task_name,problem_type,instruction,instance,solution,obj,instance_variant,solution_variant,context_index,input_format,input_index_base
QSPP,QSPP,"I work as the dispatcher planning a single run from pickup to delivery, thinking of the city as a set of intersections and one-way streets. The job is to pick one continuous route that starts at the pickup spot and ends at the drop-off, following only the allowed one-way streets. Every street taken has a normal charge and also its own little extra fee just for being used, and whenever two streets both end up on the route there can be additional combination charges — those combo fees can even depend on direction, and if both directions between a pair matter they both get added. The best route is simply the one that makes the total bill (all the street charges plus each street’s extra fee and all the pairwise combo fees for every pair of streets included) as small as possible. The final plan should be shown as a straight list of place names from pickup to delivery, with each step actually being a legal one-way move and nothing skipped or listed twice. The concrete map and numbers are shown below.

I see 16 intersections and 24 one-way streets; the intersections are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P. I'll start at A and finish at P.
I have segment 0 going from A to B.
I have segment 1 going from A to E.
I have segment 2 going from B to C.
I have segment 3 going from B to F.
I have segment 4 going from C to D.
I have segment 5 going from C to G.
I have segment 6 going from D to H.
I have segment 7 going from E to F.
I have segment 8 going from E to I.
I have segment 9 going from F to G.
I have segment 10 going from F to J.
I have segment 11 going from G to H.
I have segment 12 going from G to K.
I have segment 13 going from H to L.
I have segment 14 going from I to J.
I have segment 15 going from I to M.
I have segment 16 going from J to K.
I have segment 17 going from J to N.
I have segment 18 going from K to L.
I have segment 19 going from K to O.
I have segment 20 going from L to P.
I have segment 21 going from M to N.
I have segment 22 going from N to O.
I have segment 23 going from O to P.
I note segment 0 carries a base charge of 8.0.
I note segment 1 carries a base charge of 4.0.
I note segment 2 carries a base charge of 8.0.
I note segment 3 carries a base charge of 7.0.
I note segment 4 carries a base charge of 10.0.
I note segment 5 carries a base charge of 1.0.
I note segment 6 carries a base charge of 8.0.
I note segment 7 carries a base charge of 1.0.
I note segment 8 carries a base charge of 7.0.
I note segment 9 carries a base charge of 9.0.
I note segment 10 carries a base charge of 1.0.
I note segment 11 carries a base charge of 9.0.
I note segment 12 carries a base charge of 2.0.
I note segment 13 carries a base charge of 5.0.
I note segment 14 carries a base charge of 2.0.
I note segment 15 carries a base charge of 3.0.
I note segment 16 carries a base charge of 1.0.
I note segment 17 carries a base charge of 2.0.
I note segment 18 carries a base charge of 9.0.
I note segment 19 carries a base charge of 3.0.
I note segment 20 carries a base charge of 1.0.
I note segment 21 carries a base charge of 6.0.
I note segment 22 carries a base charge of 3.0.
I note segment 23 carries a base charge of 9.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 9.0 | 7.0 | 6.0 | 7.0 | 10.0 | 5.0 | 5.0 | 2.0 | 1.0 | 1.0 | 2.0 | 9.0 | 1.0 | 9.0 | 2.0 | 6.0 | 7.0 | 9.0 | 10.0 | 3.0 | 6.0 | 4.0 | 1.0 |
| 1 | 9.0 | 3.0 | 4.0 | 8.0 | 5.0 | 9.0 | 3.0 | 5.0 | 10.0 | 5.0 | 3.0 | 2.0 | 2.0 | 7.0 | 10.0 | 4.0 | 5.0 | 10.0 | 4.0 | 2.0 | 10.0 | 7.0 | 4.0 | 6.0 |
| 2 | 7.0 | 4.0 | 6.0 | 10.0 | 3.0 | 1.0 | 7.0 | 1.0 | 1.0 | 10.0 | 5.0 | 1.0 | 1.0 | 6.0 | 9.0 | 3.0 | 7.0 | 5.0 | 6.0 | 8.0 | 9.0 | 4.0 | 6.0 | 9.0 |
| 3 | 6.0 | 8.0 | 10.0 | 7.0 | 4.0 | 10.0 | 4.0 | 1.0 | 6.0 | 4.0 | 3.0 | 7.0 | 5.0 | 4.0 | 4.0 | 3.0 | 1.0 | 8.0 | 8.0 | 4.0 | 8.0 | 5.0 | 9.0 | 5.0 |
| 4 | 7.0 | 5.0 | 3.0 | 4.0 | 10.0 | 4.0 | 10.0 | 5.0 | 4.0 | 5.0 | 8.0 | 7.0 | 9.0 | 8.0 | 8.0 | 6.0 | 4.0 | 4.0 | 4.0 | 6.0 | 9.0 | 2.0 | 8.0 | 1.0 |
| 5 | 10.0 | 9.0 | 1.0 | 10.0 | 4.0 | 3.0 | 8.0 | 9.0 | 1.0 | 8.0 | 3.0 | 7.0 | 7.0 | 1.0 | 7.0 | 4.0 | 4.0 | 10.0 | 8.0 | 7.0 | 5.0 | 4.0 | 5.0 | 5.0 |
| 6 | 5.0 | 3.0 | 7.0 | 4.0 | 10.0 | 8.0 | 9.0 | 4.0 | 9.0 | 2.0 | 1.0 | 9.0 | 10.0 | 8.0 | 7.0 | 1.0 | 10.0 | 5.0 | 10.0 | 2.0 | 7.0 | 3.0 | 10.0 | 10.0 |
| 7 | 5.0 | 5.0 | 1.0 | 1.0 | 5.0 | 9.0 | 4.0 | 1.0 | 3.0 | 4.0 | 9.0 | 8.0 | 10.0 | 4.0 | 2.0 | 9.0 | 10.0 | 7.0 | 5.0 | 10.0 | 2.0 | 9.0 | 4.0 | 6.0 |
| 8 | 2.0 | 10.0 | 1.0 | 6.0 | 4.0 | 1.0 | 9.0 | 3.0 | 3.0 | 6.0 | 6.0 | 9.0 | 1.0 | 5.0 | 1.0 | 4.0 | 6.0 | 8.0 | 2.0 | 4.0 | 1.0 | 7.0 | 8.0 | 8.0 |
| 9 | 1.0 | 5.0 | 10.0 | 4.0 | 5.0 | 8.0 | 2.0 | 4.0 | 6.0 | 5.0 | 7.0 | 2.0 | 1.0 | 5.0 | 6.0 | 7.0 | 4.0 | 5.0 | 9.0 | 6.0 | 6.0 | 6.0 | 6.0 | 10.0 |
| 10 | 1.0 | 3.0 | 5.0 | 3.0 | 8.0 | 3.0 | 1.0 | 9.0 | 6.0 | 7.0 | 5.0 | 8.0 | 4.0 | 9.0 | 10.0 | 1.0 | 5.0 | 8.0 | 8.0 | 6.0 | 8.0 | 8.0 | 5.0 | 8.0 |
| 11 | 2.0 | 2.0 | 1.0 | 7.0 | 7.0 | 7.0 | 9.0 | 8.0 | 9.0 | 2.0 | 8.0 | 8.0 | 4.0 | 10.0 | 6.0 | 1.0 | 8.0 | 6.0 | 3.0 | 9.0 | 3.0 | 5.0 | 1.0 | 9.0 |
| 12 | 9.0 | 2.0 | 1.0 | 5.0 | 9.0 | 7.0 | 10.0 | 10.0 | 1.0 | 1.0 | 4.0 | 4.0 | 3.0 | 8.0 | 2.0 | 3.0 | 2.0 | 2.0 | 8.0 | 8.0 | 8.0 | 4.0 | 3.0 | 9.0 |
| 13 | 1.0 | 7.0 | 6.0 | 4.0 | 8.0 | 1.0 | 8.0 | 4.0 | 5.0 | 5.0 | 9.0 | 10.0 | 8.0 | 2.0 | 6.0 | 1.0 | 2.0 | 8.0 | 6.0 | 4.0 | 1.0 | 3.0 | 6.0 | 5.0 |
| 14 | 9.0 | 10.0 | 9.0 | 4.0 | 8.0 | 7.0 | 7.0 | 2.0 | 1.0 | 6.0 | 10.0 | 6.0 | 2.0 | 6.0 | 1.0 | 6.0 | 10.0 | 9.0 | 4.0 | 5.0 | 6.0 | 4.0 | 7.0 | 10.0 |
| 15 | 2.0 | 4.0 | 3.0 | 3.0 | 6.0 | 4.0 | 1.0 | 9.0 | 4.0 | 7.0 | 1.0 | 1.0 | 3.0 | 1.0 | 6.0 | 9.0 | 6.0 | 4.0 | 8.0 | 6.0 | 4.0 | 1.0 | 5.0 | 2.0 |
| 16 | 6.0 | 5.0 | 7.0 | 1.0 | 4.0 | 4.0 | 10.0 | 10.0 | 6.0 | 4.0 | 5.0 | 8.0 | 2.0 | 2.0 | 10.0 | 6.0 | 5.0 | 3.0 | 3.0 | 3.0 | 6.0 | 4.0 | 7.0 | 3.0 |
| 17 | 7.0 | 10.0 | 5.0 | 8.0 | 4.0 | 10.0 | 5.0 | 7.0 | 8.0 | 5.0 | 8.0 | 6.0 | 2.0 | 8.0 | 9.0 | 4.0 | 3.0 | 8.0 | 3.0 | 3.0 | 1.0 | 3.0 | 7.0 | 5.0 |
| 18 | 9.0 | 4.0 | 6.0 | 8.0 | 4.0 | 8.0 | 10.0 | 5.0 | 2.0 | 9.0 | 8.0 | 3.0 | 8.0 | 6.0 | 4.0 | 8.0 | 3.0 | 3.0 | 2.0 | 4.0 | 10.0 | 8.0 | 1.0 | 7.0 |
| 19 | 10.0 | 2.0 | 8.0 | 4.0 | 6.0 | 7.0 | 2.0 | 10.0 | 4.0 | 6.0 | 6.0 | 9.0 | 8.0 | 4.0 | 5.0 | 6.0 | 3.0 | 3.0 | 4.0 | 1.0 | 1.0 | 3.0 | 7.0 | 9.0 |
| 20 | 3.0 | 10.0 | 9.0 | 8.0 | 9.0 | 5.0 | 7.0 | 2.0 | 1.0 | 6.0 | 8.0 | 3.0 | 8.0 | 1.0 | 6.0 | 4.0 | 6.0 | 1.0 | 10.0 | 1.0 | 8.0 | 1.0 | 6.0 | 2.0 |
| 21 | 6.0 | 7.0 | 4.0 | 5.0 | 2.0 | 4.0 | 3.0 | 9.0 | 7.0 | 6.0 | 8.0 | 5.0 | 4.0 | 3.0 | 4.0 | 1.0 | 4.0 | 3.0 | 8.0 | 3.0 | 1.0 | 10.0 | 8.0 | 2.0 |
| 22 | 4.0 | 4.0 | 6.0 | 9.0 | 8.0 | 5.0 | 10.0 | 4.0 | 8.0 | 6.0 | 5.0 | 1.0 | 3.0 | 6.0 | 7.0 | 5.0 | 7.0 | 7.0 | 1.0 | 7.0 | 6.0 | 8.0 | 3.0 | 6.0 |
| 23 | 1.0 | 6.0 | 9.0 | 5.0 | 1.0 | 5.0 | 10.0 | 6.0 | 8.0 | 10.0 | 8.0 | 9.0 | 9.0 | 5.0 | 10.0 | 2.0 | 3.0 | 5.0 | 7.0 | 9.0 | 2.0 | 2.0 | 6.0 | 3.0 |
I'll use these details to pick one legal route from A to P that minimizes the total bill.

And when you send the final route back, please stick it in a tiny JSON box so it's easy to read and parse. Something like this is exactly the shape I expect:

{
  ""solution"": []
}

Think of that ""solution"" array as where you'll list the sequence of place names (node identifiers) from pickup to drop-off, in order — each step is a real one-way move on the map. This JSON is just a sketch of the shape I need, not the actual answer itself.

Quick reminder: use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k4_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 4, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 5, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 6, 'var_index': 5}, {'from': 3, 'to': 7, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 8, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 9, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 10, 'var_index': 12}, {'from': 7, 'to': 11, 'var_index': 13}, {'from': 8, 'to': 9, 'var_index': 14}, {'from': 8, 'to': 12, 'var_index': 15}, {'from': 9, 'to': 10, 'var_index': 16}, {'from': 9, 'to': 13, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 14, 'var_index': 19}, {'from': 11, 'to': 15, 'var_index': 20}, {'from': 12, 'to': 13, 'var_index': 21}, {'from': 13, 'to': 14, 'var_index': 22}, {'from': 14, 'to': 15, 'var_index': 23}], 'objective': {'constant': 0.0, 'linear': [8.0, 4.0, 8.0, 7.0, 10.0, 1.0, 8.0, 1.0, 7.0, 9.0, 1.0, 9.0, 2.0, 5.0, 2.0, 3.0, 1.0, 2.0, 9.0, 3.0, 1.0, 6.0, 3.0, 9.0], 'quadratic': [[10.0, 9.0, 7.0, 6.0, 7.0, 10.0, 5.0, 5.0, 2.0, 1.0, 1.0, 2.0, 9.0, 1.0, 9.0, 2.0, 6.0, 7.0, 9.0, 10.0, 3.0, 6.0, 4.0, 1.0], [9.0, 3.0, 4.0, 8.0, 5.0, 9.0, 3.0, 5.0, 10.0, 5.0, 3.0, 2.0, 2.0, 7.0, 10.0, 4.0, 5.0, 10.0, 4.0, 2.0, 10.0, 7.0, 4.0, 6.0], [7.0, 4.0, 6.0, 10.0, 3.0, 1.0, 7.0, 1.0, 1.0, 10.0, 5.0, 1.0, 1.0, 6.0, 9.0, 3.0, 7.0, 5.0, 6.0, 8.0, 9.0, 4.0, 6.0, 9.0], [6.0, 8.0, 10.0, 7.0, 4.0, 10.0, 4.0, 1.0, 6.0, 4.0, 3.0, 7.0, 5.0, 4.0, 4.0, 3.0, 1.0, 8.0, 8.0, 4.0, 8.0, 5.0, 9.0, 5.0], [7.0, 5.0, 3.0, 4.0, 10.0, 4.0, 10.0, 5.0, 4.0, 5.0, 8.0, 7.0, 9.0, 8.0, 8.0, 6.0, 4.0, 4.0, 4.0, 6.0, 9.0, 2.0, 8.0, 1.0], [10.0, 9.0, 1.0, 10.0, 4.0, 3.0, 8.0, 9.0, 1.0, 8.0, 3.0, 7.0, 7.0, 1.0, 7.0, 4.0, 4.0, 10.0, 8.0, 7.0, 5.0, 4.0, 5.0, 5.0], [5.0, 3.0, 7.0, 4.0, 10.0, 8.0, 9.0, 4.0, 9.0, 2.0, 1.0, 9.0, 10.0, 8.0, 7.0, 1.0, 10.0, 5.0, 10.0, 2.0, 7.0, 3.0, 10.0, 10.0], [5.0, 5.0, 1.0, 1.0, 5.0, 9.0, 4.0, 1.0, 3.0, 4.0, 9.0, 8.0, 10.0, 4.0, 2.0, 9.0, 10.0, 7.0, 5.0, 10.0, 2.0, 9.0, 4.0, 6.0], [2.0, 10.0, 1.0, 6.0, 4.0, 1.0, 9.0, 3.0, 3.0, 6.0, 6.0, 9.0, 1.0, 5.0, 1.0, 4.0, 6.0, 8.0, 2.0, 4.0, 1.0, 7.0, 8.0, 8.0], [1.0, 5.0, 10.0, 4.0, 5.0, 8.0, 2.0, 4.0, 6.0, 5.0, 7.0, 2.0, 1.0, 5.0, 6.0, 7.0, 4.0, 5.0, 9.0, 6.0, 6.0, 6.0, 6.0, 10.0], [1.0, 3.0, 5.0, 3.0, 8.0, 3.0, 1.0, 9.0, 6.0, 7.0, 5.0, 8.0, 4.0, 9.0, 10.0, 1.0, 5.0, 8.0, 8.0, 6.0, 8.0, 8.0, 5.0, 8.0], [2.0, 2.0, 1.0, 7.0, 7.0, 7.0, 9.0, 8.0, 9.0, 2.0, 8.0, 8.0, 4.0, 10.0, 6.0, 1.0, 8.0, 6.0, 3.0, 9.0, 3.0, 5.0, 1.0, 9.0], [9.0, 2.0, 1.0, 5.0, 9.0, 7.0, 10.0, 10.0, 1.0, 1.0, 4.0, 4.0, 3.0, 8.0, 2.0, 3.0, 2.0, 2.0, 8.0, 8.0, 8.0, 4.0, 3.0, 9.0], [1.0, 7.0, 6.0, 4.0, 8.0, 1.0, 8.0, 4.0, 5.0, 5.0, 9.0, 10.0, 8.0, 2.0, 6.0, 1.0, 2.0, 8.0, 6.0, 4.0, 1.0, 3.0, 6.0, 5.0], [9.0, 10.0, 9.0, 4.0, 8.0, 7.0, 7.0, 2.0, 1.0, 6.0, 10.0, 6.0, 2.0, 6.0, 1.0, 6.0, 10.0, 9.0, 4.0, 5.0, 6.0, 4.0, 7.0, 10.0], [2.0, 4.0, 3.0, 3.0, 6.0, 4.0, 1.0, 9.0, 4.0, 7.0, 1.0, 1.0, 3.0, 1.0, 6.0, 9.0, 6.0, 4.0, 8.0, 6.0, 4.0, 1.0, 5.0, 2.0], [6.0, 5.0, 7.0, 1.0, 4.0, 4.0, 10.0, 10.0, 6.0, 4.0, 5.0, 8.0, 2.0, 2.0, 10.0, 6.0, 5.0, 3.0, 3.0, 3.0, 6.0, 4.0, 7.0, 3.0], [7.0, 10.0, 5.0, 8.0, 4.0, 10.0, 5.0, 7.0, 8.0, 5.0, 8.0, 6.0, 2.0, 8.0, 9.0, 4.0, 3.0, 8.0, 3.0, 3.0, 1.0, 3.0, 7.0, 5.0], [9.0, 4.0, 6.0, 8.0, 4.0, 8.0, 10.0, 5.0, 2.0, 9.0, 8.0, 3.0, 8.0, 6.0, 4.0, 8.0, 3.0, 3.0, 2.0, 4.0, 10.0, 8.0, 1.0, 7.0], [10.0, 2.0, 8.0, 4.0, 6.0, 7.0, 2.0, 10.0, 4.0, 6.0, 6.0, 9.0, 8.0, 4.0, 5.0, 6.0, 3.0, 3.0, 4.0, 1.0, 1.0, 3.0, 7.0, 9.0], [3.0, 10.0, 9.0, 8.0, 9.0, 5.0, 7.0, 2.0, 1.0, 6.0, 8.0, 3.0, 8.0, 1.0, 6.0, 4.0, 6.0, 1.0, 10.0, 1.0, 8.0, 1.0, 6.0, 2.0], [6.0, 7.0, 4.0, 5.0, 2.0, 4.0, 3.0, 9.0, 7.0, 6.0, 8.0, 5.0, 4.0, 3.0, 4.0, 1.0, 4.0, 3.0, 8.0, 3.0, 1.0, 10.0, 8.0, 2.0], [4.0, 4.0, 6.0, 9.0, 8.0, 5.0, 10.0, 4.0, 8.0, 6.0, 5.0, 1.0, 3.0, 6.0, 7.0, 5.0, 7.0, 7.0, 1.0, 7.0, 6.0, 8.0, 3.0, 6.0], [1.0, 6.0, 9.0, 5.0, 1.0, 5.0, 10.0, 6.0, 8.0, 10.0, 8.0, 9.0, 9.0, 5.0, 10.0, 2.0, 3.0, 5.0, 7.0, 9.0, 2.0, 2.0, 6.0, 3.0]]}, 'source': 0, 'target': 15}","[0, 1, 5, 9, 10, 14, 15]",202.0,"{'problem_type': 'QSPP', 'num_nodes': 16, 'num_edges': 24, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P'], 'source': 'A', 'target': 'P', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 1.0}, 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'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 23, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 23, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 23, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 23, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 23, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 23, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 23, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'A', 'to': 'B', 'var_index': 0}, {'from': 'A', 'to': 'E', 'var_index': 1}, {'from': 'B', 'to': 'C', 'var_index': 2}, {'from': 'B', 'to': 'F', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'C', 'to': 'G', 'var_index': 5}, {'from': 'D', 'to': 'H', 'var_index': 6}, {'from': 'E', 'to': 'F', 'var_index': 7}, {'from': 'E', 'to': 'I', 'var_index': 8}, {'from': 'F', 'to': 'G', 'var_index': 9}, {'from': 'F', 'to': 'J', 'var_index': 10}, {'from': 'G', 'to': 'H', 'var_index': 11}, {'from': 'G', 'to': 'K', 'var_index': 12}, {'from': 'H', 'to': 'L', 'var_index': 13}, {'from': 'I', 'to': 'J', 'var_index': 14}, {'from': 'I', 'to': 'M', 'var_index': 15}, {'from': 'J', 'to': 'K', 'var_index': 16}, {'from': 'J', 'to': 'N', 'var_index': 17}, {'from': 'K', 'to': 'L', 'var_index': 18}, {'from': 'K', 'to': 'O', 'var_index': 19}, {'from': 'L', 'to': 'P', 'var_index': 20}, {'from': 'M', 'to': 'N', 'var_index': 21}, {'from': 'N', 'to': 'O', 'var_index': 22}, {'from': 'O', 'to': 'P', 'var_index': 23}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P'}}","['A', 'B', 'F', 'J', 'K', 'O', 'P']",1,nl,names
QSPP,QSPP,"On a busy morning the trail crew wanted one clean, one-directional route from the trailhead to the overlook that sticks to the marked directional paths. Each trail segment takes a certain amount of effort, some segments also carry a little extra surcharge just for taking them, and some pairs of segments create extra penalties when both are used — with the size (and sometimes the direction) of that penalty depending on which segment comes first. So the task is to pick the single continuous list of places that, when summing all the segment efforts, individual surcharges, and pair penalties, comes out with the lowest total. The map and the exact effort and penalty figures are shown below, and the final path should be the ordered sequence of locations from the trailhead to the overlook with every step legally following a one-way trail.

# num_locations=24
# num_trail_segments=23
# location_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
# trailhead_location=22
# overlook_location=23

segment_start_location,segment_end_location,segment_id
22,0,0
21,23,1
0,1,2
1,2,3
2,3,4
3,4,5
4,5,6
5,6,7
6,7,8
7,8,9
8,9,10
9,10,11
10,11,12
11,12,13
12,13,14
13,14,15
14,15,16
15,16,17
16,17,18
17,18,19
18,19,20
19,20,21
20,21,22

segment_id,base_effort
0,10.0
1,7.0
2,10.0
3,10.0
4,8.0
5,5.0
6,7.0
7,10.0
8,4.0
9,9.0
10,9.0
11,7.0
12,9.0
13,6.0
14,3.0
15,7.0
16,10.0
17,5.0
18,7.0
19,6.0
20,7.0
21,9.0
22,10.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 4.0 | 6.0 | 9.0 | 2.0 | 7.0 | 6.0 | 1.0 | 9.0 | 4.0 | 10.0 | 8.0 | 1.0 | 5.0 | 8.0 | 5.0 | 7.0 | 2.0 | 4.0 | 1.0 | 4.0 | 5.0 | 4.0 |
| 1 | 4.0 | 4.0 | 8.0 | 9.0 | 4.0 | 8.0 | 4.0 | 2.0 | 9.0 | 1.0 | 7.0 | 3.0 | 5.0 | 6.0 | 8.0 | 4.0 | 5.0 | 2.0 | 8.0 | 2.0 | 10.0 | 4.0 | 6.0 |
| 2 | 6.0 | 8.0 | 1.0 | 1.0 | 1.0 | 7.0 | 3.0 | 7.0 | 1.0 | 7.0 | 5.0 | 5.0 | 4.0 | 4.0 | 9.0 | 10.0 | 6.0 | 7.0 | 6.0 | 2.0 | 8.0 | 6.0 | 3.0 |
| 3 | 9.0 | 9.0 | 1.0 | 5.0 | 4.0 | 3.0 | 3.0 | 3.0 | 4.0 | 4.0 | 5.0 | 4.0 | 4.0 | 8.0 | 5.0 | 2.0 | 3.0 | 6.0 | 7.0 | 4.0 | 2.0 | 5.0 | 4.0 |
| 4 | 2.0 | 4.0 | 1.0 | 4.0 | 1.0 | 9.0 | 4.0 | 10.0 | 1.0 | 10.0 | 2.0 | 10.0 | 9.0 | 5.0 | 3.0 | 8.0 | 3.0 | 3.0 | 10.0 | 4.0 | 9.0 | 5.0 | 6.0 |
| 5 | 7.0 | 8.0 | 7.0 | 3.0 | 9.0 | 8.0 | 5.0 | 5.0 | 6.0 | 2.0 | 3.0 | 3.0 | 3.0 | 3.0 | 1.0 | 3.0 | 3.0 | 5.0 | 6.0 | 1.0 | 9.0 | 6.0 | 10.0 |
| 6 | 6.0 | 4.0 | 3.0 | 3.0 | 4.0 | 5.0 | 2.0 | 1.0 | 6.0 | 4.0 | 6.0 | 2.0 | 1.0 | 1.0 | 4.0 | 4.0 | 7.0 | 9.0 | 3.0 | 9.0 | 10.0 | 6.0 | 10.0 |
| 7 | 1.0 | 2.0 | 7.0 | 3.0 | 10.0 | 5.0 | 1.0 | 1.0 | 2.0 | 6.0 | 1.0 | 4.0 | 7.0 | 3.0 | 2.0 | 8.0 | 1.0 | 7.0 | 2.0 | 4.0 | 4.0 | 5.0 | 4.0 |
| 8 | 9.0 | 9.0 | 1.0 | 4.0 | 1.0 | 6.0 | 6.0 | 2.0 | 5.0 | 9.0 | 7.0 | 9.0 | 8.0 | 1.0 | 6.0 | 2.0 | 2.0 | 9.0 | 4.0 | 9.0 | 1.0 | 8.0 | 5.0 |
| 9 | 4.0 | 1.0 | 7.0 | 4.0 | 10.0 | 2.0 | 4.0 | 6.0 | 9.0 | 3.0 | 2.0 | 10.0 | 6.0 | 4.0 | 8.0 | 2.0 | 10.0 | 6.0 | 4.0 | 7.0 | 5.0 | 10.0 | 7.0 |
| 10 | 10.0 | 7.0 | 5.0 | 5.0 | 2.0 | 3.0 | 6.0 | 1.0 | 7.0 | 2.0 | 6.0 | 9.0 | 1.0 | 6.0 | 8.0 | 9.0 | 3.0 | 2.0 | 3.0 | 10.0 | 5.0 | 9.0 | 8.0 |
| 11 | 8.0 | 3.0 | 5.0 | 4.0 | 10.0 | 3.0 | 2.0 | 4.0 | 9.0 | 10.0 | 9.0 | 1.0 | 8.0 | 8.0 | 4.0 | 5.0 | 4.0 | 5.0 | 8.0 | 6.0 | 2.0 | 1.0 | 8.0 |
| 12 | 1.0 | 5.0 | 4.0 | 4.0 | 9.0 | 3.0 | 1.0 | 7.0 | 8.0 | 6.0 | 1.0 | 8.0 | 1.0 | 7.0 | 9.0 | 1.0 | 4.0 | 5.0 | 3.0 | 1.0 | 7.0 | 7.0 | 8.0 |
| 13 | 5.0 | 6.0 | 4.0 | 8.0 | 5.0 | 3.0 | 1.0 | 3.0 | 1.0 | 4.0 | 6.0 | 8.0 | 7.0 | 9.0 | 5.0 | 1.0 | 2.0 | 8.0 | 10.0 | 4.0 | 5.0 | 4.0 | 4.0 |
| 14 | 8.0 | 8.0 | 9.0 | 5.0 | 3.0 | 1.0 | 4.0 | 2.0 | 6.0 | 8.0 | 8.0 | 4.0 | 9.0 | 5.0 | 4.0 | 2.0 | 10.0 | 3.0 | 5.0 | 10.0 | 10.0 | 6.0 | 10.0 |
| 15 | 5.0 | 4.0 | 10.0 | 2.0 | 8.0 | 3.0 | 4.0 | 8.0 | 2.0 | 2.0 | 9.0 | 5.0 | 1.0 | 1.0 | 2.0 | 5.0 | 8.0 | 2.0 | 9.0 | 4.0 | 2.0 | 3.0 | 10.0 |
| 16 | 7.0 | 5.0 | 6.0 | 3.0 | 3.0 | 3.0 | 7.0 | 1.0 | 2.0 | 10.0 | 3.0 | 4.0 | 4.0 | 2.0 | 10.0 | 8.0 | 1.0 | 8.0 | 3.0 | 5.0 | 8.0 | 4.0 | 8.0 |
| 17 | 2.0 | 2.0 | 7.0 | 6.0 | 3.0 | 5.0 | 9.0 | 7.0 | 9.0 | 6.0 | 2.0 | 5.0 | 5.0 | 8.0 | 3.0 | 2.0 | 8.0 | 4.0 | 3.0 | 2.0 | 1.0 | 2.0 | 10.0 |
| 18 | 4.0 | 8.0 | 6.0 | 7.0 | 10.0 | 6.0 | 3.0 | 2.0 | 4.0 | 4.0 | 3.0 | 8.0 | 3.0 | 10.0 | 5.0 | 9.0 | 3.0 | 3.0 | 9.0 | 4.0 | 3.0 | 10.0 | 6.0 |
| 19 | 1.0 | 2.0 | 2.0 | 4.0 | 4.0 | 1.0 | 9.0 | 4.0 | 9.0 | 7.0 | 10.0 | 6.0 | 1.0 | 4.0 | 10.0 | 4.0 | 5.0 | 2.0 | 4.0 | 5.0 | 7.0 | 3.0 | 3.0 |
| 20 | 4.0 | 10.0 | 8.0 | 2.0 | 9.0 | 9.0 | 10.0 | 4.0 | 1.0 | 5.0 | 5.0 | 2.0 | 7.0 | 5.0 | 10.0 | 2.0 | 8.0 | 1.0 | 3.0 | 7.0 | 8.0 | 1.0 | 9.0 |
| 21 | 5.0 | 4.0 | 6.0 | 5.0 | 5.0 | 6.0 | 6.0 | 5.0 | 8.0 | 10.0 | 9.0 | 1.0 | 7.0 | 4.0 | 6.0 | 3.0 | 4.0 | 2.0 | 10.0 | 3.0 | 1.0 | 6.0 | 9.0 |
| 22 | 4.0 | 6.0 | 3.0 | 4.0 | 6.0 | 10.0 | 10.0 | 4.0 | 5.0 | 7.0 | 8.0 | 8.0 | 8.0 | 4.0 | 10.0 | 10.0 | 8.0 | 10.0 | 6.0 | 3.0 | 9.0 | 9.0 | 3.0 |

Also, when you give the final route, please put it in a tiny JSON sketch like this so it's easy to parse:

{
  ""solution"": []
}

Here ""solution"" is where you list the ordered sequence of place names from the trailhead to the overlook — just the node identifiers, in order (no extra numbers or cost labels). Think of this as the simple form to fill out with the route; it's only showing the shape, not the actual answer.

Please use the exact identifiers shown in the map/input and don’t rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 23, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}, {'from': 19, 'to': 20, 'var_index': 21}, {'from': 20, 'to': 21, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [10.0, 7.0, 10.0, 10.0, 8.0, 5.0, 7.0, 10.0, 4.0, 9.0, 9.0, 7.0, 9.0, 6.0, 3.0, 7.0, 10.0, 5.0, 7.0, 6.0, 7.0, 9.0, 10.0], 'quadratic': [[1.0, 4.0, 6.0, 9.0, 2.0, 7.0, 6.0, 1.0, 9.0, 4.0, 10.0, 8.0, 1.0, 5.0, 8.0, 5.0, 7.0, 2.0, 4.0, 1.0, 4.0, 5.0, 4.0], [4.0, 4.0, 8.0, 9.0, 4.0, 8.0, 4.0, 2.0, 9.0, 1.0, 7.0, 3.0, 5.0, 6.0, 8.0, 4.0, 5.0, 2.0, 8.0, 2.0, 10.0, 4.0, 6.0], [6.0, 8.0, 1.0, 1.0, 1.0, 7.0, 3.0, 7.0, 1.0, 7.0, 5.0, 5.0, 4.0, 4.0, 9.0, 10.0, 6.0, 7.0, 6.0, 2.0, 8.0, 6.0, 3.0], [9.0, 9.0, 1.0, 5.0, 4.0, 3.0, 3.0, 3.0, 4.0, 4.0, 5.0, 4.0, 4.0, 8.0, 5.0, 2.0, 3.0, 6.0, 7.0, 4.0, 2.0, 5.0, 4.0], [2.0, 4.0, 1.0, 4.0, 1.0, 9.0, 4.0, 10.0, 1.0, 10.0, 2.0, 10.0, 9.0, 5.0, 3.0, 8.0, 3.0, 3.0, 10.0, 4.0, 9.0, 5.0, 6.0], [7.0, 8.0, 7.0, 3.0, 9.0, 8.0, 5.0, 5.0, 6.0, 2.0, 3.0, 3.0, 3.0, 3.0, 1.0, 3.0, 3.0, 5.0, 6.0, 1.0, 9.0, 6.0, 10.0], [6.0, 4.0, 3.0, 3.0, 4.0, 5.0, 2.0, 1.0, 6.0, 4.0, 6.0, 2.0, 1.0, 1.0, 4.0, 4.0, 7.0, 9.0, 3.0, 9.0, 10.0, 6.0, 10.0], [1.0, 2.0, 7.0, 3.0, 10.0, 5.0, 1.0, 1.0, 2.0, 6.0, 1.0, 4.0, 7.0, 3.0, 2.0, 8.0, 1.0, 7.0, 2.0, 4.0, 4.0, 5.0, 4.0], [9.0, 9.0, 1.0, 4.0, 1.0, 6.0, 6.0, 2.0, 5.0, 9.0, 7.0, 9.0, 8.0, 1.0, 6.0, 2.0, 2.0, 9.0, 4.0, 9.0, 1.0, 8.0, 5.0], [4.0, 1.0, 7.0, 4.0, 10.0, 2.0, 4.0, 6.0, 9.0, 3.0, 2.0, 10.0, 6.0, 4.0, 8.0, 2.0, 10.0, 6.0, 4.0, 7.0, 5.0, 10.0, 7.0], [10.0, 7.0, 5.0, 5.0, 2.0, 3.0, 6.0, 1.0, 7.0, 2.0, 6.0, 9.0, 1.0, 6.0, 8.0, 9.0, 3.0, 2.0, 3.0, 10.0, 5.0, 9.0, 8.0], [8.0, 3.0, 5.0, 4.0, 10.0, 3.0, 2.0, 4.0, 9.0, 10.0, 9.0, 1.0, 8.0, 8.0, 4.0, 5.0, 4.0, 5.0, 8.0, 6.0, 2.0, 1.0, 8.0], [1.0, 5.0, 4.0, 4.0, 9.0, 3.0, 1.0, 7.0, 8.0, 6.0, 1.0, 8.0, 1.0, 7.0, 9.0, 1.0, 4.0, 5.0, 3.0, 1.0, 7.0, 7.0, 8.0], [5.0, 6.0, 4.0, 8.0, 5.0, 3.0, 1.0, 3.0, 1.0, 4.0, 6.0, 8.0, 7.0, 9.0, 5.0, 1.0, 2.0, 8.0, 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'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 23, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}, {'from': 19, 'to': 20, 'var_index': 21}, {'from': 20, 'to': 21, 'var_index': 22}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23}}","[22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23]",2,csv,0
QSPP,QSPP,"I’m looking at a router map and have to pick one single route from the start node to the end node that actually follows the arrows between routers. The “score” of a route is what happens when all the link delays are added up, plus any extra interference hits that appear whenever certain pairs of links are used together (and some links even carry a little extra hit just for being used). The better route is simply the one with the lowest total of those link delays and pairwise interference amounts. The route must be one continuous path from the source to the destination, each hop must be a real directed link, and the answer will be shown below with the concrete details.

There are 23 routers and 62 directed links listed as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23; the route must start at 22 and end at 23.
I see a directed link from 22 to 1 labeled 0.
I see a directed link from 22 to 2 labeled 1.
I see a directed link from 22 to 3 labeled 2.
I see a directed link from 22 to 4 labeled 3.
I see a directed link from 22 to 5 labeled 4.
I see a directed link from 22 to 6 labeled 5.
I see a directed link from 22 to 7 labeled 6.
I see a directed link from 22 to 8 labeled 7.
I see a directed link from 22 to 9 labeled 8.
I see a directed link from 22 to 10 labeled 9.
I see a directed link from 22 to 11 labeled 10.
I see a directed link from 22 to 12 labeled 11.
I see a directed link from 22 to 13 labeled 12.
I see a directed link from 22 to 14 labeled 13.
I see a directed link from 22 to 15 labeled 14.
I see a directed link from 22 to 16 labeled 15.
I see a directed link from 22 to 17 labeled 16.
I see a directed link from 22 to 18 labeled 17.
I see a directed link from 22 to 19 labeled 18.
I see a directed link from 22 to 20 labeled 19.
I see a directed link from 22 to 21 labeled 20.
I see a directed link from 1 to 23 labeled 21.
I see a directed link from 2 to 23 labeled 22.
I see a directed link from 3 to 23 labeled 23.
I see a directed link from 4 to 23 labeled 24.
I see a directed link from 5 to 23 labeled 25.
I see a directed link from 6 to 23 labeled 26.
I see a directed link from 7 to 23 labeled 27.
I see a directed link from 8 to 23 labeled 28.
I see a directed link from 9 to 23 labeled 29.
I see a directed link from 10 to 23 labeled 30.
I see a directed link from 11 to 23 labeled 31.
I see a directed link from 12 to 23 labeled 32.
I see a directed link from 13 to 23 labeled 33.
I see a directed link from 14 to 23 labeled 34.
I see a directed link from 15 to 23 labeled 35.
I see a directed link from 16 to 23 labeled 36.
I see a directed link from 17 to 23 labeled 37.
I see a directed link from 18 to 23 labeled 38.
I see a directed link from 19 to 23 labeled 39.
I see a directed link from 20 to 23 labeled 40.
I see a directed link from 21 to 23 labeled 41.
I see a directed link from 1 to 2 labeled 42.
I see a directed link from 2 to 3 labeled 43.
I see a directed link from 3 to 4 labeled 44.
I see a directed link from 4 to 5 labeled 45.
I see a directed link from 5 to 6 labeled 46.
I see a directed link from 6 to 7 labeled 47.
I see a directed link from 7 to 8 labeled 48.
I see a directed link from 8 to 9 labeled 49.
I see a directed link from 9 to 10 labeled 50.
I see a directed link from 10 to 11 labeled 51.
I see a directed link from 11 to 12 labeled 52.
I see a directed link from 12 to 13 labeled 53.
I see a directed link from 13 to 14 labeled 54.
I see a directed link from 14 to 15 labeled 55.
I see a directed link from 15 to 16 labeled 56.
I see a directed link from 16 to 17 labeled 57.
I see a directed link from 17 to 18 labeled 58.
I see a directed link from 18 to 19 labeled 59.
I see a directed link from 19 to 20 labeled 60.
I see a directed link from 20 to 21 labeled 61.
If I use link 0 it adds a base latency of 7.0.
If I use link 1 it adds a base latency of 9.0.
If I use link 2 it adds a base latency of 6.0.
If I use link 3 it adds a base latency of 1.0.
If I use link 4 it adds a base latency of 7.0.
If I use link 5 it adds a base latency of 6.0.
If I use link 6 it adds a base latency of 6.0.
If I use link 7 it adds a base latency of 2.0.
If I use link 8 it adds a base latency of 4.0.
If I use link 9 it adds a base latency of 1.0.
If I use link 10 it adds a base latency of 6.0.
If I use link 11 it adds a base latency of 10.0.
If I use link 12 it adds a base latency of 8.0.
If I use link 13 it adds a base latency of 6.0.
If I use link 14 it adds a base latency of 5.0.
If I use link 15 it adds a base latency of 9.0.
If I use link 16 it adds a base latency of 1.0.
If I use link 17 it adds a base latency of 3.0.
If I use link 18 it adds a base latency of 6.0.
If I use link 19 it adds a base latency of 4.0.
If I use link 20 it adds a base latency of 10.0.
If I use link 21 it adds a base latency of 3.0.
If I use link 22 it adds a base latency of 7.0.
If I use link 23 it adds a base latency of 4.0.
If I use link 24 it adds a base latency of 4.0.
If I use link 25 it adds a base latency of 5.0.
If I use link 26 it adds a base latency of 5.0.
If I use link 27 it adds a base latency of 2.0.
If I use link 28 it adds a base latency of 3.0.
If I use link 29 it adds a base latency of 8.0.
If I use link 30 it adds a base latency of 3.0.
If I use link 31 it adds a base latency of 5.0.
If I use link 32 it adds a base latency of 9.0.
If I use link 33 it adds a base latency of 4.0.
If I use link 34 it adds a base latency of 8.0.
If I use link 35 it adds a base latency of 1.0.
If I use link 36 it adds a base latency of 10.0.
If I use link 37 it adds a base latency of 2.0.
If I use link 38 it adds a base latency of 7.0.
If I use link 39 it adds a base latency of 6.0.
If I use link 40 it adds a base latency of 1.0.
If I use link 41 it adds a base latency of 4.0.
If I use link 42 it adds a base latency of 8.0.
If I use link 43 it adds a base latency of 4.0.
If I use link 44 it adds a base latency of 2.0.
If I use link 45 it adds a base latency of 8.0.
If I use link 46 it adds a base latency of 1.0.
If I use link 47 it adds a base latency of 3.0.
If I use link 48 it adds a base latency of 7.0.
If I use link 49 it adds a base latency of 7.0.
If I use link 50 it adds a base latency of 5.0.
If I use link 51 it adds a base latency of 2.0.
If I use link 52 it adds a base latency of 4.0.
If I use link 53 it adds a base latency of 3.0.
If I use link 54 it adds a base latency of 9.0.
If I use link 55 it adds a base latency of 1.0.
If I use link 56 it adds a base latency of 8.0.
If I use link 57 it adds a base latency of 4.0.
If I use link 58 it adds a base latency of 5.0.
If I use link 59 it adds a base latency of 1.0.
If I use link 60 it adds a base latency of 5.0.
If I use link 61 it adds a base latency of 1.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (link_i_id, link_j_id). If two links with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| link_i_id\link_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 7.0 | 5.0 | 3.0 | 1.0 | 4.0 | 8.0 | 9.0 | 2.0 | 3.0 | 1.0 | 7.0 | 9.0 | 7.0 | 6.0 | 9.0 | 7.0 | 9.0 | 10.0 | 10.0 | 6.0 | 1.0 | 2.0 | 9.0 | 4.0 | 6.0 | 10.0 | 6.0 | 1.0 | 3.0 | 9.0 | 7.0 | 10.0 | 5.0 | 3.0 | 8.0 | 7.0 | 5.0 | 9.0 | 10.0 | 4.0 | 2.0 | 2.0 | 10.0 | 8.0 | 5.0 | 4.0 | 8.0 | 5.0 | 8.0 | 7.0 | 10.0 | 8.0 | 9.0 | 8.0 | 2.0 | 1.0 | 9.0 | 5.0 | 2.0 | 5.0 | 9.0 |
| 1 | 7.0 | 8.0 | 4.0 | 5.0 | 8.0 | 5.0 | 5.0 | 10.0 | 9.0 | 10.0 | 4.0 | 2.0 | 4.0 | 8.0 | 5.0 | 10.0 | 9.0 | 10.0 | 1.0 | 8.0 | 2.0 | 9.0 | 6.0 | 2.0 | 4.0 | 1.0 | 6.0 | 8.0 | 3.0 | 3.0 | 10.0 | 1.0 | 9.0 | 2.0 | 1.0 | 5.0 | 2.0 | 4.0 | 7.0 | 1.0 | 2.0 | 10.0 | 6.0 | 2.0 | 1.0 | 1.0 | 6.0 | 1.0 | 8.0 | 4.0 | 3.0 | 7.0 | 9.0 | 1.0 | 6.0 | 2.0 | 1.0 | 9.0 | 3.0 | 2.0 | 7.0 | 8.0 |
| 2 | 5.0 | 4.0 | 1.0 | 10.0 | 6.0 | 9.0 | 4.0 | 9.0 | 10.0 | 6.0 | 4.0 | 8.0 | 6.0 | 7.0 | 7.0 | 2.0 | 4.0 | 2.0 | 1.0 | 9.0 | 2.0 | 3.0 | 5.0 | 6.0 | 8.0 | 3.0 | 8.0 | 3.0 | 10.0 | 10.0 | 5.0 | 5.0 | 9.0 | 3.0 | 4.0 | 10.0 | 10.0 | 6.0 | 4.0 | 3.0 | 2.0 | 5.0 | 4.0 | 3.0 | 9.0 | 1.0 | 9.0 | 2.0 | 10.0 | 9.0 | 4.0 | 7.0 | 8.0 | 1.0 | 5.0 | 1.0 | 1.0 | 7.0 | 3.0 | 10.0 | 9.0 | 7.0 |
| 3 | 3.0 | 5.0 | 10.0 | 1.0 | 10.0 | 4.0 | 7.0 | 9.0 | 6.0 | 7.0 | 9.0 | 6.0 | 3.0 | 3.0 | 6.0 | 8.0 | 10.0 | 8.0 | 3.0 | 8.0 | 9.0 | 9.0 | 1.0 | 2.0 | 3.0 | 7.0 | 2.0 | 5.0 | 6.0 | 6.0 | 4.0 | 1.0 | 4.0 | 8.0 | 10.0 | 3.0 | 3.0 | 1.0 | 3.0 | 5.0 | 4.0 | 4.0 | 3.0 | 4.0 | 3.0 | 2.0 | 1.0 | 8.0 | 3.0 | 7.0 | 1.0 | 4.0 | 6.0 | 8.0 | 1.0 | 3.0 | 9.0 | 10.0 | 7.0 | 9.0 | 6.0 | 8.0 |
| 4 | 1.0 | 8.0 | 6.0 | 10.0 | 10.0 | 7.0 | 6.0 | 10.0 | 6.0 | 2.0 | 6.0 | 4.0 | 10.0 | 7.0 | 10.0 | 1.0 | 3.0 | 8.0 | 8.0 | 6.0 | 1.0 | 8.0 | 8.0 | 3.0 | 3.0 | 2.0 | 3.0 | 10.0 | 2.0 | 9.0 | 2.0 | 8.0 | 5.0 | 1.0 | 4.0 | 7.0 | 6.0 | 2.0 | 1.0 | 8.0 | 9.0 | 8.0 | 6.0 | 5.0 | 5.0 | 3.0 | 1.0 | 3.0 | 7.0 | 3.0 | 5.0 | 4.0 | 10.0 | 9.0 | 4.0 | 1.0 | 3.0 | 2.0 | 4.0 | 3.0 | 4.0 | 3.0 |
| 5 | 4.0 | 5.0 | 9.0 | 4.0 | 7.0 | 6.0 | 8.0 | 9.0 | 3.0 | 9.0 | 10.0 | 8.0 | 3.0 | 4.0 | 3.0 | 3.0 | 9.0 | 6.0 | 8.0 | 2.0 | 6.0 | 7.0 | 8.0 | 1.0 | 3.0 | 6.0 | 8.0 | 9.0 | 2.0 | 1.0 | 6.0 | 6.0 | 6.0 | 2.0 | 10.0 | 4.0 | 2.0 | 8.0 | 2.0 | 6.0 | 7.0 | 7.0 | 2.0 | 9.0 | 10.0 | 10.0 | 8.0 | 10.0 | 7.0 | 9.0 | 8.0 | 6.0 | 2.0 | 9.0 | 10.0 | 2.0 | 2.0 | 8.0 | 9.0 | 8.0 | 2.0 | 6.0 |
| 6 | 8.0 | 5.0 | 4.0 | 7.0 | 6.0 | 8.0 | 9.0 | 4.0 | 6.0 | 4.0 | 6.0 | 8.0 | 10.0 | 2.0 | 7.0 | 2.0 | 1.0 | 3.0 | 6.0 | 6.0 | 5.0 | 8.0 | 3.0 | 8.0 | 10.0 | 6.0 | 7.0 | 3.0 | 4.0 | 2.0 | 5.0 | 5.0 | 3.0 | 4.0 | 9.0 | 7.0 | 9.0 | 7.0 | 5.0 | 7.0 | 6.0 | 8.0 | 2.0 | 5.0 | 2.0 | 8.0 | 5.0 | 9.0 | 5.0 | 5.0 | 2.0 | 10.0 | 2.0 | 8.0 | 4.0 | 1.0 | 1.0 | 7.0 | 9.0 | 10.0 | 9.0 | 7.0 |
| 7 | 9.0 | 10.0 | 9.0 | 9.0 | 10.0 | 9.0 | 4.0 | 2.0 | 6.0 | 8.0 | 1.0 | 3.0 | 1.0 | 3.0 | 1.0 | 2.0 | 3.0 | 9.0 | 1.0 | 6.0 | 3.0 | 7.0 | 3.0 | 3.0 | 5.0 | 5.0 | 6.0 | 9.0 | 8.0 | 1.0 | 10.0 | 9.0 | 1.0 | 5.0 | 5.0 | 5.0 | 4.0 | 9.0 | 2.0 | 6.0 | 2.0 | 9.0 | 5.0 | 6.0 | 5.0 | 6.0 | 3.0 | 3.0 | 6.0 | 9.0 | 9.0 | 5.0 | 5.0 | 3.0 | 7.0 | 8.0 | 2.0 | 6.0 | 7.0 | 10.0 | 9.0 | 2.0 |
| 8 | 2.0 | 9.0 | 10.0 | 6.0 | 6.0 | 3.0 | 6.0 | 6.0 | 7.0 | 4.0 | 9.0 | 2.0 | 7.0 | 9.0 | 7.0 | 10.0 | 7.0 | 6.0 | 8.0 | 4.0 | 1.0 | 7.0 | 4.0 | 7.0 | 5.0 | 1.0 | 7.0 | 7.0 | 4.0 | 6.0 | 6.0 | 9.0 | 6.0 | 10.0 | 10.0 | 8.0 | 1.0 | 4.0 | 10.0 | 2.0 | 10.0 | 2.0 | 8.0 | 8.0 | 7.0 | 10.0 | 8.0 | 10.0 | 2.0 | 4.0 | 1.0 | 9.0 | 2.0 | 1.0 | 9.0 | 5.0 | 6.0 | 5.0 | 6.0 | 8.0 | 3.0 | 8.0 |
| 9 | 3.0 | 10.0 | 6.0 | 7.0 | 2.0 | 9.0 | 4.0 | 8.0 | 4.0 | 5.0 | 5.0 | 6.0 | 5.0 | 9.0 | 2.0 | 3.0 | 3.0 | 6.0 | 3.0 | 6.0 | 4.0 | 9.0 | 2.0 | 10.0 | 7.0 | 2.0 | 3.0 | 9.0 | 3.0 | 10.0 | 6.0 | 6.0 | 3.0 | 7.0 | 9.0 | 6.0 | 9.0 | 1.0 | 3.0 | 8.0 | 8.0 | 8.0 | 5.0 | 4.0 | 3.0 | 6.0 | 1.0 | 3.0 | 1.0 | 9.0 | 2.0 | 7.0 | 9.0 | 2.0 | 7.0 | 2.0 | 3.0 | 6.0 | 2.0 | 3.0 | 4.0 | 2.0 |
| 10 | 1.0 | 4.0 | 4.0 | 9.0 | 6.0 | 10.0 | 6.0 | 1.0 | 9.0 | 5.0 | 6.0 | 5.0 | 2.0 | 3.0 | 7.0 | 6.0 | 1.0 | 6.0 | 10.0 | 3.0 | 2.0 | 1.0 | 4.0 | 6.0 | 10.0 | 2.0 | 2.0 | 4.0 | 6.0 | 10.0 | 1.0 | 1.0 | 1.0 | 8.0 | 6.0 | 6.0 | 8.0 | 3.0 | 9.0 | 9.0 | 5.0 | 10.0 | 5.0 | 7.0 | 1.0 | 9.0 | 7.0 | 2.0 | 4.0 | 3.0 | 2.0 | 1.0 | 6.0 | 2.0 | 6.0 | 3.0 | 4.0 | 4.0 | 2.0 | 3.0 | 8.0 | 8.0 |
| 11 | 7.0 | 2.0 | 8.0 | 6.0 | 4.0 | 8.0 | 8.0 | 3.0 | 2.0 | 6.0 | 5.0 | 5.0 | 9.0 | 9.0 | 9.0 | 3.0 | 4.0 | 3.0 | 2.0 | 5.0 | 5.0 | 2.0 | 7.0 | 10.0 | 8.0 | 6.0 | 7.0 | 9.0 | 10.0 | 5.0 | 5.0 | 7.0 | 1.0 | 5.0 | 3.0 | 7.0 | 7.0 | 2.0 | 9.0 | 1.0 | 2.0 | 3.0 | 3.0 | 1.0 | 7.0 | 8.0 | 8.0 | 5.0 | 3.0 | 6.0 | 2.0 | 6.0 | 3.0 | 6.0 | 3.0 | 4.0 | 10.0 | 2.0 | 10.0 | 3.0 | 9.0 | 6.0 |
| 12 | 9.0 | 4.0 | 6.0 | 3.0 | 10.0 | 3.0 | 10.0 | 1.0 | 7.0 | 5.0 | 2.0 | 9.0 | 4.0 | 7.0 | 7.0 | 4.0 | 1.0 | 10.0 | 2.0 | 6.0 | 9.0 | 1.0 | 4.0 | 6.0 | 8.0 | 3.0 | 7.0 | 4.0 | 1.0 | 8.0 | 8.0 | 3.0 | 1.0 | 7.0 | 3.0 | 2.0 | 10.0 | 10.0 | 8.0 | 10.0 | 8.0 | 1.0 | 10.0 | 3.0 | 7.0 | 1.0 | 7.0 | 7.0 | 9.0 | 6.0 | 9.0 | 9.0 | 7.0 | 5.0 | 1.0 | 7.0 | 2.0 | 8.0 | 3.0 | 2.0 | 9.0 | 8.0 |
| 13 | 7.0 | 8.0 | 7.0 | 3.0 | 7.0 | 4.0 | 2.0 | 3.0 | 9.0 | 9.0 | 3.0 | 9.0 | 7.0 | 9.0 | 9.0 | 10.0 | 3.0 | 5.0 | 8.0 | 2.0 | 5.0 | 6.0 | 2.0 | 10.0 | 10.0 | 5.0 | 10.0 | 10.0 | 6.0 | 6.0 | 9.0 | 7.0 | 8.0 | 2.0 | 10.0 | 5.0 | 8.0 | 2.0 | 1.0 | 10.0 | 10.0 | 10.0 | 6.0 | 4.0 | 3.0 | 4.0 | 9.0 | 7.0 | 6.0 | 9.0 | 3.0 | 6.0 | 4.0 | 8.0 | 10.0 | 7.0 | 1.0 | 3.0 | 6.0 | 9.0 | 8.0 | 4.0 |
| 14 | 6.0 | 5.0 | 7.0 | 6.0 | 10.0 | 3.0 | 7.0 | 1.0 | 7.0 | 2.0 | 7.0 | 9.0 | 7.0 | 9.0 | 5.0 | 7.0 | 3.0 | 7.0 | 5.0 | 4.0 | 1.0 | 9.0 | 1.0 | 5.0 | 1.0 | 7.0 | 6.0 | 5.0 | 1.0 | 8.0 | 8.0 | 2.0 | 7.0 | 4.0 | 7.0 | 6.0 | 9.0 | 8.0 | 1.0 | 4.0 | 1.0 | 10.0 | 9.0 | 9.0 | 4.0 | 5.0 | 7.0 | 3.0 | 9.0 | 6.0 | 7.0 | 5.0 | 6.0 | 8.0 | 2.0 | 6.0 | 7.0 | 6.0 | 7.0 | 6.0 | 5.0 | 8.0 |
| 15 | 9.0 | 10.0 | 2.0 | 8.0 | 1.0 | 3.0 | 2.0 | 2.0 | 10.0 | 3.0 | 6.0 | 3.0 | 4.0 | 10.0 | 7.0 | 8.0 | 2.0 | 6.0 | 1.0 | 8.0 | 2.0 | 3.0 | 4.0 | 5.0 | 3.0 | 1.0 | 7.0 | 1.0 | 3.0 | 9.0 | 1.0 | 10.0 | 5.0 | 5.0 | 2.0 | 2.0 | 2.0 | 6.0 | 10.0 | 5.0 | 6.0 | 6.0 | 1.0 | 8.0 | 3.0 | 7.0 | 7.0 | 8.0 | 9.0 | 5.0 | 3.0 | 9.0 | 10.0 | 10.0 | 1.0 | 3.0 | 9.0 | 4.0 | 2.0 | 4.0 | 8.0 | 5.0 |
| 16 | 7.0 | 9.0 | 4.0 | 10.0 | 3.0 | 9.0 | 1.0 | 3.0 | 7.0 | 3.0 | 1.0 | 4.0 | 1.0 | 3.0 | 3.0 | 2.0 | 7.0 | 1.0 | 4.0 | 3.0 | 2.0 | 4.0 | 6.0 | 3.0 | 4.0 | 7.0 | 7.0 | 7.0 | 4.0 | 1.0 | 2.0 | 10.0 | 2.0 | 9.0 | 3.0 | 9.0 | 8.0 | 6.0 | 1.0 | 7.0 | 3.0 | 3.0 | 1.0 | 2.0 | 4.0 | 9.0 | 10.0 | 4.0 | 2.0 | 4.0 | 7.0 | 10.0 | 5.0 | 1.0 | 8.0 | 6.0 | 6.0 | 7.0 | 5.0 | 6.0 | 7.0 | 10.0 |
| 17 | 9.0 | 10.0 | 2.0 | 8.0 | 8.0 | 6.0 | 3.0 | 9.0 | 6.0 | 6.0 | 6.0 | 3.0 | 10.0 | 5.0 | 7.0 | 6.0 | 1.0 | 7.0 | 2.0 | 1.0 | 6.0 | 7.0 | 8.0 | 2.0 | 8.0 | 6.0 | 7.0 | 3.0 | 2.0 | 6.0 | 6.0 | 8.0 | 7.0 | 7.0 | 7.0 | 6.0 | 2.0 | 9.0 | 7.0 | 7.0 | 1.0 | 2.0 | 2.0 | 10.0 | 3.0 | 4.0 | 4.0 | 6.0 | 7.0 | 4.0 | 3.0 | 5.0 | 1.0 | 1.0 | 4.0 | 8.0 | 8.0 | 6.0 | 3.0 | 3.0 | 8.0 | 3.0 |
| 18 | 10.0 | 1.0 | 1.0 | 3.0 | 8.0 | 8.0 | 6.0 | 1.0 | 8.0 | 3.0 | 10.0 | 2.0 | 2.0 | 8.0 | 5.0 | 1.0 | 4.0 | 2.0 | 10.0 | 4.0 | 7.0 | 5.0 | 3.0 | 6.0 | 2.0 | 3.0 | 9.0 | 4.0 | 9.0 | 8.0 | 4.0 | 3.0 | 9.0 | 2.0 | 2.0 | 8.0 | 9.0 | 9.0 | 4.0 | 10.0 | 10.0 | 1.0 | 2.0 | 8.0 | 4.0 | 1.0 | 10.0 | 6.0 | 1.0 | 7.0 | 1.0 | 8.0 | 2.0 | 1.0 | 5.0 | 3.0 | 6.0 | 3.0 | 4.0 | 3.0 | 1.0 | 7.0 |
| 19 | 10.0 | 8.0 | 9.0 | 8.0 | 6.0 | 2.0 | 6.0 | 6.0 | 4.0 | 6.0 | 3.0 | 5.0 | 6.0 | 2.0 | 4.0 | 8.0 | 3.0 | 1.0 | 4.0 | 6.0 | 5.0 | 1.0 | 8.0 | 6.0 | 3.0 | 4.0 | 10.0 | 2.0 | 3.0 | 4.0 | 8.0 | 1.0 | 9.0 | 6.0 | 2.0 | 3.0 | 1.0 | 8.0 | 4.0 | 4.0 | 1.0 | 8.0 | 1.0 | 9.0 | 10.0 | 5.0 | 8.0 | 8.0 | 5.0 | 6.0 | 9.0 | 5.0 | 6.0 | 8.0 | 4.0 | 6.0 | 9.0 | 5.0 | 1.0 | 10.0 | 8.0 | 3.0 |
| 20 | 6.0 | 2.0 | 2.0 | 9.0 | 1.0 | 6.0 | 5.0 | 3.0 | 1.0 | 4.0 | 2.0 | 5.0 | 9.0 | 5.0 | 1.0 | 2.0 | 2.0 | 6.0 | 7.0 | 5.0 | 3.0 | 4.0 | 1.0 | 10.0 | 3.0 | 9.0 | 4.0 | 5.0 | 4.0 | 1.0 | 8.0 | 5.0 | 1.0 | 4.0 | 7.0 | 8.0 | 7.0 | 10.0 | 6.0 | 3.0 | 9.0 | 9.0 | 9.0 | 6.0 | 6.0 | 5.0 | 5.0 | 8.0 | 7.0 | 8.0 | 3.0 | 1.0 | 9.0 | 7.0 | 7.0 | 1.0 | 9.0 | 5.0 | 2.0 | 7.0 | 7.0 | 3.0 |
| 21 | 1.0 | 9.0 | 3.0 | 9.0 | 8.0 | 7.0 | 8.0 | 7.0 | 7.0 | 9.0 | 1.0 | 2.0 | 1.0 | 6.0 | 9.0 | 3.0 | 4.0 | 7.0 | 5.0 | 1.0 | 4.0 | 1.0 | 8.0 | 4.0 | 3.0 | 7.0 | 9.0 | 10.0 | 10.0 | 2.0 | 4.0 | 8.0 | 4.0 | 5.0 | 1.0 | 4.0 | 4.0 | 5.0 | 5.0 | 4.0 | 3.0 | 1.0 | 7.0 | 9.0 | 6.0 | 2.0 | 9.0 | 5.0 | 7.0 | 3.0 | 6.0 | 1.0 | 1.0 | 5.0 | 9.0 | 1.0 | 7.0 | 3.0 | 1.0 | 9.0 | 3.0 | 3.0 |
| 22 | 2.0 | 6.0 | 5.0 | 1.0 | 8.0 | 8.0 | 3.0 | 3.0 | 4.0 | 2.0 | 4.0 | 7.0 | 4.0 | 2.0 | 1.0 | 4.0 | 6.0 | 8.0 | 3.0 | 8.0 | 1.0 | 8.0 | 2.0 | 8.0 | 7.0 | 9.0 | 4.0 | 4.0 | 3.0 | 5.0 | 9.0 | 10.0 | 2.0 | 8.0 | 3.0 | 10.0 | 5.0 | 7.0 | 1.0 | 2.0 | 6.0 | 2.0 | 5.0 | 10.0 | 1.0 | 2.0 | 5.0 | 5.0 | 4.0 | 10.0 | 4.0 | 7.0 | 1.0 | 6.0 | 1.0 | 8.0 | 5.0 | 5.0 | 4.0 | 9.0 | 3.0 | 1.0 |
| 23 | 9.0 | 2.0 | 6.0 | 2.0 | 3.0 | 1.0 | 8.0 | 3.0 | 7.0 | 10.0 | 6.0 | 10.0 | 6.0 | 10.0 | 5.0 | 5.0 | 3.0 | 2.0 | 6.0 | 6.0 | 10.0 | 4.0 | 8.0 | 1.0 | 3.0 | 8.0 | 2.0 | 6.0 | 7.0 | 2.0 | 1.0 | 1.0 | 6.0 | 7.0 | 4.0 | 2.0 | 10.0 | 10.0 | 9.0 | 4.0 | 2.0 | 9.0 | 7.0 | 5.0 | 9.0 | 10.0 | 5.0 | 7.0 | 8.0 | 2.0 | 2.0 | 2.0 | 2.0 | 2.0 | 5.0 | 2.0 | 7.0 | 3.0 | 5.0 | 1.0 | 4.0 | 2.0 |
| 24 | 4.0 | 4.0 | 8.0 | 3.0 | 3.0 | 3.0 | 10.0 | 5.0 | 5.0 | 7.0 | 10.0 | 8.0 | 8.0 | 10.0 | 1.0 | 3.0 | 4.0 | 8.0 | 2.0 | 3.0 | 3.0 | 3.0 | 7.0 | 3.0 | 2.0 | 2.0 | 3.0 | 3.0 | 3.0 | 6.0 | 7.0 | 10.0 | 3.0 | 3.0 | 2.0 | 1.0 | 10.0 | 3.0 | 3.0 | 2.0 | 8.0 | 4.0 | 4.0 | 8.0 | 1.0 | 3.0 | 3.0 | 9.0 | 9.0 | 6.0 | 3.0 | 9.0 | 9.0 | 2.0 | 2.0 | 7.0 | 3.0 | 5.0 | 3.0 | 6.0 | 6.0 | 8.0 |
| 25 | 6.0 | 1.0 | 3.0 | 7.0 | 2.0 | 6.0 | 6.0 | 5.0 | 1.0 | 2.0 | 2.0 | 6.0 | 3.0 | 5.0 | 7.0 | 1.0 | 7.0 | 6.0 | 3.0 | 4.0 | 9.0 | 7.0 | 9.0 | 8.0 | 2.0 | 4.0 | 1.0 | 2.0 | 5.0 | 5.0 | 4.0 | 10.0 | 10.0 | 8.0 | 2.0 | 10.0 | 10.0 | 3.0 | 4.0 | 6.0 | 10.0 | 8.0 | 9.0 | 8.0 | 2.0 | 4.0 | 6.0 | 2.0 | 2.0 | 3.0 | 3.0 | 7.0 | 5.0 | 8.0 | 5.0 | 5.0 | 4.0 | 9.0 | 2.0 | 6.0 | 7.0 | 6.0 |
| 26 | 10.0 | 6.0 | 8.0 | 2.0 | 3.0 | 8.0 | 7.0 | 6.0 | 7.0 | 3.0 | 2.0 | 7.0 | 7.0 | 10.0 | 6.0 | 7.0 | 7.0 | 7.0 | 9.0 | 10.0 | 4.0 | 9.0 | 4.0 | 2.0 | 3.0 | 1.0 | 10.0 | 4.0 | 7.0 | 2.0 | 3.0 | 3.0 | 5.0 | 1.0 | 1.0 | 8.0 | 4.0 | 5.0 | 9.0 | 10.0 | 5.0 | 1.0 | 2.0 | 2.0 | 7.0 | 10.0 | 6.0 | 7.0 | 3.0 | 6.0 | 9.0 | 5.0 | 2.0 | 7.0 | 6.0 | 7.0 | 3.0 | 6.0 | 9.0 | 1.0 | 8.0 | 8.0 |
| 27 | 6.0 | 8.0 | 3.0 | 5.0 | 10.0 | 9.0 | 3.0 | 9.0 | 7.0 | 9.0 | 4.0 | 9.0 | 4.0 | 10.0 | 5.0 | 1.0 | 7.0 | 3.0 | 4.0 | 2.0 | 5.0 | 10.0 | 4.0 | 6.0 | 3.0 | 2.0 | 4.0 | 8.0 | 4.0 | 1.0 | 10.0 | 6.0 | 1.0 | 2.0 | 7.0 | 5.0 | 4.0 | 3.0 | 4.0 | 1.0 | 8.0 | 6.0 | 3.0 | 7.0 | 9.0 | 1.0 | 10.0 | 2.0 | 3.0 | 2.0 | 4.0 | 7.0 | 4.0 | 1.0 | 2.0 | 8.0 | 1.0 | 8.0 | 10.0 | 3.0 | 2.0 | 4.0 |
| 28 | 1.0 | 3.0 | 10.0 | 6.0 | 2.0 | 2.0 | 4.0 | 8.0 | 4.0 | 3.0 | 6.0 | 10.0 | 1.0 | 6.0 | 1.0 | 3.0 | 4.0 | 2.0 | 9.0 | 3.0 | 4.0 | 10.0 | 3.0 | 7.0 | 3.0 | 5.0 | 7.0 | 4.0 | 1.0 | 3.0 | 1.0 | 8.0 | 6.0 | 2.0 | 8.0 | 4.0 | 9.0 | 2.0 | 9.0 | 7.0 | 5.0 | 9.0 | 5.0 | 7.0 | 2.0 | 5.0 | 4.0 | 3.0 | 1.0 | 10.0 | 9.0 | 1.0 | 9.0 | 10.0 | 4.0 | 3.0 | 6.0 | 4.0 | 2.0 | 1.0 | 10.0 | 9.0 |
| 29 | 3.0 | 3.0 | 10.0 | 6.0 | 9.0 | 1.0 | 2.0 | 1.0 | 6.0 | 10.0 | 10.0 | 5.0 | 8.0 | 6.0 | 8.0 | 9.0 | 1.0 | 6.0 | 8.0 | 4.0 | 1.0 | 2.0 | 5.0 | 2.0 | 6.0 | 5.0 | 2.0 | 1.0 | 3.0 | 3.0 | 2.0 | 2.0 | 5.0 | 3.0 | 1.0 | 2.0 | 2.0 | 6.0 | 6.0 | 9.0 | 4.0 | 4.0 | 5.0 | 1.0 | 1.0 | 5.0 | 2.0 | 1.0 | 3.0 | 5.0 | 10.0 | 9.0 | 10.0 | 1.0 | 6.0 | 9.0 | 4.0 | 10.0 | 7.0 | 5.0 | 6.0 | 10.0 |
| 30 | 9.0 | 10.0 | 5.0 | 4.0 | 2.0 | 6.0 | 5.0 | 10.0 | 6.0 | 6.0 | 1.0 | 5.0 | 8.0 | 9.0 | 8.0 | 1.0 | 2.0 | 6.0 | 4.0 | 8.0 | 8.0 | 4.0 | 9.0 | 1.0 | 7.0 | 4.0 | 3.0 | 10.0 | 1.0 | 2.0 | 4.0 | 9.0 | 8.0 | 8.0 | 6.0 | 7.0 | 6.0 | 4.0 | 7.0 | 2.0 | 8.0 | 9.0 | 8.0 | 10.0 | 5.0 | 2.0 | 6.0 | 5.0 | 8.0 | 3.0 | 6.0 | 7.0 | 7.0 | 7.0 | 9.0 | 7.0 | 10.0 | 10.0 | 8.0 | 6.0 | 5.0 | 2.0 |
| 31 | 7.0 | 1.0 | 5.0 | 1.0 | 8.0 | 6.0 | 5.0 | 9.0 | 9.0 | 6.0 | 1.0 | 7.0 | 3.0 | 7.0 | 2.0 | 10.0 | 10.0 | 8.0 | 3.0 | 1.0 | 5.0 | 8.0 | 10.0 | 1.0 | 10.0 | 10.0 | 3.0 | 6.0 | 8.0 | 2.0 | 9.0 | 5.0 | 8.0 | 9.0 | 6.0 | 5.0 | 6.0 | 6.0 | 1.0 | 6.0 | 5.0 | 10.0 | 4.0 | 5.0 | 10.0 | 8.0 | 7.0 | 9.0 | 8.0 | 1.0 | 7.0 | 7.0 | 4.0 | 1.0 | 5.0 | 5.0 | 8.0 | 4.0 | 2.0 | 6.0 | 9.0 | 5.0 |
| 32 | 10.0 | 9.0 | 9.0 | 4.0 | 5.0 | 6.0 | 3.0 | 1.0 | 6.0 | 3.0 | 1.0 | 1.0 | 1.0 | 8.0 | 7.0 | 5.0 | 2.0 | 7.0 | 9.0 | 9.0 | 1.0 | 4.0 | 2.0 | 6.0 | 3.0 | 10.0 | 5.0 | 1.0 | 6.0 | 5.0 | 8.0 | 8.0 | 2.0 | 9.0 | 3.0 | 10.0 | 8.0 | 4.0 | 8.0 | 3.0 | 1.0 | 7.0 | 4.0 | 8.0 | 1.0 | 10.0 | 3.0 | 2.0 | 5.0 | 6.0 | 3.0 | 1.0 | 4.0 | 5.0 | 5.0 | 3.0 | 1.0 | 7.0 | 8.0 | 3.0 | 1.0 | 7.0 |
| 33 | 5.0 | 2.0 | 3.0 | 8.0 | 1.0 | 2.0 | 4.0 | 5.0 | 10.0 | 7.0 | 8.0 | 5.0 | 7.0 | 2.0 | 4.0 | 5.0 | 9.0 | 7.0 | 2.0 | 6.0 | 4.0 | 5.0 | 8.0 | 7.0 | 3.0 | 8.0 | 1.0 | 2.0 | 2.0 | 3.0 | 8.0 | 9.0 | 9.0 | 4.0 | 8.0 | 9.0 | 10.0 | 4.0 | 6.0 | 8.0 | 1.0 | 1.0 | 6.0 | 4.0 | 10.0 | 10.0 | 1.0 | 10.0 | 1.0 | 8.0 | 4.0 | 5.0 | 3.0 | 5.0 | 6.0 | 4.0 | 10.0 | 8.0 | 9.0 | 2.0 | 7.0 | 6.0 |
| 34 | 3.0 | 1.0 | 4.0 | 10.0 | 4.0 | 10.0 | 9.0 | 5.0 | 10.0 | 9.0 | 6.0 | 3.0 | 3.0 | 10.0 | 7.0 | 2.0 | 3.0 | 7.0 | 2.0 | 2.0 | 7.0 | 1.0 | 3.0 | 4.0 | 2.0 | 2.0 | 1.0 | 7.0 | 8.0 | 1.0 | 6.0 | 6.0 | 3.0 | 8.0 | 8.0 | 1.0 | 6.0 | 4.0 | 7.0 | 4.0 | 3.0 | 5.0 | 3.0 | 8.0 | 5.0 | 8.0 | 6.0 | 9.0 | 2.0 | 3.0 | 10.0 | 3.0 | 5.0 | 9.0 | 1.0 | 5.0 | 2.0 | 5.0 | 2.0 | 6.0 | 3.0 | 2.0 |
| 35 | 8.0 | 5.0 | 10.0 | 3.0 | 7.0 | 4.0 | 7.0 | 5.0 | 8.0 | 6.0 | 6.0 | 7.0 | 2.0 | 5.0 | 6.0 | 2.0 | 9.0 | 6.0 | 8.0 | 3.0 | 8.0 | 4.0 | 10.0 | 2.0 | 1.0 | 10.0 | 8.0 | 5.0 | 4.0 | 2.0 | 7.0 | 5.0 | 10.0 | 9.0 | 1.0 | 4.0 | 9.0 | 6.0 | 6.0 | 7.0 | 7.0 | 4.0 | 7.0 | 2.0 | 6.0 | 6.0 | 9.0 | 8.0 | 5.0 | 7.0 | 8.0 | 2.0 | 9.0 | 1.0 | 1.0 | 9.0 | 6.0 | 9.0 | 4.0 | 8.0 | 2.0 | 1.0 |
| 36 | 7.0 | 2.0 | 10.0 | 3.0 | 6.0 | 2.0 | 9.0 | 4.0 | 1.0 | 9.0 | 8.0 | 7.0 | 10.0 | 8.0 | 9.0 | 2.0 | 8.0 | 2.0 | 9.0 | 1.0 | 7.0 | 4.0 | 5.0 | 10.0 | 10.0 | 10.0 | 4.0 | 4.0 | 9.0 | 2.0 | 6.0 | 6.0 | 8.0 | 10.0 | 6.0 | 9.0 | 2.0 | 10.0 | 2.0 | 3.0 | 8.0 | 3.0 | 10.0 | 8.0 | 4.0 | 1.0 | 1.0 | 9.0 | 2.0 | 6.0 | 1.0 | 5.0 | 4.0 | 2.0 | 7.0 | 4.0 | 7.0 | 8.0 | 5.0 | 9.0 | 4.0 | 4.0 |
| 37 | 5.0 | 4.0 | 6.0 | 1.0 | 2.0 | 8.0 | 7.0 | 9.0 | 4.0 | 1.0 | 3.0 | 2.0 | 10.0 | 2.0 | 8.0 | 6.0 | 6.0 | 9.0 | 9.0 | 8.0 | 10.0 | 5.0 | 7.0 | 10.0 | 3.0 | 3.0 | 5.0 | 3.0 | 2.0 | 6.0 | 4.0 | 6.0 | 4.0 | 4.0 | 4.0 | 6.0 | 10.0 | 1.0 | 8.0 | 7.0 | 9.0 | 9.0 | 4.0 | 10.0 | 2.0 | 9.0 | 2.0 | 4.0 | 1.0 | 1.0 | 8.0 | 9.0 | 1.0 | 1.0 | 9.0 | 2.0 | 2.0 | 7.0 | 7.0 | 10.0 | 2.0 | 10.0 |
| 38 | 9.0 | 7.0 | 4.0 | 3.0 | 1.0 | 2.0 | 5.0 | 2.0 | 10.0 | 3.0 | 9.0 | 9.0 | 8.0 | 1.0 | 1.0 | 10.0 | 1.0 | 7.0 | 4.0 | 4.0 | 6.0 | 5.0 | 1.0 | 9.0 | 3.0 | 4.0 | 9.0 | 4.0 | 9.0 | 6.0 | 7.0 | 1.0 | 8.0 | 6.0 | 7.0 | 6.0 | 2.0 | 8.0 | 5.0 | 5.0 | 9.0 | 9.0 | 10.0 | 1.0 | 7.0 | 9.0 | 5.0 | 2.0 | 4.0 | 5.0 | 2.0 | 3.0 | 7.0 | 6.0 | 9.0 | 7.0 | 10.0 | 6.0 | 9.0 | 4.0 | 6.0 | 2.0 |
| 39 | 10.0 | 1.0 | 3.0 | 5.0 | 8.0 | 6.0 | 7.0 | 6.0 | 2.0 | 8.0 | 9.0 | 1.0 | 10.0 | 10.0 | 4.0 | 5.0 | 7.0 | 7.0 | 10.0 | 4.0 | 3.0 | 4.0 | 2.0 | 4.0 | 2.0 | 6.0 | 10.0 | 1.0 | 7.0 | 9.0 | 2.0 | 6.0 | 3.0 | 8.0 | 4.0 | 7.0 | 3.0 | 7.0 | 5.0 | 5.0 | 2.0 | 3.0 | 7.0 | 10.0 | 2.0 | 1.0 | 8.0 | 10.0 | 10.0 | 3.0 | 10.0 | 7.0 | 6.0 | 7.0 | 1.0 | 9.0 | 4.0 | 5.0 | 4.0 | 9.0 | 1.0 | 2.0 |
| 40 | 4.0 | 2.0 | 2.0 | 4.0 | 9.0 | 7.0 | 6.0 | 2.0 | 10.0 | 8.0 | 5.0 | 2.0 | 8.0 | 10.0 | 1.0 | 6.0 | 3.0 | 1.0 | 10.0 | 1.0 | 9.0 | 3.0 | 6.0 | 2.0 | 8.0 | 10.0 | 5.0 | 8.0 | 5.0 | 4.0 | 8.0 | 5.0 | 1.0 | 1.0 | 3.0 | 7.0 | 8.0 | 9.0 | 9.0 | 2.0 | 8.0 | 5.0 | 4.0 | 7.0 | 5.0 | 6.0 | 9.0 | 5.0 | 6.0 | 4.0 | 4.0 | 7.0 | 8.0 | 8.0 | 3.0 | 10.0 | 10.0 | 6.0 | 7.0 | 7.0 | 1.0 | 3.0 |
| 41 | 2.0 | 10.0 | 5.0 | 4.0 | 8.0 | 7.0 | 8.0 | 9.0 | 2.0 | 8.0 | 10.0 | 3.0 | 1.0 | 10.0 | 10.0 | 6.0 | 3.0 | 2.0 | 1.0 | 8.0 | 9.0 | 1.0 | 2.0 | 9.0 | 4.0 | 8.0 | 1.0 | 6.0 | 9.0 | 4.0 | 9.0 | 10.0 | 7.0 | 1.0 | 5.0 | 4.0 | 3.0 | 9.0 | 9.0 | 3.0 | 5.0 | 9.0 | 10.0 | 5.0 | 5.0 | 7.0 | 9.0 | 7.0 | 2.0 | 8.0 | 2.0 | 8.0 | 7.0 | 2.0 | 4.0 | 4.0 | 4.0 | 1.0 | 7.0 | 1.0 | 10.0 | 5.0 |
| 42 | 2.0 | 6.0 | 4.0 | 3.0 | 6.0 | 2.0 | 2.0 | 5.0 | 8.0 | 5.0 | 5.0 | 3.0 | 10.0 | 6.0 | 9.0 | 1.0 | 1.0 | 2.0 | 2.0 | 1.0 | 9.0 | 7.0 | 5.0 | 7.0 | 4.0 | 9.0 | 2.0 | 3.0 | 5.0 | 5.0 | 8.0 | 4.0 | 4.0 | 6.0 | 3.0 | 7.0 | 10.0 | 4.0 | 10.0 | 7.0 | 4.0 | 10.0 | 9.0 | 10.0 | 9.0 | 4.0 | 4.0 | 9.0 | 3.0 | 8.0 | 10.0 | 6.0 | 8.0 | 4.0 | 1.0 | 9.0 | 9.0 | 3.0 | 9.0 | 10.0 | 3.0 | 1.0 |
| 43 | 10.0 | 2.0 | 3.0 | 4.0 | 5.0 | 9.0 | 5.0 | 6.0 | 8.0 | 4.0 | 7.0 | 1.0 | 3.0 | 4.0 | 9.0 | 8.0 | 2.0 | 10.0 | 8.0 | 9.0 | 6.0 | 9.0 | 10.0 | 5.0 | 8.0 | 8.0 | 2.0 | 7.0 | 7.0 | 1.0 | 10.0 | 5.0 | 8.0 | 4.0 | 8.0 | 2.0 | 8.0 | 10.0 | 1.0 | 10.0 | 7.0 | 5.0 | 10.0 | 2.0 | 5.0 | 5.0 | 1.0 | 4.0 | 5.0 | 3.0 | 3.0 | 7.0 | 7.0 | 4.0 | 7.0 | 7.0 | 7.0 | 10.0 | 10.0 | 7.0 | 10.0 | 3.0 |
| 44 | 8.0 | 1.0 | 9.0 | 3.0 | 5.0 | 10.0 | 2.0 | 5.0 | 7.0 | 3.0 | 1.0 | 7.0 | 7.0 | 3.0 | 4.0 | 3.0 | 4.0 | 3.0 | 4.0 | 10.0 | 6.0 | 6.0 | 1.0 | 9.0 | 1.0 | 2.0 | 7.0 | 9.0 | 2.0 | 1.0 | 5.0 | 10.0 | 1.0 | 10.0 | 5.0 | 6.0 | 4.0 | 2.0 | 7.0 | 2.0 | 5.0 | 5.0 | 9.0 | 5.0 | 5.0 | 3.0 | 1.0 | 1.0 | 4.0 | 3.0 | 10.0 | 10.0 | 1.0 | 10.0 | 8.0 | 9.0 | 2.0 | 2.0 | 5.0 | 3.0 | 5.0 | 7.0 |
| 45 | 5.0 | 1.0 | 1.0 | 2.0 | 3.0 | 10.0 | 8.0 | 6.0 | 10.0 | 6.0 | 9.0 | 8.0 | 1.0 | 4.0 | 5.0 | 7.0 | 9.0 | 4.0 | 1.0 | 5.0 | 5.0 | 2.0 | 2.0 | 10.0 | 3.0 | 4.0 | 10.0 | 1.0 | 5.0 | 5.0 | 2.0 | 8.0 | 10.0 | 10.0 | 8.0 | 6.0 | 1.0 | 9.0 | 9.0 | 1.0 | 6.0 | 7.0 | 4.0 | 5.0 | 3.0 | 3.0 | 9.0 | 2.0 | 3.0 | 9.0 | 1.0 | 10.0 | 1.0 | 8.0 | 3.0 | 6.0 | 10.0 | 7.0 | 8.0 | 2.0 | 8.0 | 3.0 |
| 46 | 4.0 | 6.0 | 9.0 | 1.0 | 1.0 | 8.0 | 5.0 | 3.0 | 8.0 | 1.0 | 7.0 | 8.0 | 7.0 | 9.0 | 7.0 | 7.0 | 10.0 | 4.0 | 10.0 | 8.0 | 5.0 | 9.0 | 5.0 | 5.0 | 3.0 | 6.0 | 6.0 | 10.0 | 4.0 | 2.0 | 6.0 | 7.0 | 3.0 | 1.0 | 6.0 | 9.0 | 1.0 | 2.0 | 5.0 | 8.0 | 9.0 | 9.0 | 4.0 | 1.0 | 1.0 | 9.0 | 2.0 | 8.0 | 3.0 | 7.0 | 6.0 | 2.0 | 4.0 | 4.0 | 8.0 | 2.0 | 3.0 | 7.0 | 2.0 | 7.0 | 5.0 | 6.0 |
| 47 | 8.0 | 1.0 | 2.0 | 8.0 | 3.0 | 10.0 | 9.0 | 3.0 | 10.0 | 3.0 | 2.0 | 5.0 | 7.0 | 7.0 | 3.0 | 8.0 | 4.0 | 6.0 | 6.0 | 8.0 | 8.0 | 5.0 | 5.0 | 7.0 | 9.0 | 2.0 | 7.0 | 2.0 | 3.0 | 1.0 | 5.0 | 9.0 | 2.0 | 10.0 | 9.0 | 8.0 | 9.0 | 4.0 | 2.0 | 10.0 | 5.0 | 7.0 | 9.0 | 4.0 | 1.0 | 2.0 | 8.0 | 3.0 | 7.0 | 3.0 | 2.0 | 4.0 | 6.0 | 5.0 | 9.0 | 4.0 | 5.0 | 2.0 | 4.0 | 10.0 | 2.0 | 9.0 |
| 48 | 5.0 | 8.0 | 10.0 | 3.0 | 7.0 | 7.0 | 5.0 | 6.0 | 2.0 | 1.0 | 4.0 | 3.0 | 9.0 | 6.0 | 9.0 | 9.0 | 2.0 | 7.0 | 1.0 | 5.0 | 7.0 | 7.0 | 4.0 | 8.0 | 9.0 | 2.0 | 3.0 | 3.0 | 1.0 | 3.0 | 8.0 | 8.0 | 5.0 | 1.0 | 2.0 | 5.0 | 2.0 | 1.0 | 4.0 | 10.0 | 6.0 | 2.0 | 3.0 | 5.0 | 4.0 | 3.0 | 3.0 | 7.0 | 7.0 | 2.0 | 1.0 | 8.0 | 7.0 | 9.0 | 8.0 | 6.0 | 9.0 | 7.0 | 5.0 | 6.0 | 5.0 | 4.0 |
| 49 | 8.0 | 4.0 | 9.0 | 7.0 | 3.0 | 9.0 | 5.0 | 9.0 | 4.0 | 9.0 | 3.0 | 6.0 | 6.0 | 9.0 | 6.0 | 5.0 | 4.0 | 4.0 | 7.0 | 6.0 | 8.0 | 3.0 | 10.0 | 2.0 | 6.0 | 3.0 | 6.0 | 2.0 | 10.0 | 5.0 | 3.0 | 1.0 | 6.0 | 8.0 | 3.0 | 7.0 | 6.0 | 1.0 | 5.0 | 3.0 | 4.0 | 8.0 | 8.0 | 3.0 | 3.0 | 9.0 | 7.0 | 3.0 | 2.0 | 7.0 | 5.0 | 4.0 | 1.0 | 5.0 | 1.0 | 1.0 | 3.0 | 1.0 | 2.0 | 1.0 | 9.0 | 9.0 |
| 50 | 7.0 | 3.0 | 4.0 | 1.0 | 5.0 | 8.0 | 2.0 | 9.0 | 1.0 | 2.0 | 2.0 | 2.0 | 9.0 | 3.0 | 7.0 | 3.0 | 7.0 | 3.0 | 1.0 | 9.0 | 3.0 | 6.0 | 4.0 | 2.0 | 3.0 | 3.0 | 9.0 | 4.0 | 9.0 | 10.0 | 6.0 | 7.0 | 3.0 | 4.0 | 10.0 | 8.0 | 1.0 | 8.0 | 2.0 | 10.0 | 4.0 | 2.0 | 10.0 | 3.0 | 10.0 | 1.0 | 6.0 | 2.0 | 1.0 | 5.0 | 10.0 | 4.0 | 8.0 | 3.0 | 6.0 | 4.0 | 10.0 | 9.0 | 8.0 | 3.0 | 9.0 | 10.0 |
| 51 | 10.0 | 7.0 | 7.0 | 4.0 | 4.0 | 6.0 | 10.0 | 5.0 | 9.0 | 7.0 | 1.0 | 6.0 | 9.0 | 6.0 | 5.0 | 9.0 | 10.0 | 5.0 | 8.0 | 5.0 | 1.0 | 1.0 | 7.0 | 2.0 | 9.0 | 7.0 | 5.0 | 7.0 | 1.0 | 9.0 | 7.0 | 7.0 | 1.0 | 5.0 | 3.0 | 2.0 | 5.0 | 9.0 | 3.0 | 7.0 | 7.0 | 8.0 | 6.0 | 7.0 | 10.0 | 10.0 | 2.0 | 4.0 | 8.0 | 4.0 | 4.0 | 4.0 | 10.0 | 3.0 | 2.0 | 5.0 | 2.0 | 4.0 | 1.0 | 9.0 | 9.0 | 8.0 |
| 52 | 8.0 | 9.0 | 8.0 | 6.0 | 10.0 | 2.0 | 2.0 | 5.0 | 2.0 | 9.0 | 6.0 | 3.0 | 7.0 | 4.0 | 6.0 | 10.0 | 5.0 | 1.0 | 2.0 | 6.0 | 9.0 | 1.0 | 1.0 | 2.0 | 9.0 | 5.0 | 2.0 | 4.0 | 9.0 | 10.0 | 7.0 | 4.0 | 4.0 | 3.0 | 5.0 | 9.0 | 4.0 | 1.0 | 7.0 | 6.0 | 8.0 | 7.0 | 8.0 | 7.0 | 1.0 | 1.0 | 4.0 | 6.0 | 7.0 | 1.0 | 8.0 | 10.0 | 10.0 | 9.0 | 5.0 | 6.0 | 8.0 | 4.0 | 3.0 | 5.0 | 7.0 | 5.0 |
| 53 | 9.0 | 1.0 | 1.0 | 8.0 | 9.0 | 9.0 | 8.0 | 3.0 | 1.0 | 2.0 | 2.0 | 6.0 | 5.0 | 8.0 | 8.0 | 10.0 | 1.0 | 1.0 | 1.0 | 8.0 | 7.0 | 5.0 | 6.0 | 2.0 | 2.0 | 8.0 | 7.0 | 1.0 | 10.0 | 1.0 | 7.0 | 1.0 | 5.0 | 5.0 | 9.0 | 1.0 | 2.0 | 1.0 | 6.0 | 7.0 | 8.0 | 2.0 | 4.0 | 4.0 | 10.0 | 8.0 | 4.0 | 5.0 | 9.0 | 5.0 | 3.0 | 3.0 | 9.0 | 6.0 | 1.0 | 9.0 | 1.0 | 4.0 | 3.0 | 7.0 | 6.0 | 1.0 |
| 54 | 8.0 | 6.0 | 5.0 | 1.0 | 4.0 | 10.0 | 4.0 | 7.0 | 9.0 | 7.0 | 6.0 | 3.0 | 1.0 | 10.0 | 2.0 | 1.0 | 8.0 | 4.0 | 5.0 | 4.0 | 7.0 | 9.0 | 1.0 | 5.0 | 2.0 | 5.0 | 6.0 | 2.0 | 4.0 | 6.0 | 9.0 | 5.0 | 5.0 | 6.0 | 1.0 | 1.0 | 7.0 | 9.0 | 9.0 | 1.0 | 3.0 | 4.0 | 1.0 | 7.0 | 8.0 | 3.0 | 8.0 | 9.0 | 8.0 | 1.0 | 6.0 | 2.0 | 5.0 | 1.0 | 2.0 | 7.0 | 9.0 | 7.0 | 5.0 | 5.0 | 3.0 | 7.0 |
| 55 | 2.0 | 2.0 | 1.0 | 3.0 | 1.0 | 2.0 | 1.0 | 8.0 | 5.0 | 2.0 | 3.0 | 4.0 | 7.0 | 7.0 | 6.0 | 3.0 | 6.0 | 8.0 | 3.0 | 6.0 | 1.0 | 1.0 | 8.0 | 2.0 | 7.0 | 5.0 | 7.0 | 8.0 | 3.0 | 9.0 | 7.0 | 5.0 | 3.0 | 4.0 | 5.0 | 9.0 | 4.0 | 2.0 | 7.0 | 9.0 | 10.0 | 4.0 | 9.0 | 7.0 | 9.0 | 6.0 | 2.0 | 4.0 | 6.0 | 1.0 | 4.0 | 5.0 | 6.0 | 9.0 | 7.0 | 8.0 | 9.0 | 7.0 | 8.0 | 9.0 | 1.0 | 10.0 |
| 56 | 1.0 | 1.0 | 1.0 | 9.0 | 3.0 | 2.0 | 1.0 | 2.0 | 6.0 | 3.0 | 4.0 | 10.0 | 2.0 | 1.0 | 7.0 | 9.0 | 6.0 | 8.0 | 6.0 | 9.0 | 9.0 | 7.0 | 5.0 | 7.0 | 3.0 | 4.0 | 3.0 | 1.0 | 6.0 | 4.0 | 10.0 | 8.0 | 1.0 | 10.0 | 2.0 | 6.0 | 7.0 | 2.0 | 10.0 | 4.0 | 10.0 | 4.0 | 9.0 | 7.0 | 2.0 | 10.0 | 3.0 | 5.0 | 9.0 | 3.0 | 10.0 | 2.0 | 8.0 | 1.0 | 9.0 | 9.0 | 1.0 | 6.0 | 5.0 | 10.0 | 1.0 | 5.0 |
| 57 | 9.0 | 9.0 | 7.0 | 10.0 | 2.0 | 8.0 | 7.0 | 6.0 | 5.0 | 6.0 | 4.0 | 2.0 | 8.0 | 3.0 | 6.0 | 4.0 | 7.0 | 6.0 | 3.0 | 5.0 | 5.0 | 3.0 | 5.0 | 3.0 | 5.0 | 9.0 | 6.0 | 8.0 | 4.0 | 10.0 | 10.0 | 4.0 | 7.0 | 8.0 | 5.0 | 9.0 | 8.0 | 7.0 | 6.0 | 5.0 | 6.0 | 1.0 | 3.0 | 10.0 | 2.0 | 7.0 | 7.0 | 2.0 | 7.0 | 1.0 | 9.0 | 4.0 | 4.0 | 4.0 | 7.0 | 7.0 | 6.0 | 7.0 | 4.0 | 6.0 | 10.0 | 9.0 |
| 58 | 5.0 | 3.0 | 3.0 | 7.0 | 4.0 | 9.0 | 9.0 | 7.0 | 6.0 | 2.0 | 2.0 | 10.0 | 3.0 | 6.0 | 7.0 | 2.0 | 5.0 | 3.0 | 4.0 | 1.0 | 2.0 | 1.0 | 4.0 | 5.0 | 3.0 | 2.0 | 9.0 | 10.0 | 2.0 | 7.0 | 8.0 | 2.0 | 8.0 | 9.0 | 2.0 | 4.0 | 5.0 | 7.0 | 9.0 | 4.0 | 7.0 | 7.0 | 9.0 | 10.0 | 5.0 | 8.0 | 2.0 | 4.0 | 5.0 | 2.0 | 8.0 | 1.0 | 3.0 | 3.0 | 5.0 | 8.0 | 5.0 | 4.0 | 4.0 | 4.0 | 4.0 | 10.0 |
| 59 | 2.0 | 2.0 | 10.0 | 9.0 | 3.0 | 8.0 | 10.0 | 10.0 | 8.0 | 3.0 | 3.0 | 3.0 | 2.0 | 9.0 | 6.0 | 4.0 | 6.0 | 3.0 | 3.0 | 10.0 | 7.0 | 9.0 | 9.0 | 1.0 | 6.0 | 6.0 | 1.0 | 3.0 | 1.0 | 5.0 | 6.0 | 6.0 | 3.0 | 2.0 | 6.0 | 8.0 | 9.0 | 10.0 | 4.0 | 9.0 | 7.0 | 1.0 | 10.0 | 7.0 | 3.0 | 2.0 | 7.0 | 10.0 | 6.0 | 1.0 | 3.0 | 9.0 | 5.0 | 7.0 | 5.0 | 9.0 | 10.0 | 6.0 | 4.0 | 4.0 | 1.0 | 2.0 |
| 60 | 5.0 | 7.0 | 9.0 | 6.0 | 4.0 | 2.0 | 9.0 | 9.0 | 3.0 | 4.0 | 8.0 | 9.0 | 9.0 | 8.0 | 5.0 | 8.0 | 7.0 | 8.0 | 1.0 | 8.0 | 7.0 | 3.0 | 3.0 | 4.0 | 6.0 | 7.0 | 8.0 | 2.0 | 10.0 | 6.0 | 5.0 | 9.0 | 1.0 | 7.0 | 3.0 | 2.0 | 4.0 | 2.0 | 6.0 | 1.0 | 1.0 | 10.0 | 3.0 | 10.0 | 5.0 | 8.0 | 5.0 | 2.0 | 5.0 | 9.0 | 9.0 | 9.0 | 7.0 | 6.0 | 3.0 | 1.0 | 1.0 | 10.0 | 4.0 | 1.0 | 2.0 | 5.0 |
| 61 | 9.0 | 8.0 | 7.0 | 8.0 | 3.0 | 6.0 | 7.0 | 2.0 | 8.0 | 2.0 | 8.0 | 6.0 | 8.0 | 4.0 | 8.0 | 5.0 | 10.0 | 3.0 | 7.0 | 3.0 | 3.0 | 3.0 | 1.0 | 2.0 | 8.0 | 6.0 | 8.0 | 4.0 | 9.0 | 10.0 | 2.0 | 5.0 | 7.0 | 6.0 | 2.0 | 1.0 | 4.0 | 10.0 | 2.0 | 2.0 | 3.0 | 5.0 | 1.0 | 3.0 | 7.0 | 3.0 | 6.0 | 9.0 | 4.0 | 9.0 | 10.0 | 8.0 | 5.0 | 1.0 | 7.0 | 10.0 | 5.0 | 9.0 | 10.0 | 2.0 | 5.0 | 5.0 |
I'll list each link, its base latency, and any pairwise interference below so I can pick the continuous path with the lowest total score.

I'll put the route in a simple JSON layout so it's easy to copy/paste and see the shape I expect.

{
  ""solution"": []
}

Here ""solution"" is meant to be a list (in order) of the node identifiers that form the single directed path from the start to the end. Think of it like filling in a short form: just the sequence of router names or numbers, first the start, last the destination, and every step must be a real arrow in the map. This JSON is just a sketch of the shape I want, not the final answer itself.

Please use the exact identifiers from the instance input — do not rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], 'edges': [{'from': 21, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 1, 'var_index': 1}, {'from': 21, 'to': 2, 'var_index': 2}, {'from': 21, 'to': 3, 'var_index': 3}, {'from': 21, 'to': 4, 'var_index': 4}, {'from': 21, 'to': 5, 'var_index': 5}, {'from': 21, 'to': 6, 'var_index': 6}, {'from': 21, 'to': 7, 'var_index': 7}, {'from': 21, 'to': 8, 'var_index': 8}, {'from': 21, 'to': 9, 'var_index': 9}, {'from': 21, 'to': 10, 'var_index': 10}, {'from': 21, 'to': 11, 'var_index': 11}, {'from': 21, 'to': 12, 'var_index': 12}, {'from': 21, 'to': 13, 'var_index': 13}, {'from': 21, 'to': 14, 'var_index': 14}, {'from': 21, 'to': 15, 'var_index': 15}, {'from': 21, 'to': 16, 'var_index': 16}, {'from': 21, 'to': 17, 'var_index': 17}, {'from': 21, 'to': 18, 'var_index': 18}, {'from': 21, 'to': 19, 'var_index': 19}, {'from': 21, 'to': 20, 'var_index': 20}, {'from': 0, 'to': 22, 'var_index': 21}, {'from': 1, 'to': 22, 'var_index': 22}, {'from': 2, 'to': 22, 'var_index': 23}, {'from': 3, 'to': 22, 'var_index': 24}, {'from': 4, 'to': 22, 'var_index': 25}, {'from': 5, 'to': 22, 'var_index': 26}, {'from': 6, 'to': 22, 'var_index': 27}, {'from': 7, 'to': 22, 'var_index': 28}, {'from': 8, 'to': 22, 'var_index': 29}, {'from': 9, 'to': 22, 'var_index': 30}, {'from': 10, 'to': 22, 'var_index': 31}, {'from': 11, 'to': 22, 'var_index': 32}, {'from': 12, 'to': 22, 'var_index': 33}, {'from': 13, 'to': 22, 'var_index': 34}, {'from': 14, 'to': 22, 'var_index': 35}, {'from': 15, 'to': 22, 'var_index': 36}, {'from': 16, 'to': 22, 'var_index': 37}, {'from': 17, 'to': 22, 'var_index': 38}, {'from': 18, 'to': 22, 'var_index': 39}, {'from': 19, 'to': 22, 'var_index': 40}, {'from': 20, 'to': 22, 'var_index': 41}, {'from': 0, 'to': 1, 'var_index': 42}, {'from': 1, 'to': 2, 'var_index': 43}, {'from': 2, 'to': 3, 'var_index': 44}, {'from': 3, 'to': 4, 'var_index': 45}, {'from': 4, 'to': 5, 'var_index': 46}, {'from': 5, 'to': 6, 'var_index': 47}, {'from': 6, 'to': 7, 'var_index': 48}, {'from': 7, 'to': 8, 'var_index': 49}, {'from': 8, 'to': 9, 'var_index': 50}, {'from': 9, 'to': 10, 'var_index': 51}, {'from': 10, 'to': 11, 'var_index': 52}, {'from': 11, 'to': 12, 'var_index': 53}, {'from': 12, 'to': 13, 'var_index': 54}, {'from': 13, 'to': 14, 'var_index': 55}, {'from': 14, 'to': 15, 'var_index': 56}, {'from': 15, 'to': 16, 'var_index': 57}, {'from': 16, 'to': 17, 'var_index': 58}, {'from': 17, 'to': 18, 'var_index': 59}, {'from': 18, 'to': 19, 'var_index': 60}, {'from': 19, 'to': 20, 'var_index': 61}], 'objective': {'constant': 0.0, 'linear': [7.0, 9.0, 6.0, 1.0, 7.0, 6.0, 6.0, 2.0, 4.0, 1.0, 6.0, 10.0, 8.0, 6.0, 5.0, 9.0, 1.0, 3.0, 6.0, 4.0, 10.0, 3.0, 7.0, 4.0, 4.0, 5.0, 5.0, 2.0, 3.0, 8.0, 3.0, 5.0, 9.0, 4.0, 8.0, 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56, 'quadratic_cost': 10.0}, {'var_i': 59, 'var_j': 57, 'quadratic_cost': 6.0}, {'var_i': 59, 'var_j': 58, 'quadratic_cost': 4.0}, {'var_i': 59, 'var_j': 59, 'quadratic_cost': 4.0}, {'var_i': 59, 'var_j': 60, 'quadratic_cost': 1.0}, {'var_i': 59, 'var_j': 61, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 60, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 60, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 60, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 60, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 60, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 27, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 60, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 60, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 60, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 38, 'quadratic_cost': 6.0}, {'var_i': 60, 'var_j': 39, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 40, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 41, 'quadratic_cost': 10.0}, {'var_i': 60, 'var_j': 42, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 43, 'quadratic_cost': 10.0}, {'var_i': 60, 'var_j': 44, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 45, 'quadratic_cost': 8.0}, {'var_i': 60, 'var_j': 46, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 47, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 48, 'quadratic_cost': 5.0}, {'var_i': 60, 'var_j': 49, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 50, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 51, 'quadratic_cost': 9.0}, {'var_i': 60, 'var_j': 52, 'quadratic_cost': 7.0}, {'var_i': 60, 'var_j': 53, 'quadratic_cost': 6.0}, {'var_i': 60, 'var_j': 54, 'quadratic_cost': 3.0}, {'var_i': 60, 'var_j': 55, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 56, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 57, 'quadratic_cost': 10.0}, {'var_i': 60, 'var_j': 58, 'quadratic_cost': 4.0}, {'var_i': 60, 'var_j': 59, 'quadratic_cost': 1.0}, {'var_i': 60, 'var_j': 60, 'quadratic_cost': 2.0}, {'var_i': 60, 'var_j': 61, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 61, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 61, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 61, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 61, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 61, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 25, 'quadratic_cost': 6.0}, {'var_i': 61, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 61, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 61, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 33, 'quadratic_cost': 6.0}, {'var_i': 61, 'var_j': 34, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 35, 'quadratic_cost': 1.0}, {'var_i': 61, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 61, 'var_j': 37, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 38, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 39, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 40, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 41, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 42, 'quadratic_cost': 1.0}, {'var_i': 61, 'var_j': 43, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 44, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 45, 'quadratic_cost': 3.0}, {'var_i': 61, 'var_j': 46, 'quadratic_cost': 6.0}, {'var_i': 61, 'var_j': 47, 'quadratic_cost': 9.0}, {'var_i': 61, 'var_j': 48, 'quadratic_cost': 4.0}, {'var_i': 61, 'var_j': 49, 'quadratic_cost': 9.0}, {'var_i': 61, 'var_j': 50, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 51, 'quadratic_cost': 8.0}, {'var_i': 61, 'var_j': 52, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 53, 'quadratic_cost': 1.0}, {'var_i': 61, 'var_j': 54, 'quadratic_cost': 7.0}, {'var_i': 61, 'var_j': 55, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 56, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 57, 'quadratic_cost': 9.0}, {'var_i': 61, 'var_j': 58, 'quadratic_cost': 10.0}, {'var_i': 61, 'var_j': 59, 'quadratic_cost': 2.0}, {'var_i': 61, 'var_j': 60, 'quadratic_cost': 5.0}, {'var_i': 61, 'var_j': 61, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 22, 'to': 1, 'var_index': 0}, {'from': 22, 'to': 2, 'var_index': 1}, {'from': 22, 'to': 3, 'var_index': 2}, {'from': 22, 'to': 4, 'var_index': 3}, {'from': 22, 'to': 5, 'var_index': 4}, {'from': 22, 'to': 6, 'var_index': 5}, {'from': 22, 'to': 7, 'var_index': 6}, {'from': 22, 'to': 8, 'var_index': 7}, {'from': 22, 'to': 9, 'var_index': 8}, {'from': 22, 'to': 10, 'var_index': 9}, {'from': 22, 'to': 11, 'var_index': 10}, {'from': 22, 'to': 12, 'var_index': 11}, {'from': 22, 'to': 13, 'var_index': 12}, {'from': 22, 'to': 14, 'var_index': 13}, {'from': 22, 'to': 15, 'var_index': 14}, {'from': 22, 'to': 16, 'var_index': 15}, {'from': 22, 'to': 17, 'var_index': 16}, {'from': 22, 'to': 18, 'var_index': 17}, {'from': 22, 'to': 19, 'var_index': 18}, {'from': 22, 'to': 20, 'var_index': 19}, {'from': 22, 'to': 21, 'var_index': 20}, {'from': 1, 'to': 23, 'var_index': 21}, {'from': 2, 'to': 23, 'var_index': 22}, {'from': 3, 'to': 23, 'var_index': 23}, {'from': 4, 'to': 23, 'var_index': 24}, {'from': 5, 'to': 23, 'var_index': 25}, {'from': 6, 'to': 23, 'var_index': 26}, {'from': 7, 'to': 23, 'var_index': 27}, {'from': 8, 'to': 23, 'var_index': 28}, {'from': 9, 'to': 23, 'var_index': 29}, {'from': 10, 'to': 23, 'var_index': 30}, {'from': 11, 'to': 23, 'var_index': 31}, {'from': 12, 'to': 23, 'var_index': 32}, {'from': 13, 'to': 23, 'var_index': 33}, {'from': 14, 'to': 23, 'var_index': 34}, {'from': 15, 'to': 23, 'var_index': 35}, {'from': 16, 'to': 23, 'var_index': 36}, {'from': 17, 'to': 23, 'var_index': 37}, {'from': 18, 'to': 23, 'var_index': 38}, {'from': 19, 'to': 23, 'var_index': 39}, {'from': 20, 'to': 23, 'var_index': 40}, {'from': 21, 'to': 23, 'var_index': 41}, {'from': 1, 'to': 2, 'var_index': 42}, {'from': 2, 'to': 3, 'var_index': 43}, {'from': 3, 'to': 4, 'var_index': 44}, {'from': 4, 'to': 5, 'var_index': 45}, {'from': 5, 'to': 6, 'var_index': 46}, {'from': 6, 'to': 7, 'var_index': 47}, {'from': 7, 'to': 8, 'var_index': 48}, {'from': 8, 'to': 9, 'var_index': 49}, {'from': 9, 'to': 10, 'var_index': 50}, {'from': 10, 'to': 11, 'var_index': 51}, {'from': 11, 'to': 12, 'var_index': 52}, {'from': 12, 'to': 13, 'var_index': 53}, {'from': 13, 'to': 14, 'var_index': 54}, {'from': 14, 'to': 15, 'var_index': 55}, {'from': 15, 'to': 16, 'var_index': 56}, {'from': 16, 'to': 17, 'var_index': 57}, {'from': 17, 'to': 18, 'var_index': 58}, {'from': 18, 'to': 19, 'var_index': 59}, {'from': 19, 'to': 20, 'var_index': 60}, {'from': 20, 'to': 21, 'var_index': 61}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23}}","[22, 4, 23]",3,nl,1
QSPP,QSPP,"We manage a stretch of conveyors between the loading station and the packing station and need to decide on exactly one route that follows the arrows on the belts. Every conveyor segment burns energy and may have a one-off surcharge for using it, and sometimes two particular segments together trigger another small fee. The winner is simply the one route whose total bill — the sum of each segment’s cost plus any extra charges for pairs of segments used together — is smallest. The route must be a single, connected sequence from the loading spot to packing, with each connection actually existing and no duplicates; the specific map and costs appear below.

{
  ""total_locations"": 18,
  ""total_conveyor_segments"": 17,
  ""location_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17
  ],
  ""loading_station"": 16,
  ""packing_station"": 17,
  ""edges"": [
    {
      ""segment_tail_location"": 16,
      ""segment_head_location"": 0,
      ""segment_id"": 0
    },
    {
      ""segment_tail_location"": 15,
      ""segment_head_location"": 17,
      ""segment_id"": 1
    },
    {
      ""segment_tail_location"": 0,
      ""segment_head_location"": 1,
      ""segment_id"": 2
    },
    {
      ""segment_tail_location"": 1,
      ""segment_head_location"": 2,
      ""segment_id"": 3
    },
    {
      ""segment_tail_location"": 2,
      ""segment_head_location"": 3,
      ""segment_id"": 4
    },
    {
      ""segment_tail_location"": 3,
      ""segment_head_location"": 4,
      ""segment_id"": 5
    },
    {
      ""segment_tail_location"": 4,
      ""segment_head_location"": 5,
      ""segment_id"": 6
    },
    {
      ""segment_tail_location"": 5,
      ""segment_head_location"": 6,
      ""segment_id"": 7
    },
    {
      ""segment_tail_location"": 6,
      ""segment_head_location"": 7,
      ""segment_id"": 8
    },
    {
      ""segment_tail_location"": 7,
      ""segment_head_location"": 8,
      ""segment_id"": 9
    },
    {
      ""segment_tail_location"": 8,
      ""segment_head_location"": 9,
      ""segment_id"": 10
    },
    {
      ""segment_tail_location"": 9,
      ""segment_head_location"": 10,
      ""segment_id"": 11
    },
    {
      ""segment_tail_location"": 10,
      ""segment_head_location"": 11,
      ""segment_id"": 12
    },
    {
      ""segment_tail_location"": 11,
      ""segment_head_location"": 12,
      ""segment_id"": 13
    },
    {
      ""segment_tail_location"": 12,
      ""segment_head_location"": 13,
      ""segment_id"": 14
    },
    {
      ""segment_tail_location"": 13,
      ""segment_head_location"": 14,
      ""segment_id"": 15
    },
    {
      ""segment_tail_location"": 14,
      ""segment_head_location"": 15,
      ""segment_id"": 16
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""energy_and_usage_surcharge"": 6.0
    },
    {
      ""segment_id"": 1,
      ""energy_and_usage_surcharge"": 1.0
    },
    {
      ""segment_id"": 2,
      ""energy_and_usage_surcharge"": 4.0
    },
    {
      ""segment_id"": 3,
      ""energy_and_usage_surcharge"": 5.0
    },
    {
      ""segment_id"": 4,
      ""energy_and_usage_surcharge"": 3.0
    },
    {
      ""segment_id"": 5,
      ""energy_and_usage_surcharge"": 9.0
    },
    {
      ""segment_id"": 6,
      ""energy_and_usage_surcharge"": 8.0
    },
    {
      ""segment_id"": 7,
      ""energy_and_usage_surcharge"": 5.0
    },
    {
      ""segment_id"": 8,
      ""energy_and_usage_surcharge"": 6.0
    },
    {
      ""segment_id"": 9,
      ""energy_and_usage_surcharge"": 1.0
    },
    {
      ""segment_id"": 10,
      ""energy_and_usage_surcharge"": 4.0
    },
    {
      ""segment_id"": 11,
      ""energy_and_usage_surcharge"": 1.0
    },
    {
      ""segment_id"": 12,
      ""energy_and_usage_surcharge"": 1.0
    },
    {
      ""segment_id"": 13,
      ""energy_and_usage_surcharge"": 6.0
    },
    {
      ""segment_id"": 14,
      ""energy_and_usage_surcharge"": 3.0
    },
    {
      ""segment_id"": 15,
      ""energy_and_usage_surcharge"": 10.0
    },
    {
      ""segment_id"": 16,
      ""energy_and_usage_surcharge"": 7.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 8.0 | 9.0 | 4.0 | 8.0 | 8.0 | 9.0 | 6.0 | 4.0 | 7.0 | 3.0 | 3.0 | 5.0 | 9.0 | 10.0 | 5.0 | 6.0 |
| 1 | 8.0 | 4.0 | 9.0 | 10.0 | 4.0 | 8.0 | 2.0 | 10.0 | 6.0 | 5.0 | 5.0 | 4.0 | 6.0 | 7.0 | 2.0 | 2.0 | 9.0 |
| 2 | 9.0 | 9.0 | 2.0 | 2.0 | 7.0 | 10.0 | 2.0 | 1.0 | 8.0 | 5.0 | 4.0 | 5.0 | 3.0 | 6.0 | 9.0 | 6.0 | 1.0 |
| 3 | 4.0 | 10.0 | 2.0 | 6.0 | 2.0 | 9.0 | 6.0 | 5.0 | 7.0 | 7.0 | 6.0 | 8.0 | 6.0 | 10.0 | 1.0 | 6.0 | 1.0 |
| 4 | 8.0 | 4.0 | 7.0 | 2.0 | 9.0 | 2.0 | 2.0 | 2.0 | 9.0 | 7.0 | 5.0 | 10.0 | 7.0 | 8.0 | 10.0 | 5.0 | 8.0 |
| 5 | 8.0 | 8.0 | 10.0 | 9.0 | 2.0 | 6.0 | 6.0 | 8.0 | 7.0 | 4.0 | 1.0 | 8.0 | 10.0 | 9.0 | 2.0 | 2.0 | 4.0 |
| 6 | 9.0 | 2.0 | 2.0 | 6.0 | 2.0 | 6.0 | 6.0 | 5.0 | 9.0 | 2.0 | 7.0 | 10.0 | 9.0 | 4.0 | 9.0 | 6.0 | 3.0 |
| 7 | 6.0 | 10.0 | 1.0 | 5.0 | 2.0 | 8.0 | 5.0 | 1.0 | 4.0 | 10.0 | 10.0 | 10.0 | 7.0 | 7.0 | 9.0 | 8.0 | 1.0 |
| 8 | 4.0 | 6.0 | 8.0 | 7.0 | 9.0 | 7.0 | 9.0 | 4.0 | 4.0 | 6.0 | 1.0 | 10.0 | 8.0 | 6.0 | 8.0 | 9.0 | 1.0 |
| 9 | 7.0 | 5.0 | 5.0 | 7.0 | 7.0 | 4.0 | 2.0 | 10.0 | 6.0 | 10.0 | 8.0 | 10.0 | 2.0 | 6.0 | 9.0 | 3.0 | 5.0 |
| 10 | 3.0 | 5.0 | 4.0 | 6.0 | 5.0 | 1.0 | 7.0 | 10.0 | 1.0 | 8.0 | 1.0 | 10.0 | 7.0 | 3.0 | 7.0 | 2.0 | 10.0 |
| 11 | 3.0 | 4.0 | 5.0 | 8.0 | 10.0 | 8.0 | 10.0 | 10.0 | 10.0 | 10.0 | 10.0 | 8.0 | 6.0 | 9.0 | 6.0 | 8.0 | 8.0 |
| 12 | 5.0 | 6.0 | 3.0 | 6.0 | 7.0 | 10.0 | 9.0 | 7.0 | 8.0 | 2.0 | 7.0 | 6.0 | 3.0 | 4.0 | 10.0 | 3.0 | 2.0 |
| 13 | 9.0 | 7.0 | 6.0 | 10.0 | 8.0 | 9.0 | 4.0 | 7.0 | 6.0 | 6.0 | 3.0 | 9.0 | 4.0 | 4.0 | 10.0 | 4.0 | 4.0 |
| 14 | 10.0 | 2.0 | 9.0 | 1.0 | 10.0 | 2.0 | 9.0 | 9.0 | 8.0 | 9.0 | 7.0 | 6.0 | 10.0 | 10.0 | 1.0 | 5.0 | 4.0 |
| 15 | 5.0 | 2.0 | 6.0 | 6.0 | 5.0 | 2.0 | 6.0 | 8.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 4.0 | 5.0 | 2.0 | 4.0 |
| 16 | 6.0 | 9.0 | 1.0 | 1.0 | 8.0 | 4.0 | 3.0 | 1.0 | 1.0 | 5.0 | 10.0 | 8.0 | 2.0 | 4.0 | 4.0 | 4.0 | 5.0 |

Also, when you send the chosen route back, please put it in a tiny JSON shape so it's easy to read and machine-friendly. Something like this:

{
  ""solution"": []
}

Here, ""solution"" is just a list of node identifiers in order from the loading spot to the packing spot — first item is the source, last item is the target. Think of it like filling out a one-line route on a form; this block just shows the expected shape, not the actual route itself.

Please use the node identifiers exactly as they appear in the instance input — no renaming, no made-up labels — and don't include any edge IDs or cost numbers, only node names. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 15, 'to': 17, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [6.0, 1.0, 4.0, 5.0, 3.0, 9.0, 8.0, 5.0, 6.0, 1.0, 4.0, 1.0, 1.0, 6.0, 3.0, 10.0, 7.0], 'quadratic': [[3.0, 8.0, 9.0, 4.0, 8.0, 8.0, 9.0, 6.0, 4.0, 7.0, 3.0, 3.0, 5.0, 9.0, 10.0, 5.0, 6.0], [8.0, 4.0, 9.0, 10.0, 4.0, 8.0, 2.0, 10.0, 6.0, 5.0, 5.0, 4.0, 6.0, 7.0, 2.0, 2.0, 9.0], [9.0, 9.0, 2.0, 2.0, 7.0, 10.0, 2.0, 1.0, 8.0, 5.0, 4.0, 5.0, 3.0, 6.0, 9.0, 6.0, 1.0], [4.0, 10.0, 2.0, 6.0, 2.0, 9.0, 6.0, 5.0, 7.0, 7.0, 6.0, 8.0, 6.0, 10.0, 1.0, 6.0, 1.0], [8.0, 4.0, 7.0, 2.0, 9.0, 2.0, 2.0, 2.0, 9.0, 7.0, 5.0, 10.0, 7.0, 8.0, 10.0, 5.0, 8.0], [8.0, 8.0, 10.0, 9.0, 2.0, 6.0, 6.0, 8.0, 7.0, 4.0, 1.0, 8.0, 10.0, 9.0, 2.0, 2.0, 4.0], [9.0, 2.0, 2.0, 6.0, 2.0, 6.0, 6.0, 5.0, 9.0, 2.0, 7.0, 10.0, 9.0, 4.0, 9.0, 6.0, 3.0], [6.0, 10.0, 1.0, 5.0, 2.0, 8.0, 5.0, 1.0, 4.0, 10.0, 10.0, 10.0, 7.0, 7.0, 9.0, 8.0, 1.0], [4.0, 6.0, 8.0, 7.0, 9.0, 7.0, 9.0, 4.0, 4.0, 6.0, 1.0, 10.0, 8.0, 6.0, 8.0, 9.0, 1.0], [7.0, 5.0, 5.0, 7.0, 7.0, 4.0, 2.0, 10.0, 6.0, 10.0, 8.0, 10.0, 2.0, 6.0, 9.0, 3.0, 5.0], [3.0, 5.0, 4.0, 6.0, 5.0, 1.0, 7.0, 10.0, 1.0, 8.0, 1.0, 10.0, 7.0, 3.0, 7.0, 2.0, 10.0], [3.0, 4.0, 5.0, 8.0, 10.0, 8.0, 10.0, 10.0, 10.0, 10.0, 10.0, 8.0, 6.0, 9.0, 6.0, 8.0, 8.0], [5.0, 6.0, 3.0, 6.0, 7.0, 10.0, 9.0, 7.0, 8.0, 2.0, 7.0, 6.0, 3.0, 4.0, 10.0, 3.0, 2.0], [9.0, 7.0, 6.0, 10.0, 8.0, 9.0, 4.0, 7.0, 6.0, 6.0, 3.0, 9.0, 4.0, 4.0, 10.0, 4.0, 4.0], [10.0, 2.0, 9.0, 1.0, 10.0, 2.0, 9.0, 9.0, 8.0, 9.0, 7.0, 6.0, 10.0, 10.0, 1.0, 5.0, 4.0], [5.0, 2.0, 6.0, 6.0, 5.0, 2.0, 6.0, 8.0, 9.0, 3.0, 2.0, 8.0, 3.0, 4.0, 5.0, 2.0, 4.0], [6.0, 9.0, 1.0, 1.0, 8.0, 4.0, 3.0, 1.0, 1.0, 5.0, 10.0, 8.0, 2.0, 4.0, 4.0, 4.0, 5.0]]}, 'source': 16, 'target': 17}","[16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17]",1795.0,"{'problem_type': 'QSPP', 'num_nodes': 18, 'num_edges': 17, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'source': 16, 'target': 17, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 3.0}, {'var_index': 5, 'linear_cost': 9.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 6.0}, {'var_index': 9, 'linear_cost': 1.0}, {'var_index': 10, 'linear_cost': 4.0}, {'var_index': 11, 'linear_cost': 1.0}, {'var_index': 12, 'linear_cost': 1.0}, {'var_index': 13, 'linear_cost': 6.0}, {'var_index': 14, 'linear_cost': 3.0}, {'var_index': 15, 'linear_cost': 10.0}, {'var_index': 16, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 15, 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QSPP,QSPP,"Many people on the planning team are comparing possible single-channel routes from the reservoir inlet to the treatment outfall, all of which must follow the arrows on the canal map. Every candidate has to be a single, uninterrupted path—no skipping pieces, no splitting, no revisiting the same segment. Each canal segment brings its own pumping/erosion cost plus a usage surcharge, and some pairs of consecutive segments bring extra charges when used together (those extra charges can vary with the order of the two segments). The route we want is simply the one that results in the lowest total bill after summing every segment’s charges and any extra pairwise fees. The map and cost details are shown below.

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  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_segment_id, second_segment_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_segment_id\second_segment_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 9.0 | 2.0 | 6.0 | 1.0 | 1.0 | 4.0 | 4.0 | 1.0 | 2.0 | 7.0 | 2.0 | 5.0 | 8.0 | 7.0 | 7.0 | 8.0 | 1.0 | 1.0 | 8.0 | 4.0 | 7.0 | 10.0 | 7.0 | 3.0 | 1.0 | 10.0 | 8.0 | 6.0 | 3.0 | 1.0 | 1.0 | 2.0 | 8.0 | 10.0 | 4.0 | 9.0 | 7.0 | 1.0 | 9.0 | 3.0 | 7.0 | 8.0 | 4.0 | 7.0 | 7.0 | 3.0 | 3.0 | 5.0 | 2.0 | 9.0 | 3.0 | 4.0 | 3.0 | 10.0 | 5.0 |
| 1 | 9.0 | 9.0 | 5.0 | 5.0 | 10.0 | 9.0 | 9.0 | 2.0 | 6.0 | 5.0 | 10.0 | 3.0 | 3.0 | 9.0 | 4.0 | 10.0 | 9.0 | 3.0 | 8.0 | 8.0 | 7.0 | 5.0 | 3.0 | 5.0 | 5.0 | 3.0 | 4.0 | 5.0 | 2.0 | 10.0 | 4.0 | 1.0 | 10.0 | 6.0 | 3.0 | 4.0 | 6.0 | 4.0 | 9.0 | 2.0 | 1.0 | 3.0 | 4.0 | 8.0 | 2.0 | 4.0 | 4.0 | 10.0 | 4.0 | 3.0 | 4.0 | 8.0 | 8.0 | 6.0 | 10.0 | 4.0 |
| 2 | 2.0 | 5.0 | 8.0 | 10.0 | 7.0 | 5.0 | 5.0 | 4.0 | 4.0 | 10.0 | 10.0 | 9.0 | 10.0 | 9.0 | 9.0 | 6.0 | 10.0 | 8.0 | 2.0 | 4.0 | 9.0 | 4.0 | 4.0 | 1.0 | 1.0 | 7.0 | 7.0 | 3.0 | 8.0 | 1.0 | 7.0 | 7.0 | 6.0 | 10.0 | 7.0 | 7.0 | 1.0 | 8.0 | 10.0 | 9.0 | 1.0 | 6.0 | 5.0 | 6.0 | 7.0 | 2.0 | 6.0 | 9.0 | 8.0 | 6.0 | 8.0 | 9.0 | 1.0 | 10.0 | 1.0 | 6.0 |
| 3 | 6.0 | 5.0 | 10.0 | 2.0 | 9.0 | 7.0 | 2.0 | 2.0 | 10.0 | 4.0 | 4.0 | 10.0 | 3.0 | 9.0 | 10.0 | 6.0 | 4.0 | 5.0 | 7.0 | 8.0 | 4.0 | 10.0 | 1.0 | 2.0 | 1.0 | 1.0 | 6.0 | 8.0 | 1.0 | 3.0 | 6.0 | 5.0 | 4.0 | 8.0 | 10.0 | 1.0 | 6.0 | 9.0 | 4.0 | 5.0 | 4.0 | 4.0 | 3.0 | 6.0 | 1.0 | 4.0 | 3.0 | 8.0 | 7.0 | 8.0 | 1.0 | 10.0 | 2.0 | 9.0 | 1.0 | 9.0 |
| 4 | 1.0 | 10.0 | 7.0 | 9.0 | 7.0 | 7.0 | 10.0 | 10.0 | 4.0 | 10.0 | 2.0 | 7.0 | 6.0 | 8.0 | 5.0 | 5.0 | 2.0 | 5.0 | 6.0 | 2.0 | 4.0 | 7.0 | 3.0 | 6.0 | 1.0 | 7.0 | 6.0 | 9.0 | 10.0 | 5.0 | 3.0 | 7.0 | 8.0 | 4.0 | 9.0 | 6.0 | 5.0 | 7.0 | 6.0 | 5.0 | 1.0 | 8.0 | 7.0 | 3.0 | 3.0 | 10.0 | 2.0 | 7.0 | 4.0 | 7.0 | 8.0 | 3.0 | 6.0 | 7.0 | 3.0 | 5.0 |
| 5 | 1.0 | 9.0 | 5.0 | 7.0 | 7.0 | 8.0 | 4.0 | 2.0 | 2.0 | 4.0 | 8.0 | 3.0 | 5.0 | 5.0 | 10.0 | 4.0 | 3.0 | 5.0 | 9.0 | 7.0 | 6.0 | 10.0 | 5.0 | 6.0 | 7.0 | 3.0 | 4.0 | 5.0 | 9.0 | 9.0 | 6.0 | 10.0 | 6.0 | 4.0 | 8.0 | 6.0 | 1.0 | 10.0 | 7.0 | 2.0 | 2.0 | 1.0 | 1.0 | 1.0 | 3.0 | 6.0 | 8.0 | 1.0 | 2.0 | 10.0 | 2.0 | 2.0 | 6.0 | 2.0 | 8.0 | 2.0 |
| 6 | 4.0 | 9.0 | 5.0 | 2.0 | 10.0 | 4.0 | 10.0 | 7.0 | 7.0 | 5.0 | 5.0 | 10.0 | 4.0 | 3.0 | 1.0 | 3.0 | 3.0 | 6.0 | 6.0 | 8.0 | 9.0 | 3.0 | 8.0 | 4.0 | 7.0 | 4.0 | 6.0 | 2.0 | 8.0 | 6.0 | 1.0 | 4.0 | 4.0 | 3.0 | 1.0 | 9.0 | 1.0 | 6.0 | 7.0 | 7.0 | 8.0 | 2.0 | 6.0 | 9.0 | 9.0 | 7.0 | 4.0 | 8.0 | 1.0 | 3.0 | 8.0 | 2.0 | 4.0 | 10.0 | 3.0 | 6.0 |
| 7 | 4.0 | 2.0 | 4.0 | 2.0 | 10.0 | 2.0 | 7.0 | 1.0 | 6.0 | 3.0 | 8.0 | 5.0 | 10.0 | 6.0 | 4.0 | 1.0 | 8.0 | 5.0 | 6.0 | 1.0 | 8.0 | 6.0 | 5.0 | 10.0 | 2.0 | 1.0 | 9.0 | 10.0 | 9.0 | 10.0 | 6.0 | 5.0 | 1.0 | 6.0 | 5.0 | 9.0 | 8.0 | 5.0 | 2.0 | 1.0 | 6.0 | 2.0 | 9.0 | 10.0 | 10.0 | 5.0 | 6.0 | 5.0 | 9.0 | 5.0 | 6.0 | 7.0 | 2.0 | 10.0 | 3.0 | 9.0 |
| 8 | 1.0 | 6.0 | 4.0 | 10.0 | 4.0 | 2.0 | 7.0 | 6.0 | 6.0 | 3.0 | 6.0 | 6.0 | 7.0 | 1.0 | 6.0 | 4.0 | 3.0 | 1.0 | 10.0 | 2.0 | 2.0 | 3.0 | 4.0 | 2.0 | 6.0 | 7.0 | 7.0 | 6.0 | 10.0 | 9.0 | 8.0 | 3.0 | 5.0 | 7.0 | 8.0 | 9.0 | 6.0 | 7.0 | 1.0 | 2.0 | 9.0 | 10.0 | 2.0 | 9.0 | 1.0 | 4.0 | 6.0 | 3.0 | 2.0 | 4.0 | 2.0 | 5.0 | 8.0 | 5.0 | 5.0 | 2.0 |
| 9 | 2.0 | 5.0 | 10.0 | 4.0 | 10.0 | 4.0 | 5.0 | 3.0 | 3.0 | 9.0 | 10.0 | 5.0 | 5.0 | 10.0 | 2.0 | 1.0 | 5.0 | 6.0 | 10.0 | 5.0 | 10.0 | 9.0 | 3.0 | 5.0 | 7.0 | 10.0 | 9.0 | 1.0 | 7.0 | 4.0 | 5.0 | 3.0 | 8.0 | 4.0 | 8.0 | 9.0 | 5.0 | 9.0 | 9.0 | 3.0 | 1.0 | 7.0 | 10.0 | 2.0 | 10.0 | 5.0 | 5.0 | 1.0 | 7.0 | 1.0 | 4.0 | 6.0 | 1.0 | 1.0 | 5.0 | 10.0 |
| 10 | 7.0 | 10.0 | 10.0 | 4.0 | 2.0 | 8.0 | 5.0 | 8.0 | 6.0 | 10.0 | 3.0 | 9.0 | 2.0 | 4.0 | 6.0 | 9.0 | 4.0 | 2.0 | 9.0 | 10.0 | 1.0 | 10.0 | 7.0 | 2.0 | 7.0 | 1.0 | 6.0 | 7.0 | 1.0 | 5.0 | 1.0 | 7.0 | 6.0 | 2.0 | 1.0 | 6.0 | 10.0 | 3.0 | 3.0 | 2.0 | 4.0 | 3.0 | 5.0 | 9.0 | 6.0 | 3.0 | 2.0 | 1.0 | 8.0 | 7.0 | 5.0 | 10.0 | 1.0 | 10.0 | 8.0 | 5.0 |
| 11 | 2.0 | 3.0 | 9.0 | 10.0 | 7.0 | 3.0 | 10.0 | 5.0 | 6.0 | 5.0 | 9.0 | 4.0 | 4.0 | 9.0 | 3.0 | 7.0 | 5.0 | 10.0 | 7.0 | 7.0 | 2.0 | 1.0 | 6.0 | 5.0 | 8.0 | 2.0 | 3.0 | 2.0 | 6.0 | 7.0 | 9.0 | 9.0 | 6.0 | 10.0 | 2.0 | 7.0 | 8.0 | 8.0 | 4.0 | 7.0 | 9.0 | 5.0 | 4.0 | 8.0 | 8.0 | 8.0 | 1.0 | 5.0 | 6.0 | 8.0 | 6.0 | 6.0 | 9.0 | 4.0 | 2.0 | 9.0 |
| 12 | 5.0 | 3.0 | 10.0 | 3.0 | 6.0 | 5.0 | 4.0 | 10.0 | 7.0 | 5.0 | 2.0 | 4.0 | 9.0 | 3.0 | 7.0 | 10.0 | 3.0 | 2.0 | 7.0 | 9.0 | 1.0 | 8.0 | 5.0 | 2.0 | 8.0 | 4.0 | 5.0 | 9.0 | 4.0 | 1.0 | 2.0 | 3.0 | 2.0 | 3.0 | 9.0 | 1.0 | 4.0 | 7.0 | 9.0 | 10.0 | 4.0 | 10.0 | 7.0 | 6.0 | 1.0 | 2.0 | 10.0 | 10.0 | 7.0 | 3.0 | 4.0 | 1.0 | 3.0 | 2.0 | 1.0 | 4.0 |
| 13 | 8.0 | 9.0 | 9.0 | 9.0 | 8.0 | 5.0 | 3.0 | 6.0 | 1.0 | 10.0 | 4.0 | 9.0 | 3.0 | 4.0 | 5.0 | 2.0 | 6.0 | 3.0 | 6.0 | 2.0 | 9.0 | 5.0 | 7.0 | 1.0 | 1.0 | 4.0 | 10.0 | 9.0 | 2.0 | 6.0 | 8.0 | 4.0 | 6.0 | 4.0 | 4.0 | 4.0 | 10.0 | 8.0 | 2.0 | 1.0 | 7.0 | 7.0 | 4.0 | 7.0 | 6.0 | 5.0 | 2.0 | 5.0 | 10.0 | 8.0 | 10.0 | 2.0 | 6.0 | 8.0 | 7.0 | 7.0 |
| 14 | 7.0 | 4.0 | 9.0 | 10.0 | 5.0 | 10.0 | 1.0 | 4.0 | 6.0 | 2.0 | 6.0 | 3.0 | 7.0 | 5.0 | 2.0 | 4.0 | 1.0 | 10.0 | 5.0 | 1.0 | 5.0 | 10.0 | 6.0 | 6.0 | 2.0 | 1.0 | 2.0 | 4.0 | 4.0 | 7.0 | 5.0 | 2.0 | 2.0 | 7.0 | 5.0 | 7.0 | 6.0 | 6.0 | 9.0 | 7.0 | 3.0 | 7.0 | 2.0 | 4.0 | 10.0 | 2.0 | 7.0 | 2.0 | 1.0 | 9.0 | 1.0 | 2.0 | 2.0 | 2.0 | 2.0 | 10.0 |
| 15 | 7.0 | 10.0 | 6.0 | 6.0 | 5.0 | 4.0 | 3.0 | 1.0 | 4.0 | 1.0 | 9.0 | 7.0 | 10.0 | 2.0 | 4.0 | 3.0 | 8.0 | 8.0 | 4.0 | 6.0 | 3.0 | 10.0 | 3.0 | 6.0 | 7.0 | 10.0 | 1.0 | 2.0 | 9.0 | 10.0 | 3.0 | 3.0 | 3.0 | 4.0 | 2.0 | 8.0 | 9.0 | 10.0 | 6.0 | 7.0 | 1.0 | 7.0 | 10.0 | 7.0 | 9.0 | 1.0 | 2.0 | 5.0 | 2.0 | 10.0 | 7.0 | 10.0 | 7.0 | 6.0 | 4.0 | 2.0 |
| 16 | 8.0 | 9.0 | 10.0 | 4.0 | 2.0 | 3.0 | 3.0 | 8.0 | 3.0 | 5.0 | 4.0 | 5.0 | 3.0 | 6.0 | 1.0 | 8.0 | 10.0 | 2.0 | 8.0 | 5.0 | 9.0 | 2.0 | 4.0 | 4.0 | 8.0 | 4.0 | 5.0 | 8.0 | 1.0 | 9.0 | 10.0 | 5.0 | 7.0 | 1.0 | 3.0 | 1.0 | 1.0 | 5.0 | 3.0 | 8.0 | 8.0 | 2.0 | 5.0 | 2.0 | 8.0 | 5.0 | 5.0 | 7.0 | 3.0 | 8.0 | 6.0 | 10.0 | 9.0 | 6.0 | 5.0 | 8.0 |
| 17 | 1.0 | 3.0 | 8.0 | 5.0 | 5.0 | 5.0 | 6.0 | 5.0 | 1.0 | 6.0 | 2.0 | 10.0 | 2.0 | 3.0 | 10.0 | 8.0 | 2.0 | 8.0 | 8.0 | 1.0 | 6.0 | 1.0 | 3.0 | 8.0 | 7.0 | 10.0 | 8.0 | 8.0 | 2.0 | 10.0 | 7.0 | 2.0 | 9.0 | 2.0 | 3.0 | 8.0 | 6.0 | 9.0 | 6.0 | 9.0 | 9.0 | 1.0 | 5.0 | 9.0 | 6.0 | 10.0 | 5.0 | 8.0 | 8.0 | 4.0 | 7.0 | 10.0 | 3.0 | 5.0 | 6.0 | 4.0 |
| 18 | 1.0 | 8.0 | 2.0 | 7.0 | 6.0 | 9.0 | 6.0 | 6.0 | 10.0 | 10.0 | 9.0 | 7.0 | 7.0 | 6.0 | 5.0 | 4.0 | 8.0 | 8.0 | 8.0 | 7.0 | 10.0 | 6.0 | 10.0 | 8.0 | 3.0 | 6.0 | 7.0 | 10.0 | 10.0 | 2.0 | 7.0 | 7.0 | 5.0 | 6.0 | 10.0 | 2.0 | 2.0 | 4.0 | 5.0 | 7.0 | 10.0 | 7.0 | 8.0 | 3.0 | 1.0 | 6.0 | 9.0 | 6.0 | 5.0 | 6.0 | 1.0 | 4.0 | 6.0 | 10.0 | 4.0 | 10.0 |
| 19 | 8.0 | 8.0 | 4.0 | 8.0 | 2.0 | 7.0 | 8.0 | 1.0 | 2.0 | 5.0 | 10.0 | 7.0 | 9.0 | 2.0 | 1.0 | 6.0 | 5.0 | 1.0 | 7.0 | 8.0 | 8.0 | 5.0 | 4.0 | 7.0 | 1.0 | 2.0 | 2.0 | 8.0 | 1.0 | 1.0 | 9.0 | 10.0 | 3.0 | 10.0 | 1.0 | 4.0 | 7.0 | 5.0 | 5.0 | 10.0 | 4.0 | 4.0 | 9.0 | 8.0 | 7.0 | 2.0 | 3.0 | 3.0 | 1.0 | 5.0 | 5.0 | 10.0 | 2.0 | 1.0 | 5.0 | 3.0 |
| 20 | 4.0 | 7.0 | 9.0 | 4.0 | 4.0 | 6.0 | 9.0 | 8.0 | 2.0 | 10.0 | 1.0 | 2.0 | 1.0 | 9.0 | 5.0 | 3.0 | 9.0 | 6.0 | 10.0 | 8.0 | 8.0 | 4.0 | 7.0 | 8.0 | 7.0 | 1.0 | 2.0 | 3.0 | 7.0 | 2.0 | 1.0 | 7.0 | 6.0 | 6.0 | 10.0 | 4.0 | 2.0 | 9.0 | 9.0 | 1.0 | 3.0 | 6.0 | 6.0 | 5.0 | 9.0 | 7.0 | 1.0 | 3.0 | 5.0 | 4.0 | 7.0 | 5.0 | 4.0 | 10.0 | 4.0 | 1.0 |
| 21 | 7.0 | 5.0 | 4.0 | 10.0 | 7.0 | 10.0 | 3.0 | 6.0 | 3.0 | 9.0 | 10.0 | 1.0 | 8.0 | 5.0 | 10.0 | 10.0 | 2.0 | 1.0 | 6.0 | 5.0 | 4.0 | 1.0 | 10.0 | 10.0 | 1.0 | 10.0 | 3.0 | 7.0 | 3.0 | 6.0 | 4.0 | 6.0 | 6.0 | 10.0 | 7.0 | 9.0 | 5.0 | 1.0 | 10.0 | 10.0 | 8.0 | 2.0 | 2.0 | 4.0 | 1.0 | 1.0 | 6.0 | 5.0 | 6.0 | 10.0 | 5.0 | 2.0 | 7.0 | 3.0 | 3.0 | 8.0 |
| 22 | 10.0 | 3.0 | 4.0 | 1.0 | 3.0 | 5.0 | 8.0 | 5.0 | 4.0 | 3.0 | 7.0 | 6.0 | 5.0 | 7.0 | 6.0 | 3.0 | 4.0 | 3.0 | 10.0 | 4.0 | 7.0 | 10.0 | 4.0 | 1.0 | 3.0 | 10.0 | 6.0 | 8.0 | 4.0 | 1.0 | 1.0 | 2.0 | 7.0 | 10.0 | 2.0 | 4.0 | 8.0 | 2.0 | 2.0 | 10.0 | 9.0 | 3.0 | 1.0 | 7.0 | 1.0 | 4.0 | 9.0 | 6.0 | 3.0 | 4.0 | 9.0 | 9.0 | 5.0 | 2.0 | 9.0 | 6.0 |
| 23 | 7.0 | 5.0 | 1.0 | 2.0 | 6.0 | 6.0 | 4.0 | 10.0 | 2.0 | 5.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 6.0 | 4.0 | 8.0 | 8.0 | 7.0 | 8.0 | 10.0 | 1.0 | 7.0 | 1.0 | 4.0 | 3.0 | 8.0 | 3.0 | 3.0 | 3.0 | 8.0 | 7.0 | 3.0 | 5.0 | 8.0 | 1.0 | 3.0 | 4.0 | 5.0 | 1.0 | 8.0 | 7.0 | 2.0 | 1.0 | 4.0 | 7.0 | 3.0 | 6.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 6.0 | 7.0 |
| 24 | 3.0 | 5.0 | 1.0 | 1.0 | 1.0 | 7.0 | 7.0 | 2.0 | 6.0 | 7.0 | 7.0 | 8.0 | 8.0 | 1.0 | 2.0 | 7.0 | 8.0 | 7.0 | 3.0 | 1.0 | 7.0 | 1.0 | 3.0 | 1.0 | 6.0 | 5.0 | 5.0 | 8.0 | 9.0 | 4.0 | 7.0 | 1.0 | 3.0 | 4.0 | 8.0 | 3.0 | 3.0 | 1.0 | 4.0 | 8.0 | 2.0 | 10.0 | 9.0 | 4.0 | 2.0 | 1.0 | 3.0 | 2.0 | 10.0 | 6.0 | 5.0 | 1.0 | 8.0 | 10.0 | 2.0 | 6.0 |
| 25 | 1.0 | 3.0 | 7.0 | 1.0 | 7.0 | 3.0 | 4.0 | 1.0 | 7.0 | 10.0 | 1.0 | 2.0 | 4.0 | 4.0 | 1.0 | 10.0 | 4.0 | 10.0 | 6.0 | 2.0 | 1.0 | 10.0 | 10.0 | 4.0 | 5.0 | 8.0 | 2.0 | 7.0 | 7.0 | 5.0 | 5.0 | 3.0 | 9.0 | 9.0 | 3.0 | 1.0 | 6.0 | 10.0 | 8.0 | 8.0 | 6.0 | 10.0 | 3.0 | 5.0 | 2.0 | 6.0 | 10.0 | 8.0 | 10.0 | 8.0 | 8.0 | 10.0 | 7.0 | 4.0 | 4.0 | 3.0 |
| 26 | 10.0 | 4.0 | 7.0 | 6.0 | 6.0 | 4.0 | 6.0 | 9.0 | 7.0 | 9.0 | 6.0 | 3.0 | 5.0 | 10.0 | 2.0 | 1.0 | 5.0 | 8.0 | 7.0 | 2.0 | 2.0 | 3.0 | 6.0 | 3.0 | 5.0 | 2.0 | 2.0 | 3.0 | 4.0 | 2.0 | 4.0 | 7.0 | 2.0 | 9.0 | 9.0 | 4.0 | 8.0 | 5.0 | 7.0 | 4.0 | 2.0 | 1.0 | 1.0 | 1.0 | 4.0 | 2.0 | 10.0 | 6.0 | 4.0 | 5.0 | 4.0 | 6.0 | 2.0 | 5.0 | 6.0 | 2.0 |
| 27 | 8.0 | 5.0 | 3.0 | 8.0 | 9.0 | 5.0 | 2.0 | 10.0 | 6.0 | 1.0 | 7.0 | 2.0 | 9.0 | 9.0 | 4.0 | 2.0 | 8.0 | 8.0 | 10.0 | 8.0 | 3.0 | 7.0 | 8.0 | 8.0 | 8.0 | 7.0 | 3.0 | 10.0 | 4.0 | 5.0 | 4.0 | 5.0 | 5.0 | 4.0 | 7.0 | 3.0 | 10.0 | 9.0 | 4.0 | 5.0 | 7.0 | 3.0 | 3.0 | 6.0 | 2.0 | 4.0 | 10.0 | 3.0 | 9.0 | 10.0 | 2.0 | 4.0 | 6.0 | 5.0 | 6.0 | 7.0 |
| 28 | 6.0 | 2.0 | 8.0 | 1.0 | 10.0 | 9.0 | 8.0 | 9.0 | 10.0 | 7.0 | 1.0 | 6.0 | 4.0 | 2.0 | 4.0 | 9.0 | 1.0 | 2.0 | 10.0 | 1.0 | 7.0 | 3.0 | 4.0 | 3.0 | 9.0 | 7.0 | 4.0 | 4.0 | 9.0 | 9.0 | 8.0 | 2.0 | 6.0 | 9.0 | 10.0 | 6.0 | 2.0 | 9.0 | 3.0 | 2.0 | 7.0 | 1.0 | 4.0 | 9.0 | 5.0 | 7.0 | 9.0 | 2.0 | 3.0 | 5.0 | 6.0 | 3.0 | 8.0 | 7.0 | 10.0 | 2.0 |
| 29 | 3.0 | 10.0 | 1.0 | 3.0 | 5.0 | 9.0 | 6.0 | 10.0 | 9.0 | 4.0 | 5.0 | 7.0 | 1.0 | 6.0 | 7.0 | 10.0 | 9.0 | 10.0 | 2.0 | 1.0 | 2.0 | 6.0 | 1.0 | 3.0 | 4.0 | 5.0 | 2.0 | 5.0 | 9.0 | 5.0 | 9.0 | 4.0 | 6.0 | 7.0 | 9.0 | 3.0 | 3.0 | 3.0 | 1.0 | 9.0 | 6.0 | 9.0 | 3.0 | 9.0 | 5.0 | 2.0 | 2.0 | 10.0 | 7.0 | 10.0 | 7.0 | 8.0 | 4.0 | 9.0 | 4.0 | 3.0 |
| 30 | 1.0 | 4.0 | 7.0 | 6.0 | 3.0 | 6.0 | 1.0 | 6.0 | 8.0 | 5.0 | 1.0 | 9.0 | 2.0 | 8.0 | 5.0 | 3.0 | 10.0 | 7.0 | 7.0 | 9.0 | 1.0 | 4.0 | 1.0 | 3.0 | 7.0 | 5.0 | 4.0 | 4.0 | 8.0 | 9.0 | 10.0 | 2.0 | 4.0 | 3.0 | 2.0 | 6.0 | 8.0 | 5.0 | 6.0 | 5.0 | 10.0 | 6.0 | 6.0 | 3.0 | 3.0 | 3.0 | 4.0 | 10.0 | 2.0 | 3.0 | 8.0 | 9.0 | 10.0 | 7.0 | 4.0 | 4.0 |
| 31 | 1.0 | 1.0 | 7.0 | 5.0 | 7.0 | 10.0 | 4.0 | 5.0 | 3.0 | 3.0 | 7.0 | 9.0 | 3.0 | 4.0 | 2.0 | 3.0 | 5.0 | 2.0 | 7.0 | 10.0 | 7.0 | 6.0 | 2.0 | 8.0 | 1.0 | 3.0 | 7.0 | 5.0 | 2.0 | 4.0 | 2.0 | 7.0 | 8.0 | 7.0 | 5.0 | 4.0 | 10.0 | 1.0 | 6.0 | 5.0 | 8.0 | 8.0 | 9.0 | 10.0 | 7.0 | 10.0 | 3.0 | 10.0 | 2.0 | 2.0 | 5.0 | 1.0 | 6.0 | 3.0 | 2.0 | 9.0 |
| 32 | 2.0 | 10.0 | 6.0 | 4.0 | 8.0 | 6.0 | 4.0 | 1.0 | 5.0 | 8.0 | 6.0 | 6.0 | 2.0 | 6.0 | 2.0 | 3.0 | 7.0 | 9.0 | 5.0 | 3.0 | 6.0 | 6.0 | 7.0 | 7.0 | 3.0 | 9.0 | 2.0 | 5.0 | 6.0 | 6.0 | 4.0 | 8.0 | 5.0 | 7.0 | 7.0 | 1.0 | 8.0 | 10.0 | 6.0 | 5.0 | 9.0 | 8.0 | 4.0 | 4.0 | 4.0 | 4.0 | 5.0 | 6.0 | 8.0 | 4.0 | 9.0 | 3.0 | 3.0 | 10.0 | 5.0 | 3.0 |
| 33 | 8.0 | 6.0 | 10.0 | 8.0 | 4.0 | 4.0 | 3.0 | 6.0 | 7.0 | 4.0 | 2.0 | 10.0 | 3.0 | 4.0 | 7.0 | 4.0 | 1.0 | 2.0 | 6.0 | 10.0 | 6.0 | 10.0 | 10.0 | 3.0 | 4.0 | 9.0 | 9.0 | 4.0 | 9.0 | 7.0 | 3.0 | 7.0 | 7.0 | 10.0 | 7.0 | 9.0 | 3.0 | 4.0 | 8.0 | 6.0 | 10.0 | 9.0 | 1.0 | 9.0 | 9.0 | 1.0 | 6.0 | 3.0 | 3.0 | 8.0 | 3.0 | 7.0 | 6.0 | 4.0 | 4.0 | 9.0 |
| 34 | 10.0 | 3.0 | 7.0 | 10.0 | 9.0 | 8.0 | 1.0 | 5.0 | 8.0 | 8.0 | 1.0 | 2.0 | 9.0 | 4.0 | 5.0 | 2.0 | 3.0 | 3.0 | 10.0 | 1.0 | 10.0 | 7.0 | 2.0 | 5.0 | 8.0 | 3.0 | 9.0 | 7.0 | 10.0 | 9.0 | 2.0 | 5.0 | 7.0 | 7.0 | 1.0 | 7.0 | 8.0 | 9.0 | 7.0 | 4.0 | 3.0 | 3.0 | 6.0 | 2.0 | 2.0 | 1.0 | 3.0 | 5.0 | 1.0 | 4.0 | 1.0 | 7.0 | 5.0 | 10.0 | 5.0 | 4.0 |
| 35 | 4.0 | 4.0 | 7.0 | 1.0 | 6.0 | 6.0 | 9.0 | 9.0 | 9.0 | 9.0 | 6.0 | 7.0 | 1.0 | 4.0 | 7.0 | 8.0 | 1.0 | 8.0 | 2.0 | 4.0 | 4.0 | 9.0 | 4.0 | 8.0 | 3.0 | 1.0 | 4.0 | 3.0 | 6.0 | 3.0 | 6.0 | 4.0 | 1.0 | 9.0 | 7.0 | 6.0 | 6.0 | 3.0 | 3.0 | 9.0 | 7.0 | 8.0 | 9.0 | 7.0 | 2.0 | 3.0 | 7.0 | 2.0 | 1.0 | 5.0 | 5.0 | 3.0 | 10.0 | 7.0 | 4.0 | 7.0 |
| 36 | 9.0 | 6.0 | 1.0 | 6.0 | 5.0 | 1.0 | 1.0 | 8.0 | 6.0 | 5.0 | 10.0 | 8.0 | 4.0 | 10.0 | 6.0 | 9.0 | 1.0 | 6.0 | 2.0 | 7.0 | 2.0 | 5.0 | 8.0 | 1.0 | 3.0 | 6.0 | 8.0 | 10.0 | 2.0 | 3.0 | 8.0 | 10.0 | 8.0 | 3.0 | 8.0 | 6.0 | 9.0 | 9.0 | 9.0 | 4.0 | 5.0 | 5.0 | 3.0 | 2.0 | 9.0 | 4.0 | 10.0 | 6.0 | 1.0 | 8.0 | 3.0 | 2.0 | 9.0 | 9.0 | 4.0 | 2.0 |
| 37 | 7.0 | 4.0 | 8.0 | 9.0 | 7.0 | 10.0 | 6.0 | 5.0 | 7.0 | 9.0 | 3.0 | 8.0 | 7.0 | 8.0 | 6.0 | 10.0 | 5.0 | 9.0 | 4.0 | 5.0 | 9.0 | 1.0 | 2.0 | 3.0 | 1.0 | 10.0 | 5.0 | 9.0 | 9.0 | 3.0 | 5.0 | 1.0 | 10.0 | 4.0 | 9.0 | 3.0 | 9.0 | 7.0 | 9.0 | 4.0 | 5.0 | 6.0 | 3.0 | 2.0 | 5.0 | 4.0 | 2.0 | 2.0 | 5.0 | 4.0 | 3.0 | 4.0 | 5.0 | 4.0 | 9.0 | 2.0 |
| 38 | 1.0 | 9.0 | 10.0 | 4.0 | 6.0 | 7.0 | 7.0 | 2.0 | 1.0 | 9.0 | 3.0 | 4.0 | 9.0 | 2.0 | 9.0 | 6.0 | 3.0 | 6.0 | 5.0 | 5.0 | 9.0 | 10.0 | 2.0 | 4.0 | 4.0 | 8.0 | 7.0 | 4.0 | 3.0 | 1.0 | 6.0 | 6.0 | 6.0 | 8.0 | 7.0 | 3.0 | 9.0 | 9.0 | 3.0 | 4.0 | 5.0 | 8.0 | 7.0 | 1.0 | 8.0 | 10.0 | 2.0 | 5.0 | 10.0 | 3.0 | 1.0 | 8.0 | 10.0 | 4.0 | 7.0 | 9.0 |
| 39 | 9.0 | 2.0 | 9.0 | 5.0 | 5.0 | 2.0 | 7.0 | 1.0 | 2.0 | 3.0 | 2.0 | 7.0 | 10.0 | 1.0 | 7.0 | 7.0 | 8.0 | 9.0 | 7.0 | 10.0 | 1.0 | 10.0 | 10.0 | 5.0 | 8.0 | 8.0 | 4.0 | 5.0 | 2.0 | 9.0 | 5.0 | 5.0 | 5.0 | 6.0 | 4.0 | 9.0 | 4.0 | 4.0 | 4.0 | 9.0 | 5.0 | 5.0 | 8.0 | 6.0 | 3.0 | 1.0 | 7.0 | 6.0 | 6.0 | 3.0 | 5.0 | 2.0 | 6.0 | 1.0 | 3.0 | 2.0 |
| 40 | 3.0 | 1.0 | 1.0 | 4.0 | 1.0 | 2.0 | 8.0 | 6.0 | 9.0 | 1.0 | 4.0 | 9.0 | 4.0 | 7.0 | 3.0 | 1.0 | 8.0 | 9.0 | 10.0 | 4.0 | 3.0 | 8.0 | 9.0 | 1.0 | 2.0 | 6.0 | 2.0 | 7.0 | 7.0 | 6.0 | 10.0 | 8.0 | 9.0 | 10.0 | 3.0 | 7.0 | 5.0 | 5.0 | 5.0 | 5.0 | 10.0 | 5.0 | 6.0 | 3.0 | 10.0 | 8.0 | 10.0 | 5.0 | 9.0 | 6.0 | 9.0 | 10.0 | 10.0 | 8.0 | 5.0 | 9.0 |
| 41 | 7.0 | 3.0 | 6.0 | 4.0 | 8.0 | 1.0 | 2.0 | 2.0 | 10.0 | 7.0 | 3.0 | 5.0 | 10.0 | 7.0 | 7.0 | 7.0 | 2.0 | 1.0 | 7.0 | 4.0 | 6.0 | 2.0 | 3.0 | 8.0 | 10.0 | 10.0 | 1.0 | 3.0 | 1.0 | 9.0 | 6.0 | 8.0 | 8.0 | 9.0 | 3.0 | 8.0 | 5.0 | 6.0 | 8.0 | 5.0 | 5.0 | 2.0 | 3.0 | 6.0 | 7.0 | 2.0 | 1.0 | 9.0 | 9.0 | 3.0 | 5.0 | 5.0 | 3.0 | 10.0 | 5.0 | 5.0 |
| 42 | 8.0 | 4.0 | 5.0 | 3.0 | 7.0 | 1.0 | 6.0 | 9.0 | 2.0 | 10.0 | 5.0 | 4.0 | 7.0 | 4.0 | 2.0 | 10.0 | 5.0 | 5.0 | 8.0 | 9.0 | 6.0 | 2.0 | 1.0 | 7.0 | 9.0 | 3.0 | 1.0 | 3.0 | 4.0 | 3.0 | 6.0 | 9.0 | 4.0 | 1.0 | 6.0 | 9.0 | 3.0 | 3.0 | 7.0 | 8.0 | 6.0 | 3.0 | 10.0 | 10.0 | 6.0 | 4.0 | 5.0 | 4.0 | 6.0 | 8.0 | 9.0 | 9.0 | 3.0 | 9.0 | 5.0 | 9.0 |
| 43 | 4.0 | 8.0 | 6.0 | 6.0 | 3.0 | 1.0 | 9.0 | 10.0 | 9.0 | 2.0 | 9.0 | 8.0 | 6.0 | 7.0 | 4.0 | 7.0 | 2.0 | 9.0 | 3.0 | 8.0 | 5.0 | 4.0 | 7.0 | 2.0 | 4.0 | 5.0 | 1.0 | 6.0 | 9.0 | 9.0 | 3.0 | 10.0 | 4.0 | 9.0 | 2.0 | 7.0 | 2.0 | 2.0 | 1.0 | 6.0 | 3.0 | 6.0 | 10.0 | 10.0 | 10.0 | 7.0 | 9.0 | 7.0 | 1.0 | 5.0 | 7.0 | 7.0 | 2.0 | 8.0 | 2.0 | 2.0 |
| 44 | 7.0 | 2.0 | 7.0 | 1.0 | 3.0 | 3.0 | 9.0 | 10.0 | 1.0 | 10.0 | 6.0 | 8.0 | 1.0 | 6.0 | 10.0 | 9.0 | 8.0 | 6.0 | 1.0 | 7.0 | 9.0 | 1.0 | 1.0 | 1.0 | 2.0 | 2.0 | 4.0 | 2.0 | 5.0 | 5.0 | 3.0 | 7.0 | 4.0 | 9.0 | 2.0 | 2.0 | 9.0 | 5.0 | 8.0 | 3.0 | 10.0 | 7.0 | 6.0 | 10.0 | 8.0 | 2.0 | 9.0 | 6.0 | 10.0 | 2.0 | 7.0 | 1.0 | 8.0 | 10.0 | 8.0 | 7.0 |
| 45 | 7.0 | 4.0 | 2.0 | 4.0 | 10.0 | 6.0 | 7.0 | 5.0 | 4.0 | 5.0 | 3.0 | 8.0 | 2.0 | 5.0 | 2.0 | 1.0 | 5.0 | 10.0 | 6.0 | 2.0 | 7.0 | 1.0 | 4.0 | 4.0 | 1.0 | 6.0 | 2.0 | 4.0 | 7.0 | 2.0 | 3.0 | 10.0 | 4.0 | 1.0 | 1.0 | 3.0 | 4.0 | 4.0 | 10.0 | 1.0 | 8.0 | 2.0 | 4.0 | 7.0 | 2.0 | 7.0 | 3.0 | 6.0 | 8.0 | 4.0 | 8.0 | 2.0 | 4.0 | 6.0 | 10.0 | 1.0 |
| 46 | 3.0 | 4.0 | 6.0 | 3.0 | 2.0 | 8.0 | 4.0 | 6.0 | 6.0 | 5.0 | 2.0 | 1.0 | 10.0 | 2.0 | 7.0 | 2.0 | 5.0 | 5.0 | 9.0 | 3.0 | 1.0 | 6.0 | 9.0 | 7.0 | 3.0 | 10.0 | 10.0 | 10.0 | 9.0 | 2.0 | 4.0 | 3.0 | 5.0 | 6.0 | 3.0 | 7.0 | 10.0 | 2.0 | 2.0 | 7.0 | 10.0 | 1.0 | 5.0 | 9.0 | 9.0 | 3.0 | 1.0 | 6.0 | 6.0 | 8.0 | 10.0 | 10.0 | 3.0 | 8.0 | 10.0 | 9.0 |
| 47 | 3.0 | 10.0 | 9.0 | 8.0 | 7.0 | 1.0 | 8.0 | 5.0 | 3.0 | 1.0 | 1.0 | 5.0 | 10.0 | 5.0 | 2.0 | 5.0 | 7.0 | 8.0 | 6.0 | 3.0 | 3.0 | 5.0 | 6.0 | 3.0 | 2.0 | 8.0 | 6.0 | 3.0 | 2.0 | 10.0 | 10.0 | 10.0 | 6.0 | 3.0 | 5.0 | 2.0 | 6.0 | 2.0 | 5.0 | 6.0 | 5.0 | 9.0 | 4.0 | 7.0 | 6.0 | 6.0 | 6.0 | 3.0 | 6.0 | 5.0 | 4.0 | 8.0 | 1.0 | 6.0 | 9.0 | 4.0 |
| 48 | 5.0 | 4.0 | 8.0 | 7.0 | 4.0 | 2.0 | 1.0 | 9.0 | 2.0 | 7.0 | 8.0 | 6.0 | 7.0 | 10.0 | 1.0 | 2.0 | 3.0 | 8.0 | 5.0 | 1.0 | 5.0 | 6.0 | 3.0 | 6.0 | 10.0 | 10.0 | 4.0 | 9.0 | 3.0 | 7.0 | 2.0 | 2.0 | 8.0 | 3.0 | 1.0 | 1.0 | 1.0 | 5.0 | 10.0 | 6.0 | 9.0 | 9.0 | 6.0 | 1.0 | 10.0 | 8.0 | 6.0 | 6.0 | 6.0 | 4.0 | 5.0 | 7.0 | 8.0 | 2.0 | 8.0 | 6.0 |
| 49 | 2.0 | 3.0 | 6.0 | 8.0 | 7.0 | 10.0 | 3.0 | 5.0 | 4.0 | 1.0 | 7.0 | 8.0 | 3.0 | 8.0 | 9.0 | 10.0 | 8.0 | 4.0 | 6.0 | 5.0 | 4.0 | 10.0 | 4.0 | 1.0 | 6.0 | 8.0 | 5.0 | 10.0 | 5.0 | 10.0 | 3.0 | 2.0 | 4.0 | 8.0 | 4.0 | 5.0 | 8.0 | 4.0 | 3.0 | 3.0 | 6.0 | 3.0 | 8.0 | 5.0 | 2.0 | 4.0 | 8.0 | 5.0 | 4.0 | 6.0 | 1.0 | 7.0 | 9.0 | 4.0 | 8.0 | 2.0 |
| 50 | 9.0 | 4.0 | 8.0 | 1.0 | 8.0 | 2.0 | 8.0 | 6.0 | 2.0 | 4.0 | 5.0 | 6.0 | 4.0 | 10.0 | 1.0 | 7.0 | 6.0 | 7.0 | 1.0 | 5.0 | 7.0 | 5.0 | 9.0 | 8.0 | 5.0 | 8.0 | 4.0 | 2.0 | 6.0 | 7.0 | 8.0 | 5.0 | 9.0 | 3.0 | 1.0 | 5.0 | 3.0 | 3.0 | 1.0 | 5.0 | 9.0 | 5.0 | 9.0 | 7.0 | 7.0 | 8.0 | 10.0 | 4.0 | 5.0 | 1.0 | 7.0 | 2.0 | 6.0 | 2.0 | 10.0 | 5.0 |
| 51 | 3.0 | 8.0 | 9.0 | 10.0 | 3.0 | 2.0 | 2.0 | 7.0 | 5.0 | 6.0 | 10.0 | 6.0 | 1.0 | 2.0 | 2.0 | 10.0 | 10.0 | 10.0 | 4.0 | 10.0 | 5.0 | 2.0 | 9.0 | 8.0 | 1.0 | 10.0 | 6.0 | 4.0 | 3.0 | 8.0 | 9.0 | 1.0 | 3.0 | 7.0 | 7.0 | 3.0 | 2.0 | 4.0 | 8.0 | 2.0 | 10.0 | 5.0 | 9.0 | 7.0 | 1.0 | 2.0 | 10.0 | 8.0 | 7.0 | 7.0 | 2.0 | 2.0 | 6.0 | 9.0 | 4.0 | 8.0 |
| 52 | 4.0 | 8.0 | 1.0 | 2.0 | 6.0 | 6.0 | 4.0 | 2.0 | 8.0 | 1.0 | 1.0 | 9.0 | 3.0 | 6.0 | 2.0 | 7.0 | 9.0 | 3.0 | 6.0 | 2.0 | 4.0 | 7.0 | 5.0 | 8.0 | 8.0 | 7.0 | 2.0 | 6.0 | 8.0 | 4.0 | 10.0 | 6.0 | 3.0 | 6.0 | 5.0 | 10.0 | 9.0 | 5.0 | 10.0 | 6.0 | 10.0 | 3.0 | 3.0 | 2.0 | 8.0 | 4.0 | 3.0 | 1.0 | 8.0 | 9.0 | 6.0 | 6.0 | 9.0 | 9.0 | 8.0 | 4.0 |
| 53 | 3.0 | 6.0 | 10.0 | 9.0 | 7.0 | 2.0 | 10.0 | 10.0 | 5.0 | 1.0 | 10.0 | 4.0 | 2.0 | 8.0 | 2.0 | 6.0 | 6.0 | 5.0 | 10.0 | 1.0 | 10.0 | 3.0 | 2.0 | 1.0 | 10.0 | 4.0 | 5.0 | 5.0 | 7.0 | 9.0 | 7.0 | 3.0 | 10.0 | 4.0 | 10.0 | 7.0 | 9.0 | 4.0 | 4.0 | 1.0 | 8.0 | 10.0 | 9.0 | 8.0 | 10.0 | 6.0 | 8.0 | 6.0 | 2.0 | 4.0 | 2.0 | 9.0 | 9.0 | 4.0 | 9.0 | 10.0 |
| 54 | 10.0 | 10.0 | 1.0 | 1.0 | 3.0 | 8.0 | 3.0 | 3.0 | 5.0 | 5.0 | 8.0 | 2.0 | 1.0 | 7.0 | 2.0 | 4.0 | 5.0 | 6.0 | 4.0 | 5.0 | 4.0 | 3.0 | 9.0 | 6.0 | 2.0 | 4.0 | 6.0 | 6.0 | 10.0 | 4.0 | 4.0 | 2.0 | 5.0 | 4.0 | 5.0 | 4.0 | 4.0 | 9.0 | 7.0 | 3.0 | 5.0 | 5.0 | 5.0 | 2.0 | 8.0 | 10.0 | 10.0 | 9.0 | 8.0 | 8.0 | 10.0 | 4.0 | 8.0 | 9.0 | 5.0 | 7.0 |
| 55 | 5.0 | 4.0 | 6.0 | 9.0 | 5.0 | 2.0 | 6.0 | 9.0 | 2.0 | 10.0 | 5.0 | 9.0 | 4.0 | 7.0 | 10.0 | 2.0 | 8.0 | 4.0 | 10.0 | 3.0 | 1.0 | 8.0 | 6.0 | 7.0 | 6.0 | 3.0 | 2.0 | 7.0 | 2.0 | 3.0 | 4.0 | 9.0 | 3.0 | 9.0 | 4.0 | 7.0 | 2.0 | 2.0 | 9.0 | 2.0 | 9.0 | 5.0 | 9.0 | 2.0 | 7.0 | 1.0 | 9.0 | 4.0 | 6.0 | 2.0 | 5.0 | 8.0 | 4.0 | 10.0 | 7.0 | 8.0 |

When you send the chosen route back, please tuck it into a tiny JSON sketch so it's easy to parse. Nothing fancy — just the one key below holding the ordered list of nodes from source to target:

{
  ""solution"": []
}

Think of ""solution"" as the form field where you drop the path: that array should contain the node identifiers in order (start at the reservoir inlet, end at the treatment outfall), and nothing else — node IDs only, no edge IDs, no costs. This JSON is just a template showing the shape I expect, not the actual path itself.

Please use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 1, 'var_index': 1}, {'from': 19, 'to': 2, 'var_index': 2}, {'from': 19, 'to': 3, 'var_index': 3}, {'from': 19, 'to': 4, 'var_index': 4}, {'from': 19, 'to': 5, 'var_index': 5}, {'from': 19, 'to': 6, 'var_index': 6}, {'from': 19, 'to': 7, 'var_index': 7}, {'from': 19, 'to': 8, 'var_index': 8}, {'from': 19, 'to': 9, 'var_index': 9}, {'from': 19, 'to': 10, 'var_index': 10}, {'from': 19, 'to': 11, 'var_index': 11}, {'from': 19, 'to': 12, 'var_index': 12}, {'from': 19, 'to': 13, 'var_index': 13}, {'from': 19, 'to': 14, 'var_index': 14}, {'from': 19, 'to': 15, 'var_index': 15}, {'from': 19, 'to': 16, 'var_index': 16}, {'from': 19, 'to': 17, 'var_index': 17}, {'from': 19, 'to': 18, 'var_index': 18}, {'from': 0, 'to': 20, 'var_index': 19}, {'from': 1, 'to': 20, 'var_index': 20}, {'from': 2, 'to': 20, 'var_index': 21}, {'from': 3, 'to': 20, 'var_index': 22}, {'from': 4, 'to': 20, 'var_index': 23}, {'from': 5, 'to': 20, 'var_index': 24}, {'from': 6, 'to': 20, 'var_index': 25}, {'from': 7, 'to': 20, 'var_index': 26}, {'from': 8, 'to': 20, 'var_index': 27}, {'from': 9, 'to': 20, 'var_index': 28}, {'from': 10, 'to': 20, 'var_index': 29}, {'from': 11, 'to': 20, 'var_index': 30}, {'from': 12, 'to': 20, 'var_index': 31}, {'from': 13, 'to': 20, 'var_index': 32}, {'from': 14, 'to': 20, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 20, 'var_index': 35}, {'from': 17, 'to': 20, 'var_index': 36}, {'from': 18, 'to': 20, 'var_index': 37}, {'from': 0, 'to': 1, 'var_index': 38}, {'from': 1, 'to': 2, 'var_index': 39}, {'from': 2, 'to': 3, 'var_index': 40}, {'from': 3, 'to': 4, 'var_index': 41}, {'from': 4, 'to': 5, 'var_index': 42}, {'from': 5, 'to': 6, 'var_index': 43}, {'from': 6, 'to': 7, 'var_index': 44}, {'from': 7, 'to': 8, 'var_index': 45}, {'from': 8, 'to': 9, 'var_index': 46}, {'from': 9, 'to': 10, 'var_index': 47}, {'from': 10, 'to': 11, 'var_index': 48}, {'from': 11, 'to': 12, 'var_index': 49}, {'from': 12, 'to': 13, 'var_index': 50}, {'from': 13, 'to': 14, 'var_index': 51}, {'from': 14, 'to': 15, 'var_index': 52}, {'from': 15, 'to': 16, 'var_index': 53}, {'from': 16, 'to': 17, 'var_index': 54}, {'from': 17, 'to': 18, 'var_index': 55}], 'objective': {'constant': 0.0, 'linear': [8.0, 3.0, 8.0, 4.0, 2.0, 5.0, 8.0, 8.0, 7.0, 2.0, 3.0, 6.0, 9.0, 4.0, 10.0, 2.0, 6.0, 9.0, 8.0, 9.0, 2.0, 1.0, 3.0, 2.0, 8.0, 4.0, 3.0, 7.0, 2.0, 4.0, 5.0, 6.0, 7.0, 3.0, 3.0, 4.0, 9.0, 4.0, 8.0, 2.0, 7.0, 1.0, 6.0, 10.0, 5.0, 4.0, 2.0, 2.0, 2.0, 6.0, 1.0, 8.0, 5.0, 7.0, 5.0, 3.0], 'quadratic': [[1.0, 9.0, 2.0, 6.0, 1.0, 1.0, 4.0, 4.0, 1.0, 2.0, 7.0, 2.0, 5.0, 8.0, 7.0, 7.0, 8.0, 1.0, 1.0, 8.0, 4.0, 7.0, 10.0, 7.0, 3.0, 1.0, 10.0, 8.0, 6.0, 3.0, 1.0, 1.0, 2.0, 8.0, 10.0, 4.0, 9.0, 7.0, 1.0, 9.0, 3.0, 7.0, 8.0, 4.0, 7.0, 7.0, 3.0, 3.0, 5.0, 2.0, 9.0, 3.0, 4.0, 3.0, 10.0, 5.0], [9.0, 9.0, 5.0, 5.0, 10.0, 9.0, 9.0, 2.0, 6.0, 5.0, 10.0, 3.0, 3.0, 9.0, 4.0, 10.0, 9.0, 3.0, 8.0, 8.0, 7.0, 5.0, 3.0, 5.0, 5.0, 3.0, 4.0, 5.0, 2.0, 10.0, 4.0, 1.0, 10.0, 6.0, 3.0, 4.0, 6.0, 4.0, 9.0, 2.0, 1.0, 3.0, 4.0, 8.0, 2.0, 4.0, 4.0, 10.0, 4.0, 3.0, 4.0, 8.0, 8.0, 6.0, 10.0, 4.0], [2.0, 5.0, 8.0, 10.0, 7.0, 5.0, 5.0, 4.0, 4.0, 10.0, 10.0, 9.0, 10.0, 9.0, 9.0, 6.0, 10.0, 8.0, 2.0, 4.0, 9.0, 4.0, 4.0, 1.0, 1.0, 7.0, 7.0, 3.0, 8.0, 1.0, 7.0, 7.0, 6.0, 10.0, 7.0, 7.0, 1.0, 8.0, 10.0, 9.0, 1.0, 6.0, 5.0, 6.0, 7.0, 2.0, 6.0, 9.0, 8.0, 6.0, 8.0, 9.0, 1.0, 10.0, 1.0, 6.0], [6.0, 5.0, 10.0, 2.0, 9.0, 7.0, 2.0, 2.0, 10.0, 4.0, 4.0, 10.0, 3.0, 9.0, 10.0, 6.0, 4.0, 5.0, 7.0, 8.0, 4.0, 10.0, 1.0, 2.0, 1.0, 1.0, 6.0, 8.0, 1.0, 3.0, 6.0, 5.0, 4.0, 8.0, 10.0, 1.0, 6.0, 9.0, 4.0, 5.0, 4.0, 4.0, 3.0, 6.0, 1.0, 4.0, 3.0, 8.0, 7.0, 8.0, 1.0, 10.0, 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{'var_i': 54, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 54, 'var_j': 32, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 33, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 34, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 35, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 37, 'quadratic_cost': 9.0}, {'var_i': 54, 'var_j': 38, 'quadratic_cost': 7.0}, {'var_i': 54, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 54, 'var_j': 40, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 41, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 42, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 43, 'quadratic_cost': 2.0}, {'var_i': 54, 'var_j': 44, 'quadratic_cost': 8.0}, {'var_i': 54, 'var_j': 45, 'quadratic_cost': 10.0}, {'var_i': 54, 'var_j': 46, 'quadratic_cost': 10.0}, {'var_i': 54, 'var_j': 47, 'quadratic_cost': 9.0}, {'var_i': 54, 'var_j': 48, 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{'var_i': 55, 'var_j': 51, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 52, 'quadratic_cost': 4.0}, {'var_i': 55, 'var_j': 53, 'quadratic_cost': 10.0}, {'var_i': 55, 'var_j': 54, 'quadratic_cost': 7.0}, {'var_i': 55, 'var_j': 55, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 1, 'var_index': 1}, {'from': 19, 'to': 2, 'var_index': 2}, {'from': 19, 'to': 3, 'var_index': 3}, {'from': 19, 'to': 4, 'var_index': 4}, {'from': 19, 'to': 5, 'var_index': 5}, {'from': 19, 'to': 6, 'var_index': 6}, {'from': 19, 'to': 7, 'var_index': 7}, {'from': 19, 'to': 8, 'var_index': 8}, {'from': 19, 'to': 9, 'var_index': 9}, {'from': 19, 'to': 10, 'var_index': 10}, {'from': 19, 'to': 11, 'var_index': 11}, {'from': 19, 'to': 12, 'var_index': 12}, {'from': 19, 'to': 13, 'var_index': 13}, {'from': 19, 'to': 14, 'var_index': 14}, {'from': 19, 'to': 15, 'var_index': 15}, {'from': 19, 'to': 16, 'var_index': 16}, {'from': 19, 'to': 17, 'var_index': 17}, {'from': 19, 'to': 18, 'var_index': 18}, {'from': 0, 'to': 20, 'var_index': 19}, {'from': 1, 'to': 20, 'var_index': 20}, {'from': 2, 'to': 20, 'var_index': 21}, {'from': 3, 'to': 20, 'var_index': 22}, {'from': 4, 'to': 20, 'var_index': 23}, {'from': 5, 'to': 20, 'var_index': 24}, {'from': 6, 'to': 20, 'var_index': 25}, {'from': 7, 'to': 20, 'var_index': 26}, {'from': 8, 'to': 20, 'var_index': 27}, {'from': 9, 'to': 20, 'var_index': 28}, {'from': 10, 'to': 20, 'var_index': 29}, {'from': 11, 'to': 20, 'var_index': 30}, {'from': 12, 'to': 20, 'var_index': 31}, {'from': 13, 'to': 20, 'var_index': 32}, {'from': 14, 'to': 20, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 20, 'var_index': 35}, {'from': 17, 'to': 20, 'var_index': 36}, {'from': 18, 'to': 20, 'var_index': 37}, {'from': 0, 'to': 1, 'var_index': 38}, {'from': 1, 'to': 2, 'var_index': 39}, {'from': 2, 'to': 3, 'var_index': 40}, {'from': 3, 'to': 4, 'var_index': 41}, {'from': 4, 'to': 5, 'var_index': 42}, {'from': 5, 'to': 6, 'var_index': 43}, {'from': 6, 'to': 7, 'var_index': 44}, {'from': 7, 'to': 8, 'var_index': 45}, {'from': 8, 'to': 9, 'var_index': 46}, {'from': 9, 'to': 10, 'var_index': 47}, {'from': 10, 'to': 11, 'var_index': 48}, {'from': 11, 'to': 12, 'var_index': 49}, {'from': 12, 'to': 13, 'var_index': 50}, {'from': 13, 'to': 14, 'var_index': 51}, {'from': 14, 'to': 15, 'var_index': 52}, {'from': 15, 'to': 16, 'var_index': 53}, {'from': 16, 'to': 17, 'var_index': 54}, {'from': 17, 'to': 18, 'var_index': 55}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20}}","[19, 15, 20]",5,json,0
QSPP,QSPP,"I’m imagining a transit planner staring at a city map, trying to pick one single route for a bus to go from the depot to the terminal. The choice has to be a continuous, allowed one-way path that follows the direction of each road, starts at the depot and ends at the terminal — nothing magical, no teleporting or skipping segments, and the plan will be written down as a list of locations. Each road taken carries a basic fuel/toll charge and sometimes an extra tag that applies when that road is used; on top of that, certain pairs of road segments bump up the bill if both are on the trip. The trick is to pick the route that makes the total bill smallest by adding every road’s basic charge, any per-road use charges, and every extra charge for pairs of segments that appear together. The concrete map and numbers are shown below.

In that concrete map there are 24 locations and 23 directed road segments; the valid location IDs are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, the trip must start at 23 and end at 24.

| road_start_location | road_end_location | road_segment_id |
|---|---|---|
| 23 | 1 | 0 |
| 22 | 24 | 1 |
| 1 | 2 | 2 |
| 2 | 3 | 3 |
| 3 | 4 | 4 |
| 4 | 5 | 5 |
| 5 | 6 | 6 |
| 6 | 7 | 7 |
| 7 | 8 | 8 |
| 8 | 9 | 9 |
| 9 | 10 | 10 |
| 10 | 11 | 11 |
| 11 | 12 | 12 |
| 12 | 13 | 13 |
| 13 | 14 | 14 |
| 14 | 15 | 15 |
| 15 | 16 | 16 |
| 16 | 17 | 17 |
| 17 | 18 | 18 |
| 18 | 19 | 19 |
| 19 | 20 | 20 |
| 20 | 21 | 21 |
| 21 | 22 | 22 |

| road_segment_id | base_fuel_toll_cost |
|---|---|
| 0 | 7.0 |
| 1 | 1.0 |
| 2 | 10.0 |
| 3 | 7.0 |
| 4 | 4.0 |
| 5 | 4.0 |
| 6 | 3.0 |
| 7 | 6.0 |
| 8 | 4.0 |
| 9 | 2.0 |
| 10 | 10.0 |
| 11 | 4.0 |
| 12 | 10.0 |
| 13 | 5.0 |
| 14 | 5.0 |
| 15 | 2.0 |
| 16 | 2.0 |
| 17 | 3.0 |
| 18 | 3.0 |
| 19 | 3.0 |
| 20 | 4.0 |
| 21 | 10.0 |
| 22 | 3.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two road_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 9.0 | 4.0 | 3.0 | 10.0 | 1.0 | 6.0 | 8.0 | 9.0 | 5.0 | 1.0 | 1.0 | 3.0 | 2.0 | 2.0 | 6.0 | 9.0 | 10.0 | 4.0 | 10.0 | 8.0 | 3.0 | 5.0 |
| 1 | 9.0 | 9.0 | 10.0 | 1.0 | 10.0 | 2.0 | 2.0 | 9.0 | 9.0 | 9.0 | 8.0 | 7.0 | 6.0 | 5.0 | 3.0 | 9.0 | 1.0 | 3.0 | 7.0 | 5.0 | 2.0 | 9.0 | 10.0 |
| 2 | 4.0 | 10.0 | 10.0 | 10.0 | 5.0 | 4.0 | 7.0 | 2.0 | 3.0 | 10.0 | 1.0 | 5.0 | 8.0 | 9.0 | 3.0 | 2.0 | 4.0 | 7.0 | 10.0 | 8.0 | 1.0 | 3.0 | 5.0 |
| 3 | 3.0 | 1.0 | 10.0 | 4.0 | 5.0 | 8.0 | 5.0 | 4.0 | 2.0 | 2.0 | 4.0 | 1.0 | 3.0 | 4.0 | 3.0 | 6.0 | 10.0 | 3.0 | 1.0 | 5.0 | 7.0 | 3.0 | 1.0 |
| 4 | 10.0 | 10.0 | 5.0 | 5.0 | 8.0 | 1.0 | 6.0 | 1.0 | 4.0 | 4.0 | 5.0 | 10.0 | 1.0 | 2.0 | 5.0 | 8.0 | 4.0 | 2.0 | 2.0 | 9.0 | 3.0 | 1.0 | 2.0 |
| 5 | 1.0 | 2.0 | 4.0 | 8.0 | 1.0 | 4.0 | 9.0 | 8.0 | 1.0 | 4.0 | 5.0 | 10.0 | 2.0 | 9.0 | 4.0 | 10.0 | 4.0 | 6.0 | 9.0 | 3.0 | 1.0 | 7.0 | 8.0 |
| 6 | 6.0 | 2.0 | 7.0 | 5.0 | 6.0 | 9.0 | 1.0 | 1.0 | 5.0 | 5.0 | 7.0 | 1.0 | 10.0 | 4.0 | 5.0 | 5.0 | 3.0 | 10.0 | 5.0 | 8.0 | 2.0 | 4.0 | 10.0 |
| 7 | 8.0 | 9.0 | 2.0 | 4.0 | 1.0 | 8.0 | 1.0 | 10.0 | 7.0 | 10.0 | 4.0 | 10.0 | 8.0 | 1.0 | 1.0 | 3.0 | 5.0 | 9.0 | 9.0 | 2.0 | 7.0 | 8.0 | 10.0 |
| 8 | 9.0 | 9.0 | 3.0 | 2.0 | 4.0 | 1.0 | 5.0 | 7.0 | 8.0 | 9.0 | 3.0 | 2.0 | 9.0 | 3.0 | 8.0 | 6.0 | 8.0 | 7.0 | 1.0 | 8.0 | 6.0 | 1.0 | 6.0 |
| 9 | 5.0 | 9.0 | 10.0 | 2.0 | 4.0 | 4.0 | 5.0 | 10.0 | 9.0 | 10.0 | 6.0 | 5.0 | 9.0 | 3.0 | 9.0 | 7.0 | 2.0 | 2.0 | 2.0 | 1.0 | 3.0 | 4.0 | 3.0 |
| 10 | 1.0 | 8.0 | 1.0 | 4.0 | 5.0 | 5.0 | 7.0 | 4.0 | 3.0 | 6.0 | 5.0 | 5.0 | 1.0 | 7.0 | 7.0 | 5.0 | 2.0 | 6.0 | 7.0 | 7.0 | 2.0 | 9.0 | 6.0 |
| 11 | 1.0 | 7.0 | 5.0 | 1.0 | 10.0 | 10.0 | 1.0 | 10.0 | 2.0 | 5.0 | 5.0 | 10.0 | 8.0 | 5.0 | 7.0 | 5.0 | 5.0 | 5.0 | 8.0 | 5.0 | 1.0 | 5.0 | 5.0 |
| 12 | 3.0 | 6.0 | 8.0 | 3.0 | 1.0 | 2.0 | 10.0 | 8.0 | 9.0 | 9.0 | 1.0 | 8.0 | 8.0 | 4.0 | 6.0 | 8.0 | 10.0 | 2.0 | 3.0 | 10.0 | 8.0 | 10.0 | 1.0 |
| 13 | 2.0 | 5.0 | 9.0 | 4.0 | 2.0 | 9.0 | 4.0 | 1.0 | 3.0 | 3.0 | 7.0 | 5.0 | 4.0 | 8.0 | 2.0 | 7.0 | 7.0 | 10.0 | 8.0 | 5.0 | 2.0 | 7.0 | 1.0 |
| 14 | 2.0 | 3.0 | 3.0 | 3.0 | 5.0 | 4.0 | 5.0 | 1.0 | 8.0 | 9.0 | 7.0 | 7.0 | 6.0 | 2.0 | 2.0 | 4.0 | 10.0 | 1.0 | 1.0 | 8.0 | 5.0 | 6.0 | 7.0 |
| 15 | 6.0 | 9.0 | 2.0 | 6.0 | 8.0 | 10.0 | 5.0 | 3.0 | 6.0 | 7.0 | 5.0 | 5.0 | 8.0 | 7.0 | 4.0 | 7.0 | 3.0 | 9.0 | 9.0 | 10.0 | 6.0 | 5.0 | 6.0 |
| 16 | 9.0 | 1.0 | 4.0 | 10.0 | 4.0 | 4.0 | 3.0 | 5.0 | 8.0 | 2.0 | 2.0 | 5.0 | 10.0 | 7.0 | 10.0 | 3.0 | 3.0 | 6.0 | 8.0 | 4.0 | 7.0 | 9.0 | 8.0 |
| 17 | 10.0 | 3.0 | 7.0 | 3.0 | 2.0 | 6.0 | 10.0 | 9.0 | 7.0 | 2.0 | 6.0 | 5.0 | 2.0 | 10.0 | 1.0 | 9.0 | 6.0 | 10.0 | 2.0 | 6.0 | 2.0 | 9.0 | 9.0 |
| 18 | 4.0 | 7.0 | 10.0 | 1.0 | 2.0 | 9.0 | 5.0 | 9.0 | 1.0 | 2.0 | 7.0 | 8.0 | 3.0 | 8.0 | 1.0 | 9.0 | 8.0 | 2.0 | 6.0 | 2.0 | 2.0 | 3.0 | 4.0 |
| 19 | 10.0 | 5.0 | 8.0 | 5.0 | 9.0 | 3.0 | 8.0 | 2.0 | 8.0 | 1.0 | 7.0 | 5.0 | 10.0 | 5.0 | 8.0 | 10.0 | 4.0 | 6.0 | 2.0 | 8.0 | 9.0 | 8.0 | 7.0 |
| 20 | 8.0 | 2.0 | 1.0 | 7.0 | 3.0 | 1.0 | 2.0 | 7.0 | 6.0 | 3.0 | 2.0 | 1.0 | 8.0 | 2.0 | 5.0 | 6.0 | 7.0 | 2.0 | 2.0 | 9.0 | 5.0 | 3.0 | 4.0 |
| 21 | 3.0 | 9.0 | 3.0 | 3.0 | 1.0 | 7.0 | 4.0 | 8.0 | 1.0 | 4.0 | 9.0 | 5.0 | 10.0 | 7.0 | 6.0 | 5.0 | 9.0 | 9.0 | 3.0 | 8.0 | 3.0 | 5.0 | 1.0 |
| 22 | 5.0 | 10.0 | 5.0 | 1.0 | 2.0 | 8.0 | 10.0 | 10.0 | 6.0 | 3.0 | 6.0 | 5.0 | 1.0 | 1.0 | 7.0 | 6.0 | 8.0 | 9.0 | 4.0 | 7.0 | 4.0 | 1.0 | 5.0 |

With those details, the planner's task is to pick a continuous one-way path that minimizes the total bill.

You can just hand the final route back in a tiny JSON snippet — keeps things neat. Below is the shape I expect:

{
  ""solution"": []
}

This little object is just a form: put the chosen path into the solution array as a sequence of NODE identifiers (start with the source/depot and end with the target/terminal). Use only node names, in order, and make sure each consecutive pair follows a directed edge on the map. The JSON above is only a sketch of the expected shape, not the actual route.

Please use the exact identifiers given in the instance input — don’t rename nodes or invent new labels, and don’t include any edge identifiers. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 23, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}, {'from': 19, 'to': 20, 'var_index': 21}, {'from': 20, 'to': 21, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [7.0, 1.0, 10.0, 7.0, 4.0, 4.0, 3.0, 6.0, 4.0, 2.0, 10.0, 4.0, 10.0, 5.0, 5.0, 2.0, 2.0, 3.0, 3.0, 3.0, 4.0, 10.0, 3.0], 'quadratic': [[8.0, 9.0, 4.0, 3.0, 10.0, 1.0, 6.0, 8.0, 9.0, 5.0, 1.0, 1.0, 3.0, 2.0, 2.0, 6.0, 9.0, 10.0, 4.0, 10.0, 8.0, 3.0, 5.0], [9.0, 9.0, 10.0, 1.0, 10.0, 2.0, 2.0, 9.0, 9.0, 9.0, 8.0, 7.0, 6.0, 5.0, 3.0, 9.0, 1.0, 3.0, 7.0, 5.0, 2.0, 9.0, 10.0], [4.0, 10.0, 10.0, 10.0, 5.0, 4.0, 7.0, 2.0, 3.0, 10.0, 1.0, 5.0, 8.0, 9.0, 3.0, 2.0, 4.0, 7.0, 10.0, 8.0, 1.0, 3.0, 5.0], [3.0, 1.0, 10.0, 4.0, 5.0, 8.0, 5.0, 4.0, 2.0, 2.0, 4.0, 1.0, 3.0, 4.0, 3.0, 6.0, 10.0, 3.0, 1.0, 5.0, 7.0, 3.0, 1.0], [10.0, 10.0, 5.0, 5.0, 8.0, 1.0, 6.0, 1.0, 4.0, 4.0, 5.0, 10.0, 1.0, 2.0, 5.0, 8.0, 4.0, 2.0, 2.0, 9.0, 3.0, 1.0, 2.0], [1.0, 2.0, 4.0, 8.0, 1.0, 4.0, 9.0, 8.0, 1.0, 4.0, 5.0, 10.0, 2.0, 9.0, 4.0, 10.0, 4.0, 6.0, 9.0, 3.0, 1.0, 7.0, 8.0], [6.0, 2.0, 7.0, 5.0, 6.0, 9.0, 1.0, 1.0, 5.0, 5.0, 7.0, 1.0, 10.0, 4.0, 5.0, 5.0, 3.0, 10.0, 5.0, 8.0, 2.0, 4.0, 10.0], [8.0, 9.0, 2.0, 4.0, 1.0, 8.0, 1.0, 10.0, 7.0, 10.0, 4.0, 10.0, 8.0, 1.0, 1.0, 3.0, 5.0, 9.0, 9.0, 2.0, 7.0, 8.0, 10.0], [9.0, 9.0, 3.0, 2.0, 4.0, 1.0, 5.0, 7.0, 8.0, 9.0, 3.0, 2.0, 9.0, 3.0, 8.0, 6.0, 8.0, 7.0, 1.0, 8.0, 6.0, 1.0, 6.0], [5.0, 9.0, 10.0, 2.0, 4.0, 4.0, 5.0, 10.0, 9.0, 10.0, 6.0, 5.0, 9.0, 3.0, 9.0, 7.0, 2.0, 2.0, 2.0, 1.0, 3.0, 4.0, 3.0], [1.0, 8.0, 1.0, 4.0, 5.0, 5.0, 7.0, 4.0, 3.0, 6.0, 5.0, 5.0, 1.0, 7.0, 7.0, 5.0, 2.0, 6.0, 7.0, 7.0, 2.0, 9.0, 6.0], [1.0, 7.0, 5.0, 1.0, 10.0, 10.0, 1.0, 10.0, 2.0, 5.0, 5.0, 10.0, 8.0, 5.0, 7.0, 5.0, 5.0, 5.0, 8.0, 5.0, 1.0, 5.0, 5.0], [3.0, 6.0, 8.0, 3.0, 1.0, 2.0, 10.0, 8.0, 9.0, 9.0, 1.0, 8.0, 8.0, 4.0, 6.0, 8.0, 10.0, 2.0, 3.0, 10.0, 8.0, 10.0, 1.0], [2.0, 5.0, 9.0, 4.0, 2.0, 9.0, 4.0, 1.0, 3.0, 3.0, 7.0, 5.0, 4.0, 8.0, 2.0, 7.0, 7.0, 10.0, 8.0, 5.0, 2.0, 7.0, 1.0], [2.0, 3.0, 3.0, 3.0, 5.0, 4.0, 5.0, 1.0, 8.0, 9.0, 7.0, 7.0, 6.0, 2.0, 2.0, 4.0, 10.0, 1.0, 1.0, 8.0, 5.0, 6.0, 7.0], [6.0, 9.0, 2.0, 6.0, 8.0, 10.0, 5.0, 3.0, 6.0, 7.0, 5.0, 5.0, 8.0, 7.0, 4.0, 7.0, 3.0, 9.0, 9.0, 10.0, 6.0, 5.0, 6.0], [9.0, 1.0, 4.0, 10.0, 4.0, 4.0, 3.0, 5.0, 8.0, 2.0, 2.0, 5.0, 10.0, 7.0, 10.0, 3.0, 3.0, 6.0, 8.0, 4.0, 7.0, 9.0, 8.0], [10.0, 3.0, 7.0, 3.0, 2.0, 6.0, 10.0, 9.0, 7.0, 2.0, 6.0, 5.0, 2.0, 10.0, 1.0, 9.0, 6.0, 10.0, 2.0, 6.0, 2.0, 9.0, 9.0], [4.0, 7.0, 10.0, 1.0, 2.0, 9.0, 5.0, 9.0, 1.0, 2.0, 7.0, 8.0, 3.0, 8.0, 1.0, 9.0, 8.0, 2.0, 6.0, 2.0, 2.0, 3.0, 4.0], [10.0, 5.0, 8.0, 5.0, 9.0, 3.0, 8.0, 2.0, 8.0, 1.0, 7.0, 5.0, 10.0, 5.0, 8.0, 10.0, 4.0, 6.0, 2.0, 8.0, 9.0, 8.0, 7.0], [8.0, 2.0, 1.0, 7.0, 3.0, 1.0, 2.0, 7.0, 6.0, 3.0, 2.0, 1.0, 8.0, 2.0, 5.0, 6.0, 7.0, 2.0, 2.0, 9.0, 5.0, 3.0, 4.0], [3.0, 9.0, 3.0, 3.0, 1.0, 7.0, 4.0, 8.0, 1.0, 4.0, 9.0, 5.0, 10.0, 7.0, 6.0, 5.0, 9.0, 9.0, 3.0, 8.0, 3.0, 5.0, 1.0], [5.0, 10.0, 5.0, 1.0, 2.0, 8.0, 10.0, 10.0, 6.0, 3.0, 6.0, 5.0, 1.0, 1.0, 7.0, 6.0, 8.0, 9.0, 4.0, 7.0, 4.0, 1.0, 5.0]]}, 'source': 22, 'target': 23}","[22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23]",2964.0,"{'problem_type': 'QSPP', 'num_nodes': 24, 'num_edges': 23, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'source': 23, 'target': 24, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 10.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 3.0}, {'var_index': 7, 'linear_cost': 6.0}, {'var_index': 8, 'linear_cost': 4.0}, {'var_index': 9, 'linear_cost': 2.0}, {'var_index': 10, 'linear_cost': 10.0}, {'var_index': 11, 'linear_cost': 4.0}, {'var_index': 12, 'linear_cost': 10.0}, {'var_index': 13, 'linear_cost': 5.0}, {'var_index': 14, 'linear_cost': 5.0}, {'var_index': 15, 'linear_cost': 2.0}, {'var_index': 16, 'linear_cost': 2.0}, {'var_index': 17, 'linear_cost': 3.0}, {'var_index': 18, 'linear_cost': 3.0}, {'var_index': 19, 'linear_cost': 3.0}, {'var_index': 20, 'linear_cost': 4.0}, {'var_index': 21, 'linear_cost': 10.0}, {'var_index': 22, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 4, 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'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 23, 'to': 1, 'var_index': 0}, {'from': 22, 'to': 24, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}, {'from': 15, 'to': 16, 'var_index': 16}, {'from': 16, 'to': 17, 'var_index': 17}, {'from': 17, 'to': 18, 'var_index': 18}, {'from': 18, 'to': 19, 'var_index': 19}, {'from': 19, 'to': 20, 'var_index': 20}, {'from': 20, 'to': 21, 'var_index': 21}, {'from': 21, 'to': 22, 'var_index': 22}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23, 23: 24}}","[23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24]",6,markdown_table,1
QSPP,QSPP,"Out on the bench there’s a single-route problem: route one signal from the input pad to the output pad by choosing a single directed chain of connections that’s allowed by the layout. Judge a candidate chain by summing each segment’s own leakage/resistance penalty and adding any extra penalties that come from every pair of segments on that chain interacting with each other — aim for the chain with the lowest overall sum. The result must be a single, unbroken sequence of locations starting at the input and ending at the output that steps only along valid directed links, and the specific map and numbers are shown below.

Here on the bench the map below lists 24 locations and 65 directed segments; valid location IDs are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. The signal must start at 22 and finish at 23.

| segment_from_location | segment_to_location | segment_id |
|---|---|---|
| 22 | 0 | 0 |
| 22 | 1 | 1 |
| 22 | 2 | 2 |
| 22 | 3 | 3 |
| 22 | 4 | 4 |
| 22 | 5 | 5 |
| 22 | 6 | 6 |
| 22 | 7 | 7 |
| 22 | 8 | 8 |
| 22 | 9 | 9 |
| 22 | 10 | 10 |
| 22 | 11 | 11 |
| 22 | 12 | 12 |
| 22 | 13 | 13 |
| 22 | 14 | 14 |
| 22 | 15 | 15 |
| 22 | 16 | 16 |
| 22 | 17 | 17 |
| 22 | 18 | 18 |
| 22 | 19 | 19 |
| 22 | 20 | 20 |
| 22 | 21 | 21 |
| 0 | 23 | 22 |
| 1 | 23 | 23 |
| 2 | 23 | 24 |
| 3 | 23 | 25 |
| 4 | 23 | 26 |
| 5 | 23 | 27 |
| 6 | 23 | 28 |
| 7 | 23 | 29 |
| 8 | 23 | 30 |
| 9 | 23 | 31 |
| 10 | 23 | 32 |
| 11 | 23 | 33 |
| 12 | 23 | 34 |
| 13 | 23 | 35 |
| 14 | 23 | 36 |
| 15 | 23 | 37 |
| 16 | 23 | 38 |
| 17 | 23 | 39 |
| 18 | 23 | 40 |
| 19 | 23 | 41 |
| 20 | 23 | 42 |
| 21 | 23 | 43 |
| 0 | 1 | 44 |
| 1 | 2 | 45 |
| 2 | 3 | 46 |
| 3 | 4 | 47 |
| 4 | 5 | 48 |
| 5 | 6 | 49 |
| 6 | 7 | 50 |
| 7 | 8 | 51 |
| 8 | 9 | 52 |
| 9 | 10 | 53 |
| 10 | 11 | 54 |
| 11 | 12 | 55 |
| 12 | 13 | 56 |
| 13 | 14 | 57 |
| 14 | 15 | 58 |
| 15 | 16 | 59 |
| 16 | 17 | 60 |
| 17 | 18 | 61 |
| 18 | 19 | 62 |
| 19 | 20 | 63 |
| 20 | 21 | 64 |

| segment_id | leakage_resistance_cost |
|---|---|
| 0 | 4.0 |
| 1 | 1.0 |
| 2 | 4.0 |
| 3 | 7.0 |
| 4 | 2.0 |
| 5 | 6.0 |
| 6 | 3.0 |
| 7 | 8.0 |
| 8 | 4.0 |
| 9 | 4.0 |
| 10 | 7.0 |
| 11 | 4.0 |
| 12 | 2.0 |
| 13 | 7.0 |
| 14 | 4.0 |
| 15 | 10.0 |
| 16 | 9.0 |
| 17 | 1.0 |
| 18 | 2.0 |
| 19 | 9.0 |
| 20 | 5.0 |
| 21 | 9.0 |
| 22 | 1.0 |
| 23 | 9.0 |
| 24 | 5.0 |
| 25 | 8.0 |
| 26 | 5.0 |
| 27 | 7.0 |
| 28 | 6.0 |
| 29 | 6.0 |
| 30 | 8.0 |
| 31 | 4.0 |
| 32 | 10.0 |
| 33 | 3.0 |
| 34 | 5.0 |
| 35 | 1.0 |
| 36 | 6.0 |
| 37 | 5.0 |
| 38 | 9.0 |
| 39 | 3.0 |
| 40 | 3.0 |
| 41 | 8.0 |
| 42 | 4.0 |
| 43 | 9.0 |
| 44 | 10.0 |
| 45 | 3.0 |
| 46 | 2.0 |
| 47 | 4.0 |
| 48 | 6.0 |
| 49 | 10.0 |
| 50 | 4.0 |
| 51 | 10.0 |
| 52 | 5.0 |
| 53 | 2.0 |
| 54 | 8.0 |
| 55 | 5.0 |
| 56 | 4.0 |
| 57 | 2.0 |
| 58 | 1.0 |
| 59 | 1.0 |
| 60 | 2.0 |
| 61 | 3.0 |
| 62 | 7.0 |
| 63 | 4.0 |
| 64 | 5.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 7.0 | 4.0 | 3.0 | 5.0 | 2.0 | 4.0 | 10.0 | 9.0 | 10.0 | 1.0 | 1.0 | 6.0 | 9.0 | 9.0 | 3.0 | 6.0 | 5.0 | 5.0 | 5.0 | 7.0 | 8.0 | 1.0 | 3.0 | 8.0 | 2.0 | 1.0 | 9.0 | 6.0 | 8.0 | 8.0 | 2.0 | 3.0 | 8.0 | 2.0 | 2.0 | 8.0 | 2.0 | 5.0 | 8.0 | 7.0 | 1.0 | 7.0 | 3.0 | 6.0 | 1.0 | 10.0 | 5.0 | 10.0 | 2.0 | 6.0 | 5.0 | 10.0 | 5.0 | 4.0 | 5.0 | 1.0 | 4.0 | 9.0 | 6.0 | 5.0 | 1.0 | 3.0 | 3.0 | 5.0 |
| 1 | 7.0 | 7.0 | 3.0 | 3.0 | 2.0 | 9.0 | 1.0 | 2.0 | 7.0 | 9.0 | 6.0 | 6.0 | 1.0 | 7.0 | 1.0 | 8.0 | 7.0 | 9.0 | 8.0 | 9.0 | 8.0 | 7.0 | 1.0 | 1.0 | 2.0 | 6.0 | 4.0 | 1.0 | 6.0 | 1.0 | 10.0 | 5.0 | 4.0 | 9.0 | 7.0 | 2.0 | 3.0 | 10.0 | 10.0 | 4.0 | 2.0 | 2.0 | 4.0 | 4.0 | 9.0 | 2.0 | 1.0 | 5.0 | 5.0 | 10.0 | 6.0 | 6.0 | 7.0 | 4.0 | 5.0 | 1.0 | 8.0 | 7.0 | 4.0 | 8.0 | 8.0 | 8.0 | 10.0 | 3.0 | 8.0 |
| 2 | 4.0 | 3.0 | 9.0 | 10.0 | 5.0 | 8.0 | 1.0 | 3.0 | 9.0 | 8.0 | 2.0 | 2.0 | 1.0 | 5.0 | 10.0 | 7.0 | 6.0 | 1.0 | 5.0 | 6.0 | 10.0 | 9.0 | 2.0 | 10.0 | 6.0 | 6.0 | 5.0 | 1.0 | 7.0 | 7.0 | 7.0 | 1.0 | 4.0 | 2.0 | 3.0 | 7.0 | 6.0 | 5.0 | 3.0 | 5.0 | 6.0 | 8.0 | 6.0 | 8.0 | 2.0 | 6.0 | 5.0 | 5.0 | 5.0 | 4.0 | 9.0 | 9.0 | 10.0 | 4.0 | 9.0 | 6.0 | 4.0 | 6.0 | 3.0 | 9.0 | 9.0 | 9.0 | 8.0 | 3.0 | 2.0 |
| 3 | 3.0 | 3.0 | 10.0 | 4.0 | 6.0 | 5.0 | 7.0 | 4.0 | 5.0 | 9.0 | 8.0 | 7.0 | 8.0 | 5.0 | 10.0 | 7.0 | 2.0 | 9.0 | 4.0 | 7.0 | 10.0 | 1.0 | 6.0 | 2.0 | 8.0 | 10.0 | 8.0 | 6.0 | 7.0 | 4.0 | 5.0 | 9.0 | 1.0 | 8.0 | 10.0 | 1.0 | 10.0 | 9.0 | 10.0 | 9.0 | 7.0 | 4.0 | 10.0 | 5.0 | 7.0 | 3.0 | 7.0 | 1.0 | 3.0 | 8.0 | 6.0 | 2.0 | 1.0 | 10.0 | 5.0 | 10.0 | 6.0 | 4.0 | 10.0 | 7.0 | 6.0 | 10.0 | 5.0 | 5.0 | 6.0 |
| 4 | 5.0 | 2.0 | 5.0 | 6.0 | 2.0 | 2.0 | 9.0 | 5.0 | 6.0 | 3.0 | 8.0 | 8.0 | 10.0 | 6.0 | 3.0 | 10.0 | 7.0 | 9.0 | 2.0 | 8.0 | 3.0 | 7.0 | 8.0 | 5.0 | 10.0 | 6.0 | 1.0 | 5.0 | 5.0 | 7.0 | 8.0 | 7.0 | 10.0 | 9.0 | 5.0 | 2.0 | 10.0 | 1.0 | 9.0 | 9.0 | 6.0 | 1.0 | 8.0 | 3.0 | 6.0 | 3.0 | 2.0 | 7.0 | 10.0 | 4.0 | 4.0 | 9.0 | 5.0 | 5.0 | 2.0 | 8.0 | 5.0 | 4.0 | 6.0 | 7.0 | 10.0 | 2.0 | 9.0 | 10.0 | 1.0 |
| 5 | 2.0 | 9.0 | 8.0 | 5.0 | 2.0 | 10.0 | 1.0 | 1.0 | 5.0 | 2.0 | 8.0 | 6.0 | 1.0 | 8.0 | 1.0 | 8.0 | 5.0 | 7.0 | 7.0 | 9.0 | 8.0 | 4.0 | 8.0 | 4.0 | 8.0 | 5.0 | 9.0 | 6.0 | 3.0 | 6.0 | 7.0 | 4.0 | 2.0 | 9.0 | 2.0 | 7.0 | 7.0 | 8.0 | 4.0 | 9.0 | 2.0 | 8.0 | 4.0 | 1.0 | 1.0 | 1.0 | 7.0 | 5.0 | 9.0 | 7.0 | 7.0 | 4.0 | 6.0 | 2.0 | 4.0 | 8.0 | 4.0 | 4.0 | 3.0 | 1.0 | 4.0 | 4.0 | 4.0 | 7.0 | 8.0 |
| 6 | 4.0 | 1.0 | 1.0 | 7.0 | 9.0 | 1.0 | 3.0 | 7.0 | 6.0 | 4.0 | 8.0 | 3.0 | 10.0 | 2.0 | 10.0 | 3.0 | 6.0 | 1.0 | 4.0 | 8.0 | 5.0 | 10.0 | 3.0 | 6.0 | 8.0 | 10.0 | 2.0 | 8.0 | 4.0 | 5.0 | 6.0 | 8.0 | 10.0 | 6.0 | 3.0 | 1.0 | 2.0 | 5.0 | 8.0 | 2.0 | 8.0 | 4.0 | 2.0 | 2.0 | 3.0 | 7.0 | 4.0 | 3.0 | 2.0 | 10.0 | 10.0 | 8.0 | 6.0 | 10.0 | 8.0 | 4.0 | 9.0 | 6.0 | 3.0 | 10.0 | 10.0 | 3.0 | 2.0 | 7.0 | 7.0 |
| 7 | 10.0 | 2.0 | 3.0 | 4.0 | 5.0 | 1.0 | 7.0 | 5.0 | 9.0 | 6.0 | 8.0 | 8.0 | 9.0 | 10.0 | 2.0 | 8.0 | 4.0 | 2.0 | 4.0 | 6.0 | 7.0 | 3.0 | 8.0 | 6.0 | 7.0 | 1.0 | 10.0 | 9.0 | 5.0 | 1.0 | 4.0 | 7.0 | 6.0 | 8.0 | 3.0 | 1.0 | 10.0 | 1.0 | 7.0 | 5.0 | 9.0 | 9.0 | 8.0 | 9.0 | 9.0 | 9.0 | 6.0 | 7.0 | 6.0 | 7.0 | 4.0 | 7.0 | 2.0 | 5.0 | 3.0 | 3.0 | 10.0 | 5.0 | 10.0 | 2.0 | 10.0 | 5.0 | 9.0 | 4.0 | 1.0 |
| 8 | 9.0 | 7.0 | 9.0 | 5.0 | 6.0 | 5.0 | 6.0 | 9.0 | 7.0 | 10.0 | 2.0 | 1.0 | 6.0 | 9.0 | 8.0 | 6.0 | 5.0 | 7.0 | 5.0 | 3.0 | 3.0 | 6.0 | 10.0 | 4.0 | 3.0 | 10.0 | 4.0 | 8.0 | 8.0 | 9.0 | 10.0 | 2.0 | 6.0 | 4.0 | 10.0 | 3.0 | 5.0 | 10.0 | 4.0 | 5.0 | 9.0 | 3.0 | 8.0 | 4.0 | 10.0 | 9.0 | 8.0 | 8.0 | 5.0 | 4.0 | 1.0 | 3.0 | 4.0 | 2.0 | 8.0 | 8.0 | 7.0 | 1.0 | 1.0 | 8.0 | 10.0 | 1.0 | 2.0 | 8.0 | 2.0 |
| 9 | 10.0 | 9.0 | 8.0 | 9.0 | 3.0 | 2.0 | 4.0 | 6.0 | 10.0 | 6.0 | 5.0 | 3.0 | 2.0 | 3.0 | 7.0 | 2.0 | 10.0 | 6.0 | 9.0 | 5.0 | 8.0 | 10.0 | 10.0 | 4.0 | 9.0 | 9.0 | 3.0 | 4.0 | 4.0 | 3.0 | 6.0 | 1.0 | 7.0 | 6.0 | 9.0 | 9.0 | 9.0 | 3.0 | 7.0 | 7.0 | 8.0 | 5.0 | 5.0 | 3.0 | 3.0 | 7.0 | 4.0 | 3.0 | 2.0 | 8.0 | 1.0 | 6.0 | 9.0 | 6.0 | 8.0 | 6.0 | 1.0 | 10.0 | 6.0 | 6.0 | 9.0 | 9.0 | 9.0 | 8.0 | 7.0 |
| 10 | 1.0 | 6.0 | 2.0 | 8.0 | 8.0 | 8.0 | 8.0 | 8.0 | 2.0 | 5.0 | 6.0 | 6.0 | 2.0 | 3.0 | 2.0 | 6.0 | 8.0 | 9.0 | 1.0 | 5.0 | 4.0 | 1.0 | 1.0 | 9.0 | 2.0 | 1.0 | 5.0 | 10.0 | 5.0 | 9.0 | 8.0 | 9.0 | 5.0 | 2.0 | 2.0 | 4.0 | 10.0 | 8.0 | 3.0 | 1.0 | 2.0 | 10.0 | 9.0 | 2.0 | 10.0 | 5.0 | 5.0 | 4.0 | 8.0 | 2.0 | 1.0 | 1.0 | 2.0 | 2.0 | 6.0 | 8.0 | 6.0 | 4.0 | 4.0 | 2.0 | 1.0 | 5.0 | 4.0 | 9.0 | 2.0 |
| 11 | 1.0 | 6.0 | 2.0 | 7.0 | 8.0 | 6.0 | 3.0 | 8.0 | 1.0 | 3.0 | 6.0 | 9.0 | 10.0 | 3.0 | 9.0 | 8.0 | 3.0 | 5.0 | 1.0 | 2.0 | 10.0 | 2.0 | 7.0 | 5.0 | 8.0 | 10.0 | 2.0 | 6.0 | 5.0 | 9.0 | 5.0 | 4.0 | 9.0 | 9.0 | 9.0 | 5.0 | 10.0 | 5.0 | 7.0 | 2.0 | 5.0 | 2.0 | 7.0 | 2.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 7.0 | 2.0 | 5.0 | 7.0 | 3.0 | 10.0 | 1.0 | 2.0 | 5.0 | 2.0 | 6.0 | 4.0 | 10.0 | 9.0 | 10.0 | 3.0 |
| 12 | 6.0 | 1.0 | 1.0 | 8.0 | 10.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 2.0 | 10.0 | 5.0 | 4.0 | 10.0 | 8.0 | 4.0 | 9.0 | 8.0 | 2.0 | 7.0 | 10.0 | 3.0 | 7.0 | 10.0 | 4.0 | 3.0 | 1.0 | 7.0 | 6.0 | 2.0 | 1.0 | 9.0 | 6.0 | 4.0 | 5.0 | 5.0 | 9.0 | 5.0 | 10.0 | 9.0 | 2.0 | 7.0 | 3.0 | 5.0 | 2.0 | 1.0 | 4.0 | 5.0 | 9.0 | 4.0 | 1.0 | 2.0 | 10.0 | 6.0 | 8.0 | 8.0 | 8.0 | 2.0 | 4.0 | 1.0 | 1.0 | 6.0 | 1.0 | 1.0 |
| 13 | 9.0 | 7.0 | 5.0 | 5.0 | 6.0 | 8.0 | 2.0 | 10.0 | 9.0 | 3.0 | 3.0 | 3.0 | 4.0 | 8.0 | 9.0 | 6.0 | 6.0 | 2.0 | 7.0 | 8.0 | 5.0 | 2.0 | 6.0 | 7.0 | 4.0 | 3.0 | 2.0 | 3.0 | 5.0 | 10.0 | 6.0 | 7.0 | 2.0 | 2.0 | 3.0 | 1.0 | 5.0 | 4.0 | 6.0 | 4.0 | 7.0 | 3.0 | 1.0 | 2.0 | 4.0 | 10.0 | 1.0 | 8.0 | 5.0 | 7.0 | 7.0 | 8.0 | 2.0 | 9.0 | 10.0 | 1.0 | 6.0 | 4.0 | 2.0 | 5.0 | 2.0 | 7.0 | 1.0 | 3.0 | 7.0 |
| 14 | 9.0 | 1.0 | 10.0 | 10.0 | 3.0 | 1.0 | 10.0 | 2.0 | 8.0 | 7.0 | 2.0 | 9.0 | 10.0 | 9.0 | 2.0 | 5.0 | 9.0 | 7.0 | 1.0 | 4.0 | 7.0 | 4.0 | 8.0 | 1.0 | 2.0 | 3.0 | 9.0 | 7.0 | 9.0 | 1.0 | 2.0 | 9.0 | 3.0 | 7.0 | 10.0 | 4.0 | 9.0 | 6.0 | 6.0 | 2.0 | 10.0 | 5.0 | 1.0 | 9.0 | 4.0 | 5.0 | 9.0 | 6.0 | 1.0 | 3.0 | 5.0 | 8.0 | 4.0 | 10.0 | 3.0 | 7.0 | 7.0 | 8.0 | 1.0 | 9.0 | 2.0 | 10.0 | 3.0 | 3.0 | 5.0 |
| 15 | 3.0 | 8.0 | 7.0 | 7.0 | 10.0 | 8.0 | 3.0 | 8.0 | 6.0 | 2.0 | 6.0 | 8.0 | 8.0 | 6.0 | 5.0 | 8.0 | 3.0 | 9.0 | 1.0 | 7.0 | 7.0 | 9.0 | 1.0 | 10.0 | 5.0 | 3.0 | 2.0 | 4.0 | 3.0 | 9.0 | 4.0 | 5.0 | 1.0 | 9.0 | 8.0 | 9.0 | 4.0 | 10.0 | 8.0 | 4.0 | 1.0 | 6.0 | 10.0 | 1.0 | 7.0 | 2.0 | 10.0 | 7.0 | 1.0 | 4.0 | 7.0 | 5.0 | 5.0 | 10.0 | 9.0 | 1.0 | 3.0 | 9.0 | 1.0 | 4.0 | 8.0 | 6.0 | 4.0 | 1.0 | 2.0 |
| 16 | 6.0 | 7.0 | 6.0 | 2.0 | 7.0 | 5.0 | 6.0 | 4.0 | 5.0 | 10.0 | 8.0 | 3.0 | 4.0 | 6.0 | 9.0 | 3.0 | 8.0 | 4.0 | 4.0 | 10.0 | 5.0 | 7.0 | 1.0 | 5.0 | 6.0 | 5.0 | 5.0 | 6.0 | 9.0 | 10.0 | 1.0 | 1.0 | 10.0 | 7.0 | 9.0 | 6.0 | 1.0 | 1.0 | 10.0 | 6.0 | 4.0 | 6.0 | 4.0 | 6.0 | 10.0 | 5.0 | 1.0 | 4.0 | 6.0 | 4.0 | 9.0 | 8.0 | 3.0 | 2.0 | 6.0 | 7.0 | 8.0 | 2.0 | 2.0 | 8.0 | 8.0 | 9.0 | 4.0 | 2.0 | 10.0 |
| 17 | 5.0 | 9.0 | 1.0 | 9.0 | 9.0 | 7.0 | 1.0 | 2.0 | 7.0 | 6.0 | 9.0 | 5.0 | 9.0 | 2.0 | 7.0 | 9.0 | 4.0 | 2.0 | 9.0 | 9.0 | 1.0 | 6.0 | 5.0 | 7.0 | 2.0 | 8.0 | 6.0 | 7.0 | 2.0 | 1.0 | 4.0 | 5.0 | 10.0 | 2.0 | 3.0 | 2.0 | 2.0 | 4.0 | 6.0 | 7.0 | 6.0 | 10.0 | 3.0 | 1.0 | 5.0 | 7.0 | 2.0 | 5.0 | 2.0 | 5.0 | 4.0 | 9.0 | 9.0 | 9.0 | 4.0 | 10.0 | 8.0 | 9.0 | 5.0 | 7.0 | 8.0 | 6.0 | 5.0 | 7.0 | 2.0 |
| 18 | 5.0 | 8.0 | 5.0 | 4.0 | 2.0 | 7.0 | 4.0 | 4.0 | 5.0 | 9.0 | 1.0 | 1.0 | 8.0 | 7.0 | 1.0 | 1.0 | 4.0 | 9.0 | 8.0 | 4.0 | 5.0 | 5.0 | 4.0 | 5.0 | 9.0 | 4.0 | 1.0 | 2.0 | 2.0 | 4.0 | 9.0 | 9.0 | 2.0 | 2.0 | 6.0 | 2.0 | 2.0 | 1.0 | 3.0 | 3.0 | 1.0 | 9.0 | 1.0 | 4.0 | 2.0 | 3.0 | 1.0 | 5.0 | 6.0 | 5.0 | 7.0 | 3.0 | 6.0 | 7.0 | 8.0 | 10.0 | 4.0 | 5.0 | 6.0 | 4.0 | 7.0 | 4.0 | 8.0 | 9.0 | 3.0 |
| 19 | 5.0 | 9.0 | 6.0 | 7.0 | 8.0 | 9.0 | 8.0 | 6.0 | 3.0 | 5.0 | 5.0 | 2.0 | 2.0 | 8.0 | 4.0 | 7.0 | 10.0 | 9.0 | 4.0 | 2.0 | 2.0 | 10.0 | 6.0 | 2.0 | 9.0 | 1.0 | 7.0 | 4.0 | 9.0 | 4.0 | 2.0 | 3.0 | 5.0 | 8.0 | 9.0 | 9.0 | 3.0 | 5.0 | 1.0 | 2.0 | 7.0 | 2.0 | 4.0 | 10.0 | 8.0 | 9.0 | 2.0 | 4.0 | 10.0 | 5.0 | 7.0 | 4.0 | 7.0 | 7.0 | 7.0 | 8.0 | 2.0 | 6.0 | 6.0 | 10.0 | 1.0 | 4.0 | 8.0 | 6.0 | 3.0 |
| 20 | 7.0 | 8.0 | 10.0 | 10.0 | 3.0 | 8.0 | 5.0 | 7.0 | 3.0 | 8.0 | 4.0 | 10.0 | 7.0 | 5.0 | 7.0 | 7.0 | 5.0 | 1.0 | 5.0 | 2.0 | 9.0 | 8.0 | 2.0 | 9.0 | 5.0 | 3.0 | 3.0 | 1.0 | 8.0 | 9.0 | 2.0 | 9.0 | 3.0 | 8.0 | 7.0 | 4.0 | 7.0 | 2.0 | 4.0 | 6.0 | 7.0 | 5.0 | 9.0 | 9.0 | 5.0 | 10.0 | 6.0 | 5.0 | 6.0 | 8.0 | 9.0 | 3.0 | 6.0 | 7.0 | 4.0 | 6.0 | 10.0 | 2.0 | 3.0 | 8.0 | 3.0 | 2.0 | 10.0 | 2.0 | 2.0 |
| 21 | 8.0 | 7.0 | 9.0 | 1.0 | 7.0 | 4.0 | 10.0 | 3.0 | 6.0 | 10.0 | 1.0 | 2.0 | 10.0 | 2.0 | 4.0 | 9.0 | 7.0 | 6.0 | 5.0 | 10.0 | 8.0 | 8.0 | 1.0 | 2.0 | 5.0 | 5.0 | 3.0 | 6.0 | 4.0 | 4.0 | 3.0 | 6.0 | 1.0 | 1.0 | 10.0 | 8.0 | 1.0 | 9.0 | 7.0 | 6.0 | 6.0 | 9.0 | 7.0 | 4.0 | 4.0 | 9.0 | 7.0 | 7.0 | 10.0 | 6.0 | 7.0 | 3.0 | 8.0 | 2.0 | 2.0 | 4.0 | 1.0 | 1.0 | 10.0 | 5.0 | 1.0 | 7.0 | 10.0 | 6.0 | 8.0 |
| 22 | 1.0 | 1.0 | 2.0 | 6.0 | 8.0 | 8.0 | 3.0 | 8.0 | 10.0 | 10.0 | 1.0 | 7.0 | 3.0 | 6.0 | 8.0 | 1.0 | 1.0 | 5.0 | 4.0 | 6.0 | 2.0 | 1.0 | 4.0 | 4.0 | 2.0 | 1.0 | 10.0 | 1.0 | 9.0 | 7.0 | 5.0 | 1.0 | 8.0 | 3.0 | 8.0 | 7.0 | 10.0 | 6.0 | 2.0 | 4.0 | 4.0 | 8.0 | 5.0 | 10.0 | 7.0 | 8.0 | 10.0 | 8.0 | 9.0 | 6.0 | 10.0 | 9.0 | 2.0 | 10.0 | 5.0 | 6.0 | 10.0 | 6.0 | 9.0 | 7.0 | 10.0 | 9.0 | 5.0 | 8.0 | 4.0 |
| 23 | 3.0 | 1.0 | 10.0 | 2.0 | 5.0 | 4.0 | 6.0 | 6.0 | 4.0 | 4.0 | 9.0 | 5.0 | 7.0 | 7.0 | 1.0 | 10.0 | 5.0 | 7.0 | 5.0 | 2.0 | 9.0 | 2.0 | 4.0 | 4.0 | 5.0 | 5.0 | 1.0 | 1.0 | 2.0 | 6.0 | 10.0 | 10.0 | 6.0 | 8.0 | 7.0 | 2.0 | 6.0 | 4.0 | 1.0 | 6.0 | 1.0 | 5.0 | 7.0 | 9.0 | 8.0 | 2.0 | 4.0 | 4.0 | 6.0 | 9.0 | 7.0 | 9.0 | 5.0 | 6.0 | 10.0 | 5.0 | 1.0 | 10.0 | 3.0 | 10.0 | 4.0 | 7.0 | 10.0 | 4.0 | 9.0 |
| 24 | 8.0 | 2.0 | 6.0 | 8.0 | 10.0 | 8.0 | 8.0 | 7.0 | 3.0 | 9.0 | 2.0 | 8.0 | 10.0 | 4.0 | 2.0 | 5.0 | 6.0 | 2.0 | 9.0 | 9.0 | 5.0 | 5.0 | 2.0 | 5.0 | 1.0 | 1.0 | 4.0 | 1.0 | 9.0 | 10.0 | 9.0 | 1.0 | 7.0 | 10.0 | 9.0 | 1.0 | 5.0 | 10.0 | 4.0 | 4.0 | 7.0 | 7.0 | 8.0 | 2.0 | 5.0 | 6.0 | 2.0 | 7.0 | 4.0 | 1.0 | 2.0 | 8.0 | 5.0 | 2.0 | 7.0 | 6.0 | 7.0 | 7.0 | 9.0 | 7.0 | 5.0 | 4.0 | 10.0 | 7.0 | 3.0 |
| 25 | 2.0 | 6.0 | 6.0 | 10.0 | 6.0 | 5.0 | 10.0 | 1.0 | 10.0 | 9.0 | 1.0 | 10.0 | 4.0 | 3.0 | 3.0 | 3.0 | 5.0 | 8.0 | 4.0 | 1.0 | 3.0 | 5.0 | 1.0 | 5.0 | 1.0 | 4.0 | 10.0 | 10.0 | 9.0 | 6.0 | 6.0 | 2.0 | 3.0 | 6.0 | 2.0 | 3.0 | 2.0 | 6.0 | 8.0 | 6.0 | 9.0 | 2.0 | 4.0 | 9.0 | 7.0 | 2.0 | 8.0 | 5.0 | 2.0 | 10.0 | 1.0 | 2.0 | 8.0 | 3.0 | 4.0 | 5.0 | 2.0 | 9.0 | 3.0 | 4.0 | 8.0 | 3.0 | 10.0 | 3.0 | 3.0 |
| 26 | 1.0 | 4.0 | 5.0 | 8.0 | 1.0 | 9.0 | 2.0 | 10.0 | 4.0 | 3.0 | 5.0 | 2.0 | 3.0 | 2.0 | 9.0 | 2.0 | 5.0 | 6.0 | 1.0 | 7.0 | 3.0 | 3.0 | 10.0 | 1.0 | 4.0 | 10.0 | 1.0 | 7.0 | 9.0 | 10.0 | 6.0 | 10.0 | 8.0 | 8.0 | 10.0 | 8.0 | 2.0 | 2.0 | 5.0 | 8.0 | 1.0 | 5.0 | 10.0 | 1.0 | 1.0 | 10.0 | 10.0 | 3.0 | 7.0 | 5.0 | 10.0 | 8.0 | 2.0 | 3.0 | 5.0 | 10.0 | 2.0 | 8.0 | 4.0 | 7.0 | 7.0 | 1.0 | 10.0 | 2.0 | 9.0 |
| 27 | 9.0 | 1.0 | 1.0 | 6.0 | 5.0 | 6.0 | 8.0 | 9.0 | 8.0 | 4.0 | 10.0 | 6.0 | 1.0 | 3.0 | 7.0 | 4.0 | 6.0 | 7.0 | 2.0 | 4.0 | 1.0 | 6.0 | 1.0 | 1.0 | 1.0 | 10.0 | 7.0 | 5.0 | 6.0 | 3.0 | 1.0 | 9.0 | 10.0 | 5.0 | 7.0 | 6.0 | 5.0 | 5.0 | 1.0 | 5.0 | 4.0 | 10.0 | 8.0 | 4.0 | 10.0 | 8.0 | 8.0 | 1.0 | 4.0 | 9.0 | 2.0 | 8.0 | 8.0 | 5.0 | 2.0 | 9.0 | 5.0 | 4.0 | 10.0 | 5.0 | 10.0 | 8.0 | 7.0 | 8.0 | 6.0 |
| 28 | 6.0 | 6.0 | 7.0 | 7.0 | 5.0 | 3.0 | 4.0 | 5.0 | 8.0 | 4.0 | 5.0 | 5.0 | 7.0 | 5.0 | 9.0 | 3.0 | 9.0 | 2.0 | 2.0 | 9.0 | 8.0 | 4.0 | 9.0 | 2.0 | 9.0 | 9.0 | 9.0 | 6.0 | 5.0 | 4.0 | 1.0 | 7.0 | 9.0 | 3.0 | 9.0 | 9.0 | 7.0 | 2.0 | 5.0 | 5.0 | 8.0 | 7.0 | 6.0 | 2.0 | 7.0 | 6.0 | 5.0 | 5.0 | 3.0 | 9.0 | 4.0 | 3.0 | 1.0 | 8.0 | 10.0 | 4.0 | 8.0 | 3.0 | 1.0 | 3.0 | 8.0 | 10.0 | 8.0 | 7.0 | 8.0 |
| 29 | 8.0 | 1.0 | 7.0 | 4.0 | 7.0 | 6.0 | 5.0 | 1.0 | 9.0 | 3.0 | 9.0 | 9.0 | 6.0 | 10.0 | 1.0 | 9.0 | 10.0 | 1.0 | 4.0 | 4.0 | 9.0 | 4.0 | 7.0 | 6.0 | 10.0 | 6.0 | 10.0 | 3.0 | 4.0 | 3.0 | 2.0 | 9.0 | 7.0 | 3.0 | 5.0 | 4.0 | 3.0 | 7.0 | 9.0 | 5.0 | 3.0 | 5.0 | 8.0 | 6.0 | 9.0 | 1.0 | 4.0 | 7.0 | 7.0 | 3.0 | 2.0 | 9.0 | 3.0 | 6.0 | 2.0 | 5.0 | 8.0 | 5.0 | 6.0 | 9.0 | 4.0 | 6.0 | 10.0 | 8.0 | 2.0 |
| 30 | 8.0 | 10.0 | 7.0 | 5.0 | 8.0 | 7.0 | 6.0 | 4.0 | 10.0 | 6.0 | 8.0 | 5.0 | 2.0 | 6.0 | 2.0 | 4.0 | 1.0 | 4.0 | 9.0 | 2.0 | 2.0 | 3.0 | 5.0 | 10.0 | 9.0 | 6.0 | 6.0 | 1.0 | 1.0 | 2.0 | 10.0 | 9.0 | 6.0 | 6.0 | 8.0 | 3.0 | 4.0 | 1.0 | 7.0 | 8.0 | 6.0 | 5.0 | 8.0 | 2.0 | 1.0 | 1.0 | 9.0 | 6.0 | 3.0 | 3.0 | 8.0 | 8.0 | 5.0 | 6.0 | 7.0 | 4.0 | 2.0 | 3.0 | 1.0 | 6.0 | 9.0 | 2.0 | 9.0 | 2.0 | 6.0 |
| 31 | 2.0 | 5.0 | 1.0 | 9.0 | 7.0 | 4.0 | 8.0 | 7.0 | 2.0 | 1.0 | 9.0 | 4.0 | 1.0 | 7.0 | 9.0 | 5.0 | 1.0 | 5.0 | 9.0 | 3.0 | 9.0 | 6.0 | 1.0 | 10.0 | 1.0 | 2.0 | 10.0 | 9.0 | 7.0 | 9.0 | 9.0 | 1.0 | 10.0 | 7.0 | 10.0 | 7.0 | 2.0 | 7.0 | 4.0 | 6.0 | 9.0 | 8.0 | 2.0 | 8.0 | 7.0 | 9.0 | 6.0 | 9.0 | 1.0 | 1.0 | 1.0 | 2.0 | 8.0 | 2.0 | 4.0 | 3.0 | 1.0 | 5.0 | 4.0 | 6.0 | 1.0 | 3.0 | 7.0 | 8.0 | 4.0 |
| 32 | 3.0 | 4.0 | 4.0 | 1.0 | 10.0 | 2.0 | 10.0 | 6.0 | 6.0 | 7.0 | 5.0 | 9.0 | 9.0 | 2.0 | 3.0 | 1.0 | 10.0 | 10.0 | 2.0 | 5.0 | 3.0 | 1.0 | 8.0 | 6.0 | 7.0 | 3.0 | 8.0 | 10.0 | 9.0 | 7.0 | 6.0 | 10.0 | 6.0 | 9.0 | 8.0 | 8.0 | 7.0 | 10.0 | 2.0 | 7.0 | 3.0 | 9.0 | 8.0 | 8.0 | 5.0 | 8.0 | 9.0 | 2.0 | 9.0 | 8.0 | 1.0 | 9.0 | 9.0 | 1.0 | 9.0 | 1.0 | 2.0 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 5.0 | 10.0 | 6.0 |
| 33 | 8.0 | 9.0 | 2.0 | 8.0 | 9.0 | 9.0 | 6.0 | 8.0 | 4.0 | 6.0 | 2.0 | 9.0 | 6.0 | 2.0 | 7.0 | 9.0 | 7.0 | 2.0 | 2.0 | 8.0 | 8.0 | 1.0 | 3.0 | 8.0 | 10.0 | 6.0 | 8.0 | 5.0 | 3.0 | 3.0 | 6.0 | 7.0 | 9.0 | 8.0 | 4.0 | 9.0 | 5.0 | 1.0 | 5.0 | 8.0 | 5.0 | 9.0 | 7.0 | 7.0 | 7.0 | 7.0 | 5.0 | 7.0 | 5.0 | 4.0 | 4.0 | 7.0 | 9.0 | 9.0 | 2.0 | 9.0 | 8.0 | 2.0 | 1.0 | 7.0 | 3.0 | 6.0 | 4.0 | 10.0 | 8.0 |
| 34 | 2.0 | 7.0 | 3.0 | 10.0 | 5.0 | 2.0 | 3.0 | 3.0 | 10.0 | 9.0 | 2.0 | 9.0 | 4.0 | 3.0 | 10.0 | 8.0 | 9.0 | 3.0 | 6.0 | 9.0 | 7.0 | 10.0 | 8.0 | 7.0 | 9.0 | 2.0 | 10.0 | 7.0 | 9.0 | 5.0 | 8.0 | 10.0 | 8.0 | 4.0 | 3.0 | 8.0 | 2.0 | 9.0 | 2.0 | 5.0 | 10.0 | 8.0 | 6.0 | 4.0 | 2.0 | 5.0 | 8.0 | 9.0 | 4.0 | 1.0 | 10.0 | 6.0 | 1.0 | 7.0 | 1.0 | 6.0 | 3.0 | 1.0 | 5.0 | 4.0 | 9.0 | 3.0 | 7.0 | 7.0 | 10.0 |
| 35 | 2.0 | 2.0 | 7.0 | 1.0 | 2.0 | 7.0 | 1.0 | 1.0 | 3.0 | 9.0 | 4.0 | 5.0 | 5.0 | 1.0 | 4.0 | 9.0 | 6.0 | 2.0 | 2.0 | 9.0 | 4.0 | 8.0 | 7.0 | 2.0 | 1.0 | 3.0 | 8.0 | 6.0 | 9.0 | 4.0 | 3.0 | 7.0 | 8.0 | 9.0 | 8.0 | 5.0 | 9.0 | 10.0 | 2.0 | 9.0 | 7.0 | 3.0 | 8.0 | 5.0 | 4.0 | 2.0 | 8.0 | 10.0 | 6.0 | 8.0 | 3.0 | 3.0 | 9.0 | 10.0 | 4.0 | 5.0 | 10.0 | 5.0 | 2.0 | 9.0 | 3.0 | 4.0 | 4.0 | 4.0 | 8.0 |
| 36 | 8.0 | 3.0 | 6.0 | 10.0 | 10.0 | 7.0 | 2.0 | 10.0 | 5.0 | 9.0 | 10.0 | 10.0 | 5.0 | 5.0 | 9.0 | 4.0 | 1.0 | 2.0 | 2.0 | 3.0 | 7.0 | 1.0 | 10.0 | 6.0 | 5.0 | 2.0 | 2.0 | 5.0 | 7.0 | 3.0 | 4.0 | 2.0 | 7.0 | 5.0 | 2.0 | 9.0 | 1.0 | 5.0 | 10.0 | 4.0 | 7.0 | 9.0 | 4.0 | 4.0 | 1.0 | 6.0 | 9.0 | 1.0 | 2.0 | 3.0 | 9.0 | 2.0 | 9.0 | 8.0 | 3.0 | 5.0 | 10.0 | 1.0 | 5.0 | 5.0 | 8.0 | 7.0 | 10.0 | 1.0 | 4.0 |
| 37 | 2.0 | 10.0 | 5.0 | 9.0 | 1.0 | 8.0 | 5.0 | 1.0 | 10.0 | 3.0 | 8.0 | 5.0 | 9.0 | 4.0 | 6.0 | 10.0 | 1.0 | 4.0 | 1.0 | 5.0 | 2.0 | 9.0 | 6.0 | 4.0 | 10.0 | 6.0 | 2.0 | 5.0 | 2.0 | 7.0 | 1.0 | 7.0 | 10.0 | 1.0 | 9.0 | 10.0 | 5.0 | 1.0 | 2.0 | 5.0 | 4.0 | 4.0 | 3.0 | 9.0 | 1.0 | 3.0 | 1.0 | 4.0 | 4.0 | 9.0 | 6.0 | 4.0 | 6.0 | 1.0 | 6.0 | 4.0 | 1.0 | 10.0 | 9.0 | 3.0 | 5.0 | 9.0 | 4.0 | 2.0 | 2.0 |
| 38 | 5.0 | 10.0 | 3.0 | 10.0 | 9.0 | 4.0 | 8.0 | 7.0 | 4.0 | 7.0 | 3.0 | 7.0 | 5.0 | 6.0 | 6.0 | 8.0 | 10.0 | 6.0 | 3.0 | 1.0 | 4.0 | 7.0 | 2.0 | 1.0 | 4.0 | 8.0 | 5.0 | 1.0 | 5.0 | 9.0 | 7.0 | 4.0 | 2.0 | 5.0 | 2.0 | 2.0 | 10.0 | 2.0 | 1.0 | 10.0 | 4.0 | 10.0 | 9.0 | 5.0 | 3.0 | 9.0 | 3.0 | 8.0 | 8.0 | 9.0 | 6.0 | 7.0 | 1.0 | 4.0 | 9.0 | 4.0 | 9.0 | 6.0 | 4.0 | 4.0 | 10.0 | 10.0 | 6.0 | 9.0 | 7.0 |
| 39 | 8.0 | 4.0 | 5.0 | 9.0 | 9.0 | 9.0 | 2.0 | 5.0 | 5.0 | 7.0 | 1.0 | 2.0 | 10.0 | 4.0 | 2.0 | 4.0 | 6.0 | 7.0 | 3.0 | 2.0 | 6.0 | 6.0 | 4.0 | 6.0 | 4.0 | 6.0 | 8.0 | 5.0 | 5.0 | 5.0 | 8.0 | 6.0 | 7.0 | 8.0 | 5.0 | 9.0 | 4.0 | 5.0 | 10.0 | 3.0 | 7.0 | 2.0 | 2.0 | 9.0 | 8.0 | 7.0 | 3.0 | 3.0 | 2.0 | 8.0 | 8.0 | 5.0 | 10.0 | 3.0 | 4.0 | 10.0 | 4.0 | 7.0 | 6.0 | 7.0 | 4.0 | 1.0 | 3.0 | 5.0 | 8.0 |
| 40 | 7.0 | 2.0 | 6.0 | 7.0 | 6.0 | 2.0 | 8.0 | 9.0 | 9.0 | 8.0 | 2.0 | 5.0 | 9.0 | 7.0 | 10.0 | 1.0 | 4.0 | 6.0 | 1.0 | 7.0 | 7.0 | 6.0 | 4.0 | 1.0 | 7.0 | 9.0 | 1.0 | 4.0 | 8.0 | 3.0 | 6.0 | 9.0 | 3.0 | 5.0 | 10.0 | 7.0 | 7.0 | 4.0 | 4.0 | 7.0 | 1.0 | 7.0 | 3.0 | 3.0 | 7.0 | 3.0 | 8.0 | 6.0 | 9.0 | 8.0 | 1.0 | 5.0 | 7.0 | 1.0 | 8.0 | 3.0 | 8.0 | 7.0 | 2.0 | 1.0 | 4.0 | 9.0 | 8.0 | 1.0 | 1.0 |
| 41 | 1.0 | 2.0 | 8.0 | 4.0 | 1.0 | 8.0 | 4.0 | 9.0 | 3.0 | 5.0 | 10.0 | 2.0 | 2.0 | 3.0 | 5.0 | 6.0 | 6.0 | 10.0 | 9.0 | 2.0 | 5.0 | 9.0 | 8.0 | 5.0 | 7.0 | 2.0 | 5.0 | 10.0 | 7.0 | 5.0 | 5.0 | 8.0 | 9.0 | 9.0 | 8.0 | 3.0 | 9.0 | 4.0 | 10.0 | 2.0 | 7.0 | 8.0 | 10.0 | 7.0 | 1.0 | 10.0 | 5.0 | 2.0 | 7.0 | 7.0 | 5.0 | 9.0 | 5.0 | 8.0 | 9.0 | 3.0 | 3.0 | 6.0 | 2.0 | 6.0 | 1.0 | 9.0 | 3.0 | 4.0 | 10.0 |
| 42 | 7.0 | 4.0 | 6.0 | 10.0 | 8.0 | 4.0 | 2.0 | 8.0 | 8.0 | 5.0 | 9.0 | 7.0 | 7.0 | 1.0 | 1.0 | 10.0 | 4.0 | 3.0 | 1.0 | 4.0 | 9.0 | 7.0 | 5.0 | 7.0 | 8.0 | 4.0 | 10.0 | 8.0 | 6.0 | 8.0 | 8.0 | 2.0 | 8.0 | 7.0 | 6.0 | 8.0 | 4.0 | 3.0 | 9.0 | 2.0 | 3.0 | 10.0 | 5.0 | 6.0 | 4.0 | 4.0 | 1.0 | 2.0 | 6.0 | 4.0 | 6.0 | 3.0 | 3.0 | 1.0 | 6.0 | 9.0 | 2.0 | 10.0 | 3.0 | 3.0 | 7.0 | 1.0 | 2.0 | 3.0 | 4.0 |
| 43 | 3.0 | 4.0 | 8.0 | 5.0 | 3.0 | 1.0 | 2.0 | 9.0 | 4.0 | 3.0 | 2.0 | 2.0 | 3.0 | 2.0 | 9.0 | 1.0 | 6.0 | 1.0 | 4.0 | 10.0 | 9.0 | 4.0 | 10.0 | 9.0 | 2.0 | 9.0 | 1.0 | 4.0 | 2.0 | 6.0 | 2.0 | 8.0 | 8.0 | 7.0 | 4.0 | 5.0 | 4.0 | 9.0 | 5.0 | 9.0 | 3.0 | 7.0 | 6.0 | 10.0 | 3.0 | 10.0 | 1.0 | 5.0 | 4.0 | 7.0 | 8.0 | 10.0 | 9.0 | 5.0 | 5.0 | 3.0 | 9.0 | 9.0 | 2.0 | 7.0 | 8.0 | 7.0 | 9.0 | 2.0 | 10.0 |
| 44 | 6.0 | 9.0 | 2.0 | 7.0 | 6.0 | 1.0 | 3.0 | 9.0 | 10.0 | 3.0 | 10.0 | 3.0 | 5.0 | 4.0 | 4.0 | 7.0 | 10.0 | 5.0 | 2.0 | 8.0 | 5.0 | 4.0 | 7.0 | 8.0 | 5.0 | 7.0 | 1.0 | 10.0 | 7.0 | 9.0 | 1.0 | 7.0 | 5.0 | 7.0 | 2.0 | 4.0 | 1.0 | 1.0 | 3.0 | 8.0 | 7.0 | 1.0 | 4.0 | 3.0 | 7.0 | 10.0 | 4.0 | 4.0 | 9.0 | 8.0 | 10.0 | 9.0 | 9.0 | 2.0 | 3.0 | 6.0 | 4.0 | 9.0 | 5.0 | 5.0 | 6.0 | 1.0 | 10.0 | 2.0 | 6.0 |
| 45 | 1.0 | 2.0 | 6.0 | 3.0 | 3.0 | 1.0 | 7.0 | 9.0 | 9.0 | 7.0 | 5.0 | 9.0 | 2.0 | 10.0 | 5.0 | 2.0 | 5.0 | 7.0 | 3.0 | 9.0 | 10.0 | 9.0 | 8.0 | 2.0 | 6.0 | 2.0 | 10.0 | 8.0 | 6.0 | 1.0 | 1.0 | 9.0 | 8.0 | 7.0 | 5.0 | 2.0 | 6.0 | 3.0 | 9.0 | 7.0 | 3.0 | 10.0 | 4.0 | 10.0 | 10.0 | 10.0 | 7.0 | 3.0 | 2.0 | 2.0 | 1.0 | 8.0 | 6.0 | 6.0 | 7.0 | 7.0 | 10.0 | 3.0 | 3.0 | 1.0 | 3.0 | 10.0 | 5.0 | 2.0 | 4.0 |
| 46 | 10.0 | 1.0 | 5.0 | 7.0 | 2.0 | 7.0 | 4.0 | 6.0 | 8.0 | 4.0 | 5.0 | 9.0 | 1.0 | 1.0 | 9.0 | 10.0 | 1.0 | 2.0 | 1.0 | 2.0 | 6.0 | 7.0 | 10.0 | 4.0 | 2.0 | 8.0 | 10.0 | 8.0 | 5.0 | 4.0 | 9.0 | 6.0 | 9.0 | 5.0 | 8.0 | 8.0 | 9.0 | 1.0 | 3.0 | 3.0 | 8.0 | 5.0 | 1.0 | 1.0 | 4.0 | 7.0 | 9.0 | 6.0 | 3.0 | 4.0 | 1.0 | 9.0 | 5.0 | 1.0 | 10.0 | 6.0 | 5.0 | 10.0 | 2.0 | 1.0 | 7.0 | 1.0 | 3.0 | 9.0 | 2.0 |
| 47 | 5.0 | 5.0 | 5.0 | 1.0 | 7.0 | 5.0 | 3.0 | 7.0 | 8.0 | 3.0 | 4.0 | 4.0 | 4.0 | 8.0 | 6.0 | 7.0 | 4.0 | 5.0 | 5.0 | 4.0 | 5.0 | 7.0 | 8.0 | 4.0 | 7.0 | 5.0 | 3.0 | 1.0 | 5.0 | 7.0 | 6.0 | 9.0 | 2.0 | 7.0 | 9.0 | 10.0 | 1.0 | 4.0 | 8.0 | 3.0 | 6.0 | 2.0 | 2.0 | 5.0 | 4.0 | 3.0 | 6.0 | 5.0 | 7.0 | 8.0 | 4.0 | 4.0 | 5.0 | 4.0 | 7.0 | 2.0 | 4.0 | 7.0 | 1.0 | 1.0 | 7.0 | 3.0 | 8.0 | 1.0 | 7.0 |
| 48 | 10.0 | 5.0 | 5.0 | 3.0 | 10.0 | 9.0 | 2.0 | 6.0 | 5.0 | 2.0 | 8.0 | 8.0 | 5.0 | 5.0 | 1.0 | 1.0 | 6.0 | 2.0 | 6.0 | 10.0 | 6.0 | 10.0 | 9.0 | 6.0 | 4.0 | 2.0 | 7.0 | 4.0 | 3.0 | 7.0 | 3.0 | 1.0 | 9.0 | 5.0 | 4.0 | 6.0 | 2.0 | 4.0 | 8.0 | 2.0 | 9.0 | 7.0 | 6.0 | 4.0 | 9.0 | 2.0 | 3.0 | 7.0 | 8.0 | 9.0 | 2.0 | 10.0 | 6.0 | 4.0 | 4.0 | 6.0 | 10.0 | 7.0 | 2.0 | 4.0 | 4.0 | 5.0 | 4.0 | 8.0 | 4.0 |
| 49 | 2.0 | 10.0 | 4.0 | 8.0 | 4.0 | 7.0 | 10.0 | 7.0 | 4.0 | 8.0 | 2.0 | 7.0 | 9.0 | 7.0 | 3.0 | 4.0 | 4.0 | 5.0 | 5.0 | 5.0 | 8.0 | 6.0 | 6.0 | 9.0 | 1.0 | 10.0 | 5.0 | 9.0 | 9.0 | 3.0 | 3.0 | 1.0 | 8.0 | 4.0 | 1.0 | 8.0 | 3.0 | 9.0 | 9.0 | 8.0 | 8.0 | 7.0 | 4.0 | 7.0 | 8.0 | 2.0 | 4.0 | 8.0 | 9.0 | 1.0 | 1.0 | 5.0 | 8.0 | 4.0 | 6.0 | 8.0 | 2.0 | 4.0 | 1.0 | 10.0 | 3.0 | 5.0 | 10.0 | 1.0 | 8.0 |
| 50 | 6.0 | 6.0 | 9.0 | 6.0 | 4.0 | 7.0 | 10.0 | 4.0 | 1.0 | 1.0 | 1.0 | 2.0 | 4.0 | 7.0 | 5.0 | 7.0 | 9.0 | 4.0 | 7.0 | 7.0 | 9.0 | 7.0 | 10.0 | 7.0 | 2.0 | 1.0 | 10.0 | 2.0 | 4.0 | 2.0 | 8.0 | 1.0 | 1.0 | 4.0 | 10.0 | 3.0 | 9.0 | 6.0 | 6.0 | 8.0 | 1.0 | 5.0 | 6.0 | 8.0 | 10.0 | 1.0 | 1.0 | 4.0 | 2.0 | 1.0 | 4.0 | 7.0 | 3.0 | 3.0 | 10.0 | 3.0 | 5.0 | 1.0 | 3.0 | 9.0 | 7.0 | 4.0 | 8.0 | 9.0 | 9.0 |
| 51 | 5.0 | 6.0 | 9.0 | 2.0 | 9.0 | 4.0 | 8.0 | 7.0 | 3.0 | 6.0 | 1.0 | 5.0 | 1.0 | 8.0 | 8.0 | 5.0 | 8.0 | 9.0 | 3.0 | 4.0 | 3.0 | 3.0 | 9.0 | 9.0 | 8.0 | 2.0 | 8.0 | 8.0 | 3.0 | 9.0 | 8.0 | 2.0 | 9.0 | 7.0 | 6.0 | 3.0 | 2.0 | 4.0 | 7.0 | 5.0 | 5.0 | 9.0 | 3.0 | 10.0 | 9.0 | 8.0 | 9.0 | 4.0 | 10.0 | 5.0 | 7.0 | 1.0 | 6.0 | 8.0 | 8.0 | 5.0 | 8.0 | 8.0 | 9.0 | 7.0 | 3.0 | 10.0 | 5.0 | 1.0 | 10.0 |
| 52 | 10.0 | 7.0 | 10.0 | 1.0 | 5.0 | 6.0 | 6.0 | 2.0 | 4.0 | 9.0 | 2.0 | 7.0 | 2.0 | 2.0 | 4.0 | 5.0 | 3.0 | 9.0 | 6.0 | 7.0 | 6.0 | 8.0 | 2.0 | 5.0 | 5.0 | 8.0 | 2.0 | 8.0 | 1.0 | 3.0 | 5.0 | 8.0 | 9.0 | 9.0 | 1.0 | 9.0 | 9.0 | 6.0 | 1.0 | 10.0 | 7.0 | 5.0 | 3.0 | 9.0 | 9.0 | 6.0 | 5.0 | 5.0 | 6.0 | 8.0 | 3.0 | 6.0 | 6.0 | 1.0 | 1.0 | 7.0 | 7.0 | 1.0 | 6.0 | 7.0 | 1.0 | 4.0 | 10.0 | 5.0 | 8.0 |
| 53 | 5.0 | 4.0 | 4.0 | 10.0 | 5.0 | 2.0 | 10.0 | 5.0 | 2.0 | 6.0 | 2.0 | 3.0 | 10.0 | 9.0 | 10.0 | 10.0 | 2.0 | 9.0 | 7.0 | 7.0 | 7.0 | 2.0 | 10.0 | 6.0 | 2.0 | 3.0 | 3.0 | 5.0 | 8.0 | 6.0 | 6.0 | 2.0 | 1.0 | 9.0 | 7.0 | 10.0 | 8.0 | 1.0 | 4.0 | 3.0 | 1.0 | 8.0 | 1.0 | 5.0 | 2.0 | 6.0 | 1.0 | 4.0 | 4.0 | 4.0 | 3.0 | 8.0 | 1.0 | 7.0 | 6.0 | 5.0 | 3.0 | 5.0 | 9.0 | 4.0 | 6.0 | 9.0 | 6.0 | 1.0 | 6.0 |
| 54 | 4.0 | 5.0 | 9.0 | 5.0 | 2.0 | 4.0 | 8.0 | 3.0 | 8.0 | 8.0 | 6.0 | 10.0 | 6.0 | 10.0 | 3.0 | 9.0 | 6.0 | 4.0 | 8.0 | 7.0 | 4.0 | 2.0 | 5.0 | 10.0 | 7.0 | 4.0 | 5.0 | 2.0 | 10.0 | 2.0 | 7.0 | 4.0 | 9.0 | 2.0 | 1.0 | 4.0 | 3.0 | 6.0 | 9.0 | 4.0 | 8.0 | 9.0 | 6.0 | 5.0 | 3.0 | 7.0 | 10.0 | 7.0 | 4.0 | 6.0 | 10.0 | 8.0 | 1.0 | 6.0 | 4.0 | 7.0 | 8.0 | 10.0 | 7.0 | 7.0 | 1.0 | 6.0 | 5.0 | 2.0 | 2.0 |
| 55 | 5.0 | 1.0 | 6.0 | 10.0 | 8.0 | 8.0 | 4.0 | 3.0 | 8.0 | 6.0 | 8.0 | 1.0 | 8.0 | 1.0 | 7.0 | 1.0 | 7.0 | 10.0 | 10.0 | 8.0 | 6.0 | 4.0 | 6.0 | 5.0 | 6.0 | 5.0 | 10.0 | 9.0 | 4.0 | 5.0 | 4.0 | 3.0 | 1.0 | 9.0 | 6.0 | 5.0 | 5.0 | 4.0 | 4.0 | 10.0 | 3.0 | 3.0 | 9.0 | 3.0 | 6.0 | 7.0 | 6.0 | 2.0 | 6.0 | 8.0 | 3.0 | 5.0 | 7.0 | 5.0 | 7.0 | 10.0 | 9.0 | 2.0 | 5.0 | 1.0 | 5.0 | 8.0 | 6.0 | 10.0 | 9.0 |
| 56 | 1.0 | 8.0 | 4.0 | 6.0 | 5.0 | 4.0 | 9.0 | 10.0 | 7.0 | 1.0 | 6.0 | 2.0 | 8.0 | 6.0 | 7.0 | 3.0 | 8.0 | 8.0 | 4.0 | 2.0 | 10.0 | 1.0 | 10.0 | 1.0 | 7.0 | 2.0 | 2.0 | 5.0 | 8.0 | 8.0 | 2.0 | 1.0 | 2.0 | 8.0 | 3.0 | 10.0 | 10.0 | 1.0 | 9.0 | 4.0 | 8.0 | 3.0 | 2.0 | 9.0 | 4.0 | 10.0 | 5.0 | 4.0 | 10.0 | 2.0 | 5.0 | 8.0 | 7.0 | 3.0 | 8.0 | 9.0 | 8.0 | 2.0 | 2.0 | 8.0 | 10.0 | 6.0 | 6.0 | 4.0 | 5.0 |
| 57 | 4.0 | 7.0 | 6.0 | 4.0 | 4.0 | 4.0 | 6.0 | 5.0 | 1.0 | 10.0 | 4.0 | 5.0 | 8.0 | 4.0 | 8.0 | 9.0 | 2.0 | 9.0 | 5.0 | 6.0 | 2.0 | 1.0 | 6.0 | 10.0 | 7.0 | 9.0 | 8.0 | 4.0 | 3.0 | 5.0 | 3.0 | 5.0 | 9.0 | 2.0 | 1.0 | 5.0 | 1.0 | 10.0 | 6.0 | 7.0 | 7.0 | 6.0 | 10.0 | 9.0 | 9.0 | 3.0 | 10.0 | 7.0 | 7.0 | 4.0 | 1.0 | 8.0 | 1.0 | 5.0 | 10.0 | 2.0 | 2.0 | 3.0 | 7.0 | 1.0 | 7.0 | 2.0 | 5.0 | 9.0 | 8.0 |
| 58 | 9.0 | 4.0 | 3.0 | 10.0 | 6.0 | 3.0 | 3.0 | 10.0 | 1.0 | 6.0 | 4.0 | 2.0 | 2.0 | 2.0 | 1.0 | 1.0 | 2.0 | 5.0 | 6.0 | 6.0 | 3.0 | 10.0 | 9.0 | 3.0 | 9.0 | 3.0 | 4.0 | 10.0 | 1.0 | 6.0 | 1.0 | 4.0 | 10.0 | 1.0 | 5.0 | 2.0 | 5.0 | 9.0 | 4.0 | 6.0 | 2.0 | 2.0 | 3.0 | 2.0 | 5.0 | 3.0 | 2.0 | 1.0 | 2.0 | 1.0 | 3.0 | 9.0 | 6.0 | 9.0 | 7.0 | 5.0 | 2.0 | 7.0 | 3.0 | 2.0 | 6.0 | 6.0 | 1.0 | 3.0 | 3.0 |
| 59 | 6.0 | 8.0 | 9.0 | 7.0 | 7.0 | 1.0 | 10.0 | 2.0 | 8.0 | 6.0 | 2.0 | 6.0 | 4.0 | 5.0 | 9.0 | 4.0 | 8.0 | 7.0 | 4.0 | 10.0 | 8.0 | 5.0 | 7.0 | 10.0 | 7.0 | 4.0 | 7.0 | 5.0 | 3.0 | 9.0 | 6.0 | 6.0 | 8.0 | 7.0 | 4.0 | 9.0 | 5.0 | 3.0 | 4.0 | 7.0 | 1.0 | 6.0 | 3.0 | 7.0 | 5.0 | 1.0 | 1.0 | 1.0 | 4.0 | 10.0 | 9.0 | 7.0 | 7.0 | 4.0 | 7.0 | 1.0 | 8.0 | 1.0 | 2.0 | 4.0 | 5.0 | 9.0 | 4.0 | 6.0 | 10.0 |
| 60 | 5.0 | 8.0 | 9.0 | 6.0 | 10.0 | 4.0 | 10.0 | 10.0 | 10.0 | 9.0 | 1.0 | 4.0 | 1.0 | 2.0 | 2.0 | 8.0 | 8.0 | 8.0 | 7.0 | 1.0 | 3.0 | 1.0 | 10.0 | 4.0 | 5.0 | 8.0 | 7.0 | 10.0 | 8.0 | 4.0 | 9.0 | 1.0 | 6.0 | 3.0 | 9.0 | 3.0 | 8.0 | 5.0 | 10.0 | 4.0 | 4.0 | 1.0 | 7.0 | 8.0 | 6.0 | 3.0 | 7.0 | 7.0 | 4.0 | 3.0 | 7.0 | 3.0 | 1.0 | 6.0 | 1.0 | 5.0 | 10.0 | 7.0 | 6.0 | 5.0 | 6.0 | 3.0 | 4.0 | 6.0 | 5.0 |
| 61 | 1.0 | 8.0 | 9.0 | 10.0 | 2.0 | 4.0 | 3.0 | 5.0 | 1.0 | 9.0 | 5.0 | 10.0 | 1.0 | 7.0 | 10.0 | 6.0 | 9.0 | 6.0 | 4.0 | 4.0 | 2.0 | 7.0 | 9.0 | 7.0 | 4.0 | 3.0 | 1.0 | 8.0 | 10.0 | 6.0 | 2.0 | 3.0 | 2.0 | 6.0 | 3.0 | 4.0 | 7.0 | 9.0 | 10.0 | 1.0 | 9.0 | 9.0 | 1.0 | 7.0 | 1.0 | 10.0 | 1.0 | 3.0 | 5.0 | 5.0 | 4.0 | 10.0 | 4.0 | 9.0 | 6.0 | 8.0 | 6.0 | 2.0 | 6.0 | 9.0 | 3.0 | 7.0 | 9.0 | 9.0 | 3.0 |
| 62 | 3.0 | 10.0 | 8.0 | 5.0 | 9.0 | 4.0 | 2.0 | 9.0 | 2.0 | 9.0 | 4.0 | 9.0 | 6.0 | 1.0 | 3.0 | 4.0 | 4.0 | 5.0 | 8.0 | 8.0 | 10.0 | 10.0 | 5.0 | 10.0 | 10.0 | 10.0 | 10.0 | 7.0 | 8.0 | 10.0 | 9.0 | 7.0 | 5.0 | 4.0 | 7.0 | 4.0 | 10.0 | 4.0 | 6.0 | 3.0 | 8.0 | 3.0 | 2.0 | 9.0 | 10.0 | 5.0 | 3.0 | 8.0 | 4.0 | 10.0 | 8.0 | 5.0 | 10.0 | 6.0 | 5.0 | 6.0 | 6.0 | 5.0 | 1.0 | 4.0 | 4.0 | 9.0 | 3.0 | 3.0 | 10.0 |
| 63 | 3.0 | 3.0 | 3.0 | 5.0 | 10.0 | 7.0 | 7.0 | 4.0 | 8.0 | 8.0 | 9.0 | 10.0 | 1.0 | 3.0 | 3.0 | 1.0 | 2.0 | 7.0 | 9.0 | 6.0 | 2.0 | 6.0 | 8.0 | 4.0 | 7.0 | 3.0 | 2.0 | 8.0 | 7.0 | 8.0 | 2.0 | 8.0 | 10.0 | 10.0 | 7.0 | 4.0 | 1.0 | 2.0 | 9.0 | 5.0 | 1.0 | 4.0 | 3.0 | 2.0 | 2.0 | 2.0 | 9.0 | 1.0 | 8.0 | 1.0 | 9.0 | 1.0 | 5.0 | 1.0 | 2.0 | 10.0 | 4.0 | 9.0 | 3.0 | 6.0 | 6.0 | 9.0 | 3.0 | 1.0 | 6.0 |
| 64 | 5.0 | 8.0 | 2.0 | 6.0 | 1.0 | 8.0 | 7.0 | 1.0 | 2.0 | 7.0 | 2.0 | 3.0 | 1.0 | 7.0 | 5.0 | 2.0 | 10.0 | 2.0 | 3.0 | 3.0 | 2.0 | 8.0 | 4.0 | 9.0 | 3.0 | 3.0 | 9.0 | 6.0 | 8.0 | 2.0 | 6.0 | 4.0 | 6.0 | 8.0 | 10.0 | 8.0 | 4.0 | 2.0 | 7.0 | 8.0 | 1.0 | 10.0 | 4.0 | 10.0 | 6.0 | 4.0 | 2.0 | 7.0 | 4.0 | 8.0 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 9.0 | 5.0 | 8.0 | 3.0 | 10.0 | 5.0 | 3.0 | 10.0 | 6.0 | 3.0 |

Choose a single directed chain from 22 to 23 that minimizes the total of all listed penalties.

When you send back the chosen route, slip it into a tiny JSON snippet so it's easy to read and validate.

{
  ""solution"": []
}

The ""solution"" field is just an ordered list of node identifiers — the path from the input pad to the output pad. Treat it like a short form: list the starting location first, the ending location last, and put each intermediate location in order. This JSON is only a sketch of the expected shape, not the actual answer.

Please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 1, 'var_index': 1}, {'from': 22, 'to': 2, 'var_index': 2}, {'from': 22, 'to': 3, 'var_index': 3}, {'from': 22, 'to': 4, 'var_index': 4}, {'from': 22, 'to': 5, 'var_index': 5}, {'from': 22, 'to': 6, 'var_index': 6}, {'from': 22, 'to': 7, 'var_index': 7}, {'from': 22, 'to': 8, 'var_index': 8}, {'from': 22, 'to': 9, 'var_index': 9}, {'from': 22, 'to': 10, 'var_index': 10}, {'from': 22, 'to': 11, 'var_index': 11}, {'from': 22, 'to': 12, 'var_index': 12}, {'from': 22, 'to': 13, 'var_index': 13}, {'from': 22, 'to': 14, 'var_index': 14}, {'from': 22, 'to': 15, 'var_index': 15}, {'from': 22, 'to': 16, 'var_index': 16}, {'from': 22, 'to': 17, 'var_index': 17}, {'from': 22, 'to': 18, 'var_index': 18}, {'from': 22, 'to': 19, 'var_index': 19}, {'from': 22, 'to': 20, 'var_index': 20}, {'from': 22, 'to': 21, 'var_index': 21}, {'from': 0, 'to': 23, 'var_index': 22}, {'from': 1, 'to': 23, 'var_index': 23}, {'from': 2, 'to': 23, 'var_index': 24}, {'from': 3, 'to': 23, 'var_index': 25}, {'from': 4, 'to': 23, 'var_index': 26}, {'from': 5, 'to': 23, 'var_index': 27}, {'from': 6, 'to': 23, 'var_index': 28}, {'from': 7, 'to': 23, 'var_index': 29}, {'from': 8, 'to': 23, 'var_index': 30}, {'from': 9, 'to': 23, 'var_index': 31}, {'from': 10, 'to': 23, 'var_index': 32}, {'from': 11, 'to': 23, 'var_index': 33}, {'from': 12, 'to': 23, 'var_index': 34}, {'from': 13, 'to': 23, 'var_index': 35}, {'from': 14, 'to': 23, 'var_index': 36}, {'from': 15, 'to': 23, 'var_index': 37}, {'from': 16, 'to': 23, 'var_index': 38}, {'from': 17, 'to': 23, 'var_index': 39}, {'from': 18, 'to': 23, 'var_index': 40}, {'from': 19, 'to': 23, 'var_index': 41}, {'from': 20, 'to': 23, 'var_index': 42}, {'from': 21, 'to': 23, 'var_index': 43}, {'from': 0, 'to': 1, 'var_index': 44}, {'from': 1, 'to': 2, 'var_index': 45}, {'from': 2, 'to': 3, 'var_index': 46}, {'from': 3, 'to': 4, 'var_index': 47}, {'from': 4, 'to': 5, 'var_index': 48}, {'from': 5, 'to': 6, 'var_index': 49}, {'from': 6, 'to': 7, 'var_index': 50}, {'from': 7, 'to': 8, 'var_index': 51}, {'from': 8, 'to': 9, 'var_index': 52}, {'from': 9, 'to': 10, 'var_index': 53}, {'from': 10, 'to': 11, 'var_index': 54}, {'from': 11, 'to': 12, 'var_index': 55}, {'from': 12, 'to': 13, 'var_index': 56}, {'from': 13, 'to': 14, 'var_index': 57}, {'from': 14, 'to': 15, 'var_index': 58}, {'from': 15, 'to': 16, 'var_index': 59}, {'from': 16, 'to': 17, 'var_index': 60}, {'from': 17, 'to': 18, 'var_index': 61}, {'from': 18, 'to': 19, 'var_index': 62}, {'from': 19, 'to': 20, 'var_index': 63}, {'from': 20, 'to': 21, 'var_index': 64}], 'objective': {'constant': 0.0, 'linear': [4.0, 1.0, 4.0, 7.0, 2.0, 6.0, 3.0, 8.0, 4.0, 4.0, 7.0, 4.0, 2.0, 7.0, 4.0, 10.0, 9.0, 1.0, 2.0, 9.0, 5.0, 9.0, 1.0, 9.0, 5.0, 8.0, 5.0, 7.0, 6.0, 6.0, 8.0, 4.0, 10.0, 3.0, 5.0, 1.0, 6.0, 5.0, 9.0, 3.0, 3.0, 8.0, 4.0, 9.0, 10.0, 3.0, 2.0, 4.0, 6.0, 10.0, 4.0, 10.0, 5.0, 2.0, 8.0, 5.0, 4.0, 2.0, 1.0, 1.0, 2.0, 3.0, 7.0, 4.0, 5.0], 'quadratic': [[9.0, 7.0, 4.0, 3.0, 5.0, 2.0, 4.0, 10.0, 9.0, 10.0, 1.0, 1.0, 6.0, 9.0, 9.0, 3.0, 6.0, 5.0, 5.0, 5.0, 7.0, 8.0, 1.0, 3.0, 8.0, 2.0, 1.0, 9.0, 6.0, 8.0, 8.0, 2.0, 3.0, 8.0, 2.0, 2.0, 8.0, 2.0, 5.0, 8.0, 7.0, 1.0, 7.0, 3.0, 6.0, 1.0, 10.0, 5.0, 10.0, 2.0, 6.0, 5.0, 10.0, 5.0, 4.0, 5.0, 1.0, 4.0, 9.0, 6.0, 5.0, 1.0, 3.0, 3.0, 5.0], [7.0, 7.0, 3.0, 3.0, 2.0, 9.0, 1.0, 2.0, 7.0, 9.0, 6.0, 6.0, 1.0, 7.0, 1.0, 8.0, 7.0, 9.0, 8.0, 9.0, 8.0, 7.0, 1.0, 1.0, 2.0, 6.0, 4.0, 1.0, 6.0, 1.0, 10.0, 5.0, 4.0, 9.0, 7.0, 2.0, 3.0, 10.0, 10.0, 4.0, 2.0, 2.0, 4.0, 4.0, 9.0, 2.0, 1.0, 5.0, 5.0, 10.0, 6.0, 6.0, 7.0, 4.0, 5.0, 1.0, 8.0, 7.0, 4.0, 8.0, 8.0, 8.0, 10.0, 3.0, 8.0], [4.0, 3.0, 9.0, 10.0, 5.0, 8.0, 1.0, 3.0, 9.0, 8.0, 2.0, 2.0, 1.0, 5.0, 10.0, 7.0, 6.0, 1.0, 5.0, 6.0, 10.0, 9.0, 2.0, 10.0, 6.0, 6.0, 5.0, 1.0, 7.0, 7.0, 7.0, 1.0, 4.0, 2.0, 3.0, 7.0, 6.0, 5.0, 3.0, 5.0, 6.0, 8.0, 6.0, 8.0, 2.0, 6.0, 5.0, 5.0, 5.0, 4.0, 9.0, 9.0, 10.0, 4.0, 9.0, 6.0, 4.0, 6.0, 3.0, 9.0, 9.0, 9.0, 8.0, 3.0, 2.0], [3.0, 3.0, 10.0, 4.0, 6.0, 5.0, 7.0, 4.0, 5.0, 9.0, 8.0, 7.0, 8.0, 5.0, 10.0, 7.0, 2.0, 9.0, 4.0, 7.0, 10.0, 1.0, 6.0, 2.0, 8.0, 10.0, 8.0, 6.0, 7.0, 4.0, 5.0, 9.0, 1.0, 8.0, 10.0, 1.0, 10.0, 9.0, 10.0, 9.0, 7.0, 4.0, 10.0, 5.0, 7.0, 3.0, 7.0, 1.0, 3.0, 8.0, 6.0, 2.0, 1.0, 10.0, 5.0, 10.0, 6.0, 4.0, 10.0, 7.0, 6.0, 10.0, 5.0, 5.0, 6.0], [5.0, 2.0, 5.0, 6.0, 2.0, 2.0, 9.0, 5.0, 6.0, 3.0, 8.0, 8.0, 10.0, 6.0, 3.0, 10.0, 7.0, 9.0, 2.0, 8.0, 3.0, 7.0, 8.0, 5.0, 10.0, 6.0, 1.0, 5.0, 5.0, 7.0, 8.0, 7.0, 10.0, 9.0, 5.0, 2.0, 10.0, 1.0, 9.0, 9.0, 6.0, 1.0, 8.0, 3.0, 6.0, 3.0, 2.0, 7.0, 10.0, 4.0, 4.0, 9.0, 5.0, 5.0, 2.0, 8.0, 5.0, 4.0, 6.0, 7.0, 10.0, 2.0, 9.0, 10.0, 1.0], [2.0, 9.0, 8.0, 5.0, 2.0, 10.0, 1.0, 1.0, 5.0, 2.0, 8.0, 6.0, 1.0, 8.0, 1.0, 8.0, 5.0, 7.0, 7.0, 9.0, 8.0, 4.0, 8.0, 4.0, 8.0, 5.0, 9.0, 6.0, 3.0, 6.0, 7.0, 4.0, 2.0, 9.0, 2.0, 7.0, 7.0, 8.0, 4.0, 9.0, 2.0, 8.0, 4.0, 1.0, 1.0, 1.0, 7.0, 5.0, 9.0, 7.0, 7.0, 4.0, 6.0, 2.0, 4.0, 8.0, 4.0, 4.0, 3.0, 1.0, 4.0, 4.0, 4.0, 7.0, 8.0], [4.0, 1.0, 1.0, 7.0, 9.0, 1.0, 3.0, 7.0, 6.0, 4.0, 8.0, 3.0, 10.0, 2.0, 10.0, 3.0, 6.0, 1.0, 4.0, 8.0, 5.0, 10.0, 3.0, 6.0, 8.0, 10.0, 2.0, 8.0, 4.0, 5.0, 6.0, 8.0, 10.0, 6.0, 3.0, 1.0, 2.0, 5.0, 8.0, 2.0, 8.0, 4.0, 2.0, 2.0, 3.0, 7.0, 4.0, 3.0, 2.0, 10.0, 10.0, 8.0, 6.0, 10.0, 8.0, 4.0, 9.0, 6.0, 3.0, 10.0, 10.0, 3.0, 2.0, 7.0, 7.0], [10.0, 2.0, 3.0, 4.0, 5.0, 1.0, 7.0, 5.0, 9.0, 6.0, 8.0, 8.0, 9.0, 10.0, 2.0, 8.0, 4.0, 2.0, 4.0, 6.0, 7.0, 3.0, 8.0, 6.0, 7.0, 1.0, 10.0, 9.0, 5.0, 1.0, 4.0, 7.0, 6.0, 8.0, 3.0, 1.0, 10.0, 1.0, 7.0, 5.0, 9.0, 9.0, 8.0, 9.0, 9.0, 9.0, 6.0, 7.0, 6.0, 7.0, 4.0, 7.0, 2.0, 5.0, 3.0, 3.0, 10.0, 5.0, 10.0, 2.0, 10.0, 5.0, 9.0, 4.0, 1.0], [9.0, 7.0, 9.0, 5.0, 6.0, 5.0, 6.0, 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'quadratic_cost': 5.0}, {'var_i': 63, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 63, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 63, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 63, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 63, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 63, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 63, 'var_j': 24, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 26, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 27, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 63, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 63, 'var_j': 34, 'quadratic_cost': 7.0}, {'var_i': 63, 'var_j': 35, 'quadratic_cost': 4.0}, {'var_i': 63, 'var_j': 36, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 38, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 39, 'quadratic_cost': 5.0}, {'var_i': 63, 'var_j': 40, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 41, 'quadratic_cost': 4.0}, {'var_i': 63, 'var_j': 42, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 43, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 44, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 45, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 46, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 47, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 48, 'quadratic_cost': 8.0}, {'var_i': 63, 'var_j': 49, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 50, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 51, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 52, 'quadratic_cost': 5.0}, {'var_i': 63, 'var_j': 53, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 54, 'quadratic_cost': 2.0}, {'var_i': 63, 'var_j': 55, 'quadratic_cost': 10.0}, {'var_i': 63, 'var_j': 56, 'quadratic_cost': 4.0}, {'var_i': 63, 'var_j': 57, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 58, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 59, 'quadratic_cost': 6.0}, {'var_i': 63, 'var_j': 60, 'quadratic_cost': 6.0}, {'var_i': 63, 'var_j': 61, 'quadratic_cost': 9.0}, {'var_i': 63, 'var_j': 62, 'quadratic_cost': 3.0}, {'var_i': 63, 'var_j': 63, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 64, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 24, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 31, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 33, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 34, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 35, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 38, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 39, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 40, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 41, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 42, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 43, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 44, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 45, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 46, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 47, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 48, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 49, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 50, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 51, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 52, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 53, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 54, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 55, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 56, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 57, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 58, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 59, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 60, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 61, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 62, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 63, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 64, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 1, 'var_index': 1}, {'from': 22, 'to': 2, 'var_index': 2}, {'from': 22, 'to': 3, 'var_index': 3}, {'from': 22, 'to': 4, 'var_index': 4}, {'from': 22, 'to': 5, 'var_index': 5}, {'from': 22, 'to': 6, 'var_index': 6}, {'from': 22, 'to': 7, 'var_index': 7}, {'from': 22, 'to': 8, 'var_index': 8}, {'from': 22, 'to': 9, 'var_index': 9}, {'from': 22, 'to': 10, 'var_index': 10}, {'from': 22, 'to': 11, 'var_index': 11}, {'from': 22, 'to': 12, 'var_index': 12}, {'from': 22, 'to': 13, 'var_index': 13}, {'from': 22, 'to': 14, 'var_index': 14}, {'from': 22, 'to': 15, 'var_index': 15}, {'from': 22, 'to': 16, 'var_index': 16}, {'from': 22, 'to': 17, 'var_index': 17}, {'from': 22, 'to': 18, 'var_index': 18}, {'from': 22, 'to': 19, 'var_index': 19}, {'from': 22, 'to': 20, 'var_index': 20}, {'from': 22, 'to': 21, 'var_index': 21}, {'from': 0, 'to': 23, 'var_index': 22}, {'from': 1, 'to': 23, 'var_index': 23}, {'from': 2, 'to': 23, 'var_index': 24}, {'from': 3, 'to': 23, 'var_index': 25}, {'from': 4, 'to': 23, 'var_index': 26}, {'from': 5, 'to': 23, 'var_index': 27}, {'from': 6, 'to': 23, 'var_index': 28}, {'from': 7, 'to': 23, 'var_index': 29}, {'from': 8, 'to': 23, 'var_index': 30}, {'from': 9, 'to': 23, 'var_index': 31}, {'from': 10, 'to': 23, 'var_index': 32}, {'from': 11, 'to': 23, 'var_index': 33}, {'from': 12, 'to': 23, 'var_index': 34}, {'from': 13, 'to': 23, 'var_index': 35}, {'from': 14, 'to': 23, 'var_index': 36}, {'from': 15, 'to': 23, 'var_index': 37}, {'from': 16, 'to': 23, 'var_index': 38}, {'from': 17, 'to': 23, 'var_index': 39}, {'from': 18, 'to': 23, 'var_index': 40}, {'from': 19, 'to': 23, 'var_index': 41}, {'from': 20, 'to': 23, 'var_index': 42}, {'from': 21, 'to': 23, 'var_index': 43}, {'from': 0, 'to': 1, 'var_index': 44}, {'from': 1, 'to': 2, 'var_index': 45}, {'from': 2, 'to': 3, 'var_index': 46}, {'from': 3, 'to': 4, 'var_index': 47}, {'from': 4, 'to': 5, 'var_index': 48}, {'from': 5, 'to': 6, 'var_index': 49}, {'from': 6, 'to': 7, 'var_index': 50}, {'from': 7, 'to': 8, 'var_index': 51}, {'from': 8, 'to': 9, 'var_index': 52}, {'from': 9, 'to': 10, 'var_index': 53}, {'from': 10, 'to': 11, 'var_index': 54}, {'from': 11, 'to': 12, 'var_index': 55}, {'from': 12, 'to': 13, 'var_index': 56}, {'from': 13, 'to': 14, 'var_index': 57}, {'from': 14, 'to': 15, 'var_index': 58}, {'from': 15, 'to': 16, 'var_index': 59}, {'from': 16, 'to': 17, 'var_index': 60}, {'from': 17, 'to': 18, 'var_index': 61}, {'from': 18, 'to': 19, 'var_index': 62}, {'from': 19, 'to': 20, 'var_index': 63}, {'from': 20, 'to': 21, 'var_index': 64}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23}}","[22, 4, 23]",7,markdown_table,0
QSPP,QSPP,"Back at the warehouse, the task is to send one robot from the pick area to the drop area along a single, allowed-direction aisle route and to spell out every location it passes. The trip time is built from the fixed time of each aisle segment on that route plus extra congestion penalties that apply whenever particular segment pairs are both present; a few segments also carry their own small extra time. The sensible plan is the one route whose combined time — base times plus any pairwise and per-segment penalties — is smallest, and the exact layout and penalty values are shown below.

Below are the layout and penalty details for 17 locations and 44 aisles: locations ordered as A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q; the robot starts at P and must end at Q.

| aisle_from | aisle_to | aisle_segment_id |
|---|---|---|
| P | A | 0 |
| P | B | 1 |
| P | C | 2 |
| P | D | 3 |
| P | E | 4 |
| P | F | 5 |
| P | G | 6 |
| P | H | 7 |
| P | I | 8 |
| P | J | 9 |
| P | K | 10 |
| P | L | 11 |
| P | M | 12 |
| P | N | 13 |
| P | O | 14 |
| A | Q | 15 |
| B | Q | 16 |
| C | Q | 17 |
| D | Q | 18 |
| E | Q | 19 |
| F | Q | 20 |
| G | Q | 21 |
| H | Q | 22 |
| I | Q | 23 |
| J | Q | 24 |
| K | Q | 25 |
| L | Q | 26 |
| M | Q | 27 |
| N | Q | 28 |
| O | Q | 29 |
| A | B | 30 |
| B | C | 31 |
| C | D | 32 |
| D | E | 33 |
| E | F | 34 |
| F | G | 35 |
| G | H | 36 |
| H | I | 37 |
| I | J | 38 |
| J | K | 39 |
| K | L | 40 |
| L | M | 41 |
| M | N | 42 |
| N | O | 43 |

| aisle_segment_id | traversal_time |
|---|---|
| 0 | 9.0 |
| 1 | 3.0 |
| 2 | 2.0 |
| 3 | 8.0 |
| 4 | 7.0 |
| 5 | 5.0 |
| 6 | 7.0 |
| 7 | 10.0 |
| 8 | 8.0 |
| 9 | 8.0 |
| 10 | 10.0 |
| 11 | 10.0 |
| 12 | 3.0 |
| 13 | 5.0 |
| 14 | 7.0 |
| 15 | 6.0 |
| 16 | 7.0 |
| 17 | 6.0 |
| 18 | 7.0 |
| 19 | 2.0 |
| 20 | 3.0 |
| 21 | 5.0 |
| 22 | 8.0 |
| 23 | 2.0 |
| 24 | 3.0 |
| 25 | 3.0 |
| 26 | 10.0 |
| 27 | 7.0 |
| 28 | 6.0 |
| 29 | 7.0 |
| 30 | 5.0 |
| 31 | 9.0 |
| 32 | 7.0 |
| 33 | 7.0 |
| 34 | 2.0 |
| 35 | 9.0 |
| 36 | 9.0 |
| 37 | 9.0 |
| 38 | 7.0 |
| 39 | 2.0 |
| 40 | 10.0 |
| 41 | 2.0 |
| 42 | 10.0 |
| 43 | 3.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (aisle_i_id, aisle_j_id). If two aisle_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| aisle_i_id\aisle_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 4.0 | 2.0 | 8.0 | 9.0 | 4.0 | 3.0 | 1.0 | 3.0 | 6.0 | 7.0 | 8.0 | 1.0 | 7.0 | 8.0 | 8.0 | 8.0 | 1.0 | 10.0 | 8.0 | 8.0 | 5.0 | 7.0 | 6.0 | 1.0 | 2.0 | 4.0 | 6.0 | 9.0 | 7.0 | 2.0 | 3.0 | 5.0 | 3.0 | 7.0 | 10.0 | 8.0 | 8.0 | 10.0 | 8.0 | 6.0 | 10.0 | 10.0 | 3.0 |
| 1 | 4.0 | 6.0 | 1.0 | 5.0 | 1.0 | 9.0 | 9.0 | 3.0 | 10.0 | 5.0 | 2.0 | 6.0 | 4.0 | 7.0 | 8.0 | 4.0 | 6.0 | 8.0 | 6.0 | 7.0 | 5.0 | 4.0 | 5.0 | 5.0 | 8.0 | 6.0 | 10.0 | 9.0 | 3.0 | 7.0 | 1.0 | 6.0 | 4.0 | 4.0 | 4.0 | 6.0 | 6.0 | 7.0 | 6.0 | 3.0 | 5.0 | 6.0 | 9.0 | 1.0 |
| 2 | 2.0 | 1.0 | 10.0 | 1.0 | 9.0 | 6.0 | 1.0 | 5.0 | 5.0 | 9.0 | 9.0 | 2.0 | 9.0 | 4.0 | 5.0 | 7.0 | 7.0 | 7.0 | 3.0 | 5.0 | 10.0 | 4.0 | 1.0 | 1.0 | 5.0 | 2.0 | 8.0 | 6.0 | 2.0 | 9.0 | 7.0 | 6.0 | 1.0 | 7.0 | 7.0 | 4.0 | 9.0 | 4.0 | 7.0 | 1.0 | 8.0 | 10.0 | 2.0 | 8.0 |
| 3 | 8.0 | 5.0 | 1.0 | 5.0 | 4.0 | 1.0 | 6.0 | 6.0 | 7.0 | 4.0 | 8.0 | 3.0 | 6.0 | 10.0 | 9.0 | 6.0 | 3.0 | 5.0 | 5.0 | 7.0 | 8.0 | 9.0 | 7.0 | 8.0 | 8.0 | 5.0 | 9.0 | 1.0 | 3.0 | 5.0 | 9.0 | 6.0 | 6.0 | 9.0 | 4.0 | 3.0 | 10.0 | 1.0 | 5.0 | 7.0 | 6.0 | 4.0 | 7.0 | 9.0 |
| 4 | 9.0 | 1.0 | 9.0 | 4.0 | 9.0 | 8.0 | 2.0 | 10.0 | 1.0 | 7.0 | 9.0 | 1.0 | 7.0 | 5.0 | 3.0 | 8.0 | 5.0 | 5.0 | 8.0 | 3.0 | 6.0 | 4.0 | 6.0 | 10.0 | 9.0 | 7.0 | 5.0 | 6.0 | 2.0 | 3.0 | 2.0 | 8.0 | 7.0 | 7.0 | 10.0 | 2.0 | 7.0 | 9.0 | 6.0 | 1.0 | 8.0 | 1.0 | 8.0 | 8.0 |
| 5 | 4.0 | 9.0 | 6.0 | 1.0 | 8.0 | 3.0 | 3.0 | 3.0 | 2.0 | 10.0 | 2.0 | 10.0 | 5.0 | 6.0 | 5.0 | 6.0 | 7.0 | 5.0 | 8.0 | 7.0 | 1.0 | 4.0 | 9.0 | 4.0 | 3.0 | 3.0 | 3.0 | 2.0 | 10.0 | 7.0 | 6.0 | 6.0 | 9.0 | 9.0 | 8.0 | 10.0 | 7.0 | 5.0 | 7.0 | 10.0 | 8.0 | 4.0 | 9.0 | 10.0 |
| 6 | 3.0 | 9.0 | 1.0 | 6.0 | 2.0 | 3.0 | 9.0 | 8.0 | 10.0 | 7.0 | 10.0 | 3.0 | 10.0 | 1.0 | 10.0 | 2.0 | 6.0 | 5.0 | 7.0 | 1.0 | 8.0 | 9.0 | 6.0 | 3.0 | 6.0 | 10.0 | 4.0 | 1.0 | 3.0 | 9.0 | 5.0 | 4.0 | 4.0 | 1.0 | 3.0 | 1.0 | 10.0 | 5.0 | 1.0 | 1.0 | 7.0 | 6.0 | 5.0 | 4.0 |
| 7 | 1.0 | 3.0 | 5.0 | 6.0 | 10.0 | 3.0 | 8.0 | 10.0 | 9.0 | 3.0 | 7.0 | 1.0 | 4.0 | 7.0 | 7.0 | 3.0 | 6.0 | 10.0 | 4.0 | 8.0 | 1.0 | 5.0 | 7.0 | 4.0 | 8.0 | 1.0 | 10.0 | 1.0 | 4.0 | 3.0 | 2.0 | 4.0 | 5.0 | 1.0 | 2.0 | 3.0 | 3.0 | 5.0 | 9.0 | 5.0 | 7.0 | 7.0 | 8.0 | 6.0 |
| 8 | 3.0 | 10.0 | 5.0 | 7.0 | 1.0 | 2.0 | 10.0 | 9.0 | 4.0 | 5.0 | 9.0 | 5.0 | 5.0 | 2.0 | 2.0 | 1.0 | 3.0 | 9.0 | 5.0 | 2.0 | 3.0 | 8.0 | 9.0 | 9.0 | 1.0 | 7.0 | 7.0 | 1.0 | 8.0 | 9.0 | 9.0 | 4.0 | 3.0 | 5.0 | 9.0 | 7.0 | 4.0 | 3.0 | 9.0 | 6.0 | 1.0 | 10.0 | 1.0 | 4.0 |
| 9 | 6.0 | 5.0 | 9.0 | 4.0 | 7.0 | 10.0 | 7.0 | 3.0 | 5.0 | 4.0 | 2.0 | 5.0 | 1.0 | 1.0 | 10.0 | 1.0 | 2.0 | 6.0 | 10.0 | 5.0 | 9.0 | 2.0 | 2.0 | 7.0 | 10.0 | 1.0 | 4.0 | 10.0 | 7.0 | 5.0 | 3.0 | 7.0 | 1.0 | 9.0 | 2.0 | 2.0 | 2.0 | 8.0 | 5.0 | 2.0 | 2.0 | 5.0 | 9.0 | 2.0 |
| 10 | 7.0 | 2.0 | 9.0 | 8.0 | 9.0 | 2.0 | 10.0 | 7.0 | 9.0 | 2.0 | 8.0 | 4.0 | 6.0 | 4.0 | 9.0 | 3.0 | 8.0 | 5.0 | 1.0 | 8.0 | 9.0 | 4.0 | 10.0 | 5.0 | 7.0 | 6.0 | 6.0 | 10.0 | 5.0 | 2.0 | 6.0 | 8.0 | 7.0 | 2.0 | 1.0 | 9.0 | 8.0 | 1.0 | 9.0 | 3.0 | 1.0 | 7.0 | 5.0 | 7.0 |
| 11 | 8.0 | 6.0 | 2.0 | 3.0 | 1.0 | 10.0 | 3.0 | 1.0 | 5.0 | 5.0 | 4.0 | 2.0 | 9.0 | 6.0 | 6.0 | 3.0 | 4.0 | 5.0 | 3.0 | 5.0 | 3.0 | 10.0 | 10.0 | 8.0 | 6.0 | 2.0 | 3.0 | 4.0 | 10.0 | 5.0 | 2.0 | 1.0 | 8.0 | 4.0 | 7.0 | 6.0 | 3.0 | 7.0 | 6.0 | 1.0 | 3.0 | 7.0 | 1.0 | 6.0 |
| 12 | 1.0 | 4.0 | 9.0 | 6.0 | 7.0 | 5.0 | 10.0 | 4.0 | 5.0 | 1.0 | 6.0 | 9.0 | 10.0 | 6.0 | 5.0 | 1.0 | 9.0 | 6.0 | 3.0 | 6.0 | 6.0 | 1.0 | 9.0 | 8.0 | 2.0 | 6.0 | 9.0 | 2.0 | 10.0 | 7.0 | 7.0 | 2.0 | 7.0 | 3.0 | 8.0 | 8.0 | 9.0 | 4.0 | 3.0 | 6.0 | 8.0 | 9.0 | 2.0 | 9.0 |
| 13 | 7.0 | 7.0 | 4.0 | 10.0 | 5.0 | 6.0 | 1.0 | 7.0 | 2.0 | 1.0 | 4.0 | 6.0 | 6.0 | 5.0 | 7.0 | 7.0 | 6.0 | 3.0 | 4.0 | 10.0 | 8.0 | 2.0 | 4.0 | 2.0 | 7.0 | 3.0 | 9.0 | 3.0 | 3.0 | 10.0 | 4.0 | 9.0 | 6.0 | 6.0 | 2.0 | 8.0 | 2.0 | 8.0 | 2.0 | 6.0 | 9.0 | 7.0 | 8.0 | 6.0 |
| 14 | 8.0 | 8.0 | 5.0 | 9.0 | 3.0 | 5.0 | 10.0 | 7.0 | 2.0 | 10.0 | 9.0 | 6.0 | 5.0 | 7.0 | 10.0 | 6.0 | 3.0 | 9.0 | 4.0 | 8.0 | 1.0 | 9.0 | 9.0 | 9.0 | 1.0 | 2.0 | 6.0 | 10.0 | 5.0 | 3.0 | 3.0 | 5.0 | 9.0 | 5.0 | 5.0 | 1.0 | 2.0 | 4.0 | 6.0 | 7.0 | 10.0 | 9.0 | 5.0 | 10.0 |
| 15 | 8.0 | 4.0 | 7.0 | 6.0 | 8.0 | 6.0 | 2.0 | 3.0 | 1.0 | 1.0 | 3.0 | 3.0 | 1.0 | 7.0 | 6.0 | 3.0 | 3.0 | 1.0 | 8.0 | 4.0 | 1.0 | 5.0 | 7.0 | 10.0 | 10.0 | 2.0 | 1.0 | 7.0 | 10.0 | 7.0 | 10.0 | 9.0 | 3.0 | 7.0 | 6.0 | 4.0 | 1.0 | 2.0 | 1.0 | 10.0 | 4.0 | 4.0 | 6.0 | 3.0 |
| 16 | 8.0 | 6.0 | 7.0 | 3.0 | 5.0 | 7.0 | 6.0 | 6.0 | 3.0 | 2.0 | 8.0 | 4.0 | 9.0 | 6.0 | 3.0 | 3.0 | 6.0 | 4.0 | 3.0 | 2.0 | 6.0 | 4.0 | 4.0 | 10.0 | 8.0 | 5.0 | 10.0 | 2.0 | 1.0 | 10.0 | 9.0 | 4.0 | 9.0 | 3.0 | 6.0 | 1.0 | 5.0 | 2.0 | 1.0 | 10.0 | 6.0 | 1.0 | 10.0 | 4.0 |
| 17 | 1.0 | 8.0 | 7.0 | 5.0 | 5.0 | 5.0 | 5.0 | 10.0 | 9.0 | 6.0 | 5.0 | 5.0 | 6.0 | 3.0 | 9.0 | 1.0 | 4.0 | 1.0 | 1.0 | 4.0 | 5.0 | 9.0 | 2.0 | 2.0 | 4.0 | 7.0 | 4.0 | 6.0 | 3.0 | 9.0 | 10.0 | 1.0 | 10.0 | 9.0 | 4.0 | 1.0 | 7.0 | 1.0 | 1.0 | 10.0 | 8.0 | 9.0 | 1.0 | 2.0 |
| 18 | 10.0 | 6.0 | 3.0 | 5.0 | 8.0 | 8.0 | 7.0 | 4.0 | 5.0 | 10.0 | 1.0 | 3.0 | 3.0 | 4.0 | 4.0 | 8.0 | 3.0 | 1.0 | 3.0 | 8.0 | 7.0 | 2.0 | 4.0 | 3.0 | 7.0 | 8.0 | 8.0 | 8.0 | 8.0 | 3.0 | 3.0 | 2.0 | 8.0 | 6.0 | 4.0 | 5.0 | 10.0 | 4.0 | 4.0 | 6.0 | 1.0 | 4.0 | 9.0 | 5.0 |
| 19 | 8.0 | 7.0 | 5.0 | 7.0 | 3.0 | 7.0 | 1.0 | 8.0 | 2.0 | 5.0 | 8.0 | 5.0 | 6.0 | 10.0 | 8.0 | 4.0 | 2.0 | 4.0 | 8.0 | 2.0 | 1.0 | 10.0 | 8.0 | 3.0 | 5.0 | 9.0 | 6.0 | 3.0 | 7.0 | 2.0 | 6.0 | 5.0 | 4.0 | 10.0 | 2.0 | 3.0 | 1.0 | 7.0 | 6.0 | 8.0 | 6.0 | 6.0 | 5.0 | 2.0 |
| 20 | 8.0 | 5.0 | 10.0 | 8.0 | 6.0 | 1.0 | 8.0 | 1.0 | 3.0 | 9.0 | 9.0 | 3.0 | 6.0 | 8.0 | 1.0 | 1.0 | 6.0 | 5.0 | 7.0 | 1.0 | 8.0 | 10.0 | 7.0 | 1.0 | 4.0 | 3.0 | 6.0 | 5.0 | 7.0 | 7.0 | 5.0 | 9.0 | 4.0 | 4.0 | 10.0 | 7.0 | 3.0 | 4.0 | 1.0 | 5.0 | 7.0 | 9.0 | 2.0 | 4.0 |
| 21 | 5.0 | 4.0 | 4.0 | 9.0 | 4.0 | 4.0 | 9.0 | 5.0 | 8.0 | 2.0 | 4.0 | 10.0 | 1.0 | 2.0 | 9.0 | 5.0 | 4.0 | 9.0 | 2.0 | 10.0 | 10.0 | 10.0 | 9.0 | 10.0 | 2.0 | 2.0 | 10.0 | 5.0 | 3.0 | 7.0 | 4.0 | 9.0 | 5.0 | 2.0 | 7.0 | 7.0 | 7.0 | 7.0 | 3.0 | 10.0 | 4.0 | 4.0 | 2.0 | 2.0 |
| 22 | 7.0 | 5.0 | 1.0 | 7.0 | 6.0 | 9.0 | 6.0 | 7.0 | 9.0 | 2.0 | 10.0 | 10.0 | 9.0 | 4.0 | 9.0 | 7.0 | 4.0 | 2.0 | 4.0 | 8.0 | 7.0 | 9.0 | 3.0 | 10.0 | 1.0 | 4.0 | 9.0 | 9.0 | 2.0 | 3.0 | 1.0 | 10.0 | 2.0 | 6.0 | 10.0 | 3.0 | 1.0 | 3.0 | 9.0 | 1.0 | 7.0 | 4.0 | 1.0 | 10.0 |
| 23 | 6.0 | 5.0 | 1.0 | 8.0 | 10.0 | 4.0 | 3.0 | 4.0 | 9.0 | 7.0 | 5.0 | 8.0 | 8.0 | 2.0 | 9.0 | 10.0 | 10.0 | 2.0 | 3.0 | 3.0 | 1.0 | 10.0 | 10.0 | 3.0 | 10.0 | 6.0 | 4.0 | 9.0 | 5.0 | 2.0 | 7.0 | 7.0 | 7.0 | 9.0 | 8.0 | 3.0 | 9.0 | 10.0 | 9.0 | 8.0 | 7.0 | 2.0 | 3.0 | 4.0 |
| 24 | 1.0 | 8.0 | 5.0 | 8.0 | 9.0 | 3.0 | 6.0 | 8.0 | 1.0 | 10.0 | 7.0 | 6.0 | 2.0 | 7.0 | 1.0 | 10.0 | 8.0 | 4.0 | 7.0 | 5.0 | 4.0 | 2.0 | 1.0 | 10.0 | 10.0 | 6.0 | 2.0 | 9.0 | 9.0 | 3.0 | 1.0 | 10.0 | 3.0 | 6.0 | 10.0 | 1.0 | 9.0 | 2.0 | 4.0 | 3.0 | 9.0 | 5.0 | 5.0 | 8.0 |
| 25 | 2.0 | 6.0 | 2.0 | 5.0 | 7.0 | 3.0 | 10.0 | 1.0 | 7.0 | 1.0 | 6.0 | 2.0 | 6.0 | 3.0 | 2.0 | 2.0 | 5.0 | 7.0 | 8.0 | 9.0 | 3.0 | 2.0 | 4.0 | 6.0 | 6.0 | 5.0 | 6.0 | 10.0 | 4.0 | 4.0 | 8.0 | 3.0 | 3.0 | 5.0 | 3.0 | 10.0 | 10.0 | 10.0 | 8.0 | 5.0 | 10.0 | 4.0 | 9.0 | 8.0 |
| 26 | 4.0 | 10.0 | 8.0 | 9.0 | 5.0 | 3.0 | 4.0 | 10.0 | 7.0 | 4.0 | 6.0 | 3.0 | 9.0 | 9.0 | 6.0 | 1.0 | 10.0 | 4.0 | 8.0 | 6.0 | 6.0 | 10.0 | 9.0 | 4.0 | 2.0 | 6.0 | 2.0 | 9.0 | 3.0 | 3.0 | 6.0 | 9.0 | 1.0 | 1.0 | 8.0 | 10.0 | 3.0 | 3.0 | 4.0 | 9.0 | 6.0 | 5.0 | 9.0 | 10.0 |
| 27 | 6.0 | 9.0 | 6.0 | 1.0 | 6.0 | 2.0 | 1.0 | 1.0 | 1.0 | 10.0 | 10.0 | 4.0 | 2.0 | 3.0 | 10.0 | 7.0 | 2.0 | 6.0 | 8.0 | 3.0 | 5.0 | 5.0 | 9.0 | 9.0 | 9.0 | 10.0 | 9.0 | 3.0 | 10.0 | 6.0 | 9.0 | 10.0 | 7.0 | 5.0 | 8.0 | 9.0 | 4.0 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 4.0 | 6.0 |
| 28 | 9.0 | 3.0 | 2.0 | 3.0 | 2.0 | 10.0 | 3.0 | 4.0 | 8.0 | 7.0 | 5.0 | 10.0 | 10.0 | 3.0 | 5.0 | 10.0 | 1.0 | 3.0 | 8.0 | 7.0 | 7.0 | 3.0 | 2.0 | 5.0 | 9.0 | 4.0 | 3.0 | 10.0 | 9.0 | 8.0 | 2.0 | 6.0 | 9.0 | 2.0 | 4.0 | 7.0 | 4.0 | 8.0 | 5.0 | 4.0 | 6.0 | 6.0 | 10.0 | 1.0 |
| 29 | 7.0 | 7.0 | 9.0 | 5.0 | 3.0 | 7.0 | 9.0 | 3.0 | 9.0 | 5.0 | 2.0 | 5.0 | 7.0 | 10.0 | 3.0 | 7.0 | 10.0 | 9.0 | 3.0 | 2.0 | 7.0 | 7.0 | 3.0 | 2.0 | 3.0 | 4.0 | 3.0 | 6.0 | 8.0 | 8.0 | 6.0 | 6.0 | 7.0 | 4.0 | 3.0 | 8.0 | 9.0 | 1.0 | 8.0 | 1.0 | 3.0 | 5.0 | 4.0 | 4.0 |
| 30 | 2.0 | 1.0 | 7.0 | 9.0 | 2.0 | 6.0 | 5.0 | 2.0 | 9.0 | 3.0 | 6.0 | 2.0 | 7.0 | 4.0 | 3.0 | 10.0 | 9.0 | 10.0 | 3.0 | 6.0 | 5.0 | 4.0 | 1.0 | 7.0 | 1.0 | 8.0 | 6.0 | 9.0 | 2.0 | 6.0 | 7.0 | 1.0 | 1.0 | 4.0 | 9.0 | 1.0 | 3.0 | 2.0 | 10.0 | 4.0 | 5.0 | 10.0 | 1.0 | 2.0 |
| 31 | 3.0 | 6.0 | 6.0 | 6.0 | 8.0 | 6.0 | 4.0 | 4.0 | 4.0 | 7.0 | 8.0 | 1.0 | 2.0 | 9.0 | 5.0 | 9.0 | 4.0 | 1.0 | 2.0 | 5.0 | 9.0 | 9.0 | 10.0 | 7.0 | 10.0 | 3.0 | 9.0 | 10.0 | 6.0 | 6.0 | 1.0 | 4.0 | 4.0 | 2.0 | 1.0 | 5.0 | 6.0 | 6.0 | 8.0 | 2.0 | 5.0 | 10.0 | 5.0 | 1.0 |
| 32 | 5.0 | 4.0 | 1.0 | 6.0 | 7.0 | 9.0 | 4.0 | 5.0 | 3.0 | 1.0 | 7.0 | 8.0 | 7.0 | 6.0 | 9.0 | 3.0 | 9.0 | 10.0 | 8.0 | 4.0 | 4.0 | 5.0 | 2.0 | 7.0 | 3.0 | 3.0 | 1.0 | 7.0 | 9.0 | 7.0 | 1.0 | 4.0 | 5.0 | 7.0 | 6.0 | 6.0 | 6.0 | 10.0 | 5.0 | 5.0 | 7.0 | 6.0 | 2.0 | 3.0 |
| 33 | 3.0 | 4.0 | 7.0 | 9.0 | 7.0 | 9.0 | 1.0 | 1.0 | 5.0 | 9.0 | 2.0 | 4.0 | 3.0 | 6.0 | 5.0 | 7.0 | 3.0 | 9.0 | 6.0 | 10.0 | 4.0 | 2.0 | 6.0 | 9.0 | 6.0 | 5.0 | 1.0 | 5.0 | 2.0 | 4.0 | 4.0 | 2.0 | 7.0 | 10.0 | 8.0 | 9.0 | 3.0 | 10.0 | 9.0 | 1.0 | 10.0 | 2.0 | 2.0 | 2.0 |
| 34 | 7.0 | 4.0 | 7.0 | 4.0 | 10.0 | 8.0 | 3.0 | 2.0 | 9.0 | 2.0 | 1.0 | 7.0 | 8.0 | 2.0 | 5.0 | 6.0 | 6.0 | 4.0 | 4.0 | 2.0 | 10.0 | 7.0 | 10.0 | 8.0 | 10.0 | 3.0 | 8.0 | 8.0 | 4.0 | 3.0 | 9.0 | 1.0 | 6.0 | 8.0 | 7.0 | 2.0 | 5.0 | 1.0 | 8.0 | 3.0 | 5.0 | 8.0 | 9.0 | 3.0 |
| 35 | 10.0 | 6.0 | 4.0 | 3.0 | 2.0 | 10.0 | 1.0 | 3.0 | 7.0 | 2.0 | 9.0 | 6.0 | 8.0 | 8.0 | 1.0 | 4.0 | 1.0 | 1.0 | 5.0 | 3.0 | 7.0 | 7.0 | 3.0 | 3.0 | 1.0 | 10.0 | 10.0 | 9.0 | 7.0 | 8.0 | 1.0 | 5.0 | 6.0 | 9.0 | 2.0 | 4.0 | 9.0 | 2.0 | 2.0 | 9.0 | 10.0 | 4.0 | 4.0 | 2.0 |
| 36 | 8.0 | 6.0 | 9.0 | 10.0 | 7.0 | 7.0 | 10.0 | 3.0 | 4.0 | 2.0 | 8.0 | 3.0 | 9.0 | 2.0 | 2.0 | 1.0 | 5.0 | 7.0 | 10.0 | 1.0 | 3.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 3.0 | 4.0 | 4.0 | 9.0 | 3.0 | 6.0 | 6.0 | 3.0 | 5.0 | 9.0 | 1.0 | 4.0 | 7.0 | 3.0 | 6.0 | 5.0 | 8.0 | 8.0 |
| 37 | 8.0 | 7.0 | 4.0 | 1.0 | 9.0 | 5.0 | 5.0 | 5.0 | 3.0 | 8.0 | 1.0 | 7.0 | 4.0 | 8.0 | 4.0 | 2.0 | 2.0 | 1.0 | 4.0 | 7.0 | 4.0 | 7.0 | 3.0 | 10.0 | 2.0 | 10.0 | 3.0 | 9.0 | 8.0 | 1.0 | 2.0 | 6.0 | 10.0 | 10.0 | 1.0 | 2.0 | 4.0 | 1.0 | 4.0 | 10.0 | 3.0 | 6.0 | 9.0 | 9.0 |
| 38 | 10.0 | 6.0 | 7.0 | 5.0 | 6.0 | 7.0 | 1.0 | 9.0 | 9.0 | 5.0 | 9.0 | 6.0 | 3.0 | 2.0 | 6.0 | 1.0 | 1.0 | 1.0 | 4.0 | 6.0 | 1.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 4.0 | 10.0 | 5.0 | 8.0 | 10.0 | 8.0 | 5.0 | 9.0 | 8.0 | 2.0 | 7.0 | 4.0 | 6.0 | 1.0 | 6.0 | 3.0 | 5.0 | 1.0 |
| 39 | 8.0 | 3.0 | 1.0 | 7.0 | 1.0 | 10.0 | 1.0 | 5.0 | 6.0 | 2.0 | 3.0 | 1.0 | 6.0 | 6.0 | 7.0 | 10.0 | 10.0 | 10.0 | 6.0 | 8.0 | 5.0 | 10.0 | 1.0 | 8.0 | 3.0 | 5.0 | 9.0 | 8.0 | 4.0 | 1.0 | 4.0 | 2.0 | 5.0 | 1.0 | 3.0 | 9.0 | 3.0 | 10.0 | 1.0 | 3.0 | 5.0 | 1.0 | 2.0 | 5.0 |
| 40 | 6.0 | 5.0 | 8.0 | 6.0 | 8.0 | 8.0 | 7.0 | 7.0 | 1.0 | 2.0 | 1.0 | 3.0 | 8.0 | 9.0 | 10.0 | 4.0 | 6.0 | 8.0 | 1.0 | 6.0 | 7.0 | 4.0 | 7.0 | 7.0 | 9.0 | 10.0 | 6.0 | 6.0 | 6.0 | 3.0 | 5.0 | 5.0 | 7.0 | 10.0 | 5.0 | 10.0 | 6.0 | 3.0 | 6.0 | 5.0 | 2.0 | 4.0 | 3.0 | 3.0 |
| 41 | 10.0 | 6.0 | 10.0 | 4.0 | 1.0 | 4.0 | 6.0 | 7.0 | 10.0 | 5.0 | 7.0 | 7.0 | 9.0 | 7.0 | 9.0 | 4.0 | 1.0 | 9.0 | 4.0 | 6.0 | 9.0 | 4.0 | 4.0 | 2.0 | 5.0 | 4.0 | 5.0 | 2.0 | 6.0 | 5.0 | 10.0 | 10.0 | 6.0 | 2.0 | 8.0 | 4.0 | 5.0 | 6.0 | 3.0 | 1.0 | 4.0 | 3.0 | 2.0 | 6.0 |
| 42 | 10.0 | 9.0 | 2.0 | 7.0 | 8.0 | 9.0 | 5.0 | 8.0 | 1.0 | 9.0 | 5.0 | 1.0 | 2.0 | 8.0 | 5.0 | 6.0 | 10.0 | 1.0 | 9.0 | 5.0 | 2.0 | 2.0 | 1.0 | 3.0 | 5.0 | 9.0 | 9.0 | 4.0 | 10.0 | 4.0 | 1.0 | 5.0 | 2.0 | 2.0 | 9.0 | 4.0 | 8.0 | 9.0 | 5.0 | 2.0 | 3.0 | 2.0 | 8.0 | 5.0 |
| 43 | 3.0 | 1.0 | 8.0 | 9.0 | 8.0 | 10.0 | 4.0 | 6.0 | 4.0 | 2.0 | 7.0 | 6.0 | 9.0 | 6.0 | 10.0 | 3.0 | 4.0 | 2.0 | 5.0 | 2.0 | 4.0 | 2.0 | 10.0 | 4.0 | 8.0 | 8.0 | 10.0 | 6.0 | 1.0 | 4.0 | 2.0 | 1.0 | 3.0 | 2.0 | 3.0 | 2.0 | 8.0 | 9.0 | 1.0 | 5.0 | 3.0 | 6.0 | 5.0 | 7.0 |

The sensible plan is the single allowed-direction route whose combined traversal times and any congestion or per-segment penalties are smallest.

Oh, and one small thing — when you send the chosen route, please put it into a tiny JSON object so it's easy to read and validate. The structure should look like this:

{
  ""solution"": []
}

The idea is simple: put the nodes, in order, inside that ""solution"" array — from the pick area (source) to the drop area (target). Keep it casual: just the node identifiers, nothing else (no edge IDs, no costs, no extra labels).

This JSON is just the sketch of the shape we want, not the actual answer itself.

Also, please use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'edges': [{'from': 15, 'to': 0, 'var_index': 0}, {'from': 15, 'to': 1, 'var_index': 1}, {'from': 15, 'to': 2, 'var_index': 2}, {'from': 15, 'to': 3, 'var_index': 3}, {'from': 15, 'to': 4, 'var_index': 4}, {'from': 15, 'to': 5, 'var_index': 5}, {'from': 15, 'to': 6, 'var_index': 6}, {'from': 15, 'to': 7, 'var_index': 7}, {'from': 15, 'to': 8, 'var_index': 8}, {'from': 15, 'to': 9, 'var_index': 9}, {'from': 15, 'to': 10, 'var_index': 10}, {'from': 15, 'to': 11, 'var_index': 11}, {'from': 15, 'to': 12, 'var_index': 12}, {'from': 15, 'to': 13, 'var_index': 13}, {'from': 15, 'to': 14, 'var_index': 14}, {'from': 0, 'to': 16, 'var_index': 15}, {'from': 1, 'to': 16, 'var_index': 16}, {'from': 2, 'to': 16, 'var_index': 17}, {'from': 3, 'to': 16, 'var_index': 18}, {'from': 4, 'to': 16, 'var_index': 19}, {'from': 5, 'to': 16, 'var_index': 20}, {'from': 6, 'to': 16, 'var_index': 21}, {'from': 7, 'to': 16, 'var_index': 22}, {'from': 8, 'to': 16, 'var_index': 23}, {'from': 9, 'to': 16, 'var_index': 24}, {'from': 10, 'to': 16, 'var_index': 25}, {'from': 11, 'to': 16, 'var_index': 26}, {'from': 12, 'to': 16, 'var_index': 27}, {'from': 13, 'to': 16, 'var_index': 28}, {'from': 14, 'to': 16, 'var_index': 29}, {'from': 0, 'to': 1, 'var_index': 30}, {'from': 1, 'to': 2, 'var_index': 31}, {'from': 2, 'to': 3, 'var_index': 32}, {'from': 3, 'to': 4, 'var_index': 33}, {'from': 4, 'to': 5, 'var_index': 34}, {'from': 5, 'to': 6, 'var_index': 35}, {'from': 6, 'to': 7, 'var_index': 36}, {'from': 7, 'to': 8, 'var_index': 37}, {'from': 8, 'to': 9, 'var_index': 38}, {'from': 9, 'to': 10, 'var_index': 39}, {'from': 10, 'to': 11, 'var_index': 40}, {'from': 11, 'to': 12, 'var_index': 41}, {'from': 12, 'to': 13, 'var_index': 42}, {'from': 13, 'to': 14, 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'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 43, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 43, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 33, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 36, 'quadratic_cost': 8.0}, {'var_i': 43, 'var_j': 37, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 39, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 40, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 41, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 42, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 43, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'P', 'to': 'A', 'var_index': 0}, {'from': 'P', 'to': 'B', 'var_index': 1}, {'from': 'P', 'to': 'C', 'var_index': 2}, {'from': 'P', 'to': 'D', 'var_index': 3}, {'from': 'P', 'to': 'E', 'var_index': 4}, {'from': 'P', 'to': 'F', 'var_index': 5}, {'from': 'P', 'to': 'G', 'var_index': 6}, {'from': 'P', 'to': 'H', 'var_index': 7}, {'from': 'P', 'to': 'I', 'var_index': 8}, {'from': 'P', 'to': 'J', 'var_index': 9}, {'from': 'P', 'to': 'K', 'var_index': 10}, {'from': 'P', 'to': 'L', 'var_index': 11}, {'from': 'P', 'to': 'M', 'var_index': 12}, {'from': 'P', 'to': 'N', 'var_index': 13}, {'from': 'P', 'to': 'O', 'var_index': 14}, {'from': 'A', 'to': 'Q', 'var_index': 15}, {'from': 'B', 'to': 'Q', 'var_index': 16}, {'from': 'C', 'to': 'Q', 'var_index': 17}, {'from': 'D', 'to': 'Q', 'var_index': 18}, {'from': 'E', 'to': 'Q', 'var_index': 19}, {'from': 'F', 'to': 'Q', 'var_index': 20}, {'from': 'G', 'to': 'Q', 'var_index': 21}, {'from': 'H', 'to': 'Q', 'var_index': 22}, {'from': 'I', 'to': 'Q', 'var_index': 23}, {'from': 'J', 'to': 'Q', 'var_index': 24}, {'from': 'K', 'to': 'Q', 'var_index': 25}, {'from': 'L', 'to': 'Q', 'var_index': 26}, {'from': 'M', 'to': 'Q', 'var_index': 27}, {'from': 'N', 'to': 'Q', 'var_index': 28}, {'from': 'O', 'to': 'Q', 'var_index': 29}, {'from': 'A', 'to': 'B', 'var_index': 30}, {'from': 'B', 'to': 'C', 'var_index': 31}, {'from': 'C', 'to': 'D', 'var_index': 32}, {'from': 'D', 'to': 'E', 'var_index': 33}, {'from': 'E', 'to': 'F', 'var_index': 34}, {'from': 'F', 'to': 'G', 'var_index': 35}, {'from': 'G', 'to': 'H', 'var_index': 36}, {'from': 'H', 'to': 'I', 'var_index': 37}, {'from': 'I', 'to': 'J', 'var_index': 38}, {'from': 'J', 'to': 'K', 'var_index': 39}, {'from': 'K', 'to': 'L', 'var_index': 40}, {'from': 'L', 'to': 'M', 'var_index': 41}, {'from': 'M', 'to': 'N', 'var_index': 42}, {'from': 'N', 'to': 'O', 'var_index': 43}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q'}}","['P', 'F', 'Q']",8,markdown_table,names
QSPP,QSPP,"Someone in logistics sketched out a network of sea lanes where every segment has a basic tariff, but certain segment pairs together cause additional handling fees. The practical choice is to select a single legal, one-way path from the origin port to the destination and compute the total charge by summing each segment’s tariff and any extra pairwise charges that apply when both segments appear on the path. The selection must be one uninterrupted path along allowed lanes, beginning at the origin and ending at the destination, with no missing links or repeated corridor usage. The exact graph and fee numbers appear below.

{
  ""number_of_ports"": 25,
  ""number_of_corridor_segments"": 40,
  ""port_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19,
    20,
    21,
    22,
    23,
    24
  ],
  ""origin_port"": 0,
  ""destination_port"": 24,
  ""edges"": [
    {
      ""corridor_start_port"": 0,
      ""corridor_end_port"": 1,
      ""corridor_id"": 0
    },
    {
      ""corridor_start_port"": 0,
      ""corridor_end_port"": 5,
      ""corridor_id"": 1
    },
    {
      ""corridor_start_port"": 1,
      ""corridor_end_port"": 2,
      ""corridor_id"": 2
    },
    {
      ""corridor_start_port"": 1,
      ""corridor_end_port"": 6,
      ""corridor_id"": 3
    },
    {
      ""corridor_start_port"": 2,
      ""corridor_end_port"": 3,
      ""corridor_id"": 4
    },
    {
      ""corridor_start_port"": 2,
      ""corridor_end_port"": 7,
      ""corridor_id"": 5
    },
    {
      ""corridor_start_port"": 3,
      ""corridor_end_port"": 4,
      ""corridor_id"": 6
    },
    {
      ""corridor_start_port"": 3,
      ""corridor_end_port"": 8,
      ""corridor_id"": 7
    },
    {
      ""corridor_start_port"": 4,
      ""corridor_end_port"": 9,
      ""corridor_id"": 8
    },
    {
      ""corridor_start_port"": 5,
      ""corridor_end_port"": 6,
      ""corridor_id"": 9
    },
    {
      ""corridor_start_port"": 5,
      ""corridor_end_port"": 10,
      ""corridor_id"": 10
    },
    {
      ""corridor_start_port"": 6,
      ""corridor_end_port"": 7,
      ""corridor_id"": 11
    },
    {
      ""corridor_start_port"": 6,
      ""corridor_end_port"": 11,
      ""corridor_id"": 12
    },
    {
      ""corridor_start_port"": 7,
      ""corridor_end_port"": 8,
      ""corridor_id"": 13
    },
    {
      ""corridor_start_port"": 7,
      ""corridor_end_port"": 12,
      ""corridor_id"": 14
    },
    {
      ""corridor_start_port"": 8,
      ""corridor_end_port"": 9,
      ""corridor_id"": 15
    },
    {
      ""corridor_start_port"": 8,
      ""corridor_end_port"": 13,
      ""corridor_id"": 16
    },
    {
      ""corridor_start_port"": 9,
      ""corridor_end_port"": 14,
      ""corridor_id"": 17
    },
    {
      ""corridor_start_port"": 10,
      ""corridor_end_port"": 11,
      ""corridor_id"": 18
    },
    {
      ""corridor_start_port"": 10,
      ""corridor_end_port"": 15,
      ""corridor_id"": 19
    },
    {
      ""corridor_start_port"": 11,
      ""corridor_end_port"": 12,
      ""corridor_id"": 20
    },
    {
      ""corridor_start_port"": 11,
      ""corridor_end_port"": 16,
      ""corridor_id"": 21
    },
    {
      ""corridor_start_port"": 12,
      ""corridor_end_port"": 13,
      ""corridor_id"": 22
    },
    {
      ""corridor_start_port"": 12,
      ""corridor_end_port"": 17,
      ""corridor_id"": 23
    },
    {
      ""corridor_start_port"": 13,
      ""corridor_end_port"": 14,
      ""corridor_id"": 24
    },
    {
      ""corridor_start_port"": 13,
      ""corridor_end_port"": 18,
      ""corridor_id"": 25
    },
    {
      ""corridor_start_port"": 14,
      ""corridor_end_port"": 19,
      ""corridor_id"": 26
    },
    {
      ""corridor_start_port"": 15,
      ""corridor_end_port"": 16,
      ""corridor_id"": 27
    },
    {
      ""corridor_start_port"": 15,
      ""corridor_end_port"": 20,
      ""corridor_id"": 28
    },
    {
      ""corridor_start_port"": 16,
      ""corridor_end_port"": 17,
      ""corridor_id"": 29
    },
    {
      ""corridor_start_port"": 16,
      ""corridor_end_port"": 21,
      ""corridor_id"": 30
    },
    {
      ""corridor_start_port"": 17,
      ""corridor_end_port"": 18,
      ""corridor_id"": 31
    },
    {
      ""corridor_start_port"": 17,
      ""corridor_end_port"": 22,
      ""corridor_id"": 32
    },
    {
      ""corridor_start_port"": 18,
      ""corridor_end_port"": 19,
      ""corridor_id"": 33
    },
    {
      ""corridor_start_port"": 18,
      ""corridor_end_port"": 23,
      ""corridor_id"": 34
    },
    {
      ""corridor_start_port"": 19,
      ""corridor_end_port"": 24,
      ""corridor_id"": 35
    },
    {
      ""corridor_start_port"": 20,
      ""corridor_end_port"": 21,
      ""corridor_id"": 36
    },
    {
      ""corridor_start_port"": 21,
      ""corridor_end_port"": 22,
      ""corridor_id"": 37
    },
    {
      ""corridor_start_port"": 22,
      ""corridor_end_port"": 23,
      ""corridor_id"": 38
    },
    {
      ""corridor_start_port"": 23,
      ""corridor_end_port"": 24,
      ""corridor_id"": 39
    }
  ],
  ""linear_costs"": [
    {
      ""corridor_id"": 0,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 1,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 2,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 3,
      ""corridor_tariff"": 9.0
    },
    {
      ""corridor_id"": 4,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 5,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 6,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 7,
      ""corridor_tariff"": 6.0
    },
    {
      ""corridor_id"": 8,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 9,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 10,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 11,
      ""corridor_tariff"": 6.0
    },
    {
      ""corridor_id"": 12,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 13,
      ""corridor_tariff"": 6.0
    },
    {
      ""corridor_id"": 14,
      ""corridor_tariff"": 9.0
    },
    {
      ""corridor_id"": 15,
      ""corridor_tariff"": 4.0
    },
    {
      ""corridor_id"": 16,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 17,
      ""corridor_tariff"": 10.0
    },
    {
      ""corridor_id"": 18,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 19,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 20,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 21,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 22,
      ""corridor_tariff"": 9.0
    },
    {
      ""corridor_id"": 23,
      ""corridor_tariff"": 9.0
    },
    {
      ""corridor_id"": 24,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 25,
      ""corridor_tariff"": 1.0
    },
    {
      ""corridor_id"": 26,
      ""corridor_tariff"": 8.0
    },
    {
      ""corridor_id"": 27,
      ""corridor_tariff"": 8.0
    },
    {
      ""corridor_id"": 28,
      ""corridor_tariff"": 3.0
    },
    {
      ""corridor_id"": 29,
      ""corridor_tariff"": 3.0
    },
    {
      ""corridor_id"": 30,
      ""corridor_tariff"": 2.0
    },
    {
      ""corridor_id"": 31,
      ""corridor_tariff"": 8.0
    },
    {
      ""corridor_id"": 32,
      ""corridor_tariff"": 6.0
    },
    {
      ""corridor_id"": 33,
      ""corridor_tariff"": 10.0
    },
    {
      ""corridor_id"": 34,
      ""corridor_tariff"": 4.0
    },
    {
      ""corridor_id"": 35,
      ""corridor_tariff"": 4.0
    },
    {
      ""corridor_id"": 36,
      ""corridor_tariff"": 4.0
    },
    {
      ""corridor_id"": 37,
      ""corridor_tariff"": 9.0
    },
    {
      ""corridor_id"": 38,
      ""corridor_tariff"": 7.0
    },
    {
      ""corridor_id"": 39,
      ""corridor_tariff"": 5.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 9.0 | 3.0 | 3.0 | 3.0 | 5.0 | 8.0 | 4.0 | 5.0 | 7.0 | 3.0 | 9.0 | 2.0 | 3.0 | 9.0 | 6.0 | 9.0 | 9.0 | 2.0 | 4.0 | 7.0 | 5.0 | 10.0 | 7.0 | 6.0 | 3.0 | 5.0 | 9.0 | 1.0 | 1.0 | 5.0 | 4.0 | 7.0 | 5.0 | 2.0 | 1.0 | 7.0 | 4.0 | 5.0 | 9.0 |
| 1 | 9.0 | 10.0 | 10.0 | 4.0 | 7.0 | 5.0 | 2.0 | 9.0 | 6.0 | 3.0 | 7.0 | 6.0 | 10.0 | 3.0 | 7.0 | 2.0 | 1.0 | 3.0 | 3.0 | 10.0 | 4.0 | 3.0 | 9.0 | 8.0 | 8.0 | 4.0 | 2.0 | 8.0 | 5.0 | 4.0 | 9.0 | 10.0 | 5.0 | 2.0 | 2.0 | 6.0 | 7.0 | 8.0 | 8.0 | 3.0 |
| 2 | 3.0 | 10.0 | 1.0 | 4.0 | 6.0 | 6.0 | 5.0 | 9.0 | 5.0 | 5.0 | 4.0 | 4.0 | 5.0 | 3.0 | 9.0 | 3.0 | 8.0 | 5.0 | 1.0 | 8.0 | 7.0 | 1.0 | 10.0 | 4.0 | 3.0 | 1.0 | 6.0 | 10.0 | 5.0 | 8.0 | 4.0 | 10.0 | 6.0 | 2.0 | 2.0 | 1.0 | 5.0 | 6.0 | 1.0 | 8.0 |
| 3 | 3.0 | 4.0 | 4.0 | 3.0 | 2.0 | 4.0 | 4.0 | 5.0 | 6.0 | 8.0 | 7.0 | 9.0 | 9.0 | 1.0 | 2.0 | 9.0 | 5.0 | 5.0 | 2.0 | 8.0 | 7.0 | 4.0 | 5.0 | 8.0 | 9.0 | 3.0 | 3.0 | 4.0 | 5.0 | 1.0 | 8.0 | 9.0 | 1.0 | 7.0 | 9.0 | 5.0 | 6.0 | 8.0 | 3.0 | 3.0 |
| 4 | 3.0 | 7.0 | 6.0 | 2.0 | 10.0 | 10.0 | 5.0 | 3.0 | 1.0 | 3.0 | 2.0 | 7.0 | 3.0 | 2.0 | 10.0 | 4.0 | 5.0 | 5.0 | 5.0 | 6.0 | 5.0 | 8.0 | 6.0 | 6.0 | 3.0 | 9.0 | 7.0 | 2.0 | 4.0 | 3.0 | 3.0 | 9.0 | 1.0 | 4.0 | 2.0 | 5.0 | 6.0 | 9.0 | 6.0 | 6.0 |
| 5 | 5.0 | 5.0 | 6.0 | 4.0 | 10.0 | 6.0 | 6.0 | 8.0 | 3.0 | 4.0 | 1.0 | 2.0 | 6.0 | 6.0 | 2.0 | 10.0 | 10.0 | 6.0 | 8.0 | 1.0 | 5.0 | 4.0 | 2.0 | 2.0 | 3.0 | 3.0 | 9.0 | 6.0 | 1.0 | 3.0 | 1.0 | 6.0 | 6.0 | 5.0 | 5.0 | 8.0 | 5.0 | 10.0 | 8.0 | 5.0 |
| 6 | 8.0 | 2.0 | 5.0 | 4.0 | 5.0 | 6.0 | 9.0 | 4.0 | 9.0 | 7.0 | 4.0 | 10.0 | 6.0 | 1.0 | 3.0 | 7.0 | 4.0 | 1.0 | 4.0 | 2.0 | 8.0 | 8.0 | 10.0 | 4.0 | 9.0 | 6.0 | 5.0 | 8.0 | 5.0 | 1.0 | 2.0 | 4.0 | 1.0 | 2.0 | 6.0 | 9.0 | 1.0 | 6.0 | 7.0 | 7.0 |
| 7 | 4.0 | 9.0 | 9.0 | 5.0 | 3.0 | 8.0 | 4.0 | 6.0 | 6.0 | 8.0 | 4.0 | 2.0 | 4.0 | 4.0 | 7.0 | 2.0 | 10.0 | 5.0 | 4.0 | 10.0 | 7.0 | 5.0 | 10.0 | 8.0 | 6.0 | 6.0 | 5.0 | 10.0 | 1.0 | 8.0 | 1.0 | 6.0 | 3.0 | 8.0 | 7.0 | 2.0 | 5.0 | 9.0 | 1.0 | 2.0 |
| 8 | 5.0 | 6.0 | 5.0 | 6.0 | 1.0 | 3.0 | 9.0 | 6.0 | 10.0 | 5.0 | 8.0 | 10.0 | 7.0 | 9.0 | 3.0 | 2.0 | 3.0 | 4.0 | 9.0 | 8.0 | 1.0 | 4.0 | 10.0 | 1.0 | 4.0 | 4.0 | 1.0 | 8.0 | 8.0 | 9.0 | 1.0 | 6.0 | 8.0 | 9.0 | 8.0 | 9.0 | 7.0 | 4.0 | 2.0 | 3.0 |
| 9 | 7.0 | 3.0 | 5.0 | 8.0 | 3.0 | 4.0 | 7.0 | 8.0 | 5.0 | 1.0 | 10.0 | 5.0 | 1.0 | 7.0 | 3.0 | 2.0 | 6.0 | 5.0 | 7.0 | 7.0 | 7.0 | 5.0 | 2.0 | 6.0 | 1.0 | 8.0 | 9.0 | 9.0 | 4.0 | 3.0 | 8.0 | 2.0 | 1.0 | 4.0 | 7.0 | 6.0 | 6.0 | 3.0 | 3.0 | 6.0 |
| 10 | 3.0 | 7.0 | 4.0 | 7.0 | 2.0 | 1.0 | 4.0 | 4.0 | 8.0 | 10.0 | 4.0 | 6.0 | 9.0 | 9.0 | 5.0 | 3.0 | 9.0 | 7.0 | 9.0 | 4.0 | 9.0 | 5.0 | 5.0 | 9.0 | 5.0 | 2.0 | 7.0 | 9.0 | 7.0 | 5.0 | 9.0 | 9.0 | 9.0 | 7.0 | 8.0 | 3.0 | 9.0 | 3.0 | 3.0 | 9.0 |
| 11 | 9.0 | 6.0 | 4.0 | 9.0 | 7.0 | 2.0 | 10.0 | 2.0 | 10.0 | 5.0 | 6.0 | 7.0 | 2.0 | 3.0 | 6.0 | 7.0 | 1.0 | 4.0 | 2.0 | 10.0 | 2.0 | 5.0 | 2.0 | 10.0 | 9.0 | 4.0 | 2.0 | 8.0 | 6.0 | 3.0 | 7.0 | 8.0 | 8.0 | 3.0 | 5.0 | 7.0 | 2.0 | 9.0 | 9.0 | 3.0 |
| 12 | 2.0 | 10.0 | 5.0 | 9.0 | 3.0 | 6.0 | 6.0 | 4.0 | 7.0 | 1.0 | 9.0 | 2.0 | 6.0 | 2.0 | 2.0 | 7.0 | 8.0 | 6.0 | 7.0 | 10.0 | 3.0 | 1.0 | 9.0 | 9.0 | 3.0 | 3.0 | 5.0 | 6.0 | 7.0 | 6.0 | 4.0 | 5.0 | 7.0 | 7.0 | 7.0 | 6.0 | 10.0 | 8.0 | 7.0 | 1.0 |
| 13 | 3.0 | 3.0 | 3.0 | 1.0 | 2.0 | 6.0 | 1.0 | 4.0 | 9.0 | 7.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 6.0 | 2.0 | 10.0 | 1.0 | 8.0 | 6.0 | 1.0 | 8.0 | 1.0 | 10.0 | 6.0 | 2.0 | 3.0 | 3.0 | 1.0 | 5.0 | 5.0 | 7.0 | 2.0 | 5.0 | 1.0 | 6.0 | 1.0 | 5.0 | 8.0 |
| 14 | 9.0 | 7.0 | 9.0 | 2.0 | 10.0 | 2.0 | 3.0 | 7.0 | 3.0 | 3.0 | 5.0 | 6.0 | 2.0 | 3.0 | 5.0 | 9.0 | 8.0 | 8.0 | 3.0 | 4.0 | 2.0 | 5.0 | 9.0 | 3.0 | 5.0 | 9.0 | 2.0 | 9.0 | 4.0 | 6.0 | 5.0 | 9.0 | 10.0 | 7.0 | 3.0 | 2.0 | 10.0 | 9.0 | 3.0 | 3.0 |
| 15 | 6.0 | 2.0 | 3.0 | 9.0 | 4.0 | 10.0 | 7.0 | 2.0 | 2.0 | 2.0 | 3.0 | 7.0 | 7.0 | 6.0 | 9.0 | 5.0 | 9.0 | 9.0 | 1.0 | 4.0 | 10.0 | 10.0 | 6.0 | 3.0 | 4.0 | 7.0 | 3.0 | 6.0 | 7.0 | 2.0 | 6.0 | 2.0 | 3.0 | 9.0 | 4.0 | 4.0 | 3.0 | 10.0 | 6.0 | 1.0 |
| 16 | 9.0 | 1.0 | 8.0 | 5.0 | 5.0 | 10.0 | 4.0 | 10.0 | 3.0 | 6.0 | 9.0 | 1.0 | 8.0 | 2.0 | 8.0 | 9.0 | 2.0 | 9.0 | 7.0 | 7.0 | 7.0 | 10.0 | 8.0 | 2.0 | 10.0 | 8.0 | 9.0 | 4.0 | 6.0 | 1.0 | 6.0 | 3.0 | 6.0 | 9.0 | 7.0 | 3.0 | 9.0 | 10.0 | 3.0 | 8.0 |
| 17 | 9.0 | 3.0 | 5.0 | 5.0 | 5.0 | 6.0 | 1.0 | 5.0 | 4.0 | 5.0 | 7.0 | 4.0 | 6.0 | 10.0 | 8.0 | 9.0 | 9.0 | 1.0 | 5.0 | 9.0 | 10.0 | 8.0 | 5.0 | 9.0 | 4.0 | 5.0 | 10.0 | 1.0 | 2.0 | 4.0 | 2.0 | 4.0 | 7.0 | 1.0 | 2.0 | 9.0 | 4.0 | 4.0 | 6.0 | 8.0 |
| 18 | 2.0 | 3.0 | 1.0 | 2.0 | 5.0 | 8.0 | 4.0 | 4.0 | 9.0 | 7.0 | 9.0 | 2.0 | 7.0 | 1.0 | 3.0 | 1.0 | 7.0 | 5.0 | 10.0 | 8.0 | 7.0 | 7.0 | 5.0 | 9.0 | 8.0 | 1.0 | 5.0 | 5.0 | 7.0 | 3.0 | 9.0 | 6.0 | 10.0 | 10.0 | 6.0 | 2.0 | 8.0 | 9.0 | 3.0 | 3.0 |
| 19 | 4.0 | 10.0 | 8.0 | 8.0 | 6.0 | 1.0 | 2.0 | 10.0 | 8.0 | 7.0 | 4.0 | 10.0 | 10.0 | 8.0 | 4.0 | 4.0 | 7.0 | 9.0 | 8.0 | 7.0 | 4.0 | 5.0 | 3.0 | 10.0 | 4.0 | 7.0 | 10.0 | 4.0 | 10.0 | 4.0 | 8.0 | 1.0 | 3.0 | 2.0 | 1.0 | 10.0 | 1.0 | 6.0 | 5.0 | 10.0 |
| 20 | 7.0 | 4.0 | 7.0 | 7.0 | 5.0 | 5.0 | 8.0 | 7.0 | 1.0 | 7.0 | 9.0 | 2.0 | 3.0 | 6.0 | 2.0 | 10.0 | 7.0 | 10.0 | 7.0 | 4.0 | 9.0 | 4.0 | 8.0 | 8.0 | 8.0 | 5.0 | 7.0 | 7.0 | 3.0 | 9.0 | 5.0 | 2.0 | 7.0 | 5.0 | 3.0 | 10.0 | 5.0 | 9.0 | 8.0 | 7.0 |
| 21 | 5.0 | 3.0 | 1.0 | 4.0 | 8.0 | 4.0 | 8.0 | 5.0 | 4.0 | 5.0 | 5.0 | 5.0 | 1.0 | 1.0 | 5.0 | 10.0 | 10.0 | 8.0 | 7.0 | 5.0 | 4.0 | 5.0 | 9.0 | 10.0 | 1.0 | 1.0 | 5.0 | 1.0 | 6.0 | 6.0 | 3.0 | 3.0 | 1.0 | 7.0 | 8.0 | 1.0 | 7.0 | 4.0 | 10.0 | 8.0 |
| 22 | 10.0 | 9.0 | 10.0 | 5.0 | 6.0 | 2.0 | 10.0 | 10.0 | 10.0 | 2.0 | 5.0 | 2.0 | 9.0 | 8.0 | 9.0 | 6.0 | 8.0 | 5.0 | 5.0 | 3.0 | 8.0 | 9.0 | 10.0 | 9.0 | 4.0 | 10.0 | 1.0 | 8.0 | 9.0 | 1.0 | 4.0 | 2.0 | 2.0 | 6.0 | 5.0 | 7.0 | 4.0 | 3.0 | 8.0 | 10.0 |
| 23 | 7.0 | 8.0 | 4.0 | 8.0 | 6.0 | 2.0 | 4.0 | 8.0 | 1.0 | 6.0 | 9.0 | 10.0 | 9.0 | 1.0 | 3.0 | 3.0 | 2.0 | 9.0 | 9.0 | 10.0 | 8.0 | 10.0 | 9.0 | 6.0 | 6.0 | 7.0 | 10.0 | 6.0 | 10.0 | 3.0 | 2.0 | 6.0 | 6.0 | 7.0 | 3.0 | 1.0 | 8.0 | 7.0 | 7.0 | 2.0 |
| 24 | 6.0 | 8.0 | 3.0 | 9.0 | 3.0 | 3.0 | 9.0 | 6.0 | 4.0 | 1.0 | 5.0 | 9.0 | 3.0 | 10.0 | 5.0 | 4.0 | 10.0 | 4.0 | 8.0 | 4.0 | 8.0 | 1.0 | 4.0 | 6.0 | 3.0 | 1.0 | 3.0 | 6.0 | 7.0 | 6.0 | 8.0 | 8.0 | 3.0 | 5.0 | 10.0 | 6.0 | 6.0 | 1.0 | 5.0 | 2.0 |
| 25 | 3.0 | 4.0 | 1.0 | 3.0 | 9.0 | 3.0 | 6.0 | 6.0 | 4.0 | 8.0 | 2.0 | 4.0 | 3.0 | 6.0 | 9.0 | 7.0 | 8.0 | 5.0 | 1.0 | 7.0 | 5.0 | 1.0 | 10.0 | 7.0 | 1.0 | 4.0 | 6.0 | 9.0 | 2.0 | 6.0 | 8.0 | 7.0 | 7.0 | 3.0 | 9.0 | 5.0 | 2.0 | 4.0 | 7.0 | 6.0 |
| 26 | 5.0 | 2.0 | 6.0 | 3.0 | 7.0 | 9.0 | 5.0 | 5.0 | 1.0 | 9.0 | 7.0 | 2.0 | 5.0 | 2.0 | 2.0 | 3.0 | 9.0 | 10.0 | 5.0 | 10.0 | 7.0 | 5.0 | 1.0 | 10.0 | 3.0 | 6.0 | 7.0 | 5.0 | 5.0 | 5.0 | 4.0 | 8.0 | 8.0 | 4.0 | 4.0 | 6.0 | 10.0 | 6.0 | 10.0 | 8.0 |
| 27 | 9.0 | 8.0 | 10.0 | 4.0 | 2.0 | 6.0 | 8.0 | 10.0 | 8.0 | 9.0 | 9.0 | 8.0 | 6.0 | 3.0 | 9.0 | 6.0 | 4.0 | 1.0 | 5.0 | 4.0 | 7.0 | 1.0 | 8.0 | 6.0 | 6.0 | 9.0 | 5.0 | 7.0 | 1.0 | 5.0 | 10.0 | 5.0 | 8.0 | 9.0 | 2.0 | 10.0 | 4.0 | 1.0 | 4.0 | 2.0 |
| 28 | 1.0 | 5.0 | 5.0 | 5.0 | 4.0 | 1.0 | 5.0 | 1.0 | 8.0 | 4.0 | 7.0 | 6.0 | 7.0 | 3.0 | 4.0 | 7.0 | 6.0 | 2.0 | 7.0 | 10.0 | 3.0 | 6.0 | 9.0 | 10.0 | 7.0 | 2.0 | 5.0 | 1.0 | 4.0 | 9.0 | 1.0 | 1.0 | 5.0 | 4.0 | 6.0 | 1.0 | 9.0 | 3.0 | 1.0 | 6.0 |
| 29 | 1.0 | 4.0 | 8.0 | 1.0 | 3.0 | 3.0 | 1.0 | 8.0 | 9.0 | 3.0 | 5.0 | 3.0 | 6.0 | 1.0 | 6.0 | 2.0 | 1.0 | 4.0 | 3.0 | 4.0 | 9.0 | 6.0 | 1.0 | 3.0 | 6.0 | 6.0 | 5.0 | 5.0 | 9.0 | 6.0 | 3.0 | 7.0 | 1.0 | 8.0 | 10.0 | 1.0 | 6.0 | 7.0 | 5.0 | 9.0 |
| 30 | 5.0 | 9.0 | 4.0 | 8.0 | 3.0 | 1.0 | 2.0 | 1.0 | 1.0 | 8.0 | 9.0 | 7.0 | 4.0 | 5.0 | 5.0 | 6.0 | 6.0 | 2.0 | 9.0 | 8.0 | 5.0 | 3.0 | 4.0 | 2.0 | 8.0 | 8.0 | 4.0 | 10.0 | 1.0 | 3.0 | 3.0 | 6.0 | 8.0 | 3.0 | 3.0 | 1.0 | 4.0 | 8.0 | 9.0 | 2.0 |
| 31 | 4.0 | 10.0 | 10.0 | 9.0 | 9.0 | 6.0 | 4.0 | 6.0 | 6.0 | 2.0 | 9.0 | 8.0 | 5.0 | 5.0 | 9.0 | 2.0 | 3.0 | 4.0 | 6.0 | 1.0 | 2.0 | 3.0 | 2.0 | 6.0 | 8.0 | 7.0 | 8.0 | 5.0 | 1.0 | 7.0 | 6.0 | 3.0 | 4.0 | 8.0 | 6.0 | 8.0 | 9.0 | 6.0 | 3.0 | 7.0 |
| 32 | 7.0 | 5.0 | 6.0 | 1.0 | 1.0 | 6.0 | 1.0 | 3.0 | 8.0 | 1.0 | 9.0 | 8.0 | 7.0 | 7.0 | 10.0 | 3.0 | 6.0 | 7.0 | 10.0 | 3.0 | 7.0 | 1.0 | 2.0 | 6.0 | 3.0 | 7.0 | 8.0 | 8.0 | 5.0 | 1.0 | 8.0 | 4.0 | 10.0 | 1.0 | 3.0 | 2.0 | 8.0 | 1.0 | 7.0 | 9.0 |
| 33 | 5.0 | 2.0 | 2.0 | 7.0 | 4.0 | 5.0 | 2.0 | 8.0 | 9.0 | 4.0 | 7.0 | 3.0 | 7.0 | 2.0 | 7.0 | 9.0 | 9.0 | 1.0 | 10.0 | 2.0 | 5.0 | 7.0 | 6.0 | 7.0 | 5.0 | 3.0 | 4.0 | 9.0 | 4.0 | 8.0 | 3.0 | 8.0 | 1.0 | 7.0 | 3.0 | 10.0 | 6.0 | 7.0 | 3.0 | 1.0 |
| 34 | 2.0 | 2.0 | 2.0 | 9.0 | 2.0 | 5.0 | 6.0 | 7.0 | 8.0 | 7.0 | 8.0 | 5.0 | 7.0 | 5.0 | 3.0 | 4.0 | 7.0 | 2.0 | 6.0 | 1.0 | 3.0 | 8.0 | 5.0 | 3.0 | 10.0 | 9.0 | 4.0 | 2.0 | 6.0 | 10.0 | 3.0 | 6.0 | 3.0 | 3.0 | 3.0 | 2.0 | 6.0 | 8.0 | 6.0 | 8.0 |
| 35 | 1.0 | 6.0 | 1.0 | 5.0 | 5.0 | 8.0 | 9.0 | 2.0 | 9.0 | 6.0 | 3.0 | 7.0 | 6.0 | 1.0 | 2.0 | 4.0 | 3.0 | 9.0 | 2.0 | 10.0 | 10.0 | 1.0 | 7.0 | 1.0 | 6.0 | 5.0 | 6.0 | 10.0 | 1.0 | 1.0 | 1.0 | 8.0 | 2.0 | 10.0 | 2.0 | 6.0 | 6.0 | 4.0 | 6.0 | 2.0 |
| 36 | 7.0 | 7.0 | 5.0 | 6.0 | 6.0 | 5.0 | 1.0 | 5.0 | 7.0 | 6.0 | 9.0 | 2.0 | 10.0 | 6.0 | 10.0 | 3.0 | 9.0 | 4.0 | 8.0 | 1.0 | 5.0 | 7.0 | 4.0 | 8.0 | 6.0 | 2.0 | 10.0 | 4.0 | 9.0 | 6.0 | 4.0 | 9.0 | 8.0 | 6.0 | 6.0 | 6.0 | 9.0 | 10.0 | 9.0 | 9.0 |
| 37 | 4.0 | 8.0 | 6.0 | 8.0 | 9.0 | 10.0 | 6.0 | 9.0 | 4.0 | 3.0 | 3.0 | 9.0 | 8.0 | 1.0 | 9.0 | 10.0 | 10.0 | 4.0 | 9.0 | 6.0 | 9.0 | 4.0 | 3.0 | 7.0 | 1.0 | 4.0 | 6.0 | 1.0 | 3.0 | 7.0 | 8.0 | 6.0 | 1.0 | 7.0 | 8.0 | 4.0 | 10.0 | 8.0 | 5.0 | 5.0 |
| 38 | 5.0 | 8.0 | 1.0 | 3.0 | 6.0 | 8.0 | 7.0 | 1.0 | 2.0 | 3.0 | 3.0 | 9.0 | 7.0 | 5.0 | 3.0 | 6.0 | 3.0 | 6.0 | 3.0 | 5.0 | 8.0 | 10.0 | 8.0 | 7.0 | 5.0 | 7.0 | 10.0 | 4.0 | 1.0 | 5.0 | 9.0 | 3.0 | 7.0 | 3.0 | 6.0 | 6.0 | 9.0 | 5.0 | 8.0 | 1.0 |
| 39 | 9.0 | 3.0 | 8.0 | 3.0 | 6.0 | 5.0 | 7.0 | 2.0 | 3.0 | 6.0 | 9.0 | 3.0 | 1.0 | 8.0 | 3.0 | 1.0 | 8.0 | 8.0 | 3.0 | 10.0 | 7.0 | 8.0 | 10.0 | 2.0 | 2.0 | 6.0 | 8.0 | 2.0 | 6.0 | 9.0 | 2.0 | 7.0 | 9.0 | 1.0 | 8.0 | 2.0 | 9.0 | 5.0 | 1.0 | 6.0 |

Also, when you give the actual answer, please stick to a tiny JSON shape so it’s easy to parse — nothing fancy, just a single top-level key called solution with the path inside. Here’s the little sketch I expect:

{
  ""solution"": []
}

In that sketch, ""solution"" should be a list containing the nodes of the chosen route in order, from the origin to the destination. Think of it like filling in a short form: one sequence of place names, nothing else — no edge identifiers, no costs, just the node names in path order. This JSON is only a template showing the expected shape, not the actual path.

Also be sure to use the node identifiers exactly as they appear in the instance input — don’t rename them or invent new labels. For example:
- Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'objective': {'constant': 0.0, 'linear': [1.0, 1.0, 7.0, 9.0, 2.0, 1.0, 7.0, 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{'var_i': 36, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 33, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 34, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 36, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 37, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 38, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 39, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 25, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 26, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 28, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 31, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 34, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 35, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 36, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 37, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 38, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 39, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 24, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 29, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 33, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 34, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 36, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 38, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 39, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 25, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 27, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 28, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 32, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 34, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 36, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 39, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23, 24: 24}}","[0, 5, 6, 7, 8, 13, 18, 19, 24]",9,json,0
QSPP,QSPP,"We’re organizing visitor flow and need to choose exactly one one-way path from the lobby to the keynote stage that follows the direction signs through the exhibit halls. Every hallway adds a base walking cost, some hallways have an extra obstacle cost when used, and certain hallway pairs create additional delay when both are included — so the “best” route is the one with the smallest total of all those pieces added together. The route must be a connected list of places, starting at the entrance and ending at the keynote, and the answer should only list location names in order (no corridor identifiers or cost figures). The specific map and numbers appear below.

# total_locations_count=18
# total_corridors_count=32
# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R
# entrance_location=Q
# keynote_location=R

corridor_from,corridor_to,corridor_id
Q,A,0
Q,E,1
Q,I,2
Q,M,3
D,R,4
H,R,5
L,R,6
P,R,7
A,B,8
A,E,9
B,C,10
B,F,11
C,D,12
C,G,13
D,H,14
E,F,15
E,I,16
F,G,17
F,J,18
G,H,19
G,K,20
H,L,21
I,J,22
I,M,23
J,K,24
J,N,25
K,L,26
K,O,27
L,P,28
M,N,29
N,O,30
O,P,31

corridor_id,walking_cost
0,2.0
1,7.0
2,8.0
3,10.0
4,7.0
5,8.0
6,3.0
7,2.0
8,2.0
9,1.0
10,7.0
11,7.0
12,1.0
13,4.0
14,6.0
15,6.0
16,6.0
17,2.0
18,6.0
19,8.0
20,4.0
21,5.0
22,10.0
23,7.0
24,4.0
25,4.0
26,7.0
27,6.0
28,8.0
29,8.0
30,8.0
31,10.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 2.0 | 9.0 | 3.0 | 8.0 | 3.0 | 3.0 | 2.0 | 1.0 | 2.0 | 2.0 | 3.0 | 1.0 | 4.0 | 4.0 | 2.0 | 10.0 | 9.0 | 7.0 | 9.0 | 4.0 | 2.0 | 2.0 | 10.0 | 3.0 | 1.0 | 6.0 | 5.0 | 1.0 | 3.0 | 5.0 | 1.0 |
| 1 | 2.0 | 5.0 | 3.0 | 4.0 | 1.0 | 7.0 | 10.0 | 5.0 | 2.0 | 3.0 | 1.0 | 2.0 | 9.0 | 4.0 | 6.0 | 7.0 | 8.0 | 7.0 | 3.0 | 10.0 | 1.0 | 3.0 | 6.0 | 9.0 | 1.0 | 10.0 | 7.0 | 9.0 | 5.0 | 4.0 | 10.0 | 1.0 |
| 2 | 9.0 | 3.0 | 4.0 | 3.0 | 8.0 | 8.0 | 9.0 | 8.0 | 6.0 | 3.0 | 4.0 | 1.0 | 2.0 | 5.0 | 10.0 | 8.0 | 9.0 | 2.0 | 5.0 | 9.0 | 5.0 | 2.0 | 5.0 | 2.0 | 7.0 | 4.0 | 8.0 | 4.0 | 10.0 | 2.0 | 10.0 | 2.0 |
| 3 | 3.0 | 4.0 | 3.0 | 5.0 | 6.0 | 2.0 | 7.0 | 2.0 | 3.0 | 1.0 | 10.0 | 5.0 | 3.0 | 5.0 | 2.0 | 3.0 | 10.0 | 1.0 | 3.0 | 7.0 | 10.0 | 5.0 | 4.0 | 5.0 | 6.0 | 9.0 | 3.0 | 8.0 | 3.0 | 5.0 | 3.0 | 8.0 |
| 4 | 8.0 | 1.0 | 8.0 | 6.0 | 8.0 | 3.0 | 1.0 | 2.0 | 3.0 | 6.0 | 1.0 | 8.0 | 10.0 | 2.0 | 5.0 | 9.0 | 7.0 | 2.0 | 1.0 | 5.0 | 5.0 | 9.0 | 3.0 | 5.0 | 4.0 | 5.0 | 8.0 | 10.0 | 5.0 | 9.0 | 2.0 | 9.0 |
| 5 | 3.0 | 7.0 | 8.0 | 2.0 | 3.0 | 7.0 | 9.0 | 7.0 | 7.0 | 1.0 | 3.0 | 4.0 | 3.0 | 5.0 | 10.0 | 7.0 | 9.0 | 1.0 | 8.0 | 4.0 | 7.0 | 6.0 | 5.0 | 1.0 | 6.0 | 5.0 | 3.0 | 2.0 | 3.0 | 8.0 | 8.0 | 3.0 |
| 6 | 3.0 | 10.0 | 9.0 | 7.0 | 1.0 | 9.0 | 6.0 | 10.0 | 3.0 | 1.0 | 4.0 | 1.0 | 2.0 | 7.0 | 6.0 | 3.0 | 5.0 | 10.0 | 6.0 | 8.0 | 6.0 | 1.0 | 6.0 | 4.0 | 5.0 | 4.0 | 8.0 | 7.0 | 8.0 | 8.0 | 4.0 | 3.0 |
| 7 | 2.0 | 5.0 | 8.0 | 2.0 | 2.0 | 7.0 | 10.0 | 3.0 | 9.0 | 9.0 | 9.0 | 9.0 | 8.0 | 6.0 | 2.0 | 6.0 | 5.0 | 9.0 | 7.0 | 6.0 | 1.0 | 2.0 | 5.0 | 9.0 | 6.0 | 2.0 | 6.0 | 5.0 | 5.0 | 1.0 | 10.0 | 4.0 |
| 8 | 1.0 | 2.0 | 6.0 | 3.0 | 3.0 | 7.0 | 3.0 | 9.0 | 8.0 | 8.0 | 6.0 | 10.0 | 7.0 | 3.0 | 7.0 | 10.0 | 6.0 | 10.0 | 2.0 | 6.0 | 10.0 | 7.0 | 4.0 | 4.0 | 2.0 | 10.0 | 4.0 | 4.0 | 7.0 | 10.0 | 7.0 | 9.0 |
| 9 | 2.0 | 3.0 | 3.0 | 1.0 | 6.0 | 1.0 | 1.0 | 9.0 | 8.0 | 2.0 | 8.0 | 5.0 | 7.0 | 10.0 | 8.0 | 1.0 | 10.0 | 6.0 | 1.0 | 5.0 | 2.0 | 2.0 | 2.0 | 10.0 | 6.0 | 5.0 | 10.0 | 5.0 | 3.0 | 9.0 | 3.0 | 10.0 |
| 10 | 2.0 | 1.0 | 4.0 | 10.0 | 1.0 | 3.0 | 4.0 | 9.0 | 6.0 | 8.0 | 2.0 | 3.0 | 4.0 | 5.0 | 3.0 | 3.0 | 10.0 | 8.0 | 2.0 | 6.0 | 1.0 | 7.0 | 5.0 | 1.0 | 6.0 | 3.0 | 3.0 | 5.0 | 8.0 | 5.0 | 2.0 | 8.0 |
| 11 | 3.0 | 2.0 | 1.0 | 5.0 | 8.0 | 4.0 | 1.0 | 9.0 | 10.0 | 5.0 | 3.0 | 1.0 | 8.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 6.0 | 4.0 | 8.0 | 1.0 | 6.0 | 2.0 | 2.0 | 7.0 | 6.0 | 8.0 | 7.0 | 4.0 | 7.0 | 9.0 |
| 12 | 1.0 | 9.0 | 2.0 | 3.0 | 10.0 | 3.0 | 2.0 | 8.0 | 7.0 | 7.0 | 4.0 | 8.0 | 8.0 | 9.0 | 1.0 | 7.0 | 7.0 | 2.0 | 5.0 | 6.0 | 5.0 | 3.0 | 10.0 | 3.0 | 10.0 | 5.0 | 3.0 | 3.0 | 7.0 | 5.0 | 7.0 | 5.0 |
| 13 | 4.0 | 4.0 | 5.0 | 5.0 | 2.0 | 5.0 | 7.0 | 6.0 | 3.0 | 10.0 | 5.0 | 2.0 | 9.0 | 2.0 | 5.0 | 10.0 | 10.0 | 1.0 | 3.0 | 8.0 | 8.0 | 10.0 | 1.0 | 5.0 | 4.0 | 4.0 | 3.0 | 9.0 | 10.0 | 5.0 | 3.0 | 2.0 |
| 14 | 4.0 | 6.0 | 10.0 | 2.0 | 5.0 | 10.0 | 6.0 | 2.0 | 7.0 | 8.0 | 3.0 | 8.0 | 1.0 | 5.0 | 9.0 | 1.0 | 6.0 | 6.0 | 2.0 | 3.0 | 7.0 | 4.0 | 8.0 | 3.0 | 4.0 | 9.0 | 1.0 | 10.0 | 1.0 | 4.0 | 5.0 | 3.0 |
| 15 | 2.0 | 7.0 | 8.0 | 3.0 | 9.0 | 7.0 | 3.0 | 6.0 | 10.0 | 1.0 | 3.0 | 5.0 | 7.0 | 10.0 | 1.0 | 9.0 | 5.0 | 8.0 | 1.0 | 6.0 | 7.0 | 1.0 | 6.0 | 6.0 | 3.0 | 7.0 | 4.0 | 5.0 | 5.0 | 2.0 | 5.0 | 9.0 |
| 16 | 10.0 | 8.0 | 9.0 | 10.0 | 7.0 | 9.0 | 5.0 | 5.0 | 6.0 | 10.0 | 10.0 | 9.0 | 7.0 | 10.0 | 6.0 | 5.0 | 3.0 | 7.0 | 7.0 | 3.0 | 3.0 | 6.0 | 6.0 | 2.0 | 3.0 | 7.0 | 3.0 | 3.0 | 2.0 | 7.0 | 2.0 | 8.0 |
| 17 | 9.0 | 7.0 | 2.0 | 1.0 | 2.0 | 1.0 | 10.0 | 9.0 | 10.0 | 6.0 | 8.0 | 9.0 | 2.0 | 1.0 | 6.0 | 8.0 | 7.0 | 8.0 | 1.0 | 2.0 | 5.0 | 9.0 | 7.0 | 6.0 | 3.0 | 5.0 | 5.0 | 8.0 | 10.0 | 1.0 | 3.0 | 10.0 |
| 18 | 7.0 | 3.0 | 5.0 | 3.0 | 1.0 | 8.0 | 6.0 | 7.0 | 2.0 | 1.0 | 2.0 | 6.0 | 5.0 | 3.0 | 2.0 | 1.0 | 7.0 | 1.0 | 3.0 | 9.0 | 8.0 | 4.0 | 8.0 | 4.0 | 7.0 | 5.0 | 2.0 | 4.0 | 10.0 | 2.0 | 2.0 | 7.0 |
| 19 | 9.0 | 10.0 | 9.0 | 7.0 | 5.0 | 4.0 | 8.0 | 6.0 | 6.0 | 5.0 | 6.0 | 4.0 | 6.0 | 8.0 | 3.0 | 6.0 | 3.0 | 2.0 | 9.0 | 8.0 | 10.0 | 8.0 | 1.0 | 4.0 | 8.0 | 7.0 | 2.0 | 4.0 | 9.0 | 6.0 | 4.0 | 5.0 |
| 20 | 4.0 | 1.0 | 5.0 | 10.0 | 5.0 | 7.0 | 6.0 | 1.0 | 10.0 | 2.0 | 1.0 | 8.0 | 5.0 | 8.0 | 7.0 | 7.0 | 3.0 | 5.0 | 8.0 | 10.0 | 8.0 | 7.0 | 3.0 | 7.0 | 6.0 | 2.0 | 9.0 | 10.0 | 8.0 | 1.0 | 5.0 | 3.0 |
| 21 | 2.0 | 3.0 | 2.0 | 5.0 | 9.0 | 6.0 | 1.0 | 2.0 | 7.0 | 2.0 | 7.0 | 1.0 | 3.0 | 10.0 | 4.0 | 1.0 | 6.0 | 9.0 | 4.0 | 8.0 | 7.0 | 6.0 | 4.0 | 9.0 | 8.0 | 10.0 | 2.0 | 4.0 | 4.0 | 5.0 | 5.0 | 9.0 |
| 22 | 2.0 | 6.0 | 5.0 | 4.0 | 3.0 | 5.0 | 6.0 | 5.0 | 4.0 | 2.0 | 5.0 | 6.0 | 10.0 | 1.0 | 8.0 | 6.0 | 6.0 | 7.0 | 8.0 | 1.0 | 3.0 | 4.0 | 8.0 | 8.0 | 7.0 | 1.0 | 9.0 | 7.0 | 4.0 | 10.0 | 10.0 | 6.0 |
| 23 | 10.0 | 9.0 | 2.0 | 5.0 | 5.0 | 1.0 | 4.0 | 9.0 | 4.0 | 10.0 | 1.0 | 2.0 | 3.0 | 5.0 | 3.0 | 6.0 | 2.0 | 6.0 | 4.0 | 4.0 | 7.0 | 9.0 | 8.0 | 8.0 | 4.0 | 8.0 | 8.0 | 9.0 | 5.0 | 9.0 | 2.0 | 3.0 |
| 24 | 3.0 | 1.0 | 7.0 | 6.0 | 4.0 | 6.0 | 5.0 | 6.0 | 2.0 | 6.0 | 6.0 | 2.0 | 10.0 | 4.0 | 4.0 | 3.0 | 3.0 | 3.0 | 7.0 | 8.0 | 6.0 | 8.0 | 7.0 | 4.0 | 7.0 | 4.0 | 6.0 | 8.0 | 4.0 | 1.0 | 2.0 | 2.0 |
| 25 | 1.0 | 10.0 | 4.0 | 9.0 | 5.0 | 5.0 | 4.0 | 2.0 | 10.0 | 5.0 | 3.0 | 7.0 | 5.0 | 4.0 | 9.0 | 7.0 | 7.0 | 5.0 | 5.0 | 7.0 | 2.0 | 10.0 | 1.0 | 8.0 | 4.0 | 5.0 | 7.0 | 4.0 | 1.0 | 8.0 | 4.0 | 8.0 |
| 26 | 6.0 | 7.0 | 8.0 | 3.0 | 8.0 | 3.0 | 8.0 | 6.0 | 4.0 | 10.0 | 3.0 | 6.0 | 3.0 | 3.0 | 1.0 | 4.0 | 3.0 | 5.0 | 2.0 | 2.0 | 9.0 | 2.0 | 9.0 | 8.0 | 6.0 | 7.0 | 7.0 | 4.0 | 10.0 | 1.0 | 3.0 | 9.0 |
| 27 | 5.0 | 9.0 | 4.0 | 8.0 | 10.0 | 2.0 | 7.0 | 5.0 | 4.0 | 5.0 | 5.0 | 8.0 | 3.0 | 9.0 | 10.0 | 5.0 | 3.0 | 8.0 | 4.0 | 4.0 | 10.0 | 4.0 | 7.0 | 9.0 | 8.0 | 4.0 | 4.0 | 5.0 | 7.0 | 8.0 | 9.0 | 6.0 |
| 28 | 1.0 | 5.0 | 10.0 | 3.0 | 5.0 | 3.0 | 8.0 | 5.0 | 7.0 | 3.0 | 8.0 | 7.0 | 7.0 | 10.0 | 1.0 | 5.0 | 2.0 | 10.0 | 10.0 | 9.0 | 8.0 | 4.0 | 4.0 | 5.0 | 4.0 | 1.0 | 10.0 | 7.0 | 3.0 | 10.0 | 9.0 | 10.0 |
| 29 | 3.0 | 4.0 | 2.0 | 5.0 | 9.0 | 8.0 | 8.0 | 1.0 | 10.0 | 9.0 | 5.0 | 4.0 | 5.0 | 5.0 | 4.0 | 2.0 | 7.0 | 1.0 | 2.0 | 6.0 | 1.0 | 5.0 | 10.0 | 9.0 | 1.0 | 8.0 | 1.0 | 8.0 | 10.0 | 2.0 | 4.0 | 7.0 |
| 30 | 5.0 | 10.0 | 10.0 | 3.0 | 2.0 | 8.0 | 4.0 | 10.0 | 7.0 | 3.0 | 2.0 | 7.0 | 7.0 | 3.0 | 5.0 | 5.0 | 2.0 | 3.0 | 2.0 | 4.0 | 5.0 | 5.0 | 10.0 | 2.0 | 2.0 | 4.0 | 3.0 | 9.0 | 9.0 | 4.0 | 2.0 | 1.0 |
| 31 | 1.0 | 1.0 | 2.0 | 8.0 | 9.0 | 3.0 | 3.0 | 4.0 | 9.0 | 10.0 | 8.0 | 9.0 | 5.0 | 2.0 | 3.0 | 9.0 | 8.0 | 10.0 | 7.0 | 5.0 | 3.0 | 9.0 | 6.0 | 3.0 | 2.0 | 8.0 | 9.0 | 6.0 | 10.0 | 7.0 | 1.0 | 5.0 |

Oh, and when you send back the route, please use this simple JSON layout so it's easy to check automatically:

{
  ""solution"": []
}

The ""solution"" array is where you put the ordered list of place names (the locations you walk through) from the entrance to the keynote stage. Keep it casual: just the location identifiers in order, nothing else — no corridor IDs, no cost numbers. This JSON is just a sketch of the shape I want, not the actual answer itself.

Use the node identifiers exactly as they appear in the instance input — no renaming and no new labels.  
Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 4, 'var_index': 1}, {'from': 16, 'to': 8, 'var_index': 2}, {'from': 16, 'to': 12, 'var_index': 3}, {'from': 3, 'to': 17, 'var_index': 4}, {'from': 7, 'to': 17, 'var_index': 5}, {'from': 11, 'to': 17, 'var_index': 6}, {'from': 15, 'to': 17, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 0, 'to': 4, 'var_index': 9}, {'from': 1, 'to': 2, 'var_index': 10}, {'from': 1, 'to': 5, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 2, 'to': 6, 'var_index': 13}, {'from': 3, 'to': 7, 'var_index': 14}, {'from': 4, 'to': 5, 'var_index': 15}, {'from': 4, 'to': 8, 'var_index': 16}, {'from': 5, 'to': 6, 'var_index': 17}, {'from': 5, 'to': 9, 'var_index': 18}, {'from': 6, 'to': 7, 'var_index': 19}, {'from': 6, 'to': 10, 'var_index': 20}, {'from': 7, 'to': 11, 'var_index': 21}, {'from': 8, 'to': 9, 'var_index': 22}, {'from': 8, 'to': 12, 'var_index': 23}, {'from': 9, 'to': 10, 'var_index': 24}, {'from': 9, 'to': 13, 'var_index': 25}, {'from': 10, 'to': 11, 'var_index': 26}, {'from': 10, 'to': 14, 'var_index': 27}, {'from': 11, 'to': 15, 'var_index': 28}, {'from': 12, 'to': 13, 'var_index': 29}, {'from': 13, 'to': 14, 'var_index': 30}, {'from': 14, 'to': 15, 'var_index': 31}], 'objective': {'constant': 0.0, 'linear': [2.0, 7.0, 8.0, 10.0, 7.0, 8.0, 3.0, 2.0, 2.0, 1.0, 7.0, 7.0, 1.0, 4.0, 6.0, 6.0, 6.0, 2.0, 6.0, 8.0, 4.0, 5.0, 10.0, 7.0, 4.0, 4.0, 7.0, 6.0, 8.0, 8.0, 8.0, 10.0], 'quadratic': [[6.0, 2.0, 9.0, 3.0, 8.0, 3.0, 3.0, 2.0, 1.0, 2.0, 2.0, 3.0, 1.0, 4.0, 4.0, 2.0, 10.0, 9.0, 7.0, 9.0, 4.0, 2.0, 2.0, 10.0, 3.0, 1.0, 6.0, 5.0, 1.0, 3.0, 5.0, 1.0], [2.0, 5.0, 3.0, 4.0, 1.0, 7.0, 10.0, 5.0, 2.0, 3.0, 1.0, 2.0, 9.0, 4.0, 6.0, 7.0, 8.0, 7.0, 3.0, 10.0, 1.0, 3.0, 6.0, 9.0, 1.0, 10.0, 7.0, 9.0, 5.0, 4.0, 10.0, 1.0], [9.0, 3.0, 4.0, 3.0, 8.0, 8.0, 9.0, 8.0, 6.0, 3.0, 4.0, 1.0, 2.0, 5.0, 10.0, 8.0, 9.0, 2.0, 5.0, 9.0, 5.0, 2.0, 5.0, 2.0, 7.0, 4.0, 8.0, 4.0, 10.0, 2.0, 10.0, 2.0], [3.0, 4.0, 3.0, 5.0, 6.0, 2.0, 7.0, 2.0, 3.0, 1.0, 10.0, 5.0, 3.0, 5.0, 2.0, 3.0, 10.0, 1.0, 3.0, 7.0, 10.0, 5.0, 4.0, 5.0, 6.0, 9.0, 3.0, 8.0, 3.0, 5.0, 3.0, 8.0], [8.0, 1.0, 8.0, 6.0, 8.0, 3.0, 1.0, 2.0, 3.0, 6.0, 1.0, 8.0, 10.0, 2.0, 5.0, 9.0, 7.0, 2.0, 1.0, 5.0, 5.0, 9.0, 3.0, 5.0, 4.0, 5.0, 8.0, 10.0, 5.0, 9.0, 2.0, 9.0], [3.0, 7.0, 8.0, 2.0, 3.0, 7.0, 9.0, 7.0, 7.0, 1.0, 3.0, 4.0, 3.0, 5.0, 10.0, 7.0, 9.0, 1.0, 8.0, 4.0, 7.0, 6.0, 5.0, 1.0, 6.0, 5.0, 3.0, 2.0, 3.0, 8.0, 8.0, 3.0], [3.0, 10.0, 9.0, 7.0, 1.0, 9.0, 6.0, 10.0, 3.0, 1.0, 4.0, 1.0, 2.0, 7.0, 6.0, 3.0, 5.0, 10.0, 6.0, 8.0, 6.0, 1.0, 6.0, 4.0, 5.0, 4.0, 8.0, 7.0, 8.0, 8.0, 4.0, 3.0], [2.0, 5.0, 8.0, 2.0, 2.0, 7.0, 10.0, 3.0, 9.0, 9.0, 9.0, 9.0, 8.0, 6.0, 2.0, 6.0, 5.0, 9.0, 7.0, 6.0, 1.0, 2.0, 5.0, 9.0, 6.0, 2.0, 6.0, 5.0, 5.0, 1.0, 10.0, 4.0], [1.0, 2.0, 6.0, 3.0, 3.0, 7.0, 3.0, 9.0, 8.0, 8.0, 6.0, 10.0, 7.0, 3.0, 7.0, 10.0, 6.0, 10.0, 2.0, 6.0, 10.0, 7.0, 4.0, 4.0, 2.0, 10.0, 4.0, 4.0, 7.0, 10.0, 7.0, 9.0], [2.0, 3.0, 3.0, 1.0, 6.0, 1.0, 1.0, 9.0, 8.0, 2.0, 8.0, 5.0, 7.0, 10.0, 8.0, 1.0, 10.0, 6.0, 1.0, 5.0, 2.0, 2.0, 2.0, 10.0, 6.0, 5.0, 10.0, 5.0, 3.0, 9.0, 3.0, 10.0], [2.0, 1.0, 4.0, 10.0, 1.0, 3.0, 4.0, 9.0, 6.0, 8.0, 2.0, 3.0, 4.0, 5.0, 3.0, 3.0, 10.0, 8.0, 2.0, 6.0, 1.0, 7.0, 5.0, 1.0, 6.0, 3.0, 3.0, 5.0, 8.0, 5.0, 2.0, 8.0], [3.0, 2.0, 1.0, 5.0, 8.0, 4.0, 1.0, 9.0, 10.0, 5.0, 3.0, 1.0, 8.0, 2.0, 8.0, 5.0, 9.0, 9.0, 6.0, 4.0, 8.0, 1.0, 6.0, 2.0, 2.0, 7.0, 6.0, 8.0, 7.0, 4.0, 7.0, 9.0], [1.0, 9.0, 2.0, 3.0, 10.0, 3.0, 2.0, 8.0, 7.0, 7.0, 4.0, 8.0, 8.0, 9.0, 1.0, 7.0, 7.0, 2.0, 5.0, 6.0, 5.0, 3.0, 10.0, 3.0, 10.0, 5.0, 3.0, 3.0, 7.0, 5.0, 7.0, 5.0], [4.0, 4.0, 5.0, 5.0, 2.0, 5.0, 7.0, 6.0, 3.0, 10.0, 5.0, 2.0, 9.0, 2.0, 5.0, 10.0, 10.0, 1.0, 3.0, 8.0, 8.0, 10.0, 1.0, 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2.0}, {'var_i': 31, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 31, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 'Q', 'to': 'A', 'var_index': 0}, {'from': 'Q', 'to': 'E', 'var_index': 1}, {'from': 'Q', 'to': 'I', 'var_index': 2}, {'from': 'Q', 'to': 'M', 'var_index': 3}, {'from': 'D', 'to': 'R', 'var_index': 4}, {'from': 'H', 'to': 'R', 'var_index': 5}, {'from': 'L', 'to': 'R', 'var_index': 6}, {'from': 'P', 'to': 'R', 'var_index': 7}, {'from': 'A', 'to': 'B', 'var_index': 8}, {'from': 'A', 'to': 'E', 'var_index': 9}, {'from': 'B', 'to': 'C', 'var_index': 10}, {'from': 'B', 'to': 'F', 'var_index': 11}, {'from': 'C', 'to': 'D', 'var_index': 12}, {'from': 'C', 'to': 'G', 'var_index': 13}, {'from': 'D', 'to': 'H', 'var_index': 14}, {'from': 'E', 'to': 'F', 'var_index': 15}, {'from': 'E', 'to': 'I', 'var_index': 16}, {'from': 'F', 'to': 'G', 'var_index': 17}, {'from': 'F', 'to': 'J', 'var_index': 18}, {'from': 'G', 'to': 'H', 'var_index': 19}, {'from': 'G', 'to': 'K', 'var_index': 20}, {'from': 'H', 'to': 'L', 'var_index': 21}, {'from': 'I', 'to': 'J', 'var_index': 22}, {'from': 'I', 'to': 'M', 'var_index': 23}, {'from': 'J', 'to': 'K', 'var_index': 24}, {'from': 'J', 'to': 'N', 'var_index': 25}, {'from': 'K', 'to': 'L', 'var_index': 26}, {'from': 'K', 'to': 'O', 'var_index': 27}, {'from': 'L', 'to': 'P', 'var_index': 28}, {'from': 'M', 'to': 'N', 'var_index': 29}, {'from': 'N', 'to': 'O', 'var_index': 30}, {'from': 'O', 'to': 'P', 'var_index': 31}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R'}}","['Q', 'A', 'B', 'C', 'D', 'R']",10,csv,names
QSPP,QSPP,"I’m the build engineer trying to stitch together a single chain of build steps from the root module to the final artifact, following every dependency in the right direction. The trick is that every step has its own compile time plus a little overhead whenever it runs, and certain pairs of steps cause extra cache-miss slowdowns if both of them end up in the chain (sometimes the slowdown depends on which one comes before the other). The whole point is to make the total build finish as fast as possible by picking one valid, dependency-respecting chain and adding up the per-step times, the per-step overheads, and any pairwise penalties that occur. Nothing in the chain can be skipped or duplicated — it has to be one continuous route from source to target. The concrete build graph and the exact times and penalties are shown below.

The concrete build graph below has 24 modules and 65 dependency edges; the modules are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. I start at 22 and must end at 23.

| dependency_from_module | dependency_to_module | build_step_id |
|---|---|---|
| 22 | 0 | 0 |
| 22 | 1 | 1 |
| 22 | 2 | 2 |
| 22 | 3 | 3 |
| 22 | 4 | 4 |
| 22 | 5 | 5 |
| 22 | 6 | 6 |
| 22 | 7 | 7 |
| 22 | 8 | 8 |
| 22 | 9 | 9 |
| 22 | 10 | 10 |
| 22 | 11 | 11 |
| 22 | 12 | 12 |
| 22 | 13 | 13 |
| 22 | 14 | 14 |
| 22 | 15 | 15 |
| 22 | 16 | 16 |
| 22 | 17 | 17 |
| 22 | 18 | 18 |
| 22 | 19 | 19 |
| 22 | 20 | 20 |
| 22 | 21 | 21 |
| 0 | 23 | 22 |
| 1 | 23 | 23 |
| 2 | 23 | 24 |
| 3 | 23 | 25 |
| 4 | 23 | 26 |
| 5 | 23 | 27 |
| 6 | 23 | 28 |
| 7 | 23 | 29 |
| 8 | 23 | 30 |
| 9 | 23 | 31 |
| 10 | 23 | 32 |
| 11 | 23 | 33 |
| 12 | 23 | 34 |
| 13 | 23 | 35 |
| 14 | 23 | 36 |
| 15 | 23 | 37 |
| 16 | 23 | 38 |
| 17 | 23 | 39 |
| 18 | 23 | 40 |
| 19 | 23 | 41 |
| 20 | 23 | 42 |
| 21 | 23 | 43 |
| 0 | 1 | 44 |
| 1 | 2 | 45 |
| 2 | 3 | 46 |
| 3 | 4 | 47 |
| 4 | 5 | 48 |
| 5 | 6 | 49 |
| 6 | 7 | 50 |
| 7 | 8 | 51 |
| 8 | 9 | 52 |
| 9 | 10 | 53 |
| 10 | 11 | 54 |
| 11 | 12 | 55 |
| 12 | 13 | 56 |
| 13 | 14 | 57 |
| 14 | 15 | 58 |
| 15 | 16 | 59 |
| 16 | 17 | 60 |
| 17 | 18 | 61 |
| 18 | 19 | 62 |
| 19 | 20 | 63 |
| 20 | 21 | 64 |

| build_step_id_ref | step_compile_time |
|---|---|
| 0 | 5.0 |
| 1 | 7.0 |
| 2 | 8.0 |
| 3 | 9.0 |
| 4 | 1.0 |
| 5 | 2.0 |
| 6 | 5.0 |
| 7 | 2.0 |
| 8 | 3.0 |
| 9 | 8.0 |
| 10 | 1.0 |
| 11 | 6.0 |
| 12 | 4.0 |
| 13 | 9.0 |
| 14 | 3.0 |
| 15 | 3.0 |
| 16 | 6.0 |
| 17 | 3.0 |
| 18 | 6.0 |
| 19 | 9.0 |
| 20 | 1.0 |
| 21 | 3.0 |
| 22 | 6.0 |
| 23 | 10.0 |
| 24 | 1.0 |
| 25 | 6.0 |
| 26 | 6.0 |
| 27 | 9.0 |
| 28 | 6.0 |
| 29 | 8.0 |
| 30 | 6.0 |
| 31 | 8.0 |
| 32 | 1.0 |
| 33 | 1.0 |
| 34 | 4.0 |
| 35 | 3.0 |
| 36 | 4.0 |
| 37 | 10.0 |
| 38 | 4.0 |
| 39 | 2.0 |
| 40 | 2.0 |
| 41 | 1.0 |
| 42 | 4.0 |
| 43 | 6.0 |
| 44 | 2.0 |
| 45 | 7.0 |
| 46 | 9.0 |
| 47 | 9.0 |
| 48 | 1.0 |
| 49 | 8.0 |
| 50 | 6.0 |
| 51 | 8.0 |
| 52 | 2.0 |
| 53 | 9.0 |
| 54 | 4.0 |
| 55 | 4.0 |
| 56 | 5.0 |
| 57 | 3.0 |
| 58 | 3.0 |
| 59 | 5.0 |
| 60 | 10.0 |
| 61 | 9.0 |
| 62 | 3.0 |
| 63 | 1.0 |
| 64 | 5.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (step_i_id, step_j_id). If two build_steps with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| step_i_id\step_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 9.0 | 3.0 | 2.0 | 7.0 | 1.0 | 10.0 | 4.0 | 4.0 | 2.0 | 5.0 | 3.0 | 10.0 | 1.0 | 8.0 | 7.0 | 6.0 | 7.0 | 8.0 | 9.0 | 9.0 | 7.0 | 2.0 | 5.0 | 8.0 | 8.0 | 4.0 | 7.0 | 5.0 | 1.0 | 2.0 | 4.0 | 1.0 | 6.0 | 2.0 | 1.0 | 1.0 | 10.0 | 5.0 | 6.0 | 9.0 | 5.0 | 2.0 | 4.0 | 8.0 | 6.0 | 9.0 | 2.0 | 5.0 | 10.0 | 6.0 | 5.0 | 6.0 | 8.0 | 7.0 | 1.0 | 8.0 | 4.0 | 8.0 | 8.0 | 3.0 | 6.0 | 7.0 | 6.0 | 10.0 |
| 1 | 9.0 | 6.0 | 2.0 | 5.0 | 7.0 | 3.0 | 7.0 | 9.0 | 1.0 | 8.0 | 5.0 | 10.0 | 3.0 | 1.0 | 7.0 | 4.0 | 1.0 | 7.0 | 1.0 | 6.0 | 9.0 | 8.0 | 7.0 | 3.0 | 5.0 | 3.0 | 1.0 | 9.0 | 9.0 | 9.0 | 3.0 | 7.0 | 4.0 | 2.0 | 5.0 | 5.0 | 3.0 | 5.0 | 3.0 | 4.0 | 9.0 | 2.0 | 7.0 | 5.0 | 4.0 | 8.0 | 2.0 | 7.0 | 3.0 | 6.0 | 1.0 | 1.0 | 5.0 | 3.0 | 8.0 | 9.0 | 10.0 | 2.0 | 2.0 | 9.0 | 3.0 | 10.0 | 3.0 | 10.0 | 6.0 |
| 2 | 3.0 | 2.0 | 5.0 | 6.0 | 4.0 | 5.0 | 9.0 | 5.0 | 9.0 | 8.0 | 10.0 | 6.0 | 6.0 | 9.0 | 7.0 | 10.0 | 6.0 | 5.0 | 4.0 | 4.0 | 9.0 | 6.0 | 9.0 | 6.0 | 7.0 | 1.0 | 2.0 | 1.0 | 3.0 | 5.0 | 1.0 | 8.0 | 6.0 | 4.0 | 8.0 | 8.0 | 5.0 | 1.0 | 5.0 | 1.0 | 8.0 | 4.0 | 4.0 | 4.0 | 7.0 | 9.0 | 5.0 | 6.0 | 2.0 | 9.0 | 8.0 | 3.0 | 3.0 | 8.0 | 2.0 | 10.0 | 4.0 | 5.0 | 5.0 | 4.0 | 1.0 | 8.0 | 4.0 | 2.0 | 2.0 |
| 3 | 2.0 | 5.0 | 6.0 | 5.0 | 6.0 | 3.0 | 9.0 | 7.0 | 1.0 | 5.0 | 7.0 | 2.0 | 7.0 | 3.0 | 7.0 | 3.0 | 4.0 | 4.0 | 3.0 | 10.0 | 10.0 | 9.0 | 9.0 | 8.0 | 4.0 | 6.0 | 6.0 | 3.0 | 1.0 | 9.0 | 9.0 | 8.0 | 9.0 | 10.0 | 8.0 | 9.0 | 4.0 | 8.0 | 2.0 | 6.0 | 2.0 | 1.0 | 6.0 | 8.0 | 6.0 | 8.0 | 2.0 | 10.0 | 1.0 | 1.0 | 10.0 | 5.0 | 6.0 | 2.0 | 8.0 | 2.0 | 2.0 | 8.0 | 5.0 | 2.0 | 8.0 | 7.0 | 5.0 | 2.0 | 3.0 |
| 4 | 7.0 | 7.0 | 4.0 | 6.0 | 3.0 | 7.0 | 1.0 | 1.0 | 7.0 | 8.0 | 4.0 | 7.0 | 3.0 | 4.0 | 1.0 | 6.0 | 7.0 | 7.0 | 2.0 | 6.0 | 7.0 | 7.0 | 7.0 | 1.0 | 8.0 | 6.0 | 10.0 | 7.0 | 9.0 | 8.0 | 6.0 | 10.0 | 10.0 | 4.0 | 8.0 | 5.0 | 2.0 | 5.0 | 1.0 | 5.0 | 10.0 | 9.0 | 6.0 | 2.0 | 1.0 | 2.0 | 9.0 | 5.0 | 9.0 | 5.0 | 6.0 | 1.0 | 10.0 | 6.0 | 10.0 | 4.0 | 7.0 | 5.0 | 9.0 | 5.0 | 9.0 | 4.0 | 6.0 | 9.0 | 6.0 |
| 5 | 1.0 | 3.0 | 5.0 | 3.0 | 7.0 | 9.0 | 1.0 | 3.0 | 6.0 | 1.0 | 4.0 | 6.0 | 9.0 | 10.0 | 10.0 | 7.0 | 3.0 | 7.0 | 7.0 | 2.0 | 7.0 | 4.0 | 1.0 | 5.0 | 10.0 | 2.0 | 1.0 | 1.0 | 5.0 | 9.0 | 6.0 | 7.0 | 1.0 | 8.0 | 10.0 | 9.0 | 6.0 | 7.0 | 6.0 | 2.0 | 4.0 | 6.0 | 6.0 | 5.0 | 7.0 | 8.0 | 2.0 | 3.0 | 7.0 | 9.0 | 3.0 | 8.0 | 9.0 | 8.0 | 2.0 | 10.0 | 6.0 | 6.0 | 8.0 | 7.0 | 1.0 | 2.0 | 5.0 | 5.0 | 2.0 |
| 6 | 10.0 | 7.0 | 9.0 | 9.0 | 1.0 | 1.0 | 2.0 | 7.0 | 4.0 | 5.0 | 2.0 | 7.0 | 6.0 | 5.0 | 8.0 | 7.0 | 7.0 | 8.0 | 10.0 | 8.0 | 7.0 | 8.0 | 1.0 | 3.0 | 10.0 | 6.0 | 6.0 | 8.0 | 2.0 | 9.0 | 7.0 | 10.0 | 4.0 | 3.0 | 2.0 | 10.0 | 8.0 | 4.0 | 5.0 | 7.0 | 10.0 | 5.0 | 3.0 | 10.0 | 8.0 | 3.0 | 7.0 | 5.0 | 7.0 | 5.0 | 4.0 | 3.0 | 4.0 | 8.0 | 10.0 | 9.0 | 6.0 | 7.0 | 2.0 | 10.0 | 9.0 | 6.0 | 7.0 | 6.0 | 10.0 |
| 7 | 4.0 | 9.0 | 5.0 | 7.0 | 1.0 | 3.0 | 7.0 | 5.0 | 5.0 | 8.0 | 1.0 | 8.0 | 6.0 | 10.0 | 2.0 | 1.0 | 5.0 | 5.0 | 10.0 | 7.0 | 9.0 | 7.0 | 4.0 | 8.0 | 4.0 | 5.0 | 1.0 | 4.0 | 4.0 | 1.0 | 7.0 | 7.0 | 8.0 | 7.0 | 9.0 | 7.0 | 3.0 | 9.0 | 2.0 | 9.0 | 9.0 | 5.0 | 9.0 | 1.0 | 3.0 | 8.0 | 7.0 | 2.0 | 4.0 | 10.0 | 3.0 | 6.0 | 5.0 | 9.0 | 10.0 | 8.0 | 2.0 | 2.0 | 8.0 | 7.0 | 5.0 | 4.0 | 4.0 | 5.0 | 1.0 |
| 8 | 4.0 | 1.0 | 9.0 | 1.0 | 7.0 | 6.0 | 4.0 | 5.0 | 9.0 | 10.0 | 9.0 | 9.0 | 3.0 | 6.0 | 3.0 | 8.0 | 7.0 | 9.0 | 10.0 | 6.0 | 4.0 | 1.0 | 3.0 | 7.0 | 6.0 | 10.0 | 1.0 | 4.0 | 9.0 | 5.0 | 4.0 | 3.0 | 8.0 | 6.0 | 6.0 | 6.0 | 5.0 | 9.0 | 10.0 | 8.0 | 7.0 | 6.0 | 1.0 | 7.0 | 1.0 | 7.0 | 5.0 | 7.0 | 7.0 | 6.0 | 10.0 | 1.0 | 6.0 | 9.0 | 3.0 | 6.0 | 5.0 | 9.0 | 1.0 | 7.0 | 9.0 | 5.0 | 9.0 | 10.0 | 1.0 |
| 9 | 2.0 | 8.0 | 8.0 | 5.0 | 8.0 | 1.0 | 5.0 | 8.0 | 10.0 | 5.0 | 4.0 | 6.0 | 7.0 | 6.0 | 1.0 | 2.0 | 1.0 | 6.0 | 2.0 | 10.0 | 7.0 | 4.0 | 8.0 | 10.0 | 7.0 | 5.0 | 4.0 | 3.0 | 10.0 | 3.0 | 2.0 | 10.0 | 10.0 | 6.0 | 6.0 | 5.0 | 2.0 | 8.0 | 5.0 | 10.0 | 2.0 | 10.0 | 7.0 | 1.0 | 6.0 | 5.0 | 8.0 | 3.0 | 8.0 | 7.0 | 5.0 | 8.0 | 7.0 | 3.0 | 9.0 | 3.0 | 9.0 | 8.0 | 2.0 | 4.0 | 7.0 | 7.0 | 2.0 | 4.0 | 3.0 |
| 10 | 5.0 | 5.0 | 10.0 | 7.0 | 4.0 | 4.0 | 2.0 | 1.0 | 9.0 | 4.0 | 1.0 | 2.0 | 8.0 | 4.0 | 2.0 | 9.0 | 1.0 | 3.0 | 1.0 | 5.0 | 6.0 | 4.0 | 9.0 | 10.0 | 3.0 | 5.0 | 2.0 | 6.0 | 8.0 | 7.0 | 8.0 | 4.0 | 4.0 | 3.0 | 5.0 | 3.0 | 5.0 | 3.0 | 6.0 | 9.0 | 1.0 | 7.0 | 6.0 | 6.0 | 10.0 | 4.0 | 9.0 | 4.0 | 3.0 | 6.0 | 10.0 | 2.0 | 7.0 | 3.0 | 3.0 | 1.0 | 5.0 | 4.0 | 7.0 | 6.0 | 4.0 | 9.0 | 6.0 | 1.0 | 1.0 |
| 11 | 3.0 | 10.0 | 6.0 | 2.0 | 7.0 | 6.0 | 7.0 | 8.0 | 9.0 | 6.0 | 2.0 | 7.0 | 9.0 | 3.0 | 3.0 | 4.0 | 6.0 | 7.0 | 5.0 | 3.0 | 9.0 | 2.0 | 2.0 | 9.0 | 7.0 | 2.0 | 1.0 | 6.0 | 10.0 | 8.0 | 2.0 | 7.0 | 6.0 | 8.0 | 9.0 | 7.0 | 1.0 | 4.0 | 2.0 | 3.0 | 6.0 | 6.0 | 9.0 | 1.0 | 5.0 | 5.0 | 4.0 | 5.0 | 10.0 | 2.0 | 7.0 | 2.0 | 8.0 | 3.0 | 6.0 | 6.0 | 3.0 | 3.0 | 3.0 | 3.0 | 10.0 | 1.0 | 6.0 | 7.0 | 2.0 |
| 12 | 10.0 | 3.0 | 6.0 | 7.0 | 3.0 | 9.0 | 6.0 | 6.0 | 3.0 | 7.0 | 8.0 | 9.0 | 1.0 | 7.0 | 1.0 | 5.0 | 6.0 | 1.0 | 9.0 | 3.0 | 3.0 | 1.0 | 9.0 | 10.0 | 7.0 | 7.0 | 4.0 | 2.0 | 6.0 | 9.0 | 9.0 | 10.0 | 5.0 | 8.0 | 8.0 | 4.0 | 6.0 | 2.0 | 2.0 | 7.0 | 7.0 | 3.0 | 1.0 | 1.0 | 10.0 | 2.0 | 4.0 | 7.0 | 3.0 | 2.0 | 1.0 | 3.0 | 3.0 | 2.0 | 3.0 | 2.0 | 1.0 | 1.0 | 8.0 | 7.0 | 10.0 | 7.0 | 3.0 | 10.0 | 10.0 |
| 13 | 1.0 | 1.0 | 9.0 | 3.0 | 4.0 | 10.0 | 5.0 | 10.0 | 6.0 | 6.0 | 4.0 | 3.0 | 7.0 | 8.0 | 6.0 | 6.0 | 10.0 | 7.0 | 3.0 | 7.0 | 3.0 | 2.0 | 8.0 | 4.0 | 5.0 | 7.0 | 7.0 | 7.0 | 4.0 | 3.0 | 4.0 | 7.0 | 5.0 | 8.0 | 9.0 | 3.0 | 5.0 | 5.0 | 7.0 | 3.0 | 2.0 | 5.0 | 6.0 | 8.0 | 2.0 | 7.0 | 7.0 | 9.0 | 5.0 | 3.0 | 2.0 | 7.0 | 1.0 | 1.0 | 1.0 | 2.0 | 4.0 | 8.0 | 8.0 | 10.0 | 5.0 | 9.0 | 8.0 | 10.0 | 6.0 |
| 14 | 8.0 | 7.0 | 7.0 | 7.0 | 1.0 | 10.0 | 8.0 | 2.0 | 3.0 | 1.0 | 2.0 | 3.0 | 1.0 | 6.0 | 2.0 | 10.0 | 7.0 | 5.0 | 9.0 | 9.0 | 10.0 | 2.0 | 1.0 | 1.0 | 7.0 | 2.0 | 5.0 | 2.0 | 1.0 | 7.0 | 8.0 | 1.0 | 2.0 | 1.0 | 6.0 | 8.0 | 8.0 | 7.0 | 5.0 | 5.0 | 4.0 | 4.0 | 5.0 | 9.0 | 8.0 | 7.0 | 8.0 | 8.0 | 5.0 | 8.0 | 6.0 | 4.0 | 6.0 | 10.0 | 1.0 | 6.0 | 6.0 | 7.0 | 1.0 | 6.0 | 6.0 | 7.0 | 7.0 | 9.0 | 6.0 |
| 15 | 7.0 | 4.0 | 10.0 | 3.0 | 6.0 | 7.0 | 7.0 | 1.0 | 8.0 | 2.0 | 9.0 | 4.0 | 5.0 | 6.0 | 10.0 | 3.0 | 5.0 | 9.0 | 2.0 | 10.0 | 5.0 | 2.0 | 8.0 | 8.0 | 4.0 | 10.0 | 5.0 | 10.0 | 3.0 | 2.0 | 5.0 | 6.0 | 4.0 | 9.0 | 9.0 | 5.0 | 9.0 | 7.0 | 3.0 | 5.0 | 5.0 | 6.0 | 3.0 | 8.0 | 2.0 | 6.0 | 4.0 | 10.0 | 5.0 | 3.0 | 10.0 | 4.0 | 6.0 | 9.0 | 9.0 | 3.0 | 6.0 | 10.0 | 7.0 | 10.0 | 9.0 | 4.0 | 3.0 | 2.0 | 2.0 |
| 16 | 6.0 | 1.0 | 6.0 | 4.0 | 7.0 | 3.0 | 7.0 | 5.0 | 7.0 | 1.0 | 1.0 | 6.0 | 6.0 | 10.0 | 7.0 | 5.0 | 4.0 | 6.0 | 1.0 | 5.0 | 8.0 | 4.0 | 5.0 | 8.0 | 9.0 | 2.0 | 4.0 | 4.0 | 2.0 | 8.0 | 7.0 | 4.0 | 2.0 | 6.0 | 10.0 | 9.0 | 10.0 | 2.0 | 9.0 | 4.0 | 4.0 | 9.0 | 6.0 | 6.0 | 7.0 | 3.0 | 10.0 | 10.0 | 5.0 | 4.0 | 9.0 | 10.0 | 2.0 | 7.0 | 6.0 | 5.0 | 4.0 | 6.0 | 1.0 | 4.0 | 4.0 | 1.0 | 1.0 | 8.0 | 3.0 |
| 17 | 7.0 | 7.0 | 5.0 | 4.0 | 7.0 | 7.0 | 8.0 | 5.0 | 9.0 | 6.0 | 3.0 | 7.0 | 1.0 | 7.0 | 5.0 | 9.0 | 6.0 | 10.0 | 9.0 | 3.0 | 9.0 | 8.0 | 7.0 | 8.0 | 7.0 | 3.0 | 2.0 | 10.0 | 3.0 | 2.0 | 6.0 | 10.0 | 2.0 | 2.0 | 4.0 | 7.0 | 5.0 | 9.0 | 8.0 | 10.0 | 9.0 | 7.0 | 4.0 | 2.0 | 7.0 | 9.0 | 6.0 | 4.0 | 3.0 | 5.0 | 1.0 | 7.0 | 5.0 | 2.0 | 5.0 | 2.0 | 8.0 | 1.0 | 6.0 | 10.0 | 6.0 | 9.0 | 1.0 | 4.0 | 1.0 |
| 18 | 8.0 | 1.0 | 4.0 | 3.0 | 2.0 | 7.0 | 10.0 | 10.0 | 10.0 | 2.0 | 1.0 | 5.0 | 9.0 | 3.0 | 9.0 | 2.0 | 1.0 | 9.0 | 1.0 | 7.0 | 4.0 | 5.0 | 6.0 | 1.0 | 3.0 | 8.0 | 9.0 | 5.0 | 7.0 | 2.0 | 5.0 | 5.0 | 1.0 | 10.0 | 5.0 | 3.0 | 10.0 | 5.0 | 9.0 | 9.0 | 2.0 | 1.0 | 5.0 | 10.0 | 1.0 | 9.0 | 1.0 | 9.0 | 4.0 | 1.0 | 9.0 | 3.0 | 8.0 | 5.0 | 1.0 | 10.0 | 6.0 | 6.0 | 3.0 | 10.0 | 2.0 | 9.0 | 10.0 | 3.0 | 1.0 |
| 19 | 9.0 | 6.0 | 4.0 | 10.0 | 6.0 | 2.0 | 8.0 | 7.0 | 6.0 | 10.0 | 5.0 | 3.0 | 3.0 | 7.0 | 9.0 | 10.0 | 5.0 | 3.0 | 7.0 | 8.0 | 5.0 | 10.0 | 3.0 | 10.0 | 6.0 | 3.0 | 7.0 | 8.0 | 6.0 | 2.0 | 5.0 | 4.0 | 8.0 | 6.0 | 9.0 | 2.0 | 4.0 | 1.0 | 8.0 | 6.0 | 6.0 | 1.0 | 1.0 | 1.0 | 1.0 | 3.0 | 7.0 | 2.0 | 3.0 | 8.0 | 10.0 | 1.0 | 10.0 | 8.0 | 10.0 | 5.0 | 4.0 | 2.0 | 4.0 | 6.0 | 1.0 | 1.0 | 4.0 | 2.0 | 4.0 |
| 20 | 9.0 | 9.0 | 9.0 | 10.0 | 7.0 | 7.0 | 7.0 | 9.0 | 4.0 | 7.0 | 6.0 | 9.0 | 3.0 | 3.0 | 10.0 | 5.0 | 8.0 | 9.0 | 4.0 | 5.0 | 8.0 | 10.0 | 9.0 | 1.0 | 3.0 | 1.0 | 3.0 | 5.0 | 1.0 | 2.0 | 2.0 | 3.0 | 8.0 | 7.0 | 3.0 | 4.0 | 3.0 | 6.0 | 6.0 | 8.0 | 3.0 | 7.0 | 9.0 | 4.0 | 2.0 | 3.0 | 4.0 | 9.0 | 10.0 | 3.0 | 1.0 | 6.0 | 5.0 | 1.0 | 8.0 | 6.0 | 5.0 | 3.0 | 4.0 | 7.0 | 5.0 | 10.0 | 3.0 | 5.0 | 5.0 |
| 21 | 7.0 | 8.0 | 6.0 | 9.0 | 7.0 | 4.0 | 8.0 | 7.0 | 1.0 | 4.0 | 4.0 | 2.0 | 1.0 | 2.0 | 2.0 | 2.0 | 4.0 | 8.0 | 5.0 | 10.0 | 10.0 | 8.0 | 10.0 | 3.0 | 1.0 | 6.0 | 2.0 | 6.0 | 3.0 | 6.0 | 2.0 | 4.0 | 7.0 | 6.0 | 6.0 | 6.0 | 9.0 | 1.0 | 2.0 | 3.0 | 10.0 | 8.0 | 6.0 | 6.0 | 10.0 | 10.0 | 9.0 | 1.0 | 4.0 | 10.0 | 7.0 | 10.0 | 1.0 | 3.0 | 3.0 | 6.0 | 3.0 | 8.0 | 2.0 | 4.0 | 8.0 | 5.0 | 3.0 | 7.0 | 2.0 |
| 22 | 2.0 | 7.0 | 9.0 | 9.0 | 7.0 | 1.0 | 1.0 | 4.0 | 3.0 | 8.0 | 9.0 | 2.0 | 9.0 | 8.0 | 1.0 | 8.0 | 5.0 | 7.0 | 6.0 | 3.0 | 9.0 | 10.0 | 1.0 | 4.0 | 3.0 | 1.0 | 4.0 | 5.0 | 4.0 | 5.0 | 3.0 | 5.0 | 4.0 | 8.0 | 5.0 | 8.0 | 4.0 | 3.0 | 10.0 | 9.0 | 5.0 | 1.0 | 9.0 | 1.0 | 7.0 | 10.0 | 10.0 | 7.0 | 9.0 | 9.0 | 5.0 | 3.0 | 5.0 | 10.0 | 8.0 | 5.0 | 7.0 | 8.0 | 3.0 | 1.0 | 2.0 | 4.0 | 7.0 | 3.0 | 8.0 |
| 23 | 5.0 | 3.0 | 6.0 | 8.0 | 1.0 | 5.0 | 3.0 | 8.0 | 7.0 | 10.0 | 10.0 | 9.0 | 10.0 | 4.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 10.0 | 1.0 | 3.0 | 4.0 | 10.0 | 1.0 | 9.0 | 6.0 | 9.0 | 2.0 | 9.0 | 9.0 | 1.0 | 5.0 | 5.0 | 9.0 | 10.0 | 5.0 | 1.0 | 4.0 | 6.0 | 2.0 | 4.0 | 9.0 | 6.0 | 8.0 | 8.0 | 6.0 | 2.0 | 6.0 | 3.0 | 9.0 | 2.0 | 10.0 | 2.0 | 10.0 | 9.0 | 7.0 | 5.0 | 1.0 | 2.0 | 1.0 | 3.0 | 1.0 | 2.0 | 6.0 |
| 24 | 8.0 | 5.0 | 7.0 | 4.0 | 8.0 | 10.0 | 10.0 | 4.0 | 6.0 | 7.0 | 3.0 | 7.0 | 7.0 | 5.0 | 7.0 | 4.0 | 9.0 | 7.0 | 3.0 | 6.0 | 3.0 | 1.0 | 3.0 | 1.0 | 10.0 | 2.0 | 4.0 | 7.0 | 8.0 | 3.0 | 3.0 | 10.0 | 4.0 | 9.0 | 2.0 | 5.0 | 8.0 | 8.0 | 1.0 | 6.0 | 10.0 | 3.0 | 4.0 | 8.0 | 4.0 | 3.0 | 9.0 | 10.0 | 2.0 | 9.0 | 3.0 | 9.0 | 3.0 | 2.0 | 8.0 | 6.0 | 3.0 | 10.0 | 1.0 | 5.0 | 2.0 | 3.0 | 6.0 | 9.0 | 9.0 |
| 25 | 8.0 | 3.0 | 1.0 | 6.0 | 6.0 | 2.0 | 6.0 | 5.0 | 10.0 | 5.0 | 5.0 | 2.0 | 7.0 | 7.0 | 2.0 | 10.0 | 2.0 | 3.0 | 8.0 | 3.0 | 1.0 | 6.0 | 1.0 | 9.0 | 2.0 | 10.0 | 1.0 | 4.0 | 7.0 | 5.0 | 10.0 | 6.0 | 2.0 | 10.0 | 9.0 | 8.0 | 6.0 | 9.0 | 6.0 | 7.0 | 9.0 | 7.0 | 7.0 | 9.0 | 6.0 | 9.0 | 7.0 | 6.0 | 8.0 | 8.0 | 9.0 | 8.0 | 7.0 | 6.0 | 4.0 | 7.0 | 10.0 | 3.0 | 7.0 | 8.0 | 6.0 | 7.0 | 8.0 | 10.0 | 10.0 |
| 26 | 4.0 | 1.0 | 2.0 | 6.0 | 10.0 | 1.0 | 6.0 | 1.0 | 1.0 | 4.0 | 2.0 | 1.0 | 4.0 | 7.0 | 5.0 | 5.0 | 4.0 | 2.0 | 9.0 | 7.0 | 3.0 | 2.0 | 4.0 | 6.0 | 4.0 | 1.0 | 3.0 | 9.0 | 4.0 | 7.0 | 8.0 | 10.0 | 6.0 | 5.0 | 5.0 | 8.0 | 2.0 | 1.0 | 7.0 | 9.0 | 8.0 | 5.0 | 10.0 | 6.0 | 2.0 | 3.0 | 9.0 | 6.0 | 1.0 | 7.0 | 8.0 | 4.0 | 8.0 | 9.0 | 2.0 | 7.0 | 2.0 | 6.0 | 8.0 | 5.0 | 6.0 | 10.0 | 4.0 | 7.0 | 10.0 |
| 27 | 7.0 | 9.0 | 1.0 | 3.0 | 7.0 | 1.0 | 8.0 | 4.0 | 4.0 | 3.0 | 6.0 | 6.0 | 2.0 | 7.0 | 2.0 | 10.0 | 4.0 | 10.0 | 5.0 | 8.0 | 5.0 | 6.0 | 5.0 | 9.0 | 7.0 | 4.0 | 9.0 | 4.0 | 3.0 | 2.0 | 8.0 | 2.0 | 7.0 | 10.0 | 7.0 | 3.0 | 4.0 | 1.0 | 9.0 | 3.0 | 6.0 | 3.0 | 5.0 | 6.0 | 5.0 | 1.0 | 2.0 | 8.0 | 8.0 | 6.0 | 8.0 | 3.0 | 5.0 | 9.0 | 10.0 | 4.0 | 2.0 | 4.0 | 4.0 | 5.0 | 6.0 | 10.0 | 10.0 | 4.0 | 7.0 |
| 28 | 5.0 | 9.0 | 3.0 | 1.0 | 9.0 | 5.0 | 2.0 | 4.0 | 9.0 | 10.0 | 8.0 | 10.0 | 6.0 | 4.0 | 1.0 | 3.0 | 2.0 | 3.0 | 7.0 | 6.0 | 1.0 | 3.0 | 4.0 | 2.0 | 8.0 | 7.0 | 4.0 | 3.0 | 7.0 | 6.0 | 5.0 | 5.0 | 3.0 | 6.0 | 7.0 | 9.0 | 4.0 | 7.0 | 9.0 | 6.0 | 10.0 | 9.0 | 9.0 | 1.0 | 7.0 | 1.0 | 4.0 | 9.0 | 1.0 | 4.0 | 1.0 | 5.0 | 3.0 | 1.0 | 9.0 | 6.0 | 5.0 | 1.0 | 5.0 | 4.0 | 8.0 | 8.0 | 7.0 | 7.0 | 1.0 |
| 29 | 1.0 | 9.0 | 5.0 | 9.0 | 8.0 | 9.0 | 9.0 | 1.0 | 5.0 | 3.0 | 7.0 | 8.0 | 9.0 | 3.0 | 7.0 | 2.0 | 8.0 | 2.0 | 2.0 | 2.0 | 2.0 | 6.0 | 5.0 | 9.0 | 3.0 | 5.0 | 7.0 | 2.0 | 6.0 | 5.0 | 2.0 | 5.0 | 9.0 | 8.0 | 1.0 | 1.0 | 10.0 | 4.0 | 10.0 | 3.0 | 8.0 | 8.0 | 5.0 | 7.0 | 3.0 | 2.0 | 1.0 | 3.0 | 3.0 | 6.0 | 3.0 | 8.0 | 4.0 | 4.0 | 6.0 | 5.0 | 9.0 | 5.0 | 7.0 | 5.0 | 2.0 | 10.0 | 10.0 | 4.0 | 8.0 |
| 30 | 2.0 | 3.0 | 1.0 | 9.0 | 6.0 | 6.0 | 7.0 | 7.0 | 4.0 | 2.0 | 8.0 | 2.0 | 9.0 | 4.0 | 8.0 | 5.0 | 7.0 | 6.0 | 5.0 | 5.0 | 2.0 | 2.0 | 3.0 | 9.0 | 3.0 | 10.0 | 8.0 | 8.0 | 5.0 | 2.0 | 7.0 | 2.0 | 10.0 | 7.0 | 4.0 | 6.0 | 5.0 | 2.0 | 6.0 | 10.0 | 5.0 | 9.0 | 2.0 | 9.0 | 8.0 | 3.0 | 7.0 | 4.0 | 9.0 | 3.0 | 2.0 | 8.0 | 6.0 | 8.0 | 10.0 | 1.0 | 8.0 | 6.0 | 1.0 | 10.0 | 10.0 | 8.0 | 9.0 | 1.0 | 4.0 |
| 31 | 4.0 | 7.0 | 8.0 | 8.0 | 10.0 | 7.0 | 10.0 | 7.0 | 3.0 | 10.0 | 4.0 | 7.0 | 10.0 | 7.0 | 1.0 | 6.0 | 4.0 | 10.0 | 5.0 | 4.0 | 3.0 | 4.0 | 5.0 | 1.0 | 10.0 | 6.0 | 10.0 | 2.0 | 5.0 | 5.0 | 2.0 | 5.0 | 6.0 | 6.0 | 3.0 | 1.0 | 4.0 | 10.0 | 5.0 | 6.0 | 7.0 | 5.0 | 4.0 | 1.0 | 7.0 | 2.0 | 4.0 | 10.0 | 9.0 | 3.0 | 4.0 | 3.0 | 8.0 | 9.0 | 3.0 | 8.0 | 10.0 | 9.0 | 9.0 | 5.0 | 7.0 | 4.0 | 2.0 | 5.0 | 10.0 |
| 32 | 1.0 | 4.0 | 6.0 | 9.0 | 10.0 | 1.0 | 4.0 | 8.0 | 8.0 | 10.0 | 4.0 | 6.0 | 5.0 | 5.0 | 2.0 | 4.0 | 2.0 | 2.0 | 1.0 | 8.0 | 8.0 | 7.0 | 4.0 | 5.0 | 4.0 | 2.0 | 6.0 | 7.0 | 3.0 | 9.0 | 10.0 | 6.0 | 4.0 | 2.0 | 2.0 | 1.0 | 10.0 | 2.0 | 9.0 | 4.0 | 3.0 | 7.0 | 10.0 | 7.0 | 8.0 | 2.0 | 3.0 | 6.0 | 4.0 | 5.0 | 1.0 | 8.0 | 10.0 | 7.0 | 10.0 | 8.0 | 2.0 | 1.0 | 10.0 | 8.0 | 6.0 | 1.0 | 4.0 | 3.0 | 9.0 |
| 33 | 6.0 | 2.0 | 4.0 | 10.0 | 4.0 | 8.0 | 3.0 | 7.0 | 6.0 | 6.0 | 3.0 | 8.0 | 8.0 | 8.0 | 1.0 | 9.0 | 6.0 | 2.0 | 10.0 | 6.0 | 7.0 | 6.0 | 8.0 | 5.0 | 9.0 | 10.0 | 5.0 | 10.0 | 6.0 | 8.0 | 7.0 | 6.0 | 2.0 | 3.0 | 9.0 | 2.0 | 3.0 | 4.0 | 4.0 | 5.0 | 9.0 | 5.0 | 5.0 | 6.0 | 5.0 | 7.0 | 9.0 | 2.0 | 8.0 | 3.0 | 5.0 | 9.0 | 8.0 | 2.0 | 8.0 | 4.0 | 7.0 | 5.0 | 9.0 | 5.0 | 3.0 | 1.0 | 10.0 | 4.0 | 6.0 |
| 34 | 2.0 | 5.0 | 8.0 | 8.0 | 8.0 | 10.0 | 2.0 | 9.0 | 6.0 | 6.0 | 5.0 | 9.0 | 8.0 | 9.0 | 6.0 | 9.0 | 10.0 | 4.0 | 5.0 | 9.0 | 3.0 | 6.0 | 5.0 | 9.0 | 2.0 | 9.0 | 5.0 | 7.0 | 7.0 | 1.0 | 4.0 | 3.0 | 2.0 | 9.0 | 5.0 | 8.0 | 2.0 | 10.0 | 3.0 | 1.0 | 10.0 | 9.0 | 3.0 | 8.0 | 10.0 | 6.0 | 6.0 | 8.0 | 5.0 | 7.0 | 7.0 | 9.0 | 2.0 | 7.0 | 9.0 | 8.0 | 6.0 | 7.0 | 8.0 | 8.0 | 8.0 | 2.0 | 7.0 | 9.0 | 5.0 |
| 35 | 1.0 | 5.0 | 8.0 | 9.0 | 5.0 | 9.0 | 10.0 | 7.0 | 6.0 | 5.0 | 3.0 | 7.0 | 4.0 | 3.0 | 8.0 | 5.0 | 9.0 | 7.0 | 3.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 | 5.0 | 8.0 | 8.0 | 3.0 | 9.0 | 1.0 | 6.0 | 1.0 | 1.0 | 2.0 | 8.0 | 2.0 | 6.0 | 4.0 | 10.0 | 10.0 | 8.0 | 7.0 | 3.0 | 5.0 | 10.0 | 2.0 | 1.0 | 3.0 | 9.0 | 4.0 | 4.0 | 8.0 | 4.0 | 3.0 | 4.0 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 5.0 | 7.0 | 7.0 | 3.0 | 1.0 |
| 36 | 1.0 | 3.0 | 5.0 | 4.0 | 2.0 | 6.0 | 8.0 | 3.0 | 5.0 | 2.0 | 5.0 | 1.0 | 6.0 | 5.0 | 8.0 | 9.0 | 10.0 | 5.0 | 10.0 | 4.0 | 3.0 | 9.0 | 4.0 | 5.0 | 8.0 | 6.0 | 2.0 | 4.0 | 4.0 | 10.0 | 5.0 | 4.0 | 10.0 | 3.0 | 2.0 | 6.0 | 2.0 | 1.0 | 4.0 | 4.0 | 10.0 | 8.0 | 8.0 | 7.0 | 8.0 | 6.0 | 8.0 | 5.0 | 9.0 | 10.0 | 5.0 | 3.0 | 3.0 | 4.0 | 8.0 | 9.0 | 2.0 | 2.0 | 9.0 | 5.0 | 9.0 | 9.0 | 8.0 | 6.0 | 2.0 |
| 37 | 10.0 | 5.0 | 1.0 | 8.0 | 5.0 | 7.0 | 4.0 | 9.0 | 9.0 | 8.0 | 3.0 | 4.0 | 2.0 | 5.0 | 7.0 | 7.0 | 2.0 | 9.0 | 5.0 | 1.0 | 6.0 | 1.0 | 3.0 | 1.0 | 8.0 | 9.0 | 1.0 | 1.0 | 7.0 | 4.0 | 2.0 | 10.0 | 2.0 | 4.0 | 10.0 | 4.0 | 1.0 | 1.0 | 9.0 | 10.0 | 8.0 | 4.0 | 5.0 | 1.0 | 2.0 | 7.0 | 3.0 | 7.0 | 4.0 | 7.0 | 5.0 | 3.0 | 10.0 | 6.0 | 2.0 | 6.0 | 7.0 | 4.0 | 1.0 | 1.0 | 5.0 | 10.0 | 6.0 | 9.0 | 2.0 |
| 38 | 5.0 | 3.0 | 5.0 | 2.0 | 1.0 | 6.0 | 5.0 | 2.0 | 10.0 | 5.0 | 6.0 | 2.0 | 2.0 | 7.0 | 5.0 | 3.0 | 9.0 | 8.0 | 9.0 | 8.0 | 6.0 | 2.0 | 10.0 | 4.0 | 1.0 | 6.0 | 7.0 | 9.0 | 9.0 | 10.0 | 6.0 | 5.0 | 9.0 | 4.0 | 3.0 | 10.0 | 4.0 | 9.0 | 5.0 | 4.0 | 2.0 | 2.0 | 7.0 | 1.0 | 10.0 | 9.0 | 7.0 | 3.0 | 8.0 | 4.0 | 10.0 | 5.0 | 6.0 | 6.0 | 1.0 | 1.0 | 3.0 | 9.0 | 3.0 | 3.0 | 3.0 | 4.0 | 8.0 | 7.0 | 8.0 |
| 39 | 6.0 | 4.0 | 1.0 | 6.0 | 5.0 | 2.0 | 7.0 | 9.0 | 8.0 | 10.0 | 9.0 | 3.0 | 7.0 | 3.0 | 5.0 | 5.0 | 4.0 | 10.0 | 9.0 | 6.0 | 8.0 | 3.0 | 9.0 | 6.0 | 6.0 | 7.0 | 9.0 | 3.0 | 6.0 | 3.0 | 10.0 | 6.0 | 4.0 | 5.0 | 1.0 | 10.0 | 4.0 | 10.0 | 4.0 | 3.0 | 6.0 | 6.0 | 2.0 | 3.0 | 9.0 | 10.0 | 8.0 | 4.0 | 10.0 | 4.0 | 2.0 | 6.0 | 5.0 | 5.0 | 3.0 | 6.0 | 3.0 | 5.0 | 1.0 | 6.0 | 4.0 | 7.0 | 9.0 | 6.0 | 3.0 |
| 40 | 9.0 | 9.0 | 8.0 | 2.0 | 10.0 | 4.0 | 10.0 | 9.0 | 7.0 | 2.0 | 1.0 | 6.0 | 7.0 | 2.0 | 4.0 | 5.0 | 4.0 | 9.0 | 2.0 | 6.0 | 3.0 | 10.0 | 5.0 | 2.0 | 10.0 | 9.0 | 8.0 | 6.0 | 10.0 | 8.0 | 5.0 | 7.0 | 3.0 | 9.0 | 10.0 | 8.0 | 10.0 | 8.0 | 2.0 | 6.0 | 2.0 | 9.0 | 3.0 | 3.0 | 7.0 | 1.0 | 6.0 | 8.0 | 10.0 | 2.0 | 6.0 | 4.0 | 7.0 | 10.0 | 3.0 | 8.0 | 1.0 | 6.0 | 9.0 | 5.0 | 3.0 | 9.0 | 3.0 | 3.0 | 10.0 |
| 41 | 5.0 | 2.0 | 4.0 | 1.0 | 9.0 | 6.0 | 5.0 | 5.0 | 6.0 | 10.0 | 7.0 | 6.0 | 3.0 | 5.0 | 4.0 | 6.0 | 9.0 | 7.0 | 1.0 | 1.0 | 7.0 | 8.0 | 1.0 | 4.0 | 3.0 | 7.0 | 5.0 | 3.0 | 9.0 | 8.0 | 9.0 | 5.0 | 7.0 | 5.0 | 9.0 | 7.0 | 8.0 | 4.0 | 2.0 | 6.0 | 9.0 | 2.0 | 7.0 | 6.0 | 4.0 | 1.0 | 2.0 | 5.0 | 9.0 | 5.0 | 7.0 | 7.0 | 5.0 | 3.0 | 1.0 | 7.0 | 7.0 | 7.0 | 4.0 | 5.0 | 10.0 | 6.0 | 2.0 | 6.0 | 10.0 |
| 42 | 2.0 | 7.0 | 4.0 | 6.0 | 6.0 | 6.0 | 3.0 | 9.0 | 1.0 | 7.0 | 6.0 | 9.0 | 1.0 | 6.0 | 5.0 | 3.0 | 6.0 | 4.0 | 5.0 | 1.0 | 9.0 | 6.0 | 9.0 | 9.0 | 4.0 | 7.0 | 10.0 | 5.0 | 9.0 | 5.0 | 2.0 | 4.0 | 10.0 | 5.0 | 3.0 | 3.0 | 8.0 | 5.0 | 7.0 | 2.0 | 3.0 | 7.0 | 7.0 | 1.0 | 2.0 | 7.0 | 8.0 | 10.0 | 3.0 | 4.0 | 1.0 | 5.0 | 9.0 | 7.0 | 10.0 | 8.0 | 9.0 | 2.0 | 6.0 | 8.0 | 7.0 | 7.0 | 1.0 | 8.0 | 9.0 |
| 43 | 4.0 | 5.0 | 4.0 | 8.0 | 2.0 | 5.0 | 10.0 | 1.0 | 7.0 | 1.0 | 6.0 | 1.0 | 1.0 | 8.0 | 9.0 | 8.0 | 6.0 | 2.0 | 10.0 | 1.0 | 4.0 | 6.0 | 1.0 | 6.0 | 8.0 | 9.0 | 6.0 | 6.0 | 1.0 | 7.0 | 9.0 | 1.0 | 7.0 | 6.0 | 8.0 | 5.0 | 7.0 | 1.0 | 1.0 | 3.0 | 3.0 | 6.0 | 1.0 | 9.0 | 4.0 | 7.0 | 2.0 | 3.0 | 6.0 | 2.0 | 5.0 | 1.0 | 4.0 | 2.0 | 4.0 | 6.0 | 1.0 | 4.0 | 3.0 | 4.0 | 7.0 | 5.0 | 8.0 | 6.0 | 10.0 |
| 44 | 8.0 | 4.0 | 7.0 | 6.0 | 1.0 | 7.0 | 8.0 | 3.0 | 1.0 | 6.0 | 10.0 | 5.0 | 10.0 | 2.0 | 8.0 | 2.0 | 7.0 | 7.0 | 1.0 | 1.0 | 2.0 | 10.0 | 7.0 | 8.0 | 4.0 | 6.0 | 2.0 | 5.0 | 7.0 | 3.0 | 8.0 | 7.0 | 8.0 | 5.0 | 10.0 | 10.0 | 8.0 | 2.0 | 10.0 | 9.0 | 7.0 | 4.0 | 2.0 | 4.0 | 6.0 | 5.0 | 2.0 | 8.0 | 3.0 | 10.0 | 6.0 | 8.0 | 4.0 | 7.0 | 5.0 | 2.0 | 9.0 | 2.0 | 6.0 | 2.0 | 7.0 | 9.0 | 3.0 | 1.0 | 10.0 |
| 45 | 6.0 | 8.0 | 9.0 | 8.0 | 2.0 | 8.0 | 3.0 | 8.0 | 7.0 | 5.0 | 4.0 | 5.0 | 2.0 | 7.0 | 7.0 | 6.0 | 3.0 | 9.0 | 9.0 | 3.0 | 3.0 | 10.0 | 10.0 | 8.0 | 3.0 | 9.0 | 3.0 | 1.0 | 1.0 | 2.0 | 3.0 | 2.0 | 2.0 | 7.0 | 6.0 | 2.0 | 6.0 | 7.0 | 9.0 | 10.0 | 1.0 | 1.0 | 7.0 | 7.0 | 5.0 | 7.0 | 3.0 | 7.0 | 9.0 | 6.0 | 8.0 | 9.0 | 5.0 | 6.0 | 10.0 | 2.0 | 5.0 | 6.0 | 2.0 | 5.0 | 9.0 | 8.0 | 5.0 | 1.0 | 7.0 |
| 46 | 9.0 | 2.0 | 5.0 | 2.0 | 9.0 | 2.0 | 7.0 | 7.0 | 5.0 | 8.0 | 9.0 | 4.0 | 4.0 | 7.0 | 8.0 | 4.0 | 10.0 | 6.0 | 1.0 | 7.0 | 4.0 | 9.0 | 10.0 | 6.0 | 9.0 | 7.0 | 9.0 | 2.0 | 4.0 | 1.0 | 7.0 | 4.0 | 3.0 | 9.0 | 6.0 | 1.0 | 8.0 | 3.0 | 7.0 | 8.0 | 6.0 | 2.0 | 8.0 | 2.0 | 2.0 | 3.0 | 6.0 | 6.0 | 9.0 | 4.0 | 10.0 | 4.0 | 4.0 | 2.0 | 2.0 | 1.0 | 10.0 | 10.0 | 6.0 | 9.0 | 4.0 | 2.0 | 6.0 | 2.0 | 3.0 |
| 47 | 2.0 | 7.0 | 6.0 | 10.0 | 5.0 | 3.0 | 5.0 | 2.0 | 7.0 | 3.0 | 4.0 | 5.0 | 7.0 | 9.0 | 8.0 | 10.0 | 10.0 | 4.0 | 9.0 | 2.0 | 9.0 | 1.0 | 7.0 | 2.0 | 10.0 | 6.0 | 6.0 | 8.0 | 9.0 | 3.0 | 4.0 | 10.0 | 6.0 | 2.0 | 8.0 | 3.0 | 5.0 | 7.0 | 3.0 | 4.0 | 8.0 | 5.0 | 10.0 | 3.0 | 8.0 | 7.0 | 6.0 | 10.0 | 1.0 | 8.0 | 5.0 | 3.0 | 10.0 | 4.0 | 9.0 | 8.0 | 10.0 | 6.0 | 5.0 | 7.0 | 7.0 | 6.0 | 7.0 | 9.0 | 1.0 |
| 48 | 5.0 | 3.0 | 2.0 | 1.0 | 9.0 | 7.0 | 7.0 | 4.0 | 7.0 | 8.0 | 3.0 | 10.0 | 3.0 | 5.0 | 5.0 | 5.0 | 5.0 | 3.0 | 4.0 | 3.0 | 10.0 | 4.0 | 9.0 | 6.0 | 2.0 | 8.0 | 1.0 | 8.0 | 1.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 5.0 | 9.0 | 9.0 | 4.0 | 8.0 | 10.0 | 10.0 | 9.0 | 3.0 | 6.0 | 3.0 | 9.0 | 9.0 | 1.0 | 4.0 | 3.0 | 4.0 | 2.0 | 5.0 | 10.0 | 8.0 | 8.0 | 1.0 | 4.0 | 8.0 | 7.0 | 8.0 | 3.0 | 2.0 | 5.0 | 5.0 |
| 49 | 10.0 | 6.0 | 9.0 | 1.0 | 5.0 | 9.0 | 5.0 | 10.0 | 6.0 | 7.0 | 6.0 | 2.0 | 2.0 | 3.0 | 8.0 | 3.0 | 4.0 | 5.0 | 1.0 | 8.0 | 3.0 | 10.0 | 9.0 | 3.0 | 9.0 | 8.0 | 7.0 | 6.0 | 4.0 | 6.0 | 3.0 | 3.0 | 5.0 | 3.0 | 7.0 | 4.0 | 10.0 | 7.0 | 4.0 | 4.0 | 2.0 | 5.0 | 4.0 | 2.0 | 10.0 | 6.0 | 4.0 | 8.0 | 3.0 | 1.0 | 6.0 | 5.0 | 1.0 | 3.0 | 10.0 | 5.0 | 6.0 | 4.0 | 6.0 | 5.0 | 6.0 | 5.0 | 1.0 | 5.0 | 1.0 |
| 50 | 6.0 | 1.0 | 8.0 | 10.0 | 6.0 | 3.0 | 4.0 | 3.0 | 10.0 | 5.0 | 10.0 | 7.0 | 1.0 | 2.0 | 6.0 | 10.0 | 9.0 | 1.0 | 9.0 | 10.0 | 1.0 | 7.0 | 5.0 | 9.0 | 3.0 | 9.0 | 8.0 | 8.0 | 1.0 | 3.0 | 2.0 | 4.0 | 1.0 | 5.0 | 7.0 | 4.0 | 5.0 | 5.0 | 10.0 | 2.0 | 6.0 | 7.0 | 1.0 | 5.0 | 6.0 | 8.0 | 10.0 | 5.0 | 4.0 | 6.0 | 1.0 | 5.0 | 3.0 | 6.0 | 7.0 | 10.0 | 7.0 | 10.0 | 7.0 | 1.0 | 2.0 | 3.0 | 6.0 | 6.0 | 10.0 |
| 51 | 5.0 | 1.0 | 3.0 | 5.0 | 1.0 | 8.0 | 3.0 | 6.0 | 1.0 | 8.0 | 2.0 | 2.0 | 3.0 | 7.0 | 4.0 | 4.0 | 10.0 | 7.0 | 3.0 | 1.0 | 6.0 | 10.0 | 3.0 | 2.0 | 9.0 | 8.0 | 4.0 | 3.0 | 5.0 | 8.0 | 8.0 | 3.0 | 8.0 | 9.0 | 9.0 | 8.0 | 3.0 | 3.0 | 5.0 | 6.0 | 4.0 | 7.0 | 5.0 | 1.0 | 8.0 | 9.0 | 4.0 | 3.0 | 2.0 | 5.0 | 5.0 | 4.0 | 5.0 | 8.0 | 8.0 | 2.0 | 3.0 | 1.0 | 2.0 | 10.0 | 8.0 | 9.0 | 7.0 | 4.0 | 7.0 |
| 52 | 6.0 | 5.0 | 3.0 | 6.0 | 10.0 | 9.0 | 4.0 | 5.0 | 6.0 | 7.0 | 7.0 | 8.0 | 3.0 | 1.0 | 6.0 | 6.0 | 2.0 | 5.0 | 8.0 | 10.0 | 5.0 | 1.0 | 5.0 | 10.0 | 3.0 | 7.0 | 8.0 | 5.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | 8.0 | 2.0 | 4.0 | 3.0 | 10.0 | 6.0 | 5.0 | 7.0 | 5.0 | 9.0 | 4.0 | 4.0 | 5.0 | 4.0 | 10.0 | 5.0 | 1.0 | 3.0 | 5.0 | 9.0 | 1.0 | 7.0 | 4.0 | 8.0 | 1.0 | 8.0 | 6.0 | 1.0 | 6.0 | 5.0 | 5.0 | 2.0 |
| 53 | 8.0 | 3.0 | 8.0 | 2.0 | 6.0 | 8.0 | 8.0 | 9.0 | 9.0 | 3.0 | 3.0 | 3.0 | 2.0 | 1.0 | 10.0 | 9.0 | 7.0 | 2.0 | 5.0 | 8.0 | 1.0 | 3.0 | 10.0 | 2.0 | 2.0 | 6.0 | 9.0 | 9.0 | 1.0 | 4.0 | 8.0 | 9.0 | 7.0 | 2.0 | 7.0 | 3.0 | 4.0 | 6.0 | 6.0 | 5.0 | 10.0 | 3.0 | 7.0 | 2.0 | 7.0 | 6.0 | 2.0 | 4.0 | 10.0 | 3.0 | 6.0 | 8.0 | 1.0 | 3.0 | 5.0 | 6.0 | 9.0 | 8.0 | 5.0 | 6.0 | 5.0 | 2.0 | 6.0 | 7.0 | 9.0 |
| 54 | 7.0 | 8.0 | 2.0 | 8.0 | 10.0 | 2.0 | 10.0 | 10.0 | 3.0 | 9.0 | 3.0 | 6.0 | 3.0 | 1.0 | 1.0 | 9.0 | 6.0 | 5.0 | 1.0 | 10.0 | 8.0 | 3.0 | 8.0 | 10.0 | 8.0 | 4.0 | 2.0 | 10.0 | 9.0 | 6.0 | 10.0 | 3.0 | 10.0 | 8.0 | 9.0 | 4.0 | 8.0 | 2.0 | 1.0 | 3.0 | 3.0 | 1.0 | 10.0 | 4.0 | 5.0 | 10.0 | 2.0 | 9.0 | 8.0 | 10.0 | 7.0 | 8.0 | 7.0 | 5.0 | 8.0 | 3.0 | 7.0 | 2.0 | 6.0 | 7.0 | 9.0 | 8.0 | 3.0 | 5.0 | 2.0 |
| 55 | 1.0 | 9.0 | 10.0 | 2.0 | 4.0 | 10.0 | 9.0 | 8.0 | 6.0 | 3.0 | 1.0 | 6.0 | 2.0 | 2.0 | 6.0 | 3.0 | 5.0 | 2.0 | 10.0 | 5.0 | 6.0 | 6.0 | 5.0 | 9.0 | 6.0 | 7.0 | 7.0 | 4.0 | 6.0 | 5.0 | 1.0 | 8.0 | 8.0 | 4.0 | 8.0 | 9.0 | 9.0 | 6.0 | 1.0 | 6.0 | 8.0 | 7.0 | 8.0 | 6.0 | 2.0 | 2.0 | 1.0 | 8.0 | 8.0 | 5.0 | 10.0 | 2.0 | 4.0 | 6.0 | 3.0 | 3.0 | 6.0 | 10.0 | 6.0 | 4.0 | 8.0 | 7.0 | 5.0 | 5.0 | 8.0 |
| 56 | 8.0 | 10.0 | 4.0 | 2.0 | 7.0 | 6.0 | 6.0 | 2.0 | 5.0 | 9.0 | 5.0 | 3.0 | 1.0 | 4.0 | 6.0 | 6.0 | 4.0 | 8.0 | 6.0 | 4.0 | 5.0 | 3.0 | 7.0 | 7.0 | 3.0 | 10.0 | 2.0 | 2.0 | 5.0 | 9.0 | 8.0 | 10.0 | 2.0 | 7.0 | 6.0 | 10.0 | 2.0 | 7.0 | 3.0 | 3.0 | 1.0 | 7.0 | 9.0 | 1.0 | 9.0 | 5.0 | 10.0 | 10.0 | 1.0 | 6.0 | 7.0 | 3.0 | 8.0 | 9.0 | 7.0 | 6.0 | 2.0 | 10.0 | 3.0 | 9.0 | 4.0 | 4.0 | 8.0 | 2.0 | 5.0 |
| 57 | 4.0 | 2.0 | 5.0 | 8.0 | 5.0 | 6.0 | 7.0 | 2.0 | 9.0 | 8.0 | 4.0 | 3.0 | 1.0 | 8.0 | 7.0 | 10.0 | 6.0 | 1.0 | 6.0 | 2.0 | 3.0 | 8.0 | 8.0 | 5.0 | 10.0 | 3.0 | 6.0 | 4.0 | 1.0 | 5.0 | 6.0 | 9.0 | 1.0 | 5.0 | 7.0 | 8.0 | 2.0 | 4.0 | 9.0 | 5.0 | 6.0 | 7.0 | 2.0 | 4.0 | 2.0 | 6.0 | 10.0 | 6.0 | 4.0 | 4.0 | 10.0 | 1.0 | 1.0 | 8.0 | 2.0 | 10.0 | 10.0 | 10.0 | 3.0 | 1.0 | 7.0 | 6.0 | 1.0 | 10.0 | 3.0 |
| 58 | 8.0 | 2.0 | 5.0 | 5.0 | 9.0 | 8.0 | 2.0 | 8.0 | 1.0 | 2.0 | 7.0 | 3.0 | 8.0 | 8.0 | 1.0 | 7.0 | 1.0 | 6.0 | 3.0 | 4.0 | 4.0 | 2.0 | 3.0 | 1.0 | 1.0 | 7.0 | 8.0 | 4.0 | 5.0 | 7.0 | 1.0 | 9.0 | 10.0 | 9.0 | 8.0 | 6.0 | 9.0 | 1.0 | 3.0 | 1.0 | 9.0 | 4.0 | 6.0 | 3.0 | 6.0 | 2.0 | 6.0 | 5.0 | 8.0 | 6.0 | 7.0 | 2.0 | 8.0 | 5.0 | 6.0 | 6.0 | 3.0 | 3.0 | 6.0 | 7.0 | 4.0 | 9.0 | 10.0 | 10.0 | 8.0 |
| 59 | 8.0 | 9.0 | 4.0 | 2.0 | 5.0 | 7.0 | 10.0 | 7.0 | 7.0 | 4.0 | 6.0 | 3.0 | 7.0 | 10.0 | 6.0 | 10.0 | 4.0 | 10.0 | 10.0 | 6.0 | 7.0 | 4.0 | 1.0 | 2.0 | 5.0 | 8.0 | 5.0 | 5.0 | 4.0 | 5.0 | 10.0 | 5.0 | 8.0 | 5.0 | 8.0 | 2.0 | 5.0 | 1.0 | 3.0 | 6.0 | 5.0 | 5.0 | 8.0 | 4.0 | 2.0 | 5.0 | 9.0 | 7.0 | 7.0 | 5.0 | 1.0 | 10.0 | 6.0 | 6.0 | 7.0 | 4.0 | 9.0 | 1.0 | 7.0 | 2.0 | 3.0 | 6.0 | 9.0 | 7.0 | 10.0 |
| 60 | 3.0 | 3.0 | 1.0 | 8.0 | 9.0 | 1.0 | 9.0 | 5.0 | 9.0 | 7.0 | 4.0 | 10.0 | 10.0 | 5.0 | 6.0 | 9.0 | 4.0 | 6.0 | 2.0 | 1.0 | 5.0 | 8.0 | 2.0 | 1.0 | 2.0 | 6.0 | 6.0 | 6.0 | 8.0 | 2.0 | 10.0 | 7.0 | 6.0 | 3.0 | 8.0 | 5.0 | 9.0 | 5.0 | 3.0 | 4.0 | 3.0 | 10.0 | 7.0 | 7.0 | 7.0 | 9.0 | 4.0 | 7.0 | 8.0 | 6.0 | 2.0 | 8.0 | 1.0 | 5.0 | 9.0 | 8.0 | 4.0 | 7.0 | 4.0 | 3.0 | 5.0 | 2.0 | 3.0 | 4.0 | 2.0 |
| 61 | 6.0 | 10.0 | 8.0 | 7.0 | 4.0 | 2.0 | 6.0 | 4.0 | 5.0 | 7.0 | 9.0 | 1.0 | 7.0 | 9.0 | 7.0 | 4.0 | 1.0 | 9.0 | 9.0 | 1.0 | 10.0 | 5.0 | 4.0 | 3.0 | 3.0 | 7.0 | 10.0 | 10.0 | 8.0 | 10.0 | 8.0 | 4.0 | 1.0 | 1.0 | 2.0 | 7.0 | 9.0 | 10.0 | 4.0 | 7.0 | 9.0 | 6.0 | 7.0 | 5.0 | 9.0 | 8.0 | 2.0 | 6.0 | 3.0 | 5.0 | 3.0 | 9.0 | 6.0 | 2.0 | 8.0 | 7.0 | 4.0 | 6.0 | 9.0 | 6.0 | 2.0 | 6.0 | 9.0 | 7.0 | 7.0 |
| 62 | 7.0 | 3.0 | 4.0 | 5.0 | 6.0 | 5.0 | 7.0 | 4.0 | 9.0 | 2.0 | 6.0 | 6.0 | 3.0 | 8.0 | 7.0 | 3.0 | 1.0 | 1.0 | 10.0 | 4.0 | 3.0 | 3.0 | 7.0 | 1.0 | 6.0 | 8.0 | 4.0 | 10.0 | 7.0 | 10.0 | 9.0 | 2.0 | 4.0 | 10.0 | 7.0 | 7.0 | 8.0 | 6.0 | 8.0 | 9.0 | 3.0 | 2.0 | 1.0 | 8.0 | 3.0 | 5.0 | 6.0 | 7.0 | 2.0 | 1.0 | 6.0 | 7.0 | 5.0 | 6.0 | 3.0 | 5.0 | 8.0 | 1.0 | 10.0 | 9.0 | 3.0 | 9.0 | 4.0 | 6.0 | 2.0 |
| 63 | 6.0 | 10.0 | 2.0 | 2.0 | 9.0 | 5.0 | 6.0 | 5.0 | 10.0 | 4.0 | 1.0 | 7.0 | 10.0 | 10.0 | 9.0 | 2.0 | 8.0 | 4.0 | 3.0 | 2.0 | 5.0 | 7.0 | 3.0 | 2.0 | 9.0 | 10.0 | 7.0 | 4.0 | 7.0 | 4.0 | 1.0 | 5.0 | 3.0 | 4.0 | 9.0 | 3.0 | 6.0 | 9.0 | 7.0 | 6.0 | 3.0 | 6.0 | 8.0 | 6.0 | 1.0 | 1.0 | 2.0 | 9.0 | 5.0 | 5.0 | 6.0 | 4.0 | 5.0 | 7.0 | 5.0 | 5.0 | 2.0 | 10.0 | 10.0 | 7.0 | 4.0 | 7.0 | 6.0 | 1.0 | 5.0 |
| 64 | 10.0 | 6.0 | 2.0 | 3.0 | 6.0 | 2.0 | 10.0 | 1.0 | 1.0 | 3.0 | 1.0 | 2.0 | 10.0 | 6.0 | 6.0 | 2.0 | 3.0 | 1.0 | 1.0 | 4.0 | 5.0 | 2.0 | 8.0 | 6.0 | 9.0 | 10.0 | 10.0 | 7.0 | 1.0 | 8.0 | 4.0 | 10.0 | 9.0 | 6.0 | 5.0 | 1.0 | 2.0 | 2.0 | 8.0 | 3.0 | 10.0 | 10.0 | 9.0 | 10.0 | 10.0 | 7.0 | 3.0 | 1.0 | 5.0 | 1.0 | 10.0 | 7.0 | 2.0 | 9.0 | 2.0 | 8.0 | 5.0 | 3.0 | 8.0 | 10.0 | 2.0 | 7.0 | 2.0 | 5.0 | 1.0 |

I’ll choose one continuous, dependency-respecting route from 22 to 23 that minimizes the sum of per-step compile times, per-step overheads, and any cache-miss penalties.

Also, to keep things machine-friendly, please give the chosen chain in a tiny JSON layout — just a single key with the node sequence as the value.

{
  ""solution"": []
}

This little sketch shows the shape I expect: ""solution"" should hold the ordered list of node identifiers that form the chain from the root module to the final artifact. Think of it as the short form of a form field — just list the locations in order, start to finish. This is only a template showing the expected shape, not the actual path itself.

Please make sure to use the exact node identifiers from the instance input, with no renaming or invented labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 1, 'var_index': 1}, {'from': 22, 'to': 2, 'var_index': 2}, {'from': 22, 'to': 3, 'var_index': 3}, {'from': 22, 'to': 4, 'var_index': 4}, {'from': 22, 'to': 5, 'var_index': 5}, {'from': 22, 'to': 6, 'var_index': 6}, {'from': 22, 'to': 7, 'var_index': 7}, {'from': 22, 'to': 8, 'var_index': 8}, {'from': 22, 'to': 9, 'var_index': 9}, {'from': 22, 'to': 10, 'var_index': 10}, {'from': 22, 'to': 11, 'var_index': 11}, {'from': 22, 'to': 12, 'var_index': 12}, {'from': 22, 'to': 13, 'var_index': 13}, {'from': 22, 'to': 14, 'var_index': 14}, {'from': 22, 'to': 15, 'var_index': 15}, {'from': 22, 'to': 16, 'var_index': 16}, {'from': 22, 'to': 17, 'var_index': 17}, {'from': 22, 'to': 18, 'var_index': 18}, {'from': 22, 'to': 19, 'var_index': 19}, {'from': 22, 'to': 20, 'var_index': 20}, {'from': 22, 'to': 21, 'var_index': 21}, {'from': 0, 'to': 23, 'var_index': 22}, {'from': 1, 'to': 23, 'var_index': 23}, {'from': 2, 'to': 23, 'var_index': 24}, {'from': 3, 'to': 23, 'var_index': 25}, {'from': 4, 'to': 23, 'var_index': 26}, {'from': 5, 'to': 23, 'var_index': 27}, {'from': 6, 'to': 23, 'var_index': 28}, {'from': 7, 'to': 23, 'var_index': 29}, {'from': 8, 'to': 23, 'var_index': 30}, {'from': 9, 'to': 23, 'var_index': 31}, {'from': 10, 'to': 23, 'var_index': 32}, {'from': 11, 'to': 23, 'var_index': 33}, {'from': 12, 'to': 23, 'var_index': 34}, {'from': 13, 'to': 23, 'var_index': 35}, {'from': 14, 'to': 23, 'var_index': 36}, {'from': 15, 'to': 23, 'var_index': 37}, {'from': 16, 'to': 23, 'var_index': 38}, {'from': 17, 'to': 23, 'var_index': 39}, {'from': 18, 'to': 23, 'var_index': 40}, {'from': 19, 'to': 23, 'var_index': 41}, {'from': 20, 'to': 23, 'var_index': 42}, {'from': 21, 'to': 23, 'var_index': 43}, {'from': 0, 'to': 1, 'var_index': 44}, {'from': 1, 'to': 2, 'var_index': 45}, {'from': 2, 'to': 3, 'var_index': 46}, {'from': 3, 'to': 4, 'var_index': 47}, {'from': 4, 'to': 5, 'var_index': 48}, {'from': 5, 'to': 6, 'var_index': 49}, {'from': 6, 'to': 7, 'var_index': 50}, {'from': 7, 'to': 8, 'var_index': 51}, {'from': 8, 'to': 9, 'var_index': 52}, {'from': 9, 'to': 10, 'var_index': 53}, {'from': 10, 'to': 11, 'var_index': 54}, {'from': 11, 'to': 12, 'var_index': 55}, {'from': 12, 'to': 13, 'var_index': 56}, {'from': 13, 'to': 14, 'var_index': 57}, {'from': 14, 'to': 15, 'var_index': 58}, {'from': 15, 'to': 16, 'var_index': 59}, {'from': 16, 'to': 17, 'var_index': 60}, {'from': 17, 'to': 18, 'var_index': 61}, {'from': 18, 'to': 19, 'var_index': 62}, {'from': 19, 'to': 20, 'var_index': 63}, {'from': 20, 'to': 21, 'var_index': 64}], 'objective': {'constant': 0.0, 'linear': [5.0, 7.0, 8.0, 9.0, 1.0, 2.0, 5.0, 2.0, 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{'var_i': 63, 'var_j': 63, 'quadratic_cost': 1.0}, {'var_i': 63, 'var_j': 64, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 24, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 25, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 64, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 32, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 33, 'quadratic_cost': 6.0}, {'var_i': 64, 'var_j': 34, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 35, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 36, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 38, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 40, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 41, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 42, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 43, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 44, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 45, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 46, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 47, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 48, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 49, 'quadratic_cost': 1.0}, {'var_i': 64, 'var_j': 50, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 51, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 52, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 53, 'quadratic_cost': 9.0}, {'var_i': 64, 'var_j': 54, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 55, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 56, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 57, 'quadratic_cost': 3.0}, {'var_i': 64, 'var_j': 58, 'quadratic_cost': 8.0}, {'var_i': 64, 'var_j': 59, 'quadratic_cost': 10.0}, {'var_i': 64, 'var_j': 60, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 61, 'quadratic_cost': 7.0}, {'var_i': 64, 'var_j': 62, 'quadratic_cost': 2.0}, {'var_i': 64, 'var_j': 63, 'quadratic_cost': 5.0}, {'var_i': 64, 'var_j': 64, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 1, 'var_index': 1}, {'from': 22, 'to': 2, 'var_index': 2}, {'from': 22, 'to': 3, 'var_index': 3}, {'from': 22, 'to': 4, 'var_index': 4}, {'from': 22, 'to': 5, 'var_index': 5}, {'from': 22, 'to': 6, 'var_index': 6}, {'from': 22, 'to': 7, 'var_index': 7}, {'from': 22, 'to': 8, 'var_index': 8}, {'from': 22, 'to': 9, 'var_index': 9}, {'from': 22, 'to': 10, 'var_index': 10}, {'from': 22, 'to': 11, 'var_index': 11}, {'from': 22, 'to': 12, 'var_index': 12}, {'from': 22, 'to': 13, 'var_index': 13}, {'from': 22, 'to': 14, 'var_index': 14}, {'from': 22, 'to': 15, 'var_index': 15}, {'from': 22, 'to': 16, 'var_index': 16}, {'from': 22, 'to': 17, 'var_index': 17}, {'from': 22, 'to': 18, 'var_index': 18}, {'from': 22, 'to': 19, 'var_index': 19}, {'from': 22, 'to': 20, 'var_index': 20}, {'from': 22, 'to': 21, 'var_index': 21}, {'from': 0, 'to': 23, 'var_index': 22}, {'from': 1, 'to': 23, 'var_index': 23}, {'from': 2, 'to': 23, 'var_index': 24}, {'from': 3, 'to': 23, 'var_index': 25}, {'from': 4, 'to': 23, 'var_index': 26}, {'from': 5, 'to': 23, 'var_index': 27}, {'from': 6, 'to': 23, 'var_index': 28}, {'from': 7, 'to': 23, 'var_index': 29}, {'from': 8, 'to': 23, 'var_index': 30}, {'from': 9, 'to': 23, 'var_index': 31}, {'from': 10, 'to': 23, 'var_index': 32}, {'from': 11, 'to': 23, 'var_index': 33}, {'from': 12, 'to': 23, 'var_index': 34}, {'from': 13, 'to': 23, 'var_index': 35}, {'from': 14, 'to': 23, 'var_index': 36}, {'from': 15, 'to': 23, 'var_index': 37}, {'from': 16, 'to': 23, 'var_index': 38}, {'from': 17, 'to': 23, 'var_index': 39}, {'from': 18, 'to': 23, 'var_index': 40}, {'from': 19, 'to': 23, 'var_index': 41}, {'from': 20, 'to': 23, 'var_index': 42}, {'from': 21, 'to': 23, 'var_index': 43}, {'from': 0, 'to': 1, 'var_index': 44}, {'from': 1, 'to': 2, 'var_index': 45}, {'from': 2, 'to': 3, 'var_index': 46}, {'from': 3, 'to': 4, 'var_index': 47}, {'from': 4, 'to': 5, 'var_index': 48}, {'from': 5, 'to': 6, 'var_index': 49}, {'from': 6, 'to': 7, 'var_index': 50}, {'from': 7, 'to': 8, 'var_index': 51}, {'from': 8, 'to': 9, 'var_index': 52}, {'from': 9, 'to': 10, 'var_index': 53}, {'from': 10, 'to': 11, 'var_index': 54}, {'from': 11, 'to': 12, 'var_index': 55}, {'from': 12, 'to': 13, 'var_index': 56}, {'from': 13, 'to': 14, 'var_index': 57}, {'from': 14, 'to': 15, 'var_index': 58}, {'from': 15, 'to': 16, 'var_index': 59}, {'from': 16, 'to': 17, 'var_index': 60}, {'from': 17, 'to': 18, 'var_index': 61}, {'from': 18, 'to': 19, 'var_index': 62}, {'from': 19, 'to': 20, 'var_index': 63}, {'from': 20, 'to': 21, 'var_index': 64}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23}}","[22, 10, 23]",11,markdown_table,0
QSPP,QSPP,"I was sketching an evacuation plan the other day: imagine a building with one assembly area and one safe zone, and a web of one-way exit corridors between rooms. The job is to pick a single, continuous one-way route from the assembly area to the safe zone that actually follows those corridors step by step — no gaps, no branching, and each move must be along an existing directed corridor. Each corridor carries its own hazard surcharge, and some pairs of corridors trigger extra penalties when both are used on the same route (sometimes the extra hit depends on which corridor comes before the other, and some corridors even have an extra cost just for being used at all). The plan that works best is the one with the lowest total exposure when you add up every corridor’s base surcharge plus every extra penalty that applies because certain corridor combos appear together. The concrete map and the numbers for each corridor are shown below.

# total_rooms=18
# total_corridors=47
# room_list=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R
# assembly_area_id=Q
# safe_zone_id=R

corridor_from,corridor_to,corridor_id
Q,A,0
Q,B,1
Q,C,2
Q,D,3
Q,E,4
Q,F,5
Q,G,6
Q,H,7
Q,I,8
Q,J,9
Q,K,10
Q,L,11
Q,M,12
Q,N,13
Q,O,14
Q,P,15
A,R,16
B,R,17
C,R,18
D,R,19
E,R,20
F,R,21
G,R,22
H,R,23
I,R,24
J,R,25
K,R,26
L,R,27
M,R,28
N,R,29
O,R,30
P,R,31
A,B,32
B,C,33
C,D,34
D,E,35
E,F,36
F,G,37
G,H,38
H,I,39
I,J,40
J,K,41
K,L,42
L,M,43
M,N,44
N,O,45
O,P,46

corridor_ref,hazard_surcharge
0,6.0
1,4.0
2,10.0
3,8.0
4,2.0
5,5.0
6,2.0
7,4.0
8,2.0
9,1.0
10,4.0
11,5.0
12,3.0
13,9.0
14,2.0
15,10.0
16,1.0
17,4.0
18,10.0
19,8.0
20,2.0
21,5.0
22,6.0
23,3.0
24,3.0
25,7.0
26,1.0
27,5.0
28,2.0
29,7.0
30,9.0
31,3.0
32,10.0
33,7.0
34,1.0
35,7.0
36,5.0
37,1.0
38,10.0
39,6.0
40,3.0
41,4.0
42,1.0
43,3.0
44,10.0
45,10.0
46,2.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_ref, corridor_j_ref). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_ref\corridor_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 10.0 | 5.0 | 4.0 | 2.0 | 2.0 | 6.0 | 6.0 | 3.0 | 10.0 | 1.0 | 6.0 | 1.0 | 1.0 | 8.0 | 1.0 | 1.0 | 6.0 | 4.0 | 8.0 | 3.0 | 3.0 | 9.0 | 2.0 | 7.0 | 10.0 | 5.0 | 10.0 | 9.0 | 2.0 | 8.0 | 5.0 | 10.0 | 9.0 | 9.0 | 6.0 | 1.0 | 2.0 | 9.0 | 5.0 | 2.0 | 7.0 | 8.0 | 8.0 | 4.0 | 5.0 | 5.0 |
| 1 | 10.0 | 4.0 | 3.0 | 2.0 | 5.0 | 5.0 | 8.0 | 4.0 | 9.0 | 8.0 | 8.0 | 6.0 | 4.0 | 2.0 | 3.0 | 2.0 | 5.0 | 4.0 | 5.0 | 6.0 | 3.0 | 5.0 | 2.0 | 10.0 | 10.0 | 8.0 | 3.0 | 8.0 | 10.0 | 2.0 | 10.0 | 9.0 | 7.0 | 3.0 | 9.0 | 10.0 | 9.0 | 1.0 | 5.0 | 9.0 | 8.0 | 1.0 | 9.0 | 4.0 | 1.0 | 9.0 | 6.0 |
| 2 | 5.0 | 3.0 | 9.0 | 10.0 | 6.0 | 6.0 | 5.0 | 9.0 | 2.0 | 10.0 | 8.0 | 1.0 | 6.0 | 10.0 | 2.0 | 3.0 | 4.0 | 5.0 | 3.0 | 9.0 | 6.0 | 3.0 | 9.0 | 3.0 | 3.0 | 3.0 | 6.0 | 1.0 | 4.0 | 3.0 | 5.0 | 2.0 | 1.0 | 5.0 | 3.0 | 4.0 | 7.0 | 3.0 | 4.0 | 5.0 | 10.0 | 5.0 | 5.0 | 7.0 | 5.0 | 4.0 | 2.0 |
| 3 | 4.0 | 2.0 | 10.0 | 5.0 | 7.0 | 8.0 | 7.0 | 2.0 | 8.0 | 9.0 | 7.0 | 6.0 | 3.0 | 4.0 | 7.0 | 9.0 | 7.0 | 2.0 | 3.0 | 7.0 | 7.0 | 5.0 | 2.0 | 5.0 | 8.0 | 1.0 | 6.0 | 9.0 | 10.0 | 10.0 | 9.0 | 5.0 | 6.0 | 4.0 | 1.0 | 7.0 | 1.0 | 6.0 | 1.0 | 9.0 | 1.0 | 5.0 | 3.0 | 3.0 | 1.0 | 7.0 | 10.0 |
| 4 | 2.0 | 5.0 | 6.0 | 7.0 | 3.0 | 4.0 | 5.0 | 8.0 | 4.0 | 1.0 | 8.0 | 10.0 | 5.0 | 10.0 | 5.0 | 8.0 | 9.0 | 5.0 | 3.0 | 7.0 | 1.0 | 8.0 | 1.0 | 6.0 | 4.0 | 2.0 | 10.0 | 2.0 | 4.0 | 1.0 | 2.0 | 9.0 | 5.0 | 5.0 | 5.0 | 6.0 | 4.0 | 4.0 | 8.0 | 10.0 | 3.0 | 6.0 | 8.0 | 7.0 | 1.0 | 9.0 | 1.0 |
| 5 | 2.0 | 5.0 | 6.0 | 8.0 | 4.0 | 9.0 | 1.0 | 1.0 | 5.0 | 4.0 | 2.0 | 3.0 | 5.0 | 6.0 | 9.0 | 5.0 | 4.0 | 1.0 | 9.0 | 5.0 | 2.0 | 5.0 | 7.0 | 3.0 | 4.0 | 4.0 | 8.0 | 3.0 | 1.0 | 9.0 | 10.0 | 10.0 | 7.0 | 4.0 | 1.0 | 9.0 | 8.0 | 1.0 | 6.0 | 1.0 | 8.0 | 7.0 | 4.0 | 5.0 | 1.0 | 5.0 | 2.0 |
| 6 | 6.0 | 8.0 | 5.0 | 7.0 | 5.0 | 1.0 | 6.0 | 9.0 | 2.0 | 5.0 | 6.0 | 2.0 | 4.0 | 5.0 | 6.0 | 4.0 | 10.0 | 5.0 | 6.0 | 7.0 | 9.0 | 3.0 | 2.0 | 3.0 | 10.0 | 6.0 | 7.0 | 4.0 | 9.0 | 9.0 | 7.0 | 8.0 | 5.0 | 1.0 | 7.0 | 9.0 | 1.0 | 1.0 | 3.0 | 3.0 | 9.0 | 2.0 | 6.0 | 2.0 | 5.0 | 8.0 | 3.0 |
| 7 | 6.0 | 4.0 | 9.0 | 2.0 | 8.0 | 1.0 | 9.0 | 10.0 | 4.0 | 6.0 | 5.0 | 6.0 | 2.0 | 3.0 | 4.0 | 7.0 | 9.0 | 5.0 | 7.0 | 4.0 | 2.0 | 6.0 | 6.0 | 4.0 | 6.0 | 3.0 | 8.0 | 8.0 | 9.0 | 5.0 | 6.0 | 6.0 | 2.0 | 6.0 | 1.0 | 8.0 | 8.0 | 9.0 | 3.0 | 2.0 | 9.0 | 9.0 | 5.0 | 6.0 | 2.0 | 5.0 | 5.0 |
| 8 | 3.0 | 9.0 | 2.0 | 8.0 | 4.0 | 5.0 | 2.0 | 4.0 | 5.0 | 3.0 | 3.0 | 6.0 | 8.0 | 8.0 | 9.0 | 9.0 | 1.0 | 7.0 | 4.0 | 2.0 | 6.0 | 7.0 | 9.0 | 5.0 | 4.0 | 3.0 | 9.0 | 10.0 | 8.0 | 9.0 | 7.0 | 9.0 | 7.0 | 4.0 | 5.0 | 2.0 | 9.0 | 2.0 | 3.0 | 1.0 | 5.0 | 6.0 | 8.0 | 4.0 | 4.0 | 4.0 | 1.0 |
| 9 | 10.0 | 8.0 | 10.0 | 9.0 | 1.0 | 4.0 | 5.0 | 6.0 | 3.0 | 3.0 | 6.0 | 8.0 | 7.0 | 4.0 | 2.0 | 9.0 | 8.0 | 5.0 | 9.0 | 7.0 | 3.0 | 6.0 | 8.0 | 10.0 | 5.0 | 2.0 | 7.0 | 5.0 | 5.0 | 7.0 | 5.0 | 9.0 | 2.0 | 8.0 | 6.0 | 10.0 | 9.0 | 10.0 | 8.0 | 3.0 | 7.0 | 10.0 | 8.0 | 4.0 | 1.0 | 1.0 | 1.0 |
| 10 | 1.0 | 8.0 | 8.0 | 7.0 | 8.0 | 2.0 | 6.0 | 5.0 | 3.0 | 6.0 | 5.0 | 4.0 | 8.0 | 3.0 | 3.0 | 10.0 | 10.0 | 5.0 | 6.0 | 4.0 | 7.0 | 9.0 | 7.0 | 4.0 | 2.0 | 9.0 | 10.0 | 3.0 | 10.0 | 8.0 | 2.0 | 9.0 | 8.0 | 7.0 | 10.0 | 10.0 | 5.0 | 8.0 | 10.0 | 7.0 | 9.0 | 1.0 | 7.0 | 2.0 | 10.0 | 5.0 | 5.0 |
| 11 | 6.0 | 6.0 | 1.0 | 6.0 | 10.0 | 3.0 | 2.0 | 6.0 | 6.0 | 8.0 | 4.0 | 10.0 | 9.0 | 8.0 | 6.0 | 3.0 | 5.0 | 7.0 | 4.0 | 8.0 | 2.0 | 10.0 | 6.0 | 10.0 | 10.0 | 1.0 | 6.0 | 2.0 | 10.0 | 1.0 | 9.0 | 1.0 | 4.0 | 3.0 | 4.0 | 2.0 | 10.0 | 2.0 | 6.0 | 5.0 | 8.0 | 5.0 | 7.0 | 2.0 | 3.0 | 6.0 | 9.0 |
| 12 | 1.0 | 4.0 | 6.0 | 3.0 | 5.0 | 5.0 | 4.0 | 2.0 | 8.0 | 7.0 | 8.0 | 9.0 | 8.0 | 10.0 | 10.0 | 7.0 | 7.0 | 6.0 | 7.0 | 1.0 | 3.0 | 3.0 | 8.0 | 2.0 | 3.0 | 9.0 | 9.0 | 9.0 | 7.0 | 5.0 | 9.0 | 2.0 | 1.0 | 7.0 | 6.0 | 6.0 | 4.0 | 4.0 | 10.0 | 6.0 | 3.0 | 8.0 | 8.0 | 5.0 | 5.0 | 1.0 | 10.0 |
| 13 | 1.0 | 2.0 | 10.0 | 4.0 | 10.0 | 6.0 | 5.0 | 3.0 | 8.0 | 4.0 | 3.0 | 8.0 | 10.0 | 5.0 | 9.0 | 3.0 | 7.0 | 1.0 | 1.0 | 5.0 | 3.0 | 9.0 | 5.0 | 7.0 | 9.0 | 1.0 | 4.0 | 5.0 | 9.0 | 5.0 | 1.0 | 6.0 | 6.0 | 10.0 | 3.0 | 3.0 | 4.0 | 2.0 | 2.0 | 1.0 | 3.0 | 8.0 | 4.0 | 10.0 | 10.0 | 1.0 | 10.0 |
| 14 | 8.0 | 3.0 | 2.0 | 7.0 | 5.0 | 9.0 | 6.0 | 4.0 | 9.0 | 2.0 | 3.0 | 6.0 | 10.0 | 9.0 | 6.0 | 4.0 | 10.0 | 9.0 | 5.0 | 1.0 | 3.0 | 1.0 | 4.0 | 1.0 | 1.0 | 4.0 | 2.0 | 10.0 | 1.0 | 2.0 | 7.0 | 9.0 | 3.0 | 1.0 | 9.0 | 1.0 | 8.0 | 1.0 | 9.0 | 2.0 | 10.0 | 2.0 | 3.0 | 3.0 | 10.0 | 6.0 | 1.0 |
| 15 | 1.0 | 2.0 | 3.0 | 9.0 | 8.0 | 5.0 | 4.0 | 7.0 | 9.0 | 9.0 | 10.0 | 3.0 | 7.0 | 3.0 | 4.0 | 8.0 | 8.0 | 7.0 | 9.0 | 8.0 | 6.0 | 3.0 | 1.0 | 9.0 | 8.0 | 9.0 | 9.0 | 2.0 | 6.0 | 4.0 | 5.0 | 1.0 | 3.0 | 6.0 | 8.0 | 10.0 | 3.0 | 4.0 | 1.0 | 1.0 | 7.0 | 5.0 | 3.0 | 5.0 | 6.0 | 8.0 | 1.0 |
| 16 | 1.0 | 5.0 | 4.0 | 7.0 | 9.0 | 4.0 | 10.0 | 9.0 | 1.0 | 8.0 | 10.0 | 5.0 | 7.0 | 7.0 | 10.0 | 8.0 | 2.0 | 8.0 | 7.0 | 10.0 | 8.0 | 3.0 | 9.0 | 8.0 | 1.0 | 7.0 | 7.0 | 8.0 | 2.0 | 9.0 | 10.0 | 9.0 | 1.0 | 10.0 | 10.0 | 10.0 | 1.0 | 3.0 | 9.0 | 5.0 | 1.0 | 6.0 | 5.0 | 6.0 | 8.0 | 10.0 | 5.0 |
| 17 | 6.0 | 4.0 | 5.0 | 2.0 | 5.0 | 1.0 | 5.0 | 5.0 | 7.0 | 5.0 | 5.0 | 7.0 | 6.0 | 1.0 | 9.0 | 7.0 | 8.0 | 3.0 | 7.0 | 9.0 | 6.0 | 10.0 | 3.0 | 10.0 | 7.0 | 5.0 | 3.0 | 8.0 | 1.0 | 5.0 | 9.0 | 7.0 | 4.0 | 4.0 | 10.0 | 7.0 | 3.0 | 4.0 | 4.0 | 4.0 | 7.0 | 8.0 | 6.0 | 4.0 | 6.0 | 3.0 | 7.0 |
| 18 | 4.0 | 5.0 | 3.0 | 3.0 | 3.0 | 9.0 | 6.0 | 7.0 | 4.0 | 9.0 | 6.0 | 4.0 | 7.0 | 1.0 | 5.0 | 9.0 | 7.0 | 7.0 | 3.0 | 2.0 | 8.0 | 5.0 | 9.0 | 4.0 | 8.0 | 9.0 | 1.0 | 5.0 | 8.0 | 2.0 | 9.0 | 8.0 | 8.0 | 2.0 | 1.0 | 4.0 | 1.0 | 4.0 | 3.0 | 3.0 | 6.0 | 3.0 | 10.0 | 6.0 | 7.0 | 10.0 | 9.0 |
| 19 | 8.0 | 6.0 | 9.0 | 7.0 | 7.0 | 5.0 | 7.0 | 4.0 | 2.0 | 7.0 | 4.0 | 8.0 | 1.0 | 5.0 | 1.0 | 8.0 | 10.0 | 9.0 | 2.0 | 9.0 | 1.0 | 10.0 | 8.0 | 5.0 | 4.0 | 1.0 | 2.0 | 1.0 | 2.0 | 2.0 | 6.0 | 8.0 | 3.0 | 5.0 | 2.0 | 7.0 | 1.0 | 6.0 | 2.0 | 5.0 | 5.0 | 3.0 | 1.0 | 2.0 | 3.0 | 5.0 | 6.0 |
| 20 | 3.0 | 3.0 | 6.0 | 7.0 | 1.0 | 2.0 | 9.0 | 2.0 | 6.0 | 3.0 | 7.0 | 2.0 | 3.0 | 3.0 | 3.0 | 6.0 | 8.0 | 6.0 | 8.0 | 1.0 | 5.0 | 6.0 | 9.0 | 6.0 | 4.0 | 10.0 | 2.0 | 6.0 | 6.0 | 9.0 | 9.0 | 6.0 | 10.0 | 1.0 | 10.0 | 6.0 | 5.0 | 6.0 | 1.0 | 10.0 | 7.0 | 9.0 | 9.0 | 1.0 | 5.0 | 2.0 | 8.0 |
| 21 | 3.0 | 5.0 | 3.0 | 5.0 | 8.0 | 5.0 | 3.0 | 6.0 | 7.0 | 6.0 | 9.0 | 10.0 | 3.0 | 9.0 | 1.0 | 3.0 | 3.0 | 10.0 | 5.0 | 10.0 | 6.0 | 1.0 | 8.0 | 4.0 | 5.0 | 5.0 | 10.0 | 7.0 | 1.0 | 10.0 | 7.0 | 5.0 | 10.0 | 6.0 | 3.0 | 2.0 | 10.0 | 10.0 | 8.0 | 10.0 | 1.0 | 2.0 | 1.0 | 8.0 | 1.0 | 7.0 | 5.0 |
| 22 | 9.0 | 2.0 | 9.0 | 2.0 | 1.0 | 7.0 | 2.0 | 6.0 | 9.0 | 8.0 | 7.0 | 6.0 | 8.0 | 5.0 | 4.0 | 1.0 | 9.0 | 3.0 | 9.0 | 8.0 | 9.0 | 8.0 | 9.0 | 5.0 | 3.0 | 8.0 | 5.0 | 2.0 | 10.0 | 4.0 | 3.0 | 2.0 | 10.0 | 7.0 | 9.0 | 8.0 | 10.0 | 7.0 | 3.0 | 4.0 | 2.0 | 4.0 | 6.0 | 5.0 | 1.0 | 3.0 | 5.0 |
| 23 | 2.0 | 10.0 | 3.0 | 5.0 | 6.0 | 3.0 | 3.0 | 4.0 | 5.0 | 10.0 | 4.0 | 10.0 | 2.0 | 7.0 | 1.0 | 9.0 | 8.0 | 10.0 | 4.0 | 5.0 | 6.0 | 4.0 | 5.0 | 5.0 | 2.0 | 3.0 | 10.0 | 7.0 | 9.0 | 1.0 | 2.0 | 7.0 | 2.0 | 1.0 | 3.0 | 6.0 | 3.0 | 6.0 | 2.0 | 5.0 | 1.0 | 6.0 | 4.0 | 1.0 | 3.0 | 3.0 | 9.0 |
| 24 | 7.0 | 10.0 | 3.0 | 8.0 | 4.0 | 4.0 | 10.0 | 6.0 | 4.0 | 5.0 | 2.0 | 10.0 | 3.0 | 9.0 | 1.0 | 8.0 | 1.0 | 7.0 | 8.0 | 4.0 | 4.0 | 5.0 | 3.0 | 2.0 | 10.0 | 2.0 | 10.0 | 10.0 | 6.0 | 8.0 | 1.0 | 10.0 | 9.0 | 1.0 | 8.0 | 8.0 | 5.0 | 7.0 | 8.0 | 5.0 | 10.0 | 2.0 | 8.0 | 8.0 | 10.0 | 2.0 | 2.0 |
| 25 | 10.0 | 8.0 | 3.0 | 1.0 | 2.0 | 4.0 | 6.0 | 3.0 | 3.0 | 2.0 | 9.0 | 1.0 | 9.0 | 1.0 | 4.0 | 9.0 | 7.0 | 5.0 | 9.0 | 1.0 | 10.0 | 5.0 | 8.0 | 3.0 | 2.0 | 8.0 | 8.0 | 2.0 | 10.0 | 7.0 | 9.0 | 10.0 | 5.0 | 6.0 | 9.0 | 2.0 | 9.0 | 9.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 5.0 | 3.0 | 1.0 | 2.0 |
| 26 | 5.0 | 3.0 | 6.0 | 6.0 | 10.0 | 8.0 | 7.0 | 8.0 | 9.0 | 7.0 | 10.0 | 6.0 | 9.0 | 4.0 | 2.0 | 9.0 | 7.0 | 3.0 | 1.0 | 2.0 | 2.0 | 10.0 | 5.0 | 10.0 | 10.0 | 8.0 | 2.0 | 2.0 | 2.0 | 2.0 | 1.0 | 10.0 | 7.0 | 1.0 | 1.0 | 1.0 | 8.0 | 9.0 | 3.0 | 7.0 | 2.0 | 1.0 | 10.0 | 8.0 | 8.0 | 6.0 | 6.0 |
| 27 | 10.0 | 8.0 | 1.0 | 9.0 | 2.0 | 3.0 | 4.0 | 8.0 | 10.0 | 5.0 | 3.0 | 2.0 | 9.0 | 5.0 | 10.0 | 2.0 | 8.0 | 8.0 | 5.0 | 1.0 | 6.0 | 7.0 | 2.0 | 7.0 | 10.0 | 2.0 | 2.0 | 3.0 | 1.0 | 4.0 | 9.0 | 8.0 | 1.0 | 7.0 | 7.0 | 3.0 | 5.0 | 5.0 | 5.0 | 2.0 | 3.0 | 8.0 | 9.0 | 7.0 | 9.0 | 4.0 | 4.0 |
| 28 | 9.0 | 10.0 | 4.0 | 10.0 | 4.0 | 1.0 | 9.0 | 9.0 | 8.0 | 5.0 | 10.0 | 10.0 | 7.0 | 9.0 | 1.0 | 6.0 | 2.0 | 1.0 | 8.0 | 2.0 | 6.0 | 1.0 | 10.0 | 9.0 | 6.0 | 10.0 | 2.0 | 1.0 | 4.0 | 4.0 | 7.0 | 10.0 | 7.0 | 9.0 | 1.0 | 1.0 | 10.0 | 10.0 | 2.0 | 10.0 | 10.0 | 8.0 | 8.0 | 3.0 | 6.0 | 1.0 | 5.0 |
| 29 | 2.0 | 2.0 | 3.0 | 10.0 | 1.0 | 9.0 | 9.0 | 5.0 | 9.0 | 7.0 | 8.0 | 1.0 | 5.0 | 5.0 | 2.0 | 4.0 | 9.0 | 5.0 | 2.0 | 2.0 | 9.0 | 10.0 | 4.0 | 1.0 | 8.0 | 7.0 | 2.0 | 4.0 | 4.0 | 3.0 | 2.0 | 8.0 | 5.0 | 1.0 | 5.0 | 4.0 | 10.0 | 8.0 | 8.0 | 3.0 | 5.0 | 5.0 | 3.0 | 1.0 | 3.0 | 7.0 | 1.0 |
| 30 | 8.0 | 10.0 | 5.0 | 9.0 | 2.0 | 10.0 | 7.0 | 6.0 | 7.0 | 5.0 | 2.0 | 9.0 | 9.0 | 1.0 | 7.0 | 5.0 | 10.0 | 9.0 | 9.0 | 6.0 | 9.0 | 7.0 | 3.0 | 2.0 | 1.0 | 9.0 | 1.0 | 9.0 | 7.0 | 2.0 | 4.0 | 1.0 | 3.0 | 6.0 | 2.0 | 6.0 | 8.0 | 8.0 | 4.0 | 5.0 | 7.0 | 10.0 | 4.0 | 5.0 | 1.0 | 9.0 | 1.0 |
| 31 | 5.0 | 9.0 | 2.0 | 5.0 | 9.0 | 10.0 | 8.0 | 6.0 | 9.0 | 9.0 | 9.0 | 1.0 | 2.0 | 6.0 | 9.0 | 1.0 | 9.0 | 7.0 | 8.0 | 8.0 | 6.0 | 5.0 | 2.0 | 7.0 | 10.0 | 10.0 | 10.0 | 8.0 | 10.0 | 8.0 | 1.0 | 1.0 | 6.0 | 4.0 | 2.0 | 4.0 | 9.0 | 1.0 | 7.0 | 1.0 | 7.0 | 5.0 | 3.0 | 1.0 | 1.0 | 2.0 | 2.0 |
| 32 | 10.0 | 7.0 | 1.0 | 6.0 | 5.0 | 7.0 | 5.0 | 2.0 | 7.0 | 2.0 | 8.0 | 4.0 | 1.0 | 6.0 | 3.0 | 3.0 | 1.0 | 4.0 | 8.0 | 3.0 | 10.0 | 10.0 | 10.0 | 2.0 | 9.0 | 5.0 | 7.0 | 1.0 | 7.0 | 5.0 | 3.0 | 6.0 | 4.0 | 7.0 | 3.0 | 8.0 | 2.0 | 3.0 | 3.0 | 7.0 | 7.0 | 1.0 | 7.0 | 9.0 | 2.0 | 3.0 | 6.0 |
| 33 | 9.0 | 3.0 | 5.0 | 4.0 | 5.0 | 4.0 | 1.0 | 6.0 | 4.0 | 8.0 | 7.0 | 3.0 | 7.0 | 10.0 | 1.0 | 6.0 | 10.0 | 4.0 | 2.0 | 5.0 | 1.0 | 6.0 | 7.0 | 1.0 | 1.0 | 6.0 | 1.0 | 7.0 | 9.0 | 1.0 | 6.0 | 4.0 | 7.0 | 2.0 | 4.0 | 2.0 | 7.0 | 9.0 | 4.0 | 3.0 | 5.0 | 9.0 | 6.0 | 2.0 | 1.0 | 7.0 | 10.0 |
| 34 | 9.0 | 9.0 | 3.0 | 1.0 | 5.0 | 1.0 | 7.0 | 1.0 | 5.0 | 6.0 | 10.0 | 4.0 | 6.0 | 3.0 | 9.0 | 8.0 | 10.0 | 10.0 | 1.0 | 2.0 | 10.0 | 3.0 | 9.0 | 3.0 | 8.0 | 9.0 | 1.0 | 7.0 | 1.0 | 5.0 | 2.0 | 2.0 | 3.0 | 4.0 | 4.0 | 5.0 | 4.0 | 8.0 | 5.0 | 10.0 | 6.0 | 5.0 | 10.0 | 3.0 | 10.0 | 4.0 | 8.0 |
| 35 | 6.0 | 10.0 | 4.0 | 7.0 | 6.0 | 9.0 | 9.0 | 8.0 | 2.0 | 10.0 | 10.0 | 2.0 | 6.0 | 3.0 | 1.0 | 10.0 | 10.0 | 7.0 | 4.0 | 7.0 | 6.0 | 2.0 | 8.0 | 6.0 | 8.0 | 2.0 | 1.0 | 3.0 | 1.0 | 4.0 | 6.0 | 4.0 | 8.0 | 2.0 | 5.0 | 7.0 | 4.0 | 6.0 | 1.0 | 10.0 | 8.0 | 4.0 | 10.0 | 7.0 | 4.0 | 5.0 | 8.0 |
| 36 | 1.0 | 9.0 | 7.0 | 1.0 | 4.0 | 8.0 | 1.0 | 8.0 | 9.0 | 9.0 | 5.0 | 10.0 | 4.0 | 4.0 | 8.0 | 3.0 | 1.0 | 3.0 | 1.0 | 1.0 | 5.0 | 10.0 | 10.0 | 3.0 | 5.0 | 9.0 | 8.0 | 5.0 | 10.0 | 10.0 | 8.0 | 9.0 | 2.0 | 7.0 | 4.0 | 4.0 | 9.0 | 9.0 | 5.0 | 10.0 | 4.0 | 5.0 | 9.0 | 2.0 | 4.0 | 6.0 | 4.0 |
| 37 | 2.0 | 1.0 | 3.0 | 6.0 | 4.0 | 1.0 | 1.0 | 9.0 | 2.0 | 10.0 | 8.0 | 2.0 | 4.0 | 2.0 | 1.0 | 4.0 | 3.0 | 4.0 | 4.0 | 6.0 | 6.0 | 10.0 | 7.0 | 6.0 | 7.0 | 9.0 | 9.0 | 5.0 | 10.0 | 8.0 | 8.0 | 1.0 | 3.0 | 9.0 | 8.0 | 6.0 | 9.0 | 10.0 | 9.0 | 7.0 | 6.0 | 9.0 | 9.0 | 2.0 | 3.0 | 3.0 | 8.0 |
| 38 | 9.0 | 5.0 | 4.0 | 1.0 | 8.0 | 6.0 | 3.0 | 3.0 | 3.0 | 8.0 | 10.0 | 6.0 | 10.0 | 2.0 | 9.0 | 1.0 | 9.0 | 4.0 | 3.0 | 2.0 | 1.0 | 8.0 | 3.0 | 2.0 | 8.0 | 9.0 | 3.0 | 5.0 | 2.0 | 8.0 | 4.0 | 7.0 | 3.0 | 4.0 | 5.0 | 1.0 | 5.0 | 9.0 | 10.0 | 5.0 | 4.0 | 4.0 | 1.0 | 6.0 | 3.0 | 10.0 | 1.0 |
| 39 | 5.0 | 9.0 | 5.0 | 9.0 | 10.0 | 1.0 | 3.0 | 2.0 | 1.0 | 3.0 | 7.0 | 5.0 | 6.0 | 1.0 | 2.0 | 1.0 | 5.0 | 4.0 | 3.0 | 5.0 | 10.0 | 10.0 | 4.0 | 5.0 | 5.0 | 3.0 | 7.0 | 2.0 | 10.0 | 3.0 | 5.0 | 1.0 | 7.0 | 3.0 | 10.0 | 10.0 | 10.0 | 7.0 | 5.0 | 5.0 | 4.0 | 6.0 | 2.0 | 6.0 | 7.0 | 8.0 | 3.0 |
| 40 | 2.0 | 8.0 | 10.0 | 1.0 | 3.0 | 8.0 | 9.0 | 9.0 | 5.0 | 7.0 | 9.0 | 8.0 | 3.0 | 3.0 | 10.0 | 7.0 | 1.0 | 7.0 | 6.0 | 5.0 | 7.0 | 1.0 | 2.0 | 1.0 | 10.0 | 2.0 | 2.0 | 3.0 | 10.0 | 5.0 | 7.0 | 7.0 | 7.0 | 5.0 | 6.0 | 8.0 | 4.0 | 6.0 | 4.0 | 4.0 | 3.0 | 5.0 | 4.0 | 10.0 | 3.0 | 1.0 | 9.0 |
| 41 | 7.0 | 1.0 | 5.0 | 5.0 | 6.0 | 7.0 | 2.0 | 9.0 | 6.0 | 10.0 | 1.0 | 5.0 | 8.0 | 8.0 | 2.0 | 5.0 | 6.0 | 8.0 | 3.0 | 3.0 | 9.0 | 2.0 | 4.0 | 6.0 | 2.0 | 8.0 | 1.0 | 8.0 | 8.0 | 5.0 | 10.0 | 5.0 | 1.0 | 9.0 | 5.0 | 4.0 | 5.0 | 9.0 | 4.0 | 6.0 | 5.0 | 1.0 | 5.0 | 5.0 | 6.0 | 8.0 | 8.0 |
| 42 | 8.0 | 9.0 | 5.0 | 3.0 | 8.0 | 4.0 | 6.0 | 5.0 | 8.0 | 8.0 | 7.0 | 7.0 | 8.0 | 4.0 | 3.0 | 3.0 | 5.0 | 6.0 | 10.0 | 1.0 | 9.0 | 1.0 | 6.0 | 4.0 | 8.0 | 3.0 | 10.0 | 9.0 | 8.0 | 3.0 | 4.0 | 3.0 | 7.0 | 6.0 | 10.0 | 10.0 | 9.0 | 9.0 | 1.0 | 2.0 | 4.0 | 5.0 | 9.0 | 7.0 | 10.0 | 6.0 | 1.0 |
| 43 | 8.0 | 4.0 | 7.0 | 3.0 | 7.0 | 5.0 | 2.0 | 6.0 | 4.0 | 4.0 | 2.0 | 2.0 | 5.0 | 10.0 | 3.0 | 5.0 | 6.0 | 4.0 | 6.0 | 2.0 | 1.0 | 8.0 | 5.0 | 1.0 | 8.0 | 5.0 | 8.0 | 7.0 | 3.0 | 1.0 | 5.0 | 1.0 | 9.0 | 2.0 | 3.0 | 7.0 | 2.0 | 2.0 | 6.0 | 6.0 | 10.0 | 5.0 | 7.0 | 7.0 | 3.0 | 7.0 | 6.0 |
| 44 | 4.0 | 1.0 | 5.0 | 1.0 | 1.0 | 1.0 | 5.0 | 2.0 | 4.0 | 1.0 | 10.0 | 3.0 | 5.0 | 10.0 | 10.0 | 6.0 | 8.0 | 6.0 | 7.0 | 3.0 | 5.0 | 1.0 | 1.0 | 3.0 | 10.0 | 3.0 | 8.0 | 9.0 | 6.0 | 3.0 | 1.0 | 1.0 | 2.0 | 1.0 | 10.0 | 4.0 | 4.0 | 3.0 | 3.0 | 7.0 | 3.0 | 6.0 | 10.0 | 3.0 | 3.0 | 4.0 | 5.0 |
| 45 | 5.0 | 9.0 | 4.0 | 7.0 | 9.0 | 5.0 | 8.0 | 5.0 | 4.0 | 1.0 | 5.0 | 6.0 | 1.0 | 1.0 | 6.0 | 8.0 | 10.0 | 3.0 | 10.0 | 5.0 | 2.0 | 7.0 | 3.0 | 3.0 | 2.0 | 1.0 | 6.0 | 4.0 | 1.0 | 7.0 | 9.0 | 2.0 | 3.0 | 7.0 | 4.0 | 5.0 | 6.0 | 3.0 | 10.0 | 8.0 | 1.0 | 8.0 | 6.0 | 7.0 | 4.0 | 2.0 | 6.0 |
| 46 | 5.0 | 6.0 | 2.0 | 10.0 | 1.0 | 2.0 | 3.0 | 5.0 | 1.0 | 1.0 | 5.0 | 9.0 | 10.0 | 10.0 | 1.0 | 1.0 | 5.0 | 7.0 | 9.0 | 6.0 | 8.0 | 5.0 | 5.0 | 9.0 | 2.0 | 2.0 | 6.0 | 4.0 | 5.0 | 1.0 | 1.0 | 2.0 | 6.0 | 10.0 | 8.0 | 8.0 | 4.0 | 8.0 | 1.0 | 3.0 | 9.0 | 8.0 | 1.0 | 6.0 | 5.0 | 6.0 | 7.0 |

Oh, and when you send the actual route back, please stick to a tiny, predictable JSON shape so it's easy to check automatically. Something casual like this is perfect:

{
  ""solution"": []
}

Here ""solution"" is just a single list where you'll put the nodes of the chosen route in order, from the assembly area (source) to the safe zone (target). Think of it as the one-line form field for the path — the example above is only the shape, not the answer itself. Please use the node labels exactly as they appear in the problem instance and don't invent or rename anything.

- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Keep it simple and readable, and I’ll take it from there.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 1, 'var_index': 1}, {'from': 16, 'to': 2, 'var_index': 2}, {'from': 16, 'to': 3, 'var_index': 3}, {'from': 16, 'to': 4, 'var_index': 4}, {'from': 16, 'to': 5, 'var_index': 5}, {'from': 16, 'to': 6, 'var_index': 6}, {'from': 16, 'to': 7, 'var_index': 7}, {'from': 16, 'to': 8, 'var_index': 8}, {'from': 16, 'to': 9, 'var_index': 9}, {'from': 16, 'to': 10, 'var_index': 10}, {'from': 16, 'to': 11, 'var_index': 11}, {'from': 16, 'to': 12, 'var_index': 12}, {'from': 16, 'to': 13, 'var_index': 13}, {'from': 16, 'to': 14, 'var_index': 14}, {'from': 16, 'to': 15, 'var_index': 15}, {'from': 0, 'to': 17, 'var_index': 16}, {'from': 1, 'to': 17, 'var_index': 17}, {'from': 2, 'to': 17, 'var_index': 18}, {'from': 3, 'to': 17, 'var_index': 19}, {'from': 4, 'to': 17, 'var_index': 20}, {'from': 5, 'to': 17, 'var_index': 21}, {'from': 6, 'to': 17, 'var_index': 22}, {'from': 7, 'to': 17, 'var_index': 23}, {'from': 8, 'to': 17, 'var_index': 24}, {'from': 9, 'to': 17, 'var_index': 25}, {'from': 10, 'to': 17, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 17, 'var_index': 28}, {'from': 13, 'to': 17, 'var_index': 29}, {'from': 14, 'to': 17, 'var_index': 30}, {'from': 15, 'to': 17, 'var_index': 31}, {'from': 0, 'to': 1, 'var_index': 32}, {'from': 1, 'to': 2, 'var_index': 33}, {'from': 2, 'to': 3, 'var_index': 34}, {'from': 3, 'to': 4, 'var_index': 35}, {'from': 4, 'to': 5, 'var_index': 36}, {'from': 5, 'to': 6, 'var_index': 37}, {'from': 6, 'to': 7, 'var_index': 38}, {'from': 7, 'to': 8, 'var_index': 39}, {'from': 8, 'to': 9, 'var_index': 40}, {'from': 9, 'to': 10, 'var_index': 41}, {'from': 10, 'to': 11, 'var_index': 42}, {'from': 11, 'to': 12, 'var_index': 43}, {'from': 12, 'to': 13, 'var_index': 44}, {'from': 13, 'to': 14, 'var_index': 45}, {'from': 14, 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'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 45, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 46, 'quadratic_cost': 6.0}, {'var_i': 44, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 44, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 44, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 44, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 44, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 44, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 44, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 44, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 44, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 44, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 44, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 44, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 44, 'var_j': 27, 'quadratic_cost': 9.0}, {'var_i': 44, 'var_j': 28, 'quadratic_cost': 6.0}, {'var_i': 44, 'var_j': 29, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 44, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 44, 'var_j': 34, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 35, 'quadratic_cost': 4.0}, {'var_i': 44, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 44, 'var_j': 37, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 38, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 39, 'quadratic_cost': 7.0}, {'var_i': 44, 'var_j': 40, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 41, 'quadratic_cost': 6.0}, {'var_i': 44, 'var_j': 42, 'quadratic_cost': 10.0}, {'var_i': 44, 'var_j': 43, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 44, 'quadratic_cost': 3.0}, {'var_i': 44, 'var_j': 45, 'quadratic_cost': 4.0}, {'var_i': 44, 'var_j': 46, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 45, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 45, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 45, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 45, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 45, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 45, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 45, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 45, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 45, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 45, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 45, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 45, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 45, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 45, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 45, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 45, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 45, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 26, 'quadratic_cost': 6.0}, {'var_i': 45, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 45, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 45, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 45, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 45, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 45, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 45, 'var_j': 34, 'quadratic_cost': 4.0}, {'var_i': 45, 'var_j': 35, 'quadratic_cost': 5.0}, {'var_i': 45, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 45, 'var_j': 37, 'quadratic_cost': 3.0}, {'var_i': 45, 'var_j': 38, 'quadratic_cost': 10.0}, {'var_i': 45, 'var_j': 39, 'quadratic_cost': 8.0}, {'var_i': 45, 'var_j': 40, 'quadratic_cost': 1.0}, {'var_i': 45, 'var_j': 41, 'quadratic_cost': 8.0}, {'var_i': 45, 'var_j': 42, 'quadratic_cost': 6.0}, {'var_i': 45, 'var_j': 43, 'quadratic_cost': 7.0}, {'var_i': 45, 'var_j': 44, 'quadratic_cost': 4.0}, {'var_i': 45, 'var_j': 45, 'quadratic_cost': 2.0}, {'var_i': 45, 'var_j': 46, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 46, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 26, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 46, 'var_j': 28, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 29, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 34, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 35, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 36, 'quadratic_cost': 4.0}, {'var_i': 46, 'var_j': 37, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 46, 'var_j': 40, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 41, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 42, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 43, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 44, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 45, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 46, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'Q', 'to': 'A', 'var_index': 0}, {'from': 'Q', 'to': 'B', 'var_index': 1}, {'from': 'Q', 'to': 'C', 'var_index': 2}, {'from': 'Q', 'to': 'D', 'var_index': 3}, {'from': 'Q', 'to': 'E', 'var_index': 4}, {'from': 'Q', 'to': 'F', 'var_index': 5}, {'from': 'Q', 'to': 'G', 'var_index': 6}, {'from': 'Q', 'to': 'H', 'var_index': 7}, {'from': 'Q', 'to': 'I', 'var_index': 8}, {'from': 'Q', 'to': 'J', 'var_index': 9}, {'from': 'Q', 'to': 'K', 'var_index': 10}, {'from': 'Q', 'to': 'L', 'var_index': 11}, {'from': 'Q', 'to': 'M', 'var_index': 12}, {'from': 'Q', 'to': 'N', 'var_index': 13}, {'from': 'Q', 'to': 'O', 'var_index': 14}, {'from': 'Q', 'to': 'P', 'var_index': 15}, {'from': 'A', 'to': 'R', 'var_index': 16}, {'from': 'B', 'to': 'R', 'var_index': 17}, {'from': 'C', 'to': 'R', 'var_index': 18}, {'from': 'D', 'to': 'R', 'var_index': 19}, {'from': 'E', 'to': 'R', 'var_index': 20}, {'from': 'F', 'to': 'R', 'var_index': 21}, {'from': 'G', 'to': 'R', 'var_index': 22}, {'from': 'H', 'to': 'R', 'var_index': 23}, {'from': 'I', 'to': 'R', 'var_index': 24}, {'from': 'J', 'to': 'R', 'var_index': 25}, {'from': 'K', 'to': 'R', 'var_index': 26}, {'from': 'L', 'to': 'R', 'var_index': 27}, {'from': 'M', 'to': 'R', 'var_index': 28}, {'from': 'N', 'to': 'R', 'var_index': 29}, {'from': 'O', 'to': 'R', 'var_index': 30}, {'from': 'P', 'to': 'R', 'var_index': 31}, {'from': 'A', 'to': 'B', 'var_index': 32}, {'from': 'B', 'to': 'C', 'var_index': 33}, {'from': 'C', 'to': 'D', 'var_index': 34}, {'from': 'D', 'to': 'E', 'var_index': 35}, {'from': 'E', 'to': 'F', 'var_index': 36}, {'from': 'F', 'to': 'G', 'var_index': 37}, {'from': 'G', 'to': 'H', 'var_index': 38}, {'from': 'H', 'to': 'I', 'var_index': 39}, {'from': 'I', 'to': 'J', 'var_index': 40}, {'from': 'J', 'to': 'K', 'var_index': 41}, {'from': 'K', 'to': 'L', 'var_index': 42}, {'from': 'L', 'to': 'M', 'var_index': 43}, {'from': 'M', 'to': 'N', 'var_index': 44}, {'from': 'N', 'to': 'O', 'var_index': 45}, {'from': 'O', 'to': 'P', 'var_index': 46}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R'}}","['Q', 'E', 'R']",12,csv,names
QSPP,QSPP,"We were putting together a distribution map and needed exactly one directed chain from our content source to the audience endpoint. Every hop in that chain has a base activation fee, and certain combinations of hops cause extra overlap charges when both are used — those combination charges can be asymmetric, so if channel A and channel B are both in the chain you include A’s extra cost with B and B’s extra cost with A. The task is to choose one uninterrupted, direction-respecting route (start at the origin, end at the audience, and every consecutive pair must be a valid one-way connection) and keep everything in that single sequence — don’t split or create multiple routes. The winner is the route with the smallest total bill: sum all the individual activation fees plus all pairwise overlap costs for channels that appear together. Concrete channel names, fees, and overlap rules are listed below.

# num_locations=20
# num_channel_hops=19
# location_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
# content_origin_node=19
# audience_endpoint_node=20

hop_from_location,hop_to_location,channel_hop_id
19,1,0
18,20,1
1,2,2
2,3,3
3,4,4
4,5,5
5,6,6
6,7,7
7,8,8
8,9,9
9,10,10
10,11,11
11,12,12
12,13,13
13,14,14
14,15,15
15,16,16
16,17,17
17,18,18

channel_hop_id,activation_fee
0,8.0
1,3.0
2,3.0
3,1.0
4,10.0
5,5.0
6,7.0
7,2.0
8,2.0
9,3.0
10,2.0
11,4.0
12,10.0
13,9.0
14,5.0
15,8.0
16,9.0
17,7.0
18,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (channel_i_id, channel_j_id). If two channel_hops with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| channel_i_id\channel_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 2.0 | 10.0 | 5.0 | 9.0 | 7.0 | 2.0 | 6.0 | 7.0 | 5.0 | 4.0 | 1.0 | 5.0 | 3.0 | 5.0 | 5.0 | 5.0 | 2.0 | 3.0 |
| 1 | 2.0 | 10.0 | 9.0 | 6.0 | 10.0 | 4.0 | 3.0 | 2.0 | 10.0 | 2.0 | 9.0 | 9.0 | 4.0 | 2.0 | 10.0 | 2.0 | 2.0 | 7.0 | 9.0 |
| 2 | 10.0 | 9.0 | 1.0 | 5.0 | 10.0 | 2.0 | 4.0 | 6.0 | 8.0 | 6.0 | 7.0 | 4.0 | 6.0 | 4.0 | 4.0 | 1.0 | 3.0 | 8.0 | 10.0 |
| 3 | 5.0 | 6.0 | 5.0 | 4.0 | 6.0 | 3.0 | 1.0 | 7.0 | 8.0 | 1.0 | 6.0 | 10.0 | 6.0 | 5.0 | 4.0 | 7.0 | 8.0 | 9.0 | 5.0 |
| 4 | 9.0 | 10.0 | 10.0 | 6.0 | 4.0 | 2.0 | 5.0 | 4.0 | 8.0 | 5.0 | 10.0 | 8.0 | 1.0 | 6.0 | 7.0 | 5.0 | 4.0 | 4.0 | 10.0 |
| 5 | 7.0 | 4.0 | 2.0 | 3.0 | 2.0 | 5.0 | 5.0 | 5.0 | 2.0 | 10.0 | 2.0 | 2.0 | 6.0 | 7.0 | 5.0 | 4.0 | 4.0 | 4.0 | 9.0 |
| 6 | 2.0 | 3.0 | 4.0 | 1.0 | 5.0 | 5.0 | 6.0 | 4.0 | 3.0 | 8.0 | 9.0 | 10.0 | 6.0 | 8.0 | 9.0 | 3.0 | 10.0 | 6.0 | 3.0 |
| 7 | 6.0 | 2.0 | 6.0 | 7.0 | 4.0 | 5.0 | 4.0 | 1.0 | 3.0 | 7.0 | 1.0 | 7.0 | 1.0 | 1.0 | 2.0 | 4.0 | 1.0 | 10.0 | 5.0 |
| 8 | 7.0 | 10.0 | 8.0 | 8.0 | 8.0 | 2.0 | 3.0 | 3.0 | 9.0 | 7.0 | 4.0 | 5.0 | 2.0 | 4.0 | 9.0 | 6.0 | 10.0 | 1.0 | 9.0 |
| 9 | 5.0 | 2.0 | 6.0 | 1.0 | 5.0 | 10.0 | 8.0 | 7.0 | 7.0 | 3.0 | 1.0 | 4.0 | 5.0 | 3.0 | 10.0 | 9.0 | 10.0 | 9.0 | 10.0 |
| 10 | 4.0 | 9.0 | 7.0 | 6.0 | 10.0 | 2.0 | 9.0 | 1.0 | 4.0 | 1.0 | 6.0 | 6.0 | 5.0 | 2.0 | 8.0 | 1.0 | 6.0 | 9.0 | 10.0 |
| 11 | 1.0 | 9.0 | 4.0 | 10.0 | 8.0 | 2.0 | 10.0 | 7.0 | 5.0 | 4.0 | 6.0 | 2.0 | 9.0 | 3.0 | 4.0 | 4.0 | 10.0 | 6.0 | 10.0 |
| 12 | 5.0 | 4.0 | 6.0 | 6.0 | 1.0 | 6.0 | 6.0 | 1.0 | 2.0 | 5.0 | 5.0 | 9.0 | 5.0 | 7.0 | 4.0 | 2.0 | 10.0 | 7.0 | 2.0 |
| 13 | 3.0 | 2.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 1.0 | 4.0 | 3.0 | 2.0 | 3.0 | 7.0 | 2.0 | 4.0 | 7.0 | 5.0 | 1.0 | 6.0 |
| 14 | 5.0 | 10.0 | 4.0 | 4.0 | 7.0 | 5.0 | 9.0 | 2.0 | 9.0 | 10.0 | 8.0 | 4.0 | 4.0 | 4.0 | 8.0 | 1.0 | 9.0 | 1.0 | 8.0 |
| 15 | 5.0 | 2.0 | 1.0 | 7.0 | 5.0 | 4.0 | 3.0 | 4.0 | 6.0 | 9.0 | 1.0 | 4.0 | 2.0 | 7.0 | 1.0 | 9.0 | 1.0 | 2.0 | 1.0 |
| 16 | 5.0 | 2.0 | 3.0 | 8.0 | 4.0 | 4.0 | 10.0 | 1.0 | 10.0 | 10.0 | 6.0 | 10.0 | 10.0 | 5.0 | 9.0 | 1.0 | 6.0 | 5.0 | 2.0 |
| 17 | 2.0 | 7.0 | 8.0 | 9.0 | 4.0 | 4.0 | 6.0 | 10.0 | 1.0 | 9.0 | 9.0 | 6.0 | 7.0 | 1.0 | 1.0 | 2.0 | 5.0 | 9.0 | 5.0 |
| 18 | 3.0 | 9.0 | 10.0 | 5.0 | 10.0 | 9.0 | 3.0 | 5.0 | 9.0 | 10.0 | 10.0 | 10.0 | 2.0 | 6.0 | 8.0 | 1.0 | 2.0 | 5.0 | 10.0 |

Oh, and when you send back the final route, please drop it into this tiny JSON shape so it's easy to read and parse:

{
  ""solution"": []
}

Think of ""solution"" as the single ordered list of node names that form the path from the origin to the audience endpoint — just the node identifiers in order, nothing else. This JSON is just a sketch of the expected shape, not the actual answer; fill that array with the nodes of your chosen route.

Also, please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example:
- ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 17, 'to': 19, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}], 'objective': {'constant': 0.0, 'linear': [8.0, 3.0, 3.0, 1.0, 10.0, 5.0, 7.0, 2.0, 2.0, 3.0, 2.0, 4.0, 10.0, 9.0, 5.0, 8.0, 9.0, 7.0, 7.0], 'quadratic': [[8.0, 2.0, 10.0, 5.0, 9.0, 7.0, 2.0, 6.0, 7.0, 5.0, 4.0, 1.0, 5.0, 3.0, 5.0, 5.0, 5.0, 2.0, 3.0], [2.0, 10.0, 9.0, 6.0, 10.0, 4.0, 3.0, 2.0, 10.0, 2.0, 9.0, 9.0, 4.0, 2.0, 10.0, 2.0, 2.0, 7.0, 9.0], [10.0, 9.0, 1.0, 5.0, 10.0, 2.0, 4.0, 6.0, 8.0, 6.0, 7.0, 4.0, 6.0, 4.0, 4.0, 1.0, 3.0, 8.0, 10.0], [5.0, 6.0, 5.0, 4.0, 6.0, 3.0, 1.0, 7.0, 8.0, 1.0, 6.0, 10.0, 6.0, 5.0, 4.0, 7.0, 8.0, 9.0, 5.0], [9.0, 10.0, 10.0, 6.0, 4.0, 2.0, 5.0, 4.0, 8.0, 5.0, 10.0, 8.0, 1.0, 6.0, 7.0, 5.0, 4.0, 4.0, 10.0], [7.0, 4.0, 2.0, 3.0, 2.0, 5.0, 5.0, 5.0, 2.0, 10.0, 2.0, 2.0, 6.0, 7.0, 5.0, 4.0, 4.0, 4.0, 9.0], [2.0, 3.0, 4.0, 1.0, 5.0, 5.0, 6.0, 4.0, 3.0, 8.0, 9.0, 10.0, 6.0, 8.0, 9.0, 3.0, 10.0, 6.0, 3.0], [6.0, 2.0, 6.0, 7.0, 4.0, 5.0, 4.0, 1.0, 3.0, 7.0, 1.0, 7.0, 1.0, 1.0, 2.0, 4.0, 1.0, 10.0, 5.0], [7.0, 10.0, 8.0, 8.0, 8.0, 2.0, 3.0, 3.0, 9.0, 7.0, 4.0, 5.0, 2.0, 4.0, 9.0, 6.0, 10.0, 1.0, 9.0], [5.0, 2.0, 6.0, 1.0, 5.0, 10.0, 8.0, 7.0, 7.0, 3.0, 1.0, 4.0, 5.0, 3.0, 10.0, 9.0, 10.0, 9.0, 10.0], [4.0, 9.0, 7.0, 6.0, 10.0, 2.0, 9.0, 1.0, 4.0, 1.0, 6.0, 6.0, 5.0, 2.0, 8.0, 1.0, 6.0, 9.0, 10.0], [1.0, 9.0, 4.0, 10.0, 8.0, 2.0, 10.0, 7.0, 5.0, 4.0, 6.0, 2.0, 9.0, 3.0, 4.0, 4.0, 10.0, 6.0, 10.0], [5.0, 4.0, 6.0, 6.0, 1.0, 6.0, 6.0, 1.0, 2.0, 5.0, 5.0, 9.0, 5.0, 7.0, 4.0, 2.0, 10.0, 7.0, 2.0], [3.0, 2.0, 4.0, 5.0, 6.0, 7.0, 8.0, 1.0, 4.0, 3.0, 2.0, 3.0, 7.0, 2.0, 4.0, 7.0, 5.0, 1.0, 6.0], [5.0, 10.0, 4.0, 4.0, 7.0, 5.0, 9.0, 2.0, 9.0, 10.0, 8.0, 4.0, 4.0, 4.0, 8.0, 1.0, 9.0, 1.0, 8.0], [5.0, 2.0, 1.0, 7.0, 5.0, 4.0, 3.0, 4.0, 6.0, 9.0, 1.0, 4.0, 2.0, 7.0, 1.0, 9.0, 1.0, 2.0, 1.0], [5.0, 2.0, 3.0, 8.0, 4.0, 4.0, 10.0, 1.0, 10.0, 10.0, 6.0, 10.0, 10.0, 5.0, 9.0, 1.0, 6.0, 5.0, 2.0], [2.0, 7.0, 8.0, 9.0, 4.0, 4.0, 6.0, 10.0, 1.0, 9.0, 9.0, 6.0, 7.0, 1.0, 1.0, 2.0, 5.0, 9.0, 5.0], [3.0, 9.0, 10.0, 5.0, 10.0, 9.0, 3.0, 5.0, 9.0, 10.0, 10.0, 10.0, 2.0, 6.0, 8.0, 1.0, 2.0, 5.0, 10.0]]}, 'source': 18, 'target': 19}","[18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]",2065.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 19, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'source': 19, 'target': 20, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 5.0}, {'var_index': 6, 'linear_cost': 7.0}, {'var_index': 7, 'linear_cost': 2.0}, {'var_index': 8, 'linear_cost': 2.0}, {'var_index': 9, 'linear_cost': 3.0}, {'var_index': 10, 'linear_cost': 2.0}, {'var_index': 11, 'linear_cost': 4.0}, {'var_index': 12, 'linear_cost': 10.0}, {'var_index': 13, 'linear_cost': 9.0}, {'var_index': 14, 'linear_cost': 5.0}, {'var_index': 15, 'linear_cost': 8.0}, {'var_index': 16, 'linear_cost': 9.0}, {'var_index': 17, 'linear_cost': 7.0}, {'var_index': 18, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 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'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 4, 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'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 19, 'to': 1, 'var_index': 0}, {'from': 18, 'to': 20, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}, {'from': 15, 'to': 16, 'var_index': 16}, {'from': 16, 'to': 17, 'var_index': 17}, {'from': 17, 'to': 18, 'var_index': 18}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20}}","[19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20]",13,csv,1
QSPP,QSPP,"Someone is routing a delivery drone: pick one one-way path from launch to landing that follows the allowed airways. Each airway has its own battery/wind penalty, and some have an extra built-in penalty when they’re used. Pairs of airways can also interact — if both are flown there’s an additional interference penalty, and that interaction can depend on which airway comes first in the trip. The idea is to choose the single legal route that ends up with the smallest total of all those penalties, computed by adding each airway’s individual penalty plus any extra penalties for every pair that appears on the trip. Concrete corridor choices and penalty values are shown below.

{
  ""total_locations_count"": 16,
  ""total_corridors_count"": 23,
  ""location_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16
  ],
  ""launch_site"": 15,
  ""landing_pad"": 16,
  ""edges"": [
    {
      ""corridor_tail"": 15,
      ""corridor_head"": 1,
      ""corridor_id"": 0
    },
    {
      ""corridor_tail"": 15,
      ""corridor_head"": 8,
      ""corridor_id"": 1
    },
    {
      ""corridor_tail"": 7,
      ""corridor_head"": 16,
      ""corridor_id"": 2
    },
    {
      ""corridor_tail"": 14,
      ""corridor_head"": 16,
      ""corridor_id"": 3
    },
    {
      ""corridor_tail"": 1,
      ""corridor_head"": 2,
      ""corridor_id"": 4
    },
    {
      ""corridor_tail"": 1,
      ""corridor_head"": 8,
      ""corridor_id"": 5
    },
    {
      ""corridor_tail"": 2,
      ""corridor_head"": 3,
      ""corridor_id"": 6
    },
    {
      ""corridor_tail"": 2,
      ""corridor_head"": 9,
      ""corridor_id"": 7
    },
    {
      ""corridor_tail"": 3,
      ""corridor_head"": 4,
      ""corridor_id"": 8
    },
    {
      ""corridor_tail"": 3,
      ""corridor_head"": 10,
      ""corridor_id"": 9
    },
    {
      ""corridor_tail"": 4,
      ""corridor_head"": 5,
      ""corridor_id"": 10
    },
    {
      ""corridor_tail"": 4,
      ""corridor_head"": 11,
      ""corridor_id"": 11
    },
    {
      ""corridor_tail"": 5,
      ""corridor_head"": 6,
      ""corridor_id"": 12
    },
    {
      ""corridor_tail"": 5,
      ""corridor_head"": 12,
      ""corridor_id"": 13
    },
    {
      ""corridor_tail"": 6,
      ""corridor_head"": 7,
      ""corridor_id"": 14
    },
    {
      ""corridor_tail"": 6,
      ""corridor_head"": 13,
      ""corridor_id"": 15
    },
    {
      ""corridor_tail"": 7,
      ""corridor_head"": 14,
      ""corridor_id"": 16
    },
    {
      ""corridor_tail"": 8,
      ""corridor_head"": 9,
      ""corridor_id"": 17
    },
    {
      ""corridor_tail"": 9,
      ""corridor_head"": 10,
      ""corridor_id"": 18
    },
    {
      ""corridor_tail"": 10,
      ""corridor_head"": 11,
      ""corridor_id"": 19
    },
    {
      ""corridor_tail"": 11,
      ""corridor_head"": 12,
      ""corridor_id"": 20
    },
    {
      ""corridor_tail"": 12,
      ""corridor_head"": 13,
      ""corridor_id"": 21
    },
    {
      ""corridor_tail"": 13,
      ""corridor_head"": 14,
      ""corridor_id"": 22
    }
  ],
  ""linear_costs"": [
    {
      ""corridor_id"": 0,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 1,
      ""per_corridor_penalty"": 7.0
    },
    {
      ""corridor_id"": 2,
      ""per_corridor_penalty"": 1.0
    },
    {
      ""corridor_id"": 3,
      ""per_corridor_penalty"": 5.0
    },
    {
      ""corridor_id"": 4,
      ""per_corridor_penalty"": 8.0
    },
    {
      ""corridor_id"": 5,
      ""per_corridor_penalty"": 4.0
    },
    {
      ""corridor_id"": 6,
      ""per_corridor_penalty"": 5.0
    },
    {
      ""corridor_id"": 7,
      ""per_corridor_penalty"": 7.0
    },
    {
      ""corridor_id"": 8,
      ""per_corridor_penalty"": 6.0
    },
    {
      ""corridor_id"": 9,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 10,
      ""per_corridor_penalty"": 10.0
    },
    {
      ""corridor_id"": 11,
      ""per_corridor_penalty"": 3.0
    },
    {
      ""corridor_id"": 12,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 13,
      ""per_corridor_penalty"": 8.0
    },
    {
      ""corridor_id"": 14,
      ""per_corridor_penalty"": 8.0
    },
    {
      ""corridor_id"": 15,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 16,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 17,
      ""per_corridor_penalty"": 5.0
    },
    {
      ""corridor_id"": 18,
      ""per_corridor_penalty"": 6.0
    },
    {
      ""corridor_id"": 19,
      ""per_corridor_penalty"": 7.0
    },
    {
      ""corridor_id"": 20,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 21,
      ""per_corridor_penalty"": 9.0
    },
    {
      ""corridor_id"": 22,
      ""per_corridor_penalty"": 4.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 4.0 | 8.0 | 9.0 | 10.0 | 6.0 | 9.0 | 6.0 | 1.0 | 4.0 | 8.0 | 10.0 | 10.0 | 8.0 | 7.0 | 3.0 | 1.0 | 1.0 | 6.0 | 5.0 | 4.0 | 10.0 | 3.0 |
| 1 | 4.0 | 8.0 | 1.0 | 10.0 | 8.0 | 5.0 | 1.0 | 1.0 | 6.0 | 1.0 | 9.0 | 4.0 | 6.0 | 10.0 | 7.0 | 7.0 | 10.0 | 2.0 | 1.0 | 3.0 | 10.0 | 2.0 | 10.0 |
| 2 | 8.0 | 1.0 | 4.0 | 10.0 | 5.0 | 8.0 | 3.0 | 2.0 | 9.0 | 9.0 | 3.0 | 9.0 | 1.0 | 2.0 | 6.0 | 4.0 | 4.0 | 7.0 | 3.0 | 3.0 | 2.0 | 10.0 | 4.0 |
| 3 | 9.0 | 10.0 | 10.0 | 7.0 | 9.0 | 4.0 | 10.0 | 9.0 | 4.0 | 7.0 | 10.0 | 5.0 | 7.0 | 3.0 | 2.0 | 10.0 | 8.0 | 10.0 | 3.0 | 3.0 | 1.0 | 1.0 | 9.0 |
| 4 | 10.0 | 8.0 | 5.0 | 9.0 | 5.0 | 4.0 | 2.0 | 7.0 | 3.0 | 5.0 | 1.0 | 8.0 | 6.0 | 5.0 | 6.0 | 6.0 | 2.0 | 10.0 | 4.0 | 3.0 | 5.0 | 3.0 | 8.0 |
| 5 | 6.0 | 5.0 | 8.0 | 4.0 | 4.0 | 4.0 | 10.0 | 1.0 | 1.0 | 8.0 | 2.0 | 4.0 | 9.0 | 4.0 | 6.0 | 7.0 | 2.0 | 10.0 | 7.0 | 10.0 | 2.0 | 10.0 | 5.0 |
| 6 | 9.0 | 1.0 | 3.0 | 10.0 | 2.0 | 10.0 | 3.0 | 2.0 | 2.0 | 8.0 | 5.0 | 8.0 | 4.0 | 1.0 | 5.0 | 4.0 | 6.0 | 6.0 | 3.0 | 9.0 | 1.0 | 8.0 | 10.0 |
| 7 | 6.0 | 1.0 | 2.0 | 9.0 | 7.0 | 1.0 | 2.0 | 3.0 | 1.0 | 4.0 | 4.0 | 1.0 | 5.0 | 6.0 | 7.0 | 6.0 | 6.0 | 1.0 | 3.0 | 5.0 | 1.0 | 10.0 | 3.0 |
| 8 | 1.0 | 6.0 | 9.0 | 4.0 | 3.0 | 1.0 | 2.0 | 1.0 | 1.0 | 4.0 | 4.0 | 8.0 | 1.0 | 4.0 | 10.0 | 6.0 | 2.0 | 4.0 | 1.0 | 5.0 | 2.0 | 9.0 | 10.0 |
| 9 | 4.0 | 1.0 | 9.0 | 7.0 | 5.0 | 8.0 | 8.0 | 4.0 | 4.0 | 9.0 | 2.0 | 2.0 | 3.0 | 8.0 | 6.0 | 8.0 | 9.0 | 9.0 | 2.0 | 10.0 | 2.0 | 7.0 | 6.0 |
| 10 | 8.0 | 9.0 | 3.0 | 10.0 | 1.0 | 2.0 | 5.0 | 4.0 | 4.0 | 2.0 | 3.0 | 5.0 | 9.0 | 3.0 | 3.0 | 4.0 | 8.0 | 5.0 | 8.0 | 8.0 | 5.0 | 4.0 | 2.0 |
| 11 | 10.0 | 4.0 | 9.0 | 5.0 | 8.0 | 4.0 | 8.0 | 1.0 | 8.0 | 2.0 | 5.0 | 6.0 | 5.0 | 8.0 | 4.0 | 8.0 | 10.0 | 7.0 | 7.0 | 3.0 | 8.0 | 2.0 | 2.0 |
| 12 | 10.0 | 6.0 | 1.0 | 7.0 | 6.0 | 9.0 | 4.0 | 5.0 | 1.0 | 3.0 | 9.0 | 5.0 | 6.0 | 10.0 | 2.0 | 5.0 | 6.0 | 1.0 | 3.0 | 8.0 | 4.0 | 7.0 | 9.0 |
| 13 | 8.0 | 10.0 | 2.0 | 3.0 | 5.0 | 4.0 | 1.0 | 6.0 | 4.0 | 8.0 | 3.0 | 8.0 | 10.0 | 4.0 | 3.0 | 10.0 | 9.0 | 10.0 | 10.0 | 2.0 | 3.0 | 10.0 | 3.0 |
| 14 | 7.0 | 7.0 | 6.0 | 2.0 | 6.0 | 6.0 | 5.0 | 7.0 | 10.0 | 6.0 | 3.0 | 4.0 | 2.0 | 3.0 | 5.0 | 7.0 | 5.0 | 6.0 | 2.0 | 4.0 | 1.0 | 2.0 | 2.0 |
| 15 | 3.0 | 7.0 | 4.0 | 10.0 | 6.0 | 7.0 | 4.0 | 6.0 | 6.0 | 8.0 | 4.0 | 8.0 | 5.0 | 10.0 | 7.0 | 6.0 | 10.0 | 5.0 | 9.0 | 7.0 | 1.0 | 5.0 | 2.0 |
| 16 | 1.0 | 10.0 | 4.0 | 8.0 | 2.0 | 2.0 | 6.0 | 6.0 | 2.0 | 9.0 | 8.0 | 10.0 | 6.0 | 9.0 | 5.0 | 10.0 | 2.0 | 7.0 | 2.0 | 8.0 | 7.0 | 5.0 | 7.0 |
| 17 | 1.0 | 2.0 | 7.0 | 10.0 | 10.0 | 10.0 | 6.0 | 1.0 | 4.0 | 9.0 | 5.0 | 7.0 | 1.0 | 10.0 | 6.0 | 5.0 | 7.0 | 7.0 | 5.0 | 6.0 | 4.0 | 3.0 | 6.0 |
| 18 | 6.0 | 1.0 | 3.0 | 3.0 | 4.0 | 7.0 | 3.0 | 3.0 | 1.0 | 2.0 | 8.0 | 7.0 | 3.0 | 10.0 | 2.0 | 9.0 | 2.0 | 5.0 | 6.0 | 7.0 | 9.0 | 7.0 | 10.0 |
| 19 | 5.0 | 3.0 | 3.0 | 3.0 | 3.0 | 10.0 | 9.0 | 5.0 | 5.0 | 10.0 | 8.0 | 3.0 | 8.0 | 2.0 | 4.0 | 7.0 | 8.0 | 6.0 | 7.0 | 2.0 | 3.0 | 10.0 | 6.0 |
| 20 | 4.0 | 10.0 | 2.0 | 1.0 | 5.0 | 2.0 | 1.0 | 1.0 | 2.0 | 2.0 | 5.0 | 8.0 | 4.0 | 3.0 | 1.0 | 1.0 | 7.0 | 4.0 | 9.0 | 3.0 | 9.0 | 8.0 | 3.0 |
| 21 | 10.0 | 2.0 | 10.0 | 1.0 | 3.0 | 10.0 | 8.0 | 10.0 | 9.0 | 7.0 | 4.0 | 2.0 | 7.0 | 10.0 | 2.0 | 5.0 | 5.0 | 3.0 | 7.0 | 10.0 | 8.0 | 9.0 | 1.0 |
| 22 | 3.0 | 10.0 | 4.0 | 9.0 | 8.0 | 5.0 | 10.0 | 3.0 | 10.0 | 6.0 | 2.0 | 2.0 | 9.0 | 3.0 | 2.0 | 2.0 | 7.0 | 6.0 | 10.0 | 6.0 | 3.0 | 1.0 | 5.0 |

Oh, and when you reply with the chosen route, please use a tiny JSON layout so it's easy to check automatically — something like this:

{
  ""solution"": []
}

""solution"" should hold the route as an ordered list of node identifiers (launch point first, landing point last). Just list the node names in order — nothing else. This is only a sketch of the expected shape, not the actual answer.

Please use each node identifier exactly as it appears in the instance input — don't rename them or invent new labels.

- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 'edges': [{'from': 14, 'to': 0, 'var_index': 0}, {'from': 14, 'to': 7, 'var_index': 1}, {'from': 6, 'to': 15, 'var_index': 2}, {'from': 13, 'to': 15, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 7, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 8, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 9, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 10, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 11, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 12, 'var_index': 15}, {'from': 6, 'to': 13, 'var_index': 16}, {'from': 7, 'to': 8, 'var_index': 17}, {'from': 8, 'to': 9, 'var_index': 18}, {'from': 9, 'to': 10, 'var_index': 19}, {'from': 10, 'to': 11, 'var_index': 20}, {'from': 11, 'to': 12, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [9.0, 7.0, 1.0, 5.0, 8.0, 4.0, 5.0, 7.0, 6.0, 9.0, 10.0, 3.0, 9.0, 8.0, 8.0, 9.0, 9.0, 5.0, 6.0, 7.0, 9.0, 9.0, 4.0], 'quadratic': [[7.0, 4.0, 8.0, 9.0, 10.0, 6.0, 9.0, 6.0, 1.0, 4.0, 8.0, 10.0, 10.0, 8.0, 7.0, 3.0, 1.0, 1.0, 6.0, 5.0, 4.0, 10.0, 3.0], [4.0, 8.0, 1.0, 10.0, 8.0, 5.0, 1.0, 1.0, 6.0, 1.0, 9.0, 4.0, 6.0, 10.0, 7.0, 7.0, 10.0, 2.0, 1.0, 3.0, 10.0, 2.0, 10.0], [8.0, 1.0, 4.0, 10.0, 5.0, 8.0, 3.0, 2.0, 9.0, 9.0, 3.0, 9.0, 1.0, 2.0, 6.0, 4.0, 4.0, 7.0, 3.0, 3.0, 2.0, 10.0, 4.0], [9.0, 10.0, 10.0, 7.0, 9.0, 4.0, 10.0, 9.0, 4.0, 7.0, 10.0, 5.0, 7.0, 3.0, 2.0, 10.0, 8.0, 10.0, 3.0, 3.0, 1.0, 1.0, 9.0], [10.0, 8.0, 5.0, 9.0, 5.0, 4.0, 2.0, 7.0, 3.0, 5.0, 1.0, 8.0, 6.0, 5.0, 6.0, 6.0, 2.0, 10.0, 4.0, 3.0, 5.0, 3.0, 8.0], [6.0, 5.0, 8.0, 4.0, 4.0, 4.0, 10.0, 1.0, 1.0, 8.0, 2.0, 4.0, 9.0, 4.0, 6.0, 7.0, 2.0, 10.0, 7.0, 10.0, 2.0, 10.0, 5.0], [9.0, 1.0, 3.0, 10.0, 2.0, 10.0, 3.0, 2.0, 2.0, 8.0, 5.0, 8.0, 4.0, 1.0, 5.0, 4.0, 6.0, 6.0, 3.0, 9.0, 1.0, 8.0, 10.0], [6.0, 1.0, 2.0, 9.0, 7.0, 1.0, 2.0, 3.0, 1.0, 4.0, 4.0, 1.0, 5.0, 6.0, 7.0, 6.0, 6.0, 1.0, 3.0, 5.0, 1.0, 10.0, 3.0], [1.0, 6.0, 9.0, 4.0, 3.0, 1.0, 2.0, 1.0, 1.0, 4.0, 4.0, 8.0, 1.0, 4.0, 10.0, 6.0, 2.0, 4.0, 1.0, 5.0, 2.0, 9.0, 10.0], [4.0, 1.0, 9.0, 7.0, 5.0, 8.0, 8.0, 4.0, 4.0, 9.0, 2.0, 2.0, 3.0, 8.0, 6.0, 8.0, 9.0, 9.0, 2.0, 10.0, 2.0, 7.0, 6.0], [8.0, 9.0, 3.0, 10.0, 1.0, 2.0, 5.0, 4.0, 4.0, 2.0, 3.0, 5.0, 9.0, 3.0, 3.0, 4.0, 8.0, 5.0, 8.0, 8.0, 5.0, 4.0, 2.0], [10.0, 4.0, 9.0, 5.0, 8.0, 4.0, 8.0, 1.0, 8.0, 2.0, 5.0, 6.0, 5.0, 8.0, 4.0, 8.0, 10.0, 7.0, 7.0, 3.0, 8.0, 2.0, 2.0], [10.0, 6.0, 1.0, 7.0, 6.0, 9.0, 4.0, 5.0, 1.0, 3.0, 9.0, 5.0, 6.0, 10.0, 2.0, 5.0, 6.0, 1.0, 3.0, 8.0, 4.0, 7.0, 9.0], [8.0, 10.0, 2.0, 3.0, 5.0, 4.0, 1.0, 6.0, 4.0, 8.0, 3.0, 8.0, 10.0, 4.0, 3.0, 10.0, 9.0, 10.0, 10.0, 2.0, 3.0, 10.0, 3.0], [7.0, 7.0, 6.0, 2.0, 6.0, 6.0, 5.0, 7.0, 10.0, 6.0, 3.0, 4.0, 2.0, 3.0, 5.0, 7.0, 5.0, 6.0, 2.0, 4.0, 1.0, 2.0, 2.0], [3.0, 7.0, 4.0, 10.0, 6.0, 7.0, 4.0, 6.0, 6.0, 8.0, 4.0, 8.0, 5.0, 10.0, 7.0, 6.0, 10.0, 5.0, 9.0, 7.0, 1.0, 5.0, 2.0], [1.0, 10.0, 4.0, 8.0, 2.0, 2.0, 6.0, 6.0, 2.0, 9.0, 8.0, 10.0, 6.0, 9.0, 5.0, 10.0, 2.0, 7.0, 2.0, 8.0, 7.0, 5.0, 7.0], [1.0, 2.0, 7.0, 10.0, 10.0, 10.0, 6.0, 1.0, 4.0, 9.0, 5.0, 7.0, 1.0, 10.0, 6.0, 5.0, 7.0, 7.0, 5.0, 6.0, 4.0, 3.0, 6.0], [6.0, 1.0, 3.0, 3.0, 4.0, 7.0, 3.0, 3.0, 1.0, 2.0, 8.0, 7.0, 3.0, 10.0, 2.0, 9.0, 2.0, 5.0, 6.0, 7.0, 9.0, 7.0, 10.0], [5.0, 3.0, 3.0, 3.0, 3.0, 10.0, 9.0, 5.0, 5.0, 10.0, 8.0, 3.0, 8.0, 2.0, 4.0, 7.0, 8.0, 6.0, 7.0, 2.0, 3.0, 10.0, 6.0], [4.0, 10.0, 2.0, 1.0, 5.0, 2.0, 1.0, 1.0, 2.0, 2.0, 5.0, 8.0, 4.0, 3.0, 1.0, 1.0, 7.0, 4.0, 9.0, 3.0, 9.0, 8.0, 3.0], [10.0, 2.0, 10.0, 1.0, 3.0, 10.0, 8.0, 10.0, 9.0, 7.0, 4.0, 2.0, 7.0, 10.0, 2.0, 5.0, 5.0, 3.0, 7.0, 10.0, 8.0, 9.0, 1.0], [3.0, 10.0, 4.0, 9.0, 8.0, 5.0, 10.0, 3.0, 10.0, 6.0, 2.0, 2.0, 9.0, 3.0, 2.0, 2.0, 7.0, 6.0, 10.0, 6.0, 3.0, 1.0, 5.0]]}, 'source': 14, 'target': 15}","[14, 0, 1, 2, 3, 4, 5, 6, 15]",376.0,"{'problem_type': 'QSPP', 'num_nodes': 16, 'num_edges': 23, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'source': 15, 'target': 16, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 7.0}, {'var_index': 2, 'linear_cost': 1.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 5.0}, {'var_index': 7, 'linear_cost': 7.0}, {'var_index': 8, 'linear_cost': 6.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 10.0}, {'var_index': 11, 'linear_cost': 3.0}, {'var_index': 12, 'linear_cost': 9.0}, {'var_index': 13, 'linear_cost': 8.0}, {'var_index': 14, 'linear_cost': 8.0}, {'var_index': 15, 'linear_cost': 9.0}, {'var_index': 16, 'linear_cost': 9.0}, {'var_index': 17, 'linear_cost': 5.0}, {'var_index': 18, 'linear_cost': 6.0}, {'var_index': 19, 'linear_cost': 7.0}, {'var_index': 20, 'linear_cost': 9.0}, {'var_index': 21, 'linear_cost': 9.0}, {'var_index': 22, 'linear_cost': 4.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 22, 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QSPP,QSPP,"I’m putting together a single lesson run that starts at the intro topic and finishes at the wrap-up, and I need to pick one straight sequence of topics where each next topic is a valid follow-up to the one before. Every topic on that line adds some prep time, and some pairs of topics create extra work or awkward overlap if they both show up, so the best plan is the one that ends up with the least total prep when you add each topic’s prep plus any extra friction between pairs. Nothing can be skipped or taught twice — it has to be one continuous path from intro to summary that follows the prerequisite order. The concrete diagram and numbers will be shown below.

{
  ""num_topics"": 25,
  ""num_transitions"": 40,
  ""topic_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I"",
    ""J"",
    ""K"",
    ""L"",
    ""M"",
    ""N"",
    ""O"",
    ""P"",
    ""Q"",
    ""R"",
    ""S"",
    ""T"",
    ""U"",
    ""V"",
    ""W"",
    ""X"",
    ""Y""
  ],
  ""intro_topic"": ""A"",
  ""wrap_up_topic"": ""Y"",
  ""edges"": [
    {
      ""prerequisite_topic"": ""A"",
      ""next_topic"": ""B"",
      ""transition_id"": 0
    },
    {
      ""prerequisite_topic"": ""A"",
      ""next_topic"": ""F"",
      ""transition_id"": 1
    },
    {
      ""prerequisite_topic"": ""B"",
      ""next_topic"": ""C"",
      ""transition_id"": 2
    },
    {
      ""prerequisite_topic"": ""B"",
      ""next_topic"": ""G"",
      ""transition_id"": 3
    },
    {
      ""prerequisite_topic"": ""C"",
      ""next_topic"": ""D"",
      ""transition_id"": 4
    },
    {
      ""prerequisite_topic"": ""C"",
      ""next_topic"": ""H"",
      ""transition_id"": 5
    },
    {
      ""prerequisite_topic"": ""D"",
      ""next_topic"": ""E"",
      ""transition_id"": 6
    },
    {
      ""prerequisite_topic"": ""D"",
      ""next_topic"": ""I"",
      ""transition_id"": 7
    },
    {
      ""prerequisite_topic"": ""E"",
      ""next_topic"": ""J"",
      ""transition_id"": 8
    },
    {
      ""prerequisite_topic"": ""F"",
      ""next_topic"": ""G"",
      ""transition_id"": 9
    },
    {
      ""prerequisite_topic"": ""F"",
      ""next_topic"": ""K"",
      ""transition_id"": 10
    },
    {
      ""prerequisite_topic"": ""G"",
      ""next_topic"": ""H"",
      ""transition_id"": 11
    },
    {
      ""prerequisite_topic"": ""G"",
      ""next_topic"": ""L"",
      ""transition_id"": 12
    },
    {
      ""prerequisite_topic"": ""H"",
      ""next_topic"": ""I"",
      ""transition_id"": 13
    },
    {
      ""prerequisite_topic"": ""H"",
      ""next_topic"": ""M"",
      ""transition_id"": 14
    },
    {
      ""prerequisite_topic"": ""I"",
      ""next_topic"": ""J"",
      ""transition_id"": 15
    },
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      ""prerequisite_topic"": ""I"",
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      ""transition_id"": 16
    },
    {
      ""prerequisite_topic"": ""J"",
      ""next_topic"": ""O"",
      ""transition_id"": 17
    },
    {
      ""prerequisite_topic"": ""K"",
      ""next_topic"": ""L"",
      ""transition_id"": 18
    },
    {
      ""prerequisite_topic"": ""K"",
      ""next_topic"": ""P"",
      ""transition_id"": 19
    },
    {
      ""prerequisite_topic"": ""L"",
      ""next_topic"": ""M"",
      ""transition_id"": 20
    },
    {
      ""prerequisite_topic"": ""L"",
      ""next_topic"": ""Q"",
      ""transition_id"": 21
    },
    {
      ""prerequisite_topic"": ""M"",
      ""next_topic"": ""N"",
      ""transition_id"": 22
    },
    {
      ""prerequisite_topic"": ""M"",
      ""next_topic"": ""R"",
      ""transition_id"": 23
    },
    {
      ""prerequisite_topic"": ""N"",
      ""next_topic"": ""O"",
      ""transition_id"": 24
    },
    {
      ""prerequisite_topic"": ""N"",
      ""next_topic"": ""S"",
      ""transition_id"": 25
    },
    {
      ""prerequisite_topic"": ""O"",
      ""next_topic"": ""T"",
      ""transition_id"": 26
    },
    {
      ""prerequisite_topic"": ""P"",
      ""next_topic"": ""Q"",
      ""transition_id"": 27
    },
    {
      ""prerequisite_topic"": ""P"",
      ""next_topic"": ""U"",
      ""transition_id"": 28
    },
    {
      ""prerequisite_topic"": ""Q"",
      ""next_topic"": ""R"",
      ""transition_id"": 29
    },
    {
      ""prerequisite_topic"": ""Q"",
      ""next_topic"": ""V"",
      ""transition_id"": 30
    },
    {
      ""prerequisite_topic"": ""R"",
      ""next_topic"": ""S"",
      ""transition_id"": 31
    },
    {
      ""prerequisite_topic"": ""R"",
      ""next_topic"": ""W"",
      ""transition_id"": 32
    },
    {
      ""prerequisite_topic"": ""S"",
      ""next_topic"": ""T"",
      ""transition_id"": 33
    },
    {
      ""prerequisite_topic"": ""S"",
      ""next_topic"": ""X"",
      ""transition_id"": 34
    },
    {
      ""prerequisite_topic"": ""T"",
      ""next_topic"": ""Y"",
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    },
    {
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      ""transition_id"": 36
    },
    {
      ""prerequisite_topic"": ""V"",
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    },
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      ""prerequisite_topic"": ""W"",
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      ""transition_id"": 38
    },
    {
      ""prerequisite_topic"": ""X"",
      ""next_topic"": ""Y"",
      ""transition_id"": 39
    }
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    {
      ""transition_id"": 31,
      ""prep_overhead"": 2.0
    },
    {
      ""transition_id"": 32,
      ""prep_overhead"": 8.0
    },
    {
      ""transition_id"": 33,
      ""prep_overhead"": 4.0
    },
    {
      ""transition_id"": 34,
      ""prep_overhead"": 4.0
    },
    {
      ""transition_id"": 35,
      ""prep_overhead"": 6.0
    },
    {
      ""transition_id"": 36,
      ""prep_overhead"": 9.0
    },
    {
      ""transition_id"": 37,
      ""prep_overhead"": 4.0
    },
    {
      ""transition_id"": 38,
      ""prep_overhead"": 6.0
    },
    {
      ""transition_id"": 39,
      ""prep_overhead"": 1.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (transition_i_id, transition_j_id). If two transitions with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| transition_i_id\transition_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 6.0 | 10.0 | 7.0 | 5.0 | 1.0 | 10.0 | 1.0 | 4.0 | 6.0 | 8.0 | 9.0 | 7.0 | 7.0 | 9.0 | 8.0 | 2.0 | 10.0 | 3.0 | 3.0 | 5.0 | 6.0 | 8.0 | 1.0 | 3.0 | 2.0 | 6.0 | 5.0 | 7.0 | 4.0 | 2.0 | 7.0 | 7.0 | 3.0 | 5.0 | 10.0 | 1.0 | 10.0 | 8.0 | 7.0 |
| 1 | 6.0 | 8.0 | 1.0 | 6.0 | 4.0 | 2.0 | 3.0 | 10.0 | 5.0 | 2.0 | 9.0 | 7.0 | 1.0 | 4.0 | 6.0 | 4.0 | 6.0 | 3.0 | 6.0 | 6.0 | 4.0 | 6.0 | 4.0 | 10.0 | 2.0 | 6.0 | 1.0 | 5.0 | 3.0 | 5.0 | 10.0 | 6.0 | 2.0 | 7.0 | 6.0 | 4.0 | 5.0 | 7.0 | 8.0 | 1.0 |
| 2 | 10.0 | 1.0 | 6.0 | 5.0 | 1.0 | 5.0 | 10.0 | 2.0 | 7.0 | 1.0 | 10.0 | 9.0 | 10.0 | 1.0 | 7.0 | 4.0 | 8.0 | 10.0 | 5.0 | 4.0 | 3.0 | 8.0 | 8.0 | 2.0 | 6.0 | 3.0 | 7.0 | 7.0 | 6.0 | 1.0 | 2.0 | 1.0 | 9.0 | 4.0 | 2.0 | 10.0 | 2.0 | 2.0 | 8.0 | 5.0 |
| 3 | 7.0 | 6.0 | 5.0 | 9.0 | 4.0 | 9.0 | 4.0 | 5.0 | 10.0 | 4.0 | 6.0 | 9.0 | 8.0 | 7.0 | 5.0 | 3.0 | 8.0 | 3.0 | 6.0 | 10.0 | 4.0 | 10.0 | 6.0 | 8.0 | 8.0 | 7.0 | 9.0 | 1.0 | 2.0 | 3.0 | 2.0 | 5.0 | 3.0 | 8.0 | 5.0 | 3.0 | 4.0 | 10.0 | 10.0 | 5.0 |
| 4 | 5.0 | 4.0 | 1.0 | 4.0 | 10.0 | 8.0 | 8.0 | 6.0 | 3.0 | 3.0 | 7.0 | 7.0 | 8.0 | 7.0 | 1.0 | 9.0 | 6.0 | 6.0 | 6.0 | 10.0 | 9.0 | 6.0 | 9.0 | 9.0 | 6.0 | 7.0 | 4.0 | 6.0 | 7.0 | 10.0 | 6.0 | 7.0 | 6.0 | 2.0 | 3.0 | 10.0 | 10.0 | 3.0 | 10.0 | 3.0 |
| 5 | 1.0 | 2.0 | 5.0 | 9.0 | 8.0 | 4.0 | 10.0 | 9.0 | 10.0 | 9.0 | 6.0 | 10.0 | 4.0 | 8.0 | 9.0 | 8.0 | 8.0 | 5.0 | 1.0 | 5.0 | 5.0 | 6.0 | 10.0 | 2.0 | 3.0 | 6.0 | 5.0 | 4.0 | 9.0 | 4.0 | 3.0 | 2.0 | 2.0 | 4.0 | 5.0 | 8.0 | 9.0 | 2.0 | 8.0 | 8.0 |
| 6 | 10.0 | 3.0 | 10.0 | 4.0 | 8.0 | 10.0 | 4.0 | 9.0 | 2.0 | 8.0 | 4.0 | 3.0 | 3.0 | 7.0 | 10.0 | 6.0 | 4.0 | 8.0 | 10.0 | 6.0 | 10.0 | 6.0 | 4.0 | 10.0 | 10.0 | 6.0 | 10.0 | 7.0 | 4.0 | 9.0 | 4.0 | 2.0 | 2.0 | 1.0 | 2.0 | 7.0 | 5.0 | 3.0 | 3.0 | 7.0 |
| 7 | 1.0 | 10.0 | 2.0 | 5.0 | 6.0 | 9.0 | 9.0 | 8.0 | 10.0 | 6.0 | 9.0 | 1.0 | 8.0 | 9.0 | 9.0 | 1.0 | 8.0 | 7.0 | 8.0 | 4.0 | 5.0 | 6.0 | 7.0 | 1.0 | 3.0 | 5.0 | 2.0 | 3.0 | 10.0 | 4.0 | 2.0 | 3.0 | 8.0 | 7.0 | 7.0 | 1.0 | 3.0 | 6.0 | 5.0 | 9.0 |
| 8 | 4.0 | 5.0 | 7.0 | 10.0 | 3.0 | 10.0 | 2.0 | 10.0 | 2.0 | 7.0 | 10.0 | 9.0 | 1.0 | 4.0 | 4.0 | 3.0 | 5.0 | 5.0 | 7.0 | 7.0 | 1.0 | 1.0 | 4.0 | 7.0 | 5.0 | 10.0 | 6.0 | 5.0 | 5.0 | 4.0 | 1.0 | 4.0 | 8.0 | 5.0 | 10.0 | 3.0 | 7.0 | 4.0 | 10.0 | 5.0 |
| 9 | 6.0 | 2.0 | 1.0 | 4.0 | 3.0 | 9.0 | 8.0 | 6.0 | 7.0 | 8.0 | 1.0 | 2.0 | 8.0 | 8.0 | 2.0 | 4.0 | 7.0 | 1.0 | 9.0 | 4.0 | 10.0 | 3.0 | 5.0 | 10.0 | 9.0 | 6.0 | 6.0 | 6.0 | 9.0 | 5.0 | 1.0 | 4.0 | 6.0 | 1.0 | 5.0 | 5.0 | 8.0 | 6.0 | 10.0 | 2.0 |
| 10 | 8.0 | 9.0 | 10.0 | 6.0 | 7.0 | 6.0 | 4.0 | 9.0 | 10.0 | 1.0 | 10.0 | 8.0 | 4.0 | 10.0 | 5.0 | 8.0 | 4.0 | 7.0 | 3.0 | 3.0 | 1.0 | 5.0 | 6.0 | 6.0 | 2.0 | 8.0 | 9.0 | 10.0 | 8.0 | 7.0 | 2.0 | 2.0 | 3.0 | 7.0 | 7.0 | 7.0 | 5.0 | 4.0 | 3.0 | 5.0 |
| 11 | 9.0 | 7.0 | 9.0 | 9.0 | 7.0 | 10.0 | 3.0 | 1.0 | 9.0 | 2.0 | 8.0 | 2.0 | 3.0 | 1.0 | 2.0 | 2.0 | 9.0 | 10.0 | 1.0 | 4.0 | 5.0 | 2.0 | 1.0 | 6.0 | 6.0 | 6.0 | 2.0 | 1.0 | 6.0 | 7.0 | 1.0 | 2.0 | 5.0 | 2.0 | 5.0 | 5.0 | 2.0 | 4.0 | 1.0 | 5.0 |
| 12 | 7.0 | 1.0 | 10.0 | 8.0 | 8.0 | 4.0 | 3.0 | 8.0 | 1.0 | 8.0 | 4.0 | 3.0 | 1.0 | 10.0 | 9.0 | 3.0 | 8.0 | 9.0 | 3.0 | 2.0 | 5.0 | 9.0 | 7.0 | 1.0 | 6.0 | 8.0 | 5.0 | 2.0 | 6.0 | 10.0 | 5.0 | 6.0 | 3.0 | 7.0 | 3.0 | 3.0 | 6.0 | 2.0 | 1.0 | 7.0 |
| 13 | 7.0 | 4.0 | 1.0 | 7.0 | 7.0 | 8.0 | 7.0 | 9.0 | 4.0 | 8.0 | 10.0 | 1.0 | 10.0 | 1.0 | 7.0 | 3.0 | 10.0 | 5.0 | 5.0 | 6.0 | 6.0 | 1.0 | 6.0 | 10.0 | 4.0 | 10.0 | 7.0 | 5.0 | 7.0 | 7.0 | 1.0 | 2.0 | 7.0 | 4.0 | 7.0 | 7.0 | 4.0 | 7.0 | 8.0 | 1.0 |
| 14 | 9.0 | 6.0 | 7.0 | 5.0 | 1.0 | 9.0 | 10.0 | 9.0 | 4.0 | 2.0 | 5.0 | 2.0 | 9.0 | 7.0 | 10.0 | 7.0 | 6.0 | 6.0 | 9.0 | 8.0 | 5.0 | 1.0 | 9.0 | 5.0 | 9.0 | 5.0 | 10.0 | 5.0 | 3.0 | 7.0 | 9.0 | 4.0 | 10.0 | 8.0 | 3.0 | 6.0 | 8.0 | 3.0 | 2.0 | 3.0 |
| 15 | 8.0 | 4.0 | 4.0 | 3.0 | 9.0 | 8.0 | 6.0 | 1.0 | 3.0 | 4.0 | 8.0 | 2.0 | 3.0 | 3.0 | 7.0 | 8.0 | 4.0 | 6.0 | 3.0 | 10.0 | 1.0 | 2.0 | 2.0 | 9.0 | 6.0 | 3.0 | 6.0 | 6.0 | 3.0 | 6.0 | 5.0 | 8.0 | 10.0 | 3.0 | 9.0 | 10.0 | 9.0 | 4.0 | 5.0 | 4.0 |
| 16 | 2.0 | 6.0 | 8.0 | 8.0 | 6.0 | 8.0 | 4.0 | 8.0 | 5.0 | 7.0 | 4.0 | 9.0 | 8.0 | 10.0 | 6.0 | 4.0 | 2.0 | 4.0 | 1.0 | 8.0 | 1.0 | 5.0 | 6.0 | 6.0 | 2.0 | 3.0 | 9.0 | 9.0 | 2.0 | 7.0 | 4.0 | 10.0 | 8.0 | 6.0 | 8.0 | 4.0 | 6.0 | 6.0 | 1.0 | 7.0 |
| 17 | 10.0 | 3.0 | 10.0 | 3.0 | 6.0 | 5.0 | 8.0 | 7.0 | 5.0 | 1.0 | 7.0 | 10.0 | 9.0 | 5.0 | 6.0 | 6.0 | 4.0 | 3.0 | 10.0 | 1.0 | 1.0 | 3.0 | 2.0 | 3.0 | 1.0 | 7.0 | 8.0 | 1.0 | 7.0 | 5.0 | 1.0 | 4.0 | 8.0 | 10.0 | 1.0 | 2.0 | 4.0 | 8.0 | 5.0 | 9.0 |
| 18 | 3.0 | 6.0 | 5.0 | 6.0 | 6.0 | 1.0 | 10.0 | 8.0 | 7.0 | 9.0 | 3.0 | 1.0 | 3.0 | 5.0 | 9.0 | 3.0 | 1.0 | 10.0 | 7.0 | 5.0 | 7.0 | 6.0 | 2.0 | 7.0 | 7.0 | 2.0 | 9.0 | 2.0 | 10.0 | 6.0 | 1.0 | 7.0 | 7.0 | 5.0 | 6.0 | 7.0 | 8.0 | 10.0 | 10.0 | 2.0 |
| 19 | 3.0 | 6.0 | 4.0 | 10.0 | 10.0 | 5.0 | 6.0 | 4.0 | 7.0 | 4.0 | 3.0 | 4.0 | 2.0 | 6.0 | 8.0 | 10.0 | 8.0 | 1.0 | 5.0 | 3.0 | 1.0 | 9.0 | 9.0 | 9.0 | 6.0 | 6.0 | 2.0 | 4.0 | 8.0 | 7.0 | 3.0 | 4.0 | 3.0 | 7.0 | 4.0 | 8.0 | 6.0 | 9.0 | 7.0 | 9.0 |
| 20 | 5.0 | 4.0 | 3.0 | 4.0 | 9.0 | 5.0 | 10.0 | 5.0 | 1.0 | 10.0 | 1.0 | 5.0 | 5.0 | 6.0 | 5.0 | 1.0 | 1.0 | 1.0 | 7.0 | 1.0 | 8.0 | 7.0 | 5.0 | 8.0 | 6.0 | 3.0 | 2.0 | 1.0 | 3.0 | 6.0 | 4.0 | 8.0 | 1.0 | 9.0 | 2.0 | 7.0 | 6.0 | 2.0 | 1.0 | 3.0 |
| 21 | 6.0 | 6.0 | 8.0 | 10.0 | 6.0 | 6.0 | 6.0 | 6.0 | 1.0 | 3.0 | 5.0 | 2.0 | 9.0 | 1.0 | 1.0 | 2.0 | 5.0 | 3.0 | 6.0 | 9.0 | 7.0 | 4.0 | 1.0 | 8.0 | 3.0 | 5.0 | 5.0 | 2.0 | 5.0 | 1.0 | 10.0 | 8.0 | 1.0 | 2.0 | 1.0 | 3.0 | 8.0 | 4.0 | 8.0 | 5.0 |
| 22 | 8.0 | 4.0 | 8.0 | 6.0 | 9.0 | 10.0 | 4.0 | 7.0 | 4.0 | 5.0 | 6.0 | 1.0 | 7.0 | 6.0 | 9.0 | 2.0 | 6.0 | 2.0 | 2.0 | 9.0 | 5.0 | 1.0 | 10.0 | 4.0 | 4.0 | 7.0 | 1.0 | 4.0 | 3.0 | 8.0 | 7.0 | 3.0 | 2.0 | 6.0 | 1.0 | 10.0 | 4.0 | 2.0 | 8.0 | 1.0 |
| 23 | 1.0 | 10.0 | 2.0 | 8.0 | 9.0 | 2.0 | 10.0 | 1.0 | 7.0 | 10.0 | 6.0 | 6.0 | 1.0 | 10.0 | 5.0 | 9.0 | 6.0 | 3.0 | 7.0 | 9.0 | 8.0 | 8.0 | 4.0 | 5.0 | 3.0 | 1.0 | 5.0 | 6.0 | 2.0 | 10.0 | 4.0 | 8.0 | 2.0 | 4.0 | 8.0 | 5.0 | 7.0 | 7.0 | 4.0 | 1.0 |
| 24 | 3.0 | 2.0 | 6.0 | 8.0 | 6.0 | 3.0 | 10.0 | 3.0 | 5.0 | 9.0 | 2.0 | 6.0 | 6.0 | 4.0 | 9.0 | 6.0 | 2.0 | 1.0 | 7.0 | 6.0 | 6.0 | 3.0 | 4.0 | 3.0 | 6.0 | 10.0 | 10.0 | 1.0 | 1.0 | 10.0 | 2.0 | 4.0 | 5.0 | 9.0 | 7.0 | 5.0 | 8.0 | 2.0 | 2.0 | 2.0 |
| 25 | 2.0 | 6.0 | 3.0 | 7.0 | 7.0 | 6.0 | 6.0 | 5.0 | 10.0 | 6.0 | 8.0 | 6.0 | 8.0 | 10.0 | 5.0 | 3.0 | 3.0 | 7.0 | 2.0 | 6.0 | 3.0 | 5.0 | 7.0 | 1.0 | 10.0 | 5.0 | 6.0 | 10.0 | 1.0 | 4.0 | 9.0 | 10.0 | 10.0 | 3.0 | 5.0 | 1.0 | 2.0 | 2.0 | 10.0 | 5.0 |
| 26 | 6.0 | 1.0 | 7.0 | 9.0 | 4.0 | 5.0 | 10.0 | 2.0 | 6.0 | 6.0 | 9.0 | 2.0 | 5.0 | 7.0 | 10.0 | 6.0 | 9.0 | 8.0 | 9.0 | 2.0 | 2.0 | 5.0 | 1.0 | 5.0 | 10.0 | 6.0 | 4.0 | 9.0 | 8.0 | 2.0 | 1.0 | 4.0 | 9.0 | 10.0 | 1.0 | 8.0 | 7.0 | 5.0 | 3.0 | 2.0 |
| 27 | 5.0 | 5.0 | 7.0 | 1.0 | 6.0 | 4.0 | 7.0 | 3.0 | 5.0 | 6.0 | 10.0 | 1.0 | 2.0 | 5.0 | 5.0 | 6.0 | 9.0 | 1.0 | 2.0 | 4.0 | 1.0 | 2.0 | 4.0 | 6.0 | 1.0 | 10.0 | 9.0 | 4.0 | 6.0 | 3.0 | 2.0 | 9.0 | 8.0 | 2.0 | 3.0 | 10.0 | 2.0 | 6.0 | 7.0 | 6.0 |
| 28 | 7.0 | 3.0 | 6.0 | 2.0 | 7.0 | 9.0 | 4.0 | 10.0 | 5.0 | 9.0 | 8.0 | 6.0 | 6.0 | 7.0 | 3.0 | 3.0 | 2.0 | 7.0 | 10.0 | 8.0 | 3.0 | 5.0 | 3.0 | 2.0 | 1.0 | 1.0 | 8.0 | 6.0 | 6.0 | 8.0 | 3.0 | 5.0 | 4.0 | 5.0 | 5.0 | 3.0 | 1.0 | 3.0 | 3.0 | 10.0 |
| 29 | 4.0 | 5.0 | 1.0 | 3.0 | 10.0 | 4.0 | 9.0 | 4.0 | 4.0 | 5.0 | 7.0 | 7.0 | 10.0 | 7.0 | 7.0 | 6.0 | 7.0 | 5.0 | 6.0 | 7.0 | 6.0 | 1.0 | 8.0 | 10.0 | 10.0 | 4.0 | 2.0 | 3.0 | 8.0 | 3.0 | 10.0 | 3.0 | 6.0 | 10.0 | 8.0 | 3.0 | 4.0 | 10.0 | 9.0 | 8.0 |
| 30 | 2.0 | 10.0 | 2.0 | 2.0 | 6.0 | 3.0 | 4.0 | 2.0 | 1.0 | 1.0 | 2.0 | 1.0 | 5.0 | 1.0 | 9.0 | 5.0 | 4.0 | 1.0 | 1.0 | 3.0 | 4.0 | 10.0 | 7.0 | 4.0 | 2.0 | 9.0 | 1.0 | 2.0 | 3.0 | 10.0 | 1.0 | 10.0 | 6.0 | 9.0 | 3.0 | 3.0 | 1.0 | 2.0 | 4.0 | 7.0 |
| 31 | 7.0 | 6.0 | 1.0 | 5.0 | 7.0 | 2.0 | 2.0 | 3.0 | 4.0 | 4.0 | 2.0 | 2.0 | 6.0 | 2.0 | 4.0 | 8.0 | 10.0 | 4.0 | 7.0 | 4.0 | 8.0 | 8.0 | 3.0 | 8.0 | 4.0 | 10.0 | 4.0 | 9.0 | 5.0 | 3.0 | 10.0 | 10.0 | 3.0 | 9.0 | 2.0 | 6.0 | 8.0 | 8.0 | 4.0 | 3.0 |
| 32 | 7.0 | 2.0 | 9.0 | 3.0 | 6.0 | 2.0 | 2.0 | 8.0 | 8.0 | 6.0 | 3.0 | 5.0 | 3.0 | 7.0 | 10.0 | 10.0 | 8.0 | 8.0 | 7.0 | 3.0 | 1.0 | 1.0 | 2.0 | 2.0 | 5.0 | 10.0 | 9.0 | 8.0 | 4.0 | 6.0 | 6.0 | 3.0 | 4.0 | 3.0 | 8.0 | 2.0 | 9.0 | 1.0 | 7.0 | 7.0 |
| 33 | 3.0 | 7.0 | 4.0 | 8.0 | 2.0 | 4.0 | 1.0 | 7.0 | 5.0 | 1.0 | 7.0 | 2.0 | 7.0 | 4.0 | 8.0 | 3.0 | 6.0 | 10.0 | 5.0 | 7.0 | 9.0 | 2.0 | 6.0 | 4.0 | 9.0 | 3.0 | 10.0 | 2.0 | 5.0 | 10.0 | 9.0 | 9.0 | 3.0 | 5.0 | 7.0 | 4.0 | 6.0 | 7.0 | 6.0 | 1.0 |
| 34 | 5.0 | 6.0 | 2.0 | 5.0 | 3.0 | 5.0 | 2.0 | 7.0 | 10.0 | 5.0 | 7.0 | 5.0 | 3.0 | 7.0 | 3.0 | 9.0 | 8.0 | 1.0 | 6.0 | 4.0 | 2.0 | 1.0 | 1.0 | 8.0 | 7.0 | 5.0 | 1.0 | 3.0 | 5.0 | 8.0 | 3.0 | 2.0 | 8.0 | 7.0 | 9.0 | 7.0 | 9.0 | 9.0 | 5.0 | 3.0 |
| 35 | 10.0 | 4.0 | 10.0 | 3.0 | 10.0 | 8.0 | 7.0 | 1.0 | 3.0 | 5.0 | 7.0 | 5.0 | 3.0 | 7.0 | 6.0 | 10.0 | 4.0 | 2.0 | 7.0 | 8.0 | 7.0 | 3.0 | 10.0 | 5.0 | 5.0 | 1.0 | 8.0 | 10.0 | 3.0 | 3.0 | 3.0 | 6.0 | 2.0 | 4.0 | 7.0 | 3.0 | 3.0 | 4.0 | 4.0 | 10.0 |
| 36 | 1.0 | 5.0 | 2.0 | 4.0 | 10.0 | 9.0 | 5.0 | 3.0 | 7.0 | 8.0 | 5.0 | 2.0 | 6.0 | 4.0 | 8.0 | 9.0 | 6.0 | 4.0 | 8.0 | 6.0 | 6.0 | 8.0 | 4.0 | 7.0 | 8.0 | 2.0 | 7.0 | 2.0 | 1.0 | 4.0 | 1.0 | 8.0 | 9.0 | 6.0 | 9.0 | 3.0 | 10.0 | 6.0 | 2.0 | 7.0 |
| 37 | 10.0 | 7.0 | 2.0 | 10.0 | 3.0 | 2.0 | 3.0 | 6.0 | 4.0 | 6.0 | 4.0 | 4.0 | 2.0 | 7.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | 9.0 | 2.0 | 4.0 | 2.0 | 7.0 | 2.0 | 2.0 | 5.0 | 6.0 | 3.0 | 10.0 | 2.0 | 8.0 | 1.0 | 7.0 | 9.0 | 4.0 | 6.0 | 6.0 | 5.0 | 10.0 |
| 38 | 8.0 | 8.0 | 8.0 | 10.0 | 10.0 | 8.0 | 3.0 | 5.0 | 10.0 | 10.0 | 3.0 | 1.0 | 1.0 | 8.0 | 2.0 | 5.0 | 1.0 | 5.0 | 10.0 | 7.0 | 1.0 | 8.0 | 8.0 | 4.0 | 2.0 | 10.0 | 3.0 | 7.0 | 3.0 | 9.0 | 4.0 | 4.0 | 7.0 | 6.0 | 5.0 | 4.0 | 2.0 | 5.0 | 2.0 | 4.0 |
| 39 | 7.0 | 1.0 | 5.0 | 5.0 | 3.0 | 8.0 | 7.0 | 9.0 | 5.0 | 2.0 | 5.0 | 5.0 | 7.0 | 1.0 | 3.0 | 4.0 | 7.0 | 9.0 | 2.0 | 9.0 | 3.0 | 5.0 | 1.0 | 1.0 | 2.0 | 5.0 | 2.0 | 6.0 | 10.0 | 8.0 | 7.0 | 3.0 | 7.0 | 1.0 | 3.0 | 10.0 | 7.0 | 10.0 | 4.0 | 1.0 |

Oh, and one more thing — when you send the final pick, please put it in a tiny JSON sketch so I can read it cleanly. Something simple like this:

{
  ""solution"": []
}

Here ""solution"" is the spot where you’d list the chosen straight sequence of topic nodes (start with the intro node, end with the wrap-up node). Think of it like a short form: the array is just the ordered list of topic names in the path. This is just a template to show the expected shape, not the actual answer — fill that array with the nodes when you have the final path.

Please remember: use the exact identifiers from the instance input — don’t rename anything or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 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'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 26, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 35, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 36, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 37, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 38, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 39, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 'A', 'to': 'B', 'var_index': 0}, {'from': 'A', 'to': 'F', 'var_index': 1}, {'from': 'B', 'to': 'C', 'var_index': 2}, {'from': 'B', 'to': 'G', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'C', 'to': 'H', 'var_index': 5}, {'from': 'D', 'to': 'E', 'var_index': 6}, {'from': 'D', 'to': 'I', 'var_index': 7}, {'from': 'E', 'to': 'J', 'var_index': 8}, {'from': 'F', 'to': 'G', 'var_index': 9}, {'from': 'F', 'to': 'K', 'var_index': 10}, {'from': 'G', 'to': 'H', 'var_index': 11}, {'from': 'G', 'to': 'L', 'var_index': 12}, {'from': 'H', 'to': 'I', 'var_index': 13}, {'from': 'H', 'to': 'M', 'var_index': 14}, {'from': 'I', 'to': 'J', 'var_index': 15}, {'from': 'I', 'to': 'N', 'var_index': 16}, {'from': 'J', 'to': 'O', 'var_index': 17}, {'from': 'K', 'to': 'L', 'var_index': 18}, {'from': 'K', 'to': 'P', 'var_index': 19}, {'from': 'L', 'to': 'M', 'var_index': 20}, {'from': 'L', 'to': 'Q', 'var_index': 21}, {'from': 'M', 'to': 'N', 'var_index': 22}, {'from': 'M', 'to': 'R', 'var_index': 23}, {'from': 'N', 'to': 'O', 'var_index': 24}, {'from': 'N', 'to': 'S', 'var_index': 25}, {'from': 'O', 'to': 'T', 'var_index': 26}, {'from': 'P', 'to': 'Q', 'var_index': 27}, {'from': 'P', 'to': 'U', 'var_index': 28}, {'from': 'Q', 'to': 'R', 'var_index': 29}, {'from': 'Q', 'to': 'V', 'var_index': 30}, {'from': 'R', 'to': 'S', 'var_index': 31}, {'from': 'R', 'to': 'W', 'var_index': 32}, {'from': 'S', 'to': 'T', 'var_index': 33}, {'from': 'S', 'to': 'X', 'var_index': 34}, {'from': 'T', 'to': 'Y', 'var_index': 35}, {'from': 'U', 'to': 'V', 'var_index': 36}, {'from': 'V', 'to': 'W', 'var_index': 37}, {'from': 'W', 'to': 'X', 'var_index': 38}, {'from': 'X', 'to': 'Y', 'var_index': 39}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V', 22: 'W', 23: 'X', 24: 'Y'}}","['A', 'F', 'G', 'H', 'M', 'N', 'S', 'X', 'Y']",15,json,names
QSPP,QSPP,"I can imagine the control plan as a little map story: send the batch from the intake valve to the delivery manifold along one directed route through the pipes. Every pipe piece in that route costs something to run and carries a per-piece maintenance surcharge, and whenever particular pieces are combined in the same run there can be extra coupling charges that apply only if both are included (and order can matter). The sensible way to pick is to sum each piece’s base fee plus its maintenance add-on, then include all the extra charges for every pair that’s used together — the route with the lowest total cost is the one to choose. The path must be continuous, start at intake and end at delivery, listed as locations only with nothing left out, and the concrete network and cost numbers are shown below.

Below I list the concrete network: 19 locations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 18 directed segments; the run starts at 18 and ends at 19.

| segment_from_location | segment_to_location | segment_id |
|---|---|---|
| 18 | 1 | 0 |
| 17 | 19 | 1 |
| 1 | 2 | 2 |
| 2 | 3 | 3 |
| 3 | 4 | 4 |
| 4 | 5 | 5 |
| 5 | 6 | 6 |
| 6 | 7 | 7 |
| 7 | 8 | 8 |
| 8 | 9 | 9 |
| 9 | 10 | 10 |
| 10 | 11 | 11 |
| 11 | 12 | 12 |
| 12 | 13 | 13 |
| 13 | 14 | 14 |
| 14 | 15 | 15 |
| 15 | 16 | 16 |
| 16 | 17 | 17 |

| segment_id | segment_operational_plus_maintenance_cost |
|---|---|
| 0 | 4.0 |
| 1 | 6.0 |
| 2 | 2.0 |
| 3 | 4.0 |
| 4 | 7.0 |
| 5 | 10.0 |
| 6 | 5.0 |
| 7 | 3.0 |
| 8 | 7.0 |
| 9 | 2.0 |
| 10 | 2.0 |
| 11 | 1.0 |
| 12 | 1.0 |
| 13 | 5.0 |
| 14 | 2.0 |
| 15 | 1.0 |
| 16 | 3.0 |
| 17 | 9.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 9.0 | 4.0 | 6.0 | 8.0 | 1.0 | 3.0 | 9.0 | 5.0 | 2.0 | 2.0 | 3.0 | 3.0 | 2.0 | 3.0 | 4.0 | 3.0 | 2.0 |
| 1 | 9.0 | 3.0 | 8.0 | 4.0 | 5.0 | 8.0 | 1.0 | 1.0 | 1.0 | 4.0 | 2.0 | 5.0 | 4.0 | 2.0 | 5.0 | 1.0 | 1.0 | 3.0 |
| 2 | 4.0 | 8.0 | 7.0 | 4.0 | 8.0 | 1.0 | 6.0 | 6.0 | 6.0 | 10.0 | 8.0 | 2.0 | 9.0 | 9.0 | 3.0 | 8.0 | 10.0 | 10.0 |
| 3 | 6.0 | 4.0 | 4.0 | 1.0 | 9.0 | 8.0 | 7.0 | 10.0 | 2.0 | 8.0 | 5.0 | 1.0 | 4.0 | 1.0 | 7.0 | 3.0 | 1.0 | 10.0 |
| 4 | 8.0 | 5.0 | 8.0 | 9.0 | 2.0 | 9.0 | 10.0 | 7.0 | 7.0 | 2.0 | 2.0 | 3.0 | 3.0 | 9.0 | 1.0 | 10.0 | 4.0 | 4.0 |
| 5 | 1.0 | 8.0 | 1.0 | 8.0 | 9.0 | 2.0 | 9.0 | 3.0 | 8.0 | 2.0 | 8.0 | 4.0 | 4.0 | 9.0 | 4.0 | 8.0 | 5.0 | 9.0 |
| 6 | 3.0 | 1.0 | 6.0 | 7.0 | 10.0 | 9.0 | 9.0 | 2.0 | 2.0 | 6.0 | 3.0 | 1.0 | 2.0 | 8.0 | 5.0 | 9.0 | 5.0 | 5.0 |
| 7 | 9.0 | 1.0 | 6.0 | 10.0 | 7.0 | 3.0 | 2.0 | 7.0 | 7.0 | 9.0 | 8.0 | 4.0 | 5.0 | 8.0 | 2.0 | 4.0 | 3.0 | 3.0 |
| 8 | 5.0 | 1.0 | 6.0 | 2.0 | 7.0 | 8.0 | 2.0 | 7.0 | 9.0 | 8.0 | 3.0 | 7.0 | 9.0 | 8.0 | 6.0 | 4.0 | 1.0 | 3.0 |
| 9 | 2.0 | 4.0 | 10.0 | 8.0 | 2.0 | 2.0 | 6.0 | 9.0 | 8.0 | 9.0 | 10.0 | 2.0 | 8.0 | 3.0 | 7.0 | 2.0 | 8.0 | 10.0 |
| 10 | 2.0 | 2.0 | 8.0 | 5.0 | 2.0 | 8.0 | 3.0 | 8.0 | 3.0 | 10.0 | 3.0 | 6.0 | 9.0 | 2.0 | 10.0 | 2.0 | 8.0 | 7.0 |
| 11 | 3.0 | 5.0 | 2.0 | 1.0 | 3.0 | 4.0 | 1.0 | 4.0 | 7.0 | 2.0 | 6.0 | 4.0 | 10.0 | 10.0 | 3.0 | 10.0 | 2.0 | 9.0 |
| 12 | 3.0 | 4.0 | 9.0 | 4.0 | 3.0 | 4.0 | 2.0 | 5.0 | 9.0 | 8.0 | 9.0 | 10.0 | 9.0 | 8.0 | 2.0 | 1.0 | 4.0 | 5.0 |
| 13 | 2.0 | 2.0 | 9.0 | 1.0 | 9.0 | 9.0 | 8.0 | 8.0 | 8.0 | 3.0 | 2.0 | 10.0 | 8.0 | 6.0 | 10.0 | 5.0 | 2.0 | 5.0 |
| 14 | 3.0 | 5.0 | 3.0 | 7.0 | 1.0 | 4.0 | 5.0 | 2.0 | 6.0 | 7.0 | 10.0 | 3.0 | 2.0 | 10.0 | 7.0 | 2.0 | 4.0 | 8.0 |
| 15 | 4.0 | 1.0 | 8.0 | 3.0 | 10.0 | 8.0 | 9.0 | 4.0 | 4.0 | 2.0 | 2.0 | 10.0 | 1.0 | 5.0 | 2.0 | 8.0 | 8.0 | 10.0 |
| 16 | 3.0 | 1.0 | 10.0 | 1.0 | 4.0 | 5.0 | 5.0 | 3.0 | 1.0 | 8.0 | 8.0 | 2.0 | 4.0 | 2.0 | 4.0 | 8.0 | 3.0 | 1.0 |
| 17 | 2.0 | 3.0 | 10.0 | 10.0 | 4.0 | 9.0 | 5.0 | 3.0 | 3.0 | 10.0 | 7.0 | 9.0 | 5.0 | 5.0 | 8.0 | 10.0 | 1.0 | 10.0 |

I will then sum each segment's fee and maintenance surcharge plus all listed coupling charges, and pick the continuous path from 18 to 19 with the lowest total.

Also, when you send back the path, please use a tiny JSON layout so it's clear and machine-friendly — just one top-level key called ""solution"" whose value is the ordered list of node names from intake to delivery.

{
  ""solution"": []
}

This ""solution"" array should hold the node sequence only (start at the intake/source, end at the delivery/target), nothing else — no edge identifiers, no costs. Think of the JSON above as a simple form: the field name tells you where to put the ordered list of locations, and the empty list is just a placeholder you should replace with the actual path when you submit it. It's just a sketch of the expected shape, not the answer itself.

Please be sure to use the exact node identifiers from the instance input — do not rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'edges': [{'from': 17, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 18, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}], 'objective': {'constant': 0.0, 'linear': [4.0, 6.0, 2.0, 4.0, 7.0, 10.0, 5.0, 3.0, 7.0, 2.0, 2.0, 1.0, 1.0, 5.0, 2.0, 1.0, 3.0, 9.0], 'quadratic': [[10.0, 9.0, 4.0, 6.0, 8.0, 1.0, 3.0, 9.0, 5.0, 2.0, 2.0, 3.0, 3.0, 2.0, 3.0, 4.0, 3.0, 2.0], [9.0, 3.0, 8.0, 4.0, 5.0, 8.0, 1.0, 1.0, 1.0, 4.0, 2.0, 5.0, 4.0, 2.0, 5.0, 1.0, 1.0, 3.0], [4.0, 8.0, 7.0, 4.0, 8.0, 1.0, 6.0, 6.0, 6.0, 10.0, 8.0, 2.0, 9.0, 9.0, 3.0, 8.0, 10.0, 10.0], [6.0, 4.0, 4.0, 1.0, 9.0, 8.0, 7.0, 10.0, 2.0, 8.0, 5.0, 1.0, 4.0, 1.0, 7.0, 3.0, 1.0, 10.0], [8.0, 5.0, 8.0, 9.0, 2.0, 9.0, 10.0, 7.0, 7.0, 2.0, 2.0, 3.0, 3.0, 9.0, 1.0, 10.0, 4.0, 4.0], [1.0, 8.0, 1.0, 8.0, 9.0, 2.0, 9.0, 3.0, 8.0, 2.0, 8.0, 4.0, 4.0, 9.0, 4.0, 8.0, 5.0, 9.0], [3.0, 1.0, 6.0, 7.0, 10.0, 9.0, 9.0, 2.0, 2.0, 6.0, 3.0, 1.0, 2.0, 8.0, 5.0, 9.0, 5.0, 5.0], [9.0, 1.0, 6.0, 10.0, 7.0, 3.0, 2.0, 7.0, 7.0, 9.0, 8.0, 4.0, 5.0, 8.0, 2.0, 4.0, 3.0, 3.0], [5.0, 1.0, 6.0, 2.0, 7.0, 8.0, 2.0, 7.0, 9.0, 8.0, 3.0, 7.0, 9.0, 8.0, 6.0, 4.0, 1.0, 3.0], [2.0, 4.0, 10.0, 8.0, 2.0, 2.0, 6.0, 9.0, 8.0, 9.0, 10.0, 2.0, 8.0, 3.0, 7.0, 2.0, 8.0, 10.0], [2.0, 2.0, 8.0, 5.0, 2.0, 8.0, 3.0, 8.0, 3.0, 10.0, 3.0, 6.0, 9.0, 2.0, 10.0, 2.0, 8.0, 7.0], [3.0, 5.0, 2.0, 1.0, 3.0, 4.0, 1.0, 4.0, 7.0, 2.0, 6.0, 4.0, 10.0, 10.0, 3.0, 10.0, 2.0, 9.0], [3.0, 4.0, 9.0, 4.0, 3.0, 4.0, 2.0, 5.0, 9.0, 8.0, 9.0, 10.0, 9.0, 8.0, 2.0, 1.0, 4.0, 5.0], [2.0, 2.0, 9.0, 1.0, 9.0, 9.0, 8.0, 8.0, 8.0, 3.0, 2.0, 10.0, 8.0, 6.0, 10.0, 5.0, 2.0, 5.0], [3.0, 5.0, 3.0, 7.0, 1.0, 4.0, 5.0, 2.0, 6.0, 7.0, 10.0, 3.0, 2.0, 10.0, 7.0, 2.0, 4.0, 8.0], [4.0, 1.0, 8.0, 3.0, 10.0, 8.0, 9.0, 4.0, 4.0, 2.0, 2.0, 10.0, 1.0, 5.0, 2.0, 8.0, 8.0, 10.0], [3.0, 1.0, 10.0, 1.0, 4.0, 5.0, 5.0, 3.0, 1.0, 8.0, 8.0, 2.0, 4.0, 2.0, 4.0, 8.0, 3.0, 1.0], [2.0, 3.0, 10.0, 10.0, 4.0, 9.0, 5.0, 3.0, 3.0, 10.0, 7.0, 9.0, 5.0, 5.0, 8.0, 10.0, 1.0, 10.0]]}, 'source': 17, 'target': 18}","[17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18]",1797.0,"{'problem_type': 'QSPP', 'num_nodes': 19, 'num_edges': 18, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'source': 18, 'target': 19, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 2.0}, {'var_index': 3, 'linear_cost': 4.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 5.0}, {'var_index': 7, 'linear_cost': 3.0}, {'var_index': 8, 'linear_cost': 7.0}, {'var_index': 9, 'linear_cost': 2.0}, {'var_index': 10, 'linear_cost': 2.0}, {'var_index': 11, 'linear_cost': 1.0}, {'var_index': 12, 'linear_cost': 1.0}, {'var_index': 13, 'linear_cost': 5.0}, {'var_index': 14, 'linear_cost': 2.0}, {'var_index': 15, 'linear_cost': 1.0}, {'var_index': 16, 'linear_cost': 3.0}, {'var_index': 17, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 18, 'to': 1, 'var_index': 0}, {'from': 17, 'to': 19, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}, {'from': 15, 'to': 16, 'var_index': 16}, {'from': 16, 'to': 17, 'var_index': 17}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19}}","[18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]",16,markdown_table,1
QSPP,QSPP,"Once there’s a panel and an outlet to link, the installer needs to pick exactly one route through the directed conduits that connect them. Every piece of conduit has a base material and connector cost, and some pieces also impose an extra cost simply for being in the route; beyond that, certain ordered pairs of pieces interact and add interference costs when both are used — since order can matter, the interference from a pair is made up of the contributions from both directions. The job is to lay out one continuous path from the panel to the outlet (no branching, no multiple runs) that results in the smallest possible total when adding up all segment fees and any interaction penalties. The full network and cost details will be provided below.

Below are the specifics: 19 locations, 18 directed conduit segments; location IDs A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S; panel at R; outlet at S.
Conduit segment 0 runs from R to A.
Conduit segment 1 runs from Q to S.
Conduit segment 2 runs from A to B.
Conduit segment 3 runs from B to C.
Conduit segment 4 runs from C to D.
Conduit segment 5 runs from D to E.
Conduit segment 6 runs from E to F.
Conduit segment 7 runs from F to G.
Conduit segment 8 runs from G to H.
Conduit segment 9 runs from H to I.
Conduit segment 10 runs from I to J.
Conduit segment 11 runs from J to K.
Conduit segment 12 runs from K to L.
Conduit segment 13 runs from L to M.
Conduit segment 14 runs from M to N.
Conduit segment 15 runs from N to O.
Conduit segment 16 runs from O to P.
Conduit segment 17 runs from P to Q.
The base material and connector fee for 0 is 5.0.
The base material and connector fee for 1 is 1.0.
The base material and connector fee for 2 is 2.0.
The base material and connector fee for 3 is 5.0.
The base material and connector fee for 4 is 9.0.
The base material and connector fee for 5 is 5.0.
The base material and connector fee for 6 is 2.0.
The base material and connector fee for 7 is 8.0.
The base material and connector fee for 8 is 5.0.
The base material and connector fee for 9 is 5.0.
The base material and connector fee for 10 is 1.0.
The base material and connector fee for 11 is 10.0.
The base material and connector fee for 12 is 3.0.
The base material and connector fee for 13 is 10.0.
The base material and connector fee for 14 is 7.0.
The base material and connector fee for 15 is 6.0.
The base material and connector fee for 16 is 7.0.
The base material and connector fee for 17 is 9.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_conduit_segment_id, second_conduit_segment_id). If two conduit_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| first_conduit_segment_id\second_conduit_segment_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 1.0 | 7.0 | 3.0 | 3.0 | 5.0 | 10.0 | 1.0 | 2.0 | 8.0 | 8.0 | 6.0 | 8.0 | 8.0 | 5.0 | 10.0 | 4.0 | 1.0 |
| 1 | 1.0 | 2.0 | 6.0 | 1.0 | 5.0 | 1.0 | 5.0 | 4.0 | 2.0 | 8.0 | 4.0 | 9.0 | 10.0 | 6.0 | 10.0 | 9.0 | 9.0 | 2.0 |
| 2 | 7.0 | 6.0 | 1.0 | 5.0 | 1.0 | 10.0 | 7.0 | 4.0 | 8.0 | 2.0 | 5.0 | 5.0 | 1.0 | 3.0 | 5.0 | 5.0 | 5.0 | 10.0 |
| 3 | 3.0 | 1.0 | 5.0 | 2.0 | 10.0 | 3.0 | 8.0 | 4.0 | 3.0 | 1.0 | 5.0 | 9.0 | 9.0 | 10.0 | 1.0 | 10.0 | 8.0 | 5.0 |
| 4 | 3.0 | 5.0 | 1.0 | 10.0 | 9.0 | 1.0 | 8.0 | 8.0 | 2.0 | 2.0 | 5.0 | 8.0 | 6.0 | 4.0 | 8.0 | 1.0 | 1.0 | 8.0 |
| 5 | 5.0 | 1.0 | 10.0 | 3.0 | 1.0 | 9.0 | 5.0 | 5.0 | 3.0 | 8.0 | 7.0 | 8.0 | 5.0 | 8.0 | 6.0 | 5.0 | 3.0 | 3.0 |
| 6 | 10.0 | 5.0 | 7.0 | 8.0 | 8.0 | 5.0 | 9.0 | 6.0 | 7.0 | 4.0 | 2.0 | 2.0 | 7.0 | 5.0 | 8.0 | 6.0 | 9.0 | 8.0 |
| 7 | 1.0 | 4.0 | 4.0 | 4.0 | 8.0 | 5.0 | 6.0 | 9.0 | 3.0 | 6.0 | 1.0 | 5.0 | 7.0 | 10.0 | 8.0 | 8.0 | 2.0 | 8.0 |
| 8 | 2.0 | 2.0 | 8.0 | 3.0 | 2.0 | 3.0 | 7.0 | 3.0 | 5.0 | 7.0 | 2.0 | 3.0 | 6.0 | 1.0 | 7.0 | 8.0 | 2.0 | 3.0 |
| 9 | 8.0 | 8.0 | 2.0 | 1.0 | 2.0 | 8.0 | 4.0 | 6.0 | 7.0 | 10.0 | 5.0 | 1.0 | 4.0 | 6.0 | 9.0 | 9.0 | 7.0 | 5.0 |
| 10 | 8.0 | 4.0 | 5.0 | 5.0 | 5.0 | 7.0 | 2.0 | 1.0 | 2.0 | 5.0 | 3.0 | 9.0 | 3.0 | 8.0 | 6.0 | 10.0 | 6.0 | 1.0 |
| 11 | 6.0 | 9.0 | 5.0 | 9.0 | 8.0 | 8.0 | 2.0 | 5.0 | 3.0 | 1.0 | 9.0 | 1.0 | 6.0 | 9.0 | 3.0 | 6.0 | 3.0 | 1.0 |
| 12 | 8.0 | 10.0 | 1.0 | 9.0 | 6.0 | 5.0 | 7.0 | 7.0 | 6.0 | 4.0 | 3.0 | 6.0 | 7.0 | 7.0 | 6.0 | 4.0 | 9.0 | 8.0 |
| 13 | 8.0 | 6.0 | 3.0 | 10.0 | 4.0 | 8.0 | 5.0 | 10.0 | 1.0 | 6.0 | 8.0 | 9.0 | 7.0 | 10.0 | 4.0 | 7.0 | 2.0 | 8.0 |
| 14 | 5.0 | 10.0 | 5.0 | 1.0 | 8.0 | 6.0 | 8.0 | 8.0 | 7.0 | 9.0 | 6.0 | 3.0 | 6.0 | 4.0 | 5.0 | 8.0 | 1.0 | 3.0 |
| 15 | 10.0 | 9.0 | 5.0 | 10.0 | 1.0 | 5.0 | 6.0 | 8.0 | 8.0 | 9.0 | 10.0 | 6.0 | 4.0 | 7.0 | 8.0 | 4.0 | 5.0 | 10.0 |
| 16 | 4.0 | 9.0 | 5.0 | 8.0 | 1.0 | 3.0 | 9.0 | 2.0 | 2.0 | 7.0 | 6.0 | 3.0 | 9.0 | 2.0 | 1.0 | 5.0 | 8.0 | 6.0 |
| 17 | 1.0 | 2.0 | 10.0 | 5.0 | 8.0 | 3.0 | 8.0 | 8.0 | 3.0 | 5.0 | 1.0 | 1.0 | 8.0 | 8.0 | 3.0 | 10.0 | 6.0 | 6.0 |
The installer will use these entries to select the single continuous path with the lowest total cost.

Oh — when you send me the final picked route, just tuck it into a tiny JSON wrapper so it's easy to read and check. Something like this:

{
  ""solution"": []
}

Here ""solution"" is where you'll list the path as a plain sequence of node identifiers, from the panel (source) to the outlet (target), in order. Think of it like filling in a short form: put each node name in the array, left-to-right along the route. This block is just a sketch of the shape I expect, not the actual answer — you'll replace the empty array with the actual node sequence.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'edges': [{'from': 17, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 18, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}], 'objective': {'constant': 0.0, 'linear': [5.0, 1.0, 2.0, 5.0, 9.0, 5.0, 2.0, 8.0, 5.0, 5.0, 1.0, 10.0, 3.0, 10.0, 7.0, 6.0, 7.0, 9.0], 'quadratic': [[3.0, 1.0, 7.0, 3.0, 3.0, 5.0, 10.0, 1.0, 2.0, 8.0, 8.0, 6.0, 8.0, 8.0, 5.0, 10.0, 4.0, 1.0], [1.0, 2.0, 6.0, 1.0, 5.0, 1.0, 5.0, 4.0, 2.0, 8.0, 4.0, 9.0, 10.0, 6.0, 10.0, 9.0, 9.0, 2.0], [7.0, 6.0, 1.0, 5.0, 1.0, 10.0, 7.0, 4.0, 8.0, 2.0, 5.0, 5.0, 1.0, 3.0, 5.0, 5.0, 5.0, 10.0], [3.0, 1.0, 5.0, 2.0, 10.0, 3.0, 8.0, 4.0, 3.0, 1.0, 5.0, 9.0, 9.0, 10.0, 1.0, 10.0, 8.0, 5.0], [3.0, 5.0, 1.0, 10.0, 9.0, 1.0, 8.0, 8.0, 2.0, 2.0, 5.0, 8.0, 6.0, 4.0, 8.0, 1.0, 1.0, 8.0], [5.0, 1.0, 10.0, 3.0, 1.0, 9.0, 5.0, 5.0, 3.0, 8.0, 7.0, 8.0, 5.0, 8.0, 6.0, 5.0, 3.0, 3.0], [10.0, 5.0, 7.0, 8.0, 8.0, 5.0, 9.0, 6.0, 7.0, 4.0, 2.0, 2.0, 7.0, 5.0, 8.0, 6.0, 9.0, 8.0], [1.0, 4.0, 4.0, 4.0, 8.0, 5.0, 6.0, 9.0, 3.0, 6.0, 1.0, 5.0, 7.0, 10.0, 8.0, 8.0, 2.0, 8.0], [2.0, 2.0, 8.0, 3.0, 2.0, 3.0, 7.0, 3.0, 5.0, 7.0, 2.0, 3.0, 6.0, 1.0, 7.0, 8.0, 2.0, 3.0], [8.0, 8.0, 2.0, 1.0, 2.0, 8.0, 4.0, 6.0, 7.0, 10.0, 5.0, 1.0, 4.0, 6.0, 9.0, 9.0, 7.0, 5.0], [8.0, 4.0, 5.0, 5.0, 5.0, 7.0, 2.0, 1.0, 2.0, 5.0, 3.0, 9.0, 3.0, 8.0, 6.0, 10.0, 6.0, 1.0], [6.0, 9.0, 5.0, 9.0, 8.0, 8.0, 2.0, 5.0, 3.0, 1.0, 9.0, 1.0, 6.0, 9.0, 3.0, 6.0, 3.0, 1.0], [8.0, 10.0, 1.0, 9.0, 6.0, 5.0, 7.0, 7.0, 6.0, 4.0, 3.0, 6.0, 7.0, 7.0, 6.0, 4.0, 9.0, 8.0], [8.0, 6.0, 3.0, 10.0, 4.0, 8.0, 5.0, 10.0, 1.0, 6.0, 8.0, 9.0, 7.0, 10.0, 4.0, 7.0, 2.0, 8.0], [5.0, 10.0, 5.0, 1.0, 8.0, 6.0, 8.0, 8.0, 7.0, 9.0, 6.0, 3.0, 6.0, 4.0, 5.0, 8.0, 1.0, 3.0], [10.0, 9.0, 5.0, 10.0, 1.0, 5.0, 6.0, 8.0, 8.0, 9.0, 10.0, 6.0, 4.0, 7.0, 8.0, 4.0, 5.0, 10.0], [4.0, 9.0, 5.0, 8.0, 1.0, 3.0, 9.0, 2.0, 2.0, 7.0, 6.0, 3.0, 9.0, 2.0, 1.0, 5.0, 8.0, 6.0], [1.0, 2.0, 10.0, 5.0, 8.0, 3.0, 8.0, 8.0, 3.0, 5.0, 1.0, 1.0, 8.0, 8.0, 3.0, 10.0, 6.0, 6.0]]}, 'source': 17, 'target': 18}","[17, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18]",1877.0,"{'problem_type': 'QSPP', 'num_nodes': 19, 'num_edges': 18, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S'], 'source': 'R', 'target': 'S', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 2.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 5.0}, {'var_index': 6, 'linear_cost': 2.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 5.0}, {'var_index': 9, 'linear_cost': 5.0}, {'var_index': 10, 'linear_cost': 1.0}, {'var_index': 11, 'linear_cost': 10.0}, {'var_index': 12, 'linear_cost': 3.0}, {'var_index': 13, 'linear_cost': 10.0}, {'var_index': 14, 'linear_cost': 7.0}, {'var_index': 15, 'linear_cost': 6.0}, {'var_index': 16, 'linear_cost': 7.0}, {'var_index': 17, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 'R', 'to': 'A', 'var_index': 0}, {'from': 'Q', 'to': 'S', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}, {'from': 'H', 'to': 'I', 'var_index': 9}, {'from': 'I', 'to': 'J', 'var_index': 10}, {'from': 'J', 'to': 'K', 'var_index': 11}, {'from': 'K', 'to': 'L', 'var_index': 12}, {'from': 'L', 'to': 'M', 'var_index': 13}, {'from': 'M', 'to': 'N', 'var_index': 14}, {'from': 'N', 'to': 'O', 'var_index': 15}, {'from': 'O', 'to': 'P', 'var_index': 16}, {'from': 'P', 'to': 'Q', 'var_index': 17}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S'}}","['R', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'S']",17,nl,names
QSPP,QSPP,"I’m imagining a lazy morning stroll from the city gate to the central plaza where the aim is simple: pick one continuous, one-way route that leaves the walker as comfortable as possible. Every block walked adds some base tiredness, some blocks are steep so they tack on an extra penalty if included, and certain combinations of streets make the walk noticeably worse when they’re both on the same route. The “better” route is just the one that ends up with the smallest total of those things — total base fatigue plus any steep-block penalties plus any extra pairwise awkwardness when two particular blocks are used together. The walk has to be a single, lawful path following the one-way lanes from gate to plaza without skipping or stitching together separate trips. The exact map and numbers are shown below.

{
  ""total_locations"": 25,
  ""total_blocks"": 40,
  ""location_list"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I"",
    ""J"",
    ""K"",
    ""L"",
    ""M"",
    ""N"",
    ""O"",
    ""P"",
    ""Q"",
    ""R"",
    ""S"",
    ""T"",
    ""U"",
    ""V"",
    ""W"",
    ""X"",
    ""Y""
  ],
  ""city_gate"": ""A"",
  ""central_plaza"": ""Y"",
  ""edges"": [
    {
      ""block_start_location"": ""A"",
      ""block_end_location"": ""B"",
      ""block_identifier"": 0
    },
    {
      ""block_start_location"": ""A"",
      ""block_end_location"": ""F"",
      ""block_identifier"": 1
    },
    {
      ""block_start_location"": ""B"",
      ""block_end_location"": ""C"",
      ""block_identifier"": 2
    },
    {
      ""block_start_location"": ""B"",
      ""block_end_location"": ""G"",
      ""block_identifier"": 3
    },
    {
      ""block_start_location"": ""C"",
      ""block_end_location"": ""D"",
      ""block_identifier"": 4
    },
    {
      ""block_start_location"": ""C"",
      ""block_end_location"": ""H"",
      ""block_identifier"": 5
    },
    {
      ""block_start_location"": ""D"",
      ""block_end_location"": ""E"",
      ""block_identifier"": 6
    },
    {
      ""block_start_location"": ""D"",
      ""block_end_location"": ""I"",
      ""block_identifier"": 7
    },
    {
      ""block_start_location"": ""E"",
      ""block_end_location"": ""J"",
      ""block_identifier"": 8
    },
    {
      ""block_start_location"": ""F"",
      ""block_end_location"": ""G"",
      ""block_identifier"": 9
    },
    {
      ""block_start_location"": ""F"",
      ""block_end_location"": ""K"",
      ""block_identifier"": 10
    },
    {
      ""block_start_location"": ""G"",
      ""block_end_location"": ""H"",
      ""block_identifier"": 11
    },
    {
      ""block_start_location"": ""G"",
      ""block_end_location"": ""L"",
      ""block_identifier"": 12
    },
    {
      ""block_start_location"": ""H"",
      ""block_end_location"": ""I"",
      ""block_identifier"": 13
    },
    {
      ""block_start_location"": ""H"",
      ""block_end_location"": ""M"",
      ""block_identifier"": 14
    },
    {
      ""block_start_location"": ""I"",
      ""block_end_location"": ""J"",
      ""block_identifier"": 15
    },
    {
      ""block_start_location"": ""I"",
      ""block_end_location"": ""N"",
      ""block_identifier"": 16
    },
    {
      ""block_start_location"": ""J"",
      ""block_end_location"": ""O"",
      ""block_identifier"": 17
    },
    {
      ""block_start_location"": ""K"",
      ""block_end_location"": ""L"",
      ""block_identifier"": 18
    },
    {
      ""block_start_location"": ""K"",
      ""block_end_location"": ""P"",
      ""block_identifier"": 19
    },
    {
      ""block_start_location"": ""L"",
      ""block_end_location"": ""M"",
      ""block_identifier"": 20
    },
    {
      ""block_start_location"": ""L"",
      ""block_end_location"": ""Q"",
      ""block_identifier"": 21
    },
    {
      ""block_start_location"": ""M"",
      ""block_end_location"": ""N"",
      ""block_identifier"": 22
    },
    {
      ""block_start_location"": ""M"",
      ""block_end_location"": ""R"",
      ""block_identifier"": 23
    },
    {
      ""block_start_location"": ""N"",
      ""block_end_location"": ""O"",
      ""block_identifier"": 24
    },
    {
      ""block_start_location"": ""N"",
      ""block_end_location"": ""S"",
      ""block_identifier"": 25
    },
    {
      ""block_start_location"": ""O"",
      ""block_end_location"": ""T"",
      ""block_identifier"": 26
    },
    {
      ""block_start_location"": ""P"",
      ""block_end_location"": ""Q"",
      ""block_identifier"": 27
    },
    {
      ""block_start_location"": ""P"",
      ""block_end_location"": ""U"",
      ""block_identifier"": 28
    },
    {
      ""block_start_location"": ""Q"",
      ""block_end_location"": ""R"",
      ""block_identifier"": 29
    },
    {
      ""block_start_location"": ""Q"",
      ""block_end_location"": ""V"",
      ""block_identifier"": 30
    },
    {
      ""block_start_location"": ""R"",
      ""block_end_location"": ""S"",
      ""block_identifier"": 31
    },
    {
      ""block_start_location"": ""R"",
      ""block_end_location"": ""W"",
      ""block_identifier"": 32
    },
    {
      ""block_start_location"": ""S"",
      ""block_end_location"": ""T"",
      ""block_identifier"": 33
    },
    {
      ""block_start_location"": ""S"",
      ""block_end_location"": ""X"",
      ""block_identifier"": 34
    },
    {
      ""block_start_location"": ""T"",
      ""block_end_location"": ""Y"",
      ""block_identifier"": 35
    },
    {
      ""block_start_location"": ""U"",
      ""block_end_location"": ""V"",
      ""block_identifier"": 36
    },
    {
      ""block_start_location"": ""V"",
      ""block_end_location"": ""W"",
      ""block_identifier"": 37
    },
    {
      ""block_start_location"": ""W"",
      ""block_end_location"": ""X"",
      ""block_identifier"": 38
    },
    {
      ""block_start_location"": ""X"",
      ""block_end_location"": ""Y"",
      ""block_identifier"": 39
    }
  ],
  ""linear_costs"": [
    {
      ""block_identifier"": 0,
      ""block_base_fatigue"": 6.0
    },
    {
      ""block_identifier"": 1,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 2,
      ""block_base_fatigue"": 4.0
    },
    {
      ""block_identifier"": 3,
      ""block_base_fatigue"": 10.0
    },
    {
      ""block_identifier"": 4,
      ""block_base_fatigue"": 6.0
    },
    {
      ""block_identifier"": 5,
      ""block_base_fatigue"": 5.0
    },
    {
      ""block_identifier"": 6,
      ""block_base_fatigue"": 9.0
    },
    {
      ""block_identifier"": 7,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 8,
      ""block_base_fatigue"": 9.0
    },
    {
      ""block_identifier"": 9,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 10,
      ""block_base_fatigue"": 6.0
    },
    {
      ""block_identifier"": 11,
      ""block_base_fatigue"": 2.0
    },
    {
      ""block_identifier"": 12,
      ""block_base_fatigue"": 4.0
    },
    {
      ""block_identifier"": 13,
      ""block_base_fatigue"": 9.0
    },
    {
      ""block_identifier"": 14,
      ""block_base_fatigue"": 1.0
    },
    {
      ""block_identifier"": 15,
      ""block_base_fatigue"": 7.0
    },
    {
      ""block_identifier"": 16,
      ""block_base_fatigue"": 1.0
    },
    {
      ""block_identifier"": 17,
      ""block_base_fatigue"": 3.0
    },
    {
      ""block_identifier"": 18,
      ""block_base_fatigue"": 5.0
    },
    {
      ""block_identifier"": 19,
      ""block_base_fatigue"": 4.0
    },
    {
      ""block_identifier"": 20,
      ""block_base_fatigue"": 9.0
    },
    {
      ""block_identifier"": 21,
      ""block_base_fatigue"": 2.0
    },
    {
      ""block_identifier"": 22,
      ""block_base_fatigue"": 4.0
    },
    {
      ""block_identifier"": 23,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 24,
      ""block_base_fatigue"": 9.0
    },
    {
      ""block_identifier"": 25,
      ""block_base_fatigue"": 7.0
    },
    {
      ""block_identifier"": 26,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 27,
      ""block_base_fatigue"": 4.0
    },
    {
      ""block_identifier"": 28,
      ""block_base_fatigue"": 3.0
    },
    {
      ""block_identifier"": 29,
      ""block_base_fatigue"": 5.0
    },
    {
      ""block_identifier"": 30,
      ""block_base_fatigue"": 6.0
    },
    {
      ""block_identifier"": 31,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 32,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 33,
      ""block_base_fatigue"": 2.0
    },
    {
      ""block_identifier"": 34,
      ""block_base_fatigue"": 6.0
    },
    {
      ""block_identifier"": 35,
      ""block_base_fatigue"": 1.0
    },
    {
      ""block_identifier"": 36,
      ""block_base_fatigue"": 1.0
    },
    {
      ""block_identifier"": 37,
      ""block_base_fatigue"": 8.0
    },
    {
      ""block_identifier"": 38,
      ""block_base_fatigue"": 1.0
    },
    {
      ""block_identifier"": 39,
      ""block_base_fatigue"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_block_identifier, second_block_identifier). If two block_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_block_identifier\second_block_identifier | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 2.0 | 1.0 | 2.0 | 8.0 | 10.0 | 6.0 | 3.0 | 10.0 | 8.0 | 1.0 | 3.0 | 4.0 | 1.0 | 4.0 | 7.0 | 1.0 | 10.0 | 7.0 | 6.0 | 1.0 | 1.0 | 7.0 | 9.0 | 8.0 | 1.0 | 5.0 | 3.0 | 7.0 | 3.0 | 7.0 | 3.0 | 2.0 | 8.0 | 8.0 | 4.0 | 7.0 | 10.0 | 8.0 | 5.0 |
| 1 | 2.0 | 9.0 | 3.0 | 9.0 | 10.0 | 6.0 | 4.0 | 10.0 | 8.0 | 2.0 | 7.0 | 6.0 | 8.0 | 7.0 | 9.0 | 3.0 | 8.0 | 7.0 | 7.0 | 8.0 | 4.0 | 9.0 | 5.0 | 7.0 | 3.0 | 7.0 | 5.0 | 5.0 | 3.0 | 10.0 | 8.0 | 3.0 | 10.0 | 10.0 | 6.0 | 9.0 | 5.0 | 3.0 | 10.0 | 5.0 |
| 2 | 1.0 | 3.0 | 4.0 | 9.0 | 8.0 | 2.0 | 8.0 | 10.0 | 6.0 | 4.0 | 1.0 | 7.0 | 1.0 | 2.0 | 10.0 | 5.0 | 3.0 | 9.0 | 1.0 | 4.0 | 7.0 | 5.0 | 9.0 | 3.0 | 3.0 | 9.0 | 4.0 | 4.0 | 7.0 | 2.0 | 2.0 | 10.0 | 3.0 | 2.0 | 7.0 | 7.0 | 8.0 | 5.0 | 2.0 | 3.0 |
| 3 | 2.0 | 9.0 | 9.0 | 3.0 | 4.0 | 10.0 | 5.0 | 7.0 | 6.0 | 3.0 | 7.0 | 10.0 | 6.0 | 1.0 | 1.0 | 7.0 | 5.0 | 7.0 | 1.0 | 2.0 | 5.0 | 6.0 | 5.0 | 5.0 | 6.0 | 8.0 | 2.0 | 7.0 | 2.0 | 6.0 | 6.0 | 8.0 | 2.0 | 8.0 | 2.0 | 1.0 | 3.0 | 1.0 | 2.0 | 2.0 |
| 4 | 8.0 | 10.0 | 8.0 | 4.0 | 4.0 | 6.0 | 2.0 | 10.0 | 1.0 | 8.0 | 10.0 | 5.0 | 9.0 | 7.0 | 1.0 | 3.0 | 5.0 | 9.0 | 4.0 | 10.0 | 2.0 | 7.0 | 6.0 | 1.0 | 3.0 | 6.0 | 7.0 | 9.0 | 2.0 | 1.0 | 3.0 | 1.0 | 10.0 | 8.0 | 9.0 | 2.0 | 10.0 | 4.0 | 4.0 | 6.0 |
| 5 | 10.0 | 6.0 | 2.0 | 10.0 | 6.0 | 7.0 | 2.0 | 3.0 | 1.0 | 3.0 | 1.0 | 10.0 | 10.0 | 9.0 | 9.0 | 3.0 | 9.0 | 3.0 | 4.0 | 4.0 | 8.0 | 7.0 | 1.0 | 8.0 | 5.0 | 2.0 | 6.0 | 5.0 | 7.0 | 5.0 | 8.0 | 10.0 | 9.0 | 1.0 | 9.0 | 7.0 | 3.0 | 2.0 | 7.0 | 5.0 |
| 6 | 6.0 | 4.0 | 8.0 | 5.0 | 2.0 | 2.0 | 6.0 | 3.0 | 7.0 | 7.0 | 4.0 | 4.0 | 8.0 | 6.0 | 5.0 | 2.0 | 4.0 | 7.0 | 2.0 | 7.0 | 3.0 | 3.0 | 4.0 | 6.0 | 5.0 | 8.0 | 1.0 | 9.0 | 8.0 | 4.0 | 10.0 | 10.0 | 5.0 | 1.0 | 8.0 | 3.0 | 2.0 | 3.0 | 4.0 | 7.0 |
| 7 | 3.0 | 10.0 | 10.0 | 7.0 | 10.0 | 3.0 | 3.0 | 4.0 | 9.0 | 5.0 | 4.0 | 9.0 | 1.0 | 3.0 | 1.0 | 1.0 | 3.0 | 6.0 | 9.0 | 6.0 | 1.0 | 10.0 | 9.0 | 1.0 | 9.0 | 9.0 | 7.0 | 5.0 | 3.0 | 5.0 | 6.0 | 3.0 | 8.0 | 10.0 | 6.0 | 2.0 | 7.0 | 2.0 | 4.0 | 8.0 |
| 8 | 10.0 | 8.0 | 6.0 | 6.0 | 1.0 | 1.0 | 7.0 | 9.0 | 8.0 | 7.0 | 5.0 | 7.0 | 8.0 | 3.0 | 9.0 | 2.0 | 6.0 | 7.0 | 7.0 | 10.0 | 7.0 | 7.0 | 10.0 | 6.0 | 8.0 | 7.0 | 5.0 | 8.0 | 9.0 | 5.0 | 9.0 | 3.0 | 10.0 | 7.0 | 2.0 | 4.0 | 5.0 | 8.0 | 10.0 | 5.0 |
| 9 | 8.0 | 2.0 | 4.0 | 3.0 | 8.0 | 3.0 | 7.0 | 5.0 | 7.0 | 4.0 | 3.0 | 3.0 | 3.0 | 1.0 | 2.0 | 8.0 | 3.0 | 9.0 | 6.0 | 3.0 | 2.0 | 4.0 | 7.0 | 9.0 | 10.0 | 4.0 | 9.0 | 7.0 | 4.0 | 6.0 | 9.0 | 7.0 | 3.0 | 3.0 | 9.0 | 10.0 | 10.0 | 10.0 | 6.0 | 9.0 |
| 10 | 1.0 | 7.0 | 1.0 | 7.0 | 10.0 | 1.0 | 4.0 | 4.0 | 5.0 | 3.0 | 2.0 | 10.0 | 9.0 | 6.0 | 7.0 | 6.0 | 9.0 | 9.0 | 4.0 | 1.0 | 7.0 | 3.0 | 3.0 | 10.0 | 9.0 | 3.0 | 1.0 | 6.0 | 7.0 | 4.0 | 5.0 | 2.0 | 1.0 | 10.0 | 4.0 | 10.0 | 5.0 | 7.0 | 6.0 | 3.0 |
| 11 | 3.0 | 6.0 | 7.0 | 10.0 | 5.0 | 10.0 | 4.0 | 9.0 | 7.0 | 3.0 | 10.0 | 10.0 | 8.0 | 5.0 | 10.0 | 3.0 | 1.0 | 2.0 | 8.0 | 7.0 | 4.0 | 3.0 | 6.0 | 3.0 | 1.0 | 2.0 | 3.0 | 7.0 | 10.0 | 6.0 | 7.0 | 9.0 | 4.0 | 10.0 | 1.0 | 6.0 | 10.0 | 9.0 | 9.0 | 10.0 |
| 12 | 4.0 | 8.0 | 1.0 | 6.0 | 9.0 | 10.0 | 8.0 | 1.0 | 8.0 | 3.0 | 9.0 | 8.0 | 6.0 | 2.0 | 6.0 | 3.0 | 7.0 | 8.0 | 2.0 | 6.0 | 1.0 | 10.0 | 3.0 | 4.0 | 2.0 | 1.0 | 1.0 | 10.0 | 3.0 | 6.0 | 7.0 | 1.0 | 7.0 | 10.0 | 2.0 | 5.0 | 8.0 | 6.0 | 3.0 | 5.0 |
| 13 | 1.0 | 7.0 | 2.0 | 1.0 | 7.0 | 9.0 | 6.0 | 3.0 | 3.0 | 1.0 | 6.0 | 5.0 | 2.0 | 9.0 | 4.0 | 3.0 | 2.0 | 6.0 | 9.0 | 3.0 | 4.0 | 9.0 | 9.0 | 4.0 | 10.0 | 10.0 | 1.0 | 5.0 | 7.0 | 10.0 | 7.0 | 8.0 | 1.0 | 8.0 | 10.0 | 9.0 | 6.0 | 2.0 | 9.0 | 4.0 |
| 14 | 4.0 | 9.0 | 10.0 | 1.0 | 1.0 | 9.0 | 5.0 | 1.0 | 9.0 | 2.0 | 7.0 | 10.0 | 6.0 | 4.0 | 7.0 | 8.0 | 3.0 | 6.0 | 3.0 | 6.0 | 1.0 | 10.0 | 4.0 | 8.0 | 3.0 | 3.0 | 3.0 | 6.0 | 1.0 | 10.0 | 9.0 | 2.0 | 2.0 | 6.0 | 1.0 | 5.0 | 9.0 | 8.0 | 8.0 | 7.0 |
| 15 | 7.0 | 3.0 | 5.0 | 7.0 | 3.0 | 3.0 | 2.0 | 1.0 | 2.0 | 8.0 | 6.0 | 3.0 | 3.0 | 3.0 | 8.0 | 5.0 | 8.0 | 4.0 | 8.0 | 6.0 | 6.0 | 2.0 | 5.0 | 6.0 | 1.0 | 1.0 | 3.0 | 3.0 | 4.0 | 9.0 | 4.0 | 1.0 | 8.0 | 4.0 | 3.0 | 8.0 | 9.0 | 2.0 | 9.0 | 9.0 |
| 16 | 1.0 | 8.0 | 3.0 | 5.0 | 5.0 | 9.0 | 4.0 | 3.0 | 6.0 | 3.0 | 9.0 | 1.0 | 7.0 | 2.0 | 3.0 | 8.0 | 4.0 | 9.0 | 9.0 | 3.0 | 2.0 | 8.0 | 6.0 | 4.0 | 7.0 | 1.0 | 9.0 | 5.0 | 6.0 | 8.0 | 6.0 | 8.0 | 4.0 | 1.0 | 1.0 | 2.0 | 2.0 | 2.0 | 9.0 | 10.0 |
| 17 | 10.0 | 7.0 | 9.0 | 7.0 | 9.0 | 3.0 | 7.0 | 6.0 | 7.0 | 9.0 | 9.0 | 2.0 | 8.0 | 6.0 | 6.0 | 4.0 | 9.0 | 2.0 | 10.0 | 4.0 | 9.0 | 1.0 | 10.0 | 1.0 | 7.0 | 10.0 | 3.0 | 6.0 | 8.0 | 3.0 | 6.0 | 10.0 | 6.0 | 4.0 | 4.0 | 2.0 | 2.0 | 10.0 | 3.0 | 4.0 |
| 18 | 7.0 | 7.0 | 1.0 | 1.0 | 4.0 | 4.0 | 2.0 | 9.0 | 7.0 | 6.0 | 4.0 | 8.0 | 2.0 | 9.0 | 3.0 | 8.0 | 9.0 | 10.0 | 6.0 | 2.0 | 4.0 | 10.0 | 2.0 | 5.0 | 1.0 | 5.0 | 4.0 | 6.0 | 7.0 | 10.0 | 3.0 | 1.0 | 8.0 | 3.0 | 10.0 | 10.0 | 5.0 | 9.0 | 2.0 | 10.0 |
| 19 | 6.0 | 8.0 | 4.0 | 2.0 | 10.0 | 4.0 | 7.0 | 6.0 | 10.0 | 3.0 | 1.0 | 7.0 | 6.0 | 3.0 | 6.0 | 6.0 | 3.0 | 4.0 | 2.0 | 8.0 | 9.0 | 4.0 | 6.0 | 10.0 | 6.0 | 8.0 | 10.0 | 9.0 | 1.0 | 9.0 | 5.0 | 3.0 | 1.0 | 8.0 | 10.0 | 3.0 | 9.0 | 7.0 | 8.0 | 8.0 |
| 20 | 1.0 | 4.0 | 7.0 | 5.0 | 2.0 | 8.0 | 3.0 | 1.0 | 7.0 | 2.0 | 7.0 | 4.0 | 1.0 | 4.0 | 1.0 | 6.0 | 2.0 | 9.0 | 4.0 | 9.0 | 10.0 | 10.0 | 8.0 | 6.0 | 1.0 | 6.0 | 4.0 | 10.0 | 2.0 | 5.0 | 5.0 | 8.0 | 3.0 | 5.0 | 2.0 | 8.0 | 9.0 | 5.0 | 3.0 | 9.0 |
| 21 | 1.0 | 9.0 | 5.0 | 6.0 | 7.0 | 7.0 | 3.0 | 10.0 | 7.0 | 4.0 | 3.0 | 3.0 | 10.0 | 9.0 | 10.0 | 2.0 | 8.0 | 1.0 | 10.0 | 4.0 | 10.0 | 2.0 | 1.0 | 5.0 | 8.0 | 6.0 | 3.0 | 9.0 | 1.0 | 7.0 | 5.0 | 6.0 | 4.0 | 10.0 | 6.0 | 5.0 | 8.0 | 9.0 | 3.0 | 9.0 |
| 22 | 7.0 | 5.0 | 9.0 | 5.0 | 6.0 | 1.0 | 4.0 | 9.0 | 10.0 | 7.0 | 3.0 | 6.0 | 3.0 | 9.0 | 4.0 | 5.0 | 6.0 | 10.0 | 2.0 | 6.0 | 8.0 | 1.0 | 5.0 | 10.0 | 5.0 | 5.0 | 4.0 | 6.0 | 6.0 | 10.0 | 7.0 | 3.0 | 7.0 | 8.0 | 6.0 | 10.0 | 1.0 | 1.0 | 3.0 | 5.0 |
| 23 | 9.0 | 7.0 | 3.0 | 5.0 | 1.0 | 8.0 | 6.0 | 1.0 | 6.0 | 9.0 | 10.0 | 3.0 | 4.0 | 4.0 | 8.0 | 6.0 | 4.0 | 1.0 | 5.0 | 10.0 | 6.0 | 5.0 | 10.0 | 9.0 | 10.0 | 6.0 | 8.0 | 9.0 | 2.0 | 7.0 | 5.0 | 7.0 | 8.0 | 10.0 | 2.0 | 4.0 | 5.0 | 2.0 | 6.0 | 2.0 |
| 24 | 8.0 | 3.0 | 3.0 | 6.0 | 3.0 | 5.0 | 5.0 | 9.0 | 8.0 | 10.0 | 9.0 | 1.0 | 2.0 | 10.0 | 3.0 | 1.0 | 7.0 | 7.0 | 1.0 | 6.0 | 1.0 | 8.0 | 5.0 | 10.0 | 10.0 | 10.0 | 5.0 | 2.0 | 4.0 | 7.0 | 6.0 | 3.0 | 9.0 | 5.0 | 8.0 | 10.0 | 3.0 | 5.0 | 4.0 | 2.0 |
| 25 | 1.0 | 7.0 | 9.0 | 8.0 | 6.0 | 2.0 | 8.0 | 9.0 | 7.0 | 4.0 | 3.0 | 2.0 | 1.0 | 10.0 | 3.0 | 1.0 | 1.0 | 10.0 | 5.0 | 8.0 | 6.0 | 6.0 | 5.0 | 6.0 | 10.0 | 9.0 | 6.0 | 7.0 | 2.0 | 2.0 | 6.0 | 1.0 | 9.0 | 6.0 | 10.0 | 8.0 | 2.0 | 9.0 | 2.0 | 1.0 |
| 26 | 5.0 | 5.0 | 4.0 | 2.0 | 7.0 | 6.0 | 1.0 | 7.0 | 5.0 | 9.0 | 1.0 | 3.0 | 1.0 | 1.0 | 3.0 | 3.0 | 9.0 | 3.0 | 4.0 | 10.0 | 4.0 | 3.0 | 4.0 | 8.0 | 5.0 | 6.0 | 2.0 | 10.0 | 10.0 | 2.0 | 2.0 | 2.0 | 2.0 | 9.0 | 3.0 | 8.0 | 10.0 | 1.0 | 3.0 | 4.0 |
| 27 | 3.0 | 5.0 | 4.0 | 7.0 | 9.0 | 5.0 | 9.0 | 5.0 | 8.0 | 7.0 | 6.0 | 7.0 | 10.0 | 5.0 | 6.0 | 3.0 | 5.0 | 6.0 | 6.0 | 9.0 | 10.0 | 9.0 | 6.0 | 9.0 | 2.0 | 7.0 | 10.0 | 3.0 | 5.0 | 8.0 | 5.0 | 10.0 | 8.0 | 6.0 | 3.0 | 5.0 | 7.0 | 3.0 | 3.0 | 4.0 |
| 28 | 7.0 | 3.0 | 7.0 | 2.0 | 2.0 | 7.0 | 8.0 | 3.0 | 9.0 | 4.0 | 7.0 | 10.0 | 3.0 | 7.0 | 1.0 | 4.0 | 6.0 | 8.0 | 7.0 | 1.0 | 2.0 | 1.0 | 6.0 | 2.0 | 4.0 | 2.0 | 10.0 | 5.0 | 1.0 | 10.0 | 8.0 | 4.0 | 3.0 | 7.0 | 6.0 | 9.0 | 7.0 | 1.0 | 4.0 | 8.0 |
| 29 | 3.0 | 10.0 | 2.0 | 6.0 | 1.0 | 5.0 | 4.0 | 5.0 | 5.0 | 6.0 | 4.0 | 6.0 | 6.0 | 10.0 | 10.0 | 9.0 | 8.0 | 3.0 | 10.0 | 9.0 | 5.0 | 7.0 | 10.0 | 7.0 | 7.0 | 2.0 | 2.0 | 8.0 | 10.0 | 3.0 | 2.0 | 9.0 | 5.0 | 4.0 | 3.0 | 9.0 | 8.0 | 10.0 | 2.0 | 7.0 |
| 30 | 7.0 | 8.0 | 2.0 | 6.0 | 3.0 | 8.0 | 10.0 | 6.0 | 9.0 | 9.0 | 5.0 | 7.0 | 7.0 | 7.0 | 9.0 | 4.0 | 6.0 | 6.0 | 3.0 | 5.0 | 5.0 | 5.0 | 7.0 | 5.0 | 6.0 | 6.0 | 2.0 | 5.0 | 8.0 | 2.0 | 9.0 | 10.0 | 3.0 | 7.0 | 3.0 | 1.0 | 8.0 | 5.0 | 7.0 | 7.0 |
| 31 | 3.0 | 3.0 | 10.0 | 8.0 | 1.0 | 10.0 | 10.0 | 3.0 | 3.0 | 7.0 | 2.0 | 9.0 | 1.0 | 8.0 | 2.0 | 1.0 | 8.0 | 10.0 | 1.0 | 3.0 | 8.0 | 6.0 | 3.0 | 7.0 | 3.0 | 1.0 | 2.0 | 10.0 | 4.0 | 9.0 | 10.0 | 6.0 | 6.0 | 6.0 | 6.0 | 8.0 | 2.0 | 5.0 | 10.0 | 9.0 |
| 32 | 2.0 | 10.0 | 3.0 | 2.0 | 10.0 | 9.0 | 5.0 | 8.0 | 10.0 | 3.0 | 1.0 | 4.0 | 7.0 | 1.0 | 2.0 | 8.0 | 4.0 | 6.0 | 8.0 | 1.0 | 3.0 | 4.0 | 7.0 | 8.0 | 9.0 | 9.0 | 2.0 | 8.0 | 3.0 | 5.0 | 3.0 | 6.0 | 10.0 | 4.0 | 10.0 | 2.0 | 2.0 | 8.0 | 8.0 | 6.0 |
| 33 | 8.0 | 10.0 | 2.0 | 8.0 | 8.0 | 1.0 | 1.0 | 10.0 | 7.0 | 3.0 | 10.0 | 10.0 | 10.0 | 8.0 | 6.0 | 4.0 | 1.0 | 4.0 | 3.0 | 8.0 | 5.0 | 10.0 | 8.0 | 10.0 | 5.0 | 6.0 | 9.0 | 6.0 | 7.0 | 4.0 | 7.0 | 6.0 | 4.0 | 10.0 | 5.0 | 2.0 | 9.0 | 10.0 | 10.0 | 1.0 |
| 34 | 8.0 | 6.0 | 7.0 | 2.0 | 9.0 | 9.0 | 8.0 | 6.0 | 2.0 | 9.0 | 4.0 | 1.0 | 2.0 | 10.0 | 1.0 | 3.0 | 1.0 | 4.0 | 10.0 | 10.0 | 2.0 | 6.0 | 6.0 | 2.0 | 8.0 | 10.0 | 3.0 | 3.0 | 6.0 | 3.0 | 3.0 | 6.0 | 10.0 | 5.0 | 8.0 | 5.0 | 7.0 | 3.0 | 5.0 | 2.0 |
| 35 | 4.0 | 9.0 | 7.0 | 1.0 | 2.0 | 7.0 | 3.0 | 2.0 | 4.0 | 10.0 | 10.0 | 6.0 | 5.0 | 9.0 | 5.0 | 8.0 | 2.0 | 2.0 | 10.0 | 3.0 | 8.0 | 5.0 | 10.0 | 4.0 | 10.0 | 8.0 | 8.0 | 5.0 | 9.0 | 9.0 | 1.0 | 8.0 | 2.0 | 2.0 | 5.0 | 5.0 | 6.0 | 3.0 | 6.0 | 2.0 |
| 36 | 7.0 | 5.0 | 8.0 | 3.0 | 10.0 | 3.0 | 2.0 | 7.0 | 5.0 | 10.0 | 5.0 | 10.0 | 8.0 | 6.0 | 9.0 | 9.0 | 2.0 | 2.0 | 5.0 | 9.0 | 9.0 | 8.0 | 1.0 | 5.0 | 3.0 | 2.0 | 10.0 | 7.0 | 7.0 | 8.0 | 8.0 | 2.0 | 2.0 | 9.0 | 7.0 | 6.0 | 5.0 | 3.0 | 1.0 | 8.0 |
| 37 | 10.0 | 3.0 | 5.0 | 1.0 | 4.0 | 2.0 | 3.0 | 2.0 | 8.0 | 10.0 | 7.0 | 9.0 | 6.0 | 2.0 | 8.0 | 2.0 | 2.0 | 10.0 | 9.0 | 7.0 | 5.0 | 9.0 | 1.0 | 2.0 | 5.0 | 9.0 | 1.0 | 3.0 | 1.0 | 10.0 | 5.0 | 5.0 | 8.0 | 10.0 | 3.0 | 3.0 | 3.0 | 10.0 | 5.0 | 6.0 |
| 38 | 8.0 | 10.0 | 2.0 | 2.0 | 4.0 | 7.0 | 4.0 | 4.0 | 10.0 | 6.0 | 6.0 | 9.0 | 3.0 | 9.0 | 8.0 | 9.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 3.0 | 3.0 | 6.0 | 4.0 | 2.0 | 3.0 | 3.0 | 4.0 | 2.0 | 7.0 | 10.0 | 8.0 | 10.0 | 5.0 | 6.0 | 1.0 | 5.0 | 2.0 | 1.0 |
| 39 | 5.0 | 5.0 | 3.0 | 2.0 | 6.0 | 5.0 | 7.0 | 8.0 | 5.0 | 9.0 | 3.0 | 10.0 | 5.0 | 4.0 | 7.0 | 9.0 | 10.0 | 4.0 | 10.0 | 8.0 | 9.0 | 9.0 | 5.0 | 2.0 | 2.0 | 1.0 | 4.0 | 4.0 | 8.0 | 7.0 | 7.0 | 9.0 | 6.0 | 1.0 | 2.0 | 2.0 | 8.0 | 6.0 | 1.0 | 7.0 |

While we’re at it, it’s handy to tuck the final path into a tiny JSON snippet so whatever reads this can pick it up easily — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of ""solution"" as the list where you’ll put the nodes in order from the city gate (source) to the central plaza (target). Keep it simple: an ordered array of NODE identifiers only, one after the other, like a little map trail. This JSON is just a sketch of the shape I want back, not the actual path answer itself.

Please be sure to use the node identifiers exactly as they appear in the instance input — don’t rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'objective': {'constant': 0.0, 'linear': [6.0, 8.0, 4.0, 10.0, 6.0, 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'quadratic_cost': 9.0}, {'var_i': 34, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 25, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 28, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 29, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 30, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 31, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 33, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 34, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 35, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 36, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 37, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 38, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 39, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 35, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 35, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 35, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 35, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 33, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 34, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 35, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 37, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 38, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 39, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 24, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 33, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 34, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 36, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 37, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 39, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 24, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 26, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 35, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 36, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 37, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 38, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 39, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 34, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 36, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 38, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 39, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 26, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 34, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 36, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 37, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 39, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'A', 'to': 'B', 'var_index': 0}, {'from': 'A', 'to': 'F', 'var_index': 1}, {'from': 'B', 'to': 'C', 'var_index': 2}, {'from': 'B', 'to': 'G', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'C', 'to': 'H', 'var_index': 5}, {'from': 'D', 'to': 'E', 'var_index': 6}, {'from': 'D', 'to': 'I', 'var_index': 7}, {'from': 'E', 'to': 'J', 'var_index': 8}, {'from': 'F', 'to': 'G', 'var_index': 9}, {'from': 'F', 'to': 'K', 'var_index': 10}, {'from': 'G', 'to': 'H', 'var_index': 11}, {'from': 'G', 'to': 'L', 'var_index': 12}, {'from': 'H', 'to': 'I', 'var_index': 13}, {'from': 'H', 'to': 'M', 'var_index': 14}, {'from': 'I', 'to': 'J', 'var_index': 15}, {'from': 'I', 'to': 'N', 'var_index': 16}, {'from': 'J', 'to': 'O', 'var_index': 17}, {'from': 'K', 'to': 'L', 'var_index': 18}, {'from': 'K', 'to': 'P', 'var_index': 19}, {'from': 'L', 'to': 'M', 'var_index': 20}, {'from': 'L', 'to': 'Q', 'var_index': 21}, {'from': 'M', 'to': 'N', 'var_index': 22}, {'from': 'M', 'to': 'R', 'var_index': 23}, {'from': 'N', 'to': 'O', 'var_index': 24}, {'from': 'N', 'to': 'S', 'var_index': 25}, {'from': 'O', 'to': 'T', 'var_index': 26}, {'from': 'P', 'to': 'Q', 'var_index': 27}, {'from': 'P', 'to': 'U', 'var_index': 28}, {'from': 'Q', 'to': 'R', 'var_index': 29}, {'from': 'Q', 'to': 'V', 'var_index': 30}, {'from': 'R', 'to': 'S', 'var_index': 31}, {'from': 'R', 'to': 'W', 'var_index': 32}, {'from': 'S', 'to': 'T', 'var_index': 33}, {'from': 'S', 'to': 'X', 'var_index': 34}, {'from': 'T', 'to': 'Y', 'var_index': 35}, {'from': 'U', 'to': 'V', 'var_index': 36}, {'from': 'V', 'to': 'W', 'var_index': 37}, {'from': 'W', 'to': 'X', 'var_index': 38}, {'from': 'X', 'to': 'Y', 'var_index': 39}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V', 22: 'W', 23: 'X', 24: 'Y'}}","['A', 'B', 'G', 'H', 'I', 'N', 'S', 'X', 'Y']",18,json,names
QSPP,QSPP,"I walk the factory floor in my head: the inspector needs to pick one straight route from the start station to the final station that follows the conveyor flow, stepping only along the allowed connections. The “best” route is simply the one that ends up taking the least total time — that total is built from the travel time along each link, the setup time every time a station is inspected, and extra slowdowns that kick in when certain pairs of stations are both on the route (sometimes the order matters). The route has to be a single continuous path from the beginning to the end with no invented shortcuts, and the exact station map and times will be shown below.

# total_stations=22
# total_transitions=39
# station_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22
# start_station=21
# final_station=22

transition_from_station,transition_to_station,transition_id
21,1,0
21,6,1
21,11,2
21,16,3
5,22,4
10,22,5
15,22,6
20,22,7
1,2,8
1,6,9
2,3,10
2,7,11
3,4,12
3,8,13
4,5,14
4,9,15
5,10,16
6,7,17
6,11,18
7,8,19
7,12,20
8,9,21
8,13,22
9,10,23
9,14,24
10,15,25
11,12,26
11,16,27
12,13,28
12,17,29
13,14,30
13,18,31
14,15,32
14,19,33
15,20,34
16,17,35
17,18,36
18,19,37
19,20,38

transition_id,transition_base_time
0,8.0
1,2.0
2,6.0
3,5.0
4,9.0
5,9.0
6,6.0
7,7.0
8,2.0
9,2.0
10,6.0
11,10.0
12,1.0
13,5.0
14,4.0
15,7.0
16,1.0
17,6.0
18,1.0
19,3.0
20,8.0
21,4.0
22,9.0
23,2.0
24,8.0
25,5.0
26,1.0
27,7.0
28,4.0
29,2.0
30,2.0
31,8.0
32,4.0
33,3.0
34,8.0
35,5.0
36,3.0
37,7.0
38,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (transition_i_id, transition_j_id). If two transitions with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| transition_i_id\transition_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 8.0 | 8.0 | 4.0 | 8.0 | 10.0 | 10.0 | 10.0 | 7.0 | 8.0 | 1.0 | 5.0 | 8.0 | 3.0 | 7.0 | 10.0 | 3.0 | 5.0 | 6.0 | 4.0 | 9.0 | 7.0 | 2.0 | 7.0 | 2.0 | 9.0 | 3.0 | 7.0 | 9.0 | 7.0 | 5.0 | 10.0 | 4.0 | 6.0 | 6.0 | 3.0 | 10.0 | 3.0 | 3.0 |
| 1 | 8.0 | 6.0 | 6.0 | 2.0 | 3.0 | 3.0 | 3.0 | 3.0 | 6.0 | 10.0 | 7.0 | 2.0 | 4.0 | 9.0 | 3.0 | 10.0 | 9.0 | 3.0 | 7.0 | 2.0 | 7.0 | 8.0 | 3.0 | 5.0 | 9.0 | 3.0 | 3.0 | 5.0 | 8.0 | 6.0 | 8.0 | 5.0 | 8.0 | 8.0 | 10.0 | 3.0 | 5.0 | 10.0 | 10.0 |
| 2 | 8.0 | 6.0 | 9.0 | 6.0 | 7.0 | 3.0 | 7.0 | 6.0 | 6.0 | 3.0 | 4.0 | 3.0 | 5.0 | 8.0 | 2.0 | 2.0 | 4.0 | 10.0 | 5.0 | 4.0 | 3.0 | 7.0 | 5.0 | 8.0 | 2.0 | 8.0 | 3.0 | 9.0 | 9.0 | 10.0 | 10.0 | 7.0 | 1.0 | 4.0 | 8.0 | 4.0 | 10.0 | 2.0 | 1.0 |
| 3 | 4.0 | 2.0 | 6.0 | 6.0 | 1.0 | 8.0 | 4.0 | 5.0 | 8.0 | 5.0 | 5.0 | 2.0 | 1.0 | 10.0 | 5.0 | 8.0 | 1.0 | 5.0 | 1.0 | 3.0 | 5.0 | 6.0 | 7.0 | 5.0 | 2.0 | 9.0 | 2.0 | 2.0 | 3.0 | 10.0 | 5.0 | 3.0 | 7.0 | 6.0 | 8.0 | 9.0 | 1.0 | 3.0 | 9.0 |
| 4 | 8.0 | 3.0 | 7.0 | 1.0 | 9.0 | 8.0 | 5.0 | 8.0 | 5.0 | 3.0 | 7.0 | 9.0 | 7.0 | 4.0 | 9.0 | 10.0 | 10.0 | 5.0 | 8.0 | 8.0 | 10.0 | 7.0 | 7.0 | 1.0 | 4.0 | 8.0 | 6.0 | 3.0 | 1.0 | 3.0 | 9.0 | 9.0 | 7.0 | 2.0 | 4.0 | 3.0 | 3.0 | 1.0 | 2.0 |
| 5 | 10.0 | 3.0 | 3.0 | 8.0 | 8.0 | 8.0 | 7.0 | 3.0 | 1.0 | 7.0 | 9.0 | 9.0 | 6.0 | 9.0 | 4.0 | 3.0 | 8.0 | 7.0 | 9.0 | 9.0 | 1.0 | 9.0 | 4.0 | 3.0 | 7.0 | 9.0 | 9.0 | 8.0 | 7.0 | 8.0 | 1.0 | 7.0 | 7.0 | 2.0 | 5.0 | 9.0 | 4.0 | 2.0 | 2.0 |
| 6 | 10.0 | 3.0 | 7.0 | 4.0 | 5.0 | 7.0 | 6.0 | 4.0 | 3.0 | 1.0 | 1.0 | 5.0 | 7.0 | 6.0 | 5.0 | 10.0 | 10.0 | 5.0 | 9.0 | 2.0 | 2.0 | 8.0 | 7.0 | 3.0 | 3.0 | 9.0 | 3.0 | 7.0 | 5.0 | 10.0 | 8.0 | 9.0 | 1.0 | 4.0 | 9.0 | 3.0 | 8.0 | 1.0 | 6.0 |
| 7 | 10.0 | 3.0 | 6.0 | 5.0 | 8.0 | 3.0 | 4.0 | 5.0 | 9.0 | 8.0 | 2.0 | 6.0 | 2.0 | 6.0 | 10.0 | 10.0 | 5.0 | 2.0 | 2.0 | 10.0 | 2.0 | 6.0 | 9.0 | 3.0 | 5.0 | 3.0 | 7.0 | 3.0 | 1.0 | 8.0 | 3.0 | 2.0 | 7.0 | 1.0 | 3.0 | 2.0 | 6.0 | 9.0 | 10.0 |
| 8 | 7.0 | 6.0 | 6.0 | 8.0 | 5.0 | 1.0 | 3.0 | 9.0 | 2.0 | 5.0 | 3.0 | 3.0 | 3.0 | 8.0 | 6.0 | 5.0 | 9.0 | 10.0 | 10.0 | 3.0 | 8.0 | 10.0 | 3.0 | 3.0 | 9.0 | 5.0 | 2.0 | 7.0 | 5.0 | 5.0 | 9.0 | 6.0 | 4.0 | 8.0 | 6.0 | 9.0 | 6.0 | 1.0 | 7.0 |
| 9 | 8.0 | 10.0 | 3.0 | 5.0 | 3.0 | 7.0 | 1.0 | 8.0 | 5.0 | 1.0 | 10.0 | 7.0 | 6.0 | 2.0 | 1.0 | 7.0 | 5.0 | 4.0 | 4.0 | 4.0 | 8.0 | 4.0 | 4.0 | 4.0 | 2.0 | 1.0 | 8.0 | 10.0 | 10.0 | 5.0 | 6.0 | 4.0 | 4.0 | 6.0 | 6.0 | 7.0 | 8.0 | 4.0 | 9.0 |
| 10 | 1.0 | 7.0 | 4.0 | 5.0 | 7.0 | 9.0 | 1.0 | 2.0 | 3.0 | 10.0 | 1.0 | 4.0 | 8.0 | 9.0 | 7.0 | 4.0 | 1.0 | 7.0 | 1.0 | 7.0 | 5.0 | 3.0 | 6.0 | 4.0 | 5.0 | 10.0 | 5.0 | 5.0 | 8.0 | 2.0 | 7.0 | 9.0 | 2.0 | 7.0 | 6.0 | 6.0 | 2.0 | 5.0 | 8.0 |
| 11 | 5.0 | 2.0 | 3.0 | 2.0 | 9.0 | 9.0 | 5.0 | 6.0 | 3.0 | 7.0 | 4.0 | 3.0 | 10.0 | 1.0 | 1.0 | 4.0 | 2.0 | 3.0 | 2.0 | 7.0 | 2.0 | 6.0 | 3.0 | 5.0 | 5.0 | 5.0 | 9.0 | 1.0 | 2.0 | 10.0 | 7.0 | 8.0 | 3.0 | 8.0 | 6.0 | 2.0 | 6.0 | 2.0 | 1.0 |
| 12 | 8.0 | 4.0 | 5.0 | 1.0 | 7.0 | 6.0 | 7.0 | 2.0 | 3.0 | 6.0 | 8.0 | 10.0 | 4.0 | 2.0 | 1.0 | 2.0 | 2.0 | 1.0 | 2.0 | 1.0 | 9.0 | 3.0 | 2.0 | 10.0 | 9.0 | 6.0 | 9.0 | 2.0 | 1.0 | 3.0 | 6.0 | 2.0 | 6.0 | 10.0 | 5.0 | 3.0 | 5.0 | 3.0 | 10.0 |
| 13 | 3.0 | 9.0 | 8.0 | 10.0 | 4.0 | 9.0 | 6.0 | 6.0 | 8.0 | 2.0 | 9.0 | 1.0 | 2.0 | 8.0 | 4.0 | 9.0 | 2.0 | 10.0 | 2.0 | 6.0 | 5.0 | 3.0 | 2.0 | 7.0 | 4.0 | 8.0 | 3.0 | 6.0 | 1.0 | 10.0 | 2.0 | 9.0 | 3.0 | 7.0 | 9.0 | 9.0 | 8.0 | 4.0 | 10.0 |
| 14 | 7.0 | 3.0 | 2.0 | 5.0 | 9.0 | 4.0 | 5.0 | 10.0 | 6.0 | 1.0 | 7.0 | 1.0 | 1.0 | 4.0 | 4.0 | 6.0 | 3.0 | 4.0 | 5.0 | 7.0 | 9.0 | 2.0 | 10.0 | 2.0 | 5.0 | 8.0 | 8.0 | 3.0 | 7.0 | 3.0 | 6.0 | 5.0 | 8.0 | 10.0 | 5.0 | 1.0 | 10.0 | 3.0 | 4.0 |
| 15 | 10.0 | 10.0 | 2.0 | 8.0 | 10.0 | 3.0 | 10.0 | 10.0 | 5.0 | 7.0 | 4.0 | 4.0 | 2.0 | 9.0 | 6.0 | 4.0 | 9.0 | 1.0 | 3.0 | 10.0 | 7.0 | 5.0 | 10.0 | 1.0 | 2.0 | 1.0 | 1.0 | 5.0 | 4.0 | 10.0 | 1.0 | 2.0 | 1.0 | 3.0 | 5.0 | 4.0 | 9.0 | 1.0 | 1.0 |
| 16 | 3.0 | 9.0 | 4.0 | 1.0 | 10.0 | 8.0 | 10.0 | 5.0 | 9.0 | 5.0 | 1.0 | 2.0 | 2.0 | 2.0 | 3.0 | 9.0 | 4.0 | 1.0 | 1.0 | 9.0 | 8.0 | 5.0 | 7.0 | 2.0 | 3.0 | 8.0 | 2.0 | 7.0 | 3.0 | 7.0 | 9.0 | 9.0 | 7.0 | 3.0 | 9.0 | 4.0 | 9.0 | 5.0 | 1.0 |
| 17 | 5.0 | 3.0 | 10.0 | 5.0 | 5.0 | 7.0 | 5.0 | 2.0 | 10.0 | 4.0 | 7.0 | 3.0 | 1.0 | 10.0 | 4.0 | 1.0 | 1.0 | 8.0 | 6.0 | 4.0 | 4.0 | 10.0 | 5.0 | 5.0 | 2.0 | 9.0 | 2.0 | 10.0 | 3.0 | 8.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 8.0 | 1.0 | 10.0 | 6.0 |
| 18 | 6.0 | 7.0 | 5.0 | 1.0 | 8.0 | 9.0 | 9.0 | 2.0 | 10.0 | 4.0 | 1.0 | 2.0 | 2.0 | 2.0 | 5.0 | 3.0 | 1.0 | 6.0 | 9.0 | 5.0 | 3.0 | 4.0 | 1.0 | 6.0 | 3.0 | 5.0 | 3.0 | 8.0 | 2.0 | 4.0 | 2.0 | 7.0 | 10.0 | 3.0 | 7.0 | 5.0 | 4.0 | 7.0 | 1.0 |
| 19 | 4.0 | 2.0 | 4.0 | 3.0 | 8.0 | 9.0 | 2.0 | 10.0 | 3.0 | 4.0 | 7.0 | 7.0 | 1.0 | 6.0 | 7.0 | 10.0 | 9.0 | 4.0 | 5.0 | 7.0 | 9.0 | 6.0 | 8.0 | 1.0 | 4.0 | 1.0 | 4.0 | 10.0 | 8.0 | 10.0 | 10.0 | 2.0 | 10.0 | 5.0 | 10.0 | 10.0 | 1.0 | 7.0 | 4.0 |
| 20 | 9.0 | 7.0 | 3.0 | 5.0 | 10.0 | 1.0 | 2.0 | 2.0 | 8.0 | 8.0 | 5.0 | 2.0 | 9.0 | 5.0 | 9.0 | 7.0 | 8.0 | 4.0 | 3.0 | 9.0 | 1.0 | 8.0 | 2.0 | 1.0 | 5.0 | 6.0 | 1.0 | 3.0 | 6.0 | 5.0 | 1.0 | 4.0 | 9.0 | 1.0 | 3.0 | 10.0 | 3.0 | 3.0 | 4.0 |
| 21 | 7.0 | 8.0 | 7.0 | 6.0 | 7.0 | 9.0 | 8.0 | 6.0 | 10.0 | 4.0 | 3.0 | 6.0 | 3.0 | 3.0 | 2.0 | 5.0 | 5.0 | 10.0 | 4.0 | 6.0 | 8.0 | 6.0 | 9.0 | 9.0 | 9.0 | 2.0 | 5.0 | 7.0 | 8.0 | 2.0 | 4.0 | 8.0 | 6.0 | 4.0 | 7.0 | 4.0 | 4.0 | 10.0 | 9.0 |
| 22 | 2.0 | 3.0 | 5.0 | 7.0 | 7.0 | 4.0 | 7.0 | 9.0 | 3.0 | 4.0 | 6.0 | 3.0 | 2.0 | 2.0 | 10.0 | 10.0 | 7.0 | 5.0 | 1.0 | 8.0 | 2.0 | 9.0 | 5.0 | 3.0 | 6.0 | 1.0 | 3.0 | 10.0 | 10.0 | 10.0 | 3.0 | 4.0 | 2.0 | 10.0 | 7.0 | 7.0 | 2.0 | 10.0 | 1.0 |
| 23 | 7.0 | 5.0 | 8.0 | 5.0 | 1.0 | 3.0 | 3.0 | 3.0 | 3.0 | 4.0 | 4.0 | 5.0 | 10.0 | 7.0 | 2.0 | 1.0 | 2.0 | 5.0 | 6.0 | 1.0 | 1.0 | 9.0 | 3.0 | 2.0 | 5.0 | 8.0 | 2.0 | 2.0 | 9.0 | 4.0 | 10.0 | 2.0 | 10.0 | 1.0 | 6.0 | 2.0 | 7.0 | 4.0 | 9.0 |
| 24 | 2.0 | 9.0 | 2.0 | 2.0 | 4.0 | 7.0 | 3.0 | 5.0 | 9.0 | 2.0 | 5.0 | 5.0 | 9.0 | 4.0 | 5.0 | 2.0 | 3.0 | 2.0 | 3.0 | 4.0 | 5.0 | 9.0 | 6.0 | 5.0 | 9.0 | 5.0 | 8.0 | 2.0 | 5.0 | 8.0 | 9.0 | 7.0 | 1.0 | 8.0 | 2.0 | 8.0 | 6.0 | 6.0 | 8.0 |
| 25 | 9.0 | 3.0 | 8.0 | 9.0 | 8.0 | 9.0 | 9.0 | 3.0 | 5.0 | 1.0 | 10.0 | 5.0 | 6.0 | 8.0 | 8.0 | 1.0 | 8.0 | 9.0 | 5.0 | 1.0 | 6.0 | 2.0 | 1.0 | 8.0 | 5.0 | 3.0 | 10.0 | 10.0 | 7.0 | 6.0 | 1.0 | 8.0 | 4.0 | 8.0 | 7.0 | 4.0 | 3.0 | 7.0 | 2.0 |
| 26 | 3.0 | 3.0 | 3.0 | 2.0 | 6.0 | 9.0 | 3.0 | 7.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 3.0 | 8.0 | 1.0 | 2.0 | 2.0 | 3.0 | 4.0 | 1.0 | 5.0 | 3.0 | 2.0 | 8.0 | 10.0 | 10.0 | 10.0 | 2.0 | 10.0 | 3.0 | 1.0 | 10.0 | 6.0 | 10.0 | 5.0 | 5.0 | 5.0 | 1.0 |
| 27 | 7.0 | 5.0 | 9.0 | 2.0 | 3.0 | 8.0 | 7.0 | 3.0 | 7.0 | 10.0 | 5.0 | 1.0 | 2.0 | 6.0 | 3.0 | 5.0 | 7.0 | 10.0 | 8.0 | 10.0 | 3.0 | 7.0 | 10.0 | 2.0 | 2.0 | 10.0 | 10.0 | 4.0 | 9.0 | 3.0 | 9.0 | 6.0 | 1.0 | 8.0 | 1.0 | 6.0 | 3.0 | 7.0 | 4.0 |
| 28 | 9.0 | 8.0 | 9.0 | 3.0 | 1.0 | 7.0 | 5.0 | 1.0 | 5.0 | 10.0 | 8.0 | 2.0 | 1.0 | 1.0 | 7.0 | 4.0 | 3.0 | 3.0 | 2.0 | 8.0 | 6.0 | 8.0 | 10.0 | 9.0 | 5.0 | 7.0 | 2.0 | 9.0 | 10.0 | 5.0 | 8.0 | 2.0 | 8.0 | 9.0 | 10.0 | 1.0 | 9.0 | 8.0 | 2.0 |
| 29 | 7.0 | 6.0 | 10.0 | 10.0 | 3.0 | 8.0 | 10.0 | 8.0 | 5.0 | 5.0 | 2.0 | 10.0 | 3.0 | 10.0 | 3.0 | 10.0 | 7.0 | 8.0 | 4.0 | 10.0 | 5.0 | 2.0 | 10.0 | 4.0 | 8.0 | 6.0 | 10.0 | 3.0 | 5.0 | 6.0 | 6.0 | 2.0 | 9.0 | 4.0 | 9.0 | 2.0 | 9.0 | 4.0 | 9.0 |
| 30 | 5.0 | 8.0 | 10.0 | 5.0 | 9.0 | 1.0 | 8.0 | 3.0 | 9.0 | 6.0 | 7.0 | 7.0 | 6.0 | 2.0 | 6.0 | 1.0 | 9.0 | 2.0 | 2.0 | 10.0 | 1.0 | 4.0 | 3.0 | 10.0 | 9.0 | 1.0 | 3.0 | 9.0 | 8.0 | 6.0 | 5.0 | 3.0 | 10.0 | 6.0 | 4.0 | 5.0 | 10.0 | 3.0 | 10.0 |
| 31 | 10.0 | 5.0 | 7.0 | 3.0 | 9.0 | 7.0 | 9.0 | 2.0 | 6.0 | 4.0 | 9.0 | 8.0 | 2.0 | 9.0 | 5.0 | 2.0 | 9.0 | 5.0 | 7.0 | 2.0 | 4.0 | 8.0 | 4.0 | 2.0 | 7.0 | 8.0 | 1.0 | 6.0 | 2.0 | 2.0 | 3.0 | 6.0 | 8.0 | 3.0 | 1.0 | 4.0 | 7.0 | 9.0 | 1.0 |
| 32 | 4.0 | 8.0 | 1.0 | 7.0 | 7.0 | 7.0 | 1.0 | 7.0 | 4.0 | 4.0 | 2.0 | 3.0 | 6.0 | 3.0 | 8.0 | 1.0 | 7.0 | 2.0 | 10.0 | 10.0 | 9.0 | 6.0 | 2.0 | 10.0 | 1.0 | 4.0 | 10.0 | 1.0 | 8.0 | 9.0 | 10.0 | 8.0 | 2.0 | 8.0 | 4.0 | 6.0 | 4.0 | 1.0 | 9.0 |
| 33 | 6.0 | 8.0 | 4.0 | 6.0 | 2.0 | 2.0 | 4.0 | 1.0 | 8.0 | 6.0 | 7.0 | 8.0 | 10.0 | 7.0 | 10.0 | 3.0 | 3.0 | 1.0 | 3.0 | 5.0 | 1.0 | 4.0 | 10.0 | 1.0 | 8.0 | 8.0 | 6.0 | 8.0 | 9.0 | 4.0 | 6.0 | 3.0 | 8.0 | 6.0 | 4.0 | 5.0 | 7.0 | 5.0 | 10.0 |
| 34 | 6.0 | 10.0 | 8.0 | 8.0 | 4.0 | 5.0 | 9.0 | 3.0 | 6.0 | 6.0 | 6.0 | 6.0 | 5.0 | 9.0 | 5.0 | 5.0 | 9.0 | 6.0 | 7.0 | 10.0 | 3.0 | 7.0 | 7.0 | 6.0 | 2.0 | 7.0 | 10.0 | 1.0 | 10.0 | 9.0 | 4.0 | 1.0 | 4.0 | 4.0 | 4.0 | 4.0 | 2.0 | 6.0 | 3.0 |
| 35 | 3.0 | 3.0 | 4.0 | 9.0 | 3.0 | 9.0 | 3.0 | 2.0 | 9.0 | 7.0 | 6.0 | 2.0 | 3.0 | 9.0 | 1.0 | 4.0 | 4.0 | 8.0 | 5.0 | 10.0 | 10.0 | 4.0 | 7.0 | 2.0 | 8.0 | 4.0 | 5.0 | 6.0 | 1.0 | 2.0 | 5.0 | 4.0 | 6.0 | 5.0 | 4.0 | 8.0 | 6.0 | 2.0 | 8.0 |
| 36 | 10.0 | 5.0 | 10.0 | 1.0 | 3.0 | 4.0 | 8.0 | 6.0 | 6.0 | 8.0 | 2.0 | 6.0 | 5.0 | 8.0 | 10.0 | 9.0 | 9.0 | 1.0 | 4.0 | 1.0 | 3.0 | 4.0 | 2.0 | 7.0 | 6.0 | 3.0 | 5.0 | 3.0 | 9.0 | 9.0 | 10.0 | 7.0 | 4.0 | 7.0 | 2.0 | 6.0 | 2.0 | 5.0 | 9.0 |
| 37 | 3.0 | 10.0 | 2.0 | 3.0 | 1.0 | 2.0 | 1.0 | 9.0 | 1.0 | 4.0 | 5.0 | 2.0 | 3.0 | 4.0 | 3.0 | 1.0 | 5.0 | 10.0 | 7.0 | 7.0 | 3.0 | 10.0 | 10.0 | 4.0 | 6.0 | 7.0 | 5.0 | 7.0 | 8.0 | 4.0 | 3.0 | 9.0 | 1.0 | 5.0 | 6.0 | 2.0 | 5.0 | 9.0 | 6.0 |
| 38 | 3.0 | 10.0 | 1.0 | 9.0 | 2.0 | 2.0 | 6.0 | 10.0 | 7.0 | 9.0 | 8.0 | 1.0 | 10.0 | 10.0 | 4.0 | 1.0 | 1.0 | 6.0 | 1.0 | 4.0 | 4.0 | 9.0 | 1.0 | 9.0 | 8.0 | 2.0 | 1.0 | 4.0 | 2.0 | 9.0 | 10.0 | 1.0 | 9.0 | 10.0 | 3.0 | 8.0 | 9.0 | 6.0 | 1.0 |

Also, when you hand me the chosen route, tuck it into a tiny JSON envelope like this — nice and simple:

{
  ""solution"": []
}

""solution"" should be an array holding the node identifiers in order, from the start station to the final station. Think of it like filling in a short form: just list the station names (nodes) you walk through, in sequence. This block is only a sketch of the expected shape, not the actual answer itself.

Please use the node identifiers exactly as they appear in the instance input — do not rename them or introduce new labels, and do not include any edge IDs or cost tags (only node names belong in the path). 

Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 20, 'to': 5, 'var_index': 1}, {'from': 20, 'to': 10, 'var_index': 2}, {'from': 20, 'to': 15, 'var_index': 3}, {'from': 4, 'to': 21, 'var_index': 4}, {'from': 9, 'to': 21, 'var_index': 5}, {'from': 14, 'to': 21, 'var_index': 6}, {'from': 19, 'to': 21, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 0, 'to': 5, 'var_index': 9}, {'from': 1, 'to': 2, 'var_index': 10}, {'from': 1, 'to': 6, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 2, 'to': 7, 'var_index': 13}, {'from': 3, 'to': 4, 'var_index': 14}, {'from': 3, 'to': 8, 'var_index': 15}, {'from': 4, 'to': 9, 'var_index': 16}, {'from': 5, 'to': 6, 'var_index': 17}, {'from': 5, 'to': 10, 'var_index': 18}, {'from': 6, 'to': 7, 'var_index': 19}, {'from': 6, 'to': 11, 'var_index': 20}, {'from': 7, 'to': 8, 'var_index': 21}, {'from': 7, 'to': 12, 'var_index': 22}, {'from': 8, 'to': 9, 'var_index': 23}, {'from': 8, 'to': 13, 'var_index': 24}, {'from': 9, 'to': 14, 'var_index': 25}, {'from': 10, 'to': 11, 'var_index': 26}, {'from': 10, 'to': 15, 'var_index': 27}, {'from': 11, 'to': 12, 'var_index': 28}, {'from': 11, 'to': 16, 'var_index': 29}, {'from': 12, 'to': 13, 'var_index': 30}, {'from': 12, 'to': 17, 'var_index': 31}, {'from': 13, 'to': 14, 'var_index': 32}, {'from': 13, 'to': 18, 'var_index': 33}, {'from': 14, 'to': 19, 'var_index': 34}, {'from': 15, 'to': 16, 'var_index': 35}, {'from': 16, 'to': 17, 'var_index': 36}, {'from': 17, 'to': 18, 'var_index': 37}, {'from': 18, 'to': 19, 'var_index': 38}], 'objective': {'constant': 0.0, 'linear': [8.0, 2.0, 6.0, 5.0, 9.0, 9.0, 6.0, 7.0, 2.0, 2.0, 6.0, 10.0, 1.0, 5.0, 4.0, 7.0, 1.0, 6.0, 1.0, 3.0, 8.0, 4.0, 9.0, 2.0, 8.0, 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'quadratic_cost': 1.0}, {'var_i': 35, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 35, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 25, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 28, 'quadratic_cost': 1.0}, {'var_i': 35, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 31, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 33, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 34, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 35, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 38, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 32, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 34, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 36, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 38, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 30, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 33, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 34, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 36, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 37, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 38, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 26, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 28, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 32, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 35, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 36, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 37, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 38, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 21, 'to': 1, 'var_index': 0}, {'from': 21, 'to': 6, 'var_index': 1}, {'from': 21, 'to': 11, 'var_index': 2}, {'from': 21, 'to': 16, 'var_index': 3}, {'from': 5, 'to': 22, 'var_index': 4}, {'from': 10, 'to': 22, 'var_index': 5}, {'from': 15, 'to': 22, 'var_index': 6}, {'from': 20, 'to': 22, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 6, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 7, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 8, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 9, 'var_index': 15}, {'from': 5, 'to': 10, 'var_index': 16}, {'from': 6, 'to': 7, 'var_index': 17}, {'from': 6, 'to': 11, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 12, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 13, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 14, 'var_index': 24}, {'from': 10, 'to': 15, 'var_index': 25}, {'from': 11, 'to': 12, 'var_index': 26}, {'from': 11, 'to': 16, 'var_index': 27}, {'from': 12, 'to': 13, 'var_index': 28}, {'from': 12, 'to': 17, 'var_index': 29}, {'from': 13, 'to': 14, 'var_index': 30}, {'from': 13, 'to': 18, 'var_index': 31}, {'from': 14, 'to': 15, 'var_index': 32}, {'from': 14, 'to': 19, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 17, 'var_index': 35}, {'from': 17, 'to': 18, 'var_index': 36}, {'from': 18, 'to': 19, 'var_index': 37}, {'from': 19, 'to': 20, 'var_index': 38}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22}}","[21, 1, 2, 3, 4, 5, 22]",19,csv,1
QSPP,QSPP,"I need to map out one straight course sequence that starts at the intro seminar and ends at the capstone, following every prerequisite link like stepping stones. The plan is to pick a single chain of classes — no detours, no doubling back, no taking extra courses off the path — and for each class count its normal workload plus the admin fee that comes with signing up. Also watch out: some pairs of classes create extra friction when they’re both taken (and a few classes carry a little extra burden just by themselves), so the total effort is the sum of all those per-course loads and fees plus any extra pairwise difficulties. The goal is to make that total as small as possible. Concrete details about the courses, fees, and pairwise frictions are shown below.

There are 22 total courses and 21 prerequisite links among 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21; my sequence must start at 20 and end at 21.

| prereq_from_course | prereq_to_course | prereq_link_id |
|---|---|---|
| 20 | 0 | 0 |
| 19 | 21 | 1 |
| 0 | 1 | 2 |
| 1 | 2 | 3 |
| 2 | 3 | 4 |
| 3 | 4 | 5 |
| 4 | 5 | 6 |
| 5 | 6 | 7 |
| 6 | 7 | 8 |
| 7 | 8 | 9 |
| 8 | 9 | 10 |
| 9 | 10 | 11 |
| 10 | 11 | 12 |
| 11 | 12 | 13 |
| 12 | 13 | 14 |
| 13 | 14 | 15 |
| 14 | 15 | 16 |
| 15 | 16 | 17 |
| 16 | 17 | 18 |
| 17 | 18 | 19 |
| 18 | 19 | 20 |

| prereq_link_id | course_workload_plus_admin_fee |
|---|---|
| 0 | 9.0 |
| 1 | 2.0 |
| 2 | 5.0 |
| 3 | 6.0 |
| 4 | 10.0 |
| 5 | 6.0 |
| 6 | 3.0 |
| 7 | 2.0 |
| 8 | 1.0 |
| 9 | 5.0 |
| 10 | 5.0 |
| 11 | 9.0 |
| 12 | 5.0 |
| 13 | 1.0 |
| 14 | 6.0 |
| 15 | 10.0 |
| 16 | 4.0 |
| 17 | 7.0 |
| 18 | 4.0 |
| 19 | 6.0 |
| 20 | 3.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (prereq_link_i_id, prereq_link_j_id). If two prereq_links with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| prereq_link_i_id\prereq_link_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 5.0 | 9.0 | 8.0 | 4.0 | 7.0 | 9.0 | 6.0 | 10.0 | 8.0 | 3.0 | 8.0 | 10.0 | 8.0 | 1.0 | 8.0 | 9.0 | 4.0 | 7.0 | 5.0 | 6.0 |
| 1 | 5.0 | 3.0 | 7.0 | 4.0 | 1.0 | 6.0 | 5.0 | 3.0 | 5.0 | 4.0 | 10.0 | 1.0 | 3.0 | 1.0 | 9.0 | 2.0 | 8.0 | 6.0 | 6.0 | 2.0 | 5.0 |
| 2 | 9.0 | 7.0 | 3.0 | 6.0 | 9.0 | 8.0 | 7.0 | 10.0 | 6.0 | 5.0 | 8.0 | 6.0 | 10.0 | 8.0 | 8.0 | 7.0 | 6.0 | 6.0 | 10.0 | 3.0 | 10.0 |
| 3 | 8.0 | 4.0 | 6.0 | 1.0 | 6.0 | 2.0 | 2.0 | 5.0 | 7.0 | 4.0 | 9.0 | 4.0 | 1.0 | 6.0 | 9.0 | 2.0 | 2.0 | 5.0 | 2.0 | 4.0 | 3.0 |
| 4 | 4.0 | 1.0 | 9.0 | 6.0 | 4.0 | 10.0 | 8.0 | 10.0 | 8.0 | 2.0 | 4.0 | 4.0 | 8.0 | 6.0 | 8.0 | 10.0 | 9.0 | 7.0 | 8.0 | 6.0 | 6.0 |
| 5 | 7.0 | 6.0 | 8.0 | 2.0 | 10.0 | 4.0 | 4.0 | 4.0 | 8.0 | 8.0 | 6.0 | 9.0 | 2.0 | 1.0 | 2.0 | 9.0 | 9.0 | 4.0 | 5.0 | 1.0 | 4.0 |
| 6 | 9.0 | 5.0 | 7.0 | 2.0 | 8.0 | 4.0 | 2.0 | 8.0 | 8.0 | 10.0 | 1.0 | 9.0 | 5.0 | 10.0 | 5.0 | 6.0 | 6.0 | 6.0 | 6.0 | 2.0 | 7.0 |
| 7 | 6.0 | 3.0 | 10.0 | 5.0 | 10.0 | 4.0 | 8.0 | 1.0 | 3.0 | 5.0 | 10.0 | 5.0 | 9.0 | 7.0 | 8.0 | 9.0 | 7.0 | 2.0 | 4.0 | 5.0 | 7.0 |
| 8 | 10.0 | 5.0 | 6.0 | 7.0 | 8.0 | 8.0 | 8.0 | 3.0 | 7.0 | 8.0 | 1.0 | 9.0 | 7.0 | 10.0 | 9.0 | 10.0 | 6.0 | 7.0 | 1.0 | 10.0 | 10.0 |
| 9 | 8.0 | 4.0 | 5.0 | 4.0 | 2.0 | 8.0 | 10.0 | 5.0 | 8.0 | 3.0 | 8.0 | 7.0 | 6.0 | 5.0 | 10.0 | 6.0 | 8.0 | 5.0 | 2.0 | 6.0 | 2.0 |
| 10 | 3.0 | 10.0 | 8.0 | 9.0 | 4.0 | 6.0 | 1.0 | 10.0 | 1.0 | 8.0 | 4.0 | 4.0 | 8.0 | 9.0 | 4.0 | 5.0 | 2.0 | 9.0 | 2.0 | 3.0 | 7.0 |
| 11 | 8.0 | 1.0 | 6.0 | 4.0 | 4.0 | 9.0 | 9.0 | 5.0 | 9.0 | 7.0 | 4.0 | 6.0 | 8.0 | 3.0 | 9.0 | 8.0 | 4.0 | 9.0 | 9.0 | 6.0 | 6.0 |
| 12 | 10.0 | 3.0 | 10.0 | 1.0 | 8.0 | 2.0 | 5.0 | 9.0 | 7.0 | 6.0 | 8.0 | 8.0 | 9.0 | 8.0 | 9.0 | 7.0 | 10.0 | 7.0 | 3.0 | 5.0 | 8.0 |
| 13 | 8.0 | 1.0 | 8.0 | 6.0 | 6.0 | 1.0 | 10.0 | 7.0 | 10.0 | 5.0 | 9.0 | 3.0 | 8.0 | 9.0 | 2.0 | 7.0 | 9.0 | 4.0 | 8.0 | 1.0 | 10.0 |
| 14 | 1.0 | 9.0 | 8.0 | 9.0 | 8.0 | 2.0 | 5.0 | 8.0 | 9.0 | 10.0 | 4.0 | 9.0 | 9.0 | 2.0 | 4.0 | 2.0 | 5.0 | 2.0 | 5.0 | 6.0 | 6.0 |
| 15 | 8.0 | 2.0 | 7.0 | 2.0 | 10.0 | 9.0 | 6.0 | 9.0 | 10.0 | 6.0 | 5.0 | 8.0 | 7.0 | 7.0 | 2.0 | 3.0 | 6.0 | 9.0 | 2.0 | 1.0 | 10.0 |
| 16 | 9.0 | 8.0 | 6.0 | 2.0 | 9.0 | 9.0 | 6.0 | 7.0 | 6.0 | 8.0 | 2.0 | 4.0 | 10.0 | 9.0 | 5.0 | 6.0 | 4.0 | 7.0 | 2.0 | 10.0 | 5.0 |
| 17 | 4.0 | 6.0 | 6.0 | 5.0 | 7.0 | 4.0 | 6.0 | 2.0 | 7.0 | 5.0 | 9.0 | 9.0 | 7.0 | 4.0 | 2.0 | 9.0 | 7.0 | 10.0 | 5.0 | 4.0 | 3.0 |
| 18 | 7.0 | 6.0 | 10.0 | 2.0 | 8.0 | 5.0 | 6.0 | 4.0 | 1.0 | 2.0 | 2.0 | 9.0 | 3.0 | 8.0 | 5.0 | 2.0 | 2.0 | 5.0 | 4.0 | 8.0 | 2.0 |
| 19 | 5.0 | 2.0 | 3.0 | 4.0 | 6.0 | 1.0 | 2.0 | 5.0 | 10.0 | 6.0 | 3.0 | 6.0 | 5.0 | 1.0 | 6.0 | 1.0 | 10.0 | 4.0 | 8.0 | 8.0 | 3.0 |
| 20 | 6.0 | 5.0 | 10.0 | 3.0 | 6.0 | 4.0 | 7.0 | 7.0 | 10.0 | 2.0 | 7.0 | 6.0 | 8.0 | 10.0 | 6.0 | 10.0 | 5.0 | 3.0 | 2.0 | 3.0 | 8.0 |

I'll use these entries to pick one uninterrupted chain from 20 to 21 that minimizes the total effort.

Also, to keep things machine-friendly, please put the chosen course chain into a tiny JSON snippet like this:

{
  ""solution"": []
}

Here, ""solution"" should be a list of NODE identifiers only — the sequence of classes from the intro seminar to the capstone, in order. Think of it as a simple form: replace the empty array with the ordered list of nodes you picked. Don’t include any edge IDs, costs, or extra labels — just the node names, and make sure each consecutive pair is a real directed prerequisite link.

This JSON is just a sketch of the shape I expect, not the final answer itself. Also, use the identifiers exactly as they appear in the instance input — no renaming and no new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 21, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}], 'objective': {'constant': 0.0, 'linear': [9.0, 2.0, 5.0, 6.0, 10.0, 6.0, 3.0, 2.0, 1.0, 5.0, 5.0, 9.0, 5.0, 1.0, 6.0, 10.0, 4.0, 7.0, 4.0, 6.0, 3.0], 'quadratic': [[10.0, 5.0, 9.0, 8.0, 4.0, 7.0, 9.0, 6.0, 10.0, 8.0, 3.0, 8.0, 10.0, 8.0, 1.0, 8.0, 9.0, 4.0, 7.0, 5.0, 6.0], [5.0, 3.0, 7.0, 4.0, 1.0, 6.0, 5.0, 3.0, 5.0, 4.0, 10.0, 1.0, 3.0, 1.0, 9.0, 2.0, 8.0, 6.0, 6.0, 2.0, 5.0], [9.0, 7.0, 3.0, 6.0, 9.0, 8.0, 7.0, 10.0, 6.0, 5.0, 8.0, 6.0, 10.0, 8.0, 8.0, 7.0, 6.0, 6.0, 10.0, 3.0, 10.0], [8.0, 4.0, 6.0, 1.0, 6.0, 2.0, 2.0, 5.0, 7.0, 4.0, 9.0, 4.0, 1.0, 6.0, 9.0, 2.0, 2.0, 5.0, 2.0, 4.0, 3.0], [4.0, 1.0, 9.0, 6.0, 4.0, 10.0, 8.0, 10.0, 8.0, 2.0, 4.0, 4.0, 8.0, 6.0, 8.0, 10.0, 9.0, 7.0, 8.0, 6.0, 6.0], [7.0, 6.0, 8.0, 2.0, 10.0, 4.0, 4.0, 4.0, 8.0, 8.0, 6.0, 9.0, 2.0, 1.0, 2.0, 9.0, 9.0, 4.0, 5.0, 1.0, 4.0], [9.0, 5.0, 7.0, 2.0, 8.0, 4.0, 2.0, 8.0, 8.0, 10.0, 1.0, 9.0, 5.0, 10.0, 5.0, 6.0, 6.0, 6.0, 6.0, 2.0, 7.0], [6.0, 3.0, 10.0, 5.0, 10.0, 4.0, 8.0, 1.0, 3.0, 5.0, 10.0, 5.0, 9.0, 7.0, 8.0, 9.0, 7.0, 2.0, 4.0, 5.0, 7.0], [10.0, 5.0, 6.0, 7.0, 8.0, 8.0, 8.0, 3.0, 7.0, 8.0, 1.0, 9.0, 7.0, 10.0, 9.0, 10.0, 6.0, 7.0, 1.0, 10.0, 10.0], [8.0, 4.0, 5.0, 4.0, 2.0, 8.0, 10.0, 5.0, 8.0, 3.0, 8.0, 7.0, 6.0, 5.0, 10.0, 6.0, 8.0, 5.0, 2.0, 6.0, 2.0], [3.0, 10.0, 8.0, 9.0, 4.0, 6.0, 1.0, 10.0, 1.0, 8.0, 4.0, 4.0, 8.0, 9.0, 4.0, 5.0, 2.0, 9.0, 2.0, 3.0, 7.0], [8.0, 1.0, 6.0, 4.0, 4.0, 9.0, 9.0, 5.0, 9.0, 7.0, 4.0, 6.0, 8.0, 3.0, 9.0, 8.0, 4.0, 9.0, 9.0, 6.0, 6.0], [10.0, 3.0, 10.0, 1.0, 8.0, 2.0, 5.0, 9.0, 7.0, 6.0, 8.0, 8.0, 9.0, 8.0, 9.0, 7.0, 10.0, 7.0, 3.0, 5.0, 8.0], [8.0, 1.0, 8.0, 6.0, 6.0, 1.0, 10.0, 7.0, 10.0, 5.0, 9.0, 3.0, 8.0, 9.0, 2.0, 7.0, 9.0, 4.0, 8.0, 1.0, 10.0], [1.0, 9.0, 8.0, 9.0, 8.0, 2.0, 5.0, 8.0, 9.0, 10.0, 4.0, 9.0, 9.0, 2.0, 4.0, 2.0, 5.0, 2.0, 5.0, 6.0, 6.0], [8.0, 2.0, 7.0, 2.0, 10.0, 9.0, 6.0, 9.0, 10.0, 6.0, 5.0, 8.0, 7.0, 7.0, 2.0, 3.0, 6.0, 9.0, 2.0, 1.0, 10.0], [9.0, 8.0, 6.0, 2.0, 9.0, 9.0, 6.0, 7.0, 6.0, 8.0, 2.0, 4.0, 10.0, 9.0, 5.0, 6.0, 4.0, 7.0, 2.0, 10.0, 5.0], [4.0, 6.0, 6.0, 5.0, 7.0, 4.0, 6.0, 2.0, 7.0, 5.0, 9.0, 9.0, 7.0, 4.0, 2.0, 9.0, 7.0, 10.0, 5.0, 4.0, 3.0], [7.0, 6.0, 10.0, 2.0, 8.0, 5.0, 6.0, 4.0, 1.0, 2.0, 2.0, 9.0, 3.0, 8.0, 5.0, 2.0, 2.0, 5.0, 4.0, 8.0, 2.0], [5.0, 2.0, 3.0, 4.0, 6.0, 1.0, 2.0, 5.0, 10.0, 6.0, 3.0, 6.0, 5.0, 1.0, 6.0, 1.0, 10.0, 4.0, 8.0, 8.0, 3.0], [6.0, 5.0, 10.0, 3.0, 6.0, 4.0, 7.0, 7.0, 10.0, 2.0, 7.0, 6.0, 8.0, 10.0, 6.0, 10.0, 5.0, 3.0, 2.0, 3.0, 8.0]]}, 'source': 20, 'target': 21}","[20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]",2732.0,"{'problem_type': 'QSPP', 'num_nodes': 22, 'num_edges': 21, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'source': 20, 'target': 21, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 3.0}, {'var_index': 7, 'linear_cost': 2.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 5.0}, {'var_index': 10, 'linear_cost': 5.0}, {'var_index': 11, 'linear_cost': 9.0}, {'var_index': 12, 'linear_cost': 5.0}, {'var_index': 13, 'linear_cost': 1.0}, {'var_index': 14, 'linear_cost': 6.0}, {'var_index': 15, 'linear_cost': 10.0}, {'var_index': 16, 'linear_cost': 4.0}, {'var_index': 17, 'linear_cost': 7.0}, {'var_index': 18, 'linear_cost': 4.0}, {'var_index': 19, 'linear_cost': 6.0}, {'var_index': 20, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 21, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21}}","[20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]",20,markdown_table,0
QSPP,QSPP,"Someone made a map of one-way streets between home and the office and wants to pick exactly one route that keeps the total charges down. Every street on that map has a base toll; on top of that, certain street combinations trigger additional fees when both are used, and some streets can add a bit extra on their own. To judge any route, add together all the street tolls along it and then add any extra combination fees that apply — the lower the total, the better. The chosen route must follow actual one-way connections from the home node to the office node in order; the specific streets and their costs are listed below.

# total_intersections=20
# total_one_way_streets=33
# intersections=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
# home_intersection=19
# office_intersection=20

street_from_intersection,street_to_intersection,street_id
19,1,0
19,7,1
19,13,2
6,20,3
12,20,4
18,20,5
1,2,6
1,7,7
2,3,8
2,8,9
3,4,10
3,9,11
4,5,12
4,10,13
5,6,14
5,11,15
6,12,16
7,8,17
7,13,18
8,9,19
8,14,20
9,10,21
9,15,22
10,11,23
10,16,24
11,12,25
11,17,26
12,18,27
13,14,28
14,15,29
15,16,30
16,17,31
17,18,32

street_id_ref,base_toll
0,1.0
1,5.0
2,4.0
3,4.0
4,1.0
5,10.0
6,4.0
7,4.0
8,3.0
9,8.0
10,9.0
11,7.0
12,5.0
13,10.0
14,5.0
15,4.0
16,2.0
17,2.0
18,3.0
19,7.0
20,9.0
21,10.0
22,4.0
23,4.0
24,6.0
25,9.0
26,10.0
27,1.0
28,7.0
29,10.0
30,10.0
31,4.0
32,8.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_ref, street_j_ref). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| street_i_ref\street_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 4.0 | 9.0 | 8.0 | 8.0 | 9.0 | 8.0 | 10.0 | 6.0 | 9.0 | 1.0 | 5.0 | 1.0 | 8.0 | 8.0 | 8.0 | 2.0 | 3.0 | 5.0 | 2.0 | 6.0 | 8.0 | 2.0 | 8.0 | 2.0 | 5.0 | 1.0 | 3.0 | 7.0 | 7.0 | 8.0 | 8.0 | 2.0 |
| 1 | 4.0 | 2.0 | 1.0 | 4.0 | 5.0 | 8.0 | 7.0 | 6.0 | 2.0 | 9.0 | 10.0 | 5.0 | 5.0 | 6.0 | 4.0 | 9.0 | 6.0 | 1.0 | 7.0 | 10.0 | 10.0 | 1.0 | 4.0 | 9.0 | 3.0 | 4.0 | 2.0 | 4.0 | 6.0 | 8.0 | 8.0 | 2.0 | 1.0 |
| 2 | 9.0 | 1.0 | 3.0 | 2.0 | 5.0 | 9.0 | 8.0 | 4.0 | 2.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 3.0 | 1.0 | 6.0 | 9.0 | 1.0 | 9.0 | 6.0 | 6.0 | 6.0 | 4.0 | 5.0 | 8.0 | 4.0 | 9.0 | 8.0 | 8.0 | 7.0 | 6.0 | 7.0 |
| 3 | 8.0 | 4.0 | 2.0 | 2.0 | 1.0 | 2.0 | 2.0 | 1.0 | 3.0 | 1.0 | 9.0 | 3.0 | 5.0 | 1.0 | 4.0 | 4.0 | 5.0 | 7.0 | 4.0 | 8.0 | 7.0 | 6.0 | 7.0 | 2.0 | 6.0 | 1.0 | 6.0 | 5.0 | 5.0 | 6.0 | 7.0 | 10.0 | 4.0 |
| 4 | 8.0 | 5.0 | 5.0 | 1.0 | 7.0 | 3.0 | 3.0 | 9.0 | 10.0 | 3.0 | 5.0 | 9.0 | 4.0 | 3.0 | 6.0 | 8.0 | 1.0 | 9.0 | 3.0 | 3.0 | 10.0 | 10.0 | 2.0 | 9.0 | 3.0 | 1.0 | 6.0 | 10.0 | 8.0 | 7.0 | 5.0 | 4.0 | 9.0 |
| 5 | 9.0 | 8.0 | 9.0 | 2.0 | 3.0 | 2.0 | 3.0 | 9.0 | 10.0 | 1.0 | 4.0 | 9.0 | 2.0 | 2.0 | 9.0 | 9.0 | 5.0 | 5.0 | 5.0 | 2.0 | 10.0 | 9.0 | 7.0 | 3.0 | 5.0 | 10.0 | 8.0 | 5.0 | 2.0 | 1.0 | 10.0 | 6.0 | 1.0 |
| 6 | 8.0 | 7.0 | 8.0 | 2.0 | 3.0 | 3.0 | 4.0 | 7.0 | 10.0 | 5.0 | 1.0 | 6.0 | 4.0 | 5.0 | 2.0 | 5.0 | 2.0 | 5.0 | 1.0 | 5.0 | 4.0 | 6.0 | 1.0 | 10.0 | 8.0 | 2.0 | 10.0 | 8.0 | 8.0 | 6.0 | 5.0 | 8.0 | 9.0 |
| 7 | 10.0 | 6.0 | 4.0 | 1.0 | 9.0 | 9.0 | 7.0 | 1.0 | 8.0 | 4.0 | 9.0 | 2.0 | 1.0 | 9.0 | 1.0 | 10.0 | 8.0 | 10.0 | 5.0 | 10.0 | 4.0 | 8.0 | 3.0 | 6.0 | 8.0 | 10.0 | 3.0 | 9.0 | 5.0 | 1.0 | 1.0 | 10.0 | 2.0 |
| 8 | 6.0 | 2.0 | 2.0 | 3.0 | 10.0 | 10.0 | 10.0 | 8.0 | 2.0 | 8.0 | 6.0 | 9.0 | 5.0 | 5.0 | 7.0 | 8.0 | 1.0 | 5.0 | 9.0 | 4.0 | 3.0 | 7.0 | 8.0 | 7.0 | 1.0 | 6.0 | 7.0 | 5.0 | 8.0 | 1.0 | 1.0 | 8.0 | 5.0 |
| 9 | 9.0 | 9.0 | 1.0 | 1.0 | 3.0 | 1.0 | 5.0 | 4.0 | 8.0 | 4.0 | 8.0 | 5.0 | 9.0 | 10.0 | 2.0 | 10.0 | 1.0 | 6.0 | 10.0 | 9.0 | 9.0 | 2.0 | 1.0 | 3.0 | 1.0 | 2.0 | 1.0 | 4.0 | 1.0 | 4.0 | 9.0 | 10.0 | 3.0 |
| 10 | 1.0 | 10.0 | 8.0 | 9.0 | 5.0 | 4.0 | 1.0 | 9.0 | 6.0 | 8.0 | 9.0 | 5.0 | 2.0 | 10.0 | 2.0 | 6.0 | 10.0 | 6.0 | 2.0 | 7.0 | 3.0 | 4.0 | 1.0 | 7.0 | 9.0 | 3.0 | 7.0 | 1.0 | 10.0 | 7.0 | 5.0 | 5.0 | 3.0 |
| 11 | 5.0 | 5.0 | 8.0 | 3.0 | 9.0 | 9.0 | 6.0 | 2.0 | 9.0 | 5.0 | 5.0 | 7.0 | 7.0 | 3.0 | 2.0 | 7.0 | 10.0 | 9.0 | 4.0 | 6.0 | 10.0 | 9.0 | 3.0 | 4.0 | 4.0 | 10.0 | 5.0 | 4.0 | 10.0 | 5.0 | 3.0 | 7.0 | 9.0 |
| 12 | 1.0 | 5.0 | 8.0 | 5.0 | 4.0 | 2.0 | 4.0 | 1.0 | 5.0 | 9.0 | 2.0 | 7.0 | 5.0 | 8.0 | 9.0 | 2.0 | 1.0 | 10.0 | 3.0 | 3.0 | 4.0 | 5.0 | 1.0 | 8.0 | 2.0 | 9.0 | 6.0 | 1.0 | 2.0 | 6.0 | 1.0 | 3.0 | 1.0 |
| 13 | 8.0 | 6.0 | 1.0 | 1.0 | 3.0 | 2.0 | 5.0 | 9.0 | 5.0 | 10.0 | 10.0 | 3.0 | 8.0 | 8.0 | 10.0 | 10.0 | 2.0 | 9.0 | 2.0 | 3.0 | 3.0 | 1.0 | 2.0 | 7.0 | 7.0 | 2.0 | 7.0 | 4.0 | 3.0 | 5.0 | 9.0 | 2.0 | 7.0 |
| 14 | 8.0 | 4.0 | 3.0 | 4.0 | 6.0 | 9.0 | 2.0 | 1.0 | 7.0 | 2.0 | 2.0 | 2.0 | 9.0 | 10.0 | 4.0 | 2.0 | 4.0 | 7.0 | 3.0 | 5.0 | 8.0 | 10.0 | 7.0 | 10.0 | 1.0 | 6.0 | 7.0 | 2.0 | 5.0 | 4.0 | 1.0 | 7.0 | 2.0 |
| 15 | 8.0 | 9.0 | 1.0 | 4.0 | 8.0 | 9.0 | 5.0 | 10.0 | 8.0 | 10.0 | 6.0 | 7.0 | 2.0 | 10.0 | 2.0 | 4.0 | 6.0 | 3.0 | 9.0 | 4.0 | 5.0 | 1.0 | 9.0 | 4.0 | 10.0 | 1.0 | 3.0 | 1.0 | 1.0 | 5.0 | 3.0 | 3.0 | 6.0 |
| 16 | 2.0 | 6.0 | 6.0 | 5.0 | 1.0 | 5.0 | 2.0 | 8.0 | 1.0 | 1.0 | 10.0 | 10.0 | 1.0 | 2.0 | 4.0 | 6.0 | 2.0 | 1.0 | 1.0 | 4.0 | 10.0 | 6.0 | 5.0 | 6.0 | 3.0 | 4.0 | 9.0 | 5.0 | 2.0 | 2.0 | 3.0 | 7.0 | 4.0 |
| 17 | 3.0 | 1.0 | 9.0 | 7.0 | 9.0 | 5.0 | 5.0 | 10.0 | 5.0 | 6.0 | 6.0 | 9.0 | 10.0 | 9.0 | 7.0 | 3.0 | 1.0 | 7.0 | 3.0 | 9.0 | 6.0 | 3.0 | 4.0 | 7.0 | 4.0 | 9.0 | 7.0 | 3.0 | 8.0 | 6.0 | 1.0 | 1.0 | 4.0 |
| 18 | 5.0 | 7.0 | 1.0 | 4.0 | 3.0 | 5.0 | 1.0 | 5.0 | 9.0 | 10.0 | 2.0 | 4.0 | 3.0 | 2.0 | 3.0 | 9.0 | 1.0 | 3.0 | 7.0 | 5.0 | 7.0 | 10.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 9.0 | 10.0 | 2.0 | 8.0 | 7.0 | 4.0 |
| 19 | 2.0 | 10.0 | 9.0 | 8.0 | 3.0 | 2.0 | 5.0 | 10.0 | 4.0 | 9.0 | 7.0 | 6.0 | 3.0 | 3.0 | 5.0 | 4.0 | 4.0 | 9.0 | 5.0 | 5.0 | 2.0 | 10.0 | 10.0 | 10.0 | 4.0 | 1.0 | 6.0 | 10.0 | 1.0 | 5.0 | 3.0 | 8.0 | 6.0 |
| 20 | 6.0 | 10.0 | 6.0 | 7.0 | 10.0 | 10.0 | 4.0 | 4.0 | 3.0 | 9.0 | 3.0 | 10.0 | 4.0 | 3.0 | 8.0 | 5.0 | 10.0 | 6.0 | 7.0 | 2.0 | 4.0 | 3.0 | 5.0 | 8.0 | 8.0 | 6.0 | 7.0 | 8.0 | 5.0 | 5.0 | 8.0 | 10.0 | 5.0 |
| 21 | 8.0 | 1.0 | 6.0 | 6.0 | 10.0 | 9.0 | 6.0 | 8.0 | 7.0 | 2.0 | 4.0 | 9.0 | 5.0 | 1.0 | 10.0 | 1.0 | 6.0 | 3.0 | 10.0 | 10.0 | 3.0 | 3.0 | 1.0 | 8.0 | 7.0 | 10.0 | 2.0 | 1.0 | 3.0 | 6.0 | 5.0 | 3.0 | 6.0 |
| 22 | 2.0 | 4.0 | 6.0 | 7.0 | 2.0 | 7.0 | 1.0 | 3.0 | 8.0 | 1.0 | 1.0 | 3.0 | 1.0 | 2.0 | 7.0 | 9.0 | 5.0 | 4.0 | 1.0 | 10.0 | 5.0 | 1.0 | 1.0 | 3.0 | 8.0 | 1.0 | 5.0 | 5.0 | 2.0 | 1.0 | 6.0 | 8.0 | 8.0 |
| 23 | 8.0 | 9.0 | 4.0 | 2.0 | 9.0 | 3.0 | 10.0 | 6.0 | 7.0 | 3.0 | 7.0 | 4.0 | 8.0 | 7.0 | 10.0 | 4.0 | 6.0 | 7.0 | 10.0 | 10.0 | 8.0 | 8.0 | 3.0 | 6.0 | 9.0 | 7.0 | 10.0 | 5.0 | 6.0 | 5.0 | 4.0 | 10.0 | 5.0 |
| 24 | 2.0 | 3.0 | 5.0 | 6.0 | 3.0 | 5.0 | 8.0 | 8.0 | 1.0 | 1.0 | 9.0 | 4.0 | 2.0 | 7.0 | 1.0 | 10.0 | 3.0 | 4.0 | 9.0 | 4.0 | 8.0 | 7.0 | 8.0 | 9.0 | 1.0 | 6.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 2.0 | 8.0 |
| 25 | 5.0 | 4.0 | 8.0 | 1.0 | 1.0 | 10.0 | 2.0 | 10.0 | 6.0 | 2.0 | 3.0 | 10.0 | 9.0 | 2.0 | 6.0 | 1.0 | 4.0 | 9.0 | 6.0 | 1.0 | 6.0 | 10.0 | 1.0 | 7.0 | 6.0 | 5.0 | 6.0 | 7.0 | 2.0 | 1.0 | 7.0 | 9.0 | 2.0 |
| 26 | 1.0 | 2.0 | 4.0 | 6.0 | 6.0 | 8.0 | 10.0 | 3.0 | 7.0 | 1.0 | 7.0 | 5.0 | 6.0 | 7.0 | 7.0 | 3.0 | 9.0 | 7.0 | 2.0 | 6.0 | 7.0 | 2.0 | 5.0 | 10.0 | 2.0 | 6.0 | 8.0 | 7.0 | 5.0 | 6.0 | 5.0 | 1.0 | 1.0 |
| 27 | 3.0 | 4.0 | 9.0 | 5.0 | 10.0 | 5.0 | 8.0 | 9.0 | 5.0 | 4.0 | 1.0 | 4.0 | 1.0 | 4.0 | 2.0 | 1.0 | 5.0 | 3.0 | 9.0 | 10.0 | 8.0 | 1.0 | 5.0 | 5.0 | 5.0 | 7.0 | 7.0 | 3.0 | 4.0 | 5.0 | 7.0 | 1.0 | 5.0 |
| 28 | 7.0 | 6.0 | 8.0 | 5.0 | 8.0 | 2.0 | 8.0 | 5.0 | 8.0 | 1.0 | 10.0 | 10.0 | 2.0 | 3.0 | 5.0 | 1.0 | 2.0 | 8.0 | 10.0 | 1.0 | 5.0 | 3.0 | 2.0 | 6.0 | 2.0 | 2.0 | 5.0 | 4.0 | 10.0 | 4.0 | 7.0 | 10.0 | 4.0 |
| 29 | 7.0 | 8.0 | 8.0 | 6.0 | 7.0 | 1.0 | 6.0 | 1.0 | 1.0 | 4.0 | 7.0 | 5.0 | 6.0 | 5.0 | 4.0 | 5.0 | 2.0 | 6.0 | 2.0 | 5.0 | 5.0 | 6.0 | 1.0 | 5.0 | 1.0 | 1.0 | 6.0 | 5.0 | 4.0 | 5.0 | 9.0 | 6.0 | 2.0 |
| 30 | 8.0 | 8.0 | 7.0 | 7.0 | 5.0 | 10.0 | 5.0 | 1.0 | 1.0 | 9.0 | 5.0 | 3.0 | 1.0 | 9.0 | 1.0 | 3.0 | 3.0 | 1.0 | 8.0 | 3.0 | 8.0 | 5.0 | 6.0 | 4.0 | 6.0 | 7.0 | 5.0 | 7.0 | 7.0 | 9.0 | 4.0 | 7.0 | 4.0 |
| 31 | 8.0 | 2.0 | 6.0 | 10.0 | 4.0 | 6.0 | 8.0 | 10.0 | 8.0 | 10.0 | 5.0 | 7.0 | 3.0 | 2.0 | 7.0 | 3.0 | 7.0 | 1.0 | 7.0 | 8.0 | 10.0 | 3.0 | 8.0 | 10.0 | 2.0 | 9.0 | 1.0 | 1.0 | 10.0 | 6.0 | 7.0 | 9.0 | 3.0 |
| 32 | 2.0 | 1.0 | 7.0 | 4.0 | 9.0 | 1.0 | 9.0 | 2.0 | 5.0 | 3.0 | 3.0 | 9.0 | 1.0 | 7.0 | 2.0 | 6.0 | 4.0 | 4.0 | 4.0 | 6.0 | 5.0 | 6.0 | 8.0 | 5.0 | 8.0 | 2.0 | 1.0 | 5.0 | 4.0 | 2.0 | 4.0 | 3.0 | 9.0 |

If you want to hand me the route, just stick it in this simple JSON shape so I can read it easily:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the route: a straight sequence of node identifiers (the home node first, the office node last), with each consecutive pair connected by an actual one-way street. This JSON is just a sketch of the expected shape — not your final answer — so replace that empty array with the path when you're ready.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 6, 'var_index': 1}, {'from': 18, 'to': 12, 'var_index': 2}, {'from': 5, 'to': 19, 'var_index': 3}, {'from': 11, 'to': 19, 'var_index': 4}, {'from': 17, 'to': 19, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 0, 'to': 6, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 7, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 8, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 9, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 10, 'var_index': 15}, {'from': 5, 'to': 11, 'var_index': 16}, {'from': 6, 'to': 7, 'var_index': 17}, {'from': 6, 'to': 12, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 13, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 14, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 15, 'var_index': 24}, {'from': 10, 'to': 11, 'var_index': 25}, {'from': 10, 'to': 16, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 13, 'var_index': 28}, {'from': 13, 'to': 14, 'var_index': 29}, {'from': 14, 'to': 15, 'var_index': 30}, {'from': 15, 'to': 16, 'var_index': 31}, {'from': 16, 'to': 17, 'var_index': 32}], 'objective': {'constant': 0.0, 'linear': [1.0, 5.0, 4.0, 4.0, 1.0, 10.0, 4.0, 4.0, 3.0, 8.0, 9.0, 7.0, 5.0, 10.0, 5.0, 4.0, 2.0, 2.0, 3.0, 7.0, 9.0, 10.0, 4.0, 4.0, 6.0, 9.0, 10.0, 1.0, 7.0, 10.0, 10.0, 4.0, 8.0], 'quadratic': [[6.0, 4.0, 9.0, 8.0, 8.0, 9.0, 8.0, 10.0, 6.0, 9.0, 1.0, 5.0, 1.0, 8.0, 8.0, 8.0, 2.0, 3.0, 5.0, 2.0, 6.0, 8.0, 2.0, 8.0, 2.0, 5.0, 1.0, 3.0, 7.0, 7.0, 8.0, 8.0, 2.0], [4.0, 2.0, 1.0, 4.0, 5.0, 8.0, 7.0, 6.0, 2.0, 9.0, 10.0, 5.0, 5.0, 6.0, 4.0, 9.0, 6.0, 1.0, 7.0, 10.0, 10.0, 1.0, 4.0, 9.0, 3.0, 4.0, 2.0, 4.0, 6.0, 8.0, 8.0, 2.0, 1.0], [9.0, 1.0, 3.0, 2.0, 5.0, 9.0, 8.0, 4.0, 2.0, 1.0, 8.0, 8.0, 8.0, 1.0, 3.0, 1.0, 6.0, 9.0, 1.0, 9.0, 6.0, 6.0, 6.0, 4.0, 5.0, 8.0, 4.0, 9.0, 8.0, 8.0, 7.0, 6.0, 7.0], [8.0, 4.0, 2.0, 2.0, 1.0, 2.0, 2.0, 1.0, 3.0, 1.0, 9.0, 3.0, 5.0, 1.0, 4.0, 4.0, 5.0, 7.0, 4.0, 8.0, 7.0, 6.0, 7.0, 2.0, 6.0, 1.0, 6.0, 5.0, 5.0, 6.0, 7.0, 10.0, 4.0], [8.0, 5.0, 5.0, 1.0, 7.0, 3.0, 3.0, 9.0, 10.0, 3.0, 5.0, 9.0, 4.0, 3.0, 6.0, 8.0, 1.0, 9.0, 3.0, 3.0, 10.0, 10.0, 2.0, 9.0, 3.0, 1.0, 6.0, 10.0, 8.0, 7.0, 5.0, 4.0, 9.0], [9.0, 8.0, 9.0, 2.0, 3.0, 2.0, 3.0, 9.0, 10.0, 1.0, 4.0, 9.0, 2.0, 2.0, 9.0, 9.0, 5.0, 5.0, 5.0, 2.0, 10.0, 9.0, 7.0, 3.0, 5.0, 10.0, 8.0, 5.0, 2.0, 1.0, 10.0, 6.0, 1.0], [8.0, 7.0, 8.0, 2.0, 3.0, 3.0, 4.0, 7.0, 10.0, 5.0, 1.0, 6.0, 4.0, 5.0, 2.0, 5.0, 2.0, 5.0, 1.0, 5.0, 4.0, 6.0, 1.0, 10.0, 8.0, 2.0, 10.0, 8.0, 8.0, 6.0, 5.0, 8.0, 9.0], [10.0, 6.0, 4.0, 1.0, 9.0, 9.0, 7.0, 1.0, 8.0, 4.0, 9.0, 2.0, 1.0, 9.0, 1.0, 10.0, 8.0, 10.0, 5.0, 10.0, 4.0, 8.0, 3.0, 6.0, 8.0, 10.0, 3.0, 9.0, 5.0, 1.0, 1.0, 10.0, 2.0], [6.0, 2.0, 2.0, 3.0, 10.0, 10.0, 10.0, 8.0, 2.0, 8.0, 6.0, 9.0, 5.0, 5.0, 7.0, 8.0, 1.0, 5.0, 9.0, 4.0, 3.0, 7.0, 8.0, 7.0, 1.0, 6.0, 7.0, 5.0, 8.0, 1.0, 1.0, 8.0, 5.0], [9.0, 9.0, 1.0, 1.0, 3.0, 1.0, 5.0, 4.0, 8.0, 4.0, 8.0, 5.0, 9.0, 10.0, 2.0, 10.0, 1.0, 6.0, 10.0, 9.0, 9.0, 2.0, 1.0, 3.0, 1.0, 2.0, 1.0, 4.0, 1.0, 4.0, 9.0, 10.0, 3.0], [1.0, 10.0, 8.0, 9.0, 5.0, 4.0, 1.0, 9.0, 6.0, 8.0, 9.0, 5.0, 2.0, 10.0, 2.0, 6.0, 10.0, 6.0, 2.0, 7.0, 3.0, 4.0, 1.0, 7.0, 9.0, 3.0, 7.0, 1.0, 10.0, 7.0, 5.0, 5.0, 3.0], [5.0, 5.0, 8.0, 3.0, 9.0, 9.0, 6.0, 2.0, 9.0, 5.0, 5.0, 7.0, 7.0, 3.0, 2.0, 7.0, 10.0, 9.0, 4.0, 6.0, 10.0, 9.0, 3.0, 4.0, 4.0, 10.0, 5.0, 4.0, 10.0, 5.0, 3.0, 7.0, 9.0], [1.0, 5.0, 8.0, 5.0, 4.0, 2.0, 4.0, 1.0, 5.0, 9.0, 2.0, 7.0, 5.0, 8.0, 9.0, 2.0, 1.0, 10.0, 3.0, 3.0, 4.0, 5.0, 1.0, 8.0, 2.0, 9.0, 6.0, 1.0, 2.0, 6.0, 1.0, 3.0, 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6.0}, {'var_i': 28, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 27, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 32, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 26, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 29, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 31, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 32, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 23, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 26, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 26, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 32, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 19, 'to': 1, 'var_index': 0}, {'from': 19, 'to': 7, 'var_index': 1}, {'from': 19, 'to': 13, 'var_index': 2}, {'from': 6, 'to': 20, 'var_index': 3}, {'from': 12, 'to': 20, 'var_index': 4}, {'from': 18, 'to': 20, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 8, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 9, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 10, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 11, 'var_index': 15}, {'from': 6, 'to': 12, 'var_index': 16}, {'from': 7, 'to': 8, 'var_index': 17}, {'from': 7, 'to': 13, 'var_index': 18}, {'from': 8, 'to': 9, 'var_index': 19}, {'from': 8, 'to': 14, 'var_index': 20}, {'from': 9, 'to': 10, 'var_index': 21}, {'from': 9, 'to': 15, 'var_index': 22}, {'from': 10, 'to': 11, 'var_index': 23}, {'from': 10, 'to': 16, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 11, 'to': 17, 'var_index': 26}, {'from': 12, 'to': 18, 'var_index': 27}, {'from': 13, 'to': 14, 'var_index': 28}, {'from': 14, 'to': 15, 'var_index': 29}, {'from': 15, 'to': 16, 'var_index': 30}, {'from': 16, 'to': 17, 'var_index': 31}, {'from': 17, 'to': 18, 'var_index': 32}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20}}","[19, 1, 2, 3, 4, 5, 6, 20]",21,csv,1
QSPP,QSPP,"Someone arranged the day so a driver has to pick one continuous path from the warehouse to a customer, obeying one-way streets. Every hop along the road schedule has a base fuel cost, and there are extra little penalties: some that apply just for taking a particular hop, and others that only come into play when two specific hops are both included (both directions of such a pair can contribute their own penalty if both hops are used). The smartest single-route choice is the one with the lowest total bill — get that bill by summing each hop’s fuel cost and then adding any applicable single-hop and pairwise penalties. The trip must be a single, legal one-way sequence from the warehouse to the customer, listed as the intersections encountered; the concrete map and cost figures are shown below.

{
  ""total_intersections"": 22,
  ""total_one_way_segments"": 21,
  ""intersection_list"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19,
    20,
    21
  ],
  ""warehouse_intersection"": 20,
  ""customer_intersection"": 21,
  ""edges"": [
    {
      ""segment_from"": 20,
      ""segment_to"": 0,
      ""segment_id"": 0
    },
    {
      ""segment_from"": 19,
      ""segment_to"": 21,
      ""segment_id"": 1
    },
    {
      ""segment_from"": 0,
      ""segment_to"": 1,
      ""segment_id"": 2
    },
    {
      ""segment_from"": 1,
      ""segment_to"": 2,
      ""segment_id"": 3
    },
    {
      ""segment_from"": 2,
      ""segment_to"": 3,
      ""segment_id"": 4
    },
    {
      ""segment_from"": 3,
      ""segment_to"": 4,
      ""segment_id"": 5
    },
    {
      ""segment_from"": 4,
      ""segment_to"": 5,
      ""segment_id"": 6
    },
    {
      ""segment_from"": 5,
      ""segment_to"": 6,
      ""segment_id"": 7
    },
    {
      ""segment_from"": 6,
      ""segment_to"": 7,
      ""segment_id"": 8
    },
    {
      ""segment_from"": 7,
      ""segment_to"": 8,
      ""segment_id"": 9
    },
    {
      ""segment_from"": 8,
      ""segment_to"": 9,
      ""segment_id"": 10
    },
    {
      ""segment_from"": 9,
      ""segment_to"": 10,
      ""segment_id"": 11
    },
    {
      ""segment_from"": 10,
      ""segment_to"": 11,
      ""segment_id"": 12
    },
    {
      ""segment_from"": 11,
      ""segment_to"": 12,
      ""segment_id"": 13
    },
    {
      ""segment_from"": 12,
      ""segment_to"": 13,
      ""segment_id"": 14
    },
    {
      ""segment_from"": 13,
      ""segment_to"": 14,
      ""segment_id"": 15
    },
    {
      ""segment_from"": 14,
      ""segment_to"": 15,
      ""segment_id"": 16
    },
    {
      ""segment_from"": 15,
      ""segment_to"": 16,
      ""segment_id"": 17
    },
    {
      ""segment_from"": 16,
      ""segment_to"": 17,
      ""segment_id"": 18
    },
    {
      ""segment_from"": 17,
      ""segment_to"": 18,
      ""segment_id"": 19
    },
    {
      ""segment_from"": 18,
      ""segment_to"": 19,
      ""segment_id"": 20
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""fuel_cost"": 8.0
    },
    {
      ""segment_id"": 1,
      ""fuel_cost"": 4.0
    },
    {
      ""segment_id"": 2,
      ""fuel_cost"": 7.0
    },
    {
      ""segment_id"": 3,
      ""fuel_cost"": 2.0
    },
    {
      ""segment_id"": 4,
      ""fuel_cost"": 8.0
    },
    {
      ""segment_id"": 5,
      ""fuel_cost"": 4.0
    },
    {
      ""segment_id"": 6,
      ""fuel_cost"": 1.0
    },
    {
      ""segment_id"": 7,
      ""fuel_cost"": 5.0
    },
    {
      ""segment_id"": 8,
      ""fuel_cost"": 3.0
    },
    {
      ""segment_id"": 9,
      ""fuel_cost"": 2.0
    },
    {
      ""segment_id"": 10,
      ""fuel_cost"": 1.0
    },
    {
      ""segment_id"": 11,
      ""fuel_cost"": 1.0
    },
    {
      ""segment_id"": 12,
      ""fuel_cost"": 7.0
    },
    {
      ""segment_id"": 13,
      ""fuel_cost"": 6.0
    },
    {
      ""segment_id"": 14,
      ""fuel_cost"": 7.0
    },
    {
      ""segment_id"": 15,
      ""fuel_cost"": 6.0
    },
    {
      ""segment_id"": 16,
      ""fuel_cost"": 2.0
    },
    {
      ""segment_id"": 17,
      ""fuel_cost"": 1.0
    },
    {
      ""segment_id"": 18,
      ""fuel_cost"": 1.0
    },
    {
      ""segment_id"": 19,
      ""fuel_cost"": 2.0
    },
    {
      ""segment_id"": 20,
      ""fuel_cost"": 9.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 10.0 | 10.0 | 5.0 | 6.0 | 8.0 | 9.0 | 3.0 | 7.0 | 7.0 | 4.0 | 9.0 | 6.0 | 1.0 | 4.0 | 7.0 | 9.0 | 10.0 | 6.0 | 2.0 | 10.0 |
| 1 | 10.0 | 3.0 | 4.0 | 9.0 | 5.0 | 8.0 | 4.0 | 9.0 | 5.0 | 10.0 | 2.0 | 5.0 | 5.0 | 6.0 | 1.0 | 4.0 | 3.0 | 2.0 | 10.0 | 3.0 | 2.0 |
| 2 | 10.0 | 4.0 | 10.0 | 3.0 | 10.0 | 5.0 | 8.0 | 3.0 | 5.0 | 7.0 | 9.0 | 6.0 | 7.0 | 5.0 | 7.0 | 5.0 | 10.0 | 3.0 | 10.0 | 7.0 | 8.0 |
| 3 | 5.0 | 9.0 | 3.0 | 7.0 | 3.0 | 4.0 | 5.0 | 4.0 | 4.0 | 8.0 | 2.0 | 2.0 | 4.0 | 1.0 | 5.0 | 3.0 | 3.0 | 10.0 | 10.0 | 8.0 | 1.0 |
| 4 | 6.0 | 5.0 | 10.0 | 3.0 | 7.0 | 6.0 | 1.0 | 3.0 | 7.0 | 5.0 | 9.0 | 6.0 | 8.0 | 2.0 | 2.0 | 8.0 | 3.0 | 7.0 | 6.0 | 3.0 | 10.0 |
| 5 | 8.0 | 8.0 | 5.0 | 4.0 | 6.0 | 2.0 | 3.0 | 9.0 | 5.0 | 8.0 | 7.0 | 1.0 | 6.0 | 6.0 | 4.0 | 2.0 | 6.0 | 8.0 | 2.0 | 2.0 | 5.0 |
| 6 | 9.0 | 4.0 | 8.0 | 5.0 | 1.0 | 3.0 | 9.0 | 6.0 | 9.0 | 5.0 | 6.0 | 7.0 | 8.0 | 7.0 | 8.0 | 2.0 | 7.0 | 8.0 | 9.0 | 4.0 | 6.0 |
| 7 | 3.0 | 9.0 | 3.0 | 4.0 | 3.0 | 9.0 | 6.0 | 5.0 | 5.0 | 5.0 | 7.0 | 5.0 | 4.0 | 8.0 | 3.0 | 7.0 | 2.0 | 8.0 | 1.0 | 6.0 | 10.0 |
| 8 | 7.0 | 5.0 | 5.0 | 4.0 | 7.0 | 5.0 | 9.0 | 5.0 | 3.0 | 5.0 | 6.0 | 6.0 | 1.0 | 1.0 | 5.0 | 10.0 | 2.0 | 2.0 | 7.0 | 2.0 | 3.0 |
| 9 | 7.0 | 10.0 | 7.0 | 8.0 | 5.0 | 8.0 | 5.0 | 5.0 | 5.0 | 5.0 | 7.0 | 7.0 | 7.0 | 1.0 | 8.0 | 9.0 | 6.0 | 2.0 | 5.0 | 5.0 | 5.0 |
| 10 | 4.0 | 2.0 | 9.0 | 2.0 | 9.0 | 7.0 | 6.0 | 7.0 | 6.0 | 7.0 | 3.0 | 7.0 | 2.0 | 5.0 | 8.0 | 10.0 | 2.0 | 3.0 | 8.0 | 10.0 | 4.0 |
| 11 | 9.0 | 5.0 | 6.0 | 2.0 | 6.0 | 1.0 | 7.0 | 5.0 | 6.0 | 7.0 | 7.0 | 1.0 | 9.0 | 5.0 | 3.0 | 7.0 | 10.0 | 4.0 | 2.0 | 4.0 | 6.0 |
| 12 | 6.0 | 5.0 | 7.0 | 4.0 | 8.0 | 6.0 | 8.0 | 4.0 | 1.0 | 7.0 | 2.0 | 9.0 | 1.0 | 7.0 | 7.0 | 3.0 | 7.0 | 5.0 | 10.0 | 6.0 | 1.0 |
| 13 | 1.0 | 6.0 | 5.0 | 1.0 | 2.0 | 6.0 | 7.0 | 8.0 | 1.0 | 1.0 | 5.0 | 5.0 | 7.0 | 4.0 | 6.0 | 3.0 | 7.0 | 2.0 | 6.0 | 1.0 | 4.0 |
| 14 | 4.0 | 1.0 | 7.0 | 5.0 | 2.0 | 4.0 | 8.0 | 3.0 | 5.0 | 8.0 | 8.0 | 3.0 | 7.0 | 6.0 | 5.0 | 9.0 | 4.0 | 9.0 | 5.0 | 4.0 | 3.0 |
| 15 | 7.0 | 4.0 | 5.0 | 3.0 | 8.0 | 2.0 | 2.0 | 7.0 | 10.0 | 9.0 | 10.0 | 7.0 | 3.0 | 3.0 | 9.0 | 3.0 | 2.0 | 3.0 | 10.0 | 7.0 | 3.0 |
| 16 | 9.0 | 3.0 | 10.0 | 3.0 | 3.0 | 6.0 | 7.0 | 2.0 | 2.0 | 6.0 | 2.0 | 10.0 | 7.0 | 7.0 | 4.0 | 2.0 | 9.0 | 7.0 | 2.0 | 2.0 | 3.0 |
| 17 | 10.0 | 2.0 | 3.0 | 10.0 | 7.0 | 8.0 | 8.0 | 8.0 | 2.0 | 2.0 | 3.0 | 4.0 | 5.0 | 2.0 | 9.0 | 3.0 | 7.0 | 4.0 | 2.0 | 9.0 | 1.0 |
| 18 | 6.0 | 10.0 | 10.0 | 10.0 | 6.0 | 2.0 | 9.0 | 1.0 | 7.0 | 5.0 | 8.0 | 2.0 | 10.0 | 6.0 | 5.0 | 10.0 | 2.0 | 2.0 | 5.0 | 6.0 | 5.0 |
| 19 | 2.0 | 3.0 | 7.0 | 8.0 | 3.0 | 2.0 | 4.0 | 6.0 | 2.0 | 5.0 | 10.0 | 4.0 | 6.0 | 1.0 | 4.0 | 7.0 | 2.0 | 9.0 | 6.0 | 6.0 | 9.0 |
| 20 | 10.0 | 2.0 | 8.0 | 1.0 | 10.0 | 5.0 | 6.0 | 10.0 | 3.0 | 5.0 | 4.0 | 6.0 | 1.0 | 4.0 | 3.0 | 3.0 | 3.0 | 1.0 | 5.0 | 9.0 | 1.0 |

Also, when you send back the final chosen route, please put it in a tiny JSON snippet so it's easy to parse — just this shape:

{
  ""solution"": []
}

Here ""solution"" is meant to hold the ordered list of intersections (node names) you travel through, starting at the warehouse and ending at the customer. Keep it simple and human-friendly: just the nodes in order, nothing else. This JSON is just the sketch of the shape I expect, not the actual route.

Please be sure to use the exact identifiers given in the instance input — don't rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 21, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}], 'objective': {'constant': 0.0, 'linear': [8.0, 4.0, 7.0, 2.0, 8.0, 4.0, 1.0, 5.0, 3.0, 2.0, 1.0, 1.0, 7.0, 6.0, 7.0, 6.0, 2.0, 1.0, 1.0, 2.0, 9.0], 'quadratic': [[3.0, 10.0, 10.0, 5.0, 6.0, 8.0, 9.0, 3.0, 7.0, 7.0, 4.0, 9.0, 6.0, 1.0, 4.0, 7.0, 9.0, 10.0, 6.0, 2.0, 10.0], [10.0, 3.0, 4.0, 9.0, 5.0, 8.0, 4.0, 9.0, 5.0, 10.0, 2.0, 5.0, 5.0, 6.0, 1.0, 4.0, 3.0, 2.0, 10.0, 3.0, 2.0], [10.0, 4.0, 10.0, 3.0, 10.0, 5.0, 8.0, 3.0, 5.0, 7.0, 9.0, 6.0, 7.0, 5.0, 7.0, 5.0, 10.0, 3.0, 10.0, 7.0, 8.0], [5.0, 9.0, 3.0, 7.0, 3.0, 4.0, 5.0, 4.0, 4.0, 8.0, 2.0, 2.0, 4.0, 1.0, 5.0, 3.0, 3.0, 10.0, 10.0, 8.0, 1.0], [6.0, 5.0, 10.0, 3.0, 7.0, 6.0, 1.0, 3.0, 7.0, 5.0, 9.0, 6.0, 8.0, 2.0, 2.0, 8.0, 3.0, 7.0, 6.0, 3.0, 10.0], [8.0, 8.0, 5.0, 4.0, 6.0, 2.0, 3.0, 9.0, 5.0, 8.0, 7.0, 1.0, 6.0, 6.0, 4.0, 2.0, 6.0, 8.0, 2.0, 2.0, 5.0], [9.0, 4.0, 8.0, 5.0, 1.0, 3.0, 9.0, 6.0, 9.0, 5.0, 6.0, 7.0, 8.0, 7.0, 8.0, 2.0, 7.0, 8.0, 9.0, 4.0, 6.0], [3.0, 9.0, 3.0, 4.0, 3.0, 9.0, 6.0, 5.0, 5.0, 5.0, 7.0, 5.0, 4.0, 8.0, 3.0, 7.0, 2.0, 8.0, 1.0, 6.0, 10.0], [7.0, 5.0, 5.0, 4.0, 7.0, 5.0, 9.0, 5.0, 3.0, 5.0, 6.0, 6.0, 1.0, 1.0, 5.0, 10.0, 2.0, 2.0, 7.0, 2.0, 3.0], [7.0, 10.0, 7.0, 8.0, 5.0, 8.0, 5.0, 5.0, 5.0, 5.0, 7.0, 7.0, 7.0, 1.0, 8.0, 9.0, 6.0, 2.0, 5.0, 5.0, 5.0], [4.0, 2.0, 9.0, 2.0, 9.0, 7.0, 6.0, 7.0, 6.0, 7.0, 3.0, 7.0, 2.0, 5.0, 8.0, 10.0, 2.0, 3.0, 8.0, 10.0, 4.0], [9.0, 5.0, 6.0, 2.0, 6.0, 1.0, 7.0, 5.0, 6.0, 7.0, 7.0, 1.0, 9.0, 5.0, 3.0, 7.0, 10.0, 4.0, 2.0, 4.0, 6.0], [6.0, 5.0, 7.0, 4.0, 8.0, 6.0, 8.0, 4.0, 1.0, 7.0, 2.0, 9.0, 1.0, 7.0, 7.0, 3.0, 7.0, 5.0, 10.0, 6.0, 1.0], [1.0, 6.0, 5.0, 1.0, 2.0, 6.0, 7.0, 8.0, 1.0, 1.0, 5.0, 5.0, 7.0, 4.0, 6.0, 3.0, 7.0, 2.0, 6.0, 1.0, 4.0], [4.0, 1.0, 7.0, 5.0, 2.0, 4.0, 8.0, 3.0, 5.0, 8.0, 8.0, 3.0, 7.0, 6.0, 5.0, 9.0, 4.0, 9.0, 5.0, 4.0, 3.0], [7.0, 4.0, 5.0, 3.0, 8.0, 2.0, 2.0, 7.0, 10.0, 9.0, 10.0, 7.0, 3.0, 3.0, 9.0, 3.0, 2.0, 3.0, 10.0, 7.0, 3.0], [9.0, 3.0, 10.0, 3.0, 3.0, 6.0, 7.0, 2.0, 2.0, 6.0, 2.0, 10.0, 7.0, 7.0, 4.0, 2.0, 9.0, 7.0, 2.0, 2.0, 3.0], [10.0, 2.0, 3.0, 10.0, 7.0, 8.0, 8.0, 8.0, 2.0, 2.0, 3.0, 4.0, 5.0, 2.0, 9.0, 3.0, 7.0, 4.0, 2.0, 9.0, 1.0], [6.0, 10.0, 10.0, 10.0, 6.0, 2.0, 9.0, 1.0, 7.0, 5.0, 8.0, 2.0, 10.0, 6.0, 5.0, 10.0, 2.0, 2.0, 5.0, 6.0, 5.0], [2.0, 3.0, 7.0, 8.0, 3.0, 2.0, 4.0, 6.0, 2.0, 5.0, 10.0, 4.0, 6.0, 1.0, 4.0, 7.0, 2.0, 9.0, 6.0, 6.0, 9.0], [10.0, 2.0, 8.0, 1.0, 10.0, 5.0, 6.0, 10.0, 3.0, 5.0, 4.0, 6.0, 1.0, 4.0, 3.0, 3.0, 3.0, 1.0, 5.0, 9.0, 1.0]]}, 'source': 20, 'target': 21}","[20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]",2481.0,"{'problem_type': 'QSPP', 'num_nodes': 22, 'num_edges': 21, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'source': 20, 'target': 21, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 7.0}, {'var_index': 3, 'linear_cost': 2.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 1.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 3.0}, {'var_index': 9, 'linear_cost': 2.0}, {'var_index': 10, 'linear_cost': 1.0}, {'var_index': 11, 'linear_cost': 1.0}, {'var_index': 12, 'linear_cost': 7.0}, {'var_index': 13, 'linear_cost': 6.0}, {'var_index': 14, 'linear_cost': 7.0}, {'var_index': 15, 'linear_cost': 6.0}, {'var_index': 16, 'linear_cost': 2.0}, {'var_index': 17, 'linear_cost': 1.0}, {'var_index': 18, 'linear_cost': 1.0}, {'var_index': 19, 'linear_cost': 2.0}, {'var_index': 20, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 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'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 21, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21}}","[20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]",22,json,0
QSPP,QSPP,"Many people think routing is just finding a path, but in this setup each route has a little billing story: pick one one-way path from the entry location to the exit location, and remember that every link charges its own base cost. On top of that, whenever two links are both used there can be extra charges tied to that specific ordered pair — the order matters — and some links even add an extra charge just for being included. The score for a route is built by adding every link’s base cost and then adding every ordered-pair penalty for links on the route; the route with the lowest overall score is the one you want. The result must be a single valid directed path from start to finish and should be reported only as the sequence of locations (no link IDs or cost numbers). The detailed instance and costs come below.

{
  ""total_locations"": 20,
  ""total_links"": 19,
  ""location_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19
  ],
  ""ingress_node"": 18,
  ""egress_node"": 19,
  ""edges"": [
    {
      ""link_tail_node"": 18,
      ""link_head_node"": 0,
      ""link_identifier"": 0
    },
    {
      ""link_tail_node"": 17,
      ""link_head_node"": 19,
      ""link_identifier"": 1
    },
    {
      ""link_tail_node"": 0,
      ""link_head_node"": 1,
      ""link_identifier"": 2
    },
    {
      ""link_tail_node"": 1,
      ""link_head_node"": 2,
      ""link_identifier"": 3
    },
    {
      ""link_tail_node"": 2,
      ""link_head_node"": 3,
      ""link_identifier"": 4
    },
    {
      ""link_tail_node"": 3,
      ""link_head_node"": 4,
      ""link_identifier"": 5
    },
    {
      ""link_tail_node"": 4,
      ""link_head_node"": 5,
      ""link_identifier"": 6
    },
    {
      ""link_tail_node"": 5,
      ""link_head_node"": 6,
      ""link_identifier"": 7
    },
    {
      ""link_tail_node"": 6,
      ""link_head_node"": 7,
      ""link_identifier"": 8
    },
    {
      ""link_tail_node"": 7,
      ""link_head_node"": 8,
      ""link_identifier"": 9
    },
    {
      ""link_tail_node"": 8,
      ""link_head_node"": 9,
      ""link_identifier"": 10
    },
    {
      ""link_tail_node"": 9,
      ""link_head_node"": 10,
      ""link_identifier"": 11
    },
    {
      ""link_tail_node"": 10,
      ""link_head_node"": 11,
      ""link_identifier"": 12
    },
    {
      ""link_tail_node"": 11,
      ""link_head_node"": 12,
      ""link_identifier"": 13
    },
    {
      ""link_tail_node"": 12,
      ""link_head_node"": 13,
      ""link_identifier"": 14
    },
    {
      ""link_tail_node"": 13,
      ""link_head_node"": 14,
      ""link_identifier"": 15
    },
    {
      ""link_tail_node"": 14,
      ""link_head_node"": 15,
      ""link_identifier"": 16
    },
    {
      ""link_tail_node"": 15,
      ""link_head_node"": 16,
      ""link_identifier"": 17
    },
    {
      ""link_tail_node"": 16,
      ""link_head_node"": 17,
      ""link_identifier"": 18
    }
  ],
  ""linear_costs"": [
    {
      ""link_identifier"": 0,
      ""link_base_cost"": 6.0
    },
    {
      ""link_identifier"": 1,
      ""link_base_cost"": 1.0
    },
    {
      ""link_identifier"": 2,
      ""link_base_cost"": 8.0
    },
    {
      ""link_identifier"": 3,
      ""link_base_cost"": 2.0
    },
    {
      ""link_identifier"": 4,
      ""link_base_cost"": 6.0
    },
    {
      ""link_identifier"": 5,
      ""link_base_cost"": 4.0
    },
    {
      ""link_identifier"": 6,
      ""link_base_cost"": 10.0
    },
    {
      ""link_identifier"": 7,
      ""link_base_cost"": 9.0
    },
    {
      ""link_identifier"": 8,
      ""link_base_cost"": 9.0
    },
    {
      ""link_identifier"": 9,
      ""link_base_cost"": 5.0
    },
    {
      ""link_identifier"": 10,
      ""link_base_cost"": 1.0
    },
    {
      ""link_identifier"": 11,
      ""link_base_cost"": 1.0
    },
    {
      ""link_identifier"": 12,
      ""link_base_cost"": 6.0
    },
    {
      ""link_identifier"": 13,
      ""link_base_cost"": 5.0
    },
    {
      ""link_identifier"": 14,
      ""link_base_cost"": 5.0
    },
    {
      ""link_identifier"": 15,
      ""link_base_cost"": 10.0
    },
    {
      ""link_identifier"": 16,
      ""link_base_cost"": 2.0
    },
    {
      ""link_identifier"": 17,
      ""link_base_cost"": 4.0
    },
    {
      ""link_identifier"": 18,
      ""link_base_cost"": 10.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (ordered_link_i_id, ordered_link_j_id). If two link_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| ordered_link_i_id\ordered_link_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 7.0 | 1.0 | 7.0 | 3.0 | 1.0 | 7.0 | 8.0 | 7.0 | 3.0 | 8.0 | 10.0 | 1.0 | 2.0 | 10.0 | 3.0 | 10.0 | 6.0 | 10.0 |
| 1 | 7.0 | 8.0 | 9.0 | 10.0 | 8.0 | 9.0 | 10.0 | 8.0 | 4.0 | 7.0 | 2.0 | 6.0 | 4.0 | 6.0 | 9.0 | 6.0 | 6.0 | 9.0 | 5.0 |
| 2 | 1.0 | 9.0 | 7.0 | 1.0 | 1.0 | 9.0 | 1.0 | 9.0 | 1.0 | 3.0 | 10.0 | 2.0 | 1.0 | 1.0 | 9.0 | 7.0 | 5.0 | 7.0 | 1.0 |
| 3 | 7.0 | 10.0 | 1.0 | 2.0 | 10.0 | 9.0 | 1.0 | 3.0 | 5.0 | 9.0 | 4.0 | 5.0 | 8.0 | 1.0 | 9.0 | 2.0 | 3.0 | 2.0 | 9.0 |
| 4 | 3.0 | 8.0 | 1.0 | 10.0 | 1.0 | 10.0 | 8.0 | 6.0 | 2.0 | 3.0 | 2.0 | 3.0 | 9.0 | 10.0 | 7.0 | 8.0 | 1.0 | 4.0 | 7.0 |
| 5 | 1.0 | 9.0 | 9.0 | 9.0 | 10.0 | 4.0 | 7.0 | 10.0 | 3.0 | 2.0 | 5.0 | 4.0 | 8.0 | 8.0 | 5.0 | 6.0 | 3.0 | 5.0 | 10.0 |
| 6 | 7.0 | 10.0 | 1.0 | 1.0 | 8.0 | 7.0 | 3.0 | 9.0 | 5.0 | 1.0 | 10.0 | 1.0 | 8.0 | 9.0 | 1.0 | 6.0 | 5.0 | 2.0 | 4.0 |
| 7 | 8.0 | 8.0 | 9.0 | 3.0 | 6.0 | 10.0 | 9.0 | 8.0 | 4.0 | 4.0 | 4.0 | 7.0 | 5.0 | 6.0 | 10.0 | 3.0 | 5.0 | 1.0 | 8.0 |
| 8 | 7.0 | 4.0 | 1.0 | 5.0 | 2.0 | 3.0 | 5.0 | 4.0 | 4.0 | 8.0 | 5.0 | 6.0 | 6.0 | 5.0 | 3.0 | 2.0 | 2.0 | 2.0 | 10.0 |
| 9 | 3.0 | 7.0 | 3.0 | 9.0 | 3.0 | 2.0 | 1.0 | 4.0 | 8.0 | 7.0 | 8.0 | 8.0 | 1.0 | 6.0 | 4.0 | 10.0 | 5.0 | 10.0 | 5.0 |
| 10 | 8.0 | 2.0 | 10.0 | 4.0 | 2.0 | 5.0 | 10.0 | 4.0 | 5.0 | 8.0 | 4.0 | 10.0 | 3.0 | 7.0 | 5.0 | 8.0 | 2.0 | 1.0 | 1.0 |
| 11 | 10.0 | 6.0 | 2.0 | 5.0 | 3.0 | 4.0 | 1.0 | 7.0 | 6.0 | 8.0 | 10.0 | 6.0 | 5.0 | 10.0 | 2.0 | 10.0 | 5.0 | 7.0 | 5.0 |
| 12 | 1.0 | 4.0 | 1.0 | 8.0 | 9.0 | 8.0 | 8.0 | 5.0 | 6.0 | 1.0 | 3.0 | 5.0 | 4.0 | 6.0 | 2.0 | 7.0 | 6.0 | 7.0 | 5.0 |
| 13 | 2.0 | 6.0 | 1.0 | 1.0 | 10.0 | 8.0 | 9.0 | 6.0 | 5.0 | 6.0 | 7.0 | 10.0 | 6.0 | 8.0 | 8.0 | 7.0 | 4.0 | 7.0 | 6.0 |
| 14 | 10.0 | 9.0 | 9.0 | 9.0 | 7.0 | 5.0 | 1.0 | 10.0 | 3.0 | 4.0 | 5.0 | 2.0 | 2.0 | 8.0 | 1.0 | 9.0 | 4.0 | 7.0 | 6.0 |
| 15 | 3.0 | 6.0 | 7.0 | 2.0 | 8.0 | 6.0 | 6.0 | 3.0 | 2.0 | 10.0 | 8.0 | 10.0 | 7.0 | 7.0 | 9.0 | 1.0 | 8.0 | 2.0 | 10.0 |
| 16 | 10.0 | 6.0 | 5.0 | 3.0 | 1.0 | 3.0 | 5.0 | 5.0 | 2.0 | 5.0 | 2.0 | 5.0 | 6.0 | 4.0 | 4.0 | 8.0 | 9.0 | 7.0 | 8.0 |
| 17 | 6.0 | 9.0 | 7.0 | 2.0 | 4.0 | 5.0 | 2.0 | 1.0 | 2.0 | 10.0 | 1.0 | 7.0 | 7.0 | 7.0 | 7.0 | 2.0 | 7.0 | 9.0 | 7.0 |
| 18 | 10.0 | 5.0 | 1.0 | 9.0 | 7.0 | 10.0 | 4.0 | 8.0 | 10.0 | 5.0 | 1.0 | 5.0 | 5.0 | 6.0 | 6.0 | 10.0 | 8.0 | 7.0 | 3.0 |

Also, to keep things tidy, please return your chosen path using this simple JSON layout:

{
  ""solution"": []
}

Think of ""solution"" as the little form field where you drop the ordered list of locations that make up your path — start node first, end node last, each entry a node label only (no link IDs, no costs). This JSON is just a sketch of the shape I expect, not the actual answer itself.

Please use the identifiers exactly as they appear in the instance input — don't rename them or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 17, 'to': 19, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}], 'objective': {'constant': 0.0, 'linear': [6.0, 1.0, 8.0, 2.0, 6.0, 4.0, 10.0, 9.0, 9.0, 5.0, 1.0, 1.0, 6.0, 5.0, 5.0, 10.0, 2.0, 4.0, 10.0], 'quadratic': [[2.0, 7.0, 1.0, 7.0, 3.0, 1.0, 7.0, 8.0, 7.0, 3.0, 8.0, 10.0, 1.0, 2.0, 10.0, 3.0, 10.0, 6.0, 10.0], [7.0, 8.0, 9.0, 10.0, 8.0, 9.0, 10.0, 8.0, 4.0, 7.0, 2.0, 6.0, 4.0, 6.0, 9.0, 6.0, 6.0, 9.0, 5.0], [1.0, 9.0, 7.0, 1.0, 1.0, 9.0, 1.0, 9.0, 1.0, 3.0, 10.0, 2.0, 1.0, 1.0, 9.0, 7.0, 5.0, 7.0, 1.0], [7.0, 10.0, 1.0, 2.0, 10.0, 9.0, 1.0, 3.0, 5.0, 9.0, 4.0, 5.0, 8.0, 1.0, 9.0, 2.0, 3.0, 2.0, 9.0], [3.0, 8.0, 1.0, 10.0, 1.0, 10.0, 8.0, 6.0, 2.0, 3.0, 2.0, 3.0, 9.0, 10.0, 7.0, 8.0, 1.0, 4.0, 7.0], [1.0, 9.0, 9.0, 9.0, 10.0, 4.0, 7.0, 10.0, 3.0, 2.0, 5.0, 4.0, 8.0, 8.0, 5.0, 6.0, 3.0, 5.0, 10.0], [7.0, 10.0, 1.0, 1.0, 8.0, 7.0, 3.0, 9.0, 5.0, 1.0, 10.0, 1.0, 8.0, 9.0, 1.0, 6.0, 5.0, 2.0, 4.0], [8.0, 8.0, 9.0, 3.0, 6.0, 10.0, 9.0, 8.0, 4.0, 4.0, 4.0, 7.0, 5.0, 6.0, 10.0, 3.0, 5.0, 1.0, 8.0], [7.0, 4.0, 1.0, 5.0, 2.0, 3.0, 5.0, 4.0, 4.0, 8.0, 5.0, 6.0, 6.0, 5.0, 3.0, 2.0, 2.0, 2.0, 10.0], [3.0, 7.0, 3.0, 9.0, 3.0, 2.0, 1.0, 4.0, 8.0, 7.0, 8.0, 8.0, 1.0, 6.0, 4.0, 10.0, 5.0, 10.0, 5.0], [8.0, 2.0, 10.0, 4.0, 2.0, 5.0, 10.0, 4.0, 5.0, 8.0, 4.0, 10.0, 3.0, 7.0, 5.0, 8.0, 2.0, 1.0, 1.0], [10.0, 6.0, 2.0, 5.0, 3.0, 4.0, 1.0, 7.0, 6.0, 8.0, 10.0, 6.0, 5.0, 10.0, 2.0, 10.0, 5.0, 7.0, 5.0], [1.0, 4.0, 1.0, 8.0, 9.0, 8.0, 8.0, 5.0, 6.0, 1.0, 3.0, 5.0, 4.0, 6.0, 2.0, 7.0, 6.0, 7.0, 5.0], [2.0, 6.0, 1.0, 1.0, 10.0, 8.0, 9.0, 6.0, 5.0, 6.0, 7.0, 10.0, 6.0, 8.0, 8.0, 7.0, 4.0, 7.0, 6.0], [10.0, 9.0, 9.0, 9.0, 7.0, 5.0, 1.0, 10.0, 3.0, 4.0, 5.0, 2.0, 2.0, 8.0, 1.0, 9.0, 4.0, 7.0, 6.0], [3.0, 6.0, 7.0, 2.0, 8.0, 6.0, 6.0, 3.0, 2.0, 10.0, 8.0, 10.0, 7.0, 7.0, 9.0, 1.0, 8.0, 2.0, 10.0], [10.0, 6.0, 5.0, 3.0, 1.0, 3.0, 5.0, 5.0, 2.0, 5.0, 2.0, 5.0, 6.0, 4.0, 4.0, 8.0, 9.0, 7.0, 8.0], [6.0, 9.0, 7.0, 2.0, 4.0, 5.0, 2.0, 1.0, 2.0, 10.0, 1.0, 7.0, 7.0, 7.0, 7.0, 2.0, 7.0, 9.0, 7.0], [10.0, 5.0, 1.0, 9.0, 7.0, 10.0, 4.0, 8.0, 10.0, 5.0, 1.0, 5.0, 5.0, 6.0, 6.0, 10.0, 8.0, 7.0, 3.0]]}, 'source': 18, 'target': 19}","[18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]",2123.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 19, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'source': 18, 'target': 19, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 2.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 9.0}, {'var_index': 8, 'linear_cost': 9.0}, {'var_index': 9, 'linear_cost': 5.0}, {'var_index': 10, 'linear_cost': 1.0}, {'var_index': 11, 'linear_cost': 1.0}, {'var_index': 12, 'linear_cost': 6.0}, {'var_index': 13, 'linear_cost': 5.0}, {'var_index': 14, 'linear_cost': 5.0}, {'var_index': 15, 'linear_cost': 10.0}, 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'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 17, 'to': 19, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19}}","[18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]",23,json,0
QSPP,QSPP,"Many people in the neighborhood treat picking a bike route like balancing a bill: start at the park, ride along allowed one-way lanes to the plaza, and each lane adds its usual delay while some lane pairings tack on extra delay when they appear together (some lanes even have their own extra cost just by being included). The trick is to choose one continuous route whose total — adding every lane’s base delay and all the extra delays caused by specific lane combinations — comes out the smallest. The route must be a legal directed path from park to plaza, spelled out as a sequence of place names with each step supported by an actual one-way lane, and the answer should contain only those place names (no lane codes). The specific map and delay details follow below.

# total_places_count=20
# total_one_way_lanes=33
# place_names=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
# park_name=18
# plaza_name=19

lane_start_place,lane_end_place,lane_code
18,0,0
18,6,1
18,12,2
5,19,3
11,19,4
17,19,5
0,1,6
0,6,7
1,2,8
1,7,9
2,3,10
2,8,11
3,4,12
3,9,13
4,5,14
4,10,15
5,11,16
6,7,17
6,12,18
7,8,19
7,13,20
8,9,21
8,14,22
9,10,23
9,15,24
10,11,25
10,16,26
11,17,27
12,13,28
13,14,29
14,15,30
15,16,31
16,17,32

lane_code_for_linear,base_expected_delay
0,5.0
1,6.0
2,6.0
3,9.0
4,2.0
5,7.0
6,8.0
7,10.0
8,1.0
9,7.0
10,8.0
11,8.0
12,7.0
13,9.0
14,1.0
15,4.0
16,8.0
17,8.0
18,5.0
19,7.0
20,1.0
21,8.0
22,7.0
23,10.0
24,5.0
25,4.0
26,8.0
27,5.0
28,1.0
29,5.0
30,7.0
31,10.0
32,5.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (lane_i_code, lane_j_code). If two lane_codes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| lane_i_code\lane_j_code | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 1.0 | 2.0 | 2.0 | 3.0 | 8.0 | 8.0 | 8.0 | 2.0 | 1.0 | 8.0 | 9.0 | 2.0 | 3.0 | 7.0 | 10.0 | 6.0 | 9.0 | 5.0 | 9.0 | 4.0 | 5.0 | 5.0 | 3.0 | 2.0 | 2.0 | 6.0 | 10.0 | 5.0 | 9.0 | 9.0 | 10.0 | 7.0 |
| 1 | 1.0 | 5.0 | 7.0 | 6.0 | 6.0 | 3.0 | 8.0 | 3.0 | 6.0 | 2.0 | 7.0 | 8.0 | 7.0 | 10.0 | 4.0 | 10.0 | 10.0 | 2.0 | 6.0 | 4.0 | 8.0 | 1.0 | 10.0 | 3.0 | 6.0 | 6.0 | 7.0 | 6.0 | 6.0 | 10.0 | 5.0 | 10.0 | 9.0 |
| 2 | 2.0 | 7.0 | 8.0 | 7.0 | 2.0 | 9.0 | 3.0 | 1.0 | 10.0 | 2.0 | 5.0 | 9.0 | 10.0 | 2.0 | 9.0 | 10.0 | 7.0 | 6.0 | 5.0 | 1.0 | 6.0 | 9.0 | 6.0 | 8.0 | 4.0 | 3.0 | 4.0 | 6.0 | 6.0 | 1.0 | 8.0 | 9.0 | 7.0 |
| 3 | 2.0 | 6.0 | 7.0 | 1.0 | 2.0 | 9.0 | 6.0 | 4.0 | 6.0 | 1.0 | 9.0 | 2.0 | 3.0 | 5.0 | 4.0 | 4.0 | 4.0 | 8.0 | 1.0 | 7.0 | 8.0 | 10.0 | 3.0 | 1.0 | 8.0 | 2.0 | 3.0 | 4.0 | 5.0 | 2.0 | 10.0 | 10.0 | 1.0 |
| 4 | 3.0 | 6.0 | 2.0 | 2.0 | 10.0 | 10.0 | 2.0 | 7.0 | 7.0 | 2.0 | 5.0 | 2.0 | 1.0 | 9.0 | 8.0 | 4.0 | 7.0 | 3.0 | 2.0 | 5.0 | 10.0 | 7.0 | 8.0 | 9.0 | 2.0 | 3.0 | 9.0 | 2.0 | 6.0 | 3.0 | 10.0 | 8.0 | 1.0 |
| 5 | 8.0 | 3.0 | 9.0 | 9.0 | 10.0 | 4.0 | 9.0 | 6.0 | 2.0 | 7.0 | 6.0 | 2.0 | 10.0 | 1.0 | 5.0 | 9.0 | 3.0 | 5.0 | 6.0 | 2.0 | 5.0 | 1.0 | 4.0 | 2.0 | 3.0 | 5.0 | 1.0 | 3.0 | 5.0 | 5.0 | 1.0 | 7.0 | 10.0 |
| 6 | 8.0 | 8.0 | 3.0 | 6.0 | 2.0 | 9.0 | 9.0 | 7.0 | 8.0 | 10.0 | 10.0 | 6.0 | 5.0 | 10.0 | 8.0 | 5.0 | 3.0 | 9.0 | 2.0 | 6.0 | 9.0 | 9.0 | 10.0 | 1.0 | 3.0 | 9.0 | 10.0 | 3.0 | 1.0 | 2.0 | 7.0 | 7.0 | 10.0 |
| 7 | 8.0 | 3.0 | 1.0 | 4.0 | 7.0 | 6.0 | 7.0 | 6.0 | 4.0 | 8.0 | 2.0 | 8.0 | 8.0 | 4.0 | 1.0 | 10.0 | 9.0 | 2.0 | 8.0 | 4.0 | 9.0 | 5.0 | 8.0 | 8.0 | 10.0 | 7.0 | 2.0 | 5.0 | 10.0 | 1.0 | 5.0 | 1.0 | 1.0 |
| 8 | 2.0 | 6.0 | 10.0 | 6.0 | 7.0 | 2.0 | 8.0 | 4.0 | 6.0 | 6.0 | 7.0 | 10.0 | 10.0 | 7.0 | 7.0 | 10.0 | 7.0 | 6.0 | 8.0 | 3.0 | 3.0 | 3.0 | 9.0 | 1.0 | 6.0 | 8.0 | 7.0 | 3.0 | 1.0 | 8.0 | 4.0 | 2.0 | 8.0 |
| 9 | 1.0 | 2.0 | 2.0 | 1.0 | 2.0 | 7.0 | 10.0 | 8.0 | 6.0 | 3.0 | 10.0 | 3.0 | 4.0 | 2.0 | 9.0 | 8.0 | 8.0 | 3.0 | 8.0 | 7.0 | 1.0 | 5.0 | 2.0 | 3.0 | 4.0 | 4.0 | 7.0 | 6.0 | 4.0 | 7.0 | 4.0 | 1.0 | 2.0 |
| 10 | 8.0 | 7.0 | 5.0 | 9.0 | 5.0 | 6.0 | 10.0 | 2.0 | 7.0 | 10.0 | 3.0 | 7.0 | 3.0 | 9.0 | 9.0 | 6.0 | 7.0 | 9.0 | 2.0 | 4.0 | 7.0 | 1.0 | 10.0 | 5.0 | 7.0 | 9.0 | 6.0 | 1.0 | 7.0 | 10.0 | 4.0 | 1.0 | 1.0 |
| 11 | 9.0 | 8.0 | 9.0 | 2.0 | 2.0 | 2.0 | 6.0 | 8.0 | 10.0 | 3.0 | 7.0 | 1.0 | 3.0 | 4.0 | 10.0 | 8.0 | 10.0 | 10.0 | 5.0 | 1.0 | 6.0 | 4.0 | 7.0 | 7.0 | 3.0 | 9.0 | 3.0 | 5.0 | 9.0 | 3.0 | 3.0 | 7.0 | 8.0 |
| 12 | 2.0 | 7.0 | 10.0 | 3.0 | 1.0 | 10.0 | 5.0 | 8.0 | 10.0 | 4.0 | 3.0 | 3.0 | 6.0 | 6.0 | 9.0 | 7.0 | 2.0 | 2.0 | 4.0 | 7.0 | 2.0 | 6.0 | 2.0 | 4.0 | 10.0 | 2.0 | 2.0 | 7.0 | 2.0 | 8.0 | 5.0 | 7.0 | 6.0 |
| 13 | 3.0 | 10.0 | 2.0 | 5.0 | 9.0 | 1.0 | 10.0 | 4.0 | 7.0 | 2.0 | 9.0 | 4.0 | 6.0 | 7.0 | 10.0 | 8.0 | 5.0 | 9.0 | 3.0 | 6.0 | 4.0 | 9.0 | 3.0 | 8.0 | 10.0 | 3.0 | 7.0 | 10.0 | 7.0 | 9.0 | 9.0 | 6.0 | 2.0 |
| 14 | 7.0 | 4.0 | 9.0 | 4.0 | 8.0 | 5.0 | 8.0 | 1.0 | 7.0 | 9.0 | 9.0 | 10.0 | 9.0 | 10.0 | 3.0 | 6.0 | 10.0 | 1.0 | 8.0 | 6.0 | 7.0 | 7.0 | 6.0 | 7.0 | 10.0 | 3.0 | 7.0 | 8.0 | 8.0 | 2.0 | 6.0 | 2.0 | 8.0 |
| 15 | 10.0 | 10.0 | 10.0 | 4.0 | 4.0 | 9.0 | 5.0 | 10.0 | 10.0 | 8.0 | 6.0 | 8.0 | 7.0 | 8.0 | 6.0 | 5.0 | 2.0 | 4.0 | 2.0 | 10.0 | 1.0 | 8.0 | 2.0 | 4.0 | 5.0 | 1.0 | 7.0 | 3.0 | 7.0 | 6.0 | 4.0 | 9.0 | 4.0 |
| 16 | 6.0 | 10.0 | 7.0 | 4.0 | 7.0 | 3.0 | 3.0 | 9.0 | 7.0 | 8.0 | 7.0 | 10.0 | 2.0 | 5.0 | 10.0 | 2.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 | 9.0 | 6.0 | 6.0 | 6.0 | 1.0 | 2.0 | 9.0 | 1.0 | 3.0 | 6.0 | 5.0 | 4.0 |
| 17 | 9.0 | 2.0 | 6.0 | 8.0 | 3.0 | 5.0 | 9.0 | 2.0 | 6.0 | 3.0 | 9.0 | 10.0 | 2.0 | 9.0 | 1.0 | 4.0 | 4.0 | 10.0 | 9.0 | 9.0 | 4.0 | 2.0 | 2.0 | 2.0 | 10.0 | 10.0 | 7.0 | 9.0 | 9.0 | 9.0 | 9.0 | 3.0 | 4.0 |
| 18 | 5.0 | 6.0 | 5.0 | 1.0 | 2.0 | 6.0 | 2.0 | 8.0 | 8.0 | 8.0 | 2.0 | 5.0 | 4.0 | 3.0 | 8.0 | 2.0 | 6.0 | 9.0 | 6.0 | 4.0 | 4.0 | 5.0 | 1.0 | 1.0 | 2.0 | 10.0 | 6.0 | 4.0 | 3.0 | 5.0 | 5.0 | 7.0 | 9.0 |
| 19 | 9.0 | 4.0 | 1.0 | 7.0 | 5.0 | 2.0 | 6.0 | 4.0 | 3.0 | 7.0 | 4.0 | 1.0 | 7.0 | 6.0 | 6.0 | 10.0 | 8.0 | 9.0 | 4.0 | 6.0 | 5.0 | 8.0 | 4.0 | 9.0 | 6.0 | 3.0 | 4.0 | 2.0 | 10.0 | 8.0 | 9.0 | 9.0 | 4.0 |
| 20 | 4.0 | 8.0 | 6.0 | 8.0 | 10.0 | 5.0 | 9.0 | 9.0 | 3.0 | 1.0 | 7.0 | 6.0 | 2.0 | 4.0 | 7.0 | 1.0 | 10.0 | 4.0 | 4.0 | 5.0 | 6.0 | 6.0 | 6.0 | 6.0 | 4.0 | 1.0 | 1.0 | 5.0 | 9.0 | 5.0 | 8.0 | 1.0 | 10.0 |
| 21 | 5.0 | 1.0 | 9.0 | 10.0 | 7.0 | 1.0 | 9.0 | 5.0 | 3.0 | 5.0 | 1.0 | 4.0 | 6.0 | 9.0 | 7.0 | 8.0 | 9.0 | 2.0 | 5.0 | 8.0 | 6.0 | 5.0 | 6.0 | 8.0 | 4.0 | 1.0 | 8.0 | 8.0 | 9.0 | 4.0 | 1.0 | 8.0 | 9.0 |
| 22 | 5.0 | 10.0 | 6.0 | 3.0 | 8.0 | 4.0 | 10.0 | 8.0 | 9.0 | 2.0 | 10.0 | 7.0 | 2.0 | 3.0 | 6.0 | 2.0 | 6.0 | 2.0 | 1.0 | 4.0 | 6.0 | 6.0 | 2.0 | 2.0 | 2.0 | 8.0 | 1.0 | 2.0 | 5.0 | 3.0 | 7.0 | 9.0 | 1.0 |
| 23 | 3.0 | 3.0 | 8.0 | 1.0 | 9.0 | 2.0 | 1.0 | 8.0 | 1.0 | 3.0 | 5.0 | 7.0 | 4.0 | 8.0 | 7.0 | 4.0 | 6.0 | 2.0 | 1.0 | 9.0 | 6.0 | 8.0 | 2.0 | 10.0 | 6.0 | 7.0 | 5.0 | 3.0 | 5.0 | 8.0 | 10.0 | 2.0 | 7.0 |
| 24 | 2.0 | 6.0 | 4.0 | 8.0 | 2.0 | 3.0 | 3.0 | 10.0 | 6.0 | 4.0 | 7.0 | 3.0 | 10.0 | 10.0 | 10.0 | 5.0 | 6.0 | 10.0 | 2.0 | 6.0 | 4.0 | 4.0 | 2.0 | 6.0 | 9.0 | 6.0 | 9.0 | 2.0 | 9.0 | 7.0 | 1.0 | 4.0 | 7.0 |
| 25 | 2.0 | 6.0 | 3.0 | 2.0 | 3.0 | 5.0 | 9.0 | 7.0 | 8.0 | 4.0 | 9.0 | 9.0 | 2.0 | 3.0 | 3.0 | 1.0 | 1.0 | 10.0 | 10.0 | 3.0 | 1.0 | 1.0 | 8.0 | 7.0 | 6.0 | 5.0 | 1.0 | 10.0 | 10.0 | 5.0 | 9.0 | 7.0 | 8.0 |
| 26 | 6.0 | 7.0 | 4.0 | 3.0 | 9.0 | 1.0 | 10.0 | 2.0 | 7.0 | 7.0 | 6.0 | 3.0 | 2.0 | 7.0 | 7.0 | 7.0 | 2.0 | 7.0 | 6.0 | 4.0 | 1.0 | 8.0 | 1.0 | 5.0 | 9.0 | 1.0 | 7.0 | 6.0 | 6.0 | 1.0 | 3.0 | 7.0 | 7.0 |
| 27 | 10.0 | 6.0 | 6.0 | 4.0 | 2.0 | 3.0 | 3.0 | 5.0 | 3.0 | 6.0 | 1.0 | 5.0 | 7.0 | 10.0 | 8.0 | 3.0 | 9.0 | 9.0 | 4.0 | 2.0 | 5.0 | 8.0 | 2.0 | 3.0 | 2.0 | 10.0 | 6.0 | 6.0 | 10.0 | 6.0 | 8.0 | 5.0 | 7.0 |
| 28 | 5.0 | 6.0 | 6.0 | 5.0 | 6.0 | 5.0 | 1.0 | 10.0 | 1.0 | 4.0 | 7.0 | 9.0 | 2.0 | 7.0 | 8.0 | 7.0 | 1.0 | 9.0 | 3.0 | 10.0 | 9.0 | 9.0 | 5.0 | 5.0 | 9.0 | 10.0 | 6.0 | 10.0 | 9.0 | 2.0 | 6.0 | 4.0 | 6.0 |
| 29 | 9.0 | 10.0 | 1.0 | 2.0 | 3.0 | 5.0 | 2.0 | 1.0 | 8.0 | 7.0 | 10.0 | 3.0 | 8.0 | 9.0 | 2.0 | 6.0 | 3.0 | 9.0 | 5.0 | 8.0 | 5.0 | 4.0 | 3.0 | 8.0 | 7.0 | 5.0 | 1.0 | 6.0 | 2.0 | 7.0 | 8.0 | 1.0 | 6.0 |
| 30 | 9.0 | 5.0 | 8.0 | 10.0 | 10.0 | 1.0 | 7.0 | 5.0 | 4.0 | 4.0 | 4.0 | 3.0 | 5.0 | 9.0 | 6.0 | 4.0 | 6.0 | 9.0 | 5.0 | 9.0 | 8.0 | 1.0 | 7.0 | 10.0 | 1.0 | 9.0 | 3.0 | 8.0 | 6.0 | 8.0 | 9.0 | 2.0 | 9.0 |
| 31 | 10.0 | 10.0 | 9.0 | 10.0 | 8.0 | 7.0 | 7.0 | 1.0 | 2.0 | 1.0 | 1.0 | 7.0 | 7.0 | 6.0 | 2.0 | 9.0 | 5.0 | 3.0 | 7.0 | 9.0 | 1.0 | 8.0 | 9.0 | 2.0 | 4.0 | 7.0 | 7.0 | 5.0 | 4.0 | 1.0 | 2.0 | 6.0 | 3.0 |
| 32 | 7.0 | 9.0 | 7.0 | 1.0 | 1.0 | 10.0 | 10.0 | 1.0 | 8.0 | 2.0 | 1.0 | 8.0 | 6.0 | 2.0 | 8.0 | 4.0 | 4.0 | 4.0 | 9.0 | 4.0 | 10.0 | 9.0 | 1.0 | 7.0 | 7.0 | 8.0 | 7.0 | 7.0 | 6.0 | 6.0 | 9.0 | 3.0 | 9.0 |

Oh, and when you send back the route, please stick to a tiny JSON sketch like this:

{
  ""solution"": []
}

""solution"" is just the ordered list of place names from the starting spot to the destination — fill it with the node names exactly as they appear on the map, one after another. Keep it to those place names only (don’t include lane codes, edge identifiers, costs, or anything else). This JSON is just the shape I’m expecting, not the actual answer itself.

Also, all identifiers must be used exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 6, 'var_index': 1}, {'from': 18, 'to': 12, 'var_index': 2}, {'from': 5, 'to': 19, 'var_index': 3}, {'from': 11, 'to': 19, 'var_index': 4}, {'from': 17, 'to': 19, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 0, 'to': 6, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 7, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 8, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 9, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 10, 'var_index': 15}, {'from': 5, 'to': 11, 'var_index': 16}, {'from': 6, 'to': 7, 'var_index': 17}, {'from': 6, 'to': 12, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 13, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 14, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 15, 'var_index': 24}, {'from': 10, 'to': 11, 'var_index': 25}, {'from': 10, 'to': 16, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 13, 'var_index': 28}, {'from': 13, 'to': 14, 'var_index': 29}, {'from': 14, 'to': 15, 'var_index': 30}, {'from': 15, 'to': 16, 'var_index': 31}, {'from': 16, 'to': 17, 'var_index': 32}], 'objective': {'constant': 0.0, 'linear': [5.0, 6.0, 6.0, 9.0, 2.0, 7.0, 8.0, 10.0, 1.0, 7.0, 8.0, 8.0, 7.0, 9.0, 1.0, 4.0, 8.0, 8.0, 5.0, 7.0, 1.0, 8.0, 7.0, 10.0, 5.0, 4.0, 8.0, 5.0, 1.0, 5.0, 7.0, 10.0, 5.0], 'quadratic': [[9.0, 1.0, 2.0, 2.0, 3.0, 8.0, 8.0, 8.0, 2.0, 1.0, 8.0, 9.0, 2.0, 3.0, 7.0, 10.0, 6.0, 9.0, 5.0, 9.0, 4.0, 5.0, 5.0, 3.0, 2.0, 2.0, 6.0, 10.0, 5.0, 9.0, 9.0, 10.0, 7.0], [1.0, 5.0, 7.0, 6.0, 6.0, 3.0, 8.0, 3.0, 6.0, 2.0, 7.0, 8.0, 7.0, 10.0, 4.0, 10.0, 10.0, 2.0, 6.0, 4.0, 8.0, 1.0, 10.0, 3.0, 6.0, 6.0, 7.0, 6.0, 6.0, 10.0, 5.0, 10.0, 9.0], [2.0, 7.0, 8.0, 7.0, 2.0, 9.0, 3.0, 1.0, 10.0, 2.0, 5.0, 9.0, 10.0, 2.0, 9.0, 10.0, 7.0, 6.0, 5.0, 1.0, 6.0, 9.0, 6.0, 8.0, 4.0, 3.0, 4.0, 6.0, 6.0, 1.0, 8.0, 9.0, 7.0], [2.0, 6.0, 7.0, 1.0, 2.0, 9.0, 6.0, 4.0, 6.0, 1.0, 9.0, 2.0, 3.0, 5.0, 4.0, 4.0, 4.0, 8.0, 1.0, 7.0, 8.0, 10.0, 3.0, 1.0, 8.0, 2.0, 3.0, 4.0, 5.0, 2.0, 10.0, 10.0, 1.0], [3.0, 6.0, 2.0, 2.0, 10.0, 10.0, 2.0, 7.0, 7.0, 2.0, 5.0, 2.0, 1.0, 9.0, 8.0, 4.0, 7.0, 3.0, 2.0, 5.0, 10.0, 7.0, 8.0, 9.0, 2.0, 3.0, 9.0, 2.0, 6.0, 3.0, 10.0, 8.0, 1.0], [8.0, 3.0, 9.0, 9.0, 10.0, 4.0, 9.0, 6.0, 2.0, 7.0, 6.0, 2.0, 10.0, 1.0, 5.0, 9.0, 3.0, 5.0, 6.0, 2.0, 5.0, 1.0, 4.0, 2.0, 3.0, 5.0, 1.0, 3.0, 5.0, 5.0, 1.0, 7.0, 10.0], [8.0, 8.0, 3.0, 6.0, 2.0, 9.0, 9.0, 7.0, 8.0, 10.0, 10.0, 6.0, 5.0, 10.0, 8.0, 5.0, 3.0, 9.0, 2.0, 6.0, 9.0, 9.0, 10.0, 1.0, 3.0, 9.0, 10.0, 3.0, 1.0, 2.0, 7.0, 7.0, 10.0], [8.0, 3.0, 1.0, 4.0, 7.0, 6.0, 7.0, 6.0, 4.0, 8.0, 2.0, 8.0, 8.0, 4.0, 1.0, 10.0, 9.0, 2.0, 8.0, 4.0, 9.0, 5.0, 8.0, 8.0, 10.0, 7.0, 2.0, 5.0, 10.0, 1.0, 5.0, 1.0, 1.0], [2.0, 6.0, 10.0, 6.0, 7.0, 2.0, 8.0, 4.0, 6.0, 6.0, 7.0, 10.0, 10.0, 7.0, 7.0, 10.0, 7.0, 6.0, 8.0, 3.0, 3.0, 3.0, 9.0, 1.0, 6.0, 8.0, 7.0, 3.0, 1.0, 8.0, 4.0, 2.0, 8.0], [1.0, 2.0, 2.0, 1.0, 2.0, 7.0, 10.0, 8.0, 6.0, 3.0, 10.0, 3.0, 4.0, 2.0, 9.0, 8.0, 8.0, 3.0, 8.0, 7.0, 1.0, 5.0, 2.0, 3.0, 4.0, 4.0, 7.0, 6.0, 4.0, 7.0, 4.0, 1.0, 2.0], [8.0, 7.0, 5.0, 9.0, 5.0, 6.0, 10.0, 2.0, 7.0, 10.0, 3.0, 7.0, 3.0, 9.0, 9.0, 6.0, 7.0, 9.0, 2.0, 4.0, 7.0, 1.0, 10.0, 5.0, 7.0, 9.0, 6.0, 1.0, 7.0, 10.0, 4.0, 1.0, 1.0], [9.0, 8.0, 9.0, 2.0, 2.0, 2.0, 6.0, 8.0, 10.0, 3.0, 7.0, 1.0, 3.0, 4.0, 10.0, 8.0, 10.0, 10.0, 5.0, 1.0, 6.0, 4.0, 7.0, 7.0, 3.0, 9.0, 3.0, 5.0, 9.0, 3.0, 3.0, 7.0, 8.0], [2.0, 7.0, 10.0, 3.0, 1.0, 10.0, 5.0, 8.0, 10.0, 4.0, 3.0, 3.0, 6.0, 6.0, 9.0, 7.0, 2.0, 2.0, 4.0, 7.0, 2.0, 6.0, 2.0, 4.0, 10.0, 2.0, 2.0, 7.0, 2.0, 8.0, 5.0, 7.0, 6.0], [3.0, 10.0, 2.0, 5.0, 9.0, 1.0, 10.0, 4.0, 7.0, 2.0, 9.0, 4.0, 6.0, 7.0, 10.0, 8.0, 5.0, 9.0, 3.0, 6.0, 4.0, 9.0, 3.0, 8.0, 10.0, 3.0, 7.0, 10.0, 7.0, 9.0, 9.0, 6.0, 2.0], [7.0, 4.0, 9.0, 4.0, 8.0, 5.0, 8.0, 1.0, 7.0, 9.0, 9.0, 10.0, 9.0, 10.0, 3.0, 6.0, 10.0, 1.0, 8.0, 6.0, 7.0, 7.0, 6.0, 7.0, 10.0, 3.0, 7.0, 8.0, 8.0, 2.0, 6.0, 2.0, 8.0], [10.0, 10.0, 10.0, 4.0, 4.0, 9.0, 5.0, 10.0, 10.0, 8.0, 6.0, 8.0, 7.0, 8.0, 6.0, 5.0, 2.0, 4.0, 2.0, 10.0, 1.0, 8.0, 2.0, 4.0, 5.0, 1.0, 7.0, 3.0, 7.0, 6.0, 4.0, 9.0, 4.0], [6.0, 10.0, 7.0, 4.0, 7.0, 3.0, 3.0, 9.0, 7.0, 8.0, 7.0, 10.0, 2.0, 5.0, 10.0, 2.0, 2.0, 4.0, 6.0, 8.0, 10.0, 9.0, 6.0, 6.0, 6.0, 1.0, 2.0, 9.0, 1.0, 3.0, 6.0, 5.0, 4.0], [9.0, 2.0, 6.0, 8.0, 3.0, 5.0, 9.0, 2.0, 6.0, 3.0, 9.0, 10.0, 2.0, 9.0, 1.0, 4.0, 4.0, 10.0, 9.0, 9.0, 4.0, 2.0, 2.0, 2.0, 10.0, 10.0, 7.0, 9.0, 9.0, 9.0, 9.0, 3.0, 4.0], [5.0, 6.0, 5.0, 1.0, 2.0, 6.0, 2.0, 8.0, 8.0, 8.0, 2.0, 5.0, 4.0, 3.0, 8.0, 2.0, 6.0, 9.0, 6.0, 4.0, 4.0, 5.0, 1.0, 1.0, 2.0, 10.0, 6.0, 4.0, 3.0, 5.0, 5.0, 7.0, 9.0], [9.0, 4.0, 1.0, 7.0, 5.0, 2.0, 6.0, 4.0, 3.0, 7.0, 4.0, 1.0, 7.0, 6.0, 6.0, 10.0, 8.0, 9.0, 4.0, 6.0, 5.0, 8.0, 4.0, 9.0, 6.0, 3.0, 4.0, 2.0, 10.0, 8.0, 9.0, 9.0, 4.0], [4.0, 8.0, 6.0, 8.0, 10.0, 5.0, 9.0, 9.0, 3.0, 1.0, 7.0, 6.0, 2.0, 4.0, 7.0, 1.0, 10.0, 4.0, 4.0, 5.0, 6.0, 6.0, 6.0, 6.0, 4.0, 1.0, 1.0, 5.0, 9.0, 5.0, 8.0, 1.0, 10.0], [5.0, 1.0, 9.0, 10.0, 7.0, 1.0, 9.0, 5.0, 3.0, 5.0, 1.0, 4.0, 6.0, 9.0, 7.0, 8.0, 9.0, 2.0, 5.0, 8.0, 6.0, 5.0, 6.0, 8.0, 4.0, 1.0, 8.0, 8.0, 9.0, 4.0, 1.0, 8.0, 9.0], [5.0, 10.0, 6.0, 3.0, 8.0, 4.0, 10.0, 8.0, 9.0, 2.0, 10.0, 7.0, 2.0, 3.0, 6.0, 2.0, 6.0, 2.0, 1.0, 4.0, 6.0, 6.0, 2.0, 2.0, 2.0, 8.0, 1.0, 2.0, 5.0, 3.0, 7.0, 9.0, 1.0], [3.0, 3.0, 8.0, 1.0, 9.0, 2.0, 1.0, 8.0, 1.0, 3.0, 5.0, 7.0, 4.0, 8.0, 7.0, 4.0, 6.0, 2.0, 1.0, 9.0, 6.0, 8.0, 2.0, 10.0, 6.0, 7.0, 5.0, 3.0, 5.0, 8.0, 10.0, 2.0, 7.0], [2.0, 6.0, 4.0, 8.0, 2.0, 3.0, 3.0, 10.0, 6.0, 4.0, 7.0, 3.0, 10.0, 10.0, 10.0, 5.0, 6.0, 10.0, 2.0, 6.0, 4.0, 4.0, 2.0, 6.0, 9.0, 6.0, 9.0, 2.0, 9.0, 7.0, 1.0, 4.0, 7.0], [2.0, 6.0, 3.0, 2.0, 3.0, 5.0, 9.0, 7.0, 8.0, 4.0, 9.0, 9.0, 2.0, 3.0, 3.0, 1.0, 1.0, 10.0, 10.0, 3.0, 1.0, 1.0, 8.0, 7.0, 6.0, 5.0, 1.0, 10.0, 10.0, 5.0, 9.0, 7.0, 8.0], [6.0, 7.0, 4.0, 3.0, 9.0, 1.0, 10.0, 2.0, 7.0, 7.0, 6.0, 3.0, 2.0, 7.0, 7.0, 7.0, 2.0, 7.0, 6.0, 4.0, 1.0, 8.0, 1.0, 5.0, 9.0, 1.0, 7.0, 6.0, 6.0, 1.0, 3.0, 7.0, 7.0], [10.0, 6.0, 6.0, 4.0, 2.0, 3.0, 3.0, 5.0, 3.0, 6.0, 1.0, 5.0, 7.0, 10.0, 8.0, 3.0, 9.0, 9.0, 4.0, 2.0, 5.0, 8.0, 2.0, 3.0, 2.0, 10.0, 6.0, 6.0, 10.0, 6.0, 8.0, 5.0, 7.0], [5.0, 6.0, 6.0, 5.0, 6.0, 5.0, 1.0, 10.0, 1.0, 4.0, 7.0, 9.0, 2.0, 7.0, 8.0, 7.0, 1.0, 9.0, 3.0, 10.0, 9.0, 9.0, 5.0, 5.0, 9.0, 10.0, 6.0, 10.0, 9.0, 2.0, 6.0, 4.0, 6.0], [9.0, 10.0, 1.0, 2.0, 3.0, 5.0, 2.0, 1.0, 8.0, 7.0, 10.0, 3.0, 8.0, 9.0, 2.0, 6.0, 3.0, 9.0, 5.0, 8.0, 5.0, 4.0, 3.0, 8.0, 7.0, 5.0, 1.0, 6.0, 2.0, 7.0, 8.0, 1.0, 6.0], [9.0, 5.0, 8.0, 10.0, 10.0, 1.0, 7.0, 5.0, 4.0, 4.0, 4.0, 3.0, 5.0, 9.0, 6.0, 4.0, 6.0, 9.0, 5.0, 9.0, 8.0, 1.0, 7.0, 10.0, 1.0, 9.0, 3.0, 8.0, 6.0, 8.0, 9.0, 2.0, 9.0], [10.0, 10.0, 9.0, 10.0, 8.0, 7.0, 7.0, 1.0, 2.0, 1.0, 1.0, 7.0, 7.0, 6.0, 2.0, 9.0, 5.0, 3.0, 7.0, 9.0, 1.0, 8.0, 9.0, 2.0, 4.0, 7.0, 7.0, 5.0, 4.0, 1.0, 2.0, 6.0, 3.0], [7.0, 9.0, 7.0, 1.0, 1.0, 10.0, 10.0, 1.0, 8.0, 2.0, 1.0, 8.0, 6.0, 2.0, 8.0, 4.0, 4.0, 4.0, 9.0, 4.0, 10.0, 9.0, 1.0, 7.0, 7.0, 8.0, 7.0, 7.0, 6.0, 6.0, 9.0, 3.0, 9.0]]}, 'source': 18, 'target': 19}","[18, 6, 7, 8, 9, 10, 11, 19]",312.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 33, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'source': 18, 'target': 19, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 9.0}, {'var_index': 4, 'linear_cost': 2.0}, {'var_index': 5, 'linear_cost': 7.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 10.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 7.0}, {'var_index': 10, 'linear_cost': 8.0}, {'var_index': 11, 'linear_cost': 8.0}, {'var_index': 12, 'linear_cost': 7.0}, {'var_index': 13, 'linear_cost': 9.0}, {'var_index': 14, 'linear_cost': 1.0}, {'var_index': 15, 'linear_cost': 4.0}, {'var_index': 16, 'linear_cost': 8.0}, {'var_index': 17, 'linear_cost': 8.0}, {'var_index': 18, 'linear_cost': 5.0}, {'var_index': 19, 'linear_cost': 7.0}, {'var_index': 20, 'linear_cost': 1.0}, {'var_index': 21, 'linear_cost': 8.0}, {'var_index': 22, 'linear_cost': 7.0}, {'var_index': 23, 'linear_cost': 10.0}, {'var_index': 24, 'linear_cost': 5.0}, {'var_index': 25, 'linear_cost': 4.0}, {'var_index': 26, 'linear_cost': 8.0}, {'var_index': 27, 'linear_cost': 5.0}, {'var_index': 28, 'linear_cost': 1.0}, {'var_index': 29, 'linear_cost': 5.0}, {'var_index': 30, 'linear_cost': 7.0}, {'var_index': 31, 'linear_cost': 10.0}, {'var_index': 32, 'linear_cost': 5.0}], 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QSPP,QSPP,"There’s a scenario at the harbor where the operator has to send a ferry along one directed waterway from the entrance to the pier, using only the permitted one-way channels. Each channel carries a base fee, and whenever two particular channels end up used in sequence there can be an extra surcharge — so cost is the sum of the channel fees plus any surcharges for those ordered channel pairs that appear on the trip. The goal is to choose the single continuous route that comes out cheapest by that accounting. The route must be continuous and legal (entrance first, pier last, every hop along an allowed direction) and the response should list only the locations visited in order. The concrete map and charges are shown below.

{
  ""total_locations_count"": 17,
  ""total_channels_count"": 44,
  ""location_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17
  ],
  ""harbor_entrance"": 16,
  ""pier_location"": 17,
  ""edges"": [
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 1,
      ""channel_id"": 0
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 2,
      ""channel_id"": 1
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 3,
      ""channel_id"": 2
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 4,
      ""channel_id"": 3
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 5,
      ""channel_id"": 4
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 6,
      ""channel_id"": 5
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 7,
      ""channel_id"": 6
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 8,
      ""channel_id"": 7
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 9,
      ""channel_id"": 8
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 10,
      ""channel_id"": 9
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 11,
      ""channel_id"": 10
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 12,
      ""channel_id"": 11
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 13,
      ""channel_id"": 12
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 14,
      ""channel_id"": 13
    },
    {
      ""channel_from_location"": 16,
      ""channel_to_location"": 15,
      ""channel_id"": 14
    },
    {
      ""channel_from_location"": 1,
      ""channel_to_location"": 17,
      ""channel_id"": 15
    },
    {
      ""channel_from_location"": 2,
      ""channel_to_location"": 17,
      ""channel_id"": 16
    },
    {
      ""channel_from_location"": 3,
      ""channel_to_location"": 17,
      ""channel_id"": 17
    },
    {
      ""channel_from_location"": 4,
      ""channel_to_location"": 17,
      ""channel_id"": 18
    },
    {
      ""channel_from_location"": 5,
      ""channel_to_location"": 17,
      ""channel_id"": 19
    },
    {
      ""channel_from_location"": 6,
      ""channel_to_location"": 17,
      ""channel_id"": 20
    },
    {
      ""channel_from_location"": 7,
      ""channel_to_location"": 17,
      ""channel_id"": 21
    },
    {
      ""channel_from_location"": 8,
      ""channel_to_location"": 17,
      ""channel_id"": 22
    },
    {
      ""channel_from_location"": 9,
      ""channel_to_location"": 17,
      ""channel_id"": 23
    },
    {
      ""channel_from_location"": 10,
      ""channel_to_location"": 17,
      ""channel_id"": 24
    },
    {
      ""channel_from_location"": 11,
      ""channel_to_location"": 17,
      ""channel_id"": 25
    },
    {
      ""channel_from_location"": 12,
      ""channel_to_location"": 17,
      ""channel_id"": 26
    },
    {
      ""channel_from_location"": 13,
      ""channel_to_location"": 17,
      ""channel_id"": 27
    },
    {
      ""channel_from_location"": 14,
      ""channel_to_location"": 17,
      ""channel_id"": 28
    },
    {
      ""channel_from_location"": 15,
      ""channel_to_location"": 17,
      ""channel_id"": 29
    },
    {
      ""channel_from_location"": 1,
      ""channel_to_location"": 2,
      ""channel_id"": 30
    },
    {
      ""channel_from_location"": 2,
      ""channel_to_location"": 3,
      ""channel_id"": 31
    },
    {
      ""channel_from_location"": 3,
      ""channel_to_location"": 4,
      ""channel_id"": 32
    },
    {
      ""channel_from_location"": 4,
      ""channel_to_location"": 5,
      ""channel_id"": 33
    },
    {
      ""channel_from_location"": 5,
      ""channel_to_location"": 6,
      ""channel_id"": 34
    },
    {
      ""channel_from_location"": 6,
      ""channel_to_location"": 7,
      ""channel_id"": 35
    },
    {
      ""channel_from_location"": 7,
      ""channel_to_location"": 8,
      ""channel_id"": 36
    },
    {
      ""channel_from_location"": 8,
      ""channel_to_location"": 9,
      ""channel_id"": 37
    },
    {
      ""channel_from_location"": 9,
      ""channel_to_location"": 10,
      ""channel_id"": 38
    },
    {
      ""channel_from_location"": 10,
      ""channel_to_location"": 11,
      ""channel_id"": 39
    },
    {
      ""channel_from_location"": 11,
      ""channel_to_location"": 12,
      ""channel_id"": 40
    },
    {
      ""channel_from_location"": 12,
      ""channel_to_location"": 13,
      ""channel_id"": 41
    },
    {
      ""channel_from_location"": 13,
      ""channel_to_location"": 14,
      ""channel_id"": 42
    },
    {
      ""channel_from_location"": 14,
      ""channel_to_location"": 15,
      ""channel_id"": 43
    }
  ],
  ""linear_costs"": [
    {
      ""channel_id_ref"": 0,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 1,
      ""base_fee"": 1.0
    },
    {
      ""channel_id_ref"": 2,
      ""base_fee"": 9.0
    },
    {
      ""channel_id_ref"": 3,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 4,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 5,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 6,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 7,
      ""base_fee"": 1.0
    },
    {
      ""channel_id_ref"": 8,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 9,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 10,
      ""base_fee"": 10.0
    },
    {
      ""channel_id_ref"": 11,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 12,
      ""base_fee"": 9.0
    },
    {
      ""channel_id_ref"": 13,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 14,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 15,
      ""base_fee"": 9.0
    },
    {
      ""channel_id_ref"": 16,
      ""base_fee"": 2.0
    },
    {
      ""channel_id_ref"": 17,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 18,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 19,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 20,
      ""base_fee"": 2.0
    },
    {
      ""channel_id_ref"": 21,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 22,
      ""base_fee"": 3.0
    },
    {
      ""channel_id_ref"": 23,
      ""base_fee"": 6.0
    },
    {
      ""channel_id_ref"": 24,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 25,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 26,
      ""base_fee"": 10.0
    },
    {
      ""channel_id_ref"": 27,
      ""base_fee"": 1.0
    },
    {
      ""channel_id_ref"": 28,
      ""base_fee"": 8.0
    },
    {
      ""channel_id_ref"": 29,
      ""base_fee"": 10.0
    },
    {
      ""channel_id_ref"": 30,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 31,
      ""base_fee"": 10.0
    },
    {
      ""channel_id_ref"": 32,
      ""base_fee"": 9.0
    },
    {
      ""channel_id_ref"": 33,
      ""base_fee"": 9.0
    },
    {
      ""channel_id_ref"": 34,
      ""base_fee"": 2.0
    },
    {
      ""channel_id_ref"": 35,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 36,
      ""base_fee"": 10.0
    },
    {
      ""channel_id_ref"": 37,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 38,
      ""base_fee"": 4.0
    },
    {
      ""channel_id_ref"": 39,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 40,
      ""base_fee"": 3.0
    },
    {
      ""channel_id_ref"": 41,
      ""base_fee"": 5.0
    },
    {
      ""channel_id_ref"": 42,
      ""base_fee"": 7.0
    },
    {
      ""channel_id_ref"": 43,
      ""base_fee"": 7.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_channel_id, second_channel_id). If two channels with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_channel_id\second_channel_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 2.0 | 1.0 | 10.0 | 1.0 | 9.0 | 4.0 | 9.0 | 9.0 | 10.0 | 4.0 | 3.0 | 2.0 | 3.0 | 1.0 | 9.0 | 3.0 | 8.0 | 9.0 | 7.0 | 9.0 | 4.0 | 7.0 | 10.0 | 2.0 | 6.0 | 8.0 | 4.0 | 4.0 | 10.0 | 3.0 | 2.0 | 6.0 | 5.0 | 6.0 | 4.0 | 9.0 | 10.0 | 7.0 | 6.0 | 10.0 | 7.0 | 1.0 | 2.0 |
| 1 | 2.0 | 6.0 | 9.0 | 1.0 | 2.0 | 10.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 4.0 | 2.0 | 10.0 | 10.0 | 2.0 | 10.0 | 1.0 | 9.0 | 10.0 | 7.0 | 8.0 | 7.0 | 4.0 | 10.0 | 7.0 | 6.0 | 8.0 | 1.0 | 4.0 | 4.0 | 4.0 | 8.0 | 6.0 | 8.0 | 9.0 | 3.0 | 6.0 | 6.0 | 10.0 | 10.0 | 10.0 | 2.0 | 4.0 |
| 2 | 1.0 | 9.0 | 10.0 | 3.0 | 1.0 | 2.0 | 3.0 | 1.0 | 3.0 | 3.0 | 9.0 | 7.0 | 8.0 | 2.0 | 10.0 | 2.0 | 3.0 | 3.0 | 1.0 | 2.0 | 9.0 | 8.0 | 10.0 | 6.0 | 10.0 | 8.0 | 4.0 | 5.0 | 4.0 | 1.0 | 7.0 | 5.0 | 4.0 | 7.0 | 6.0 | 2.0 | 9.0 | 2.0 | 3.0 | 10.0 | 9.0 | 3.0 | 7.0 | 8.0 |
| 3 | 10.0 | 1.0 | 3.0 | 6.0 | 9.0 | 2.0 | 3.0 | 10.0 | 8.0 | 8.0 | 2.0 | 6.0 | 2.0 | 9.0 | 7.0 | 8.0 | 1.0 | 5.0 | 10.0 | 7.0 | 8.0 | 6.0 | 5.0 | 5.0 | 9.0 | 6.0 | 4.0 | 8.0 | 2.0 | 8.0 | 4.0 | 9.0 | 4.0 | 1.0 | 4.0 | 3.0 | 3.0 | 5.0 | 7.0 | 8.0 | 4.0 | 5.0 | 8.0 | 5.0 |
| 4 | 1.0 | 2.0 | 1.0 | 9.0 | 6.0 | 3.0 | 10.0 | 6.0 | 8.0 | 8.0 | 3.0 | 8.0 | 8.0 | 6.0 | 5.0 | 5.0 | 2.0 | 1.0 | 10.0 | 6.0 | 4.0 | 4.0 | 2.0 | 10.0 | 5.0 | 8.0 | 9.0 | 10.0 | 2.0 | 8.0 | 6.0 | 10.0 | 5.0 | 2.0 | 9.0 | 6.0 | 9.0 | 4.0 | 4.0 | 9.0 | 10.0 | 5.0 | 3.0 | 1.0 |
| 5 | 9.0 | 10.0 | 2.0 | 2.0 | 3.0 | 4.0 | 4.0 | 2.0 | 3.0 | 9.0 | 5.0 | 4.0 | 2.0 | 4.0 | 1.0 | 6.0 | 2.0 | 10.0 | 9.0 | 7.0 | 7.0 | 6.0 | 6.0 | 3.0 | 7.0 | 2.0 | 10.0 | 10.0 | 5.0 | 2.0 | 9.0 | 7.0 | 10.0 | 1.0 | 10.0 | 3.0 | 5.0 | 5.0 | 5.0 | 10.0 | 9.0 | 5.0 | 7.0 | 10.0 |
| 6 | 4.0 | 2.0 | 3.0 | 3.0 | 10.0 | 4.0 | 5.0 | 10.0 | 5.0 | 8.0 | 10.0 | 8.0 | 1.0 | 8.0 | 5.0 | 8.0 | 9.0 | 3.0 | 2.0 | 9.0 | 4.0 | 5.0 | 9.0 | 4.0 | 10.0 | 8.0 | 3.0 | 4.0 | 4.0 | 4.0 | 1.0 | 1.0 | 2.0 | 6.0 | 4.0 | 3.0 | 7.0 | 3.0 | 1.0 | 9.0 | 7.0 | 2.0 | 3.0 | 5.0 |
| 7 | 9.0 | 8.0 | 1.0 | 10.0 | 6.0 | 2.0 | 10.0 | 10.0 | 7.0 | 5.0 | 7.0 | 7.0 | 8.0 | 4.0 | 7.0 | 6.0 | 9.0 | 9.0 | 5.0 | 1.0 | 9.0 | 9.0 | 5.0 | 4.0 | 10.0 | 8.0 | 3.0 | 7.0 | 5.0 | 9.0 | 8.0 | 6.0 | 3.0 | 4.0 | 6.0 | 8.0 | 4.0 | 4.0 | 2.0 | 3.0 | 3.0 | 5.0 | 3.0 | 3.0 |
| 8 | 9.0 | 5.0 | 3.0 | 8.0 | 8.0 | 3.0 | 5.0 | 7.0 | 3.0 | 5.0 | 10.0 | 9.0 | 4.0 | 10.0 | 6.0 | 7.0 | 3.0 | 2.0 | 5.0 | 8.0 | 3.0 | 5.0 | 8.0 | 1.0 | 10.0 | 1.0 | 10.0 | 8.0 | 3.0 | 10.0 | 6.0 | 1.0 | 10.0 | 9.0 | 2.0 | 10.0 | 8.0 | 8.0 | 1.0 | 3.0 | 1.0 | 6.0 | 3.0 | 5.0 |
| 9 | 10.0 | 9.0 | 3.0 | 8.0 | 8.0 | 9.0 | 8.0 | 5.0 | 5.0 | 4.0 | 4.0 | 3.0 | 4.0 | 3.0 | 6.0 | 5.0 | 3.0 | 10.0 | 10.0 | 7.0 | 9.0 | 7.0 | 8.0 | 2.0 | 1.0 | 10.0 | 8.0 | 3.0 | 4.0 | 1.0 | 7.0 | 5.0 | 7.0 | 6.0 | 4.0 | 7.0 | 7.0 | 8.0 | 7.0 | 10.0 | 6.0 | 2.0 | 4.0 | 7.0 |
| 10 | 4.0 | 9.0 | 9.0 | 2.0 | 3.0 | 5.0 | 10.0 | 7.0 | 10.0 | 4.0 | 9.0 | 9.0 | 1.0 | 4.0 | 7.0 | 8.0 | 7.0 | 4.0 | 10.0 | 9.0 | 1.0 | 5.0 | 6.0 | 1.0 | 1.0 | 9.0 | 9.0 | 1.0 | 10.0 | 8.0 | 10.0 | 2.0 | 5.0 | 8.0 | 2.0 | 2.0 | 7.0 | 7.0 | 3.0 | 1.0 | 4.0 | 3.0 | 8.0 | 2.0 |
| 11 | 3.0 | 4.0 | 7.0 | 6.0 | 8.0 | 4.0 | 8.0 | 7.0 | 9.0 | 3.0 | 9.0 | 2.0 | 1.0 | 2.0 | 3.0 | 8.0 | 4.0 | 8.0 | 6.0 | 8.0 | 8.0 | 7.0 | 7.0 | 9.0 | 2.0 | 6.0 | 8.0 | 8.0 | 5.0 | 2.0 | 3.0 | 9.0 | 4.0 | 4.0 | 7.0 | 5.0 | 2.0 | 5.0 | 6.0 | 8.0 | 1.0 | 7.0 | 2.0 | 8.0 |
| 12 | 2.0 | 2.0 | 8.0 | 2.0 | 8.0 | 2.0 | 1.0 | 8.0 | 4.0 | 4.0 | 1.0 | 1.0 | 9.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 6.0 | 3.0 | 7.0 | 2.0 | 2.0 | 1.0 | 8.0 | 2.0 | 4.0 | 2.0 | 8.0 | 4.0 | 3.0 | 10.0 | 4.0 | 3.0 | 4.0 | 9.0 | 1.0 | 4.0 | 7.0 | 5.0 | 10.0 | 2.0 | 2.0 | 5.0 |
| 13 | 3.0 | 10.0 | 2.0 | 9.0 | 6.0 | 4.0 | 8.0 | 4.0 | 10.0 | 3.0 | 4.0 | 2.0 | 4.0 | 2.0 | 2.0 | 10.0 | 1.0 | 9.0 | 9.0 | 2.0 | 2.0 | 8.0 | 4.0 | 10.0 | 6.0 | 8.0 | 4.0 | 4.0 | 6.0 | 8.0 | 9.0 | 4.0 | 2.0 | 1.0 | 3.0 | 9.0 | 10.0 | 5.0 | 2.0 | 10.0 | 3.0 | 4.0 | 2.0 | 10.0 |
| 14 | 1.0 | 10.0 | 10.0 | 7.0 | 5.0 | 1.0 | 5.0 | 7.0 | 6.0 | 6.0 | 7.0 | 3.0 | 5.0 | 2.0 | 4.0 | 3.0 | 7.0 | 2.0 | 2.0 | 9.0 | 5.0 | 1.0 | 4.0 | 3.0 | 8.0 | 6.0 | 4.0 | 6.0 | 2.0 | 6.0 | 9.0 | 6.0 | 10.0 | 2.0 | 10.0 | 9.0 | 8.0 | 7.0 | 1.0 | 10.0 | 9.0 | 10.0 | 3.0 | 5.0 |
| 15 | 9.0 | 2.0 | 2.0 | 8.0 | 5.0 | 6.0 | 8.0 | 6.0 | 7.0 | 5.0 | 8.0 | 8.0 | 6.0 | 10.0 | 3.0 | 4.0 | 9.0 | 1.0 | 9.0 | 10.0 | 9.0 | 7.0 | 10.0 | 1.0 | 10.0 | 1.0 | 10.0 | 2.0 | 8.0 | 7.0 | 2.0 | 4.0 | 3.0 | 1.0 | 9.0 | 3.0 | 9.0 | 3.0 | 6.0 | 9.0 | 4.0 | 6.0 | 7.0 | 10.0 |
| 16 | 3.0 | 10.0 | 3.0 | 1.0 | 2.0 | 2.0 | 9.0 | 9.0 | 3.0 | 3.0 | 7.0 | 4.0 | 7.0 | 1.0 | 7.0 | 9.0 | 4.0 | 9.0 | 8.0 | 5.0 | 4.0 | 3.0 | 1.0 | 8.0 | 1.0 | 4.0 | 3.0 | 3.0 | 8.0 | 6.0 | 6.0 | 7.0 | 5.0 | 7.0 | 3.0 | 3.0 | 5.0 | 5.0 | 9.0 | 3.0 | 6.0 | 1.0 | 8.0 | 9.0 |
| 17 | 8.0 | 1.0 | 3.0 | 5.0 | 1.0 | 10.0 | 3.0 | 9.0 | 2.0 | 10.0 | 4.0 | 8.0 | 8.0 | 9.0 | 2.0 | 1.0 | 9.0 | 5.0 | 6.0 | 7.0 | 5.0 | 7.0 | 5.0 | 8.0 | 4.0 | 8.0 | 10.0 | 2.0 | 5.0 | 7.0 | 9.0 | 2.0 | 4.0 | 2.0 | 3.0 | 7.0 | 8.0 | 6.0 | 1.0 | 9.0 | 6.0 | 1.0 | 4.0 | 5.0 |
| 18 | 9.0 | 9.0 | 1.0 | 10.0 | 10.0 | 9.0 | 2.0 | 5.0 | 5.0 | 10.0 | 10.0 | 6.0 | 6.0 | 9.0 | 2.0 | 9.0 | 8.0 | 6.0 | 6.0 | 7.0 | 8.0 | 9.0 | 8.0 | 8.0 | 4.0 | 3.0 | 6.0 | 1.0 | 4.0 | 4.0 | 8.0 | 6.0 | 10.0 | 9.0 | 2.0 | 1.0 | 8.0 | 7.0 | 3.0 | 10.0 | 9.0 | 8.0 | 5.0 | 7.0 |
| 19 | 7.0 | 10.0 | 2.0 | 7.0 | 6.0 | 7.0 | 9.0 | 1.0 | 8.0 | 7.0 | 9.0 | 8.0 | 3.0 | 2.0 | 9.0 | 10.0 | 5.0 | 7.0 | 7.0 | 6.0 | 9.0 | 2.0 | 7.0 | 1.0 | 6.0 | 6.0 | 10.0 | 10.0 | 8.0 | 2.0 | 3.0 | 9.0 | 1.0 | 4.0 | 3.0 | 4.0 | 5.0 | 9.0 | 9.0 | 3.0 | 4.0 | 8.0 | 1.0 | 7.0 |
| 20 | 9.0 | 7.0 | 9.0 | 8.0 | 4.0 | 7.0 | 4.0 | 9.0 | 3.0 | 9.0 | 1.0 | 8.0 | 7.0 | 2.0 | 5.0 | 9.0 | 4.0 | 5.0 | 8.0 | 9.0 | 1.0 | 2.0 | 6.0 | 7.0 | 7.0 | 6.0 | 10.0 | 8.0 | 7.0 | 2.0 | 8.0 | 10.0 | 9.0 | 4.0 | 5.0 | 4.0 | 5.0 | 10.0 | 9.0 | 1.0 | 6.0 | 3.0 | 6.0 | 5.0 |
| 21 | 4.0 | 8.0 | 8.0 | 6.0 | 4.0 | 6.0 | 5.0 | 9.0 | 5.0 | 7.0 | 5.0 | 7.0 | 2.0 | 8.0 | 1.0 | 7.0 | 3.0 | 7.0 | 9.0 | 2.0 | 2.0 | 1.0 | 6.0 | 3.0 | 3.0 | 8.0 | 10.0 | 1.0 | 9.0 | 6.0 | 9.0 | 9.0 | 9.0 | 6.0 | 3.0 | 8.0 | 7.0 | 9.0 | 3.0 | 9.0 | 6.0 | 4.0 | 9.0 | 4.0 |
| 22 | 7.0 | 7.0 | 10.0 | 5.0 | 2.0 | 6.0 | 9.0 | 5.0 | 8.0 | 8.0 | 6.0 | 7.0 | 2.0 | 4.0 | 4.0 | 10.0 | 1.0 | 5.0 | 8.0 | 7.0 | 6.0 | 6.0 | 1.0 | 10.0 | 8.0 | 2.0 | 3.0 | 7.0 | 5.0 | 3.0 | 3.0 | 1.0 | 3.0 | 7.0 | 2.0 | 9.0 | 2.0 | 6.0 | 7.0 | 9.0 | 6.0 | 9.0 | 7.0 | 3.0 |
| 23 | 10.0 | 4.0 | 6.0 | 5.0 | 10.0 | 3.0 | 4.0 | 4.0 | 1.0 | 2.0 | 1.0 | 9.0 | 1.0 | 10.0 | 3.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 7.0 | 3.0 | 10.0 | 3.0 | 1.0 | 6.0 | 1.0 | 4.0 | 2.0 | 7.0 | 10.0 | 8.0 | 8.0 | 10.0 | 5.0 | 3.0 | 10.0 | 8.0 | 8.0 | 7.0 | 10.0 | 10.0 | 7.0 | 3.0 |
| 24 | 2.0 | 10.0 | 10.0 | 9.0 | 5.0 | 7.0 | 10.0 | 10.0 | 10.0 | 1.0 | 1.0 | 2.0 | 8.0 | 6.0 | 8.0 | 10.0 | 1.0 | 4.0 | 4.0 | 6.0 | 7.0 | 3.0 | 8.0 | 1.0 | 10.0 | 1.0 | 8.0 | 10.0 | 2.0 | 6.0 | 3.0 | 5.0 | 4.0 | 5.0 | 8.0 | 4.0 | 10.0 | 9.0 | 1.0 | 4.0 | 8.0 | 5.0 | 6.0 | 2.0 |
| 25 | 6.0 | 7.0 | 8.0 | 6.0 | 8.0 | 2.0 | 8.0 | 8.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 8.0 | 6.0 | 1.0 | 4.0 | 8.0 | 3.0 | 6.0 | 6.0 | 8.0 | 2.0 | 6.0 | 1.0 | 5.0 | 9.0 | 4.0 | 10.0 | 4.0 | 6.0 | 3.0 | 9.0 | 6.0 | 9.0 | 10.0 | 10.0 | 4.0 | 9.0 | 2.0 | 6.0 | 3.0 | 2.0 | 9.0 |
| 26 | 8.0 | 6.0 | 4.0 | 4.0 | 9.0 | 10.0 | 3.0 | 3.0 | 10.0 | 8.0 | 9.0 | 8.0 | 4.0 | 4.0 | 4.0 | 10.0 | 3.0 | 10.0 | 6.0 | 10.0 | 10.0 | 10.0 | 3.0 | 1.0 | 8.0 | 9.0 | 6.0 | 10.0 | 8.0 | 8.0 | 7.0 | 8.0 | 7.0 | 3.0 | 10.0 | 8.0 | 4.0 | 3.0 | 5.0 | 4.0 | 8.0 | 3.0 | 7.0 | 9.0 |
| 27 | 4.0 | 8.0 | 5.0 | 8.0 | 10.0 | 10.0 | 4.0 | 7.0 | 8.0 | 3.0 | 1.0 | 8.0 | 2.0 | 4.0 | 6.0 | 2.0 | 3.0 | 2.0 | 1.0 | 10.0 | 8.0 | 1.0 | 7.0 | 4.0 | 10.0 | 4.0 | 10.0 | 7.0 | 8.0 | 7.0 | 3.0 | 4.0 | 1.0 | 7.0 | 10.0 | 8.0 | 3.0 | 10.0 | 1.0 | 9.0 | 1.0 | 1.0 | 10.0 | 6.0 |
| 28 | 4.0 | 1.0 | 4.0 | 2.0 | 2.0 | 5.0 | 4.0 | 5.0 | 3.0 | 4.0 | 10.0 | 5.0 | 8.0 | 6.0 | 2.0 | 8.0 | 8.0 | 5.0 | 4.0 | 8.0 | 7.0 | 9.0 | 5.0 | 2.0 | 2.0 | 10.0 | 8.0 | 8.0 | 9.0 | 6.0 | 7.0 | 1.0 | 7.0 | 3.0 | 7.0 | 9.0 | 4.0 | 7.0 | 9.0 | 4.0 | 3.0 | 5.0 | 9.0 | 10.0 |
| 29 | 10.0 | 4.0 | 1.0 | 8.0 | 8.0 | 2.0 | 4.0 | 9.0 | 10.0 | 1.0 | 8.0 | 2.0 | 4.0 | 8.0 | 6.0 | 7.0 | 6.0 | 7.0 | 4.0 | 2.0 | 2.0 | 6.0 | 3.0 | 7.0 | 6.0 | 4.0 | 8.0 | 7.0 | 6.0 | 10.0 | 3.0 | 3.0 | 5.0 | 4.0 | 9.0 | 8.0 | 9.0 | 6.0 | 9.0 | 4.0 | 8.0 | 2.0 | 3.0 | 9.0 |
| 30 | 3.0 | 4.0 | 7.0 | 4.0 | 6.0 | 9.0 | 1.0 | 8.0 | 6.0 | 7.0 | 10.0 | 3.0 | 3.0 | 9.0 | 9.0 | 2.0 | 6.0 | 9.0 | 8.0 | 3.0 | 8.0 | 9.0 | 3.0 | 10.0 | 3.0 | 6.0 | 7.0 | 3.0 | 7.0 | 3.0 | 1.0 | 5.0 | 7.0 | 8.0 | 1.0 | 8.0 | 1.0 | 2.0 | 9.0 | 4.0 | 7.0 | 2.0 | 7.0 | 1.0 |
| 31 | 2.0 | 4.0 | 5.0 | 9.0 | 10.0 | 7.0 | 1.0 | 6.0 | 1.0 | 5.0 | 2.0 | 9.0 | 10.0 | 4.0 | 6.0 | 4.0 | 7.0 | 2.0 | 6.0 | 9.0 | 10.0 | 9.0 | 1.0 | 8.0 | 5.0 | 3.0 | 8.0 | 4.0 | 1.0 | 3.0 | 5.0 | 6.0 | 8.0 | 3.0 | 3.0 | 8.0 | 1.0 | 8.0 | 8.0 | 10.0 | 9.0 | 2.0 | 7.0 | 9.0 |
| 32 | 6.0 | 8.0 | 4.0 | 4.0 | 5.0 | 10.0 | 2.0 | 3.0 | 10.0 | 7.0 | 5.0 | 4.0 | 4.0 | 2.0 | 10.0 | 3.0 | 5.0 | 4.0 | 10.0 | 1.0 | 9.0 | 9.0 | 3.0 | 8.0 | 4.0 | 9.0 | 7.0 | 1.0 | 7.0 | 5.0 | 7.0 | 8.0 | 9.0 | 10.0 | 9.0 | 7.0 | 2.0 | 8.0 | 2.0 | 2.0 | 8.0 | 2.0 | 2.0 | 3.0 |
| 33 | 5.0 | 6.0 | 7.0 | 1.0 | 2.0 | 1.0 | 6.0 | 4.0 | 9.0 | 6.0 | 8.0 | 4.0 | 3.0 | 1.0 | 2.0 | 1.0 | 7.0 | 2.0 | 9.0 | 4.0 | 4.0 | 6.0 | 7.0 | 10.0 | 5.0 | 6.0 | 3.0 | 7.0 | 3.0 | 4.0 | 8.0 | 3.0 | 10.0 | 8.0 | 9.0 | 10.0 | 5.0 | 8.0 | 1.0 | 6.0 | 9.0 | 3.0 | 1.0 | 9.0 |
| 34 | 6.0 | 8.0 | 6.0 | 4.0 | 9.0 | 10.0 | 4.0 | 6.0 | 2.0 | 4.0 | 2.0 | 7.0 | 4.0 | 3.0 | 10.0 | 9.0 | 3.0 | 3.0 | 2.0 | 3.0 | 5.0 | 3.0 | 2.0 | 5.0 | 8.0 | 9.0 | 10.0 | 10.0 | 7.0 | 9.0 | 1.0 | 3.0 | 9.0 | 9.0 | 1.0 | 1.0 | 7.0 | 9.0 | 6.0 | 3.0 | 7.0 | 2.0 | 1.0 | 1.0 |
| 35 | 4.0 | 9.0 | 2.0 | 3.0 | 6.0 | 3.0 | 3.0 | 8.0 | 10.0 | 7.0 | 2.0 | 5.0 | 9.0 | 9.0 | 9.0 | 3.0 | 3.0 | 7.0 | 1.0 | 4.0 | 4.0 | 8.0 | 9.0 | 3.0 | 4.0 | 10.0 | 8.0 | 8.0 | 9.0 | 8.0 | 8.0 | 8.0 | 7.0 | 10.0 | 1.0 | 10.0 | 4.0 | 1.0 | 8.0 | 4.0 | 2.0 | 1.0 | 2.0 | 10.0 |
| 36 | 9.0 | 3.0 | 9.0 | 3.0 | 9.0 | 5.0 | 7.0 | 4.0 | 8.0 | 7.0 | 7.0 | 2.0 | 1.0 | 10.0 | 8.0 | 9.0 | 5.0 | 8.0 | 8.0 | 5.0 | 5.0 | 7.0 | 2.0 | 10.0 | 10.0 | 10.0 | 4.0 | 3.0 | 4.0 | 9.0 | 1.0 | 1.0 | 2.0 | 5.0 | 7.0 | 4.0 | 9.0 | 5.0 | 2.0 | 9.0 | 8.0 | 5.0 | 9.0 | 6.0 |
| 37 | 10.0 | 6.0 | 2.0 | 5.0 | 4.0 | 5.0 | 3.0 | 4.0 | 8.0 | 8.0 | 7.0 | 5.0 | 4.0 | 5.0 | 7.0 | 3.0 | 5.0 | 6.0 | 7.0 | 9.0 | 10.0 | 9.0 | 6.0 | 8.0 | 9.0 | 4.0 | 3.0 | 10.0 | 7.0 | 6.0 | 2.0 | 8.0 | 8.0 | 8.0 | 9.0 | 1.0 | 5.0 | 8.0 | 2.0 | 3.0 | 1.0 | 2.0 | 9.0 | 6.0 |
| 38 | 7.0 | 6.0 | 3.0 | 7.0 | 4.0 | 5.0 | 1.0 | 2.0 | 1.0 | 7.0 | 3.0 | 6.0 | 7.0 | 2.0 | 1.0 | 6.0 | 9.0 | 1.0 | 3.0 | 9.0 | 9.0 | 3.0 | 7.0 | 8.0 | 1.0 | 9.0 | 5.0 | 1.0 | 9.0 | 9.0 | 9.0 | 8.0 | 2.0 | 1.0 | 6.0 | 8.0 | 2.0 | 2.0 | 2.0 | 3.0 | 1.0 | 8.0 | 8.0 | 4.0 |
| 39 | 6.0 | 10.0 | 10.0 | 8.0 | 9.0 | 10.0 | 9.0 | 3.0 | 3.0 | 10.0 | 1.0 | 8.0 | 5.0 | 10.0 | 10.0 | 9.0 | 3.0 | 9.0 | 10.0 | 3.0 | 1.0 | 9.0 | 9.0 | 7.0 | 4.0 | 2.0 | 4.0 | 9.0 | 4.0 | 4.0 | 4.0 | 10.0 | 2.0 | 6.0 | 3.0 | 4.0 | 9.0 | 3.0 | 3.0 | 7.0 | 10.0 | 9.0 | 3.0 | 1.0 |
| 40 | 10.0 | 10.0 | 9.0 | 4.0 | 10.0 | 9.0 | 7.0 | 3.0 | 1.0 | 6.0 | 4.0 | 1.0 | 10.0 | 3.0 | 9.0 | 4.0 | 6.0 | 6.0 | 9.0 | 4.0 | 6.0 | 6.0 | 6.0 | 10.0 | 8.0 | 6.0 | 8.0 | 1.0 | 3.0 | 8.0 | 7.0 | 9.0 | 8.0 | 9.0 | 7.0 | 2.0 | 8.0 | 1.0 | 1.0 | 10.0 | 2.0 | 1.0 | 9.0 | 7.0 |
| 41 | 7.0 | 10.0 | 3.0 | 5.0 | 5.0 | 5.0 | 2.0 | 5.0 | 6.0 | 2.0 | 3.0 | 7.0 | 2.0 | 4.0 | 10.0 | 6.0 | 1.0 | 1.0 | 8.0 | 8.0 | 3.0 | 4.0 | 9.0 | 10.0 | 5.0 | 3.0 | 3.0 | 1.0 | 5.0 | 2.0 | 2.0 | 2.0 | 2.0 | 3.0 | 2.0 | 1.0 | 5.0 | 2.0 | 8.0 | 9.0 | 1.0 | 8.0 | 9.0 | 6.0 |
| 42 | 1.0 | 2.0 | 7.0 | 8.0 | 3.0 | 7.0 | 3.0 | 3.0 | 3.0 | 4.0 | 8.0 | 2.0 | 2.0 | 2.0 | 3.0 | 7.0 | 8.0 | 4.0 | 5.0 | 1.0 | 6.0 | 9.0 | 7.0 | 7.0 | 6.0 | 2.0 | 7.0 | 10.0 | 9.0 | 3.0 | 7.0 | 7.0 | 2.0 | 1.0 | 1.0 | 2.0 | 9.0 | 9.0 | 8.0 | 3.0 | 9.0 | 9.0 | 3.0 | 2.0 |
| 43 | 2.0 | 4.0 | 8.0 | 5.0 | 1.0 | 10.0 | 5.0 | 3.0 | 5.0 | 7.0 | 2.0 | 8.0 | 5.0 | 10.0 | 5.0 | 10.0 | 9.0 | 5.0 | 7.0 | 7.0 | 5.0 | 4.0 | 3.0 | 3.0 | 2.0 | 9.0 | 9.0 | 6.0 | 10.0 | 9.0 | 1.0 | 9.0 | 3.0 | 9.0 | 1.0 | 10.0 | 6.0 | 6.0 | 4.0 | 1.0 | 7.0 | 6.0 | 2.0 | 5.0 |

Also, when you send your chosen route back, please use the little JSON layout below so it's easy to parse — just a single top-level object with a solution array containing the visited locations in order.

{
  ""solution"": []
}

This JSON is just a simple sketch: ""solution"" should hold a list of the place names (nodes) you visit from the entrance to the pier, in order. Keep it casual — just the locations, nothing about channel IDs, costs, or surcharges. The JSON above shows the shape your answer should follow, but it's not the actual path.

One important note: use the exact identifiers from the problem input with no renaming and no new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'edges': [{'from': 15, 'to': 0, 'var_index': 0}, {'from': 15, 'to': 1, 'var_index': 1}, {'from': 15, 'to': 2, 'var_index': 2}, {'from': 15, 'to': 3, 'var_index': 3}, {'from': 15, 'to': 4, 'var_index': 4}, {'from': 15, 'to': 5, 'var_index': 5}, {'from': 15, 'to': 6, 'var_index': 6}, {'from': 15, 'to': 7, 'var_index': 7}, {'from': 15, 'to': 8, 'var_index': 8}, {'from': 15, 'to': 9, 'var_index': 9}, {'from': 15, 'to': 10, 'var_index': 10}, {'from': 15, 'to': 11, 'var_index': 11}, {'from': 15, 'to': 12, 'var_index': 12}, {'from': 15, 'to': 13, 'var_index': 13}, {'from': 15, 'to': 14, 'var_index': 14}, {'from': 0, 'to': 16, 'var_index': 15}, {'from': 1, 'to': 16, 'var_index': 16}, {'from': 2, 'to': 16, 'var_index': 17}, {'from': 3, 'to': 16, 'var_index': 18}, {'from': 4, 'to': 16, 'var_index': 19}, {'from': 5, 'to': 16, 'var_index': 20}, {'from': 6, 'to': 16, 'var_index': 21}, {'from': 7, 'to': 16, 'var_index': 22}, {'from': 8, 'to': 16, 'var_index': 23}, {'from': 9, 'to': 16, 'var_index': 24}, {'from': 10, 'to': 16, 'var_index': 25}, {'from': 11, 'to': 16, 'var_index': 26}, {'from': 12, 'to': 16, 'var_index': 27}, {'from': 13, 'to': 16, 'var_index': 28}, {'from': 14, 'to': 16, 'var_index': 29}, {'from': 0, 'to': 1, 'var_index': 30}, {'from': 1, 'to': 2, 'var_index': 31}, {'from': 2, 'to': 3, 'var_index': 32}, {'from': 3, 'to': 4, 'var_index': 33}, {'from': 4, 'to': 5, 'var_index': 34}, {'from': 5, 'to': 6, 'var_index': 35}, {'from': 6, 'to': 7, 'var_index': 36}, {'from': 7, 'to': 8, 'var_index': 37}, {'from': 8, 'to': 9, 'var_index': 38}, {'from': 9, 'to': 10, 'var_index': 39}, {'from': 10, 'to': 11, 'var_index': 40}, {'from': 11, 'to': 12, 'var_index': 41}, {'from': 12, 'to': 13, 'var_index': 42}, {'from': 13, 'to': 14, 'var_index': 43}], 'objective': {'constant': 0.0, 'linear': [5.0, 1.0, 9.0, 6.0, 6.0, 4.0, 4.0, 1.0, 4.0, 6.0, 10.0, 4.0, 9.0, 5.0, 6.0, 9.0, 2.0, 6.0, 5.0, 6.0, 2.0, 6.0, 3.0, 6.0, 4.0, 5.0, 10.0, 1.0, 8.0, 10.0, 5.0, 10.0, 9.0, 9.0, 2.0, 5.0, 10.0, 5.0, 4.0, 5.0, 3.0, 5.0, 7.0, 7.0], 'quadratic': [[10.0, 2.0, 1.0, 10.0, 1.0, 9.0, 4.0, 9.0, 9.0, 10.0, 4.0, 3.0, 2.0, 3.0, 1.0, 9.0, 3.0, 8.0, 9.0, 7.0, 9.0, 4.0, 7.0, 10.0, 2.0, 6.0, 8.0, 4.0, 4.0, 10.0, 3.0, 2.0, 6.0, 5.0, 6.0, 4.0, 9.0, 10.0, 7.0, 6.0, 10.0, 7.0, 1.0, 2.0], [2.0, 6.0, 9.0, 1.0, 2.0, 10.0, 2.0, 8.0, 5.0, 9.0, 9.0, 4.0, 2.0, 10.0, 10.0, 2.0, 10.0, 1.0, 9.0, 10.0, 7.0, 8.0, 7.0, 4.0, 10.0, 7.0, 6.0, 8.0, 1.0, 4.0, 4.0, 4.0, 8.0, 6.0, 8.0, 9.0, 3.0, 6.0, 6.0, 10.0, 10.0, 10.0, 2.0, 4.0], [1.0, 9.0, 10.0, 3.0, 1.0, 2.0, 3.0, 1.0, 3.0, 3.0, 9.0, 7.0, 8.0, 2.0, 10.0, 2.0, 3.0, 3.0, 1.0, 2.0, 9.0, 8.0, 10.0, 6.0, 10.0, 8.0, 4.0, 5.0, 4.0, 1.0, 7.0, 5.0, 4.0, 7.0, 6.0, 2.0, 9.0, 2.0, 3.0, 10.0, 9.0, 3.0, 7.0, 8.0], [10.0, 1.0, 3.0, 6.0, 9.0, 2.0, 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'quadratic_cost': 2.0}, {'var_i': 42, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 42, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 42, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 42, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 42, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 42, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 42, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 42, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 42, 'var_j': 26, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 42, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 29, 'quadratic_cost': 3.0}, {'var_i': 42, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 42, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 42, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 42, 'var_j': 34, 'quadratic_cost': 1.0}, {'var_i': 42, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 42, 'var_j': 36, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 37, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 38, 'quadratic_cost': 8.0}, {'var_i': 42, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 42, 'var_j': 40, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 41, 'quadratic_cost': 9.0}, {'var_i': 42, 'var_j': 42, 'quadratic_cost': 3.0}, {'var_i': 42, 'var_j': 43, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 43, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 43, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 43, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 43, 'var_j': 33, 'quadratic_cost': 9.0}, {'var_i': 43, 'var_j': 34, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 35, 'quadratic_cost': 10.0}, {'var_i': 43, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 37, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 38, 'quadratic_cost': 4.0}, {'var_i': 43, 'var_j': 39, 'quadratic_cost': 1.0}, {'var_i': 43, 'var_j': 40, 'quadratic_cost': 7.0}, {'var_i': 43, 'var_j': 41, 'quadratic_cost': 6.0}, {'var_i': 43, 'var_j': 42, 'quadratic_cost': 2.0}, {'var_i': 43, 'var_j': 43, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 16, 'to': 1, 'var_index': 0}, {'from': 16, 'to': 2, 'var_index': 1}, {'from': 16, 'to': 3, 'var_index': 2}, {'from': 16, 'to': 4, 'var_index': 3}, {'from': 16, 'to': 5, 'var_index': 4}, {'from': 16, 'to': 6, 'var_index': 5}, {'from': 16, 'to': 7, 'var_index': 6}, {'from': 16, 'to': 8, 'var_index': 7}, {'from': 16, 'to': 9, 'var_index': 8}, {'from': 16, 'to': 10, 'var_index': 9}, {'from': 16, 'to': 11, 'var_index': 10}, {'from': 16, 'to': 12, 'var_index': 11}, {'from': 16, 'to': 13, 'var_index': 12}, {'from': 16, 'to': 14, 'var_index': 13}, {'from': 16, 'to': 15, 'var_index': 14}, {'from': 1, 'to': 17, 'var_index': 15}, {'from': 2, 'to': 17, 'var_index': 16}, {'from': 3, 'to': 17, 'var_index': 17}, {'from': 4, 'to': 17, 'var_index': 18}, {'from': 5, 'to': 17, 'var_index': 19}, {'from': 6, 'to': 17, 'var_index': 20}, {'from': 7, 'to': 17, 'var_index': 21}, {'from': 8, 'to': 17, 'var_index': 22}, {'from': 9, 'to': 17, 'var_index': 23}, {'from': 10, 'to': 17, 'var_index': 24}, {'from': 11, 'to': 17, 'var_index': 25}, {'from': 12, 'to': 17, 'var_index': 26}, {'from': 13, 'to': 17, 'var_index': 27}, {'from': 14, 'to': 17, 'var_index': 28}, {'from': 15, 'to': 17, 'var_index': 29}, {'from': 1, 'to': 2, 'var_index': 30}, {'from': 2, 'to': 3, 'var_index': 31}, {'from': 3, 'to': 4, 'var_index': 32}, {'from': 4, 'to': 5, 'var_index': 33}, {'from': 5, 'to': 6, 'var_index': 34}, {'from': 6, 'to': 7, 'var_index': 35}, {'from': 7, 'to': 8, 'var_index': 36}, {'from': 8, 'to': 9, 'var_index': 37}, {'from': 9, 'to': 10, 'var_index': 38}, {'from': 10, 'to': 11, 'var_index': 39}, {'from': 11, 'to': 12, 'var_index': 40}, {'from': 12, 'to': 13, 'var_index': 41}, {'from': 13, 'to': 14, 'var_index': 42}, {'from': 14, 'to': 15, 'var_index': 43}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17}}","[16, 9, 17]",25,json,1
QSPP,QSPP,"I was asked to send a single maintenance crew from the gate to the machinery room using only the approved one-way service corridors. The crew has to pick one continuous route that follows the arrows from start to finish — no side trips, no skipping segments, and the route must begin at the gate and end at the machinery room. Each corridor has a regular access charge and also its own little surcharge just for being used, and some specific pairs of corridors add extra fees when both are taken (sometimes the extra depends on which corridor comes first). The goal is to pick the route that makes the total bill as small as possible by adding up each corridor’s access charge, any per-corridor surcharges, and every extra fee caused by any used corridor pairs. The exact layout and numbers will be shown below.

Below are the 25 locations, the 40 one-way corridors, the list of location IDs 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, the gate at 0, and the machinery room at 24.

| corridor_from | corridor_to | corridor_id |
|---|---|---|
| 0 | 1 | 0 |
| 0 | 5 | 1 |
| 1 | 2 | 2 |
| 1 | 6 | 3 |
| 2 | 3 | 4 |
| 2 | 7 | 5 |
| 3 | 4 | 6 |
| 3 | 8 | 7 |
| 4 | 9 | 8 |
| 5 | 6 | 9 |
| 5 | 10 | 10 |
| 6 | 7 | 11 |
| 6 | 11 | 12 |
| 7 | 8 | 13 |
| 7 | 12 | 14 |
| 8 | 9 | 15 |
| 8 | 13 | 16 |
| 9 | 14 | 17 |
| 10 | 11 | 18 |
| 10 | 15 | 19 |
| 11 | 12 | 20 |
| 11 | 16 | 21 |
| 12 | 13 | 22 |
| 12 | 17 | 23 |
| 13 | 14 | 24 |
| 13 | 18 | 25 |
| 14 | 19 | 26 |
| 15 | 16 | 27 |
| 15 | 20 | 28 |
| 16 | 17 | 29 |
| 16 | 21 | 30 |
| 17 | 18 | 31 |
| 17 | 22 | 32 |
| 18 | 19 | 33 |
| 18 | 23 | 34 |
| 19 | 24 | 35 |
| 20 | 21 | 36 |
| 21 | 22 | 37 |
| 22 | 23 | 38 |
| 23 | 24 | 39 |

| corridor_id | access_charge |
|---|---|
| 0 | 5.0 |
| 1 | 2.0 |
| 2 | 10.0 |
| 3 | 9.0 |
| 4 | 8.0 |
| 5 | 5.0 |
| 6 | 4.0 |
| 7 | 3.0 |
| 8 | 10.0 |
| 9 | 6.0 |
| 10 | 9.0 |
| 11 | 2.0 |
| 12 | 7.0 |
| 13 | 1.0 |
| 14 | 9.0 |
| 15 | 6.0 |
| 16 | 2.0 |
| 17 | 2.0 |
| 18 | 5.0 |
| 19 | 10.0 |
| 20 | 10.0 |
| 21 | 7.0 |
| 22 | 2.0 |
| 23 | 9.0 |
| 24 | 5.0 |
| 25 | 6.0 |
| 26 | 8.0 |
| 27 | 8.0 |
| 28 | 8.0 |
| 29 | 8.0 |
| 30 | 5.0 |
| 31 | 10.0 |
| 32 | 6.0 |
| 33 | 9.0 |
| 34 | 9.0 |
| 35 | 1.0 |
| 36 | 7.0 |
| 37 | 4.0 |
| 38 | 5.0 |
| 39 | 6.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 8.0 | 2.0 | 5.0 | 3.0 | 8.0 | 5.0 | 7.0 | 8.0 | 9.0 | 2.0 | 10.0 | 10.0 | 4.0 | 4.0 | 10.0 | 3.0 | 6.0 | 5.0 | 6.0 | 5.0 | 5.0 | 4.0 | 9.0 | 8.0 | 8.0 | 4.0 | 9.0 | 10.0 | 3.0 | 1.0 | 6.0 | 9.0 | 2.0 | 9.0 | 8.0 | 9.0 | 4.0 | 9.0 | 6.0 |
| 1 | 8.0 | 3.0 | 4.0 | 7.0 | 4.0 | 9.0 | 9.0 | 6.0 | 3.0 | 8.0 | 3.0 | 7.0 | 8.0 | 2.0 | 6.0 | 5.0 | 5.0 | 3.0 | 9.0 | 10.0 | 3.0 | 1.0 | 2.0 | 5.0 | 3.0 | 8.0 | 5.0 | 5.0 | 8.0 | 7.0 | 7.0 | 10.0 | 1.0 | 6.0 | 6.0 | 1.0 | 6.0 | 3.0 | 7.0 | 5.0 |
| 2 | 2.0 | 4.0 | 4.0 | 3.0 | 6.0 | 8.0 | 8.0 | 5.0 | 7.0 | 5.0 | 7.0 | 8.0 | 7.0 | 7.0 | 9.0 | 2.0 | 7.0 | 3.0 | 2.0 | 6.0 | 3.0 | 9.0 | 10.0 | 10.0 | 2.0 | 2.0 | 5.0 | 9.0 | 8.0 | 1.0 | 1.0 | 6.0 | 2.0 | 9.0 | 1.0 | 4.0 | 3.0 | 4.0 | 5.0 | 9.0 |
| 3 | 5.0 | 7.0 | 3.0 | 2.0 | 5.0 | 1.0 | 4.0 | 1.0 | 8.0 | 7.0 | 7.0 | 9.0 | 5.0 | 10.0 | 7.0 | 8.0 | 4.0 | 3.0 | 6.0 | 10.0 | 5.0 | 2.0 | 10.0 | 9.0 | 2.0 | 5.0 | 1.0 | 8.0 | 9.0 | 9.0 | 5.0 | 8.0 | 6.0 | 1.0 | 2.0 | 10.0 | 3.0 | 5.0 | 5.0 | 6.0 |
| 4 | 3.0 | 4.0 | 6.0 | 5.0 | 5.0 | 5.0 | 8.0 | 2.0 | 6.0 | 1.0 | 10.0 | 7.0 | 10.0 | 3.0 | 3.0 | 9.0 | 7.0 | 2.0 | 4.0 | 7.0 | 2.0 | 2.0 | 4.0 | 2.0 | 5.0 | 1.0 | 8.0 | 2.0 | 7.0 | 2.0 | 4.0 | 4.0 | 8.0 | 1.0 | 7.0 | 5.0 | 8.0 | 10.0 | 7.0 | 3.0 |
| 5 | 8.0 | 9.0 | 8.0 | 1.0 | 5.0 | 10.0 | 8.0 | 3.0 | 6.0 | 9.0 | 5.0 | 6.0 | 9.0 | 6.0 | 4.0 | 4.0 | 3.0 | 2.0 | 10.0 | 2.0 | 1.0 | 2.0 | 7.0 | 5.0 | 6.0 | 6.0 | 5.0 | 10.0 | 6.0 | 7.0 | 9.0 | 9.0 | 1.0 | 5.0 | 10.0 | 6.0 | 8.0 | 2.0 | 5.0 | 8.0 |
| 6 | 5.0 | 9.0 | 8.0 | 4.0 | 8.0 | 8.0 | 9.0 | 9.0 | 8.0 | 2.0 | 1.0 | 3.0 | 8.0 | 5.0 | 10.0 | 5.0 | 10.0 | 6.0 | 1.0 | 2.0 | 3.0 | 1.0 | 4.0 | 5.0 | 7.0 | 8.0 | 2.0 | 7.0 | 9.0 | 8.0 | 8.0 | 7.0 | 6.0 | 6.0 | 10.0 | 10.0 | 1.0 | 7.0 | 10.0 | 6.0 |
| 7 | 7.0 | 6.0 | 5.0 | 1.0 | 2.0 | 3.0 | 9.0 | 7.0 | 3.0 | 2.0 | 4.0 | 10.0 | 1.0 | 3.0 | 7.0 | 7.0 | 4.0 | 10.0 | 3.0 | 8.0 | 6.0 | 2.0 | 2.0 | 5.0 | 2.0 | 6.0 | 5.0 | 9.0 | 9.0 | 7.0 | 9.0 | 10.0 | 2.0 | 4.0 | 10.0 | 4.0 | 3.0 | 8.0 | 4.0 | 4.0 |
| 8 | 8.0 | 3.0 | 7.0 | 8.0 | 6.0 | 6.0 | 8.0 | 3.0 | 2.0 | 2.0 | 10.0 | 9.0 | 3.0 | 1.0 | 2.0 | 6.0 | 1.0 | 6.0 | 3.0 | 10.0 | 6.0 | 8.0 | 4.0 | 9.0 | 4.0 | 10.0 | 1.0 | 10.0 | 7.0 | 5.0 | 9.0 | 8.0 | 4.0 | 4.0 | 6.0 | 5.0 | 3.0 | 8.0 | 8.0 | 9.0 |
| 9 | 9.0 | 8.0 | 5.0 | 7.0 | 1.0 | 9.0 | 2.0 | 2.0 | 2.0 | 1.0 | 3.0 | 10.0 | 9.0 | 1.0 | 2.0 | 4.0 | 10.0 | 5.0 | 9.0 | 7.0 | 7.0 | 7.0 | 1.0 | 2.0 | 9.0 | 8.0 | 3.0 | 4.0 | 2.0 | 2.0 | 9.0 | 10.0 | 9.0 | 9.0 | 10.0 | 2.0 | 7.0 | 4.0 | 9.0 | 8.0 |
| 10 | 2.0 | 3.0 | 7.0 | 7.0 | 10.0 | 5.0 | 1.0 | 4.0 | 10.0 | 3.0 | 1.0 | 8.0 | 10.0 | 1.0 | 2.0 | 8.0 | 5.0 | 8.0 | 7.0 | 6.0 | 4.0 | 4.0 | 2.0 | 3.0 | 4.0 | 4.0 | 3.0 | 3.0 | 8.0 | 9.0 | 9.0 | 5.0 | 2.0 | 8.0 | 2.0 | 3.0 | 8.0 | 1.0 | 4.0 | 2.0 |
| 11 | 10.0 | 7.0 | 8.0 | 9.0 | 7.0 | 6.0 | 3.0 | 10.0 | 9.0 | 10.0 | 8.0 | 10.0 | 3.0 | 7.0 | 8.0 | 10.0 | 1.0 | 3.0 | 3.0 | 3.0 | 10.0 | 3.0 | 5.0 | 3.0 | 4.0 | 10.0 | 7.0 | 10.0 | 4.0 | 7.0 | 2.0 | 10.0 | 5.0 | 5.0 | 6.0 | 6.0 | 8.0 | 1.0 | 1.0 | 5.0 |
| 12 | 10.0 | 8.0 | 7.0 | 5.0 | 10.0 | 9.0 | 8.0 | 1.0 | 3.0 | 9.0 | 10.0 | 3.0 | 8.0 | 6.0 | 2.0 | 10.0 | 6.0 | 3.0 | 2.0 | 5.0 | 3.0 | 8.0 | 9.0 | 10.0 | 5.0 | 2.0 | 7.0 | 3.0 | 9.0 | 2.0 | 2.0 | 6.0 | 1.0 | 5.0 | 10.0 | 8.0 | 9.0 | 9.0 | 2.0 | 2.0 |
| 13 | 4.0 | 2.0 | 7.0 | 10.0 | 3.0 | 6.0 | 5.0 | 3.0 | 1.0 | 1.0 | 1.0 | 7.0 | 6.0 | 7.0 | 7.0 | 8.0 | 7.0 | 6.0 | 10.0 | 5.0 | 2.0 | 8.0 | 6.0 | 4.0 | 2.0 | 8.0 | 7.0 | 8.0 | 2.0 | 9.0 | 5.0 | 6.0 | 4.0 | 7.0 | 7.0 | 5.0 | 1.0 | 4.0 | 9.0 | 2.0 |
| 14 | 4.0 | 6.0 | 9.0 | 7.0 | 3.0 | 4.0 | 10.0 | 7.0 | 2.0 | 2.0 | 2.0 | 8.0 | 2.0 | 7.0 | 7.0 | 8.0 | 8.0 | 1.0 | 4.0 | 5.0 | 6.0 | 2.0 | 5.0 | 7.0 | 7.0 | 3.0 | 3.0 | 8.0 | 3.0 | 10.0 | 6.0 | 7.0 | 6.0 | 8.0 | 10.0 | 7.0 | 1.0 | 7.0 | 2.0 | 10.0 |
| 15 | 10.0 | 5.0 | 2.0 | 8.0 | 9.0 | 4.0 | 5.0 | 7.0 | 6.0 | 4.0 | 8.0 | 10.0 | 10.0 | 8.0 | 8.0 | 6.0 | 3.0 | 8.0 | 9.0 | 5.0 | 5.0 | 6.0 | 5.0 | 8.0 | 6.0 | 2.0 | 7.0 | 2.0 | 9.0 | 3.0 | 9.0 | 7.0 | 10.0 | 6.0 | 10.0 | 5.0 | 10.0 | 3.0 | 5.0 | 9.0 |
| 16 | 3.0 | 5.0 | 7.0 | 4.0 | 7.0 | 3.0 | 10.0 | 4.0 | 1.0 | 10.0 | 5.0 | 1.0 | 6.0 | 7.0 | 8.0 | 3.0 | 10.0 | 8.0 | 6.0 | 3.0 | 10.0 | 3.0 | 2.0 | 1.0 | 2.0 | 9.0 | 5.0 | 10.0 | 4.0 | 10.0 | 4.0 | 9.0 | 8.0 | 3.0 | 3.0 | 8.0 | 1.0 | 1.0 | 5.0 | 4.0 |
| 17 | 6.0 | 3.0 | 3.0 | 3.0 | 2.0 | 2.0 | 6.0 | 10.0 | 6.0 | 5.0 | 8.0 | 3.0 | 3.0 | 6.0 | 1.0 | 8.0 | 8.0 | 5.0 | 2.0 | 1.0 | 3.0 | 4.0 | 8.0 | 4.0 | 9.0 | 1.0 | 1.0 | 5.0 | 10.0 | 1.0 | 5.0 | 7.0 | 7.0 | 9.0 | 3.0 | 3.0 | 6.0 | 5.0 | 6.0 | 10.0 |
| 18 | 5.0 | 9.0 | 2.0 | 6.0 | 4.0 | 10.0 | 1.0 | 3.0 | 3.0 | 9.0 | 7.0 | 3.0 | 2.0 | 10.0 | 4.0 | 9.0 | 6.0 | 2.0 | 10.0 | 1.0 | 5.0 | 5.0 | 5.0 | 5.0 | 8.0 | 3.0 | 10.0 | 3.0 | 6.0 | 10.0 | 10.0 | 4.0 | 8.0 | 3.0 | 2.0 | 2.0 | 4.0 | 7.0 | 2.0 | 2.0 |
| 19 | 6.0 | 10.0 | 6.0 | 10.0 | 7.0 | 2.0 | 2.0 | 8.0 | 10.0 | 7.0 | 6.0 | 3.0 | 5.0 | 5.0 | 5.0 | 5.0 | 3.0 | 1.0 | 1.0 | 9.0 | 7.0 | 2.0 | 7.0 | 4.0 | 3.0 | 6.0 | 10.0 | 7.0 | 3.0 | 3.0 | 3.0 | 5.0 | 9.0 | 3.0 | 5.0 | 4.0 | 8.0 | 4.0 | 4.0 | 5.0 |
| 20 | 5.0 | 3.0 | 3.0 | 5.0 | 2.0 | 1.0 | 3.0 | 6.0 | 6.0 | 7.0 | 4.0 | 10.0 | 3.0 | 2.0 | 6.0 | 5.0 | 10.0 | 3.0 | 5.0 | 7.0 | 3.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 3.0 | 2.0 | 1.0 | 2.0 | 6.0 | 6.0 | 6.0 | 2.0 | 7.0 | 10.0 | 4.0 | 5.0 | 7.0 | 4.0 |
| 21 | 5.0 | 1.0 | 9.0 | 2.0 | 2.0 | 2.0 | 1.0 | 2.0 | 8.0 | 7.0 | 4.0 | 3.0 | 8.0 | 8.0 | 2.0 | 6.0 | 3.0 | 4.0 | 5.0 | 2.0 | 1.0 | 1.0 | 2.0 | 8.0 | 8.0 | 8.0 | 3.0 | 6.0 | 2.0 | 6.0 | 4.0 | 6.0 | 3.0 | 1.0 | 4.0 | 5.0 | 3.0 | 7.0 | 7.0 | 9.0 |
| 22 | 4.0 | 2.0 | 10.0 | 10.0 | 4.0 | 7.0 | 4.0 | 2.0 | 4.0 | 1.0 | 2.0 | 5.0 | 9.0 | 6.0 | 5.0 | 5.0 | 2.0 | 8.0 | 5.0 | 7.0 | 10.0 | 2.0 | 7.0 | 2.0 | 7.0 | 2.0 | 6.0 | 10.0 | 6.0 | 6.0 | 9.0 | 2.0 | 10.0 | 5.0 | 2.0 | 2.0 | 6.0 | 7.0 | 8.0 | 8.0 |
| 23 | 9.0 | 5.0 | 10.0 | 9.0 | 2.0 | 5.0 | 5.0 | 5.0 | 9.0 | 2.0 | 3.0 | 3.0 | 10.0 | 4.0 | 7.0 | 8.0 | 1.0 | 4.0 | 5.0 | 4.0 | 9.0 | 8.0 | 2.0 | 10.0 | 6.0 | 6.0 | 10.0 | 4.0 | 2.0 | 4.0 | 9.0 | 3.0 | 7.0 | 10.0 | 3.0 | 8.0 | 7.0 | 5.0 | 9.0 | 8.0 |
| 24 | 8.0 | 3.0 | 2.0 | 2.0 | 5.0 | 6.0 | 7.0 | 2.0 | 4.0 | 9.0 | 4.0 | 4.0 | 5.0 | 2.0 | 7.0 | 6.0 | 2.0 | 9.0 | 8.0 | 3.0 | 6.0 | 8.0 | 7.0 | 6.0 | 9.0 | 10.0 | 3.0 | 7.0 | 2.0 | 6.0 | 3.0 | 2.0 | 10.0 | 2.0 | 6.0 | 1.0 | 10.0 | 9.0 | 1.0 | 6.0 |
| 25 | 8.0 | 8.0 | 2.0 | 5.0 | 1.0 | 6.0 | 8.0 | 6.0 | 10.0 | 8.0 | 4.0 | 10.0 | 2.0 | 8.0 | 3.0 | 2.0 | 9.0 | 1.0 | 3.0 | 6.0 | 2.0 | 8.0 | 2.0 | 6.0 | 10.0 | 4.0 | 4.0 | 5.0 | 9.0 | 5.0 | 9.0 | 3.0 | 7.0 | 1.0 | 2.0 | 4.0 | 8.0 | 9.0 | 2.0 | 6.0 |
| 26 | 4.0 | 5.0 | 5.0 | 1.0 | 8.0 | 5.0 | 2.0 | 5.0 | 1.0 | 3.0 | 3.0 | 7.0 | 7.0 | 7.0 | 3.0 | 7.0 | 5.0 | 1.0 | 10.0 | 10.0 | 3.0 | 3.0 | 6.0 | 10.0 | 3.0 | 4.0 | 5.0 | 9.0 | 3.0 | 7.0 | 9.0 | 3.0 | 3.0 | 10.0 | 3.0 | 2.0 | 2.0 | 3.0 | 5.0 | 8.0 |
| 27 | 9.0 | 5.0 | 9.0 | 8.0 | 2.0 | 10.0 | 7.0 | 9.0 | 10.0 | 4.0 | 3.0 | 10.0 | 3.0 | 8.0 | 8.0 | 2.0 | 10.0 | 5.0 | 3.0 | 7.0 | 2.0 | 6.0 | 10.0 | 4.0 | 7.0 | 5.0 | 9.0 | 6.0 | 6.0 | 7.0 | 5.0 | 10.0 | 9.0 | 5.0 | 10.0 | 2.0 | 10.0 | 2.0 | 8.0 | 6.0 |
| 28 | 10.0 | 8.0 | 8.0 | 9.0 | 7.0 | 6.0 | 9.0 | 9.0 | 7.0 | 2.0 | 8.0 | 4.0 | 9.0 | 2.0 | 3.0 | 9.0 | 4.0 | 10.0 | 6.0 | 3.0 | 1.0 | 2.0 | 6.0 | 2.0 | 2.0 | 9.0 | 3.0 | 6.0 | 4.0 | 3.0 | 7.0 | 9.0 | 9.0 | 2.0 | 8.0 | 2.0 | 1.0 | 7.0 | 6.0 | 7.0 |
| 29 | 3.0 | 7.0 | 1.0 | 9.0 | 2.0 | 7.0 | 8.0 | 7.0 | 5.0 | 2.0 | 9.0 | 7.0 | 2.0 | 9.0 | 10.0 | 3.0 | 10.0 | 1.0 | 10.0 | 3.0 | 2.0 | 6.0 | 6.0 | 4.0 | 6.0 | 5.0 | 7.0 | 7.0 | 3.0 | 1.0 | 2.0 | 1.0 | 9.0 | 8.0 | 3.0 | 1.0 | 9.0 | 6.0 | 4.0 | 7.0 |
| 30 | 1.0 | 7.0 | 1.0 | 5.0 | 4.0 | 9.0 | 8.0 | 9.0 | 9.0 | 9.0 | 9.0 | 2.0 | 2.0 | 5.0 | 6.0 | 9.0 | 4.0 | 5.0 | 10.0 | 3.0 | 6.0 | 4.0 | 9.0 | 9.0 | 3.0 | 9.0 | 9.0 | 5.0 | 7.0 | 2.0 | 3.0 | 10.0 | 6.0 | 10.0 | 4.0 | 9.0 | 1.0 | 6.0 | 6.0 | 5.0 |
| 31 | 6.0 | 10.0 | 6.0 | 8.0 | 4.0 | 9.0 | 7.0 | 10.0 | 8.0 | 10.0 | 5.0 | 10.0 | 6.0 | 6.0 | 7.0 | 7.0 | 9.0 | 7.0 | 4.0 | 5.0 | 6.0 | 6.0 | 2.0 | 3.0 | 2.0 | 3.0 | 3.0 | 10.0 | 9.0 | 1.0 | 10.0 | 1.0 | 6.0 | 3.0 | 1.0 | 2.0 | 2.0 | 4.0 | 6.0 | 4.0 |
| 32 | 9.0 | 1.0 | 2.0 | 6.0 | 8.0 | 1.0 | 6.0 | 2.0 | 4.0 | 9.0 | 2.0 | 5.0 | 1.0 | 4.0 | 6.0 | 10.0 | 8.0 | 7.0 | 8.0 | 9.0 | 6.0 | 3.0 | 10.0 | 7.0 | 10.0 | 7.0 | 3.0 | 9.0 | 9.0 | 9.0 | 6.0 | 6.0 | 1.0 | 1.0 | 9.0 | 8.0 | 1.0 | 10.0 | 6.0 | 1.0 |
| 33 | 2.0 | 6.0 | 9.0 | 1.0 | 1.0 | 5.0 | 6.0 | 4.0 | 4.0 | 9.0 | 8.0 | 5.0 | 5.0 | 7.0 | 8.0 | 6.0 | 3.0 | 9.0 | 3.0 | 3.0 | 2.0 | 1.0 | 5.0 | 10.0 | 2.0 | 1.0 | 10.0 | 5.0 | 2.0 | 8.0 | 10.0 | 3.0 | 1.0 | 10.0 | 8.0 | 7.0 | 2.0 | 2.0 | 5.0 | 7.0 |
| 34 | 9.0 | 6.0 | 1.0 | 2.0 | 7.0 | 10.0 | 10.0 | 10.0 | 6.0 | 10.0 | 2.0 | 6.0 | 10.0 | 7.0 | 10.0 | 10.0 | 3.0 | 3.0 | 2.0 | 5.0 | 7.0 | 4.0 | 2.0 | 3.0 | 6.0 | 2.0 | 3.0 | 10.0 | 8.0 | 3.0 | 4.0 | 1.0 | 9.0 | 8.0 | 1.0 | 9.0 | 4.0 | 7.0 | 5.0 | 4.0 |
| 35 | 8.0 | 1.0 | 4.0 | 10.0 | 5.0 | 6.0 | 10.0 | 4.0 | 5.0 | 2.0 | 3.0 | 6.0 | 8.0 | 5.0 | 7.0 | 5.0 | 8.0 | 3.0 | 2.0 | 4.0 | 10.0 | 5.0 | 2.0 | 8.0 | 1.0 | 4.0 | 2.0 | 2.0 | 2.0 | 1.0 | 9.0 | 2.0 | 8.0 | 7.0 | 9.0 | 4.0 | 1.0 | 1.0 | 2.0 | 10.0 |
| 36 | 9.0 | 6.0 | 3.0 | 3.0 | 8.0 | 8.0 | 1.0 | 3.0 | 3.0 | 7.0 | 8.0 | 8.0 | 9.0 | 1.0 | 1.0 | 10.0 | 1.0 | 6.0 | 4.0 | 8.0 | 4.0 | 3.0 | 6.0 | 7.0 | 10.0 | 8.0 | 2.0 | 10.0 | 1.0 | 9.0 | 1.0 | 2.0 | 1.0 | 2.0 | 4.0 | 1.0 | 4.0 | 10.0 | 4.0 | 4.0 |
| 37 | 4.0 | 3.0 | 4.0 | 5.0 | 10.0 | 2.0 | 7.0 | 8.0 | 8.0 | 4.0 | 1.0 | 1.0 | 9.0 | 4.0 | 7.0 | 3.0 | 1.0 | 5.0 | 7.0 | 4.0 | 5.0 | 7.0 | 7.0 | 5.0 | 9.0 | 9.0 | 3.0 | 2.0 | 7.0 | 6.0 | 6.0 | 4.0 | 10.0 | 2.0 | 7.0 | 1.0 | 10.0 | 8.0 | 9.0 | 5.0 |
| 38 | 9.0 | 7.0 | 5.0 | 5.0 | 7.0 | 5.0 | 10.0 | 4.0 | 8.0 | 9.0 | 4.0 | 1.0 | 2.0 | 9.0 | 2.0 | 5.0 | 5.0 | 6.0 | 2.0 | 4.0 | 7.0 | 7.0 | 8.0 | 9.0 | 1.0 | 2.0 | 5.0 | 8.0 | 6.0 | 4.0 | 6.0 | 6.0 | 6.0 | 5.0 | 5.0 | 2.0 | 4.0 | 9.0 | 3.0 | 10.0 |
| 39 | 6.0 | 5.0 | 9.0 | 6.0 | 3.0 | 8.0 | 6.0 | 4.0 | 9.0 | 8.0 | 2.0 | 5.0 | 2.0 | 2.0 | 10.0 | 9.0 | 4.0 | 10.0 | 2.0 | 5.0 | 4.0 | 9.0 | 8.0 | 8.0 | 6.0 | 6.0 | 8.0 | 6.0 | 7.0 | 7.0 | 5.0 | 4.0 | 1.0 | 7.0 | 4.0 | 10.0 | 4.0 | 5.0 | 10.0 | 10.0 |

These entries list every corridor and charge so I can choose the single continuous route from 0 to 24 that minimizes the total bill.

Also, when you send back the chosen route, you can use a tiny JSON layout so it's easy to parse—nothing fancy, just drop the path into this shape:

{
  ""solution"": []
}

Think of the ""solution"" array as the place to list the corridor stops in order: start with the gate, then each location you pass through, and finish with the machinery room. It's just a simple form to fill out with the node names in sequence.

This JSON is only a sketch of the expected shape — you'll replace the empty array with the actual path when you give the answer.

Also, please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Don't include edge IDs or any cost labels in the response; just the sequence of node identifiers.","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'objective': {'constant': 0.0, 'linear': [5.0, 2.0, 10.0, 9.0, 8.0, 5.0, 4.0, 3.0, 10.0, 6.0, 9.0, 2.0, 7.0, 1.0, 9.0, 6.0, 2.0, 2.0, 5.0, 10.0, 10.0, 7.0, 2.0, 9.0, 5.0, 6.0, 8.0, 8.0, 8.0, 8.0, 5.0, 10.0, 6.0, 9.0, 9.0, 1.0, 7.0, 4.0, 5.0, 6.0], 'quadratic': [[5.0, 8.0, 2.0, 5.0, 3.0, 8.0, 5.0, 7.0, 8.0, 9.0, 2.0, 10.0, 10.0, 4.0, 4.0, 10.0, 3.0, 6.0, 5.0, 6.0, 5.0, 5.0, 4.0, 9.0, 8.0, 8.0, 4.0, 9.0, 10.0, 3.0, 1.0, 6.0, 9.0, 2.0, 9.0, 8.0, 9.0, 4.0, 9.0, 6.0], [8.0, 3.0, 4.0, 7.0, 4.0, 9.0, 9.0, 6.0, 3.0, 8.0, 3.0, 7.0, 8.0, 2.0, 6.0, 5.0, 5.0, 3.0, 9.0, 10.0, 3.0, 1.0, 2.0, 5.0, 3.0, 8.0, 5.0, 5.0, 8.0, 7.0, 7.0, 10.0, 1.0, 6.0, 6.0, 1.0, 6.0, 3.0, 7.0, 5.0], [2.0, 4.0, 4.0, 3.0, 6.0, 8.0, 8.0, 5.0, 7.0, 5.0, 7.0, 8.0, 7.0, 7.0, 9.0, 2.0, 7.0, 3.0, 2.0, 6.0, 3.0, 9.0, 10.0, 10.0, 2.0, 2.0, 5.0, 9.0, 8.0, 1.0, 1.0, 6.0, 2.0, 9.0, 1.0, 4.0, 3.0, 4.0, 5.0, 9.0], [5.0, 7.0, 3.0, 2.0, 5.0, 1.0, 4.0, 1.0, 8.0, 7.0, 7.0, 9.0, 5.0, 10.0, 7.0, 8.0, 4.0, 3.0, 6.0, 10.0, 5.0, 2.0, 10.0, 9.0, 2.0, 5.0, 1.0, 8.0, 9.0, 9.0, 5.0, 8.0, 6.0, 1.0, 2.0, 10.0, 3.0, 5.0, 5.0, 6.0], [3.0, 4.0, 6.0, 5.0, 5.0, 5.0, 8.0, 2.0, 6.0, 1.0, 10.0, 7.0, 10.0, 3.0, 3.0, 9.0, 7.0, 2.0, 4.0, 7.0, 2.0, 2.0, 4.0, 2.0, 5.0, 1.0, 8.0, 2.0, 7.0, 2.0, 4.0, 4.0, 8.0, 1.0, 7.0, 5.0, 8.0, 10.0, 7.0, 3.0], [8.0, 9.0, 8.0, 1.0, 5.0, 10.0, 8.0, 3.0, 6.0, 9.0, 5.0, 6.0, 9.0, 6.0, 4.0, 4.0, 3.0, 2.0, 10.0, 2.0, 1.0, 2.0, 7.0, 5.0, 6.0, 6.0, 5.0, 10.0, 6.0, 7.0, 9.0, 9.0, 1.0, 5.0, 10.0, 6.0, 8.0, 2.0, 5.0, 8.0], [5.0, 9.0, 8.0, 4.0, 8.0, 8.0, 9.0, 9.0, 8.0, 2.0, 1.0, 3.0, 8.0, 5.0, 10.0, 5.0, 10.0, 6.0, 1.0, 2.0, 3.0, 1.0, 4.0, 5.0, 7.0, 8.0, 2.0, 7.0, 9.0, 8.0, 8.0, 7.0, 6.0, 6.0, 10.0, 10.0, 1.0, 7.0, 10.0, 6.0], [7.0, 6.0, 5.0, 1.0, 2.0, 3.0, 9.0, 7.0, 3.0, 2.0, 4.0, 10.0, 1.0, 3.0, 7.0, 7.0, 4.0, 10.0, 3.0, 8.0, 6.0, 2.0, 2.0, 5.0, 2.0, 6.0, 5.0, 9.0, 9.0, 7.0, 9.0, 10.0, 2.0, 4.0, 10.0, 4.0, 3.0, 8.0, 4.0, 4.0], [8.0, 3.0, 7.0, 8.0, 6.0, 6.0, 8.0, 3.0, 2.0, 2.0, 10.0, 9.0, 3.0, 1.0, 2.0, 6.0, 1.0, 6.0, 3.0, 10.0, 6.0, 8.0, 4.0, 9.0, 4.0, 10.0, 1.0, 10.0, 7.0, 5.0, 9.0, 8.0, 4.0, 4.0, 6.0, 5.0, 3.0, 8.0, 8.0, 9.0], [9.0, 8.0, 5.0, 7.0, 1.0, 9.0, 2.0, 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'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23, 24: 24}}","[0, 5, 10, 11, 12, 13, 18, 23, 24]",26,markdown_table,0
QSPP,QSPP,"Many people treat this like picking a single subway path from the entry concourse to the platform: follow the one-way tracks, hop from station to station, and don’t split the trip. Each track segment charges a base fee, some segments tack on an extra surcharge when they’re used, and some particular combos of segments create additional penalties that only count if both are on the trip. The aim is to choose exactly one legal route, obeying the track directions and starting and ending in the right places, so that when all base fees, surcharges, and combo penalties are summed the total is as small as possible. The detailed map and the fee schedule are provided below.

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      ""segment_base_fee"": 8.0
    },
    {
      ""segment_id_for_linear_fee"": 12,
      ""segment_base_fee"": 4.0
    },
    {
      ""segment_id_for_linear_fee"": 13,
      ""segment_base_fee"": 8.0
    },
    {
      ""segment_id_for_linear_fee"": 14,
      ""segment_base_fee"": 8.0
    },
    {
      ""segment_id_for_linear_fee"": 15,
      ""segment_base_fee"": 2.0
    },
    {
      ""segment_id_for_linear_fee"": 16,
      ""segment_base_fee"": 10.0
    },
    {
      ""segment_id_for_linear_fee"": 17,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 18,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 19,
      ""segment_base_fee"": 8.0
    },
    {
      ""segment_id_for_linear_fee"": 20,
      ""segment_base_fee"": 3.0
    },
    {
      ""segment_id_for_linear_fee"": 21,
      ""segment_base_fee"": 3.0
    },
    {
      ""segment_id_for_linear_fee"": 22,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 23,
      ""segment_base_fee"": 7.0
    },
    {
      ""segment_id_for_linear_fee"": 24,
      ""segment_base_fee"": 10.0
    },
    {
      ""segment_id_for_linear_fee"": 25,
      ""segment_base_fee"": 1.0
    },
    {
      ""segment_id_for_linear_fee"": 26,
      ""segment_base_fee"": 9.0
    },
    {
      ""segment_id_for_linear_fee"": 27,
      ""segment_base_fee"": 7.0
    },
    {
      ""segment_id_for_linear_fee"": 28,
      ""segment_base_fee"": 10.0
    },
    {
      ""segment_id_for_linear_fee"": 29,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 30,
      ""segment_base_fee"": 9.0
    },
    {
      ""segment_id_for_linear_fee"": 31,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 32,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 33,
      ""segment_base_fee"": 9.0
    },
    {
      ""segment_id_for_linear_fee"": 34,
      ""segment_base_fee"": 1.0
    },
    {
      ""segment_id_for_linear_fee"": 35,
      ""segment_base_fee"": 1.0
    },
    {
      ""segment_id_for_linear_fee"": 36,
      ""segment_base_fee"": 2.0
    },
    {
      ""segment_id_for_linear_fee"": 37,
      ""segment_base_fee"": 3.0
    },
    {
      ""segment_id_for_linear_fee"": 38,
      ""segment_base_fee"": 3.0
    },
    {
      ""segment_id_for_linear_fee"": 39,
      ""segment_base_fee"": 10.0
    },
    {
      ""segment_id_for_linear_fee"": 40,
      ""segment_base_fee"": 4.0
    },
    {
      ""segment_id_for_linear_fee"": 41,
      ""segment_base_fee"": 5.0
    },
    {
      ""segment_id_for_linear_fee"": 42,
      ""segment_base_fee"": 10.0
    },
    {
      ""segment_id_for_linear_fee"": 43,
      ""segment_base_fee"": 6.0
    },
    {
      ""segment_id_for_linear_fee"": 44,
      ""segment_base_fee"": 2.0
    },
    {
      ""segment_id_for_linear_fee"": 45,
      ""segment_base_fee"": 2.0
    },
    {
      ""segment_id_for_linear_fee"": 46,
      ""segment_base_fee"": 1.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 10.0 | 2.0 | 7.0 | 5.0 | 1.0 | 9.0 | 4.0 | 7.0 | 5.0 | 6.0 | 2.0 | 8.0 | 2.0 | 1.0 | 5.0 | 8.0 | 1.0 | 7.0 | 3.0 | 3.0 | 3.0 | 9.0 | 3.0 | 1.0 | 5.0 | 9.0 | 8.0 | 4.0 | 3.0 | 6.0 | 7.0 | 3.0 | 5.0 | 2.0 | 6.0 | 3.0 | 4.0 | 7.0 | 9.0 | 10.0 | 9.0 | 1.0 | 10.0 | 5.0 | 6.0 | 6.0 |
| 1 | 10.0 | 8.0 | 3.0 | 6.0 | 5.0 | 2.0 | 5.0 | 3.0 | 8.0 | 10.0 | 6.0 | 1.0 | 10.0 | 7.0 | 10.0 | 5.0 | 5.0 | 10.0 | 9.0 | 2.0 | 8.0 | 2.0 | 1.0 | 5.0 | 1.0 | 9.0 | 6.0 | 7.0 | 9.0 | 4.0 | 6.0 | 3.0 | 10.0 | 4.0 | 1.0 | 5.0 | 10.0 | 10.0 | 3.0 | 10.0 | 7.0 | 6.0 | 3.0 | 8.0 | 1.0 | 1.0 | 2.0 |
| 2 | 2.0 | 3.0 | 3.0 | 1.0 | 9.0 | 5.0 | 4.0 | 10.0 | 6.0 | 10.0 | 2.0 | 5.0 | 3.0 | 9.0 | 9.0 | 6.0 | 10.0 | 9.0 | 10.0 | 5.0 | 9.0 | 5.0 | 4.0 | 8.0 | 10.0 | 2.0 | 9.0 | 4.0 | 7.0 | 10.0 | 5.0 | 9.0 | 3.0 | 4.0 | 9.0 | 5.0 | 5.0 | 8.0 | 3.0 | 6.0 | 5.0 | 8.0 | 3.0 | 4.0 | 9.0 | 10.0 | 8.0 |
| 3 | 7.0 | 6.0 | 1.0 | 5.0 | 3.0 | 5.0 | 1.0 | 1.0 | 2.0 | 2.0 | 6.0 | 5.0 | 1.0 | 2.0 | 10.0 | 10.0 | 7.0 | 6.0 | 9.0 | 8.0 | 2.0 | 8.0 | 9.0 | 10.0 | 10.0 | 4.0 | 6.0 | 7.0 | 4.0 | 3.0 | 10.0 | 4.0 | 1.0 | 6.0 | 1.0 | 2.0 | 8.0 | 4.0 | 3.0 | 10.0 | 7.0 | 4.0 | 8.0 | 2.0 | 9.0 | 8.0 | 3.0 |
| 4 | 5.0 | 5.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 10.0 | 2.0 | 2.0 | 2.0 | 7.0 | 1.0 | 6.0 | 3.0 | 2.0 | 9.0 | 10.0 | 2.0 | 10.0 | 2.0 | 7.0 | 4.0 | 7.0 | 10.0 | 5.0 | 9.0 | 5.0 | 7.0 | 10.0 | 5.0 | 10.0 | 3.0 | 10.0 | 3.0 | 7.0 | 3.0 | 4.0 | 7.0 | 6.0 | 2.0 | 3.0 | 5.0 | 8.0 | 7.0 | 6.0 | 8.0 |
| 5 | 1.0 | 2.0 | 5.0 | 5.0 | 8.0 | 8.0 | 1.0 | 6.0 | 8.0 | 9.0 | 4.0 | 1.0 | 8.0 | 6.0 | 7.0 | 4.0 | 2.0 | 10.0 | 3.0 | 2.0 | 4.0 | 6.0 | 9.0 | 9.0 | 4.0 | 9.0 | 10.0 | 4.0 | 2.0 | 1.0 | 7.0 | 6.0 | 4.0 | 6.0 | 5.0 | 2.0 | 8.0 | 1.0 | 2.0 | 6.0 | 10.0 | 7.0 | 6.0 | 10.0 | 5.0 | 2.0 | 3.0 |
| 6 | 9.0 | 5.0 | 4.0 | 1.0 | 3.0 | 1.0 | 9.0 | 2.0 | 2.0 | 7.0 | 7.0 | 7.0 | 9.0 | 5.0 | 6.0 | 10.0 | 8.0 | 1.0 | 3.0 | 1.0 | 10.0 | 10.0 | 9.0 | 1.0 | 7.0 | 1.0 | 8.0 | 4.0 | 6.0 | 9.0 | 8.0 | 10.0 | 4.0 | 6.0 | 9.0 | 10.0 | 5.0 | 10.0 | 6.0 | 3.0 | 4.0 | 6.0 | 8.0 | 7.0 | 4.0 | 1.0 | 2.0 |
| 7 | 4.0 | 3.0 | 10.0 | 1.0 | 10.0 | 6.0 | 2.0 | 10.0 | 2.0 | 7.0 | 8.0 | 4.0 | 1.0 | 1.0 | 1.0 | 5.0 | 8.0 | 2.0 | 5.0 | 4.0 | 10.0 | 6.0 | 2.0 | 1.0 | 1.0 | 5.0 | 2.0 | 4.0 | 6.0 | 6.0 | 1.0 | 5.0 | 3.0 | 5.0 | 9.0 | 9.0 | 6.0 | 9.0 | 8.0 | 2.0 | 5.0 | 2.0 | 4.0 | 10.0 | 1.0 | 9.0 | 5.0 |
| 8 | 7.0 | 8.0 | 6.0 | 2.0 | 2.0 | 8.0 | 2.0 | 2.0 | 6.0 | 7.0 | 4.0 | 10.0 | 2.0 | 10.0 | 7.0 | 3.0 | 2.0 | 6.0 | 9.0 | 10.0 | 4.0 | 10.0 | 6.0 | 6.0 | 1.0 | 6.0 | 7.0 | 9.0 | 6.0 | 10.0 | 4.0 | 5.0 | 5.0 | 7.0 | 6.0 | 8.0 | 2.0 | 9.0 | 7.0 | 4.0 | 2.0 | 10.0 | 2.0 | 10.0 | 6.0 | 7.0 | 2.0 |
| 9 | 5.0 | 10.0 | 10.0 | 2.0 | 2.0 | 9.0 | 7.0 | 7.0 | 7.0 | 8.0 | 7.0 | 7.0 | 1.0 | 4.0 | 1.0 | 9.0 | 2.0 | 3.0 | 7.0 | 1.0 | 4.0 | 4.0 | 8.0 | 2.0 | 7.0 | 6.0 | 6.0 | 4.0 | 1.0 | 10.0 | 5.0 | 6.0 | 1.0 | 4.0 | 9.0 | 9.0 | 5.0 | 8.0 | 7.0 | 6.0 | 4.0 | 4.0 | 1.0 | 10.0 | 8.0 | 9.0 | 3.0 |
| 10 | 6.0 | 6.0 | 2.0 | 6.0 | 2.0 | 4.0 | 7.0 | 8.0 | 4.0 | 7.0 | 4.0 | 8.0 | 3.0 | 8.0 | 5.0 | 6.0 | 8.0 | 7.0 | 7.0 | 8.0 | 5.0 | 4.0 | 3.0 | 7.0 | 7.0 | 1.0 | 6.0 | 9.0 | 4.0 | 5.0 | 10.0 | 5.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 6.0 | 3.0 | 5.0 | 1.0 | 4.0 | 2.0 | 8.0 | 9.0 | 9.0 | 7.0 |
| 11 | 2.0 | 1.0 | 5.0 | 5.0 | 7.0 | 1.0 | 7.0 | 4.0 | 10.0 | 7.0 | 8.0 | 8.0 | 10.0 | 6.0 | 9.0 | 9.0 | 3.0 | 1.0 | 4.0 | 5.0 | 6.0 | 8.0 | 7.0 | 5.0 | 3.0 | 8.0 | 1.0 | 1.0 | 6.0 | 7.0 | 2.0 | 8.0 | 10.0 | 1.0 | 10.0 | 3.0 | 9.0 | 1.0 | 5.0 | 6.0 | 9.0 | 4.0 | 1.0 | 10.0 | 7.0 | 10.0 | 2.0 |
| 12 | 8.0 | 10.0 | 3.0 | 1.0 | 1.0 | 8.0 | 9.0 | 1.0 | 2.0 | 1.0 | 3.0 | 10.0 | 8.0 | 5.0 | 10.0 | 6.0 | 9.0 | 9.0 | 6.0 | 7.0 | 3.0 | 6.0 | 10.0 | 2.0 | 7.0 | 4.0 | 2.0 | 1.0 | 7.0 | 7.0 | 8.0 | 10.0 | 3.0 | 1.0 | 4.0 | 9.0 | 2.0 | 7.0 | 6.0 | 8.0 | 8.0 | 4.0 | 3.0 | 8.0 | 6.0 | 4.0 | 6.0 |
| 13 | 2.0 | 7.0 | 9.0 | 2.0 | 6.0 | 6.0 | 5.0 | 1.0 | 10.0 | 4.0 | 8.0 | 6.0 | 5.0 | 3.0 | 8.0 | 4.0 | 8.0 | 6.0 | 9.0 | 10.0 | 10.0 | 3.0 | 8.0 | 2.0 | 5.0 | 6.0 | 7.0 | 6.0 | 10.0 | 9.0 | 9.0 | 7.0 | 3.0 | 7.0 | 5.0 | 6.0 | 2.0 | 1.0 | 5.0 | 3.0 | 3.0 | 4.0 | 10.0 | 9.0 | 5.0 | 9.0 | 5.0 |
| 14 | 1.0 | 10.0 | 9.0 | 10.0 | 3.0 | 7.0 | 6.0 | 1.0 | 7.0 | 1.0 | 5.0 | 9.0 | 10.0 | 8.0 | 7.0 | 6.0 | 10.0 | 7.0 | 4.0 | 7.0 | 4.0 | 9.0 | 2.0 | 1.0 | 1.0 | 6.0 | 5.0 | 5.0 | 4.0 | 9.0 | 1.0 | 1.0 | 1.0 | 10.0 | 4.0 | 1.0 | 8.0 | 6.0 | 9.0 | 6.0 | 8.0 | 3.0 | 9.0 | 9.0 | 7.0 | 10.0 | 7.0 |
| 15 | 5.0 | 5.0 | 6.0 | 10.0 | 2.0 | 4.0 | 10.0 | 5.0 | 3.0 | 9.0 | 6.0 | 9.0 | 6.0 | 4.0 | 6.0 | 8.0 | 8.0 | 5.0 | 10.0 | 7.0 | 6.0 | 3.0 | 2.0 | 4.0 | 9.0 | 3.0 | 2.0 | 1.0 | 4.0 | 5.0 | 7.0 | 3.0 | 3.0 | 6.0 | 5.0 | 8.0 | 1.0 | 2.0 | 8.0 | 9.0 | 5.0 | 5.0 | 2.0 | 9.0 | 2.0 | 5.0 | 9.0 |
| 16 | 8.0 | 5.0 | 10.0 | 7.0 | 9.0 | 2.0 | 8.0 | 8.0 | 2.0 | 2.0 | 8.0 | 3.0 | 9.0 | 8.0 | 10.0 | 8.0 | 9.0 | 6.0 | 3.0 | 4.0 | 3.0 | 10.0 | 3.0 | 8.0 | 5.0 | 2.0 | 6.0 | 5.0 | 3.0 | 3.0 | 9.0 | 10.0 | 6.0 | 6.0 | 4.0 | 9.0 | 1.0 | 4.0 | 1.0 | 8.0 | 5.0 | 6.0 | 3.0 | 10.0 | 3.0 | 6.0 | 2.0 |
| 17 | 1.0 | 10.0 | 9.0 | 6.0 | 10.0 | 10.0 | 1.0 | 2.0 | 6.0 | 3.0 | 7.0 | 1.0 | 9.0 | 6.0 | 7.0 | 5.0 | 6.0 | 5.0 | 9.0 | 5.0 | 10.0 | 10.0 | 7.0 | 3.0 | 9.0 | 4.0 | 8.0 | 5.0 | 7.0 | 10.0 | 2.0 | 7.0 | 9.0 | 2.0 | 6.0 | 6.0 | 5.0 | 5.0 | 2.0 | 5.0 | 4.0 | 8.0 | 10.0 | 7.0 | 5.0 | 4.0 | 4.0 |
| 18 | 7.0 | 9.0 | 10.0 | 9.0 | 2.0 | 3.0 | 3.0 | 5.0 | 9.0 | 7.0 | 7.0 | 4.0 | 6.0 | 9.0 | 4.0 | 10.0 | 3.0 | 9.0 | 1.0 | 2.0 | 2.0 | 4.0 | 10.0 | 9.0 | 7.0 | 6.0 | 6.0 | 6.0 | 1.0 | 1.0 | 1.0 | 7.0 | 4.0 | 1.0 | 2.0 | 2.0 | 10.0 | 3.0 | 4.0 | 4.0 | 3.0 | 3.0 | 3.0 | 3.0 | 1.0 | 7.0 | 2.0 |
| 19 | 3.0 | 2.0 | 5.0 | 8.0 | 10.0 | 2.0 | 1.0 | 4.0 | 10.0 | 1.0 | 8.0 | 5.0 | 7.0 | 10.0 | 7.0 | 7.0 | 4.0 | 5.0 | 2.0 | 3.0 | 5.0 | 4.0 | 10.0 | 2.0 | 2.0 | 5.0 | 7.0 | 6.0 | 2.0 | 6.0 | 5.0 | 8.0 | 9.0 | 1.0 | 1.0 | 10.0 | 6.0 | 1.0 | 4.0 | 1.0 | 9.0 | 1.0 | 7.0 | 3.0 | 9.0 | 8.0 | 7.0 |
| 20 | 3.0 | 8.0 | 9.0 | 2.0 | 2.0 | 4.0 | 10.0 | 10.0 | 4.0 | 4.0 | 5.0 | 6.0 | 3.0 | 10.0 | 4.0 | 6.0 | 3.0 | 10.0 | 2.0 | 5.0 | 5.0 | 10.0 | 10.0 | 9.0 | 1.0 | 4.0 | 2.0 | 7.0 | 2.0 | 1.0 | 2.0 | 2.0 | 5.0 | 6.0 | 3.0 | 2.0 | 1.0 | 9.0 | 2.0 | 4.0 | 1.0 | 5.0 | 2.0 | 3.0 | 7.0 | 4.0 | 6.0 |
| 21 | 3.0 | 2.0 | 5.0 | 8.0 | 7.0 | 6.0 | 10.0 | 6.0 | 10.0 | 4.0 | 4.0 | 8.0 | 6.0 | 3.0 | 9.0 | 3.0 | 10.0 | 10.0 | 4.0 | 4.0 | 10.0 | 1.0 | 6.0 | 6.0 | 1.0 | 4.0 | 10.0 | 3.0 | 3.0 | 1.0 | 10.0 | 9.0 | 5.0 | 4.0 | 2.0 | 10.0 | 6.0 | 6.0 | 2.0 | 8.0 | 6.0 | 8.0 | 5.0 | 1.0 | 1.0 | 6.0 | 10.0 |
| 22 | 9.0 | 1.0 | 4.0 | 9.0 | 4.0 | 9.0 | 9.0 | 2.0 | 6.0 | 8.0 | 3.0 | 7.0 | 10.0 | 8.0 | 2.0 | 2.0 | 3.0 | 7.0 | 10.0 | 10.0 | 10.0 | 6.0 | 6.0 | 10.0 | 9.0 | 1.0 | 3.0 | 2.0 | 8.0 | 9.0 | 10.0 | 5.0 | 10.0 | 3.0 | 1.0 | 8.0 | 3.0 | 3.0 | 2.0 | 10.0 | 6.0 | 5.0 | 9.0 | 4.0 | 1.0 | 3.0 | 9.0 |
| 23 | 3.0 | 5.0 | 8.0 | 10.0 | 7.0 | 9.0 | 1.0 | 1.0 | 6.0 | 2.0 | 7.0 | 5.0 | 2.0 | 2.0 | 1.0 | 4.0 | 8.0 | 3.0 | 9.0 | 2.0 | 9.0 | 6.0 | 10.0 | 10.0 | 9.0 | 5.0 | 1.0 | 1.0 | 6.0 | 4.0 | 5.0 | 9.0 | 9.0 | 6.0 | 5.0 | 1.0 | 8.0 | 5.0 | 6.0 | 2.0 | 6.0 | 1.0 | 3.0 | 1.0 | 2.0 | 6.0 | 1.0 |
| 24 | 1.0 | 1.0 | 10.0 | 10.0 | 10.0 | 4.0 | 7.0 | 1.0 | 1.0 | 7.0 | 7.0 | 3.0 | 7.0 | 5.0 | 1.0 | 9.0 | 5.0 | 9.0 | 7.0 | 2.0 | 1.0 | 1.0 | 9.0 | 9.0 | 1.0 | 7.0 | 8.0 | 4.0 | 4.0 | 6.0 | 7.0 | 5.0 | 6.0 | 5.0 | 3.0 | 5.0 | 10.0 | 10.0 | 2.0 | 10.0 | 8.0 | 5.0 | 3.0 | 7.0 | 9.0 | 2.0 | 4.0 |
| 25 | 5.0 | 9.0 | 2.0 | 4.0 | 5.0 | 9.0 | 1.0 | 5.0 | 6.0 | 6.0 | 1.0 | 8.0 | 4.0 | 6.0 | 6.0 | 3.0 | 2.0 | 4.0 | 6.0 | 5.0 | 4.0 | 4.0 | 1.0 | 5.0 | 7.0 | 9.0 | 7.0 | 4.0 | 5.0 | 1.0 | 5.0 | 7.0 | 10.0 | 10.0 | 1.0 | 5.0 | 5.0 | 5.0 | 5.0 | 5.0 | 9.0 | 7.0 | 7.0 | 5.0 | 8.0 | 10.0 | 10.0 |
| 26 | 9.0 | 6.0 | 9.0 | 6.0 | 9.0 | 10.0 | 8.0 | 2.0 | 7.0 | 6.0 | 6.0 | 1.0 | 2.0 | 7.0 | 5.0 | 2.0 | 6.0 | 8.0 | 6.0 | 7.0 | 2.0 | 10.0 | 3.0 | 1.0 | 8.0 | 7.0 | 8.0 | 8.0 | 8.0 | 5.0 | 10.0 | 6.0 | 4.0 | 5.0 | 10.0 | 1.0 | 4.0 | 10.0 | 2.0 | 1.0 | 6.0 | 9.0 | 10.0 | 2.0 | 4.0 | 8.0 | 9.0 |
| 27 | 8.0 | 7.0 | 4.0 | 7.0 | 5.0 | 4.0 | 4.0 | 4.0 | 9.0 | 4.0 | 9.0 | 1.0 | 1.0 | 6.0 | 5.0 | 1.0 | 5.0 | 5.0 | 6.0 | 6.0 | 7.0 | 3.0 | 2.0 | 1.0 | 4.0 | 4.0 | 8.0 | 4.0 | 5.0 | 6.0 | 1.0 | 9.0 | 1.0 | 7.0 | 5.0 | 9.0 | 8.0 | 4.0 | 10.0 | 10.0 | 6.0 | 9.0 | 2.0 | 1.0 | 8.0 | 2.0 | 1.0 |
| 28 | 4.0 | 9.0 | 7.0 | 4.0 | 7.0 | 2.0 | 6.0 | 6.0 | 6.0 | 1.0 | 4.0 | 6.0 | 7.0 | 10.0 | 4.0 | 4.0 | 3.0 | 7.0 | 1.0 | 2.0 | 2.0 | 3.0 | 8.0 | 6.0 | 4.0 | 5.0 | 8.0 | 5.0 | 2.0 | 7.0 | 7.0 | 1.0 | 2.0 | 3.0 | 10.0 | 2.0 | 4.0 | 7.0 | 6.0 | 9.0 | 7.0 | 6.0 | 2.0 | 8.0 | 7.0 | 4.0 | 6.0 |
| 29 | 3.0 | 4.0 | 10.0 | 3.0 | 10.0 | 1.0 | 9.0 | 6.0 | 10.0 | 10.0 | 5.0 | 7.0 | 7.0 | 9.0 | 9.0 | 5.0 | 3.0 | 10.0 | 1.0 | 6.0 | 1.0 | 1.0 | 9.0 | 4.0 | 6.0 | 1.0 | 5.0 | 6.0 | 7.0 | 3.0 | 10.0 | 5.0 | 4.0 | 3.0 | 6.0 | 4.0 | 8.0 | 6.0 | 7.0 | 9.0 | 7.0 | 8.0 | 10.0 | 4.0 | 10.0 | 2.0 | 1.0 |
| 30 | 6.0 | 6.0 | 5.0 | 10.0 | 5.0 | 7.0 | 8.0 | 1.0 | 4.0 | 5.0 | 10.0 | 2.0 | 8.0 | 9.0 | 1.0 | 7.0 | 9.0 | 2.0 | 1.0 | 5.0 | 2.0 | 10.0 | 10.0 | 5.0 | 7.0 | 5.0 | 10.0 | 1.0 | 7.0 | 10.0 | 8.0 | 10.0 | 4.0 | 2.0 | 4.0 | 9.0 | 5.0 | 3.0 | 9.0 | 6.0 | 4.0 | 5.0 | 9.0 | 9.0 | 6.0 | 5.0 | 8.0 |
| 31 | 7.0 | 3.0 | 9.0 | 4.0 | 10.0 | 6.0 | 10.0 | 5.0 | 5.0 | 6.0 | 5.0 | 8.0 | 10.0 | 7.0 | 1.0 | 3.0 | 10.0 | 7.0 | 7.0 | 8.0 | 2.0 | 9.0 | 5.0 | 9.0 | 5.0 | 7.0 | 6.0 | 9.0 | 1.0 | 5.0 | 10.0 | 6.0 | 7.0 | 7.0 | 2.0 | 2.0 | 1.0 | 1.0 | 3.0 | 1.0 | 3.0 | 1.0 | 10.0 | 10.0 | 2.0 | 4.0 | 6.0 |
| 32 | 3.0 | 10.0 | 3.0 | 1.0 | 3.0 | 4.0 | 4.0 | 3.0 | 5.0 | 1.0 | 7.0 | 10.0 | 3.0 | 3.0 | 1.0 | 3.0 | 6.0 | 9.0 | 4.0 | 9.0 | 5.0 | 5.0 | 10.0 | 9.0 | 6.0 | 10.0 | 4.0 | 1.0 | 2.0 | 4.0 | 4.0 | 7.0 | 4.0 | 8.0 | 7.0 | 5.0 | 5.0 | 1.0 | 10.0 | 2.0 | 4.0 | 9.0 | 2.0 | 9.0 | 3.0 | 4.0 | 6.0 |
| 33 | 5.0 | 4.0 | 4.0 | 6.0 | 10.0 | 6.0 | 6.0 | 5.0 | 7.0 | 4.0 | 1.0 | 1.0 | 1.0 | 7.0 | 10.0 | 6.0 | 6.0 | 2.0 | 1.0 | 1.0 | 6.0 | 4.0 | 3.0 | 6.0 | 5.0 | 10.0 | 5.0 | 7.0 | 3.0 | 3.0 | 2.0 | 7.0 | 8.0 | 3.0 | 4.0 | 8.0 | 2.0 | 8.0 | 1.0 | 1.0 | 2.0 | 8.0 | 3.0 | 8.0 | 7.0 | 4.0 | 4.0 |
| 34 | 2.0 | 1.0 | 9.0 | 1.0 | 3.0 | 5.0 | 9.0 | 9.0 | 6.0 | 9.0 | 9.0 | 10.0 | 4.0 | 5.0 | 4.0 | 5.0 | 4.0 | 6.0 | 2.0 | 1.0 | 3.0 | 2.0 | 1.0 | 5.0 | 3.0 | 1.0 | 10.0 | 5.0 | 10.0 | 6.0 | 4.0 | 2.0 | 7.0 | 4.0 | 5.0 | 3.0 | 2.0 | 1.0 | 9.0 | 10.0 | 3.0 | 10.0 | 7.0 | 3.0 | 8.0 | 3.0 | 2.0 |
| 35 | 6.0 | 5.0 | 5.0 | 2.0 | 7.0 | 2.0 | 10.0 | 9.0 | 8.0 | 9.0 | 9.0 | 3.0 | 9.0 | 6.0 | 1.0 | 8.0 | 9.0 | 6.0 | 2.0 | 10.0 | 2.0 | 10.0 | 8.0 | 1.0 | 5.0 | 5.0 | 1.0 | 9.0 | 2.0 | 4.0 | 9.0 | 2.0 | 5.0 | 8.0 | 3.0 | 9.0 | 2.0 | 1.0 | 6.0 | 9.0 | 2.0 | 8.0 | 10.0 | 8.0 | 10.0 | 10.0 | 5.0 |
| 36 | 3.0 | 10.0 | 5.0 | 8.0 | 3.0 | 8.0 | 5.0 | 6.0 | 2.0 | 5.0 | 10.0 | 9.0 | 2.0 | 2.0 | 8.0 | 1.0 | 1.0 | 5.0 | 10.0 | 6.0 | 1.0 | 6.0 | 3.0 | 8.0 | 10.0 | 5.0 | 4.0 | 8.0 | 4.0 | 8.0 | 5.0 | 1.0 | 5.0 | 2.0 | 2.0 | 2.0 | 6.0 | 3.0 | 10.0 | 7.0 | 9.0 | 3.0 | 1.0 | 4.0 | 3.0 | 3.0 | 2.0 |
| 37 | 4.0 | 10.0 | 8.0 | 4.0 | 4.0 | 1.0 | 10.0 | 9.0 | 9.0 | 8.0 | 6.0 | 1.0 | 7.0 | 1.0 | 6.0 | 2.0 | 4.0 | 5.0 | 3.0 | 1.0 | 9.0 | 6.0 | 3.0 | 5.0 | 10.0 | 5.0 | 10.0 | 4.0 | 7.0 | 6.0 | 3.0 | 1.0 | 1.0 | 8.0 | 1.0 | 1.0 | 3.0 | 10.0 | 10.0 | 4.0 | 8.0 | 9.0 | 9.0 | 4.0 | 4.0 | 8.0 | 7.0 |
| 38 | 7.0 | 3.0 | 3.0 | 3.0 | 7.0 | 2.0 | 6.0 | 8.0 | 7.0 | 7.0 | 3.0 | 5.0 | 6.0 | 5.0 | 9.0 | 8.0 | 1.0 | 2.0 | 4.0 | 4.0 | 2.0 | 2.0 | 2.0 | 6.0 | 2.0 | 5.0 | 2.0 | 10.0 | 6.0 | 7.0 | 9.0 | 3.0 | 10.0 | 1.0 | 9.0 | 6.0 | 10.0 | 10.0 | 1.0 | 6.0 | 4.0 | 9.0 | 4.0 | 1.0 | 6.0 | 10.0 | 10.0 |
| 39 | 9.0 | 10.0 | 6.0 | 10.0 | 6.0 | 6.0 | 3.0 | 2.0 | 4.0 | 6.0 | 5.0 | 6.0 | 8.0 | 3.0 | 6.0 | 9.0 | 8.0 | 5.0 | 4.0 | 1.0 | 4.0 | 8.0 | 10.0 | 2.0 | 10.0 | 5.0 | 1.0 | 10.0 | 9.0 | 9.0 | 6.0 | 1.0 | 2.0 | 1.0 | 10.0 | 9.0 | 7.0 | 4.0 | 6.0 | 3.0 | 9.0 | 4.0 | 6.0 | 2.0 | 1.0 | 10.0 | 6.0 |
| 40 | 10.0 | 7.0 | 5.0 | 7.0 | 2.0 | 10.0 | 4.0 | 5.0 | 2.0 | 4.0 | 1.0 | 9.0 | 8.0 | 3.0 | 8.0 | 5.0 | 5.0 | 4.0 | 3.0 | 9.0 | 1.0 | 6.0 | 6.0 | 6.0 | 8.0 | 9.0 | 6.0 | 6.0 | 7.0 | 7.0 | 4.0 | 3.0 | 4.0 | 2.0 | 3.0 | 2.0 | 9.0 | 8.0 | 4.0 | 9.0 | 2.0 | 9.0 | 3.0 | 10.0 | 9.0 | 10.0 | 5.0 |
| 41 | 9.0 | 6.0 | 8.0 | 4.0 | 3.0 | 7.0 | 6.0 | 2.0 | 10.0 | 4.0 | 4.0 | 4.0 | 4.0 | 4.0 | 3.0 | 5.0 | 6.0 | 8.0 | 3.0 | 1.0 | 5.0 | 8.0 | 5.0 | 1.0 | 5.0 | 7.0 | 9.0 | 9.0 | 6.0 | 8.0 | 5.0 | 1.0 | 9.0 | 8.0 | 10.0 | 8.0 | 3.0 | 9.0 | 9.0 | 4.0 | 9.0 | 7.0 | 3.0 | 7.0 | 7.0 | 2.0 | 9.0 |
| 42 | 1.0 | 3.0 | 3.0 | 8.0 | 5.0 | 6.0 | 8.0 | 4.0 | 2.0 | 1.0 | 2.0 | 1.0 | 3.0 | 10.0 | 9.0 | 2.0 | 3.0 | 10.0 | 3.0 | 7.0 | 2.0 | 5.0 | 9.0 | 3.0 | 3.0 | 7.0 | 10.0 | 2.0 | 2.0 | 10.0 | 9.0 | 10.0 | 2.0 | 3.0 | 7.0 | 10.0 | 1.0 | 9.0 | 4.0 | 6.0 | 3.0 | 3.0 | 7.0 | 2.0 | 1.0 | 4.0 | 1.0 |
| 43 | 10.0 | 8.0 | 4.0 | 2.0 | 8.0 | 10.0 | 7.0 | 10.0 | 10.0 | 10.0 | 8.0 | 10.0 | 8.0 | 9.0 | 9.0 | 9.0 | 10.0 | 7.0 | 3.0 | 3.0 | 3.0 | 1.0 | 4.0 | 1.0 | 7.0 | 5.0 | 2.0 | 1.0 | 8.0 | 4.0 | 9.0 | 10.0 | 9.0 | 8.0 | 3.0 | 8.0 | 4.0 | 4.0 | 1.0 | 2.0 | 10.0 | 7.0 | 2.0 | 3.0 | 7.0 | 5.0 | 4.0 |
| 44 | 5.0 | 1.0 | 9.0 | 9.0 | 7.0 | 5.0 | 4.0 | 1.0 | 6.0 | 8.0 | 9.0 | 7.0 | 6.0 | 5.0 | 7.0 | 2.0 | 3.0 | 5.0 | 1.0 | 9.0 | 7.0 | 1.0 | 1.0 | 2.0 | 9.0 | 8.0 | 4.0 | 8.0 | 7.0 | 10.0 | 6.0 | 2.0 | 3.0 | 7.0 | 8.0 | 10.0 | 3.0 | 4.0 | 6.0 | 1.0 | 9.0 | 7.0 | 1.0 | 7.0 | 7.0 | 8.0 | 10.0 |
| 45 | 6.0 | 1.0 | 10.0 | 8.0 | 6.0 | 2.0 | 1.0 | 9.0 | 7.0 | 9.0 | 9.0 | 10.0 | 4.0 | 9.0 | 10.0 | 5.0 | 6.0 | 4.0 | 7.0 | 8.0 | 4.0 | 6.0 | 3.0 | 6.0 | 2.0 | 10.0 | 8.0 | 2.0 | 4.0 | 2.0 | 5.0 | 4.0 | 4.0 | 4.0 | 3.0 | 10.0 | 3.0 | 8.0 | 10.0 | 10.0 | 10.0 | 2.0 | 4.0 | 5.0 | 8.0 | 7.0 | 9.0 |
| 46 | 6.0 | 2.0 | 8.0 | 3.0 | 8.0 | 3.0 | 2.0 | 5.0 | 2.0 | 3.0 | 7.0 | 2.0 | 6.0 | 5.0 | 7.0 | 9.0 | 2.0 | 4.0 | 2.0 | 7.0 | 6.0 | 10.0 | 9.0 | 1.0 | 4.0 | 10.0 | 9.0 | 1.0 | 6.0 | 1.0 | 8.0 | 6.0 | 6.0 | 4.0 | 2.0 | 5.0 | 2.0 | 7.0 | 10.0 | 6.0 | 5.0 | 9.0 | 1.0 | 4.0 | 10.0 | 9.0 | 7.0 |

Oh, and one more practical thing: when you send back the path, please put it into a tiny JSON object like this.

{
  ""solution"": []
}

The ""solution"" array is where you list the nodes of your chosen route in order — like station names: the first entry is the start, the last entry is the finish, and each pair of neighbors in the list must correspond to a legal one-way link on the map. Think of this JSON as just the simple form I want to see filled in, not the route itself.

Please use the exact node labels from the instance input — don’t rename them or invent new ones. 
- For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 1, 'var_index': 1}, {'from': 16, 'to': 2, 'var_index': 2}, {'from': 16, 'to': 3, 'var_index': 3}, {'from': 16, 'to': 4, 'var_index': 4}, {'from': 16, 'to': 5, 'var_index': 5}, {'from': 16, 'to': 6, 'var_index': 6}, {'from': 16, 'to': 7, 'var_index': 7}, {'from': 16, 'to': 8, 'var_index': 8}, {'from': 16, 'to': 9, 'var_index': 9}, {'from': 16, 'to': 10, 'var_index': 10}, {'from': 16, 'to': 11, 'var_index': 11}, {'from': 16, 'to': 12, 'var_index': 12}, {'from': 16, 'to': 13, 'var_index': 13}, {'from': 16, 'to': 14, 'var_index': 14}, {'from': 16, 'to': 15, 'var_index': 15}, {'from': 0, 'to': 17, 'var_index': 16}, {'from': 1, 'to': 17, 'var_index': 17}, {'from': 2, 'to': 17, 'var_index': 18}, {'from': 3, 'to': 17, 'var_index': 19}, {'from': 4, 'to': 17, 'var_index': 20}, {'from': 5, 'to': 17, 'var_index': 21}, {'from': 6, 'to': 17, 'var_index': 22}, {'from': 7, 'to': 17, 'var_index': 23}, {'from': 8, 'to': 17, 'var_index': 24}, {'from': 9, 'to': 17, 'var_index': 25}, {'from': 10, 'to': 17, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 17, 'var_index': 28}, {'from': 13, 'to': 17, 'var_index': 29}, {'from': 14, 'to': 17, 'var_index': 30}, {'from': 15, 'to': 17, 'var_index': 31}, {'from': 0, 'to': 1, 'var_index': 32}, {'from': 1, 'to': 2, 'var_index': 33}, {'from': 2, 'to': 3, 'var_index': 34}, {'from': 3, 'to': 4, 'var_index': 35}, {'from': 4, 'to': 5, 'var_index': 36}, {'from': 5, 'to': 6, 'var_index': 37}, {'from': 6, 'to': 7, 'var_index': 38}, {'from': 7, 'to': 8, 'var_index': 39}, {'from': 8, 'to': 9, 'var_index': 40}, {'from': 9, 'to': 10, 'var_index': 41}, {'from': 10, 'to': 11, 'var_index': 42}, {'from': 11, 'to': 12, 'var_index': 43}, {'from': 12, 'to': 13, 'var_index': 44}, {'from': 13, 'to': 14, 'var_index': 45}, {'from': 14, 'to': 15, 'var_index': 46}], 'objective': {'constant': 0.0, 'linear': [5.0, 2.0, 2.0, 4.0, 10.0, 5.0, 8.0, 1.0, 2.0, 2.0, 10.0, 8.0, 4.0, 8.0, 8.0, 2.0, 10.0, 6.0, 6.0, 8.0, 3.0, 3.0, 6.0, 7.0, 10.0, 1.0, 9.0, 7.0, 10.0, 6.0, 9.0, 6.0, 6.0, 9.0, 1.0, 1.0, 2.0, 3.0, 3.0, 10.0, 4.0, 5.0, 10.0, 6.0, 2.0, 2.0, 1.0], 'quadratic': [[10.0, 10.0, 2.0, 7.0, 5.0, 1.0, 9.0, 4.0, 7.0, 5.0, 6.0, 2.0, 8.0, 2.0, 1.0, 5.0, 8.0, 1.0, 7.0, 3.0, 3.0, 3.0, 9.0, 3.0, 1.0, 5.0, 9.0, 8.0, 4.0, 3.0, 6.0, 7.0, 3.0, 5.0, 2.0, 6.0, 3.0, 4.0, 7.0, 9.0, 10.0, 9.0, 1.0, 10.0, 5.0, 6.0, 6.0], [10.0, 8.0, 3.0, 6.0, 5.0, 2.0, 5.0, 3.0, 8.0, 10.0, 6.0, 1.0, 10.0, 7.0, 10.0, 5.0, 5.0, 10.0, 9.0, 2.0, 8.0, 2.0, 1.0, 5.0, 1.0, 9.0, 6.0, 7.0, 9.0, 4.0, 6.0, 3.0, 10.0, 4.0, 1.0, 5.0, 10.0, 10.0, 3.0, 10.0, 7.0, 6.0, 3.0, 8.0, 1.0, 1.0, 2.0], [2.0, 3.0, 3.0, 1.0, 9.0, 5.0, 4.0, 10.0, 6.0, 10.0, 2.0, 5.0, 3.0, 9.0, 9.0, 6.0, 10.0, 9.0, 10.0, 5.0, 9.0, 5.0, 4.0, 8.0, 10.0, 2.0, 9.0, 4.0, 7.0, 10.0, 5.0, 9.0, 3.0, 4.0, 9.0, 5.0, 5.0, 8.0, 3.0, 6.0, 5.0, 8.0, 3.0, 4.0, 9.0, 10.0, 8.0], [7.0, 6.0, 1.0, 5.0, 3.0, 5.0, 1.0, 1.0, 2.0, 2.0, 6.0, 5.0, 1.0, 2.0, 10.0, 10.0, 7.0, 6.0, 9.0, 8.0, 2.0, 8.0, 9.0, 10.0, 10.0, 4.0, 6.0, 7.0, 4.0, 3.0, 10.0, 4.0, 1.0, 6.0, 1.0, 2.0, 8.0, 4.0, 3.0, 10.0, 7.0, 4.0, 8.0, 2.0, 9.0, 8.0, 3.0], [5.0, 5.0, 9.0, 3.0, 2.0, 8.0, 3.0, 10.0, 2.0, 2.0, 2.0, 7.0, 1.0, 6.0, 3.0, 2.0, 9.0, 10.0, 2.0, 10.0, 2.0, 7.0, 4.0, 7.0, 10.0, 5.0, 9.0, 5.0, 7.0, 10.0, 5.0, 10.0, 3.0, 10.0, 3.0, 7.0, 3.0, 4.0, 7.0, 6.0, 2.0, 3.0, 5.0, 8.0, 7.0, 6.0, 8.0], [1.0, 2.0, 5.0, 5.0, 8.0, 8.0, 1.0, 6.0, 8.0, 9.0, 4.0, 1.0, 8.0, 6.0, 7.0, 4.0, 2.0, 10.0, 3.0, 2.0, 4.0, 6.0, 9.0, 9.0, 4.0, 9.0, 10.0, 4.0, 2.0, 1.0, 7.0, 6.0, 4.0, 6.0, 5.0, 2.0, 8.0, 1.0, 2.0, 6.0, 10.0, 7.0, 6.0, 10.0, 5.0, 2.0, 3.0], [9.0, 5.0, 4.0, 1.0, 3.0, 1.0, 9.0, 2.0, 2.0, 7.0, 7.0, 7.0, 9.0, 5.0, 6.0, 10.0, 8.0, 1.0, 3.0, 1.0, 10.0, 10.0, 9.0, 1.0, 7.0, 1.0, 8.0, 4.0, 6.0, 9.0, 8.0, 10.0, 4.0, 6.0, 9.0, 10.0, 5.0, 10.0, 6.0, 3.0, 4.0, 6.0, 8.0, 7.0, 4.0, 1.0, 2.0], [4.0, 3.0, 10.0, 1.0, 10.0, 6.0, 2.0, 10.0, 2.0, 7.0, 8.0, 4.0, 1.0, 1.0, 1.0, 5.0, 8.0, 2.0, 5.0, 4.0, 10.0, 6.0, 2.0, 1.0, 1.0, 5.0, 2.0, 4.0, 6.0, 6.0, 1.0, 5.0, 3.0, 5.0, 9.0, 9.0, 6.0, 9.0, 8.0, 2.0, 5.0, 2.0, 4.0, 10.0, 1.0, 9.0, 5.0], [7.0, 8.0, 6.0, 2.0, 2.0, 8.0, 2.0, 2.0, 6.0, 7.0, 4.0, 10.0, 2.0, 10.0, 7.0, 3.0, 2.0, 6.0, 9.0, 10.0, 4.0, 10.0, 6.0, 6.0, 1.0, 6.0, 7.0, 9.0, 6.0, 10.0, 4.0, 5.0, 5.0, 7.0, 6.0, 8.0, 2.0, 9.0, 7.0, 4.0, 2.0, 10.0, 2.0, 10.0, 6.0, 7.0, 2.0], [5.0, 10.0, 10.0, 2.0, 2.0, 9.0, 7.0, 7.0, 7.0, 8.0, 7.0, 7.0, 1.0, 4.0, 1.0, 9.0, 2.0, 3.0, 7.0, 1.0, 4.0, 4.0, 8.0, 2.0, 7.0, 6.0, 6.0, 4.0, 1.0, 10.0, 5.0, 6.0, 1.0, 4.0, 9.0, 9.0, 5.0, 8.0, 7.0, 6.0, 4.0, 4.0, 1.0, 10.0, 8.0, 9.0, 3.0], [6.0, 6.0, 2.0, 6.0, 2.0, 4.0, 7.0, 8.0, 4.0, 7.0, 4.0, 8.0, 3.0, 8.0, 5.0, 6.0, 8.0, 7.0, 7.0, 8.0, 5.0, 4.0, 3.0, 7.0, 7.0, 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'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 37, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 38, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 39, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 40, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 41, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 42, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 43, 'quadratic_cost': 4.0}, {'var_i': 46, 'var_j': 44, 'quadratic_cost': 10.0}, {'var_i': 46, 'var_j': 45, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 46, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'Q', 'to': 'A', 'var_index': 0}, {'from': 'Q', 'to': 'B', 'var_index': 1}, {'from': 'Q', 'to': 'C', 'var_index': 2}, {'from': 'Q', 'to': 'D', 'var_index': 3}, {'from': 'Q', 'to': 'E', 'var_index': 4}, {'from': 'Q', 'to': 'F', 'var_index': 5}, {'from': 'Q', 'to': 'G', 'var_index': 6}, {'from': 'Q', 'to': 'H', 'var_index': 7}, {'from': 'Q', 'to': 'I', 'var_index': 8}, {'from': 'Q', 'to': 'J', 'var_index': 9}, {'from': 'Q', 'to': 'K', 'var_index': 10}, {'from': 'Q', 'to': 'L', 'var_index': 11}, {'from': 'Q', 'to': 'M', 'var_index': 12}, {'from': 'Q', 'to': 'N', 'var_index': 13}, {'from': 'Q', 'to': 'O', 'var_index': 14}, {'from': 'Q', 'to': 'P', 'var_index': 15}, {'from': 'A', 'to': 'R', 'var_index': 16}, {'from': 'B', 'to': 'R', 'var_index': 17}, {'from': 'C', 'to': 'R', 'var_index': 18}, {'from': 'D', 'to': 'R', 'var_index': 19}, {'from': 'E', 'to': 'R', 'var_index': 20}, {'from': 'F', 'to': 'R', 'var_index': 21}, {'from': 'G', 'to': 'R', 'var_index': 22}, {'from': 'H', 'to': 'R', 'var_index': 23}, {'from': 'I', 'to': 'R', 'var_index': 24}, {'from': 'J', 'to': 'R', 'var_index': 25}, {'from': 'K', 'to': 'R', 'var_index': 26}, {'from': 'L', 'to': 'R', 'var_index': 27}, {'from': 'M', 'to': 'R', 'var_index': 28}, {'from': 'N', 'to': 'R', 'var_index': 29}, {'from': 'O', 'to': 'R', 'var_index': 30}, {'from': 'P', 'to': 'R', 'var_index': 31}, {'from': 'A', 'to': 'B', 'var_index': 32}, {'from': 'B', 'to': 'C', 'var_index': 33}, {'from': 'C', 'to': 'D', 'var_index': 34}, {'from': 'D', 'to': 'E', 'var_index': 35}, {'from': 'E', 'to': 'F', 'var_index': 36}, {'from': 'F', 'to': 'G', 'var_index': 37}, {'from': 'G', 'to': 'H', 'var_index': 38}, {'from': 'H', 'to': 'I', 'var_index': 39}, {'from': 'I', 'to': 'J', 'var_index': 40}, {'from': 'J', 'to': 'K', 'var_index': 41}, {'from': 'K', 'to': 'L', 'var_index': 42}, {'from': 'L', 'to': 'M', 'var_index': 43}, {'from': 'M', 'to': 'N', 'var_index': 44}, {'from': 'N', 'to': 'O', 'var_index': 45}, {'from': 'O', 'to': 'P', 'var_index': 46}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R'}}","['Q', 'I', 'R']",27,json,names
QSPP,QSPP,"Someone is trying to pick a single one-way plumbing run from the inlet to the outlet through a maze of pipes. Each pipe carries a handling cost, and whenever certain pipes are used together they produce extra losses — even a lone pipe can have its own extra hit. The task is to select one continuous route (begin at the inlet, finish at the outlet, step along existing directed connections) so that the final tally — add every pipe’s base fee and add every extra penalty for each pair of pipes that both show up on the route — is as small as possible. The exact network and the numbers for each pipe and pair are shown below.

{
  ""total_junctions"": 16,
  ""total_pipes"": 24,
  ""junction_ids"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16
  ],
  ""inlet_junction"": 1,
  ""outlet_junction"": 16,
  ""edges"": [
    {
      ""pipe_from_junction"": 1,
      ""pipe_to_junction"": 2,
      ""pipe_id"": 0
    },
    {
      ""pipe_from_junction"": 1,
      ""pipe_to_junction"": 5,
      ""pipe_id"": 1
    },
    {
      ""pipe_from_junction"": 2,
      ""pipe_to_junction"": 3,
      ""pipe_id"": 2
    },
    {
      ""pipe_from_junction"": 2,
      ""pipe_to_junction"": 6,
      ""pipe_id"": 3
    },
    {
      ""pipe_from_junction"": 3,
      ""pipe_to_junction"": 4,
      ""pipe_id"": 4
    },
    {
      ""pipe_from_junction"": 3,
      ""pipe_to_junction"": 7,
      ""pipe_id"": 5
    },
    {
      ""pipe_from_junction"": 4,
      ""pipe_to_junction"": 8,
      ""pipe_id"": 6
    },
    {
      ""pipe_from_junction"": 5,
      ""pipe_to_junction"": 6,
      ""pipe_id"": 7
    },
    {
      ""pipe_from_junction"": 5,
      ""pipe_to_junction"": 9,
      ""pipe_id"": 8
    },
    {
      ""pipe_from_junction"": 6,
      ""pipe_to_junction"": 7,
      ""pipe_id"": 9
    },
    {
      ""pipe_from_junction"": 6,
      ""pipe_to_junction"": 10,
      ""pipe_id"": 10
    },
    {
      ""pipe_from_junction"": 7,
      ""pipe_to_junction"": 8,
      ""pipe_id"": 11
    },
    {
      ""pipe_from_junction"": 7,
      ""pipe_to_junction"": 11,
      ""pipe_id"": 12
    },
    {
      ""pipe_from_junction"": 8,
      ""pipe_to_junction"": 12,
      ""pipe_id"": 13
    },
    {
      ""pipe_from_junction"": 9,
      ""pipe_to_junction"": 10,
      ""pipe_id"": 14
    },
    {
      ""pipe_from_junction"": 9,
      ""pipe_to_junction"": 13,
      ""pipe_id"": 15
    },
    {
      ""pipe_from_junction"": 10,
      ""pipe_to_junction"": 11,
      ""pipe_id"": 16
    },
    {
      ""pipe_from_junction"": 10,
      ""pipe_to_junction"": 14,
      ""pipe_id"": 17
    },
    {
      ""pipe_from_junction"": 11,
      ""pipe_to_junction"": 12,
      ""pipe_id"": 18
    },
    {
      ""pipe_from_junction"": 11,
      ""pipe_to_junction"": 15,
      ""pipe_id"": 19
    },
    {
      ""pipe_from_junction"": 12,
      ""pipe_to_junction"": 16,
      ""pipe_id"": 20
    },
    {
      ""pipe_from_junction"": 13,
      ""pipe_to_junction"": 14,
      ""pipe_id"": 21
    },
    {
      ""pipe_from_junction"": 14,
      ""pipe_to_junction"": 15,
      ""pipe_id"": 22
    },
    {
      ""pipe_from_junction"": 15,
      ""pipe_to_junction"": 16,
      ""pipe_id"": 23
    }
  ],
  ""linear_costs"": [
    {
      ""pipe_id"": 0,
      ""pipe_handling_fee"": 3.0
    },
    {
      ""pipe_id"": 1,
      ""pipe_handling_fee"": 3.0
    },
    {
      ""pipe_id"": 2,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 3,
      ""pipe_handling_fee"": 6.0
    },
    {
      ""pipe_id"": 4,
      ""pipe_handling_fee"": 8.0
    },
    {
      ""pipe_id"": 5,
      ""pipe_handling_fee"": 3.0
    },
    {
      ""pipe_id"": 6,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 7,
      ""pipe_handling_fee"": 2.0
    },
    {
      ""pipe_id"": 8,
      ""pipe_handling_fee"": 10.0
    },
    {
      ""pipe_id"": 9,
      ""pipe_handling_fee"": 9.0
    },
    {
      ""pipe_id"": 10,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 11,
      ""pipe_handling_fee"": 7.0
    },
    {
      ""pipe_id"": 12,
      ""pipe_handling_fee"": 6.0
    },
    {
      ""pipe_id"": 13,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 14,
      ""pipe_handling_fee"": 5.0
    },
    {
      ""pipe_id"": 15,
      ""pipe_handling_fee"": 1.0
    },
    {
      ""pipe_id"": 16,
      ""pipe_handling_fee"": 1.0
    },
    {
      ""pipe_id"": 17,
      ""pipe_handling_fee"": 5.0
    },
    {
      ""pipe_id"": 18,
      ""pipe_handling_fee"": 7.0
    },
    {
      ""pipe_id"": 19,
      ""pipe_handling_fee"": 5.0
    },
    {
      ""pipe_id"": 20,
      ""pipe_handling_fee"": 8.0
    },
    {
      ""pipe_id"": 21,
      ""pipe_handling_fee"": 3.0
    },
    {
      ""pipe_id"": 22,
      ""pipe_handling_fee"": 6.0
    },
    {
      ""pipe_id"": 23,
      ""pipe_handling_fee"": 5.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (pipe_i_id, pipe_j_id). If two pipes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| pipe_i_id\pipe_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 3.0 | 7.0 | 4.0 | 6.0 | 2.0 | 2.0 | 8.0 | 4.0 | 2.0 | 3.0 | 5.0 | 2.0 | 1.0 | 3.0 | 9.0 | 6.0 | 7.0 | 2.0 | 5.0 | 10.0 | 4.0 | 4.0 | 2.0 |
| 1 | 3.0 | 2.0 | 5.0 | 4.0 | 9.0 | 5.0 | 6.0 | 1.0 | 2.0 | 10.0 | 2.0 | 1.0 | 1.0 | 6.0 | 5.0 | 9.0 | 1.0 | 8.0 | 3.0 | 4.0 | 3.0 | 9.0 | 10.0 | 9.0 |
| 2 | 7.0 | 5.0 | 10.0 | 5.0 | 10.0 | 2.0 | 9.0 | 8.0 | 1.0 | 5.0 | 8.0 | 8.0 | 6.0 | 4.0 | 6.0 | 2.0 | 9.0 | 9.0 | 8.0 | 2.0 | 9.0 | 5.0 | 2.0 | 1.0 |
| 3 | 4.0 | 4.0 | 5.0 | 8.0 | 9.0 | 6.0 | 10.0 | 4.0 | 7.0 | 4.0 | 4.0 | 10.0 | 6.0 | 8.0 | 6.0 | 3.0 | 9.0 | 6.0 | 9.0 | 6.0 | 3.0 | 1.0 | 6.0 | 3.0 |
| 4 | 6.0 | 9.0 | 10.0 | 9.0 | 4.0 | 4.0 | 3.0 | 5.0 | 5.0 | 7.0 | 10.0 | 9.0 | 6.0 | 10.0 | 8.0 | 2.0 | 5.0 | 4.0 | 9.0 | 5.0 | 5.0 | 2.0 | 6.0 | 10.0 |
| 5 | 2.0 | 5.0 | 2.0 | 6.0 | 4.0 | 9.0 | 5.0 | 6.0 | 6.0 | 5.0 | 6.0 | 6.0 | 8.0 | 10.0 | 4.0 | 2.0 | 2.0 | 2.0 | 8.0 | 6.0 | 2.0 | 3.0 | 10.0 | 9.0 |
| 6 | 2.0 | 6.0 | 9.0 | 10.0 | 3.0 | 5.0 | 8.0 | 10.0 | 9.0 | 3.0 | 2.0 | 9.0 | 4.0 | 1.0 | 1.0 | 2.0 | 2.0 | 2.0 | 4.0 | 6.0 | 3.0 | 6.0 | 9.0 | 3.0 |
| 7 | 8.0 | 1.0 | 8.0 | 4.0 | 5.0 | 6.0 | 10.0 | 9.0 | 8.0 | 3.0 | 2.0 | 1.0 | 2.0 | 7.0 | 8.0 | 9.0 | 5.0 | 3.0 | 3.0 | 10.0 | 2.0 | 7.0 | 9.0 | 7.0 |
| 8 | 4.0 | 2.0 | 1.0 | 7.0 | 5.0 | 6.0 | 9.0 | 8.0 | 3.0 | 9.0 | 5.0 | 5.0 | 7.0 | 2.0 | 6.0 | 8.0 | 6.0 | 5.0 | 7.0 | 10.0 | 7.0 | 5.0 | 6.0 | 10.0 |
| 9 | 2.0 | 10.0 | 5.0 | 4.0 | 7.0 | 5.0 | 3.0 | 3.0 | 9.0 | 1.0 | 5.0 | 1.0 | 7.0 | 1.0 | 4.0 | 5.0 | 3.0 | 3.0 | 9.0 | 2.0 | 6.0 | 10.0 | 8.0 | 4.0 |
| 10 | 3.0 | 2.0 | 8.0 | 4.0 | 10.0 | 6.0 | 2.0 | 2.0 | 5.0 | 5.0 | 5.0 | 10.0 | 8.0 | 8.0 | 4.0 | 5.0 | 9.0 | 10.0 | 6.0 | 5.0 | 9.0 | 8.0 | 2.0 | 5.0 |
| 11 | 5.0 | 1.0 | 8.0 | 10.0 | 9.0 | 6.0 | 9.0 | 1.0 | 5.0 | 1.0 | 10.0 | 5.0 | 7.0 | 4.0 | 10.0 | 8.0 | 4.0 | 10.0 | 6.0 | 1.0 | 9.0 | 5.0 | 2.0 | 9.0 |
| 12 | 2.0 | 1.0 | 6.0 | 6.0 | 6.0 | 8.0 | 4.0 | 2.0 | 7.0 | 7.0 | 8.0 | 7.0 | 10.0 | 7.0 | 8.0 | 3.0 | 9.0 | 8.0 | 8.0 | 6.0 | 3.0 | 4.0 | 9.0 | 1.0 |
| 13 | 1.0 | 6.0 | 4.0 | 8.0 | 10.0 | 10.0 | 1.0 | 7.0 | 2.0 | 1.0 | 8.0 | 4.0 | 7.0 | 5.0 | 2.0 | 4.0 | 10.0 | 3.0 | 2.0 | 4.0 | 5.0 | 10.0 | 5.0 | 7.0 |
| 14 | 3.0 | 5.0 | 6.0 | 6.0 | 8.0 | 4.0 | 1.0 | 8.0 | 6.0 | 4.0 | 4.0 | 10.0 | 8.0 | 2.0 | 4.0 | 7.0 | 2.0 | 3.0 | 4.0 | 3.0 | 3.0 | 6.0 | 2.0 | 1.0 |
| 15 | 9.0 | 9.0 | 2.0 | 3.0 | 2.0 | 2.0 | 2.0 | 9.0 | 8.0 | 5.0 | 5.0 | 8.0 | 3.0 | 4.0 | 7.0 | 7.0 | 5.0 | 7.0 | 10.0 | 7.0 | 7.0 | 4.0 | 8.0 | 7.0 |
| 16 | 6.0 | 1.0 | 9.0 | 9.0 | 5.0 | 2.0 | 2.0 | 5.0 | 6.0 | 3.0 | 9.0 | 4.0 | 9.0 | 10.0 | 2.0 | 5.0 | 1.0 | 10.0 | 7.0 | 6.0 | 4.0 | 3.0 | 1.0 | 1.0 |
| 17 | 7.0 | 8.0 | 9.0 | 6.0 | 4.0 | 2.0 | 2.0 | 3.0 | 5.0 | 3.0 | 10.0 | 10.0 | 8.0 | 3.0 | 3.0 | 7.0 | 10.0 | 10.0 | 6.0 | 5.0 | 6.0 | 1.0 | 3.0 | 10.0 |
| 18 | 2.0 | 3.0 | 8.0 | 9.0 | 9.0 | 8.0 | 4.0 | 3.0 | 7.0 | 9.0 | 6.0 | 6.0 | 8.0 | 2.0 | 4.0 | 10.0 | 7.0 | 6.0 | 10.0 | 9.0 | 4.0 | 9.0 | 10.0 | 3.0 |
| 19 | 5.0 | 4.0 | 2.0 | 6.0 | 5.0 | 6.0 | 6.0 | 10.0 | 10.0 | 2.0 | 5.0 | 1.0 | 6.0 | 4.0 | 3.0 | 7.0 | 6.0 | 5.0 | 9.0 | 6.0 | 7.0 | 6.0 | 10.0 | 1.0 |
| 20 | 10.0 | 3.0 | 9.0 | 3.0 | 5.0 | 2.0 | 3.0 | 2.0 | 7.0 | 6.0 | 9.0 | 9.0 | 3.0 | 5.0 | 3.0 | 7.0 | 4.0 | 6.0 | 4.0 | 7.0 | 1.0 | 4.0 | 8.0 | 9.0 |
| 21 | 4.0 | 9.0 | 5.0 | 1.0 | 2.0 | 3.0 | 6.0 | 7.0 | 5.0 | 10.0 | 8.0 | 5.0 | 4.0 | 10.0 | 6.0 | 4.0 | 3.0 | 1.0 | 9.0 | 6.0 | 4.0 | 4.0 | 1.0 | 10.0 |
| 22 | 4.0 | 10.0 | 2.0 | 6.0 | 6.0 | 10.0 | 9.0 | 9.0 | 6.0 | 8.0 | 2.0 | 2.0 | 9.0 | 5.0 | 2.0 | 8.0 | 1.0 | 3.0 | 10.0 | 10.0 | 8.0 | 1.0 | 6.0 | 6.0 |
| 23 | 2.0 | 9.0 | 1.0 | 3.0 | 10.0 | 9.0 | 3.0 | 7.0 | 10.0 | 4.0 | 5.0 | 9.0 | 1.0 | 7.0 | 1.0 | 7.0 | 1.0 | 10.0 | 3.0 | 1.0 | 9.0 | 10.0 | 6.0 | 1.0 |

When you're ready, just reply with the chosen node sequence in a tiny JSON object — super simple, just a single field called solution that holds the list of nodes along the route. For example:

{
  ""solution"": []
}

Here ""solution"" is the list of node identifiers in order from the inlet to the outlet (first entry is the inlet, last is the outlet). Treat this JSON like a short form you fill out—it's only a sketch of the expected shape, not the actual answer itself.

Please use node identifiers exactly as they appear in the instance input — no renaming, no made-up labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k4_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 4, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 5, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 6, 'var_index': 5}, {'from': 3, 'to': 7, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 8, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 9, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 10, 'var_index': 12}, {'from': 7, 'to': 11, 'var_index': 13}, {'from': 8, 'to': 9, 'var_index': 14}, {'from': 8, 'to': 12, 'var_index': 15}, {'from': 9, 'to': 10, 'var_index': 16}, {'from': 9, 'to': 13, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 14, 'var_index': 19}, {'from': 11, 'to': 15, 'var_index': 20}, {'from': 12, 'to': 13, 'var_index': 21}, {'from': 13, 'to': 14, 'var_index': 22}, {'from': 14, 'to': 15, 'var_index': 23}], 'objective': {'constant': 0.0, 'linear': [3.0, 3.0, 4.0, 6.0, 8.0, 3.0, 4.0, 2.0, 10.0, 9.0, 4.0, 7.0, 6.0, 4.0, 5.0, 1.0, 1.0, 5.0, 7.0, 5.0, 8.0, 3.0, 6.0, 5.0], 'quadratic': [[10.0, 3.0, 7.0, 4.0, 6.0, 2.0, 2.0, 8.0, 4.0, 2.0, 3.0, 5.0, 2.0, 1.0, 3.0, 9.0, 6.0, 7.0, 2.0, 5.0, 10.0, 4.0, 4.0, 2.0], [3.0, 2.0, 5.0, 4.0, 9.0, 5.0, 6.0, 1.0, 2.0, 10.0, 2.0, 1.0, 1.0, 6.0, 5.0, 9.0, 1.0, 8.0, 3.0, 4.0, 3.0, 9.0, 10.0, 9.0], [7.0, 5.0, 10.0, 5.0, 10.0, 2.0, 9.0, 8.0, 1.0, 5.0, 8.0, 8.0, 6.0, 4.0, 6.0, 2.0, 9.0, 9.0, 8.0, 2.0, 9.0, 5.0, 2.0, 1.0], [4.0, 4.0, 5.0, 8.0, 9.0, 6.0, 10.0, 4.0, 7.0, 4.0, 4.0, 10.0, 6.0, 8.0, 6.0, 3.0, 9.0, 6.0, 9.0, 6.0, 3.0, 1.0, 6.0, 3.0], [6.0, 9.0, 10.0, 9.0, 4.0, 4.0, 3.0, 5.0, 5.0, 7.0, 10.0, 9.0, 6.0, 10.0, 8.0, 2.0, 5.0, 4.0, 9.0, 5.0, 5.0, 2.0, 6.0, 10.0], [2.0, 5.0, 2.0, 6.0, 4.0, 9.0, 5.0, 6.0, 6.0, 5.0, 6.0, 6.0, 8.0, 10.0, 4.0, 2.0, 2.0, 2.0, 8.0, 6.0, 2.0, 3.0, 10.0, 9.0], [2.0, 6.0, 9.0, 10.0, 3.0, 5.0, 8.0, 10.0, 9.0, 3.0, 2.0, 9.0, 4.0, 1.0, 1.0, 2.0, 2.0, 2.0, 4.0, 6.0, 3.0, 6.0, 9.0, 3.0], [8.0, 1.0, 8.0, 4.0, 5.0, 6.0, 10.0, 9.0, 8.0, 3.0, 2.0, 1.0, 2.0, 7.0, 8.0, 9.0, 5.0, 3.0, 3.0, 10.0, 2.0, 7.0, 9.0, 7.0], [4.0, 2.0, 1.0, 7.0, 5.0, 6.0, 9.0, 8.0, 3.0, 9.0, 5.0, 5.0, 7.0, 2.0, 6.0, 8.0, 6.0, 5.0, 7.0, 10.0, 7.0, 5.0, 6.0, 10.0], [2.0, 10.0, 5.0, 4.0, 7.0, 5.0, 3.0, 3.0, 9.0, 1.0, 5.0, 1.0, 7.0, 1.0, 4.0, 5.0, 3.0, 3.0, 9.0, 2.0, 6.0, 10.0, 8.0, 4.0], [3.0, 2.0, 8.0, 4.0, 10.0, 6.0, 2.0, 2.0, 5.0, 5.0, 5.0, 10.0, 8.0, 8.0, 4.0, 5.0, 9.0, 10.0, 6.0, 5.0, 9.0, 8.0, 2.0, 5.0], [5.0, 1.0, 8.0, 10.0, 9.0, 6.0, 9.0, 1.0, 5.0, 1.0, 10.0, 5.0, 7.0, 4.0, 10.0, 8.0, 4.0, 10.0, 6.0, 1.0, 9.0, 5.0, 2.0, 9.0], [2.0, 1.0, 6.0, 6.0, 6.0, 8.0, 4.0, 2.0, 7.0, 7.0, 8.0, 7.0, 10.0, 7.0, 8.0, 3.0, 9.0, 8.0, 8.0, 6.0, 3.0, 4.0, 9.0, 1.0], [1.0, 6.0, 4.0, 8.0, 10.0, 10.0, 1.0, 7.0, 2.0, 1.0, 8.0, 4.0, 7.0, 5.0, 2.0, 4.0, 10.0, 3.0, 2.0, 4.0, 5.0, 10.0, 5.0, 7.0], [3.0, 5.0, 6.0, 6.0, 8.0, 4.0, 1.0, 8.0, 6.0, 4.0, 4.0, 10.0, 8.0, 2.0, 4.0, 7.0, 2.0, 3.0, 4.0, 3.0, 3.0, 6.0, 2.0, 1.0], [9.0, 9.0, 2.0, 3.0, 2.0, 2.0, 2.0, 9.0, 8.0, 5.0, 5.0, 8.0, 3.0, 4.0, 7.0, 7.0, 5.0, 7.0, 10.0, 7.0, 7.0, 4.0, 8.0, 7.0], [6.0, 1.0, 9.0, 9.0, 5.0, 2.0, 2.0, 5.0, 6.0, 3.0, 9.0, 4.0, 9.0, 10.0, 2.0, 5.0, 1.0, 10.0, 7.0, 6.0, 4.0, 3.0, 1.0, 1.0], [7.0, 8.0, 9.0, 6.0, 4.0, 2.0, 2.0, 3.0, 5.0, 3.0, 10.0, 10.0, 8.0, 3.0, 3.0, 7.0, 10.0, 10.0, 6.0, 5.0, 6.0, 1.0, 3.0, 10.0], [2.0, 3.0, 8.0, 9.0, 9.0, 8.0, 4.0, 3.0, 7.0, 9.0, 6.0, 6.0, 8.0, 2.0, 4.0, 10.0, 7.0, 6.0, 10.0, 9.0, 4.0, 9.0, 10.0, 3.0], [5.0, 4.0, 2.0, 6.0, 5.0, 6.0, 6.0, 10.0, 10.0, 2.0, 5.0, 1.0, 6.0, 4.0, 3.0, 7.0, 6.0, 5.0, 9.0, 6.0, 7.0, 6.0, 10.0, 1.0], [10.0, 3.0, 9.0, 3.0, 5.0, 2.0, 3.0, 2.0, 7.0, 6.0, 9.0, 9.0, 3.0, 5.0, 3.0, 7.0, 4.0, 6.0, 4.0, 7.0, 1.0, 4.0, 8.0, 9.0], [4.0, 9.0, 5.0, 1.0, 2.0, 3.0, 6.0, 7.0, 5.0, 10.0, 8.0, 5.0, 4.0, 10.0, 6.0, 4.0, 3.0, 1.0, 9.0, 6.0, 4.0, 4.0, 1.0, 10.0], [4.0, 10.0, 2.0, 6.0, 6.0, 10.0, 9.0, 9.0, 6.0, 8.0, 2.0, 2.0, 9.0, 5.0, 2.0, 8.0, 1.0, 3.0, 10.0, 10.0, 8.0, 1.0, 6.0, 6.0], [2.0, 9.0, 1.0, 3.0, 10.0, 9.0, 3.0, 7.0, 10.0, 4.0, 5.0, 9.0, 1.0, 7.0, 1.0, 7.0, 1.0, 10.0, 3.0, 1.0, 9.0, 10.0, 6.0, 1.0]]}, 'source': 0, 'target': 15}","[0, 4, 5, 9, 10, 11, 15]",175.0,"{'problem_type': 'QSPP', 'num_nodes': 16, 'num_edges': 24, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'source': 1, 'target': 16, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 3.0}, {'var_index': 6, 'linear_cost': 4.0}, {'var_index': 7, 'linear_cost': 2.0}, {'var_index': 8, 'linear_cost': 10.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 4.0}, {'var_index': 11, 'linear_cost': 7.0}, {'var_index': 12, 'linear_cost': 6.0}, {'var_index': 13, 'linear_cost': 4.0}, {'var_index': 14, 'linear_cost': 5.0}, {'var_index': 15, 'linear_cost': 1.0}, {'var_index': 16, 'linear_cost': 1.0}, {'var_index': 17, 'linear_cost': 5.0}, {'var_index': 18, 'linear_cost': 7.0}, {'var_index': 19, 'linear_cost': 5.0}, {'var_index': 20, 'linear_cost': 8.0}, {'var_index': 21, 'linear_cost': 3.0}, {'var_index': 22, 'linear_cost': 6.0}, {'var_index': 23, 'linear_cost': 5.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 23, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 23, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 23, 'quadratic_cost': 3.0}, 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'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 17, 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{'var_i': 18, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 21, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 23, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 23, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 23, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 23, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 23, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 23, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 23, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 23, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 1, 'to': 2, 'var_index': 0}, {'from': 1, 'to': 5, 'var_index': 1}, {'from': 2, 'to': 3, 'var_index': 2}, {'from': 2, 'to': 6, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 3, 'to': 7, 'var_index': 5}, {'from': 4, 'to': 8, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 5, 'to': 9, 'var_index': 8}, {'from': 6, 'to': 7, 'var_index': 9}, {'from': 6, 'to': 10, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}, {'from': 7, 'to': 11, 'var_index': 12}, {'from': 8, 'to': 12, 'var_index': 13}, {'from': 9, 'to': 10, 'var_index': 14}, {'from': 9, 'to': 13, 'var_index': 15}, {'from': 10, 'to': 11, 'var_index': 16}, {'from': 10, 'to': 14, 'var_index': 17}, {'from': 11, 'to': 12, 'var_index': 18}, {'from': 11, 'to': 15, 'var_index': 19}, {'from': 12, 'to': 16, 'var_index': 20}, {'from': 13, 'to': 14, 'var_index': 21}, {'from': 14, 'to': 15, 'var_index': 22}, {'from': 15, 'to': 16, 'var_index': 23}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16}}","[1, 5, 6, 10, 11, 12, 16]",28,json,1
QSPP,QSPP,"I’m helping out an event planner who has to pick one clear route to move all guests from the lobby into the banquet hall using the venue’s one-way corridors. Each corridor has a basic inconvenience — like how narrow, long, or awkward it is — and some corridor combinations make things worse when used together (maybe they create pinch points or confusing turns). The aim is to pick the single continuous route that causes the least total hassle, where the total hassle is just the sum of each corridor’s basic cost plus any extra friction that arises if certain corridors are used in combination. The route has to start in the lobby, end in the banquet room, follow the direction of the passageways at every step, and be a single, unbroken sequence (no splitting guests across multiple routes or skipping/making up connections). The exact map and the numbers for each corridor and combination are shown below.

# total_locations=18
# total_corridors=32
# location_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
# lobby_node=16
# banquet_hall_node=17

corridor_from_location,corridor_to_location,corridor_id
16,0,0
16,4,1
16,8,2
16,12,3
3,17,4
7,17,5
11,17,6
15,17,7
0,1,8
0,4,9
1,2,10
1,5,11
2,3,12
2,6,13
3,7,14
4,5,15
4,8,16
5,6,17
5,9,18
6,7,19
6,10,20
7,11,21
8,9,22
8,12,23
9,10,24
9,13,25
10,11,26
10,14,27
11,15,28
12,13,29
13,14,30
14,15,31

corridor_id_ref,base_inconvenience
0,1.0
1,9.0
2,5.0
3,7.0
4,2.0
5,4.0
6,9.0
7,9.0
8,4.0
9,1.0
10,7.0
11,10.0
12,6.0
13,9.0
14,8.0
15,10.0
16,7.0
17,10.0
18,7.0
19,3.0
20,1.0
21,5.0
22,3.0
23,7.0
24,1.0
25,1.0
26,2.0
27,4.0
28,7.0
29,1.0
30,8.0
31,9.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 7.0 | 7.0 | 4.0 | 5.0 | 4.0 | 10.0 | 10.0 | 3.0 | 9.0 | 8.0 | 8.0 | 9.0 | 10.0 | 1.0 | 1.0 | 5.0 | 1.0 | 10.0 | 5.0 | 1.0 | 8.0 | 4.0 | 8.0 | 6.0 | 5.0 | 8.0 | 10.0 | 8.0 | 1.0 | 6.0 | 4.0 |
| 1 | 7.0 | 5.0 | 8.0 | 1.0 | 2.0 | 3.0 | 7.0 | 9.0 | 2.0 | 8.0 | 1.0 | 8.0 | 6.0 | 7.0 | 4.0 | 9.0 | 8.0 | 7.0 | 10.0 | 7.0 | 4.0 | 2.0 | 10.0 | 8.0 | 2.0 | 5.0 | 6.0 | 10.0 | 6.0 | 5.0 | 1.0 | 8.0 |
| 2 | 7.0 | 8.0 | 4.0 | 9.0 | 2.0 | 9.0 | 1.0 | 4.0 | 1.0 | 3.0 | 6.0 | 8.0 | 10.0 | 1.0 | 2.0 | 3.0 | 3.0 | 8.0 | 7.0 | 5.0 | 9.0 | 10.0 | 3.0 | 4.0 | 6.0 | 2.0 | 6.0 | 8.0 | 2.0 | 4.0 | 2.0 | 3.0 |
| 3 | 4.0 | 1.0 | 9.0 | 7.0 | 6.0 | 8.0 | 10.0 | 1.0 | 8.0 | 1.0 | 3.0 | 9.0 | 5.0 | 2.0 | 6.0 | 1.0 | 9.0 | 7.0 | 5.0 | 3.0 | 2.0 | 3.0 | 2.0 | 9.0 | 10.0 | 3.0 | 3.0 | 10.0 | 5.0 | 5.0 | 6.0 | 7.0 |
| 4 | 5.0 | 2.0 | 2.0 | 6.0 | 8.0 | 10.0 | 8.0 | 1.0 | 1.0 | 6.0 | 1.0 | 2.0 | 2.0 | 1.0 | 8.0 | 10.0 | 2.0 | 10.0 | 5.0 | 1.0 | 3.0 | 3.0 | 5.0 | 1.0 | 3.0 | 2.0 | 1.0 | 6.0 | 1.0 | 4.0 | 8.0 | 8.0 |
| 5 | 4.0 | 3.0 | 9.0 | 8.0 | 10.0 | 4.0 | 8.0 | 3.0 | 10.0 | 8.0 | 6.0 | 9.0 | 9.0 | 9.0 | 10.0 | 1.0 | 8.0 | 7.0 | 3.0 | 8.0 | 2.0 | 2.0 | 3.0 | 5.0 | 8.0 | 3.0 | 8.0 | 8.0 | 5.0 | 6.0 | 7.0 | 1.0 |
| 6 | 10.0 | 7.0 | 1.0 | 10.0 | 8.0 | 8.0 | 4.0 | 5.0 | 8.0 | 1.0 | 8.0 | 1.0 | 8.0 | 6.0 | 5.0 | 2.0 | 1.0 | 9.0 | 4.0 | 3.0 | 3.0 | 5.0 | 7.0 | 2.0 | 1.0 | 4.0 | 10.0 | 5.0 | 5.0 | 2.0 | 9.0 | 4.0 |
| 7 | 10.0 | 9.0 | 4.0 | 1.0 | 1.0 | 3.0 | 5.0 | 6.0 | 3.0 | 2.0 | 8.0 | 8.0 | 5.0 | 8.0 | 5.0 | 8.0 | 3.0 | 6.0 | 2.0 | 3.0 | 2.0 | 7.0 | 5.0 | 2.0 | 9.0 | 7.0 | 7.0 | 4.0 | 5.0 | 1.0 | 9.0 | 9.0 |
| 8 | 3.0 | 2.0 | 1.0 | 8.0 | 1.0 | 10.0 | 8.0 | 3.0 | 9.0 | 9.0 | 1.0 | 2.0 | 7.0 | 1.0 | 7.0 | 4.0 | 4.0 | 3.0 | 1.0 | 1.0 | 2.0 | 4.0 | 3.0 | 10.0 | 7.0 | 6.0 | 10.0 | 10.0 | 2.0 | 9.0 | 9.0 | 2.0 |
| 9 | 9.0 | 8.0 | 3.0 | 1.0 | 6.0 | 8.0 | 1.0 | 2.0 | 9.0 | 7.0 | 3.0 | 5.0 | 4.0 | 1.0 | 2.0 | 6.0 | 1.0 | 2.0 | 4.0 | 6.0 | 3.0 | 1.0 | 4.0 | 8.0 | 10.0 | 10.0 | 5.0 | 5.0 | 8.0 | 6.0 | 4.0 | 3.0 |
| 10 | 8.0 | 1.0 | 6.0 | 3.0 | 1.0 | 6.0 | 8.0 | 8.0 | 1.0 | 3.0 | 7.0 | 5.0 | 1.0 | 5.0 | 9.0 | 5.0 | 1.0 | 3.0 | 2.0 | 10.0 | 4.0 | 9.0 | 3.0 | 10.0 | 9.0 | 10.0 | 4.0 | 9.0 | 1.0 | 1.0 | 3.0 | 9.0 |
| 11 | 8.0 | 8.0 | 8.0 | 9.0 | 2.0 | 9.0 | 1.0 | 8.0 | 2.0 | 5.0 | 5.0 | 3.0 | 5.0 | 4.0 | 3.0 | 4.0 | 7.0 | 8.0 | 9.0 | 5.0 | 4.0 | 3.0 | 9.0 | 9.0 | 6.0 | 5.0 | 3.0 | 10.0 | 7.0 | 8.0 | 2.0 | 7.0 |
| 12 | 9.0 | 6.0 | 10.0 | 5.0 | 2.0 | 9.0 | 8.0 | 5.0 | 7.0 | 4.0 | 1.0 | 5.0 | 4.0 | 1.0 | 4.0 | 10.0 | 4.0 | 4.0 | 9.0 | 6.0 | 10.0 | 3.0 | 4.0 | 6.0 | 8.0 | 8.0 | 1.0 | 7.0 | 3.0 | 9.0 | 6.0 | 3.0 |
| 13 | 10.0 | 7.0 | 1.0 | 2.0 | 1.0 | 9.0 | 6.0 | 8.0 | 1.0 | 1.0 | 5.0 | 4.0 | 1.0 | 4.0 | 7.0 | 8.0 | 9.0 | 3.0 | 1.0 | 4.0 | 4.0 | 10.0 | 6.0 | 9.0 | 7.0 | 4.0 | 1.0 | 10.0 | 6.0 | 6.0 | 3.0 | 10.0 |
| 14 | 1.0 | 4.0 | 2.0 | 6.0 | 8.0 | 10.0 | 5.0 | 5.0 | 7.0 | 2.0 | 9.0 | 3.0 | 4.0 | 7.0 | 2.0 | 9.0 | 2.0 | 5.0 | 7.0 | 1.0 | 4.0 | 5.0 | 2.0 | 4.0 | 9.0 | 8.0 | 6.0 | 1.0 | 6.0 | 5.0 | 6.0 | 8.0 |
| 15 | 1.0 | 9.0 | 3.0 | 1.0 | 10.0 | 1.0 | 2.0 | 8.0 | 4.0 | 6.0 | 5.0 | 4.0 | 10.0 | 8.0 | 9.0 | 10.0 | 8.0 | 6.0 | 10.0 | 5.0 | 3.0 | 7.0 | 5.0 | 10.0 | 4.0 | 2.0 | 8.0 | 4.0 | 8.0 | 7.0 | 2.0 | 5.0 |
| 16 | 5.0 | 8.0 | 3.0 | 9.0 | 2.0 | 8.0 | 1.0 | 3.0 | 4.0 | 1.0 | 1.0 | 7.0 | 4.0 | 9.0 | 2.0 | 8.0 | 4.0 | 5.0 | 9.0 | 3.0 | 6.0 | 10.0 | 4.0 | 6.0 | 6.0 | 4.0 | 3.0 | 7.0 | 2.0 | 9.0 | 7.0 | 4.0 |
| 17 | 1.0 | 7.0 | 8.0 | 7.0 | 10.0 | 7.0 | 9.0 | 6.0 | 3.0 | 2.0 | 3.0 | 8.0 | 4.0 | 3.0 | 5.0 | 6.0 | 5.0 | 6.0 | 7.0 | 2.0 | 6.0 | 6.0 | 10.0 | 8.0 | 3.0 | 1.0 | 6.0 | 6.0 | 5.0 | 2.0 | 7.0 | 1.0 |
| 18 | 10.0 | 10.0 | 7.0 | 5.0 | 5.0 | 3.0 | 4.0 | 2.0 | 1.0 | 4.0 | 2.0 | 9.0 | 9.0 | 1.0 | 7.0 | 10.0 | 9.0 | 7.0 | 6.0 | 5.0 | 6.0 | 1.0 | 1.0 | 2.0 | 7.0 | 4.0 | 2.0 | 6.0 | 10.0 | 10.0 | 7.0 | 6.0 |
| 19 | 5.0 | 7.0 | 5.0 | 3.0 | 1.0 | 8.0 | 3.0 | 3.0 | 1.0 | 6.0 | 10.0 | 5.0 | 6.0 | 4.0 | 1.0 | 5.0 | 3.0 | 2.0 | 5.0 | 5.0 | 4.0 | 2.0 | 1.0 | 5.0 | 4.0 | 1.0 | 1.0 | 10.0 | 9.0 | 10.0 | 7.0 | 4.0 |
| 20 | 1.0 | 4.0 | 9.0 | 2.0 | 3.0 | 2.0 | 3.0 | 2.0 | 2.0 | 3.0 | 4.0 | 4.0 | 10.0 | 4.0 | 4.0 | 3.0 | 6.0 | 6.0 | 6.0 | 4.0 | 5.0 | 3.0 | 1.0 | 9.0 | 6.0 | 4.0 | 8.0 | 4.0 | 5.0 | 8.0 | 8.0 | 2.0 |
| 21 | 8.0 | 2.0 | 10.0 | 3.0 | 3.0 | 2.0 | 5.0 | 7.0 | 4.0 | 1.0 | 9.0 | 3.0 | 3.0 | 10.0 | 5.0 | 7.0 | 10.0 | 6.0 | 1.0 | 2.0 | 3.0 | 7.0 | 10.0 | 7.0 | 9.0 | 6.0 | 3.0 | 5.0 | 3.0 | 8.0 | 1.0 | 4.0 |
| 22 | 4.0 | 10.0 | 3.0 | 2.0 | 5.0 | 3.0 | 7.0 | 5.0 | 3.0 | 4.0 | 3.0 | 9.0 | 4.0 | 6.0 | 2.0 | 5.0 | 4.0 | 10.0 | 1.0 | 1.0 | 1.0 | 10.0 | 8.0 | 6.0 | 8.0 | 7.0 | 9.0 | 7.0 | 9.0 | 5.0 | 5.0 | 2.0 |
| 23 | 8.0 | 8.0 | 4.0 | 9.0 | 1.0 | 5.0 | 2.0 | 2.0 | 10.0 | 8.0 | 10.0 | 9.0 | 6.0 | 9.0 | 4.0 | 10.0 | 6.0 | 8.0 | 2.0 | 5.0 | 9.0 | 7.0 | 6.0 | 9.0 | 1.0 | 8.0 | 5.0 | 6.0 | 1.0 | 6.0 | 3.0 | 7.0 |
| 24 | 6.0 | 2.0 | 6.0 | 10.0 | 3.0 | 8.0 | 1.0 | 9.0 | 7.0 | 10.0 | 9.0 | 6.0 | 8.0 | 7.0 | 9.0 | 4.0 | 6.0 | 3.0 | 7.0 | 4.0 | 6.0 | 9.0 | 8.0 | 1.0 | 8.0 | 4.0 | 2.0 | 7.0 | 1.0 | 8.0 | 10.0 | 7.0 |
| 25 | 5.0 | 5.0 | 2.0 | 3.0 | 2.0 | 3.0 | 4.0 | 7.0 | 6.0 | 10.0 | 10.0 | 5.0 | 8.0 | 4.0 | 8.0 | 2.0 | 4.0 | 1.0 | 4.0 | 1.0 | 4.0 | 6.0 | 7.0 | 8.0 | 4.0 | 3.0 | 5.0 | 1.0 | 8.0 | 2.0 | 6.0 | 7.0 |
| 26 | 8.0 | 6.0 | 6.0 | 3.0 | 1.0 | 8.0 | 10.0 | 7.0 | 10.0 | 5.0 | 4.0 | 3.0 | 1.0 | 1.0 | 6.0 | 8.0 | 3.0 | 6.0 | 2.0 | 1.0 | 8.0 | 3.0 | 9.0 | 5.0 | 2.0 | 5.0 | 3.0 | 9.0 | 10.0 | 6.0 | 2.0 | 10.0 |
| 27 | 10.0 | 10.0 | 8.0 | 10.0 | 6.0 | 8.0 | 5.0 | 4.0 | 10.0 | 5.0 | 9.0 | 10.0 | 7.0 | 10.0 | 1.0 | 4.0 | 7.0 | 6.0 | 6.0 | 10.0 | 4.0 | 5.0 | 7.0 | 6.0 | 7.0 | 1.0 | 9.0 | 8.0 | 3.0 | 5.0 | 1.0 | 5.0 |
| 28 | 8.0 | 6.0 | 2.0 | 5.0 | 1.0 | 5.0 | 5.0 | 5.0 | 2.0 | 8.0 | 1.0 | 7.0 | 3.0 | 6.0 | 6.0 | 8.0 | 2.0 | 5.0 | 10.0 | 9.0 | 5.0 | 3.0 | 9.0 | 1.0 | 1.0 | 8.0 | 10.0 | 3.0 | 6.0 | 8.0 | 7.0 | 7.0 |
| 29 | 1.0 | 5.0 | 4.0 | 5.0 | 4.0 | 6.0 | 2.0 | 1.0 | 9.0 | 6.0 | 1.0 | 8.0 | 9.0 | 6.0 | 5.0 | 7.0 | 9.0 | 2.0 | 10.0 | 10.0 | 8.0 | 8.0 | 5.0 | 6.0 | 8.0 | 2.0 | 6.0 | 5.0 | 8.0 | 7.0 | 8.0 | 2.0 |
| 30 | 6.0 | 1.0 | 2.0 | 6.0 | 8.0 | 7.0 | 9.0 | 9.0 | 9.0 | 4.0 | 3.0 | 2.0 | 6.0 | 3.0 | 6.0 | 2.0 | 7.0 | 7.0 | 7.0 | 7.0 | 8.0 | 1.0 | 5.0 | 3.0 | 10.0 | 6.0 | 2.0 | 1.0 | 7.0 | 8.0 | 1.0 | 6.0 |
| 31 | 4.0 | 8.0 | 3.0 | 7.0 | 8.0 | 1.0 | 4.0 | 9.0 | 2.0 | 3.0 | 9.0 | 7.0 | 3.0 | 10.0 | 8.0 | 5.0 | 4.0 | 1.0 | 6.0 | 4.0 | 2.0 | 4.0 | 2.0 | 7.0 | 7.0 | 7.0 | 10.0 | 5.0 | 7.0 | 2.0 | 6.0 | 4.0 |

Oh, and to keep things easy to parse, please put the chosen route into a tiny JSON snippet like this:

{
  ""solution"": []
}

Here, ""solution"" is where you’ll list the route as an ordered array of NODE identifiers only (start with the lobby, end with the banquet room, and make sure each step follows an existing one-way corridor). This JSON is just a sketch of the shape I expect — not the actual answer itself.

Please use identifiers exactly as they appear in the instance input — no renaming and no made-up labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".

Also, don’t include corridor/edge identifiers or any cost numbers in the path — just the node names.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 4, 'var_index': 1}, {'from': 16, 'to': 8, 'var_index': 2}, {'from': 16, 'to': 12, 'var_index': 3}, {'from': 3, 'to': 17, 'var_index': 4}, {'from': 7, 'to': 17, 'var_index': 5}, {'from': 11, 'to': 17, 'var_index': 6}, {'from': 15, 'to': 17, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 0, 'to': 4, 'var_index': 9}, {'from': 1, 'to': 2, 'var_index': 10}, {'from': 1, 'to': 5, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 2, 'to': 6, 'var_index': 13}, {'from': 3, 'to': 7, 'var_index': 14}, {'from': 4, 'to': 5, 'var_index': 15}, {'from': 4, 'to': 8, 'var_index': 16}, {'from': 5, 'to': 6, 'var_index': 17}, {'from': 5, 'to': 9, 'var_index': 18}, {'from': 6, 'to': 7, 'var_index': 19}, {'from': 6, 'to': 10, 'var_index': 20}, {'from': 7, 'to': 11, 'var_index': 21}, {'from': 8, 'to': 9, 'var_index': 22}, {'from': 8, 'to': 12, 'var_index': 23}, {'from': 9, 'to': 10, 'var_index': 24}, {'from': 9, 'to': 13, 'var_index': 25}, {'from': 10, 'to': 11, 'var_index': 26}, {'from': 10, 'to': 14, 'var_index': 27}, {'from': 11, 'to': 15, 'var_index': 28}, {'from': 12, 'to': 13, 'var_index': 29}, {'from': 13, 'to': 14, 'var_index': 30}, {'from': 14, 'to': 15, 'var_index': 31}], 'objective': {'constant': 0.0, 'linear': [1.0, 9.0, 5.0, 7.0, 2.0, 4.0, 9.0, 9.0, 4.0, 1.0, 7.0, 10.0, 6.0, 9.0, 8.0, 10.0, 7.0, 10.0, 7.0, 3.0, 1.0, 5.0, 3.0, 7.0, 1.0, 1.0, 2.0, 4.0, 7.0, 1.0, 8.0, 9.0], 'quadratic': [[3.0, 7.0, 7.0, 4.0, 5.0, 4.0, 10.0, 10.0, 3.0, 9.0, 8.0, 8.0, 9.0, 10.0, 1.0, 1.0, 5.0, 1.0, 10.0, 5.0, 1.0, 8.0, 4.0, 8.0, 6.0, 5.0, 8.0, 10.0, 8.0, 1.0, 6.0, 4.0], [7.0, 5.0, 8.0, 1.0, 2.0, 3.0, 7.0, 9.0, 2.0, 8.0, 1.0, 8.0, 6.0, 7.0, 4.0, 9.0, 8.0, 7.0, 10.0, 7.0, 4.0, 2.0, 10.0, 8.0, 2.0, 5.0, 6.0, 10.0, 6.0, 5.0, 1.0, 8.0], [7.0, 8.0, 4.0, 9.0, 2.0, 9.0, 1.0, 4.0, 1.0, 3.0, 6.0, 8.0, 10.0, 1.0, 2.0, 3.0, 3.0, 8.0, 7.0, 5.0, 9.0, 10.0, 3.0, 4.0, 6.0, 2.0, 6.0, 8.0, 2.0, 4.0, 2.0, 3.0], [4.0, 1.0, 9.0, 7.0, 6.0, 8.0, 10.0, 1.0, 8.0, 1.0, 3.0, 9.0, 5.0, 2.0, 6.0, 1.0, 9.0, 7.0, 5.0, 3.0, 2.0, 3.0, 2.0, 9.0, 10.0, 3.0, 3.0, 10.0, 5.0, 5.0, 6.0, 7.0], [5.0, 2.0, 2.0, 6.0, 8.0, 10.0, 8.0, 1.0, 1.0, 6.0, 1.0, 2.0, 2.0, 1.0, 8.0, 10.0, 2.0, 10.0, 5.0, 1.0, 3.0, 3.0, 5.0, 1.0, 3.0, 2.0, 1.0, 6.0, 1.0, 4.0, 8.0, 8.0], [4.0, 3.0, 9.0, 8.0, 10.0, 4.0, 8.0, 3.0, 10.0, 8.0, 6.0, 9.0, 9.0, 9.0, 10.0, 1.0, 8.0, 7.0, 3.0, 8.0, 2.0, 2.0, 3.0, 5.0, 8.0, 3.0, 8.0, 8.0, 5.0, 6.0, 7.0, 1.0], [10.0, 7.0, 1.0, 10.0, 8.0, 8.0, 4.0, 5.0, 8.0, 1.0, 8.0, 1.0, 8.0, 6.0, 5.0, 2.0, 1.0, 9.0, 4.0, 3.0, 3.0, 5.0, 7.0, 2.0, 1.0, 4.0, 10.0, 5.0, 5.0, 2.0, 9.0, 4.0], [10.0, 9.0, 4.0, 1.0, 1.0, 3.0, 5.0, 6.0, 3.0, 2.0, 8.0, 8.0, 5.0, 8.0, 5.0, 8.0, 3.0, 6.0, 2.0, 3.0, 2.0, 7.0, 5.0, 2.0, 9.0, 7.0, 7.0, 4.0, 5.0, 1.0, 9.0, 9.0], [3.0, 2.0, 1.0, 8.0, 1.0, 10.0, 8.0, 3.0, 9.0, 9.0, 1.0, 2.0, 7.0, 1.0, 7.0, 4.0, 4.0, 3.0, 1.0, 1.0, 2.0, 4.0, 3.0, 10.0, 7.0, 6.0, 10.0, 10.0, 2.0, 9.0, 9.0, 2.0], [9.0, 8.0, 3.0, 1.0, 6.0, 8.0, 1.0, 2.0, 9.0, 7.0, 3.0, 5.0, 4.0, 1.0, 2.0, 6.0, 1.0, 2.0, 4.0, 6.0, 3.0, 1.0, 4.0, 8.0, 10.0, 10.0, 5.0, 5.0, 8.0, 6.0, 4.0, 3.0], [8.0, 1.0, 6.0, 3.0, 1.0, 6.0, 8.0, 8.0, 1.0, 3.0, 7.0, 5.0, 1.0, 5.0, 9.0, 5.0, 1.0, 3.0, 2.0, 10.0, 4.0, 9.0, 3.0, 10.0, 9.0, 10.0, 4.0, 9.0, 1.0, 1.0, 3.0, 9.0], [8.0, 8.0, 8.0, 9.0, 2.0, 9.0, 1.0, 8.0, 2.0, 5.0, 5.0, 3.0, 5.0, 4.0, 3.0, 4.0, 7.0, 8.0, 9.0, 5.0, 4.0, 3.0, 9.0, 9.0, 6.0, 5.0, 3.0, 10.0, 7.0, 8.0, 2.0, 7.0], [9.0, 6.0, 10.0, 5.0, 2.0, 9.0, 8.0, 5.0, 7.0, 4.0, 1.0, 5.0, 4.0, 1.0, 4.0, 10.0, 4.0, 4.0, 9.0, 6.0, 10.0, 3.0, 4.0, 6.0, 8.0, 8.0, 1.0, 7.0, 3.0, 9.0, 6.0, 3.0], [10.0, 7.0, 1.0, 2.0, 1.0, 9.0, 6.0, 8.0, 1.0, 1.0, 5.0, 4.0, 1.0, 4.0, 7.0, 8.0, 9.0, 3.0, 1.0, 4.0, 4.0, 10.0, 6.0, 9.0, 7.0, 4.0, 1.0, 10.0, 6.0, 6.0, 3.0, 10.0], [1.0, 4.0, 2.0, 6.0, 8.0, 10.0, 5.0, 5.0, 7.0, 2.0, 9.0, 3.0, 4.0, 7.0, 2.0, 9.0, 2.0, 5.0, 7.0, 1.0, 4.0, 5.0, 2.0, 4.0, 9.0, 8.0, 6.0, 1.0, 6.0, 5.0, 6.0, 8.0], [1.0, 9.0, 3.0, 1.0, 10.0, 1.0, 2.0, 8.0, 4.0, 6.0, 5.0, 4.0, 10.0, 8.0, 9.0, 10.0, 8.0, 6.0, 10.0, 5.0, 3.0, 7.0, 5.0, 10.0, 4.0, 2.0, 8.0, 4.0, 8.0, 7.0, 2.0, 5.0], [5.0, 8.0, 3.0, 9.0, 2.0, 8.0, 1.0, 3.0, 4.0, 1.0, 1.0, 7.0, 4.0, 9.0, 2.0, 8.0, 4.0, 5.0, 9.0, 3.0, 6.0, 10.0, 4.0, 6.0, 6.0, 4.0, 3.0, 7.0, 2.0, 9.0, 7.0, 4.0], [1.0, 7.0, 8.0, 7.0, 10.0, 7.0, 9.0, 6.0, 3.0, 2.0, 3.0, 8.0, 4.0, 3.0, 5.0, 6.0, 5.0, 6.0, 7.0, 2.0, 6.0, 6.0, 10.0, 8.0, 3.0, 1.0, 6.0, 6.0, 5.0, 2.0, 7.0, 1.0], [10.0, 10.0, 7.0, 5.0, 5.0, 3.0, 4.0, 2.0, 1.0, 4.0, 2.0, 9.0, 9.0, 1.0, 7.0, 10.0, 9.0, 7.0, 6.0, 5.0, 6.0, 1.0, 1.0, 2.0, 7.0, 4.0, 2.0, 6.0, 10.0, 10.0, 7.0, 6.0], [5.0, 7.0, 5.0, 3.0, 1.0, 8.0, 3.0, 3.0, 1.0, 6.0, 10.0, 5.0, 6.0, 4.0, 1.0, 5.0, 3.0, 2.0, 5.0, 5.0, 4.0, 2.0, 1.0, 5.0, 4.0, 1.0, 1.0, 10.0, 9.0, 10.0, 7.0, 4.0], [1.0, 4.0, 9.0, 2.0, 3.0, 2.0, 3.0, 2.0, 2.0, 3.0, 4.0, 4.0, 10.0, 4.0, 4.0, 3.0, 6.0, 6.0, 6.0, 4.0, 5.0, 3.0, 1.0, 9.0, 6.0, 4.0, 8.0, 4.0, 5.0, 8.0, 8.0, 2.0], [8.0, 2.0, 10.0, 3.0, 3.0, 2.0, 5.0, 7.0, 4.0, 1.0, 9.0, 3.0, 3.0, 10.0, 5.0, 7.0, 10.0, 6.0, 1.0, 2.0, 3.0, 7.0, 10.0, 7.0, 9.0, 6.0, 3.0, 5.0, 3.0, 8.0, 1.0, 4.0], [4.0, 10.0, 3.0, 2.0, 5.0, 3.0, 7.0, 5.0, 3.0, 4.0, 3.0, 9.0, 4.0, 6.0, 2.0, 5.0, 4.0, 10.0, 1.0, 1.0, 1.0, 10.0, 8.0, 6.0, 8.0, 7.0, 9.0, 7.0, 9.0, 5.0, 5.0, 2.0], [8.0, 8.0, 4.0, 9.0, 1.0, 5.0, 2.0, 2.0, 10.0, 8.0, 10.0, 9.0, 6.0, 9.0, 4.0, 10.0, 6.0, 8.0, 2.0, 5.0, 9.0, 7.0, 6.0, 9.0, 1.0, 8.0, 5.0, 6.0, 1.0, 6.0, 3.0, 7.0], [6.0, 2.0, 6.0, 10.0, 3.0, 8.0, 1.0, 9.0, 7.0, 10.0, 9.0, 6.0, 8.0, 7.0, 9.0, 4.0, 6.0, 3.0, 7.0, 4.0, 6.0, 9.0, 8.0, 1.0, 8.0, 4.0, 2.0, 7.0, 1.0, 8.0, 10.0, 7.0], [5.0, 5.0, 2.0, 3.0, 2.0, 3.0, 4.0, 7.0, 6.0, 10.0, 10.0, 5.0, 8.0, 4.0, 8.0, 2.0, 4.0, 1.0, 4.0, 1.0, 4.0, 6.0, 7.0, 8.0, 4.0, 3.0, 5.0, 1.0, 8.0, 2.0, 6.0, 7.0], [8.0, 6.0, 6.0, 3.0, 1.0, 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'quadratic_cost': 4.0}, {'var_i': 25, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 25, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 25, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 25, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 25, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 25, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 25, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 25, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 25, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 25, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 25, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 26, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 26, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 26, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 26, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 26, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 26, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 26, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 26, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 26, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 26, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 26, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 26, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 26, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 26, 'var_j': 27, 'quadratic_cost': 9.0}, {'var_i': 26, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 26, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 27, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 27, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 27, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 24, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 27, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 28, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 29, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 28, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 26, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 23, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 25, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 26, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 31, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 24, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 31, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 4, 'var_index': 1}, {'from': 16, 'to': 8, 'var_index': 2}, {'from': 16, 'to': 12, 'var_index': 3}, {'from': 3, 'to': 17, 'var_index': 4}, {'from': 7, 'to': 17, 'var_index': 5}, {'from': 11, 'to': 17, 'var_index': 6}, {'from': 15, 'to': 17, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 0, 'to': 4, 'var_index': 9}, {'from': 1, 'to': 2, 'var_index': 10}, {'from': 1, 'to': 5, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 2, 'to': 6, 'var_index': 13}, {'from': 3, 'to': 7, 'var_index': 14}, {'from': 4, 'to': 5, 'var_index': 15}, {'from': 4, 'to': 8, 'var_index': 16}, {'from': 5, 'to': 6, 'var_index': 17}, {'from': 5, 'to': 9, 'var_index': 18}, {'from': 6, 'to': 7, 'var_index': 19}, {'from': 6, 'to': 10, 'var_index': 20}, {'from': 7, 'to': 11, 'var_index': 21}, {'from': 8, 'to': 9, 'var_index': 22}, {'from': 8, 'to': 12, 'var_index': 23}, {'from': 9, 'to': 10, 'var_index': 24}, {'from': 9, 'to': 13, 'var_index': 25}, {'from': 10, 'to': 11, 'var_index': 26}, {'from': 10, 'to': 14, 'var_index': 27}, {'from': 11, 'to': 15, 'var_index': 28}, {'from': 12, 'to': 13, 'var_index': 29}, {'from': 13, 'to': 14, 'var_index': 30}, {'from': 14, 'to': 15, 'var_index': 31}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17}}","[16, 0, 1, 2, 3, 17]",29,csv,0
QSPP,QSPP,"Out in town a carrier needed to pick a single, legal one-way path from the depot to a mailbox. Every street costs something to serve, some streets have extra charges that kick in when they’re used, and some pairs of streets add an extra penalty if both are included on the run. The idea is to find one continuous path that ends at the mailbox and gives the lowest total bill — add up every street’s cost, any individual extra charges, and every extra penalty for street pairs that both appear on the trip. Each step must be an actual allowed one-way move from one spot to the next, and the full route must go straight from depot to mailbox. The detailed map and cost numbers are shown below.

The map shows 24 locations (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X) and 35 one-way streets; the depot is W and the mailbox is X.
Street 0 goes one-way from W to A.
Street 1 goes one-way from W to L.
Street 2 goes one-way from K to X.
Street 3 goes one-way from V to X.
Street 4 goes one-way from A to B.
Street 5 goes one-way from A to L.
Street 6 goes one-way from B to C.
Street 7 goes one-way from B to M.
Street 8 goes one-way from C to D.
Street 9 goes one-way from C to N.
Street 10 goes one-way from D to E.
Street 11 goes one-way from D to O.
Street 12 goes one-way from E to F.
Street 13 goes one-way from E to P.
Street 14 goes one-way from F to G.
Street 15 goes one-way from F to Q.
Street 16 goes one-way from G to H.
Street 17 goes one-way from G to R.
Street 18 goes one-way from H to I.
Street 19 goes one-way from H to S.
Street 20 goes one-way from I to J.
Street 21 goes one-way from I to T.
Street 22 goes one-way from J to K.
Street 23 goes one-way from J to U.
Street 24 goes one-way from K to V.
Street 25 goes one-way from L to M.
Street 26 goes one-way from M to N.
Street 27 goes one-way from N to O.
Street 28 goes one-way from O to P.
Street 29 goes one-way from P to Q.
Street 30 goes one-way from Q to R.
Street 31 goes one-way from R to S.
Street 32 goes one-way from S to T.
Street 33 goes one-way from T to U.
Street 34 goes one-way from U to V.
Serving 0 incurs a base cost of 4.0.
Serving 1 incurs a base cost of 10.0.
Serving 2 incurs a base cost of 1.0.
Serving 3 incurs a base cost of 8.0.
Serving 4 incurs a base cost of 3.0.
Serving 5 incurs a base cost of 2.0.
Serving 6 incurs a base cost of 5.0.
Serving 7 incurs a base cost of 1.0.
Serving 8 incurs a base cost of 9.0.
Serving 9 incurs a base cost of 5.0.
Serving 10 incurs a base cost of 3.0.
Serving 11 incurs a base cost of 10.0.
Serving 12 incurs a base cost of 8.0.
Serving 13 incurs a base cost of 9.0.
Serving 14 incurs a base cost of 10.0.
Serving 15 incurs a base cost of 6.0.
Serving 16 incurs a base cost of 3.0.
Serving 17 incurs a base cost of 6.0.
Serving 18 incurs a base cost of 5.0.
Serving 19 incurs a base cost of 8.0.
Serving 20 incurs a base cost of 8.0.
Serving 21 incurs a base cost of 8.0.
Serving 22 incurs a base cost of 10.0.
Serving 23 incurs a base cost of 1.0.
Serving 24 incurs a base cost of 9.0.
Serving 25 incurs a base cost of 1.0.
Serving 26 incurs a base cost of 2.0.
Serving 27 incurs a base cost of 2.0.
Serving 28 incurs a base cost of 2.0.
Serving 29 incurs a base cost of 7.0.
Serving 30 incurs a base cost of 6.0.
Serving 31 incurs a base cost of 1.0.
Serving 32 incurs a base cost of 6.0.
Serving 33 incurs a base cost of 1.0.
Serving 34 incurs a base cost of 5.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_id, street_j_id). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| street_i_id\street_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 10.0 | 4.0 | 10.0 | 10.0 | 7.0 | 6.0 | 1.0 | 9.0 | 2.0 | 3.0 | 8.0 | 3.0 | 8.0 | 9.0 | 6.0 | 4.0 | 10.0 | 2.0 | 8.0 | 1.0 | 5.0 | 1.0 | 6.0 | 7.0 | 9.0 | 2.0 | 1.0 | 9.0 | 3.0 | 1.0 | 6.0 | 1.0 | 9.0 | 10.0 |
| 1 | 10.0 | 9.0 | 2.0 | 2.0 | 8.0 | 3.0 | 5.0 | 9.0 | 10.0 | 2.0 | 6.0 | 6.0 | 4.0 | 4.0 | 4.0 | 5.0 | 9.0 | 10.0 | 3.0 | 6.0 | 8.0 | 6.0 | 4.0 | 8.0 | 3.0 | 8.0 | 6.0 | 5.0 | 4.0 | 9.0 | 4.0 | 6.0 | 10.0 | 10.0 | 4.0 |
| 2 | 4.0 | 2.0 | 3.0 | 10.0 | 6.0 | 1.0 | 3.0 | 6.0 | 7.0 | 6.0 | 8.0 | 4.0 | 8.0 | 5.0 | 6.0 | 5.0 | 3.0 | 6.0 | 8.0 | 10.0 | 4.0 | 6.0 | 2.0 | 3.0 | 7.0 | 5.0 | 4.0 | 2.0 | 8.0 | 7.0 | 5.0 | 9.0 | 3.0 | 4.0 | 7.0 |
| 3 | 10.0 | 2.0 | 10.0 | 3.0 | 2.0 | 2.0 | 5.0 | 5.0 | 9.0 | 1.0 | 8.0 | 2.0 | 6.0 | 8.0 | 7.0 | 7.0 | 2.0 | 5.0 | 6.0 | 5.0 | 4.0 | 9.0 | 5.0 | 9.0 | 7.0 | 6.0 | 6.0 | 2.0 | 6.0 | 9.0 | 4.0 | 8.0 | 2.0 | 5.0 | 6.0 |
| 4 | 10.0 | 8.0 | 6.0 | 2.0 | 8.0 | 8.0 | 10.0 | 6.0 | 6.0 | 7.0 | 9.0 | 7.0 | 9.0 | 5.0 | 9.0 | 5.0 | 3.0 | 10.0 | 3.0 | 6.0 | 6.0 | 4.0 | 2.0 | 3.0 | 7.0 | 6.0 | 3.0 | 1.0 | 4.0 | 2.0 | 6.0 | 1.0 | 6.0 | 5.0 | 7.0 |
| 5 | 7.0 | 3.0 | 1.0 | 2.0 | 8.0 | 4.0 | 7.0 | 3.0 | 1.0 | 4.0 | 1.0 | 3.0 | 4.0 | 8.0 | 4.0 | 8.0 | 6.0 | 2.0 | 2.0 | 5.0 | 10.0 | 10.0 | 4.0 | 9.0 | 6.0 | 5.0 | 2.0 | 8.0 | 8.0 | 4.0 | 8.0 | 6.0 | 2.0 | 8.0 | 6.0 |
| 6 | 6.0 | 5.0 | 3.0 | 5.0 | 10.0 | 7.0 | 2.0 | 10.0 | 7.0 | 6.0 | 6.0 | 10.0 | 8.0 | 8.0 | 9.0 | 5.0 | 7.0 | 4.0 | 8.0 | 7.0 | 5.0 | 8.0 | 9.0 | 6.0 | 4.0 | 10.0 | 8.0 | 4.0 | 9.0 | 2.0 | 10.0 | 10.0 | 9.0 | 6.0 | 1.0 |
| 7 | 1.0 | 9.0 | 6.0 | 5.0 | 6.0 | 3.0 | 10.0 | 8.0 | 9.0 | 10.0 | 6.0 | 2.0 | 4.0 | 8.0 | 1.0 | 3.0 | 7.0 | 8.0 | 2.0 | 1.0 | 6.0 | 6.0 | 5.0 | 5.0 | 1.0 | 3.0 | 2.0 | 5.0 | 2.0 | 3.0 | 2.0 | 10.0 | 1.0 | 3.0 | 4.0 |
| 8 | 9.0 | 10.0 | 7.0 | 9.0 | 6.0 | 1.0 | 7.0 | 9.0 | 3.0 | 10.0 | 6.0 | 1.0 | 1.0 | 1.0 | 3.0 | 8.0 | 9.0 | 6.0 | 5.0 | 10.0 | 4.0 | 7.0 | 1.0 | 2.0 | 8.0 | 1.0 | 7.0 | 6.0 | 2.0 | 6.0 | 5.0 | 3.0 | 9.0 | 5.0 | 3.0 |
| 9 | 2.0 | 2.0 | 6.0 | 1.0 | 7.0 | 4.0 | 6.0 | 10.0 | 10.0 | 9.0 | 5.0 | 10.0 | 3.0 | 10.0 | 3.0 | 4.0 | 2.0 | 3.0 | 2.0 | 3.0 | 10.0 | 9.0 | 8.0 | 5.0 | 8.0 | 7.0 | 8.0 | 10.0 | 1.0 | 7.0 | 4.0 | 3.0 | 6.0 | 7.0 | 9.0 |
| 10 | 3.0 | 6.0 | 8.0 | 8.0 | 9.0 | 1.0 | 6.0 | 6.0 | 6.0 | 5.0 | 7.0 | 5.0 | 3.0 | 5.0 | 7.0 | 4.0 | 3.0 | 9.0 | 9.0 | 10.0 | 1.0 | 4.0 | 10.0 | 9.0 | 8.0 | 10.0 | 1.0 | 6.0 | 2.0 | 10.0 | 2.0 | 5.0 | 10.0 | 5.0 | 6.0 |
| 11 | 8.0 | 6.0 | 4.0 | 2.0 | 7.0 | 3.0 | 10.0 | 2.0 | 1.0 | 10.0 | 5.0 | 8.0 | 6.0 | 9.0 | 6.0 | 8.0 | 2.0 | 9.0 | 5.0 | 10.0 | 9.0 | 6.0 | 5.0 | 5.0 | 9.0 | 9.0 | 6.0 | 6.0 | 3.0 | 6.0 | 6.0 | 8.0 | 8.0 | 10.0 | 9.0 |
| 12 | 3.0 | 4.0 | 8.0 | 6.0 | 9.0 | 4.0 | 8.0 | 4.0 | 1.0 | 3.0 | 3.0 | 6.0 | 2.0 | 7.0 | 5.0 | 7.0 | 10.0 | 4.0 | 7.0 | 3.0 | 3.0 | 7.0 | 10.0 | 1.0 | 8.0 | 9.0 | 1.0 | 7.0 | 9.0 | 3.0 | 2.0 | 7.0 | 9.0 | 8.0 | 9.0 |
| 13 | 8.0 | 4.0 | 5.0 | 8.0 | 5.0 | 8.0 | 8.0 | 8.0 | 1.0 | 10.0 | 5.0 | 9.0 | 7.0 | 7.0 | 2.0 | 6.0 | 8.0 | 8.0 | 7.0 | 7.0 | 9.0 | 6.0 | 2.0 | 7.0 | 8.0 | 10.0 | 4.0 | 8.0 | 5.0 | 2.0 | 2.0 | 8.0 | 3.0 | 6.0 | 3.0 |
| 14 | 9.0 | 4.0 | 6.0 | 7.0 | 9.0 | 4.0 | 9.0 | 1.0 | 3.0 | 3.0 | 7.0 | 6.0 | 5.0 | 2.0 | 9.0 | 8.0 | 7.0 | 5.0 | 10.0 | 5.0 | 4.0 | 7.0 | 5.0 | 2.0 | 4.0 | 5.0 | 7.0 | 4.0 | 3.0 | 8.0 | 8.0 | 5.0 | 4.0 | 7.0 | 7.0 |
| 15 | 6.0 | 5.0 | 5.0 | 7.0 | 5.0 | 8.0 | 5.0 | 3.0 | 8.0 | 4.0 | 4.0 | 8.0 | 7.0 | 6.0 | 8.0 | 8.0 | 9.0 | 3.0 | 4.0 | 8.0 | 8.0 | 1.0 | 8.0 | 3.0 | 6.0 | 1.0 | 1.0 | 9.0 | 3.0 | 8.0 | 9.0 | 4.0 | 8.0 | 1.0 | 10.0 |
| 16 | 4.0 | 9.0 | 3.0 | 2.0 | 3.0 | 6.0 | 7.0 | 7.0 | 9.0 | 2.0 | 3.0 | 2.0 | 10.0 | 8.0 | 7.0 | 9.0 | 7.0 | 7.0 | 7.0 | 5.0 | 6.0 | 1.0 | 4.0 | 2.0 | 10.0 | 4.0 | 2.0 | 10.0 | 2.0 | 10.0 | 2.0 | 9.0 | 9.0 | 2.0 | 9.0 |
| 17 | 10.0 | 10.0 | 6.0 | 5.0 | 10.0 | 2.0 | 4.0 | 8.0 | 6.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 5.0 | 3.0 | 7.0 | 5.0 | 6.0 | 4.0 | 7.0 | 1.0 | 2.0 | 8.0 | 9.0 | 8.0 | 1.0 | 2.0 | 10.0 | 9.0 | 10.0 | 4.0 | 3.0 | 9.0 | 6.0 |
| 18 | 2.0 | 3.0 | 8.0 | 6.0 | 3.0 | 2.0 | 8.0 | 2.0 | 5.0 | 2.0 | 9.0 | 5.0 | 7.0 | 7.0 | 10.0 | 4.0 | 7.0 | 6.0 | 3.0 | 7.0 | 9.0 | 6.0 | 1.0 | 10.0 | 8.0 | 2.0 | 10.0 | 3.0 | 5.0 | 3.0 | 2.0 | 2.0 | 2.0 | 9.0 | 4.0 |
| 19 | 8.0 | 6.0 | 10.0 | 5.0 | 6.0 | 5.0 | 7.0 | 1.0 | 10.0 | 3.0 | 10.0 | 10.0 | 3.0 | 7.0 | 5.0 | 8.0 | 5.0 | 4.0 | 7.0 | 3.0 | 9.0 | 7.0 | 9.0 | 8.0 | 4.0 | 6.0 | 1.0 | 9.0 | 7.0 | 5.0 | 9.0 | 8.0 | 7.0 | 4.0 | 8.0 |
| 20 | 1.0 | 8.0 | 4.0 | 4.0 | 6.0 | 10.0 | 5.0 | 6.0 | 4.0 | 10.0 | 1.0 | 9.0 | 3.0 | 9.0 | 4.0 | 8.0 | 6.0 | 7.0 | 9.0 | 9.0 | 2.0 | 8.0 | 2.0 | 8.0 | 8.0 | 1.0 | 6.0 | 4.0 | 1.0 | 8.0 | 6.0 | 9.0 | 4.0 | 2.0 | 1.0 |
| 21 | 5.0 | 6.0 | 6.0 | 9.0 | 4.0 | 10.0 | 8.0 | 6.0 | 7.0 | 9.0 | 4.0 | 6.0 | 7.0 | 6.0 | 7.0 | 1.0 | 1.0 | 1.0 | 6.0 | 7.0 | 8.0 | 3.0 | 7.0 | 3.0 | 7.0 | 1.0 | 6.0 | 1.0 | 5.0 | 9.0 | 4.0 | 9.0 | 10.0 | 8.0 | 4.0 |
| 22 | 1.0 | 4.0 | 2.0 | 5.0 | 2.0 | 4.0 | 9.0 | 5.0 | 1.0 | 8.0 | 10.0 | 5.0 | 10.0 | 2.0 | 5.0 | 8.0 | 4.0 | 2.0 | 1.0 | 9.0 | 2.0 | 7.0 | 6.0 | 1.0 | 9.0 | 4.0 | 7.0 | 1.0 | 5.0 | 4.0 | 10.0 | 5.0 | 3.0 | 8.0 | 7.0 |
| 23 | 6.0 | 8.0 | 3.0 | 9.0 | 3.0 | 9.0 | 6.0 | 5.0 | 2.0 | 5.0 | 9.0 | 5.0 | 1.0 | 7.0 | 2.0 | 3.0 | 2.0 | 8.0 | 10.0 | 8.0 | 8.0 | 3.0 | 1.0 | 7.0 | 8.0 | 2.0 | 7.0 | 5.0 | 4.0 | 6.0 | 9.0 | 7.0 | 10.0 | 5.0 | 1.0 |
| 24 | 7.0 | 3.0 | 7.0 | 7.0 | 7.0 | 6.0 | 4.0 | 1.0 | 8.0 | 8.0 | 8.0 | 9.0 | 8.0 | 8.0 | 4.0 | 6.0 | 10.0 | 9.0 | 8.0 | 4.0 | 8.0 | 7.0 | 9.0 | 8.0 | 5.0 | 8.0 | 8.0 | 6.0 | 8.0 | 5.0 | 7.0 | 2.0 | 3.0 | 7.0 | 4.0 |
| 25 | 9.0 | 8.0 | 5.0 | 6.0 | 6.0 | 5.0 | 10.0 | 3.0 | 1.0 | 7.0 | 10.0 | 9.0 | 9.0 | 10.0 | 5.0 | 1.0 | 4.0 | 8.0 | 2.0 | 6.0 | 1.0 | 1.0 | 4.0 | 2.0 | 8.0 | 5.0 | 8.0 | 1.0 | 9.0 | 8.0 | 6.0 | 8.0 | 3.0 | 2.0 | 2.0 |
| 26 | 2.0 | 6.0 | 4.0 | 6.0 | 3.0 | 2.0 | 8.0 | 2.0 | 7.0 | 8.0 | 1.0 | 6.0 | 1.0 | 4.0 | 7.0 | 1.0 | 2.0 | 1.0 | 10.0 | 1.0 | 6.0 | 6.0 | 7.0 | 7.0 | 8.0 | 8.0 | 2.0 | 9.0 | 3.0 | 9.0 | 7.0 | 1.0 | 6.0 | 8.0 | 3.0 |
| 27 | 1.0 | 5.0 | 2.0 | 2.0 | 1.0 | 8.0 | 4.0 | 5.0 | 6.0 | 10.0 | 6.0 | 6.0 | 7.0 | 8.0 | 4.0 | 9.0 | 10.0 | 2.0 | 3.0 | 9.0 | 4.0 | 1.0 | 1.0 | 5.0 | 6.0 | 1.0 | 9.0 | 1.0 | 1.0 | 5.0 | 7.0 | 8.0 | 4.0 | 8.0 | 10.0 |
| 28 | 9.0 | 4.0 | 8.0 | 6.0 | 4.0 | 8.0 | 9.0 | 2.0 | 2.0 | 1.0 | 2.0 | 3.0 | 9.0 | 5.0 | 3.0 | 3.0 | 2.0 | 10.0 | 5.0 | 7.0 | 1.0 | 5.0 | 5.0 | 4.0 | 8.0 | 9.0 | 3.0 | 1.0 | 9.0 | 3.0 | 5.0 | 2.0 | 4.0 | 5.0 | 4.0 |
| 29 | 3.0 | 9.0 | 7.0 | 9.0 | 2.0 | 4.0 | 2.0 | 3.0 | 6.0 | 7.0 | 10.0 | 6.0 | 3.0 | 2.0 | 8.0 | 8.0 | 10.0 | 9.0 | 3.0 | 5.0 | 8.0 | 9.0 | 4.0 | 6.0 | 5.0 | 8.0 | 9.0 | 5.0 | 3.0 | 6.0 | 1.0 | 7.0 | 8.0 | 2.0 | 1.0 |
| 30 | 1.0 | 4.0 | 5.0 | 4.0 | 6.0 | 8.0 | 10.0 | 2.0 | 5.0 | 4.0 | 2.0 | 6.0 | 2.0 | 2.0 | 8.0 | 9.0 | 2.0 | 10.0 | 2.0 | 9.0 | 6.0 | 4.0 | 10.0 | 9.0 | 7.0 | 6.0 | 7.0 | 7.0 | 5.0 | 1.0 | 4.0 | 5.0 | 8.0 | 4.0 | 8.0 |
| 31 | 6.0 | 6.0 | 9.0 | 8.0 | 1.0 | 6.0 | 10.0 | 10.0 | 3.0 | 3.0 | 5.0 | 8.0 | 7.0 | 8.0 | 5.0 | 4.0 | 9.0 | 4.0 | 2.0 | 8.0 | 9.0 | 9.0 | 5.0 | 7.0 | 2.0 | 8.0 | 1.0 | 8.0 | 2.0 | 7.0 | 5.0 | 5.0 | 8.0 | 9.0 | 3.0 |
| 32 | 1.0 | 10.0 | 3.0 | 2.0 | 6.0 | 2.0 | 9.0 | 1.0 | 9.0 | 6.0 | 10.0 | 8.0 | 9.0 | 3.0 | 4.0 | 8.0 | 9.0 | 3.0 | 2.0 | 7.0 | 4.0 | 10.0 | 3.0 | 10.0 | 3.0 | 3.0 | 6.0 | 4.0 | 4.0 | 8.0 | 8.0 | 8.0 | 10.0 | 4.0 | 7.0 |
| 33 | 9.0 | 10.0 | 4.0 | 5.0 | 5.0 | 8.0 | 6.0 | 3.0 | 5.0 | 7.0 | 5.0 | 10.0 | 8.0 | 6.0 | 7.0 | 1.0 | 2.0 | 9.0 | 9.0 | 4.0 | 2.0 | 8.0 | 8.0 | 5.0 | 7.0 | 2.0 | 8.0 | 8.0 | 5.0 | 2.0 | 4.0 | 9.0 | 4.0 | 9.0 | 5.0 |
| 34 | 10.0 | 4.0 | 7.0 | 6.0 | 7.0 | 6.0 | 1.0 | 4.0 | 3.0 | 9.0 | 6.0 | 9.0 | 9.0 | 3.0 | 7.0 | 10.0 | 9.0 | 6.0 | 4.0 | 8.0 | 1.0 | 4.0 | 7.0 | 1.0 | 4.0 | 2.0 | 3.0 | 10.0 | 4.0 | 1.0 | 8.0 | 3.0 | 7.0 | 5.0 | 3.0 |
Use these entries to pick the single legal one-way route from W to X that yields the lowest total cost.

And here's the tiny bit of structure I want you to follow for your reply — just a simple JSON shape that holds the route.

{
  ""solution"": []
}

""solution"" is where you put the chosen path as an ordered list of node identifiers, starting at the depot and ending at the mailbox. Think of it like filling in a short form: list each location you pass through in order, and make sure every step is a legal one-way move on the map. This JSON is just a sketch of the expected shape, not the actual route answer.

Please use the exact identifiers from the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Keep it simple and exact, and I'll check the path you drop into that ""solution"" array.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 11, 'var_index': 1}, {'from': 10, 'to': 23, 'var_index': 2}, {'from': 21, 'to': 23, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 11, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 12, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 13, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 14, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 15, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 16, 'var_index': 15}, {'from': 6, 'to': 7, 'var_index': 16}, {'from': 6, 'to': 17, 'var_index': 17}, {'from': 7, 'to': 8, 'var_index': 18}, {'from': 7, 'to': 18, 'var_index': 19}, {'from': 8, 'to': 9, 'var_index': 20}, {'from': 8, 'to': 19, 'var_index': 21}, {'from': 9, 'to': 10, 'var_index': 22}, {'from': 9, 'to': 20, 'var_index': 23}, {'from': 10, 'to': 21, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 12, 'to': 13, 'var_index': 26}, {'from': 13, 'to': 14, 'var_index': 27}, {'from': 14, 'to': 15, 'var_index': 28}, {'from': 15, 'to': 16, 'var_index': 29}, {'from': 16, 'to': 17, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 18, 'to': 19, 'var_index': 32}, {'from': 19, 'to': 20, 'var_index': 33}, {'from': 20, 'to': 21, 'var_index': 34}], 'objective': {'constant': 0.0, 'linear': [4.0, 10.0, 1.0, 8.0, 3.0, 2.0, 5.0, 1.0, 9.0, 5.0, 3.0, 10.0, 8.0, 9.0, 10.0, 6.0, 3.0, 6.0, 5.0, 8.0, 8.0, 8.0, 10.0, 1.0, 9.0, 1.0, 2.0, 2.0, 2.0, 7.0, 6.0, 1.0, 6.0, 1.0, 5.0], 'quadratic': [[8.0, 10.0, 4.0, 10.0, 10.0, 7.0, 6.0, 1.0, 9.0, 2.0, 3.0, 8.0, 3.0, 8.0, 9.0, 6.0, 4.0, 10.0, 2.0, 8.0, 1.0, 5.0, 1.0, 6.0, 7.0, 9.0, 2.0, 1.0, 9.0, 3.0, 1.0, 6.0, 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'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 34, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 29, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 33, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 34, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'W', 'to': 'A', 'var_index': 0}, {'from': 'W', 'to': 'L', 'var_index': 1}, {'from': 'K', 'to': 'X', 'var_index': 2}, {'from': 'V', 'to': 'X', 'var_index': 3}, {'from': 'A', 'to': 'B', 'var_index': 4}, {'from': 'A', 'to': 'L', 'var_index': 5}, {'from': 'B', 'to': 'C', 'var_index': 6}, {'from': 'B', 'to': 'M', 'var_index': 7}, {'from': 'C', 'to': 'D', 'var_index': 8}, {'from': 'C', 'to': 'N', 'var_index': 9}, {'from': 'D', 'to': 'E', 'var_index': 10}, {'from': 'D', 'to': 'O', 'var_index': 11}, {'from': 'E', 'to': 'F', 'var_index': 12}, {'from': 'E', 'to': 'P', 'var_index': 13}, {'from': 'F', 'to': 'G', 'var_index': 14}, {'from': 'F', 'to': 'Q', 'var_index': 15}, {'from': 'G', 'to': 'H', 'var_index': 16}, {'from': 'G', 'to': 'R', 'var_index': 17}, {'from': 'H', 'to': 'I', 'var_index': 18}, {'from': 'H', 'to': 'S', 'var_index': 19}, {'from': 'I', 'to': 'J', 'var_index': 20}, {'from': 'I', 'to': 'T', 'var_index': 21}, {'from': 'J', 'to': 'K', 'var_index': 22}, {'from': 'J', 'to': 'U', 'var_index': 23}, {'from': 'K', 'to': 'V', 'var_index': 24}, {'from': 'L', 'to': 'M', 'var_index': 25}, {'from': 'M', 'to': 'N', 'var_index': 26}, {'from': 'N', 'to': 'O', 'var_index': 27}, {'from': 'O', 'to': 'P', 'var_index': 28}, {'from': 'P', 'to': 'Q', 'var_index': 29}, {'from': 'Q', 'to': 'R', 'var_index': 30}, {'from': 'R', 'to': 'S', 'var_index': 31}, {'from': 'S', 'to': 'T', 'var_index': 32}, {'from': 'T', 'to': 'U', 'var_index': 33}, {'from': 'U', 'to': 'V', 'var_index': 34}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V', 22: 'W', 23: 'X'}}","['W', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'X']",30,nl,names
QSPP,QSPP,"Many people on the team treat it like a little puzzle: program a single, one-way trip for the robot from its charger to the workbench using only the approved directional lanes. Each lane adds its own energy cost, and some lane pairs introduce extra penalties when they both show up in that exact order, so the trip’s total cost is the sum of the lane energies plus any such ordered penalties. The best trip is the one with the lowest total, and the recorded answer should be just the sequence of locations from start to finish—every consecutive pair must be a real lane, with nothing else tacked on. The full map and cost numbers are given below.

Map summary: 16 locations, 15 directed lanes; valid location IDs: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P; start at O and end at P.
Lane 0 goes from O to A.
Lane 1 goes from N to P.
Lane 2 goes from A to B.
Lane 3 goes from B to C.
Lane 4 goes from C to D.
Lane 5 goes from D to E.
Lane 6 goes from E to F.
Lane 7 goes from F to G.
Lane 8 goes from G to H.
Lane 9 goes from H to I.
Lane 10 goes from I to J.
Lane 11 goes from J to K.
Lane 12 goes from K to L.
Lane 13 goes from L to M.
Lane 14 goes from M to N.
Lane 0 energy cost: 6.0.
Lane 1 energy cost: 6.0.
Lane 2 energy cost: 5.0.
Lane 3 energy cost: 7.0.
Lane 4 energy cost: 1.0.
Lane 5 energy cost: 4.0.
Lane 6 energy cost: 9.0.
Lane 7 energy cost: 5.0.
Lane 8 energy cost: 4.0.
Lane 9 energy cost: 4.0.
Lane 10 energy cost: 7.0.
Lane 11 energy cost: 8.0.
Lane 12 energy cost: 1.0.
Lane 13 energy cost: 6.0.
Lane 14 energy cost: 9.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_lane_id, second_lane_id). If two lanes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| first_lane_id\second_lane_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 4.0 | 1.0 | 7.0 | 3.0 | 10.0 | 10.0 | 10.0 | 3.0 | 10.0 | 3.0 | 10.0 | 7.0 | 5.0 | 5.0 |
| 1 | 4.0 | 1.0 | 3.0 | 8.0 | 8.0 | 8.0 | 6.0 | 6.0 | 8.0 | 5.0 | 3.0 | 9.0 | 7.0 | 1.0 | 7.0 |
| 2 | 1.0 | 3.0 | 4.0 | 6.0 | 1.0 | 3.0 | 10.0 | 5.0 | 7.0 | 8.0 | 1.0 | 3.0 | 6.0 | 3.0 | 2.0 |
| 3 | 7.0 | 8.0 | 6.0 | 1.0 | 9.0 | 5.0 | 9.0 | 8.0 | 9.0 | 9.0 | 2.0 | 2.0 | 6.0 | 10.0 | 6.0 |
| 4 | 3.0 | 8.0 | 1.0 | 9.0 | 6.0 | 9.0 | 3.0 | 6.0 | 10.0 | 4.0 | 3.0 | 9.0 | 3.0 | 7.0 | 4.0 |
| 5 | 10.0 | 8.0 | 3.0 | 5.0 | 9.0 | 10.0 | 7.0 | 3.0 | 7.0 | 8.0 | 9.0 | 6.0 | 8.0 | 4.0 | 9.0 |
| 6 | 10.0 | 6.0 | 10.0 | 9.0 | 3.0 | 7.0 | 6.0 | 10.0 | 6.0 | 5.0 | 5.0 | 4.0 | 7.0 | 1.0 | 2.0 |
| 7 | 10.0 | 6.0 | 5.0 | 8.0 | 6.0 | 3.0 | 10.0 | 10.0 | 9.0 | 10.0 | 2.0 | 9.0 | 9.0 | 7.0 | 5.0 |
| 8 | 3.0 | 8.0 | 7.0 | 9.0 | 10.0 | 7.0 | 6.0 | 9.0 | 5.0 | 1.0 | 6.0 | 6.0 | 5.0 | 7.0 | 7.0 |
| 9 | 10.0 | 5.0 | 8.0 | 9.0 | 4.0 | 8.0 | 5.0 | 10.0 | 1.0 | 2.0 | 1.0 | 8.0 | 2.0 | 5.0 | 1.0 |
| 10 | 3.0 | 3.0 | 1.0 | 2.0 | 3.0 | 9.0 | 5.0 | 2.0 | 6.0 | 1.0 | 5.0 | 9.0 | 5.0 | 3.0 | 10.0 |
| 11 | 10.0 | 9.0 | 3.0 | 2.0 | 9.0 | 6.0 | 4.0 | 9.0 | 6.0 | 8.0 | 9.0 | 1.0 | 6.0 | 6.0 | 10.0 |
| 12 | 7.0 | 7.0 | 6.0 | 6.0 | 3.0 | 8.0 | 7.0 | 9.0 | 5.0 | 2.0 | 5.0 | 6.0 | 7.0 | 8.0 | 6.0 |
| 13 | 5.0 | 1.0 | 3.0 | 10.0 | 7.0 | 4.0 | 1.0 | 7.0 | 7.0 | 5.0 | 3.0 | 6.0 | 8.0 | 8.0 | 3.0 |
| 14 | 5.0 | 7.0 | 2.0 | 6.0 | 4.0 | 9.0 | 2.0 | 5.0 | 7.0 | 1.0 | 10.0 | 10.0 | 6.0 | 3.0 | 1.0 |
Pick the lowest-total trip and record only the location sequence from O to P.

Also, when you send back the chosen trip, please drop it into a tiny JSON snippet so it's easy to read and parse. A relaxed example of the shape I expect is below.

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of locations you want the robot to drive through — just the node names from start to finish, in order. This JSON is only a sketch of the shape I want, not the actual answer itself.

Please use the node identifiers exactly as they appear in the input — do not rename them or invent new labels. For example, valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 'edges': [{'from': 14, 'to': 0, 'var_index': 0}, {'from': 13, 'to': 15, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}], 'objective': {'constant': 0.0, 'linear': [6.0, 6.0, 5.0, 7.0, 1.0, 4.0, 9.0, 5.0, 4.0, 4.0, 7.0, 8.0, 1.0, 6.0, 9.0], 'quadratic': [[4.0, 4.0, 1.0, 7.0, 3.0, 10.0, 10.0, 10.0, 3.0, 10.0, 3.0, 10.0, 7.0, 5.0, 5.0], [4.0, 1.0, 3.0, 8.0, 8.0, 8.0, 6.0, 6.0, 8.0, 5.0, 3.0, 9.0, 7.0, 1.0, 7.0], [1.0, 3.0, 4.0, 6.0, 1.0, 3.0, 10.0, 5.0, 7.0, 8.0, 1.0, 3.0, 6.0, 3.0, 2.0], [7.0, 8.0, 6.0, 1.0, 9.0, 5.0, 9.0, 8.0, 9.0, 9.0, 2.0, 2.0, 6.0, 10.0, 6.0], [3.0, 8.0, 1.0, 9.0, 6.0, 9.0, 3.0, 6.0, 10.0, 4.0, 3.0, 9.0, 3.0, 7.0, 4.0], [10.0, 8.0, 3.0, 5.0, 9.0, 10.0, 7.0, 3.0, 7.0, 8.0, 9.0, 6.0, 8.0, 4.0, 9.0], [10.0, 6.0, 10.0, 9.0, 3.0, 7.0, 6.0, 10.0, 6.0, 5.0, 5.0, 4.0, 7.0, 1.0, 2.0], [10.0, 6.0, 5.0, 8.0, 6.0, 3.0, 10.0, 10.0, 9.0, 10.0, 2.0, 9.0, 9.0, 7.0, 5.0], [3.0, 8.0, 7.0, 9.0, 10.0, 7.0, 6.0, 9.0, 5.0, 1.0, 6.0, 6.0, 5.0, 7.0, 7.0], [10.0, 5.0, 8.0, 9.0, 4.0, 8.0, 5.0, 10.0, 1.0, 2.0, 1.0, 8.0, 2.0, 5.0, 1.0], [3.0, 3.0, 1.0, 2.0, 3.0, 9.0, 5.0, 2.0, 6.0, 1.0, 5.0, 9.0, 5.0, 3.0, 10.0], [10.0, 9.0, 3.0, 2.0, 9.0, 6.0, 4.0, 9.0, 6.0, 8.0, 9.0, 1.0, 6.0, 6.0, 10.0], [7.0, 7.0, 6.0, 6.0, 3.0, 8.0, 7.0, 9.0, 5.0, 2.0, 5.0, 6.0, 7.0, 8.0, 6.0], [5.0, 1.0, 3.0, 10.0, 7.0, 4.0, 1.0, 7.0, 7.0, 5.0, 3.0, 6.0, 8.0, 8.0, 3.0], [5.0, 7.0, 2.0, 6.0, 4.0, 9.0, 2.0, 5.0, 7.0, 1.0, 10.0, 10.0, 6.0, 3.0, 1.0]]}, 'source': 14, 'target': 15}","[14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15]",1397.0,"{'problem_type': 'QSPP', 'num_nodes': 16, 'num_edges': 15, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P'], 'source': 'O', 'target': 'P', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 1.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 9.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 4.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 7.0}, {'var_index': 11, 'linear_cost': 8.0}, {'var_index': 12, 'linear_cost': 1.0}, {'var_index': 13, 'linear_cost': 6.0}, {'var_index': 14, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 'O', 'to': 'A', 'var_index': 0}, {'from': 'N', 'to': 'P', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}, {'from': 'H', 'to': 'I', 'var_index': 9}, {'from': 'I', 'to': 'J', 'var_index': 10}, {'from': 'J', 'to': 'K', 'var_index': 11}, {'from': 'K', 'to': 'L', 'var_index': 12}, {'from': 'L', 'to': 'M', 'var_index': 13}, {'from': 'M', 'to': 'N', 'var_index': 14}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P'}}","['O', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'P']",31,nl,names
QSPP,QSPP,"There's a simple scene: a visitor wants to go from the museum entrance to the viewpoint using the one-way promenades, and only one path is allowed. That path must be continuous and follow the direction signs the whole way — no splitting the trip or leaving out any segments. Each promenade costs some walking effort, some segments bring their own extra awkwardness even alone, and any time two specific promenades appear together they may add extra combined discomfort (both sides of their interaction are added up). So the trick is to pick the single allowed route that minimizes the sum of all individual efforts plus any extra awkwardness from chosen pairings. The full map with the walkway details and numbers is shown below.

# num_locations=25
# num_promenades=40
# location_ids=0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
# museum_entrance_id=0
# viewpoint_id=24

promenade_tail_location,promenade_head_location,promenade_id
0,1,0
0,5,1
1,2,2
1,6,3
2,3,4
2,7,5
3,4,6
3,8,7
4,9,8
5,6,9
5,10,10
6,7,11
6,11,12
7,8,13
7,12,14
8,9,15
8,13,16
9,14,17
10,11,18
10,15,19
11,12,20
11,16,21
12,13,22
12,17,23
13,14,24
13,18,25
14,19,26
15,16,27
15,20,28
16,17,29
16,21,30
17,18,31
17,22,32
18,19,33
18,23,34
19,24,35
20,21,36
21,22,37
22,23,38
23,24,39

promenade_id,walking_effort
0,5.0
1,9.0
2,10.0
3,1.0
4,2.0
5,2.0
6,3.0
7,8.0
8,1.0
9,7.0
10,5.0
11,8.0
12,5.0
13,8.0
14,1.0
15,3.0
16,8.0
17,1.0
18,10.0
19,6.0
20,5.0
21,9.0
22,9.0
23,2.0
24,3.0
25,3.0
26,1.0
27,10.0
28,9.0
29,3.0
30,4.0
31,9.0
32,7.0
33,3.0
34,2.0
35,5.0
36,1.0
37,3.0
38,10.0
39,8.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (promenade_i_id, promenade_j_id). If two promenades with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| promenade_i_id\promenade_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 4.0 | 5.0 | 5.0 | 9.0 | 3.0 | 1.0 | 4.0 | 9.0 | 1.0 | 9.0 | 3.0 | 10.0 | 5.0 | 1.0 | 6.0 | 6.0 | 2.0 | 5.0 | 7.0 | 8.0 | 1.0 | 7.0 | 9.0 | 9.0 | 10.0 | 8.0 | 8.0 | 8.0 | 1.0 | 2.0 | 2.0 | 3.0 | 1.0 | 6.0 | 3.0 | 3.0 | 7.0 | 7.0 | 2.0 |
| 1 | 4.0 | 4.0 | 9.0 | 6.0 | 1.0 | 1.0 | 8.0 | 9.0 | 7.0 | 1.0 | 7.0 | 7.0 | 2.0 | 6.0 | 1.0 | 4.0 | 5.0 | 7.0 | 2.0 | 9.0 | 1.0 | 10.0 | 8.0 | 3.0 | 3.0 | 1.0 | 3.0 | 4.0 | 6.0 | 4.0 | 9.0 | 4.0 | 6.0 | 1.0 | 4.0 | 8.0 | 1.0 | 1.0 | 10.0 | 3.0 |
| 2 | 5.0 | 9.0 | 10.0 | 10.0 | 7.0 | 9.0 | 8.0 | 6.0 | 7.0 | 3.0 | 1.0 | 3.0 | 3.0 | 9.0 | 3.0 | 5.0 | 8.0 | 6.0 | 4.0 | 3.0 | 3.0 | 3.0 | 4.0 | 1.0 | 9.0 | 1.0 | 5.0 | 9.0 | 6.0 | 10.0 | 5.0 | 10.0 | 3.0 | 3.0 | 9.0 | 7.0 | 7.0 | 8.0 | 9.0 | 3.0 |
| 3 | 5.0 | 6.0 | 10.0 | 3.0 | 10.0 | 7.0 | 2.0 | 10.0 | 4.0 | 9.0 | 1.0 | 6.0 | 10.0 | 10.0 | 6.0 | 1.0 | 3.0 | 2.0 | 3.0 | 8.0 | 5.0 | 6.0 | 6.0 | 1.0 | 4.0 | 8.0 | 8.0 | 9.0 | 7.0 | 5.0 | 1.0 | 6.0 | 5.0 | 9.0 | 8.0 | 3.0 | 6.0 | 2.0 | 7.0 | 3.0 |
| 4 | 9.0 | 1.0 | 7.0 | 10.0 | 3.0 | 7.0 | 3.0 | 7.0 | 7.0 | 5.0 | 5.0 | 2.0 | 6.0 | 5.0 | 10.0 | 1.0 | 1.0 | 2.0 | 7.0 | 4.0 | 3.0 | 4.0 | 10.0 | 1.0 | 7.0 | 2.0 | 10.0 | 5.0 | 8.0 | 1.0 | 9.0 | 2.0 | 8.0 | 4.0 | 5.0 | 8.0 | 4.0 | 4.0 | 3.0 | 2.0 |
| 5 | 3.0 | 1.0 | 9.0 | 7.0 | 7.0 | 1.0 | 5.0 | 3.0 | 6.0 | 8.0 | 8.0 | 9.0 | 1.0 | 8.0 | 7.0 | 3.0 | 7.0 | 1.0 | 7.0 | 2.0 | 9.0 | 5.0 | 8.0 | 2.0 | 7.0 | 1.0 | 3.0 | 5.0 | 1.0 | 1.0 | 1.0 | 10.0 | 8.0 | 5.0 | 7.0 | 9.0 | 8.0 | 4.0 | 3.0 | 9.0 |
| 6 | 1.0 | 8.0 | 8.0 | 2.0 | 3.0 | 5.0 | 1.0 | 9.0 | 8.0 | 4.0 | 4.0 | 2.0 | 3.0 | 7.0 | 3.0 | 2.0 | 6.0 | 9.0 | 3.0 | 6.0 | 1.0 | 10.0 | 5.0 | 1.0 | 7.0 | 4.0 | 8.0 | 5.0 | 3.0 | 2.0 | 8.0 | 8.0 | 1.0 | 4.0 | 7.0 | 5.0 | 6.0 | 3.0 | 3.0 | 3.0 |
| 7 | 4.0 | 9.0 | 6.0 | 10.0 | 7.0 | 3.0 | 9.0 | 8.0 | 2.0 | 7.0 | 9.0 | 10.0 | 3.0 | 3.0 | 5.0 | 1.0 | 6.0 | 8.0 | 2.0 | 10.0 | 3.0 | 1.0 | 5.0 | 1.0 | 10.0 | 8.0 | 8.0 | 5.0 | 2.0 | 3.0 | 2.0 | 7.0 | 10.0 | 9.0 | 7.0 | 6.0 | 2.0 | 6.0 | 10.0 | 10.0 |
| 8 | 9.0 | 7.0 | 7.0 | 4.0 | 7.0 | 6.0 | 8.0 | 2.0 | 9.0 | 6.0 | 8.0 | 2.0 | 10.0 | 3.0 | 3.0 | 1.0 | 9.0 | 5.0 | 1.0 | 5.0 | 4.0 | 7.0 | 4.0 | 3.0 | 2.0 | 5.0 | 10.0 | 7.0 | 6.0 | 9.0 | 6.0 | 6.0 | 10.0 | 10.0 | 4.0 | 5.0 | 7.0 | 1.0 | 2.0 | 5.0 |
| 9 | 1.0 | 1.0 | 3.0 | 9.0 | 5.0 | 8.0 | 4.0 | 7.0 | 6.0 | 2.0 | 4.0 | 10.0 | 8.0 | 3.0 | 1.0 | 1.0 | 1.0 | 10.0 | 2.0 | 7.0 | 1.0 | 5.0 | 8.0 | 3.0 | 8.0 | 6.0 | 7.0 | 6.0 | 1.0 | 2.0 | 3.0 | 5.0 | 10.0 | 2.0 | 9.0 | 9.0 | 4.0 | 5.0 | 5.0 | 10.0 |
| 10 | 9.0 | 7.0 | 1.0 | 1.0 | 5.0 | 8.0 | 4.0 | 9.0 | 8.0 | 4.0 | 1.0 | 5.0 | 7.0 | 1.0 | 7.0 | 5.0 | 1.0 | 2.0 | 4.0 | 4.0 | 4.0 | 5.0 | 6.0 | 8.0 | 6.0 | 10.0 | 7.0 | 3.0 | 10.0 | 3.0 | 8.0 | 10.0 | 6.0 | 9.0 | 8.0 | 6.0 | 4.0 | 6.0 | 2.0 | 3.0 |
| 11 | 3.0 | 7.0 | 3.0 | 6.0 | 2.0 | 9.0 | 2.0 | 10.0 | 2.0 | 10.0 | 5.0 | 6.0 | 7.0 | 8.0 | 7.0 | 7.0 | 1.0 | 9.0 | 8.0 | 6.0 | 10.0 | 10.0 | 4.0 | 10.0 | 6.0 | 2.0 | 3.0 | 6.0 | 3.0 | 1.0 | 5.0 | 3.0 | 9.0 | 6.0 | 8.0 | 5.0 | 6.0 | 6.0 | 8.0 | 5.0 |
| 12 | 10.0 | 2.0 | 3.0 | 10.0 | 6.0 | 1.0 | 3.0 | 3.0 | 10.0 | 8.0 | 7.0 | 7.0 | 10.0 | 4.0 | 6.0 | 5.0 | 1.0 | 9.0 | 2.0 | 7.0 | 8.0 | 5.0 | 1.0 | 4.0 | 2.0 | 1.0 | 10.0 | 3.0 | 6.0 | 3.0 | 3.0 | 9.0 | 3.0 | 5.0 | 7.0 | 8.0 | 9.0 | 1.0 | 9.0 | 3.0 |
| 13 | 5.0 | 6.0 | 9.0 | 10.0 | 5.0 | 8.0 | 7.0 | 3.0 | 3.0 | 3.0 | 1.0 | 8.0 | 4.0 | 10.0 | 10.0 | 8.0 | 9.0 | 10.0 | 5.0 | 3.0 | 6.0 | 3.0 | 10.0 | 1.0 | 10.0 | 4.0 | 2.0 | 5.0 | 5.0 | 5.0 | 5.0 | 2.0 | 4.0 | 2.0 | 8.0 | 10.0 | 10.0 | 1.0 | 9.0 | 6.0 |
| 14 | 1.0 | 1.0 | 3.0 | 6.0 | 10.0 | 7.0 | 3.0 | 5.0 | 3.0 | 1.0 | 7.0 | 7.0 | 6.0 | 10.0 | 1.0 | 5.0 | 2.0 | 5.0 | 2.0 | 9.0 | 6.0 | 2.0 | 8.0 | 4.0 | 7.0 | 9.0 | 7.0 | 5.0 | 3.0 | 5.0 | 5.0 | 3.0 | 7.0 | 5.0 | 1.0 | 6.0 | 4.0 | 9.0 | 8.0 | 1.0 |
| 15 | 6.0 | 4.0 | 5.0 | 1.0 | 1.0 | 3.0 | 2.0 | 1.0 | 1.0 | 1.0 | 5.0 | 7.0 | 5.0 | 8.0 | 5.0 | 5.0 | 7.0 | 1.0 | 9.0 | 8.0 | 3.0 | 8.0 | 2.0 | 6.0 | 2.0 | 1.0 | 2.0 | 3.0 | 4.0 | 7.0 | 5.0 | 2.0 | 6.0 | 9.0 | 10.0 | 9.0 | 7.0 | 6.0 | 9.0 | 2.0 |
| 16 | 6.0 | 5.0 | 8.0 | 3.0 | 1.0 | 7.0 | 6.0 | 6.0 | 9.0 | 1.0 | 1.0 | 1.0 | 1.0 | 9.0 | 2.0 | 7.0 | 7.0 | 5.0 | 10.0 | 4.0 | 7.0 | 4.0 | 10.0 | 9.0 | 1.0 | 3.0 | 10.0 | 9.0 | 7.0 | 2.0 | 7.0 | 1.0 | 7.0 | 4.0 | 3.0 | 8.0 | 7.0 | 2.0 | 3.0 | 3.0 |
| 17 | 2.0 | 7.0 | 6.0 | 2.0 | 2.0 | 1.0 | 9.0 | 8.0 | 5.0 | 10.0 | 2.0 | 9.0 | 9.0 | 10.0 | 5.0 | 1.0 | 5.0 | 6.0 | 7.0 | 10.0 | 2.0 | 7.0 | 2.0 | 3.0 | 6.0 | 7.0 | 5.0 | 7.0 | 6.0 | 2.0 | 3.0 | 9.0 | 4.0 | 2.0 | 7.0 | 9.0 | 3.0 | 4.0 | 4.0 | 8.0 |
| 18 | 5.0 | 2.0 | 4.0 | 3.0 | 7.0 | 7.0 | 3.0 | 2.0 | 1.0 | 2.0 | 4.0 | 8.0 | 2.0 | 5.0 | 2.0 | 9.0 | 10.0 | 7.0 | 2.0 | 5.0 | 3.0 | 7.0 | 9.0 | 3.0 | 4.0 | 9.0 | 9.0 | 4.0 | 5.0 | 4.0 | 2.0 | 4.0 | 9.0 | 9.0 | 7.0 | 8.0 | 10.0 | 3.0 | 6.0 | 2.0 |
| 19 | 7.0 | 9.0 | 3.0 | 8.0 | 4.0 | 2.0 | 6.0 | 10.0 | 5.0 | 7.0 | 4.0 | 6.0 | 7.0 | 3.0 | 9.0 | 8.0 | 4.0 | 10.0 | 5.0 | 4.0 | 3.0 | 10.0 | 8.0 | 5.0 | 8.0 | 8.0 | 10.0 | 10.0 | 5.0 | 4.0 | 6.0 | 2.0 | 2.0 | 2.0 | 1.0 | 4.0 | 8.0 | 6.0 | 1.0 | 4.0 |
| 20 | 8.0 | 1.0 | 3.0 | 5.0 | 3.0 | 9.0 | 1.0 | 3.0 | 4.0 | 1.0 | 4.0 | 10.0 | 8.0 | 6.0 | 6.0 | 3.0 | 7.0 | 2.0 | 3.0 | 3.0 | 10.0 | 7.0 | 4.0 | 10.0 | 9.0 | 6.0 | 6.0 | 6.0 | 5.0 | 1.0 | 9.0 | 3.0 | 2.0 | 4.0 | 8.0 | 5.0 | 1.0 | 4.0 | 2.0 | 3.0 |
| 21 | 1.0 | 10.0 | 3.0 | 6.0 | 4.0 | 5.0 | 10.0 | 1.0 | 7.0 | 5.0 | 5.0 | 10.0 | 5.0 | 3.0 | 2.0 | 8.0 | 4.0 | 7.0 | 7.0 | 10.0 | 7.0 | 8.0 | 9.0 | 1.0 | 3.0 | 10.0 | 3.0 | 9.0 | 8.0 | 5.0 | 4.0 | 6.0 | 10.0 | 6.0 | 5.0 | 4.0 | 8.0 | 2.0 | 4.0 | 9.0 |
| 22 | 7.0 | 8.0 | 4.0 | 6.0 | 10.0 | 8.0 | 5.0 | 5.0 | 4.0 | 8.0 | 6.0 | 4.0 | 1.0 | 10.0 | 8.0 | 2.0 | 10.0 | 2.0 | 9.0 | 8.0 | 4.0 | 9.0 | 7.0 | 9.0 | 3.0 | 7.0 | 3.0 | 1.0 | 1.0 | 6.0 | 5.0 | 3.0 | 8.0 | 5.0 | 5.0 | 10.0 | 1.0 | 4.0 | 5.0 | 8.0 |
| 23 | 9.0 | 3.0 | 1.0 | 1.0 | 1.0 | 2.0 | 1.0 | 1.0 | 3.0 | 3.0 | 8.0 | 10.0 | 4.0 | 1.0 | 4.0 | 6.0 | 9.0 | 3.0 | 3.0 | 5.0 | 10.0 | 1.0 | 9.0 | 10.0 | 1.0 | 5.0 | 9.0 | 5.0 | 10.0 | 6.0 | 6.0 | 10.0 | 6.0 | 8.0 | 8.0 | 6.0 | 6.0 | 8.0 | 8.0 | 4.0 |
| 24 | 9.0 | 3.0 | 9.0 | 4.0 | 7.0 | 7.0 | 7.0 | 10.0 | 2.0 | 8.0 | 6.0 | 6.0 | 2.0 | 10.0 | 7.0 | 2.0 | 1.0 | 6.0 | 4.0 | 8.0 | 9.0 | 3.0 | 3.0 | 1.0 | 5.0 | 8.0 | 7.0 | 10.0 | 3.0 | 1.0 | 10.0 | 4.0 | 7.0 | 2.0 | 10.0 | 10.0 | 10.0 | 2.0 | 2.0 | 10.0 |
| 25 | 10.0 | 1.0 | 1.0 | 8.0 | 2.0 | 1.0 | 4.0 | 8.0 | 5.0 | 6.0 | 10.0 | 2.0 | 1.0 | 4.0 | 9.0 | 1.0 | 3.0 | 7.0 | 9.0 | 8.0 | 6.0 | 10.0 | 7.0 | 5.0 | 8.0 | 3.0 | 7.0 | 5.0 | 4.0 | 10.0 | 3.0 | 7.0 | 1.0 | 5.0 | 10.0 | 8.0 | 7.0 | 9.0 | 4.0 | 3.0 |
| 26 | 8.0 | 3.0 | 5.0 | 8.0 | 10.0 | 3.0 | 8.0 | 8.0 | 10.0 | 7.0 | 7.0 | 3.0 | 10.0 | 2.0 | 7.0 | 2.0 | 10.0 | 5.0 | 9.0 | 10.0 | 6.0 | 3.0 | 3.0 | 9.0 | 7.0 | 7.0 | 1.0 | 10.0 | 7.0 | 5.0 | 10.0 | 3.0 | 9.0 | 9.0 | 5.0 | 8.0 | 5.0 | 4.0 | 3.0 | 3.0 |
| 27 | 8.0 | 4.0 | 9.0 | 9.0 | 5.0 | 5.0 | 5.0 | 5.0 | 7.0 | 6.0 | 3.0 | 6.0 | 3.0 | 5.0 | 5.0 | 3.0 | 9.0 | 7.0 | 4.0 | 10.0 | 6.0 | 9.0 | 1.0 | 5.0 | 10.0 | 5.0 | 10.0 | 8.0 | 6.0 | 3.0 | 1.0 | 3.0 | 2.0 | 7.0 | 4.0 | 2.0 | 10.0 | 1.0 | 8.0 | 5.0 |
| 28 | 8.0 | 6.0 | 6.0 | 7.0 | 8.0 | 1.0 | 3.0 | 2.0 | 6.0 | 1.0 | 10.0 | 3.0 | 6.0 | 5.0 | 3.0 | 4.0 | 7.0 | 6.0 | 5.0 | 5.0 | 5.0 | 8.0 | 1.0 | 10.0 | 3.0 | 4.0 | 7.0 | 6.0 | 9.0 | 5.0 | 4.0 | 7.0 | 4.0 | 7.0 | 1.0 | 7.0 | 6.0 | 5.0 | 8.0 | 2.0 |
| 29 | 1.0 | 4.0 | 10.0 | 5.0 | 1.0 | 1.0 | 2.0 | 3.0 | 9.0 | 2.0 | 3.0 | 1.0 | 3.0 | 5.0 | 5.0 | 7.0 | 2.0 | 2.0 | 4.0 | 4.0 | 1.0 | 5.0 | 6.0 | 6.0 | 1.0 | 10.0 | 5.0 | 3.0 | 5.0 | 4.0 | 5.0 | 1.0 | 10.0 | 4.0 | 5.0 | 10.0 | 1.0 | 9.0 | 9.0 | 4.0 |
| 30 | 2.0 | 9.0 | 5.0 | 1.0 | 9.0 | 1.0 | 8.0 | 2.0 | 6.0 | 3.0 | 8.0 | 5.0 | 3.0 | 5.0 | 5.0 | 5.0 | 7.0 | 3.0 | 2.0 | 6.0 | 9.0 | 4.0 | 5.0 | 6.0 | 10.0 | 3.0 | 10.0 | 1.0 | 4.0 | 5.0 | 5.0 | 3.0 | 9.0 | 7.0 | 4.0 | 5.0 | 6.0 | 6.0 | 5.0 | 2.0 |
| 31 | 2.0 | 4.0 | 10.0 | 6.0 | 2.0 | 10.0 | 8.0 | 7.0 | 6.0 | 5.0 | 10.0 | 3.0 | 9.0 | 2.0 | 3.0 | 2.0 | 1.0 | 9.0 | 4.0 | 2.0 | 3.0 | 6.0 | 3.0 | 10.0 | 4.0 | 7.0 | 3.0 | 3.0 | 7.0 | 1.0 | 3.0 | 1.0 | 7.0 | 10.0 | 1.0 | 3.0 | 5.0 | 1.0 | 9.0 | 1.0 |
| 32 | 3.0 | 6.0 | 3.0 | 5.0 | 8.0 | 8.0 | 1.0 | 10.0 | 10.0 | 10.0 | 6.0 | 9.0 | 3.0 | 4.0 | 7.0 | 6.0 | 7.0 | 4.0 | 9.0 | 2.0 | 2.0 | 10.0 | 8.0 | 6.0 | 7.0 | 1.0 | 9.0 | 2.0 | 4.0 | 10.0 | 9.0 | 7.0 | 6.0 | 2.0 | 1.0 | 6.0 | 10.0 | 10.0 | 8.0 | 5.0 |
| 33 | 1.0 | 1.0 | 3.0 | 9.0 | 4.0 | 5.0 | 4.0 | 9.0 | 10.0 | 2.0 | 9.0 | 6.0 | 5.0 | 2.0 | 5.0 | 9.0 | 4.0 | 2.0 | 9.0 | 2.0 | 4.0 | 6.0 | 5.0 | 8.0 | 2.0 | 5.0 | 9.0 | 7.0 | 7.0 | 4.0 | 7.0 | 10.0 | 2.0 | 8.0 | 3.0 | 9.0 | 2.0 | 1.0 | 7.0 | 2.0 |
| 34 | 6.0 | 4.0 | 9.0 | 8.0 | 5.0 | 7.0 | 7.0 | 7.0 | 4.0 | 9.0 | 8.0 | 8.0 | 7.0 | 8.0 | 1.0 | 10.0 | 3.0 | 7.0 | 7.0 | 1.0 | 8.0 | 5.0 | 5.0 | 8.0 | 10.0 | 10.0 | 5.0 | 4.0 | 1.0 | 5.0 | 4.0 | 1.0 | 1.0 | 3.0 | 6.0 | 2.0 | 10.0 | 4.0 | 7.0 | 2.0 |
| 35 | 3.0 | 8.0 | 7.0 | 3.0 | 8.0 | 9.0 | 5.0 | 6.0 | 5.0 | 9.0 | 6.0 | 5.0 | 8.0 | 10.0 | 6.0 | 9.0 | 8.0 | 9.0 | 8.0 | 4.0 | 5.0 | 4.0 | 10.0 | 6.0 | 10.0 | 8.0 | 8.0 | 2.0 | 7.0 | 10.0 | 5.0 | 3.0 | 6.0 | 9.0 | 2.0 | 4.0 | 6.0 | 5.0 | 7.0 | 10.0 |
| 36 | 3.0 | 1.0 | 7.0 | 6.0 | 4.0 | 8.0 | 6.0 | 2.0 | 7.0 | 4.0 | 4.0 | 6.0 | 9.0 | 10.0 | 4.0 | 7.0 | 7.0 | 3.0 | 10.0 | 8.0 | 1.0 | 8.0 | 1.0 | 6.0 | 10.0 | 7.0 | 5.0 | 10.0 | 6.0 | 1.0 | 6.0 | 5.0 | 10.0 | 2.0 | 10.0 | 6.0 | 6.0 | 5.0 | 5.0 | 3.0 |
| 37 | 7.0 | 1.0 | 8.0 | 2.0 | 4.0 | 4.0 | 3.0 | 6.0 | 1.0 | 5.0 | 6.0 | 6.0 | 1.0 | 1.0 | 9.0 | 6.0 | 2.0 | 4.0 | 3.0 | 6.0 | 4.0 | 2.0 | 4.0 | 8.0 | 2.0 | 9.0 | 4.0 | 1.0 | 5.0 | 9.0 | 6.0 | 1.0 | 10.0 | 1.0 | 4.0 | 5.0 | 5.0 | 2.0 | 6.0 | 7.0 |
| 38 | 7.0 | 10.0 | 9.0 | 7.0 | 3.0 | 3.0 | 3.0 | 10.0 | 2.0 | 5.0 | 2.0 | 8.0 | 9.0 | 9.0 | 8.0 | 9.0 | 3.0 | 4.0 | 6.0 | 1.0 | 2.0 | 4.0 | 5.0 | 8.0 | 2.0 | 4.0 | 3.0 | 8.0 | 8.0 | 9.0 | 5.0 | 9.0 | 8.0 | 7.0 | 7.0 | 7.0 | 5.0 | 6.0 | 10.0 | 8.0 |
| 39 | 2.0 | 3.0 | 3.0 | 3.0 | 2.0 | 9.0 | 3.0 | 10.0 | 5.0 | 10.0 | 3.0 | 5.0 | 3.0 | 6.0 | 1.0 | 2.0 | 3.0 | 8.0 | 2.0 | 4.0 | 3.0 | 9.0 | 8.0 | 4.0 | 10.0 | 3.0 | 3.0 | 5.0 | 2.0 | 4.0 | 2.0 | 1.0 | 5.0 | 2.0 | 2.0 | 10.0 | 3.0 | 7.0 | 8.0 | 10.0 |

When you send back the single chosen promenade, just drop it into a tiny JSON sketch like this so it's easy to parse — nothing fancy, just the shape I expect:

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of NODE names only: start at the museum entrance and list each node you pass through until the viewpoint, in order. Keep it human-readable and simple (for example, [""Entrance"",""A"",""Viewpoint""]), and remember this block is only a template showing the expected shape, not the actual answer.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'objective': {'constant': 0.0, 'linear': [5.0, 9.0, 10.0, 1.0, 2.0, 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{'var_i': 34, 'var_j': 30, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 33, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 34, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 36, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 37, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 38, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 39, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 35, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 35, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 9, 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{'var_i': 35, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 35, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 35, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 33, 'quadratic_cost': 9.0}, {'var_i': 35, 'var_j': 34, 'quadratic_cost': 2.0}, {'var_i': 35, 'var_j': 35, 'quadratic_cost': 4.0}, {'var_i': 35, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 35, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 35, 'var_j': 38, 'quadratic_cost': 7.0}, {'var_i': 35, 'var_j': 39, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 28, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 29, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 33, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 34, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 36, 'quadratic_cost': 6.0}, {'var_i': 36, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 38, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 20, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 26, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 28, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 37, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 34, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 35, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 36, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 38, 'quadratic_cost': 6.0}, {'var_i': 37, 'var_j': 39, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 25, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 27, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 34, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 35, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 36, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 37, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 38, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 39, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 25, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 28, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 32, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 33, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 34, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 35, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 36, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 37, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 38, 'quadratic_cost': 8.0}, {'var_i': 39, 'var_j': 39, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17, 18: 18, 19: 19, 20: 20, 21: 21, 22: 22, 23: 23, 24: 24}}","[0, 5, 10, 15, 16, 17, 18, 23, 24]",32,csv,0
QSPP,QSPP,"At the station they want one clear path for the ambulance to follow from base to the incident, using only legal one-way streets, and the preference is the path that yields the lowest total trip time. Each street in that path brings a basic travel time, and there are extra slowdowns associated with some streets individually or when certain streets appear together, so the trip’s total time is the sum of the street times plus any applicable added delays. The chosen route should be written as a single list of locations—starting at the emergency center, ending at the scene—where each consecutive pair matches a real one-way street; the detailed map and costs are provided below.

The map below lists 18 locations and 47 one-way streets: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. The ambulance starts at 16 and must end at 17.

| street_start_location | street_end_location | street_id |
|---|---|---|
| 16 | 0 | 0 |
| 16 | 1 | 1 |
| 16 | 2 | 2 |
| 16 | 3 | 3 |
| 16 | 4 | 4 |
| 16 | 5 | 5 |
| 16 | 6 | 6 |
| 16 | 7 | 7 |
| 16 | 8 | 8 |
| 16 | 9 | 9 |
| 16 | 10 | 10 |
| 16 | 11 | 11 |
| 16 | 12 | 12 |
| 16 | 13 | 13 |
| 16 | 14 | 14 |
| 16 | 15 | 15 |
| 0 | 17 | 16 |
| 1 | 17 | 17 |
| 2 | 17 | 18 |
| 3 | 17 | 19 |
| 4 | 17 | 20 |
| 5 | 17 | 21 |
| 6 | 17 | 22 |
| 7 | 17 | 23 |
| 8 | 17 | 24 |
| 9 | 17 | 25 |
| 10 | 17 | 26 |
| 11 | 17 | 27 |
| 12 | 17 | 28 |
| 13 | 17 | 29 |
| 14 | 17 | 30 |
| 15 | 17 | 31 |
| 0 | 1 | 32 |
| 1 | 2 | 33 |
| 2 | 3 | 34 |
| 3 | 4 | 35 |
| 4 | 5 | 36 |
| 5 | 6 | 37 |
| 6 | 7 | 38 |
| 7 | 8 | 39 |
| 8 | 9 | 40 |
| 9 | 10 | 41 |
| 10 | 11 | 42 |
| 11 | 12 | 43 |
| 12 | 13 | 44 |
| 13 | 14 | 45 |
| 14 | 15 | 46 |

| street_id_ref | base_travel_time |
|---|---|
| 0 | 2.0 |
| 1 | 1.0 |
| 2 | 3.0 |
| 3 | 10.0 |
| 4 | 7.0 |
| 5 | 9.0 |
| 6 | 8.0 |
| 7 | 1.0 |
| 8 | 1.0 |
| 9 | 2.0 |
| 10 | 1.0 |
| 11 | 7.0 |
| 12 | 2.0 |
| 13 | 5.0 |
| 14 | 7.0 |
| 15 | 8.0 |
| 16 | 9.0 |
| 17 | 1.0 |
| 18 | 4.0 |
| 19 | 10.0 |
| 20 | 1.0 |
| 21 | 10.0 |
| 22 | 1.0 |
| 23 | 5.0 |
| 24 | 10.0 |
| 25 | 6.0 |
| 26 | 2.0 |
| 27 | 9.0 |
| 28 | 10.0 |
| 29 | 8.0 |
| 30 | 7.0 |
| 31 | 4.0 |
| 32 | 3.0 |
| 33 | 9.0 |
| 34 | 6.0 |
| 35 | 4.0 |
| 36 | 3.0 |
| 37 | 8.0 |
| 38 | 2.0 |
| 39 | 10.0 |
| 40 | 4.0 |
| 41 | 5.0 |
| 42 | 2.0 |
| 43 | 4.0 |
| 44 | 1.0 |
| 45 | 4.0 |
| 46 | 9.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_id, street_j_id). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| street_i_id\street_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 6.0 | 8.0 | 3.0 | 4.0 | 5.0 | 4.0 | 2.0 | 4.0 | 9.0 | 10.0 | 9.0 | 3.0 | 6.0 | 5.0 | 7.0 | 7.0 | 3.0 | 6.0 | 1.0 | 10.0 | 7.0 | 3.0 | 2.0 | 7.0 | 3.0 | 10.0 | 2.0 | 10.0 | 9.0 | 1.0 | 9.0 | 1.0 | 1.0 | 7.0 | 4.0 | 3.0 | 3.0 | 8.0 | 2.0 | 9.0 | 9.0 | 4.0 | 4.0 | 1.0 | 9.0 | 7.0 |
| 1 | 6.0 | 9.0 | 9.0 | 7.0 | 6.0 | 3.0 | 10.0 | 9.0 | 2.0 | 2.0 | 5.0 | 4.0 | 6.0 | 8.0 | 10.0 | 7.0 | 7.0 | 2.0 | 7.0 | 1.0 | 2.0 | 9.0 | 5.0 | 2.0 | 7.0 | 1.0 | 1.0 | 1.0 | 2.0 | 7.0 | 8.0 | 5.0 | 3.0 | 5.0 | 9.0 | 2.0 | 8.0 | 7.0 | 1.0 | 2.0 | 4.0 | 2.0 | 4.0 | 5.0 | 7.0 | 2.0 | 1.0 |
| 2 | 8.0 | 9.0 | 1.0 | 2.0 | 5.0 | 10.0 | 9.0 | 3.0 | 8.0 | 10.0 | 2.0 | 5.0 | 3.0 | 3.0 | 1.0 | 8.0 | 7.0 | 9.0 | 3.0 | 10.0 | 2.0 | 7.0 | 7.0 | 1.0 | 1.0 | 9.0 | 3.0 | 8.0 | 7.0 | 4.0 | 3.0 | 8.0 | 2.0 | 4.0 | 5.0 | 2.0 | 7.0 | 4.0 | 1.0 | 1.0 | 6.0 | 7.0 | 8.0 | 2.0 | 7.0 | 4.0 | 9.0 |
| 3 | 3.0 | 7.0 | 2.0 | 6.0 | 7.0 | 6.0 | 10.0 | 4.0 | 2.0 | 7.0 | 5.0 | 4.0 | 9.0 | 10.0 | 7.0 | 9.0 | 8.0 | 9.0 | 6.0 | 6.0 | 10.0 | 1.0 | 5.0 | 4.0 | 10.0 | 10.0 | 2.0 | 5.0 | 2.0 | 3.0 | 9.0 | 4.0 | 3.0 | 2.0 | 10.0 | 4.0 | 5.0 | 4.0 | 4.0 | 2.0 | 10.0 | 3.0 | 3.0 | 8.0 | 2.0 | 9.0 | 1.0 |
| 4 | 4.0 | 6.0 | 5.0 | 7.0 | 8.0 | 1.0 | 9.0 | 2.0 | 9.0 | 9.0 | 5.0 | 6.0 | 4.0 | 5.0 | 3.0 | 8.0 | 1.0 | 5.0 | 3.0 | 5.0 | 10.0 | 3.0 | 10.0 | 3.0 | 1.0 | 6.0 | 4.0 | 8.0 | 5.0 | 9.0 | 7.0 | 2.0 | 10.0 | 6.0 | 1.0 | 10.0 | 3.0 | 1.0 | 8.0 | 3.0 | 8.0 | 1.0 | 2.0 | 9.0 | 9.0 | 4.0 | 5.0 |
| 5 | 5.0 | 3.0 | 10.0 | 6.0 | 1.0 | 3.0 | 10.0 | 6.0 | 6.0 | 4.0 | 3.0 | 10.0 | 9.0 | 10.0 | 9.0 | 3.0 | 10.0 | 10.0 | 7.0 | 6.0 | 3.0 | 4.0 | 6.0 | 9.0 | 2.0 | 8.0 | 10.0 | 1.0 | 6.0 | 6.0 | 9.0 | 10.0 | 2.0 | 7.0 | 9.0 | 1.0 | 10.0 | 6.0 | 7.0 | 10.0 | 10.0 | 2.0 | 2.0 | 1.0 | 7.0 | 8.0 | 3.0 |
| 6 | 4.0 | 10.0 | 9.0 | 10.0 | 9.0 | 10.0 | 1.0 | 4.0 | 4.0 | 6.0 | 8.0 | 6.0 | 3.0 | 9.0 | 9.0 | 6.0 | 1.0 | 1.0 | 7.0 | 7.0 | 5.0 | 7.0 | 10.0 | 7.0 | 3.0 | 2.0 | 1.0 | 8.0 | 7.0 | 5.0 | 5.0 | 3.0 | 6.0 | 5.0 | 9.0 | 4.0 | 3.0 | 8.0 | 3.0 | 7.0 | 6.0 | 8.0 | 6.0 | 7.0 | 6.0 | 6.0 | 7.0 |
| 7 | 2.0 | 9.0 | 3.0 | 4.0 | 2.0 | 6.0 | 4.0 | 9.0 | 8.0 | 8.0 | 3.0 | 2.0 | 3.0 | 5.0 | 2.0 | 8.0 | 1.0 | 1.0 | 9.0 | 4.0 | 2.0 | 2.0 | 7.0 | 4.0 | 7.0 | 3.0 | 3.0 | 8.0 | 1.0 | 7.0 | 3.0 | 1.0 | 3.0 | 3.0 | 2.0 | 2.0 | 2.0 | 3.0 | 2.0 | 8.0 | 2.0 | 8.0 | 5.0 | 6.0 | 1.0 | 10.0 | 10.0 |
| 8 | 4.0 | 2.0 | 8.0 | 2.0 | 9.0 | 6.0 | 4.0 | 8.0 | 6.0 | 4.0 | 10.0 | 6.0 | 3.0 | 1.0 | 9.0 | 10.0 | 1.0 | 10.0 | 8.0 | 3.0 | 3.0 | 4.0 | 6.0 | 9.0 | 10.0 | 10.0 | 10.0 | 4.0 | 9.0 | 6.0 | 9.0 | 4.0 | 5.0 | 7.0 | 9.0 | 9.0 | 4.0 | 7.0 | 1.0 | 6.0 | 1.0 | 6.0 | 2.0 | 9.0 | 7.0 | 10.0 | 10.0 |
| 9 | 9.0 | 2.0 | 10.0 | 7.0 | 9.0 | 4.0 | 6.0 | 8.0 | 4.0 | 9.0 | 10.0 | 4.0 | 1.0 | 6.0 | 7.0 | 9.0 | 2.0 | 10.0 | 5.0 | 8.0 | 3.0 | 10.0 | 9.0 | 1.0 | 6.0 | 10.0 | 2.0 | 9.0 | 3.0 | 2.0 | 8.0 | 8.0 | 2.0 | 1.0 | 3.0 | 6.0 | 2.0 | 4.0 | 1.0 | 3.0 | 3.0 | 7.0 | 10.0 | 8.0 | 10.0 | 6.0 | 10.0 |
| 10 | 10.0 | 5.0 | 2.0 | 5.0 | 5.0 | 3.0 | 8.0 | 3.0 | 10.0 | 10.0 | 10.0 | 3.0 | 8.0 | 8.0 | 2.0 | 8.0 | 5.0 | 4.0 | 4.0 | 8.0 | 9.0 | 10.0 | 8.0 | 2.0 | 5.0 | 2.0 | 7.0 | 6.0 | 10.0 | 8.0 | 1.0 | 1.0 | 9.0 | 4.0 | 6.0 | 3.0 | 1.0 | 1.0 | 8.0 | 4.0 | 8.0 | 4.0 | 2.0 | 6.0 | 2.0 | 1.0 | 1.0 |
| 11 | 9.0 | 4.0 | 5.0 | 4.0 | 6.0 | 10.0 | 6.0 | 2.0 | 6.0 | 4.0 | 3.0 | 8.0 | 8.0 | 3.0 | 7.0 | 3.0 | 9.0 | 5.0 | 4.0 | 9.0 | 8.0 | 10.0 | 2.0 | 4.0 | 7.0 | 1.0 | 4.0 | 10.0 | 4.0 | 5.0 | 2.0 | 1.0 | 4.0 | 9.0 | 10.0 | 8.0 | 9.0 | 9.0 | 6.0 | 5.0 | 1.0 | 5.0 | 2.0 | 4.0 | 3.0 | 10.0 | 9.0 |
| 12 | 3.0 | 6.0 | 3.0 | 9.0 | 4.0 | 9.0 | 3.0 | 3.0 | 3.0 | 1.0 | 8.0 | 8.0 | 3.0 | 9.0 | 1.0 | 8.0 | 4.0 | 6.0 | 9.0 | 6.0 | 7.0 | 10.0 | 8.0 | 8.0 | 2.0 | 8.0 | 5.0 | 7.0 | 4.0 | 4.0 | 10.0 | 4.0 | 7.0 | 9.0 | 10.0 | 6.0 | 10.0 | 7.0 | 6.0 | 1.0 | 5.0 | 6.0 | 3.0 | 4.0 | 10.0 | 3.0 | 8.0 |
| 13 | 6.0 | 8.0 | 3.0 | 10.0 | 5.0 | 10.0 | 9.0 | 5.0 | 1.0 | 6.0 | 8.0 | 3.0 | 9.0 | 6.0 | 4.0 | 10.0 | 6.0 | 3.0 | 2.0 | 7.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 6.0 | 6.0 | 2.0 | 8.0 | 6.0 | 9.0 | 7.0 | 9.0 | 2.0 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 2.0 | 2.0 | 4.0 | 5.0 | 6.0 | 7.0 | 5.0 | 5.0 |
| 14 | 5.0 | 10.0 | 1.0 | 7.0 | 3.0 | 9.0 | 9.0 | 2.0 | 9.0 | 7.0 | 2.0 | 7.0 | 1.0 | 4.0 | 4.0 | 3.0 | 6.0 | 4.0 | 3.0 | 5.0 | 7.0 | 3.0 | 10.0 | 7.0 | 9.0 | 10.0 | 5.0 | 1.0 | 7.0 | 4.0 | 9.0 | 9.0 | 1.0 | 5.0 | 9.0 | 2.0 | 6.0 | 3.0 | 10.0 | 8.0 | 3.0 | 6.0 | 4.0 | 7.0 | 9.0 | 8.0 | 3.0 |
| 15 | 7.0 | 7.0 | 8.0 | 9.0 | 8.0 | 3.0 | 6.0 | 8.0 | 10.0 | 9.0 | 8.0 | 3.0 | 8.0 | 10.0 | 3.0 | 1.0 | 3.0 | 10.0 | 2.0 | 10.0 | 7.0 | 3.0 | 4.0 | 10.0 | 9.0 | 4.0 | 5.0 | 2.0 | 1.0 | 8.0 | 9.0 | 3.0 | 6.0 | 4.0 | 7.0 | 8.0 | 6.0 | 1.0 | 9.0 | 1.0 | 5.0 | 9.0 | 5.0 | 5.0 | 4.0 | 1.0 | 7.0 |
| 16 | 7.0 | 7.0 | 7.0 | 8.0 | 1.0 | 10.0 | 1.0 | 1.0 | 1.0 | 2.0 | 5.0 | 9.0 | 4.0 | 6.0 | 6.0 | 3.0 | 9.0 | 8.0 | 4.0 | 7.0 | 6.0 | 2.0 | 8.0 | 9.0 | 8.0 | 3.0 | 2.0 | 8.0 | 3.0 | 1.0 | 4.0 | 1.0 | 2.0 | 7.0 | 7.0 | 2.0 | 5.0 | 10.0 | 8.0 | 5.0 | 2.0 | 8.0 | 5.0 | 8.0 | 9.0 | 9.0 | 8.0 |
| 17 | 3.0 | 2.0 | 9.0 | 9.0 | 5.0 | 10.0 | 1.0 | 1.0 | 10.0 | 10.0 | 4.0 | 5.0 | 6.0 | 3.0 | 4.0 | 10.0 | 8.0 | 5.0 | 8.0 | 2.0 | 2.0 | 7.0 | 5.0 | 1.0 | 2.0 | 5.0 | 10.0 | 5.0 | 7.0 | 1.0 | 10.0 | 9.0 | 10.0 | 5.0 | 7.0 | 4.0 | 6.0 | 3.0 | 6.0 | 8.0 | 4.0 | 1.0 | 8.0 | 3.0 | 8.0 | 9.0 | 3.0 |
| 18 | 6.0 | 7.0 | 3.0 | 6.0 | 3.0 | 7.0 | 7.0 | 9.0 | 8.0 | 5.0 | 4.0 | 4.0 | 9.0 | 2.0 | 3.0 | 2.0 | 4.0 | 8.0 | 4.0 | 2.0 | 8.0 | 3.0 | 9.0 | 8.0 | 1.0 | 6.0 | 5.0 | 4.0 | 2.0 | 6.0 | 7.0 | 7.0 | 2.0 | 5.0 | 10.0 | 1.0 | 3.0 | 4.0 | 10.0 | 4.0 | 8.0 | 2.0 | 8.0 | 7.0 | 10.0 | 3.0 | 1.0 |
| 19 | 1.0 | 1.0 | 10.0 | 6.0 | 5.0 | 6.0 | 7.0 | 4.0 | 3.0 | 8.0 | 8.0 | 9.0 | 6.0 | 7.0 | 5.0 | 10.0 | 7.0 | 2.0 | 2.0 | 5.0 | 10.0 | 1.0 | 6.0 | 2.0 | 4.0 | 10.0 | 2.0 | 5.0 | 4.0 | 8.0 | 2.0 | 9.0 | 2.0 | 10.0 | 9.0 | 5.0 | 9.0 | 3.0 | 6.0 | 7.0 | 4.0 | 3.0 | 3.0 | 1.0 | 9.0 | 3.0 | 9.0 |
| 20 | 10.0 | 2.0 | 2.0 | 10.0 | 10.0 | 3.0 | 5.0 | 2.0 | 3.0 | 3.0 | 9.0 | 8.0 | 7.0 | 3.0 | 7.0 | 7.0 | 6.0 | 2.0 | 8.0 | 10.0 | 7.0 | 6.0 | 3.0 | 7.0 | 7.0 | 4.0 | 5.0 | 4.0 | 8.0 | 6.0 | 5.0 | 7.0 | 2.0 | 9.0 | 6.0 | 5.0 | 5.0 | 1.0 | 7.0 | 10.0 | 3.0 | 3.0 | 3.0 | 6.0 | 1.0 | 3.0 | 4.0 |
| 21 | 7.0 | 9.0 | 7.0 | 1.0 | 3.0 | 4.0 | 7.0 | 2.0 | 4.0 | 10.0 | 10.0 | 10.0 | 10.0 | 9.0 | 3.0 | 3.0 | 2.0 | 7.0 | 3.0 | 1.0 | 6.0 | 10.0 | 10.0 | 10.0 | 10.0 | 6.0 | 4.0 | 10.0 | 4.0 | 7.0 | 4.0 | 2.0 | 1.0 | 6.0 | 3.0 | 3.0 | 7.0 | 9.0 | 1.0 | 10.0 | 2.0 | 4.0 | 4.0 | 3.0 | 2.0 | 7.0 | 2.0 |
| 22 | 3.0 | 5.0 | 7.0 | 5.0 | 10.0 | 6.0 | 10.0 | 7.0 | 6.0 | 9.0 | 8.0 | 2.0 | 8.0 | 9.0 | 10.0 | 4.0 | 8.0 | 5.0 | 9.0 | 6.0 | 3.0 | 10.0 | 9.0 | 5.0 | 8.0 | 9.0 | 3.0 | 4.0 | 10.0 | 10.0 | 6.0 | 6.0 | 7.0 | 2.0 | 2.0 | 1.0 | 6.0 | 4.0 | 6.0 | 2.0 | 5.0 | 4.0 | 7.0 | 3.0 | 5.0 | 1.0 | 7.0 |
| 23 | 2.0 | 2.0 | 1.0 | 4.0 | 3.0 | 9.0 | 7.0 | 4.0 | 9.0 | 1.0 | 2.0 | 4.0 | 8.0 | 4.0 | 7.0 | 10.0 | 9.0 | 1.0 | 8.0 | 2.0 | 7.0 | 10.0 | 5.0 | 4.0 | 8.0 | 7.0 | 10.0 | 2.0 | 5.0 | 5.0 | 2.0 | 1.0 | 9.0 | 8.0 | 6.0 | 4.0 | 8.0 | 7.0 | 7.0 | 6.0 | 7.0 | 3.0 | 7.0 | 8.0 | 6.0 | 4.0 | 8.0 |
| 24 | 7.0 | 7.0 | 1.0 | 10.0 | 1.0 | 2.0 | 3.0 | 7.0 | 10.0 | 6.0 | 5.0 | 7.0 | 2.0 | 8.0 | 9.0 | 9.0 | 8.0 | 2.0 | 1.0 | 4.0 | 7.0 | 10.0 | 8.0 | 8.0 | 7.0 | 3.0 | 8.0 | 8.0 | 4.0 | 1.0 | 7.0 | 9.0 | 10.0 | 9.0 | 7.0 | 4.0 | 6.0 | 3.0 | 2.0 | 1.0 | 4.0 | 2.0 | 7.0 | 5.0 | 6.0 | 9.0 | 6.0 |
| 25 | 3.0 | 1.0 | 9.0 | 10.0 | 6.0 | 8.0 | 2.0 | 3.0 | 10.0 | 10.0 | 2.0 | 1.0 | 8.0 | 6.0 | 10.0 | 4.0 | 3.0 | 5.0 | 6.0 | 10.0 | 4.0 | 6.0 | 9.0 | 7.0 | 3.0 | 1.0 | 10.0 | 6.0 | 4.0 | 7.0 | 1.0 | 2.0 | 9.0 | 10.0 | 9.0 | 10.0 | 4.0 | 3.0 | 9.0 | 1.0 | 3.0 | 8.0 | 5.0 | 3.0 | 10.0 | 7.0 | 8.0 |
| 26 | 10.0 | 1.0 | 3.0 | 2.0 | 4.0 | 10.0 | 1.0 | 3.0 | 10.0 | 2.0 | 7.0 | 4.0 | 5.0 | 6.0 | 5.0 | 5.0 | 2.0 | 10.0 | 5.0 | 2.0 | 5.0 | 4.0 | 3.0 | 10.0 | 8.0 | 10.0 | 5.0 | 2.0 | 3.0 | 6.0 | 5.0 | 9.0 | 7.0 | 3.0 | 3.0 | 4.0 | 3.0 | 8.0 | 4.0 | 10.0 | 5.0 | 2.0 | 10.0 | 1.0 | 8.0 | 9.0 | 3.0 |
| 27 | 2.0 | 1.0 | 8.0 | 5.0 | 8.0 | 1.0 | 8.0 | 8.0 | 4.0 | 9.0 | 6.0 | 10.0 | 7.0 | 2.0 | 1.0 | 2.0 | 8.0 | 5.0 | 4.0 | 5.0 | 4.0 | 10.0 | 4.0 | 2.0 | 8.0 | 6.0 | 2.0 | 9.0 | 7.0 | 10.0 | 7.0 | 5.0 | 8.0 | 7.0 | 6.0 | 1.0 | 5.0 | 10.0 | 9.0 | 3.0 | 2.0 | 9.0 | 2.0 | 3.0 | 4.0 | 10.0 | 3.0 |
| 28 | 10.0 | 2.0 | 7.0 | 2.0 | 5.0 | 6.0 | 7.0 | 1.0 | 9.0 | 3.0 | 10.0 | 4.0 | 4.0 | 8.0 | 7.0 | 1.0 | 3.0 | 7.0 | 2.0 | 4.0 | 8.0 | 4.0 | 10.0 | 5.0 | 4.0 | 4.0 | 3.0 | 7.0 | 10.0 | 1.0 | 9.0 | 2.0 | 4.0 | 6.0 | 9.0 | 7.0 | 5.0 | 2.0 | 4.0 | 6.0 | 10.0 | 4.0 | 6.0 | 3.0 | 10.0 | 9.0 | 3.0 |
| 29 | 9.0 | 7.0 | 4.0 | 3.0 | 9.0 | 6.0 | 5.0 | 7.0 | 6.0 | 2.0 | 8.0 | 5.0 | 4.0 | 6.0 | 4.0 | 8.0 | 1.0 | 1.0 | 6.0 | 8.0 | 6.0 | 7.0 | 10.0 | 5.0 | 1.0 | 7.0 | 6.0 | 10.0 | 1.0 | 1.0 | 2.0 | 6.0 | 3.0 | 3.0 | 7.0 | 5.0 | 10.0 | 8.0 | 9.0 | 2.0 | 8.0 | 6.0 | 10.0 | 10.0 | 2.0 | 9.0 | 6.0 |
| 30 | 1.0 | 8.0 | 3.0 | 9.0 | 7.0 | 9.0 | 5.0 | 3.0 | 9.0 | 8.0 | 1.0 | 2.0 | 10.0 | 9.0 | 9.0 | 9.0 | 4.0 | 10.0 | 7.0 | 2.0 | 5.0 | 4.0 | 6.0 | 2.0 | 7.0 | 1.0 | 5.0 | 7.0 | 9.0 | 2.0 | 4.0 | 4.0 | 9.0 | 6.0 | 1.0 | 7.0 | 4.0 | 2.0 | 9.0 | 6.0 | 10.0 | 6.0 | 7.0 | 3.0 | 8.0 | 5.0 | 9.0 |
| 31 | 9.0 | 5.0 | 8.0 | 4.0 | 2.0 | 10.0 | 3.0 | 1.0 | 4.0 | 8.0 | 1.0 | 1.0 | 4.0 | 7.0 | 9.0 | 3.0 | 1.0 | 9.0 | 7.0 | 9.0 | 7.0 | 2.0 | 6.0 | 1.0 | 9.0 | 2.0 | 9.0 | 5.0 | 2.0 | 6.0 | 4.0 | 2.0 | 5.0 | 6.0 | 2.0 | 7.0 | 6.0 | 2.0 | 9.0 | 6.0 | 8.0 | 2.0 | 7.0 | 3.0 | 7.0 | 7.0 | 8.0 |
| 32 | 1.0 | 3.0 | 2.0 | 3.0 | 10.0 | 2.0 | 6.0 | 3.0 | 5.0 | 2.0 | 9.0 | 4.0 | 7.0 | 9.0 | 1.0 | 6.0 | 2.0 | 10.0 | 2.0 | 2.0 | 2.0 | 1.0 | 7.0 | 9.0 | 10.0 | 9.0 | 7.0 | 8.0 | 4.0 | 3.0 | 9.0 | 5.0 | 7.0 | 9.0 | 3.0 | 6.0 | 4.0 | 10.0 | 2.0 | 8.0 | 8.0 | 1.0 | 8.0 | 5.0 | 1.0 | 5.0 | 8.0 |
| 33 | 1.0 | 5.0 | 4.0 | 2.0 | 6.0 | 7.0 | 5.0 | 3.0 | 7.0 | 1.0 | 4.0 | 9.0 | 9.0 | 2.0 | 5.0 | 4.0 | 7.0 | 5.0 | 5.0 | 10.0 | 9.0 | 6.0 | 2.0 | 8.0 | 9.0 | 10.0 | 3.0 | 7.0 | 6.0 | 3.0 | 6.0 | 6.0 | 9.0 | 5.0 | 6.0 | 9.0 | 5.0 | 7.0 | 2.0 | 7.0 | 9.0 | 6.0 | 1.0 | 5.0 | 6.0 | 3.0 | 7.0 |
| 34 | 7.0 | 9.0 | 5.0 | 10.0 | 1.0 | 9.0 | 9.0 | 2.0 | 9.0 | 3.0 | 6.0 | 10.0 | 10.0 | 9.0 | 9.0 | 7.0 | 7.0 | 7.0 | 10.0 | 9.0 | 6.0 | 3.0 | 2.0 | 6.0 | 7.0 | 9.0 | 3.0 | 6.0 | 9.0 | 7.0 | 1.0 | 2.0 | 3.0 | 6.0 | 8.0 | 3.0 | 3.0 | 2.0 | 4.0 | 3.0 | 9.0 | 3.0 | 2.0 | 10.0 | 6.0 | 5.0 | 7.0 |
| 35 | 4.0 | 2.0 | 2.0 | 4.0 | 10.0 | 1.0 | 4.0 | 2.0 | 9.0 | 6.0 | 3.0 | 8.0 | 6.0 | 10.0 | 2.0 | 8.0 | 2.0 | 4.0 | 1.0 | 5.0 | 5.0 | 3.0 | 1.0 | 4.0 | 4.0 | 10.0 | 4.0 | 1.0 | 7.0 | 5.0 | 7.0 | 7.0 | 6.0 | 9.0 | 3.0 | 4.0 | 10.0 | 5.0 | 1.0 | 8.0 | 10.0 | 6.0 | 7.0 | 9.0 | 10.0 | 6.0 | 5.0 |
| 36 | 3.0 | 8.0 | 7.0 | 5.0 | 3.0 | 10.0 | 3.0 | 2.0 | 4.0 | 2.0 | 1.0 | 9.0 | 10.0 | 8.0 | 6.0 | 6.0 | 5.0 | 6.0 | 3.0 | 9.0 | 5.0 | 7.0 | 6.0 | 8.0 | 6.0 | 4.0 | 3.0 | 5.0 | 5.0 | 10.0 | 4.0 | 6.0 | 4.0 | 5.0 | 3.0 | 10.0 | 2.0 | 8.0 | 6.0 | 9.0 | 1.0 | 9.0 | 6.0 | 4.0 | 2.0 | 3.0 | 7.0 |
| 37 | 3.0 | 7.0 | 4.0 | 4.0 | 1.0 | 6.0 | 8.0 | 3.0 | 7.0 | 4.0 | 1.0 | 9.0 | 7.0 | 6.0 | 3.0 | 1.0 | 10.0 | 3.0 | 4.0 | 3.0 | 1.0 | 9.0 | 4.0 | 7.0 | 3.0 | 3.0 | 8.0 | 10.0 | 2.0 | 8.0 | 2.0 | 2.0 | 10.0 | 7.0 | 2.0 | 5.0 | 8.0 | 2.0 | 3.0 | 1.0 | 9.0 | 2.0 | 1.0 | 1.0 | 7.0 | 7.0 | 4.0 |
| 38 | 8.0 | 1.0 | 1.0 | 4.0 | 8.0 | 7.0 | 3.0 | 2.0 | 1.0 | 1.0 | 8.0 | 6.0 | 6.0 | 2.0 | 10.0 | 9.0 | 8.0 | 6.0 | 10.0 | 6.0 | 7.0 | 1.0 | 6.0 | 7.0 | 2.0 | 9.0 | 4.0 | 9.0 | 4.0 | 9.0 | 9.0 | 9.0 | 2.0 | 2.0 | 4.0 | 1.0 | 6.0 | 3.0 | 3.0 | 8.0 | 4.0 | 5.0 | 3.0 | 4.0 | 4.0 | 6.0 | 1.0 |
| 39 | 2.0 | 2.0 | 1.0 | 2.0 | 3.0 | 10.0 | 7.0 | 8.0 | 6.0 | 3.0 | 4.0 | 5.0 | 1.0 | 2.0 | 8.0 | 1.0 | 5.0 | 8.0 | 4.0 | 7.0 | 10.0 | 10.0 | 2.0 | 6.0 | 1.0 | 1.0 | 10.0 | 3.0 | 6.0 | 2.0 | 6.0 | 6.0 | 8.0 | 7.0 | 3.0 | 8.0 | 9.0 | 1.0 | 8.0 | 9.0 | 2.0 | 8.0 | 8.0 | 4.0 | 9.0 | 4.0 | 6.0 |
| 40 | 9.0 | 4.0 | 6.0 | 10.0 | 8.0 | 10.0 | 6.0 | 2.0 | 1.0 | 3.0 | 8.0 | 1.0 | 5.0 | 2.0 | 3.0 | 5.0 | 2.0 | 4.0 | 8.0 | 4.0 | 3.0 | 2.0 | 5.0 | 7.0 | 4.0 | 3.0 | 5.0 | 2.0 | 10.0 | 8.0 | 10.0 | 8.0 | 8.0 | 9.0 | 9.0 | 10.0 | 1.0 | 9.0 | 4.0 | 2.0 | 4.0 | 8.0 | 9.0 | 10.0 | 6.0 | 8.0 | 9.0 |
| 41 | 9.0 | 2.0 | 7.0 | 3.0 | 1.0 | 2.0 | 8.0 | 8.0 | 6.0 | 7.0 | 4.0 | 5.0 | 6.0 | 4.0 | 6.0 | 9.0 | 8.0 | 1.0 | 2.0 | 3.0 | 3.0 | 4.0 | 4.0 | 3.0 | 2.0 | 8.0 | 2.0 | 9.0 | 4.0 | 6.0 | 6.0 | 2.0 | 1.0 | 6.0 | 3.0 | 6.0 | 9.0 | 2.0 | 5.0 | 8.0 | 8.0 | 1.0 | 7.0 | 1.0 | 7.0 | 7.0 | 2.0 |
| 42 | 4.0 | 4.0 | 8.0 | 3.0 | 2.0 | 2.0 | 6.0 | 5.0 | 2.0 | 10.0 | 2.0 | 2.0 | 3.0 | 5.0 | 4.0 | 5.0 | 5.0 | 8.0 | 8.0 | 3.0 | 3.0 | 4.0 | 7.0 | 7.0 | 7.0 | 5.0 | 10.0 | 2.0 | 6.0 | 10.0 | 7.0 | 7.0 | 8.0 | 1.0 | 2.0 | 7.0 | 6.0 | 1.0 | 3.0 | 8.0 | 9.0 | 7.0 | 2.0 | 1.0 | 2.0 | 9.0 | 8.0 |
| 43 | 4.0 | 5.0 | 2.0 | 8.0 | 9.0 | 1.0 | 7.0 | 6.0 | 9.0 | 8.0 | 6.0 | 4.0 | 4.0 | 6.0 | 7.0 | 5.0 | 8.0 | 3.0 | 7.0 | 1.0 | 6.0 | 3.0 | 3.0 | 8.0 | 5.0 | 3.0 | 1.0 | 3.0 | 3.0 | 10.0 | 3.0 | 3.0 | 5.0 | 5.0 | 10.0 | 9.0 | 4.0 | 1.0 | 4.0 | 4.0 | 10.0 | 1.0 | 1.0 | 6.0 | 5.0 | 10.0 | 4.0 |
| 44 | 1.0 | 7.0 | 7.0 | 2.0 | 9.0 | 7.0 | 6.0 | 1.0 | 7.0 | 10.0 | 2.0 | 3.0 | 10.0 | 7.0 | 9.0 | 4.0 | 9.0 | 8.0 | 10.0 | 9.0 | 1.0 | 2.0 | 5.0 | 6.0 | 6.0 | 10.0 | 8.0 | 4.0 | 10.0 | 2.0 | 8.0 | 7.0 | 1.0 | 6.0 | 6.0 | 10.0 | 2.0 | 7.0 | 4.0 | 9.0 | 6.0 | 7.0 | 2.0 | 5.0 | 10.0 | 1.0 | 6.0 |
| 45 | 9.0 | 2.0 | 4.0 | 9.0 | 4.0 | 8.0 | 6.0 | 10.0 | 10.0 | 6.0 | 1.0 | 10.0 | 3.0 | 5.0 | 8.0 | 1.0 | 9.0 | 9.0 | 3.0 | 3.0 | 3.0 | 7.0 | 1.0 | 4.0 | 9.0 | 7.0 | 9.0 | 10.0 | 9.0 | 9.0 | 5.0 | 7.0 | 5.0 | 3.0 | 5.0 | 6.0 | 3.0 | 7.0 | 6.0 | 4.0 | 8.0 | 7.0 | 9.0 | 10.0 | 1.0 | 10.0 | 8.0 |
| 46 | 7.0 | 1.0 | 9.0 | 1.0 | 5.0 | 3.0 | 7.0 | 10.0 | 10.0 | 10.0 | 1.0 | 9.0 | 8.0 | 5.0 | 3.0 | 7.0 | 8.0 | 3.0 | 1.0 | 9.0 | 4.0 | 2.0 | 7.0 | 8.0 | 6.0 | 8.0 | 3.0 | 3.0 | 3.0 | 6.0 | 9.0 | 8.0 | 8.0 | 7.0 | 7.0 | 5.0 | 7.0 | 4.0 | 1.0 | 6.0 | 9.0 | 2.0 | 8.0 | 4.0 | 6.0 | 8.0 | 5.0 |

They expect the chosen route to be given as a single ordered list of locations from 16 to 17.

Also, to keep things machine-friendly, please give the chosen route in a tiny JSON snippet — nothing fancy — like this:

{
  ""solution"": []
}

Think of ""solution"" as the single list of locations (nodes) starting at the emergency center and ending at the scene; replace the empty array with the sequence of node identifiers in order. This JSON is just a sketch of the shape I expect, not the answer itself.

A quick note: use only node identifiers exactly as they appear in the instance input — no renaming, no invented labels, and do not include edge identifiers or any cost labels in the path. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 1, 'var_index': 1}, {'from': 16, 'to': 2, 'var_index': 2}, {'from': 16, 'to': 3, 'var_index': 3}, {'from': 16, 'to': 4, 'var_index': 4}, {'from': 16, 'to': 5, 'var_index': 5}, {'from': 16, 'to': 6, 'var_index': 6}, {'from': 16, 'to': 7, 'var_index': 7}, {'from': 16, 'to': 8, 'var_index': 8}, {'from': 16, 'to': 9, 'var_index': 9}, {'from': 16, 'to': 10, 'var_index': 10}, {'from': 16, 'to': 11, 'var_index': 11}, {'from': 16, 'to': 12, 'var_index': 12}, {'from': 16, 'to': 13, 'var_index': 13}, {'from': 16, 'to': 14, 'var_index': 14}, {'from': 16, 'to': 15, 'var_index': 15}, {'from': 0, 'to': 17, 'var_index': 16}, {'from': 1, 'to': 17, 'var_index': 17}, {'from': 2, 'to': 17, 'var_index': 18}, {'from': 3, 'to': 17, 'var_index': 19}, {'from': 4, 'to': 17, 'var_index': 20}, {'from': 5, 'to': 17, 'var_index': 21}, {'from': 6, 'to': 17, 'var_index': 22}, {'from': 7, 'to': 17, 'var_index': 23}, {'from': 8, 'to': 17, 'var_index': 24}, {'from': 9, 'to': 17, 'var_index': 25}, {'from': 10, 'to': 17, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 17, 'var_index': 28}, {'from': 13, 'to': 17, 'var_index': 29}, {'from': 14, 'to': 17, 'var_index': 30}, {'from': 15, 'to': 17, 'var_index': 31}, {'from': 0, 'to': 1, 'var_index': 32}, {'from': 1, 'to': 2, 'var_index': 33}, {'from': 2, 'to': 3, 'var_index': 34}, {'from': 3, 'to': 4, 'var_index': 35}, {'from': 4, 'to': 5, 'var_index': 36}, {'from': 5, 'to': 6, 'var_index': 37}, {'from': 6, 'to': 7, 'var_index': 38}, {'from': 7, 'to': 8, 'var_index': 39}, {'from': 8, 'to': 9, 'var_index': 40}, {'from': 9, 'to': 10, 'var_index': 41}, {'from': 10, 'to': 11, 'var_index': 42}, {'from': 11, 'to': 12, 'var_index': 43}, {'from': 12, 'to': 13, 'var_index': 44}, {'from': 13, 'to': 14, 'var_index': 45}, {'from': 14, 'to': 15, 'var_index': 46}], 'objective': {'constant': 0.0, 'linear': [2.0, 1.0, 3.0, 10.0, 7.0, 9.0, 8.0, 1.0, 1.0, 2.0, 1.0, 7.0, 2.0, 5.0, 7.0, 8.0, 9.0, 1.0, 4.0, 10.0, 1.0, 10.0, 1.0, 5.0, 10.0, 6.0, 2.0, 9.0, 10.0, 8.0, 7.0, 4.0, 3.0, 9.0, 6.0, 4.0, 3.0, 8.0, 2.0, 10.0, 4.0, 5.0, 2.0, 4.0, 1.0, 4.0, 9.0], 'quadratic': [[8.0, 6.0, 8.0, 3.0, 4.0, 5.0, 4.0, 2.0, 4.0, 9.0, 10.0, 9.0, 3.0, 6.0, 5.0, 7.0, 7.0, 3.0, 6.0, 1.0, 10.0, 7.0, 3.0, 2.0, 7.0, 3.0, 10.0, 2.0, 10.0, 9.0, 1.0, 9.0, 1.0, 1.0, 7.0, 4.0, 3.0, 3.0, 8.0, 2.0, 9.0, 9.0, 4.0, 4.0, 1.0, 9.0, 7.0], [6.0, 9.0, 9.0, 7.0, 6.0, 3.0, 10.0, 9.0, 2.0, 2.0, 5.0, 4.0, 6.0, 8.0, 10.0, 7.0, 7.0, 2.0, 7.0, 1.0, 2.0, 9.0, 5.0, 2.0, 7.0, 1.0, 1.0, 1.0, 2.0, 7.0, 8.0, 5.0, 3.0, 5.0, 9.0, 2.0, 8.0, 7.0, 1.0, 2.0, 4.0, 2.0, 4.0, 5.0, 7.0, 2.0, 1.0], [8.0, 9.0, 1.0, 2.0, 5.0, 10.0, 9.0, 3.0, 8.0, 10.0, 2.0, 5.0, 3.0, 3.0, 1.0, 8.0, 7.0, 9.0, 3.0, 10.0, 2.0, 7.0, 7.0, 1.0, 1.0, 9.0, 3.0, 8.0, 7.0, 4.0, 3.0, 8.0, 2.0, 4.0, 5.0, 2.0, 7.0, 4.0, 1.0, 1.0, 6.0, 7.0, 8.0, 2.0, 7.0, 4.0, 9.0], [3.0, 7.0, 2.0, 6.0, 7.0, 6.0, 10.0, 4.0, 2.0, 7.0, 5.0, 4.0, 9.0, 10.0, 7.0, 9.0, 8.0, 9.0, 6.0, 6.0, 10.0, 1.0, 5.0, 4.0, 10.0, 10.0, 2.0, 5.0, 2.0, 3.0, 9.0, 4.0, 3.0, 2.0, 10.0, 4.0, 5.0, 4.0, 4.0, 2.0, 10.0, 3.0, 3.0, 8.0, 2.0, 9.0, 1.0], [4.0, 6.0, 5.0, 7.0, 8.0, 1.0, 9.0, 2.0, 9.0, 9.0, 5.0, 6.0, 4.0, 5.0, 3.0, 8.0, 1.0, 5.0, 3.0, 5.0, 10.0, 3.0, 10.0, 3.0, 1.0, 6.0, 4.0, 8.0, 5.0, 9.0, 7.0, 2.0, 10.0, 6.0, 1.0, 10.0, 3.0, 1.0, 8.0, 3.0, 8.0, 1.0, 2.0, 9.0, 9.0, 4.0, 5.0], [5.0, 3.0, 10.0, 6.0, 1.0, 3.0, 10.0, 6.0, 6.0, 4.0, 3.0, 10.0, 9.0, 10.0, 9.0, 3.0, 10.0, 10.0, 7.0, 6.0, 3.0, 4.0, 6.0, 9.0, 2.0, 8.0, 10.0, 1.0, 6.0, 6.0, 9.0, 10.0, 2.0, 7.0, 9.0, 1.0, 10.0, 6.0, 7.0, 10.0, 10.0, 2.0, 2.0, 1.0, 7.0, 8.0, 3.0], [4.0, 10.0, 9.0, 10.0, 9.0, 10.0, 1.0, 4.0, 4.0, 6.0, 8.0, 6.0, 3.0, 9.0, 9.0, 6.0, 1.0, 1.0, 7.0, 7.0, 5.0, 7.0, 10.0, 7.0, 3.0, 2.0, 1.0, 8.0, 7.0, 5.0, 5.0, 3.0, 6.0, 5.0, 9.0, 4.0, 3.0, 8.0, 3.0, 7.0, 6.0, 8.0, 6.0, 7.0, 6.0, 6.0, 7.0], [2.0, 9.0, 3.0, 4.0, 2.0, 6.0, 4.0, 9.0, 8.0, 8.0, 3.0, 2.0, 3.0, 5.0, 2.0, 8.0, 1.0, 1.0, 9.0, 4.0, 2.0, 2.0, 7.0, 4.0, 7.0, 3.0, 3.0, 8.0, 1.0, 7.0, 3.0, 1.0, 3.0, 3.0, 2.0, 2.0, 2.0, 3.0, 2.0, 8.0, 2.0, 8.0, 5.0, 6.0, 1.0, 10.0, 10.0], [4.0, 2.0, 8.0, 2.0, 9.0, 6.0, 4.0, 8.0, 6.0, 4.0, 10.0, 6.0, 3.0, 1.0, 9.0, 10.0, 1.0, 10.0, 8.0, 3.0, 3.0, 4.0, 6.0, 9.0, 10.0, 10.0, 10.0, 4.0, 9.0, 6.0, 9.0, 4.0, 5.0, 7.0, 9.0, 9.0, 4.0, 7.0, 1.0, 6.0, 1.0, 6.0, 2.0, 9.0, 7.0, 10.0, 10.0], [9.0, 2.0, 10.0, 7.0, 9.0, 4.0, 6.0, 8.0, 4.0, 9.0, 10.0, 4.0, 1.0, 6.0, 7.0, 9.0, 2.0, 10.0, 5.0, 8.0, 3.0, 10.0, 9.0, 1.0, 6.0, 10.0, 2.0, 9.0, 3.0, 2.0, 8.0, 8.0, 2.0, 1.0, 3.0, 6.0, 2.0, 4.0, 1.0, 3.0, 3.0, 7.0, 10.0, 8.0, 10.0, 6.0, 10.0], [10.0, 5.0, 2.0, 5.0, 5.0, 3.0, 8.0, 3.0, 10.0, 10.0, 10.0, 3.0, 8.0, 8.0, 2.0, 8.0, 5.0, 4.0, 4.0, 8.0, 9.0, 10.0, 8.0, 2.0, 5.0, 2.0, 7.0, 6.0, 10.0, 8.0, 1.0, 1.0, 9.0, 4.0, 6.0, 3.0, 1.0, 1.0, 8.0, 4.0, 8.0, 4.0, 2.0, 6.0, 2.0, 1.0, 1.0], [9.0, 4.0, 5.0, 4.0, 6.0, 10.0, 6.0, 2.0, 6.0, 4.0, 3.0, 8.0, 8.0, 3.0, 7.0, 3.0, 9.0, 5.0, 4.0, 9.0, 8.0, 10.0, 2.0, 4.0, 7.0, 1.0, 4.0, 10.0, 4.0, 5.0, 2.0, 1.0, 4.0, 9.0, 10.0, 8.0, 9.0, 9.0, 6.0, 5.0, 1.0, 5.0, 2.0, 4.0, 3.0, 10.0, 9.0], [3.0, 6.0, 3.0, 9.0, 4.0, 9.0, 3.0, 3.0, 3.0, 1.0, 8.0, 8.0, 3.0, 9.0, 1.0, 8.0, 4.0, 6.0, 9.0, 6.0, 7.0, 10.0, 8.0, 8.0, 2.0, 8.0, 5.0, 7.0, 4.0, 4.0, 10.0, 4.0, 7.0, 9.0, 10.0, 6.0, 10.0, 7.0, 6.0, 1.0, 5.0, 6.0, 3.0, 4.0, 10.0, 3.0, 8.0], [6.0, 8.0, 3.0, 10.0, 5.0, 10.0, 9.0, 5.0, 1.0, 6.0, 8.0, 3.0, 9.0, 6.0, 4.0, 10.0, 6.0, 3.0, 2.0, 7.0, 3.0, 9.0, 9.0, 4.0, 8.0, 6.0, 6.0, 2.0, 8.0, 6.0, 9.0, 7.0, 9.0, 2.0, 9.0, 10.0, 8.0, 6.0, 2.0, 2.0, 2.0, 4.0, 5.0, 6.0, 7.0, 5.0, 5.0], [5.0, 10.0, 1.0, 7.0, 3.0, 9.0, 9.0, 2.0, 9.0, 7.0, 2.0, 7.0, 1.0, 4.0, 4.0, 3.0, 6.0, 4.0, 3.0, 5.0, 7.0, 3.0, 10.0, 7.0, 9.0, 10.0, 5.0, 1.0, 7.0, 4.0, 9.0, 9.0, 1.0, 5.0, 9.0, 2.0, 6.0, 3.0, 10.0, 8.0, 3.0, 6.0, 4.0, 7.0, 9.0, 8.0, 3.0], [7.0, 7.0, 8.0, 9.0, 8.0, 3.0, 6.0, 8.0, 10.0, 9.0, 8.0, 3.0, 8.0, 10.0, 3.0, 1.0, 3.0, 10.0, 2.0, 10.0, 7.0, 3.0, 4.0, 10.0, 9.0, 4.0, 5.0, 2.0, 1.0, 8.0, 9.0, 3.0, 6.0, 4.0, 7.0, 8.0, 6.0, 1.0, 9.0, 1.0, 5.0, 9.0, 5.0, 5.0, 4.0, 1.0, 7.0], [7.0, 7.0, 7.0, 8.0, 1.0, 10.0, 1.0, 1.0, 1.0, 2.0, 5.0, 9.0, 4.0, 6.0, 6.0, 3.0, 9.0, 8.0, 4.0, 7.0, 6.0, 2.0, 8.0, 9.0, 8.0, 3.0, 2.0, 8.0, 3.0, 1.0, 4.0, 1.0, 2.0, 7.0, 7.0, 2.0, 5.0, 10.0, 8.0, 5.0, 2.0, 8.0, 5.0, 8.0, 9.0, 9.0, 8.0], [3.0, 2.0, 9.0, 9.0, 5.0, 10.0, 1.0, 1.0, 10.0, 10.0, 4.0, 5.0, 6.0, 3.0, 4.0, 10.0, 8.0, 5.0, 8.0, 2.0, 2.0, 7.0, 5.0, 1.0, 2.0, 5.0, 10.0, 5.0, 7.0, 1.0, 10.0, 9.0, 10.0, 5.0, 7.0, 4.0, 6.0, 3.0, 6.0, 8.0, 4.0, 1.0, 8.0, 3.0, 8.0, 9.0, 3.0], [6.0, 7.0, 3.0, 6.0, 3.0, 7.0, 7.0, 9.0, 8.0, 5.0, 4.0, 4.0, 9.0, 2.0, 3.0, 2.0, 4.0, 8.0, 4.0, 2.0, 8.0, 3.0, 9.0, 8.0, 1.0, 6.0, 5.0, 4.0, 2.0, 6.0, 7.0, 7.0, 2.0, 5.0, 10.0, 1.0, 3.0, 4.0, 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46, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 26, 'quadratic_cost': 3.0}, {'var_i': 46, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 46, 'var_j': 28, 'quadratic_cost': 3.0}, {'var_i': 46, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 34, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 35, 'quadratic_cost': 5.0}, {'var_i': 46, 'var_j': 36, 'quadratic_cost': 7.0}, {'var_i': 46, 'var_j': 37, 'quadratic_cost': 4.0}, {'var_i': 46, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 46, 'var_j': 39, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 40, 'quadratic_cost': 9.0}, {'var_i': 46, 'var_j': 41, 'quadratic_cost': 2.0}, {'var_i': 46, 'var_j': 42, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 43, 'quadratic_cost': 4.0}, {'var_i': 46, 'var_j': 44, 'quadratic_cost': 6.0}, {'var_i': 46, 'var_j': 45, 'quadratic_cost': 8.0}, {'var_i': 46, 'var_j': 46, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 16, 'to': 1, 'var_index': 1}, {'from': 16, 'to': 2, 'var_index': 2}, {'from': 16, 'to': 3, 'var_index': 3}, {'from': 16, 'to': 4, 'var_index': 4}, {'from': 16, 'to': 5, 'var_index': 5}, {'from': 16, 'to': 6, 'var_index': 6}, {'from': 16, 'to': 7, 'var_index': 7}, {'from': 16, 'to': 8, 'var_index': 8}, {'from': 16, 'to': 9, 'var_index': 9}, {'from': 16, 'to': 10, 'var_index': 10}, {'from': 16, 'to': 11, 'var_index': 11}, {'from': 16, 'to': 12, 'var_index': 12}, {'from': 16, 'to': 13, 'var_index': 13}, {'from': 16, 'to': 14, 'var_index': 14}, {'from': 16, 'to': 15, 'var_index': 15}, {'from': 0, 'to': 17, 'var_index': 16}, {'from': 1, 'to': 17, 'var_index': 17}, {'from': 2, 'to': 17, 'var_index': 18}, {'from': 3, 'to': 17, 'var_index': 19}, {'from': 4, 'to': 17, 'var_index': 20}, {'from': 5, 'to': 17, 'var_index': 21}, {'from': 6, 'to': 17, 'var_index': 22}, {'from': 7, 'to': 17, 'var_index': 23}, {'from': 8, 'to': 17, 'var_index': 24}, {'from': 9, 'to': 17, 'var_index': 25}, {'from': 10, 'to': 17, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 17, 'var_index': 28}, {'from': 13, 'to': 17, 'var_index': 29}, {'from': 14, 'to': 17, 'var_index': 30}, {'from': 15, 'to': 17, 'var_index': 31}, {'from': 0, 'to': 1, 'var_index': 32}, {'from': 1, 'to': 2, 'var_index': 33}, {'from': 2, 'to': 3, 'var_index': 34}, {'from': 3, 'to': 4, 'var_index': 35}, {'from': 4, 'to': 5, 'var_index': 36}, {'from': 5, 'to': 6, 'var_index': 37}, {'from': 6, 'to': 7, 'var_index': 38}, {'from': 7, 'to': 8, 'var_index': 39}, {'from': 8, 'to': 9, 'var_index': 40}, {'from': 9, 'to': 10, 'var_index': 41}, {'from': 10, 'to': 11, 'var_index': 42}, {'from': 11, 'to': 12, 'var_index': 43}, {'from': 12, 'to': 13, 'var_index': 44}, {'from': 13, 'to': 14, 'var_index': 45}, {'from': 14, 'to': 15, 'var_index': 46}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17}}","[16, 2, 17]",33,markdown_table,0
QSPP,QSPP,"Backstage there’s a request to route supplies along a single, permitted route from the service gate to the stage, following only the designated one‑way pathways. Each pathway has a normal cost, and certain pathways, or particular pairs of pathways used together, add extra penalties to the bill, so the final cost is simply the sum of every pathway’s base charge plus any extra charges that apply when specific pathways coincide. The job is to pick one uninterrupted chain of locations — start at the gate, move along real one‑way links step by step, finish at the staging area — that produces the smallest possible total when all those costs are added. The full map and the numeric details are available below.

# total_locations=20
# total_thoroughfares=53
# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T
# service_gate=S
# staging_area=T

thoroughfare_start_location,thoroughfare_end_location,thoroughfare_id
S,A,0
S,B,1
S,C,2
S,D,3
S,E,4
S,F,5
S,G,6
S,H,7
S,I,8
S,J,9
S,K,10
S,L,11
S,M,12
S,N,13
S,O,14
S,P,15
S,Q,16
S,R,17
A,T,18
B,T,19
C,T,20
D,T,21
E,T,22
F,T,23
G,T,24
H,T,25
I,T,26
J,T,27
K,T,28
L,T,29
M,T,30
N,T,31
O,T,32
P,T,33
Q,T,34
R,T,35
A,B,36
B,C,37
C,D,38
D,E,39
E,F,40
F,G,41
G,H,42
H,I,43
I,J,44
J,K,45
K,L,46
L,M,47
M,N,48
N,O,49
O,P,50
P,Q,51
Q,R,52

thoroughfare_id,base_transport_cost
0,9.0
1,1.0
2,2.0
3,7.0
4,3.0
5,10.0
6,10.0
7,4.0
8,7.0
9,8.0
10,10.0
11,5.0
12,1.0
13,7.0
14,8.0
15,10.0
16,3.0
17,5.0
18,1.0
19,10.0
20,1.0
21,7.0
22,1.0
23,2.0
24,10.0
25,2.0
26,10.0
27,1.0
28,10.0
29,2.0
30,7.0
31,8.0
32,9.0
33,3.0
34,6.0
35,9.0
36,8.0
37,4.0
38,8.0
39,8.0
40,4.0
41,5.0
42,4.0
43,10.0
44,9.0
45,10.0
46,8.0
47,3.0
48,6.0
49,1.0
50,5.0
51,8.0
52,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (thoroughfare_i_id, thoroughfare_j_id). If two thoroughfares with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| thoroughfare_i_id\thoroughfare_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 6.0 | 5.0 | 5.0 | 10.0 | 9.0 | 4.0 | 2.0 | 6.0 | 7.0 | 5.0 | 1.0 | 9.0 | 3.0 | 7.0 | 2.0 | 9.0 | 3.0 | 2.0 | 7.0 | 1.0 | 6.0 | 2.0 | 10.0 | 1.0 | 9.0 | 2.0 | 10.0 | 9.0 | 2.0 | 4.0 | 5.0 | 2.0 | 6.0 | 2.0 | 10.0 | 9.0 | 1.0 | 6.0 | 7.0 | 4.0 | 7.0 | 3.0 | 5.0 | 1.0 | 4.0 | 3.0 | 5.0 | 10.0 | 8.0 | 7.0 | 6.0 | 6.0 |
| 1 | 6.0 | 4.0 | 3.0 | 8.0 | 6.0 | 10.0 | 9.0 | 10.0 | 9.0 | 1.0 | 8.0 | 9.0 | 8.0 | 6.0 | 1.0 | 8.0 | 3.0 | 9.0 | 3.0 | 4.0 | 6.0 | 1.0 | 8.0 | 3.0 | 3.0 | 3.0 | 6.0 | 6.0 | 10.0 | 9.0 | 4.0 | 10.0 | 8.0 | 5.0 | 6.0 | 3.0 | 3.0 | 9.0 | 3.0 | 6.0 | 2.0 | 9.0 | 9.0 | 7.0 | 6.0 | 8.0 | 3.0 | 3.0 | 3.0 | 4.0 | 9.0 | 4.0 | 9.0 |
| 2 | 5.0 | 3.0 | 10.0 | 10.0 | 4.0 | 3.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 9.0 | 8.0 | 7.0 | 4.0 | 5.0 | 8.0 | 1.0 | 3.0 | 2.0 | 5.0 | 3.0 | 3.0 | 3.0 | 4.0 | 10.0 | 6.0 | 4.0 | 6.0 | 5.0 | 8.0 | 3.0 | 4.0 | 8.0 | 8.0 | 10.0 | 7.0 | 9.0 | 1.0 | 10.0 | 3.0 | 3.0 | 10.0 | 1.0 | 5.0 | 10.0 | 10.0 | 4.0 | 5.0 | 8.0 | 9.0 | 2.0 | 8.0 |
| 3 | 5.0 | 8.0 | 10.0 | 6.0 | 10.0 | 6.0 | 7.0 | 1.0 | 5.0 | 9.0 | 2.0 | 1.0 | 10.0 | 4.0 | 4.0 | 2.0 | 4.0 | 9.0 | 10.0 | 7.0 | 2.0 | 2.0 | 4.0 | 5.0 | 4.0 | 7.0 | 2.0 | 8.0 | 3.0 | 9.0 | 4.0 | 4.0 | 4.0 | 5.0 | 4.0 | 10.0 | 8.0 | 5.0 | 6.0 | 1.0 | 7.0 | 3.0 | 10.0 | 9.0 | 3.0 | 10.0 | 8.0 | 4.0 | 8.0 | 6.0 | 7.0 | 5.0 | 5.0 |
| 4 | 10.0 | 6.0 | 4.0 | 10.0 | 5.0 | 10.0 | 10.0 | 4.0 | 10.0 | 4.0 | 4.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 7.0 | 6.0 | 9.0 | 7.0 | 2.0 | 1.0 | 4.0 | 1.0 | 6.0 | 3.0 | 1.0 | 7.0 | 4.0 | 8.0 | 1.0 | 2.0 | 3.0 | 7.0 | 6.0 | 7.0 | 9.0 | 9.0 | 2.0 | 6.0 | 8.0 | 1.0 | 2.0 | 9.0 | 9.0 | 5.0 | 6.0 | 3.0 | 3.0 | 2.0 | 3.0 | 5.0 | 3.0 |
| 5 | 9.0 | 10.0 | 3.0 | 6.0 | 10.0 | 3.0 | 5.0 | 9.0 | 9.0 | 8.0 | 2.0 | 5.0 | 1.0 | 4.0 | 10.0 | 10.0 | 5.0 | 3.0 | 3.0 | 1.0 | 5.0 | 7.0 | 6.0 | 5.0 | 7.0 | 5.0 | 9.0 | 1.0 | 3.0 | 2.0 | 2.0 | 10.0 | 5.0 | 3.0 | 8.0 | 7.0 | 7.0 | 8.0 | 9.0 | 7.0 | 3.0 | 4.0 | 5.0 | 10.0 | 10.0 | 3.0 | 3.0 | 4.0 | 4.0 | 9.0 | 1.0 | 7.0 | 9.0 |
| 6 | 4.0 | 9.0 | 1.0 | 7.0 | 10.0 | 5.0 | 1.0 | 4.0 | 6.0 | 6.0 | 4.0 | 2.0 | 10.0 | 6.0 | 8.0 | 10.0 | 6.0 | 2.0 | 2.0 | 9.0 | 9.0 | 10.0 | 5.0 | 7.0 | 9.0 | 4.0 | 10.0 | 10.0 | 4.0 | 9.0 | 8.0 | 6.0 | 7.0 | 2.0 | 9.0 | 2.0 | 5.0 | 10.0 | 6.0 | 6.0 | 9.0 | 3.0 | 4.0 | 4.0 | 10.0 | 3.0 | 3.0 | 9.0 | 3.0 | 2.0 | 10.0 | 3.0 | 6.0 |
| 7 | 2.0 | 10.0 | 10.0 | 1.0 | 4.0 | 9.0 | 4.0 | 8.0 | 3.0 | 2.0 | 4.0 | 5.0 | 5.0 | 3.0 | 8.0 | 9.0 | 6.0 | 3.0 | 10.0 | 9.0 | 9.0 | 5.0 | 5.0 | 4.0 | 4.0 | 5.0 | 4.0 | 8.0 | 3.0 | 3.0 | 3.0 | 5.0 | 4.0 | 5.0 | 6.0 | 5.0 | 4.0 | 2.0 | 3.0 | 9.0 | 9.0 | 6.0 | 9.0 | 2.0 | 5.0 | 2.0 | 5.0 | 6.0 | 6.0 | 5.0 | 7.0 | 3.0 | 7.0 |
| 8 | 6.0 | 9.0 | 9.0 | 5.0 | 10.0 | 9.0 | 6.0 | 3.0 | 7.0 | 3.0 | 3.0 | 10.0 | 5.0 | 7.0 | 5.0 | 6.0 | 3.0 | 1.0 | 6.0 | 7.0 | 10.0 | 4.0 | 1.0 | 3.0 | 8.0 | 1.0 | 3.0 | 2.0 | 8.0 | 10.0 | 5.0 | 8.0 | 8.0 | 5.0 | 2.0 | 2.0 | 8.0 | 1.0 | 6.0 | 9.0 | 2.0 | 8.0 | 5.0 | 1.0 | 5.0 | 6.0 | 7.0 | 3.0 | 10.0 | 1.0 | 10.0 | 8.0 | 9.0 |
| 9 | 7.0 | 1.0 | 6.0 | 9.0 | 4.0 | 8.0 | 6.0 | 2.0 | 3.0 | 7.0 | 6.0 | 7.0 | 6.0 | 2.0 | 7.0 | 4.0 | 5.0 | 9.0 | 2.0 | 9.0 | 7.0 | 8.0 | 8.0 | 5.0 | 4.0 | 5.0 | 1.0 | 8.0 | 1.0 | 10.0 | 2.0 | 9.0 | 4.0 | 8.0 | 6.0 | 1.0 | 4.0 | 4.0 | 2.0 | 8.0 | 5.0 | 8.0 | 6.0 | 9.0 | 5.0 | 7.0 | 8.0 | 2.0 | 1.0 | 10.0 | 5.0 | 3.0 | 10.0 |
| 10 | 5.0 | 8.0 | 2.0 | 2.0 | 4.0 | 2.0 | 4.0 | 4.0 | 3.0 | 6.0 | 2.0 | 3.0 | 5.0 | 9.0 | 4.0 | 9.0 | 6.0 | 3.0 | 9.0 | 1.0 | 3.0 | 1.0 | 1.0 | 9.0 | 9.0 | 2.0 | 5.0 | 8.0 | 5.0 | 4.0 | 2.0 | 5.0 | 8.0 | 1.0 | 1.0 | 6.0 | 10.0 | 2.0 | 3.0 | 1.0 | 10.0 | 9.0 | 9.0 | 2.0 | 8.0 | 6.0 | 5.0 | 1.0 | 6.0 | 1.0 | 10.0 | 1.0 | 7.0 |
| 11 | 1.0 | 9.0 | 9.0 | 1.0 | 2.0 | 5.0 | 2.0 | 5.0 | 10.0 | 7.0 | 3.0 | 6.0 | 1.0 | 7.0 | 1.0 | 3.0 | 5.0 | 2.0 | 6.0 | 6.0 | 2.0 | 3.0 | 7.0 | 4.0 | 8.0 | 7.0 | 7.0 | 8.0 | 2.0 | 7.0 | 7.0 | 9.0 | 5.0 | 9.0 | 4.0 | 9.0 | 2.0 | 1.0 | 7.0 | 7.0 | 7.0 | 8.0 | 5.0 | 5.0 | 1.0 | 5.0 | 8.0 | 8.0 | 7.0 | 9.0 | 9.0 | 8.0 | 7.0 |
| 12 | 9.0 | 8.0 | 8.0 | 10.0 | 8.0 | 1.0 | 10.0 | 5.0 | 5.0 | 6.0 | 5.0 | 1.0 | 3.0 | 7.0 | 9.0 | 9.0 | 2.0 | 8.0 | 8.0 | 9.0 | 8.0 | 4.0 | 4.0 | 2.0 | 2.0 | 9.0 | 7.0 | 6.0 | 5.0 | 6.0 | 1.0 | 6.0 | 2.0 | 2.0 | 9.0 | 6.0 | 6.0 | 1.0 | 2.0 | 6.0 | 3.0 | 1.0 | 6.0 | 2.0 | 5.0 | 2.0 | 5.0 | 4.0 | 1.0 | 2.0 | 2.0 | 9.0 | 3.0 |
| 13 | 3.0 | 6.0 | 7.0 | 4.0 | 5.0 | 4.0 | 6.0 | 3.0 | 7.0 | 2.0 | 9.0 | 7.0 | 7.0 | 5.0 | 5.0 | 10.0 | 6.0 | 3.0 | 2.0 | 5.0 | 10.0 | 3.0 | 5.0 | 6.0 | 1.0 | 2.0 | 8.0 | 10.0 | 9.0 | 2.0 | 2.0 | 2.0 | 8.0 | 7.0 | 5.0 | 4.0 | 9.0 | 6.0 | 4.0 | 6.0 | 4.0 | 6.0 | 5.0 | 1.0 | 5.0 | 2.0 | 4.0 | 3.0 | 7.0 | 5.0 | 4.0 | 1.0 | 3.0 |
| 14 | 7.0 | 1.0 | 4.0 | 4.0 | 9.0 | 10.0 | 8.0 | 8.0 | 5.0 | 7.0 | 4.0 | 1.0 | 9.0 | 5.0 | 6.0 | 1.0 | 7.0 | 5.0 | 8.0 | 2.0 | 8.0 | 10.0 | 7.0 | 4.0 | 7.0 | 2.0 | 1.0 | 7.0 | 4.0 | 8.0 | 5.0 | 8.0 | 3.0 | 8.0 | 5.0 | 10.0 | 9.0 | 6.0 | 2.0 | 1.0 | 3.0 | 9.0 | 9.0 | 6.0 | 8.0 | 4.0 | 9.0 | 3.0 | 3.0 | 3.0 | 4.0 | 7.0 | 8.0 |
| 15 | 2.0 | 8.0 | 5.0 | 2.0 | 9.0 | 10.0 | 10.0 | 9.0 | 6.0 | 4.0 | 9.0 | 3.0 | 9.0 | 10.0 | 1.0 | 1.0 | 3.0 | 7.0 | 5.0 | 8.0 | 9.0 | 1.0 | 2.0 | 7.0 | 4.0 | 6.0 | 6.0 | 4.0 | 7.0 | 3.0 | 3.0 | 6.0 | 5.0 | 7.0 | 1.0 | 1.0 | 3.0 | 8.0 | 1.0 | 6.0 | 3.0 | 3.0 | 2.0 | 10.0 | 1.0 | 4.0 | 5.0 | 9.0 | 5.0 | 5.0 | 6.0 | 2.0 | 1.0 |
| 16 | 9.0 | 3.0 | 8.0 | 4.0 | 7.0 | 5.0 | 6.0 | 6.0 | 3.0 | 5.0 | 6.0 | 5.0 | 2.0 | 6.0 | 7.0 | 3.0 | 8.0 | 1.0 | 8.0 | 9.0 | 6.0 | 6.0 | 5.0 | 5.0 | 6.0 | 4.0 | 10.0 | 4.0 | 7.0 | 8.0 | 8.0 | 5.0 | 4.0 | 10.0 | 1.0 | 1.0 | 8.0 | 2.0 | 7.0 | 6.0 | 6.0 | 7.0 | 9.0 | 4.0 | 6.0 | 1.0 | 8.0 | 1.0 | 3.0 | 4.0 | 3.0 | 3.0 | 4.0 |
| 17 | 3.0 | 9.0 | 1.0 | 9.0 | 6.0 | 3.0 | 2.0 | 3.0 | 1.0 | 9.0 | 3.0 | 2.0 | 8.0 | 3.0 | 5.0 | 7.0 | 1.0 | 5.0 | 3.0 | 9.0 | 2.0 | 8.0 | 6.0 | 4.0 | 9.0 | 4.0 | 1.0 | 10.0 | 1.0 | 9.0 | 3.0 | 5.0 | 2.0 | 1.0 | 3.0 | 6.0 | 9.0 | 4.0 | 7.0 | 5.0 | 7.0 | 1.0 | 6.0 | 2.0 | 8.0 | 3.0 | 10.0 | 9.0 | 1.0 | 4.0 | 10.0 | 10.0 | 3.0 |
| 18 | 2.0 | 3.0 | 3.0 | 10.0 | 9.0 | 3.0 | 2.0 | 10.0 | 6.0 | 2.0 | 9.0 | 6.0 | 8.0 | 2.0 | 8.0 | 5.0 | 8.0 | 3.0 | 3.0 | 5.0 | 2.0 | 3.0 | 2.0 | 10.0 | 10.0 | 7.0 | 6.0 | 8.0 | 6.0 | 1.0 | 2.0 | 3.0 | 9.0 | 4.0 | 10.0 | 7.0 | 6.0 | 10.0 | 9.0 | 1.0 | 4.0 | 5.0 | 6.0 | 8.0 | 1.0 | 1.0 | 5.0 | 3.0 | 10.0 | 6.0 | 2.0 | 1.0 | 6.0 |
| 19 | 7.0 | 4.0 | 2.0 | 7.0 | 7.0 | 1.0 | 9.0 | 9.0 | 7.0 | 9.0 | 1.0 | 6.0 | 9.0 | 5.0 | 2.0 | 8.0 | 9.0 | 9.0 | 5.0 | 6.0 | 8.0 | 2.0 | 6.0 | 4.0 | 8.0 | 1.0 | 6.0 | 10.0 | 4.0 | 4.0 | 2.0 | 2.0 | 2.0 | 2.0 | 10.0 | 2.0 | 4.0 | 4.0 | 4.0 | 1.0 | 9.0 | 8.0 | 8.0 | 2.0 | 10.0 | 8.0 | 7.0 | 6.0 | 3.0 | 2.0 | 5.0 | 4.0 | 7.0 |
| 20 | 1.0 | 6.0 | 5.0 | 2.0 | 2.0 | 5.0 | 9.0 | 9.0 | 10.0 | 7.0 | 3.0 | 2.0 | 8.0 | 10.0 | 8.0 | 9.0 | 6.0 | 2.0 | 2.0 | 8.0 | 2.0 | 7.0 | 8.0 | 3.0 | 9.0 | 3.0 | 1.0 | 10.0 | 9.0 | 2.0 | 7.0 | 7.0 | 8.0 | 4.0 | 2.0 | 8.0 | 2.0 | 4.0 | 2.0 | 2.0 | 7.0 | 4.0 | 5.0 | 4.0 | 6.0 | 1.0 | 5.0 | 10.0 | 2.0 | 3.0 | 2.0 | 3.0 | 6.0 |
| 21 | 6.0 | 1.0 | 3.0 | 2.0 | 1.0 | 7.0 | 10.0 | 5.0 | 4.0 | 8.0 | 1.0 | 3.0 | 4.0 | 3.0 | 10.0 | 1.0 | 6.0 | 8.0 | 3.0 | 2.0 | 7.0 | 7.0 | 7.0 | 9.0 | 9.0 | 3.0 | 1.0 | 1.0 | 4.0 | 5.0 | 5.0 | 1.0 | 4.0 | 9.0 | 1.0 | 4.0 | 7.0 | 7.0 | 7.0 | 2.0 | 10.0 | 1.0 | 1.0 | 8.0 | 6.0 | 9.0 | 9.0 | 3.0 | 3.0 | 9.0 | 8.0 | 10.0 | 8.0 |
| 22 | 2.0 | 8.0 | 3.0 | 4.0 | 4.0 | 6.0 | 5.0 | 5.0 | 1.0 | 8.0 | 1.0 | 7.0 | 4.0 | 5.0 | 7.0 | 2.0 | 5.0 | 6.0 | 2.0 | 6.0 | 8.0 | 7.0 | 5.0 | 9.0 | 4.0 | 5.0 | 9.0 | 9.0 | 7.0 | 10.0 | 9.0 | 9.0 | 2.0 | 3.0 | 2.0 | 8.0 | 6.0 | 1.0 | 2.0 | 3.0 | 10.0 | 1.0 | 7.0 | 4.0 | 4.0 | 8.0 | 8.0 | 6.0 | 7.0 | 6.0 | 4.0 | 1.0 | 9.0 |
| 23 | 10.0 | 3.0 | 3.0 | 5.0 | 1.0 | 5.0 | 7.0 | 4.0 | 3.0 | 5.0 | 9.0 | 4.0 | 2.0 | 6.0 | 4.0 | 7.0 | 5.0 | 4.0 | 10.0 | 4.0 | 3.0 | 9.0 | 9.0 | 10.0 | 3.0 | 8.0 | 8.0 | 1.0 | 9.0 | 7.0 | 10.0 | 6.0 | 2.0 | 1.0 | 1.0 | 4.0 | 9.0 | 3.0 | 8.0 | 7.0 | 8.0 | 9.0 | 8.0 | 10.0 | 7.0 | 5.0 | 1.0 | 9.0 | 9.0 | 9.0 | 10.0 | 2.0 | 3.0 |
| 24 | 1.0 | 3.0 | 4.0 | 4.0 | 6.0 | 7.0 | 9.0 | 4.0 | 8.0 | 4.0 | 9.0 | 8.0 | 2.0 | 1.0 | 7.0 | 4.0 | 6.0 | 9.0 | 10.0 | 8.0 | 9.0 | 9.0 | 4.0 | 3.0 | 10.0 | 4.0 | 1.0 | 3.0 | 8.0 | 3.0 | 4.0 | 1.0 | 3.0 | 10.0 | 4.0 | 4.0 | 2.0 | 10.0 | 10.0 | 6.0 | 3.0 | 9.0 | 3.0 | 9.0 | 2.0 | 6.0 | 2.0 | 2.0 | 6.0 | 4.0 | 9.0 | 10.0 | 3.0 |
| 25 | 9.0 | 3.0 | 10.0 | 7.0 | 3.0 | 5.0 | 4.0 | 5.0 | 1.0 | 5.0 | 2.0 | 7.0 | 9.0 | 2.0 | 2.0 | 6.0 | 4.0 | 4.0 | 7.0 | 1.0 | 3.0 | 3.0 | 5.0 | 8.0 | 4.0 | 4.0 | 4.0 | 2.0 | 6.0 | 9.0 | 8.0 | 2.0 | 7.0 | 4.0 | 2.0 | 6.0 | 7.0 | 7.0 | 3.0 | 3.0 | 8.0 | 5.0 | 8.0 | 5.0 | 3.0 | 2.0 | 4.0 | 4.0 | 8.0 | 3.0 | 6.0 | 8.0 | 1.0 |
| 26 | 2.0 | 6.0 | 6.0 | 2.0 | 1.0 | 9.0 | 10.0 | 4.0 | 3.0 | 1.0 | 5.0 | 7.0 | 7.0 | 8.0 | 1.0 | 6.0 | 10.0 | 1.0 | 6.0 | 6.0 | 1.0 | 1.0 | 9.0 | 8.0 | 1.0 | 4.0 | 5.0 | 5.0 | 7.0 | 6.0 | 1.0 | 3.0 | 9.0 | 8.0 | 5.0 | 8.0 | 3.0 | 3.0 | 2.0 | 7.0 | 1.0 | 2.0 | 9.0 | 5.0 | 6.0 | 2.0 | 1.0 | 4.0 | 6.0 | 10.0 | 10.0 | 4.0 | 1.0 |
| 27 | 10.0 | 6.0 | 4.0 | 8.0 | 7.0 | 1.0 | 10.0 | 8.0 | 2.0 | 8.0 | 8.0 | 8.0 | 6.0 | 10.0 | 7.0 | 4.0 | 4.0 | 10.0 | 8.0 | 10.0 | 10.0 | 1.0 | 9.0 | 1.0 | 3.0 | 2.0 | 5.0 | 9.0 | 2.0 | 2.0 | 1.0 | 8.0 | 3.0 | 1.0 | 9.0 | 5.0 | 3.0 | 6.0 | 6.0 | 7.0 | 9.0 | 10.0 | 7.0 | 8.0 | 7.0 | 1.0 | 2.0 | 10.0 | 10.0 | 3.0 | 5.0 | 2.0 | 4.0 |
| 28 | 9.0 | 10.0 | 6.0 | 3.0 | 4.0 | 3.0 | 4.0 | 3.0 | 8.0 | 1.0 | 5.0 | 2.0 | 5.0 | 9.0 | 4.0 | 7.0 | 7.0 | 1.0 | 6.0 | 4.0 | 9.0 | 4.0 | 7.0 | 9.0 | 8.0 | 6.0 | 7.0 | 2.0 | 4.0 | 9.0 | 2.0 | 7.0 | 1.0 | 9.0 | 9.0 | 6.0 | 3.0 | 10.0 | 4.0 | 2.0 | 6.0 | 10.0 | 7.0 | 6.0 | 7.0 | 7.0 | 2.0 | 1.0 | 10.0 | 7.0 | 8.0 | 9.0 | 2.0 |
| 29 | 2.0 | 9.0 | 5.0 | 9.0 | 8.0 | 2.0 | 9.0 | 3.0 | 10.0 | 10.0 | 4.0 | 7.0 | 6.0 | 2.0 | 8.0 | 3.0 | 8.0 | 9.0 | 1.0 | 4.0 | 2.0 | 5.0 | 10.0 | 7.0 | 3.0 | 9.0 | 6.0 | 2.0 | 9.0 | 7.0 | 1.0 | 2.0 | 3.0 | 8.0 | 10.0 | 5.0 | 10.0 | 4.0 | 10.0 | 8.0 | 10.0 | 2.0 | 10.0 | 7.0 | 2.0 | 4.0 | 10.0 | 7.0 | 9.0 | 10.0 | 10.0 | 1.0 | 6.0 |
| 30 | 4.0 | 4.0 | 8.0 | 4.0 | 1.0 | 2.0 | 8.0 | 3.0 | 5.0 | 2.0 | 2.0 | 7.0 | 1.0 | 2.0 | 5.0 | 3.0 | 8.0 | 3.0 | 2.0 | 2.0 | 7.0 | 5.0 | 9.0 | 10.0 | 4.0 | 8.0 | 1.0 | 1.0 | 2.0 | 1.0 | 7.0 | 2.0 | 9.0 | 3.0 | 10.0 | 7.0 | 3.0 | 10.0 | 8.0 | 1.0 | 5.0 | 6.0 | 8.0 | 5.0 | 6.0 | 2.0 | 9.0 | 8.0 | 7.0 | 1.0 | 3.0 | 10.0 | 3.0 |
| 31 | 5.0 | 10.0 | 3.0 | 4.0 | 2.0 | 10.0 | 6.0 | 5.0 | 8.0 | 9.0 | 5.0 | 9.0 | 6.0 | 2.0 | 8.0 | 6.0 | 5.0 | 5.0 | 3.0 | 2.0 | 7.0 | 1.0 | 9.0 | 6.0 | 1.0 | 2.0 | 3.0 | 8.0 | 7.0 | 2.0 | 2.0 | 9.0 | 6.0 | 4.0 | 9.0 | 1.0 | 7.0 | 10.0 | 5.0 | 5.0 | 1.0 | 3.0 | 1.0 | 3.0 | 9.0 | 9.0 | 3.0 | 1.0 | 5.0 | 4.0 | 2.0 | 9.0 | 4.0 |
| 32 | 2.0 | 8.0 | 4.0 | 4.0 | 3.0 | 5.0 | 7.0 | 4.0 | 8.0 | 4.0 | 8.0 | 5.0 | 2.0 | 8.0 | 3.0 | 5.0 | 4.0 | 2.0 | 9.0 | 2.0 | 8.0 | 4.0 | 2.0 | 2.0 | 3.0 | 7.0 | 9.0 | 3.0 | 1.0 | 3.0 | 9.0 | 6.0 | 7.0 | 5.0 | 10.0 | 5.0 | 9.0 | 4.0 | 4.0 | 4.0 | 3.0 | 1.0 | 9.0 | 5.0 | 7.0 | 5.0 | 9.0 | 3.0 | 5.0 | 9.0 | 9.0 | 5.0 | 4.0 |
| 33 | 6.0 | 5.0 | 8.0 | 5.0 | 7.0 | 3.0 | 2.0 | 5.0 | 5.0 | 8.0 | 1.0 | 9.0 | 2.0 | 7.0 | 8.0 | 7.0 | 10.0 | 1.0 | 4.0 | 2.0 | 4.0 | 9.0 | 3.0 | 1.0 | 10.0 | 4.0 | 8.0 | 1.0 | 9.0 | 8.0 | 3.0 | 4.0 | 5.0 | 2.0 | 9.0 | 10.0 | 9.0 | 3.0 | 2.0 | 9.0 | 5.0 | 9.0 | 3.0 | 7.0 | 3.0 | 9.0 | 2.0 | 1.0 | 2.0 | 8.0 | 9.0 | 5.0 | 5.0 |
| 34 | 2.0 | 6.0 | 8.0 | 4.0 | 6.0 | 8.0 | 9.0 | 6.0 | 2.0 | 6.0 | 1.0 | 4.0 | 9.0 | 5.0 | 5.0 | 1.0 | 1.0 | 3.0 | 10.0 | 10.0 | 2.0 | 1.0 | 2.0 | 1.0 | 4.0 | 2.0 | 5.0 | 9.0 | 9.0 | 10.0 | 10.0 | 9.0 | 10.0 | 9.0 | 7.0 | 5.0 | 2.0 | 5.0 | 4.0 | 10.0 | 1.0 | 8.0 | 6.0 | 7.0 | 1.0 | 3.0 | 7.0 | 10.0 | 7.0 | 5.0 | 9.0 | 3.0 | 8.0 |
| 35 | 10.0 | 3.0 | 10.0 | 10.0 | 7.0 | 7.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 9.0 | 6.0 | 4.0 | 10.0 | 1.0 | 1.0 | 6.0 | 7.0 | 2.0 | 8.0 | 4.0 | 8.0 | 4.0 | 4.0 | 6.0 | 8.0 | 5.0 | 6.0 | 5.0 | 7.0 | 1.0 | 5.0 | 10.0 | 5.0 | 3.0 | 6.0 | 8.0 | 4.0 | 9.0 | 10.0 | 6.0 | 5.0 | 1.0 | 9.0 | 3.0 | 1.0 | 10.0 | 5.0 | 2.0 | 9.0 | 1.0 | 3.0 |
| 36 | 9.0 | 3.0 | 7.0 | 8.0 | 9.0 | 7.0 | 5.0 | 4.0 | 8.0 | 4.0 | 10.0 | 2.0 | 6.0 | 9.0 | 9.0 | 3.0 | 8.0 | 9.0 | 6.0 | 4.0 | 2.0 | 7.0 | 6.0 | 9.0 | 2.0 | 7.0 | 3.0 | 3.0 | 3.0 | 10.0 | 3.0 | 7.0 | 9.0 | 9.0 | 2.0 | 6.0 | 4.0 | 9.0 | 6.0 | 8.0 | 1.0 | 1.0 | 10.0 | 8.0 | 7.0 | 1.0 | 5.0 | 5.0 | 6.0 | 6.0 | 1.0 | 6.0 | 6.0 |
| 37 | 1.0 | 9.0 | 9.0 | 5.0 | 9.0 | 8.0 | 10.0 | 2.0 | 1.0 | 4.0 | 2.0 | 1.0 | 1.0 | 6.0 | 6.0 | 8.0 | 2.0 | 4.0 | 10.0 | 4.0 | 4.0 | 7.0 | 1.0 | 3.0 | 10.0 | 7.0 | 3.0 | 6.0 | 10.0 | 4.0 | 10.0 | 10.0 | 4.0 | 3.0 | 5.0 | 8.0 | 9.0 | 9.0 | 5.0 | 2.0 | 2.0 | 8.0 | 6.0 | 5.0 | 3.0 | 5.0 | 4.0 | 5.0 | 6.0 | 3.0 | 4.0 | 9.0 | 7.0 |
| 38 | 6.0 | 3.0 | 1.0 | 6.0 | 2.0 | 9.0 | 6.0 | 3.0 | 6.0 | 2.0 | 3.0 | 7.0 | 2.0 | 4.0 | 2.0 | 1.0 | 7.0 | 7.0 | 9.0 | 4.0 | 2.0 | 7.0 | 2.0 | 8.0 | 10.0 | 3.0 | 2.0 | 6.0 | 4.0 | 10.0 | 8.0 | 5.0 | 4.0 | 2.0 | 4.0 | 4.0 | 6.0 | 5.0 | 8.0 | 8.0 | 8.0 | 4.0 | 4.0 | 3.0 | 1.0 | 1.0 | 4.0 | 1.0 | 5.0 | 2.0 | 8.0 | 4.0 | 2.0 |
| 39 | 7.0 | 6.0 | 10.0 | 1.0 | 6.0 | 7.0 | 6.0 | 9.0 | 9.0 | 8.0 | 1.0 | 7.0 | 6.0 | 6.0 | 1.0 | 6.0 | 6.0 | 5.0 | 1.0 | 1.0 | 2.0 | 2.0 | 3.0 | 7.0 | 6.0 | 3.0 | 7.0 | 7.0 | 2.0 | 8.0 | 1.0 | 5.0 | 4.0 | 9.0 | 10.0 | 9.0 | 8.0 | 2.0 | 8.0 | 7.0 | 4.0 | 1.0 | 1.0 | 4.0 | 10.0 | 4.0 | 6.0 | 3.0 | 5.0 | 10.0 | 9.0 | 10.0 | 4.0 |
| 40 | 4.0 | 2.0 | 3.0 | 7.0 | 8.0 | 3.0 | 9.0 | 9.0 | 2.0 | 5.0 | 10.0 | 7.0 | 3.0 | 4.0 | 3.0 | 3.0 | 6.0 | 7.0 | 4.0 | 9.0 | 7.0 | 10.0 | 10.0 | 8.0 | 3.0 | 8.0 | 1.0 | 9.0 | 6.0 | 10.0 | 5.0 | 1.0 | 3.0 | 5.0 | 1.0 | 10.0 | 1.0 | 2.0 | 8.0 | 4.0 | 1.0 | 5.0 | 9.0 | 9.0 | 6.0 | 8.0 | 8.0 | 7.0 | 10.0 | 2.0 | 8.0 | 6.0 | 1.0 |
| 41 | 7.0 | 9.0 | 3.0 | 3.0 | 1.0 | 4.0 | 3.0 | 6.0 | 8.0 | 8.0 | 9.0 | 8.0 | 1.0 | 6.0 | 9.0 | 3.0 | 7.0 | 1.0 | 5.0 | 8.0 | 4.0 | 1.0 | 1.0 | 9.0 | 9.0 | 5.0 | 2.0 | 10.0 | 10.0 | 2.0 | 6.0 | 3.0 | 1.0 | 9.0 | 8.0 | 6.0 | 1.0 | 8.0 | 4.0 | 1.0 | 5.0 | 8.0 | 10.0 | 4.0 | 9.0 | 6.0 | 5.0 | 8.0 | 8.0 | 6.0 | 1.0 | 9.0 | 3.0 |
| 42 | 3.0 | 9.0 | 10.0 | 10.0 | 2.0 | 5.0 | 4.0 | 9.0 | 5.0 | 6.0 | 9.0 | 5.0 | 6.0 | 5.0 | 9.0 | 2.0 | 9.0 | 6.0 | 6.0 | 8.0 | 5.0 | 1.0 | 7.0 | 8.0 | 3.0 | 8.0 | 9.0 | 7.0 | 7.0 | 10.0 | 8.0 | 1.0 | 9.0 | 3.0 | 6.0 | 5.0 | 10.0 | 6.0 | 4.0 | 1.0 | 9.0 | 10.0 | 1.0 | 5.0 | 4.0 | 3.0 | 2.0 | 1.0 | 7.0 | 9.0 | 7.0 | 8.0 | 8.0 |
| 43 | 5.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 4.0 | 2.0 | 1.0 | 9.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 10.0 | 4.0 | 2.0 | 8.0 | 2.0 | 4.0 | 8.0 | 4.0 | 10.0 | 9.0 | 5.0 | 5.0 | 8.0 | 6.0 | 7.0 | 5.0 | 3.0 | 5.0 | 7.0 | 7.0 | 1.0 | 8.0 | 5.0 | 3.0 | 4.0 | 9.0 | 4.0 | 5.0 | 6.0 | 6.0 | 5.0 | 9.0 | 8.0 | 5.0 | 1.0 | 3.0 | 6.0 | 9.0 |
| 44 | 1.0 | 6.0 | 5.0 | 3.0 | 9.0 | 10.0 | 10.0 | 5.0 | 5.0 | 5.0 | 8.0 | 1.0 | 5.0 | 5.0 | 8.0 | 1.0 | 6.0 | 8.0 | 1.0 | 10.0 | 6.0 | 6.0 | 4.0 | 7.0 | 2.0 | 3.0 | 6.0 | 7.0 | 7.0 | 2.0 | 6.0 | 9.0 | 7.0 | 3.0 | 1.0 | 9.0 | 7.0 | 3.0 | 1.0 | 10.0 | 6.0 | 9.0 | 4.0 | 6.0 | 8.0 | 10.0 | 4.0 | 1.0 | 9.0 | 3.0 | 6.0 | 10.0 | 6.0 |
| 45 | 4.0 | 8.0 | 10.0 | 10.0 | 5.0 | 3.0 | 3.0 | 2.0 | 6.0 | 7.0 | 6.0 | 5.0 | 2.0 | 2.0 | 4.0 | 4.0 | 1.0 | 3.0 | 1.0 | 8.0 | 1.0 | 9.0 | 8.0 | 5.0 | 6.0 | 2.0 | 2.0 | 1.0 | 7.0 | 4.0 | 2.0 | 9.0 | 5.0 | 9.0 | 3.0 | 3.0 | 1.0 | 5.0 | 1.0 | 4.0 | 8.0 | 6.0 | 3.0 | 5.0 | 10.0 | 8.0 | 5.0 | 8.0 | 2.0 | 6.0 | 6.0 | 3.0 | 4.0 |
| 46 | 3.0 | 3.0 | 10.0 | 8.0 | 6.0 | 3.0 | 3.0 | 5.0 | 7.0 | 8.0 | 5.0 | 8.0 | 5.0 | 4.0 | 9.0 | 5.0 | 8.0 | 10.0 | 5.0 | 7.0 | 5.0 | 9.0 | 8.0 | 1.0 | 2.0 | 4.0 | 1.0 | 2.0 | 2.0 | 10.0 | 9.0 | 3.0 | 9.0 | 2.0 | 7.0 | 1.0 | 5.0 | 4.0 | 4.0 | 6.0 | 8.0 | 5.0 | 2.0 | 9.0 | 4.0 | 5.0 | 9.0 | 10.0 | 3.0 | 7.0 | 10.0 | 3.0 | 10.0 |
| 47 | 5.0 | 3.0 | 4.0 | 4.0 | 3.0 | 4.0 | 9.0 | 6.0 | 3.0 | 2.0 | 1.0 | 8.0 | 4.0 | 3.0 | 3.0 | 9.0 | 1.0 | 9.0 | 3.0 | 6.0 | 10.0 | 3.0 | 6.0 | 9.0 | 2.0 | 4.0 | 4.0 | 10.0 | 1.0 | 7.0 | 8.0 | 1.0 | 3.0 | 1.0 | 10.0 | 10.0 | 5.0 | 5.0 | 1.0 | 3.0 | 7.0 | 8.0 | 1.0 | 8.0 | 1.0 | 8.0 | 10.0 | 1.0 | 2.0 | 1.0 | 4.0 | 6.0 | 4.0 |
| 48 | 10.0 | 3.0 | 5.0 | 8.0 | 3.0 | 4.0 | 3.0 | 6.0 | 10.0 | 1.0 | 6.0 | 7.0 | 1.0 | 7.0 | 3.0 | 5.0 | 3.0 | 1.0 | 10.0 | 3.0 | 2.0 | 3.0 | 7.0 | 9.0 | 6.0 | 8.0 | 6.0 | 10.0 | 10.0 | 9.0 | 7.0 | 5.0 | 5.0 | 2.0 | 7.0 | 5.0 | 6.0 | 6.0 | 5.0 | 5.0 | 10.0 | 8.0 | 7.0 | 5.0 | 9.0 | 2.0 | 3.0 | 2.0 | 9.0 | 1.0 | 2.0 | 7.0 | 5.0 |
| 49 | 8.0 | 4.0 | 8.0 | 6.0 | 2.0 | 9.0 | 2.0 | 5.0 | 1.0 | 10.0 | 1.0 | 9.0 | 2.0 | 5.0 | 3.0 | 5.0 | 4.0 | 4.0 | 6.0 | 2.0 | 3.0 | 9.0 | 6.0 | 9.0 | 4.0 | 3.0 | 10.0 | 3.0 | 7.0 | 10.0 | 1.0 | 4.0 | 9.0 | 8.0 | 5.0 | 2.0 | 6.0 | 3.0 | 2.0 | 10.0 | 2.0 | 6.0 | 9.0 | 1.0 | 3.0 | 6.0 | 7.0 | 1.0 | 1.0 | 3.0 | 1.0 | 7.0 | 5.0 |
| 50 | 7.0 | 9.0 | 9.0 | 7.0 | 3.0 | 1.0 | 10.0 | 7.0 | 10.0 | 5.0 | 10.0 | 9.0 | 2.0 | 4.0 | 4.0 | 6.0 | 3.0 | 10.0 | 2.0 | 5.0 | 2.0 | 8.0 | 4.0 | 10.0 | 9.0 | 6.0 | 10.0 | 5.0 | 8.0 | 10.0 | 3.0 | 2.0 | 9.0 | 9.0 | 9.0 | 9.0 | 1.0 | 4.0 | 8.0 | 9.0 | 8.0 | 1.0 | 7.0 | 3.0 | 6.0 | 6.0 | 10.0 | 4.0 | 2.0 | 1.0 | 6.0 | 7.0 | 3.0 |
| 51 | 6.0 | 4.0 | 2.0 | 5.0 | 5.0 | 7.0 | 3.0 | 3.0 | 8.0 | 3.0 | 1.0 | 8.0 | 9.0 | 1.0 | 7.0 | 2.0 | 3.0 | 10.0 | 1.0 | 4.0 | 3.0 | 10.0 | 1.0 | 2.0 | 10.0 | 8.0 | 4.0 | 2.0 | 9.0 | 1.0 | 10.0 | 9.0 | 5.0 | 5.0 | 3.0 | 1.0 | 6.0 | 9.0 | 4.0 | 10.0 | 6.0 | 9.0 | 8.0 | 6.0 | 10.0 | 3.0 | 3.0 | 6.0 | 7.0 | 7.0 | 7.0 | 5.0 | 6.0 |
| 52 | 6.0 | 9.0 | 8.0 | 5.0 | 3.0 | 9.0 | 6.0 | 7.0 | 9.0 | 10.0 | 7.0 | 7.0 | 3.0 | 3.0 | 8.0 | 1.0 | 4.0 | 3.0 | 6.0 | 7.0 | 6.0 | 8.0 | 9.0 | 3.0 | 3.0 | 1.0 | 1.0 | 4.0 | 2.0 | 6.0 | 3.0 | 4.0 | 4.0 | 5.0 | 8.0 | 3.0 | 6.0 | 7.0 | 2.0 | 4.0 | 1.0 | 3.0 | 8.0 | 9.0 | 6.0 | 4.0 | 10.0 | 4.0 | 5.0 | 5.0 | 3.0 | 6.0 | 5.0 |

Also, when you give the final reply, please put the chosen route into a tiny JSON layout — nothing fancy, just a single top-level key called ""solution"" whose value is the path as an array.

{
  ""solution"": []
}

This little block is just a sketch of the shape I expect: the ""solution"" array is where you'll list the chain of locations from the service gate to the stage, in order, using node identifiers only (start node first, end node last). Think of it like filling in a short form — the JSON shows the fields, but it's not the actual answer until you fill that array with the nodes of the path.

One more thing: use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7"".""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 1, 'var_index': 1}, {'from': 18, 'to': 2, 'var_index': 2}, {'from': 18, 'to': 3, 'var_index': 3}, {'from': 18, 'to': 4, 'var_index': 4}, {'from': 18, 'to': 5, 'var_index': 5}, {'from': 18, 'to': 6, 'var_index': 6}, {'from': 18, 'to': 7, 'var_index': 7}, {'from': 18, 'to': 8, 'var_index': 8}, {'from': 18, 'to': 9, 'var_index': 9}, {'from': 18, 'to': 10, 'var_index': 10}, {'from': 18, 'to': 11, 'var_index': 11}, {'from': 18, 'to': 12, 'var_index': 12}, {'from': 18, 'to': 13, 'var_index': 13}, {'from': 18, 'to': 14, 'var_index': 14}, {'from': 18, 'to': 15, 'var_index': 15}, {'from': 18, 'to': 16, 'var_index': 16}, {'from': 18, 'to': 17, 'var_index': 17}, {'from': 0, 'to': 19, 'var_index': 18}, {'from': 1, 'to': 19, 'var_index': 19}, {'from': 2, 'to': 19, 'var_index': 20}, {'from': 3, 'to': 19, 'var_index': 21}, {'from': 4, 'to': 19, 'var_index': 22}, {'from': 5, 'to': 19, 'var_index': 23}, {'from': 6, 'to': 19, 'var_index': 24}, {'from': 7, 'to': 19, 'var_index': 25}, {'from': 8, 'to': 19, 'var_index': 26}, {'from': 9, 'to': 19, 'var_index': 27}, {'from': 10, 'to': 19, 'var_index': 28}, {'from': 11, 'to': 19, 'var_index': 29}, {'from': 12, 'to': 19, 'var_index': 30}, {'from': 13, 'to': 19, 'var_index': 31}, {'from': 14, 'to': 19, 'var_index': 32}, {'from': 15, 'to': 19, 'var_index': 33}, {'from': 16, 'to': 19, 'var_index': 34}, {'from': 17, 'to': 19, 'var_index': 35}, {'from': 0, 'to': 1, 'var_index': 36}, {'from': 1, 'to': 2, 'var_index': 37}, {'from': 2, 'to': 3, 'var_index': 38}, {'from': 3, 'to': 4, 'var_index': 39}, {'from': 4, 'to': 5, 'var_index': 40}, {'from': 5, 'to': 6, 'var_index': 41}, {'from': 6, 'to': 7, 'var_index': 42}, {'from': 7, 'to': 8, 'var_index': 43}, {'from': 8, 'to': 9, 'var_index': 44}, {'from': 9, 'to': 10, 'var_index': 45}, {'from': 10, 'to': 11, 'var_index': 46}, {'from': 11, 'to': 12, 'var_index': 47}, {'from': 12, 'to': 13, 'var_index': 48}, {'from': 13, 'to': 14, 'var_index': 49}, {'from': 14, 'to': 15, 'var_index': 50}, {'from': 15, 'to': 16, 'var_index': 51}, {'from': 16, 'to': 17, 'var_index': 52}], 'objective': {'constant': 0.0, 'linear': [9.0, 1.0, 2.0, 7.0, 3.0, 10.0, 10.0, 4.0, 7.0, 8.0, 10.0, 5.0, 1.0, 7.0, 8.0, 10.0, 3.0, 5.0, 1.0, 10.0, 1.0, 7.0, 1.0, 2.0, 10.0, 2.0, 10.0, 1.0, 10.0, 2.0, 7.0, 8.0, 9.0, 3.0, 6.0, 9.0, 8.0, 4.0, 8.0, 8.0, 4.0, 5.0, 4.0, 10.0, 9.0, 10.0, 8.0, 3.0, 6.0, 1.0, 5.0, 8.0, 7.0], 'quadratic': [[2.0, 6.0, 5.0, 5.0, 10.0, 9.0, 4.0, 2.0, 6.0, 7.0, 5.0, 1.0, 9.0, 3.0, 7.0, 2.0, 9.0, 3.0, 2.0, 7.0, 1.0, 6.0, 2.0, 10.0, 1.0, 9.0, 2.0, 10.0, 9.0, 2.0, 4.0, 5.0, 2.0, 6.0, 2.0, 10.0, 9.0, 1.0, 6.0, 7.0, 4.0, 7.0, 3.0, 5.0, 1.0, 4.0, 3.0, 5.0, 10.0, 8.0, 7.0, 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30}, {'from': 'N', 'to': 'T', 'var_index': 31}, {'from': 'O', 'to': 'T', 'var_index': 32}, {'from': 'P', 'to': 'T', 'var_index': 33}, {'from': 'Q', 'to': 'T', 'var_index': 34}, {'from': 'R', 'to': 'T', 'var_index': 35}, {'from': 'A', 'to': 'B', 'var_index': 36}, {'from': 'B', 'to': 'C', 'var_index': 37}, {'from': 'C', 'to': 'D', 'var_index': 38}, {'from': 'D', 'to': 'E', 'var_index': 39}, {'from': 'E', 'to': 'F', 'var_index': 40}, {'from': 'F', 'to': 'G', 'var_index': 41}, {'from': 'G', 'to': 'H', 'var_index': 42}, {'from': 'H', 'to': 'I', 'var_index': 43}, {'from': 'I', 'to': 'J', 'var_index': 44}, {'from': 'J', 'to': 'K', 'var_index': 45}, {'from': 'K', 'to': 'L', 'var_index': 46}, {'from': 'L', 'to': 'M', 'var_index': 47}, {'from': 'M', 'to': 'N', 'var_index': 48}, {'from': 'N', 'to': 'O', 'var_index': 49}, {'from': 'O', 'to': 'P', 'var_index': 50}, {'from': 'P', 'to': 'Q', 'var_index': 51}, {'from': 'Q', 'to': 'R', 'var_index': 52}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T'}}","['S', 'A', 'T']",34,csv,names
QSPP,QSPP,"Someone on the team needs to commit to one specific path a user would take from the landing page to checkout — no branching, no skipping, just one continuous set of clicks following the site’s links. Each click has a baseline cost in friction, and when certain clicks are combined the pair can cause additional losses (order can matter, and some clicks even carry an extra standalone penalty). The idea is to pick the one route that ends up with the least total friction by summing all individual frictions and any extra pairwise hits. The chosen route must begin at landing, end at checkout, only follow existing links in sequence, and the actual page map and cost numbers appear below.

{
  ""total_pages"": 18,
  ""total_links"": 17,
  ""page_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9,
    10,
    11,
    12,
    13,
    14,
    15,
    16,
    17
  ],
  ""landing_page"": 16,
  ""checkout_page"": 17,
  ""edges"": [
    {
      ""link_from_page"": 16,
      ""link_to_page"": 0,
      ""link_identifier"": 0
    },
    {
      ""link_from_page"": 15,
      ""link_to_page"": 17,
      ""link_identifier"": 1
    },
    {
      ""link_from_page"": 0,
      ""link_to_page"": 1,
      ""link_identifier"": 2
    },
    {
      ""link_from_page"": 1,
      ""link_to_page"": 2,
      ""link_identifier"": 3
    },
    {
      ""link_from_page"": 2,
      ""link_to_page"": 3,
      ""link_identifier"": 4
    },
    {
      ""link_from_page"": 3,
      ""link_to_page"": 4,
      ""link_identifier"": 5
    },
    {
      ""link_from_page"": 4,
      ""link_to_page"": 5,
      ""link_identifier"": 6
    },
    {
      ""link_from_page"": 5,
      ""link_to_page"": 6,
      ""link_identifier"": 7
    },
    {
      ""link_from_page"": 6,
      ""link_to_page"": 7,
      ""link_identifier"": 8
    },
    {
      ""link_from_page"": 7,
      ""link_to_page"": 8,
      ""link_identifier"": 9
    },
    {
      ""link_from_page"": 8,
      ""link_to_page"": 9,
      ""link_identifier"": 10
    },
    {
      ""link_from_page"": 9,
      ""link_to_page"": 10,
      ""link_identifier"": 11
    },
    {
      ""link_from_page"": 10,
      ""link_to_page"": 11,
      ""link_identifier"": 12
    },
    {
      ""link_from_page"": 11,
      ""link_to_page"": 12,
      ""link_identifier"": 13
    },
    {
      ""link_from_page"": 12,
      ""link_to_page"": 13,
      ""link_identifier"": 14
    },
    {
      ""link_from_page"": 13,
      ""link_to_page"": 14,
      ""link_identifier"": 15
    },
    {
      ""link_from_page"": 14,
      ""link_to_page"": 15,
      ""link_identifier"": 16
    }
  ],
  ""linear_costs"": [
    {
      ""link_id_for_cost"": 0,
      ""click_friction"": 3.0
    },
    {
      ""link_id_for_cost"": 1,
      ""click_friction"": 2.0
    },
    {
      ""link_id_for_cost"": 2,
      ""click_friction"": 6.0
    },
    {
      ""link_id_for_cost"": 3,
      ""click_friction"": 1.0
    },
    {
      ""link_id_for_cost"": 4,
      ""click_friction"": 9.0
    },
    {
      ""link_id_for_cost"": 5,
      ""click_friction"": 8.0
    },
    {
      ""link_id_for_cost"": 6,
      ""click_friction"": 7.0
    },
    {
      ""link_id_for_cost"": 7,
      ""click_friction"": 1.0
    },
    {
      ""link_id_for_cost"": 8,
      ""click_friction"": 10.0
    },
    {
      ""link_id_for_cost"": 9,
      ""click_friction"": 10.0
    },
    {
      ""link_id_for_cost"": 10,
      ""click_friction"": 10.0
    },
    {
      ""link_id_for_cost"": 11,
      ""click_friction"": 9.0
    },
    {
      ""link_id_for_cost"": 12,
      ""click_friction"": 7.0
    },
    {
      ""link_id_for_cost"": 13,
      ""click_friction"": 9.0
    },
    {
      ""link_id_for_cost"": 14,
      ""click_friction"": 4.0
    },
    {
      ""link_id_for_cost"": 15,
      ""click_friction"": 10.0
    },
    {
      ""link_id_for_cost"": 16,
      ""click_friction"": 10.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_link_in_pair, second_link_in_pair). If two link_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_link_in_pair\second_link_in_pair | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 9.0 | 3.0 | 8.0 | 6.0 | 8.0 | 2.0 | 8.0 | 7.0 | 7.0 | 8.0 | 8.0 | 7.0 | 3.0 | 5.0 | 6.0 | 4.0 |
| 1 | 9.0 | 1.0 | 2.0 | 9.0 | 7.0 | 10.0 | 4.0 | 3.0 | 5.0 | 10.0 | 9.0 | 7.0 | 9.0 | 9.0 | 4.0 | 5.0 | 9.0 |
| 2 | 3.0 | 2.0 | 5.0 | 10.0 | 4.0 | 7.0 | 2.0 | 1.0 | 3.0 | 8.0 | 7.0 | 3.0 | 1.0 | 10.0 | 7.0 | 10.0 | 10.0 |
| 3 | 8.0 | 9.0 | 10.0 | 7.0 | 3.0 | 6.0 | 7.0 | 10.0 | 5.0 | 4.0 | 10.0 | 10.0 | 7.0 | 2.0 | 3.0 | 1.0 | 2.0 |
| 4 | 6.0 | 7.0 | 4.0 | 3.0 | 8.0 | 1.0 | 1.0 | 7.0 | 5.0 | 7.0 | 5.0 | 2.0 | 4.0 | 8.0 | 8.0 | 7.0 | 5.0 |
| 5 | 8.0 | 10.0 | 7.0 | 6.0 | 1.0 | 9.0 | 9.0 | 7.0 | 10.0 | 6.0 | 1.0 | 9.0 | 1.0 | 7.0 | 5.0 | 8.0 | 4.0 |
| 6 | 2.0 | 4.0 | 2.0 | 7.0 | 1.0 | 9.0 | 7.0 | 5.0 | 7.0 | 6.0 | 2.0 | 8.0 | 8.0 | 8.0 | 2.0 | 2.0 | 7.0 |
| 7 | 8.0 | 3.0 | 1.0 | 10.0 | 7.0 | 7.0 | 5.0 | 7.0 | 8.0 | 2.0 | 9.0 | 6.0 | 6.0 | 4.0 | 4.0 | 6.0 | 4.0 |
| 8 | 7.0 | 5.0 | 3.0 | 5.0 | 5.0 | 10.0 | 7.0 | 8.0 | 2.0 | 1.0 | 6.0 | 4.0 | 1.0 | 4.0 | 6.0 | 6.0 | 4.0 |
| 9 | 7.0 | 10.0 | 8.0 | 4.0 | 7.0 | 6.0 | 6.0 | 2.0 | 1.0 | 2.0 | 8.0 | 10.0 | 1.0 | 5.0 | 4.0 | 8.0 | 10.0 |
| 10 | 8.0 | 9.0 | 7.0 | 10.0 | 5.0 | 1.0 | 2.0 | 9.0 | 6.0 | 8.0 | 5.0 | 10.0 | 6.0 | 8.0 | 2.0 | 1.0 | 5.0 |
| 11 | 8.0 | 7.0 | 3.0 | 10.0 | 2.0 | 9.0 | 8.0 | 6.0 | 4.0 | 10.0 | 10.0 | 7.0 | 2.0 | 3.0 | 3.0 | 9.0 | 2.0 |
| 12 | 7.0 | 9.0 | 1.0 | 7.0 | 4.0 | 1.0 | 8.0 | 6.0 | 1.0 | 1.0 | 6.0 | 2.0 | 1.0 | 2.0 | 7.0 | 5.0 | 4.0 |
| 13 | 3.0 | 9.0 | 10.0 | 2.0 | 8.0 | 7.0 | 8.0 | 4.0 | 4.0 | 5.0 | 8.0 | 3.0 | 2.0 | 3.0 | 9.0 | 9.0 | 7.0 |
| 14 | 5.0 | 4.0 | 7.0 | 3.0 | 8.0 | 5.0 | 2.0 | 4.0 | 6.0 | 4.0 | 2.0 | 3.0 | 7.0 | 9.0 | 7.0 | 5.0 | 7.0 |
| 15 | 6.0 | 5.0 | 10.0 | 1.0 | 7.0 | 8.0 | 2.0 | 6.0 | 6.0 | 8.0 | 1.0 | 9.0 | 5.0 | 9.0 | 5.0 | 4.0 | 2.0 |
| 16 | 4.0 | 9.0 | 10.0 | 2.0 | 5.0 | 4.0 | 7.0 | 4.0 | 4.0 | 10.0 | 5.0 | 2.0 | 4.0 | 7.0 | 7.0 | 2.0 | 6.0 |

Also, when you send back the specific route you picked, please put it in a tiny JSON snippet so it's easy to read and machine-friendly. Just drop the sequence of page NODE names into the solution array, like this:

{
  ""solution"": []
}

The idea: ""solution"" should be the ordered list of pages (node identifiers) from the landing page to checkout — just the page names in order, nothing else. Treat the JSON above like a simple form: solution = [first page, next page, ..., checkout]. This is just a sketch of the shape I expect, not the actual answer.

One more thing — use the exact identifiers as they appear in the instance input. Do not rename them or invent new labels. Valid identifiers look like:
- plain numbers such as ""1"" or ""23""
- single capital letters like ""A"" or ""B""
- a capital letter followed by digits like ""A1"" or ""X7""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 15, 'to': 17, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [3.0, 2.0, 6.0, 1.0, 9.0, 8.0, 7.0, 1.0, 10.0, 10.0, 10.0, 9.0, 7.0, 9.0, 4.0, 10.0, 10.0], 'quadratic': [[7.0, 9.0, 3.0, 8.0, 6.0, 8.0, 2.0, 8.0, 7.0, 7.0, 8.0, 8.0, 7.0, 3.0, 5.0, 6.0, 4.0], [9.0, 1.0, 2.0, 9.0, 7.0, 10.0, 4.0, 3.0, 5.0, 10.0, 9.0, 7.0, 9.0, 9.0, 4.0, 5.0, 9.0], [3.0, 2.0, 5.0, 10.0, 4.0, 7.0, 2.0, 1.0, 3.0, 8.0, 7.0, 3.0, 1.0, 10.0, 7.0, 10.0, 10.0], [8.0, 9.0, 10.0, 7.0, 3.0, 6.0, 7.0, 10.0, 5.0, 4.0, 10.0, 10.0, 7.0, 2.0, 3.0, 1.0, 2.0], [6.0, 7.0, 4.0, 3.0, 8.0, 1.0, 1.0, 7.0, 5.0, 7.0, 5.0, 2.0, 4.0, 8.0, 8.0, 7.0, 5.0], [8.0, 10.0, 7.0, 6.0, 1.0, 9.0, 9.0, 7.0, 10.0, 6.0, 1.0, 9.0, 1.0, 7.0, 5.0, 8.0, 4.0], [2.0, 4.0, 2.0, 7.0, 1.0, 9.0, 7.0, 5.0, 7.0, 6.0, 2.0, 8.0, 8.0, 8.0, 2.0, 2.0, 7.0], [8.0, 3.0, 1.0, 10.0, 7.0, 7.0, 5.0, 7.0, 8.0, 2.0, 9.0, 6.0, 6.0, 4.0, 4.0, 6.0, 4.0], [7.0, 5.0, 3.0, 5.0, 5.0, 10.0, 7.0, 8.0, 2.0, 1.0, 6.0, 4.0, 1.0, 4.0, 6.0, 6.0, 4.0], [7.0, 10.0, 8.0, 4.0, 7.0, 6.0, 6.0, 2.0, 1.0, 2.0, 8.0, 10.0, 1.0, 5.0, 4.0, 8.0, 10.0], [8.0, 9.0, 7.0, 10.0, 5.0, 1.0, 2.0, 9.0, 6.0, 8.0, 5.0, 10.0, 6.0, 8.0, 2.0, 1.0, 5.0], [8.0, 7.0, 3.0, 10.0, 2.0, 9.0, 8.0, 6.0, 4.0, 10.0, 10.0, 7.0, 2.0, 3.0, 3.0, 9.0, 2.0], [7.0, 9.0, 1.0, 7.0, 4.0, 1.0, 8.0, 6.0, 1.0, 1.0, 6.0, 2.0, 1.0, 2.0, 7.0, 5.0, 4.0], [3.0, 9.0, 10.0, 2.0, 8.0, 7.0, 8.0, 4.0, 4.0, 5.0, 8.0, 3.0, 2.0, 3.0, 9.0, 9.0, 7.0], [5.0, 4.0, 7.0, 3.0, 8.0, 5.0, 2.0, 4.0, 6.0, 4.0, 2.0, 3.0, 7.0, 9.0, 7.0, 5.0, 7.0], [6.0, 5.0, 10.0, 1.0, 7.0, 8.0, 2.0, 6.0, 6.0, 8.0, 1.0, 9.0, 5.0, 9.0, 5.0, 4.0, 2.0], [4.0, 9.0, 10.0, 2.0, 5.0, 4.0, 7.0, 4.0, 4.0, 10.0, 5.0, 2.0, 4.0, 7.0, 7.0, 2.0, 6.0]]}, 'source': 16, 'target': 17}","[16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17]",1746.0,"{'problem_type': 'QSPP', 'num_nodes': 18, 'num_edges': 17, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'source': 16, 'target': 17, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 8.0}, {'var_index': 6, 'linear_cost': 7.0}, {'var_index': 7, 'linear_cost': 1.0}, {'var_index': 8, 'linear_cost': 10.0}, {'var_index': 9, 'linear_cost': 10.0}, {'var_index': 10, 'linear_cost': 10.0}, {'var_index': 11, 'linear_cost': 9.0}, {'var_index': 12, 'linear_cost': 7.0}, {'var_index': 13, 'linear_cost': 9.0}, {'var_index': 14, 'linear_cost': 4.0}, {'var_index': 15, 'linear_cost': 10.0}, {'var_index': 16, 'linear_cost': 10.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 3, 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{'var_i': 12, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 16, 'to': 0, 'var_index': 0}, {'from': 15, 'to': 17, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9, 10: 10, 11: 11, 12: 12, 13: 13, 14: 14, 15: 15, 16: 16, 17: 17}}","[16, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17]",35,json,0
QSPP,QSPP,"We’re planning a one-way path through a line of machines: from the starting station to the final assembly, following only the allowed connections. Every machine-to-machine move has a base operating cost, and certain combinations of moves add extra combined setup costs whenever both moves are used (and some moves carry an additional standalone setup). The task is to pick one continuous sequence of moves so that, when summing all the individual move costs and all the extra combination costs that apply, the overall expense is as low as it can be. The chosen path must be a single coherent route beginning at the start and ending at the finish, using only valid forward steps. The concrete details are listed below.

Concretely, we have 23 stations and 38 allowed moves; the stations are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, the start station is 22, and the final assembly station is 23.

| move_from_station | move_to_station | move_id |
|---|---|---|
| 22 | 1 | 0 |
| 22 | 8 | 1 |
| 22 | 15 | 2 |
| 7 | 23 | 3 |
| 14 | 23 | 4 |
| 21 | 23 | 5 |
| 1 | 2 | 6 |
| 1 | 8 | 7 |
| 2 | 3 | 8 |
| 2 | 9 | 9 |
| 3 | 4 | 10 |
| 3 | 10 | 11 |
| 4 | 5 | 12 |
| 4 | 11 | 13 |
| 5 | 6 | 14 |
| 5 | 12 | 15 |
| 6 | 7 | 16 |
| 6 | 13 | 17 |
| 7 | 14 | 18 |
| 8 | 9 | 19 |
| 8 | 15 | 20 |
| 9 | 10 | 21 |
| 9 | 16 | 22 |
| 10 | 11 | 23 |
| 10 | 17 | 24 |
| 11 | 12 | 25 |
| 11 | 18 | 26 |
| 12 | 13 | 27 |
| 12 | 19 | 28 |
| 13 | 14 | 29 |
| 13 | 20 | 30 |
| 14 | 21 | 31 |
| 15 | 16 | 32 |
| 16 | 17 | 33 |
| 17 | 18 | 34 |
| 18 | 19 | 35 |
| 19 | 20 | 36 |
| 20 | 21 | 37 |

| move_id | operating_cost |
|---|---|
| 0 | 4.0 |
| 1 | 6.0 |
| 2 | 1.0 |
| 3 | 9.0 |
| 4 | 8.0 |
| 5 | 1.0 |
| 6 | 1.0 |
| 7 | 4.0 |
| 8 | 8.0 |
| 9 | 7.0 |
| 10 | 8.0 |
| 11 | 1.0 |
| 12 | 1.0 |
| 13 | 5.0 |
| 14 | 10.0 |
| 15 | 3.0 |
| 16 | 2.0 |
| 17 | 2.0 |
| 18 | 5.0 |
| 19 | 7.0 |
| 20 | 3.0 |
| 21 | 5.0 |
| 22 | 7.0 |
| 23 | 9.0 |
| 24 | 6.0 |
| 25 | 3.0 |
| 26 | 5.0 |
| 27 | 1.0 |
| 28 | 10.0 |
| 29 | 10.0 |
| 30 | 9.0 |
| 31 | 8.0 |
| 32 | 9.0 |
| 33 | 5.0 |
| 34 | 4.0 |
| 35 | 10.0 |
| 36 | 3.0 |
| 37 | 3.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (move_i_id, move_j_id). If two moves with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| move_i_id\move_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 6.0 | 5.0 | 6.0 | 5.0 | 6.0 | 5.0 | 10.0 | 6.0 | 3.0 | 5.0 | 9.0 | 1.0 | 2.0 | 8.0 | 5.0 | 7.0 | 8.0 | 4.0 | 6.0 | 10.0 | 3.0 | 4.0 | 7.0 | 4.0 | 3.0 | 1.0 | 4.0 | 8.0 | 1.0 | 3.0 | 3.0 | 1.0 | 6.0 | 5.0 | 9.0 | 7.0 | 1.0 |
| 1 | 6.0 | 8.0 | 6.0 | 1.0 | 1.0 | 10.0 | 4.0 | 7.0 | 3.0 | 5.0 | 8.0 | 7.0 | 8.0 | 6.0 | 5.0 | 10.0 | 8.0 | 8.0 | 4.0 | 5.0 | 9.0 | 8.0 | 3.0 | 10.0 | 1.0 | 7.0 | 1.0 | 8.0 | 1.0 | 3.0 | 7.0 | 9.0 | 4.0 | 10.0 | 3.0 | 3.0 | 8.0 | 4.0 |
| 2 | 5.0 | 6.0 | 6.0 | 4.0 | 7.0 | 1.0 | 9.0 | 8.0 | 3.0 | 4.0 | 5.0 | 4.0 | 9.0 | 4.0 | 4.0 | 7.0 | 10.0 | 7.0 | 10.0 | 4.0 | 10.0 | 7.0 | 2.0 | 9.0 | 9.0 | 3.0 | 9.0 | 7.0 | 7.0 | 9.0 | 8.0 | 10.0 | 8.0 | 8.0 | 2.0 | 5.0 | 6.0 | 4.0 |
| 3 | 6.0 | 1.0 | 4.0 | 7.0 | 5.0 | 5.0 | 5.0 | 6.0 | 2.0 | 7.0 | 10.0 | 8.0 | 9.0 | 5.0 | 5.0 | 4.0 | 5.0 | 8.0 | 2.0 | 10.0 | 10.0 | 5.0 | 1.0 | 4.0 | 5.0 | 2.0 | 1.0 | 4.0 | 2.0 | 2.0 | 4.0 | 5.0 | 2.0 | 4.0 | 8.0 | 4.0 | 2.0 | 8.0 |
| 4 | 5.0 | 1.0 | 7.0 | 5.0 | 3.0 | 4.0 | 3.0 | 7.0 | 8.0 | 3.0 | 8.0 | 5.0 | 10.0 | 6.0 | 4.0 | 10.0 | 4.0 | 2.0 | 6.0 | 10.0 | 5.0 | 2.0 | 7.0 | 8.0 | 4.0 | 3.0 | 9.0 | 3.0 | 7.0 | 6.0 | 1.0 | 4.0 | 3.0 | 5.0 | 7.0 | 8.0 | 7.0 | 9.0 |
| 5 | 6.0 | 10.0 | 1.0 | 5.0 | 4.0 | 4.0 | 6.0 | 1.0 | 6.0 | 8.0 | 7.0 | 1.0 | 8.0 | 9.0 | 6.0 | 10.0 | 9.0 | 9.0 | 7.0 | 1.0 | 9.0 | 9.0 | 4.0 | 10.0 | 8.0 | 9.0 | 5.0 | 5.0 | 3.0 | 4.0 | 2.0 | 9.0 | 8.0 | 1.0 | 3.0 | 7.0 | 4.0 | 5.0 |
| 6 | 5.0 | 4.0 | 9.0 | 5.0 | 3.0 | 6.0 | 1.0 | 6.0 | 5.0 | 3.0 | 9.0 | 2.0 | 1.0 | 1.0 | 7.0 | 2.0 | 4.0 | 9.0 | 3.0 | 10.0 | 6.0 | 10.0 | 4.0 | 7.0 | 6.0 | 1.0 | 8.0 | 4.0 | 2.0 | 8.0 | 6.0 | 1.0 | 10.0 | 8.0 | 2.0 | 5.0 | 4.0 | 1.0 |
| 7 | 10.0 | 7.0 | 8.0 | 6.0 | 7.0 | 1.0 | 6.0 | 5.0 | 2.0 | 7.0 | 10.0 | 4.0 | 3.0 | 5.0 | 4.0 | 5.0 | 4.0 | 9.0 | 1.0 | 5.0 | 2.0 | 7.0 | 3.0 | 9.0 | 10.0 | 7.0 | 1.0 | 10.0 | 2.0 | 5.0 | 9.0 | 10.0 | 9.0 | 4.0 | 5.0 | 1.0 | 10.0 | 4.0 |
| 8 | 6.0 | 3.0 | 3.0 | 2.0 | 8.0 | 6.0 | 5.0 | 2.0 | 3.0 | 8.0 | 5.0 | 3.0 | 8.0 | 10.0 | 2.0 | 1.0 | 5.0 | 7.0 | 6.0 | 8.0 | 6.0 | 8.0 | 3.0 | 4.0 | 9.0 | 8.0 | 5.0 | 6.0 | 8.0 | 7.0 | 2.0 | 7.0 | 7.0 | 9.0 | 10.0 | 2.0 | 5.0 | 1.0 |
| 9 | 3.0 | 5.0 | 4.0 | 7.0 | 3.0 | 8.0 | 3.0 | 7.0 | 8.0 | 2.0 | 5.0 | 1.0 | 2.0 | 5.0 | 5.0 | 6.0 | 7.0 | 3.0 | 4.0 | 5.0 | 10.0 | 10.0 | 3.0 | 2.0 | 1.0 | 7.0 | 4.0 | 7.0 | 1.0 | 3.0 | 9.0 | 4.0 | 10.0 | 9.0 | 2.0 | 7.0 | 10.0 | 5.0 |
| 10 | 5.0 | 8.0 | 5.0 | 10.0 | 8.0 | 7.0 | 9.0 | 10.0 | 5.0 | 5.0 | 5.0 | 3.0 | 7.0 | 7.0 | 7.0 | 7.0 | 7.0 | 10.0 | 7.0 | 5.0 | 4.0 | 8.0 | 1.0 | 4.0 | 9.0 | 4.0 | 5.0 | 9.0 | 6.0 | 2.0 | 1.0 | 8.0 | 10.0 | 4.0 | 2.0 | 6.0 | 7.0 | 3.0 |
| 11 | 9.0 | 7.0 | 4.0 | 8.0 | 5.0 | 1.0 | 2.0 | 4.0 | 3.0 | 1.0 | 3.0 | 8.0 | 10.0 | 7.0 | 6.0 | 9.0 | 9.0 | 10.0 | 3.0 | 7.0 | 6.0 | 6.0 | 6.0 | 10.0 | 1.0 | 6.0 | 7.0 | 8.0 | 1.0 | 2.0 | 9.0 | 10.0 | 7.0 | 10.0 | 8.0 | 6.0 | 3.0 | 8.0 |
| 12 | 1.0 | 8.0 | 9.0 | 9.0 | 10.0 | 8.0 | 1.0 | 3.0 | 8.0 | 2.0 | 7.0 | 10.0 | 9.0 | 10.0 | 9.0 | 4.0 | 4.0 | 7.0 | 10.0 | 4.0 | 6.0 | 6.0 | 4.0 | 4.0 | 5.0 | 10.0 | 8.0 | 6.0 | 10.0 | 1.0 | 9.0 | 6.0 | 3.0 | 7.0 | 8.0 | 9.0 | 9.0 | 9.0 |
| 13 | 2.0 | 6.0 | 4.0 | 5.0 | 6.0 | 9.0 | 1.0 | 5.0 | 10.0 | 5.0 | 7.0 | 7.0 | 10.0 | 4.0 | 4.0 | 6.0 | 6.0 | 2.0 | 3.0 | 3.0 | 6.0 | 1.0 | 4.0 | 1.0 | 10.0 | 5.0 | 6.0 | 5.0 | 10.0 | 5.0 | 4.0 | 4.0 | 2.0 | 2.0 | 6.0 | 6.0 | 1.0 | 7.0 |
| 14 | 8.0 | 5.0 | 4.0 | 5.0 | 4.0 | 6.0 | 7.0 | 4.0 | 2.0 | 5.0 | 7.0 | 6.0 | 9.0 | 4.0 | 3.0 | 5.0 | 1.0 | 4.0 | 6.0 | 2.0 | 7.0 | 5.0 | 3.0 | 10.0 | 8.0 | 2.0 | 7.0 | 4.0 | 9.0 | 2.0 | 3.0 | 1.0 | 4.0 | 5.0 | 8.0 | 3.0 | 7.0 | 1.0 |
| 15 | 5.0 | 10.0 | 7.0 | 4.0 | 10.0 | 10.0 | 2.0 | 5.0 | 1.0 | 6.0 | 7.0 | 9.0 | 4.0 | 6.0 | 5.0 | 2.0 | 5.0 | 6.0 | 7.0 | 2.0 | 7.0 | 10.0 | 7.0 | 5.0 | 2.0 | 8.0 | 3.0 | 8.0 | 7.0 | 1.0 | 4.0 | 1.0 | 8.0 | 10.0 | 5.0 | 9.0 | 8.0 | 9.0 |
| 16 | 7.0 | 8.0 | 10.0 | 5.0 | 4.0 | 9.0 | 4.0 | 4.0 | 5.0 | 7.0 | 7.0 | 9.0 | 4.0 | 6.0 | 1.0 | 5.0 | 1.0 | 7.0 | 9.0 | 8.0 | 5.0 | 9.0 | 3.0 | 10.0 | 1.0 | 7.0 | 3.0 | 1.0 | 8.0 | 8.0 | 9.0 | 4.0 | 1.0 | 8.0 | 5.0 | 2.0 | 1.0 | 5.0 |
| 17 | 8.0 | 8.0 | 7.0 | 8.0 | 2.0 | 9.0 | 9.0 | 9.0 | 7.0 | 3.0 | 10.0 | 10.0 | 7.0 | 2.0 | 4.0 | 6.0 | 7.0 | 3.0 | 1.0 | 4.0 | 4.0 | 10.0 | 4.0 | 2.0 | 3.0 | 7.0 | 8.0 | 1.0 | 7.0 | 3.0 | 8.0 | 1.0 | 4.0 | 10.0 | 8.0 | 3.0 | 4.0 | 2.0 |
| 18 | 4.0 | 4.0 | 10.0 | 2.0 | 6.0 | 7.0 | 3.0 | 1.0 | 6.0 | 4.0 | 7.0 | 3.0 | 10.0 | 3.0 | 6.0 | 7.0 | 9.0 | 1.0 | 7.0 | 7.0 | 4.0 | 7.0 | 6.0 | 3.0 | 7.0 | 2.0 | 7.0 | 3.0 | 9.0 | 3.0 | 5.0 | 9.0 | 9.0 | 1.0 | 4.0 | 4.0 | 2.0 | 7.0 |
| 19 | 6.0 | 5.0 | 4.0 | 10.0 | 10.0 | 1.0 | 10.0 | 5.0 | 8.0 | 5.0 | 5.0 | 7.0 | 4.0 | 3.0 | 2.0 | 2.0 | 8.0 | 4.0 | 7.0 | 6.0 | 2.0 | 9.0 | 10.0 | 10.0 | 7.0 | 1.0 | 7.0 | 7.0 | 6.0 | 4.0 | 1.0 | 8.0 | 5.0 | 7.0 | 7.0 | 3.0 | 9.0 | 9.0 |
| 20 | 10.0 | 9.0 | 10.0 | 10.0 | 5.0 | 9.0 | 6.0 | 2.0 | 6.0 | 10.0 | 4.0 | 6.0 | 6.0 | 6.0 | 7.0 | 7.0 | 5.0 | 4.0 | 4.0 | 2.0 | 6.0 | 7.0 | 2.0 | 8.0 | 4.0 | 10.0 | 10.0 | 2.0 | 6.0 | 4.0 | 9.0 | 9.0 | 1.0 | 4.0 | 10.0 | 9.0 | 10.0 | 2.0 |
| 21 | 3.0 | 8.0 | 7.0 | 5.0 | 2.0 | 9.0 | 10.0 | 7.0 | 8.0 | 10.0 | 8.0 | 6.0 | 6.0 | 1.0 | 5.0 | 10.0 | 9.0 | 10.0 | 7.0 | 9.0 | 7.0 | 4.0 | 2.0 | 4.0 | 10.0 | 2.0 | 10.0 | 3.0 | 8.0 | 2.0 | 4.0 | 10.0 | 6.0 | 4.0 | 8.0 | 5.0 | 6.0 | 1.0 |
| 22 | 4.0 | 3.0 | 2.0 | 1.0 | 7.0 | 4.0 | 4.0 | 3.0 | 3.0 | 3.0 | 1.0 | 6.0 | 4.0 | 4.0 | 3.0 | 7.0 | 3.0 | 4.0 | 6.0 | 10.0 | 2.0 | 2.0 | 5.0 | 5.0 | 6.0 | 4.0 | 10.0 | 6.0 | 7.0 | 7.0 | 1.0 | 7.0 | 4.0 | 10.0 | 8.0 | 3.0 | 10.0 | 7.0 |
| 23 | 7.0 | 10.0 | 9.0 | 4.0 | 8.0 | 10.0 | 7.0 | 9.0 | 4.0 | 2.0 | 4.0 | 10.0 | 4.0 | 1.0 | 10.0 | 5.0 | 10.0 | 2.0 | 3.0 | 10.0 | 8.0 | 4.0 | 5.0 | 8.0 | 2.0 | 6.0 | 7.0 | 10.0 | 1.0 | 7.0 | 10.0 | 7.0 | 10.0 | 9.0 | 4.0 | 9.0 | 8.0 | 8.0 |
| 24 | 4.0 | 1.0 | 9.0 | 5.0 | 4.0 | 8.0 | 6.0 | 10.0 | 9.0 | 1.0 | 9.0 | 1.0 | 5.0 | 10.0 | 8.0 | 2.0 | 1.0 | 3.0 | 7.0 | 7.0 | 4.0 | 10.0 | 6.0 | 2.0 | 7.0 | 4.0 | 5.0 | 8.0 | 10.0 | 3.0 | 3.0 | 2.0 | 10.0 | 8.0 | 4.0 | 8.0 | 4.0 | 9.0 |
| 25 | 3.0 | 7.0 | 3.0 | 2.0 | 3.0 | 9.0 | 1.0 | 7.0 | 8.0 | 7.0 | 4.0 | 6.0 | 10.0 | 5.0 | 2.0 | 8.0 | 7.0 | 7.0 | 2.0 | 1.0 | 10.0 | 2.0 | 4.0 | 6.0 | 4.0 | 3.0 | 4.0 | 7.0 | 10.0 | 8.0 | 7.0 | 3.0 | 6.0 | 2.0 | 1.0 | 7.0 | 4.0 | 7.0 |
| 26 | 1.0 | 1.0 | 9.0 | 1.0 | 9.0 | 5.0 | 8.0 | 1.0 | 5.0 | 4.0 | 5.0 | 7.0 | 8.0 | 6.0 | 7.0 | 3.0 | 3.0 | 8.0 | 7.0 | 7.0 | 10.0 | 10.0 | 10.0 | 7.0 | 5.0 | 4.0 | 7.0 | 7.0 | 7.0 | 8.0 | 9.0 | 6.0 | 2.0 | 10.0 | 4.0 | 2.0 | 8.0 | 9.0 |
| 27 | 4.0 | 8.0 | 7.0 | 4.0 | 3.0 | 5.0 | 4.0 | 10.0 | 6.0 | 7.0 | 9.0 | 8.0 | 6.0 | 5.0 | 4.0 | 8.0 | 1.0 | 1.0 | 3.0 | 7.0 | 2.0 | 3.0 | 6.0 | 10.0 | 8.0 | 7.0 | 7.0 | 9.0 | 8.0 | 4.0 | 3.0 | 4.0 | 5.0 | 6.0 | 2.0 | 9.0 | 3.0 | 5.0 |
| 28 | 8.0 | 1.0 | 7.0 | 2.0 | 7.0 | 3.0 | 2.0 | 2.0 | 8.0 | 1.0 | 6.0 | 1.0 | 10.0 | 10.0 | 9.0 | 7.0 | 8.0 | 7.0 | 9.0 | 6.0 | 6.0 | 8.0 | 7.0 | 1.0 | 10.0 | 10.0 | 7.0 | 8.0 | 5.0 | 2.0 | 3.0 | 10.0 | 4.0 | 9.0 | 7.0 | 1.0 | 9.0 | 7.0 |
| 29 | 1.0 | 3.0 | 9.0 | 2.0 | 6.0 | 4.0 | 8.0 | 5.0 | 7.0 | 3.0 | 2.0 | 2.0 | 1.0 | 5.0 | 2.0 | 1.0 | 8.0 | 3.0 | 3.0 | 4.0 | 4.0 | 2.0 | 7.0 | 7.0 | 3.0 | 8.0 | 8.0 | 4.0 | 2.0 | 1.0 | 6.0 | 8.0 | 2.0 | 3.0 | 9.0 | 4.0 | 5.0 | 4.0 |
| 30 | 3.0 | 7.0 | 8.0 | 4.0 | 1.0 | 2.0 | 6.0 | 9.0 | 2.0 | 9.0 | 1.0 | 9.0 | 9.0 | 4.0 | 3.0 | 4.0 | 9.0 | 8.0 | 5.0 | 1.0 | 9.0 | 4.0 | 1.0 | 10.0 | 3.0 | 7.0 | 9.0 | 3.0 | 3.0 | 6.0 | 7.0 | 4.0 | 1.0 | 3.0 | 9.0 | 4.0 | 10.0 | 9.0 |
| 31 | 3.0 | 9.0 | 10.0 | 5.0 | 4.0 | 9.0 | 1.0 | 10.0 | 7.0 | 4.0 | 8.0 | 10.0 | 6.0 | 4.0 | 1.0 | 1.0 | 4.0 | 1.0 | 9.0 | 8.0 | 9.0 | 10.0 | 7.0 | 7.0 | 2.0 | 3.0 | 6.0 | 4.0 | 10.0 | 8.0 | 4.0 | 2.0 | 10.0 | 9.0 | 1.0 | 8.0 | 1.0 | 8.0 |
| 32 | 1.0 | 4.0 | 8.0 | 2.0 | 3.0 | 8.0 | 10.0 | 9.0 | 7.0 | 10.0 | 10.0 | 7.0 | 3.0 | 2.0 | 4.0 | 8.0 | 1.0 | 4.0 | 9.0 | 5.0 | 1.0 | 6.0 | 4.0 | 10.0 | 10.0 | 6.0 | 2.0 | 5.0 | 4.0 | 2.0 | 1.0 | 10.0 | 8.0 | 2.0 | 3.0 | 8.0 | 9.0 | 2.0 |
| 33 | 6.0 | 10.0 | 8.0 | 4.0 | 5.0 | 1.0 | 8.0 | 4.0 | 9.0 | 9.0 | 4.0 | 10.0 | 7.0 | 2.0 | 5.0 | 10.0 | 8.0 | 10.0 | 1.0 | 7.0 | 4.0 | 4.0 | 10.0 | 9.0 | 8.0 | 2.0 | 10.0 | 6.0 | 9.0 | 3.0 | 3.0 | 9.0 | 2.0 | 2.0 | 8.0 | 7.0 | 7.0 | 2.0 |
| 34 | 5.0 | 3.0 | 2.0 | 8.0 | 7.0 | 3.0 | 2.0 | 5.0 | 10.0 | 2.0 | 2.0 | 8.0 | 8.0 | 6.0 | 8.0 | 5.0 | 5.0 | 8.0 | 4.0 | 7.0 | 10.0 | 8.0 | 8.0 | 4.0 | 4.0 | 1.0 | 4.0 | 2.0 | 7.0 | 9.0 | 9.0 | 1.0 | 3.0 | 8.0 | 8.0 | 2.0 | 1.0 | 8.0 |
| 35 | 9.0 | 3.0 | 5.0 | 4.0 | 8.0 | 7.0 | 5.0 | 1.0 | 2.0 | 7.0 | 6.0 | 6.0 | 9.0 | 6.0 | 3.0 | 9.0 | 2.0 | 3.0 | 4.0 | 3.0 | 9.0 | 5.0 | 3.0 | 9.0 | 8.0 | 7.0 | 2.0 | 9.0 | 1.0 | 4.0 | 4.0 | 8.0 | 8.0 | 7.0 | 2.0 | 9.0 | 2.0 | 1.0 |
| 36 | 7.0 | 8.0 | 6.0 | 2.0 | 7.0 | 4.0 | 4.0 | 10.0 | 5.0 | 10.0 | 7.0 | 3.0 | 9.0 | 1.0 | 7.0 | 8.0 | 1.0 | 4.0 | 2.0 | 9.0 | 10.0 | 6.0 | 10.0 | 8.0 | 4.0 | 4.0 | 8.0 | 3.0 | 9.0 | 5.0 | 10.0 | 1.0 | 9.0 | 7.0 | 1.0 | 2.0 | 3.0 | 2.0 |
| 37 | 1.0 | 4.0 | 4.0 | 8.0 | 9.0 | 5.0 | 1.0 | 4.0 | 1.0 | 5.0 | 3.0 | 8.0 | 9.0 | 7.0 | 1.0 | 9.0 | 5.0 | 2.0 | 7.0 | 9.0 | 2.0 | 1.0 | 7.0 | 8.0 | 9.0 | 7.0 | 9.0 | 5.0 | 7.0 | 4.0 | 9.0 | 8.0 | 2.0 | 2.0 | 8.0 | 1.0 | 2.0 | 5.0 |

We’ll select the single coherent route from 22 to 23 that minimizes the sum of all operating and setup costs.

Also, when you send back the chosen route, just stick it into a tiny JSON object so it's easy to parse — something like this:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the nodes in order: start node first, finish node last, and every step in between must follow a valid forward connection. This JSON is only a sketch of the shape I expect you to follow — in your final reply replace the empty array with the actual sequence of node identifiers for the path.

Please use the identifiers exactly as they appear in the instance input — no renaming and no new labels.
""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], 'edges': [{'from': 21, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 7, 'var_index': 1}, {'from': 21, 'to': 14, 'var_index': 2}, {'from': 6, 'to': 22, 'var_index': 3}, {'from': 13, 'to': 22, 'var_index': 4}, {'from': 20, 'to': 22, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 0, 'to': 7, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 8, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 9, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 10, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 11, 'var_index': 15}, {'from': 5, 'to': 6, 'var_index': 16}, {'from': 5, 'to': 12, 'var_index': 17}, {'from': 6, 'to': 13, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 14, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 15, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 16, 'var_index': 24}, {'from': 10, 'to': 11, 'var_index': 25}, {'from': 10, 'to': 17, 'var_index': 26}, {'from': 11, 'to': 12, 'var_index': 27}, {'from': 11, 'to': 18, 'var_index': 28}, {'from': 12, 'to': 13, 'var_index': 29}, {'from': 12, 'to': 19, 'var_index': 30}, {'from': 13, 'to': 20, 'var_index': 31}, {'from': 14, 'to': 15, 'var_index': 32}, {'from': 15, 'to': 16, 'var_index': 33}, {'from': 16, 'to': 17, 'var_index': 34}, {'from': 17, 'to': 18, 'var_index': 35}, {'from': 18, 'to': 19, 'var_index': 36}, {'from': 19, 'to': 20, 'var_index': 37}], 'objective': {'constant': 0.0, 'linear': [4.0, 6.0, 1.0, 9.0, 8.0, 1.0, 1.0, 4.0, 8.0, 7.0, 8.0, 1.0, 1.0, 5.0, 10.0, 3.0, 2.0, 2.0, 5.0, 7.0, 3.0, 5.0, 7.0, 9.0, 6.0, 3.0, 5.0, 1.0, 10.0, 10.0, 9.0, 8.0, 9.0, 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10.0}, {'var_i': 36, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 25, 'quadratic_cost': 4.0}, {'var_i': 36, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 36, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 29, 'quadratic_cost': 5.0}, {'var_i': 36, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 36, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 32, 'quadratic_cost': 9.0}, {'var_i': 36, 'var_j': 33, 'quadratic_cost': 7.0}, {'var_i': 36, 'var_j': 34, 'quadratic_cost': 1.0}, {'var_i': 36, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 36, 'var_j': 36, 'quadratic_cost': 3.0}, {'var_i': 36, 'var_j': 37, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 37, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 24, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 37, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 37, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 37, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 37, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 33, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 34, 'quadratic_cost': 8.0}, {'var_i': 37, 'var_j': 35, 'quadratic_cost': 1.0}, {'var_i': 37, 'var_j': 36, 'quadratic_cost': 2.0}, {'var_i': 37, 'var_j': 37, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 22, 'to': 1, 'var_index': 0}, {'from': 22, 'to': 8, 'var_index': 1}, {'from': 22, 'to': 15, 'var_index': 2}, {'from': 7, 'to': 23, 'var_index': 3}, {'from': 14, 'to': 23, 'var_index': 4}, {'from': 21, 'to': 23, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 8, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 9, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 10, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 11, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 12, 'var_index': 15}, {'from': 6, 'to': 7, 'var_index': 16}, {'from': 6, 'to': 13, 'var_index': 17}, {'from': 7, 'to': 14, 'var_index': 18}, {'from': 8, 'to': 9, 'var_index': 19}, {'from': 8, 'to': 15, 'var_index': 20}, {'from': 9, 'to': 10, 'var_index': 21}, {'from': 9, 'to': 16, 'var_index': 22}, {'from': 10, 'to': 11, 'var_index': 23}, {'from': 10, 'to': 17, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 11, 'to': 18, 'var_index': 26}, {'from': 12, 'to': 13, 'var_index': 27}, {'from': 12, 'to': 19, 'var_index': 28}, {'from': 13, 'to': 14, 'var_index': 29}, {'from': 13, 'to': 20, 'var_index': 30}, {'from': 14, 'to': 21, 'var_index': 31}, {'from': 15, 'to': 16, 'var_index': 32}, {'from': 16, 'to': 17, 'var_index': 33}, {'from': 17, 'to': 18, 'var_index': 34}, {'from': 18, 'to': 19, 'var_index': 35}, {'from': 19, 'to': 20, 'var_index': 36}, {'from': 20, 'to': 21, 'var_index': 37}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23}}","[22, 15, 16, 17, 18, 19, 20, 21, 23]",36,markdown_table,1
QSPP,QSPP,"Someone in dispatch needs a single, clean routing: a continuous sequence of controlled corridors from the departure fix to the arrival fix, following the assigned directions on each corridor. Each corridor costs a bit of fuel, and certain combinations of two corridors together rack up additional penalties, so the plan’s score is just the sum of all those per-leg costs plus any pairwise penalties caused by legs flown together. The aim is to pick the one route that ends up with the lowest total cost, and the route must start at the departure fix, end at the arrival fix, and be made up of connected, directionally allowed legs — listed only as the fixes in order. The full details and numbers are shown below.

# num_fixes=21
# num_corridors=20
# fixes_list=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
# departure_fix=20
# arrival_fix=21

corridor_from_fix,corridor_to_fix,corridor_leg_id
20,1,0
19,21,1
1,2,2
2,3,3
3,4,4
4,5,5
5,6,6
6,7,7
7,8,8
8,9,9
9,10,10
10,11,11
11,12,12
12,13,13
13,14,14
14,15,15
15,16,16
16,17,17
17,18,18
18,19,19

corridor_leg_id,fuel_penalty_per_leg
0,6.0
1,9.0
2,8.0
3,1.0
4,6.0
5,2.0
6,2.0
7,9.0
8,4.0
9,9.0
10,4.0
11,9.0
12,4.0
13,2.0
14,1.0
15,4.0
16,2.0
17,10.0
18,8.0
19,6.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_leg_i_id, corridor_leg_j_id). If two corridor_legs with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_leg_i_id\corridor_leg_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 1.0 | 8.0 | 4.0 | 2.0 | 4.0 | 2.0 | 5.0 | 5.0 | 7.0 | 9.0 | 6.0 | 7.0 | 8.0 | 10.0 | 9.0 | 3.0 | 5.0 | 1.0 | 1.0 |
| 1 | 1.0 | 6.0 | 8.0 | 10.0 | 7.0 | 10.0 | 4.0 | 6.0 | 4.0 | 7.0 | 3.0 | 5.0 | 1.0 | 10.0 | 2.0 | 9.0 | 3.0 | 5.0 | 10.0 | 2.0 |
| 2 | 8.0 | 8.0 | 4.0 | 9.0 | 5.0 | 5.0 | 6.0 | 6.0 | 7.0 | 9.0 | 2.0 | 3.0 | 2.0 | 8.0 | 2.0 | 2.0 | 3.0 | 7.0 | 3.0 | 1.0 |
| 3 | 4.0 | 10.0 | 9.0 | 10.0 | 5.0 | 7.0 | 1.0 | 6.0 | 9.0 | 1.0 | 3.0 | 9.0 | 6.0 | 4.0 | 8.0 | 1.0 | 6.0 | 9.0 | 2.0 | 10.0 |
| 4 | 2.0 | 7.0 | 5.0 | 5.0 | 9.0 | 2.0 | 8.0 | 6.0 | 5.0 | 2.0 | 7.0 | 7.0 | 4.0 | 6.0 | 5.0 | 5.0 | 10.0 | 5.0 | 2.0 | 8.0 |
| 5 | 4.0 | 10.0 | 5.0 | 7.0 | 2.0 | 7.0 | 7.0 | 5.0 | 8.0 | 5.0 | 2.0 | 6.0 | 1.0 | 4.0 | 4.0 | 6.0 | 3.0 | 7.0 | 9.0 | 1.0 |
| 6 | 2.0 | 4.0 | 6.0 | 1.0 | 8.0 | 7.0 | 9.0 | 9.0 | 5.0 | 8.0 | 5.0 | 5.0 | 3.0 | 8.0 | 6.0 | 8.0 | 5.0 | 8.0 | 3.0 | 1.0 |
| 7 | 5.0 | 6.0 | 6.0 | 6.0 | 6.0 | 5.0 | 9.0 | 1.0 | 1.0 | 2.0 | 4.0 | 9.0 | 7.0 | 3.0 | 6.0 | 6.0 | 8.0 | 3.0 | 6.0 | 7.0 |
| 8 | 5.0 | 4.0 | 7.0 | 9.0 | 5.0 | 8.0 | 5.0 | 1.0 | 10.0 | 4.0 | 6.0 | 8.0 | 9.0 | 2.0 | 4.0 | 1.0 | 4.0 | 5.0 | 10.0 | 7.0 |
| 9 | 7.0 | 7.0 | 9.0 | 1.0 | 2.0 | 5.0 | 8.0 | 2.0 | 4.0 | 2.0 | 3.0 | 8.0 | 2.0 | 10.0 | 8.0 | 3.0 | 7.0 | 1.0 | 6.0 | 3.0 |
| 10 | 9.0 | 3.0 | 2.0 | 3.0 | 7.0 | 2.0 | 5.0 | 4.0 | 6.0 | 3.0 | 2.0 | 9.0 | 1.0 | 3.0 | 9.0 | 1.0 | 2.0 | 10.0 | 1.0 | 1.0 |
| 11 | 6.0 | 5.0 | 3.0 | 9.0 | 7.0 | 6.0 | 5.0 | 9.0 | 8.0 | 8.0 | 9.0 | 9.0 | 2.0 | 10.0 | 10.0 | 1.0 | 4.0 | 7.0 | 5.0 | 3.0 |
| 12 | 7.0 | 1.0 | 2.0 | 6.0 | 4.0 | 1.0 | 3.0 | 7.0 | 9.0 | 2.0 | 1.0 | 2.0 | 10.0 | 1.0 | 7.0 | 10.0 | 1.0 | 8.0 | 2.0 | 3.0 |
| 13 | 8.0 | 10.0 | 8.0 | 4.0 | 6.0 | 4.0 | 8.0 | 3.0 | 2.0 | 10.0 | 3.0 | 10.0 | 1.0 | 1.0 | 3.0 | 9.0 | 2.0 | 2.0 | 2.0 | 3.0 |
| 14 | 10.0 | 2.0 | 2.0 | 8.0 | 5.0 | 4.0 | 6.0 | 6.0 | 4.0 | 8.0 | 9.0 | 10.0 | 7.0 | 3.0 | 1.0 | 2.0 | 10.0 | 4.0 | 7.0 | 9.0 |
| 15 | 9.0 | 9.0 | 2.0 | 1.0 | 5.0 | 6.0 | 8.0 | 6.0 | 1.0 | 3.0 | 1.0 | 1.0 | 10.0 | 9.0 | 2.0 | 6.0 | 3.0 | 6.0 | 3.0 | 1.0 |
| 16 | 3.0 | 3.0 | 3.0 | 6.0 | 10.0 | 3.0 | 5.0 | 8.0 | 4.0 | 7.0 | 2.0 | 4.0 | 1.0 | 2.0 | 10.0 | 3.0 | 9.0 | 3.0 | 4.0 | 3.0 |
| 17 | 5.0 | 5.0 | 7.0 | 9.0 | 5.0 | 7.0 | 8.0 | 3.0 | 5.0 | 1.0 | 10.0 | 7.0 | 8.0 | 2.0 | 4.0 | 6.0 | 3.0 | 2.0 | 7.0 | 1.0 |
| 18 | 1.0 | 10.0 | 3.0 | 2.0 | 2.0 | 9.0 | 3.0 | 6.0 | 10.0 | 6.0 | 1.0 | 5.0 | 2.0 | 2.0 | 7.0 | 3.0 | 4.0 | 7.0 | 3.0 | 4.0 |
| 19 | 1.0 | 2.0 | 1.0 | 10.0 | 8.0 | 1.0 | 1.0 | 7.0 | 7.0 | 3.0 | 1.0 | 3.0 | 3.0 | 3.0 | 9.0 | 1.0 | 3.0 | 1.0 | 4.0 | 4.0 |

You can just drop the final route into a tiny JSON snippet like this when you're ready — it keeps things simple and easy to parse.

{
  ""solution"": []
}

This ""solution"" array is where the chosen route goes: list the fixes (node identifiers) in order from the departure fix to the arrival fix, nothing else. Think of it like filling in a short form — first stop, next stop, …, last stop. The JSON above is just a sketch of the shape we expect, not the actual route.

Please make sure to use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 20, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}], 'objective': {'constant': 0.0, 'linear': [6.0, 9.0, 8.0, 1.0, 6.0, 2.0, 2.0, 9.0, 4.0, 9.0, 4.0, 9.0, 4.0, 2.0, 1.0, 4.0, 2.0, 10.0, 8.0, 6.0], 'quadratic': [[4.0, 1.0, 8.0, 4.0, 2.0, 4.0, 2.0, 5.0, 5.0, 7.0, 9.0, 6.0, 7.0, 8.0, 10.0, 9.0, 3.0, 5.0, 1.0, 1.0], [1.0, 6.0, 8.0, 10.0, 7.0, 10.0, 4.0, 6.0, 4.0, 7.0, 3.0, 5.0, 1.0, 10.0, 2.0, 9.0, 3.0, 5.0, 10.0, 2.0], [8.0, 8.0, 4.0, 9.0, 5.0, 5.0, 6.0, 6.0, 7.0, 9.0, 2.0, 3.0, 2.0, 8.0, 2.0, 2.0, 3.0, 7.0, 3.0, 1.0], [4.0, 10.0, 9.0, 10.0, 5.0, 7.0, 1.0, 6.0, 9.0, 1.0, 3.0, 9.0, 6.0, 4.0, 8.0, 1.0, 6.0, 9.0, 2.0, 10.0], [2.0, 7.0, 5.0, 5.0, 9.0, 2.0, 8.0, 6.0, 5.0, 2.0, 7.0, 7.0, 4.0, 6.0, 5.0, 5.0, 10.0, 5.0, 2.0, 8.0], [4.0, 10.0, 5.0, 7.0, 2.0, 7.0, 7.0, 5.0, 8.0, 5.0, 2.0, 6.0, 1.0, 4.0, 4.0, 6.0, 3.0, 7.0, 9.0, 1.0], [2.0, 4.0, 6.0, 1.0, 8.0, 7.0, 9.0, 9.0, 5.0, 8.0, 5.0, 5.0, 3.0, 8.0, 6.0, 8.0, 5.0, 8.0, 3.0, 1.0], [5.0, 6.0, 6.0, 6.0, 6.0, 5.0, 9.0, 1.0, 1.0, 2.0, 4.0, 9.0, 7.0, 3.0, 6.0, 6.0, 8.0, 3.0, 6.0, 7.0], [5.0, 4.0, 7.0, 9.0, 5.0, 8.0, 5.0, 1.0, 10.0, 4.0, 6.0, 8.0, 9.0, 2.0, 4.0, 1.0, 4.0, 5.0, 10.0, 7.0], [7.0, 7.0, 9.0, 1.0, 2.0, 5.0, 8.0, 2.0, 4.0, 2.0, 3.0, 8.0, 2.0, 10.0, 8.0, 3.0, 7.0, 1.0, 6.0, 3.0], [9.0, 3.0, 2.0, 3.0, 7.0, 2.0, 5.0, 4.0, 6.0, 3.0, 2.0, 9.0, 1.0, 3.0, 9.0, 1.0, 2.0, 10.0, 1.0, 1.0], [6.0, 5.0, 3.0, 9.0, 7.0, 6.0, 5.0, 9.0, 8.0, 8.0, 9.0, 9.0, 2.0, 10.0, 10.0, 1.0, 4.0, 7.0, 5.0, 3.0], [7.0, 1.0, 2.0, 6.0, 4.0, 1.0, 3.0, 7.0, 9.0, 2.0, 1.0, 2.0, 10.0, 1.0, 7.0, 10.0, 1.0, 8.0, 2.0, 3.0], [8.0, 10.0, 8.0, 4.0, 6.0, 4.0, 8.0, 3.0, 2.0, 10.0, 3.0, 10.0, 1.0, 1.0, 3.0, 9.0, 2.0, 2.0, 2.0, 3.0], [10.0, 2.0, 2.0, 8.0, 5.0, 4.0, 6.0, 6.0, 4.0, 8.0, 9.0, 10.0, 7.0, 3.0, 1.0, 2.0, 10.0, 4.0, 7.0, 9.0], [9.0, 9.0, 2.0, 1.0, 5.0, 6.0, 8.0, 6.0, 1.0, 3.0, 1.0, 1.0, 10.0, 9.0, 2.0, 6.0, 3.0, 6.0, 3.0, 1.0], [3.0, 3.0, 3.0, 6.0, 10.0, 3.0, 5.0, 8.0, 4.0, 7.0, 2.0, 4.0, 1.0, 2.0, 10.0, 3.0, 9.0, 3.0, 4.0, 3.0], [5.0, 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11, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 20, 'to': 1, 'var_index': 0}, {'from': 19, 'to': 21, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}, {'from': 15, 'to': 16, 'var_index': 16}, {'from': 16, 'to': 17, 'var_index': 17}, {'from': 17, 'to': 18, 'var_index': 18}, {'from': 18, 'to': 19, 'var_index': 19}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21}}","[20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]",37,csv,1
QSPP,QSPP,"Many people treat a grocery run as a little puzzle: start at the entrance, follow the arrows through one continuous path, and finish at checkout. Each bit of aisle walked brings its own cost, and some pairs of bits interact badly and add extra cost when both are part of the same trip. The aim is to choose one valid, arrow-abiding route and total its cost by summing every segment’s cost and any pairwise penalties for segments that appear together. Don’t skip segments or hop between disconnected aisles; the full layout and the detailed costs are listed below.

# num_locations=17
# num_aisle_segments=16
# location_ids=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
# entrance_location=16
# checkout_location=17

segment_start_location,segment_end_location,segment_id
16,1,0
15,17,1
1,2,2
2,3,3
3,4,4
4,5,5
5,6,6
6,7,7
7,8,8
8,9,9
9,10,10
10,11,11
11,12,12
12,13,13
13,14,14
14,15,15

segment_id,segment_cost
0,7.0
1,8.0
2,6.0
3,8.0
4,4.0
5,8.0
6,4.0
7,8.0
8,2.0
9,9.0
10,9.0
11,2.0
12,10.0
13,6.0
14,9.0
15,2.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 8.0 | 8.0 | 9.0 | 7.0 | 5.0 | 3.0 | 5.0 | 7.0 | 4.0 | 10.0 | 6.0 | 6.0 | 2.0 | 3.0 | 2.0 |
| 1 | 8.0 | 8.0 | 3.0 | 4.0 | 2.0 | 6.0 | 10.0 | 1.0 | 8.0 | 3.0 | 9.0 | 9.0 | 4.0 | 8.0 | 3.0 | 1.0 |
| 2 | 8.0 | 3.0 | 8.0 | 10.0 | 8.0 | 2.0 | 4.0 | 5.0 | 6.0 | 5.0 | 6.0 | 1.0 | 1.0 | 8.0 | 6.0 | 8.0 |
| 3 | 9.0 | 4.0 | 10.0 | 5.0 | 6.0 | 3.0 | 4.0 | 10.0 | 7.0 | 5.0 | 9.0 | 10.0 | 2.0 | 3.0 | 6.0 | 9.0 |
| 4 | 7.0 | 2.0 | 8.0 | 6.0 | 5.0 | 4.0 | 8.0 | 5.0 | 1.0 | 9.0 | 7.0 | 6.0 | 5.0 | 2.0 | 1.0 | 3.0 |
| 5 | 5.0 | 6.0 | 2.0 | 3.0 | 4.0 | 2.0 | 2.0 | 10.0 | 8.0 | 3.0 | 5.0 | 1.0 | 7.0 | 10.0 | 10.0 | 8.0 |
| 6 | 3.0 | 10.0 | 4.0 | 4.0 | 8.0 | 2.0 | 8.0 | 4.0 | 3.0 | 2.0 | 10.0 | 4.0 | 2.0 | 2.0 | 5.0 | 8.0 |
| 7 | 5.0 | 1.0 | 5.0 | 10.0 | 5.0 | 10.0 | 4.0 | 7.0 | 1.0 | 10.0 | 7.0 | 8.0 | 5.0 | 8.0 | 10.0 | 6.0 |
| 8 | 7.0 | 8.0 | 6.0 | 7.0 | 1.0 | 8.0 | 3.0 | 1.0 | 9.0 | 6.0 | 5.0 | 7.0 | 6.0 | 6.0 | 6.0 | 10.0 |
| 9 | 4.0 | 3.0 | 5.0 | 5.0 | 9.0 | 3.0 | 2.0 | 10.0 | 6.0 | 2.0 | 3.0 | 1.0 | 7.0 | 6.0 | 7.0 | 2.0 |
| 10 | 10.0 | 9.0 | 6.0 | 9.0 | 7.0 | 5.0 | 10.0 | 7.0 | 5.0 | 3.0 | 4.0 | 5.0 | 3.0 | 6.0 | 2.0 | 7.0 |
| 11 | 6.0 | 9.0 | 1.0 | 10.0 | 6.0 | 1.0 | 4.0 | 8.0 | 7.0 | 1.0 | 5.0 | 1.0 | 10.0 | 6.0 | 9.0 | 7.0 |
| 12 | 6.0 | 4.0 | 1.0 | 2.0 | 5.0 | 7.0 | 2.0 | 5.0 | 6.0 | 7.0 | 3.0 | 10.0 | 9.0 | 4.0 | 10.0 | 3.0 |
| 13 | 2.0 | 8.0 | 8.0 | 3.0 | 2.0 | 10.0 | 2.0 | 8.0 | 6.0 | 6.0 | 6.0 | 6.0 | 4.0 | 4.0 | 10.0 | 7.0 |
| 14 | 3.0 | 3.0 | 6.0 | 6.0 | 1.0 | 10.0 | 5.0 | 10.0 | 6.0 | 7.0 | 2.0 | 9.0 | 10.0 | 10.0 | 3.0 | 7.0 |
| 15 | 2.0 | 1.0 | 8.0 | 9.0 | 3.0 | 8.0 | 8.0 | 6.0 | 10.0 | 2.0 | 7.0 | 7.0 | 3.0 | 7.0 | 7.0 | 8.0 |

Oh, and when you send back the chosen route, please tuck it into this tiny JSON shape so it's easy to read:

{
  ""solution"": []
}

Think of that ""solution"" list as the single continuous route: put the node names in order from the entrance to checkout (first entry is the source, last is the target), and only list node identifiers — no edge IDs, no costs. This block is just a sketch of the shape we want, not the actual answer.

Please use the exact node identifiers from the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'edges': [{'from': 15, 'to': 0, 'var_index': 0}, {'from': 14, 'to': 16, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}], 'objective': {'constant': 0.0, 'linear': [7.0, 8.0, 6.0, 8.0, 4.0, 8.0, 4.0, 8.0, 2.0, 9.0, 9.0, 2.0, 10.0, 6.0, 9.0, 2.0], 'quadratic': [[4.0, 8.0, 8.0, 9.0, 7.0, 5.0, 3.0, 5.0, 7.0, 4.0, 10.0, 6.0, 6.0, 2.0, 3.0, 2.0], [8.0, 8.0, 3.0, 4.0, 2.0, 6.0, 10.0, 1.0, 8.0, 3.0, 9.0, 9.0, 4.0, 8.0, 3.0, 1.0], [8.0, 3.0, 8.0, 10.0, 8.0, 2.0, 4.0, 5.0, 6.0, 5.0, 6.0, 1.0, 1.0, 8.0, 6.0, 8.0], [9.0, 4.0, 10.0, 5.0, 6.0, 3.0, 4.0, 10.0, 7.0, 5.0, 9.0, 10.0, 2.0, 3.0, 6.0, 9.0], [7.0, 2.0, 8.0, 6.0, 5.0, 4.0, 8.0, 5.0, 1.0, 9.0, 7.0, 6.0, 5.0, 2.0, 1.0, 3.0], [5.0, 6.0, 2.0, 3.0, 4.0, 2.0, 2.0, 10.0, 8.0, 3.0, 5.0, 1.0, 7.0, 10.0, 10.0, 8.0], [3.0, 10.0, 4.0, 4.0, 8.0, 2.0, 8.0, 4.0, 3.0, 2.0, 10.0, 4.0, 2.0, 2.0, 5.0, 8.0], [5.0, 1.0, 5.0, 10.0, 5.0, 10.0, 4.0, 7.0, 1.0, 10.0, 7.0, 8.0, 5.0, 8.0, 10.0, 6.0], [7.0, 8.0, 6.0, 7.0, 1.0, 8.0, 3.0, 1.0, 9.0, 6.0, 5.0, 7.0, 6.0, 6.0, 6.0, 10.0], [4.0, 3.0, 5.0, 5.0, 9.0, 3.0, 2.0, 10.0, 6.0, 2.0, 3.0, 1.0, 7.0, 6.0, 7.0, 2.0], [10.0, 9.0, 6.0, 9.0, 7.0, 5.0, 10.0, 7.0, 5.0, 3.0, 4.0, 5.0, 3.0, 6.0, 2.0, 7.0], [6.0, 9.0, 1.0, 10.0, 6.0, 1.0, 4.0, 8.0, 7.0, 1.0, 5.0, 1.0, 10.0, 6.0, 9.0, 7.0], [6.0, 4.0, 1.0, 2.0, 5.0, 7.0, 2.0, 5.0, 6.0, 7.0, 3.0, 10.0, 9.0, 4.0, 10.0, 3.0], [2.0, 8.0, 8.0, 3.0, 2.0, 10.0, 2.0, 8.0, 6.0, 6.0, 6.0, 6.0, 4.0, 4.0, 10.0, 7.0], [3.0, 3.0, 6.0, 6.0, 1.0, 10.0, 5.0, 10.0, 6.0, 7.0, 2.0, 9.0, 10.0, 10.0, 3.0, 7.0], [2.0, 1.0, 8.0, 9.0, 3.0, 8.0, 8.0, 6.0, 10.0, 2.0, 7.0, 7.0, 3.0, 7.0, 7.0, 8.0]]}, 'source': 15, 'target': 16}","[15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16]",1545.0,"{'problem_type': 'QSPP', 'num_nodes': 17, 'num_edges': 16, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 'source': 16, 'target': 17, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 8.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 8.0}, {'var_index': 6, 'linear_cost': 4.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 2.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 9.0}, {'var_index': 11, 'linear_cost': 2.0}, {'var_index': 12, 'linear_cost': 10.0}, {'var_index': 13, 'linear_cost': 6.0}, {'var_index': 14, 'linear_cost': 9.0}, {'var_index': 15, 'linear_cost': 2.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 16, 'to': 1, 'var_index': 0}, {'from': 15, 'to': 17, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17}}","[16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17]",38,csv,1
QSPP,QSPP,"We had a pile of parcels and a single conveyor belt system to move each package from intake to the sorting chute, and the tricky bit was picking which continuous belt path to use. Every belt costs something to run, and certain combinations of belts cause extra wear when both are used; that added wear can even be different depending on the order the belts are hit. A belt can also have its own extra wear if it’s used at all. What makes one choice better than another is the total tally: total running costs plus every extra wear charge for every pair of belts that appear on the chosen path. The package must follow one uninterrupted route that respects the belt directions and lists the locations in order — nothing left out or patched together. The exact map and cost details appear below.

# num_locations=24
# num_belts=23
# locations=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
# intake_location=23
# sorting_chute_location=24

belt_from_location,belt_to_location,belt_segment_id
23,1,0
22,24,1
1,2,2
2,3,3
3,4,4
4,5,5
5,6,6
6,7,7
7,8,8
8,9,9
9,10,10
10,11,11
11,12,12
12,13,13
13,14,14
14,15,15
15,16,16
16,17,17
17,18,18
18,19,19
19,20,20
20,21,21
21,22,22

belt_segment_id,operating_cost
0,9.0
1,10.0
2,1.0
3,5.0
4,5.0
5,5.0
6,4.0
7,1.0
8,10.0
9,10.0
10,10.0
11,6.0
12,3.0
13,5.0
14,7.0
15,4.0
16,2.0
17,5.0
18,6.0
19,5.0
20,9.0
21,4.0
22,1.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (belt_i_id, belt_j_id). If two belt_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| belt_i_id\belt_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 5.0 | 9.0 | 1.0 | 2.0 | 9.0 | 7.0 | 6.0 | 4.0 | 8.0 | 1.0 | 10.0 | 6.0 | 6.0 | 3.0 | 10.0 | 7.0 | 9.0 | 8.0 | 9.0 | 7.0 | 3.0 | 1.0 |
| 1 | 5.0 | 10.0 | 1.0 | 10.0 | 7.0 | 8.0 | 4.0 | 6.0 | 10.0 | 9.0 | 3.0 | 2.0 | 6.0 | 5.0 | 2.0 | 9.0 | 5.0 | 8.0 | 8.0 | 4.0 | 8.0 | 7.0 | 5.0 |
| 2 | 9.0 | 1.0 | 8.0 | 5.0 | 7.0 | 3.0 | 2.0 | 2.0 | 9.0 | 5.0 | 3.0 | 7.0 | 1.0 | 9.0 | 7.0 | 1.0 | 9.0 | 9.0 | 9.0 | 2.0 | 4.0 | 7.0 | 1.0 |
| 3 | 1.0 | 10.0 | 5.0 | 5.0 | 5.0 | 6.0 | 3.0 | 1.0 | 7.0 | 2.0 | 1.0 | 3.0 | 6.0 | 3.0 | 5.0 | 10.0 | 6.0 | 2.0 | 2.0 | 10.0 | 6.0 | 10.0 | 4.0 |
| 4 | 2.0 | 7.0 | 7.0 | 5.0 | 5.0 | 3.0 | 3.0 | 1.0 | 6.0 | 8.0 | 4.0 | 6.0 | 1.0 | 2.0 | 5.0 | 4.0 | 8.0 | 3.0 | 4.0 | 1.0 | 10.0 | 3.0 | 6.0 |
| 5 | 9.0 | 8.0 | 3.0 | 6.0 | 3.0 | 6.0 | 10.0 | 2.0 | 5.0 | 6.0 | 4.0 | 4.0 | 8.0 | 9.0 | 3.0 | 1.0 | 10.0 | 4.0 | 3.0 | 5.0 | 2.0 | 7.0 | 3.0 |
| 6 | 7.0 | 4.0 | 2.0 | 3.0 | 3.0 | 10.0 | 2.0 | 8.0 | 1.0 | 10.0 | 10.0 | 2.0 | 4.0 | 5.0 | 7.0 | 8.0 | 5.0 | 1.0 | 3.0 | 7.0 | 8.0 | 3.0 | 9.0 |
| 7 | 6.0 | 6.0 | 2.0 | 1.0 | 1.0 | 2.0 | 8.0 | 2.0 | 3.0 | 6.0 | 8.0 | 2.0 | 9.0 | 5.0 | 10.0 | 1.0 | 6.0 | 9.0 | 5.0 | 7.0 | 4.0 | 2.0 | 8.0 |
| 8 | 4.0 | 10.0 | 9.0 | 7.0 | 6.0 | 5.0 | 1.0 | 3.0 | 9.0 | 3.0 | 8.0 | 8.0 | 2.0 | 5.0 | 4.0 | 2.0 | 10.0 | 10.0 | 4.0 | 10.0 | 3.0 | 8.0 | 1.0 |
| 9 | 8.0 | 9.0 | 5.0 | 2.0 | 8.0 | 6.0 | 10.0 | 6.0 | 3.0 | 5.0 | 8.0 | 1.0 | 7.0 | 4.0 | 8.0 | 1.0 | 4.0 | 9.0 | 10.0 | 3.0 | 2.0 | 6.0 | 3.0 |
| 10 | 1.0 | 3.0 | 3.0 | 1.0 | 4.0 | 4.0 | 10.0 | 8.0 | 8.0 | 8.0 | 1.0 | 4.0 | 2.0 | 7.0 | 3.0 | 9.0 | 7.0 | 6.0 | 2.0 | 8.0 | 3.0 | 2.0 | 1.0 |
| 11 | 10.0 | 2.0 | 7.0 | 3.0 | 6.0 | 4.0 | 2.0 | 2.0 | 8.0 | 1.0 | 4.0 | 8.0 | 5.0 | 3.0 | 7.0 | 4.0 | 4.0 | 9.0 | 5.0 | 3.0 | 4.0 | 8.0 | 9.0 |
| 12 | 6.0 | 6.0 | 1.0 | 6.0 | 1.0 | 8.0 | 4.0 | 9.0 | 2.0 | 7.0 | 2.0 | 5.0 | 8.0 | 3.0 | 3.0 | 3.0 | 3.0 | 2.0 | 5.0 | 1.0 | 10.0 | 3.0 | 5.0 |
| 13 | 6.0 | 5.0 | 9.0 | 3.0 | 2.0 | 9.0 | 5.0 | 5.0 | 5.0 | 4.0 | 7.0 | 3.0 | 3.0 | 7.0 | 8.0 | 8.0 | 3.0 | 10.0 | 8.0 | 7.0 | 3.0 | 10.0 | 10.0 |
| 14 | 3.0 | 2.0 | 7.0 | 5.0 | 5.0 | 3.0 | 7.0 | 10.0 | 4.0 | 8.0 | 3.0 | 7.0 | 3.0 | 8.0 | 7.0 | 10.0 | 4.0 | 1.0 | 10.0 | 1.0 | 6.0 | 3.0 | 6.0 |
| 15 | 10.0 | 9.0 | 1.0 | 10.0 | 4.0 | 1.0 | 8.0 | 1.0 | 2.0 | 1.0 | 9.0 | 4.0 | 3.0 | 8.0 | 10.0 | 1.0 | 1.0 | 1.0 | 5.0 | 7.0 | 2.0 | 2.0 | 1.0 |
| 16 | 7.0 | 5.0 | 9.0 | 6.0 | 8.0 | 10.0 | 5.0 | 6.0 | 10.0 | 4.0 | 7.0 | 4.0 | 3.0 | 3.0 | 4.0 | 1.0 | 3.0 | 2.0 | 6.0 | 3.0 | 2.0 | 9.0 | 7.0 |
| 17 | 9.0 | 8.0 | 9.0 | 2.0 | 3.0 | 4.0 | 1.0 | 9.0 | 10.0 | 9.0 | 6.0 | 9.0 | 2.0 | 10.0 | 1.0 | 1.0 | 2.0 | 1.0 | 5.0 | 3.0 | 4.0 | 6.0 | 6.0 |
| 18 | 8.0 | 8.0 | 9.0 | 2.0 | 4.0 | 3.0 | 3.0 | 5.0 | 4.0 | 10.0 | 2.0 | 5.0 | 5.0 | 8.0 | 10.0 | 5.0 | 6.0 | 5.0 | 8.0 | 9.0 | 1.0 | 9.0 | 2.0 |
| 19 | 9.0 | 4.0 | 2.0 | 10.0 | 1.0 | 5.0 | 7.0 | 7.0 | 10.0 | 3.0 | 8.0 | 3.0 | 1.0 | 7.0 | 1.0 | 7.0 | 3.0 | 3.0 | 9.0 | 9.0 | 9.0 | 9.0 | 8.0 |
| 20 | 7.0 | 8.0 | 4.0 | 6.0 | 10.0 | 2.0 | 8.0 | 4.0 | 3.0 | 2.0 | 3.0 | 4.0 | 10.0 | 3.0 | 6.0 | 2.0 | 2.0 | 4.0 | 1.0 | 9.0 | 10.0 | 2.0 | 6.0 |
| 21 | 3.0 | 7.0 | 7.0 | 10.0 | 3.0 | 7.0 | 3.0 | 2.0 | 8.0 | 6.0 | 2.0 | 8.0 | 3.0 | 10.0 | 3.0 | 2.0 | 9.0 | 6.0 | 9.0 | 9.0 | 2.0 | 7.0 | 9.0 |
| 22 | 1.0 | 5.0 | 1.0 | 4.0 | 6.0 | 3.0 | 9.0 | 8.0 | 1.0 | 3.0 | 1.0 | 9.0 | 5.0 | 10.0 | 6.0 | 1.0 | 7.0 | 6.0 | 2.0 | 8.0 | 6.0 | 9.0 | 10.0 |

Oh, and when you send the chosen route back, please stick to a tiny JSON shape so whatever reads it later knows what to expect. Here’s the layout to use:

{
  ""solution"": []
}

Think of this as a little form: put the path you picked into the solution array as an ordered list of node names, starting with the intake (source) and ending with the sorting chute (target). Keep it simple — just the node identifiers in order, nothing else — and this block is only a sketch of the shape, not the actual answer.

Please make sure you use the exact node identifiers from the instance input — don’t rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 21, 'to': 23, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}, {'from': 19, 'to': 20, 'var_index': 21}, {'from': 20, 'to': 21, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [9.0, 10.0, 1.0, 5.0, 5.0, 5.0, 4.0, 1.0, 10.0, 10.0, 10.0, 6.0, 3.0, 5.0, 7.0, 4.0, 2.0, 5.0, 6.0, 5.0, 9.0, 4.0, 1.0], 'quadratic': [[1.0, 5.0, 9.0, 1.0, 2.0, 9.0, 7.0, 6.0, 4.0, 8.0, 1.0, 10.0, 6.0, 6.0, 3.0, 10.0, 7.0, 9.0, 8.0, 9.0, 7.0, 3.0, 1.0], [5.0, 10.0, 1.0, 10.0, 7.0, 8.0, 4.0, 6.0, 10.0, 9.0, 3.0, 2.0, 6.0, 5.0, 2.0, 9.0, 5.0, 8.0, 8.0, 4.0, 8.0, 7.0, 5.0], [9.0, 1.0, 8.0, 5.0, 7.0, 3.0, 2.0, 2.0, 9.0, 5.0, 3.0, 7.0, 1.0, 9.0, 7.0, 1.0, 9.0, 9.0, 9.0, 2.0, 4.0, 7.0, 1.0], [1.0, 10.0, 5.0, 5.0, 5.0, 6.0, 3.0, 1.0, 7.0, 2.0, 1.0, 3.0, 6.0, 3.0, 5.0, 10.0, 6.0, 2.0, 2.0, 10.0, 6.0, 10.0, 4.0], [2.0, 7.0, 7.0, 5.0, 5.0, 3.0, 3.0, 1.0, 6.0, 8.0, 4.0, 6.0, 1.0, 2.0, 5.0, 4.0, 8.0, 3.0, 4.0, 1.0, 10.0, 3.0, 6.0], [9.0, 8.0, 3.0, 6.0, 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5.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 23, 'to': 1, 'var_index': 0}, {'from': 22, 'to': 24, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}, {'from': 7, 'to': 8, 'var_index': 8}, {'from': 8, 'to': 9, 'var_index': 9}, {'from': 9, 'to': 10, 'var_index': 10}, {'from': 10, 'to': 11, 'var_index': 11}, {'from': 11, 'to': 12, 'var_index': 12}, {'from': 12, 'to': 13, 'var_index': 13}, {'from': 13, 'to': 14, 'var_index': 14}, {'from': 14, 'to': 15, 'var_index': 15}, {'from': 15, 'to': 16, 'var_index': 16}, {'from': 16, 'to': 17, 'var_index': 17}, {'from': 17, 'to': 18, 'var_index': 18}, {'from': 18, 'to': 19, 'var_index': 19}, {'from': 19, 'to': 20, 'var_index': 20}, {'from': 20, 'to': 21, 'var_index': 21}, {'from': 21, 'to': 22, 'var_index': 22}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23, 23: 24}}","[23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24]",39,csv,1
QSPP,QSPP,"We need to pick one straight patrol from the guard room to the checkpoint, following the one-way flow of halls and doors. Every hallway has a base cost to patrol, and some pairs of hallways create extra added effort if both are on the same route. Even an individual hallway can have its own extra overhead. The task is simple in words: choose a single legal route (start at the guard room, end at the checkpoint, follow only the allowed directions) and make sure the sum of all hallway costs plus any pairwise extra costs is as small as possible. The concrete map and cost details come next below.

# total_locations=25
# total_corridors=24
# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y
# guard_room_id=X
# checkpoint_id=Y

corridor_start_location,corridor_end_location,corridor_id
X,A,0
W,Y,1
A,B,2
B,C,3
C,D,4
D,E,5
E,F,6
F,G,7
G,H,8
H,I,9
I,J,10
J,K,11
K,L,12
L,M,13
M,N,14
N,O,15
O,P,16
P,Q,17
Q,R,18
R,S,19
S,T,20
T,U,21
U,V,22
V,W,23

corridor_id_ref,base_patrol_cost
0,1.0
1,6.0
2,4.0
3,9.0
4,2.0
5,7.0
6,9.0
7,4.0
8,1.0
9,4.0
10,4.0
11,2.0
12,7.0
13,6.0
14,1.0
15,10.0
16,9.0
17,6.0
18,5.0
19,7.0
20,4.0
21,10.0
22,8.0
23,9.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 6.0 | 5.0 | 7.0 | 9.0 | 6.0 | 5.0 | 2.0 | 10.0 | 5.0 | 6.0 | 3.0 | 7.0 | 4.0 | 3.0 | 3.0 | 6.0 | 9.0 | 1.0 | 2.0 | 3.0 | 5.0 | 4.0 | 6.0 |
| 1 | 6.0 | 6.0 | 10.0 | 8.0 | 3.0 | 6.0 | 8.0 | 2.0 | 7.0 | 3.0 | 7.0 | 3.0 | 2.0 | 3.0 | 5.0 | 3.0 | 6.0 | 5.0 | 2.0 | 8.0 | 4.0 | 2.0 | 2.0 | 7.0 |
| 2 | 5.0 | 10.0 | 1.0 | 5.0 | 10.0 | 10.0 | 7.0 | 10.0 | 5.0 | 8.0 | 1.0 | 8.0 | 8.0 | 10.0 | 7.0 | 1.0 | 9.0 | 8.0 | 9.0 | 1.0 | 4.0 | 9.0 | 2.0 | 1.0 |
| 3 | 7.0 | 8.0 | 5.0 | 6.0 | 9.0 | 5.0 | 1.0 | 3.0 | 3.0 | 2.0 | 2.0 | 7.0 | 1.0 | 5.0 | 2.0 | 6.0 | 7.0 | 5.0 | 8.0 | 10.0 | 2.0 | 6.0 | 4.0 | 6.0 |
| 4 | 9.0 | 3.0 | 10.0 | 9.0 | 3.0 | 10.0 | 10.0 | 4.0 | 6.0 | 3.0 | 6.0 | 6.0 | 6.0 | 7.0 | 3.0 | 8.0 | 2.0 | 7.0 | 5.0 | 5.0 | 6.0 | 9.0 | 7.0 | 5.0 |
| 5 | 6.0 | 6.0 | 10.0 | 5.0 | 10.0 | 8.0 | 4.0 | 4.0 | 9.0 | 5.0 | 6.0 | 2.0 | 7.0 | 2.0 | 1.0 | 6.0 | 1.0 | 2.0 | 1.0 | 2.0 | 2.0 | 8.0 | 5.0 | 6.0 |
| 6 | 5.0 | 8.0 | 7.0 | 1.0 | 10.0 | 4.0 | 4.0 | 4.0 | 10.0 | 6.0 | 2.0 | 3.0 | 5.0 | 1.0 | 2.0 | 2.0 | 6.0 | 1.0 | 7.0 | 1.0 | 2.0 | 1.0 | 6.0 | 4.0 |
| 7 | 2.0 | 2.0 | 10.0 | 3.0 | 4.0 | 4.0 | 4.0 | 4.0 | 3.0 | 2.0 | 9.0 | 3.0 | 3.0 | 5.0 | 6.0 | 3.0 | 8.0 | 10.0 | 4.0 | 8.0 | 2.0 | 8.0 | 1.0 | 9.0 |
| 8 | 10.0 | 7.0 | 5.0 | 3.0 | 6.0 | 9.0 | 10.0 | 3.0 | 5.0 | 7.0 | 10.0 | 6.0 | 4.0 | 6.0 | 8.0 | 9.0 | 6.0 | 9.0 | 2.0 | 6.0 | 4.0 | 8.0 | 4.0 | 5.0 |
| 9 | 5.0 | 3.0 | 8.0 | 2.0 | 3.0 | 5.0 | 6.0 | 2.0 | 7.0 | 6.0 | 5.0 | 1.0 | 2.0 | 4.0 | 3.0 | 6.0 | 5.0 | 1.0 | 9.0 | 4.0 | 10.0 | 2.0 | 4.0 | 1.0 |
| 10 | 6.0 | 7.0 | 1.0 | 2.0 | 6.0 | 6.0 | 2.0 | 9.0 | 10.0 | 5.0 | 2.0 | 1.0 | 5.0 | 3.0 | 8.0 | 4.0 | 6.0 | 7.0 | 3.0 | 10.0 | 9.0 | 8.0 | 1.0 | 6.0 |
| 11 | 3.0 | 3.0 | 8.0 | 7.0 | 6.0 | 2.0 | 3.0 | 3.0 | 6.0 | 1.0 | 1.0 | 8.0 | 7.0 | 2.0 | 3.0 | 1.0 | 5.0 | 8.0 | 5.0 | 4.0 | 1.0 | 1.0 | 3.0 | 7.0 |
| 12 | 7.0 | 2.0 | 8.0 | 1.0 | 6.0 | 7.0 | 5.0 | 3.0 | 4.0 | 2.0 | 5.0 | 7.0 | 5.0 | 3.0 | 7.0 | 2.0 | 4.0 | 2.0 | 2.0 | 6.0 | 7.0 | 9.0 | 9.0 | 5.0 |
| 13 | 4.0 | 3.0 | 10.0 | 5.0 | 7.0 | 2.0 | 1.0 | 5.0 | 6.0 | 4.0 | 3.0 | 2.0 | 3.0 | 7.0 | 4.0 | 7.0 | 1.0 | 4.0 | 3.0 | 1.0 | 4.0 | 3.0 | 6.0 | 7.0 |
| 14 | 3.0 | 5.0 | 7.0 | 2.0 | 3.0 | 1.0 | 2.0 | 6.0 | 8.0 | 3.0 | 8.0 | 3.0 | 7.0 | 4.0 | 10.0 | 7.0 | 4.0 | 5.0 | 7.0 | 8.0 | 3.0 | 5.0 | 7.0 | 9.0 |
| 15 | 3.0 | 3.0 | 1.0 | 6.0 | 8.0 | 6.0 | 2.0 | 3.0 | 9.0 | 6.0 | 4.0 | 1.0 | 2.0 | 7.0 | 7.0 | 6.0 | 5.0 | 8.0 | 2.0 | 4.0 | 5.0 | 7.0 | 3.0 | 3.0 |
| 16 | 6.0 | 6.0 | 9.0 | 7.0 | 2.0 | 1.0 | 6.0 | 8.0 | 6.0 | 5.0 | 6.0 | 5.0 | 4.0 | 1.0 | 4.0 | 5.0 | 4.0 | 2.0 | 10.0 | 4.0 | 9.0 | 6.0 | 10.0 | 9.0 |
| 17 | 9.0 | 5.0 | 8.0 | 5.0 | 7.0 | 2.0 | 1.0 | 10.0 | 9.0 | 1.0 | 7.0 | 8.0 | 2.0 | 4.0 | 5.0 | 8.0 | 2.0 | 10.0 | 4.0 | 4.0 | 1.0 | 2.0 | 9.0 | 4.0 |
| 18 | 1.0 | 2.0 | 9.0 | 8.0 | 5.0 | 1.0 | 7.0 | 4.0 | 2.0 | 9.0 | 3.0 | 5.0 | 2.0 | 3.0 | 7.0 | 2.0 | 10.0 | 4.0 | 10.0 | 5.0 | 4.0 | 10.0 | 1.0 | 2.0 |
| 19 | 2.0 | 8.0 | 1.0 | 10.0 | 5.0 | 2.0 | 1.0 | 8.0 | 6.0 | 4.0 | 10.0 | 4.0 | 6.0 | 1.0 | 8.0 | 4.0 | 4.0 | 4.0 | 5.0 | 9.0 | 5.0 | 7.0 | 3.0 | 7.0 |
| 20 | 3.0 | 4.0 | 4.0 | 2.0 | 6.0 | 2.0 | 2.0 | 2.0 | 4.0 | 10.0 | 9.0 | 1.0 | 7.0 | 4.0 | 3.0 | 5.0 | 9.0 | 1.0 | 4.0 | 5.0 | 3.0 | 3.0 | 2.0 | 7.0 |
| 21 | 5.0 | 2.0 | 9.0 | 6.0 | 9.0 | 8.0 | 1.0 | 8.0 | 8.0 | 2.0 | 8.0 | 1.0 | 9.0 | 3.0 | 5.0 | 7.0 | 6.0 | 2.0 | 10.0 | 7.0 | 3.0 | 2.0 | 5.0 | 7.0 |
| 22 | 4.0 | 2.0 | 2.0 | 4.0 | 7.0 | 5.0 | 6.0 | 1.0 | 4.0 | 4.0 | 1.0 | 3.0 | 9.0 | 6.0 | 7.0 | 3.0 | 10.0 | 9.0 | 1.0 | 3.0 | 2.0 | 5.0 | 2.0 | 1.0 |
| 23 | 6.0 | 7.0 | 1.0 | 6.0 | 5.0 | 6.0 | 4.0 | 9.0 | 5.0 | 1.0 | 6.0 | 7.0 | 5.0 | 7.0 | 9.0 | 3.0 | 9.0 | 4.0 | 2.0 | 7.0 | 7.0 | 7.0 | 1.0 | 6.0 |

Also, when you send back the chosen route, please use this simple JSON layout so it's easy to read and check:

{
  ""solution"": []
}

Here, ""solution"" should be an array containing the sequence of NODE identifiers from the guard room (source) to the checkpoint (target), in order. Keep it light — just the node names, nothing about hallway IDs or costs. This JSON is just a sketch of the expected shape, not the actual answer.

Please use the exact node identifiers as they appear in the instance input — do not rename or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 23, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 24, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}, {'from': 17, 'to': 18, 'var_index': 19}, {'from': 18, 'to': 19, 'var_index': 20}, {'from': 19, 'to': 20, 'var_index': 21}, {'from': 20, 'to': 21, 'var_index': 22}, {'from': 21, 'to': 22, 'var_index': 23}], 'objective': {'constant': 0.0, 'linear': [1.0, 6.0, 4.0, 9.0, 2.0, 7.0, 9.0, 4.0, 1.0, 4.0, 4.0, 2.0, 7.0, 6.0, 1.0, 10.0, 9.0, 6.0, 5.0, 7.0, 4.0, 10.0, 8.0, 9.0], 'quadratic': [[5.0, 6.0, 5.0, 7.0, 9.0, 6.0, 5.0, 2.0, 10.0, 5.0, 6.0, 3.0, 7.0, 4.0, 3.0, 3.0, 6.0, 9.0, 1.0, 2.0, 3.0, 5.0, 4.0, 6.0], [6.0, 6.0, 10.0, 8.0, 3.0, 6.0, 8.0, 2.0, 7.0, 3.0, 7.0, 3.0, 2.0, 3.0, 5.0, 3.0, 6.0, 5.0, 2.0, 8.0, 4.0, 2.0, 2.0, 7.0], [5.0, 10.0, 1.0, 5.0, 10.0, 10.0, 7.0, 10.0, 5.0, 8.0, 1.0, 8.0, 8.0, 10.0, 7.0, 1.0, 9.0, 8.0, 9.0, 1.0, 4.0, 9.0, 2.0, 1.0], [7.0, 8.0, 5.0, 6.0, 9.0, 5.0, 1.0, 3.0, 3.0, 2.0, 2.0, 7.0, 1.0, 5.0, 2.0, 6.0, 7.0, 5.0, 8.0, 10.0, 2.0, 6.0, 4.0, 6.0], [9.0, 3.0, 10.0, 9.0, 3.0, 10.0, 10.0, 4.0, 6.0, 3.0, 6.0, 6.0, 6.0, 7.0, 3.0, 8.0, 2.0, 7.0, 5.0, 5.0, 6.0, 9.0, 7.0, 5.0], [6.0, 6.0, 10.0, 5.0, 10.0, 8.0, 4.0, 4.0, 9.0, 5.0, 6.0, 2.0, 7.0, 2.0, 1.0, 6.0, 1.0, 2.0, 1.0, 2.0, 2.0, 8.0, 5.0, 6.0], [5.0, 8.0, 7.0, 1.0, 10.0, 4.0, 4.0, 4.0, 10.0, 6.0, 2.0, 3.0, 5.0, 1.0, 2.0, 2.0, 6.0, 1.0, 7.0, 1.0, 2.0, 1.0, 6.0, 4.0], [2.0, 2.0, 10.0, 3.0, 4.0, 4.0, 4.0, 4.0, 3.0, 2.0, 9.0, 3.0, 3.0, 5.0, 6.0, 3.0, 8.0, 10.0, 4.0, 8.0, 2.0, 8.0, 1.0, 9.0], [10.0, 7.0, 5.0, 3.0, 6.0, 9.0, 10.0, 3.0, 5.0, 7.0, 10.0, 6.0, 4.0, 6.0, 8.0, 9.0, 6.0, 9.0, 2.0, 6.0, 4.0, 8.0, 4.0, 5.0], [5.0, 3.0, 8.0, 2.0, 3.0, 5.0, 6.0, 2.0, 7.0, 6.0, 5.0, 1.0, 2.0, 4.0, 3.0, 6.0, 5.0, 1.0, 9.0, 4.0, 10.0, 2.0, 4.0, 1.0], [6.0, 7.0, 1.0, 2.0, 6.0, 6.0, 2.0, 9.0, 10.0, 5.0, 2.0, 1.0, 5.0, 3.0, 8.0, 4.0, 6.0, 7.0, 3.0, 10.0, 9.0, 8.0, 1.0, 6.0], [3.0, 3.0, 8.0, 7.0, 6.0, 2.0, 3.0, 3.0, 6.0, 1.0, 1.0, 8.0, 7.0, 2.0, 3.0, 1.0, 5.0, 8.0, 5.0, 4.0, 1.0, 1.0, 3.0, 7.0], [7.0, 2.0, 8.0, 1.0, 6.0, 7.0, 5.0, 3.0, 4.0, 2.0, 5.0, 7.0, 5.0, 3.0, 7.0, 2.0, 4.0, 2.0, 2.0, 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2.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 23, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 23, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 23, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 23, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 23, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 23, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 23, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 23, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 23, 'var_j': 23, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 'X', 'to': 'A', 'var_index': 0}, {'from': 'W', 'to': 'Y', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}, {'from': 'H', 'to': 'I', 'var_index': 9}, {'from': 'I', 'to': 'J', 'var_index': 10}, {'from': 'J', 'to': 'K', 'var_index': 11}, {'from': 'K', 'to': 'L', 'var_index': 12}, {'from': 'L', 'to': 'M', 'var_index': 13}, {'from': 'M', 'to': 'N', 'var_index': 14}, {'from': 'N', 'to': 'O', 'var_index': 15}, {'from': 'O', 'to': 'P', 'var_index': 16}, {'from': 'P', 'to': 'Q', 'var_index': 17}, {'from': 'Q', 'to': 'R', 'var_index': 18}, {'from': 'R', 'to': 'S', 'var_index': 19}, {'from': 'S', 'to': 'T', 'var_index': 20}, {'from': 'T', 'to': 'U', 'var_index': 21}, {'from': 'U', 'to': 'V', 'var_index': 22}, {'from': 'V', 'to': 'W', 'var_index': 23}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V', 22: 'W', 23: 'X', 24: 'Y'}}","['X', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'Y']",40,csv,names
QSPP,QSPP,"Someone on the team described it like planning a courier route through a set of conveyor belts: each belt moves the package forward but charges a fee, and certain belt combinations create extra handling fees if they’re used together — some belts also have a small handling surcharge by themselves. The task is to pick exactly one conveyor route from the pickup point to the delivery point so the total handling bill (every belt’s fee plus any extra pair fees) is as low as it can be. The route has to follow the arrows on the belts so every step is valid, and the final report should only list the sequence of locations visited — keep the internal belt codes and pricing out of that list. The full map and fee table are shown below.

# location_count=21
# links_count=56
# locations=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21
# pickup_location=20
# delivery_location=21

link_from_location,link_to_location,link_code
20,1,0
20,2,1
20,3,2
20,4,3
20,5,4
20,6,5
20,7,6
20,8,7
20,9,8
20,10,9
20,11,10
20,12,11
20,13,12
20,14,13
20,15,14
20,16,15
20,17,16
20,18,17
20,19,18
1,21,19
2,21,20
3,21,21
4,21,22
5,21,23
6,21,24
7,21,25
8,21,26
9,21,27
10,21,28
11,21,29
12,21,30
13,21,31
14,21,32
15,21,33
16,21,34
17,21,35
18,21,36
19,21,37
1,2,38
2,3,39
3,4,40
4,5,41
5,6,42
6,7,43
7,8,44
8,9,45
9,10,46
10,11,47
11,12,48
12,13,49
13,14,50
14,15,51
15,16,52
16,17,53
17,18,54
18,19,55

link_code,link_fee
0,1.0
1,4.0
2,7.0
3,1.0
4,3.0
5,10.0
6,6.0
7,10.0
8,4.0
9,2.0
10,1.0
11,2.0
12,8.0
13,9.0
14,8.0
15,5.0
16,5.0
17,2.0
18,2.0
19,7.0
20,3.0
21,6.0
22,5.0
23,9.0
24,7.0
25,8.0
26,3.0
27,2.0
28,2.0
29,10.0
30,5.0
31,10.0
32,3.0
33,2.0
34,9.0
35,2.0
36,9.0
37,1.0
38,10.0
39,5.0
40,4.0
41,10.0
42,8.0
43,7.0
44,3.0
45,7.0
46,10.0
47,2.0
48,9.0
49,9.0
50,2.0
51,2.0
52,8.0
53,6.0
54,7.0
55,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (link_i_code, link_j_code). If two link_codes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| link_i_code\link_j_code | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 6.0 | 9.0 | 10.0 | 4.0 | 9.0 | 4.0 | 1.0 | 8.0 | 9.0 | 2.0 | 2.0 | 10.0 | 5.0 | 7.0 | 9.0 | 2.0 | 8.0 | 2.0 | 4.0 | 3.0 | 2.0 | 3.0 | 3.0 | 7.0 | 8.0 | 8.0 | 4.0 | 1.0 | 4.0 | 2.0 | 8.0 | 7.0 | 5.0 | 4.0 | 9.0 | 9.0 | 9.0 | 5.0 | 2.0 | 5.0 | 4.0 | 3.0 | 5.0 | 10.0 | 8.0 | 6.0 | 8.0 | 9.0 | 8.0 | 8.0 | 10.0 | 1.0 | 7.0 | 3.0 | 8.0 |
| 1 | 6.0 | 8.0 | 9.0 | 3.0 | 8.0 | 2.0 | 3.0 | 10.0 | 7.0 | 3.0 | 7.0 | 7.0 | 4.0 | 2.0 | 1.0 | 9.0 | 6.0 | 4.0 | 2.0 | 4.0 | 7.0 | 3.0 | 10.0 | 5.0 | 9.0 | 1.0 | 4.0 | 3.0 | 10.0 | 8.0 | 3.0 | 2.0 | 2.0 | 6.0 | 9.0 | 5.0 | 10.0 | 1.0 | 1.0 | 7.0 | 4.0 | 5.0 | 5.0 | 6.0 | 1.0 | 1.0 | 6.0 | 1.0 | 8.0 | 10.0 | 10.0 | 1.0 | 6.0 | 3.0 | 3.0 | 10.0 |
| 2 | 9.0 | 9.0 | 5.0 | 1.0 | 10.0 | 5.0 | 2.0 | 10.0 | 1.0 | 3.0 | 9.0 | 3.0 | 4.0 | 7.0 | 1.0 | 3.0 | 3.0 | 2.0 | 3.0 | 1.0 | 5.0 | 6.0 | 3.0 | 3.0 | 10.0 | 5.0 | 9.0 | 2.0 | 8.0 | 9.0 | 1.0 | 8.0 | 2.0 | 2.0 | 1.0 | 9.0 | 6.0 | 8.0 | 6.0 | 5.0 | 3.0 | 5.0 | 7.0 | 4.0 | 7.0 | 3.0 | 8.0 | 3.0 | 3.0 | 4.0 | 3.0 | 5.0 | 6.0 | 8.0 | 10.0 | 10.0 |
| 3 | 10.0 | 3.0 | 1.0 | 3.0 | 2.0 | 3.0 | 1.0 | 10.0 | 7.0 | 5.0 | 8.0 | 10.0 | 7.0 | 10.0 | 7.0 | 3.0 | 7.0 | 7.0 | 3.0 | 4.0 | 9.0 | 10.0 | 7.0 | 9.0 | 4.0 | 6.0 | 7.0 | 2.0 | 4.0 | 3.0 | 4.0 | 6.0 | 1.0 | 4.0 | 1.0 | 8.0 | 2.0 | 4.0 | 4.0 | 10.0 | 2.0 | 10.0 | 7.0 | 7.0 | 1.0 | 8.0 | 5.0 | 8.0 | 7.0 | 7.0 | 8.0 | 9.0 | 8.0 | 2.0 | 5.0 | 1.0 |
| 4 | 4.0 | 8.0 | 10.0 | 2.0 | 4.0 | 6.0 | 7.0 | 9.0 | 4.0 | 9.0 | 5.0 | 6.0 | 10.0 | 5.0 | 8.0 | 3.0 | 1.0 | 6.0 | 6.0 | 3.0 | 8.0 | 7.0 | 7.0 | 9.0 | 8.0 | 8.0 | 6.0 | 7.0 | 8.0 | 3.0 | 3.0 | 6.0 | 8.0 | 3.0 | 5.0 | 10.0 | 9.0 | 8.0 | 8.0 | 9.0 | 9.0 | 4.0 | 4.0 | 5.0 | 6.0 | 8.0 | 9.0 | 3.0 | 3.0 | 1.0 | 2.0 | 7.0 | 2.0 | 2.0 | 6.0 | 6.0 |
| 5 | 9.0 | 2.0 | 5.0 | 3.0 | 6.0 | 5.0 | 6.0 | 4.0 | 7.0 | 1.0 | 9.0 | 1.0 | 2.0 | 5.0 | 9.0 | 6.0 | 7.0 | 8.0 | 4.0 | 4.0 | 10.0 | 3.0 | 4.0 | 5.0 | 1.0 | 7.0 | 7.0 | 5.0 | 5.0 | 9.0 | 9.0 | 2.0 | 1.0 | 5.0 | 4.0 | 7.0 | 7.0 | 4.0 | 1.0 | 5.0 | 6.0 | 1.0 | 1.0 | 6.0 | 3.0 | 5.0 | 9.0 | 2.0 | 2.0 | 9.0 | 3.0 | 8.0 | 3.0 | 3.0 | 4.0 | 10.0 |
| 6 | 4.0 | 3.0 | 2.0 | 1.0 | 7.0 | 6.0 | 9.0 | 5.0 | 5.0 | 6.0 | 3.0 | 6.0 | 7.0 | 7.0 | 4.0 | 9.0 | 9.0 | 6.0 | 1.0 | 4.0 | 4.0 | 10.0 | 3.0 | 8.0 | 3.0 | 10.0 | 1.0 | 8.0 | 8.0 | 1.0 | 8.0 | 2.0 | 9.0 | 5.0 | 1.0 | 3.0 | 6.0 | 2.0 | 5.0 | 10.0 | 6.0 | 9.0 | 7.0 | 6.0 | 4.0 | 6.0 | 10.0 | 6.0 | 8.0 | 4.0 | 2.0 | 6.0 | 6.0 | 1.0 | 2.0 | 2.0 |
| 7 | 1.0 | 10.0 | 10.0 | 10.0 | 9.0 | 4.0 | 5.0 | 1.0 | 7.0 | 3.0 | 10.0 | 5.0 | 10.0 | 10.0 | 7.0 | 2.0 | 6.0 | 7.0 | 6.0 | 8.0 | 4.0 | 7.0 | 2.0 | 10.0 | 6.0 | 9.0 | 8.0 | 10.0 | 7.0 | 1.0 | 5.0 | 4.0 | 6.0 | 5.0 | 7.0 | 10.0 | 8.0 | 9.0 | 4.0 | 10.0 | 4.0 | 8.0 | 10.0 | 10.0 | 1.0 | 10.0 | 1.0 | 9.0 | 1.0 | 5.0 | 2.0 | 6.0 | 6.0 | 4.0 | 5.0 | 3.0 |
| 8 | 8.0 | 7.0 | 1.0 | 7.0 | 4.0 | 7.0 | 5.0 | 7.0 | 7.0 | 6.0 | 6.0 | 1.0 | 7.0 | 6.0 | 6.0 | 7.0 | 3.0 | 4.0 | 7.0 | 4.0 | 4.0 | 9.0 | 5.0 | 8.0 | 5.0 | 8.0 | 3.0 | 10.0 | 1.0 | 3.0 | 8.0 | 10.0 | 8.0 | 5.0 | 8.0 | 6.0 | 3.0 | 1.0 | 9.0 | 2.0 | 2.0 | 5.0 | 3.0 | 8.0 | 6.0 | 10.0 | 9.0 | 7.0 | 9.0 | 5.0 | 8.0 | 8.0 | 7.0 | 3.0 | 1.0 | 2.0 |
| 9 | 9.0 | 3.0 | 3.0 | 5.0 | 9.0 | 1.0 | 6.0 | 3.0 | 6.0 | 8.0 | 6.0 | 9.0 | 5.0 | 4.0 | 5.0 | 10.0 | 7.0 | 9.0 | 4.0 | 1.0 | 6.0 | 5.0 | 5.0 | 8.0 | 3.0 | 6.0 | 7.0 | 10.0 | 6.0 | 2.0 | 1.0 | 10.0 | 6.0 | 7.0 | 5.0 | 3.0 | 6.0 | 1.0 | 1.0 | 7.0 | 3.0 | 10.0 | 1.0 | 4.0 | 3.0 | 8.0 | 4.0 | 10.0 | 10.0 | 9.0 | 4.0 | 7.0 | 4.0 | 7.0 | 2.0 | 6.0 |
| 10 | 2.0 | 7.0 | 9.0 | 8.0 | 5.0 | 9.0 | 3.0 | 10.0 | 6.0 | 6.0 | 10.0 | 6.0 | 6.0 | 5.0 | 3.0 | 9.0 | 2.0 | 7.0 | 10.0 | 2.0 | 5.0 | 9.0 | 7.0 | 3.0 | 8.0 | 2.0 | 10.0 | 5.0 | 3.0 | 10.0 | 6.0 | 1.0 | 7.0 | 1.0 | 1.0 | 6.0 | 2.0 | 6.0 | 2.0 | 4.0 | 6.0 | 1.0 | 2.0 | 6.0 | 2.0 | 5.0 | 10.0 | 9.0 | 1.0 | 10.0 | 7.0 | 2.0 | 5.0 | 7.0 | 2.0 | 5.0 |
| 11 | 2.0 | 7.0 | 3.0 | 10.0 | 6.0 | 1.0 | 6.0 | 5.0 | 1.0 | 9.0 | 6.0 | 10.0 | 10.0 | 9.0 | 8.0 | 2.0 | 5.0 | 2.0 | 4.0 | 3.0 | 9.0 | 4.0 | 9.0 | 3.0 | 3.0 | 7.0 | 4.0 | 7.0 | 8.0 | 4.0 | 4.0 | 5.0 | 7.0 | 8.0 | 4.0 | 9.0 | 5.0 | 5.0 | 4.0 | 2.0 | 4.0 | 3.0 | 1.0 | 7.0 | 7.0 | 3.0 | 9.0 | 3.0 | 1.0 | 5.0 | 2.0 | 7.0 | 10.0 | 2.0 | 2.0 | 7.0 |
| 12 | 10.0 | 4.0 | 4.0 | 7.0 | 10.0 | 2.0 | 7.0 | 10.0 | 7.0 | 5.0 | 6.0 | 10.0 | 6.0 | 9.0 | 5.0 | 8.0 | 6.0 | 8.0 | 2.0 | 7.0 | 7.0 | 2.0 | 7.0 | 9.0 | 3.0 | 5.0 | 10.0 | 10.0 | 1.0 | 6.0 | 9.0 | 2.0 | 2.0 | 10.0 | 3.0 | 1.0 | 5.0 | 4.0 | 5.0 | 6.0 | 3.0 | 5.0 | 6.0 | 5.0 | 6.0 | 7.0 | 1.0 | 1.0 | 3.0 | 8.0 | 7.0 | 7.0 | 4.0 | 1.0 | 6.0 | 10.0 |
| 13 | 5.0 | 2.0 | 7.0 | 10.0 | 5.0 | 5.0 | 7.0 | 10.0 | 6.0 | 4.0 | 5.0 | 9.0 | 9.0 | 6.0 | 6.0 | 2.0 | 5.0 | 6.0 | 5.0 | 3.0 | 8.0 | 4.0 | 3.0 | 9.0 | 10.0 | 5.0 | 4.0 | 6.0 | 4.0 | 4.0 | 8.0 | 3.0 | 4.0 | 3.0 | 1.0 | 8.0 | 4.0 | 4.0 | 1.0 | 7.0 | 5.0 | 7.0 | 9.0 | 1.0 | 2.0 | 10.0 | 4.0 | 3.0 | 4.0 | 10.0 | 7.0 | 3.0 | 3.0 | 9.0 | 5.0 | 8.0 |
| 14 | 7.0 | 1.0 | 1.0 | 7.0 | 8.0 | 9.0 | 4.0 | 7.0 | 6.0 | 5.0 | 3.0 | 8.0 | 5.0 | 6.0 | 6.0 | 2.0 | 10.0 | 10.0 | 4.0 | 9.0 | 2.0 | 4.0 | 9.0 | 9.0 | 4.0 | 4.0 | 7.0 | 5.0 | 4.0 | 10.0 | 1.0 | 8.0 | 3.0 | 3.0 | 4.0 | 8.0 | 4.0 | 7.0 | 8.0 | 1.0 | 3.0 | 10.0 | 5.0 | 1.0 | 5.0 | 10.0 | 8.0 | 7.0 | 7.0 | 7.0 | 10.0 | 3.0 | 8.0 | 1.0 | 9.0 | 3.0 |
| 15 | 9.0 | 9.0 | 3.0 | 3.0 | 3.0 | 6.0 | 9.0 | 2.0 | 7.0 | 10.0 | 9.0 | 2.0 | 8.0 | 2.0 | 2.0 | 6.0 | 3.0 | 5.0 | 9.0 | 5.0 | 9.0 | 4.0 | 10.0 | 10.0 | 4.0 | 7.0 | 4.0 | 9.0 | 2.0 | 2.0 | 3.0 | 4.0 | 2.0 | 6.0 | 5.0 | 5.0 | 7.0 | 2.0 | 3.0 | 1.0 | 10.0 | 3.0 | 9.0 | 2.0 | 8.0 | 5.0 | 3.0 | 1.0 | 9.0 | 9.0 | 5.0 | 1.0 | 3.0 | 1.0 | 5.0 | 3.0 |
| 16 | 2.0 | 6.0 | 3.0 | 7.0 | 1.0 | 7.0 | 9.0 | 6.0 | 3.0 | 7.0 | 2.0 | 5.0 | 6.0 | 5.0 | 10.0 | 3.0 | 9.0 | 6.0 | 9.0 | 10.0 | 6.0 | 7.0 | 1.0 | 4.0 | 4.0 | 7.0 | 4.0 | 7.0 | 10.0 | 5.0 | 7.0 | 7.0 | 10.0 | 7.0 | 9.0 | 9.0 | 1.0 | 7.0 | 5.0 | 5.0 | 2.0 | 5.0 | 10.0 | 1.0 | 1.0 | 5.0 | 9.0 | 2.0 | 3.0 | 4.0 | 10.0 | 3.0 | 4.0 | 2.0 | 9.0 | 2.0 |
| 17 | 8.0 | 4.0 | 2.0 | 7.0 | 6.0 | 8.0 | 6.0 | 7.0 | 4.0 | 9.0 | 7.0 | 2.0 | 8.0 | 6.0 | 10.0 | 5.0 | 6.0 | 7.0 | 6.0 | 9.0 | 8.0 | 8.0 | 2.0 | 9.0 | 8.0 | 5.0 | 2.0 | 8.0 | 2.0 | 3.0 | 5.0 | 10.0 | 7.0 | 1.0 | 2.0 | 2.0 | 6.0 | 2.0 | 4.0 | 10.0 | 3.0 | 4.0 | 1.0 | 2.0 | 9.0 | 3.0 | 8.0 | 2.0 | 9.0 | 8.0 | 7.0 | 10.0 | 9.0 | 6.0 | 10.0 | 9.0 |
| 18 | 2.0 | 2.0 | 3.0 | 3.0 | 6.0 | 4.0 | 1.0 | 6.0 | 7.0 | 4.0 | 10.0 | 4.0 | 2.0 | 5.0 | 4.0 | 9.0 | 9.0 | 6.0 | 7.0 | 8.0 | 6.0 | 9.0 | 1.0 | 2.0 | 5.0 | 6.0 | 8.0 | 10.0 | 3.0 | 3.0 | 7.0 | 7.0 | 5.0 | 6.0 | 3.0 | 3.0 | 4.0 | 3.0 | 4.0 | 8.0 | 8.0 | 9.0 | 1.0 | 2.0 | 6.0 | 6.0 | 5.0 | 9.0 | 10.0 | 7.0 | 1.0 | 2.0 | 3.0 | 3.0 | 6.0 | 9.0 |
| 19 | 4.0 | 4.0 | 1.0 | 4.0 | 3.0 | 4.0 | 4.0 | 8.0 | 4.0 | 1.0 | 2.0 | 3.0 | 7.0 | 3.0 | 9.0 | 5.0 | 10.0 | 9.0 | 8.0 | 7.0 | 1.0 | 9.0 | 8.0 | 3.0 | 4.0 | 8.0 | 6.0 | 10.0 | 7.0 | 3.0 | 10.0 | 6.0 | 2.0 | 6.0 | 1.0 | 7.0 | 4.0 | 7.0 | 3.0 | 6.0 | 5.0 | 2.0 | 9.0 | 9.0 | 10.0 | 6.0 | 3.0 | 5.0 | 4.0 | 9.0 | 7.0 | 10.0 | 5.0 | 5.0 | 6.0 | 3.0 |
| 20 | 3.0 | 7.0 | 5.0 | 9.0 | 8.0 | 10.0 | 4.0 | 4.0 | 4.0 | 6.0 | 5.0 | 9.0 | 7.0 | 8.0 | 2.0 | 9.0 | 6.0 | 8.0 | 6.0 | 1.0 | 6.0 | 5.0 | 10.0 | 2.0 | 6.0 | 8.0 | 6.0 | 3.0 | 9.0 | 4.0 | 1.0 | 6.0 | 1.0 | 2.0 | 2.0 | 7.0 | 6.0 | 9.0 | 7.0 | 3.0 | 10.0 | 4.0 | 3.0 | 7.0 | 2.0 | 4.0 | 6.0 | 1.0 | 3.0 | 6.0 | 5.0 | 6.0 | 6.0 | 3.0 | 5.0 | 3.0 |
| 21 | 2.0 | 3.0 | 6.0 | 10.0 | 7.0 | 3.0 | 10.0 | 7.0 | 9.0 | 5.0 | 9.0 | 4.0 | 2.0 | 4.0 | 4.0 | 4.0 | 7.0 | 8.0 | 9.0 | 9.0 | 5.0 | 10.0 | 2.0 | 5.0 | 4.0 | 6.0 | 10.0 | 4.0 | 8.0 | 1.0 | 2.0 | 9.0 | 3.0 | 8.0 | 10.0 | 6.0 | 1.0 | 6.0 | 2.0 | 8.0 | 3.0 | 2.0 | 9.0 | 6.0 | 9.0 | 2.0 | 9.0 | 7.0 | 10.0 | 1.0 | 2.0 | 1.0 | 9.0 | 6.0 | 7.0 | 3.0 |
| 22 | 3.0 | 10.0 | 3.0 | 7.0 | 7.0 | 4.0 | 3.0 | 2.0 | 5.0 | 5.0 | 7.0 | 9.0 | 7.0 | 3.0 | 9.0 | 10.0 | 1.0 | 2.0 | 1.0 | 8.0 | 10.0 | 2.0 | 7.0 | 6.0 | 8.0 | 4.0 | 4.0 | 4.0 | 3.0 | 2.0 | 10.0 | 1.0 | 10.0 | 7.0 | 5.0 | 1.0 | 3.0 | 9.0 | 8.0 | 8.0 | 1.0 | 1.0 | 8.0 | 5.0 | 9.0 | 2.0 | 4.0 | 10.0 | 4.0 | 4.0 | 6.0 | 9.0 | 3.0 | 10.0 | 7.0 | 1.0 |
| 23 | 3.0 | 5.0 | 3.0 | 9.0 | 9.0 | 5.0 | 8.0 | 10.0 | 8.0 | 8.0 | 3.0 | 3.0 | 9.0 | 9.0 | 9.0 | 10.0 | 4.0 | 9.0 | 2.0 | 3.0 | 2.0 | 5.0 | 6.0 | 6.0 | 7.0 | 10.0 | 1.0 | 2.0 | 6.0 | 9.0 | 5.0 | 7.0 | 5.0 | 4.0 | 8.0 | 7.0 | 4.0 | 9.0 | 9.0 | 4.0 | 3.0 | 7.0 | 2.0 | 7.0 | 5.0 | 10.0 | 9.0 | 9.0 | 9.0 | 5.0 | 8.0 | 8.0 | 6.0 | 10.0 | 7.0 | 7.0 |
| 24 | 7.0 | 9.0 | 10.0 | 4.0 | 8.0 | 1.0 | 3.0 | 6.0 | 5.0 | 3.0 | 8.0 | 3.0 | 3.0 | 10.0 | 4.0 | 4.0 | 4.0 | 8.0 | 5.0 | 4.0 | 6.0 | 4.0 | 8.0 | 7.0 | 7.0 | 6.0 | 1.0 | 3.0 | 2.0 | 5.0 | 6.0 | 7.0 | 10.0 | 3.0 | 9.0 | 10.0 | 10.0 | 5.0 | 6.0 | 7.0 | 6.0 | 6.0 | 10.0 | 10.0 | 2.0 | 10.0 | 1.0 | 3.0 | 9.0 | 1.0 | 7.0 | 10.0 | 6.0 | 2.0 | 9.0 | 2.0 |
| 25 | 8.0 | 1.0 | 5.0 | 6.0 | 8.0 | 7.0 | 10.0 | 9.0 | 8.0 | 6.0 | 2.0 | 7.0 | 5.0 | 5.0 | 4.0 | 7.0 | 7.0 | 5.0 | 6.0 | 8.0 | 8.0 | 6.0 | 4.0 | 10.0 | 6.0 | 9.0 | 7.0 | 8.0 | 9.0 | 7.0 | 6.0 | 10.0 | 10.0 | 8.0 | 5.0 | 7.0 | 6.0 | 3.0 | 2.0 | 8.0 | 8.0 | 9.0 | 7.0 | 6.0 | 2.0 | 10.0 | 1.0 | 1.0 | 4.0 | 2.0 | 6.0 | 4.0 | 10.0 | 2.0 | 3.0 | 9.0 |
| 26 | 8.0 | 4.0 | 9.0 | 7.0 | 6.0 | 7.0 | 1.0 | 8.0 | 3.0 | 7.0 | 10.0 | 4.0 | 10.0 | 4.0 | 7.0 | 4.0 | 4.0 | 2.0 | 8.0 | 6.0 | 6.0 | 10.0 | 4.0 | 1.0 | 1.0 | 7.0 | 3.0 | 4.0 | 10.0 | 6.0 | 1.0 | 7.0 | 4.0 | 4.0 | 9.0 | 5.0 | 8.0 | 10.0 | 3.0 | 3.0 | 7.0 | 5.0 | 1.0 | 7.0 | 7.0 | 4.0 | 3.0 | 6.0 | 9.0 | 1.0 | 5.0 | 1.0 | 8.0 | 9.0 | 6.0 | 3.0 |
| 27 | 4.0 | 3.0 | 2.0 | 2.0 | 7.0 | 5.0 | 8.0 | 10.0 | 10.0 | 10.0 | 5.0 | 7.0 | 10.0 | 6.0 | 5.0 | 9.0 | 7.0 | 8.0 | 10.0 | 10.0 | 3.0 | 4.0 | 4.0 | 2.0 | 3.0 | 8.0 | 4.0 | 7.0 | 1.0 | 5.0 | 8.0 | 3.0 | 4.0 | 4.0 | 1.0 | 9.0 | 6.0 | 6.0 | 1.0 | 2.0 | 7.0 | 9.0 | 4.0 | 5.0 | 10.0 | 9.0 | 6.0 | 6.0 | 7.0 | 3.0 | 3.0 | 2.0 | 9.0 | 3.0 | 5.0 | 2.0 |
| 28 | 1.0 | 10.0 | 8.0 | 4.0 | 8.0 | 5.0 | 8.0 | 7.0 | 1.0 | 6.0 | 3.0 | 8.0 | 1.0 | 4.0 | 4.0 | 2.0 | 10.0 | 2.0 | 3.0 | 7.0 | 9.0 | 8.0 | 3.0 | 6.0 | 2.0 | 9.0 | 10.0 | 1.0 | 9.0 | 2.0 | 5.0 | 2.0 | 1.0 | 6.0 | 8.0 | 2.0 | 7.0 | 1.0 | 9.0 | 1.0 | 1.0 | 3.0 | 5.0 | 3.0 | 10.0 | 5.0 | 9.0 | 5.0 | 3.0 | 10.0 | 7.0 | 8.0 | 3.0 | 8.0 | 9.0 | 9.0 |
| 29 | 4.0 | 8.0 | 9.0 | 3.0 | 3.0 | 9.0 | 1.0 | 1.0 | 3.0 | 2.0 | 10.0 | 4.0 | 6.0 | 4.0 | 10.0 | 2.0 | 5.0 | 3.0 | 3.0 | 3.0 | 4.0 | 1.0 | 2.0 | 9.0 | 5.0 | 7.0 | 6.0 | 5.0 | 2.0 | 10.0 | 10.0 | 4.0 | 10.0 | 3.0 | 3.0 | 4.0 | 10.0 | 9.0 | 3.0 | 10.0 | 2.0 | 5.0 | 7.0 | 2.0 | 1.0 | 8.0 | 2.0 | 3.0 | 10.0 | 10.0 | 8.0 | 8.0 | 9.0 | 6.0 | 3.0 | 9.0 |
| 30 | 2.0 | 3.0 | 1.0 | 4.0 | 3.0 | 9.0 | 8.0 | 5.0 | 8.0 | 1.0 | 6.0 | 4.0 | 9.0 | 8.0 | 1.0 | 3.0 | 7.0 | 5.0 | 7.0 | 10.0 | 1.0 | 2.0 | 10.0 | 5.0 | 6.0 | 6.0 | 1.0 | 8.0 | 5.0 | 10.0 | 2.0 | 9.0 | 1.0 | 5.0 | 1.0 | 10.0 | 3.0 | 9.0 | 7.0 | 10.0 | 2.0 | 10.0 | 9.0 | 10.0 | 1.0 | 4.0 | 7.0 | 8.0 | 8.0 | 5.0 | 10.0 | 9.0 | 8.0 | 2.0 | 8.0 | 9.0 |
| 31 | 8.0 | 2.0 | 8.0 | 6.0 | 6.0 | 2.0 | 2.0 | 4.0 | 10.0 | 10.0 | 1.0 | 5.0 | 2.0 | 3.0 | 8.0 | 4.0 | 7.0 | 10.0 | 7.0 | 6.0 | 6.0 | 9.0 | 1.0 | 7.0 | 7.0 | 10.0 | 7.0 | 3.0 | 2.0 | 4.0 | 9.0 | 8.0 | 7.0 | 10.0 | 5.0 | 4.0 | 3.0 | 1.0 | 4.0 | 2.0 | 2.0 | 1.0 | 9.0 | 1.0 | 1.0 | 7.0 | 7.0 | 10.0 | 3.0 | 5.0 | 10.0 | 4.0 | 3.0 | 4.0 | 10.0 | 4.0 |
| 32 | 7.0 | 2.0 | 2.0 | 1.0 | 8.0 | 1.0 | 9.0 | 6.0 | 8.0 | 6.0 | 7.0 | 7.0 | 2.0 | 4.0 | 3.0 | 2.0 | 10.0 | 7.0 | 5.0 | 2.0 | 1.0 | 3.0 | 10.0 | 5.0 | 10.0 | 10.0 | 4.0 | 4.0 | 1.0 | 10.0 | 1.0 | 7.0 | 7.0 | 9.0 | 6.0 | 7.0 | 3.0 | 1.0 | 4.0 | 9.0 | 2.0 | 8.0 | 5.0 | 9.0 | 4.0 | 6.0 | 9.0 | 1.0 | 1.0 | 1.0 | 6.0 | 4.0 | 8.0 | 10.0 | 10.0 | 9.0 |
| 33 | 5.0 | 6.0 | 2.0 | 4.0 | 3.0 | 5.0 | 5.0 | 5.0 | 5.0 | 7.0 | 1.0 | 8.0 | 10.0 | 3.0 | 3.0 | 6.0 | 7.0 | 1.0 | 6.0 | 6.0 | 2.0 | 8.0 | 7.0 | 4.0 | 3.0 | 8.0 | 4.0 | 4.0 | 6.0 | 3.0 | 5.0 | 10.0 | 9.0 | 9.0 | 7.0 | 10.0 | 6.0 | 5.0 | 6.0 | 3.0 | 2.0 | 4.0 | 9.0 | 10.0 | 3.0 | 8.0 | 9.0 | 6.0 | 9.0 | 9.0 | 8.0 | 3.0 | 5.0 | 9.0 | 1.0 | 8.0 |
| 34 | 4.0 | 9.0 | 1.0 | 1.0 | 5.0 | 4.0 | 1.0 | 7.0 | 8.0 | 5.0 | 1.0 | 4.0 | 3.0 | 1.0 | 4.0 | 5.0 | 9.0 | 2.0 | 3.0 | 1.0 | 2.0 | 10.0 | 5.0 | 8.0 | 9.0 | 5.0 | 9.0 | 1.0 | 8.0 | 3.0 | 1.0 | 5.0 | 6.0 | 7.0 | 8.0 | 4.0 | 5.0 | 4.0 | 3.0 | 2.0 | 9.0 | 6.0 | 2.0 | 6.0 | 6.0 | 8.0 | 10.0 | 4.0 | 4.0 | 9.0 | 5.0 | 2.0 | 6.0 | 2.0 | 4.0 | 2.0 |
| 35 | 9.0 | 5.0 | 9.0 | 8.0 | 10.0 | 7.0 | 3.0 | 10.0 | 6.0 | 3.0 | 6.0 | 9.0 | 1.0 | 8.0 | 8.0 | 5.0 | 9.0 | 2.0 | 3.0 | 7.0 | 7.0 | 6.0 | 1.0 | 7.0 | 10.0 | 7.0 | 5.0 | 9.0 | 2.0 | 4.0 | 10.0 | 4.0 | 7.0 | 10.0 | 4.0 | 7.0 | 5.0 | 1.0 | 3.0 | 5.0 | 10.0 | 10.0 | 9.0 | 4.0 | 10.0 | 9.0 | 10.0 | 2.0 | 5.0 | 1.0 | 8.0 | 1.0 | 4.0 | 8.0 | 2.0 | 3.0 |
| 36 | 9.0 | 10.0 | 6.0 | 2.0 | 9.0 | 7.0 | 6.0 | 8.0 | 3.0 | 6.0 | 2.0 | 5.0 | 5.0 | 4.0 | 4.0 | 7.0 | 1.0 | 6.0 | 4.0 | 4.0 | 6.0 | 1.0 | 3.0 | 4.0 | 10.0 | 6.0 | 8.0 | 6.0 | 7.0 | 10.0 | 3.0 | 3.0 | 3.0 | 6.0 | 5.0 | 5.0 | 4.0 | 7.0 | 3.0 | 5.0 | 10.0 | 6.0 | 7.0 | 9.0 | 6.0 | 6.0 | 3.0 | 5.0 | 3.0 | 7.0 | 10.0 | 9.0 | 6.0 | 1.0 | 9.0 | 2.0 |
| 37 | 9.0 | 1.0 | 8.0 | 4.0 | 8.0 | 4.0 | 2.0 | 9.0 | 1.0 | 1.0 | 6.0 | 5.0 | 4.0 | 4.0 | 7.0 | 2.0 | 7.0 | 2.0 | 3.0 | 7.0 | 9.0 | 6.0 | 9.0 | 9.0 | 5.0 | 3.0 | 10.0 | 6.0 | 1.0 | 9.0 | 9.0 | 1.0 | 1.0 | 5.0 | 4.0 | 1.0 | 7.0 | 8.0 | 2.0 | 4.0 | 9.0 | 4.0 | 4.0 | 6.0 | 5.0 | 10.0 | 7.0 | 5.0 | 10.0 | 3.0 | 3.0 | 10.0 | 7.0 | 2.0 | 5.0 | 4.0 |
| 38 | 5.0 | 1.0 | 6.0 | 4.0 | 8.0 | 1.0 | 5.0 | 4.0 | 9.0 | 1.0 | 2.0 | 4.0 | 5.0 | 1.0 | 8.0 | 3.0 | 5.0 | 4.0 | 4.0 | 3.0 | 7.0 | 2.0 | 8.0 | 9.0 | 6.0 | 2.0 | 3.0 | 1.0 | 9.0 | 3.0 | 7.0 | 4.0 | 4.0 | 6.0 | 3.0 | 3.0 | 3.0 | 2.0 | 6.0 | 5.0 | 1.0 | 1.0 | 7.0 | 10.0 | 10.0 | 9.0 | 9.0 | 9.0 | 9.0 | 1.0 | 6.0 | 1.0 | 5.0 | 4.0 | 7.0 | 1.0 |
| 39 | 2.0 | 7.0 | 5.0 | 10.0 | 9.0 | 5.0 | 10.0 | 10.0 | 2.0 | 7.0 | 4.0 | 2.0 | 6.0 | 7.0 | 1.0 | 1.0 | 5.0 | 10.0 | 8.0 | 6.0 | 3.0 | 8.0 | 8.0 | 4.0 | 7.0 | 8.0 | 3.0 | 2.0 | 1.0 | 10.0 | 10.0 | 2.0 | 9.0 | 3.0 | 2.0 | 5.0 | 5.0 | 4.0 | 5.0 | 3.0 | 9.0 | 4.0 | 6.0 | 7.0 | 5.0 | 3.0 | 3.0 | 10.0 | 4.0 | 10.0 | 8.0 | 5.0 | 10.0 | 2.0 | 2.0 | 7.0 |
| 40 | 5.0 | 4.0 | 3.0 | 2.0 | 9.0 | 6.0 | 6.0 | 4.0 | 2.0 | 3.0 | 6.0 | 4.0 | 3.0 | 5.0 | 3.0 | 10.0 | 2.0 | 3.0 | 8.0 | 5.0 | 10.0 | 3.0 | 1.0 | 3.0 | 6.0 | 8.0 | 7.0 | 7.0 | 1.0 | 2.0 | 2.0 | 2.0 | 2.0 | 2.0 | 9.0 | 10.0 | 10.0 | 9.0 | 1.0 | 9.0 | 1.0 | 8.0 | 1.0 | 9.0 | 10.0 | 9.0 | 8.0 | 10.0 | 2.0 | 9.0 | 5.0 | 1.0 | 8.0 | 10.0 | 5.0 | 10.0 |
| 41 | 4.0 | 5.0 | 5.0 | 10.0 | 4.0 | 1.0 | 9.0 | 8.0 | 5.0 | 10.0 | 1.0 | 3.0 | 5.0 | 7.0 | 10.0 | 3.0 | 5.0 | 4.0 | 9.0 | 2.0 | 4.0 | 2.0 | 1.0 | 7.0 | 6.0 | 9.0 | 5.0 | 9.0 | 3.0 | 5.0 | 10.0 | 1.0 | 8.0 | 4.0 | 6.0 | 10.0 | 6.0 | 4.0 | 1.0 | 4.0 | 8.0 | 1.0 | 3.0 | 9.0 | 5.0 | 1.0 | 2.0 | 5.0 | 3.0 | 6.0 | 10.0 | 9.0 | 6.0 | 7.0 | 3.0 | 1.0 |
| 42 | 3.0 | 5.0 | 7.0 | 7.0 | 4.0 | 1.0 | 7.0 | 10.0 | 3.0 | 1.0 | 2.0 | 1.0 | 6.0 | 9.0 | 5.0 | 9.0 | 10.0 | 1.0 | 1.0 | 9.0 | 3.0 | 9.0 | 8.0 | 2.0 | 10.0 | 7.0 | 1.0 | 4.0 | 5.0 | 7.0 | 9.0 | 9.0 | 5.0 | 9.0 | 2.0 | 9.0 | 7.0 | 4.0 | 7.0 | 6.0 | 1.0 | 3.0 | 8.0 | 4.0 | 6.0 | 7.0 | 5.0 | 6.0 | 9.0 | 3.0 | 7.0 | 8.0 | 9.0 | 7.0 | 9.0 | 3.0 |
| 43 | 5.0 | 6.0 | 4.0 | 7.0 | 5.0 | 6.0 | 6.0 | 10.0 | 8.0 | 4.0 | 6.0 | 7.0 | 5.0 | 1.0 | 1.0 | 2.0 | 1.0 | 2.0 | 2.0 | 9.0 | 7.0 | 6.0 | 5.0 | 7.0 | 10.0 | 6.0 | 7.0 | 5.0 | 3.0 | 2.0 | 10.0 | 1.0 | 9.0 | 10.0 | 6.0 | 4.0 | 9.0 | 6.0 | 10.0 | 7.0 | 9.0 | 9.0 | 4.0 | 8.0 | 3.0 | 4.0 | 4.0 | 5.0 | 1.0 | 7.0 | 9.0 | 2.0 | 4.0 | 7.0 | 10.0 | 5.0 |
| 44 | 10.0 | 1.0 | 7.0 | 1.0 | 6.0 | 3.0 | 4.0 | 1.0 | 6.0 | 3.0 | 2.0 | 7.0 | 6.0 | 2.0 | 5.0 | 8.0 | 1.0 | 9.0 | 6.0 | 10.0 | 2.0 | 9.0 | 9.0 | 5.0 | 2.0 | 2.0 | 7.0 | 10.0 | 10.0 | 1.0 | 1.0 | 1.0 | 4.0 | 3.0 | 6.0 | 10.0 | 6.0 | 5.0 | 10.0 | 5.0 | 10.0 | 5.0 | 6.0 | 3.0 | 8.0 | 1.0 | 8.0 | 6.0 | 2.0 | 7.0 | 9.0 | 1.0 | 5.0 | 10.0 | 10.0 | 2.0 |
| 45 | 8.0 | 1.0 | 3.0 | 8.0 | 8.0 | 5.0 | 6.0 | 10.0 | 10.0 | 8.0 | 5.0 | 3.0 | 7.0 | 10.0 | 10.0 | 5.0 | 5.0 | 3.0 | 6.0 | 6.0 | 4.0 | 2.0 | 2.0 | 10.0 | 10.0 | 10.0 | 4.0 | 9.0 | 5.0 | 8.0 | 4.0 | 7.0 | 6.0 | 8.0 | 8.0 | 9.0 | 6.0 | 10.0 | 9.0 | 3.0 | 9.0 | 1.0 | 7.0 | 4.0 | 1.0 | 9.0 | 9.0 | 3.0 | 2.0 | 2.0 | 1.0 | 5.0 | 2.0 | 10.0 | 5.0 | 8.0 |
| 46 | 6.0 | 6.0 | 8.0 | 5.0 | 9.0 | 9.0 | 10.0 | 1.0 | 9.0 | 4.0 | 10.0 | 9.0 | 1.0 | 4.0 | 8.0 | 3.0 | 9.0 | 8.0 | 5.0 | 3.0 | 6.0 | 9.0 | 4.0 | 9.0 | 1.0 | 1.0 | 3.0 | 6.0 | 9.0 | 2.0 | 7.0 | 7.0 | 9.0 | 9.0 | 10.0 | 10.0 | 3.0 | 7.0 | 9.0 | 3.0 | 8.0 | 2.0 | 5.0 | 4.0 | 8.0 | 9.0 | 7.0 | 5.0 | 4.0 | 8.0 | 5.0 | 3.0 | 9.0 | 3.0 | 1.0 | 4.0 |
| 47 | 8.0 | 1.0 | 3.0 | 8.0 | 3.0 | 2.0 | 6.0 | 9.0 | 7.0 | 10.0 | 9.0 | 3.0 | 1.0 | 3.0 | 7.0 | 1.0 | 2.0 | 2.0 | 9.0 | 5.0 | 1.0 | 7.0 | 10.0 | 9.0 | 3.0 | 1.0 | 6.0 | 6.0 | 5.0 | 3.0 | 8.0 | 10.0 | 1.0 | 6.0 | 4.0 | 2.0 | 5.0 | 5.0 | 9.0 | 10.0 | 10.0 | 5.0 | 6.0 | 5.0 | 6.0 | 3.0 | 5.0 | 6.0 | 8.0 | 7.0 | 9.0 | 7.0 | 5.0 | 4.0 | 7.0 | 2.0 |
| 48 | 9.0 | 8.0 | 3.0 | 7.0 | 3.0 | 2.0 | 8.0 | 1.0 | 9.0 | 10.0 | 1.0 | 1.0 | 3.0 | 4.0 | 7.0 | 9.0 | 3.0 | 9.0 | 10.0 | 4.0 | 3.0 | 10.0 | 4.0 | 9.0 | 9.0 | 4.0 | 9.0 | 7.0 | 3.0 | 10.0 | 8.0 | 3.0 | 1.0 | 9.0 | 4.0 | 5.0 | 3.0 | 10.0 | 9.0 | 4.0 | 2.0 | 3.0 | 9.0 | 1.0 | 2.0 | 2.0 | 4.0 | 8.0 | 3.0 | 10.0 | 4.0 | 7.0 | 4.0 | 3.0 | 9.0 | 6.0 |
| 49 | 8.0 | 10.0 | 4.0 | 7.0 | 1.0 | 9.0 | 4.0 | 5.0 | 5.0 | 9.0 | 10.0 | 5.0 | 8.0 | 10.0 | 7.0 | 9.0 | 4.0 | 8.0 | 7.0 | 9.0 | 6.0 | 1.0 | 4.0 | 5.0 | 1.0 | 2.0 | 1.0 | 3.0 | 10.0 | 10.0 | 5.0 | 5.0 | 1.0 | 9.0 | 9.0 | 1.0 | 7.0 | 3.0 | 1.0 | 10.0 | 9.0 | 6.0 | 3.0 | 7.0 | 7.0 | 2.0 | 8.0 | 7.0 | 10.0 | 5.0 | 5.0 | 5.0 | 5.0 | 10.0 | 1.0 | 1.0 |
| 50 | 8.0 | 10.0 | 3.0 | 8.0 | 2.0 | 3.0 | 2.0 | 2.0 | 8.0 | 4.0 | 7.0 | 2.0 | 7.0 | 7.0 | 10.0 | 5.0 | 10.0 | 7.0 | 1.0 | 7.0 | 5.0 | 2.0 | 6.0 | 8.0 | 7.0 | 6.0 | 5.0 | 3.0 | 7.0 | 8.0 | 10.0 | 10.0 | 6.0 | 8.0 | 5.0 | 8.0 | 10.0 | 3.0 | 6.0 | 8.0 | 5.0 | 10.0 | 7.0 | 9.0 | 9.0 | 1.0 | 5.0 | 9.0 | 4.0 | 5.0 | 7.0 | 1.0 | 7.0 | 3.0 | 1.0 | 2.0 |
| 51 | 10.0 | 1.0 | 5.0 | 9.0 | 7.0 | 8.0 | 6.0 | 6.0 | 8.0 | 7.0 | 2.0 | 7.0 | 7.0 | 3.0 | 3.0 | 1.0 | 3.0 | 10.0 | 2.0 | 10.0 | 6.0 | 1.0 | 9.0 | 8.0 | 10.0 | 4.0 | 1.0 | 2.0 | 8.0 | 8.0 | 9.0 | 4.0 | 4.0 | 3.0 | 2.0 | 1.0 | 9.0 | 10.0 | 1.0 | 5.0 | 1.0 | 9.0 | 8.0 | 2.0 | 1.0 | 5.0 | 3.0 | 7.0 | 7.0 | 5.0 | 1.0 | 5.0 | 9.0 | 1.0 | 9.0 | 4.0 |
| 52 | 1.0 | 6.0 | 6.0 | 8.0 | 2.0 | 3.0 | 6.0 | 6.0 | 7.0 | 4.0 | 5.0 | 10.0 | 4.0 | 3.0 | 8.0 | 3.0 | 4.0 | 9.0 | 3.0 | 5.0 | 6.0 | 9.0 | 3.0 | 6.0 | 6.0 | 10.0 | 8.0 | 9.0 | 3.0 | 9.0 | 8.0 | 3.0 | 8.0 | 5.0 | 6.0 | 4.0 | 6.0 | 7.0 | 5.0 | 10.0 | 8.0 | 6.0 | 9.0 | 4.0 | 5.0 | 2.0 | 9.0 | 5.0 | 4.0 | 5.0 | 7.0 | 9.0 | 7.0 | 10.0 | 4.0 | 7.0 |
| 53 | 7.0 | 3.0 | 8.0 | 2.0 | 2.0 | 3.0 | 1.0 | 4.0 | 3.0 | 7.0 | 7.0 | 2.0 | 1.0 | 9.0 | 1.0 | 1.0 | 2.0 | 6.0 | 3.0 | 5.0 | 3.0 | 6.0 | 10.0 | 10.0 | 2.0 | 2.0 | 9.0 | 3.0 | 8.0 | 6.0 | 2.0 | 4.0 | 10.0 | 9.0 | 2.0 | 8.0 | 1.0 | 2.0 | 4.0 | 2.0 | 10.0 | 7.0 | 7.0 | 7.0 | 10.0 | 10.0 | 3.0 | 4.0 | 3.0 | 10.0 | 3.0 | 1.0 | 10.0 | 3.0 | 3.0 | 9.0 |
| 54 | 3.0 | 3.0 | 10.0 | 5.0 | 6.0 | 4.0 | 2.0 | 5.0 | 1.0 | 2.0 | 2.0 | 2.0 | 6.0 | 5.0 | 9.0 | 5.0 | 9.0 | 10.0 | 6.0 | 6.0 | 5.0 | 7.0 | 7.0 | 7.0 | 9.0 | 3.0 | 6.0 | 5.0 | 9.0 | 3.0 | 8.0 | 10.0 | 10.0 | 1.0 | 4.0 | 2.0 | 9.0 | 5.0 | 7.0 | 2.0 | 5.0 | 3.0 | 9.0 | 10.0 | 10.0 | 5.0 | 1.0 | 7.0 | 9.0 | 1.0 | 1.0 | 9.0 | 4.0 | 3.0 | 5.0 | 8.0 |
| 55 | 8.0 | 10.0 | 10.0 | 1.0 | 6.0 | 10.0 | 2.0 | 3.0 | 2.0 | 6.0 | 5.0 | 7.0 | 10.0 | 8.0 | 3.0 | 3.0 | 2.0 | 9.0 | 9.0 | 3.0 | 3.0 | 3.0 | 1.0 | 7.0 | 2.0 | 9.0 | 3.0 | 2.0 | 9.0 | 9.0 | 9.0 | 4.0 | 9.0 | 8.0 | 2.0 | 3.0 | 2.0 | 4.0 | 1.0 | 7.0 | 10.0 | 1.0 | 3.0 | 5.0 | 2.0 | 8.0 | 4.0 | 2.0 | 6.0 | 1.0 | 2.0 | 4.0 | 7.0 | 9.0 | 8.0 | 4.0 |

Also, when you send the route back, it'd be great if you pop it into a tiny JSON snippet so it's easy to read and machine-friendly — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of that as a little form: ""solution"" should be the ordered list of locations (nodes) you travel through from pickup to delivery, first entry the source and last the target. Keep it simple and human: just the location names in order, no belt codes or cost bits. This block is just the expected shape — it’s a sketch, not the actual answer.

One more thing: use the node identifiers exactly as they appear in the instance input — do not rename or invent labels.  

Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 1, 'var_index': 1}, {'from': 19, 'to': 2, 'var_index': 2}, {'from': 19, 'to': 3, 'var_index': 3}, {'from': 19, 'to': 4, 'var_index': 4}, {'from': 19, 'to': 5, 'var_index': 5}, {'from': 19, 'to': 6, 'var_index': 6}, {'from': 19, 'to': 7, 'var_index': 7}, {'from': 19, 'to': 8, 'var_index': 8}, {'from': 19, 'to': 9, 'var_index': 9}, {'from': 19, 'to': 10, 'var_index': 10}, {'from': 19, 'to': 11, 'var_index': 11}, {'from': 19, 'to': 12, 'var_index': 12}, {'from': 19, 'to': 13, 'var_index': 13}, {'from': 19, 'to': 14, 'var_index': 14}, {'from': 19, 'to': 15, 'var_index': 15}, {'from': 19, 'to': 16, 'var_index': 16}, {'from': 19, 'to': 17, 'var_index': 17}, {'from': 19, 'to': 18, 'var_index': 18}, {'from': 0, 'to': 20, 'var_index': 19}, {'from': 1, 'to': 20, 'var_index': 20}, {'from': 2, 'to': 20, 'var_index': 21}, {'from': 3, 'to': 20, 'var_index': 22}, {'from': 4, 'to': 20, 'var_index': 23}, {'from': 5, 'to': 20, 'var_index': 24}, {'from': 6, 'to': 20, 'var_index': 25}, {'from': 7, 'to': 20, 'var_index': 26}, {'from': 8, 'to': 20, 'var_index': 27}, {'from': 9, 'to': 20, 'var_index': 28}, {'from': 10, 'to': 20, 'var_index': 29}, {'from': 11, 'to': 20, 'var_index': 30}, {'from': 12, 'to': 20, 'var_index': 31}, {'from': 13, 'to': 20, 'var_index': 32}, {'from': 14, 'to': 20, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 20, 'var_index': 35}, {'from': 17, 'to': 20, 'var_index': 36}, {'from': 18, 'to': 20, 'var_index': 37}, {'from': 0, 'to': 1, 'var_index': 38}, {'from': 1, 'to': 2, 'var_index': 39}, {'from': 2, 'to': 3, 'var_index': 40}, {'from': 3, 'to': 4, 'var_index': 41}, {'from': 4, 'to': 5, 'var_index': 42}, {'from': 5, 'to': 6, 'var_index': 43}, {'from': 6, 'to': 7, 'var_index': 44}, {'from': 7, 'to': 8, 'var_index': 45}, {'from': 8, 'to': 9, 'var_index': 46}, {'from': 9, 'to': 10, 'var_index': 47}, {'from': 10, 'to': 11, 'var_index': 48}, {'from': 11, 'to': 12, 'var_index': 49}, {'from': 12, 'to': 13, 'var_index': 50}, {'from': 13, 'to': 14, 'var_index': 51}, {'from': 14, 'to': 15, 'var_index': 52}, {'from': 15, 'to': 16, 'var_index': 53}, {'from': 16, 'to': 17, 'var_index': 54}, {'from': 17, 'to': 18, 'var_index': 55}], 'objective': {'constant': 0.0, 'linear': [1.0, 4.0, 7.0, 1.0, 3.0, 10.0, 6.0, 10.0, 4.0, 2.0, 1.0, 2.0, 8.0, 9.0, 8.0, 5.0, 5.0, 2.0, 2.0, 7.0, 3.0, 6.0, 5.0, 9.0, 7.0, 8.0, 3.0, 2.0, 2.0, 10.0, 5.0, 10.0, 3.0, 2.0, 9.0, 2.0, 9.0, 1.0, 10.0, 5.0, 4.0, 10.0, 8.0, 7.0, 3.0, 7.0, 10.0, 2.0, 9.0, 9.0, 2.0, 2.0, 8.0, 6.0, 7.0, 7.0], 'quadratic': [[10.0, 6.0, 9.0, 10.0, 4.0, 9.0, 4.0, 1.0, 8.0, 9.0, 2.0, 2.0, 10.0, 5.0, 7.0, 9.0, 2.0, 8.0, 2.0, 4.0, 3.0, 2.0, 3.0, 3.0, 7.0, 8.0, 8.0, 4.0, 1.0, 4.0, 2.0, 8.0, 7.0, 5.0, 4.0, 9.0, 9.0, 9.0, 5.0, 2.0, 5.0, 4.0, 3.0, 5.0, 10.0, 8.0, 6.0, 8.0, 9.0, 8.0, 8.0, 10.0, 1.0, 7.0, 3.0, 8.0], [6.0, 8.0, 9.0, 3.0, 8.0, 2.0, 3.0, 10.0, 7.0, 3.0, 7.0, 7.0, 4.0, 2.0, 1.0, 9.0, 6.0, 4.0, 2.0, 4.0, 7.0, 3.0, 10.0, 5.0, 9.0, 1.0, 4.0, 3.0, 10.0, 8.0, 3.0, 2.0, 2.0, 6.0, 9.0, 5.0, 10.0, 1.0, 1.0, 7.0, 4.0, 5.0, 5.0, 6.0, 1.0, 1.0, 6.0, 1.0, 8.0, 10.0, 10.0, 1.0, 6.0, 3.0, 3.0, 10.0], [9.0, 9.0, 5.0, 1.0, 10.0, 5.0, 2.0, 10.0, 1.0, 3.0, 9.0, 3.0, 4.0, 7.0, 1.0, 3.0, 3.0, 2.0, 3.0, 1.0, 5.0, 6.0, 3.0, 3.0, 10.0, 5.0, 9.0, 2.0, 8.0, 9.0, 1.0, 8.0, 2.0, 2.0, 1.0, 9.0, 6.0, 8.0, 6.0, 5.0, 3.0, 5.0, 7.0, 4.0, 7.0, 3.0, 8.0, 3.0, 3.0, 4.0, 3.0, 5.0, 6.0, 8.0, 10.0, 10.0], [10.0, 3.0, 1.0, 3.0, 2.0, 3.0, 1.0, 10.0, 7.0, 5.0, 8.0, 10.0, 7.0, 10.0, 7.0, 3.0, 7.0, 7.0, 3.0, 4.0, 9.0, 10.0, 7.0, 9.0, 4.0, 6.0, 7.0, 2.0, 4.0, 3.0, 4.0, 6.0, 1.0, 4.0, 1.0, 8.0, 2.0, 4.0, 4.0, 10.0, 2.0, 10.0, 7.0, 7.0, 1.0, 8.0, 5.0, 8.0, 7.0, 7.0, 8.0, 9.0, 8.0, 2.0, 5.0, 1.0], [4.0, 8.0, 10.0, 2.0, 4.0, 6.0, 7.0, 9.0, 4.0, 9.0, 5.0, 6.0, 10.0, 5.0, 8.0, 3.0, 1.0, 6.0, 6.0, 3.0, 8.0, 7.0, 7.0, 9.0, 8.0, 8.0, 6.0, 7.0, 8.0, 3.0, 3.0, 6.0, 8.0, 3.0, 5.0, 10.0, 9.0, 8.0, 8.0, 9.0, 9.0, 4.0, 4.0, 5.0, 6.0, 8.0, 9.0, 3.0, 3.0, 1.0, 2.0, 7.0, 2.0, 2.0, 6.0, 6.0], [9.0, 2.0, 5.0, 3.0, 6.0, 5.0, 6.0, 4.0, 7.0, 1.0, 9.0, 1.0, 2.0, 5.0, 9.0, 6.0, 7.0, 8.0, 4.0, 4.0, 10.0, 3.0, 4.0, 5.0, 1.0, 7.0, 7.0, 5.0, 5.0, 9.0, 9.0, 2.0, 1.0, 5.0, 4.0, 7.0, 7.0, 4.0, 1.0, 5.0, 6.0, 1.0, 1.0, 6.0, 3.0, 5.0, 9.0, 2.0, 2.0, 9.0, 3.0, 8.0, 3.0, 3.0, 4.0, 10.0], [4.0, 3.0, 2.0, 1.0, 7.0, 6.0, 9.0, 5.0, 5.0, 6.0, 3.0, 6.0, 7.0, 7.0, 4.0, 9.0, 9.0, 6.0, 1.0, 4.0, 4.0, 10.0, 3.0, 8.0, 3.0, 10.0, 1.0, 8.0, 8.0, 1.0, 8.0, 2.0, 9.0, 5.0, 1.0, 3.0, 6.0, 2.0, 5.0, 10.0, 6.0, 9.0, 7.0, 6.0, 4.0, 6.0, 10.0, 6.0, 8.0, 4.0, 2.0, 6.0, 6.0, 1.0, 2.0, 2.0], [1.0, 10.0, 10.0, 10.0, 9.0, 4.0, 5.0, 1.0, 7.0, 3.0, 10.0, 5.0, 10.0, 10.0, 7.0, 2.0, 6.0, 7.0, 6.0, 8.0, 4.0, 7.0, 2.0, 10.0, 6.0, 9.0, 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'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 48, 'quadratic_cost': 6.0}, {'var_i': 55, 'var_j': 49, 'quadratic_cost': 1.0}, {'var_i': 55, 'var_j': 50, 'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 51, 'quadratic_cost': 4.0}, {'var_i': 55, 'var_j': 52, 'quadratic_cost': 7.0}, {'var_i': 55, 'var_j': 53, 'quadratic_cost': 9.0}, {'var_i': 55, 'var_j': 54, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 55, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 20, 'to': 1, 'var_index': 0}, {'from': 20, 'to': 2, 'var_index': 1}, {'from': 20, 'to': 3, 'var_index': 2}, {'from': 20, 'to': 4, 'var_index': 3}, {'from': 20, 'to': 5, 'var_index': 4}, {'from': 20, 'to': 6, 'var_index': 5}, {'from': 20, 'to': 7, 'var_index': 6}, {'from': 20, 'to': 8, 'var_index': 7}, {'from': 20, 'to': 9, 'var_index': 8}, {'from': 20, 'to': 10, 'var_index': 9}, {'from': 20, 'to': 11, 'var_index': 10}, {'from': 20, 'to': 12, 'var_index': 11}, {'from': 20, 'to': 13, 'var_index': 12}, {'from': 20, 'to': 14, 'var_index': 13}, {'from': 20, 'to': 15, 'var_index': 14}, {'from': 20, 'to': 16, 'var_index': 15}, {'from': 20, 'to': 17, 'var_index': 16}, {'from': 20, 'to': 18, 'var_index': 17}, {'from': 20, 'to': 19, 'var_index': 18}, {'from': 1, 'to': 21, 'var_index': 19}, {'from': 2, 'to': 21, 'var_index': 20}, {'from': 3, 'to': 21, 'var_index': 21}, {'from': 4, 'to': 21, 'var_index': 22}, {'from': 5, 'to': 21, 'var_index': 23}, {'from': 6, 'to': 21, 'var_index': 24}, {'from': 7, 'to': 21, 'var_index': 25}, {'from': 8, 'to': 21, 'var_index': 26}, {'from': 9, 'to': 21, 'var_index': 27}, {'from': 10, 'to': 21, 'var_index': 28}, {'from': 11, 'to': 21, 'var_index': 29}, {'from': 12, 'to': 21, 'var_index': 30}, {'from': 13, 'to': 21, 'var_index': 31}, {'from': 14, 'to': 21, 'var_index': 32}, {'from': 15, 'to': 21, 'var_index': 33}, {'from': 16, 'to': 21, 'var_index': 34}, {'from': 17, 'to': 21, 'var_index': 35}, {'from': 18, 'to': 21, 'var_index': 36}, {'from': 19, 'to': 21, 'var_index': 37}, {'from': 1, 'to': 2, 'var_index': 38}, {'from': 2, 'to': 3, 'var_index': 39}, {'from': 3, 'to': 4, 'var_index': 40}, {'from': 4, 'to': 5, 'var_index': 41}, {'from': 5, 'to': 6, 'var_index': 42}, {'from': 6, 'to': 7, 'var_index': 43}, {'from': 7, 'to': 8, 'var_index': 44}, {'from': 8, 'to': 9, 'var_index': 45}, {'from': 9, 'to': 10, 'var_index': 46}, {'from': 10, 'to': 11, 'var_index': 47}, {'from': 11, 'to': 12, 'var_index': 48}, {'from': 12, 'to': 13, 'var_index': 49}, {'from': 13, 'to': 14, 'var_index': 50}, {'from': 14, 'to': 15, 'var_index': 51}, {'from': 15, 'to': 16, 'var_index': 52}, {'from': 16, 'to': 17, 'var_index': 53}, {'from': 17, 'to': 18, 'var_index': 54}, {'from': 18, 'to': 19, 'var_index': 55}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21}}","[20, 19, 21]",41,csv,1
QSPP,QSPP,"I was imagining a day out on the mountain: start at the trailhead and follow the one-way, signposted routes up to the summit. The job is to pick one continuous trail that goes from the start to the top without jumping around or breaking the route, and that respects the uphill/downhill directions posted along the way. Each trail segment has its usual level of effort, and some combinations of segments add extra annoyances when taken together — the total toll of a route is just the sum of every segment’s effort plus any extra trouble that pops up between particular pairs of segments. The goal is to pick the single route with the smallest total toll, and the exact map, segment efforts, and interaction details are shown below.

# total_locations=20
# total_trail_segments=33
# location_ids=A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T
# trailhead=S
# summit=T

segment_start_location,segment_end_location,segment_id
S,A,0
S,G,1
S,M,2
F,T,3
L,T,4
R,T,5
A,B,6
A,G,7
B,C,8
B,H,9
C,D,10
C,I,11
D,E,12
D,J,13
E,F,14
E,K,15
F,L,16
G,H,17
G,M,18
H,I,19
H,N,20
I,J,21
I,O,22
J,K,23
J,P,24
K,L,25
K,Q,26
L,R,27
M,N,28
N,O,29
O,P,30
P,Q,31
Q,R,32

segment_ref_id,segment_effort
0,3.0
1,5.0
2,3.0
3,8.0
4,2.0
5,9.0
6,7.0
7,7.0
8,2.0
9,8.0
10,3.0
11,3.0
12,8.0
13,4.0
14,10.0
15,3.0
16,10.0
17,6.0
18,8.0
19,8.0
20,6.0
21,2.0
22,1.0
23,4.0
24,9.0
25,9.0
26,6.0
27,10.0
28,4.0
29,10.0
30,3.0
31,10.0
32,3.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 5.0 | 7.0 | 10.0 | 3.0 | 2.0 | 7.0 | 2.0 | 5.0 | 3.0 | 10.0 | 5.0 | 5.0 | 9.0 | 3.0 | 9.0 | 3.0 | 7.0 | 6.0 | 6.0 | 6.0 | 3.0 | 10.0 | 9.0 | 6.0 | 7.0 | 10.0 | 10.0 | 10.0 | 6.0 | 8.0 | 6.0 | 1.0 |
| 1 | 5.0 | 6.0 | 10.0 | 9.0 | 8.0 | 3.0 | 6.0 | 10.0 | 9.0 | 2.0 | 6.0 | 8.0 | 8.0 | 5.0 | 4.0 | 2.0 | 10.0 | 9.0 | 6.0 | 5.0 | 10.0 | 9.0 | 1.0 | 9.0 | 3.0 | 9.0 | 1.0 | 7.0 | 2.0 | 8.0 | 4.0 | 6.0 | 8.0 |
| 2 | 7.0 | 10.0 | 10.0 | 5.0 | 10.0 | 4.0 | 9.0 | 1.0 | 4.0 | 7.0 | 8.0 | 1.0 | 7.0 | 4.0 | 6.0 | 2.0 | 1.0 | 9.0 | 4.0 | 4.0 | 7.0 | 6.0 | 1.0 | 1.0 | 6.0 | 4.0 | 8.0 | 1.0 | 9.0 | 2.0 | 2.0 | 8.0 | 9.0 |
| 3 | 10.0 | 9.0 | 5.0 | 3.0 | 8.0 | 1.0 | 10.0 | 2.0 | 5.0 | 9.0 | 6.0 | 3.0 | 4.0 | 7.0 | 7.0 | 8.0 | 9.0 | 8.0 | 6.0 | 9.0 | 6.0 | 6.0 | 8.0 | 4.0 | 3.0 | 6.0 | 3.0 | 8.0 | 10.0 | 1.0 | 5.0 | 6.0 | 2.0 |
| 4 | 3.0 | 8.0 | 10.0 | 8.0 | 3.0 | 9.0 | 10.0 | 9.0 | 7.0 | 3.0 | 8.0 | 1.0 | 9.0 | 10.0 | 3.0 | 10.0 | 9.0 | 8.0 | 6.0 | 2.0 | 7.0 | 10.0 | 1.0 | 4.0 | 10.0 | 9.0 | 1.0 | 2.0 | 2.0 | 4.0 | 10.0 | 4.0 | 6.0 |
| 5 | 2.0 | 3.0 | 4.0 | 1.0 | 9.0 | 8.0 | 10.0 | 9.0 | 7.0 | 1.0 | 5.0 | 1.0 | 1.0 | 3.0 | 10.0 | 1.0 | 7.0 | 7.0 | 5.0 | 1.0 | 9.0 | 2.0 | 1.0 | 9.0 | 5.0 | 8.0 | 3.0 | 10.0 | 6.0 | 5.0 | 3.0 | 8.0 | 8.0 |
| 6 | 7.0 | 6.0 | 9.0 | 10.0 | 10.0 | 10.0 | 5.0 | 9.0 | 1.0 | 5.0 | 2.0 | 6.0 | 8.0 | 2.0 | 3.0 | 3.0 | 7.0 | 5.0 | 10.0 | 5.0 | 10.0 | 8.0 | 8.0 | 5.0 | 10.0 | 1.0 | 1.0 | 5.0 | 4.0 | 1.0 | 10.0 | 7.0 | 6.0 |
| 7 | 2.0 | 10.0 | 1.0 | 2.0 | 9.0 | 9.0 | 9.0 | 4.0 | 2.0 | 4.0 | 4.0 | 1.0 | 2.0 | 8.0 | 4.0 | 7.0 | 10.0 | 6.0 | 6.0 | 9.0 | 4.0 | 9.0 | 4.0 | 2.0 | 3.0 | 3.0 | 10.0 | 8.0 | 1.0 | 4.0 | 3.0 | 10.0 | 9.0 |
| 8 | 5.0 | 9.0 | 4.0 | 5.0 | 7.0 | 7.0 | 1.0 | 2.0 | 7.0 | 1.0 | 3.0 | 4.0 | 8.0 | 6.0 | 3.0 | 6.0 | 4.0 | 10.0 | 9.0 | 8.0 | 1.0 | 10.0 | 10.0 | 2.0 | 6.0 | 6.0 | 9.0 | 5.0 | 6.0 | 10.0 | 2.0 | 6.0 | 7.0 |
| 9 | 3.0 | 2.0 | 7.0 | 9.0 | 3.0 | 1.0 | 5.0 | 4.0 | 1.0 | 10.0 | 7.0 | 3.0 | 7.0 | 8.0 | 9.0 | 10.0 | 9.0 | 5.0 | 3.0 | 6.0 | 5.0 | 3.0 | 5.0 | 9.0 | 2.0 | 5.0 | 9.0 | 4.0 | 6.0 | 8.0 | 6.0 | 1.0 | 2.0 |
| 10 | 10.0 | 6.0 | 8.0 | 6.0 | 8.0 | 5.0 | 2.0 | 4.0 | 3.0 | 7.0 | 8.0 | 3.0 | 5.0 | 7.0 | 5.0 | 10.0 | 10.0 | 4.0 | 9.0 | 8.0 | 4.0 | 6.0 | 8.0 | 8.0 | 4.0 | 5.0 | 3.0 | 4.0 | 7.0 | 6.0 | 8.0 | 5.0 | 4.0 |
| 11 | 5.0 | 8.0 | 1.0 | 3.0 | 1.0 | 1.0 | 6.0 | 1.0 | 4.0 | 3.0 | 3.0 | 5.0 | 8.0 | 8.0 | 7.0 | 1.0 | 4.0 | 5.0 | 3.0 | 7.0 | 6.0 | 5.0 | 1.0 | 9.0 | 5.0 | 6.0 | 3.0 | 5.0 | 10.0 | 5.0 | 10.0 | 8.0 | 3.0 |
| 12 | 5.0 | 8.0 | 7.0 | 4.0 | 9.0 | 1.0 | 8.0 | 2.0 | 8.0 | 7.0 | 5.0 | 8.0 | 6.0 | 6.0 | 8.0 | 10.0 | 1.0 | 1.0 | 9.0 | 6.0 | 1.0 | 9.0 | 8.0 | 8.0 | 8.0 | 8.0 | 1.0 | 3.0 | 5.0 | 8.0 | 6.0 | 3.0 | 4.0 |
| 13 | 9.0 | 5.0 | 4.0 | 7.0 | 10.0 | 3.0 | 2.0 | 8.0 | 6.0 | 8.0 | 7.0 | 8.0 | 6.0 | 3.0 | 10.0 | 6.0 | 1.0 | 6.0 | 5.0 | 2.0 | 4.0 | 4.0 | 2.0 | 4.0 | 10.0 | 9.0 | 8.0 | 1.0 | 8.0 | 8.0 | 2.0 | 4.0 | 2.0 |
| 14 | 3.0 | 4.0 | 6.0 | 7.0 | 3.0 | 10.0 | 3.0 | 4.0 | 3.0 | 9.0 | 5.0 | 7.0 | 8.0 | 10.0 | 8.0 | 5.0 | 3.0 | 5.0 | 4.0 | 4.0 | 3.0 | 4.0 | 8.0 | 5.0 | 8.0 | 2.0 | 3.0 | 1.0 | 3.0 | 10.0 | 4.0 | 4.0 | 3.0 |
| 15 | 9.0 | 2.0 | 2.0 | 8.0 | 10.0 | 1.0 | 3.0 | 7.0 | 6.0 | 10.0 | 10.0 | 1.0 | 10.0 | 6.0 | 5.0 | 9.0 | 2.0 | 7.0 | 10.0 | 10.0 | 2.0 | 8.0 | 7.0 | 5.0 | 7.0 | 6.0 | 9.0 | 7.0 | 6.0 | 7.0 | 1.0 | 2.0 | 5.0 |
| 16 | 3.0 | 10.0 | 1.0 | 9.0 | 9.0 | 7.0 | 7.0 | 10.0 | 4.0 | 9.0 | 10.0 | 4.0 | 1.0 | 1.0 | 3.0 | 2.0 | 10.0 | 10.0 | 3.0 | 5.0 | 8.0 | 6.0 | 8.0 | 5.0 | 2.0 | 7.0 | 5.0 | 8.0 | 4.0 | 5.0 | 9.0 | 5.0 | 9.0 |
| 17 | 7.0 | 9.0 | 9.0 | 8.0 | 8.0 | 7.0 | 5.0 | 6.0 | 10.0 | 5.0 | 4.0 | 5.0 | 1.0 | 6.0 | 5.0 | 7.0 | 10.0 | 4.0 | 6.0 | 8.0 | 3.0 | 6.0 | 5.0 | 1.0 | 6.0 | 3.0 | 4.0 | 7.0 | 4.0 | 4.0 | 1.0 | 7.0 | 2.0 |
| 18 | 6.0 | 6.0 | 4.0 | 6.0 | 6.0 | 5.0 | 10.0 | 6.0 | 9.0 | 3.0 | 9.0 | 3.0 | 9.0 | 5.0 | 4.0 | 10.0 | 3.0 | 6.0 | 9.0 | 9.0 | 1.0 | 6.0 | 6.0 | 3.0 | 5.0 | 8.0 | 4.0 | 10.0 | 7.0 | 5.0 | 2.0 | 4.0 | 5.0 |
| 19 | 6.0 | 5.0 | 4.0 | 9.0 | 2.0 | 1.0 | 5.0 | 9.0 | 8.0 | 6.0 | 8.0 | 7.0 | 6.0 | 2.0 | 4.0 | 10.0 | 5.0 | 8.0 | 9.0 | 4.0 | 2.0 | 3.0 | 6.0 | 8.0 | 6.0 | 1.0 | 3.0 | 7.0 | 1.0 | 8.0 | 2.0 | 7.0 | 4.0 |
| 20 | 6.0 | 10.0 | 7.0 | 6.0 | 7.0 | 9.0 | 10.0 | 4.0 | 1.0 | 5.0 | 4.0 | 6.0 | 1.0 | 4.0 | 3.0 | 2.0 | 8.0 | 3.0 | 1.0 | 2.0 | 7.0 | 8.0 | 9.0 | 3.0 | 3.0 | 2.0 | 9.0 | 5.0 | 7.0 | 10.0 | 10.0 | 2.0 | 6.0 |
| 21 | 3.0 | 9.0 | 6.0 | 6.0 | 10.0 | 2.0 | 8.0 | 9.0 | 10.0 | 3.0 | 6.0 | 5.0 | 9.0 | 4.0 | 4.0 | 8.0 | 6.0 | 6.0 | 6.0 | 3.0 | 8.0 | 10.0 | 10.0 | 8.0 | 6.0 | 8.0 | 10.0 | 6.0 | 9.0 | 6.0 | 7.0 | 7.0 | 4.0 |
| 22 | 10.0 | 1.0 | 1.0 | 8.0 | 1.0 | 1.0 | 8.0 | 4.0 | 10.0 | 5.0 | 8.0 | 1.0 | 8.0 | 2.0 | 8.0 | 7.0 | 8.0 | 5.0 | 6.0 | 6.0 | 9.0 | 10.0 | 7.0 | 1.0 | 7.0 | 9.0 | 1.0 | 9.0 | 5.0 | 6.0 | 5.0 | 1.0 | 8.0 |
| 23 | 9.0 | 9.0 | 1.0 | 4.0 | 4.0 | 9.0 | 5.0 | 2.0 | 2.0 | 9.0 | 8.0 | 9.0 | 8.0 | 4.0 | 5.0 | 5.0 | 5.0 | 1.0 | 3.0 | 8.0 | 3.0 | 8.0 | 1.0 | 6.0 | 3.0 | 5.0 | 1.0 | 9.0 | 5.0 | 1.0 | 10.0 | 6.0 | 5.0 |
| 24 | 6.0 | 3.0 | 6.0 | 3.0 | 10.0 | 5.0 | 10.0 | 3.0 | 6.0 | 2.0 | 4.0 | 5.0 | 8.0 | 10.0 | 8.0 | 7.0 | 2.0 | 6.0 | 5.0 | 6.0 | 3.0 | 6.0 | 7.0 | 3.0 | 2.0 | 1.0 | 1.0 | 6.0 | 5.0 | 8.0 | 5.0 | 1.0 | 1.0 |
| 25 | 7.0 | 9.0 | 4.0 | 6.0 | 9.0 | 8.0 | 1.0 | 3.0 | 6.0 | 5.0 | 5.0 | 6.0 | 8.0 | 9.0 | 2.0 | 6.0 | 7.0 | 3.0 | 8.0 | 1.0 | 2.0 | 8.0 | 9.0 | 5.0 | 1.0 | 6.0 | 9.0 | 10.0 | 7.0 | 5.0 | 5.0 | 1.0 | 9.0 |
| 26 | 10.0 | 1.0 | 8.0 | 3.0 | 1.0 | 3.0 | 1.0 | 10.0 | 9.0 | 9.0 | 3.0 | 3.0 | 1.0 | 8.0 | 3.0 | 9.0 | 5.0 | 4.0 | 4.0 | 3.0 | 9.0 | 10.0 | 1.0 | 1.0 | 1.0 | 9.0 | 8.0 | 9.0 | 4.0 | 7.0 | 8.0 | 5.0 | 10.0 |
| 27 | 10.0 | 7.0 | 1.0 | 8.0 | 2.0 | 10.0 | 5.0 | 8.0 | 5.0 | 4.0 | 4.0 | 5.0 | 3.0 | 1.0 | 1.0 | 7.0 | 8.0 | 7.0 | 10.0 | 7.0 | 5.0 | 6.0 | 9.0 | 9.0 | 6.0 | 10.0 | 9.0 | 9.0 | 5.0 | 3.0 | 7.0 | 2.0 | 10.0 |
| 28 | 10.0 | 2.0 | 9.0 | 10.0 | 2.0 | 6.0 | 4.0 | 1.0 | 6.0 | 6.0 | 7.0 | 10.0 | 5.0 | 8.0 | 3.0 | 6.0 | 4.0 | 4.0 | 7.0 | 1.0 | 7.0 | 9.0 | 5.0 | 5.0 | 5.0 | 7.0 | 4.0 | 5.0 | 7.0 | 9.0 | 8.0 | 3.0 | 2.0 |
| 29 | 6.0 | 8.0 | 2.0 | 1.0 | 4.0 | 5.0 | 1.0 | 4.0 | 10.0 | 8.0 | 6.0 | 5.0 | 8.0 | 8.0 | 10.0 | 7.0 | 5.0 | 4.0 | 5.0 | 8.0 | 10.0 | 6.0 | 6.0 | 1.0 | 8.0 | 5.0 | 7.0 | 3.0 | 9.0 | 10.0 | 6.0 | 9.0 | 7.0 |
| 30 | 8.0 | 4.0 | 2.0 | 5.0 | 10.0 | 3.0 | 10.0 | 3.0 | 2.0 | 6.0 | 8.0 | 10.0 | 6.0 | 2.0 | 4.0 | 1.0 | 9.0 | 1.0 | 2.0 | 2.0 | 10.0 | 7.0 | 5.0 | 10.0 | 5.0 | 5.0 | 8.0 | 7.0 | 8.0 | 6.0 | 7.0 | 1.0 | 3.0 |
| 31 | 6.0 | 6.0 | 8.0 | 6.0 | 4.0 | 8.0 | 7.0 | 10.0 | 6.0 | 1.0 | 5.0 | 8.0 | 3.0 | 4.0 | 4.0 | 2.0 | 5.0 | 7.0 | 4.0 | 7.0 | 2.0 | 7.0 | 1.0 | 6.0 | 1.0 | 1.0 | 5.0 | 2.0 | 3.0 | 9.0 | 1.0 | 5.0 | 3.0 |
| 32 | 1.0 | 8.0 | 9.0 | 2.0 | 6.0 | 8.0 | 6.0 | 9.0 | 7.0 | 2.0 | 4.0 | 3.0 | 4.0 | 2.0 | 3.0 | 5.0 | 9.0 | 2.0 | 5.0 | 4.0 | 6.0 | 4.0 | 8.0 | 5.0 | 1.0 | 9.0 | 10.0 | 10.0 | 2.0 | 7.0 | 3.0 | 3.0 | 3.0 |

When you send back your chosen trail, just drop it into this little JSON layout so it's easy to parse:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the trail from the trailhead to the summit — just the node names in order (start, any intermediate waypoints, then the top). Keep it simple and human: the array holds the path nodes only. This JSON is just a sketch of the shape I want, not the actual answer — you'll fill the array with the node IDs from the map when you reply.

Please make sure to use the exact identifiers exactly as they appear in the instance input — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 6, 'var_index': 1}, {'from': 18, 'to': 12, 'var_index': 2}, {'from': 5, 'to': 19, 'var_index': 3}, {'from': 11, 'to': 19, 'var_index': 4}, {'from': 17, 'to': 19, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 0, 'to': 6, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 7, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 8, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 9, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 10, 'var_index': 15}, {'from': 5, 'to': 11, 'var_index': 16}, {'from': 6, 'to': 7, 'var_index': 17}, {'from': 6, 'to': 12, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 13, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 14, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 15, 'var_index': 24}, {'from': 10, 'to': 11, 'var_index': 25}, {'from': 10, 'to': 16, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 13, 'var_index': 28}, {'from': 13, 'to': 14, 'var_index': 29}, {'from': 14, 'to': 15, 'var_index': 30}, {'from': 15, 'to': 16, 'var_index': 31}, {'from': 16, 'to': 17, 'var_index': 32}], 'objective': {'constant': 0.0, 'linear': [3.0, 5.0, 3.0, 8.0, 2.0, 9.0, 7.0, 7.0, 2.0, 8.0, 3.0, 3.0, 8.0, 4.0, 10.0, 3.0, 10.0, 6.0, 8.0, 8.0, 6.0, 2.0, 1.0, 4.0, 9.0, 9.0, 6.0, 10.0, 4.0, 10.0, 3.0, 10.0, 3.0], 'quadratic': [[1.0, 5.0, 7.0, 10.0, 3.0, 2.0, 7.0, 2.0, 5.0, 3.0, 10.0, 5.0, 5.0, 9.0, 3.0, 9.0, 3.0, 7.0, 6.0, 6.0, 6.0, 3.0, 10.0, 9.0, 6.0, 7.0, 10.0, 10.0, 10.0, 6.0, 8.0, 6.0, 1.0], [5.0, 6.0, 10.0, 9.0, 8.0, 3.0, 6.0, 10.0, 9.0, 2.0, 6.0, 8.0, 8.0, 5.0, 4.0, 2.0, 10.0, 9.0, 6.0, 5.0, 10.0, 9.0, 1.0, 9.0, 3.0, 9.0, 1.0, 7.0, 2.0, 8.0, 4.0, 6.0, 8.0], [7.0, 10.0, 10.0, 5.0, 10.0, 4.0, 9.0, 1.0, 4.0, 7.0, 8.0, 1.0, 7.0, 4.0, 6.0, 2.0, 1.0, 9.0, 4.0, 4.0, 7.0, 6.0, 1.0, 1.0, 6.0, 4.0, 8.0, 1.0, 9.0, 2.0, 2.0, 8.0, 9.0], [10.0, 9.0, 5.0, 3.0, 8.0, 1.0, 10.0, 2.0, 5.0, 9.0, 6.0, 3.0, 4.0, 7.0, 7.0, 8.0, 9.0, 8.0, 6.0, 9.0, 6.0, 6.0, 8.0, 4.0, 3.0, 6.0, 3.0, 8.0, 10.0, 1.0, 5.0, 6.0, 2.0], [3.0, 8.0, 10.0, 8.0, 3.0, 9.0, 10.0, 9.0, 7.0, 3.0, 8.0, 1.0, 9.0, 10.0, 3.0, 10.0, 9.0, 8.0, 6.0, 2.0, 7.0, 10.0, 1.0, 4.0, 10.0, 9.0, 1.0, 2.0, 2.0, 4.0, 10.0, 4.0, 6.0], [2.0, 3.0, 4.0, 1.0, 9.0, 8.0, 10.0, 9.0, 7.0, 1.0, 5.0, 1.0, 1.0, 3.0, 10.0, 1.0, 7.0, 7.0, 5.0, 1.0, 9.0, 2.0, 1.0, 9.0, 5.0, 8.0, 3.0, 10.0, 6.0, 5.0, 3.0, 8.0, 8.0], [7.0, 6.0, 9.0, 10.0, 10.0, 10.0, 5.0, 9.0, 1.0, 5.0, 2.0, 6.0, 8.0, 2.0, 3.0, 3.0, 7.0, 5.0, 10.0, 5.0, 10.0, 8.0, 8.0, 5.0, 10.0, 1.0, 1.0, 5.0, 4.0, 1.0, 10.0, 7.0, 6.0], [2.0, 10.0, 1.0, 2.0, 9.0, 9.0, 9.0, 4.0, 2.0, 4.0, 4.0, 1.0, 2.0, 8.0, 4.0, 7.0, 10.0, 6.0, 6.0, 9.0, 4.0, 9.0, 4.0, 2.0, 3.0, 3.0, 10.0, 8.0, 1.0, 4.0, 3.0, 10.0, 9.0], [5.0, 9.0, 4.0, 5.0, 7.0, 7.0, 1.0, 2.0, 7.0, 1.0, 3.0, 4.0, 8.0, 6.0, 3.0, 6.0, 4.0, 10.0, 9.0, 8.0, 1.0, 10.0, 10.0, 2.0, 6.0, 6.0, 9.0, 5.0, 6.0, 10.0, 2.0, 6.0, 7.0], [3.0, 2.0, 7.0, 9.0, 3.0, 1.0, 5.0, 4.0, 1.0, 10.0, 7.0, 3.0, 7.0, 8.0, 9.0, 10.0, 9.0, 5.0, 3.0, 6.0, 5.0, 3.0, 5.0, 9.0, 2.0, 5.0, 9.0, 4.0, 6.0, 8.0, 6.0, 1.0, 2.0], [10.0, 6.0, 8.0, 6.0, 8.0, 5.0, 2.0, 4.0, 3.0, 7.0, 8.0, 3.0, 5.0, 7.0, 5.0, 10.0, 10.0, 4.0, 9.0, 8.0, 4.0, 6.0, 8.0, 8.0, 4.0, 5.0, 3.0, 4.0, 7.0, 6.0, 8.0, 5.0, 4.0], [5.0, 8.0, 1.0, 3.0, 1.0, 1.0, 6.0, 1.0, 4.0, 3.0, 3.0, 5.0, 8.0, 8.0, 7.0, 1.0, 4.0, 5.0, 3.0, 7.0, 6.0, 5.0, 1.0, 9.0, 5.0, 6.0, 3.0, 5.0, 10.0, 5.0, 10.0, 8.0, 3.0], [5.0, 8.0, 7.0, 4.0, 9.0, 1.0, 8.0, 2.0, 8.0, 7.0, 5.0, 8.0, 6.0, 6.0, 8.0, 10.0, 1.0, 1.0, 9.0, 6.0, 1.0, 9.0, 8.0, 8.0, 8.0, 8.0, 1.0, 3.0, 5.0, 8.0, 6.0, 3.0, 4.0], [9.0, 5.0, 4.0, 7.0, 10.0, 3.0, 2.0, 8.0, 6.0, 8.0, 7.0, 8.0, 6.0, 3.0, 10.0, 6.0, 1.0, 6.0, 5.0, 2.0, 4.0, 4.0, 2.0, 4.0, 10.0, 9.0, 8.0, 1.0, 8.0, 8.0, 2.0, 4.0, 2.0], [3.0, 4.0, 6.0, 7.0, 3.0, 10.0, 3.0, 4.0, 3.0, 9.0, 5.0, 7.0, 8.0, 10.0, 8.0, 5.0, 3.0, 5.0, 4.0, 4.0, 3.0, 4.0, 8.0, 5.0, 8.0, 2.0, 3.0, 1.0, 3.0, 10.0, 4.0, 4.0, 3.0], [9.0, 2.0, 2.0, 8.0, 10.0, 1.0, 3.0, 7.0, 6.0, 10.0, 10.0, 1.0, 10.0, 6.0, 5.0, 9.0, 2.0, 7.0, 10.0, 10.0, 2.0, 8.0, 7.0, 5.0, 7.0, 6.0, 9.0, 7.0, 6.0, 7.0, 1.0, 2.0, 5.0], [3.0, 10.0, 1.0, 9.0, 9.0, 7.0, 7.0, 10.0, 4.0, 9.0, 10.0, 4.0, 1.0, 1.0, 3.0, 2.0, 10.0, 10.0, 3.0, 5.0, 8.0, 6.0, 8.0, 5.0, 2.0, 7.0, 5.0, 8.0, 4.0, 5.0, 9.0, 5.0, 9.0], [7.0, 9.0, 9.0, 8.0, 8.0, 7.0, 5.0, 6.0, 10.0, 5.0, 4.0, 5.0, 1.0, 6.0, 5.0, 7.0, 10.0, 4.0, 6.0, 8.0, 3.0, 6.0, 5.0, 1.0, 6.0, 3.0, 4.0, 7.0, 4.0, 4.0, 1.0, 7.0, 2.0], [6.0, 6.0, 4.0, 6.0, 6.0, 5.0, 10.0, 6.0, 9.0, 3.0, 9.0, 3.0, 9.0, 5.0, 4.0, 10.0, 3.0, 6.0, 9.0, 9.0, 1.0, 6.0, 6.0, 3.0, 5.0, 8.0, 4.0, 10.0, 7.0, 5.0, 2.0, 4.0, 5.0], [6.0, 5.0, 4.0, 9.0, 2.0, 1.0, 5.0, 9.0, 8.0, 6.0, 8.0, 7.0, 6.0, 2.0, 4.0, 10.0, 5.0, 8.0, 9.0, 4.0, 2.0, 3.0, 6.0, 8.0, 6.0, 1.0, 3.0, 7.0, 1.0, 8.0, 2.0, 7.0, 4.0], [6.0, 10.0, 7.0, 6.0, 7.0, 9.0, 10.0, 4.0, 1.0, 5.0, 4.0, 6.0, 1.0, 4.0, 3.0, 2.0, 8.0, 3.0, 1.0, 2.0, 7.0, 8.0, 9.0, 3.0, 3.0, 2.0, 9.0, 5.0, 7.0, 10.0, 10.0, 2.0, 6.0], [3.0, 9.0, 6.0, 6.0, 10.0, 2.0, 8.0, 9.0, 10.0, 3.0, 6.0, 5.0, 9.0, 4.0, 4.0, 8.0, 6.0, 6.0, 6.0, 3.0, 8.0, 10.0, 10.0, 8.0, 6.0, 8.0, 10.0, 6.0, 9.0, 6.0, 7.0, 7.0, 4.0], [10.0, 1.0, 1.0, 8.0, 1.0, 1.0, 8.0, 4.0, 10.0, 5.0, 8.0, 1.0, 8.0, 2.0, 8.0, 7.0, 8.0, 5.0, 6.0, 6.0, 9.0, 10.0, 7.0, 1.0, 7.0, 9.0, 1.0, 9.0, 5.0, 6.0, 5.0, 1.0, 8.0], [9.0, 9.0, 1.0, 4.0, 4.0, 9.0, 5.0, 2.0, 2.0, 9.0, 8.0, 9.0, 8.0, 4.0, 5.0, 5.0, 5.0, 1.0, 3.0, 8.0, 3.0, 8.0, 1.0, 6.0, 3.0, 5.0, 1.0, 9.0, 5.0, 1.0, 10.0, 6.0, 5.0], [6.0, 3.0, 6.0, 3.0, 10.0, 5.0, 10.0, 3.0, 6.0, 2.0, 4.0, 5.0, 8.0, 10.0, 8.0, 7.0, 2.0, 6.0, 5.0, 6.0, 3.0, 6.0, 7.0, 3.0, 2.0, 1.0, 1.0, 6.0, 5.0, 8.0, 5.0, 1.0, 1.0], [7.0, 9.0, 4.0, 6.0, 9.0, 8.0, 1.0, 3.0, 6.0, 5.0, 5.0, 6.0, 8.0, 9.0, 2.0, 6.0, 7.0, 3.0, 8.0, 1.0, 2.0, 8.0, 9.0, 5.0, 1.0, 6.0, 9.0, 10.0, 7.0, 5.0, 5.0, 1.0, 9.0], [10.0, 1.0, 8.0, 3.0, 1.0, 3.0, 1.0, 10.0, 9.0, 9.0, 3.0, 3.0, 1.0, 8.0, 3.0, 9.0, 5.0, 4.0, 4.0, 3.0, 9.0, 10.0, 1.0, 1.0, 1.0, 9.0, 8.0, 9.0, 4.0, 7.0, 8.0, 5.0, 10.0], [10.0, 7.0, 1.0, 8.0, 2.0, 10.0, 5.0, 8.0, 5.0, 4.0, 4.0, 5.0, 3.0, 1.0, 1.0, 7.0, 8.0, 7.0, 10.0, 7.0, 5.0, 6.0, 9.0, 9.0, 6.0, 10.0, 9.0, 9.0, 5.0, 3.0, 7.0, 2.0, 10.0], [10.0, 2.0, 9.0, 10.0, 2.0, 6.0, 4.0, 1.0, 6.0, 6.0, 7.0, 10.0, 5.0, 8.0, 3.0, 6.0, 4.0, 4.0, 7.0, 1.0, 7.0, 9.0, 5.0, 5.0, 5.0, 7.0, 4.0, 5.0, 7.0, 9.0, 8.0, 3.0, 2.0], [6.0, 8.0, 2.0, 1.0, 4.0, 5.0, 1.0, 4.0, 10.0, 8.0, 6.0, 5.0, 8.0, 8.0, 10.0, 7.0, 5.0, 4.0, 5.0, 8.0, 10.0, 6.0, 6.0, 1.0, 8.0, 5.0, 7.0, 3.0, 9.0, 10.0, 6.0, 9.0, 7.0], [8.0, 4.0, 2.0, 5.0, 10.0, 3.0, 10.0, 3.0, 2.0, 6.0, 8.0, 10.0, 6.0, 2.0, 4.0, 1.0, 9.0, 1.0, 2.0, 2.0, 10.0, 7.0, 5.0, 10.0, 5.0, 5.0, 8.0, 7.0, 8.0, 6.0, 7.0, 1.0, 3.0], [6.0, 6.0, 8.0, 6.0, 4.0, 8.0, 7.0, 10.0, 6.0, 1.0, 5.0, 8.0, 3.0, 4.0, 4.0, 2.0, 5.0, 7.0, 4.0, 7.0, 2.0, 7.0, 1.0, 6.0, 1.0, 1.0, 5.0, 2.0, 3.0, 9.0, 1.0, 5.0, 3.0], [1.0, 8.0, 9.0, 2.0, 6.0, 8.0, 6.0, 9.0, 7.0, 2.0, 4.0, 3.0, 4.0, 2.0, 3.0, 5.0, 9.0, 2.0, 5.0, 4.0, 6.0, 4.0, 8.0, 5.0, 1.0, 9.0, 10.0, 10.0, 2.0, 7.0, 3.0, 3.0, 3.0]]}, 'source': 18, 'target': 19}","[18, 0, 1, 2, 3, 4, 5, 19]",315.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 33, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T'], 'source': 'S', 'target': 'T', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 2.0}, {'var_index': 5, 'linear_cost': 9.0}, {'var_index': 6, 'linear_cost': 7.0}, {'var_index': 7, 'linear_cost': 7.0}, {'var_index': 8, 'linear_cost': 2.0}, {'var_index': 9, 'linear_cost': 8.0}, {'var_index': 10, 'linear_cost': 3.0}, {'var_index': 11, 'linear_cost': 3.0}, {'var_index': 12, 'linear_cost': 8.0}, {'var_index': 13, 'linear_cost': 4.0}, {'var_index': 14, 'linear_cost': 10.0}, {'var_index': 15, 'linear_cost': 3.0}, {'var_index': 16, 'linear_cost': 10.0}, {'var_index': 17, 'linear_cost': 6.0}, {'var_index': 18, 'linear_cost': 8.0}, {'var_index': 19, 'linear_cost': 8.0}, {'var_index': 20, 'linear_cost': 6.0}, {'var_index': 21, 'linear_cost': 2.0}, {'var_index': 22, 'linear_cost': 1.0}, {'var_index': 23, 'linear_cost': 4.0}, {'var_index': 24, 'linear_cost': 9.0}, {'var_index': 25, 'linear_cost': 9.0}, {'var_index': 26, 'linear_cost': 6.0}, {'var_index': 27, 'linear_cost': 10.0}, {'var_index': 28, 'linear_cost': 4.0}, {'var_index': 29, 'linear_cost': 10.0}, {'var_index': 30, 'linear_cost': 3.0}, {'var_index': 31, 'linear_cost': 10.0}, {'var_index': 32, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 31, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, 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'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 25, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 27, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 28, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 29, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 27, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 24, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 25, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 26, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 24, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 26, 'quadratic_cost': 7.0}, {'var_i': 29, 'var_j': 27, 'quadratic_cost': 3.0}, {'var_i': 29, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 22, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 23, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 24, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 28, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 30, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 27, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 28, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 29, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 30, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 32, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 22, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 23, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 26, 'quadratic_cost': 10.0}, {'var_i': 32, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 32, 'var_j': 28, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 30, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 32, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'S', 'to': 'A', 'var_index': 0}, {'from': 'S', 'to': 'G', 'var_index': 1}, {'from': 'S', 'to': 'M', 'var_index': 2}, {'from': 'F', 'to': 'T', 'var_index': 3}, {'from': 'L', 'to': 'T', 'var_index': 4}, {'from': 'R', 'to': 'T', 'var_index': 5}, {'from': 'A', 'to': 'B', 'var_index': 6}, {'from': 'A', 'to': 'G', 'var_index': 7}, {'from': 'B', 'to': 'C', 'var_index': 8}, {'from': 'B', 'to': 'H', 'var_index': 9}, {'from': 'C', 'to': 'D', 'var_index': 10}, {'from': 'C', 'to': 'I', 'var_index': 11}, {'from': 'D', 'to': 'E', 'var_index': 12}, {'from': 'D', 'to': 'J', 'var_index': 13}, {'from': 'E', 'to': 'F', 'var_index': 14}, {'from': 'E', 'to': 'K', 'var_index': 15}, {'from': 'F', 'to': 'L', 'var_index': 16}, {'from': 'G', 'to': 'H', 'var_index': 17}, {'from': 'G', 'to': 'M', 'var_index': 18}, {'from': 'H', 'to': 'I', 'var_index': 19}, {'from': 'H', 'to': 'N', 'var_index': 20}, {'from': 'I', 'to': 'J', 'var_index': 21}, {'from': 'I', 'to': 'O', 'var_index': 22}, {'from': 'J', 'to': 'K', 'var_index': 23}, {'from': 'J', 'to': 'P', 'var_index': 24}, {'from': 'K', 'to': 'L', 'var_index': 25}, {'from': 'K', 'to': 'Q', 'var_index': 26}, {'from': 'L', 'to': 'R', 'var_index': 27}, {'from': 'M', 'to': 'N', 'var_index': 28}, {'from': 'N', 'to': 'O', 'var_index': 29}, {'from': 'O', 'to': 'P', 'var_index': 30}, {'from': 'P', 'to': 'Q', 'var_index': 31}, {'from': 'Q', 'to': 'R', 'var_index': 32}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T'}}","['S', 'A', 'B', 'C', 'D', 'E', 'F', 'T']",42,csv,names
QSPP,QSPP,"I’m picturing the shift where a robot has to roll from the charging dock over the conveyor network to the assembly area, and the job is to pick one clear route that follows the arrows. Each conveyor segment has its own running cost, and some segments carry extra charges all by themselves; plus certain pairs of segments together can trigger extra penalties — and if two different segments show up in the route, any penalties that apply between them are added in both directions. The aim is to end up with the cheapest possible route once every segment cost and all those pair penalties are added up. The route must be a single continuous trip from dock to assembly along the conveyors, listing every location in order and nothing else, and the exact layout and costs will be shown below.

Below I show the exact layout: 25 locations, 40 directed conveyor segments; locations are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y; start at A, end at Y.
I see conveyor segment 0 going from A to B.
I see conveyor segment 1 going from A to F.
I see conveyor segment 2 going from B to C.
I see conveyor segment 3 going from B to G.
I see conveyor segment 4 going from C to D.
I see conveyor segment 5 going from C to H.
I see conveyor segment 6 going from D to E.
I see conveyor segment 7 going from D to I.
I see conveyor segment 8 going from E to J.
I see conveyor segment 9 going from F to G.
I see conveyor segment 10 going from F to K.
I see conveyor segment 11 going from G to H.
I see conveyor segment 12 going from G to L.
I see conveyor segment 13 going from H to I.
I see conveyor segment 14 going from H to M.
I see conveyor segment 15 going from I to J.
I see conveyor segment 16 going from I to N.
I see conveyor segment 17 going from J to O.
I see conveyor segment 18 going from K to L.
I see conveyor segment 19 going from K to P.
I see conveyor segment 20 going from L to M.
I see conveyor segment 21 going from L to Q.
I see conveyor segment 22 going from M to N.
I see conveyor segment 23 going from M to R.
I see conveyor segment 24 going from N to O.
I see conveyor segment 25 going from N to S.
I see conveyor segment 26 going from O to T.
I see conveyor segment 27 going from P to Q.
I see conveyor segment 28 going from P to U.
I see conveyor segment 29 going from Q to R.
I see conveyor segment 30 going from Q to V.
I see conveyor segment 31 going from R to S.
I see conveyor segment 32 going from R to W.
I see conveyor segment 33 going from S to T.
I see conveyor segment 34 going from S to X.
I see conveyor segment 35 going from T to Y.
I see conveyor segment 36 going from U to V.
I see conveyor segment 37 going from V to W.
I see conveyor segment 38 going from W to X.
I see conveyor segment 39 going from X to Y.
I note base operating cost 2.0 for segment 0.
I note base operating cost 4.0 for segment 1.
I note base operating cost 3.0 for segment 2.
I note base operating cost 4.0 for segment 3.
I note base operating cost 9.0 for segment 4.
I note base operating cost 8.0 for segment 5.
I note base operating cost 7.0 for segment 6.
I note base operating cost 7.0 for segment 7.
I note base operating cost 1.0 for segment 8.
I note base operating cost 4.0 for segment 9.
I note base operating cost 7.0 for segment 10.
I note base operating cost 8.0 for segment 11.
I note base operating cost 8.0 for segment 12.
I note base operating cost 3.0 for segment 13.
I note base operating cost 7.0 for segment 14.
I note base operating cost 8.0 for segment 15.
I note base operating cost 9.0 for segment 16.
I note base operating cost 6.0 for segment 17.
I note base operating cost 8.0 for segment 18.
I note base operating cost 7.0 for segment 19.
I note base operating cost 4.0 for segment 20.
I note base operating cost 8.0 for segment 21.
I note base operating cost 4.0 for segment 22.
I note base operating cost 2.0 for segment 23.
I note base operating cost 10.0 for segment 24.
I note base operating cost 9.0 for segment 25.
I note base operating cost 6.0 for segment 26.
I note base operating cost 5.0 for segment 27.
I note base operating cost 4.0 for segment 28.
I note base operating cost 8.0 for segment 29.
I note base operating cost 4.0 for segment 30.
I note base operating cost 7.0 for segment 31.
I note base operating cost 9.0 for segment 32.
I note base operating cost 2.0 for segment 33.
I note base operating cost 1.0 for segment 34.
I note base operating cost 1.0 for segment 35.
I note base operating cost 10.0 for segment 36.
I note base operating cost 3.0 for segment 37.
I note base operating cost 1.0 for segment 38.
I note base operating cost 3.0 for segment 39.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two conveyor_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 9.0 | 9.0 | 8.0 | 4.0 | 10.0 | 6.0 | 10.0 | 3.0 | 9.0 | 9.0 | 4.0 | 3.0 | 10.0 | 9.0 | 1.0 | 1.0 | 10.0 | 9.0 | 6.0 | 2.0 | 8.0 | 2.0 | 5.0 | 10.0 | 7.0 | 7.0 | 9.0 | 7.0 | 5.0 | 6.0 | 1.0 | 6.0 | 6.0 | 2.0 | 7.0 | 1.0 | 8.0 | 1.0 | 2.0 |
| 1 | 9.0 | 10.0 | 5.0 | 8.0 | 2.0 | 3.0 | 5.0 | 10.0 | 4.0 | 10.0 | 8.0 | 4.0 | 7.0 | 10.0 | 5.0 | 2.0 | 9.0 | 7.0 | 7.0 | 5.0 | 2.0 | 10.0 | 3.0 | 5.0 | 2.0 | 5.0 | 4.0 | 9.0 | 9.0 | 3.0 | 1.0 | 5.0 | 4.0 | 10.0 | 7.0 | 8.0 | 4.0 | 1.0 | 7.0 | 3.0 |
| 2 | 9.0 | 5.0 | 4.0 | 1.0 | 10.0 | 5.0 | 2.0 | 3.0 | 3.0 | 2.0 | 1.0 | 3.0 | 8.0 | 4.0 | 5.0 | 7.0 | 9.0 | 1.0 | 9.0 | 9.0 | 5.0 | 9.0 | 4.0 | 6.0 | 9.0 | 8.0 | 10.0 | 7.0 | 9.0 | 5.0 | 1.0 | 9.0 | 3.0 | 8.0 | 5.0 | 7.0 | 2.0 | 1.0 | 3.0 | 3.0 |
| 3 | 8.0 | 8.0 | 1.0 | 2.0 | 7.0 | 10.0 | 3.0 | 7.0 | 10.0 | 9.0 | 3.0 | 8.0 | 10.0 | 5.0 | 1.0 | 4.0 | 6.0 | 9.0 | 3.0 | 9.0 | 10.0 | 2.0 | 5.0 | 2.0 | 5.0 | 6.0 | 7.0 | 1.0 | 10.0 | 10.0 | 4.0 | 10.0 | 3.0 | 6.0 | 10.0 | 3.0 | 6.0 | 4.0 | 7.0 | 3.0 |
| 4 | 4.0 | 2.0 | 10.0 | 7.0 | 5.0 | 1.0 | 10.0 | 1.0 | 7.0 | 4.0 | 1.0 | 5.0 | 3.0 | 8.0 | 1.0 | 10.0 | 6.0 | 9.0 | 5.0 | 2.0 | 6.0 | 6.0 | 10.0 | 9.0 | 1.0 | 1.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 10.0 | 2.0 | 8.0 | 5.0 | 2.0 | 6.0 | 5.0 | 10.0 | 4.0 |
| 5 | 10.0 | 3.0 | 5.0 | 10.0 | 1.0 | 7.0 | 10.0 | 5.0 | 2.0 | 4.0 | 6.0 | 2.0 | 8.0 | 6.0 | 2.0 | 7.0 | 1.0 | 3.0 | 2.0 | 2.0 | 2.0 | 6.0 | 9.0 | 1.0 | 7.0 | 1.0 | 4.0 | 10.0 | 1.0 | 5.0 | 7.0 | 1.0 | 1.0 | 10.0 | 1.0 | 7.0 | 4.0 | 8.0 | 7.0 | 2.0 |
| 6 | 6.0 | 5.0 | 2.0 | 3.0 | 10.0 | 10.0 | 5.0 | 3.0 | 6.0 | 6.0 | 1.0 | 5.0 | 6.0 | 10.0 | 10.0 | 4.0 | 4.0 | 10.0 | 1.0 | 1.0 | 2.0 | 1.0 | 2.0 | 7.0 | 1.0 | 3.0 | 6.0 | 2.0 | 6.0 | 7.0 | 9.0 | 8.0 | 8.0 | 10.0 | 1.0 | 10.0 | 5.0 | 9.0 | 8.0 | 4.0 |
| 7 | 10.0 | 10.0 | 3.0 | 7.0 | 1.0 | 5.0 | 3.0 | 3.0 | 6.0 | 4.0 | 2.0 | 1.0 | 4.0 | 2.0 | 8.0 | 8.0 | 8.0 | 7.0 | 2.0 | 3.0 | 9.0 | 1.0 | 3.0 | 2.0 | 6.0 | 3.0 | 3.0 | 2.0 | 2.0 | 2.0 | 4.0 | 8.0 | 7.0 | 5.0 | 8.0 | 6.0 | 8.0 | 4.0 | 7.0 | 5.0 |
| 8 | 3.0 | 4.0 | 3.0 | 10.0 | 7.0 | 2.0 | 6.0 | 6.0 | 5.0 | 10.0 | 5.0 | 1.0 | 3.0 | 6.0 | 8.0 | 8.0 | 8.0 | 9.0 | 3.0 | 9.0 | 7.0 | 10.0 | 10.0 | 4.0 | 8.0 | 4.0 | 4.0 | 4.0 | 6.0 | 8.0 | 7.0 | 5.0 | 2.0 | 5.0 | 7.0 | 1.0 | 6.0 | 5.0 | 5.0 | 9.0 |
| 9 | 9.0 | 10.0 | 2.0 | 9.0 | 4.0 | 4.0 | 6.0 | 4.0 | 10.0 | 3.0 | 7.0 | 5.0 | 1.0 | 9.0 | 10.0 | 7.0 | 2.0 | 1.0 | 10.0 | 10.0 | 8.0 | 9.0 | 9.0 | 2.0 | 2.0 | 2.0 | 6.0 | 10.0 | 3.0 | 8.0 | 4.0 | 10.0 | 5.0 | 1.0 | 4.0 | 7.0 | 4.0 | 4.0 | 3.0 | 1.0 |
| 10 | 9.0 | 8.0 | 1.0 | 3.0 | 1.0 | 6.0 | 1.0 | 2.0 | 5.0 | 7.0 | 8.0 | 1.0 | 5.0 | 10.0 | 3.0 | 10.0 | 10.0 | 5.0 | 1.0 | 9.0 | 8.0 | 8.0 | 1.0 | 1.0 | 10.0 | 7.0 | 9.0 | 4.0 | 5.0 | 9.0 | 4.0 | 6.0 | 10.0 | 7.0 | 6.0 | 1.0 | 1.0 | 5.0 | 9.0 | 2.0 |
| 11 | 4.0 | 4.0 | 3.0 | 8.0 | 5.0 | 2.0 | 5.0 | 1.0 | 1.0 | 5.0 | 1.0 | 7.0 | 8.0 | 6.0 | 2.0 | 4.0 | 8.0 | 10.0 | 8.0 | 8.0 | 9.0 | 2.0 | 9.0 | 9.0 | 7.0 | 10.0 | 5.0 | 9.0 | 6.0 | 8.0 | 10.0 | 1.0 | 4.0 | 5.0 | 2.0 | 6.0 | 2.0 | 7.0 | 6.0 | 4.0 |
| 12 | 3.0 | 7.0 | 8.0 | 10.0 | 3.0 | 8.0 | 6.0 | 4.0 | 3.0 | 1.0 | 5.0 | 8.0 | 3.0 | 7.0 | 7.0 | 5.0 | 5.0 | 4.0 | 5.0 | 2.0 | 7.0 | 5.0 | 5.0 | 6.0 | 5.0 | 6.0 | 10.0 | 4.0 | 8.0 | 7.0 | 10.0 | 9.0 | 1.0 | 3.0 | 6.0 | 1.0 | 8.0 | 3.0 | 1.0 | 6.0 |
| 13 | 10.0 | 10.0 | 4.0 | 5.0 | 8.0 | 6.0 | 10.0 | 2.0 | 6.0 | 9.0 | 10.0 | 6.0 | 7.0 | 7.0 | 3.0 | 2.0 | 1.0 | 7.0 | 8.0 | 3.0 | 2.0 | 6.0 | 7.0 | 10.0 | 3.0 | 5.0 | 2.0 | 7.0 | 9.0 | 2.0 | 5.0 | 4.0 | 4.0 | 7.0 | 10.0 | 3.0 | 2.0 | 3.0 | 6.0 | 1.0 |
| 14 | 9.0 | 5.0 | 5.0 | 1.0 | 1.0 | 2.0 | 10.0 | 8.0 | 8.0 | 10.0 | 3.0 | 2.0 | 7.0 | 3.0 | 10.0 | 5.0 | 8.0 | 1.0 | 6.0 | 1.0 | 6.0 | 1.0 | 6.0 | 8.0 | 10.0 | 10.0 | 2.0 | 9.0 | 2.0 | 2.0 | 5.0 | 6.0 | 5.0 | 3.0 | 8.0 | 3.0 | 4.0 | 8.0 | 8.0 | 3.0 |
| 15 | 1.0 | 2.0 | 7.0 | 4.0 | 10.0 | 7.0 | 4.0 | 8.0 | 8.0 | 7.0 | 10.0 | 4.0 | 5.0 | 2.0 | 5.0 | 7.0 | 8.0 | 7.0 | 4.0 | 5.0 | 4.0 | 4.0 | 5.0 | 5.0 | 6.0 | 4.0 | 6.0 | 5.0 | 9.0 | 7.0 | 7.0 | 9.0 | 10.0 | 6.0 | 6.0 | 7.0 | 9.0 | 2.0 | 10.0 | 1.0 |
| 16 | 1.0 | 9.0 | 9.0 | 6.0 | 6.0 | 1.0 | 4.0 | 8.0 | 8.0 | 2.0 | 10.0 | 8.0 | 5.0 | 1.0 | 8.0 | 8.0 | 1.0 | 3.0 | 5.0 | 4.0 | 8.0 | 9.0 | 2.0 | 6.0 | 6.0 | 9.0 | 9.0 | 9.0 | 9.0 | 10.0 | 6.0 | 1.0 | 10.0 | 2.0 | 4.0 | 3.0 | 9.0 | 8.0 | 8.0 | 3.0 |
| 17 | 10.0 | 7.0 | 1.0 | 9.0 | 9.0 | 3.0 | 10.0 | 7.0 | 9.0 | 1.0 | 5.0 | 10.0 | 4.0 | 7.0 | 1.0 | 7.0 | 3.0 | 3.0 | 3.0 | 2.0 | 7.0 | 4.0 | 6.0 | 3.0 | 1.0 | 8.0 | 8.0 | 10.0 | 10.0 | 7.0 | 1.0 | 10.0 | 7.0 | 10.0 | 4.0 | 4.0 | 7.0 | 7.0 | 2.0 | 3.0 |
| 18 | 9.0 | 7.0 | 9.0 | 3.0 | 5.0 | 2.0 | 1.0 | 2.0 | 3.0 | 10.0 | 1.0 | 8.0 | 5.0 | 8.0 | 6.0 | 4.0 | 5.0 | 3.0 | 8.0 | 5.0 | 3.0 | 8.0 | 7.0 | 10.0 | 2.0 | 5.0 | 8.0 | 4.0 | 7.0 | 10.0 | 10.0 | 9.0 | 4.0 | 5.0 | 7.0 | 5.0 | 3.0 | 4.0 | 10.0 | 1.0 |
| 19 | 6.0 | 5.0 | 9.0 | 9.0 | 2.0 | 2.0 | 1.0 | 3.0 | 9.0 | 10.0 | 9.0 | 8.0 | 2.0 | 3.0 | 1.0 | 5.0 | 4.0 | 2.0 | 5.0 | 9.0 | 3.0 | 7.0 | 1.0 | 5.0 | 3.0 | 8.0 | 10.0 | 9.0 | 6.0 | 3.0 | 8.0 | 1.0 | 7.0 | 1.0 | 9.0 | 9.0 | 8.0 | 4.0 | 4.0 | 9.0 |
| 20 | 2.0 | 2.0 | 5.0 | 10.0 | 6.0 | 2.0 | 2.0 | 9.0 | 7.0 | 8.0 | 8.0 | 9.0 | 7.0 | 2.0 | 6.0 | 4.0 | 8.0 | 7.0 | 3.0 | 3.0 | 4.0 | 7.0 | 5.0 | 2.0 | 9.0 | 9.0 | 1.0 | 8.0 | 10.0 | 3.0 | 3.0 | 10.0 | 1.0 | 4.0 | 7.0 | 5.0 | 6.0 | 3.0 | 2.0 | 2.0 |
| 21 | 8.0 | 10.0 | 9.0 | 2.0 | 6.0 | 6.0 | 1.0 | 1.0 | 10.0 | 9.0 | 8.0 | 2.0 | 5.0 | 6.0 | 1.0 | 4.0 | 9.0 | 4.0 | 8.0 | 7.0 | 7.0 | 8.0 | 7.0 | 6.0 | 6.0 | 5.0 | 8.0 | 1.0 | 3.0 | 4.0 | 5.0 | 9.0 | 3.0 | 7.0 | 1.0 | 10.0 | 1.0 | 3.0 | 7.0 | 4.0 |
| 22 | 2.0 | 3.0 | 4.0 | 5.0 | 10.0 | 9.0 | 2.0 | 3.0 | 10.0 | 9.0 | 1.0 | 9.0 | 5.0 | 7.0 | 6.0 | 5.0 | 2.0 | 6.0 | 7.0 | 1.0 | 5.0 | 7.0 | 1.0 | 7.0 | 4.0 | 5.0 | 3.0 | 8.0 | 7.0 | 3.0 | 4.0 | 3.0 | 1.0 | 1.0 | 5.0 | 1.0 | 1.0 | 6.0 | 7.0 | 3.0 |
| 23 | 5.0 | 5.0 | 6.0 | 2.0 | 9.0 | 1.0 | 7.0 | 2.0 | 4.0 | 2.0 | 1.0 | 9.0 | 6.0 | 10.0 | 8.0 | 5.0 | 6.0 | 3.0 | 10.0 | 5.0 | 2.0 | 6.0 | 7.0 | 6.0 | 4.0 | 1.0 | 1.0 | 2.0 | 9.0 | 4.0 | 3.0 | 8.0 | 6.0 | 3.0 | 6.0 | 5.0 | 1.0 | 1.0 | 9.0 | 6.0 |
| 24 | 10.0 | 2.0 | 9.0 | 5.0 | 1.0 | 7.0 | 1.0 | 6.0 | 8.0 | 2.0 | 10.0 | 7.0 | 5.0 | 3.0 | 10.0 | 6.0 | 6.0 | 1.0 | 2.0 | 3.0 | 9.0 | 6.0 | 4.0 | 4.0 | 3.0 | 1.0 | 9.0 | 4.0 | 8.0 | 4.0 | 2.0 | 2.0 | 6.0 | 10.0 | 1.0 | 10.0 | 3.0 | 4.0 | 9.0 | 9.0 |
| 25 | 7.0 | 5.0 | 8.0 | 6.0 | 1.0 | 1.0 | 3.0 | 3.0 | 4.0 | 2.0 | 7.0 | 10.0 | 6.0 | 5.0 | 10.0 | 4.0 | 9.0 | 8.0 | 5.0 | 8.0 | 9.0 | 5.0 | 5.0 | 1.0 | 1.0 | 10.0 | 6.0 | 4.0 | 2.0 | 9.0 | 8.0 | 2.0 | 6.0 | 6.0 | 8.0 | 2.0 | 5.0 | 7.0 | 7.0 | 4.0 |
| 26 | 7.0 | 4.0 | 10.0 | 7.0 | 7.0 | 4.0 | 6.0 | 3.0 | 4.0 | 6.0 | 9.0 | 5.0 | 10.0 | 2.0 | 2.0 | 6.0 | 9.0 | 8.0 | 8.0 | 10.0 | 1.0 | 8.0 | 3.0 | 1.0 | 9.0 | 6.0 | 5.0 | 9.0 | 5.0 | 4.0 | 5.0 | 7.0 | 5.0 | 7.0 | 5.0 | 8.0 | 3.0 | 7.0 | 10.0 | 9.0 |
| 27 | 9.0 | 9.0 | 7.0 | 1.0 | 1.0 | 10.0 | 2.0 | 2.0 | 4.0 | 10.0 | 4.0 | 9.0 | 4.0 | 7.0 | 9.0 | 5.0 | 9.0 | 10.0 | 4.0 | 9.0 | 8.0 | 1.0 | 8.0 | 2.0 | 4.0 | 4.0 | 9.0 | 4.0 | 7.0 | 9.0 | 1.0 | 2.0 | 8.0 | 1.0 | 10.0 | 10.0 | 9.0 | 8.0 | 7.0 | 10.0 |
| 28 | 7.0 | 9.0 | 9.0 | 10.0 | 9.0 | 1.0 | 6.0 | 2.0 | 6.0 | 3.0 | 5.0 | 6.0 | 8.0 | 9.0 | 2.0 | 9.0 | 9.0 | 10.0 | 7.0 | 6.0 | 10.0 | 3.0 | 7.0 | 9.0 | 8.0 | 2.0 | 5.0 | 7.0 | 4.0 | 5.0 | 6.0 | 1.0 | 9.0 | 8.0 | 2.0 | 3.0 | 8.0 | 4.0 | 6.0 | 7.0 |
| 29 | 5.0 | 3.0 | 5.0 | 10.0 | 9.0 | 5.0 | 7.0 | 2.0 | 8.0 | 8.0 | 9.0 | 8.0 | 7.0 | 2.0 | 2.0 | 7.0 | 10.0 | 7.0 | 10.0 | 3.0 | 3.0 | 4.0 | 3.0 | 4.0 | 4.0 | 9.0 | 4.0 | 9.0 | 5.0 | 5.0 | 8.0 | 8.0 | 10.0 | 2.0 | 7.0 | 3.0 | 9.0 | 8.0 | 1.0 | 10.0 |
| 30 | 6.0 | 1.0 | 1.0 | 4.0 | 10.0 | 7.0 | 9.0 | 4.0 | 7.0 | 4.0 | 4.0 | 10.0 | 10.0 | 5.0 | 5.0 | 7.0 | 6.0 | 1.0 | 10.0 | 8.0 | 3.0 | 5.0 | 4.0 | 3.0 | 2.0 | 8.0 | 5.0 | 1.0 | 6.0 | 8.0 | 2.0 | 6.0 | 5.0 | 10.0 | 5.0 | 2.0 | 4.0 | 1.0 | 6.0 | 2.0 |
| 31 | 1.0 | 5.0 | 9.0 | 10.0 | 10.0 | 1.0 | 8.0 | 8.0 | 5.0 | 10.0 | 6.0 | 1.0 | 9.0 | 4.0 | 6.0 | 9.0 | 1.0 | 10.0 | 9.0 | 1.0 | 10.0 | 9.0 | 3.0 | 8.0 | 2.0 | 2.0 | 7.0 | 2.0 | 1.0 | 8.0 | 6.0 | 10.0 | 8.0 | 7.0 | 1.0 | 8.0 | 9.0 | 1.0 | 1.0 | 9.0 |
| 32 | 6.0 | 4.0 | 3.0 | 3.0 | 2.0 | 1.0 | 8.0 | 7.0 | 2.0 | 5.0 | 10.0 | 4.0 | 1.0 | 4.0 | 5.0 | 10.0 | 10.0 | 7.0 | 4.0 | 7.0 | 1.0 | 3.0 | 1.0 | 6.0 | 6.0 | 6.0 | 5.0 | 8.0 | 9.0 | 10.0 | 5.0 | 8.0 | 9.0 | 3.0 | 10.0 | 5.0 | 2.0 | 7.0 | 3.0 | 1.0 |
| 33 | 6.0 | 10.0 | 8.0 | 6.0 | 8.0 | 10.0 | 10.0 | 5.0 | 5.0 | 1.0 | 7.0 | 5.0 | 3.0 | 7.0 | 3.0 | 6.0 | 2.0 | 10.0 | 5.0 | 1.0 | 4.0 | 7.0 | 1.0 | 3.0 | 10.0 | 6.0 | 7.0 | 1.0 | 8.0 | 2.0 | 10.0 | 7.0 | 3.0 | 10.0 | 6.0 | 2.0 | 2.0 | 10.0 | 5.0 | 1.0 |
| 34 | 2.0 | 7.0 | 5.0 | 10.0 | 5.0 | 1.0 | 1.0 | 8.0 | 7.0 | 4.0 | 6.0 | 2.0 | 6.0 | 10.0 | 8.0 | 6.0 | 4.0 | 4.0 | 7.0 | 9.0 | 7.0 | 1.0 | 5.0 | 6.0 | 1.0 | 8.0 | 5.0 | 10.0 | 2.0 | 7.0 | 5.0 | 1.0 | 10.0 | 6.0 | 2.0 | 10.0 | 4.0 | 3.0 | 9.0 | 9.0 |
| 35 | 7.0 | 8.0 | 7.0 | 3.0 | 2.0 | 7.0 | 10.0 | 6.0 | 1.0 | 7.0 | 1.0 | 6.0 | 1.0 | 3.0 | 3.0 | 7.0 | 3.0 | 4.0 | 5.0 | 9.0 | 5.0 | 10.0 | 1.0 | 5.0 | 10.0 | 2.0 | 8.0 | 10.0 | 3.0 | 3.0 | 2.0 | 8.0 | 5.0 | 2.0 | 10.0 | 9.0 | 8.0 | 6.0 | 2.0 | 2.0 |
| 36 | 1.0 | 4.0 | 2.0 | 6.0 | 6.0 | 4.0 | 5.0 | 8.0 | 6.0 | 4.0 | 1.0 | 2.0 | 8.0 | 2.0 | 4.0 | 9.0 | 9.0 | 7.0 | 3.0 | 8.0 | 6.0 | 1.0 | 1.0 | 1.0 | 3.0 | 5.0 | 3.0 | 9.0 | 8.0 | 9.0 | 4.0 | 9.0 | 2.0 | 2.0 | 4.0 | 8.0 | 9.0 | 2.0 | 5.0 | 2.0 |
| 37 | 8.0 | 1.0 | 1.0 | 4.0 | 5.0 | 8.0 | 9.0 | 4.0 | 5.0 | 4.0 | 5.0 | 7.0 | 3.0 | 3.0 | 8.0 | 2.0 | 8.0 | 7.0 | 4.0 | 4.0 | 3.0 | 3.0 | 6.0 | 1.0 | 4.0 | 7.0 | 7.0 | 8.0 | 4.0 | 8.0 | 1.0 | 1.0 | 7.0 | 10.0 | 3.0 | 6.0 | 2.0 | 1.0 | 1.0 | 4.0 |
| 38 | 1.0 | 7.0 | 3.0 | 7.0 | 10.0 | 7.0 | 8.0 | 7.0 | 5.0 | 3.0 | 9.0 | 6.0 | 1.0 | 6.0 | 8.0 | 10.0 | 8.0 | 2.0 | 10.0 | 4.0 | 2.0 | 7.0 | 7.0 | 9.0 | 9.0 | 7.0 | 10.0 | 7.0 | 6.0 | 1.0 | 6.0 | 1.0 | 3.0 | 5.0 | 9.0 | 2.0 | 5.0 | 1.0 | 5.0 | 10.0 |
| 39 | 2.0 | 3.0 | 3.0 | 3.0 | 4.0 | 2.0 | 4.0 | 5.0 | 9.0 | 1.0 | 2.0 | 4.0 | 6.0 | 1.0 | 3.0 | 1.0 | 3.0 | 3.0 | 1.0 | 9.0 | 2.0 | 4.0 | 3.0 | 6.0 | 9.0 | 4.0 | 9.0 | 10.0 | 7.0 | 10.0 | 2.0 | 9.0 | 1.0 | 1.0 | 9.0 | 2.0 | 2.0 | 4.0 | 10.0 | 8.0 |
I aim to find the cheapest single continuous route from A to Y after summing all segment costs and interaction penalties.

Also, when you give the final route, tuck it into a tiny JSON sketch like this so it's easy to read and parse:

{
  ""solution"": []
}

Here ""solution"" is meant to be an ordered list of the location names (the nodes) the robot will travel through, starting at the dock and ending at the assembly area. Think of it like writing down each stop in order — this block just shows the shape I want, not the actual filled-in route.

Please use the exact identifiers from the instance input — don’t rename or invent labels. 
""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k5_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 5, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 6, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 2, 'to': 7, 'var_index': 5}, {'from': 3, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 8, 'var_index': 7}, {'from': 4, 'to': 9, 'var_index': 8}, {'from': 5, 'to': 6, 'var_index': 9}, {'from': 5, 'to': 10, 'var_index': 10}, {'from': 6, 'to': 7, 'var_index': 11}, {'from': 6, 'to': 11, 'var_index': 12}, {'from': 7, 'to': 8, 'var_index': 13}, {'from': 7, 'to': 12, 'var_index': 14}, {'from': 8, 'to': 9, 'var_index': 15}, {'from': 8, 'to': 13, 'var_index': 16}, {'from': 9, 'to': 14, 'var_index': 17}, {'from': 10, 'to': 11, 'var_index': 18}, {'from': 10, 'to': 15, 'var_index': 19}, {'from': 11, 'to': 12, 'var_index': 20}, {'from': 11, 'to': 16, 'var_index': 21}, {'from': 12, 'to': 13, 'var_index': 22}, {'from': 12, 'to': 17, 'var_index': 23}, {'from': 13, 'to': 14, 'var_index': 24}, {'from': 13, 'to': 18, 'var_index': 25}, {'from': 14, 'to': 19, 'var_index': 26}, {'from': 15, 'to': 16, 'var_index': 27}, {'from': 15, 'to': 20, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 16, 'to': 21, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 17, 'to': 22, 'var_index': 32}, {'from': 18, 'to': 19, 'var_index': 33}, {'from': 18, 'to': 23, 'var_index': 34}, {'from': 19, 'to': 24, 'var_index': 35}, {'from': 20, 'to': 21, 'var_index': 36}, {'from': 21, 'to': 22, 'var_index': 37}, {'from': 22, 'to': 23, 'var_index': 38}, {'from': 23, 'to': 24, 'var_index': 39}], 'objective': {'constant': 0.0, 'linear': [2.0, 4.0, 3.0, 4.0, 9.0, 8.0, 7.0, 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38, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 38, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 38, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 38, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 38, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 38, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 38, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 38, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 38, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 38, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 24, 'quadratic_cost': 9.0}, {'var_i': 38, 'var_j': 25, 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39, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 39, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 39, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 39, 'var_j': 24, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 25, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 39, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 31, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 32, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 39, 'var_j': 34, 'quadratic_cost': 9.0}, {'var_i': 39, 'var_j': 35, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 36, 'quadratic_cost': 2.0}, {'var_i': 39, 'var_j': 37, 'quadratic_cost': 4.0}, {'var_i': 39, 'var_j': 38, 'quadratic_cost': 10.0}, {'var_i': 39, 'var_j': 39, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 'A', 'to': 'B', 'var_index': 0}, {'from': 'A', 'to': 'F', 'var_index': 1}, {'from': 'B', 'to': 'C', 'var_index': 2}, {'from': 'B', 'to': 'G', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'C', 'to': 'H', 'var_index': 5}, {'from': 'D', 'to': 'E', 'var_index': 6}, {'from': 'D', 'to': 'I', 'var_index': 7}, {'from': 'E', 'to': 'J', 'var_index': 8}, {'from': 'F', 'to': 'G', 'var_index': 9}, {'from': 'F', 'to': 'K', 'var_index': 10}, {'from': 'G', 'to': 'H', 'var_index': 11}, {'from': 'G', 'to': 'L', 'var_index': 12}, {'from': 'H', 'to': 'I', 'var_index': 13}, {'from': 'H', 'to': 'M', 'var_index': 14}, {'from': 'I', 'to': 'J', 'var_index': 15}, {'from': 'I', 'to': 'N', 'var_index': 16}, {'from': 'J', 'to': 'O', 'var_index': 17}, {'from': 'K', 'to': 'L', 'var_index': 18}, {'from': 'K', 'to': 'P', 'var_index': 19}, {'from': 'L', 'to': 'M', 'var_index': 20}, {'from': 'L', 'to': 'Q', 'var_index': 21}, {'from': 'M', 'to': 'N', 'var_index': 22}, {'from': 'M', 'to': 'R', 'var_index': 23}, {'from': 'N', 'to': 'O', 'var_index': 24}, {'from': 'N', 'to': 'S', 'var_index': 25}, {'from': 'O', 'to': 'T', 'var_index': 26}, {'from': 'P', 'to': 'Q', 'var_index': 27}, {'from': 'P', 'to': 'U', 'var_index': 28}, {'from': 'Q', 'to': 'R', 'var_index': 29}, {'from': 'Q', 'to': 'V', 'var_index': 30}, {'from': 'R', 'to': 'S', 'var_index': 31}, {'from': 'R', 'to': 'W', 'var_index': 32}, {'from': 'S', 'to': 'T', 'var_index': 33}, {'from': 'S', 'to': 'X', 'var_index': 34}, {'from': 'T', 'to': 'Y', 'var_index': 35}, {'from': 'U', 'to': 'V', 'var_index': 36}, {'from': 'V', 'to': 'W', 'var_index': 37}, {'from': 'W', 'to': 'X', 'var_index': 38}, {'from': 'X', 'to': 'Y', 'var_index': 39}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V', 22: 'W', 23: 'X', 24: 'Y'}}","['A', 'B', 'G', 'L', 'M', 'R', 'W', 'X', 'Y']",43,nl,names
QSPP,QSPP,"There's a little puzzle in planning connecting flights: pick one uninterrupted itinerary from the first airport to the last, using only the flights that actually go from one stop to the next. Each flight carries its own cost, and some combinations of flights trigger extra fees or slowdowns when they appear together — those extras are counted only if both flights are on the same itinerary. So the aim is to choose the route whose sum of base fares plus any pairwise extras is smallest. Everything must be included in that one route — no splitting into separate trips or inventing connections. The concrete schedule and cost details follow below.

The schedule lists 21 airports and 56 directed flights; the valid airport codes are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U. The itinerary must begin at T and end at U.
Flight 0 departs T and arrives at A.
Flight 1 departs T and arrives at B.
Flight 2 departs T and arrives at C.
Flight 3 departs T and arrives at D.
Flight 4 departs T and arrives at E.
Flight 5 departs T and arrives at F.
Flight 6 departs T and arrives at G.
Flight 7 departs T and arrives at H.
Flight 8 departs T and arrives at I.
Flight 9 departs T and arrives at J.
Flight 10 departs T and arrives at K.
Flight 11 departs T and arrives at L.
Flight 12 departs T and arrives at M.
Flight 13 departs T and arrives at N.
Flight 14 departs T and arrives at O.
Flight 15 departs T and arrives at P.
Flight 16 departs T and arrives at Q.
Flight 17 departs T and arrives at R.
Flight 18 departs T and arrives at S.
Flight 19 departs A and arrives at U.
Flight 20 departs B and arrives at U.
Flight 21 departs C and arrives at U.
Flight 22 departs D and arrives at U.
Flight 23 departs E and arrives at U.
Flight 24 departs F and arrives at U.
Flight 25 departs G and arrives at U.
Flight 26 departs H and arrives at U.
Flight 27 departs I and arrives at U.
Flight 28 departs J and arrives at U.
Flight 29 departs K and arrives at U.
Flight 30 departs L and arrives at U.
Flight 31 departs M and arrives at U.
Flight 32 departs N and arrives at U.
Flight 33 departs O and arrives at U.
Flight 34 departs P and arrives at U.
Flight 35 departs Q and arrives at U.
Flight 36 departs R and arrives at U.
Flight 37 departs S and arrives at U.
Flight 38 departs A and arrives at B.
Flight 39 departs B and arrives at C.
Flight 40 departs C and arrives at D.
Flight 41 departs D and arrives at E.
Flight 42 departs E and arrives at F.
Flight 43 departs F and arrives at G.
Flight 44 departs G and arrives at H.
Flight 45 departs H and arrives at I.
Flight 46 departs I and arrives at J.
Flight 47 departs J and arrives at K.
Flight 48 departs K and arrives at L.
Flight 49 departs L and arrives at M.
Flight 50 departs M and arrives at N.
Flight 51 departs N and arrives at O.
Flight 52 departs O and arrives at P.
Flight 53 departs P and arrives at Q.
Flight 54 departs Q and arrives at R.
Flight 55 departs R and arrives at S.
If the itinerary includes flight 0, include its base fare 3.0 in the total.
If the itinerary includes flight 1, include its base fare 5.0 in the total.
If the itinerary includes flight 2, include its base fare 4.0 in the total.
If the itinerary includes flight 3, include its base fare 3.0 in the total.
If the itinerary includes flight 4, include its base fare 4.0 in the total.
If the itinerary includes flight 5, include its base fare 2.0 in the total.
If the itinerary includes flight 6, include its base fare 4.0 in the total.
If the itinerary includes flight 7, include its base fare 10.0 in the total.
If the itinerary includes flight 8, include its base fare 7.0 in the total.
If the itinerary includes flight 9, include its base fare 2.0 in the total.
If the itinerary includes flight 10, include its base fare 7.0 in the total.
If the itinerary includes flight 11, include its base fare 8.0 in the total.
If the itinerary includes flight 12, include its base fare 9.0 in the total.
If the itinerary includes flight 13, include its base fare 9.0 in the total.
If the itinerary includes flight 14, include its base fare 9.0 in the total.
If the itinerary includes flight 15, include its base fare 1.0 in the total.
If the itinerary includes flight 16, include its base fare 2.0 in the total.
If the itinerary includes flight 17, include its base fare 6.0 in the total.
If the itinerary includes flight 18, include its base fare 7.0 in the total.
If the itinerary includes flight 19, include its base fare 8.0 in the total.
If the itinerary includes flight 20, include its base fare 8.0 in the total.
If the itinerary includes flight 21, include its base fare 6.0 in the total.
If the itinerary includes flight 22, include its base fare 4.0 in the total.
If the itinerary includes flight 23, include its base fare 5.0 in the total.
If the itinerary includes flight 24, include its base fare 9.0 in the total.
If the itinerary includes flight 25, include its base fare 10.0 in the total.
If the itinerary includes flight 26, include its base fare 6.0 in the total.
If the itinerary includes flight 27, include its base fare 2.0 in the total.
If the itinerary includes flight 28, include its base fare 9.0 in the total.
If the itinerary includes flight 29, include its base fare 5.0 in the total.
If the itinerary includes flight 30, include its base fare 1.0 in the total.
If the itinerary includes flight 31, include its base fare 3.0 in the total.
If the itinerary includes flight 32, include its base fare 3.0 in the total.
If the itinerary includes flight 33, include its base fare 8.0 in the total.
If the itinerary includes flight 34, include its base fare 1.0 in the total.
If the itinerary includes flight 35, include its base fare 10.0 in the total.
If the itinerary includes flight 36, include its base fare 9.0 in the total.
If the itinerary includes flight 37, include its base fare 10.0 in the total.
If the itinerary includes flight 38, include its base fare 2.0 in the total.
If the itinerary includes flight 39, include its base fare 3.0 in the total.
If the itinerary includes flight 40, include its base fare 7.0 in the total.
If the itinerary includes flight 41, include its base fare 9.0 in the total.
If the itinerary includes flight 42, include its base fare 1.0 in the total.
If the itinerary includes flight 43, include its base fare 7.0 in the total.
If the itinerary includes flight 44, include its base fare 1.0 in the total.
If the itinerary includes flight 45, include its base fare 4.0 in the total.
If the itinerary includes flight 46, include its base fare 1.0 in the total.
If the itinerary includes flight 47, include its base fare 9.0 in the total.
If the itinerary includes flight 48, include its base fare 1.0 in the total.
If the itinerary includes flight 49, include its base fare 8.0 in the total.
If the itinerary includes flight 50, include its base fare 4.0 in the total.
If the itinerary includes flight 51, include its base fare 9.0 in the total.
If the itinerary includes flight 52, include its base fare 1.0 in the total.
If the itinerary includes flight 53, include its base fare 9.0 in the total.
If the itinerary includes flight 54, include its base fare 4.0 in the total.
If the itinerary includes flight 55, include its base fare 3.0 in the total.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (flight_i_id, flight_j_id). If two flights with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| flight_i_id\flight_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 9.0 | 7.0 | 9.0 | 1.0 | 4.0 | 2.0 | 9.0 | 8.0 | 9.0 | 10.0 | 8.0 | 8.0 | 5.0 | 3.0 | 1.0 | 7.0 | 3.0 | 3.0 | 4.0 | 5.0 | 10.0 | 1.0 | 1.0 | 5.0 | 6.0 | 1.0 | 3.0 | 9.0 | 5.0 | 7.0 | 7.0 | 9.0 | 7.0 | 8.0 | 5.0 | 1.0 | 7.0 | 7.0 | 8.0 | 9.0 | 8.0 | 5.0 | 1.0 | 10.0 | 10.0 | 3.0 | 9.0 | 6.0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 4.0 | 8.0 |
| 1 | 9.0 | 3.0 | 8.0 | 3.0 | 9.0 | 2.0 | 8.0 | 4.0 | 2.0 | 6.0 | 10.0 | 4.0 | 8.0 | 4.0 | 6.0 | 5.0 | 5.0 | 6.0 | 10.0 | 7.0 | 6.0 | 1.0 | 5.0 | 3.0 | 9.0 | 3.0 | 9.0 | 10.0 | 1.0 | 9.0 | 7.0 | 5.0 | 8.0 | 6.0 | 9.0 | 1.0 | 3.0 | 6.0 | 3.0 | 3.0 | 3.0 | 6.0 | 9.0 | 5.0 | 2.0 | 9.0 | 7.0 | 6.0 | 8.0 | 10.0 | 7.0 | 7.0 | 2.0 | 8.0 | 6.0 | 6.0 |
| 2 | 7.0 | 8.0 | 5.0 | 1.0 | 1.0 | 3.0 | 7.0 | 6.0 | 1.0 | 5.0 | 7.0 | 3.0 | 7.0 | 3.0 | 9.0 | 3.0 | 8.0 | 4.0 | 7.0 | 3.0 | 5.0 | 3.0 | 1.0 | 2.0 | 7.0 | 10.0 | 8.0 | 4.0 | 4.0 | 10.0 | 4.0 | 7.0 | 10.0 | 5.0 | 10.0 | 4.0 | 4.0 | 3.0 | 6.0 | 9.0 | 7.0 | 6.0 | 10.0 | 2.0 | 8.0 | 2.0 | 2.0 | 2.0 | 1.0 | 9.0 | 5.0 | 6.0 | 8.0 | 5.0 | 10.0 | 10.0 |
| 3 | 9.0 | 3.0 | 1.0 | 1.0 | 3.0 | 3.0 | 7.0 | 1.0 | 1.0 | 9.0 | 7.0 | 5.0 | 10.0 | 7.0 | 3.0 | 8.0 | 9.0 | 6.0 | 5.0 | 8.0 | 5.0 | 7.0 | 8.0 | 2.0 | 7.0 | 2.0 | 3.0 | 2.0 | 8.0 | 3.0 | 4.0 | 5.0 | 5.0 | 2.0 | 3.0 | 7.0 | 5.0 | 2.0 | 7.0 | 4.0 | 2.0 | 2.0 | 1.0 | 1.0 | 1.0 | 3.0 | 9.0 | 1.0 | 2.0 | 4.0 | 1.0 | 8.0 | 1.0 | 6.0 | 7.0 | 8.0 |
| 4 | 1.0 | 9.0 | 1.0 | 3.0 | 5.0 | 8.0 | 2.0 | 8.0 | 10.0 | 7.0 | 6.0 | 7.0 | 8.0 | 1.0 | 6.0 | 8.0 | 4.0 | 1.0 | 2.0 | 1.0 | 5.0 | 1.0 | 2.0 | 10.0 | 4.0 | 9.0 | 5.0 | 8.0 | 8.0 | 3.0 | 7.0 | 8.0 | 9.0 | 7.0 | 9.0 | 5.0 | 7.0 | 4.0 | 10.0 | 6.0 | 5.0 | 10.0 | 5.0 | 3.0 | 3.0 | 5.0 | 3.0 | 7.0 | 6.0 | 8.0 | 3.0 | 1.0 | 9.0 | 2.0 | 6.0 | 2.0 |
| 5 | 4.0 | 2.0 | 3.0 | 3.0 | 8.0 | 1.0 | 2.0 | 1.0 | 2.0 | 7.0 | 10.0 | 3.0 | 3.0 | 4.0 | 9.0 | 8.0 | 3.0 | 1.0 | 9.0 | 3.0 | 9.0 | 9.0 | 6.0 | 8.0 | 3.0 | 9.0 | 7.0 | 3.0 | 4.0 | 10.0 | 9.0 | 3.0 | 8.0 | 6.0 | 4.0 | 9.0 | 4.0 | 3.0 | 1.0 | 2.0 | 7.0 | 6.0 | 9.0 | 2.0 | 8.0 | 7.0 | 2.0 | 4.0 | 6.0 | 1.0 | 6.0 | 2.0 | 4.0 | 7.0 | 8.0 | 9.0 |
| 6 | 2.0 | 8.0 | 7.0 | 7.0 | 2.0 | 2.0 | 7.0 | 9.0 | 2.0 | 2.0 | 10.0 | 10.0 | 9.0 | 4.0 | 5.0 | 3.0 | 5.0 | 6.0 | 5.0 | 4.0 | 3.0 | 3.0 | 3.0 | 7.0 | 8.0 | 7.0 | 1.0 | 2.0 | 9.0 | 9.0 | 4.0 | 2.0 | 8.0 | 3.0 | 1.0 | 9.0 | 10.0 | 8.0 | 3.0 | 3.0 | 9.0 | 2.0 | 4.0 | 9.0 | 5.0 | 1.0 | 1.0 | 2.0 | 7.0 | 6.0 | 5.0 | 8.0 | 1.0 | 8.0 | 2.0 | 9.0 |
| 7 | 9.0 | 4.0 | 6.0 | 1.0 | 8.0 | 1.0 | 9.0 | 1.0 | 2.0 | 3.0 | 8.0 | 5.0 | 2.0 | 2.0 | 3.0 | 1.0 | 10.0 | 6.0 | 10.0 | 9.0 | 1.0 | 4.0 | 3.0 | 3.0 | 5.0 | 3.0 | 2.0 | 9.0 | 10.0 | 8.0 | 5.0 | 8.0 | 6.0 | 6.0 | 1.0 | 5.0 | 6.0 | 3.0 | 9.0 | 2.0 | 8.0 | 1.0 | 3.0 | 1.0 | 7.0 | 2.0 | 4.0 | 1.0 | 2.0 | 4.0 | 6.0 | 6.0 | 5.0 | 6.0 | 10.0 | 8.0 |
| 8 | 8.0 | 2.0 | 1.0 | 1.0 | 10.0 | 2.0 | 2.0 | 2.0 | 4.0 | 9.0 | 6.0 | 10.0 | 2.0 | 10.0 | 1.0 | 2.0 | 8.0 | 3.0 | 7.0 | 4.0 | 9.0 | 9.0 | 1.0 | 10.0 | 1.0 | 1.0 | 7.0 | 7.0 | 5.0 | 2.0 | 3.0 | 3.0 | 9.0 | 9.0 | 5.0 | 2.0 | 8.0 | 3.0 | 5.0 | 8.0 | 9.0 | 2.0 | 5.0 | 3.0 | 10.0 | 7.0 | 1.0 | 3.0 | 5.0 | 7.0 | 8.0 | 8.0 | 10.0 | 5.0 | 5.0 | 5.0 |
| 9 | 9.0 | 6.0 | 5.0 | 9.0 | 7.0 | 7.0 | 2.0 | 3.0 | 9.0 | 7.0 | 9.0 | 8.0 | 2.0 | 7.0 | 5.0 | 8.0 | 2.0 | 10.0 | 10.0 | 8.0 | 1.0 | 9.0 | 6.0 | 9.0 | 10.0 | 5.0 | 10.0 | 4.0 | 7.0 | 1.0 | 8.0 | 4.0 | 1.0 | 2.0 | 8.0 | 2.0 | 9.0 | 5.0 | 10.0 | 2.0 | 5.0 | 4.0 | 7.0 | 2.0 | 4.0 | 2.0 | 3.0 | 3.0 | 10.0 | 6.0 | 5.0 | 7.0 | 9.0 | 2.0 | 4.0 | 4.0 |
| 10 | 10.0 | 10.0 | 7.0 | 7.0 | 6.0 | 10.0 | 10.0 | 8.0 | 6.0 | 9.0 | 2.0 | 4.0 | 8.0 | 10.0 | 5.0 | 10.0 | 5.0 | 9.0 | 4.0 | 7.0 | 10.0 | 5.0 | 4.0 | 3.0 | 10.0 | 5.0 | 7.0 | 2.0 | 7.0 | 9.0 | 6.0 | 10.0 | 5.0 | 2.0 | 6.0 | 5.0 | 9.0 | 9.0 | 9.0 | 6.0 | 7.0 | 7.0 | 4.0 | 5.0 | 9.0 | 8.0 | 3.0 | 6.0 | 2.0 | 1.0 | 4.0 | 2.0 | 9.0 | 6.0 | 2.0 | 10.0 |
| 11 | 8.0 | 4.0 | 3.0 | 5.0 | 7.0 | 3.0 | 10.0 | 5.0 | 10.0 | 8.0 | 4.0 | 6.0 | 1.0 | 8.0 | 10.0 | 7.0 | 3.0 | 6.0 | 5.0 | 7.0 | 7.0 | 8.0 | 7.0 | 2.0 | 7.0 | 8.0 | 7.0 | 7.0 | 3.0 | 10.0 | 7.0 | 9.0 | 3.0 | 7.0 | 7.0 | 6.0 | 7.0 | 7.0 | 1.0 | 10.0 | 6.0 | 10.0 | 3.0 | 4.0 | 1.0 | 9.0 | 4.0 | 7.0 | 3.0 | 6.0 | 5.0 | 10.0 | 5.0 | 10.0 | 2.0 | 6.0 |
| 12 | 8.0 | 8.0 | 7.0 | 10.0 | 8.0 | 3.0 | 9.0 | 2.0 | 2.0 | 2.0 | 8.0 | 1.0 | 10.0 | 1.0 | 8.0 | 8.0 | 6.0 | 2.0 | 4.0 | 3.0 | 6.0 | 6.0 | 5.0 | 9.0 | 5.0 | 4.0 | 9.0 | 10.0 | 4.0 | 6.0 | 4.0 | 1.0 | 7.0 | 8.0 | 3.0 | 3.0 | 9.0 | 10.0 | 2.0 | 5.0 | 6.0 | 4.0 | 6.0 | 6.0 | 3.0 | 7.0 | 2.0 | 2.0 | 5.0 | 2.0 | 3.0 | 6.0 | 5.0 | 6.0 | 2.0 | 4.0 |
| 13 | 5.0 | 4.0 | 3.0 | 7.0 | 1.0 | 4.0 | 4.0 | 2.0 | 10.0 | 7.0 | 10.0 | 8.0 | 1.0 | 8.0 | 9.0 | 5.0 | 4.0 | 2.0 | 3.0 | 1.0 | 6.0 | 10.0 | 4.0 | 2.0 | 4.0 | 8.0 | 10.0 | 6.0 | 5.0 | 6.0 | 5.0 | 8.0 | 10.0 | 7.0 | 3.0 | 6.0 | 7.0 | 6.0 | 9.0 | 10.0 | 2.0 | 9.0 | 2.0 | 4.0 | 1.0 | 2.0 | 6.0 | 8.0 | 8.0 | 6.0 | 5.0 | 3.0 | 6.0 | 5.0 | 1.0 | 1.0 |
| 14 | 3.0 | 6.0 | 9.0 | 3.0 | 6.0 | 9.0 | 5.0 | 3.0 | 1.0 | 5.0 | 5.0 | 10.0 | 8.0 | 9.0 | 6.0 | 7.0 | 9.0 | 9.0 | 9.0 | 1.0 | 2.0 | 10.0 | 6.0 | 3.0 | 6.0 | 1.0 | 5.0 | 10.0 | 2.0 | 1.0 | 2.0 | 7.0 | 9.0 | 5.0 | 7.0 | 3.0 | 3.0 | 5.0 | 8.0 | 3.0 | 10.0 | 3.0 | 9.0 | 2.0 | 7.0 | 1.0 | 8.0 | 4.0 | 4.0 | 10.0 | 5.0 | 4.0 | 2.0 | 2.0 | 1.0 | 8.0 |
| 15 | 1.0 | 5.0 | 3.0 | 8.0 | 8.0 | 8.0 | 3.0 | 1.0 | 2.0 | 8.0 | 10.0 | 7.0 | 8.0 | 5.0 | 7.0 | 8.0 | 3.0 | 2.0 | 2.0 | 7.0 | 10.0 | 3.0 | 7.0 | 7.0 | 1.0 | 10.0 | 2.0 | 9.0 | 1.0 | 5.0 | 3.0 | 4.0 | 3.0 | 3.0 | 6.0 | 4.0 | 6.0 | 1.0 | 7.0 | 7.0 | 1.0 | 3.0 | 10.0 | 4.0 | 4.0 | 3.0 | 10.0 | 2.0 | 4.0 | 10.0 | 3.0 | 6.0 | 5.0 | 1.0 | 8.0 | 7.0 |
| 16 | 7.0 | 5.0 | 8.0 | 9.0 | 4.0 | 3.0 | 5.0 | 10.0 | 8.0 | 2.0 | 5.0 | 3.0 | 6.0 | 4.0 | 9.0 | 3.0 | 2.0 | 4.0 | 9.0 | 1.0 | 5.0 | 9.0 | 5.0 | 3.0 | 6.0 | 3.0 | 9.0 | 7.0 | 6.0 | 3.0 | 5.0 | 1.0 | 7.0 | 3.0 | 10.0 | 6.0 | 6.0 | 2.0 | 5.0 | 8.0 | 6.0 | 4.0 | 2.0 | 4.0 | 3.0 | 1.0 | 1.0 | 6.0 | 10.0 | 8.0 | 5.0 | 6.0 | 4.0 | 1.0 | 3.0 | 1.0 |
| 17 | 3.0 | 6.0 | 4.0 | 6.0 | 1.0 | 1.0 | 6.0 | 6.0 | 3.0 | 10.0 | 9.0 | 6.0 | 2.0 | 2.0 | 9.0 | 2.0 | 4.0 | 8.0 | 9.0 | 8.0 | 10.0 | 1.0 | 1.0 | 4.0 | 4.0 | 3.0 | 8.0 | 2.0 | 2.0 | 10.0 | 1.0 | 5.0 | 5.0 | 1.0 | 3.0 | 1.0 | 5.0 | 9.0 | 10.0 | 5.0 | 7.0 | 7.0 | 4.0 | 10.0 | 7.0 | 4.0 | 4.0 | 5.0 | 5.0 | 5.0 | 6.0 | 9.0 | 7.0 | 9.0 | 8.0 | 6.0 |
| 18 | 3.0 | 10.0 | 7.0 | 5.0 | 2.0 | 9.0 | 5.0 | 10.0 | 7.0 | 10.0 | 4.0 | 5.0 | 4.0 | 3.0 | 9.0 | 2.0 | 9.0 | 9.0 | 10.0 | 8.0 | 3.0 | 4.0 | 3.0 | 6.0 | 5.0 | 8.0 | 6.0 | 3.0 | 3.0 | 3.0 | 8.0 | 3.0 | 3.0 | 9.0 | 7.0 | 2.0 | 5.0 | 5.0 | 5.0 | 3.0 | 10.0 | 10.0 | 8.0 | 1.0 | 2.0 | 5.0 | 5.0 | 2.0 | 3.0 | 4.0 | 8.0 | 6.0 | 3.0 | 3.0 | 7.0 | 5.0 |
| 19 | 4.0 | 7.0 | 3.0 | 8.0 | 1.0 | 3.0 | 4.0 | 9.0 | 4.0 | 8.0 | 7.0 | 7.0 | 3.0 | 1.0 | 1.0 | 7.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 7.0 | 7.0 | 5.0 | 3.0 | 4.0 | 2.0 | 5.0 | 8.0 | 10.0 | 4.0 | 5.0 | 1.0 | 4.0 | 10.0 | 10.0 | 7.0 | 9.0 | 5.0 | 4.0 | 6.0 | 8.0 | 7.0 | 7.0 | 5.0 | 3.0 | 1.0 | 4.0 | 10.0 | 6.0 | 2.0 | 2.0 | 7.0 | 8.0 | 9.0 | 7.0 |
| 20 | 5.0 | 6.0 | 5.0 | 5.0 | 5.0 | 9.0 | 3.0 | 1.0 | 9.0 | 1.0 | 10.0 | 7.0 | 6.0 | 6.0 | 2.0 | 10.0 | 5.0 | 10.0 | 3.0 | 1.0 | 3.0 | 4.0 | 7.0 | 2.0 | 7.0 | 8.0 | 9.0 | 8.0 | 10.0 | 1.0 | 6.0 | 9.0 | 6.0 | 9.0 | 7.0 | 7.0 | 5.0 | 6.0 | 2.0 | 1.0 | 8.0 | 4.0 | 3.0 | 2.0 | 6.0 | 4.0 | 6.0 | 10.0 | 3.0 | 5.0 | 1.0 | 9.0 | 8.0 | 10.0 | 9.0 | 5.0 |
| 21 | 10.0 | 1.0 | 3.0 | 7.0 | 1.0 | 9.0 | 3.0 | 4.0 | 9.0 | 9.0 | 5.0 | 8.0 | 6.0 | 10.0 | 10.0 | 3.0 | 9.0 | 1.0 | 4.0 | 7.0 | 4.0 | 7.0 | 9.0 | 7.0 | 1.0 | 5.0 | 4.0 | 1.0 | 9.0 | 3.0 | 6.0 | 10.0 | 4.0 | 10.0 | 10.0 | 10.0 | 5.0 | 6.0 | 6.0 | 9.0 | 5.0 | 3.0 | 6.0 | 3.0 | 4.0 | 6.0 | 6.0 | 10.0 | 8.0 | 2.0 | 8.0 | 1.0 | 7.0 | 4.0 | 6.0 | 9.0 |
| 22 | 1.0 | 5.0 | 1.0 | 8.0 | 2.0 | 6.0 | 3.0 | 3.0 | 1.0 | 6.0 | 4.0 | 7.0 | 5.0 | 4.0 | 6.0 | 7.0 | 5.0 | 1.0 | 3.0 | 7.0 | 7.0 | 9.0 | 10.0 | 9.0 | 5.0 | 10.0 | 10.0 | 7.0 | 1.0 | 5.0 | 1.0 | 2.0 | 7.0 | 6.0 | 1.0 | 6.0 | 6.0 | 2.0 | 2.0 | 6.0 | 7.0 | 10.0 | 2.0 | 5.0 | 1.0 | 6.0 | 3.0 | 5.0 | 1.0 | 9.0 | 1.0 | 7.0 | 9.0 | 5.0 | 8.0 | 9.0 |
| 23 | 1.0 | 3.0 | 2.0 | 2.0 | 10.0 | 8.0 | 7.0 | 3.0 | 10.0 | 9.0 | 3.0 | 2.0 | 9.0 | 2.0 | 3.0 | 7.0 | 3.0 | 4.0 | 6.0 | 5.0 | 2.0 | 7.0 | 9.0 | 5.0 | 2.0 | 3.0 | 4.0 | 1.0 | 10.0 | 2.0 | 7.0 | 2.0 | 6.0 | 4.0 | 6.0 | 8.0 | 1.0 | 1.0 | 9.0 | 1.0 | 5.0 | 3.0 | 3.0 | 8.0 | 10.0 | 3.0 | 10.0 | 3.0 | 5.0 | 10.0 | 2.0 | 3.0 | 7.0 | 7.0 | 10.0 | 1.0 |
| 24 | 5.0 | 9.0 | 7.0 | 7.0 | 4.0 | 3.0 | 8.0 | 5.0 | 1.0 | 10.0 | 10.0 | 7.0 | 5.0 | 4.0 | 6.0 | 1.0 | 6.0 | 4.0 | 5.0 | 3.0 | 7.0 | 1.0 | 5.0 | 2.0 | 3.0 | 9.0 | 5.0 | 7.0 | 6.0 | 5.0 | 3.0 | 8.0 | 10.0 | 4.0 | 4.0 | 9.0 | 2.0 | 4.0 | 3.0 | 1.0 | 5.0 | 6.0 | 5.0 | 7.0 | 4.0 | 7.0 | 2.0 | 6.0 | 7.0 | 8.0 | 9.0 | 4.0 | 3.0 | 3.0 | 8.0 | 7.0 |
| 25 | 6.0 | 3.0 | 10.0 | 2.0 | 9.0 | 9.0 | 7.0 | 3.0 | 1.0 | 5.0 | 5.0 | 8.0 | 4.0 | 8.0 | 1.0 | 10.0 | 3.0 | 3.0 | 8.0 | 4.0 | 8.0 | 5.0 | 10.0 | 3.0 | 9.0 | 10.0 | 10.0 | 9.0 | 2.0 | 1.0 | 1.0 | 5.0 | 7.0 | 2.0 | 8.0 | 2.0 | 2.0 | 5.0 | 9.0 | 9.0 | 1.0 | 2.0 | 2.0 | 4.0 | 6.0 | 2.0 | 6.0 | 7.0 | 5.0 | 5.0 | 8.0 | 6.0 | 10.0 | 6.0 | 7.0 | 2.0 |
| 26 | 1.0 | 9.0 | 8.0 | 3.0 | 5.0 | 7.0 | 1.0 | 2.0 | 7.0 | 10.0 | 7.0 | 7.0 | 9.0 | 10.0 | 5.0 | 2.0 | 9.0 | 8.0 | 6.0 | 2.0 | 9.0 | 4.0 | 10.0 | 4.0 | 5.0 | 10.0 | 1.0 | 2.0 | 4.0 | 3.0 | 7.0 | 10.0 | 5.0 | 2.0 | 1.0 | 10.0 | 5.0 | 7.0 | 1.0 | 6.0 | 7.0 | 6.0 | 7.0 | 10.0 | 9.0 | 5.0 | 4.0 | 8.0 | 2.0 | 6.0 | 6.0 | 7.0 | 10.0 | 8.0 | 1.0 | 5.0 |
| 27 | 3.0 | 10.0 | 4.0 | 2.0 | 8.0 | 3.0 | 2.0 | 9.0 | 7.0 | 4.0 | 2.0 | 7.0 | 10.0 | 6.0 | 10.0 | 9.0 | 7.0 | 2.0 | 3.0 | 5.0 | 8.0 | 1.0 | 7.0 | 1.0 | 7.0 | 9.0 | 2.0 | 7.0 | 5.0 | 2.0 | 6.0 | 8.0 | 8.0 | 4.0 | 8.0 | 1.0 | 7.0 | 4.0 | 1.0 | 7.0 | 4.0 | 7.0 | 1.0 | 1.0 | 8.0 | 4.0 | 6.0 | 8.0 | 1.0 | 1.0 | 3.0 | 10.0 | 8.0 | 3.0 | 8.0 | 9.0 |
| 28 | 9.0 | 1.0 | 4.0 | 8.0 | 8.0 | 4.0 | 9.0 | 10.0 | 5.0 | 7.0 | 7.0 | 3.0 | 4.0 | 5.0 | 2.0 | 1.0 | 6.0 | 2.0 | 3.0 | 8.0 | 10.0 | 9.0 | 1.0 | 10.0 | 6.0 | 2.0 | 4.0 | 5.0 | 6.0 | 7.0 | 2.0 | 5.0 | 8.0 | 10.0 | 4.0 | 9.0 | 1.0 | 1.0 | 10.0 | 6.0 | 10.0 | 10.0 | 9.0 | 1.0 | 9.0 | 4.0 | 6.0 | 5.0 | 9.0 | 1.0 | 3.0 | 6.0 | 1.0 | 6.0 | 7.0 | 7.0 |
| 29 | 5.0 | 9.0 | 10.0 | 3.0 | 3.0 | 10.0 | 9.0 | 8.0 | 2.0 | 1.0 | 9.0 | 10.0 | 6.0 | 6.0 | 1.0 | 5.0 | 3.0 | 10.0 | 3.0 | 10.0 | 1.0 | 3.0 | 5.0 | 2.0 | 5.0 | 1.0 | 3.0 | 2.0 | 7.0 | 6.0 | 3.0 | 10.0 | 1.0 | 2.0 | 6.0 | 2.0 | 3.0 | 1.0 | 9.0 | 1.0 | 9.0 | 8.0 | 2.0 | 5.0 | 8.0 | 5.0 | 6.0 | 2.0 | 8.0 | 3.0 | 4.0 | 2.0 | 9.0 | 4.0 | 10.0 | 7.0 |
| 30 | 7.0 | 7.0 | 4.0 | 4.0 | 7.0 | 9.0 | 4.0 | 5.0 | 3.0 | 8.0 | 6.0 | 7.0 | 4.0 | 5.0 | 2.0 | 3.0 | 5.0 | 1.0 | 8.0 | 4.0 | 6.0 | 6.0 | 1.0 | 7.0 | 3.0 | 1.0 | 7.0 | 6.0 | 2.0 | 3.0 | 1.0 | 10.0 | 10.0 | 6.0 | 2.0 | 9.0 | 6.0 | 5.0 | 10.0 | 8.0 | 7.0 | 7.0 | 5.0 | 1.0 | 9.0 | 3.0 | 2.0 | 4.0 | 3.0 | 8.0 | 4.0 | 9.0 | 3.0 | 9.0 | 6.0 | 6.0 |
| 31 | 7.0 | 5.0 | 7.0 | 5.0 | 8.0 | 3.0 | 2.0 | 8.0 | 3.0 | 4.0 | 10.0 | 9.0 | 1.0 | 8.0 | 7.0 | 4.0 | 1.0 | 5.0 | 3.0 | 5.0 | 9.0 | 10.0 | 2.0 | 2.0 | 8.0 | 5.0 | 10.0 | 8.0 | 5.0 | 10.0 | 10.0 | 1.0 | 1.0 | 8.0 | 1.0 | 9.0 | 1.0 | 10.0 | 8.0 | 8.0 | 3.0 | 10.0 | 9.0 | 6.0 | 6.0 | 6.0 | 4.0 | 1.0 | 6.0 | 3.0 | 4.0 | 2.0 | 1.0 | 2.0 | 9.0 | 4.0 |
| 32 | 9.0 | 8.0 | 10.0 | 5.0 | 9.0 | 8.0 | 8.0 | 6.0 | 9.0 | 1.0 | 5.0 | 3.0 | 7.0 | 10.0 | 9.0 | 3.0 | 7.0 | 5.0 | 3.0 | 1.0 | 6.0 | 4.0 | 7.0 | 6.0 | 10.0 | 7.0 | 5.0 | 8.0 | 8.0 | 1.0 | 10.0 | 1.0 | 5.0 | 2.0 | 7.0 | 5.0 | 6.0 | 8.0 | 4.0 | 8.0 | 5.0 | 9.0 | 8.0 | 6.0 | 7.0 | 6.0 | 9.0 | 4.0 | 1.0 | 7.0 | 7.0 | 6.0 | 6.0 | 9.0 | 5.0 | 3.0 |
| 33 | 7.0 | 6.0 | 5.0 | 2.0 | 7.0 | 6.0 | 3.0 | 6.0 | 9.0 | 2.0 | 2.0 | 7.0 | 8.0 | 7.0 | 5.0 | 3.0 | 3.0 | 1.0 | 9.0 | 4.0 | 9.0 | 10.0 | 6.0 | 4.0 | 4.0 | 2.0 | 2.0 | 4.0 | 10.0 | 2.0 | 6.0 | 8.0 | 2.0 | 7.0 | 5.0 | 8.0 | 7.0 | 4.0 | 8.0 | 5.0 | 5.0 | 7.0 | 4.0 | 7.0 | 5.0 | 3.0 | 5.0 | 4.0 | 3.0 | 4.0 | 8.0 | 10.0 | 5.0 | 10.0 | 3.0 | 9.0 |
| 34 | 8.0 | 9.0 | 10.0 | 3.0 | 9.0 | 4.0 | 1.0 | 1.0 | 5.0 | 8.0 | 6.0 | 7.0 | 3.0 | 3.0 | 7.0 | 6.0 | 10.0 | 3.0 | 7.0 | 10.0 | 7.0 | 10.0 | 1.0 | 6.0 | 4.0 | 8.0 | 1.0 | 8.0 | 4.0 | 6.0 | 2.0 | 1.0 | 7.0 | 5.0 | 7.0 | 10.0 | 3.0 | 3.0 | 1.0 | 9.0 | 2.0 | 4.0 | 10.0 | 8.0 | 2.0 | 1.0 | 7.0 | 3.0 | 6.0 | 1.0 | 8.0 | 5.0 | 4.0 | 7.0 | 2.0 | 7.0 |
| 35 | 5.0 | 1.0 | 4.0 | 7.0 | 5.0 | 9.0 | 9.0 | 5.0 | 2.0 | 2.0 | 5.0 | 6.0 | 3.0 | 6.0 | 3.0 | 4.0 | 6.0 | 1.0 | 2.0 | 10.0 | 7.0 | 10.0 | 6.0 | 8.0 | 9.0 | 2.0 | 10.0 | 1.0 | 9.0 | 2.0 | 9.0 | 9.0 | 5.0 | 8.0 | 10.0 | 5.0 | 10.0 | 9.0 | 2.0 | 2.0 | 9.0 | 5.0 | 10.0 | 1.0 | 1.0 | 7.0 | 2.0 | 6.0 | 10.0 | 2.0 | 3.0 | 3.0 | 4.0 | 2.0 | 5.0 | 9.0 |
| 36 | 1.0 | 3.0 | 4.0 | 5.0 | 7.0 | 4.0 | 10.0 | 6.0 | 8.0 | 9.0 | 9.0 | 7.0 | 9.0 | 7.0 | 3.0 | 6.0 | 6.0 | 5.0 | 5.0 | 7.0 | 5.0 | 5.0 | 6.0 | 1.0 | 2.0 | 2.0 | 5.0 | 7.0 | 1.0 | 3.0 | 6.0 | 1.0 | 6.0 | 7.0 | 3.0 | 10.0 | 4.0 | 6.0 | 2.0 | 4.0 | 9.0 | 5.0 | 10.0 | 10.0 | 7.0 | 1.0 | 1.0 | 1.0 | 3.0 | 8.0 | 4.0 | 3.0 | 2.0 | 10.0 | 4.0 | 7.0 |
| 37 | 7.0 | 6.0 | 3.0 | 2.0 | 4.0 | 3.0 | 8.0 | 3.0 | 3.0 | 5.0 | 9.0 | 7.0 | 10.0 | 6.0 | 5.0 | 1.0 | 2.0 | 9.0 | 5.0 | 9.0 | 6.0 | 6.0 | 2.0 | 1.0 | 4.0 | 5.0 | 7.0 | 4.0 | 1.0 | 1.0 | 5.0 | 10.0 | 8.0 | 4.0 | 3.0 | 9.0 | 6.0 | 9.0 | 6.0 | 6.0 | 10.0 | 6.0 | 10.0 | 10.0 | 4.0 | 8.0 | 6.0 | 4.0 | 9.0 | 9.0 | 6.0 | 5.0 | 5.0 | 4.0 | 1.0 | 6.0 |
| 38 | 7.0 | 3.0 | 6.0 | 7.0 | 10.0 | 1.0 | 3.0 | 9.0 | 5.0 | 10.0 | 9.0 | 1.0 | 2.0 | 9.0 | 8.0 | 7.0 | 5.0 | 10.0 | 5.0 | 5.0 | 2.0 | 6.0 | 2.0 | 9.0 | 3.0 | 9.0 | 1.0 | 1.0 | 10.0 | 9.0 | 10.0 | 8.0 | 4.0 | 8.0 | 1.0 | 2.0 | 2.0 | 6.0 | 2.0 | 3.0 | 10.0 | 4.0 | 4.0 | 4.0 | 7.0 | 3.0 | 2.0 | 1.0 | 10.0 | 4.0 | 4.0 | 1.0 | 5.0 | 8.0 | 7.0 | 5.0 |
| 39 | 8.0 | 3.0 | 9.0 | 4.0 | 6.0 | 2.0 | 3.0 | 2.0 | 8.0 | 2.0 | 6.0 | 10.0 | 5.0 | 10.0 | 3.0 | 7.0 | 8.0 | 5.0 | 3.0 | 4.0 | 1.0 | 9.0 | 6.0 | 1.0 | 1.0 | 9.0 | 6.0 | 7.0 | 6.0 | 1.0 | 8.0 | 8.0 | 8.0 | 5.0 | 9.0 | 2.0 | 4.0 | 6.0 | 3.0 | 2.0 | 5.0 | 9.0 | 6.0 | 5.0 | 6.0 | 5.0 | 2.0 | 10.0 | 4.0 | 6.0 | 2.0 | 5.0 | 3.0 | 9.0 | 8.0 | 7.0 |
| 40 | 9.0 | 3.0 | 7.0 | 2.0 | 5.0 | 7.0 | 9.0 | 8.0 | 9.0 | 5.0 | 7.0 | 6.0 | 6.0 | 2.0 | 10.0 | 1.0 | 6.0 | 7.0 | 10.0 | 6.0 | 8.0 | 5.0 | 7.0 | 5.0 | 5.0 | 1.0 | 7.0 | 4.0 | 10.0 | 9.0 | 7.0 | 3.0 | 5.0 | 5.0 | 2.0 | 9.0 | 9.0 | 10.0 | 10.0 | 5.0 | 8.0 | 2.0 | 10.0 | 7.0 | 4.0 | 6.0 | 8.0 | 2.0 | 2.0 | 1.0 | 3.0 | 4.0 | 1.0 | 5.0 | 10.0 | 9.0 |
| 41 | 8.0 | 6.0 | 6.0 | 2.0 | 10.0 | 6.0 | 2.0 | 1.0 | 2.0 | 4.0 | 7.0 | 10.0 | 4.0 | 9.0 | 3.0 | 3.0 | 4.0 | 7.0 | 10.0 | 8.0 | 4.0 | 3.0 | 10.0 | 3.0 | 6.0 | 2.0 | 6.0 | 7.0 | 10.0 | 8.0 | 7.0 | 10.0 | 9.0 | 7.0 | 4.0 | 5.0 | 5.0 | 6.0 | 4.0 | 9.0 | 2.0 | 2.0 | 5.0 | 7.0 | 7.0 | 3.0 | 9.0 | 6.0 | 3.0 | 4.0 | 8.0 | 2.0 | 9.0 | 4.0 | 1.0 | 5.0 |
| 42 | 5.0 | 9.0 | 10.0 | 1.0 | 5.0 | 9.0 | 4.0 | 3.0 | 5.0 | 7.0 | 4.0 | 3.0 | 6.0 | 2.0 | 9.0 | 10.0 | 2.0 | 4.0 | 8.0 | 7.0 | 3.0 | 6.0 | 2.0 | 3.0 | 5.0 | 2.0 | 7.0 | 1.0 | 9.0 | 2.0 | 5.0 | 9.0 | 8.0 | 4.0 | 10.0 | 10.0 | 10.0 | 10.0 | 4.0 | 6.0 | 10.0 | 5.0 | 8.0 | 2.0 | 8.0 | 5.0 | 3.0 | 9.0 | 3.0 | 8.0 | 3.0 | 1.0 | 5.0 | 1.0 | 9.0 | 6.0 |
| 43 | 1.0 | 5.0 | 2.0 | 1.0 | 3.0 | 2.0 | 9.0 | 1.0 | 3.0 | 2.0 | 5.0 | 4.0 | 6.0 | 4.0 | 2.0 | 4.0 | 4.0 | 10.0 | 1.0 | 7.0 | 2.0 | 3.0 | 5.0 | 8.0 | 7.0 | 4.0 | 10.0 | 1.0 | 1.0 | 5.0 | 1.0 | 6.0 | 6.0 | 7.0 | 8.0 | 1.0 | 10.0 | 10.0 | 4.0 | 5.0 | 7.0 | 7.0 | 2.0 | 1.0 | 2.0 | 6.0 | 7.0 | 4.0 | 10.0 | 4.0 | 8.0 | 1.0 | 3.0 | 1.0 | 10.0 | 10.0 |
| 44 | 10.0 | 2.0 | 8.0 | 1.0 | 3.0 | 8.0 | 5.0 | 7.0 | 10.0 | 4.0 | 9.0 | 1.0 | 3.0 | 1.0 | 7.0 | 4.0 | 3.0 | 7.0 | 2.0 | 5.0 | 6.0 | 4.0 | 1.0 | 10.0 | 4.0 | 6.0 | 9.0 | 8.0 | 9.0 | 8.0 | 9.0 | 6.0 | 7.0 | 5.0 | 2.0 | 1.0 | 7.0 | 4.0 | 7.0 | 6.0 | 4.0 | 7.0 | 8.0 | 2.0 | 1.0 | 5.0 | 5.0 | 2.0 | 5.0 | 8.0 | 6.0 | 7.0 | 9.0 | 7.0 | 10.0 | 6.0 |
| 45 | 10.0 | 9.0 | 2.0 | 3.0 | 5.0 | 7.0 | 1.0 | 2.0 | 7.0 | 2.0 | 8.0 | 9.0 | 7.0 | 2.0 | 1.0 | 3.0 | 1.0 | 4.0 | 5.0 | 3.0 | 4.0 | 6.0 | 6.0 | 3.0 | 7.0 | 2.0 | 5.0 | 4.0 | 4.0 | 5.0 | 3.0 | 6.0 | 6.0 | 3.0 | 1.0 | 7.0 | 1.0 | 8.0 | 3.0 | 5.0 | 6.0 | 3.0 | 5.0 | 6.0 | 5.0 | 7.0 | 6.0 | 6.0 | 9.0 | 7.0 | 3.0 | 9.0 | 2.0 | 7.0 | 3.0 | 5.0 |
| 46 | 3.0 | 7.0 | 2.0 | 9.0 | 3.0 | 2.0 | 1.0 | 4.0 | 1.0 | 3.0 | 3.0 | 4.0 | 2.0 | 6.0 | 8.0 | 10.0 | 1.0 | 4.0 | 5.0 | 1.0 | 6.0 | 6.0 | 3.0 | 10.0 | 2.0 | 6.0 | 4.0 | 6.0 | 6.0 | 6.0 | 2.0 | 4.0 | 9.0 | 5.0 | 7.0 | 2.0 | 1.0 | 6.0 | 2.0 | 2.0 | 8.0 | 9.0 | 3.0 | 7.0 | 5.0 | 6.0 | 2.0 | 1.0 | 1.0 | 1.0 | 4.0 | 3.0 | 1.0 | 7.0 | 7.0 | 4.0 |
| 47 | 9.0 | 6.0 | 2.0 | 1.0 | 7.0 | 4.0 | 2.0 | 1.0 | 3.0 | 3.0 | 6.0 | 7.0 | 2.0 | 8.0 | 4.0 | 2.0 | 6.0 | 5.0 | 2.0 | 4.0 | 10.0 | 10.0 | 5.0 | 3.0 | 6.0 | 7.0 | 8.0 | 8.0 | 5.0 | 2.0 | 4.0 | 1.0 | 4.0 | 4.0 | 3.0 | 6.0 | 1.0 | 4.0 | 1.0 | 10.0 | 2.0 | 6.0 | 9.0 | 4.0 | 2.0 | 6.0 | 1.0 | 1.0 | 4.0 | 9.0 | 5.0 | 9.0 | 9.0 | 2.0 | 8.0 | 1.0 |
| 48 | 6.0 | 8.0 | 1.0 | 2.0 | 6.0 | 6.0 | 7.0 | 2.0 | 5.0 | 10.0 | 2.0 | 3.0 | 5.0 | 8.0 | 4.0 | 4.0 | 10.0 | 5.0 | 3.0 | 10.0 | 3.0 | 8.0 | 1.0 | 5.0 | 7.0 | 5.0 | 2.0 | 1.0 | 9.0 | 8.0 | 3.0 | 6.0 | 1.0 | 3.0 | 6.0 | 10.0 | 3.0 | 9.0 | 10.0 | 4.0 | 2.0 | 3.0 | 3.0 | 10.0 | 5.0 | 9.0 | 1.0 | 4.0 | 6.0 | 9.0 | 3.0 | 10.0 | 1.0 | 9.0 | 2.0 | 7.0 |
| 49 | 1.0 | 10.0 | 9.0 | 4.0 | 8.0 | 1.0 | 6.0 | 4.0 | 7.0 | 6.0 | 1.0 | 6.0 | 2.0 | 6.0 | 10.0 | 10.0 | 8.0 | 5.0 | 4.0 | 6.0 | 5.0 | 2.0 | 9.0 | 10.0 | 8.0 | 5.0 | 6.0 | 1.0 | 1.0 | 3.0 | 8.0 | 3.0 | 7.0 | 4.0 | 1.0 | 2.0 | 8.0 | 9.0 | 4.0 | 6.0 | 1.0 | 4.0 | 8.0 | 4.0 | 8.0 | 7.0 | 1.0 | 9.0 | 9.0 | 5.0 | 7.0 | 9.0 | 1.0 | 4.0 | 2.0 | 5.0 |
| 50 | 2.0 | 7.0 | 5.0 | 1.0 | 3.0 | 6.0 | 5.0 | 6.0 | 8.0 | 5.0 | 4.0 | 5.0 | 3.0 | 5.0 | 5.0 | 3.0 | 5.0 | 6.0 | 8.0 | 2.0 | 1.0 | 8.0 | 1.0 | 2.0 | 9.0 | 8.0 | 6.0 | 3.0 | 3.0 | 4.0 | 4.0 | 4.0 | 7.0 | 8.0 | 8.0 | 3.0 | 4.0 | 6.0 | 4.0 | 2.0 | 3.0 | 8.0 | 3.0 | 8.0 | 6.0 | 3.0 | 4.0 | 5.0 | 3.0 | 7.0 | 2.0 | 2.0 | 9.0 | 5.0 | 10.0 | 8.0 |
| 51 | 3.0 | 7.0 | 6.0 | 8.0 | 1.0 | 2.0 | 8.0 | 6.0 | 8.0 | 7.0 | 2.0 | 10.0 | 6.0 | 3.0 | 4.0 | 6.0 | 6.0 | 9.0 | 6.0 | 2.0 | 9.0 | 1.0 | 7.0 | 3.0 | 4.0 | 6.0 | 7.0 | 10.0 | 6.0 | 2.0 | 9.0 | 2.0 | 6.0 | 10.0 | 5.0 | 3.0 | 3.0 | 5.0 | 1.0 | 5.0 | 4.0 | 2.0 | 1.0 | 1.0 | 7.0 | 9.0 | 3.0 | 9.0 | 10.0 | 9.0 | 2.0 | 8.0 | 5.0 | 3.0 | 6.0 | 1.0 |
| 52 | 4.0 | 2.0 | 8.0 | 1.0 | 9.0 | 4.0 | 1.0 | 5.0 | 10.0 | 9.0 | 9.0 | 5.0 | 5.0 | 6.0 | 2.0 | 5.0 | 4.0 | 7.0 | 3.0 | 7.0 | 8.0 | 7.0 | 9.0 | 7.0 | 3.0 | 10.0 | 10.0 | 8.0 | 1.0 | 9.0 | 3.0 | 1.0 | 6.0 | 5.0 | 4.0 | 4.0 | 2.0 | 5.0 | 5.0 | 3.0 | 1.0 | 9.0 | 5.0 | 3.0 | 9.0 | 2.0 | 1.0 | 9.0 | 1.0 | 1.0 | 9.0 | 5.0 | 3.0 | 3.0 | 4.0 | 8.0 |
| 53 | 5.0 | 8.0 | 5.0 | 6.0 | 2.0 | 7.0 | 8.0 | 6.0 | 5.0 | 2.0 | 6.0 | 10.0 | 6.0 | 5.0 | 2.0 | 1.0 | 1.0 | 9.0 | 3.0 | 8.0 | 10.0 | 4.0 | 5.0 | 7.0 | 3.0 | 6.0 | 8.0 | 3.0 | 6.0 | 4.0 | 9.0 | 2.0 | 9.0 | 10.0 | 7.0 | 2.0 | 10.0 | 4.0 | 8.0 | 9.0 | 5.0 | 4.0 | 1.0 | 1.0 | 7.0 | 7.0 | 7.0 | 2.0 | 9.0 | 4.0 | 5.0 | 3.0 | 3.0 | 1.0 | 9.0 | 9.0 |
| 54 | 4.0 | 6.0 | 10.0 | 7.0 | 6.0 | 8.0 | 2.0 | 10.0 | 5.0 | 4.0 | 2.0 | 2.0 | 2.0 | 1.0 | 1.0 | 8.0 | 3.0 | 8.0 | 7.0 | 9.0 | 9.0 | 6.0 | 8.0 | 10.0 | 8.0 | 7.0 | 1.0 | 8.0 | 7.0 | 10.0 | 6.0 | 9.0 | 5.0 | 3.0 | 2.0 | 5.0 | 4.0 | 1.0 | 7.0 | 8.0 | 10.0 | 1.0 | 9.0 | 10.0 | 10.0 | 3.0 | 7.0 | 8.0 | 2.0 | 2.0 | 10.0 | 6.0 | 4.0 | 9.0 | 6.0 | 8.0 |
| 55 | 8.0 | 6.0 | 10.0 | 8.0 | 2.0 | 9.0 | 9.0 | 8.0 | 5.0 | 4.0 | 10.0 | 6.0 | 4.0 | 1.0 | 8.0 | 7.0 | 1.0 | 6.0 | 5.0 | 7.0 | 5.0 | 9.0 | 9.0 | 1.0 | 7.0 | 2.0 | 5.0 | 9.0 | 7.0 | 7.0 | 6.0 | 4.0 | 3.0 | 9.0 | 7.0 | 9.0 | 7.0 | 6.0 | 5.0 | 7.0 | 9.0 | 5.0 | 6.0 | 10.0 | 6.0 | 5.0 | 4.0 | 1.0 | 7.0 | 5.0 | 8.0 | 1.0 | 8.0 | 9.0 | 8.0 | 4.0 |
Use these lines to compute each route's total (base fares plus any pairwise extras) and choose the single uninterrupted itinerary with the smallest sum.

Also, when you send back the chosen itinerary, please put it in a tiny JSON object like this:

{
  ""solution"": []
}

Here ""solution"" should be an array listing the node identifiers in order from the starting airport to the final one — just the node names, nothing else. Think of it like filling in a short form: the array is the stops along the route (first is the source, last is the target). This JSON is just a sketch of the shape I expect, not the actual answer itself.

Please make sure to use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels.

- For example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".

Alright — pick the best uninterrupted route and return it in that JSON shape.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 1, 'var_index': 1}, {'from': 19, 'to': 2, 'var_index': 2}, {'from': 19, 'to': 3, 'var_index': 3}, {'from': 19, 'to': 4, 'var_index': 4}, {'from': 19, 'to': 5, 'var_index': 5}, {'from': 19, 'to': 6, 'var_index': 6}, {'from': 19, 'to': 7, 'var_index': 7}, {'from': 19, 'to': 8, 'var_index': 8}, {'from': 19, 'to': 9, 'var_index': 9}, {'from': 19, 'to': 10, 'var_index': 10}, {'from': 19, 'to': 11, 'var_index': 11}, {'from': 19, 'to': 12, 'var_index': 12}, {'from': 19, 'to': 13, 'var_index': 13}, {'from': 19, 'to': 14, 'var_index': 14}, {'from': 19, 'to': 15, 'var_index': 15}, {'from': 19, 'to': 16, 'var_index': 16}, {'from': 19, 'to': 17, 'var_index': 17}, {'from': 19, 'to': 18, 'var_index': 18}, {'from': 0, 'to': 20, 'var_index': 19}, {'from': 1, 'to': 20, 'var_index': 20}, {'from': 2, 'to': 20, 'var_index': 21}, {'from': 3, 'to': 20, 'var_index': 22}, {'from': 4, 'to': 20, 'var_index': 23}, {'from': 5, 'to': 20, 'var_index': 24}, {'from': 6, 'to': 20, 'var_index': 25}, {'from': 7, 'to': 20, 'var_index': 26}, {'from': 8, 'to': 20, 'var_index': 27}, {'from': 9, 'to': 20, 'var_index': 28}, {'from': 10, 'to': 20, 'var_index': 29}, {'from': 11, 'to': 20, 'var_index': 30}, {'from': 12, 'to': 20, 'var_index': 31}, {'from': 13, 'to': 20, 'var_index': 32}, {'from': 14, 'to': 20, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 20, 'var_index': 35}, {'from': 17, 'to': 20, 'var_index': 36}, {'from': 18, 'to': 20, 'var_index': 37}, {'from': 0, 'to': 1, 'var_index': 38}, {'from': 1, 'to': 2, 'var_index': 39}, {'from': 2, 'to': 3, 'var_index': 40}, {'from': 3, 'to': 4, 'var_index': 41}, {'from': 4, 'to': 5, 'var_index': 42}, {'from': 5, 'to': 6, 'var_index': 43}, {'from': 6, 'to': 7, 'var_index': 44}, {'from': 7, 'to': 8, 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52, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 53, 'quadratic_cost': 9.0}, {'var_i': 55, 'var_j': 54, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 55, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 'T', 'to': 'A', 'var_index': 0}, {'from': 'T', 'to': 'B', 'var_index': 1}, {'from': 'T', 'to': 'C', 'var_index': 2}, {'from': 'T', 'to': 'D', 'var_index': 3}, {'from': 'T', 'to': 'E', 'var_index': 4}, {'from': 'T', 'to': 'F', 'var_index': 5}, {'from': 'T', 'to': 'G', 'var_index': 6}, {'from': 'T', 'to': 'H', 'var_index': 7}, {'from': 'T', 'to': 'I', 'var_index': 8}, {'from': 'T', 'to': 'J', 'var_index': 9}, {'from': 'T', 'to': 'K', 'var_index': 10}, {'from': 'T', 'to': 'L', 'var_index': 11}, {'from': 'T', 'to': 'M', 'var_index': 12}, {'from': 'T', 'to': 'N', 'var_index': 13}, {'from': 'T', 'to': 'O', 'var_index': 14}, {'from': 'T', 'to': 'P', 'var_index': 15}, {'from': 'T', 'to': 'Q', 'var_index': 16}, {'from': 'T', 'to': 'R', 'var_index': 17}, {'from': 'T', 'to': 'S', 'var_index': 18}, {'from': 'A', 'to': 'U', 'var_index': 19}, {'from': 'B', 'to': 'U', 'var_index': 20}, {'from': 'C', 'to': 'U', 'var_index': 21}, {'from': 'D', 'to': 'U', 'var_index': 22}, {'from': 'E', 'to': 'U', 'var_index': 23}, {'from': 'F', 'to': 'U', 'var_index': 24}, {'from': 'G', 'to': 'U', 'var_index': 25}, {'from': 'H', 'to': 'U', 'var_index': 26}, {'from': 'I', 'to': 'U', 'var_index': 27}, {'from': 'J', 'to': 'U', 'var_index': 28}, {'from': 'K', 'to': 'U', 'var_index': 29}, {'from': 'L', 'to': 'U', 'var_index': 30}, {'from': 'M', 'to': 'U', 'var_index': 31}, {'from': 'N', 'to': 'U', 'var_index': 32}, {'from': 'O', 'to': 'U', 'var_index': 33}, {'from': 'P', 'to': 'U', 'var_index': 34}, {'from': 'Q', 'to': 'U', 'var_index': 35}, {'from': 'R', 'to': 'U', 'var_index': 36}, {'from': 'S', 'to': 'U', 'var_index': 37}, {'from': 'A', 'to': 'B', 'var_index': 38}, {'from': 'B', 'to': 'C', 'var_index': 39}, {'from': 'C', 'to': 'D', 'var_index': 40}, {'from': 'D', 'to': 'E', 'var_index': 41}, {'from': 'E', 'to': 'F', 'var_index': 42}, {'from': 'F', 'to': 'G', 'var_index': 43}, {'from': 'G', 'to': 'H', 'var_index': 44}, {'from': 'H', 'to': 'I', 'var_index': 45}, {'from': 'I', 'to': 'J', 'var_index': 46}, {'from': 'J', 'to': 'K', 'var_index': 47}, {'from': 'K', 'to': 'L', 'var_index': 48}, {'from': 'L', 'to': 'M', 'var_index': 49}, {'from': 'M', 'to': 'N', 'var_index': 50}, {'from': 'N', 'to': 'O', 'var_index': 51}, {'from': 'O', 'to': 'P', 'var_index': 52}, {'from': 'P', 'to': 'Q', 'var_index': 53}, {'from': 'Q', 'to': 'R', 'var_index': 54}, {'from': 'R', 'to': 'S', 'var_index': 55}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U'}}","['T', 'F', 'U']",44,nl,names
QSPP,QSPP,"Many people on campus follow one-way pedestrian arrows, and for this task a messenger must pick a single such route from the administration building to the research block. Each segment has a baseline effort, some segments also carry an extra standalone penalty, and certain pairs of segments generate additional penalties only if both are included in the same path. To compare routes, add up all baseline efforts plus any standalone penalties and any pair penalties that apply, and take the single continuous, one-way route with the lowest combined score. The specific walkway details and penalty values are provided below.

{
  ""total_locations_count"": 20,
  ""total_walkways_count"": 19,
  ""location_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I"",
    ""J"",
    ""K"",
    ""L"",
    ""M"",
    ""N"",
    ""O"",
    ""P"",
    ""Q"",
    ""R"",
    ""S"",
    ""T""
  ],
  ""administration_building_node"": ""S"",
  ""research_block_node"": ""T"",
  ""edges"": [
    {
      ""walkway_from_node"": ""S"",
      ""walkway_to_node"": ""A"",
      ""walkway_segment_id"": 0
    },
    {
      ""walkway_from_node"": ""R"",
      ""walkway_to_node"": ""T"",
      ""walkway_segment_id"": 1
    },
    {
      ""walkway_from_node"": ""A"",
      ""walkway_to_node"": ""B"",
      ""walkway_segment_id"": 2
    },
    {
      ""walkway_from_node"": ""B"",
      ""walkway_to_node"": ""C"",
      ""walkway_segment_id"": 3
    },
    {
      ""walkway_from_node"": ""C"",
      ""walkway_to_node"": ""D"",
      ""walkway_segment_id"": 4
    },
    {
      ""walkway_from_node"": ""D"",
      ""walkway_to_node"": ""E"",
      ""walkway_segment_id"": 5
    },
    {
      ""walkway_from_node"": ""E"",
      ""walkway_to_node"": ""F"",
      ""walkway_segment_id"": 6
    },
    {
      ""walkway_from_node"": ""F"",
      ""walkway_to_node"": ""G"",
      ""walkway_segment_id"": 7
    },
    {
      ""walkway_from_node"": ""G"",
      ""walkway_to_node"": ""H"",
      ""walkway_segment_id"": 8
    },
    {
      ""walkway_from_node"": ""H"",
      ""walkway_to_node"": ""I"",
      ""walkway_segment_id"": 9
    },
    {
      ""walkway_from_node"": ""I"",
      ""walkway_to_node"": ""J"",
      ""walkway_segment_id"": 10
    },
    {
      ""walkway_from_node"": ""J"",
      ""walkway_to_node"": ""K"",
      ""walkway_segment_id"": 11
    },
    {
      ""walkway_from_node"": ""K"",
      ""walkway_to_node"": ""L"",
      ""walkway_segment_id"": 12
    },
    {
      ""walkway_from_node"": ""L"",
      ""walkway_to_node"": ""M"",
      ""walkway_segment_id"": 13
    },
    {
      ""walkway_from_node"": ""M"",
      ""walkway_to_node"": ""N"",
      ""walkway_segment_id"": 14
    },
    {
      ""walkway_from_node"": ""N"",
      ""walkway_to_node"": ""O"",
      ""walkway_segment_id"": 15
    },
    {
      ""walkway_from_node"": ""O"",
      ""walkway_to_node"": ""P"",
      ""walkway_segment_id"": 16
    },
    {
      ""walkway_from_node"": ""P"",
      ""walkway_to_node"": ""Q"",
      ""walkway_segment_id"": 17
    },
    {
      ""walkway_from_node"": ""Q"",
      ""walkway_to_node"": ""R"",
      ""walkway_segment_id"": 18
    }
  ],
  ""linear_costs"": [
    {
      ""walkway_segment_ref"": 0,
      ""baseline_effort"": 5.0
    },
    {
      ""walkway_segment_ref"": 1,
      ""baseline_effort"": 3.0
    },
    {
      ""walkway_segment_ref"": 2,
      ""baseline_effort"": 8.0
    },
    {
      ""walkway_segment_ref"": 3,
      ""baseline_effort"": 7.0
    },
    {
      ""walkway_segment_ref"": 4,
      ""baseline_effort"": 10.0
    },
    {
      ""walkway_segment_ref"": 5,
      ""baseline_effort"": 4.0
    },
    {
      ""walkway_segment_ref"": 6,
      ""baseline_effort"": 3.0
    },
    {
      ""walkway_segment_ref"": 7,
      ""baseline_effort"": 1.0
    },
    {
      ""walkway_segment_ref"": 8,
      ""baseline_effort"": 4.0
    },
    {
      ""walkway_segment_ref"": 9,
      ""baseline_effort"": 2.0
    },
    {
      ""walkway_segment_ref"": 10,
      ""baseline_effort"": 8.0
    },
    {
      ""walkway_segment_ref"": 11,
      ""baseline_effort"": 8.0
    },
    {
      ""walkway_segment_ref"": 12,
      ""baseline_effort"": 5.0
    },
    {
      ""walkway_segment_ref"": 13,
      ""baseline_effort"": 4.0
    },
    {
      ""walkway_segment_ref"": 14,
      ""baseline_effort"": 6.0
    },
    {
      ""walkway_segment_ref"": 15,
      ""baseline_effort"": 9.0
    },
    {
      ""walkway_segment_ref"": 16,
      ""baseline_effort"": 1.0
    },
    {
      ""walkway_segment_ref"": 17,
      ""baseline_effort"": 9.0
    },
    {
      ""walkway_segment_ref"": 18,
      ""baseline_effort"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_ref, segment_j_ref). If two walkway_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_ref\segment_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 1.0 | 5.0 | 2.0 | 4.0 | 10.0 | 5.0 | 2.0 | 4.0 | 2.0 | 8.0 | 9.0 | 5.0 | 3.0 | 9.0 | 7.0 | 3.0 | 6.0 | 6.0 |
| 1 | 1.0 | 3.0 | 4.0 | 10.0 | 9.0 | 2.0 | 7.0 | 4.0 | 6.0 | 8.0 | 6.0 | 6.0 | 3.0 | 2.0 | 1.0 | 7.0 | 8.0 | 2.0 | 10.0 |
| 2 | 5.0 | 4.0 | 8.0 | 8.0 | 1.0 | 10.0 | 10.0 | 3.0 | 2.0 | 1.0 | 6.0 | 5.0 | 1.0 | 6.0 | 3.0 | 4.0 | 2.0 | 5.0 | 7.0 |
| 3 | 2.0 | 10.0 | 8.0 | 5.0 | 2.0 | 2.0 | 10.0 | 8.0 | 9.0 | 4.0 | 2.0 | 9.0 | 8.0 | 7.0 | 10.0 | 4.0 | 8.0 | 7.0 | 4.0 |
| 4 | 4.0 | 9.0 | 1.0 | 2.0 | 10.0 | 8.0 | 4.0 | 7.0 | 1.0 | 6.0 | 1.0 | 6.0 | 3.0 | 3.0 | 6.0 | 6.0 | 8.0 | 6.0 | 3.0 |
| 5 | 10.0 | 2.0 | 10.0 | 2.0 | 8.0 | 2.0 | 5.0 | 10.0 | 4.0 | 2.0 | 7.0 | 9.0 | 5.0 | 9.0 | 5.0 | 5.0 | 2.0 | 4.0 | 4.0 |
| 6 | 5.0 | 7.0 | 10.0 | 10.0 | 4.0 | 5.0 | 4.0 | 7.0 | 2.0 | 5.0 | 10.0 | 4.0 | 8.0 | 7.0 | 4.0 | 1.0 | 8.0 | 1.0 | 8.0 |
| 7 | 2.0 | 4.0 | 3.0 | 8.0 | 7.0 | 10.0 | 7.0 | 10.0 | 7.0 | 4.0 | 2.0 | 2.0 | 9.0 | 9.0 | 2.0 | 6.0 | 4.0 | 2.0 | 8.0 |
| 8 | 4.0 | 6.0 | 2.0 | 9.0 | 1.0 | 4.0 | 2.0 | 7.0 | 7.0 | 6.0 | 3.0 | 2.0 | 2.0 | 4.0 | 6.0 | 7.0 | 3.0 | 2.0 | 10.0 |
| 9 | 2.0 | 8.0 | 1.0 | 4.0 | 6.0 | 2.0 | 5.0 | 4.0 | 6.0 | 9.0 | 1.0 | 6.0 | 1.0 | 4.0 | 10.0 | 2.0 | 4.0 | 8.0 | 9.0 |
| 10 | 8.0 | 6.0 | 6.0 | 2.0 | 1.0 | 7.0 | 10.0 | 2.0 | 3.0 | 1.0 | 4.0 | 5.0 | 3.0 | 4.0 | 3.0 | 3.0 | 10.0 | 6.0 | 3.0 |
| 11 | 9.0 | 6.0 | 5.0 | 9.0 | 6.0 | 9.0 | 4.0 | 2.0 | 2.0 | 6.0 | 5.0 | 2.0 | 7.0 | 2.0 | 4.0 | 9.0 | 1.0 | 4.0 | 4.0 |
| 12 | 5.0 | 3.0 | 1.0 | 8.0 | 3.0 | 5.0 | 8.0 | 9.0 | 2.0 | 1.0 | 3.0 | 7.0 | 1.0 | 9.0 | 9.0 | 4.0 | 3.0 | 8.0 | 5.0 |
| 13 | 3.0 | 2.0 | 6.0 | 7.0 | 3.0 | 9.0 | 7.0 | 9.0 | 4.0 | 4.0 | 4.0 | 2.0 | 9.0 | 2.0 | 6.0 | 5.0 | 6.0 | 9.0 | 1.0 |
| 14 | 9.0 | 1.0 | 3.0 | 10.0 | 6.0 | 5.0 | 4.0 | 2.0 | 6.0 | 10.0 | 3.0 | 4.0 | 9.0 | 6.0 | 8.0 | 6.0 | 5.0 | 9.0 | 10.0 |
| 15 | 7.0 | 7.0 | 4.0 | 4.0 | 6.0 | 5.0 | 1.0 | 6.0 | 7.0 | 2.0 | 3.0 | 9.0 | 4.0 | 5.0 | 6.0 | 8.0 | 7.0 | 8.0 | 4.0 |
| 16 | 3.0 | 8.0 | 2.0 | 8.0 | 8.0 | 2.0 | 8.0 | 4.0 | 3.0 | 4.0 | 10.0 | 1.0 | 3.0 | 6.0 | 5.0 | 7.0 | 10.0 | 3.0 | 5.0 |
| 17 | 6.0 | 2.0 | 5.0 | 7.0 | 6.0 | 4.0 | 1.0 | 2.0 | 2.0 | 8.0 | 6.0 | 4.0 | 8.0 | 9.0 | 9.0 | 8.0 | 3.0 | 5.0 | 1.0 |
| 18 | 6.0 | 10.0 | 7.0 | 4.0 | 3.0 | 4.0 | 8.0 | 8.0 | 10.0 | 9.0 | 3.0 | 4.0 | 5.0 | 1.0 | 10.0 | 4.0 | 5.0 | 1.0 | 9.0 |

When you send back the chosen route, just drop it into a tiny JSON snippet so it's easy to read and check. Here's the shape to use:

{
  ""solution"": []
}

Think of that ""solution"" array as the little form field where you list the path: the nodes in order from the administration building (source) to the research block (target). Keep it simple — it's just a sketch of the shape we expect, not the actual route itself.

Please use the exact identifiers as they appear in the instance input; don't rename them or make up new labels.
- for example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 17, 'to': 19, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}, {'from': 7, 'to': 8, 'var_index': 9}, {'from': 8, 'to': 9, 'var_index': 10}, {'from': 9, 'to': 10, 'var_index': 11}, {'from': 10, 'to': 11, 'var_index': 12}, {'from': 11, 'to': 12, 'var_index': 13}, {'from': 12, 'to': 13, 'var_index': 14}, {'from': 13, 'to': 14, 'var_index': 15}, {'from': 14, 'to': 15, 'var_index': 16}, {'from': 15, 'to': 16, 'var_index': 17}, {'from': 16, 'to': 17, 'var_index': 18}], 'objective': {'constant': 0.0, 'linear': [5.0, 3.0, 8.0, 7.0, 10.0, 4.0, 3.0, 1.0, 4.0, 2.0, 8.0, 8.0, 5.0, 4.0, 6.0, 9.0, 1.0, 9.0, 3.0], 'quadratic': [[1.0, 1.0, 5.0, 2.0, 4.0, 10.0, 5.0, 2.0, 4.0, 2.0, 8.0, 9.0, 5.0, 3.0, 9.0, 7.0, 3.0, 6.0, 6.0], [1.0, 3.0, 4.0, 10.0, 9.0, 2.0, 7.0, 4.0, 6.0, 8.0, 6.0, 6.0, 3.0, 2.0, 1.0, 7.0, 8.0, 2.0, 10.0], [5.0, 4.0, 8.0, 8.0, 1.0, 10.0, 10.0, 3.0, 2.0, 1.0, 6.0, 5.0, 1.0, 6.0, 3.0, 4.0, 2.0, 5.0, 7.0], [2.0, 10.0, 8.0, 5.0, 2.0, 2.0, 10.0, 8.0, 9.0, 4.0, 2.0, 9.0, 8.0, 7.0, 10.0, 4.0, 8.0, 7.0, 4.0], [4.0, 9.0, 1.0, 2.0, 10.0, 8.0, 4.0, 7.0, 1.0, 6.0, 1.0, 6.0, 3.0, 3.0, 6.0, 6.0, 8.0, 6.0, 3.0], [10.0, 2.0, 10.0, 2.0, 8.0, 2.0, 5.0, 10.0, 4.0, 2.0, 7.0, 9.0, 5.0, 9.0, 5.0, 5.0, 2.0, 4.0, 4.0], [5.0, 7.0, 10.0, 10.0, 4.0, 5.0, 4.0, 7.0, 2.0, 5.0, 10.0, 4.0, 8.0, 7.0, 4.0, 1.0, 8.0, 1.0, 8.0], [2.0, 4.0, 3.0, 8.0, 7.0, 10.0, 7.0, 10.0, 7.0, 4.0, 2.0, 2.0, 9.0, 9.0, 2.0, 6.0, 4.0, 2.0, 8.0], [4.0, 6.0, 2.0, 9.0, 1.0, 4.0, 2.0, 7.0, 7.0, 6.0, 3.0, 2.0, 2.0, 4.0, 6.0, 7.0, 3.0, 2.0, 10.0], [2.0, 8.0, 1.0, 4.0, 6.0, 2.0, 5.0, 4.0, 6.0, 9.0, 1.0, 6.0, 1.0, 4.0, 10.0, 2.0, 4.0, 8.0, 9.0], [8.0, 6.0, 6.0, 2.0, 1.0, 7.0, 10.0, 2.0, 3.0, 1.0, 4.0, 5.0, 3.0, 4.0, 3.0, 3.0, 10.0, 6.0, 3.0], [9.0, 6.0, 5.0, 9.0, 6.0, 9.0, 4.0, 2.0, 2.0, 6.0, 5.0, 2.0, 7.0, 2.0, 4.0, 9.0, 1.0, 4.0, 4.0], [5.0, 3.0, 1.0, 8.0, 3.0, 5.0, 8.0, 9.0, 2.0, 1.0, 3.0, 7.0, 1.0, 9.0, 9.0, 4.0, 3.0, 8.0, 5.0], [3.0, 2.0, 6.0, 7.0, 3.0, 9.0, 7.0, 9.0, 4.0, 4.0, 4.0, 2.0, 9.0, 2.0, 6.0, 5.0, 6.0, 9.0, 1.0], [9.0, 1.0, 3.0, 10.0, 6.0, 5.0, 4.0, 2.0, 6.0, 10.0, 3.0, 4.0, 9.0, 6.0, 8.0, 6.0, 5.0, 9.0, 10.0], [7.0, 7.0, 4.0, 4.0, 6.0, 5.0, 1.0, 6.0, 7.0, 2.0, 3.0, 9.0, 4.0, 5.0, 6.0, 8.0, 7.0, 8.0, 4.0], [3.0, 8.0, 2.0, 8.0, 8.0, 2.0, 8.0, 4.0, 3.0, 4.0, 10.0, 1.0, 3.0, 6.0, 5.0, 7.0, 10.0, 3.0, 5.0], [6.0, 2.0, 5.0, 7.0, 6.0, 4.0, 1.0, 2.0, 2.0, 8.0, 6.0, 4.0, 8.0, 9.0, 9.0, 8.0, 3.0, 5.0, 1.0], [6.0, 10.0, 7.0, 4.0, 3.0, 4.0, 8.0, 8.0, 10.0, 9.0, 3.0, 4.0, 5.0, 1.0, 10.0, 4.0, 5.0, 1.0, 9.0]]}, 'source': 18, 'target': 19}","[18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]",1996.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 19, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T'], 'source': 'S', 'target': 'T', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 3.0}, {'var_index': 7, 'linear_cost': 1.0}, {'var_index': 8, 'linear_cost': 4.0}, {'var_index': 9, 'linear_cost': 2.0}, {'var_index': 10, 'linear_cost': 8.0}, {'var_index': 11, 'linear_cost': 8.0}, {'var_index': 12, 'linear_cost': 5.0}, {'var_index': 13, 'linear_cost': 4.0}, {'var_index': 14, 'linear_cost': 6.0}, {'var_index': 15, 'linear_cost': 9.0}, {'var_index': 16, 'linear_cost': 1.0}, {'var_index': 17, 'linear_cost': 9.0}, {'var_index': 18, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 18, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 2, 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'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 'S', 'to': 'A', 'var_index': 0}, {'from': 'R', 'to': 'T', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}, {'from': 'H', 'to': 'I', 'var_index': 9}, {'from': 'I', 'to': 'J', 'var_index': 10}, {'from': 'J', 'to': 'K', 'var_index': 11}, {'from': 'K', 'to': 'L', 'var_index': 12}, {'from': 'L', 'to': 'M', 'var_index': 13}, {'from': 'M', 'to': 'N', 'var_index': 14}, {'from': 'N', 'to': 'O', 'var_index': 15}, {'from': 'O', 'to': 'P', 'var_index': 16}, {'from': 'P', 'to': 'Q', 'var_index': 17}, {'from': 'Q', 'to': 'R', 'var_index': 18}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T'}}","['S', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'T']",45,json,names
QSPP,QSPP,"Someone suggested a walking route challenge: start at the square, finish at the viewpoint, obey all one-way signs, and try to make the whole walk as easy as possible. The task is to select exactly one legal route from start to finish and list the sequence of places visited in order. The way to tell which route is better is simple in practice — add up the base tiredness for every leg of the trip, and then add any extra discomfort that comes from particular pairs of legs being combined (certain legs even add a tiny extra cost by themselves). The full map and the specific costs are shown below.

The map shows 24 places and 35 permitted one-way legs; the place identifiers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, the start is 23 and the finish is 24.

| leg_from_place | leg_to_place | leg_identifier |
|---|---|---|
| 23 | 1 | 0 |
| 23 | 12 | 1 |
| 11 | 24 | 2 |
| 22 | 24 | 3 |
| 1 | 2 | 4 |
| 1 | 12 | 5 |
| 2 | 3 | 6 |
| 2 | 13 | 7 |
| 3 | 4 | 8 |
| 3 | 14 | 9 |
| 4 | 5 | 10 |
| 4 | 15 | 11 |
| 5 | 6 | 12 |
| 5 | 16 | 13 |
| 6 | 7 | 14 |
| 6 | 17 | 15 |
| 7 | 8 | 16 |
| 7 | 18 | 17 |
| 8 | 9 | 18 |
| 8 | 19 | 19 |
| 9 | 10 | 20 |
| 9 | 20 | 21 |
| 10 | 11 | 22 |
| 10 | 21 | 23 |
| 11 | 22 | 24 |
| 12 | 13 | 25 |
| 13 | 14 | 26 |
| 14 | 15 | 27 |
| 15 | 16 | 28 |
| 16 | 17 | 29 |
| 17 | 18 | 30 |
| 18 | 19 | 31 |
| 19 | 20 | 32 |
| 20 | 21 | 33 |
| 21 | 22 | 34 |

| leg_id_ref | base_fatigue |
|---|---|
| 0 | 1.0 |
| 1 | 2.0 |
| 2 | 9.0 |
| 3 | 10.0 |
| 4 | 2.0 |
| 5 | 5.0 |
| 6 | 8.0 |
| 7 | 2.0 |
| 8 | 4.0 |
| 9 | 1.0 |
| 10 | 7.0 |
| 11 | 9.0 |
| 12 | 9.0 |
| 13 | 7.0 |
| 14 | 6.0 |
| 15 | 2.0 |
| 16 | 2.0 |
| 17 | 5.0 |
| 18 | 5.0 |
| 19 | 2.0 |
| 20 | 7.0 |
| 21 | 7.0 |
| 22 | 2.0 |
| 23 | 10.0 |
| 24 | 1.0 |
| 25 | 1.0 |
| 26 | 9.0 |
| 27 | 3.0 |
| 28 | 8.0 |
| 29 | 9.0 |
| 30 | 5.0 |
| 31 | 2.0 |
| 32 | 5.0 |
| 33 | 3.0 |
| 34 | 9.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_leg_id_ref, second_leg_id_ref). If two leg_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| first_leg_id_ref\second_leg_id_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 1.0 | 7.0 | 4.0 | 3.0 | 3.0 | 9.0 | 2.0 | 5.0 | 6.0 | 10.0 | 6.0 | 7.0 | 3.0 | 2.0 | 4.0 | 1.0 | 8.0 | 5.0 | 6.0 | 9.0 | 3.0 | 2.0 | 7.0 | 5.0 | 9.0 | 10.0 | 6.0 | 1.0 | 10.0 | 2.0 | 6.0 | 5.0 | 9.0 | 1.0 |
| 1 | 1.0 | 9.0 | 8.0 | 3.0 | 1.0 | 10.0 | 3.0 | 3.0 | 1.0 | 10.0 | 3.0 | 6.0 | 4.0 | 3.0 | 6.0 | 8.0 | 6.0 | 3.0 | 4.0 | 3.0 | 10.0 | 1.0 | 9.0 | 2.0 | 3.0 | 5.0 | 8.0 | 3.0 | 8.0 | 2.0 | 3.0 | 7.0 | 9.0 | 2.0 | 6.0 |
| 2 | 7.0 | 8.0 | 9.0 | 1.0 | 6.0 | 2.0 | 2.0 | 3.0 | 9.0 | 9.0 | 4.0 | 3.0 | 7.0 | 6.0 | 5.0 | 9.0 | 9.0 | 1.0 | 10.0 | 3.0 | 9.0 | 6.0 | 2.0 | 6.0 | 10.0 | 4.0 | 9.0 | 4.0 | 6.0 | 6.0 | 6.0 | 1.0 | 2.0 | 3.0 | 1.0 |
| 3 | 4.0 | 3.0 | 1.0 | 6.0 | 10.0 | 9.0 | 3.0 | 10.0 | 9.0 | 3.0 | 5.0 | 9.0 | 6.0 | 9.0 | 4.0 | 1.0 | 2.0 | 3.0 | 3.0 | 8.0 | 9.0 | 5.0 | 4.0 | 2.0 | 3.0 | 8.0 | 4.0 | 6.0 | 7.0 | 4.0 | 9.0 | 10.0 | 7.0 | 5.0 | 9.0 |
| 4 | 3.0 | 1.0 | 6.0 | 10.0 | 10.0 | 5.0 | 2.0 | 6.0 | 6.0 | 4.0 | 10.0 | 1.0 | 10.0 | 1.0 | 5.0 | 2.0 | 5.0 | 8.0 | 4.0 | 5.0 | 10.0 | 8.0 | 4.0 | 1.0 | 8.0 | 4.0 | 7.0 | 5.0 | 1.0 | 4.0 | 6.0 | 9.0 | 10.0 | 3.0 | 8.0 |
| 5 | 3.0 | 10.0 | 2.0 | 9.0 | 5.0 | 3.0 | 2.0 | 1.0 | 8.0 | 8.0 | 1.0 | 9.0 | 8.0 | 5.0 | 5.0 | 2.0 | 3.0 | 10.0 | 4.0 | 3.0 | 1.0 | 8.0 | 5.0 | 10.0 | 1.0 | 10.0 | 9.0 | 6.0 | 5.0 | 8.0 | 3.0 | 5.0 | 4.0 | 7.0 | 3.0 |
| 6 | 9.0 | 3.0 | 2.0 | 3.0 | 2.0 | 2.0 | 9.0 | 1.0 | 2.0 | 7.0 | 6.0 | 10.0 | 5.0 | 9.0 | 4.0 | 8.0 | 7.0 | 5.0 | 9.0 | 1.0 | 5.0 | 8.0 | 6.0 | 1.0 | 10.0 | 5.0 | 6.0 | 7.0 | 5.0 | 4.0 | 7.0 | 5.0 | 7.0 | 5.0 | 5.0 |
| 7 | 2.0 | 3.0 | 3.0 | 10.0 | 6.0 | 1.0 | 1.0 | 3.0 | 9.0 | 1.0 | 6.0 | 4.0 | 10.0 | 8.0 | 8.0 | 9.0 | 7.0 | 7.0 | 10.0 | 1.0 | 9.0 | 6.0 | 8.0 | 10.0 | 9.0 | 7.0 | 6.0 | 1.0 | 9.0 | 10.0 | 4.0 | 8.0 | 2.0 | 8.0 | 10.0 |
| 8 | 5.0 | 1.0 | 9.0 | 9.0 | 6.0 | 8.0 | 2.0 | 9.0 | 2.0 | 7.0 | 10.0 | 5.0 | 5.0 | 9.0 | 8.0 | 1.0 | 10.0 | 2.0 | 7.0 | 9.0 | 6.0 | 10.0 | 6.0 | 9.0 | 5.0 | 3.0 | 4.0 | 7.0 | 6.0 | 9.0 | 7.0 | 3.0 | 1.0 | 10.0 | 1.0 |
| 9 | 6.0 | 10.0 | 9.0 | 3.0 | 4.0 | 8.0 | 7.0 | 1.0 | 7.0 | 10.0 | 9.0 | 1.0 | 2.0 | 1.0 | 7.0 | 9.0 | 9.0 | 2.0 | 6.0 | 5.0 | 5.0 | 5.0 | 8.0 | 8.0 | 3.0 | 6.0 | 5.0 | 1.0 | 1.0 | 10.0 | 1.0 | 6.0 | 3.0 | 9.0 | 2.0 |
| 10 | 10.0 | 3.0 | 4.0 | 5.0 | 10.0 | 1.0 | 6.0 | 6.0 | 10.0 | 9.0 | 9.0 | 5.0 | 3.0 | 6.0 | 8.0 | 1.0 | 5.0 | 8.0 | 5.0 | 3.0 | 5.0 | 9.0 | 7.0 | 10.0 | 3.0 | 7.0 | 5.0 | 3.0 | 8.0 | 7.0 | 1.0 | 4.0 | 7.0 | 7.0 | 5.0 |
| 11 | 6.0 | 6.0 | 3.0 | 9.0 | 1.0 | 9.0 | 10.0 | 4.0 | 5.0 | 1.0 | 5.0 | 4.0 | 1.0 | 5.0 | 4.0 | 9.0 | 8.0 | 7.0 | 10.0 | 7.0 | 8.0 | 6.0 | 9.0 | 2.0 | 6.0 | 1.0 | 2.0 | 9.0 | 2.0 | 7.0 | 7.0 | 9.0 | 8.0 | 10.0 | 8.0 |
| 12 | 7.0 | 4.0 | 7.0 | 6.0 | 10.0 | 8.0 | 5.0 | 10.0 | 5.0 | 2.0 | 3.0 | 1.0 | 5.0 | 3.0 | 1.0 | 7.0 | 1.0 | 1.0 | 1.0 | 10.0 | 8.0 | 10.0 | 7.0 | 7.0 | 5.0 | 7.0 | 6.0 | 2.0 | 8.0 | 6.0 | 6.0 | 3.0 | 3.0 | 1.0 | 6.0 |
| 13 | 3.0 | 3.0 | 6.0 | 9.0 | 1.0 | 5.0 | 9.0 | 8.0 | 9.0 | 1.0 | 6.0 | 5.0 | 3.0 | 1.0 | 8.0 | 8.0 | 2.0 | 10.0 | 1.0 | 4.0 | 2.0 | 9.0 | 6.0 | 5.0 | 3.0 | 2.0 | 1.0 | 4.0 | 6.0 | 10.0 | 2.0 | 7.0 | 5.0 | 7.0 | 8.0 |
| 14 | 2.0 | 6.0 | 5.0 | 4.0 | 5.0 | 5.0 | 4.0 | 8.0 | 8.0 | 7.0 | 8.0 | 4.0 | 1.0 | 8.0 | 8.0 | 8.0 | 10.0 | 4.0 | 10.0 | 1.0 | 5.0 | 5.0 | 9.0 | 5.0 | 4.0 | 4.0 | 7.0 | 5.0 | 4.0 | 8.0 | 9.0 | 6.0 | 4.0 | 10.0 | 2.0 |
| 15 | 4.0 | 8.0 | 9.0 | 1.0 | 2.0 | 2.0 | 8.0 | 9.0 | 1.0 | 9.0 | 1.0 | 9.0 | 7.0 | 8.0 | 8.0 | 10.0 | 1.0 | 8.0 | 5.0 | 6.0 | 1.0 | 2.0 | 1.0 | 7.0 | 10.0 | 10.0 | 10.0 | 8.0 | 2.0 | 5.0 | 3.0 | 1.0 | 7.0 | 7.0 | 6.0 |
| 16 | 1.0 | 6.0 | 9.0 | 2.0 | 5.0 | 3.0 | 7.0 | 7.0 | 10.0 | 9.0 | 5.0 | 8.0 | 1.0 | 2.0 | 10.0 | 1.0 | 2.0 | 2.0 | 1.0 | 5.0 | 9.0 | 7.0 | 5.0 | 1.0 | 5.0 | 6.0 | 7.0 | 9.0 | 7.0 | 4.0 | 7.0 | 5.0 | 1.0 | 3.0 | 7.0 |
| 17 | 8.0 | 3.0 | 1.0 | 3.0 | 8.0 | 10.0 | 5.0 | 7.0 | 2.0 | 2.0 | 8.0 | 7.0 | 1.0 | 10.0 | 4.0 | 8.0 | 2.0 | 8.0 | 9.0 | 4.0 | 5.0 | 4.0 | 3.0 | 7.0 | 9.0 | 5.0 | 4.0 | 6.0 | 9.0 | 3.0 | 8.0 | 5.0 | 7.0 | 5.0 | 4.0 |
| 18 | 5.0 | 4.0 | 10.0 | 3.0 | 4.0 | 4.0 | 9.0 | 10.0 | 7.0 | 6.0 | 5.0 | 10.0 | 1.0 | 1.0 | 10.0 | 5.0 | 1.0 | 9.0 | 2.0 | 8.0 | 4.0 | 8.0 | 1.0 | 8.0 | 6.0 | 4.0 | 3.0 | 8.0 | 1.0 | 9.0 | 6.0 | 5.0 | 2.0 | 5.0 | 7.0 |
| 19 | 6.0 | 3.0 | 3.0 | 8.0 | 5.0 | 3.0 | 1.0 | 1.0 | 9.0 | 5.0 | 3.0 | 7.0 | 10.0 | 4.0 | 1.0 | 6.0 | 5.0 | 4.0 | 8.0 | 8.0 | 10.0 | 9.0 | 5.0 | 9.0 | 5.0 | 1.0 | 8.0 | 1.0 | 7.0 | 6.0 | 2.0 | 2.0 | 4.0 | 3.0 | 9.0 |
| 20 | 9.0 | 10.0 | 9.0 | 9.0 | 10.0 | 1.0 | 5.0 | 9.0 | 6.0 | 5.0 | 5.0 | 8.0 | 8.0 | 2.0 | 5.0 | 1.0 | 9.0 | 5.0 | 4.0 | 10.0 | 9.0 | 3.0 | 8.0 | 6.0 | 9.0 | 7.0 | 4.0 | 10.0 | 5.0 | 8.0 | 6.0 | 1.0 | 4.0 | 5.0 | 3.0 |
| 21 | 3.0 | 1.0 | 6.0 | 5.0 | 8.0 | 8.0 | 8.0 | 6.0 | 10.0 | 5.0 | 9.0 | 6.0 | 10.0 | 9.0 | 5.0 | 2.0 | 7.0 | 4.0 | 8.0 | 9.0 | 3.0 | 10.0 | 6.0 | 9.0 | 6.0 | 9.0 | 2.0 | 5.0 | 10.0 | 7.0 | 5.0 | 2.0 | 2.0 | 4.0 | 2.0 |
| 22 | 2.0 | 9.0 | 2.0 | 4.0 | 4.0 | 5.0 | 6.0 | 8.0 | 6.0 | 8.0 | 7.0 | 9.0 | 7.0 | 6.0 | 9.0 | 1.0 | 5.0 | 3.0 | 1.0 | 5.0 | 8.0 | 6.0 | 9.0 | 4.0 | 10.0 | 4.0 | 7.0 | 2.0 | 4.0 | 6.0 | 3.0 | 7.0 | 9.0 | 4.0 | 4.0 |
| 23 | 7.0 | 2.0 | 6.0 | 2.0 | 1.0 | 10.0 | 1.0 | 10.0 | 9.0 | 8.0 | 10.0 | 2.0 | 7.0 | 5.0 | 5.0 | 7.0 | 1.0 | 7.0 | 8.0 | 9.0 | 6.0 | 9.0 | 4.0 | 7.0 | 2.0 | 2.0 | 9.0 | 3.0 | 5.0 | 5.0 | 9.0 | 10.0 | 10.0 | 9.0 | 10.0 |
| 24 | 5.0 | 3.0 | 10.0 | 3.0 | 8.0 | 1.0 | 10.0 | 9.0 | 5.0 | 3.0 | 3.0 | 6.0 | 5.0 | 3.0 | 4.0 | 10.0 | 5.0 | 9.0 | 6.0 | 5.0 | 9.0 | 6.0 | 10.0 | 2.0 | 2.0 | 7.0 | 6.0 | 8.0 | 5.0 | 2.0 | 3.0 | 2.0 | 4.0 | 4.0 | 5.0 |
| 25 | 9.0 | 5.0 | 4.0 | 8.0 | 4.0 | 10.0 | 5.0 | 7.0 | 3.0 | 6.0 | 7.0 | 1.0 | 7.0 | 2.0 | 4.0 | 10.0 | 6.0 | 5.0 | 4.0 | 1.0 | 7.0 | 9.0 | 4.0 | 2.0 | 7.0 | 6.0 | 7.0 | 2.0 | 3.0 | 8.0 | 1.0 | 8.0 | 10.0 | 1.0 | 8.0 |
| 26 | 10.0 | 8.0 | 9.0 | 4.0 | 7.0 | 9.0 | 6.0 | 6.0 | 4.0 | 5.0 | 5.0 | 2.0 | 6.0 | 1.0 | 7.0 | 10.0 | 7.0 | 4.0 | 3.0 | 8.0 | 4.0 | 2.0 | 7.0 | 9.0 | 6.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 8.0 | 7.0 | 5.0 | 4.0 | 4.0 |
| 27 | 6.0 | 3.0 | 4.0 | 6.0 | 5.0 | 6.0 | 7.0 | 1.0 | 7.0 | 1.0 | 3.0 | 9.0 | 2.0 | 4.0 | 5.0 | 8.0 | 9.0 | 6.0 | 8.0 | 1.0 | 10.0 | 5.0 | 2.0 | 3.0 | 8.0 | 2.0 | 9.0 | 9.0 | 2.0 | 6.0 | 4.0 | 3.0 | 2.0 | 8.0 | 7.0 |
| 28 | 1.0 | 8.0 | 6.0 | 7.0 | 1.0 | 5.0 | 5.0 | 9.0 | 6.0 | 1.0 | 8.0 | 2.0 | 8.0 | 6.0 | 4.0 | 2.0 | 7.0 | 9.0 | 1.0 | 7.0 | 5.0 | 10.0 | 4.0 | 5.0 | 5.0 | 3.0 | 9.0 | 2.0 | 9.0 | 7.0 | 9.0 | 2.0 | 4.0 | 5.0 | 7.0 |
| 29 | 10.0 | 2.0 | 6.0 | 4.0 | 4.0 | 8.0 | 4.0 | 10.0 | 9.0 | 10.0 | 7.0 | 7.0 | 6.0 | 10.0 | 8.0 | 5.0 | 4.0 | 3.0 | 9.0 | 6.0 | 8.0 | 7.0 | 6.0 | 5.0 | 2.0 | 8.0 | 10.0 | 6.0 | 7.0 | 2.0 | 4.0 | 6.0 | 5.0 | 4.0 | 8.0 |
| 30 | 2.0 | 3.0 | 6.0 | 9.0 | 6.0 | 3.0 | 7.0 | 4.0 | 7.0 | 1.0 | 1.0 | 7.0 | 6.0 | 2.0 | 9.0 | 3.0 | 7.0 | 8.0 | 6.0 | 2.0 | 6.0 | 5.0 | 3.0 | 9.0 | 3.0 | 1.0 | 8.0 | 4.0 | 9.0 | 4.0 | 9.0 | 1.0 | 4.0 | 10.0 | 9.0 |
| 31 | 6.0 | 7.0 | 1.0 | 10.0 | 9.0 | 5.0 | 5.0 | 8.0 | 3.0 | 6.0 | 4.0 | 9.0 | 3.0 | 7.0 | 6.0 | 1.0 | 5.0 | 5.0 | 5.0 | 2.0 | 1.0 | 2.0 | 7.0 | 10.0 | 2.0 | 8.0 | 7.0 | 3.0 | 2.0 | 6.0 | 1.0 | 3.0 | 4.0 | 2.0 | 10.0 |
| 32 | 5.0 | 9.0 | 2.0 | 7.0 | 10.0 | 4.0 | 7.0 | 2.0 | 1.0 | 3.0 | 7.0 | 8.0 | 3.0 | 5.0 | 4.0 | 7.0 | 1.0 | 7.0 | 2.0 | 4.0 | 4.0 | 2.0 | 9.0 | 10.0 | 4.0 | 10.0 | 5.0 | 2.0 | 4.0 | 5.0 | 4.0 | 4.0 | 6.0 | 4.0 | 8.0 |
| 33 | 9.0 | 2.0 | 3.0 | 5.0 | 3.0 | 7.0 | 5.0 | 8.0 | 10.0 | 9.0 | 7.0 | 10.0 | 1.0 | 7.0 | 10.0 | 7.0 | 3.0 | 5.0 | 5.0 | 3.0 | 5.0 | 4.0 | 4.0 | 9.0 | 4.0 | 1.0 | 4.0 | 8.0 | 5.0 | 4.0 | 10.0 | 2.0 | 4.0 | 10.0 | 1.0 |
| 34 | 1.0 | 6.0 | 1.0 | 9.0 | 8.0 | 3.0 | 5.0 | 10.0 | 1.0 | 2.0 | 5.0 | 8.0 | 6.0 | 8.0 | 2.0 | 6.0 | 7.0 | 4.0 | 7.0 | 9.0 | 3.0 | 2.0 | 4.0 | 10.0 | 5.0 | 8.0 | 4.0 | 7.0 | 7.0 | 8.0 | 9.0 | 10.0 | 8.0 | 1.0 | 3.0 |

Select exactly one legal route from 23 to 24 that minimizes the sum of base tiredness and any pairwise discomfort.

If you're ready to give the route, just drop the sequence of places into this tiny JSON snippet and send it back — nice and simple:

{
  ""solution"": []
}

Think of ""solution"" as the field where you list the walk: a straight sequence of node names from the square (start) to the viewpoint (finish). Keep it informal — it's just a little form to fill in, not a technical report. This JSON is only a sketch of the shape I expect, so replace the empty list with the actual ordered nodes you choose.

Please make sure you use the node identifiers exactly as they appear in the instance input — don't rename them or invent new ones. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 11, 'var_index': 1}, {'from': 10, 'to': 23, 'var_index': 2}, {'from': 21, 'to': 23, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 11, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 12, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 13, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 14, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 15, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 16, 'var_index': 15}, {'from': 6, 'to': 7, 'var_index': 16}, {'from': 6, 'to': 17, 'var_index': 17}, {'from': 7, 'to': 8, 'var_index': 18}, {'from': 7, 'to': 18, 'var_index': 19}, {'from': 8, 'to': 9, 'var_index': 20}, {'from': 8, 'to': 19, 'var_index': 21}, {'from': 9, 'to': 10, 'var_index': 22}, {'from': 9, 'to': 20, 'var_index': 23}, {'from': 10, 'to': 21, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 12, 'to': 13, 'var_index': 26}, {'from': 13, 'to': 14, 'var_index': 27}, {'from': 14, 'to': 15, 'var_index': 28}, {'from': 15, 'to': 16, 'var_index': 29}, {'from': 16, 'to': 17, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 18, 'to': 19, 'var_index': 32}, {'from': 19, 'to': 20, 'var_index': 33}, {'from': 20, 'to': 21, 'var_index': 34}], 'objective': {'constant': 0.0, 'linear': [1.0, 2.0, 9.0, 10.0, 2.0, 5.0, 8.0, 2.0, 4.0, 1.0, 7.0, 9.0, 9.0, 7.0, 6.0, 2.0, 2.0, 5.0, 5.0, 2.0, 7.0, 7.0, 2.0, 10.0, 1.0, 1.0, 9.0, 3.0, 8.0, 9.0, 5.0, 2.0, 5.0, 3.0, 9.0], 'quadratic': [[5.0, 1.0, 7.0, 4.0, 3.0, 3.0, 9.0, 2.0, 5.0, 6.0, 10.0, 6.0, 7.0, 3.0, 2.0, 4.0, 1.0, 8.0, 5.0, 6.0, 9.0, 3.0, 2.0, 7.0, 5.0, 9.0, 10.0, 6.0, 1.0, 10.0, 2.0, 6.0, 5.0, 9.0, 1.0], [1.0, 9.0, 8.0, 3.0, 1.0, 10.0, 3.0, 3.0, 1.0, 10.0, 3.0, 6.0, 4.0, 3.0, 6.0, 8.0, 6.0, 3.0, 4.0, 3.0, 10.0, 1.0, 9.0, 2.0, 3.0, 5.0, 8.0, 3.0, 8.0, 2.0, 3.0, 7.0, 9.0, 2.0, 6.0], [7.0, 8.0, 9.0, 1.0, 6.0, 2.0, 2.0, 3.0, 9.0, 9.0, 4.0, 3.0, 7.0, 6.0, 5.0, 9.0, 9.0, 1.0, 10.0, 3.0, 9.0, 6.0, 2.0, 6.0, 10.0, 4.0, 9.0, 4.0, 6.0, 6.0, 6.0, 1.0, 2.0, 3.0, 1.0], [4.0, 3.0, 1.0, 6.0, 10.0, 9.0, 3.0, 10.0, 9.0, 3.0, 5.0, 9.0, 6.0, 9.0, 4.0, 1.0, 2.0, 3.0, 3.0, 8.0, 9.0, 5.0, 4.0, 2.0, 3.0, 8.0, 4.0, 6.0, 7.0, 4.0, 9.0, 10.0, 7.0, 5.0, 9.0], [3.0, 1.0, 6.0, 10.0, 10.0, 5.0, 2.0, 6.0, 6.0, 4.0, 10.0, 1.0, 10.0, 1.0, 5.0, 2.0, 5.0, 8.0, 4.0, 5.0, 10.0, 8.0, 4.0, 1.0, 8.0, 4.0, 7.0, 5.0, 1.0, 4.0, 6.0, 9.0, 10.0, 3.0, 8.0], [3.0, 10.0, 2.0, 9.0, 5.0, 3.0, 2.0, 1.0, 8.0, 8.0, 1.0, 9.0, 8.0, 5.0, 5.0, 2.0, 3.0, 10.0, 4.0, 3.0, 1.0, 8.0, 5.0, 10.0, 1.0, 10.0, 9.0, 6.0, 5.0, 8.0, 3.0, 5.0, 4.0, 7.0, 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{'var_i': 33, 'var_j': 28, 'quadratic_cost': 5.0}, {'var_i': 33, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 33, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 33, 'var_j': 31, 'quadratic_cost': 2.0}, {'var_i': 33, 'var_j': 32, 'quadratic_cost': 4.0}, {'var_i': 33, 'var_j': 33, 'quadratic_cost': 10.0}, {'var_i': 33, 'var_j': 34, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 34, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 34, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 34, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 34, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 34, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 23, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 24, 'quadratic_cost': 5.0}, {'var_i': 34, 'var_j': 25, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 26, 'quadratic_cost': 4.0}, {'var_i': 34, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 34, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 34, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 34, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 34, 'var_j': 33, 'quadratic_cost': 1.0}, {'var_i': 34, 'var_j': 34, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 23, 'to': 1, 'var_index': 0}, {'from': 23, 'to': 12, 'var_index': 1}, {'from': 11, 'to': 24, 'var_index': 2}, {'from': 22, 'to': 24, 'var_index': 3}, {'from': 1, 'to': 2, 'var_index': 4}, {'from': 1, 'to': 12, 'var_index': 5}, {'from': 2, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 13, 'var_index': 7}, {'from': 3, 'to': 4, 'var_index': 8}, {'from': 3, 'to': 14, 'var_index': 9}, {'from': 4, 'to': 5, 'var_index': 10}, {'from': 4, 'to': 15, 'var_index': 11}, {'from': 5, 'to': 6, 'var_index': 12}, {'from': 5, 'to': 16, 'var_index': 13}, {'from': 6, 'to': 7, 'var_index': 14}, {'from': 6, 'to': 17, 'var_index': 15}, {'from': 7, 'to': 8, 'var_index': 16}, {'from': 7, 'to': 18, 'var_index': 17}, {'from': 8, 'to': 9, 'var_index': 18}, {'from': 8, 'to': 19, 'var_index': 19}, {'from': 9, 'to': 10, 'var_index': 20}, {'from': 9, 'to': 20, 'var_index': 21}, {'from': 10, 'to': 11, 'var_index': 22}, {'from': 10, 'to': 21, 'var_index': 23}, {'from': 11, 'to': 22, 'var_index': 24}, {'from': 12, 'to': 13, 'var_index': 25}, {'from': 13, 'to': 14, 'var_index': 26}, {'from': 14, 'to': 15, 'var_index': 27}, {'from': 15, 'to': 16, 'var_index': 28}, {'from': 16, 'to': 17, 'var_index': 29}, {'from': 17, 'to': 18, 'var_index': 30}, {'from': 18, 'to': 19, 'var_index': 31}, {'from': 19, 'to': 20, 'var_index': 32}, {'from': 20, 'to': 21, 'var_index': 33}, {'from': 21, 'to': 22, 'var_index': 34}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20, 20: 21, 21: 22, 22: 23, 23: 24}}","[23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24]",46,markdown_table,1
QSPP,QSPP,"Many people on a busy set know the drill: choose one path to move the equipment from the storage area to the shooting area, and make sure it follows the one-way corridors. Each corridor has its own handling charge, a few have a built-in extra cost, and some corridor combinations create additional trouble if both are used — sometimes that trouble is different depending on the order. The practical rule is to pick a single continuous route, start at storage and finish at the set without splitting the move, and keep the total expense (the sum of all corridor charges and any pairwise extras) as low as you can. The exact diagram and price list are shown below.

There are 20 locations and 33 one-way corridors — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20; start at 19 and finish at 20.
Corridor 0 runs from 19 to 1.
Corridor 1 runs from 19 to 7.
Corridor 2 runs from 19 to 13.
Corridor 3 runs from 6 to 20.
Corridor 4 runs from 12 to 20.
Corridor 5 runs from 18 to 20.
Corridor 6 runs from 1 to 2.
Corridor 7 runs from 1 to 7.
Corridor 8 runs from 2 to 3.
Corridor 9 runs from 2 to 8.
Corridor 10 runs from 3 to 4.
Corridor 11 runs from 3 to 9.
Corridor 12 runs from 4 to 5.
Corridor 13 runs from 4 to 10.
Corridor 14 runs from 5 to 6.
Corridor 15 runs from 5 to 11.
Corridor 16 runs from 6 to 12.
Corridor 17 runs from 7 to 8.
Corridor 18 runs from 7 to 13.
Corridor 19 runs from 8 to 9.
Corridor 20 runs from 8 to 14.
Corridor 21 runs from 9 to 10.
Corridor 22 runs from 9 to 15.
Corridor 23 runs from 10 to 11.
Corridor 24 runs from 10 to 16.
Corridor 25 runs from 11 to 12.
Corridor 26 runs from 11 to 17.
Corridor 27 runs from 12 to 18.
Corridor 28 runs from 13 to 14.
Corridor 29 runs from 14 to 15.
Corridor 30 runs from 15 to 16.
Corridor 31 runs from 16 to 17.
Corridor 32 runs from 17 to 18.
Using corridor 0 incurs a handling charge of 5.0.
Using corridor 1 incurs a handling charge of 3.0.
Using corridor 2 incurs a handling charge of 2.0.
Using corridor 3 incurs a handling charge of 3.0.
Using corridor 4 incurs a handling charge of 6.0.
Using corridor 5 incurs a handling charge of 5.0.
Using corridor 6 incurs a handling charge of 2.0.
Using corridor 7 incurs a handling charge of 1.0.
Using corridor 8 incurs a handling charge of 7.0.
Using corridor 9 incurs a handling charge of 4.0.
Using corridor 10 incurs a handling charge of 7.0.
Using corridor 11 incurs a handling charge of 3.0.
Using corridor 12 incurs a handling charge of 5.0.
Using corridor 13 incurs a handling charge of 8.0.
Using corridor 14 incurs a handling charge of 2.0.
Using corridor 15 incurs a handling charge of 5.0.
Using corridor 16 incurs a handling charge of 1.0.
Using corridor 17 incurs a handling charge of 9.0.
Using corridor 18 incurs a handling charge of 6.0.
Using corridor 19 incurs a handling charge of 6.0.
Using corridor 20 incurs a handling charge of 10.0.
Using corridor 21 incurs a handling charge of 1.0.
Using corridor 22 incurs a handling charge of 1.0.
Using corridor 23 incurs a handling charge of 1.0.
Using corridor 24 incurs a handling charge of 5.0.
Using corridor 25 incurs a handling charge of 8.0.
Using corridor 26 incurs a handling charge of 6.0.
Using corridor 27 incurs a handling charge of 4.0.
Using corridor 28 incurs a handling charge of 6.0.
Using corridor 29 incurs a handling charge of 8.0.
Using corridor 30 incurs a handling charge of 5.0.
Using corridor 31 incurs a handling charge of 1.0.
Using corridor 32 incurs a handling charge of 4.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 5.0 | 1.0 | 10.0 | 3.0 | 9.0 | 1.0 | 7.0 | 2.0 | 3.0 | 4.0 | 10.0 | 9.0 | 2.0 | 3.0 | 6.0 | 1.0 | 10.0 | 5.0 | 6.0 | 9.0 | 7.0 | 5.0 | 7.0 | 2.0 | 4.0 | 1.0 | 8.0 | 4.0 | 6.0 | 9.0 | 10.0 | 2.0 |
| 1 | 5.0 | 9.0 | 4.0 | 8.0 | 6.0 | 9.0 | 6.0 | 7.0 | 10.0 | 8.0 | 5.0 | 7.0 | 1.0 | 1.0 | 3.0 | 8.0 | 1.0 | 10.0 | 5.0 | 2.0 | 3.0 | 6.0 | 6.0 | 10.0 | 6.0 | 9.0 | 4.0 | 10.0 | 5.0 | 10.0 | 5.0 | 4.0 | 7.0 |
| 2 | 1.0 | 4.0 | 7.0 | 7.0 | 7.0 | 6.0 | 9.0 | 4.0 | 4.0 | 2.0 | 1.0 | 7.0 | 5.0 | 7.0 | 9.0 | 1.0 | 3.0 | 7.0 | 2.0 | 2.0 | 8.0 | 4.0 | 3.0 | 2.0 | 5.0 | 10.0 | 9.0 | 7.0 | 3.0 | 10.0 | 10.0 | 2.0 | 10.0 |
| 3 | 10.0 | 8.0 | 7.0 | 6.0 | 2.0 | 8.0 | 10.0 | 2.0 | 1.0 | 2.0 | 7.0 | 1.0 | 5.0 | 6.0 | 3.0 | 1.0 | 6.0 | 4.0 | 10.0 | 6.0 | 4.0 | 9.0 | 4.0 | 2.0 | 9.0 | 5.0 | 9.0 | 8.0 | 10.0 | 10.0 | 7.0 | 10.0 | 7.0 |
| 4 | 3.0 | 6.0 | 7.0 | 2.0 | 9.0 | 8.0 | 9.0 | 3.0 | 5.0 | 6.0 | 8.0 | 10.0 | 7.0 | 6.0 | 9.0 | 10.0 | 6.0 | 3.0 | 10.0 | 8.0 | 8.0 | 10.0 | 10.0 | 9.0 | 9.0 | 9.0 | 5.0 | 7.0 | 8.0 | 1.0 | 3.0 | 6.0 | 8.0 |
| 5 | 9.0 | 9.0 | 6.0 | 8.0 | 8.0 | 5.0 | 1.0 | 9.0 | 6.0 | 10.0 | 2.0 | 4.0 | 6.0 | 4.0 | 9.0 | 7.0 | 1.0 | 1.0 | 6.0 | 9.0 | 6.0 | 6.0 | 7.0 | 6.0 | 1.0 | 3.0 | 10.0 | 4.0 | 7.0 | 3.0 | 5.0 | 2.0 | 7.0 |
| 6 | 1.0 | 6.0 | 9.0 | 10.0 | 9.0 | 1.0 | 9.0 | 6.0 | 10.0 | 7.0 | 6.0 | 6.0 | 2.0 | 2.0 | 1.0 | 7.0 | 5.0 | 2.0 | 1.0 | 9.0 | 8.0 | 10.0 | 8.0 | 10.0 | 5.0 | 1.0 | 6.0 | 1.0 | 6.0 | 5.0 | 6.0 | 3.0 | 6.0 |
| 7 | 7.0 | 7.0 | 4.0 | 2.0 | 3.0 | 9.0 | 6.0 | 1.0 | 5.0 | 6.0 | 1.0 | 3.0 | 9.0 | 4.0 | 8.0 | 1.0 | 8.0 | 10.0 | 4.0 | 6.0 | 4.0 | 1.0 | 5.0 | 4.0 | 5.0 | 7.0 | 6.0 | 10.0 | 6.0 | 8.0 | 3.0 | 10.0 | 8.0 |
| 8 | 2.0 | 10.0 | 4.0 | 1.0 | 5.0 | 6.0 | 10.0 | 5.0 | 3.0 | 9.0 | 9.0 | 9.0 | 8.0 | 1.0 | 5.0 | 2.0 | 3.0 | 6.0 | 6.0 | 2.0 | 10.0 | 1.0 | 4.0 | 10.0 | 3.0 | 4.0 | 9.0 | 10.0 | 6.0 | 4.0 | 5.0 | 8.0 | 8.0 |
| 9 | 3.0 | 8.0 | 2.0 | 2.0 | 6.0 | 10.0 | 7.0 | 6.0 | 9.0 | 3.0 | 1.0 | 8.0 | 7.0 | 2.0 | 8.0 | 10.0 | 1.0 | 6.0 | 7.0 | 4.0 | 2.0 | 1.0 | 8.0 | 1.0 | 10.0 | 2.0 | 2.0 | 1.0 | 5.0 | 9.0 | 2.0 | 3.0 | 5.0 |
| 10 | 4.0 | 5.0 | 1.0 | 7.0 | 8.0 | 2.0 | 6.0 | 1.0 | 9.0 | 1.0 | 2.0 | 7.0 | 6.0 | 2.0 | 8.0 | 4.0 | 7.0 | 1.0 | 1.0 | 6.0 | 9.0 | 3.0 | 4.0 | 5.0 | 10.0 | 5.0 | 6.0 | 3.0 | 8.0 | 1.0 | 9.0 | 6.0 | 5.0 |
| 11 | 10.0 | 7.0 | 7.0 | 1.0 | 10.0 | 4.0 | 6.0 | 3.0 | 9.0 | 8.0 | 7.0 | 10.0 | 1.0 | 3.0 | 6.0 | 6.0 | 5.0 | 4.0 | 2.0 | 8.0 | 4.0 | 8.0 | 8.0 | 10.0 | 8.0 | 4.0 | 7.0 | 1.0 | 2.0 | 5.0 | 10.0 | 5.0 | 4.0 |
| 12 | 9.0 | 1.0 | 5.0 | 5.0 | 7.0 | 6.0 | 2.0 | 9.0 | 8.0 | 7.0 | 6.0 | 1.0 | 7.0 | 3.0 | 3.0 | 6.0 | 4.0 | 6.0 | 2.0 | 10.0 | 10.0 | 7.0 | 8.0 | 1.0 | 10.0 | 3.0 | 9.0 | 10.0 | 10.0 | 1.0 | 2.0 | 1.0 | 8.0 |
| 13 | 2.0 | 1.0 | 7.0 | 6.0 | 6.0 | 4.0 | 2.0 | 4.0 | 1.0 | 2.0 | 2.0 | 3.0 | 3.0 | 8.0 | 6.0 | 5.0 | 1.0 | 10.0 | 6.0 | 5.0 | 5.0 | 3.0 | 7.0 | 10.0 | 7.0 | 6.0 | 1.0 | 3.0 | 8.0 | 1.0 | 2.0 | 2.0 | 7.0 |
| 14 | 3.0 | 3.0 | 9.0 | 3.0 | 9.0 | 9.0 | 1.0 | 8.0 | 5.0 | 8.0 | 8.0 | 6.0 | 3.0 | 6.0 | 10.0 | 8.0 | 10.0 | 4.0 | 2.0 | 8.0 | 9.0 | 6.0 | 9.0 | 2.0 | 10.0 | 10.0 | 6.0 | 7.0 | 1.0 | 10.0 | 9.0 | 1.0 | 7.0 |
| 15 | 6.0 | 8.0 | 1.0 | 1.0 | 10.0 | 7.0 | 7.0 | 1.0 | 2.0 | 10.0 | 4.0 | 6.0 | 6.0 | 5.0 | 8.0 | 9.0 | 7.0 | 2.0 | 6.0 | 5.0 | 4.0 | 10.0 | 5.0 | 10.0 | 1.0 | 7.0 | 10.0 | 3.0 | 8.0 | 5.0 | 8.0 | 6.0 | 8.0 |
| 16 | 1.0 | 1.0 | 3.0 | 6.0 | 6.0 | 1.0 | 5.0 | 8.0 | 3.0 | 1.0 | 7.0 | 5.0 | 4.0 | 1.0 | 10.0 | 7.0 | 6.0 | 7.0 | 4.0 | 2.0 | 5.0 | 9.0 | 3.0 | 1.0 | 10.0 | 4.0 | 9.0 | 4.0 | 7.0 | 1.0 | 1.0 | 9.0 | 9.0 |
| 17 | 10.0 | 10.0 | 7.0 | 4.0 | 3.0 | 1.0 | 2.0 | 10.0 | 6.0 | 6.0 | 1.0 | 4.0 | 6.0 | 10.0 | 4.0 | 2.0 | 7.0 | 7.0 | 3.0 | 5.0 | 10.0 | 9.0 | 3.0 | 9.0 | 1.0 | 2.0 | 6.0 | 9.0 | 8.0 | 6.0 | 10.0 | 9.0 | 9.0 |
| 18 | 5.0 | 5.0 | 2.0 | 10.0 | 10.0 | 6.0 | 1.0 | 4.0 | 6.0 | 7.0 | 1.0 | 2.0 | 2.0 | 6.0 | 2.0 | 6.0 | 4.0 | 3.0 | 3.0 | 9.0 | 5.0 | 6.0 | 9.0 | 2.0 | 1.0 | 9.0 | 2.0 | 2.0 | 1.0 | 5.0 | 1.0 | 2.0 | 2.0 |
| 19 | 6.0 | 2.0 | 2.0 | 6.0 | 8.0 | 9.0 | 9.0 | 6.0 | 2.0 | 4.0 | 6.0 | 8.0 | 10.0 | 5.0 | 8.0 | 5.0 | 2.0 | 5.0 | 9.0 | 8.0 | 3.0 | 10.0 | 4.0 | 2.0 | 1.0 | 2.0 | 6.0 | 8.0 | 1.0 | 2.0 | 2.0 | 3.0 | 6.0 |
| 20 | 9.0 | 3.0 | 8.0 | 4.0 | 8.0 | 6.0 | 8.0 | 4.0 | 10.0 | 2.0 | 9.0 | 4.0 | 10.0 | 5.0 | 9.0 | 4.0 | 5.0 | 10.0 | 5.0 | 3.0 | 9.0 | 1.0 | 3.0 | 2.0 | 9.0 | 3.0 | 1.0 | 10.0 | 8.0 | 3.0 | 5.0 | 6.0 | 9.0 |
| 21 | 7.0 | 6.0 | 4.0 | 9.0 | 10.0 | 6.0 | 10.0 | 1.0 | 1.0 | 1.0 | 3.0 | 8.0 | 7.0 | 3.0 | 6.0 | 10.0 | 9.0 | 9.0 | 6.0 | 10.0 | 1.0 | 2.0 | 4.0 | 3.0 | 2.0 | 3.0 | 8.0 | 3.0 | 1.0 | 4.0 | 8.0 | 7.0 | 1.0 |
| 22 | 5.0 | 6.0 | 3.0 | 4.0 | 10.0 | 7.0 | 8.0 | 5.0 | 4.0 | 8.0 | 4.0 | 8.0 | 8.0 | 7.0 | 9.0 | 5.0 | 3.0 | 3.0 | 9.0 | 4.0 | 3.0 | 4.0 | 10.0 | 9.0 | 10.0 | 9.0 | 7.0 | 7.0 | 10.0 | 1.0 | 4.0 | 6.0 | 3.0 |
| 23 | 7.0 | 10.0 | 2.0 | 2.0 | 9.0 | 6.0 | 10.0 | 4.0 | 10.0 | 1.0 | 5.0 | 10.0 | 1.0 | 10.0 | 2.0 | 10.0 | 1.0 | 9.0 | 2.0 | 2.0 | 2.0 | 3.0 | 9.0 | 3.0 | 4.0 | 9.0 | 6.0 | 9.0 | 7.0 | 4.0 | 1.0 | 8.0 | 8.0 |
| 24 | 2.0 | 6.0 | 5.0 | 9.0 | 9.0 | 1.0 | 5.0 | 5.0 | 3.0 | 10.0 | 10.0 | 8.0 | 10.0 | 7.0 | 10.0 | 1.0 | 10.0 | 1.0 | 1.0 | 1.0 | 9.0 | 2.0 | 10.0 | 4.0 | 2.0 | 7.0 | 2.0 | 6.0 | 4.0 | 4.0 | 1.0 | 10.0 | 3.0 |
| 25 | 4.0 | 9.0 | 10.0 | 5.0 | 9.0 | 3.0 | 1.0 | 7.0 | 4.0 | 2.0 | 5.0 | 4.0 | 3.0 | 6.0 | 10.0 | 7.0 | 4.0 | 2.0 | 9.0 | 2.0 | 3.0 | 3.0 | 9.0 | 9.0 | 7.0 | 7.0 | 1.0 | 5.0 | 2.0 | 9.0 | 5.0 | 9.0 | 1.0 |
| 26 | 1.0 | 4.0 | 9.0 | 9.0 | 5.0 | 10.0 | 6.0 | 6.0 | 9.0 | 2.0 | 6.0 | 7.0 | 9.0 | 1.0 | 6.0 | 10.0 | 9.0 | 6.0 | 2.0 | 6.0 | 1.0 | 8.0 | 7.0 | 6.0 | 2.0 | 1.0 | 8.0 | 2.0 | 9.0 | 1.0 | 8.0 | 5.0 | 8.0 |
| 27 | 8.0 | 10.0 | 7.0 | 8.0 | 7.0 | 4.0 | 1.0 | 10.0 | 10.0 | 1.0 | 3.0 | 1.0 | 10.0 | 3.0 | 7.0 | 3.0 | 4.0 | 9.0 | 2.0 | 8.0 | 10.0 | 3.0 | 7.0 | 9.0 | 6.0 | 5.0 | 2.0 | 1.0 | 7.0 | 10.0 | 9.0 | 5.0 | 6.0 |
| 28 | 4.0 | 5.0 | 3.0 | 10.0 | 8.0 | 7.0 | 6.0 | 6.0 | 6.0 | 5.0 | 8.0 | 2.0 | 10.0 | 8.0 | 1.0 | 8.0 | 7.0 | 8.0 | 1.0 | 1.0 | 8.0 | 1.0 | 10.0 | 7.0 | 4.0 | 2.0 | 9.0 | 7.0 | 4.0 | 2.0 | 2.0 | 3.0 | 4.0 |
| 29 | 6.0 | 10.0 | 10.0 | 10.0 | 1.0 | 3.0 | 5.0 | 8.0 | 4.0 | 9.0 | 1.0 | 5.0 | 1.0 | 1.0 | 10.0 | 5.0 | 1.0 | 6.0 | 5.0 | 2.0 | 3.0 | 4.0 | 1.0 | 4.0 | 4.0 | 9.0 | 1.0 | 10.0 | 2.0 | 5.0 | 6.0 | 8.0 | 7.0 |
| 30 | 9.0 | 5.0 | 10.0 | 7.0 | 3.0 | 5.0 | 6.0 | 3.0 | 5.0 | 2.0 | 9.0 | 10.0 | 2.0 | 2.0 | 9.0 | 8.0 | 1.0 | 10.0 | 1.0 | 2.0 | 5.0 | 8.0 | 4.0 | 1.0 | 1.0 | 5.0 | 8.0 | 9.0 | 2.0 | 6.0 | 10.0 | 10.0 | 5.0 |
| 31 | 10.0 | 4.0 | 2.0 | 10.0 | 6.0 | 2.0 | 3.0 | 10.0 | 8.0 | 3.0 | 6.0 | 5.0 | 1.0 | 2.0 | 1.0 | 6.0 | 9.0 | 9.0 | 2.0 | 3.0 | 6.0 | 7.0 | 6.0 | 8.0 | 10.0 | 9.0 | 5.0 | 5.0 | 3.0 | 8.0 | 10.0 | 8.0 | 7.0 |
| 32 | 2.0 | 7.0 | 10.0 | 7.0 | 8.0 | 7.0 | 6.0 | 8.0 | 8.0 | 5.0 | 5.0 | 4.0 | 8.0 | 7.0 | 7.0 | 8.0 | 9.0 | 9.0 | 2.0 | 6.0 | 9.0 | 1.0 | 3.0 | 8.0 | 3.0 | 1.0 | 8.0 | 6.0 | 4.0 | 7.0 | 5.0 | 7.0 | 3.0 |
Pick a single continuous route and keep the total expense as low as you can.

You can just drop the path into a tiny JSON snippet when you're ready — keeps things tidy and easy to check. Here's the little shape I expect:

{
  ""solution"": []
}

Think of ""solution"" as the place where you'll list the chosen route as a simple array of node names, from the storage spot to the shooting area. It's just a sketch for the format — not the actual answer — so fill that array with the nodes in order when you submit the final route.

Please make sure to use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels.  
Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'edges': [{'from': 18, 'to': 0, 'var_index': 0}, {'from': 18, 'to': 6, 'var_index': 1}, {'from': 18, 'to': 12, 'var_index': 2}, {'from': 5, 'to': 19, 'var_index': 3}, {'from': 11, 'to': 19, 'var_index': 4}, {'from': 17, 'to': 19, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 0, 'to': 6, 'var_index': 7}, {'from': 1, 'to': 2, 'var_index': 8}, {'from': 1, 'to': 7, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}, {'from': 2, 'to': 8, 'var_index': 11}, {'from': 3, 'to': 4, 'var_index': 12}, {'from': 3, 'to': 9, 'var_index': 13}, {'from': 4, 'to': 5, 'var_index': 14}, {'from': 4, 'to': 10, 'var_index': 15}, {'from': 5, 'to': 11, 'var_index': 16}, {'from': 6, 'to': 7, 'var_index': 17}, {'from': 6, 'to': 12, 'var_index': 18}, {'from': 7, 'to': 8, 'var_index': 19}, {'from': 7, 'to': 13, 'var_index': 20}, {'from': 8, 'to': 9, 'var_index': 21}, {'from': 8, 'to': 14, 'var_index': 22}, {'from': 9, 'to': 10, 'var_index': 23}, {'from': 9, 'to': 15, 'var_index': 24}, {'from': 10, 'to': 11, 'var_index': 25}, {'from': 10, 'to': 16, 'var_index': 26}, {'from': 11, 'to': 17, 'var_index': 27}, {'from': 12, 'to': 13, 'var_index': 28}, {'from': 13, 'to': 14, 'var_index': 29}, {'from': 14, 'to': 15, 'var_index': 30}, {'from': 15, 'to': 16, 'var_index': 31}, {'from': 16, 'to': 17, 'var_index': 32}], 'objective': {'constant': 0.0, 'linear': [5.0, 3.0, 2.0, 3.0, 6.0, 5.0, 2.0, 1.0, 7.0, 4.0, 7.0, 3.0, 5.0, 8.0, 2.0, 5.0, 1.0, 9.0, 6.0, 6.0, 10.0, 1.0, 1.0, 1.0, 5.0, 8.0, 6.0, 4.0, 6.0, 8.0, 5.0, 1.0, 4.0], 'quadratic': [[5.0, 5.0, 1.0, 10.0, 3.0, 9.0, 1.0, 7.0, 2.0, 3.0, 4.0, 10.0, 9.0, 2.0, 3.0, 6.0, 1.0, 10.0, 5.0, 6.0, 9.0, 7.0, 5.0, 7.0, 2.0, 4.0, 1.0, 8.0, 4.0, 6.0, 9.0, 10.0, 2.0], [5.0, 9.0, 4.0, 8.0, 6.0, 9.0, 6.0, 7.0, 10.0, 8.0, 5.0, 7.0, 1.0, 1.0, 3.0, 8.0, 1.0, 10.0, 5.0, 2.0, 3.0, 6.0, 6.0, 10.0, 6.0, 9.0, 4.0, 10.0, 5.0, 10.0, 5.0, 4.0, 7.0], [1.0, 4.0, 7.0, 7.0, 7.0, 6.0, 9.0, 4.0, 4.0, 2.0, 1.0, 7.0, 5.0, 7.0, 9.0, 1.0, 3.0, 7.0, 2.0, 2.0, 8.0, 4.0, 3.0, 2.0, 5.0, 10.0, 9.0, 7.0, 3.0, 10.0, 10.0, 2.0, 10.0], [10.0, 8.0, 7.0, 6.0, 2.0, 8.0, 10.0, 2.0, 1.0, 2.0, 7.0, 1.0, 5.0, 6.0, 3.0, 1.0, 6.0, 4.0, 10.0, 6.0, 4.0, 9.0, 4.0, 2.0, 9.0, 5.0, 9.0, 8.0, 10.0, 10.0, 7.0, 10.0, 7.0], [3.0, 6.0, 7.0, 2.0, 9.0, 8.0, 9.0, 3.0, 5.0, 6.0, 8.0, 10.0, 7.0, 6.0, 9.0, 10.0, 6.0, 3.0, 10.0, 8.0, 8.0, 10.0, 10.0, 9.0, 9.0, 9.0, 5.0, 7.0, 8.0, 1.0, 3.0, 6.0, 8.0], [9.0, 9.0, 6.0, 8.0, 8.0, 5.0, 1.0, 9.0, 6.0, 10.0, 2.0, 4.0, 6.0, 4.0, 9.0, 7.0, 1.0, 1.0, 6.0, 9.0, 6.0, 6.0, 7.0, 6.0, 1.0, 3.0, 10.0, 4.0, 7.0, 3.0, 5.0, 2.0, 7.0], [1.0, 6.0, 9.0, 10.0, 9.0, 1.0, 9.0, 6.0, 10.0, 7.0, 6.0, 6.0, 2.0, 2.0, 1.0, 7.0, 5.0, 2.0, 1.0, 9.0, 8.0, 10.0, 8.0, 10.0, 5.0, 1.0, 6.0, 1.0, 6.0, 5.0, 6.0, 3.0, 6.0], [7.0, 7.0, 4.0, 2.0, 3.0, 9.0, 6.0, 1.0, 5.0, 6.0, 1.0, 3.0, 9.0, 4.0, 8.0, 1.0, 8.0, 10.0, 4.0, 6.0, 4.0, 1.0, 5.0, 4.0, 5.0, 7.0, 6.0, 10.0, 6.0, 8.0, 3.0, 10.0, 8.0], [2.0, 10.0, 4.0, 1.0, 5.0, 6.0, 10.0, 5.0, 3.0, 9.0, 9.0, 9.0, 8.0, 1.0, 5.0, 2.0, 3.0, 6.0, 6.0, 2.0, 10.0, 1.0, 4.0, 10.0, 3.0, 4.0, 9.0, 10.0, 6.0, 4.0, 5.0, 8.0, 8.0], [3.0, 8.0, 2.0, 2.0, 6.0, 10.0, 7.0, 6.0, 9.0, 3.0, 1.0, 8.0, 7.0, 2.0, 8.0, 10.0, 1.0, 6.0, 7.0, 4.0, 2.0, 1.0, 8.0, 1.0, 10.0, 2.0, 2.0, 1.0, 5.0, 9.0, 2.0, 3.0, 5.0], [4.0, 5.0, 1.0, 7.0, 8.0, 2.0, 6.0, 1.0, 9.0, 1.0, 2.0, 7.0, 6.0, 2.0, 8.0, 4.0, 7.0, 1.0, 1.0, 6.0, 9.0, 3.0, 4.0, 5.0, 10.0, 5.0, 6.0, 3.0, 8.0, 1.0, 9.0, 6.0, 5.0], [10.0, 7.0, 7.0, 1.0, 10.0, 4.0, 6.0, 3.0, 9.0, 8.0, 7.0, 10.0, 1.0, 3.0, 6.0, 6.0, 5.0, 4.0, 2.0, 8.0, 4.0, 8.0, 8.0, 10.0, 8.0, 4.0, 7.0, 1.0, 2.0, 5.0, 10.0, 5.0, 4.0], [9.0, 1.0, 5.0, 5.0, 7.0, 6.0, 2.0, 9.0, 8.0, 7.0, 6.0, 1.0, 7.0, 3.0, 3.0, 6.0, 4.0, 6.0, 2.0, 10.0, 10.0, 7.0, 8.0, 1.0, 10.0, 3.0, 9.0, 10.0, 10.0, 1.0, 2.0, 1.0, 8.0], [2.0, 1.0, 7.0, 6.0, 6.0, 4.0, 2.0, 4.0, 1.0, 2.0, 2.0, 3.0, 3.0, 8.0, 6.0, 5.0, 1.0, 10.0, 6.0, 5.0, 5.0, 3.0, 7.0, 10.0, 7.0, 6.0, 1.0, 3.0, 8.0, 1.0, 2.0, 2.0, 7.0], [3.0, 3.0, 9.0, 3.0, 9.0, 9.0, 1.0, 8.0, 5.0, 8.0, 8.0, 6.0, 3.0, 6.0, 10.0, 8.0, 10.0, 4.0, 2.0, 8.0, 9.0, 6.0, 9.0, 2.0, 10.0, 10.0, 6.0, 7.0, 1.0, 10.0, 9.0, 1.0, 7.0], [6.0, 8.0, 1.0, 1.0, 10.0, 7.0, 7.0, 1.0, 2.0, 10.0, 4.0, 6.0, 6.0, 5.0, 8.0, 9.0, 7.0, 2.0, 6.0, 5.0, 4.0, 10.0, 5.0, 10.0, 1.0, 7.0, 10.0, 3.0, 8.0, 5.0, 8.0, 6.0, 8.0], [1.0, 1.0, 3.0, 6.0, 6.0, 1.0, 5.0, 8.0, 3.0, 1.0, 7.0, 5.0, 4.0, 1.0, 10.0, 7.0, 6.0, 7.0, 4.0, 2.0, 5.0, 9.0, 3.0, 1.0, 10.0, 4.0, 9.0, 4.0, 7.0, 1.0, 1.0, 9.0, 9.0], [10.0, 10.0, 7.0, 4.0, 3.0, 1.0, 2.0, 10.0, 6.0, 6.0, 1.0, 4.0, 6.0, 10.0, 4.0, 2.0, 7.0, 7.0, 3.0, 5.0, 10.0, 9.0, 3.0, 9.0, 1.0, 2.0, 6.0, 9.0, 8.0, 6.0, 10.0, 9.0, 9.0], [5.0, 5.0, 2.0, 10.0, 10.0, 6.0, 1.0, 4.0, 6.0, 7.0, 1.0, 2.0, 2.0, 6.0, 2.0, 6.0, 4.0, 3.0, 3.0, 9.0, 5.0, 6.0, 9.0, 2.0, 1.0, 9.0, 2.0, 2.0, 1.0, 5.0, 1.0, 2.0, 2.0], [6.0, 2.0, 2.0, 6.0, 8.0, 9.0, 9.0, 6.0, 2.0, 4.0, 6.0, 8.0, 10.0, 5.0, 8.0, 5.0, 2.0, 5.0, 9.0, 8.0, 3.0, 10.0, 4.0, 2.0, 1.0, 2.0, 6.0, 8.0, 1.0, 2.0, 2.0, 3.0, 6.0], [9.0, 3.0, 8.0, 4.0, 8.0, 6.0, 8.0, 4.0, 10.0, 2.0, 9.0, 4.0, 10.0, 5.0, 9.0, 4.0, 5.0, 10.0, 5.0, 3.0, 9.0, 1.0, 3.0, 2.0, 9.0, 3.0, 1.0, 10.0, 8.0, 3.0, 5.0, 6.0, 9.0], [7.0, 6.0, 4.0, 9.0, 10.0, 6.0, 10.0, 1.0, 1.0, 1.0, 3.0, 8.0, 7.0, 3.0, 6.0, 10.0, 9.0, 9.0, 6.0, 10.0, 1.0, 2.0, 4.0, 3.0, 2.0, 3.0, 8.0, 3.0, 1.0, 4.0, 8.0, 7.0, 1.0], [5.0, 6.0, 3.0, 4.0, 10.0, 7.0, 8.0, 5.0, 4.0, 8.0, 4.0, 8.0, 8.0, 7.0, 9.0, 5.0, 3.0, 3.0, 9.0, 4.0, 3.0, 4.0, 10.0, 9.0, 10.0, 9.0, 7.0, 7.0, 10.0, 1.0, 4.0, 6.0, 3.0], [7.0, 10.0, 2.0, 2.0, 9.0, 6.0, 10.0, 4.0, 10.0, 1.0, 5.0, 10.0, 1.0, 10.0, 2.0, 10.0, 1.0, 9.0, 2.0, 2.0, 2.0, 3.0, 9.0, 3.0, 4.0, 9.0, 6.0, 9.0, 7.0, 4.0, 1.0, 8.0, 8.0], [2.0, 6.0, 5.0, 9.0, 9.0, 1.0, 5.0, 5.0, 3.0, 10.0, 10.0, 8.0, 10.0, 7.0, 10.0, 1.0, 10.0, 1.0, 1.0, 1.0, 9.0, 2.0, 10.0, 4.0, 2.0, 7.0, 2.0, 6.0, 4.0, 4.0, 1.0, 10.0, 3.0], [4.0, 9.0, 10.0, 5.0, 9.0, 3.0, 1.0, 7.0, 4.0, 2.0, 5.0, 4.0, 3.0, 6.0, 10.0, 7.0, 4.0, 2.0, 9.0, 2.0, 3.0, 3.0, 9.0, 9.0, 7.0, 7.0, 1.0, 5.0, 2.0, 9.0, 5.0, 9.0, 1.0], [1.0, 4.0, 9.0, 9.0, 5.0, 10.0, 6.0, 6.0, 9.0, 2.0, 6.0, 7.0, 9.0, 1.0, 6.0, 10.0, 9.0, 6.0, 2.0, 6.0, 1.0, 8.0, 7.0, 6.0, 2.0, 1.0, 8.0, 2.0, 9.0, 1.0, 8.0, 5.0, 8.0], [8.0, 10.0, 7.0, 8.0, 7.0, 4.0, 1.0, 10.0, 10.0, 1.0, 3.0, 1.0, 10.0, 3.0, 7.0, 3.0, 4.0, 9.0, 2.0, 8.0, 10.0, 3.0, 7.0, 9.0, 6.0, 5.0, 2.0, 1.0, 7.0, 10.0, 9.0, 5.0, 6.0], [4.0, 5.0, 3.0, 10.0, 8.0, 7.0, 6.0, 6.0, 6.0, 5.0, 8.0, 2.0, 10.0, 8.0, 1.0, 8.0, 7.0, 8.0, 1.0, 1.0, 8.0, 1.0, 10.0, 7.0, 4.0, 2.0, 9.0, 7.0, 4.0, 2.0, 2.0, 3.0, 4.0], [6.0, 10.0, 10.0, 10.0, 1.0, 3.0, 5.0, 8.0, 4.0, 9.0, 1.0, 5.0, 1.0, 1.0, 10.0, 5.0, 1.0, 6.0, 5.0, 2.0, 3.0, 4.0, 1.0, 4.0, 4.0, 9.0, 1.0, 10.0, 2.0, 5.0, 6.0, 8.0, 7.0], [9.0, 5.0, 10.0, 7.0, 3.0, 5.0, 6.0, 3.0, 5.0, 2.0, 9.0, 10.0, 2.0, 2.0, 9.0, 8.0, 1.0, 10.0, 1.0, 2.0, 5.0, 8.0, 4.0, 1.0, 1.0, 5.0, 8.0, 9.0, 2.0, 6.0, 10.0, 10.0, 5.0], [10.0, 4.0, 2.0, 10.0, 6.0, 2.0, 3.0, 10.0, 8.0, 3.0, 6.0, 5.0, 1.0, 2.0, 1.0, 6.0, 9.0, 9.0, 2.0, 3.0, 6.0, 7.0, 6.0, 8.0, 10.0, 9.0, 5.0, 5.0, 3.0, 8.0, 10.0, 8.0, 7.0], [2.0, 7.0, 10.0, 7.0, 8.0, 7.0, 6.0, 8.0, 8.0, 5.0, 5.0, 4.0, 8.0, 7.0, 7.0, 8.0, 9.0, 9.0, 2.0, 6.0, 9.0, 1.0, 3.0, 8.0, 3.0, 1.0, 8.0, 6.0, 4.0, 7.0, 5.0, 7.0, 3.0]]}, 'source': 18, 'target': 19}","[18, 0, 1, 2, 3, 4, 5, 19]",299.0,"{'problem_type': 'QSPP', 'num_nodes': 20, 'num_edges': 33, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'source': 19, 'target': 20, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 2.0}, {'var_index': 3, 'linear_cost': 3.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 5.0}, {'var_index': 6, 'linear_cost': 2.0}, {'var_index': 7, 'linear_cost': 1.0}, {'var_index': 8, 'linear_cost': 7.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 7.0}, {'var_index': 11, 'linear_cost': 3.0}, {'var_index': 12, 'linear_cost': 5.0}, {'var_index': 13, 'linear_cost': 8.0}, {'var_index': 14, 'linear_cost': 2.0}, {'var_index': 15, 'linear_cost': 5.0}, {'var_index': 16, 'linear_cost': 1.0}, {'var_index': 17, 'linear_cost': 9.0}, {'var_index': 18, 'linear_cost': 6.0}, {'var_index': 19, 'linear_cost': 6.0}, {'var_index': 20, 'linear_cost': 10.0}, {'var_index': 21, 'linear_cost': 1.0}, {'var_index': 22, 'linear_cost': 1.0}, {'var_index': 23, 'linear_cost': 1.0}, {'var_index': 24, 'linear_cost': 5.0}, {'var_index': 25, 'linear_cost': 8.0}, {'var_index': 26, 'linear_cost': 6.0}, {'var_index': 27, 'linear_cost': 4.0}, {'var_index': 28, 'linear_cost': 6.0}, {'var_index': 29, 'linear_cost': 8.0}, {'var_index': 30, 'linear_cost': 5.0}, {'var_index': 31, 'linear_cost': 1.0}, {'var_index': 32, 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{'var_i': 26, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 26, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 26, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 26, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 26, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 20, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 26, 'var_j': 23, 'quadratic_cost': 6.0}, {'var_i': 26, 'var_j': 24, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 27, 'quadratic_cost': 2.0}, {'var_i': 26, 'var_j': 28, 'quadratic_cost': 9.0}, {'var_i': 26, 'var_j': 29, 'quadratic_cost': 1.0}, {'var_i': 26, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 26, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 26, 'var_j': 32, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 27, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 27, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 27, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 27, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 27, 'var_j': 22, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 23, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 24, 'quadratic_cost': 6.0}, {'var_i': 27, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 26, 'quadratic_cost': 2.0}, {'var_i': 27, 'var_j': 27, 'quadratic_cost': 1.0}, {'var_i': 27, 'var_j': 28, 'quadratic_cost': 7.0}, {'var_i': 27, 'var_j': 29, 'quadratic_cost': 10.0}, {'var_i': 27, 'var_j': 30, 'quadratic_cost': 9.0}, {'var_i': 27, 'var_j': 31, 'quadratic_cost': 5.0}, {'var_i': 27, 'var_j': 32, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 28, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 28, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 28, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 28, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 28, 'var_j': 23, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 25, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 26, 'quadratic_cost': 9.0}, {'var_i': 28, 'var_j': 27, 'quadratic_cost': 7.0}, {'var_i': 28, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 28, 'var_j': 29, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 28, 'var_j': 31, 'quadratic_cost': 3.0}, {'var_i': 28, 'var_j': 32, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 29, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 29, 'var_j': 21, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 23, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 24, 'quadratic_cost': 4.0}, {'var_i': 29, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 29, 'var_j': 26, 'quadratic_cost': 1.0}, {'var_i': 29, 'var_j': 27, 'quadratic_cost': 10.0}, {'var_i': 29, 'var_j': 28, 'quadratic_cost': 2.0}, {'var_i': 29, 'var_j': 29, 'quadratic_cost': 5.0}, {'var_i': 29, 'var_j': 30, 'quadratic_cost': 6.0}, {'var_i': 29, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 29, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 30, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 30, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 22, 'quadratic_cost': 4.0}, {'var_i': 30, 'var_j': 23, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 24, 'quadratic_cost': 1.0}, {'var_i': 30, 'var_j': 25, 'quadratic_cost': 5.0}, {'var_i': 30, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 30, 'var_j': 27, 'quadratic_cost': 9.0}, {'var_i': 30, 'var_j': 28, 'quadratic_cost': 2.0}, {'var_i': 30, 'var_j': 29, 'quadratic_cost': 6.0}, {'var_i': 30, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 30, 'var_j': 32, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 31, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 31, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 31, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 21, 'quadratic_cost': 7.0}, {'var_i': 31, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 31, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 24, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 25, 'quadratic_cost': 9.0}, {'var_i': 31, 'var_j': 26, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 27, 'quadratic_cost': 5.0}, {'var_i': 31, 'var_j': 28, 'quadratic_cost': 3.0}, {'var_i': 31, 'var_j': 29, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 30, 'quadratic_cost': 10.0}, {'var_i': 31, 'var_j': 31, 'quadratic_cost': 8.0}, {'var_i': 31, 'var_j': 32, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 32, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 32, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 32, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 23, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 24, 'quadratic_cost': 3.0}, {'var_i': 32, 'var_j': 25, 'quadratic_cost': 1.0}, {'var_i': 32, 'var_j': 26, 'quadratic_cost': 8.0}, {'var_i': 32, 'var_j': 27, 'quadratic_cost': 6.0}, {'var_i': 32, 'var_j': 28, 'quadratic_cost': 4.0}, {'var_i': 32, 'var_j': 29, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 30, 'quadratic_cost': 5.0}, {'var_i': 32, 'var_j': 31, 'quadratic_cost': 7.0}, {'var_i': 32, 'var_j': 32, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 19, 'to': 1, 'var_index': 0}, {'from': 19, 'to': 7, 'var_index': 1}, {'from': 19, 'to': 13, 'var_index': 2}, {'from': 6, 'to': 20, 'var_index': 3}, {'from': 12, 'to': 20, 'var_index': 4}, {'from': 18, 'to': 20, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 8, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 9, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 10, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 11, 'var_index': 15}, {'from': 6, 'to': 12, 'var_index': 16}, {'from': 7, 'to': 8, 'var_index': 17}, {'from': 7, 'to': 13, 'var_index': 18}, {'from': 8, 'to': 9, 'var_index': 19}, {'from': 8, 'to': 14, 'var_index': 20}, {'from': 9, 'to': 10, 'var_index': 21}, {'from': 9, 'to': 15, 'var_index': 22}, {'from': 10, 'to': 11, 'var_index': 23}, {'from': 10, 'to': 16, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 11, 'to': 17, 'var_index': 26}, {'from': 12, 'to': 18, 'var_index': 27}, {'from': 13, 'to': 14, 'var_index': 28}, {'from': 14, 'to': 15, 'var_index': 29}, {'from': 15, 'to': 16, 'var_index': 30}, {'from': 16, 'to': 17, 'var_index': 31}, {'from': 17, 'to': 18, 'var_index': 32}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, 13: 14, 14: 15, 15: 16, 16: 17, 17: 18, 18: 19, 19: 20}}","[19, 1, 2, 3, 4, 5, 6, 20]",47,nl,1
QSPP,QSPP,"We were in charge of picking one routed run from the main tank to the receiving tank, always following the one-way valves. The route had to be a single, uninterrupted chain of tank-to-tank hops that begins at the source and finishes at the destination. Every hop has a base cost, and certain combinations of hops add little extra fees only if both are part of the same run — some hops even add a self-fee when used. To evaluate any candidate run, add up each hop’s base cost and all the extra pairwise (and self) fees that apply; the best run is simply the one with the lowest total. The specific layout and cost figures are listed below.

We recorded that the network has 22 tanks and 39 directed segments; the valid tank IDs are A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V; any chosen route must start at U and end at V.

| segment_from_tank | segment_to_tank | segment_id |
|---|---|---|
| U | A | 0 |
| U | F | 1 |
| U | K | 2 |
| U | P | 3 |
| E | V | 4 |
| J | V | 5 |
| O | V | 6 |
| T | V | 7 |
| A | B | 8 |
| A | F | 9 |
| B | C | 10 |
| B | G | 11 |
| C | D | 12 |
| C | H | 13 |
| D | E | 14 |
| D | I | 15 |
| E | J | 16 |
| F | G | 17 |
| F | K | 18 |
| G | H | 19 |
| G | L | 20 |
| H | I | 21 |
| H | M | 22 |
| I | J | 23 |
| I | N | 24 |
| J | O | 25 |
| K | L | 26 |
| K | P | 27 |
| L | M | 28 |
| L | Q | 29 |
| M | N | 30 |
| M | R | 31 |
| N | O | 32 |
| N | S | 33 |
| O | T | 34 |
| P | Q | 35 |
| Q | R | 36 |
| R | S | 37 |
| S | T | 38 |

| segment_id | base_transfer_cost |
|---|---|
| 0 | 9.0 |
| 1 | 8.0 |
| 2 | 10.0 |
| 3 | 6.0 |
| 4 | 6.0 |
| 5 | 5.0 |
| 6 | 10.0 |
| 7 | 8.0 |
| 8 | 4.0 |
| 9 | 5.0 |
| 10 | 1.0 |
| 11 | 7.0 |
| 12 | 9.0 |
| 13 | 4.0 |
| 14 | 10.0 |
| 15 | 2.0 |
| 16 | 1.0 |
| 17 | 1.0 |
| 18 | 10.0 |
| 19 | 10.0 |
| 20 | 2.0 |
| 21 | 7.0 |
| 22 | 3.0 |
| 23 | 10.0 |
| 24 | 2.0 |
| 25 | 1.0 |
| 26 | 8.0 |
| 27 | 1.0 |
| 28 | 7.0 |
| 29 | 7.0 |
| 30 | 2.0 |
| 31 | 2.0 |
| 32 | 3.0 |
| 33 | 2.0 |
| 34 | 10.0 |
| 35 | 8.0 |
| 36 | 3.0 |
| 37 | 9.0 |
| 38 | 4.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 1.0 | 10.0 | 1.0 | 10.0 | 1.0 | 1.0 | 3.0 | 9.0 | 5.0 | 2.0 | 5.0 | 5.0 | 8.0 | 8.0 | 3.0 | 9.0 | 4.0 | 1.0 | 2.0 | 6.0 | 8.0 | 4.0 | 4.0 | 6.0 | 10.0 | 1.0 | 3.0 | 8.0 | 7.0 | 9.0 | 7.0 | 7.0 | 10.0 | 7.0 | 8.0 | 4.0 | 5.0 | 9.0 |
| 1 | 1.0 | 6.0 | 4.0 | 10.0 | 4.0 | 7.0 | 9.0 | 8.0 | 2.0 | 1.0 | 2.0 | 1.0 | 8.0 | 10.0 | 8.0 | 7.0 | 7.0 | 9.0 | 6.0 | 8.0 | 5.0 | 10.0 | 1.0 | 5.0 | 4.0 | 4.0 | 8.0 | 4.0 | 6.0 | 10.0 | 3.0 | 1.0 | 4.0 | 10.0 | 9.0 | 8.0 | 8.0 | 4.0 | 3.0 |
| 2 | 10.0 | 4.0 | 8.0 | 8.0 | 10.0 | 6.0 | 2.0 | 10.0 | 8.0 | 3.0 | 7.0 | 6.0 | 6.0 | 3.0 | 3.0 | 9.0 | 6.0 | 2.0 | 6.0 | 3.0 | 7.0 | 4.0 | 9.0 | 3.0 | 9.0 | 1.0 | 1.0 | 4.0 | 1.0 | 1.0 | 7.0 | 1.0 | 3.0 | 3.0 | 5.0 | 3.0 | 2.0 | 1.0 | 9.0 |
| 3 | 1.0 | 10.0 | 8.0 | 4.0 | 5.0 | 8.0 | 2.0 | 3.0 | 7.0 | 3.0 | 7.0 | 7.0 | 3.0 | 8.0 | 7.0 | 5.0 | 2.0 | 5.0 | 5.0 | 1.0 | 3.0 | 4.0 | 3.0 | 2.0 | 3.0 | 2.0 | 6.0 | 8.0 | 2.0 | 5.0 | 9.0 | 6.0 | 9.0 | 9.0 | 4.0 | 4.0 | 5.0 | 4.0 | 6.0 |
| 4 | 10.0 | 4.0 | 10.0 | 5.0 | 6.0 | 2.0 | 4.0 | 2.0 | 10.0 | 1.0 | 1.0 | 1.0 | 2.0 | 6.0 | 9.0 | 4.0 | 5.0 | 8.0 | 10.0 | 9.0 | 5.0 | 3.0 | 3.0 | 8.0 | 6.0 | 5.0 | 7.0 | 8.0 | 1.0 | 9.0 | 4.0 | 3.0 | 6.0 | 7.0 | 9.0 | 2.0 | 5.0 | 5.0 | 1.0 |
| 5 | 1.0 | 7.0 | 6.0 | 8.0 | 2.0 | 5.0 | 8.0 | 4.0 | 8.0 | 3.0 | 1.0 | 9.0 | 4.0 | 4.0 | 2.0 | 2.0 | 8.0 | 9.0 | 3.0 | 3.0 | 4.0 | 5.0 | 4.0 | 6.0 | 10.0 | 1.0 | 10.0 | 3.0 | 2.0 | 1.0 | 7.0 | 6.0 | 1.0 | 10.0 | 5.0 | 4.0 | 3.0 | 1.0 | 7.0 |
| 6 | 1.0 | 9.0 | 2.0 | 2.0 | 4.0 | 8.0 | 7.0 | 2.0 | 9.0 | 10.0 | 10.0 | 4.0 | 6.0 | 9.0 | 8.0 | 3.0 | 3.0 | 10.0 | 5.0 | 7.0 | 5.0 | 6.0 | 6.0 | 7.0 | 10.0 | 9.0 | 10.0 | 3.0 | 2.0 | 9.0 | 8.0 | 7.0 | 1.0 | 5.0 | 10.0 | 6.0 | 3.0 | 10.0 | 7.0 |
| 7 | 3.0 | 8.0 | 10.0 | 3.0 | 2.0 | 4.0 | 2.0 | 5.0 | 2.0 | 5.0 | 8.0 | 4.0 | 10.0 | 3.0 | 8.0 | 6.0 | 2.0 | 8.0 | 10.0 | 10.0 | 3.0 | 9.0 | 4.0 | 2.0 | 7.0 | 6.0 | 9.0 | 1.0 | 4.0 | 6.0 | 9.0 | 9.0 | 3.0 | 4.0 | 5.0 | 4.0 | 6.0 | 5.0 | 10.0 |
| 8 | 9.0 | 2.0 | 8.0 | 7.0 | 10.0 | 8.0 | 9.0 | 2.0 | 7.0 | 3.0 | 6.0 | 2.0 | 10.0 | 7.0 | 10.0 | 9.0 | 7.0 | 2.0 | 9.0 | 10.0 | 10.0 | 4.0 | 10.0 | 5.0 | 1.0 | 1.0 | 7.0 | 4.0 | 7.0 | 10.0 | 7.0 | 1.0 | 9.0 | 5.0 | 4.0 | 4.0 | 8.0 | 4.0 | 5.0 |
| 9 | 5.0 | 1.0 | 3.0 | 3.0 | 1.0 | 3.0 | 10.0 | 5.0 | 3.0 | 6.0 | 4.0 | 10.0 | 9.0 | 3.0 | 3.0 | 8.0 | 8.0 | 9.0 | 7.0 | 1.0 | 6.0 | 2.0 | 10.0 | 4.0 | 10.0 | 7.0 | 9.0 | 6.0 | 10.0 | 10.0 | 9.0 | 5.0 | 7.0 | 3.0 | 4.0 | 9.0 | 1.0 | 3.0 | 9.0 |
| 10 | 2.0 | 2.0 | 7.0 | 7.0 | 1.0 | 1.0 | 10.0 | 8.0 | 6.0 | 4.0 | 8.0 | 7.0 | 10.0 | 8.0 | 3.0 | 8.0 | 7.0 | 6.0 | 1.0 | 2.0 | 9.0 | 2.0 | 10.0 | 7.0 | 7.0 | 3.0 | 1.0 | 1.0 | 8.0 | 10.0 | 8.0 | 6.0 | 10.0 | 7.0 | 7.0 | 7.0 | 1.0 | 8.0 | 2.0 |
| 11 | 5.0 | 1.0 | 6.0 | 7.0 | 1.0 | 9.0 | 4.0 | 4.0 | 2.0 | 10.0 | 7.0 | 2.0 | 6.0 | 10.0 | 6.0 | 7.0 | 1.0 | 4.0 | 5.0 | 5.0 | 10.0 | 3.0 | 9.0 | 1.0 | 9.0 | 5.0 | 1.0 | 3.0 | 6.0 | 10.0 | 4.0 | 5.0 | 5.0 | 2.0 | 5.0 | 8.0 | 2.0 | 10.0 | 7.0 |
| 12 | 5.0 | 8.0 | 6.0 | 3.0 | 2.0 | 4.0 | 6.0 | 10.0 | 10.0 | 9.0 | 10.0 | 6.0 | 8.0 | 1.0 | 6.0 | 5.0 | 4.0 | 6.0 | 8.0 | 7.0 | 9.0 | 8.0 | 8.0 | 10.0 | 10.0 | 8.0 | 9.0 | 1.0 | 1.0 | 9.0 | 6.0 | 7.0 | 1.0 | 10.0 | 8.0 | 1.0 | 8.0 | 8.0 | 4.0 |
| 13 | 8.0 | 10.0 | 3.0 | 8.0 | 6.0 | 4.0 | 9.0 | 3.0 | 7.0 | 3.0 | 8.0 | 10.0 | 1.0 | 2.0 | 1.0 | 8.0 | 6.0 | 3.0 | 5.0 | 1.0 | 7.0 | 4.0 | 3.0 | 5.0 | 2.0 | 9.0 | 1.0 | 4.0 | 2.0 | 4.0 | 8.0 | 5.0 | 2.0 | 2.0 | 6.0 | 2.0 | 8.0 | 10.0 | 4.0 |
| 14 | 8.0 | 8.0 | 3.0 | 7.0 | 9.0 | 2.0 | 8.0 | 8.0 | 10.0 | 3.0 | 3.0 | 6.0 | 6.0 | 1.0 | 9.0 | 8.0 | 10.0 | 8.0 | 1.0 | 8.0 | 7.0 | 5.0 | 6.0 | 1.0 | 4.0 | 2.0 | 1.0 | 3.0 | 10.0 | 3.0 | 1.0 | 3.0 | 10.0 | 7.0 | 4.0 | 8.0 | 7.0 | 2.0 | 8.0 |
| 15 | 3.0 | 7.0 | 9.0 | 5.0 | 4.0 | 2.0 | 3.0 | 6.0 | 9.0 | 8.0 | 8.0 | 7.0 | 5.0 | 8.0 | 8.0 | 2.0 | 2.0 | 6.0 | 5.0 | 4.0 | 3.0 | 6.0 | 8.0 | 7.0 | 5.0 | 4.0 | 6.0 | 8.0 | 6.0 | 5.0 | 2.0 | 1.0 | 7.0 | 6.0 | 8.0 | 4.0 | 6.0 | 10.0 | 5.0 |
| 16 | 9.0 | 7.0 | 6.0 | 2.0 | 5.0 | 8.0 | 3.0 | 2.0 | 7.0 | 8.0 | 7.0 | 1.0 | 4.0 | 6.0 | 10.0 | 2.0 | 9.0 | 8.0 | 6.0 | 8.0 | 7.0 | 6.0 | 2.0 | 6.0 | 6.0 | 7.0 | 8.0 | 5.0 | 8.0 | 4.0 | 8.0 | 4.0 | 6.0 | 5.0 | 7.0 | 2.0 | 8.0 | 7.0 | 10.0 |
| 17 | 4.0 | 9.0 | 2.0 | 5.0 | 8.0 | 9.0 | 10.0 | 8.0 | 2.0 | 9.0 | 6.0 | 4.0 | 6.0 | 3.0 | 8.0 | 6.0 | 8.0 | 9.0 | 1.0 | 1.0 | 4.0 | 8.0 | 7.0 | 1.0 | 2.0 | 8.0 | 2.0 | 7.0 | 9.0 | 10.0 | 9.0 | 2.0 | 10.0 | 1.0 | 3.0 | 4.0 | 8.0 | 5.0 | 10.0 |
| 18 | 1.0 | 6.0 | 6.0 | 5.0 | 10.0 | 3.0 | 5.0 | 10.0 | 9.0 | 7.0 | 1.0 | 5.0 | 8.0 | 5.0 | 1.0 | 5.0 | 6.0 | 1.0 | 3.0 | 1.0 | 6.0 | 7.0 | 9.0 | 8.0 | 10.0 | 1.0 | 6.0 | 10.0 | 2.0 | 9.0 | 1.0 | 9.0 | 2.0 | 4.0 | 10.0 | 5.0 | 3.0 | 1.0 | 1.0 |
| 19 | 2.0 | 8.0 | 3.0 | 1.0 | 9.0 | 3.0 | 7.0 | 10.0 | 10.0 | 1.0 | 2.0 | 5.0 | 7.0 | 1.0 | 8.0 | 4.0 | 8.0 | 1.0 | 1.0 | 1.0 | 2.0 | 10.0 | 8.0 | 1.0 | 10.0 | 5.0 | 9.0 | 5.0 | 2.0 | 9.0 | 5.0 | 9.0 | 8.0 | 2.0 | 5.0 | 6.0 | 2.0 | 8.0 | 1.0 |
| 20 | 6.0 | 5.0 | 7.0 | 3.0 | 5.0 | 4.0 | 5.0 | 3.0 | 10.0 | 6.0 | 9.0 | 10.0 | 9.0 | 7.0 | 7.0 | 3.0 | 7.0 | 4.0 | 6.0 | 2.0 | 3.0 | 2.0 | 3.0 | 3.0 | 8.0 | 6.0 | 5.0 | 5.0 | 6.0 | 10.0 | 9.0 | 1.0 | 10.0 | 8.0 | 7.0 | 1.0 | 6.0 | 7.0 | 2.0 |
| 21 | 8.0 | 10.0 | 4.0 | 4.0 | 3.0 | 5.0 | 6.0 | 9.0 | 4.0 | 2.0 | 2.0 | 3.0 | 8.0 | 4.0 | 5.0 | 6.0 | 6.0 | 8.0 | 7.0 | 10.0 | 2.0 | 9.0 | 8.0 | 8.0 | 6.0 | 7.0 | 10.0 | 6.0 | 5.0 | 5.0 | 1.0 | 10.0 | 4.0 | 6.0 | 5.0 | 8.0 | 9.0 | 5.0 | 8.0 |
| 22 | 4.0 | 1.0 | 9.0 | 3.0 | 3.0 | 4.0 | 6.0 | 4.0 | 10.0 | 10.0 | 10.0 | 9.0 | 8.0 | 3.0 | 6.0 | 8.0 | 2.0 | 7.0 | 9.0 | 8.0 | 3.0 | 8.0 | 10.0 | 10.0 | 5.0 | 5.0 | 2.0 | 1.0 | 5.0 | 2.0 | 2.0 | 6.0 | 5.0 | 6.0 | 7.0 | 8.0 | 2.0 | 1.0 | 1.0 |
| 23 | 4.0 | 5.0 | 3.0 | 2.0 | 8.0 | 6.0 | 7.0 | 2.0 | 5.0 | 4.0 | 7.0 | 1.0 | 10.0 | 5.0 | 1.0 | 7.0 | 6.0 | 1.0 | 8.0 | 1.0 | 3.0 | 8.0 | 10.0 | 7.0 | 10.0 | 1.0 | 6.0 | 9.0 | 1.0 | 7.0 | 1.0 | 4.0 | 8.0 | 2.0 | 2.0 | 10.0 | 10.0 | 9.0 | 5.0 |
| 24 | 6.0 | 4.0 | 9.0 | 3.0 | 6.0 | 10.0 | 10.0 | 7.0 | 1.0 | 10.0 | 7.0 | 9.0 | 10.0 | 2.0 | 4.0 | 5.0 | 6.0 | 2.0 | 10.0 | 10.0 | 8.0 | 6.0 | 5.0 | 10.0 | 7.0 | 8.0 | 8.0 | 8.0 | 10.0 | 5.0 | 2.0 | 2.0 | 3.0 | 5.0 | 10.0 | 10.0 | 6.0 | 4.0 | 9.0 |
| 25 | 10.0 | 4.0 | 1.0 | 2.0 | 5.0 | 1.0 | 9.0 | 6.0 | 1.0 | 7.0 | 3.0 | 5.0 | 8.0 | 9.0 | 2.0 | 4.0 | 7.0 | 8.0 | 1.0 | 5.0 | 6.0 | 7.0 | 5.0 | 1.0 | 8.0 | 2.0 | 3.0 | 4.0 | 10.0 | 8.0 | 1.0 | 4.0 | 4.0 | 9.0 | 5.0 | 6.0 | 5.0 | 10.0 | 2.0 |
| 26 | 1.0 | 8.0 | 1.0 | 6.0 | 7.0 | 10.0 | 10.0 | 9.0 | 7.0 | 9.0 | 1.0 | 1.0 | 9.0 | 1.0 | 1.0 | 6.0 | 8.0 | 2.0 | 6.0 | 9.0 | 5.0 | 10.0 | 2.0 | 6.0 | 8.0 | 3.0 | 3.0 | 6.0 | 9.0 | 3.0 | 2.0 | 7.0 | 1.0 | 10.0 | 3.0 | 7.0 | 9.0 | 6.0 | 1.0 |
| 27 | 3.0 | 4.0 | 4.0 | 8.0 | 8.0 | 3.0 | 3.0 | 1.0 | 4.0 | 6.0 | 1.0 | 3.0 | 1.0 | 4.0 | 3.0 | 8.0 | 5.0 | 7.0 | 10.0 | 5.0 | 5.0 | 6.0 | 1.0 | 9.0 | 8.0 | 4.0 | 6.0 | 6.0 | 5.0 | 7.0 | 4.0 | 6.0 | 7.0 | 2.0 | 8.0 | 1.0 | 5.0 | 10.0 | 3.0 |
| 28 | 8.0 | 6.0 | 1.0 | 2.0 | 1.0 | 2.0 | 2.0 | 4.0 | 7.0 | 10.0 | 8.0 | 6.0 | 1.0 | 2.0 | 10.0 | 6.0 | 8.0 | 9.0 | 2.0 | 2.0 | 6.0 | 5.0 | 5.0 | 1.0 | 10.0 | 10.0 | 9.0 | 5.0 | 10.0 | 2.0 | 3.0 | 5.0 | 7.0 | 4.0 | 5.0 | 8.0 | 5.0 | 9.0 | 1.0 |
| 29 | 7.0 | 10.0 | 1.0 | 5.0 | 9.0 | 1.0 | 9.0 | 6.0 | 10.0 | 10.0 | 10.0 | 10.0 | 9.0 | 4.0 | 3.0 | 5.0 | 4.0 | 10.0 | 9.0 | 9.0 | 10.0 | 5.0 | 2.0 | 7.0 | 5.0 | 8.0 | 3.0 | 7.0 | 2.0 | 4.0 | 4.0 | 9.0 | 5.0 | 10.0 | 4.0 | 8.0 | 8.0 | 7.0 | 8.0 |
| 30 | 9.0 | 3.0 | 7.0 | 9.0 | 4.0 | 7.0 | 8.0 | 9.0 | 7.0 | 9.0 | 8.0 | 4.0 | 6.0 | 8.0 | 1.0 | 2.0 | 8.0 | 9.0 | 1.0 | 5.0 | 9.0 | 1.0 | 2.0 | 1.0 | 2.0 | 1.0 | 2.0 | 4.0 | 3.0 | 4.0 | 8.0 | 4.0 | 7.0 | 2.0 | 6.0 | 8.0 | 4.0 | 7.0 | 5.0 |
| 31 | 7.0 | 1.0 | 1.0 | 6.0 | 3.0 | 6.0 | 7.0 | 9.0 | 1.0 | 5.0 | 6.0 | 5.0 | 7.0 | 5.0 | 3.0 | 1.0 | 4.0 | 2.0 | 9.0 | 9.0 | 1.0 | 10.0 | 6.0 | 4.0 | 2.0 | 4.0 | 7.0 | 6.0 | 5.0 | 9.0 | 4.0 | 5.0 | 1.0 | 8.0 | 2.0 | 1.0 | 9.0 | 7.0 | 4.0 |
| 32 | 7.0 | 4.0 | 3.0 | 9.0 | 6.0 | 1.0 | 1.0 | 3.0 | 9.0 | 7.0 | 10.0 | 5.0 | 1.0 | 2.0 | 10.0 | 7.0 | 6.0 | 10.0 | 2.0 | 8.0 | 10.0 | 4.0 | 5.0 | 8.0 | 3.0 | 4.0 | 1.0 | 7.0 | 7.0 | 5.0 | 7.0 | 1.0 | 3.0 | 3.0 | 1.0 | 10.0 | 7.0 | 10.0 | 7.0 |
| 33 | 10.0 | 10.0 | 3.0 | 9.0 | 7.0 | 10.0 | 5.0 | 4.0 | 5.0 | 3.0 | 7.0 | 2.0 | 10.0 | 2.0 | 7.0 | 6.0 | 5.0 | 1.0 | 4.0 | 2.0 | 8.0 | 6.0 | 6.0 | 2.0 | 5.0 | 9.0 | 10.0 | 2.0 | 4.0 | 10.0 | 2.0 | 8.0 | 3.0 | 3.0 | 7.0 | 10.0 | 1.0 | 7.0 | 5.0 |
| 34 | 7.0 | 9.0 | 5.0 | 4.0 | 9.0 | 5.0 | 10.0 | 5.0 | 4.0 | 4.0 | 7.0 | 5.0 | 8.0 | 6.0 | 4.0 | 8.0 | 7.0 | 3.0 | 10.0 | 5.0 | 7.0 | 5.0 | 7.0 | 2.0 | 10.0 | 5.0 | 3.0 | 8.0 | 5.0 | 4.0 | 6.0 | 2.0 | 1.0 | 7.0 | 1.0 | 8.0 | 9.0 | 4.0 | 6.0 |
| 35 | 8.0 | 8.0 | 3.0 | 4.0 | 2.0 | 4.0 | 6.0 | 4.0 | 4.0 | 9.0 | 7.0 | 8.0 | 1.0 | 2.0 | 8.0 | 4.0 | 2.0 | 4.0 | 5.0 | 6.0 | 1.0 | 8.0 | 8.0 | 10.0 | 10.0 | 6.0 | 7.0 | 1.0 | 8.0 | 8.0 | 8.0 | 1.0 | 10.0 | 10.0 | 8.0 | 6.0 | 6.0 | 5.0 | 10.0 |
| 36 | 4.0 | 8.0 | 2.0 | 5.0 | 5.0 | 3.0 | 3.0 | 6.0 | 8.0 | 1.0 | 1.0 | 2.0 | 8.0 | 8.0 | 7.0 | 6.0 | 8.0 | 8.0 | 3.0 | 2.0 | 6.0 | 9.0 | 2.0 | 10.0 | 6.0 | 5.0 | 9.0 | 5.0 | 5.0 | 8.0 | 4.0 | 9.0 | 7.0 | 1.0 | 9.0 | 6.0 | 7.0 | 5.0 | 2.0 |
| 37 | 5.0 | 4.0 | 1.0 | 4.0 | 5.0 | 1.0 | 10.0 | 5.0 | 4.0 | 3.0 | 8.0 | 10.0 | 8.0 | 10.0 | 2.0 | 10.0 | 7.0 | 5.0 | 1.0 | 8.0 | 7.0 | 5.0 | 1.0 | 9.0 | 4.0 | 10.0 | 6.0 | 10.0 | 9.0 | 7.0 | 7.0 | 7.0 | 10.0 | 7.0 | 4.0 | 5.0 | 5.0 | 10.0 | 8.0 |
| 38 | 9.0 | 3.0 | 9.0 | 6.0 | 1.0 | 7.0 | 7.0 | 10.0 | 5.0 | 9.0 | 2.0 | 7.0 | 4.0 | 4.0 | 8.0 | 5.0 | 10.0 | 10.0 | 1.0 | 1.0 | 2.0 | 8.0 | 1.0 | 5.0 | 9.0 | 2.0 | 1.0 | 3.0 | 1.0 | 8.0 | 5.0 | 4.0 | 7.0 | 5.0 | 6.0 | 10.0 | 2.0 | 8.0 | 3.0 |

We then evaluated candidate runs by summing those base and interaction costs and chose the run with the lowest total.

Oh, and when you send back the chosen route, please put it in a tiny JSON snippet so it's easy to parse. Something casual like this will do:

{
  ""solution"": []
}

Think of ""solution"" as the place where you list the tanks (node names) in order from the starting tank to the receiving tank — just the node identifiers, nothing else (no hop/edge IDs, no costs). This JSON is just a sketch of the shape I expect, not the actual run.

Please use the exact node identifiers from the instance input — don't rename them or invent new labels. 
for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 'edges': [{'from': 20, 'to': 0, 'var_index': 0}, {'from': 20, 'to': 5, 'var_index': 1}, {'from': 20, 'to': 10, 'var_index': 2}, {'from': 20, 'to': 15, 'var_index': 3}, {'from': 4, 'to': 21, 'var_index': 4}, {'from': 9, 'to': 21, 'var_index': 5}, {'from': 14, 'to': 21, 'var_index': 6}, {'from': 19, 'to': 21, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 0, 'to': 5, 'var_index': 9}, {'from': 1, 'to': 2, 'var_index': 10}, {'from': 1, 'to': 6, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 2, 'to': 7, 'var_index': 13}, {'from': 3, 'to': 4, 'var_index': 14}, {'from': 3, 'to': 8, 'var_index': 15}, {'from': 4, 'to': 9, 'var_index': 16}, {'from': 5, 'to': 6, 'var_index': 17}, {'from': 5, 'to': 10, 'var_index': 18}, {'from': 6, 'to': 7, 'var_index': 19}, {'from': 6, 'to': 11, 'var_index': 20}, {'from': 7, 'to': 8, 'var_index': 21}, {'from': 7, 'to': 12, 'var_index': 22}, {'from': 8, 'to': 9, 'var_index': 23}, {'from': 8, 'to': 13, 'var_index': 24}, {'from': 9, 'to': 14, 'var_index': 25}, {'from': 10, 'to': 11, 'var_index': 26}, {'from': 10, 'to': 15, 'var_index': 27}, {'from': 11, 'to': 12, 'var_index': 28}, {'from': 11, 'to': 16, 'var_index': 29}, {'from': 12, 'to': 13, 'var_index': 30}, {'from': 12, 'to': 17, 'var_index': 31}, {'from': 13, 'to': 14, 'var_index': 32}, {'from': 13, 'to': 18, 'var_index': 33}, {'from': 14, 'to': 19, 'var_index': 34}, {'from': 15, 'to': 16, 'var_index': 35}, {'from': 16, 'to': 17, 'var_index': 36}, {'from': 17, 'to': 18, 'var_index': 37}, {'from': 18, 'to': 19, 'var_index': 38}], 'objective': {'constant': 0.0, 'linear': [9.0, 8.0, 10.0, 6.0, 6.0, 5.0, 10.0, 8.0, 4.0, 5.0, 1.0, 7.0, 9.0, 4.0, 10.0, 2.0, 1.0, 1.0, 10.0, 10.0, 2.0, 7.0, 3.0, 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'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U', 21: 'V'}}","['U', 'K', 'L', 'M', 'N', 'O', 'V']",48,markdown_table,names
QSPP,QSPP,"Out in the yard a gardener must pick one single line of hoses and valves from the water source to the flower bed, walking the water along only the allowed one‑way connections. The route needs to be continuous — a clear start at the source and a clear finish at the bed, using existing links and not leaving out or repeating segments. Each link has a basic upkeep cost, and some links also interact: using a particular link might add its own extra cost, and certain pairs of links together trigger additional charges that can depend on which comes first. To choose, total up the upkeep for every used link and then add any extra charges for every pair of links that are both in the route; the route with the lowest overall total is the goal. The exact network and cost details are listed below.

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    {
      ""segment_start_location"": ""K"",
      ""segment_end_location"": ""L"",
      ""segment_id"": 48
    },
    {
      ""segment_start_location"": ""L"",
      ""segment_end_location"": ""M"",
      ""segment_id"": 49
    },
    {
      ""segment_start_location"": ""M"",
      ""segment_end_location"": ""N"",
      ""segment_id"": 50
    },
    {
      ""segment_start_location"": ""N"",
      ""segment_end_location"": ""O"",
      ""segment_id"": 51
    },
    {
      ""segment_start_location"": ""O"",
      ""segment_end_location"": ""P"",
      ""segment_id"": 52
    },
    {
      ""segment_start_location"": ""P"",
      ""segment_end_location"": ""Q"",
      ""segment_id"": 53
    },
    {
      ""segment_start_location"": ""Q"",
      ""segment_end_location"": ""R"",
      ""segment_id"": 54
    },
    {
      ""segment_start_location"": ""R"",
      ""segment_end_location"": ""S"",
      ""segment_id"": 55
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 1,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 2,
      ""maintenance_cost"": 7.0
    },
    {
      ""segment_id"": 3,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 4,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 5,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 6,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 7,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 8,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 9,
      ""maintenance_cost"": 7.0
    },
    {
      ""segment_id"": 10,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 11,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 12,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 13,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 14,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 15,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 16,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 17,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 18,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 19,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 20,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 21,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 22,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 23,
      ""maintenance_cost"": 1.0
    },
    {
      ""segment_id"": 24,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 25,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 26,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 27,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 28,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 29,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 30,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 31,
      ""maintenance_cost"": 7.0
    },
    {
      ""segment_id"": 32,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 33,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 34,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 35,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 36,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 37,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 38,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 39,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 40,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 41,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 42,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 43,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 44,
      ""maintenance_cost"": 8.0
    },
    {
      ""segment_id"": 45,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 46,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 47,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 48,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 49,
      ""maintenance_cost"": 10.0
    },
    {
      ""segment_id"": 50,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 51,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 52,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 53,
      ""maintenance_cost"": 1.0
    },
    {
      ""segment_id"": 54,
      ""maintenance_cost"": 1.0
    },
    {
      ""segment_id"": 55,
      ""maintenance_cost"": 7.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 2.0 | 10.0 | 10.0 | 8.0 | 7.0 | 3.0 | 6.0 | 8.0 | 4.0 | 10.0 | 1.0 | 7.0 | 4.0 | 4.0 | 7.0 | 4.0 | 4.0 | 4.0 | 3.0 | 2.0 | 3.0 | 5.0 | 7.0 | 6.0 | 7.0 | 3.0 | 6.0 | 10.0 | 5.0 | 10.0 | 9.0 | 4.0 | 10.0 | 1.0 | 4.0 | 10.0 | 4.0 | 10.0 | 5.0 | 2.0 | 10.0 | 1.0 | 10.0 | 6.0 | 4.0 | 6.0 | 3.0 | 9.0 | 1.0 | 2.0 | 2.0 | 9.0 | 3.0 | 5.0 | 1.0 |
| 1 | 2.0 | 1.0 | 5.0 | 7.0 | 1.0 | 1.0 | 3.0 | 6.0 | 10.0 | 6.0 | 3.0 | 3.0 | 10.0 | 7.0 | 5.0 | 6.0 | 4.0 | 5.0 | 8.0 | 9.0 | 7.0 | 8.0 | 7.0 | 4.0 | 8.0 | 8.0 | 8.0 | 10.0 | 8.0 | 8.0 | 9.0 | 5.0 | 7.0 | 7.0 | 10.0 | 5.0 | 9.0 | 7.0 | 5.0 | 2.0 | 4.0 | 7.0 | 4.0 | 1.0 | 7.0 | 9.0 | 4.0 | 6.0 | 5.0 | 4.0 | 2.0 | 3.0 | 5.0 | 9.0 | 8.0 | 6.0 |
| 2 | 10.0 | 5.0 | 7.0 | 7.0 | 9.0 | 9.0 | 5.0 | 4.0 | 3.0 | 4.0 | 4.0 | 9.0 | 10.0 | 7.0 | 1.0 | 3.0 | 3.0 | 6.0 | 1.0 | 8.0 | 2.0 | 8.0 | 6.0 | 8.0 | 7.0 | 9.0 | 7.0 | 1.0 | 2.0 | 1.0 | 3.0 | 7.0 | 9.0 | 3.0 | 1.0 | 6.0 | 9.0 | 6.0 | 1.0 | 2.0 | 1.0 | 4.0 | 8.0 | 9.0 | 3.0 | 4.0 | 9.0 | 2.0 | 8.0 | 8.0 | 5.0 | 4.0 | 1.0 | 5.0 | 6.0 | 4.0 |
| 3 | 10.0 | 7.0 | 7.0 | 1.0 | 7.0 | 2.0 | 5.0 | 6.0 | 8.0 | 10.0 | 1.0 | 2.0 | 4.0 | 9.0 | 9.0 | 3.0 | 2.0 | 4.0 | 10.0 | 2.0 | 10.0 | 1.0 | 4.0 | 7.0 | 10.0 | 5.0 | 1.0 | 7.0 | 6.0 | 6.0 | 1.0 | 1.0 | 1.0 | 7.0 | 5.0 | 6.0 | 2.0 | 7.0 | 1.0 | 9.0 | 3.0 | 9.0 | 1.0 | 10.0 | 6.0 | 4.0 | 3.0 | 4.0 | 3.0 | 6.0 | 7.0 | 10.0 | 9.0 | 3.0 | 5.0 | 4.0 |
| 4 | 8.0 | 1.0 | 9.0 | 7.0 | 4.0 | 10.0 | 5.0 | 8.0 | 9.0 | 8.0 | 10.0 | 9.0 | 5.0 | 3.0 | 10.0 | 2.0 | 7.0 | 4.0 | 9.0 | 6.0 | 9.0 | 4.0 | 3.0 | 6.0 | 1.0 | 2.0 | 6.0 | 3.0 | 8.0 | 6.0 | 10.0 | 4.0 | 6.0 | 6.0 | 3.0 | 4.0 | 5.0 | 7.0 | 5.0 | 4.0 | 2.0 | 8.0 | 7.0 | 7.0 | 4.0 | 1.0 | 5.0 | 3.0 | 10.0 | 2.0 | 2.0 | 1.0 | 4.0 | 2.0 | 5.0 | 10.0 |
| 5 | 7.0 | 1.0 | 9.0 | 2.0 | 10.0 | 3.0 | 2.0 | 6.0 | 5.0 | 1.0 | 4.0 | 5.0 | 10.0 | 6.0 | 8.0 | 9.0 | 1.0 | 3.0 | 3.0 | 5.0 | 6.0 | 4.0 | 2.0 | 4.0 | 2.0 | 1.0 | 2.0 | 7.0 | 7.0 | 5.0 | 6.0 | 5.0 | 6.0 | 4.0 | 7.0 | 7.0 | 8.0 | 4.0 | 10.0 | 10.0 | 10.0 | 8.0 | 1.0 | 9.0 | 7.0 | 6.0 | 7.0 | 1.0 | 2.0 | 1.0 | 8.0 | 3.0 | 4.0 | 8.0 | 4.0 | 3.0 |
| 6 | 3.0 | 3.0 | 5.0 | 5.0 | 5.0 | 2.0 | 8.0 | 10.0 | 8.0 | 3.0 | 4.0 | 3.0 | 10.0 | 7.0 | 8.0 | 2.0 | 3.0 | 3.0 | 7.0 | 4.0 | 5.0 | 3.0 | 5.0 | 3.0 | 4.0 | 7.0 | 4.0 | 8.0 | 4.0 | 7.0 | 4.0 | 2.0 | 6.0 | 8.0 | 9.0 | 6.0 | 3.0 | 7.0 | 7.0 | 10.0 | 10.0 | 8.0 | 3.0 | 5.0 | 8.0 | 1.0 | 1.0 | 5.0 | 10.0 | 4.0 | 3.0 | 6.0 | 6.0 | 8.0 | 6.0 | 2.0 |
| 7 | 6.0 | 6.0 | 4.0 | 6.0 | 8.0 | 6.0 | 10.0 | 4.0 | 9.0 | 2.0 | 10.0 | 3.0 | 4.0 | 9.0 | 2.0 | 5.0 | 5.0 | 3.0 | 7.0 | 2.0 | 5.0 | 2.0 | 5.0 | 7.0 | 10.0 | 5.0 | 9.0 | 4.0 | 8.0 | 7.0 | 6.0 | 10.0 | 4.0 | 7.0 | 1.0 | 7.0 | 6.0 | 9.0 | 9.0 | 3.0 | 1.0 | 7.0 | 4.0 | 8.0 | 10.0 | 9.0 | 8.0 | 9.0 | 5.0 | 7.0 | 9.0 | 1.0 | 7.0 | 4.0 | 9.0 | 8.0 |
| 8 | 8.0 | 10.0 | 3.0 | 8.0 | 9.0 | 5.0 | 8.0 | 9.0 | 10.0 | 1.0 | 2.0 | 10.0 | 7.0 | 6.0 | 6.0 | 3.0 | 2.0 | 2.0 | 2.0 | 7.0 | 8.0 | 7.0 | 6.0 | 5.0 | 9.0 | 2.0 | 1.0 | 3.0 | 5.0 | 10.0 | 7.0 | 7.0 | 1.0 | 7.0 | 4.0 | 1.0 | 3.0 | 4.0 | 5.0 | 3.0 | 10.0 | 6.0 | 6.0 | 2.0 | 8.0 | 9.0 | 9.0 | 4.0 | 9.0 | 6.0 | 3.0 | 3.0 | 4.0 | 6.0 | 9.0 | 9.0 |
| 9 | 4.0 | 6.0 | 4.0 | 10.0 | 8.0 | 1.0 | 3.0 | 2.0 | 1.0 | 1.0 | 3.0 | 3.0 | 7.0 | 4.0 | 1.0 | 7.0 | 4.0 | 9.0 | 3.0 | 8.0 | 1.0 | 2.0 | 2.0 | 9.0 | 2.0 | 5.0 | 6.0 | 4.0 | 3.0 | 6.0 | 6.0 | 9.0 | 7.0 | 5.0 | 10.0 | 4.0 | 5.0 | 6.0 | 2.0 | 9.0 | 4.0 | 10.0 | 8.0 | 6.0 | 8.0 | 4.0 | 10.0 | 2.0 | 10.0 | 1.0 | 7.0 | 5.0 | 8.0 | 6.0 | 3.0 | 2.0 |
| 10 | 10.0 | 3.0 | 4.0 | 1.0 | 10.0 | 4.0 | 4.0 | 10.0 | 2.0 | 3.0 | 7.0 | 3.0 | 3.0 | 8.0 | 6.0 | 9.0 | 9.0 | 1.0 | 3.0 | 2.0 | 9.0 | 5.0 | 1.0 | 7.0 | 2.0 | 1.0 | 8.0 | 3.0 | 6.0 | 7.0 | 2.0 | 6.0 | 4.0 | 8.0 | 5.0 | 9.0 | 6.0 | 5.0 | 2.0 | 8.0 | 9.0 | 3.0 | 7.0 | 6.0 | 5.0 | 8.0 | 6.0 | 7.0 | 7.0 | 3.0 | 1.0 | 10.0 | 7.0 | 10.0 | 9.0 | 3.0 |
| 11 | 1.0 | 3.0 | 9.0 | 2.0 | 9.0 | 5.0 | 3.0 | 3.0 | 10.0 | 3.0 | 3.0 | 1.0 | 4.0 | 5.0 | 2.0 | 7.0 | 7.0 | 2.0 | 5.0 | 10.0 | 9.0 | 6.0 | 10.0 | 5.0 | 10.0 | 7.0 | 2.0 | 7.0 | 4.0 | 10.0 | 1.0 | 4.0 | 8.0 | 10.0 | 2.0 | 5.0 | 7.0 | 5.0 | 3.0 | 2.0 | 10.0 | 1.0 | 5.0 | 5.0 | 2.0 | 4.0 | 4.0 | 7.0 | 5.0 | 3.0 | 3.0 | 4.0 | 5.0 | 4.0 | 6.0 | 5.0 |
| 12 | 7.0 | 10.0 | 10.0 | 4.0 | 5.0 | 10.0 | 10.0 | 4.0 | 7.0 | 7.0 | 3.0 | 4.0 | 7.0 | 6.0 | 2.0 | 9.0 | 4.0 | 4.0 | 9.0 | 3.0 | 2.0 | 1.0 | 2.0 | 10.0 | 2.0 | 6.0 | 2.0 | 10.0 | 1.0 | 9.0 | 3.0 | 9.0 | 5.0 | 8.0 | 1.0 | 10.0 | 4.0 | 9.0 | 5.0 | 4.0 | 7.0 | 8.0 | 1.0 | 10.0 | 5.0 | 2.0 | 4.0 | 10.0 | 1.0 | 3.0 | 2.0 | 3.0 | 5.0 | 5.0 | 8.0 | 9.0 |
| 13 | 4.0 | 7.0 | 7.0 | 9.0 | 3.0 | 6.0 | 7.0 | 9.0 | 6.0 | 4.0 | 8.0 | 5.0 | 6.0 | 6.0 | 8.0 | 7.0 | 5.0 | 4.0 | 8.0 | 7.0 | 4.0 | 3.0 | 7.0 | 6.0 | 7.0 | 1.0 | 5.0 | 5.0 | 8.0 | 6.0 | 2.0 | 10.0 | 2.0 | 1.0 | 2.0 | 1.0 | 7.0 | 4.0 | 9.0 | 2.0 | 6.0 | 3.0 | 1.0 | 4.0 | 8.0 | 4.0 | 1.0 | 6.0 | 7.0 | 8.0 | 7.0 | 10.0 | 6.0 | 9.0 | 2.0 | 7.0 |
| 14 | 4.0 | 5.0 | 1.0 | 9.0 | 10.0 | 8.0 | 8.0 | 2.0 | 6.0 | 1.0 | 6.0 | 2.0 | 2.0 | 8.0 | 2.0 | 2.0 | 10.0 | 8.0 | 1.0 | 2.0 | 5.0 | 6.0 | 3.0 | 2.0 | 4.0 | 4.0 | 5.0 | 5.0 | 4.0 | 8.0 | 1.0 | 9.0 | 10.0 | 6.0 | 10.0 | 1.0 | 6.0 | 9.0 | 4.0 | 5.0 | 5.0 | 7.0 | 6.0 | 9.0 | 10.0 | 1.0 | 1.0 | 7.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 5.0 | 7.0 | 3.0 |
| 15 | 7.0 | 6.0 | 3.0 | 3.0 | 2.0 | 9.0 | 2.0 | 5.0 | 3.0 | 7.0 | 9.0 | 7.0 | 9.0 | 7.0 | 2.0 | 5.0 | 9.0 | 9.0 | 3.0 | 3.0 | 6.0 | 2.0 | 3.0 | 6.0 | 4.0 | 2.0 | 3.0 | 3.0 | 3.0 | 3.0 | 9.0 | 7.0 | 1.0 | 5.0 | 10.0 | 8.0 | 7.0 | 6.0 | 5.0 | 5.0 | 10.0 | 6.0 | 7.0 | 3.0 | 4.0 | 6.0 | 7.0 | 6.0 | 2.0 | 1.0 | 9.0 | 3.0 | 9.0 | 1.0 | 7.0 | 3.0 |
| 16 | 4.0 | 4.0 | 3.0 | 2.0 | 7.0 | 1.0 | 3.0 | 5.0 | 2.0 | 4.0 | 9.0 | 7.0 | 4.0 | 5.0 | 10.0 | 9.0 | 8.0 | 3.0 | 8.0 | 4.0 | 4.0 | 9.0 | 5.0 | 7.0 | 3.0 | 7.0 | 10.0 | 4.0 | 9.0 | 1.0 | 6.0 | 9.0 | 5.0 | 3.0 | 3.0 | 1.0 | 1.0 | 1.0 | 9.0 | 4.0 | 4.0 | 2.0 | 10.0 | 1.0 | 6.0 | 8.0 | 10.0 | 6.0 | 9.0 | 2.0 | 7.0 | 7.0 | 1.0 | 10.0 | 9.0 | 7.0 |
| 17 | 4.0 | 5.0 | 6.0 | 4.0 | 4.0 | 3.0 | 3.0 | 3.0 | 2.0 | 9.0 | 1.0 | 2.0 | 4.0 | 4.0 | 8.0 | 9.0 | 3.0 | 6.0 | 5.0 | 5.0 | 5.0 | 6.0 | 3.0 | 1.0 | 6.0 | 8.0 | 8.0 | 5.0 | 6.0 | 9.0 | 1.0 | 9.0 | 9.0 | 9.0 | 3.0 | 9.0 | 5.0 | 8.0 | 4.0 | 5.0 | 7.0 | 10.0 | 10.0 | 5.0 | 6.0 | 9.0 | 10.0 | 10.0 | 8.0 | 10.0 | 2.0 | 7.0 | 7.0 | 1.0 | 5.0 | 3.0 |
| 18 | 4.0 | 8.0 | 1.0 | 10.0 | 9.0 | 3.0 | 7.0 | 7.0 | 2.0 | 3.0 | 3.0 | 5.0 | 9.0 | 8.0 | 1.0 | 3.0 | 8.0 | 5.0 | 10.0 | 10.0 | 5.0 | 4.0 | 7.0 | 8.0 | 6.0 | 3.0 | 1.0 | 4.0 | 3.0 | 1.0 | 1.0 | 4.0 | 3.0 | 4.0 | 1.0 | 1.0 | 2.0 | 10.0 | 9.0 | 4.0 | 3.0 | 10.0 | 2.0 | 4.0 | 3.0 | 1.0 | 6.0 | 1.0 | 3.0 | 8.0 | 2.0 | 4.0 | 4.0 | 9.0 | 2.0 | 1.0 |
| 19 | 3.0 | 9.0 | 8.0 | 2.0 | 6.0 | 5.0 | 4.0 | 2.0 | 7.0 | 8.0 | 2.0 | 10.0 | 3.0 | 7.0 | 2.0 | 3.0 | 4.0 | 5.0 | 10.0 | 9.0 | 3.0 | 9.0 | 10.0 | 10.0 | 1.0 | 9.0 | 10.0 | 9.0 | 2.0 | 10.0 | 9.0 | 2.0 | 2.0 | 4.0 | 5.0 | 2.0 | 2.0 | 2.0 | 8.0 | 1.0 | 7.0 | 6.0 | 3.0 | 9.0 | 10.0 | 5.0 | 10.0 | 7.0 | 2.0 | 3.0 | 4.0 | 9.0 | 9.0 | 1.0 | 8.0 | 8.0 |
| 20 | 2.0 | 7.0 | 2.0 | 10.0 | 9.0 | 6.0 | 5.0 | 5.0 | 8.0 | 1.0 | 9.0 | 9.0 | 2.0 | 4.0 | 5.0 | 6.0 | 4.0 | 5.0 | 5.0 | 3.0 | 4.0 | 10.0 | 7.0 | 5.0 | 8.0 | 3.0 | 6.0 | 7.0 | 6.0 | 9.0 | 6.0 | 7.0 | 5.0 | 4.0 | 3.0 | 8.0 | 10.0 | 7.0 | 5.0 | 3.0 | 5.0 | 2.0 | 6.0 | 10.0 | 1.0 | 3.0 | 3.0 | 4.0 | 5.0 | 9.0 | 4.0 | 1.0 | 9.0 | 5.0 | 9.0 | 10.0 |
| 21 | 3.0 | 8.0 | 8.0 | 1.0 | 4.0 | 4.0 | 3.0 | 2.0 | 7.0 | 2.0 | 5.0 | 6.0 | 1.0 | 3.0 | 6.0 | 2.0 | 9.0 | 6.0 | 4.0 | 9.0 | 10.0 | 6.0 | 1.0 | 10.0 | 2.0 | 3.0 | 8.0 | 2.0 | 7.0 | 7.0 | 6.0 | 2.0 | 6.0 | 1.0 | 5.0 | 2.0 | 1.0 | 9.0 | 4.0 | 3.0 | 7.0 | 2.0 | 4.0 | 4.0 | 3.0 | 3.0 | 5.0 | 3.0 | 4.0 | 8.0 | 8.0 | 4.0 | 7.0 | 8.0 | 10.0 | 6.0 |
| 22 | 5.0 | 7.0 | 6.0 | 4.0 | 3.0 | 2.0 | 5.0 | 5.0 | 6.0 | 2.0 | 1.0 | 10.0 | 2.0 | 7.0 | 3.0 | 3.0 | 5.0 | 3.0 | 7.0 | 10.0 | 7.0 | 1.0 | 7.0 | 9.0 | 7.0 | 7.0 | 7.0 | 5.0 | 6.0 | 10.0 | 6.0 | 6.0 | 6.0 | 2.0 | 8.0 | 2.0 | 2.0 | 9.0 | 9.0 | 8.0 | 1.0 | 5.0 | 5.0 | 3.0 | 5.0 | 1.0 | 6.0 | 7.0 | 5.0 | 7.0 | 7.0 | 2.0 | 7.0 | 4.0 | 8.0 | 5.0 |
| 23 | 7.0 | 4.0 | 8.0 | 7.0 | 6.0 | 4.0 | 3.0 | 7.0 | 5.0 | 9.0 | 7.0 | 5.0 | 10.0 | 6.0 | 2.0 | 6.0 | 7.0 | 1.0 | 8.0 | 10.0 | 5.0 | 10.0 | 9.0 | 2.0 | 3.0 | 4.0 | 1.0 | 5.0 | 1.0 | 3.0 | 10.0 | 3.0 | 10.0 | 10.0 | 8.0 | 8.0 | 3.0 | 5.0 | 10.0 | 10.0 | 6.0 | 7.0 | 3.0 | 9.0 | 8.0 | 2.0 | 8.0 | 6.0 | 6.0 | 8.0 | 4.0 | 8.0 | 4.0 | 6.0 | 4.0 | 10.0 |
| 24 | 6.0 | 8.0 | 7.0 | 10.0 | 1.0 | 2.0 | 4.0 | 10.0 | 9.0 | 2.0 | 2.0 | 10.0 | 2.0 | 7.0 | 4.0 | 4.0 | 3.0 | 6.0 | 6.0 | 1.0 | 8.0 | 2.0 | 7.0 | 3.0 | 8.0 | 3.0 | 5.0 | 4.0 | 5.0 | 8.0 | 9.0 | 3.0 | 7.0 | 1.0 | 2.0 | 3.0 | 1.0 | 6.0 | 8.0 | 8.0 | 8.0 | 8.0 | 3.0 | 5.0 | 8.0 | 8.0 | 2.0 | 8.0 | 6.0 | 3.0 | 1.0 | 9.0 | 1.0 | 8.0 | 6.0 | 4.0 |
| 25 | 7.0 | 8.0 | 9.0 | 5.0 | 2.0 | 1.0 | 7.0 | 5.0 | 2.0 | 5.0 | 1.0 | 7.0 | 6.0 | 1.0 | 4.0 | 2.0 | 7.0 | 8.0 | 3.0 | 9.0 | 3.0 | 3.0 | 7.0 | 4.0 | 3.0 | 9.0 | 2.0 | 1.0 | 4.0 | 1.0 | 8.0 | 5.0 | 3.0 | 2.0 | 6.0 | 3.0 | 8.0 | 10.0 | 5.0 | 7.0 | 5.0 | 4.0 | 5.0 | 5.0 | 1.0 | 6.0 | 4.0 | 3.0 | 10.0 | 10.0 | 3.0 | 9.0 | 1.0 | 3.0 | 1.0 | 8.0 |
| 26 | 3.0 | 8.0 | 7.0 | 1.0 | 6.0 | 2.0 | 4.0 | 9.0 | 1.0 | 6.0 | 8.0 | 2.0 | 2.0 | 5.0 | 5.0 | 3.0 | 10.0 | 8.0 | 1.0 | 10.0 | 6.0 | 8.0 | 7.0 | 1.0 | 5.0 | 2.0 | 7.0 | 8.0 | 6.0 | 7.0 | 9.0 | 7.0 | 9.0 | 8.0 | 6.0 | 5.0 | 7.0 | 3.0 | 1.0 | 3.0 | 2.0 | 8.0 | 2.0 | 3.0 | 4.0 | 6.0 | 7.0 | 1.0 | 9.0 | 9.0 | 10.0 | 5.0 | 3.0 | 5.0 | 3.0 | 4.0 |
| 27 | 6.0 | 10.0 | 1.0 | 7.0 | 3.0 | 7.0 | 8.0 | 4.0 | 3.0 | 4.0 | 3.0 | 7.0 | 10.0 | 5.0 | 5.0 | 3.0 | 4.0 | 5.0 | 4.0 | 9.0 | 7.0 | 2.0 | 5.0 | 5.0 | 4.0 | 1.0 | 8.0 | 4.0 | 8.0 | 6.0 | 6.0 | 10.0 | 3.0 | 10.0 | 5.0 | 1.0 | 9.0 | 3.0 | 4.0 | 7.0 | 9.0 | 8.0 | 5.0 | 1.0 | 9.0 | 4.0 | 10.0 | 6.0 | 3.0 | 6.0 | 1.0 | 10.0 | 8.0 | 6.0 | 9.0 | 8.0 |
| 28 | 10.0 | 8.0 | 2.0 | 6.0 | 8.0 | 7.0 | 4.0 | 8.0 | 5.0 | 3.0 | 6.0 | 4.0 | 1.0 | 8.0 | 4.0 | 3.0 | 9.0 | 6.0 | 3.0 | 2.0 | 6.0 | 7.0 | 6.0 | 1.0 | 5.0 | 4.0 | 6.0 | 8.0 | 3.0 | 2.0 | 5.0 | 10.0 | 8.0 | 4.0 | 5.0 | 1.0 | 3.0 | 8.0 | 9.0 | 5.0 | 7.0 | 8.0 | 6.0 | 10.0 | 8.0 | 2.0 | 7.0 | 8.0 | 9.0 | 4.0 | 8.0 | 9.0 | 2.0 | 2.0 | 10.0 | 7.0 |
| 29 | 5.0 | 8.0 | 1.0 | 6.0 | 6.0 | 5.0 | 7.0 | 7.0 | 10.0 | 6.0 | 7.0 | 10.0 | 9.0 | 6.0 | 8.0 | 3.0 | 1.0 | 9.0 | 1.0 | 10.0 | 9.0 | 7.0 | 10.0 | 3.0 | 8.0 | 1.0 | 7.0 | 6.0 | 2.0 | 2.0 | 9.0 | 1.0 | 7.0 | 3.0 | 2.0 | 3.0 | 9.0 | 9.0 | 6.0 | 3.0 | 5.0 | 3.0 | 1.0 | 4.0 | 4.0 | 4.0 | 5.0 | 2.0 | 4.0 | 4.0 | 10.0 | 10.0 | 3.0 | 6.0 | 4.0 | 6.0 |
| 30 | 10.0 | 9.0 | 3.0 | 1.0 | 10.0 | 6.0 | 4.0 | 6.0 | 7.0 | 6.0 | 2.0 | 1.0 | 3.0 | 2.0 | 1.0 | 9.0 | 6.0 | 1.0 | 1.0 | 9.0 | 6.0 | 6.0 | 6.0 | 10.0 | 9.0 | 8.0 | 9.0 | 6.0 | 5.0 | 9.0 | 8.0 | 5.0 | 2.0 | 10.0 | 8.0 | 1.0 | 6.0 | 6.0 | 6.0 | 4.0 | 4.0 | 7.0 | 2.0 | 1.0 | 8.0 | 8.0 | 3.0 | 10.0 | 8.0 | 5.0 | 7.0 | 3.0 | 3.0 | 1.0 | 8.0 | 2.0 |
| 31 | 9.0 | 5.0 | 7.0 | 1.0 | 4.0 | 5.0 | 2.0 | 10.0 | 7.0 | 9.0 | 6.0 | 4.0 | 9.0 | 10.0 | 9.0 | 7.0 | 9.0 | 9.0 | 4.0 | 2.0 | 7.0 | 2.0 | 6.0 | 3.0 | 3.0 | 5.0 | 7.0 | 10.0 | 10.0 | 1.0 | 5.0 | 7.0 | 10.0 | 6.0 | 10.0 | 1.0 | 1.0 | 2.0 | 7.0 | 3.0 | 6.0 | 3.0 | 5.0 | 7.0 | 4.0 | 10.0 | 3.0 | 9.0 | 6.0 | 5.0 | 7.0 | 10.0 | 2.0 | 1.0 | 1.0 | 10.0 |
| 32 | 4.0 | 7.0 | 9.0 | 1.0 | 6.0 | 6.0 | 6.0 | 4.0 | 1.0 | 7.0 | 4.0 | 8.0 | 5.0 | 2.0 | 10.0 | 1.0 | 5.0 | 9.0 | 3.0 | 2.0 | 5.0 | 6.0 | 6.0 | 10.0 | 7.0 | 3.0 | 9.0 | 3.0 | 8.0 | 7.0 | 2.0 | 10.0 | 1.0 | 5.0 | 10.0 | 6.0 | 10.0 | 9.0 | 4.0 | 7.0 | 2.0 | 2.0 | 2.0 | 1.0 | 9.0 | 3.0 | 9.0 | 6.0 | 7.0 | 2.0 | 9.0 | 8.0 | 6.0 | 2.0 | 10.0 | 2.0 |
| 33 | 10.0 | 7.0 | 3.0 | 7.0 | 6.0 | 4.0 | 8.0 | 7.0 | 7.0 | 5.0 | 8.0 | 10.0 | 8.0 | 1.0 | 6.0 | 5.0 | 3.0 | 9.0 | 4.0 | 4.0 | 4.0 | 1.0 | 2.0 | 10.0 | 1.0 | 2.0 | 8.0 | 10.0 | 4.0 | 3.0 | 10.0 | 6.0 | 5.0 | 10.0 | 9.0 | 1.0 | 5.0 | 4.0 | 8.0 | 3.0 | 6.0 | 9.0 | 8.0 | 9.0 | 2.0 | 10.0 | 4.0 | 6.0 | 3.0 | 2.0 | 9.0 | 1.0 | 5.0 | 2.0 | 6.0 | 4.0 |
| 34 | 1.0 | 10.0 | 1.0 | 5.0 | 3.0 | 7.0 | 9.0 | 1.0 | 4.0 | 10.0 | 5.0 | 2.0 | 1.0 | 2.0 | 10.0 | 10.0 | 3.0 | 3.0 | 1.0 | 5.0 | 3.0 | 5.0 | 8.0 | 8.0 | 2.0 | 6.0 | 6.0 | 5.0 | 5.0 | 2.0 | 8.0 | 10.0 | 10.0 | 9.0 | 8.0 | 10.0 | 6.0 | 2.0 | 4.0 | 10.0 | 2.0 | 3.0 | 9.0 | 4.0 | 10.0 | 8.0 | 8.0 | 2.0 | 4.0 | 3.0 | 7.0 | 2.0 | 1.0 | 7.0 | 3.0 | 1.0 |
| 35 | 4.0 | 5.0 | 6.0 | 6.0 | 4.0 | 7.0 | 6.0 | 7.0 | 1.0 | 4.0 | 9.0 | 5.0 | 10.0 | 1.0 | 1.0 | 8.0 | 1.0 | 9.0 | 1.0 | 2.0 | 8.0 | 2.0 | 2.0 | 8.0 | 3.0 | 3.0 | 5.0 | 1.0 | 1.0 | 3.0 | 1.0 | 1.0 | 6.0 | 1.0 | 10.0 | 1.0 | 7.0 | 1.0 | 4.0 | 4.0 | 3.0 | 3.0 | 4.0 | 3.0 | 9.0 | 3.0 | 9.0 | 2.0 | 1.0 | 8.0 | 4.0 | 1.0 | 8.0 | 7.0 | 9.0 | 6.0 |
| 36 | 10.0 | 9.0 | 9.0 | 2.0 | 5.0 | 8.0 | 3.0 | 6.0 | 3.0 | 5.0 | 6.0 | 7.0 | 4.0 | 7.0 | 6.0 | 7.0 | 1.0 | 5.0 | 2.0 | 2.0 | 10.0 | 1.0 | 2.0 | 3.0 | 1.0 | 8.0 | 7.0 | 9.0 | 3.0 | 9.0 | 6.0 | 1.0 | 10.0 | 5.0 | 6.0 | 7.0 | 10.0 | 4.0 | 5.0 | 7.0 | 7.0 | 8.0 | 6.0 | 3.0 | 4.0 | 8.0 | 2.0 | 5.0 | 7.0 | 5.0 | 4.0 | 3.0 | 10.0 | 9.0 | 8.0 | 3.0 |
| 37 | 4.0 | 7.0 | 6.0 | 7.0 | 7.0 | 4.0 | 7.0 | 9.0 | 4.0 | 6.0 | 5.0 | 5.0 | 9.0 | 4.0 | 9.0 | 6.0 | 1.0 | 8.0 | 10.0 | 2.0 | 7.0 | 9.0 | 9.0 | 5.0 | 6.0 | 10.0 | 3.0 | 3.0 | 8.0 | 9.0 | 6.0 | 2.0 | 9.0 | 4.0 | 2.0 | 1.0 | 4.0 | 6.0 | 8.0 | 5.0 | 5.0 | 6.0 | 1.0 | 3.0 | 2.0 | 3.0 | 9.0 | 2.0 | 10.0 | 10.0 | 8.0 | 2.0 | 10.0 | 2.0 | 5.0 | 7.0 |
| 38 | 10.0 | 5.0 | 1.0 | 1.0 | 5.0 | 10.0 | 7.0 | 9.0 | 5.0 | 2.0 | 2.0 | 3.0 | 5.0 | 9.0 | 4.0 | 5.0 | 9.0 | 4.0 | 9.0 | 8.0 | 5.0 | 4.0 | 9.0 | 10.0 | 8.0 | 5.0 | 1.0 | 4.0 | 9.0 | 6.0 | 6.0 | 7.0 | 4.0 | 8.0 | 4.0 | 4.0 | 5.0 | 8.0 | 5.0 | 4.0 | 5.0 | 7.0 | 4.0 | 3.0 | 2.0 | 7.0 | 4.0 | 9.0 | 6.0 | 3.0 | 7.0 | 1.0 | 5.0 | 5.0 | 7.0 | 1.0 |
| 39 | 5.0 | 2.0 | 2.0 | 9.0 | 4.0 | 10.0 | 10.0 | 3.0 | 3.0 | 9.0 | 8.0 | 2.0 | 4.0 | 2.0 | 5.0 | 5.0 | 4.0 | 5.0 | 4.0 | 1.0 | 3.0 | 3.0 | 8.0 | 10.0 | 8.0 | 7.0 | 3.0 | 7.0 | 5.0 | 3.0 | 4.0 | 3.0 | 7.0 | 3.0 | 10.0 | 4.0 | 7.0 | 5.0 | 4.0 | 5.0 | 1.0 | 4.0 | 4.0 | 9.0 | 8.0 | 6.0 | 9.0 | 6.0 | 1.0 | 6.0 | 8.0 | 2.0 | 9.0 | 7.0 | 3.0 | 2.0 |
| 40 | 2.0 | 4.0 | 1.0 | 3.0 | 2.0 | 10.0 | 10.0 | 1.0 | 10.0 | 4.0 | 9.0 | 10.0 | 7.0 | 6.0 | 5.0 | 10.0 | 4.0 | 7.0 | 3.0 | 7.0 | 5.0 | 7.0 | 1.0 | 6.0 | 8.0 | 5.0 | 2.0 | 9.0 | 7.0 | 5.0 | 4.0 | 6.0 | 2.0 | 6.0 | 2.0 | 3.0 | 7.0 | 5.0 | 5.0 | 1.0 | 8.0 | 1.0 | 7.0 | 1.0 | 8.0 | 8.0 | 7.0 | 2.0 | 9.0 | 1.0 | 7.0 | 4.0 | 1.0 | 7.0 | 9.0 | 5.0 |
| 41 | 10.0 | 7.0 | 4.0 | 9.0 | 8.0 | 8.0 | 8.0 | 7.0 | 6.0 | 10.0 | 3.0 | 1.0 | 8.0 | 3.0 | 7.0 | 6.0 | 2.0 | 10.0 | 10.0 | 6.0 | 2.0 | 2.0 | 5.0 | 7.0 | 8.0 | 4.0 | 8.0 | 8.0 | 8.0 | 3.0 | 7.0 | 3.0 | 2.0 | 9.0 | 3.0 | 3.0 | 8.0 | 6.0 | 7.0 | 4.0 | 1.0 | 6.0 | 7.0 | 10.0 | 5.0 | 10.0 | 10.0 | 7.0 | 4.0 | 5.0 | 6.0 | 2.0 | 1.0 | 7.0 | 1.0 | 7.0 |
| 42 | 1.0 | 4.0 | 8.0 | 1.0 | 7.0 | 1.0 | 3.0 | 4.0 | 6.0 | 8.0 | 7.0 | 5.0 | 1.0 | 1.0 | 6.0 | 7.0 | 10.0 | 10.0 | 2.0 | 3.0 | 6.0 | 4.0 | 5.0 | 3.0 | 3.0 | 5.0 | 2.0 | 5.0 | 6.0 | 1.0 | 2.0 | 5.0 | 2.0 | 8.0 | 9.0 | 4.0 | 6.0 | 1.0 | 4.0 | 4.0 | 7.0 | 7.0 | 4.0 | 6.0 | 3.0 | 8.0 | 10.0 | 6.0 | 3.0 | 3.0 | 3.0 | 7.0 | 8.0 | 5.0 | 7.0 | 9.0 |
| 43 | 10.0 | 1.0 | 9.0 | 10.0 | 7.0 | 9.0 | 5.0 | 8.0 | 2.0 | 6.0 | 6.0 | 5.0 | 10.0 | 4.0 | 9.0 | 3.0 | 1.0 | 5.0 | 4.0 | 9.0 | 10.0 | 4.0 | 3.0 | 9.0 | 5.0 | 5.0 | 3.0 | 1.0 | 10.0 | 4.0 | 1.0 | 7.0 | 1.0 | 9.0 | 4.0 | 3.0 | 3.0 | 3.0 | 3.0 | 9.0 | 1.0 | 10.0 | 6.0 | 2.0 | 9.0 | 3.0 | 7.0 | 3.0 | 2.0 | 3.0 | 9.0 | 8.0 | 4.0 | 1.0 | 2.0 | 6.0 |
| 44 | 6.0 | 7.0 | 3.0 | 6.0 | 4.0 | 7.0 | 8.0 | 10.0 | 8.0 | 8.0 | 5.0 | 2.0 | 5.0 | 8.0 | 10.0 | 4.0 | 6.0 | 6.0 | 3.0 | 10.0 | 1.0 | 3.0 | 5.0 | 8.0 | 8.0 | 1.0 | 4.0 | 9.0 | 8.0 | 4.0 | 8.0 | 4.0 | 9.0 | 2.0 | 10.0 | 9.0 | 4.0 | 2.0 | 2.0 | 8.0 | 8.0 | 5.0 | 3.0 | 9.0 | 9.0 | 9.0 | 5.0 | 1.0 | 6.0 | 5.0 | 1.0 | 1.0 | 5.0 | 7.0 | 3.0 | 9.0 |
| 45 | 4.0 | 9.0 | 4.0 | 4.0 | 1.0 | 6.0 | 1.0 | 9.0 | 9.0 | 4.0 | 8.0 | 4.0 | 2.0 | 4.0 | 1.0 | 6.0 | 8.0 | 9.0 | 1.0 | 5.0 | 3.0 | 3.0 | 1.0 | 2.0 | 8.0 | 6.0 | 6.0 | 4.0 | 2.0 | 4.0 | 8.0 | 10.0 | 3.0 | 10.0 | 8.0 | 3.0 | 8.0 | 3.0 | 7.0 | 6.0 | 8.0 | 10.0 | 8.0 | 3.0 | 9.0 | 10.0 | 2.0 | 2.0 | 7.0 | 1.0 | 8.0 | 8.0 | 5.0 | 7.0 | 4.0 | 8.0 |
| 46 | 6.0 | 4.0 | 9.0 | 3.0 | 5.0 | 7.0 | 1.0 | 8.0 | 9.0 | 10.0 | 6.0 | 4.0 | 4.0 | 1.0 | 1.0 | 7.0 | 10.0 | 10.0 | 6.0 | 10.0 | 3.0 | 5.0 | 6.0 | 8.0 | 2.0 | 4.0 | 7.0 | 10.0 | 7.0 | 5.0 | 3.0 | 3.0 | 9.0 | 4.0 | 8.0 | 9.0 | 2.0 | 9.0 | 4.0 | 9.0 | 7.0 | 10.0 | 10.0 | 7.0 | 5.0 | 2.0 | 8.0 | 1.0 | 6.0 | 4.0 | 4.0 | 8.0 | 9.0 | 10.0 | 4.0 | 10.0 |
| 47 | 3.0 | 6.0 | 2.0 | 4.0 | 3.0 | 1.0 | 5.0 | 9.0 | 4.0 | 2.0 | 7.0 | 7.0 | 10.0 | 6.0 | 7.0 | 6.0 | 6.0 | 10.0 | 1.0 | 7.0 | 4.0 | 3.0 | 7.0 | 6.0 | 8.0 | 3.0 | 1.0 | 6.0 | 8.0 | 2.0 | 10.0 | 9.0 | 6.0 | 6.0 | 2.0 | 2.0 | 5.0 | 2.0 | 9.0 | 6.0 | 2.0 | 7.0 | 6.0 | 3.0 | 1.0 | 2.0 | 1.0 | 8.0 | 10.0 | 1.0 | 8.0 | 8.0 | 7.0 | 3.0 | 10.0 | 7.0 |
| 48 | 9.0 | 5.0 | 8.0 | 3.0 | 10.0 | 2.0 | 10.0 | 5.0 | 9.0 | 10.0 | 7.0 | 5.0 | 1.0 | 7.0 | 2.0 | 2.0 | 9.0 | 8.0 | 3.0 | 2.0 | 5.0 | 4.0 | 5.0 | 6.0 | 6.0 | 10.0 | 9.0 | 3.0 | 9.0 | 4.0 | 8.0 | 6.0 | 7.0 | 3.0 | 4.0 | 1.0 | 7.0 | 10.0 | 6.0 | 1.0 | 9.0 | 4.0 | 3.0 | 2.0 | 6.0 | 7.0 | 6.0 | 10.0 | 10.0 | 5.0 | 1.0 | 6.0 | 2.0 | 1.0 | 5.0 | 8.0 |
| 49 | 1.0 | 4.0 | 8.0 | 6.0 | 2.0 | 1.0 | 4.0 | 7.0 | 6.0 | 1.0 | 3.0 | 3.0 | 3.0 | 8.0 | 8.0 | 1.0 | 2.0 | 10.0 | 8.0 | 3.0 | 9.0 | 8.0 | 7.0 | 8.0 | 3.0 | 10.0 | 9.0 | 6.0 | 4.0 | 4.0 | 5.0 | 5.0 | 2.0 | 2.0 | 3.0 | 8.0 | 5.0 | 10.0 | 3.0 | 6.0 | 1.0 | 5.0 | 3.0 | 3.0 | 5.0 | 1.0 | 4.0 | 1.0 | 5.0 | 6.0 | 8.0 | 7.0 | 10.0 | 8.0 | 1.0 | 2.0 |
| 50 | 2.0 | 2.0 | 5.0 | 7.0 | 2.0 | 8.0 | 3.0 | 9.0 | 3.0 | 7.0 | 1.0 | 3.0 | 2.0 | 7.0 | 5.0 | 9.0 | 7.0 | 2.0 | 2.0 | 4.0 | 4.0 | 8.0 | 7.0 | 4.0 | 1.0 | 3.0 | 10.0 | 1.0 | 8.0 | 10.0 | 7.0 | 7.0 | 9.0 | 9.0 | 7.0 | 4.0 | 4.0 | 8.0 | 7.0 | 8.0 | 7.0 | 6.0 | 3.0 | 9.0 | 1.0 | 8.0 | 4.0 | 8.0 | 1.0 | 8.0 | 3.0 | 6.0 | 4.0 | 9.0 | 10.0 | 8.0 |
| 51 | 2.0 | 3.0 | 4.0 | 10.0 | 1.0 | 3.0 | 6.0 | 1.0 | 3.0 | 5.0 | 10.0 | 4.0 | 3.0 | 10.0 | 9.0 | 3.0 | 7.0 | 7.0 | 4.0 | 9.0 | 1.0 | 4.0 | 2.0 | 8.0 | 9.0 | 9.0 | 5.0 | 10.0 | 9.0 | 10.0 | 3.0 | 10.0 | 8.0 | 1.0 | 2.0 | 1.0 | 3.0 | 2.0 | 1.0 | 2.0 | 4.0 | 2.0 | 7.0 | 8.0 | 1.0 | 8.0 | 8.0 | 8.0 | 6.0 | 7.0 | 6.0 | 7.0 | 8.0 | 10.0 | 1.0 | 3.0 |
| 52 | 9.0 | 5.0 | 1.0 | 9.0 | 4.0 | 4.0 | 6.0 | 7.0 | 4.0 | 8.0 | 7.0 | 5.0 | 5.0 | 6.0 | 9.0 | 9.0 | 1.0 | 7.0 | 4.0 | 9.0 | 9.0 | 7.0 | 7.0 | 4.0 | 1.0 | 1.0 | 3.0 | 8.0 | 2.0 | 3.0 | 3.0 | 2.0 | 6.0 | 5.0 | 1.0 | 8.0 | 10.0 | 10.0 | 5.0 | 9.0 | 1.0 | 1.0 | 8.0 | 4.0 | 5.0 | 5.0 | 9.0 | 7.0 | 2.0 | 10.0 | 4.0 | 8.0 | 8.0 | 10.0 | 10.0 | 10.0 |
| 53 | 3.0 | 9.0 | 5.0 | 3.0 | 2.0 | 8.0 | 8.0 | 4.0 | 6.0 | 6.0 | 10.0 | 4.0 | 5.0 | 9.0 | 5.0 | 1.0 | 10.0 | 1.0 | 9.0 | 1.0 | 5.0 | 8.0 | 4.0 | 6.0 | 8.0 | 3.0 | 5.0 | 6.0 | 2.0 | 6.0 | 1.0 | 1.0 | 2.0 | 2.0 | 7.0 | 7.0 | 9.0 | 2.0 | 5.0 | 7.0 | 7.0 | 7.0 | 5.0 | 1.0 | 7.0 | 7.0 | 10.0 | 3.0 | 1.0 | 8.0 | 9.0 | 10.0 | 10.0 | 3.0 | 2.0 | 1.0 |
| 54 | 5.0 | 8.0 | 6.0 | 5.0 | 5.0 | 4.0 | 6.0 | 9.0 | 9.0 | 3.0 | 9.0 | 6.0 | 8.0 | 2.0 | 7.0 | 7.0 | 9.0 | 5.0 | 2.0 | 8.0 | 9.0 | 10.0 | 8.0 | 4.0 | 6.0 | 1.0 | 3.0 | 9.0 | 10.0 | 4.0 | 8.0 | 1.0 | 10.0 | 6.0 | 3.0 | 9.0 | 8.0 | 5.0 | 7.0 | 3.0 | 9.0 | 1.0 | 7.0 | 2.0 | 3.0 | 4.0 | 4.0 | 10.0 | 5.0 | 1.0 | 10.0 | 1.0 | 10.0 | 2.0 | 1.0 | 6.0 |
| 55 | 1.0 | 6.0 | 4.0 | 4.0 | 10.0 | 3.0 | 2.0 | 8.0 | 9.0 | 2.0 | 3.0 | 5.0 | 9.0 | 7.0 | 3.0 | 3.0 | 7.0 | 3.0 | 1.0 | 8.0 | 10.0 | 6.0 | 5.0 | 10.0 | 4.0 | 8.0 | 4.0 | 8.0 | 7.0 | 6.0 | 2.0 | 10.0 | 2.0 | 4.0 | 1.0 | 6.0 | 3.0 | 7.0 | 1.0 | 2.0 | 5.0 | 7.0 | 9.0 | 6.0 | 9.0 | 8.0 | 10.0 | 7.0 | 8.0 | 2.0 | 8.0 | 3.0 | 10.0 | 1.0 | 6.0 | 9.0 |

If it helps, when you send back your chosen route just put it into this little JSON layout so it's easy to pick up programmatically — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of ""solution"" as the spot where you'll drop the sequence of node names that form the path from the water source to the flower bed (a simple list like [""Source"",""X"",""Y"",""Bed""] — just as an example sketch). This JSON is just a template showing the expected shape; it's not the actual answer yet.

Also a quick reminder: use the exact node identifiers given in the instance, do not rename them or invent new labels — they must match character-for-character.  
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 'edges': [{'from': 19, 'to': 0, 'var_index': 0}, {'from': 19, 'to': 1, 'var_index': 1}, {'from': 19, 'to': 2, 'var_index': 2}, {'from': 19, 'to': 3, 'var_index': 3}, {'from': 19, 'to': 4, 'var_index': 4}, {'from': 19, 'to': 5, 'var_index': 5}, {'from': 19, 'to': 6, 'var_index': 6}, {'from': 19, 'to': 7, 'var_index': 7}, {'from': 19, 'to': 8, 'var_index': 8}, {'from': 19, 'to': 9, 'var_index': 9}, {'from': 19, 'to': 10, 'var_index': 10}, {'from': 19, 'to': 11, 'var_index': 11}, {'from': 19, 'to': 12, 'var_index': 12}, {'from': 19, 'to': 13, 'var_index': 13}, {'from': 19, 'to': 14, 'var_index': 14}, {'from': 19, 'to': 15, 'var_index': 15}, {'from': 19, 'to': 16, 'var_index': 16}, {'from': 19, 'to': 17, 'var_index': 17}, {'from': 19, 'to': 18, 'var_index': 18}, {'from': 0, 'to': 20, 'var_index': 19}, {'from': 1, 'to': 20, 'var_index': 20}, {'from': 2, 'to': 20, 'var_index': 21}, {'from': 3, 'to': 20, 'var_index': 22}, {'from': 4, 'to': 20, 'var_index': 23}, {'from': 5, 'to': 20, 'var_index': 24}, {'from': 6, 'to': 20, 'var_index': 25}, {'from': 7, 'to': 20, 'var_index': 26}, {'from': 8, 'to': 20, 'var_index': 27}, {'from': 9, 'to': 20, 'var_index': 28}, {'from': 10, 'to': 20, 'var_index': 29}, {'from': 11, 'to': 20, 'var_index': 30}, {'from': 12, 'to': 20, 'var_index': 31}, {'from': 13, 'to': 20, 'var_index': 32}, {'from': 14, 'to': 20, 'var_index': 33}, {'from': 15, 'to': 20, 'var_index': 34}, {'from': 16, 'to': 20, 'var_index': 35}, {'from': 17, 'to': 20, 'var_index': 36}, {'from': 18, 'to': 20, 'var_index': 37}, {'from': 0, 'to': 1, 'var_index': 38}, {'from': 1, 'to': 2, 'var_index': 39}, {'from': 2, 'to': 3, 'var_index': 40}, {'from': 3, 'to': 4, 'var_index': 41}, {'from': 4, 'to': 5, 'var_index': 42}, {'from': 5, 'to': 6, 'var_index': 43}, {'from': 6, 'to': 7, 'var_index': 44}, {'from': 7, 'to': 8, 'var_index': 45}, {'from': 8, 'to': 9, 'var_index': 46}, {'from': 9, 'to': 10, 'var_index': 47}, {'from': 10, 'to': 11, 'var_index': 48}, {'from': 11, 'to': 12, 'var_index': 49}, {'from': 12, 'to': 13, 'var_index': 50}, {'from': 13, 'to': 14, 'var_index': 51}, {'from': 14, 'to': 15, 'var_index': 52}, {'from': 15, 'to': 16, 'var_index': 53}, {'from': 16, 'to': 17, 'var_index': 54}, {'from': 17, 'to': 18, 'var_index': 55}], 'objective': {'constant': 0.0, 'linear': [6.0, 4.0, 7.0, 8.0, 2.0, 4.0, 2.0, 9.0, 8.0, 7.0, 9.0, 4.0, 3.0, 4.0, 8.0, 3.0, 2.0, 8.0, 8.0, 9.0, 2.0, 5.0, 6.0, 1.0, 10.0, 6.0, 10.0, 2.0, 10.0, 6.0, 3.0, 7.0, 9.0, 2.0, 9.0, 10.0, 4.0, 4.0, 2.0, 3.0, 5.0, 5.0, 5.0, 9.0, 8.0, 4.0, 3.0, 10.0, 5.0, 10.0, 4.0, 5.0, 3.0, 1.0, 1.0, 7.0], 'quadratic': [[10.0, 2.0, 10.0, 10.0, 8.0, 7.0, 3.0, 6.0, 8.0, 4.0, 10.0, 1.0, 7.0, 4.0, 4.0, 7.0, 4.0, 4.0, 4.0, 3.0, 2.0, 3.0, 5.0, 7.0, 6.0, 7.0, 3.0, 6.0, 10.0, 5.0, 10.0, 9.0, 4.0, 10.0, 1.0, 4.0, 10.0, 4.0, 10.0, 5.0, 2.0, 10.0, 1.0, 10.0, 6.0, 4.0, 6.0, 3.0, 9.0, 1.0, 2.0, 2.0, 9.0, 3.0, 5.0, 1.0], [2.0, 1.0, 5.0, 7.0, 1.0, 1.0, 3.0, 6.0, 10.0, 6.0, 3.0, 3.0, 10.0, 7.0, 5.0, 6.0, 4.0, 5.0, 8.0, 9.0, 7.0, 8.0, 7.0, 4.0, 8.0, 8.0, 8.0, 10.0, 8.0, 8.0, 9.0, 5.0, 7.0, 7.0, 10.0, 5.0, 9.0, 7.0, 5.0, 2.0, 4.0, 7.0, 4.0, 1.0, 7.0, 9.0, 4.0, 6.0, 5.0, 4.0, 2.0, 3.0, 5.0, 9.0, 8.0, 6.0], [10.0, 5.0, 7.0, 7.0, 9.0, 9.0, 5.0, 4.0, 3.0, 4.0, 4.0, 9.0, 10.0, 7.0, 1.0, 3.0, 3.0, 6.0, 1.0, 8.0, 2.0, 8.0, 6.0, 8.0, 7.0, 9.0, 7.0, 1.0, 2.0, 1.0, 3.0, 7.0, 9.0, 3.0, 1.0, 6.0, 9.0, 6.0, 1.0, 2.0, 1.0, 4.0, 8.0, 9.0, 3.0, 4.0, 9.0, 2.0, 8.0, 8.0, 5.0, 4.0, 1.0, 5.0, 6.0, 4.0], [10.0, 7.0, 7.0, 1.0, 7.0, 2.0, 5.0, 6.0, 8.0, 10.0, 1.0, 2.0, 4.0, 9.0, 9.0, 3.0, 2.0, 4.0, 10.0, 2.0, 10.0, 1.0, 4.0, 7.0, 10.0, 5.0, 1.0, 7.0, 6.0, 6.0, 1.0, 1.0, 1.0, 7.0, 5.0, 6.0, 2.0, 7.0, 1.0, 9.0, 3.0, 9.0, 1.0, 10.0, 6.0, 4.0, 3.0, 4.0, 3.0, 6.0, 7.0, 10.0, 9.0, 3.0, 5.0, 4.0], [8.0, 1.0, 9.0, 7.0, 4.0, 10.0, 5.0, 8.0, 9.0, 8.0, 10.0, 9.0, 5.0, 3.0, 10.0, 2.0, 7.0, 4.0, 9.0, 6.0, 9.0, 4.0, 3.0, 6.0, 1.0, 2.0, 6.0, 3.0, 8.0, 6.0, 10.0, 4.0, 6.0, 6.0, 3.0, 4.0, 5.0, 7.0, 5.0, 4.0, 2.0, 8.0, 7.0, 7.0, 4.0, 1.0, 5.0, 3.0, 10.0, 2.0, 2.0, 1.0, 4.0, 2.0, 5.0, 10.0], [7.0, 1.0, 9.0, 2.0, 10.0, 3.0, 2.0, 6.0, 5.0, 1.0, 4.0, 5.0, 10.0, 6.0, 8.0, 9.0, 1.0, 3.0, 3.0, 5.0, 6.0, 4.0, 2.0, 4.0, 2.0, 1.0, 2.0, 7.0, 7.0, 5.0, 6.0, 5.0, 6.0, 4.0, 7.0, 7.0, 8.0, 4.0, 10.0, 10.0, 10.0, 8.0, 1.0, 9.0, 7.0, 6.0, 7.0, 1.0, 2.0, 1.0, 8.0, 3.0, 4.0, 8.0, 4.0, 3.0], [3.0, 3.0, 5.0, 5.0, 5.0, 2.0, 8.0, 10.0, 8.0, 3.0, 4.0, 3.0, 10.0, 7.0, 8.0, 2.0, 3.0, 3.0, 7.0, 4.0, 5.0, 3.0, 5.0, 3.0, 4.0, 7.0, 4.0, 8.0, 4.0, 7.0, 4.0, 2.0, 6.0, 8.0, 9.0, 6.0, 3.0, 7.0, 7.0, 10.0, 10.0, 8.0, 3.0, 5.0, 8.0, 1.0, 1.0, 5.0, 10.0, 4.0, 3.0, 6.0, 6.0, 8.0, 6.0, 2.0], [6.0, 6.0, 4.0, 6.0, 8.0, 6.0, 10.0, 4.0, 9.0, 2.0, 10.0, 3.0, 4.0, 9.0, 2.0, 5.0, 5.0, 3.0, 7.0, 2.0, 5.0, 2.0, 5.0, 7.0, 10.0, 5.0, 9.0, 4.0, 8.0, 7.0, 6.0, 10.0, 4.0, 7.0, 1.0, 7.0, 6.0, 9.0, 9.0, 3.0, 1.0, 7.0, 4.0, 8.0, 10.0, 9.0, 8.0, 9.0, 5.0, 7.0, 9.0, 1.0, 7.0, 4.0, 9.0, 8.0], [8.0, 10.0, 3.0, 8.0, 9.0, 5.0, 8.0, 9.0, 10.0, 1.0, 2.0, 10.0, 7.0, 6.0, 6.0, 3.0, 2.0, 2.0, 2.0, 7.0, 8.0, 7.0, 6.0, 5.0, 9.0, 2.0, 1.0, 3.0, 5.0, 10.0, 7.0, 7.0, 1.0, 7.0, 4.0, 1.0, 3.0, 4.0, 5.0, 3.0, 10.0, 6.0, 6.0, 2.0, 8.0, 9.0, 9.0, 4.0, 9.0, 6.0, 3.0, 3.0, 4.0, 6.0, 9.0, 9.0], [4.0, 6.0, 4.0, 10.0, 8.0, 1.0, 3.0, 2.0, 1.0, 1.0, 3.0, 3.0, 7.0, 4.0, 1.0, 7.0, 4.0, 9.0, 3.0, 8.0, 1.0, 2.0, 2.0, 9.0, 2.0, 5.0, 6.0, 4.0, 3.0, 6.0, 6.0, 9.0, 7.0, 5.0, 10.0, 4.0, 5.0, 6.0, 2.0, 9.0, 4.0, 10.0, 8.0, 6.0, 8.0, 4.0, 10.0, 2.0, 10.0, 1.0, 7.0, 5.0, 8.0, 6.0, 3.0, 2.0], [10.0, 3.0, 4.0, 1.0, 10.0, 4.0, 4.0, 10.0, 2.0, 3.0, 7.0, 3.0, 3.0, 8.0, 6.0, 9.0, 9.0, 1.0, 3.0, 2.0, 9.0, 5.0, 1.0, 7.0, 2.0, 1.0, 8.0, 3.0, 6.0, 7.0, 2.0, 6.0, 4.0, 8.0, 5.0, 9.0, 6.0, 5.0, 2.0, 8.0, 9.0, 3.0, 7.0, 6.0, 5.0, 8.0, 6.0, 7.0, 7.0, 3.0, 1.0, 10.0, 7.0, 10.0, 9.0, 3.0], [1.0, 3.0, 9.0, 2.0, 9.0, 5.0, 3.0, 3.0, 10.0, 3.0, 3.0, 1.0, 4.0, 5.0, 2.0, 7.0, 7.0, 2.0, 5.0, 10.0, 9.0, 6.0, 10.0, 5.0, 10.0, 7.0, 2.0, 7.0, 4.0, 10.0, 1.0, 4.0, 8.0, 10.0, 2.0, 5.0, 7.0, 5.0, 3.0, 2.0, 10.0, 1.0, 5.0, 5.0, 2.0, 4.0, 4.0, 7.0, 5.0, 3.0, 3.0, 4.0, 5.0, 4.0, 6.0, 5.0], [7.0, 10.0, 10.0, 4.0, 5.0, 10.0, 10.0, 4.0, 7.0, 7.0, 3.0, 4.0, 7.0, 6.0, 2.0, 9.0, 4.0, 4.0, 9.0, 3.0, 2.0, 1.0, 2.0, 10.0, 2.0, 6.0, 2.0, 10.0, 1.0, 9.0, 3.0, 9.0, 5.0, 8.0, 1.0, 10.0, 4.0, 9.0, 5.0, 4.0, 7.0, 8.0, 1.0, 10.0, 5.0, 2.0, 4.0, 10.0, 1.0, 3.0, 2.0, 3.0, 5.0, 5.0, 8.0, 9.0], [4.0, 7.0, 7.0, 9.0, 3.0, 6.0, 7.0, 9.0, 6.0, 4.0, 8.0, 5.0, 6.0, 6.0, 8.0, 7.0, 5.0, 4.0, 8.0, 7.0, 4.0, 3.0, 7.0, 6.0, 7.0, 1.0, 5.0, 5.0, 8.0, 6.0, 2.0, 10.0, 2.0, 1.0, 2.0, 1.0, 7.0, 4.0, 9.0, 2.0, 6.0, 3.0, 1.0, 4.0, 8.0, 4.0, 1.0, 6.0, 7.0, 8.0, 7.0, 10.0, 6.0, 9.0, 2.0, 7.0], [4.0, 5.0, 1.0, 9.0, 10.0, 8.0, 8.0, 2.0, 6.0, 1.0, 6.0, 2.0, 2.0, 8.0, 2.0, 2.0, 10.0, 8.0, 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{'var_i': 54, 'var_j': 27, 'quadratic_cost': 9.0}, {'var_i': 54, 'var_j': 28, 'quadratic_cost': 10.0}, {'var_i': 54, 'var_j': 29, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 30, 'quadratic_cost': 8.0}, {'var_i': 54, 'var_j': 31, 'quadratic_cost': 1.0}, {'var_i': 54, 'var_j': 32, 'quadratic_cost': 10.0}, {'var_i': 54, 'var_j': 33, 'quadratic_cost': 6.0}, {'var_i': 54, 'var_j': 34, 'quadratic_cost': 3.0}, {'var_i': 54, 'var_j': 35, 'quadratic_cost': 9.0}, {'var_i': 54, 'var_j': 36, 'quadratic_cost': 8.0}, {'var_i': 54, 'var_j': 37, 'quadratic_cost': 5.0}, {'var_i': 54, 'var_j': 38, 'quadratic_cost': 7.0}, {'var_i': 54, 'var_j': 39, 'quadratic_cost': 3.0}, {'var_i': 54, 'var_j': 40, 'quadratic_cost': 9.0}, {'var_i': 54, 'var_j': 41, 'quadratic_cost': 1.0}, {'var_i': 54, 'var_j': 42, 'quadratic_cost': 7.0}, {'var_i': 54, 'var_j': 43, 'quadratic_cost': 2.0}, {'var_i': 54, 'var_j': 44, 'quadratic_cost': 3.0}, {'var_i': 54, 'var_j': 45, 'quadratic_cost': 4.0}, {'var_i': 54, 'var_j': 46, 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'quadratic_cost': 6.0}, {'var_i': 55, 'var_j': 30, 'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 31, 'quadratic_cost': 10.0}, {'var_i': 55, 'var_j': 32, 'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 33, 'quadratic_cost': 4.0}, {'var_i': 55, 'var_j': 34, 'quadratic_cost': 1.0}, {'var_i': 55, 'var_j': 35, 'quadratic_cost': 6.0}, {'var_i': 55, 'var_j': 36, 'quadratic_cost': 3.0}, {'var_i': 55, 'var_j': 37, 'quadratic_cost': 7.0}, {'var_i': 55, 'var_j': 38, 'quadratic_cost': 1.0}, {'var_i': 55, 'var_j': 39, 'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 40, 'quadratic_cost': 5.0}, {'var_i': 55, 'var_j': 41, 'quadratic_cost': 7.0}, {'var_i': 55, 'var_j': 42, 'quadratic_cost': 9.0}, {'var_i': 55, 'var_j': 43, 'quadratic_cost': 6.0}, {'var_i': 55, 'var_j': 44, 'quadratic_cost': 9.0}, {'var_i': 55, 'var_j': 45, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 46, 'quadratic_cost': 10.0}, {'var_i': 55, 'var_j': 47, 'quadratic_cost': 7.0}, {'var_i': 55, 'var_j': 48, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 49, 'quadratic_cost': 2.0}, {'var_i': 55, 'var_j': 50, 'quadratic_cost': 8.0}, {'var_i': 55, 'var_j': 51, 'quadratic_cost': 3.0}, {'var_i': 55, 'var_j': 52, 'quadratic_cost': 10.0}, {'var_i': 55, 'var_j': 53, 'quadratic_cost': 1.0}, {'var_i': 55, 'var_j': 54, 'quadratic_cost': 6.0}, {'var_i': 55, 'var_j': 55, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 'T', 'to': 'A', 'var_index': 0}, {'from': 'T', 'to': 'B', 'var_index': 1}, {'from': 'T', 'to': 'C', 'var_index': 2}, {'from': 'T', 'to': 'D', 'var_index': 3}, {'from': 'T', 'to': 'E', 'var_index': 4}, {'from': 'T', 'to': 'F', 'var_index': 5}, {'from': 'T', 'to': 'G', 'var_index': 6}, {'from': 'T', 'to': 'H', 'var_index': 7}, {'from': 'T', 'to': 'I', 'var_index': 8}, {'from': 'T', 'to': 'J', 'var_index': 9}, {'from': 'T', 'to': 'K', 'var_index': 10}, {'from': 'T', 'to': 'L', 'var_index': 11}, {'from': 'T', 'to': 'M', 'var_index': 12}, {'from': 'T', 'to': 'N', 'var_index': 13}, {'from': 'T', 'to': 'O', 'var_index': 14}, {'from': 'T', 'to': 'P', 'var_index': 15}, {'from': 'T', 'to': 'Q', 'var_index': 16}, {'from': 'T', 'to': 'R', 'var_index': 17}, {'from': 'T', 'to': 'S', 'var_index': 18}, {'from': 'A', 'to': 'U', 'var_index': 19}, {'from': 'B', 'to': 'U', 'var_index': 20}, {'from': 'C', 'to': 'U', 'var_index': 21}, {'from': 'D', 'to': 'U', 'var_index': 22}, {'from': 'E', 'to': 'U', 'var_index': 23}, {'from': 'F', 'to': 'U', 'var_index': 24}, {'from': 'G', 'to': 'U', 'var_index': 25}, {'from': 'H', 'to': 'U', 'var_index': 26}, {'from': 'I', 'to': 'U', 'var_index': 27}, {'from': 'J', 'to': 'U', 'var_index': 28}, {'from': 'K', 'to': 'U', 'var_index': 29}, {'from': 'L', 'to': 'U', 'var_index': 30}, {'from': 'M', 'to': 'U', 'var_index': 31}, {'from': 'N', 'to': 'U', 'var_index': 32}, {'from': 'O', 'to': 'U', 'var_index': 33}, {'from': 'P', 'to': 'U', 'var_index': 34}, {'from': 'Q', 'to': 'U', 'var_index': 35}, {'from': 'R', 'to': 'U', 'var_index': 36}, {'from': 'S', 'to': 'U', 'var_index': 37}, {'from': 'A', 'to': 'B', 'var_index': 38}, {'from': 'B', 'to': 'C', 'var_index': 39}, {'from': 'C', 'to': 'D', 'var_index': 40}, {'from': 'D', 'to': 'E', 'var_index': 41}, {'from': 'E', 'to': 'F', 'var_index': 42}, {'from': 'F', 'to': 'G', 'var_index': 43}, {'from': 'G', 'to': 'H', 'var_index': 44}, {'from': 'H', 'to': 'I', 'var_index': 45}, {'from': 'I', 'to': 'J', 'var_index': 46}, {'from': 'J', 'to': 'K', 'var_index': 47}, {'from': 'K', 'to': 'L', 'var_index': 48}, {'from': 'L', 'to': 'M', 'var_index': 49}, {'from': 'M', 'to': 'N', 'var_index': 50}, {'from': 'N', 'to': 'O', 'var_index': 51}, {'from': 'O', 'to': 'P', 'var_index': 52}, {'from': 'P', 'to': 'Q', 'var_index': 53}, {'from': 'Q', 'to': 'R', 'var_index': 54}, {'from': 'R', 'to': 'S', 'var_index': 55}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J', 10: 'K', 11: 'L', 12: 'M', 13: 'N', 14: 'O', 15: 'P', 16: 'Q', 17: 'R', 18: 'S', 19: 'T', 20: 'U'}}","['T', 'L', 'U']",49,json,names
QSPP,QSPP,"I pictured a small inspection team moving through the water network from the entry valve to the exit gate, following only the pipes that let the water flow the right way. They have to pick one continuous route and list the places they pass in order — starting at the entry and finishing at the exit — with every step following a permitted flow. Each pipe on the route takes some inspection time, and some pipe combinations create extra headaches if both are inspected, plus a few pipes have their own extra penalties. The goal is to pick the single route that makes the total inspection burden as small as possible by adding up each segment’s time and any extra penalties for pairs (including any self-penalties). The concrete map, times, and penalty details are shown below.

I see 24 distinct junctions and 35 directed pipe segments; the valid locations are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, the entry valve is at 22 and the exit gate at 23.

| pipe_from_node | pipe_to_node | pipe_segment_id |
|---|---|---|
| 22 | 0 | 0 |
| 22 | 11 | 1 |
| 10 | 23 | 2 |
| 21 | 23 | 3 |
| 0 | 1 | 4 |
| 0 | 11 | 5 |
| 1 | 2 | 6 |
| 1 | 12 | 7 |
| 2 | 3 | 8 |
| 2 | 13 | 9 |
| 3 | 4 | 10 |
| 3 | 14 | 11 |
| 4 | 5 | 12 |
| 4 | 15 | 13 |
| 5 | 6 | 14 |
| 5 | 16 | 15 |
| 6 | 7 | 16 |
| 6 | 17 | 17 |
| 7 | 8 | 18 |
| 7 | 18 | 19 |
| 8 | 9 | 20 |
| 8 | 19 | 21 |
| 9 | 10 | 22 |
| 9 | 20 | 23 |
| 10 | 21 | 24 |
| 11 | 12 | 25 |
| 12 | 13 | 26 |
| 13 | 14 | 27 |
| 14 | 15 | 28 |
| 15 | 16 | 29 |
| 16 | 17 | 30 |
| 17 | 18 | 31 |
| 18 | 19 | 32 |
| 19 | 20 | 33 |
| 20 | 21 | 34 |

| pipe_segment_id | inspection_time |
|---|---|
| 0 | 7.0 |
| 1 | 6.0 |
| 2 | 4.0 |
| 3 | 3.0 |
| 4 | 9.0 |
| 5 | 10.0 |
| 6 | 2.0 |
| 7 | 5.0 |
| 8 | 4.0 |
| 9 | 2.0 |
| 10 | 7.0 |
| 11 | 6.0 |
| 12 | 5.0 |
| 13 | 6.0 |
| 14 | 5.0 |
| 15 | 2.0 |
| 16 | 7.0 |
| 17 | 3.0 |
| 18 | 8.0 |
| 19 | 1.0 |
| 20 | 2.0 |
| 21 | 3.0 |
| 22 | 6.0 |
| 23 | 7.0 |
| 24 | 8.0 |
| 25 | 8.0 |
| 26 | 2.0 |
| 27 | 2.0 |
| 28 | 4.0 |
| 29 | 7.0 |
| 30 | 10.0 |
| 31 | 9.0 |
| 32 | 6.0 |
| 33 | 8.0 |
| 34 | 7.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (pipe_i_id, pipe_j_id). If two pipe_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| pipe_i_id\pipe_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 7.0 | 5.0 | 9.0 | 6.0 | 1.0 | 9.0 | 1.0 | 7.0 | 7.0 | 6.0 | 1.0 | 1.0 | 7.0 | 9.0 | 10.0 | 8.0 | 7.0 | 10.0 | 2.0 | 9.0 | 4.0 | 6.0 | 10.0 | 8.0 | 7.0 | 6.0 | 2.0 | 9.0 | 10.0 | 1.0 | 6.0 | 3.0 | 3.0 | 10.0 |
| 1 | 7.0 | 10.0 | 10.0 | 10.0 | 9.0 | 1.0 | 10.0 | 4.0 | 3.0 | 5.0 | 10.0 | 4.0 | 5.0 | 3.0 | 8.0 | 6.0 | 8.0 | 7.0 | 8.0 | 5.0 | 10.0 | 8.0 | 10.0 | 2.0 | 6.0 | 1.0 | 5.0 | 6.0 | 9.0 | 2.0 | 7.0 | 10.0 | 1.0 | 9.0 | 3.0 |
| 2 | 5.0 | 10.0 | 8.0 | 3.0 | 4.0 | 5.0 | 9.0 | 2.0 | 1.0 | 4.0 | 10.0 | 2.0 | 4.0 | 4.0 | 2.0 | 10.0 | 6.0 | 10.0 | 6.0 | 1.0 | 2.0 | 7.0 | 5.0 | 10.0 | 5.0 | 2.0 | 3.0 | 2.0 | 3.0 | 9.0 | 6.0 | 6.0 | 4.0 | 2.0 | 6.0 |
| 3 | 9.0 | 10.0 | 3.0 | 2.0 | 1.0 | 5.0 | 8.0 | 4.0 | 2.0 | 5.0 | 2.0 | 8.0 | 4.0 | 8.0 | 4.0 | 10.0 | 8.0 | 5.0 | 1.0 | 8.0 | 5.0 | 3.0 | 7.0 | 4.0 | 10.0 | 3.0 | 2.0 | 4.0 | 9.0 | 10.0 | 3.0 | 6.0 | 8.0 | 8.0 | 10.0 |
| 4 | 6.0 | 9.0 | 4.0 | 1.0 | 9.0 | 6.0 | 2.0 | 2.0 | 10.0 | 9.0 | 6.0 | 6.0 | 1.0 | 2.0 | 2.0 | 10.0 | 7.0 | 4.0 | 2.0 | 6.0 | 9.0 | 4.0 | 3.0 | 2.0 | 10.0 | 3.0 | 10.0 | 10.0 | 1.0 | 2.0 | 9.0 | 6.0 | 1.0 | 1.0 | 2.0 |
| 5 | 1.0 | 1.0 | 5.0 | 5.0 | 6.0 | 2.0 | 5.0 | 1.0 | 6.0 | 7.0 | 9.0 | 6.0 | 9.0 | 8.0 | 10.0 | 2.0 | 9.0 | 4.0 | 10.0 | 8.0 | 6.0 | 6.0 | 9.0 | 8.0 | 5.0 | 3.0 | 2.0 | 4.0 | 8.0 | 7.0 | 5.0 | 4.0 | 8.0 | 10.0 | 8.0 |
| 6 | 9.0 | 10.0 | 9.0 | 8.0 | 2.0 | 5.0 | 9.0 | 2.0 | 3.0 | 1.0 | 8.0 | 9.0 | 6.0 | 3.0 | 9.0 | 9.0 | 5.0 | 8.0 | 6.0 | 10.0 | 1.0 | 4.0 | 9.0 | 3.0 | 7.0 | 8.0 | 5.0 | 2.0 | 10.0 | 8.0 | 9.0 | 5.0 | 8.0 | 9.0 | 8.0 |
| 7 | 1.0 | 4.0 | 2.0 | 4.0 | 2.0 | 1.0 | 2.0 | 9.0 | 1.0 | 5.0 | 7.0 | 1.0 | 4.0 | 4.0 | 4.0 | 8.0 | 3.0 | 6.0 | 7.0 | 10.0 | 7.0 | 7.0 | 9.0 | 4.0 | 9.0 | 9.0 | 10.0 | 3.0 | 9.0 | 4.0 | 3.0 | 10.0 | 8.0 | 2.0 | 6.0 |
| 8 | 7.0 | 3.0 | 1.0 | 2.0 | 10.0 | 6.0 | 3.0 | 1.0 | 7.0 | 1.0 | 2.0 | 2.0 | 8.0 | 6.0 | 6.0 | 8.0 | 3.0 | 8.0 | 3.0 | 2.0 | 4.0 | 6.0 | 3.0 | 8.0 | 4.0 | 7.0 | 1.0 | 3.0 | 5.0 | 6.0 | 1.0 | 1.0 | 2.0 | 3.0 | 5.0 |
| 9 | 7.0 | 5.0 | 4.0 | 5.0 | 9.0 | 7.0 | 1.0 | 5.0 | 1.0 | 7.0 | 8.0 | 5.0 | 6.0 | 8.0 | 5.0 | 6.0 | 9.0 | 6.0 | 3.0 | 4.0 | 10.0 | 5.0 | 4.0 | 8.0 | 7.0 | 7.0 | 4.0 | 8.0 | 9.0 | 2.0 | 5.0 | 6.0 | 5.0 | 9.0 | 3.0 |
| 10 | 6.0 | 10.0 | 10.0 | 2.0 | 6.0 | 9.0 | 8.0 | 7.0 | 2.0 | 8.0 | 10.0 | 7.0 | 3.0 | 6.0 | 10.0 | 10.0 | 8.0 | 7.0 | 4.0 | 8.0 | 2.0 | 3.0 | 2.0 | 2.0 | 6.0 | 5.0 | 9.0 | 10.0 | 10.0 | 6.0 | 9.0 | 10.0 | 6.0 | 7.0 | 10.0 |
| 11 | 1.0 | 4.0 | 2.0 | 8.0 | 6.0 | 6.0 | 9.0 | 1.0 | 2.0 | 5.0 | 7.0 | 8.0 | 6.0 | 3.0 | 1.0 | 7.0 | 8.0 | 9.0 | 1.0 | 9.0 | 4.0 | 7.0 | 8.0 | 1.0 | 8.0 | 8.0 | 10.0 | 9.0 | 8.0 | 3.0 | 8.0 | 5.0 | 10.0 | 6.0 | 8.0 |
| 12 | 1.0 | 5.0 | 4.0 | 4.0 | 1.0 | 9.0 | 6.0 | 4.0 | 8.0 | 6.0 | 3.0 | 6.0 | 10.0 | 2.0 | 7.0 | 2.0 | 2.0 | 5.0 | 3.0 | 4.0 | 1.0 | 4.0 | 9.0 | 3.0 | 3.0 | 4.0 | 1.0 | 3.0 | 6.0 | 5.0 | 3.0 | 8.0 | 7.0 | 5.0 | 9.0 |
| 13 | 7.0 | 3.0 | 4.0 | 8.0 | 2.0 | 8.0 | 3.0 | 4.0 | 6.0 | 8.0 | 6.0 | 3.0 | 2.0 | 5.0 | 6.0 | 8.0 | 2.0 | 8.0 | 4.0 | 1.0 | 5.0 | 5.0 | 9.0 | 1.0 | 10.0 | 8.0 | 8.0 | 7.0 | 3.0 | 6.0 | 3.0 | 9.0 | 9.0 | 2.0 | 8.0 |
| 14 | 9.0 | 8.0 | 2.0 | 4.0 | 2.0 | 10.0 | 9.0 | 4.0 | 6.0 | 5.0 | 10.0 | 1.0 | 7.0 | 6.0 | 4.0 | 6.0 | 1.0 | 6.0 | 7.0 | 5.0 | 9.0 | 10.0 | 1.0 | 2.0 | 6.0 | 7.0 | 10.0 | 10.0 | 8.0 | 9.0 | 4.0 | 10.0 | 4.0 | 9.0 | 2.0 |
| 15 | 10.0 | 6.0 | 10.0 | 10.0 | 10.0 | 2.0 | 9.0 | 8.0 | 8.0 | 6.0 | 10.0 | 7.0 | 2.0 | 8.0 | 6.0 | 4.0 | 9.0 | 3.0 | 4.0 | 1.0 | 8.0 | 3.0 | 9.0 | 4.0 | 2.0 | 2.0 | 1.0 | 3.0 | 3.0 | 9.0 | 1.0 | 5.0 | 10.0 | 7.0 | 6.0 |
| 16 | 8.0 | 8.0 | 6.0 | 8.0 | 7.0 | 9.0 | 5.0 | 3.0 | 3.0 | 9.0 | 8.0 | 8.0 | 2.0 | 2.0 | 1.0 | 9.0 | 8.0 | 8.0 | 6.0 | 9.0 | 1.0 | 9.0 | 10.0 | 7.0 | 6.0 | 4.0 | 8.0 | 8.0 | 9.0 | 8.0 | 10.0 | 5.0 | 7.0 | 10.0 | 4.0 |
| 17 | 7.0 | 7.0 | 10.0 | 5.0 | 4.0 | 4.0 | 8.0 | 6.0 | 8.0 | 6.0 | 7.0 | 9.0 | 5.0 | 8.0 | 6.0 | 3.0 | 8.0 | 6.0 | 9.0 | 6.0 | 7.0 | 7.0 | 5.0 | 6.0 | 1.0 | 1.0 | 6.0 | 1.0 | 5.0 | 5.0 | 4.0 | 1.0 | 4.0 | 7.0 | 5.0 |
| 18 | 10.0 | 8.0 | 6.0 | 1.0 | 2.0 | 10.0 | 6.0 | 7.0 | 3.0 | 3.0 | 4.0 | 1.0 | 3.0 | 4.0 | 7.0 | 4.0 | 6.0 | 9.0 | 5.0 | 4.0 | 2.0 | 9.0 | 1.0 | 10.0 | 7.0 | 6.0 | 1.0 | 1.0 | 6.0 | 1.0 | 3.0 | 2.0 | 5.0 | 5.0 | 7.0 |
| 19 | 2.0 | 5.0 | 1.0 | 8.0 | 6.0 | 8.0 | 10.0 | 10.0 | 2.0 | 4.0 | 8.0 | 9.0 | 4.0 | 1.0 | 5.0 | 1.0 | 9.0 | 6.0 | 4.0 | 8.0 | 9.0 | 1.0 | 6.0 | 8.0 | 3.0 | 10.0 | 9.0 | 6.0 | 1.0 | 8.0 | 8.0 | 1.0 | 10.0 | 10.0 | 10.0 |
| 20 | 9.0 | 10.0 | 2.0 | 5.0 | 9.0 | 6.0 | 1.0 | 7.0 | 4.0 | 10.0 | 2.0 | 4.0 | 1.0 | 5.0 | 9.0 | 8.0 | 1.0 | 7.0 | 2.0 | 9.0 | 10.0 | 9.0 | 10.0 | 4.0 | 9.0 | 4.0 | 4.0 | 8.0 | 5.0 | 10.0 | 7.0 | 2.0 | 4.0 | 10.0 | 1.0 |
| 21 | 4.0 | 8.0 | 7.0 | 3.0 | 4.0 | 6.0 | 4.0 | 7.0 | 6.0 | 5.0 | 3.0 | 7.0 | 4.0 | 5.0 | 10.0 | 3.0 | 9.0 | 7.0 | 9.0 | 1.0 | 9.0 | 6.0 | 2.0 | 5.0 | 2.0 | 8.0 | 8.0 | 8.0 | 2.0 | 7.0 | 9.0 | 6.0 | 1.0 | 5.0 | 10.0 |
| 22 | 6.0 | 10.0 | 5.0 | 7.0 | 3.0 | 9.0 | 9.0 | 9.0 | 3.0 | 4.0 | 2.0 | 8.0 | 9.0 | 9.0 | 1.0 | 9.0 | 10.0 | 5.0 | 1.0 | 6.0 | 10.0 | 2.0 | 7.0 | 8.0 | 6.0 | 7.0 | 5.0 | 6.0 | 3.0 | 6.0 | 5.0 | 4.0 | 7.0 | 9.0 | 8.0 |
| 23 | 10.0 | 2.0 | 10.0 | 4.0 | 2.0 | 8.0 | 3.0 | 4.0 | 8.0 | 8.0 | 2.0 | 1.0 | 3.0 | 1.0 | 2.0 | 4.0 | 7.0 | 6.0 | 10.0 | 8.0 | 4.0 | 5.0 | 8.0 | 9.0 | 10.0 | 7.0 | 3.0 | 9.0 | 2.0 | 10.0 | 2.0 | 3.0 | 7.0 | 2.0 | 8.0 |
| 24 | 8.0 | 6.0 | 5.0 | 10.0 | 10.0 | 5.0 | 7.0 | 9.0 | 4.0 | 7.0 | 6.0 | 8.0 | 3.0 | 10.0 | 6.0 | 2.0 | 6.0 | 1.0 | 7.0 | 3.0 | 9.0 | 2.0 | 6.0 | 10.0 | 10.0 | 2.0 | 2.0 | 5.0 | 8.0 | 3.0 | 9.0 | 3.0 | 3.0 | 2.0 | 1.0 |
| 25 | 7.0 | 1.0 | 2.0 | 3.0 | 3.0 | 3.0 | 8.0 | 9.0 | 7.0 | 7.0 | 5.0 | 8.0 | 4.0 | 8.0 | 7.0 | 2.0 | 4.0 | 1.0 | 6.0 | 10.0 | 4.0 | 8.0 | 7.0 | 7.0 | 2.0 | 3.0 | 5.0 | 4.0 | 4.0 | 9.0 | 10.0 | 3.0 | 5.0 | 5.0 | 8.0 |
| 26 | 6.0 | 5.0 | 3.0 | 2.0 | 10.0 | 2.0 | 5.0 | 10.0 | 1.0 | 4.0 | 9.0 | 10.0 | 1.0 | 8.0 | 10.0 | 1.0 | 8.0 | 6.0 | 1.0 | 9.0 | 4.0 | 8.0 | 5.0 | 3.0 | 2.0 | 5.0 | 7.0 | 3.0 | 4.0 | 6.0 | 4.0 | 9.0 | 7.0 | 2.0 | 6.0 |
| 27 | 2.0 | 6.0 | 2.0 | 4.0 | 10.0 | 4.0 | 2.0 | 3.0 | 3.0 | 8.0 | 10.0 | 9.0 | 3.0 | 7.0 | 10.0 | 3.0 | 8.0 | 1.0 | 1.0 | 6.0 | 8.0 | 8.0 | 6.0 | 9.0 | 5.0 | 4.0 | 3.0 | 3.0 | 5.0 | 5.0 | 6.0 | 5.0 | 10.0 | 6.0 | 6.0 |
| 28 | 9.0 | 9.0 | 3.0 | 9.0 | 1.0 | 8.0 | 10.0 | 9.0 | 5.0 | 9.0 | 10.0 | 8.0 | 6.0 | 3.0 | 8.0 | 3.0 | 9.0 | 5.0 | 6.0 | 1.0 | 5.0 | 2.0 | 3.0 | 2.0 | 8.0 | 4.0 | 4.0 | 5.0 | 6.0 | 5.0 | 9.0 | 7.0 | 6.0 | 2.0 | 4.0 |
| 29 | 10.0 | 2.0 | 9.0 | 10.0 | 2.0 | 7.0 | 8.0 | 4.0 | 6.0 | 2.0 | 6.0 | 3.0 | 5.0 | 6.0 | 9.0 | 9.0 | 8.0 | 5.0 | 1.0 | 8.0 | 10.0 | 7.0 | 6.0 | 10.0 | 3.0 | 9.0 | 6.0 | 5.0 | 5.0 | 2.0 | 2.0 | 1.0 | 3.0 | 6.0 | 9.0 |
| 30 | 1.0 | 7.0 | 6.0 | 3.0 | 9.0 | 5.0 | 9.0 | 3.0 | 1.0 | 5.0 | 9.0 | 8.0 | 3.0 | 3.0 | 4.0 | 1.0 | 10.0 | 4.0 | 3.0 | 8.0 | 7.0 | 9.0 | 5.0 | 2.0 | 9.0 | 10.0 | 4.0 | 6.0 | 9.0 | 2.0 | 10.0 | 9.0 | 3.0 | 6.0 | 9.0 |
| 31 | 6.0 | 10.0 | 6.0 | 6.0 | 6.0 | 4.0 | 5.0 | 10.0 | 1.0 | 6.0 | 10.0 | 5.0 | 8.0 | 9.0 | 10.0 | 5.0 | 5.0 | 1.0 | 2.0 | 1.0 | 2.0 | 6.0 | 4.0 | 3.0 | 3.0 | 3.0 | 9.0 | 5.0 | 7.0 | 1.0 | 9.0 | 10.0 | 7.0 | 9.0 | 5.0 |
| 32 | 3.0 | 1.0 | 4.0 | 8.0 | 1.0 | 8.0 | 8.0 | 8.0 | 2.0 | 5.0 | 6.0 | 10.0 | 7.0 | 9.0 | 4.0 | 10.0 | 7.0 | 4.0 | 5.0 | 10.0 | 4.0 | 1.0 | 7.0 | 7.0 | 3.0 | 5.0 | 7.0 | 10.0 | 6.0 | 3.0 | 3.0 | 7.0 | 8.0 | 4.0 | 1.0 |
| 33 | 3.0 | 9.0 | 2.0 | 8.0 | 1.0 | 10.0 | 9.0 | 2.0 | 3.0 | 9.0 | 7.0 | 6.0 | 5.0 | 2.0 | 9.0 | 7.0 | 10.0 | 7.0 | 5.0 | 10.0 | 10.0 | 5.0 | 9.0 | 2.0 | 2.0 | 5.0 | 2.0 | 6.0 | 2.0 | 6.0 | 6.0 | 9.0 | 4.0 | 3.0 | 6.0 |
| 34 | 10.0 | 3.0 | 6.0 | 10.0 | 2.0 | 8.0 | 8.0 | 6.0 | 5.0 | 3.0 | 10.0 | 8.0 | 9.0 | 8.0 | 2.0 | 6.0 | 4.0 | 5.0 | 7.0 | 10.0 | 1.0 | 10.0 | 8.0 | 8.0 | 1.0 | 8.0 | 6.0 | 6.0 | 4.0 | 9.0 | 9.0 | 5.0 | 1.0 | 6.0 | 9.0 |

I will use these details to pick the single route with the smallest total inspection burden.

Oh, and to keep things machine-friendly, please return the chosen route in a tiny JSON wrapper like this:

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of places the team walks through — start node first, end node last — and nothing else. It's just a sketch of the shape I want, not the actual answer; when you fill it in, put only the node identifiers (no edge ids, no times, no penalties).

Please use the exact identifiers from the problem input, with no renaming or invented labels.  
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'edges': [{'from': 22, 'to': 0, 'var_index': 0}, {'from': 22, 'to': 11, 'var_index': 1}, {'from': 10, 'to': 23, 'var_index': 2}, {'from': 21, 'to': 23, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 11, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 12, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 13, 'var_index': 9}, {'from': 3, 'to': 4, 'var_index': 10}, {'from': 3, 'to': 14, 'var_index': 11}, {'from': 4, 'to': 5, 'var_index': 12}, {'from': 4, 'to': 15, 'var_index': 13}, {'from': 5, 'to': 6, 'var_index': 14}, {'from': 5, 'to': 16, 'var_index': 15}, {'from': 6, 'to': 7, 'var_index': 16}, {'from': 6, 'to': 17, 'var_index': 17}, {'from': 7, 'to': 8, 'var_index': 18}, {'from': 7, 'to': 18, 'var_index': 19}, {'from': 8, 'to': 9, 'var_index': 20}, {'from': 8, 'to': 19, 'var_index': 21}, {'from': 9, 'to': 10, 'var_index': 22}, {'from': 9, 'to': 20, 'var_index': 23}, {'from': 10, 'to': 21, 'var_index': 24}, {'from': 11, 'to': 12, 'var_index': 25}, {'from': 12, 'to': 13, 'var_index': 26}, {'from': 13, 'to': 14, 'var_index': 27}, {'from': 14, 'to': 15, 'var_index': 28}, {'from': 15, 'to': 16, 'var_index': 29}, {'from': 16, 'to': 17, 'var_index': 30}, {'from': 17, 'to': 18, 'var_index': 31}, {'from': 18, 'to': 19, 'var_index': 32}, {'from': 19, 'to': 20, 'var_index': 33}, {'from': 20, 'to': 21, 'var_index': 34}], 'objective': {'constant': 0.0, 'linear': [7.0, 6.0, 4.0, 3.0, 9.0, 10.0, 2.0, 5.0, 4.0, 2.0, 7.0, 6.0, 5.0, 6.0, 5.0, 2.0, 7.0, 3.0, 8.0, 1.0, 2.0, 3.0, 6.0, 7.0, 8.0, 8.0, 2.0, 2.0, 4.0, 7.0, 10.0, 9.0, 6.0, 8.0, 7.0], 'quadratic': [[7.0, 7.0, 5.0, 9.0, 6.0, 1.0, 9.0, 1.0, 7.0, 7.0, 6.0, 1.0, 1.0, 7.0, 9.0, 10.0, 8.0, 7.0, 10.0, 2.0, 9.0, 4.0, 6.0, 10.0, 8.0, 7.0, 6.0, 2.0, 9.0, 10.0, 1.0, 6.0, 3.0, 3.0, 10.0], [7.0, 10.0, 10.0, 10.0, 9.0, 1.0, 10.0, 4.0, 3.0, 5.0, 10.0, 4.0, 5.0, 3.0, 8.0, 6.0, 8.0, 7.0, 8.0, 5.0, 10.0, 8.0, 10.0, 2.0, 6.0, 1.0, 5.0, 6.0, 9.0, 2.0, 7.0, 10.0, 1.0, 9.0, 3.0], [5.0, 10.0, 8.0, 3.0, 4.0, 5.0, 9.0, 2.0, 1.0, 4.0, 10.0, 2.0, 4.0, 4.0, 2.0, 10.0, 6.0, 10.0, 6.0, 1.0, 2.0, 7.0, 5.0, 10.0, 5.0, 2.0, 3.0, 2.0, 3.0, 9.0, 6.0, 6.0, 4.0, 2.0, 6.0], [9.0, 10.0, 3.0, 2.0, 1.0, 5.0, 8.0, 4.0, 2.0, 5.0, 2.0, 8.0, 4.0, 8.0, 4.0, 10.0, 8.0, 5.0, 1.0, 8.0, 5.0, 3.0, 7.0, 4.0, 10.0, 3.0, 2.0, 4.0, 9.0, 10.0, 3.0, 6.0, 8.0, 8.0, 10.0], [6.0, 9.0, 4.0, 1.0, 9.0, 6.0, 2.0, 2.0, 10.0, 9.0, 6.0, 6.0, 1.0, 2.0, 2.0, 10.0, 7.0, 4.0, 2.0, 6.0, 9.0, 4.0, 3.0, 2.0, 10.0, 3.0, 10.0, 10.0, 1.0, 2.0, 9.0, 6.0, 1.0, 1.0, 2.0], [1.0, 1.0, 5.0, 5.0, 6.0, 2.0, 5.0, 1.0, 6.0, 7.0, 9.0, 6.0, 9.0, 8.0, 10.0, 2.0, 9.0, 4.0, 10.0, 8.0, 6.0, 6.0, 9.0, 8.0, 5.0, 3.0, 2.0, 4.0, 8.0, 7.0, 5.0, 4.0, 8.0, 10.0, 8.0], [9.0, 10.0, 9.0, 8.0, 2.0, 5.0, 9.0, 2.0, 3.0, 1.0, 8.0, 9.0, 6.0, 3.0, 9.0, 9.0, 5.0, 8.0, 6.0, 10.0, 1.0, 4.0, 9.0, 3.0, 7.0, 8.0, 5.0, 2.0, 10.0, 8.0, 9.0, 5.0, 8.0, 9.0, 8.0], [1.0, 4.0, 2.0, 4.0, 2.0, 1.0, 2.0, 9.0, 1.0, 5.0, 7.0, 1.0, 4.0, 4.0, 4.0, 8.0, 3.0, 6.0, 7.0, 10.0, 7.0, 7.0, 9.0, 4.0, 9.0, 9.0, 10.0, 3.0, 9.0, 4.0, 3.0, 10.0, 8.0, 2.0, 6.0], [7.0, 3.0, 1.0, 2.0, 10.0, 6.0, 3.0, 1.0, 7.0, 1.0, 2.0, 2.0, 8.0, 6.0, 6.0, 8.0, 3.0, 8.0, 3.0, 2.0, 4.0, 6.0, 3.0, 8.0, 4.0, 7.0, 1.0, 3.0, 5.0, 6.0, 1.0, 1.0, 2.0, 3.0, 5.0], [7.0, 5.0, 4.0, 5.0, 9.0, 7.0, 1.0, 5.0, 1.0, 7.0, 8.0, 5.0, 6.0, 8.0, 5.0, 6.0, 9.0, 6.0, 3.0, 4.0, 10.0, 5.0, 4.0, 8.0, 7.0, 7.0, 4.0, 8.0, 9.0, 2.0, 5.0, 6.0, 5.0, 9.0, 3.0], [6.0, 10.0, 10.0, 2.0, 6.0, 9.0, 8.0, 7.0, 2.0, 8.0, 10.0, 7.0, 3.0, 6.0, 10.0, 10.0, 8.0, 7.0, 4.0, 8.0, 2.0, 3.0, 2.0, 2.0, 6.0, 5.0, 9.0, 10.0, 10.0, 6.0, 9.0, 10.0, 6.0, 7.0, 10.0], [1.0, 4.0, 2.0, 8.0, 6.0, 6.0, 9.0, 1.0, 2.0, 5.0, 7.0, 8.0, 6.0, 3.0, 1.0, 7.0, 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