KMST/KMST_L_context.csv

task_name,problem_type,instruction,instance,solution,obj,instance_variant,solution_variant,context_index,input_format,input_index_base
KMST,KMST,"There’s a planning task where a team must select a predetermined number of city blocks and connect them with newly built streets so those blocks become one connected cluster, with no closed loops of road and no duplicate segments. What separates a good plan from a bad one is how cheap the whole construction comes out: just add up the price of each new street and the smaller that total, the better the plan. The exact blocks, candidate streets, and their costs are shown below.

{
  ""total_city_blocks"": 22,
  ""candidate_streets_count"": 28,
  ""edges"": [
    {
      ""block_endpoint_u"": ""Q"",
      ""block_endpoint_v"": ""R"",
      ""construction_cost"": 396.0
    },
    {
      ""block_endpoint_u"": ""Q"",
      ""block_endpoint_v"": ""T"",
      ""construction_cost"": 268.0
    },
    {
      ""block_endpoint_u"": ""Q"",
      ""block_endpoint_v"": ""C"",
      ""construction_cost"": 2.0
    },
    {
      ""block_endpoint_u"": ""R"",
      ""block_endpoint_v"": ""J"",
      ""construction_cost"": 370.0
    },
    {
      ""block_endpoint_u"": ""R"",
      ""block_endpoint_v"": ""U"",
      ""construction_cost"": 286.0
    },
    {
      ""block_endpoint_u"": ""R"",
      ""block_endpoint_v"": ""H"",
      ""construction_cost"": 466.0
    },
    {
      ""block_endpoint_u"": ""A"",
      ""block_endpoint_v"": ""B"",
      ""construction_cost"": 578.0
    },
    {
      ""block_endpoint_u"": ""A"",
      ""block_endpoint_v"": ""C"",
      ""construction_cost"": 608.0
    },
    {
      ""block_endpoint_u"": ""A"",
      ""block_endpoint_v"": ""D"",
      ""construction_cost"": 846.0
    },
    {
      ""block_endpoint_u"": ""A"",
      ""block_endpoint_v"": ""O"",
      ""construction_cost"": 283557.0
    },
    {
      ""block_endpoint_u"": ""B"",
      ""block_endpoint_v"": ""P"",
      ""construction_cost"": 792.0
    },
    {
      ""block_endpoint_u"": ""B"",
      ""block_endpoint_v"": ""F"",
      ""construction_cost"": 1110.0
    },
    {
      ""block_endpoint_u"": ""C"",
      ""block_endpoint_v"": ""I"",
      ""construction_cost"": 466.0
    },
    {
      ""block_endpoint_u"": ""D"",
      ""block_endpoint_v"": ""P"",
      ""construction_cost"": 147.0
    },
    {
      ""block_endpoint_u"": ""D"",
      ""block_endpoint_v"": ""V"",
      ""construction_cost"": 93.0
    },
    {
      ""block_endpoint_u"": ""E"",
      ""block_endpoint_v"": ""F"",
      ""construction_cost"": 945.0
    },
    {
      ""block_endpoint_u"": ""E"",
      ""block_endpoint_v"": ""G"",
      ""construction_cost"": 290.0
    },
    {
      ""block_endpoint_u"": ""E"",
      ""block_endpoint_v"": ""O"",
      ""construction_cost"": 283557.0
    },
    {
      ""block_endpoint_u"": ""G"",
      ""block_endpoint_v"": ""S"",
      ""construction_cost"": 623.0
    },
    {
      ""block_endpoint_u"": ""H"",
      ""block_endpoint_v"": ""I"",
      ""construction_cost"": 412.0
    },
    {
      ""block_endpoint_u"": ""H"",
      ""block_endpoint_v"": ""N"",
      ""construction_cost"": 333153.0
    },
    {
      ""block_endpoint_u"": ""I"",
      ""block_endpoint_v"": ""S"",
      ""construction_cost"": 367.0
    },
    {
      ""block_endpoint_u"": ""J"",
      ""block_endpoint_v"": ""K"",
      ""construction_cost"": 303.0
    },
    {
      ""block_endpoint_u"": ""K"",
      ""block_endpoint_v"": ""U"",
      ""construction_cost"": 369.0
    },
    {
      ""block_endpoint_u"": ""N"",
      ""block_endpoint_v"": ""L"",
      ""construction_cost"": 333323.0
    },
    {
      ""block_endpoint_u"": ""M"",
      ""block_endpoint_v"": ""S"",
      ""construction_cost"": 99.0
    },
    {
      ""block_endpoint_u"": ""V"",
      ""block_endpoint_v"": ""T"",
      ""construction_cost"": 816.0
    },
    {
      ""block_endpoint_u"": ""T"",
      ""block_endpoint_v"": ""U"",
      ""construction_cost"": 383.0
    }
  ],
  ""target_blocks_to_connect"": 7
}

If you want, send back the picked street segments in a tiny JSON snippet like this so it's easy to read and process:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

That ""solution"" list is just a set of street segments: each pair like [u1, v1] means ""connect block u1 to block v1"" with a new road. Think of it like filling out a short form — the JSON shows the shape I expect, not the actual answer.

Please use the exact identifiers from the instance input when you fill this in — 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”.""","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 17, 'v': 18, 'w': 396.0}, {'u': 17, 'v': 20, 'w': 268.0}, {'u': 17, 'v': 3, 'w': 2.0}, {'u': 18, 'v': 10, 'w': 370.0}, {'u': 18, 'v': 21, 'w': 286.0}, {'u': 18, 'v': 8, 'w': 466.0}, {'u': 1, 'v': 2, 'w': 578.0}, {'u': 1, 'v': 3, 'w': 608.0}, {'u': 1, 'v': 4, 'w': 846.0}, {'u': 1, 'v': 15, 'w': 283557.0}, {'u': 2, 'v': 16, 'w': 792.0}, {'u': 2, 'v': 6, 'w': 1110.0}, {'u': 3, 'v': 9, 'w': 466.0}, {'u': 4, 'v': 16, 'w': 147.0}, {'u': 4, 'v': 22, 'w': 93.0}, {'u': 5, 'v': 6, 'w': 945.0}, {'u': 5, 'v': 7, 'w': 290.0}, {'u': 5, 'v': 15, 'w': 283557.0}, {'u': 7, 'v': 19, 'w': 623.0}, {'u': 8, 'v': 9, 'w': 412.0}, {'u': 8, 'v': 14, 'w': 333153.0}, {'u': 9, 'v': 19, 'w': 367.0}, {'u': 10, 'v': 11, 'w': 303.0}, {'u': 11, 'v': 21, 'w': 369.0}, {'u': 14, 'v': 12, 'w': 333323.0}, {'u': 13, 'v': 19, 'w': 99.0}, {'u': 22, 'v': 20, 'w': 816.0}, {'u': 20, 'v': 21, 'w': 383.0}], 'k': 7, 'source_file': 'I076.stp', 'density': 0.12121212121212122}","[[17, 20], [3, 17], [3, 9], [9, 19], [13, 19], [20, 21]]",1585.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 'Q', 'v': 'R', 'w': 396.0}, {'u': 'Q', 'v': 'T', 'w': 268.0}, {'u': 'Q', 'v': 'C', 'w': 2.0}, {'u': 'R', 'v': 'J', 'w': 370.0}, {'u': 'R', 'v': 'U', 'w': 286.0}, {'u': 'R', 'v': 'H', 'w': 466.0}, {'u': 'A', 'v': 'B', 'w': 578.0}, {'u': 'A', 'v': 'C', 'w': 608.0}, {'u': 'A', 'v': 'D', 'w': 846.0}, {'u': 'A', 'v': 'O', 'w': 283557.0}, {'u': 'B', 'v': 'P', 'w': 792.0}, {'u': 'B', 'v': 'F', 'w': 1110.0}, {'u': 'C', 'v': 'I', 'w': 466.0}, {'u': 'D', 'v': 'P', 'w': 147.0}, {'u': 'D', 'v': 'V', 'w': 93.0}, {'u': 'E', 'v': 'F', 'w': 945.0}, {'u': 'E', 'v': 'G', 'w': 290.0}, {'u': 'E', 'v': 'O', 'w': 283557.0}, {'u': 'G', 'v': 'S', 'w': 623.0}, {'u': 'H', 'v': 'I', 'w': 412.0}, {'u': 'H', 'v': 'N', 'w': 333153.0}, {'u': 'I', 'v': 'S', 'w': 367.0}, {'u': 'J', 'v': 'K', 'w': 303.0}, {'u': 'K', 'v': 'U', 'w': 369.0}, {'u': 'N', 'v': 'L', 'w': 333323.0}, {'u': 'M', 'v': 'S', 'w': 99.0}, {'u': 'V', 'v': 'T', 'w': 816.0}, {'u': 'T', 'v': 'U', 'w': 383.0}], 'density': 0.12121212121212122, 'source_file': 'I076.stp', 'k': 7}","[['Q', 'T'], ['C', 'Q'], ['C', 'I'], ['I', 'S'], ['M', 'S'], ['T', 'U']]",1,json,names
KMST,KMST,"We had to lay out a small cluster: choose a set number of racks and wire them together with straight links so every machine in that set can reach every other, without creating redundant loops that would waste cable. Decisions are judged by total cable used — sum the lengths of the chosen links, and the setup with the lowest sum is best. The rule is to include exactly the required number of servers, make sure they’re all connected, and avoid any extra circular wiring. The concrete details are shown below.

We have 25 total servers, 31 potential links, and must pick exactly 12 servers to connect without cycles.
We can connect server 1 to server 2 with cable length 1914.0.
We can connect server 1 to server 3 with cable length 734.0.
We can connect server 1 to server 4 with cable length 2039.0.
We can connect server 2 to server 8 with cable length 370.0.
We can connect server 2 to server 10 with cable length 2606.0.
We can connect server 3 to server 8 with cable length 1108.0.
We can connect server 3 to server 9 with cable length 1202.0.
We can connect server 4 to server 9 with cable length 466.0.
We can connect server 4 to server 5 with cable length 2095.0.
We can connect server 5 to server 12 with cable length 460.0.
We can connect server 10 to server 18 with cable length 105.0.
We can connect server 10 to server 20 with cable length 681.0.
We can connect server 11 to server 6 with cable length 1286.0.
We can connect server 11 to server 16 with cable length 4717.0.
We can connect server 11 to server 19 with cable length 1791.0.
We can connect server 12 to server 7 with cable length 925.0.
We can connect server 12 to server 13 with cable length 626.0.
We can connect server 13 to server 23 with cable length 1058.0.
We can connect server 13 to server 15 with cable length 4936.0.
We can connect server 14 to server 23 with cable length 227.0.
We can connect server 14 to server 6 with cable length 859.0.
We can connect server 14 to server 17 with cable length 5927.0.
We can connect server 16 to server 0 with cable length 3440.0.
We can connect server 17 to server 0 with cable length 2225.0.
We can connect server 19 to server 18 with cable length 976.0.
We can connect server 19 to server 22 with cable length 546.0.
We can connect server 20 to server 21 with cable length 85.0.
We can connect server 21 to server 22 with cable length 1039.0.
We can connect server 23 to server 24 with cable length 2582.0.
We can connect server 6 to server 7 with cable length 1829.0.
We can connect server 18 to server 7 with cable length 3682.0.
We'll minimize total cable and ensure the chosen 12 servers form a connected, loop-free cluster.

When you send back the wiring plan, just paste the chosen links in this simple JSON shape so it's easy to parse and check:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of the links you picked; each inner pair like [u1, v1] is one straight connection between two racks (order doesn't matter — it's just the two endpoints). Think of it as a little checklist of which cables to lay between which racks.

This JSON is just a sketch of the shape I expect, not the actual answer — fill in the exact pair list for your instance. Also be sure to use the 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"".""","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 31, 'edges': [{'u': 2, 'v': 3, 'w': 1914.0}, {'u': 2, 'v': 4, 'w': 734.0}, {'u': 2, 'v': 5, 'w': 2039.0}, {'u': 3, 'v': 9, 'w': 370.0}, {'u': 3, 'v': 11, 'w': 2606.0}, {'u': 4, 'v': 9, 'w': 1108.0}, {'u': 4, 'v': 10, 'w': 1202.0}, {'u': 5, 'v': 10, 'w': 466.0}, {'u': 5, 'v': 6, 'w': 2095.0}, {'u': 6, 'v': 13, 'w': 460.0}, {'u': 11, 'v': 19, 'w': 105.0}, {'u': 11, 'v': 21, 'w': 681.0}, {'u': 12, 'v': 7, 'w': 1286.0}, {'u': 12, 'v': 17, 'w': 4717.0}, {'u': 12, 'v': 20, 'w': 1791.0}, {'u': 13, 'v': 8, 'w': 925.0}, {'u': 13, 'v': 14, 'w': 626.0}, {'u': 14, 'v': 24, 'w': 1058.0}, {'u': 14, 'v': 16, 'w': 4936.0}, {'u': 15, 'v': 24, 'w': 227.0}, {'u': 15, 'v': 7, 'w': 859.0}, {'u': 15, 'v': 18, 'w': 5927.0}, {'u': 17, 'v': 1, 'w': 3440.0}, {'u': 18, 'v': 1, 'w': 2225.0}, {'u': 20, 'v': 19, 'w': 976.0}, {'u': 20, 'v': 23, 'w': 546.0}, {'u': 21, 'v': 22, 'w': 85.0}, {'u': 22, 'v': 23, 'w': 1039.0}, {'u': 24, 'v': 25, 'w': 2582.0}, {'u': 7, 'v': 8, 'w': 1829.0}, {'u': 19, 'v': 8, 'w': 3682.0}], 'k': 12, 'source_file': 'I055.stp', 'density': 0.10333333333333333}","[[6, 13], [11, 19], [11, 21], [7, 12], [12, 20], [13, 14], [14, 24], [15, 24], [7, 15], [19, 20], [21, 22]]",8154.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 31, 'edges': [{'u': 1, 'v': 2, 'w': 1914.0}, {'u': 1, 'v': 3, 'w': 734.0}, {'u': 1, 'v': 4, 'w': 2039.0}, {'u': 2, 'v': 8, 'w': 370.0}, {'u': 2, 'v': 10, 'w': 2606.0}, {'u': 3, 'v': 8, 'w': 1108.0}, {'u': 3, 'v': 9, 'w': 1202.0}, {'u': 4, 'v': 9, 'w': 466.0}, {'u': 4, 'v': 5, 'w': 2095.0}, {'u': 5, 'v': 12, 'w': 460.0}, {'u': 10, 'v': 18, 'w': 105.0}, {'u': 10, 'v': 20, 'w': 681.0}, {'u': 11, 'v': 6, 'w': 1286.0}, {'u': 11, 'v': 16, 'w': 4717.0}, {'u': 11, 'v': 19, 'w': 1791.0}, {'u': 12, 'v': 7, 'w': 925.0}, {'u': 12, 'v': 13, 'w': 626.0}, {'u': 13, 'v': 23, 'w': 1058.0}, {'u': 13, 'v': 15, 'w': 4936.0}, {'u': 14, 'v': 23, 'w': 227.0}, {'u': 14, 'v': 6, 'w': 859.0}, {'u': 14, 'v': 17, 'w': 5927.0}, {'u': 16, 'v': 0, 'w': 3440.0}, {'u': 17, 'v': 0, 'w': 2225.0}, {'u': 19, 'v': 18, 'w': 976.0}, {'u': 19, 'v': 22, 'w': 546.0}, {'u': 20, 'v': 21, 'w': 85.0}, {'u': 21, 'v': 22, 'w': 1039.0}, {'u': 23, 'v': 24, 'w': 2582.0}, {'u': 6, 'v': 7, 'w': 1829.0}, {'u': 18, 'v': 7, 'w': 3682.0}], 'density': 0.10333333333333333, 'source_file': 'I055.stp', 'k': 12}","[[5, 12], [10, 18], [10, 20], [6, 11], [11, 19], [12, 13], [13, 23], [14, 23], [6, 14], [18, 19], [20, 21]]",2,markdown_table,0
KMST,KMST,"Someone on the planning team has to pick a set number of campsites and sketch paths between them so the selected sites become one connected cluster, and there can’t be any closed loops in the path layout. Better plans are the ones with the least total trail length: just sum all the individual path lengths to compare options. The rule is to use exactly that many campsites, don’t double-count spots, and make sure none of the chosen sites are left isolated. The detailed campsite list and distances appear below.

{
  ""total_campsites"": 24,
  ""total_candidate_trails"": 30,
  ""edges"": [
    {
      ""campsite_endpoint_u"": 0,
      ""campsite_endpoint_v"": 1,
      ""trail_length"": 420.0
    },
    {
      ""campsite_endpoint_u"": 0,
      ""campsite_endpoint_v"": 7,
      ""trail_length"": 275.0
    },
    {
      ""campsite_endpoint_u"": 0,
      ""campsite_endpoint_v"": 12,
      ""trail_length"": 700.0
    },
    {
      ""campsite_endpoint_u"": 1,
      ""campsite_endpoint_v"": 6,
      ""trail_length"": 275.0
    },
    {
      ""campsite_endpoint_u"": 1,
      ""campsite_endpoint_v"": 11,
      ""trail_length"": 445.0
    },
    {
      ""campsite_endpoint_u"": 11,
      ""campsite_endpoint_v"": 21,
      ""trail_length"": 1245.0
    },
    {
      ""campsite_endpoint_u"": 11,
      ""campsite_endpoint_v"": 12,
      ""trail_length"": 160.0
    },
    {
      ""campsite_endpoint_u"": 16,
      ""campsite_endpoint_v"": 17,
      ""trail_length"": 96.0
    },
    {
      ""campsite_endpoint_u"": 16,
      ""campsite_endpoint_v"": 5,
      ""trail_length"": 481.0
    },
    {
      ""campsite_endpoint_u"": 17,
      ""campsite_endpoint_v"": 10,
      ""trail_length"": 437.0
    },
    {
      ""campsite_endpoint_u"": 22,
      ""campsite_endpoint_v"": 20,
      ""trail_length"": 1738.0
    },
    {
      ""campsite_endpoint_u"": 22,
      ""campsite_endpoint_v"": 23,
      ""trail_length"": 1243.0
    },
    {
      ""campsite_endpoint_u"": 4,
      ""campsite_endpoint_v"": 13,
      ""trail_length"": 442.0
    },
    {
      ""campsite_endpoint_u"": 4,
      ""campsite_endpoint_v"": 18,
      ""trail_length"": 1463.0
    },
    {
      ""campsite_endpoint_u"": 4,
      ""campsite_endpoint_v"": 8,
      ""trail_length"": 1045.0
    },
    {
      ""campsite_endpoint_u"": 5,
      ""campsite_endpoint_v"": 15,
      ""trail_length"": 204.0
    },
    {
      ""campsite_endpoint_u"": 19,
      ""campsite_endpoint_v"": 23,
      ""trail_length"": 414.0
    },
    {
      ""campsite_endpoint_u"": 19,
      ""campsite_endpoint_v"": 20,
      ""trail_length"": 2534.0
    },
    {
      ""campsite_endpoint_u"": 13,
      ""campsite_endpoint_v"": 14,
      ""trail_length"": 310.0
    },
    {
      ""campsite_endpoint_u"": 13,
      ""campsite_endpoint_v"": 21,
      ""trail_length"": 1339.0
    },
    {
      ""campsite_endpoint_u"": 7,
      ""campsite_endpoint_v"": 6,
      ""trail_length"": 417.0
    },
    {
      ""campsite_endpoint_u"": 14,
      ""campsite_endpoint_v"": 8,
      ""trail_length"": 408.0
    },
    {
      ""campsite_endpoint_u"": 14,
      ""campsite_endpoint_v"": 3,
      ""trail_length"": 1991.0
    },
    {
      ""campsite_endpoint_u"": 15,
      ""campsite_endpoint_v"": 3,
      ""trail_length"": 1986.0
    },
    {
      ""campsite_endpoint_u"": 15,
      ""campsite_endpoint_v"": 9,
      ""trail_length"": 464.0
    },
    {
      ""campsite_endpoint_u"": 20,
      ""campsite_endpoint_v"": 18,
      ""trail_length"": 1444.0
    },
    {
      ""campsite_endpoint_u"": 21,
      ""campsite_endpoint_v"": 18,
      ""trail_length"": 1132.0
    },
    {
      ""campsite_endpoint_u"": 9,
      ""campsite_endpoint_v"": 2,
      ""trail_length"": 1987.0
    },
    {
      ""campsite_endpoint_u"": 9,
      ""campsite_endpoint_v"": 10,
      ""trail_length"": 781.0
    },
    {
      ""campsite_endpoint_u"": 2,
      ""campsite_endpoint_v"": 3,
      ""trail_length"": 529.0
    }
  ],
  ""target_campsite_count"": 12
}

When you send back the chosen paths, please stick to a little JSON sketch like this so it's easy to read and parse:

{
  ""solution"": [[camp1, camp2], [camp3, camp4], ...]
}

Here ""solution"" is a list of the trail segments you picked; each inner pair [A, B] is a path between two campsites A and B. Think of it like filling in a simple form: each line is one selected connection. This block is just a shape example — not the real answer.

Please make sure that in your actual reply you use the exact identifiers given 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 30, 'edges': [{'u': 1, 'v': 2, 'w': 420.0}, {'u': 1, 'v': 8, 'w': 275.0}, {'u': 1, 'v': 13, 'w': 700.0}, {'u': 2, 'v': 7, 'w': 275.0}, {'u': 2, 'v': 12, 'w': 445.0}, {'u': 12, 'v': 22, 'w': 1245.0}, {'u': 12, 'v': 13, 'w': 160.0}, {'u': 17, 'v': 18, 'w': 96.0}, {'u': 17, 'v': 6, 'w': 481.0}, {'u': 18, 'v': 11, 'w': 437.0}, {'u': 23, 'v': 21, 'w': 1738.0}, {'u': 23, 'v': 24, 'w': 1243.0}, {'u': 5, 'v': 14, 'w': 442.0}, {'u': 5, 'v': 19, 'w': 1463.0}, {'u': 5, 'v': 9, 'w': 1045.0}, {'u': 6, 'v': 16, 'w': 204.0}, {'u': 20, 'v': 24, 'w': 414.0}, {'u': 20, 'v': 21, 'w': 2534.0}, {'u': 14, 'v': 15, 'w': 310.0}, {'u': 14, 'v': 22, 'w': 1339.0}, {'u': 8, 'v': 7, 'w': 417.0}, {'u': 15, 'v': 9, 'w': 408.0}, {'u': 15, 'v': 4, 'w': 1991.0}, {'u': 16, 'v': 4, 'w': 1986.0}, {'u': 16, 'v': 10, 'w': 464.0}, {'u': 21, 'v': 19, 'w': 1444.0}, {'u': 22, 'v': 19, 'w': 1132.0}, {'u': 10, 'v': 3, 'w': 1987.0}, {'u': 10, 'v': 11, 'w': 781.0}, {'u': 3, 'v': 4, 'w': 529.0}], 'k': 12, 'source_file': 'I011.stp', 'density': 0.10869565217391304}","[[1, 8], [2, 7], [2, 12], [12, 22], [12, 13], [5, 14], [14, 15], [14, 22], [7, 8], [9, 15], [19, 22]]",6448.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 30, 'edges': [{'u': 0, 'v': 1, 'w': 420.0}, {'u': 0, 'v': 7, 'w': 275.0}, {'u': 0, 'v': 12, 'w': 700.0}, {'u': 1, 'v': 6, 'w': 275.0}, {'u': 1, 'v': 11, 'w': 445.0}, {'u': 11, 'v': 21, 'w': 1245.0}, {'u': 11, 'v': 12, 'w': 160.0}, {'u': 16, 'v': 17, 'w': 96.0}, {'u': 16, 'v': 5, 'w': 481.0}, {'u': 17, 'v': 10, 'w': 437.0}, {'u': 22, 'v': 20, 'w': 1738.0}, {'u': 22, 'v': 23, 'w': 1243.0}, {'u': 4, 'v': 13, 'w': 442.0}, {'u': 4, 'v': 18, 'w': 1463.0}, {'u': 4, 'v': 8, 'w': 1045.0}, {'u': 5, 'v': 15, 'w': 204.0}, {'u': 19, 'v': 23, 'w': 414.0}, {'u': 19, 'v': 20, 'w': 2534.0}, {'u': 13, 'v': 14, 'w': 310.0}, {'u': 13, 'v': 21, 'w': 1339.0}, {'u': 7, 'v': 6, 'w': 417.0}, {'u': 14, 'v': 8, 'w': 408.0}, {'u': 14, 'v': 3, 'w': 1991.0}, {'u': 15, 'v': 3, 'w': 1986.0}, {'u': 15, 'v': 9, 'w': 464.0}, {'u': 20, 'v': 18, 'w': 1444.0}, {'u': 21, 'v': 18, 'w': 1132.0}, {'u': 9, 'v': 2, 'w': 1987.0}, {'u': 9, 'v': 10, 'w': 781.0}, {'u': 2, 'v': 3, 'w': 529.0}], 'density': 0.10869565217391304, 'source_file': 'I011.stp', 'k': 12}","[[0, 7], [1, 6], [1, 11], [11, 21], [11, 12], [4, 13], [13, 14], [13, 21], [6, 7], [8, 14], [18, 21]]",3,json,0
KMST,KMST,"We had a one-line brief from the museum director: pick a set number of exhibits and connect them with walkways so visitors can move between any two chosen exhibits, but don’t let the walkways form loops where people might walk in circles. Better layouts were simply those where the sum of the lengths of all built paths was as small as it could be — you literally add up the lengths of the chosen paths and prefer the smallest total. The selection must include exactly the pre-determined number of displays (no leaving some out or doubling up) and each chosen display must be linked so the whole group is connected without circular routes. The specific layout options and distances appear below.

# total_exhibits_available=22
# total_candidate_walkways=28
# exhibits_to_select=9
exhibit_endpoint_u,exhibit_endpoint_v,walkway_length
21,16,336.0
21,10,1907.0
21,17,1755.0
18,15,245.0
18,8,1534.0
5,9,401.0
5,20,77.0
15,16,1952.0
13,14,416.0
13,12,2076.0
6,3,473.0
6,7,96.0
6,0,345.0
6,11,158.0
7,1,345.0
7,12,155.0
19,20,663.0
19,1,407.0
0,1,109.0
0,2,428.0
1,9,424.0
2,9,104.0
2,8,1649.0
3,4,177.0
4,10,1170.0
4,11,473.0
8,10,1057.0
11,12,90.0

Also, when you send back the chosen walkways, please follow this little JSON sketch so it's easy to read and parse:

{
  ""solution"": [[""ex1"", ""ex2""], [""ex3"", ""ex4""], ...]
}

Here ""solution"" is a list of the paths you'll build; each inner pair is a walkway connecting the two exhibit IDs (so [""ex1"",""ex2""] means there's a path between exhibit ex1 and exhibit ex2). It's just a template showing the shape I expect — not the actual layout you should submit.

Please make sure to use the exact exhibit IDs from 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"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 22, 'v': 17, 'w': 336.0}, {'u': 22, 'v': 11, 'w': 1907.0}, {'u': 22, 'v': 18, 'w': 1755.0}, {'u': 19, 'v': 16, 'w': 245.0}, {'u': 19, 'v': 9, 'w': 1534.0}, {'u': 6, 'v': 10, 'w': 401.0}, {'u': 6, 'v': 21, 'w': 77.0}, {'u': 16, 'v': 17, 'w': 1952.0}, {'u': 14, 'v': 15, 'w': 416.0}, {'u': 14, 'v': 13, 'w': 2076.0}, {'u': 7, 'v': 4, 'w': 473.0}, {'u': 7, 'v': 8, 'w': 96.0}, {'u': 7, 'v': 1, 'w': 345.0}, {'u': 7, 'v': 12, 'w': 158.0}, {'u': 8, 'v': 2, 'w': 345.0}, {'u': 8, 'v': 13, 'w': 155.0}, {'u': 20, 'v': 21, 'w': 663.0}, {'u': 20, 'v': 2, 'w': 407.0}, {'u': 1, 'v': 2, 'w': 109.0}, {'u': 1, 'v': 3, 'w': 428.0}, {'u': 2, 'v': 10, 'w': 424.0}, {'u': 3, 'v': 10, 'w': 104.0}, {'u': 3, 'v': 9, 'w': 1649.0}, {'u': 4, 'v': 5, 'w': 177.0}, {'u': 5, 'v': 11, 'w': 1170.0}, {'u': 5, 'v': 12, 'w': 473.0}, {'u': 9, 'v': 11, 'w': 1057.0}, {'u': 12, 'v': 13, 'w': 90.0}], 'k': 9, 'source_file': 'I024.stp', 'density': 0.12121212121212122}","[[6, 10], [6, 21], [7, 8], [2, 8], [8, 13], [2, 10], [3, 10], [12, 13]]",1692.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 21, 'v': 16, 'w': 336.0}, {'u': 21, 'v': 10, 'w': 1907.0}, {'u': 21, 'v': 17, 'w': 1755.0}, {'u': 18, 'v': 15, 'w': 245.0}, {'u': 18, 'v': 8, 'w': 1534.0}, {'u': 5, 'v': 9, 'w': 401.0}, {'u': 5, 'v': 20, 'w': 77.0}, {'u': 15, 'v': 16, 'w': 1952.0}, {'u': 13, 'v': 14, 'w': 416.0}, {'u': 13, 'v': 12, 'w': 2076.0}, {'u': 6, 'v': 3, 'w': 473.0}, {'u': 6, 'v': 7, 'w': 96.0}, {'u': 6, 'v': 0, 'w': 345.0}, {'u': 6, 'v': 11, 'w': 158.0}, {'u': 7, 'v': 1, 'w': 345.0}, {'u': 7, 'v': 12, 'w': 155.0}, {'u': 19, 'v': 20, 'w': 663.0}, {'u': 19, 'v': 1, 'w': 407.0}, {'u': 0, 'v': 1, 'w': 109.0}, {'u': 0, 'v': 2, 'w': 428.0}, {'u': 1, 'v': 9, 'w': 424.0}, {'u': 2, 'v': 9, 'w': 104.0}, {'u': 2, 'v': 8, 'w': 1649.0}, {'u': 3, 'v': 4, 'w': 177.0}, {'u': 4, 'v': 10, 'w': 1170.0}, {'u': 4, 'v': 11, 'w': 473.0}, {'u': 8, 'v': 10, 'w': 1057.0}, {'u': 11, 'v': 12, 'w': 90.0}], 'density': 0.12121212121212122, 'source_file': 'I024.stp', 'k': 9}","[[5, 9], [5, 20], [6, 7], [1, 7], [7, 12], [1, 9], [2, 9], [11, 12]]",4,csv,0
KMST,KMST,"Many planners run into the same puzzle: select a predetermined count of towers and set up point-to-point connections so the selected towers are all connected, but there are no circular routes among the links. The decision is about picking which towers and which connections; to compare options, add up the price of every link in a plan and favor the plan with the smallest total. The number of towers is fixed, each chosen once, and they must form one continuous, loop-free network. The concrete instance and numbers follow below.

{
  ""total_towers"": 22,
  ""total_candidate_links"": 30,
  ""edges"": [
    {
      ""tower_endpoint_a"": 21,
      ""tower_endpoint_b"": 4,
      ""link_cost"": 1037.0
    },
    {
      ""tower_endpoint_a"": 21,
      ""tower_endpoint_b"": 1,
      ""link_cost"": 35217.0
    },
    {
      ""tower_endpoint_a"": 0,
      ""tower_endpoint_b"": 10,
      ""link_cost"": 2224.0
    },
    {
      ""tower_endpoint_a"": 5,
      ""tower_endpoint_b"": 6,
      ""link_cost"": 25423.0
    },
    {
      ""tower_endpoint_a"": 5,
      ""tower_endpoint_b"": 4,
      ""link_cost"": 882.0
    },
    {
      ""tower_endpoint_a"": 5,
      ""tower_endpoint_b"": 17,
      ""link_cost"": 794.0
    },
    {
      ""tower_endpoint_a"": 6,
      ""tower_endpoint_b"": 18,
      ""link_cost"": 739.0
    },
    {
      ""tower_endpoint_a"": 6,
      ""tower_endpoint_b"": 8,
      ""link_cost"": 1971.0
    },
    {
      ""tower_endpoint_a"": 11,
      ""tower_endpoint_b"": 12,
      ""link_cost"": 1339.0
    },
    {
      ""tower_endpoint_a"": 11,
      ""tower_endpoint_b"": 7,
      ""link_cost"": 784.0
    },
    {
      ""tower_endpoint_a"": 11,
      ""tower_endpoint_b"": 15,
      ""link_cost"": 7343.0
    },
    {
      ""tower_endpoint_a"": 15,
      ""tower_endpoint_b"": 14,
      ""link_cost"": 1289.0
    },
    {
      ""tower_endpoint_a"": 15,
      ""tower_endpoint_b"": 18,
      ""link_cost"": 2271.0
    },
    {
      ""tower_endpoint_a"": 16,
      ""tower_endpoint_b"": 14,
      ""link_cost"": 28251.0
    },
    {
      ""tower_endpoint_a"": 16,
      ""tower_endpoint_b"": 17,
      ""link_cost"": 1342.0
    },
    {
      ""tower_endpoint_a"": 16,
      ""tower_endpoint_b"": 13,
      ""link_cost"": 1069.0
    },
    {
      ""tower_endpoint_a"": 12,
      ""tower_endpoint_b"": 9,
      ""link_cost"": 1124.0
    },
    {
      ""tower_endpoint_a"": 12,
      ""tower_endpoint_b"": 14,
      ""link_cost"": 7014.0
    },
    {
      ""tower_endpoint_a"": 18,
      ""tower_endpoint_b"": 17,
      ""link_cost"": 25628.0
    },
    {
      ""tower_endpoint_a"": 7,
      ""tower_endpoint_b"": 2,
      ""link_cost"": 880.0
    },
    {
      ""tower_endpoint_a"": 7,
      ""tower_endpoint_b"": 8,
      ""link_cost"": 7828.0
    },
    {
      ""tower_endpoint_a"": 8,
      ""tower_endpoint_b"": 3,
      ""link_cost"": 864.0
    },
    {
      ""tower_endpoint_a"": 9,
      ""tower_endpoint_b"": 10,
      ""link_cost"": 1034.0
    },
    {
      ""tower_endpoint_a"": 9,
      ""tower_endpoint_b"": 13,
      ""link_cost"": 35282.0
    },
    {
      ""tower_endpoint_a"": 10,
      ""tower_endpoint_b"": 20,
      ""link_cost"": 35293.0
    },
    {
      ""tower_endpoint_a"": 20,
      ""tower_endpoint_b"": 13,
      ""link_cost"": 1072.0
    },
    {
      ""tower_endpoint_a"": 20,
      ""tower_endpoint_b"": 19,
      ""link_cost"": 1175.0
    },
    {
      ""tower_endpoint_a"": 1,
      ""tower_endpoint_b"": 2,
      ""link_cost"": 1089.0
    },
    {
      ""tower_endpoint_a"": 2,
      ""tower_endpoint_b"": 3,
      ""link_cost"": 7996.0
    },
    {
      ""tower_endpoint_a"": 3,
      ""tower_endpoint_b"": 4,
      ""link_cost"": 27210.0
    }
  ],
  ""towers_to_connect"": 11
}

Also, when you reply with a candidate wiring plan, please use this simple JSON shape so it's easy to parse and compare:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of that as a little form: ""solution"" is the list of chosen links, and each inner pair like [u1, v1] just means ""connect tower u1 to tower v1"". Pretty informal — it's just a sketch of the shape I expect, not the final answer itself.

All identifiers in your solution must match the instance input exactly — 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”.""","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 30, 'edges': [{'u': 22, 'v': 5, 'w': 1037.0}, {'u': 22, 'v': 2, 'w': 35217.0}, {'u': 1, 'v': 11, 'w': 2224.0}, {'u': 6, 'v': 7, 'w': 25423.0}, {'u': 6, 'v': 5, 'w': 882.0}, {'u': 6, 'v': 18, 'w': 794.0}, {'u': 7, 'v': 19, 'w': 739.0}, {'u': 7, 'v': 9, 'w': 1971.0}, {'u': 12, 'v': 13, 'w': 1339.0}, {'u': 12, 'v': 8, 'w': 784.0}, {'u': 12, 'v': 16, 'w': 7343.0}, {'u': 16, 'v': 15, 'w': 1289.0}, {'u': 16, 'v': 19, 'w': 2271.0}, {'u': 17, 'v': 15, 'w': 28251.0}, {'u': 17, 'v': 18, 'w': 1342.0}, {'u': 17, 'v': 14, 'w': 1069.0}, {'u': 13, 'v': 10, 'w': 1124.0}, {'u': 13, 'v': 15, 'w': 7014.0}, {'u': 19, 'v': 18, 'w': 25628.0}, {'u': 8, 'v': 3, 'w': 880.0}, {'u': 8, 'v': 9, 'w': 7828.0}, {'u': 9, 'v': 4, 'w': 864.0}, {'u': 10, 'v': 11, 'w': 1034.0}, {'u': 10, 'v': 14, 'w': 35282.0}, {'u': 11, 'v': 21, 'w': 35293.0}, {'u': 21, 'v': 14, 'w': 1072.0}, {'u': 21, 'v': 20, 'w': 1175.0}, {'u': 2, 'v': 3, 'w': 1089.0}, {'u': 3, 'v': 4, 'w': 7996.0}, {'u': 4, 'v': 5, 'w': 27210.0}], 'k': 11, 'source_file': 'I007.stp', 'density': 0.12987012987012986}","[[7, 19], [12, 13], [8, 12], [15, 16], [16, 19], [10, 13], [13, 15], [3, 8], [10, 11], [2, 3]]",17563.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 30, 'edges': [{'u': 21, 'v': 4, 'w': 1037.0}, {'u': 21, 'v': 1, 'w': 35217.0}, {'u': 0, 'v': 10, 'w': 2224.0}, {'u': 5, 'v': 6, 'w': 25423.0}, {'u': 5, 'v': 4, 'w': 882.0}, {'u': 5, 'v': 17, 'w': 794.0}, {'u': 6, 'v': 18, 'w': 739.0}, {'u': 6, 'v': 8, 'w': 1971.0}, {'u': 11, 'v': 12, 'w': 1339.0}, {'u': 11, 'v': 7, 'w': 784.0}, {'u': 11, 'v': 15, 'w': 7343.0}, {'u': 15, 'v': 14, 'w': 1289.0}, {'u': 15, 'v': 18, 'w': 2271.0}, {'u': 16, 'v': 14, 'w': 28251.0}, {'u': 16, 'v': 17, 'w': 1342.0}, {'u': 16, 'v': 13, 'w': 1069.0}, {'u': 12, 'v': 9, 'w': 1124.0}, {'u': 12, 'v': 14, 'w': 7014.0}, {'u': 18, 'v': 17, 'w': 25628.0}, {'u': 7, 'v': 2, 'w': 880.0}, {'u': 7, 'v': 8, 'w': 7828.0}, {'u': 8, 'v': 3, 'w': 864.0}, {'u': 9, 'v': 10, 'w': 1034.0}, {'u': 9, 'v': 13, 'w': 35282.0}, {'u': 10, 'v': 20, 'w': 35293.0}, {'u': 20, 'v': 13, 'w': 1072.0}, {'u': 20, 'v': 19, 'w': 1175.0}, {'u': 1, 'v': 2, 'w': 1089.0}, {'u': 2, 'v': 3, 'w': 7996.0}, {'u': 3, 'v': 4, 'w': 27210.0}], 'density': 0.12987012987012986, 'source_file': 'I007.stp', 'k': 11}","[[6, 18], [11, 12], [7, 11], [14, 15], [15, 18], [9, 12], [12, 14], [2, 7], [9, 10], [1, 2]]",5,json,0
KMST,KMST,"Someone on the disaster team has to decide which supply depots to open and which roads to use so those depots form one tidy, loop-free network. The smarter choice is the one that keeps total driving distance down — calculated by summing the lengths of all roads that end up in the network. The rule is clear: pick the predetermined number of depots, make sure they’re all connected, and don’t create redundant circular routes. The detailed instance with distances and nodes appears below.

# total_locations=21
# total_roads=28
# depots_to_open=8
location_u,location_v,road_distance
A,C,567.0
B,C,1741.0
B,H,24.0
B,S,263.0
C,E,597.0
D,E,1869.0
D,P,219.0
D,T,59.0
E,J,1135.0
F,Q,952.0
G,H,164.0
G,O,293.0
I,J,1387.0
I,U,554.0
I,K,621.0
J,N,1832.0
K,R,563.0
K,L,1838.0
L,M,913.0
L,N,903.0
M,N,152.0
O,P,246.0
O,S,105.0
P,S,285.0
Q,R,485.0
Q,T,523.0
R,U,598.0
T,U,498.0

Also, to keep things easy for whoever's checking this, please give the picked roads in a tiny JSON sketch like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of each pair [uX, vX] as one road you plan to keep open between two depots — the whole ""solution"" list is the final loop-free network of k depots. This block is just the shape I need; don't treat these placeholders as the actual answer.

Please make sure you use the exact depot/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”.""","{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 28, 'edges': [{'u': 1, 'v': 3, 'w': 567.0}, {'u': 2, 'v': 3, 'w': 1741.0}, {'u': 2, 'v': 8, 'w': 24.0}, {'u': 2, 'v': 19, 'w': 263.0}, {'u': 3, 'v': 5, 'w': 597.0}, {'u': 4, 'v': 5, 'w': 1869.0}, {'u': 4, 'v': 16, 'w': 219.0}, {'u': 4, 'v': 20, 'w': 59.0}, {'u': 5, 'v': 10, 'w': 1135.0}, {'u': 6, 'v': 17, 'w': 952.0}, {'u': 7, 'v': 8, 'w': 164.0}, {'u': 7, 'v': 15, 'w': 293.0}, {'u': 9, 'v': 10, 'w': 1387.0}, {'u': 9, 'v': 21, 'w': 554.0}, {'u': 9, 'v': 11, 'w': 621.0}, {'u': 10, 'v': 14, 'w': 1832.0}, {'u': 11, 'v': 18, 'w': 563.0}, {'u': 11, 'v': 12, 'w': 1838.0}, {'u': 12, 'v': 13, 'w': 913.0}, {'u': 12, 'v': 14, 'w': 903.0}, {'u': 13, 'v': 14, 'w': 152.0}, {'u': 15, 'v': 16, 'w': 246.0}, {'u': 15, 'v': 19, 'w': 105.0}, {'u': 16, 'v': 19, 'w': 285.0}, {'u': 17, 'v': 18, 'w': 485.0}, {'u': 17, 'v': 20, 'w': 523.0}, {'u': 18, 'v': 21, 'w': 598.0}, {'u': 20, 'v': 21, 'w': 498.0}], 'k': 8, 'source_file': 'I052.stp', 'density': 0.13333333333333333}","[[2, 8], [2, 19], [4, 16], [4, 20], [7, 8], [15, 16], [15, 19]]",1080.0,"{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 28, 'edges': [{'u': 'A', 'v': 'C', 'w': 567.0}, {'u': 'B', 'v': 'C', 'w': 1741.0}, {'u': 'B', 'v': 'H', 'w': 24.0}, {'u': 'B', 'v': 'S', 'w': 263.0}, {'u': 'C', 'v': 'E', 'w': 597.0}, {'u': 'D', 'v': 'E', 'w': 1869.0}, {'u': 'D', 'v': 'P', 'w': 219.0}, {'u': 'D', 'v': 'T', 'w': 59.0}, {'u': 'E', 'v': 'J', 'w': 1135.0}, {'u': 'F', 'v': 'Q', 'w': 952.0}, {'u': 'G', 'v': 'H', 'w': 164.0}, {'u': 'G', 'v': 'O', 'w': 293.0}, {'u': 'I', 'v': 'J', 'w': 1387.0}, {'u': 'I', 'v': 'U', 'w': 554.0}, {'u': 'I', 'v': 'K', 'w': 621.0}, {'u': 'J', 'v': 'N', 'w': 1832.0}, {'u': 'K', 'v': 'R', 'w': 563.0}, {'u': 'K', 'v': 'L', 'w': 1838.0}, {'u': 'L', 'v': 'M', 'w': 913.0}, {'u': 'L', 'v': 'N', 'w': 903.0}, {'u': 'M', 'v': 'N', 'w': 152.0}, {'u': 'O', 'v': 'P', 'w': 246.0}, {'u': 'O', 'v': 'S', 'w': 105.0}, {'u': 'P', 'v': 'S', 'w': 285.0}, {'u': 'Q', 'v': 'R', 'w': 485.0}, {'u': 'Q', 'v': 'T', 'w': 523.0}, {'u': 'R', 'v': 'U', 'w': 598.0}, {'u': 'T', 'v': 'U', 'w': 498.0}], 'density': 0.13333333333333333, 'source_file': 'I052.stp', 'k': 8}","[['B', 'H'], ['B', 'S'], ['D', 'P'], ['D', 'T'], ['G', 'H'], ['O', 'P'], ['O', 'S']]",6,csv,names
KMST,KMST,"Back in the control room the challenge was laid out plainly: we must pick a set number of substations and string power lines so they form one connected grouping with no circular paths. A plan is judged by how little cable and installation cost it requires — total cost equals the sum of the lengths and installation costs of the chosen lines. The selection has to include exactly that many substations, tie them into one network, and avoid any closed circuits or redundancies. The concrete details will be shown below.

# total_substations=24
# available_line_segments=29
# target_substations=12
substation_u,substation_v,line_cost
6,7,1325.0
6,12,825.0
6,9,388.0
8,9,1427.0
17,16,1206.0
19,15,503.0
19,20,1036.0
19,14,937.0
5,1,189973.0
5,0,189882.0
0,14,302.0
0,15,170.0
1,10,485.0
1,12,1088.0
2,3,528.0
2,4,387.0
2,10,231.0
3,15,326.0
3,16,360.0
4,16,509.0
4,11,230.0
20,23,400.0
10,11,369.0
10,13,339.0
21,12,562.0
21,22,1853.0
21,14,525.0
22,18,1209.0
11,13,495.0

Oh, and when you send back the plan, just put it in this shape so I can read it automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of the power lines you picked; each little pair like [u1, v1] is one line connecting the two substations named u1 and v1. It's just a quick form — the actual answer should be the real list of edges from the instance.

Please use the exact 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 29, 'edges': [{'u': 7, 'v': 8, 'w': 1325.0}, {'u': 7, 'v': 13, 'w': 825.0}, {'u': 7, 'v': 10, 'w': 388.0}, {'u': 9, 'v': 10, 'w': 1427.0}, {'u': 18, 'v': 17, 'w': 1206.0}, {'u': 20, 'v': 16, 'w': 503.0}, {'u': 20, 'v': 21, 'w': 1036.0}, {'u': 20, 'v': 15, 'w': 937.0}, {'u': 6, 'v': 2, 'w': 189973.0}, {'u': 6, 'v': 1, 'w': 189882.0}, {'u': 1, 'v': 15, 'w': 302.0}, {'u': 1, 'v': 16, 'w': 170.0}, {'u': 2, 'v': 11, 'w': 485.0}, {'u': 2, 'v': 13, 'w': 1088.0}, {'u': 3, 'v': 4, 'w': 528.0}, {'u': 3, 'v': 5, 'w': 387.0}, {'u': 3, 'v': 11, 'w': 231.0}, {'u': 4, 'v': 16, 'w': 326.0}, {'u': 4, 'v': 17, 'w': 360.0}, {'u': 5, 'v': 17, 'w': 509.0}, {'u': 5, 'v': 12, 'w': 230.0}, {'u': 21, 'v': 24, 'w': 400.0}, {'u': 11, 'v': 12, 'w': 369.0}, {'u': 11, 'v': 14, 'w': 339.0}, {'u': 22, 'v': 13, 'w': 562.0}, {'u': 22, 'v': 23, 'w': 1853.0}, {'u': 22, 'v': 15, 'w': 525.0}, {'u': 23, 'v': 19, 'w': 1209.0}, {'u': 12, 'v': 14, 'w': 495.0}], 'k': 12, 'source_file': 'I037.stp', 'density': 0.10507246376811594}","[[16, 20], [1, 15], [1, 16], [2, 11], [3, 11], [4, 16], [4, 17], [5, 17], [5, 12], [11, 12], [11, 14]]",3824.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 29, 'edges': [{'u': 6, 'v': 7, 'w': 1325.0}, {'u': 6, 'v': 12, 'w': 825.0}, {'u': 6, 'v': 9, 'w': 388.0}, {'u': 8, 'v': 9, 'w': 1427.0}, {'u': 17, 'v': 16, 'w': 1206.0}, {'u': 19, 'v': 15, 'w': 503.0}, {'u': 19, 'v': 20, 'w': 1036.0}, {'u': 19, 'v': 14, 'w': 937.0}, {'u': 5, 'v': 1, 'w': 189973.0}, {'u': 5, 'v': 0, 'w': 189882.0}, {'u': 0, 'v': 14, 'w': 302.0}, {'u': 0, 'v': 15, 'w': 170.0}, {'u': 1, 'v': 10, 'w': 485.0}, {'u': 1, 'v': 12, 'w': 1088.0}, {'u': 2, 'v': 3, 'w': 528.0}, {'u': 2, 'v': 4, 'w': 387.0}, {'u': 2, 'v': 10, 'w': 231.0}, {'u': 3, 'v': 15, 'w': 326.0}, {'u': 3, 'v': 16, 'w': 360.0}, {'u': 4, 'v': 16, 'w': 509.0}, {'u': 4, 'v': 11, 'w': 230.0}, {'u': 20, 'v': 23, 'w': 400.0}, {'u': 10, 'v': 11, 'w': 369.0}, {'u': 10, 'v': 13, 'w': 339.0}, {'u': 21, 'v': 12, 'w': 562.0}, {'u': 21, 'v': 22, 'w': 1853.0}, {'u': 21, 'v': 14, 'w': 525.0}, {'u': 22, 'v': 18, 'w': 1209.0}, {'u': 11, 'v': 13, 'w': 495.0}], 'density': 0.10507246376811594, 'source_file': 'I037.stp', 'k': 12}","[[15, 19], [0, 14], [0, 15], [1, 10], [2, 10], [3, 15], [3, 16], [4, 16], [4, 11], [10, 11], [10, 13]]",7,csv,0
KMST,KMST,"Recently the operations team was asked to pick a specific number of warehouses and sketch shuttle paths between them so they form one continuous network without any loops. What counts as a better sketch is straightforward: measure every route, add those distances together, and the smallest total wins. The chosen number of warehouses must be met exactly and no circular or duplicate routes are allowed. The exact data on warehouses and route lengths appears below.

There are 29 candidate warehouses and 38 potential routes listed; the operations team must select exactly 9 warehouses.
Route between warehouses R and S with distance 1068.0.
Route between warehouses R and Y with distance 6101.0.
Route between warehouses R and W with distance 540.0.
Route between warehouses S and L with distance 1190.0.
Route between warehouses S and AC with distance 6164.0.
Route between warehouses V and H with distance 172.0.
Route between warehouses T and U with distance 1088.0.
Route between warehouses T and W with distance 586.0.
Route between warehouses T and X with distance 6149.0.
Route between warehouses U and M with distance 6216.0.
Route between warehouses U and N with distance 7354.0.
Route between warehouses AB and L with distance 6022.0.
Route between warehouses AB and AA with distance 1170.0.
Route between warehouses AB and AC with distance 1187.0.
Route between warehouses AC and Y with distance 1018.0.
Route between warehouses W and Z with distance 6053.0.
Route between warehouses X and Z with distance 595.0.
Route between warehouses X and M with distance 1137.0.
Route between warehouses I and H with distance 497.0.
Route between warehouses I and P with distance 1375.0.
Route between warehouses N and D with distance 6369.0.
Route between warehouses Y and Z with distance 505.0.
Route between warehouses AA and K with distance 5393.0.
Route between warehouses AA and Q with distance 1726.0.
Route between warehouses M and C with distance 4002.0.
Route between warehouses E and F with distance 435.0.
Route between warehouses F and J with distance 128.0.
Route between warehouses F and Q with distance 1349.0.
Route between warehouses A and B with distance 528.0.
Route between warehouses A and G with distance 1819.0.
Route between warehouses A and O with distance 2835.0.
Route between warehouses B and K with distance 91.0.
Route between warehouses B and L with distance 1377.0.
Route between warehouses C and D with distance 2695.0.
Route between warehouses K and P with distance 1822.0.
Route between warehouses O and G with distance 1529.0.
Route between warehouses G and H with distance 1443.0.
Route between warehouses P and Q with distance 5018.0.
These entries are provided for the operations team to evaluate candidate sketches and compute the minimal total distance.

Just drop your chosen edges into this simple JSON shape when you're ready — it's just a tiny, predictable form so whatever reads it knows where to look.

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as the list of shuttle paths you picked. Each inner pair like [u1, v1] is one route connecting two warehouses (the two IDs go in there). This is only a sketch of the shape I need, not the actual answer — you'll replace those placeholders with the real IDs from the instance.

Please make sure to use the exact identifiers from the input, without renaming or inventing 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”.""","{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 38, 'edges': [{'u': 18, 'v': 19, 'w': 1068.0}, {'u': 18, 'v': 25, 'w': 6101.0}, {'u': 18, 'v': 23, 'w': 540.0}, {'u': 19, 'v': 12, 'w': 1190.0}, {'u': 19, 'v': 29, 'w': 6164.0}, {'u': 22, 'v': 8, 'w': 172.0}, {'u': 20, 'v': 21, 'w': 1088.0}, {'u': 20, 'v': 23, 'w': 586.0}, {'u': 20, 'v': 24, 'w': 6149.0}, {'u': 21, 'v': 13, 'w': 6216.0}, {'u': 21, 'v': 14, 'w': 7354.0}, {'u': 28, 'v': 12, 'w': 6022.0}, {'u': 28, 'v': 27, 'w': 1170.0}, {'u': 28, 'v': 29, 'w': 1187.0}, {'u': 29, 'v': 25, 'w': 1018.0}, {'u': 23, 'v': 26, 'w': 6053.0}, {'u': 24, 'v': 26, 'w': 595.0}, {'u': 24, 'v': 13, 'w': 1137.0}, {'u': 9, 'v': 8, 'w': 497.0}, {'u': 9, 'v': 16, 'w': 1375.0}, {'u': 14, 'v': 4, 'w': 6369.0}, {'u': 25, 'v': 26, 'w': 505.0}, {'u': 27, 'v': 11, 'w': 5393.0}, {'u': 27, 'v': 17, 'w': 1726.0}, {'u': 13, 'v': 3, 'w': 4002.0}, {'u': 5, 'v': 6, 'w': 435.0}, {'u': 6, 'v': 10, 'w': 128.0}, {'u': 6, 'v': 17, 'w': 1349.0}, {'u': 1, 'v': 2, 'w': 528.0}, {'u': 1, 'v': 7, 'w': 1819.0}, {'u': 1, 'v': 15, 'w': 2835.0}, {'u': 2, 'v': 11, 'w': 91.0}, {'u': 2, 'v': 12, 'w': 1377.0}, {'u': 3, 'v': 4, 'w': 2695.0}, {'u': 11, 'v': 16, 'w': 1822.0}, {'u': 15, 'v': 7, 'w': 1529.0}, {'u': 7, 'v': 8, 'w': 1443.0}, {'u': 16, 'v': 17, 'w': 5018.0}], 'k': 9, 'source_file': 'I050.stp', 'density': 0.09359605911330049}","[[18, 19], [18, 23], [12, 19], [20, 21], [20, 23], [1, 2], [2, 11], [2, 12]]",6468.0,"{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 38, 'edges': [{'u': 'R', 'v': 'S', 'w': 1068.0}, {'u': 'R', 'v': 'Y', 'w': 6101.0}, {'u': 'R', 'v': 'W', 'w': 540.0}, {'u': 'S', 'v': 'L', 'w': 1190.0}, {'u': 'S', 'v': 'AC', 'w': 6164.0}, {'u': 'V', 'v': 'H', 'w': 172.0}, {'u': 'T', 'v': 'U', 'w': 1088.0}, {'u': 'T', 'v': 'W', 'w': 586.0}, {'u': 'T', 'v': 'X', 'w': 6149.0}, {'u': 'U', 'v': 'M', 'w': 6216.0}, {'u': 'U', 'v': 'N', 'w': 7354.0}, {'u': 'AB', 'v': 'L', 'w': 6022.0}, {'u': 'AB', 'v': 'AA', 'w': 1170.0}, {'u': 'AB', 'v': 'AC', 'w': 1187.0}, {'u': 'AC', 'v': 'Y', 'w': 1018.0}, {'u': 'W', 'v': 'Z', 'w': 6053.0}, {'u': 'X', 'v': 'Z', 'w': 595.0}, {'u': 'X', 'v': 'M', 'w': 1137.0}, {'u': 'I', 'v': 'H', 'w': 497.0}, {'u': 'I', 'v': 'P', 'w': 1375.0}, {'u': 'N', 'v': 'D', 'w': 6369.0}, {'u': 'Y', 'v': 'Z', 'w': 505.0}, {'u': 'AA', 'v': 'K', 'w': 5393.0}, {'u': 'AA', 'v': 'Q', 'w': 1726.0}, {'u': 'M', 'v': 'C', 'w': 4002.0}, {'u': 'E', 'v': 'F', 'w': 435.0}, {'u': 'F', 'v': 'J', 'w': 128.0}, {'u': 'F', 'v': 'Q', 'w': 1349.0}, {'u': 'A', 'v': 'B', 'w': 528.0}, {'u': 'A', 'v': 'G', 'w': 1819.0}, {'u': 'A', 'v': 'O', 'w': 2835.0}, {'u': 'B', 'v': 'K', 'w': 91.0}, {'u': 'B', 'v': 'L', 'w': 1377.0}, {'u': 'C', 'v': 'D', 'w': 2695.0}, {'u': 'K', 'v': 'P', 'w': 1822.0}, {'u': 'O', 'v': 'G', 'w': 1529.0}, {'u': 'G', 'v': 'H', 'w': 1443.0}, {'u': 'P', 'v': 'Q', 'w': 5018.0}], 'density': 0.09359605911330049, 'source_file': 'I050.stp', 'k': 9}","[['R', 'S'], ['R', 'W'], ['L', 'S'], ['T', 'U'], ['T', 'W'], ['A', 'B'], ['B', 'K'], ['B', 'L']]",8,markdown_table,names
KMST,KMST,"Someone on the trail crew needs to pick a handful of scenic spots and connect them with new trails and bridges so the selected spots make a single connected system without any circular detours. The better the choice, the less total track to build — compute that by summing the lengths of every installed connector — and the team must include precisely the set number of viewpoints and avoid leaving gaps or creating duplicate/looping connections. Details for the specific case are shown below.

There are 21 available viewpoints, 25 potential connectors, and the crew must include exactly 10 viewpoints.
Potential connector between viewpoint O and viewpoint B with installation length 114.0.
Potential connector between viewpoint O and viewpoint P with installation length 222.0.
Potential connector between viewpoint O and viewpoint K with installation length 318.0.
Potential connector between viewpoint O and viewpoint A with installation length 1174.0.
Potential connector between viewpoint E and viewpoint F with installation length 553.0.
Potential connector between viewpoint E and viewpoint G with installation length 902.0.
Potential connector between viewpoint E and viewpoint L with installation length 547.0.
Potential connector between viewpoint F and viewpoint Q with installation length 119.0.
Potential connector between viewpoint F and viewpoint P with installation length 638.0.
Potential connector between viewpoint G and viewpoint T with installation length 515.0.
Potential connector between viewpoint G and viewpoint U with installation length 2406.0.
Potential connector between viewpoint H and viewpoint I with installation length 1316.0.
Potential connector between viewpoint H and viewpoint J with installation length 498.0.
Potential connector between viewpoint H and viewpoint L with installation length 432.0.
Potential connector between viewpoint J and viewpoint K with installation length 407.0.
Potential connector between viewpoint P and viewpoint L with installation length 419.0.
Potential connector between viewpoint Q and viewpoint M with installation length 640.0.
Potential connector between viewpoint Q and viewpoint R with installation length 496.0.
Potential connector between viewpoint R and viewpoint N with installation length 582.0.
Potential connector between viewpoint R and viewpoint T with installation length 264.0.
Potential connector between viewpoint S and viewpoint N with installation length 45.0.
Potential connector between viewpoint K and viewpoint L with installation length 351.0.
Potential connector between viewpoint M and viewpoint N with installation length 562.0.
Potential connector between viewpoint M and viewpoint C with installation length 221.0.
Potential connector between viewpoint C and viewpoint D with installation length 528.0.
Select connectors so the chosen 10 viewpoints form one connected, acyclic trail system minimizing the total installed length.

When you hand the chosen trail segments back, just put them in a tiny JSON snippet so it's easy to read and parse. Something like this will do:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This ""solution"" field is just the list of connectors you'll build; each pair [u, v] is a single trail or bridge linking two viewpoints (use the exact labels from the instance). The block above is only a sketch of the expected shape — not the actual answer itself.

Please use the identifiers exactly as they appear in the instance input — do not 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”.""","{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 25, 'edges': [{'u': 15, 'v': 2, 'w': 114.0}, {'u': 15, 'v': 16, 'w': 222.0}, {'u': 15, 'v': 11, 'w': 318.0}, {'u': 15, 'v': 1, 'w': 1174.0}, {'u': 5, 'v': 6, 'w': 553.0}, {'u': 5, 'v': 7, 'w': 902.0}, {'u': 5, 'v': 12, 'w': 547.0}, {'u': 6, 'v': 17, 'w': 119.0}, {'u': 6, 'v': 16, 'w': 638.0}, {'u': 7, 'v': 20, 'w': 515.0}, {'u': 7, 'v': 21, 'w': 2406.0}, {'u': 8, 'v': 9, 'w': 1316.0}, {'u': 8, 'v': 10, 'w': 498.0}, {'u': 8, 'v': 12, 'w': 432.0}, {'u': 10, 'v': 11, 'w': 407.0}, {'u': 16, 'v': 12, 'w': 419.0}, {'u': 17, 'v': 13, 'w': 640.0}, {'u': 17, 'v': 18, 'w': 496.0}, {'u': 18, 'v': 14, 'w': 582.0}, {'u': 18, 'v': 20, 'w': 264.0}, {'u': 19, 'v': 14, 'w': 45.0}, {'u': 11, 'v': 12, 'w': 351.0}, {'u': 13, 'v': 14, 'w': 562.0}, {'u': 13, 'v': 3, 'w': 221.0}, {'u': 3, 'v': 4, 'w': 528.0}], 'k': 10, 'source_file': 'I061.stp', 'density': 0.11904761904761904}","[[2, 15], [15, 16], [11, 15], [6, 17], [6, 16], [17, 18], [14, 18], [18, 20], [14, 19]]",2798.0,"{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 25, 'edges': [{'u': 'O', 'v': 'B', 'w': 114.0}, {'u': 'O', 'v': 'P', 'w': 222.0}, {'u': 'O', 'v': 'K', 'w': 318.0}, {'u': 'O', 'v': 'A', 'w': 1174.0}, {'u': 'E', 'v': 'F', 'w': 553.0}, {'u': 'E', 'v': 'G', 'w': 902.0}, {'u': 'E', 'v': 'L', 'w': 547.0}, {'u': 'F', 'v': 'Q', 'w': 119.0}, {'u': 'F', 'v': 'P', 'w': 638.0}, {'u': 'G', 'v': 'T', 'w': 515.0}, {'u': 'G', 'v': 'U', 'w': 2406.0}, {'u': 'H', 'v': 'I', 'w': 1316.0}, {'u': 'H', 'v': 'J', 'w': 498.0}, {'u': 'H', 'v': 'L', 'w': 432.0}, {'u': 'J', 'v': 'K', 'w': 407.0}, {'u': 'P', 'v': 'L', 'w': 419.0}, {'u': 'Q', 'v': 'M', 'w': 640.0}, {'u': 'Q', 'v': 'R', 'w': 496.0}, {'u': 'R', 'v': 'N', 'w': 582.0}, {'u': 'R', 'v': 'T', 'w': 264.0}, {'u': 'S', 'v': 'N', 'w': 45.0}, {'u': 'K', 'v': 'L', 'w': 351.0}, {'u': 'M', 'v': 'N', 'w': 562.0}, {'u': 'M', 'v': 'C', 'w': 221.0}, {'u': 'C', 'v': 'D', 'w': 528.0}], 'density': 0.11904761904761904, 'source_file': 'I061.stp', 'k': 10}","[['B', 'O'], ['O', 'P'], ['K', 'O'], ['F', 'Q'], ['F', 'P'], ['Q', 'R'], ['N', 'R'], ['R', 'T'], ['N', 'S']]",9,markdown_table,names
KMST,KMST,"Many coastal planners face the same choice: pick exactly a set number of docks and connect them with direct ferry legs so all picked docks are connected together, but never in a loop. The straightforward score for any plan is just the sum of the lengths of its legs — lower is better — and the chosen plan must include exactly that many docks, keep each dock unique in the plan, and avoid closed circuits. The precise figures and map are given below.

There are 29 docks, 36 possible direct routes, and the plan must select exactly 9 docks.
Direct route between dock X and dock AA with distance 925.0.
Direct route between dock X and dock U with distance 9291.0.
Direct route between dock B and dock J with distance 878.0.
Direct route between dock B and dock Q with distance 13250.0.
Direct route between dock Y and dock W with distance 926.0.
Direct route between dock Y and dock L with distance 5870.0.
Direct route between dock Y and dock AA with distance 993.0.
Direct route between dock U and dock P with distance 607.0.
Direct route between dock U and dock M with distance 867.0.
Direct route between dock AB and dock T with distance 1247.0.
Direct route between dock AB and dock AC with distance 280.0.
Direct route between dock K and dock F with distance 1390.0.
Direct route between dock K and dock E with distance 8379.0.
Direct route between dock K and dock S with distance 1233.0.
Direct route between dock AC and dock D with distance 818.0.
Direct route between dock A and dock P with distance 3946.0.
Direct route between dock Z and dock M with distance 3025.0.
Direct route between dock Z and dock AA with distance 6041.0.
Direct route between dock Z and dock L with distance 999.0.
Direct route between dock Q and dock R with distance 743.0.
Direct route between dock Q and dock V with distance 9173.0.
Direct route between dock D and dock E with distance 1949.0.
Direct route between dock D and dock G with distance 193.0.
Direct route between dock R and dock J with distance 12707.0.
Direct route between dock R and dock W with distance 9407.0.
Direct route between dock F and dock G with distance 8012.0.
Direct route between dock F and dock H with distance 519.0.
Direct route between dock G and dock O with distance 1160.0.
Direct route between dock C and dock T with distance 1322.0.
Direct route between dock I and dock J with distance 853.0.
Direct route between dock I and dock L with distance 15928.0.
Direct route between dock I and dock O with distance 790.0.
Direct route between dock V and dock W with distance 1029.0.
Direct route between dock M and dock N with distance 12176.0.
Direct route between dock N and dock O with distance 536.0.
Direct route between dock N and dock T with distance 139.0.
Select 9 unique docks to connect without loops so the sum of chosen route distances is minimized.

Oh, and when you send back your plan, please stick to this little JSON layout so it's easy to read and check:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as the list of ferry legs you picked. Each inner pair like [u1, v1] is one direct leg connecting the two dock identifiers u1 and v1. This is just a sketch of the shape I expect — not your final answer.

Please make sure to use the exact dock identifiers from the instance 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”.","{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 24, 'v': 27, 'w': 925.0}, {'u': 24, 'v': 21, 'w': 9291.0}, {'u': 2, 'v': 10, 'w': 878.0}, {'u': 2, 'v': 17, 'w': 13250.0}, {'u': 25, 'v': 23, 'w': 926.0}, {'u': 25, 'v': 12, 'w': 5870.0}, {'u': 25, 'v': 27, 'w': 993.0}, {'u': 21, 'v': 16, 'w': 607.0}, {'u': 21, 'v': 13, 'w': 867.0}, {'u': 28, 'v': 20, 'w': 1247.0}, {'u': 28, 'v': 29, 'w': 280.0}, {'u': 11, 'v': 6, 'w': 1390.0}, {'u': 11, 'v': 5, 'w': 8379.0}, {'u': 11, 'v': 19, 'w': 1233.0}, {'u': 29, 'v': 4, 'w': 818.0}, {'u': 1, 'v': 16, 'w': 3946.0}, {'u': 26, 'v': 13, 'w': 3025.0}, {'u': 26, 'v': 27, 'w': 6041.0}, {'u': 26, 'v': 12, 'w': 999.0}, {'u': 17, 'v': 18, 'w': 743.0}, {'u': 17, 'v': 22, 'w': 9173.0}, {'u': 4, 'v': 5, 'w': 1949.0}, {'u': 4, 'v': 7, 'w': 193.0}, {'u': 18, 'v': 10, 'w': 12707.0}, {'u': 18, 'v': 23, 'w': 9407.0}, {'u': 6, 'v': 7, 'w': 8012.0}, {'u': 6, 'v': 8, 'w': 519.0}, {'u': 7, 'v': 15, 'w': 1160.0}, {'u': 3, 'v': 20, 'w': 1322.0}, {'u': 9, 'v': 10, 'w': 853.0}, {'u': 9, 'v': 12, 'w': 15928.0}, {'u': 9, 'v': 15, 'w': 790.0}, {'u': 22, 'v': 23, 'w': 1029.0}, {'u': 13, 'v': 14, 'w': 12176.0}, {'u': 14, 'v': 15, 'w': 536.0}, {'u': 14, 'v': 20, 'w': 139.0}], 'k': 9, 'source_file': 'I023.stp', 'density': 0.08866995073891626}","[[28, 29], [4, 29], [4, 7], [7, 15], [9, 10], [9, 15], [14, 15], [14, 20]]",4769.0,"{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 'X', 'v': 'AA', 'w': 925.0}, {'u': 'X', 'v': 'U', 'w': 9291.0}, {'u': 'B', 'v': 'J', 'w': 878.0}, {'u': 'B', 'v': 'Q', 'w': 13250.0}, {'u': 'Y', 'v': 'W', 'w': 926.0}, {'u': 'Y', 'v': 'L', 'w': 5870.0}, {'u': 'Y', 'v': 'AA', 'w': 993.0}, {'u': 'U', 'v': 'P', 'w': 607.0}, {'u': 'U', 'v': 'M', 'w': 867.0}, {'u': 'AB', 'v': 'T', 'w': 1247.0}, {'u': 'AB', 'v': 'AC', 'w': 280.0}, {'u': 'K', 'v': 'F', 'w': 1390.0}, {'u': 'K', 'v': 'E', 'w': 8379.0}, {'u': 'K', 'v': 'S', 'w': 1233.0}, {'u': 'AC', 'v': 'D', 'w': 818.0}, {'u': 'A', 'v': 'P', 'w': 3946.0}, {'u': 'Z', 'v': 'M', 'w': 3025.0}, {'u': 'Z', 'v': 'AA', 'w': 6041.0}, {'u': 'Z', 'v': 'L', 'w': 999.0}, {'u': 'Q', 'v': 'R', 'w': 743.0}, {'u': 'Q', 'v': 'V', 'w': 9173.0}, {'u': 'D', 'v': 'E', 'w': 1949.0}, {'u': 'D', 'v': 'G', 'w': 193.0}, {'u': 'R', 'v': 'J', 'w': 12707.0}, {'u': 'R', 'v': 'W', 'w': 9407.0}, {'u': 'F', 'v': 'G', 'w': 8012.0}, {'u': 'F', 'v': 'H', 'w': 519.0}, {'u': 'G', 'v': 'O', 'w': 1160.0}, {'u': 'C', 'v': 'T', 'w': 1322.0}, {'u': 'I', 'v': 'J', 'w': 853.0}, {'u': 'I', 'v': 'L', 'w': 15928.0}, {'u': 'I', 'v': 'O', 'w': 790.0}, {'u': 'V', 'v': 'W', 'w': 1029.0}, {'u': 'M', 'v': 'N', 'w': 12176.0}, {'u': 'N', 'v': 'O', 'w': 536.0}, {'u': 'N', 'v': 'T', 'w': 139.0}], 'density': 0.08866995073891626, 'source_file': 'I023.stp', 'k': 9}","[['AB', 'AC'], ['D', 'AC'], ['D', 'G'], ['G', 'O'], ['I', 'J'], ['I', 'O'], ['N', 'O'], ['N', 'T']]",10,markdown_table,names
KMST,KMST,"Recently a team decided they’d pick a fixed number of habitat patches and create corridors so those patches are all connected, but without extra looping routes that just waste length. Plans are scored by adding up every corridor’s length; the goal is the smallest possible total while including exactly the required number of patches and not duplicating connections. The particular instance and measurements are shown below.

{
  ""total_habitat_patches"": 24,
  ""candidate_corridor_count"": 31,
  ""edges"": [
    {
      ""patch_endpoint_a"": ""I"",
      ""patch_endpoint_b"": ""X"",
      ""corridor_length"": 2843.0
    },
    {
      ""patch_endpoint_a"": ""I"",
      ""patch_endpoint_b"": ""H"",
      ""corridor_length"": 3415.0
    },
    {
      ""patch_endpoint_a"": ""I"",
      ""patch_endpoint_b"": ""S"",
      ""corridor_length"": 7044.0
    },
    {
      ""patch_endpoint_a"": ""Q"",
      ""patch_endpoint_b"": ""G"",
      ""corridor_length"": 1269.0
    },
    {
      ""patch_endpoint_a"": ""Q"",
      ""patch_endpoint_b"": ""J"",
      ""corridor_length"": 7348.0
    },
    {
      ""patch_endpoint_a"": ""Q"",
      ""patch_endpoint_b"": ""O"",
      ""corridor_length"": 3564.0
    },
    {
      ""patch_endpoint_a"": ""R"",
      ""patch_endpoint_b"": ""P"",
      ""corridor_length"": 1343.0
    },
    {
      ""patch_endpoint_a"": ""R"",
      ""patch_endpoint_b"": ""S"",
      ""corridor_length"": 2574.0
    },
    {
      ""patch_endpoint_a"": ""R"",
      ""patch_endpoint_b"": ""U"",
      ""corridor_length"": 1314.0
    },
    {
      ""patch_endpoint_a"": ""S"",
      ""patch_endpoint_b"": ""L"",
      ""corridor_length"": 1254.0
    },
    {
      ""patch_endpoint_a"": ""A"",
      ""patch_endpoint_b"": ""B"",
      ""corridor_length"": 643.0
    },
    {
      ""patch_endpoint_a"": ""A"",
      ""patch_endpoint_b"": ""D"",
      ""corridor_length"": 374.0
    },
    {
      ""patch_endpoint_a"": ""A"",
      ""patch_endpoint_b"": ""K"",
      ""corridor_length"": 5548.0
    },
    {
      ""patch_endpoint_a"": ""B"",
      ""patch_endpoint_b"": ""C"",
      ""corridor_length"": 335.0
    },
    {
      ""patch_endpoint_a"": ""C"",
      ""patch_endpoint_b"": ""D"",
      ""corridor_length"": 959.0
    },
    {
      ""patch_endpoint_a"": ""D"",
      ""patch_endpoint_b"": ""W"",
      ""corridor_length"": 2147.0
    },
    {
      ""patch_endpoint_a"": ""E"",
      ""patch_endpoint_b"": ""K"",
      ""corridor_length"": 10632.0
    },
    {
      ""patch_endpoint_a"": ""L"",
      ""patch_endpoint_b"": ""P"",
      ""corridor_length"": 2414.0
    },
    {
      ""patch_endpoint_a"": ""M"",
      ""patch_endpoint_b"": ""N"",
      ""corridor_length"": 652.0
    },
    {
      ""patch_endpoint_a"": ""M"",
      ""patch_endpoint_b"": ""P"",
      ""corridor_length"": 2548.0
    },
    {
      ""patch_endpoint_a"": ""J"",
      ""patch_endpoint_b"": ""K"",
      ""corridor_length"": 156.0
    },
    {
      ""patch_endpoint_a"": ""J"",
      ""patch_endpoint_b"": ""V"",
      ""corridor_length"": 2866.0
    },
    {
      ""patch_endpoint_a"": ""F"",
      ""patch_endpoint_b"": ""G"",
      ""corridor_length"": 1683.0
    },
    {
      ""patch_endpoint_a"": ""G"",
      ""patch_endpoint_b"": ""N"",
      ""corridor_length"": 3757.0
    },
    {
      ""patch_endpoint_a"": ""H"",
      ""patch_endpoint_b"": ""T"",
      ""corridor_length"": 1249.0
    },
    {
      ""patch_endpoint_a"": ""N"",
      ""patch_endpoint_b"": ""O"",
      ""corridor_length"": 1550.0
    },
    {
      ""patch_endpoint_a"": ""O"",
      ""patch_endpoint_b"": ""U"",
      ""corridor_length"": 4456.0
    },
    {
      ""patch_endpoint_a"": ""U"",
      ""patch_endpoint_b"": ""V"",
      ""corridor_length"": 240.0
    },
    {
      ""patch_endpoint_a"": ""V"",
      ""patch_endpoint_b"": ""W"",
      ""corridor_length"": 3786.0
    },
    {
      ""patch_endpoint_a"": ""W"",
      ""patch_endpoint_b"": ""X"",
      ""corridor_length"": 336.0
    },
    {
      ""patch_endpoint_a"": ""X"",
      ""patch_endpoint_b"": ""T"",
      ""corridor_length"": 2956.0
    }
  ],
  ""target_patches_to_connect"": 12
}

If you want the corridors listed back in a compact way, I usually give them in a tiny JSON sketch like this so it’s easy to parse:

{
  ""solution"": [[""patch1"", ""patch2""], [""patch3"", ""patch4""], [""patch5"", ""patch6""], ...]
}

Each inner pair is just one corridor linking two habitat patches, and the whole ""solution"" list is the set of corridors you’d build. This block is only a shape example — not the actual chosen corridors.

Please use the exact identifiers from the instance input when you give the real answer — don’t rename patches 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 31, 'edges': [{'u': 9, 'v': 24, 'w': 2843.0}, {'u': 9, 'v': 8, 'w': 3415.0}, {'u': 9, 'v': 19, 'w': 7044.0}, {'u': 17, 'v': 7, 'w': 1269.0}, {'u': 17, 'v': 10, 'w': 7348.0}, {'u': 17, 'v': 15, 'w': 3564.0}, {'u': 18, 'v': 16, 'w': 1343.0}, {'u': 18, 'v': 19, 'w': 2574.0}, {'u': 18, 'v': 21, 'w': 1314.0}, {'u': 19, 'v': 12, 'w': 1254.0}, {'u': 1, 'v': 2, 'w': 643.0}, {'u': 1, 'v': 4, 'w': 374.0}, {'u': 1, 'v': 11, 'w': 5548.0}, {'u': 2, 'v': 3, 'w': 335.0}, {'u': 3, 'v': 4, 'w': 959.0}, {'u': 4, 'v': 23, 'w': 2147.0}, {'u': 5, 'v': 11, 'w': 10632.0}, {'u': 12, 'v': 16, 'w': 2414.0}, {'u': 13, 'v': 14, 'w': 652.0}, {'u': 13, 'v': 16, 'w': 2548.0}, {'u': 10, 'v': 11, 'w': 156.0}, {'u': 10, 'v': 22, 'w': 2866.0}, {'u': 6, 'v': 7, 'w': 1683.0}, {'u': 7, 'v': 14, 'w': 3757.0}, {'u': 8, 'v': 20, 'w': 1249.0}, {'u': 14, 'v': 15, 'w': 1550.0}, {'u': 15, 'v': 21, 'w': 4456.0}, {'u': 21, 'v': 22, 'w': 240.0}, {'u': 22, 'v': 23, 'w': 3786.0}, {'u': 23, 'v': 24, 'w': 336.0}, {'u': 24, 'v': 20, 'w': 2956.0}], 'k': 12, 'source_file': 'I045.stp', 'density': 0.11231884057971014}","[[16, 18], [18, 21], [1, 2], [1, 4], [2, 3], [4, 23], [10, 11], [10, 22], [21, 22], [22, 23], [23, 24]]",13540.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 31, 'edges': [{'u': 'I', 'v': 'X', 'w': 2843.0}, {'u': 'I', 'v': 'H', 'w': 3415.0}, {'u': 'I', 'v': 'S', 'w': 7044.0}, {'u': 'Q', 'v': 'G', 'w': 1269.0}, {'u': 'Q', 'v': 'J', 'w': 7348.0}, {'u': 'Q', 'v': 'O', 'w': 3564.0}, {'u': 'R', 'v': 'P', 'w': 1343.0}, {'u': 'R', 'v': 'S', 'w': 2574.0}, {'u': 'R', 'v': 'U', 'w': 1314.0}, {'u': 'S', 'v': 'L', 'w': 1254.0}, {'u': 'A', 'v': 'B', 'w': 643.0}, {'u': 'A', 'v': 'D', 'w': 374.0}, {'u': 'A', 'v': 'K', 'w': 5548.0}, {'u': 'B', 'v': 'C', 'w': 335.0}, {'u': 'C', 'v': 'D', 'w': 959.0}, {'u': 'D', 'v': 'W', 'w': 2147.0}, {'u': 'E', 'v': 'K', 'w': 10632.0}, {'u': 'L', 'v': 'P', 'w': 2414.0}, {'u': 'M', 'v': 'N', 'w': 652.0}, {'u': 'M', 'v': 'P', 'w': 2548.0}, {'u': 'J', 'v': 'K', 'w': 156.0}, {'u': 'J', 'v': 'V', 'w': 2866.0}, {'u': 'F', 'v': 'G', 'w': 1683.0}, {'u': 'G', 'v': 'N', 'w': 3757.0}, {'u': 'H', 'v': 'T', 'w': 1249.0}, {'u': 'N', 'v': 'O', 'w': 1550.0}, {'u': 'O', 'v': 'U', 'w': 4456.0}, {'u': 'U', 'v': 'V', 'w': 240.0}, {'u': 'V', 'v': 'W', 'w': 3786.0}, {'u': 'W', 'v': 'X', 'w': 336.0}, {'u': 'X', 'v': 'T', 'w': 2956.0}], 'density': 0.11231884057971014, 'source_file': 'I045.stp', 'k': 12}","[['P', 'R'], ['R', 'U'], ['A', 'B'], ['A', 'D'], ['B', 'C'], ['D', 'W'], ['J', 'K'], ['J', 'V'], ['U', 'V'], ['V', 'W'], ['W', 'X']]",11,json,names
KMST,KMST,"Imagine laying out the festival’s utilities: choose exactly a set number of booths to serve, run lines between them so they’re all linked together with no circular paths, and aim to use the shortest total length of cable possible — just add up the lengths of the connections you’d install to compare layouts. No booth in the chosen set can be left out or connected more than once; they all need to sit in one connected system. The precise layout and distances are below.

Here are the 30 booths and 36 candidate direct lines; select exactly 12 booths and connect them into a single acyclic network using the listed lengths.
Potential line between booth 26 and booth 23 with length 3598.0.
Potential line between booth 26 and booth 15 with length 2879.0.
Potential line between booth 26 and booth 6 with length 4887.0.
Potential line between booth 29 and booth 30 with length 1066.0.
Potential line between booth 29 and booth 28 with length 334.0.
Potential line between booth 29 and booth 12 with length 3934.0.
Potential line between booth 30 and booth 8 with length 280.0.
Potential line between booth 30 and booth 5 with length 4870.0.
Potential line between booth 24 and booth 25 with length 2312.0.
Potential line between booth 20 and booth 18 with length 1213.0.
Potential line between booth 20 and booth 19 with length 1558.0.
Potential line between booth 10 and booth 8 with length 622.0.
Potential line between booth 10 and booth 25 with length 1643.0.
Potential line between booth 10 and booth 27 with length 9.0.
Potential line between booth 27 and booth 28 with length 770.0.
Potential line between booth 27 and booth 11 with length 2064.0.
Potential line between booth 28 and booth 2 with length 4967.0.
Potential line between booth 12 and booth 5 with length 181.0.
Potential line between booth 12 and booth 14 with length 5302.0.
Potential line between booth 13 and booth 5 with length 4405.0.
Potential line between booth 13 and booth 23 with length 1713.0.
Potential line between booth 13 and booth 4 with length 3583.0.
Potential line between booth 18 and booth 19 with length 2262.0.
Potential line between booth 18 and booth 8 with length 9523.0.
Potential line between booth 19 and booth 21 with length 4392.0.
Potential line between booth 14 and booth 15 with length 786.0.
Potential line between booth 14 and booth 7 with length 365000.0.
Potential line between booth 15 and booth 7 with length 365000.0.
Potential line between booth 1 and booth 2 with length 452.0.
Potential line between booth 2 and booth 3 with length 13674.0.
Potential line between booth 16 and booth 23 with length 1450.0.
Potential line between booth 16 and booth 17 with length 1773.0.
Potential line between booth 17 and booth 6 with length 1200.0.
Potential line between booth 17 and booth 4 with length 3710.0.
Potential line between booth 9 and booth 4 with length 3910.0.
Potential line between booth 25 and booth 22 with length 4330.0.
When ready, pick the 12 booths and minimize the total of the chosen line lengths to produce the shortest connected layout.

If you want to sketch a candidate layout back to me, just drop it in a tiny JSON blob like this:

{
  ""solution"": [[""u1"", ""v1""], [""u2"", ""v2""], ...]
}

Think of ""solution"" as a list of the cable runs you’d install — each inner pair is one connection between two booths/nodes. This is just the shape I expect (a simple list of edges), not the actual final answer.

Please make sure to use the exact 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”.""","{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 36, 'edges': [{'u': 26, 'v': 23, 'w': 3598.0}, {'u': 26, 'v': 15, 'w': 2879.0}, {'u': 26, 'v': 6, 'w': 4887.0}, {'u': 29, 'v': 30, 'w': 1066.0}, {'u': 29, 'v': 28, 'w': 334.0}, {'u': 29, 'v': 12, 'w': 3934.0}, {'u': 30, 'v': 8, 'w': 280.0}, {'u': 30, 'v': 5, 'w': 4870.0}, {'u': 24, 'v': 25, 'w': 2312.0}, {'u': 20, 'v': 18, 'w': 1213.0}, {'u': 20, 'v': 19, 'w': 1558.0}, {'u': 10, 'v': 8, 'w': 622.0}, {'u': 10, 'v': 25, 'w': 1643.0}, {'u': 10, 'v': 27, 'w': 9.0}, {'u': 27, 'v': 28, 'w': 770.0}, {'u': 27, 'v': 11, 'w': 2064.0}, {'u': 28, 'v': 2, 'w': 4967.0}, {'u': 12, 'v': 5, 'w': 181.0}, {'u': 12, 'v': 14, 'w': 5302.0}, {'u': 13, 'v': 5, 'w': 4405.0}, {'u': 13, 'v': 23, 'w': 1713.0}, {'u': 13, 'v': 4, 'w': 3583.0}, {'u': 18, 'v': 19, 'w': 2262.0}, {'u': 18, 'v': 8, 'w': 9523.0}, {'u': 19, 'v': 21, 'w': 4392.0}, {'u': 14, 'v': 15, 'w': 786.0}, {'u': 14, 'v': 7, 'w': 365000.0}, {'u': 15, 'v': 7, 'w': 365000.0}, {'u': 1, 'v': 2, 'w': 452.0}, {'u': 2, 'v': 3, 'w': 13674.0}, {'u': 16, 'v': 23, 'w': 1450.0}, {'u': 16, 'v': 17, 'w': 1773.0}, {'u': 17, 'v': 6, 'w': 1200.0}, {'u': 17, 'v': 4, 'w': 3710.0}, {'u': 9, 'v': 4, 'w': 3910.0}, {'u': 25, 'v': 22, 'w': 4330.0}], 'k': 12, 'source_file': 'I044.stp', 'density': 0.08275862068965517}","[[28, 29], [12, 29], [8, 30], [8, 10], [10, 25], [10, 27], [27, 28], [11, 27], [2, 28], [5, 12], [1, 2]]",15256.0,"{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 36, 'edges': [{'u': 26, 'v': 23, 'w': 3598.0}, {'u': 26, 'v': 15, 'w': 2879.0}, {'u': 26, 'v': 6, 'w': 4887.0}, {'u': 29, 'v': 30, 'w': 1066.0}, {'u': 29, 'v': 28, 'w': 334.0}, {'u': 29, 'v': 12, 'w': 3934.0}, {'u': 30, 'v': 8, 'w': 280.0}, {'u': 30, 'v': 5, 'w': 4870.0}, {'u': 24, 'v': 25, 'w': 2312.0}, {'u': 20, 'v': 18, 'w': 1213.0}, {'u': 20, 'v': 19, 'w': 1558.0}, {'u': 10, 'v': 8, 'w': 622.0}, {'u': 10, 'v': 25, 'w': 1643.0}, {'u': 10, 'v': 27, 'w': 9.0}, {'u': 27, 'v': 28, 'w': 770.0}, {'u': 27, 'v': 11, 'w': 2064.0}, {'u': 28, 'v': 2, 'w': 4967.0}, {'u': 12, 'v': 5, 'w': 181.0}, {'u': 12, 'v': 14, 'w': 5302.0}, {'u': 13, 'v': 5, 'w': 4405.0}, {'u': 13, 'v': 23, 'w': 1713.0}, {'u': 13, 'v': 4, 'w': 3583.0}, {'u': 18, 'v': 19, 'w': 2262.0}, {'u': 18, 'v': 8, 'w': 9523.0}, {'u': 19, 'v': 21, 'w': 4392.0}, {'u': 14, 'v': 15, 'w': 786.0}, {'u': 14, 'v': 7, 'w': 365000.0}, {'u': 15, 'v': 7, 'w': 365000.0}, {'u': 1, 'v': 2, 'w': 452.0}, {'u': 2, 'v': 3, 'w': 13674.0}, {'u': 16, 'v': 23, 'w': 1450.0}, {'u': 16, 'v': 17, 'w': 1773.0}, {'u': 17, 'v': 6, 'w': 1200.0}, {'u': 17, 'v': 4, 'w': 3710.0}, {'u': 9, 'v': 4, 'w': 3910.0}, {'u': 25, 'v': 22, 'w': 4330.0}], 'density': 0.08275862068965517, 'source_file': 'I044.stp', 'k': 12}","[[28, 29], [12, 29], [8, 30], [8, 10], [10, 25], [10, 27], [27, 28], [11, 27], [2, 28], [5, 12], [1, 2]]",12,markdown_table,1
KMST,KMST,"Around here the job is to choose exactly k stops and lay down sidewalks so the chosen stops become one continuous, loop-free network for students to use. The cost to compare different layouts is the total sidewalk length — just add up the lengths of the chosen links — and the aim is to make that sum as small as possible while including exactly the required stops and not creating any closed loops or double-counted stretches. The precise map and lengths are shown below.

{
  ""total_bus_stops"": 21,
  ""candidate_sidewalk_segments"": 25,
  ""edges"": [
    {
      ""stop_u"": 3,
      ""stop_v"": 2,
      ""sidewalk_length"": 5747.0
    },
    {
      ""stop_u"": 5,
      ""stop_v"": 6,
      ""sidewalk_length"": 7418.0
    },
    {
      ""stop_u"": 5,
      ""stop_v"": 11,
      ""sidewalk_length"": 10955.0
    },
    {
      ""stop_u"": 5,
      ""stop_v"": 8,
      ""sidewalk_length"": 2353.0
    },
    {
      ""stop_u"": 9,
      ""stop_v"": 10,
      ""sidewalk_length"": 6464.0
    },
    {
      ""stop_u"": 9,
      ""stop_v"": 7,
      ""sidewalk_length"": 1678.0
    },
    {
      ""stop_u"": 9,
      ""stop_v"": 16,
      ""sidewalk_length"": 7003.0
    },
    {
      ""stop_u"": 9,
      ""stop_v"": 1,
      ""sidewalk_length"": 7511.0
    },
    {
      ""stop_u"": 7,
      ""stop_v"": 8,
      ""sidewalk_length"": 8521.0
    },
    {
      ""stop_u"": 7,
      ""stop_v"": 6,
      ""sidewalk_length"": 681.0
    },
    {
      ""stop_u"": 8,
      ""stop_v"": 14,
      ""sidewalk_length"": 1117.0
    },
    {
      ""stop_u"": 1,
      ""stop_v"": 0,
      ""sidewalk_length"": 847.0
    },
    {
      ""stop_u"": 1,
      ""stop_v"": 16,
      ""sidewalk_length"": 5348.0
    },
    {
      ""stop_u"": 10,
      ""stop_v"": 17,
      ""sidewalk_length"": 1448.0
    },
    {
      ""stop_u"": 10,
      ""stop_v"": 15,
      ""sidewalk_length"": 10934.0
    },
    {
      ""stop_u"": 12,
      ""stop_v"": 13,
      ""sidewalk_length"": 3649.0
    },
    {
      ""stop_u"": 12,
      ""stop_v"": 15,
      ""sidewalk_length"": 3585.0
    },
    {
      ""stop_u"": 12,
      ""stop_v"": 2,
      ""sidewalk_length"": 6593.0
    },
    {
      ""stop_u"": 13,
      ""stop_v"": 19,
      ""sidewalk_length"": 4931.0
    },
    {
      ""stop_u"": 13,
      ""stop_v"": 14,
      ""sidewalk_length"": 5402.0
    },
    {
      ""stop_u"": 14,
      ""stop_v"": 15,
      ""sidewalk_length"": 2141.0
    },
    {
      ""stop_u"": 0,
      ""stop_v"": 17,
      ""sidewalk_length"": 1985.0
    },
    {
      ""stop_u"": 20,
      ""stop_v"": 2,
      ""sidewalk_length"": 18536.0
    },
    {
      ""stop_u"": 4,
      ""stop_v"": 18,
      ""sidewalk_length"": 1118.0
    },
    {
      ""stop_u"": 17,
      ""stop_v"": 18,
      ""sidewalk_length"": 351.0
    }
  ],
  ""required_stops_count"": 6
}

You can just hand the chosen sidewalk segments over in a tiny JSON snippet like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as the list of sidewalk links you picked — each pair [u, v] is one connection between stop u and stop v. This block is just the shape I expect, not the real answer: replace those u1/v1 placeholders with the actual node identifiers from the instance.

Please use the identifiers exactly as they appear in the input file — 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”.""","{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 25, 'edges': [{'u': 4, 'v': 3, 'w': 5747.0}, {'u': 6, 'v': 7, 'w': 7418.0}, {'u': 6, 'v': 12, 'w': 10955.0}, {'u': 6, 'v': 9, 'w': 2353.0}, {'u': 10, 'v': 11, 'w': 6464.0}, {'u': 10, 'v': 8, 'w': 1678.0}, {'u': 10, 'v': 17, 'w': 7003.0}, {'u': 10, 'v': 2, 'w': 7511.0}, {'u': 8, 'v': 9, 'w': 8521.0}, {'u': 8, 'v': 7, 'w': 681.0}, {'u': 9, 'v': 15, 'w': 1117.0}, {'u': 2, 'v': 1, 'w': 847.0}, {'u': 2, 'v': 17, 'w': 5348.0}, {'u': 11, 'v': 18, 'w': 1448.0}, {'u': 11, 'v': 16, 'w': 10934.0}, {'u': 13, 'v': 14, 'w': 3649.0}, {'u': 13, 'v': 16, 'w': 3585.0}, {'u': 13, 'v': 3, 'w': 6593.0}, {'u': 14, 'v': 20, 'w': 4931.0}, {'u': 14, 'v': 15, 'w': 5402.0}, {'u': 15, 'v': 16, 'w': 2141.0}, {'u': 1, 'v': 18, 'w': 1985.0}, {'u': 21, 'v': 3, 'w': 18536.0}, {'u': 5, 'v': 19, 'w': 1118.0}, {'u': 18, 'v': 19, 'w': 351.0}], 'k': 6, 'source_file': 'I019.stp', 'density': 0.11904761904761904}","[[1, 2], [11, 18], [1, 18], [5, 19], [18, 19]]",5749.0,"{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 25, 'edges': [{'u': 3, 'v': 2, 'w': 5747.0}, {'u': 5, 'v': 6, 'w': 7418.0}, {'u': 5, 'v': 11, 'w': 10955.0}, {'u': 5, 'v': 8, 'w': 2353.0}, {'u': 9, 'v': 10, 'w': 6464.0}, {'u': 9, 'v': 7, 'w': 1678.0}, {'u': 9, 'v': 16, 'w': 7003.0}, {'u': 9, 'v': 1, 'w': 7511.0}, {'u': 7, 'v': 8, 'w': 8521.0}, {'u': 7, 'v': 6, 'w': 681.0}, {'u': 8, 'v': 14, 'w': 1117.0}, {'u': 1, 'v': 0, 'w': 847.0}, {'u': 1, 'v': 16, 'w': 5348.0}, {'u': 10, 'v': 17, 'w': 1448.0}, {'u': 10, 'v': 15, 'w': 10934.0}, {'u': 12, 'v': 13, 'w': 3649.0}, {'u': 12, 'v': 15, 'w': 3585.0}, {'u': 12, 'v': 2, 'w': 6593.0}, {'u': 13, 'v': 19, 'w': 4931.0}, {'u': 13, 'v': 14, 'w': 5402.0}, {'u': 14, 'v': 15, 'w': 2141.0}, {'u': 0, 'v': 17, 'w': 1985.0}, {'u': 20, 'v': 2, 'w': 18536.0}, {'u': 4, 'v': 18, 'w': 1118.0}, {'u': 17, 'v': 18, 'w': 351.0}], 'density': 0.11904761904761904, 'source_file': 'I019.stp', 'k': 6}","[[0, 1], [10, 17], [0, 17], [4, 18], [17, 18]]",13,json,0
KMST,KMST,"Many people imagine a dig where the director just opens every route, but here the task is tighter: choose a set number of sites and link them with pathways that don’t double back into loops. The better choice is the one with the least combined path length — total everything up and choose the smallest total. Exactly the predetermined number of sites must be used, they all need to be connected, and no circular or repeated tracks are allowed. The concrete site list and the path distances follow below.

# total_sites=27
# candidate_tracks=34
# sites_to_select=14
site_endpoint_a,site_endpoint_b,track_length
W,Q,1092.0
C,O,694.0
C,Q,806.0
D,E,488.0
D,I,968.0
D,K,985.0
E,M,97.0
E,L,980.0
X,Y,703.0
X,Q,332.0
X,T,1120.0
Z,J,807.0
Z,M,63.0
Z,AA,574.0
AA,H,539.0
AA,N,33.0
F,H,212.0
I,J,451.0
I,S,162.0
J,T,144.0
O,P,1485.0
K,L,395.0
K,U,125.0
L,V,88.0
M,N,480.0
N,G,549.0
H,G,133.0
P,S,1054.0
P,B,1166.0
A,B,175.0
R,U,1440.0
R,B,1228.0
S,T,445.0
U,V,385.0

I'll just show the shape I want back — a tiny JSON snippet so it's clear how to paste the chosen edges. Nothing fancy, just the layout:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This means ""solution"" should be a list of edges, and each inner pair [u, v] is an edge connecting site u to site v. Think of it like a simple checklist: list the links you picked, one pair per link. It's just a sketch of the shape I expect, not the real 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”.""","{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 34, 'edges': [{'u': 23, 'v': 17, 'w': 1092.0}, {'u': 3, 'v': 15, 'w': 694.0}, {'u': 3, 'v': 17, 'w': 806.0}, {'u': 4, 'v': 5, 'w': 488.0}, {'u': 4, 'v': 9, 'w': 968.0}, {'u': 4, 'v': 11, 'w': 985.0}, {'u': 5, 'v': 13, 'w': 97.0}, {'u': 5, 'v': 12, 'w': 980.0}, {'u': 24, 'v': 25, 'w': 703.0}, {'u': 24, 'v': 17, 'w': 332.0}, {'u': 24, 'v': 20, 'w': 1120.0}, {'u': 26, 'v': 10, 'w': 807.0}, {'u': 26, 'v': 13, 'w': 63.0}, {'u': 26, 'v': 27, 'w': 574.0}, {'u': 27, 'v': 8, 'w': 539.0}, {'u': 27, 'v': 14, 'w': 33.0}, {'u': 6, 'v': 8, 'w': 212.0}, {'u': 9, 'v': 10, 'w': 451.0}, {'u': 9, 'v': 19, 'w': 162.0}, {'u': 10, 'v': 20, 'w': 144.0}, {'u': 15, 'v': 16, 'w': 1485.0}, {'u': 11, 'v': 12, 'w': 395.0}, {'u': 11, 'v': 21, 'w': 125.0}, {'u': 12, 'v': 22, 'w': 88.0}, {'u': 13, 'v': 14, 'w': 480.0}, {'u': 14, 'v': 7, 'w': 549.0}, {'u': 8, 'v': 7, 'w': 133.0}, {'u': 16, 'v': 19, 'w': 1054.0}, {'u': 16, 'v': 2, 'w': 1166.0}, {'u': 1, 'v': 2, 'w': 175.0}, {'u': 18, 'v': 21, 'w': 1440.0}, {'u': 18, 'v': 2, 'w': 1228.0}, {'u': 19, 'v': 20, 'w': 445.0}, {'u': 21, 'v': 22, 'w': 385.0}], 'k': 14, 'source_file': 'I047.stp', 'density': 0.09686609686609686}","[[5, 13], [5, 12], [10, 26], [13, 26], [8, 27], [14, 27], [6, 8], [10, 20], [11, 21], [12, 22], [13, 14], [7, 8], [21, 22]]",4086.0,"{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 34, 'edges': [{'u': 'W', 'v': 'Q', 'w': 1092.0}, {'u': 'C', 'v': 'O', 'w': 694.0}, {'u': 'C', 'v': 'Q', 'w': 806.0}, {'u': 'D', 'v': 'E', 'w': 488.0}, {'u': 'D', 'v': 'I', 'w': 968.0}, {'u': 'D', 'v': 'K', 'w': 985.0}, {'u': 'E', 'v': 'M', 'w': 97.0}, {'u': 'E', 'v': 'L', 'w': 980.0}, {'u': 'X', 'v': 'Y', 'w': 703.0}, {'u': 'X', 'v': 'Q', 'w': 332.0}, {'u': 'X', 'v': 'T', 'w': 1120.0}, {'u': 'Z', 'v': 'J', 'w': 807.0}, {'u': 'Z', 'v': 'M', 'w': 63.0}, {'u': 'Z', 'v': 'AA', 'w': 574.0}, {'u': 'AA', 'v': 'H', 'w': 539.0}, {'u': 'AA', 'v': 'N', 'w': 33.0}, {'u': 'F', 'v': 'H', 'w': 212.0}, {'u': 'I', 'v': 'J', 'w': 451.0}, {'u': 'I', 'v': 'S', 'w': 162.0}, {'u': 'J', 'v': 'T', 'w': 144.0}, {'u': 'O', 'v': 'P', 'w': 1485.0}, {'u': 'K', 'v': 'L', 'w': 395.0}, {'u': 'K', 'v': 'U', 'w': 125.0}, {'u': 'L', 'v': 'V', 'w': 88.0}, {'u': 'M', 'v': 'N', 'w': 480.0}, {'u': 'N', 'v': 'G', 'w': 549.0}, {'u': 'H', 'v': 'G', 'w': 133.0}, {'u': 'P', 'v': 'S', 'w': 1054.0}, {'u': 'P', 'v': 'B', 'w': 1166.0}, {'u': 'A', 'v': 'B', 'w': 175.0}, {'u': 'R', 'v': 'U', 'w': 1440.0}, {'u': 'R', 'v': 'B', 'w': 1228.0}, {'u': 'S', 'v': 'T', 'w': 445.0}, {'u': 'U', 'v': 'V', 'w': 385.0}], 'density': 0.09686609686609686, 'source_file': 'I047.stp', 'k': 14}","[['E', 'M'], ['E', 'L'], ['J', 'Z'], ['M', 'Z'], ['H', 'AA'], ['N', 'AA'], ['F', 'H'], ['J', 'T'], ['K', 'U'], ['L', 'V'], ['M', 'N'], ['G', 'H'], ['U', 'V']]",14,csv,names
KMST,KMST,"Someone in the planning office wants a compact bike network: pick exactly k stations, join them so they form one connected structure without any closed loops, and make sure every selected station is included once. Plans are compared by the total length of lanes built — just add the lane distances to see which is shortest. The map and numbers for this task are shown below.

Map shows 25 stations and 32 candidate links; select exactly 12 stations to form one connected, acyclic network.
Candidate link connecting station 21 and station 19 with length 7910.0.
Candidate link connecting station 21 and station 15 with length 1527.0.
Candidate link connecting station 21 and station 18 with length 1679.0.
Candidate link connecting station 0 and station 20 with length 2976.0.
Candidate link connecting station 0 and station 10 with length 4251.0.
Candidate link connecting station 0 and station 16 with length 6694.0.
Candidate link connecting station 24 and station 23 with length 1431.0.
Candidate link connecting station 24 and station 22 with length 2213.0.
Candidate link connecting station 24 and station 1 with length 980.0.
Candidate link connecting station 19 and station 17 with length 1866.0.
Candidate link connecting station 19 and station 20 with length 1593.0.
Candidate link connecting station 20 and station 15 with length 8210.0.
Candidate link connecting station 5 and station 9 with length 325.0.
Candidate link connecting station 5 and station 6 with length 819.0.
Candidate link connecting station 6 and station 8 with length 1298.0.
Candidate link connecting station 7 and station 13 with length 1243.0.
Candidate link connecting station 7 and station 1 with length 2912.0.
Candidate link connecting station 22 and station 23 with length 3519.0.
Candidate link connecting station 22 and station 16 with length 539.0.
Candidate link connecting station 23 and station 4 with length 1530.0.
Candidate link connecting station 16 and station 14 with length 1176.0.
Candidate link connecting station 8 and station 9 with length 1704.0.
Candidate link connecting station 8 and station 10 with length 4293.0.
Candidate link connecting station 9 and station 11 with length 3037.0.
Candidate link connecting station 10 and station 14 with length 4894.0.
Candidate link connecting station 17 and station 18 with length 7354.0.
Candidate link connecting station 11 and station 12 with length 840.0.
Candidate link connecting station 12 and station 13 with length 1490.0.
Candidate link connecting station 13 and station 14 with length 1947.0.
Candidate link connecting station 1 and station 2 with length 619.0.
Candidate link connecting station 3 and station 4 with length 722.0.
Candidate link connecting station 4 and station 15 with length 2844.0.
Compare plans by summing the lengths of chosen links; the plan with the smallest total lane length is preferred.

If you want to send the chosen lanes back to me, please use this little JSON shape so it's easy to read:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is just a list of the lanes you want to build; each lane is a pair [u, v] meaning ""connect station u with station v"". Think of it like filling out a short form — this block is only a sketch of the shape I expect, not the actual answer.

Please be sure to use the exact identifiers from 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”.""","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 32, 'edges': [{'u': 22, 'v': 20, 'w': 7910.0}, {'u': 22, 'v': 16, 'w': 1527.0}, {'u': 22, 'v': 19, 'w': 1679.0}, {'u': 1, 'v': 21, 'w': 2976.0}, {'u': 1, 'v': 11, 'w': 4251.0}, {'u': 1, 'v': 17, 'w': 6694.0}, {'u': 25, 'v': 24, 'w': 1431.0}, {'u': 25, 'v': 23, 'w': 2213.0}, {'u': 25, 'v': 2, 'w': 980.0}, {'u': 20, 'v': 18, 'w': 1866.0}, {'u': 20, 'v': 21, 'w': 1593.0}, {'u': 21, 'v': 16, 'w': 8210.0}, {'u': 6, 'v': 10, 'w': 325.0}, {'u': 6, 'v': 7, 'w': 819.0}, {'u': 7, 'v': 9, 'w': 1298.0}, {'u': 8, 'v': 14, 'w': 1243.0}, {'u': 8, 'v': 2, 'w': 2912.0}, {'u': 23, 'v': 24, 'w': 3519.0}, {'u': 23, 'v': 17, 'w': 539.0}, {'u': 24, 'v': 5, 'w': 1530.0}, {'u': 17, 'v': 15, 'w': 1176.0}, {'u': 9, 'v': 10, 'w': 1704.0}, {'u': 9, 'v': 11, 'w': 4293.0}, {'u': 10, 'v': 12, 'w': 3037.0}, {'u': 11, 'v': 15, 'w': 4894.0}, {'u': 18, 'v': 19, 'w': 7354.0}, {'u': 12, 'v': 13, 'w': 840.0}, {'u': 13, 'v': 14, 'w': 1490.0}, {'u': 14, 'v': 15, 'w': 1947.0}, {'u': 2, 'v': 3, 'w': 619.0}, {'u': 4, 'v': 5, 'w': 722.0}, {'u': 5, 'v': 16, 'w': 2844.0}], 'k': 12, 'source_file': 'I017.stp', 'density': 0.10666666666666667}","[[24, 25], [23, 25], [2, 25], [17, 23], [5, 24], [15, 17], [12, 13], [13, 14], [14, 15], [2, 3], [4, 5]]",13487.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 32, 'edges': [{'u': 21, 'v': 19, 'w': 7910.0}, {'u': 21, 'v': 15, 'w': 1527.0}, {'u': 21, 'v': 18, 'w': 1679.0}, {'u': 0, 'v': 20, 'w': 2976.0}, {'u': 0, 'v': 10, 'w': 4251.0}, {'u': 0, 'v': 16, 'w': 6694.0}, {'u': 24, 'v': 23, 'w': 1431.0}, {'u': 24, 'v': 22, 'w': 2213.0}, {'u': 24, 'v': 1, 'w': 980.0}, {'u': 19, 'v': 17, 'w': 1866.0}, {'u': 19, 'v': 20, 'w': 1593.0}, {'u': 20, 'v': 15, 'w': 8210.0}, {'u': 5, 'v': 9, 'w': 325.0}, {'u': 5, 'v': 6, 'w': 819.0}, {'u': 6, 'v': 8, 'w': 1298.0}, {'u': 7, 'v': 13, 'w': 1243.0}, {'u': 7, 'v': 1, 'w': 2912.0}, {'u': 22, 'v': 23, 'w': 3519.0}, {'u': 22, 'v': 16, 'w': 539.0}, {'u': 23, 'v': 4, 'w': 1530.0}, {'u': 16, 'v': 14, 'w': 1176.0}, {'u': 8, 'v': 9, 'w': 1704.0}, {'u': 8, 'v': 10, 'w': 4293.0}, {'u': 9, 'v': 11, 'w': 3037.0}, {'u': 10, 'v': 14, 'w': 4894.0}, {'u': 17, 'v': 18, 'w': 7354.0}, {'u': 11, 'v': 12, 'w': 840.0}, {'u': 12, 'v': 13, 'w': 1490.0}, {'u': 13, 'v': 14, 'w': 1947.0}, {'u': 1, 'v': 2, 'w': 619.0}, {'u': 3, 'v': 4, 'w': 722.0}, {'u': 4, 'v': 15, 'w': 2844.0}], 'density': 0.10666666666666667, 'source_file': 'I017.stp', 'k': 12}","[[23, 24], [22, 24], [1, 24], [16, 22], [4, 23], [14, 16], [11, 12], [12, 13], [13, 14], [1, 2], [3, 4]]",15,markdown_table,0
KMST,KMST,"We’ve been asked to connect a fixed number of vineyard parcels with irrigation lines so they form one continuous network, but we must avoid creating circular feeder routes. What makes one plan better than another is how little pipe and money it needs — add up the pipe segments you choose and that total length/cost is what matters. Exactly that predetermined number of parcels has to be chosen (no more, no less), each counted once, and all must be linked together without any loops. The exact instance — which parcels and the pipe lengths/costs — appears below.

There are 24 parcels, 27 candidate pipe segments, and we must select exactly 12 parcels to interconnect into one loop-free network.
Candidate pipe connecting parcel 3 and parcel 4 with length/cost 480.0.
Candidate pipe connecting parcel 3 and parcel 6 with length/cost 452.0.
Candidate pipe connecting parcel 3 and parcel 21 with length/cost 3132.0.
Candidate pipe connecting parcel 4 and parcel 16 with length/cost 489.0.
Candidate pipe connecting parcel 7 and parcel 13 with length/cost 1278.0.
Candidate pipe connecting parcel 8 and parcel 1 with length/cost 208.0.
Candidate pipe connecting parcel 8 and parcel 10 with length/cost 3135.0.
Candidate pipe connecting parcel 9 and parcel 1 with length/cost 505.0.
Candidate pipe connecting parcel 9 and parcel 2 with length/cost 201.0.
Candidate pipe connecting parcel 9 and parcel 21 with length/cost 1621.0.
Candidate pipe connecting parcel 10 and parcel 11 with length/cost 803.0.
Candidate pipe connecting parcel 11 and parcel 17 with length/cost 1021.0.
Candidate pipe connecting parcel 11 and parcel 13 with length/cost 376.0.
Candidate pipe connecting parcel 12 and parcel 20 with length/cost 991.0.
Candidate pipe connecting parcel 19 and parcel 20 with length/cost 581.0.
Candidate pipe connecting parcel 19 and parcel 18 with length/cost 1065.0.
Candidate pipe connecting parcel 19 and parcel 15 with length/cost 651.0.
Candidate pipe connecting parcel 20 and parcel 17 with length/cost 1908.0.
Candidate pipe connecting parcel 5 and parcel 6 with length/cost 496.0.
Candidate pipe connecting parcel 5 and parcel 17 with length/cost 591.0.
Candidate pipe connecting parcel 5 and parcel 21 with length/cost 3124.0.
Candidate pipe connecting parcel 6 and parcel 15 with length/cost 1409.0.
Candidate pipe connecting parcel 14 and parcel 21 with length/cost 2335.0.
Candidate pipe connecting parcel 15 and parcel 24 with length/cost 922.0.
Candidate pipe connecting parcel 21 and parcel 22 with length/cost 1074.0.
Candidate pipe connecting parcel 23 and parcel 24 with length/cost 1077.0.
Candidate pipe connecting parcel 24 and parcel 16 with length/cost 1379.0.
These entries let us evaluate pipe choices to connect exactly 12 parcels with minimum total length/cost while avoiding loops.

I’ll keep the answer in a simple JSON shape so it’s easy to read and parse. Think of it as a little form where each entry is one chosen pipe between two parcels.

{
  ""solution"": [[""p1"", ""p2""], [""p3"", ""p4""], ...]
}

In plain terms: ""solution"" is the list of irrigation line segments you pick. Each inner pair [""X"", ""Y""] means “connect parcel X to parcel Y.” This is just the expected shape — a sketch of how I’ll present the final plan, not the actual selection.

Please make sure to use the parcel identifiers exactly as they appear in the instance input — no renaming, 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”.","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 27, 'edges': [{'u': 3, 'v': 4, 'w': 480.0}, {'u': 3, 'v': 6, 'w': 452.0}, {'u': 3, 'v': 21, 'w': 3132.0}, {'u': 4, 'v': 16, 'w': 489.0}, {'u': 7, 'v': 13, 'w': 1278.0}, {'u': 8, 'v': 1, 'w': 208.0}, {'u': 8, 'v': 10, 'w': 3135.0}, {'u': 9, 'v': 1, 'w': 505.0}, {'u': 9, 'v': 2, 'w': 201.0}, {'u': 9, 'v': 21, 'w': 1621.0}, {'u': 10, 'v': 11, 'w': 803.0}, {'u': 11, 'v': 17, 'w': 1021.0}, {'u': 11, 'v': 13, 'w': 376.0}, {'u': 12, 'v': 20, 'w': 991.0}, {'u': 19, 'v': 20, 'w': 581.0}, {'u': 19, 'v': 18, 'w': 1065.0}, {'u': 19, 'v': 15, 'w': 651.0}, {'u': 20, 'v': 17, 'w': 1908.0}, {'u': 5, 'v': 6, 'w': 496.0}, {'u': 5, 'v': 17, 'w': 591.0}, {'u': 5, 'v': 21, 'w': 3124.0}, {'u': 6, 'v': 15, 'w': 1409.0}, {'u': 14, 'v': 21, 'w': 2335.0}, {'u': 15, 'v': 24, 'w': 922.0}, {'u': 21, 'v': 22, 'w': 1074.0}, {'u': 23, 'v': 24, 'w': 1077.0}, {'u': 24, 'v': 16, 'w': 1379.0}], 'k': 12, 'source_file': 'I047.stp', 'density': 0.09782608695652174}","[[3, 4], [3, 6], [4, 16], [10, 11], [11, 17], [11, 13], [19, 20], [15, 19], [5, 6], [5, 17], [6, 15]]",7349.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 27, 'edges': [{'u': 3, 'v': 4, 'w': 480.0}, {'u': 3, 'v': 6, 'w': 452.0}, {'u': 3, 'v': 21, 'w': 3132.0}, {'u': 4, 'v': 16, 'w': 489.0}, {'u': 7, 'v': 13, 'w': 1278.0}, {'u': 8, 'v': 1, 'w': 208.0}, {'u': 8, 'v': 10, 'w': 3135.0}, {'u': 9, 'v': 1, 'w': 505.0}, {'u': 9, 'v': 2, 'w': 201.0}, {'u': 9, 'v': 21, 'w': 1621.0}, {'u': 10, 'v': 11, 'w': 803.0}, {'u': 11, 'v': 17, 'w': 1021.0}, {'u': 11, 'v': 13, 'w': 376.0}, {'u': 12, 'v': 20, 'w': 991.0}, {'u': 19, 'v': 20, 'w': 581.0}, {'u': 19, 'v': 18, 'w': 1065.0}, {'u': 19, 'v': 15, 'w': 651.0}, {'u': 20, 'v': 17, 'w': 1908.0}, {'u': 5, 'v': 6, 'w': 496.0}, {'u': 5, 'v': 17, 'w': 591.0}, {'u': 5, 'v': 21, 'w': 3124.0}, {'u': 6, 'v': 15, 'w': 1409.0}, {'u': 14, 'v': 21, 'w': 2335.0}, {'u': 15, 'v': 24, 'w': 922.0}, {'u': 21, 'v': 22, 'w': 1074.0}, {'u': 23, 'v': 24, 'w': 1077.0}, {'u': 24, 'v': 16, 'w': 1379.0}], 'density': 0.09782608695652174, 'source_file': 'I047.stp', 'k': 12}","[[3, 4], [3, 6], [4, 16], [10, 11], [11, 17], [11, 13], [19, 20], [15, 19], [5, 6], [5, 17], [6, 15]]",16,markdown_table,1
KMST,KMST,"Someone on the team needs to pick a fixed number of sensors and hook them together with radio connections so they form a single connected web with no loops; the trick is to do this while keeping the sum of all link distances as small as possible. The way to check which choice is best is to add up the lengths of all the links used, and be sure the network contains exactly the chosen number of distinct sensors with no extras. The detailed sensor layout and distances are given below.

Below are the 28 potential links among the 22 sensors; the chosen tree must span exactly 11 sensors.
Link between sensor 0 and sensor 10 with distance 217.0.
Link between sensor 0 and sensor 18 with distance 4013.0.
Link between sensor 16 and sensor 21 with distance 8848.0.
Link between sensor 17 and sensor 6 with distance 807.0.
Link between sensor 17 and sensor 15 with distance 7325.0.
Link between sensor 18 and sensor 19 with distance 918.0.
Link between sensor 18 and sensor 20 with distance 1632.0.
Link between sensor 19 and sensor 2 with distance 1254.0.
Link between sensor 19 and sensor 4 with distance 1212.0.
Link between sensor 20 and sensor 12 with distance 106.0.
Link between sensor 20 and sensor 21 with distance 2174.0.
Link between sensor 21 and sensor 13 with distance 2250.0.
Link between sensor 1 and sensor 2 with distance 1552.0.
Link between sensor 1 and sensor 9 with distance 708.0.
Link between sensor 2 and sensor 8 with distance 699.0.
Link between sensor 3 and sensor 12 with distance 1142.0.
Link between sensor 3 and sensor 13 with distance 77.0.
Link between sensor 3 and sensor 4 with distance 1492.0.
Link between sensor 4 and sensor 12 with distance 442.0.
Link between sensor 5 and sensor 7 with distance 1490.0.
Link between sensor 6 and sensor 7 with distance 958.0.
Link between sensor 7 and sensor 11 with distance 6995.0.
Link between sensor 8 and sensor 9 with distance 1438.0.
Link between sensor 8 and sensor 11 with distance 266.0.
Link between sensor 9 and sensor 14 with distance 494.0.
Link between sensor 11 and sensor 14 with distance 1376.0.
Link between sensor 13 and sensor 15 with distance 3490.0.
Link between sensor 14 and sensor 15 with distance 1970.0.
The chosen selection should minimize the total link distance while spanning exactly 11 sensors.

If you want the answer output in a machine-friendly way, just stick to this little JSON shape:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of radio links to include in the final web. Each pair like [u1, v1] is one connection between two sensors (the order inside the pair doesn't matter — it's just the two endpoints). Think of it as a simple form: a list of links that together make the connected, loop-free network of exactly the chosen sensors.

This JSON is only a sketch of the shape I need — not the real answer. When you fill it in, use the exact sensor identifiers from the instance input, with no renaming and no extra 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”.""","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 1, 'v': 11, 'w': 217.0}, {'u': 1, 'v': 19, 'w': 4013.0}, {'u': 17, 'v': 22, 'w': 8848.0}, {'u': 18, 'v': 7, 'w': 807.0}, {'u': 18, 'v': 16, 'w': 7325.0}, {'u': 19, 'v': 20, 'w': 918.0}, {'u': 19, 'v': 21, 'w': 1632.0}, {'u': 20, 'v': 3, 'w': 1254.0}, {'u': 20, 'v': 5, 'w': 1212.0}, {'u': 21, 'v': 13, 'w': 106.0}, {'u': 21, 'v': 22, 'w': 2174.0}, {'u': 22, 'v': 14, 'w': 2250.0}, {'u': 2, 'v': 3, 'w': 1552.0}, {'u': 2, 'v': 10, 'w': 708.0}, {'u': 3, 'v': 9, 'w': 699.0}, {'u': 4, 'v': 13, 'w': 1142.0}, {'u': 4, 'v': 14, 'w': 77.0}, {'u': 4, 'v': 5, 'w': 1492.0}, {'u': 5, 'v': 13, 'w': 442.0}, {'u': 6, 'v': 8, 'w': 1490.0}, {'u': 7, 'v': 8, 'w': 958.0}, {'u': 8, 'v': 12, 'w': 6995.0}, {'u': 9, 'v': 10, 'w': 1438.0}, {'u': 9, 'v': 12, 'w': 266.0}, {'u': 10, 'v': 15, 'w': 494.0}, {'u': 12, 'v': 15, 'w': 1376.0}, {'u': 14, 'v': 16, 'w': 3490.0}, {'u': 15, 'v': 16, 'w': 1970.0}], 'k': 11, 'source_file': 'I052.stp', 'density': 0.12121212121212122}","[[3, 20], [5, 20], [13, 21], [3, 9], [4, 13], [4, 14], [5, 13], [9, 12], [10, 15], [12, 15]]",7068.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 0, 'v': 10, 'w': 217.0}, {'u': 0, 'v': 18, 'w': 4013.0}, {'u': 16, 'v': 21, 'w': 8848.0}, {'u': 17, 'v': 6, 'w': 807.0}, {'u': 17, 'v': 15, 'w': 7325.0}, {'u': 18, 'v': 19, 'w': 918.0}, {'u': 18, 'v': 20, 'w': 1632.0}, {'u': 19, 'v': 2, 'w': 1254.0}, {'u': 19, 'v': 4, 'w': 1212.0}, {'u': 20, 'v': 12, 'w': 106.0}, {'u': 20, 'v': 21, 'w': 2174.0}, {'u': 21, 'v': 13, 'w': 2250.0}, {'u': 1, 'v': 2, 'w': 1552.0}, {'u': 1, 'v': 9, 'w': 708.0}, {'u': 2, 'v': 8, 'w': 699.0}, {'u': 3, 'v': 12, 'w': 1142.0}, {'u': 3, 'v': 13, 'w': 77.0}, {'u': 3, 'v': 4, 'w': 1492.0}, {'u': 4, 'v': 12, 'w': 442.0}, {'u': 5, 'v': 7, 'w': 1490.0}, {'u': 6, 'v': 7, 'w': 958.0}, {'u': 7, 'v': 11, 'w': 6995.0}, {'u': 8, 'v': 9, 'w': 1438.0}, {'u': 8, 'v': 11, 'w': 266.0}, {'u': 9, 'v': 14, 'w': 494.0}, {'u': 11, 'v': 14, 'w': 1376.0}, {'u': 13, 'v': 15, 'w': 3490.0}, {'u': 14, 'v': 15, 'w': 1970.0}], 'density': 0.12121212121212122, 'source_file': 'I052.stp', 'k': 11}","[[2, 19], [4, 19], [12, 20], [2, 8], [3, 12], [3, 13], [4, 12], [8, 11], [9, 14], [11, 14]]",17,markdown_table,0
KMST,KMST,"On a quiet afternoon the village engineer drew up plans to connect a fixed number of wells so they all sit on one continuous supply line without any loops or repeated routes. Different connection schemes are compared by simply summing the lengths of the pipes they’d need — the scheme with the smallest sum is the cheapest and therefore best. It’s non-negotiable that exactly that many wells are included, that each is connected, and that piping never forms a circular path. The actual map, distances, and how many wells to connect are given below.

Below are 27 wells and 33 candidate pipe segments; the engineer must select connections that include exactly 11 wells in one connected, acyclic supply line.
A candidate pipe joins well AA and well U with length 1428.0.
A candidate pipe joins well AA and well K with length 1051.0.
A candidate pipe joins well K and well H with length 858.0.
A candidate pipe joins well K and well A with length 2406.0.
A candidate pipe joins well L and well C with length 66.0.
A candidate pipe joins well L and well P with length 1533.0.
A candidate pipe joins well P and well Q with length 1475.0.
A candidate pipe joins well P and well J with length 1337.0.
A candidate pipe joins well Q and well M with length 945.0.
A candidate pipe joins well Q and well E with length 64.0.
A candidate pipe joins well B and well C with length 1386.0.
A candidate pipe joins well B and well G with length 614.0.
A candidate pipe joins well R and well A with length 451.0.
A candidate pipe joins well V and well F with length 437.0.
A candidate pipe joins well V and well N with length 1336.0.
A candidate pipe joins well V and well Y with length 588.0.
A candidate pipe joins well W and well F with length 1784.0.
A candidate pipe joins well W and well X with length 540.0.
A candidate pipe joins well W and well H with length 320.0.
A candidate pipe joins well X and well S with length 654.0.
A candidate pipe joins well X and well T with length 905.0.
A candidate pipe joins well Y and well S with length 1716.0.
A candidate pipe joins well G and well J with length 655.0.
A candidate pipe joins well J and well Z with length 1516.0.
A candidate pipe joins well Z and well I with length 459.0.
A candidate pipe joins well Z and well E with length 1196.0.
A candidate pipe joins well H and well I with length 1821.0.
A candidate pipe joins well M and well N with length 50.0.
A candidate pipe joins well N and well O with length 909.0.
A candidate pipe joins well F and well D with length 48.0.
A candidate pipe joins well T and well U with length 1299.0.
A candidate pipe joins well D and well E with length 1337.0.
A candidate pipe joins well D and well I with length 1182.0.
The engineer will compare totals of chosen pipe lengths to identify the cheapest scheme that connects exactly 11 wells.

If it helps, reply with a tiny JSON snippet in that shape so I can immediately see which wells get connected. Something informal like this works:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

""solution"" should be a list of pipe links; each pair [u1, v1] means there's a single pipe between the two wells whose identifiers are u1 and v1. Think of it as filling out a simple form: each inner pair is one connection. This is just the expected shape — a sketch of the format, not the actual answer.

Please be sure to use the exact identifiers from the input, with 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”.""","{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 33, 'edges': [{'u': 27, 'v': 21, 'w': 1428.0}, {'u': 27, 'v': 11, 'w': 1051.0}, {'u': 11, 'v': 8, 'w': 858.0}, {'u': 11, 'v': 1, 'w': 2406.0}, {'u': 12, 'v': 3, 'w': 66.0}, {'u': 12, 'v': 16, 'w': 1533.0}, {'u': 16, 'v': 17, 'w': 1475.0}, {'u': 16, 'v': 10, 'w': 1337.0}, {'u': 17, 'v': 13, 'w': 945.0}, {'u': 17, 'v': 5, 'w': 64.0}, {'u': 2, 'v': 3, 'w': 1386.0}, {'u': 2, 'v': 7, 'w': 614.0}, {'u': 18, 'v': 1, 'w': 451.0}, {'u': 22, 'v': 6, 'w': 437.0}, {'u': 22, 'v': 14, 'w': 1336.0}, {'u': 22, 'v': 25, 'w': 588.0}, {'u': 23, 'v': 6, 'w': 1784.0}, {'u': 23, 'v': 24, 'w': 540.0}, {'u': 23, 'v': 8, 'w': 320.0}, {'u': 24, 'v': 19, 'w': 654.0}, {'u': 24, 'v': 20, 'w': 905.0}, {'u': 25, 'v': 19, 'w': 1716.0}, {'u': 7, 'v': 10, 'w': 655.0}, {'u': 10, 'v': 26, 'w': 1516.0}, {'u': 26, 'v': 9, 'w': 459.0}, {'u': 26, 'v': 5, 'w': 1196.0}, {'u': 8, 'v': 9, 'w': 1821.0}, {'u': 13, 'v': 14, 'w': 50.0}, {'u': 14, 'v': 15, 'w': 909.0}, {'u': 6, 'v': 4, 'w': 48.0}, {'u': 20, 'v': 21, 'w': 1299.0}, {'u': 4, 'v': 5, 'w': 1337.0}, {'u': 4, 'v': 9, 'w': 1182.0}], 'k': 11, 'source_file': 'I008.stp', 'density': 0.09401709401709402}","[[13, 17], [5, 17], [6, 22], [22, 25], [9, 26], [5, 26], [13, 14], [14, 15], [4, 6], [4, 9]]",5878.0,"{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 33, 'edges': [{'u': 'AA', 'v': 'U', 'w': 1428.0}, {'u': 'AA', 'v': 'K', 'w': 1051.0}, {'u': 'K', 'v': 'H', 'w': 858.0}, {'u': 'K', 'v': 'A', 'w': 2406.0}, {'u': 'L', 'v': 'C', 'w': 66.0}, {'u': 'L', 'v': 'P', 'w': 1533.0}, {'u': 'P', 'v': 'Q', 'w': 1475.0}, {'u': 'P', 'v': 'J', 'w': 1337.0}, {'u': 'Q', 'v': 'M', 'w': 945.0}, {'u': 'Q', 'v': 'E', 'w': 64.0}, {'u': 'B', 'v': 'C', 'w': 1386.0}, {'u': 'B', 'v': 'G', 'w': 614.0}, {'u': 'R', 'v': 'A', 'w': 451.0}, {'u': 'V', 'v': 'F', 'w': 437.0}, {'u': 'V', 'v': 'N', 'w': 1336.0}, {'u': 'V', 'v': 'Y', 'w': 588.0}, {'u': 'W', 'v': 'F', 'w': 1784.0}, {'u': 'W', 'v': 'X', 'w': 540.0}, {'u': 'W', 'v': 'H', 'w': 320.0}, {'u': 'X', 'v': 'S', 'w': 654.0}, {'u': 'X', 'v': 'T', 'w': 905.0}, {'u': 'Y', 'v': 'S', 'w': 1716.0}, {'u': 'G', 'v': 'J', 'w': 655.0}, {'u': 'J', 'v': 'Z', 'w': 1516.0}, {'u': 'Z', 'v': 'I', 'w': 459.0}, {'u': 'Z', 'v': 'E', 'w': 1196.0}, {'u': 'H', 'v': 'I', 'w': 1821.0}, {'u': 'M', 'v': 'N', 'w': 50.0}, {'u': 'N', 'v': 'O', 'w': 909.0}, {'u': 'F', 'v': 'D', 'w': 48.0}, {'u': 'T', 'v': 'U', 'w': 1299.0}, {'u': 'D', 'v': 'E', 'w': 1337.0}, {'u': 'D', 'v': 'I', 'w': 1182.0}], 'density': 0.09401709401709402, 'source_file': 'I008.stp', 'k': 11}","[['M', 'Q'], ['E', 'Q'], ['F', 'V'], ['V', 'Y'], ['I', 'Z'], ['E', 'Z'], ['M', 'N'], ['N', 'O'], ['D', 'F'], ['D', 'I']]",18,nl,names
KMST,KMST,"There’s a small project to wire a handful of buildings: pick a predetermined number of sites and connect them with fiber so they all reach each other through a single connected layout that doesn’t loop back on itself. What makes one plan better than another is simply the total cable put in — add the lengths of the chosen links and the smaller total wins. Every chosen building has to be one of the fixed number (no extras, no repeats), and the cabling must link them into a single loop-free network. The detailed map and numbers follow below.

{
  ""total_buildings"": 26,
  ""total_possible_links"": 33,
  ""edges"": [
    {
      ""building_u"": 3,
      ""building_v"": 4,
      ""link_length"": 901.0
    },
    {
      ""building_u"": 3,
      ""building_v"": 6,
      ""link_length"": 93.0
    },
    {
      ""building_u"": 3,
      ""building_v"": 19,
      ""link_length"": 13213.0
    },
    {
      ""building_u"": 4,
      ""building_v"": 5,
      ""link_length"": 93.0
    },
    {
      ""building_u"": 4,
      ""building_v"": 18,
      ""link_length"": 1967.0
    },
    {
      ""building_u"": 5,
      ""building_v"": 6,
      ""link_length"": 901.0
    },
    {
      ""building_u"": 5,
      ""building_v"": 21,
      ""link_length"": 43973.0
    },
    {
      ""building_u"": 5,
      ""building_v"": 22,
      ""link_length"": 4391.0
    },
    {
      ""building_u"": 6,
      ""building_v"": 10,
      ""link_length"": 19768.0
    },
    {
      ""building_u"": 20,
      ""building_v"": 18,
      ""link_length"": 42541.0
    },
    {
      ""building_u"": 20,
      ""building_v"": 21,
      ""link_length"": 2504.0
    },
    {
      ""building_u"": 8,
      ""building_v"": 7,
      ""link_length"": 899.0
    },
    {
      ""building_u"": 8,
      ""building_v"": 19,
      ""link_length"": 8991.0
    },
    {
      ""building_u"": 7,
      ""building_v"": 18,
      ""link_length"": 20238.0
    },
    {
      ""building_u"": 12,
      ""building_v"": 11,
      ""link_length"": 58833.0
    },
    {
      ""building_u"": 2,
      ""building_v"": 21,
      ""link_length"": 5961.0
    },
    {
      ""building_u"": 2,
      ""building_v"": 22,
      ""link_length"": 48028.0
    },
    {
      ""building_u"": 2,
      ""building_v"": 16,
      ""link_length"": 6625.0
    },
    {
      ""building_u"": 16,
      ""building_v"": 23,
      ""link_length"": 52535.0
    },
    {
      ""building_u"": 0,
      ""building_v"": 1,
      ""link_length"": 2889.0
    },
    {
      ""building_u"": 0,
      ""building_v"": 14,
      ""link_length"": 36090.0
    },
    {
      ""building_u"": 1,
      ""building_v"": 13,
      ""link_length"": 36025.0
    },
    {
      ""building_u"": 19,
      ""building_v"": 25,
      ""link_length"": 70907.0
    },
    {
      ""building_u"": 22,
      ""building_v"": 23,
      ""link_length"": 4879.0
    },
    {
      ""building_u"": 23,
      ""building_v"": 24,
      ""link_length"": 2087.0
    },
    {
      ""building_u"": 9,
      ""building_v"": 10,
      ""link_length"": 898.0
    },
    {
      ""building_u"": 9,
      ""building_v"": 11,
      ""link_length"": 3715.0
    },
    {
      ""building_u"": 9,
      ""building_v"": 17,
      ""link_length"": 456.0
    },
    {
      ""building_u"": 10,
      ""building_v"": 13,
      ""link_length"": 503.0
    },
    {
      ""building_u"": 11,
      ""building_v"": 24,
      ""link_length"": 4732.0
    },
    {
      ""building_u"": 13,
      ""building_v"": 14,
      ""link_length"": 2516.0
    },
    {
      ""building_u"": 14,
      ""building_v"": 15,
      ""link_length"": 1406.0
    },
    {
      ""building_u"": 15,
      ""building_v"": 17,
      ""link_length"": 2565.0
    }
  ],
  ""buildings_to_connect"": 8
}

If you want to tell me which links you'd pick, just drop them in a tiny JSON snippet like this and I’ll know how to read it:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is just a list of the chosen cable runs, and each pair like [u1, v1] is one link between two sites (use the site identifiers from the instance). Think of it as a simple form: a list of edges that together make the connected, loop-free layout.

This JSON is only a sketch of the expected shape — not the final plan itself.

Please make sure every identifier in your submission matches exactly what appears 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”.""","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 33, 'edges': [{'u': 4, 'v': 5, 'w': 901.0}, {'u': 4, 'v': 7, 'w': 93.0}, {'u': 4, 'v': 20, 'w': 13213.0}, {'u': 5, 'v': 6, 'w': 93.0}, {'u': 5, 'v': 19, 'w': 1967.0}, {'u': 6, 'v': 7, 'w': 901.0}, {'u': 6, 'v': 22, 'w': 43973.0}, {'u': 6, 'v': 23, 'w': 4391.0}, {'u': 7, 'v': 11, 'w': 19768.0}, {'u': 21, 'v': 19, 'w': 42541.0}, {'u': 21, 'v': 22, 'w': 2504.0}, {'u': 9, 'v': 8, 'w': 899.0}, {'u': 9, 'v': 20, 'w': 8991.0}, {'u': 8, 'v': 19, 'w': 20238.0}, {'u': 13, 'v': 12, 'w': 58833.0}, {'u': 3, 'v': 22, 'w': 5961.0}, {'u': 3, 'v': 23, 'w': 48028.0}, {'u': 3, 'v': 17, 'w': 6625.0}, {'u': 17, 'v': 24, 'w': 52535.0}, {'u': 1, 'v': 2, 'w': 2889.0}, {'u': 1, 'v': 15, 'w': 36090.0}, {'u': 2, 'v': 14, 'w': 36025.0}, {'u': 20, 'v': 26, 'w': 70907.0}, {'u': 23, 'v': 24, 'w': 4879.0}, {'u': 24, 'v': 25, 'w': 2087.0}, {'u': 10, 'v': 11, 'w': 898.0}, {'u': 10, 'v': 12, 'w': 3715.0}, {'u': 10, 'v': 18, 'w': 456.0}, {'u': 11, 'v': 14, 'w': 503.0}, {'u': 12, 'v': 25, 'w': 4732.0}, {'u': 14, 'v': 15, 'w': 2516.0}, {'u': 15, 'v': 16, 'w': 1406.0}, {'u': 16, 'v': 18, 'w': 2565.0}], 'k': 8, 'source_file': 'I001.stp', 'density': 0.10153846153846154}","[[10, 11], [10, 12], [10, 18], [11, 14], [12, 25], [14, 15], [15, 16]]",14226.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 33, 'edges': [{'u': 3, 'v': 4, 'w': 901.0}, {'u': 3, 'v': 6, 'w': 93.0}, {'u': 3, 'v': 19, 'w': 13213.0}, {'u': 4, 'v': 5, 'w': 93.0}, {'u': 4, 'v': 18, 'w': 1967.0}, {'u': 5, 'v': 6, 'w': 901.0}, {'u': 5, 'v': 21, 'w': 43973.0}, {'u': 5, 'v': 22, 'w': 4391.0}, {'u': 6, 'v': 10, 'w': 19768.0}, {'u': 20, 'v': 18, 'w': 42541.0}, {'u': 20, 'v': 21, 'w': 2504.0}, {'u': 8, 'v': 7, 'w': 899.0}, {'u': 8, 'v': 19, 'w': 8991.0}, {'u': 7, 'v': 18, 'w': 20238.0}, {'u': 12, 'v': 11, 'w': 58833.0}, {'u': 2, 'v': 21, 'w': 5961.0}, {'u': 2, 'v': 22, 'w': 48028.0}, {'u': 2, 'v': 16, 'w': 6625.0}, {'u': 16, 'v': 23, 'w': 52535.0}, {'u': 0, 'v': 1, 'w': 2889.0}, {'u': 0, 'v': 14, 'w': 36090.0}, {'u': 1, 'v': 13, 'w': 36025.0}, {'u': 19, 'v': 25, 'w': 70907.0}, {'u': 22, 'v': 23, 'w': 4879.0}, {'u': 23, 'v': 24, 'w': 2087.0}, {'u': 9, 'v': 10, 'w': 898.0}, {'u': 9, 'v': 11, 'w': 3715.0}, {'u': 9, 'v': 17, 'w': 456.0}, {'u': 10, 'v': 13, 'w': 503.0}, {'u': 11, 'v': 24, 'w': 4732.0}, {'u': 13, 'v': 14, 'w': 2516.0}, {'u': 14, 'v': 15, 'w': 1406.0}, {'u': 15, 'v': 17, 'w': 2565.0}], 'density': 0.10153846153846154, 'source_file': 'I001.stp', 'k': 8}","[[9, 10], [9, 11], [9, 17], [10, 13], [11, 24], [13, 14], [14, 15]]",19,json,0
KMST,KMST,"I’m playing the role of the city planner who has to pick a fixed number of utility poles and string cable so that every chosen pole can be reached from any other without making any closed loops. The choice is about which exact poles to include and which connections to run between them; a better choice is simply the one that needs the least amount of new cable overall — add up the length of each cable segment used and that total is what’s being kept as small as possible. It’s important that exactly the given number of poles are included, none are duplicated, and the wiring can’t form circuits (every selected pole must stay reachable from the others through the network). The map and the exact distances and numbers will be shown below.

# total_poles=30
# available_cable_segments=35
# poles_to_connect=12
pole_u_id,pole_v_id,cable_length
W,I,359.0
W,O,2302.0
W,V,3550.0
M,C,1284.0
M,AD,58.0
M,D,1853.0
A,R,1722.0
N,V,2335.0
N,J,3559.0
N,O,3663.0
AD,L,2388.0
AD,G,388.0
T,X,2625.0
O,P,489.0
Y,Z,2355.0
Y,H,258.0
Y,K,856.0
Z,I,718.0
Z,L,1482.0
P,AB,2324.0
AA,V,1656.0
Q,S,949.0
Q,K,941.0
U,AC,1491.0
C,B,339053.0
D,B,338195.0
D,F,2434.0
AB,H,766.0
AB,AC,268.0
E,L,501.0
E,X,3225.0
R,S,226.0
F,G,773.0
G,K,2021.0
H,I,2336.0

Oh, and before I give the wiring plan, I’ll show the shape I’ll use for the answer so it’s easy to copy into whatever you’re using. It’s just a tiny JSON sketch of the connections — nothing final, just the format I’ll follow.

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Each inner pair is one cable segment: the two labels are the poles (nodes) that get connected. Think of it like filling out a form where each line says ""connect this pole to that pole."" This block is only an example of the expected shape, not the actual answer.

Reminder: all identifiers must be used exactly as they appear in the instance input — don’t rename any nodes 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”.""","{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 35, 'edges': [{'u': 23, 'v': 9, 'w': 359.0}, {'u': 23, 'v': 15, 'w': 2302.0}, {'u': 23, 'v': 22, 'w': 3550.0}, {'u': 13, 'v': 3, 'w': 1284.0}, {'u': 13, 'v': 30, 'w': 58.0}, {'u': 13, 'v': 4, 'w': 1853.0}, {'u': 1, 'v': 18, 'w': 1722.0}, {'u': 14, 'v': 22, 'w': 2335.0}, {'u': 14, 'v': 10, 'w': 3559.0}, {'u': 14, 'v': 15, 'w': 3663.0}, {'u': 30, 'v': 12, 'w': 2388.0}, {'u': 30, 'v': 7, 'w': 388.0}, {'u': 20, 'v': 24, 'w': 2625.0}, {'u': 15, 'v': 16, 'w': 489.0}, {'u': 25, 'v': 26, 'w': 2355.0}, {'u': 25, 'v': 8, 'w': 258.0}, {'u': 25, 'v': 11, 'w': 856.0}, {'u': 26, 'v': 9, 'w': 718.0}, {'u': 26, 'v': 12, 'w': 1482.0}, {'u': 16, 'v': 28, 'w': 2324.0}, {'u': 27, 'v': 22, 'w': 1656.0}, {'u': 17, 'v': 19, 'w': 949.0}, {'u': 17, 'v': 11, 'w': 941.0}, {'u': 21, 'v': 29, 'w': 1491.0}, {'u': 3, 'v': 2, 'w': 339053.0}, {'u': 4, 'v': 2, 'w': 338195.0}, {'u': 4, 'v': 6, 'w': 2434.0}, {'u': 28, 'v': 8, 'w': 766.0}, {'u': 28, 'v': 29, 'w': 268.0}, {'u': 5, 'v': 12, 'w': 501.0}, {'u': 5, 'v': 24, 'w': 3225.0}, {'u': 18, 'v': 19, 'w': 226.0}, {'u': 6, 'v': 7, 'w': 773.0}, {'u': 7, 'v': 11, 'w': 2021.0}, {'u': 8, 'v': 9, 'w': 2336.0}], 'k': 12, 'source_file': 'I073.stp', 'density': 0.08045977011494253}","[[13, 30], [7, 30], [8, 25], [11, 25], [17, 19], [11, 17], [8, 28], [28, 29], [18, 19], [6, 7], [7, 11]]",7504.0,"{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 35, 'edges': [{'u': 'W', 'v': 'I', 'w': 359.0}, {'u': 'W', 'v': 'O', 'w': 2302.0}, {'u': 'W', 'v': 'V', 'w': 3550.0}, {'u': 'M', 'v': 'C', 'w': 1284.0}, {'u': 'M', 'v': 'AD', 'w': 58.0}, {'u': 'M', 'v': 'D', 'w': 1853.0}, {'u': 'A', 'v': 'R', 'w': 1722.0}, {'u': 'N', 'v': 'V', 'w': 2335.0}, {'u': 'N', 'v': 'J', 'w': 3559.0}, {'u': 'N', 'v': 'O', 'w': 3663.0}, {'u': 'AD', 'v': 'L', 'w': 2388.0}, {'u': 'AD', 'v': 'G', 'w': 388.0}, {'u': 'T', 'v': 'X', 'w': 2625.0}, {'u': 'O', 'v': 'P', 'w': 489.0}, {'u': 'Y', 'v': 'Z', 'w': 2355.0}, {'u': 'Y', 'v': 'H', 'w': 258.0}, {'u': 'Y', 'v': 'K', 'w': 856.0}, {'u': 'Z', 'v': 'I', 'w': 718.0}, {'u': 'Z', 'v': 'L', 'w': 1482.0}, {'u': 'P', 'v': 'AB', 'w': 2324.0}, {'u': 'AA', 'v': 'V', 'w': 1656.0}, {'u': 'Q', 'v': 'S', 'w': 949.0}, {'u': 'Q', 'v': 'K', 'w': 941.0}, {'u': 'U', 'v': 'AC', 'w': 1491.0}, {'u': 'C', 'v': 'B', 'w': 339053.0}, {'u': 'D', 'v': 'B', 'w': 338195.0}, {'u': 'D', 'v': 'F', 'w': 2434.0}, {'u': 'AB', 'v': 'H', 'w': 766.0}, {'u': 'AB', 'v': 'AC', 'w': 268.0}, {'u': 'E', 'v': 'L', 'w': 501.0}, {'u': 'E', 'v': 'X', 'w': 3225.0}, {'u': 'R', 'v': 'S', 'w': 226.0}, {'u': 'F', 'v': 'G', 'w': 773.0}, {'u': 'G', 'v': 'K', 'w': 2021.0}, {'u': 'H', 'v': 'I', 'w': 2336.0}], 'density': 0.08045977011494253, 'source_file': 'I073.stp', 'k': 12}","[['M', 'AD'], ['G', 'AD'], ['H', 'Y'], ['K', 'Y'], ['Q', 'S'], ['K', 'Q'], ['H', 'AB'], ['AB', 'AC'], ['R', 'S'], ['F', 'G'], ['G', 'K']]",20,csv,names
KMST,KMST,"Someone in charge of park logistics needs to open a set number of ranger posts and connect them so staff can travel between them, but they can’t create any roundabout loops and must stick to exactly k posts. Better setups are judged by how short the combined trail mileage is — you calculate it by adding every trail’s length that’s built. The plan must include every chosen post, keep the network one-piece, and avoid duplicated or circular connections. The concrete instance with distances is shown below.

The instance below lists 21 ranger posts and 27 potential trails; the planner must open exactly 6 posts and connect them into a single, loop-free network.
Potential trail connecting post 8 and post 9 with distance 524.0.
Potential trail connecting post 8 and post 2 with distance 404.0.
Potential trail connecting post 8 and post 16 with distance 222.0.
Potential trail connecting post 9 and post 3 with distance 400.0.
Potential trail connecting post 9 and post 17 with distance 151.0.
Potential trail connecting post 10 and post 11 with distance 380.0.
Potential trail connecting post 10 and post 4 with distance 393.0.
Potential trail connecting post 10 and post 19 with distance 316.0.
Potential trail connecting post 11 and post 5 with distance 392.0.
Potential trail connecting post 11 and post 21 with distance 283.0.
Potential trail connecting post 12 and post 13 with distance 380.0.
Potential trail connecting post 12 and post 20 with distance 176.0.
Potential trail connecting post 12 and post 6 with distance 333.0.
Potential trail connecting post 13 and post 21 with distance 102.0.
Potential trail connecting post 13 and post 7 with distance 326.0.
Potential trail connecting post 1 and post 14 with distance 392.0.
Potential trail connecting post 1 and post 16 with distance 540.0.
Potential trail connecting post 2 and post 3 with distance 580.0.
Potential trail connecting post 4 and post 5 with distance 414.0.
Potential trail connecting post 5 and post 17 with distance 608.0.
Potential trail connecting post 6 and post 7 with distance 446.0.
Potential trail connecting post 14 and post 15 with distance 1216.0.
Potential trail connecting post 15 and post 19 with distance 796.0.
Potential trail connecting post 15 and post 18 with distance 887.0.
Potential trail connecting post 16 and post 17 with distance 498.0.
Potential trail connecting post 19 and post 20 with distance 2.0.
Potential trail connecting post 20 and post 21 with distance 351.0.
Exactly 6 posts must be opened and connected into one connected, acyclic network minimizing total trail mileage.

If you want to hand me a candidate layout, just stick to this simple JSON shape so I can read it easily:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

""solution"" should be a list of the trail segments you plan to build. Each inner pair like [u1, v1] is one connection between two ranger posts (use the post IDs from the instance). This is just a sketch of the shape I expect, not the actual final plan.

Please use the exact identifiers from the instance input — don't rename them or invent new ones. 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"".","{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 27, 'edges': [{'u': 8, 'v': 9, 'w': 524.0}, {'u': 8, 'v': 2, 'w': 404.0}, {'u': 8, 'v': 16, 'w': 222.0}, {'u': 9, 'v': 3, 'w': 400.0}, {'u': 9, 'v': 17, 'w': 151.0}, {'u': 10, 'v': 11, 'w': 380.0}, {'u': 10, 'v': 4, 'w': 393.0}, {'u': 10, 'v': 19, 'w': 316.0}, {'u': 11, 'v': 5, 'w': 392.0}, {'u': 11, 'v': 21, 'w': 283.0}, {'u': 12, 'v': 13, 'w': 380.0}, {'u': 12, 'v': 20, 'w': 176.0}, {'u': 12, 'v': 6, 'w': 333.0}, {'u': 13, 'v': 21, 'w': 102.0}, {'u': 13, 'v': 7, 'w': 326.0}, {'u': 1, 'v': 14, 'w': 392.0}, {'u': 1, 'v': 16, 'w': 540.0}, {'u': 2, 'v': 3, 'w': 580.0}, {'u': 4, 'v': 5, 'w': 414.0}, {'u': 5, 'v': 17, 'w': 608.0}, {'u': 6, 'v': 7, 'w': 446.0}, {'u': 14, 'v': 15, 'w': 1216.0}, {'u': 15, 'v': 19, 'w': 796.0}, {'u': 15, 'v': 18, 'w': 887.0}, {'u': 16, 'v': 17, 'w': 498.0}, {'u': 19, 'v': 20, 'w': 2.0}, {'u': 20, 'v': 21, 'w': 351.0}], 'k': 6, 'source_file': 'I049.stp', 'density': 0.12857142857142856}","[[11, 21], [12, 20], [13, 21], [19, 20], [20, 21]]",914.0,"{'problem_type': 'KMST', 'num_nodes': 21, 'num_edges': 27, 'edges': [{'u': 8, 'v': 9, 'w': 524.0}, {'u': 8, 'v': 2, 'w': 404.0}, {'u': 8, 'v': 16, 'w': 222.0}, {'u': 9, 'v': 3, 'w': 400.0}, {'u': 9, 'v': 17, 'w': 151.0}, {'u': 10, 'v': 11, 'w': 380.0}, {'u': 10, 'v': 4, 'w': 393.0}, {'u': 10, 'v': 19, 'w': 316.0}, {'u': 11, 'v': 5, 'w': 392.0}, {'u': 11, 'v': 21, 'w': 283.0}, {'u': 12, 'v': 13, 'w': 380.0}, {'u': 12, 'v': 20, 'w': 176.0}, {'u': 12, 'v': 6, 'w': 333.0}, {'u': 13, 'v': 21, 'w': 102.0}, {'u': 13, 'v': 7, 'w': 326.0}, {'u': 1, 'v': 14, 'w': 392.0}, {'u': 1, 'v': 16, 'w': 540.0}, {'u': 2, 'v': 3, 'w': 580.0}, {'u': 4, 'v': 5, 'w': 414.0}, {'u': 5, 'v': 17, 'w': 608.0}, {'u': 6, 'v': 7, 'w': 446.0}, {'u': 14, 'v': 15, 'w': 1216.0}, {'u': 15, 'v': 19, 'w': 796.0}, {'u': 15, 'v': 18, 'w': 887.0}, {'u': 16, 'v': 17, 'w': 498.0}, {'u': 19, 'v': 20, 'w': 2.0}, {'u': 20, 'v': 21, 'w': 351.0}], 'density': 0.12857142857142856, 'source_file': 'I049.stp', 'k': 6}","[[11, 21], [12, 20], [13, 21], [19, 20], [20, 21]]",21,nl,1
KMST,KMST,"At a small market the organizers had to pick exactly k vendors to get utilities and plan how to string the cables between them. The cables had to make the chosen vendors part of one connected group without closing any loops, and since every cable segment had a cost, the smart choice was the plan with the smallest overall cable bill — calculated by summing the cost of each segment used. No chosen vendor could be left out or duplicated, and no wiring could create a cycle. The concrete diagram and costs follow below.

The diagram shows 29 stalls and 36 possible connectors, and the organizers must choose exactly 9 stalls to connect.
Cable segment between stall AB and stall L costs 2512.0.
Cable segment between stall AB and stall V costs 2074.0.
Cable segment between stall Q and stall R costs 2370.0.
Cable segment between stall Q and stall B costs 1318.0.
Cable segment between stall R and stall AA costs 2905.0.
Cable segment between stall S and stall U costs 2355.0.
Cable segment between stall S and stall O costs 3895.0.
Cable segment between stall S and stall P costs 217.0.
Cable segment between stall T and stall P costs 417.0.
Cable segment between stall T and stall W costs 5201.0.
Cable segment between stall T and stall D costs 2322.0.
Cable segment between stall P and stall M costs 5625.0.
Cable segment between stall U and stall G costs 744.0.
Cable segment between stall U and stall N costs 2669.0.
Cable segment between stall U and stall F costs 496998.0.
Cable segment between stall V and stall C costs 517675.0.
Cable segment between stall V and stall J costs 1132.0.
Cable segment between stall W and stall I costs 179.0.
Cable segment between stall W and stall X costs 3552.0.
Cable segment between stall A and stall AA costs 1277.0.
Cable segment between stall A and stall AC costs 4163.0.
Cable segment between stall X and stall D costs 1969.0.
Cable segment between stall X and stall Z costs 3065.0.
Cable segment between stall Y and stall AC costs 5906.0.
Cable segment between stall Y and stall C costs 2223.0.
Cable segment between stall Z and stall B costs 370.0.
Cable segment between stall Z and stall AA costs 3047.0.
Cable segment between stall C and stall I costs 2344.0.
Cable segment between stall D and stall G costs 1629.0.
Cable segment between stall E and stall F costs 377298.0.
Cable segment between stall E and stall G costs 605648.0.
Cable segment between stall H and stall I costs 732848.0.
Cable segment between stall H and stall J costs 672556.0.
Cable segment between stall J and stall L costs 4246.0.
Cable segment between stall K and stall M costs 2938.0.
Cable segment between stall N and stall O costs 2313.0.
Each line names one possible cable segment the organizers may use to form the required tree.

Oh, and when you hand me the wiring plan, just put it into this little JSON shape so I can read it easily:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

""solution"" should be a list of the cable segments you plan to use. Each inner pair [u1, v1] is one cable connecting vendor u1 to vendor v1. Think of it like a simple checklist of which stands get linked together — just the structure, not the prices or anything. This is only a sketch of the shape I expect, not the final answer itself.

Please make sure to use the exact identifiers from the instance input — do not rename them and do not 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”.""","{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 28, 'v': 12, 'w': 2512.0}, {'u': 28, 'v': 22, 'w': 2074.0}, {'u': 17, 'v': 18, 'w': 2370.0}, {'u': 17, 'v': 2, 'w': 1318.0}, {'u': 18, 'v': 27, 'w': 2905.0}, {'u': 19, 'v': 21, 'w': 2355.0}, {'u': 19, 'v': 15, 'w': 3895.0}, {'u': 19, 'v': 16, 'w': 217.0}, {'u': 20, 'v': 16, 'w': 417.0}, {'u': 20, 'v': 23, 'w': 5201.0}, {'u': 20, 'v': 4, 'w': 2322.0}, {'u': 16, 'v': 13, 'w': 5625.0}, {'u': 21, 'v': 7, 'w': 744.0}, {'u': 21, 'v': 14, 'w': 2669.0}, {'u': 21, 'v': 6, 'w': 496998.0}, {'u': 22, 'v': 3, 'w': 517675.0}, {'u': 22, 'v': 10, 'w': 1132.0}, {'u': 23, 'v': 9, 'w': 179.0}, {'u': 23, 'v': 24, 'w': 3552.0}, {'u': 1, 'v': 27, 'w': 1277.0}, {'u': 1, 'v': 29, 'w': 4163.0}, {'u': 24, 'v': 4, 'w': 1969.0}, {'u': 24, 'v': 26, 'w': 3065.0}, {'u': 25, 'v': 29, 'w': 5906.0}, {'u': 25, 'v': 3, 'w': 2223.0}, {'u': 26, 'v': 2, 'w': 370.0}, {'u': 26, 'v': 27, 'w': 3047.0}, {'u': 3, 'v': 9, 'w': 2344.0}, {'u': 4, 'v': 7, 'w': 1629.0}, {'u': 5, 'v': 6, 'w': 377298.0}, {'u': 5, 'v': 7, 'w': 605648.0}, {'u': 8, 'v': 9, 'w': 732848.0}, {'u': 8, 'v': 10, 'w': 672556.0}, {'u': 10, 'v': 12, 'w': 4246.0}, {'u': 11, 'v': 13, 'w': 2938.0}, {'u': 14, 'v': 15, 'w': 2313.0}], 'k': 9, 'source_file': 'I004.stp', 'density': 0.08866995073891626}","[[16, 19], [16, 20], [4, 20], [7, 21], [4, 24], [24, 26], [2, 26], [4, 7]]",10733.0,"{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 'AB', 'v': 'L', 'w': 2512.0}, {'u': 'AB', 'v': 'V', 'w': 2074.0}, {'u': 'Q', 'v': 'R', 'w': 2370.0}, {'u': 'Q', 'v': 'B', 'w': 1318.0}, {'u': 'R', 'v': 'AA', 'w': 2905.0}, {'u': 'S', 'v': 'U', 'w': 2355.0}, {'u': 'S', 'v': 'O', 'w': 3895.0}, {'u': 'S', 'v': 'P', 'w': 217.0}, {'u': 'T', 'v': 'P', 'w': 417.0}, {'u': 'T', 'v': 'W', 'w': 5201.0}, {'u': 'T', 'v': 'D', 'w': 2322.0}, {'u': 'P', 'v': 'M', 'w': 5625.0}, {'u': 'U', 'v': 'G', 'w': 744.0}, {'u': 'U', 'v': 'N', 'w': 2669.0}, {'u': 'U', 'v': 'F', 'w': 496998.0}, {'u': 'V', 'v': 'C', 'w': 517675.0}, {'u': 'V', 'v': 'J', 'w': 1132.0}, {'u': 'W', 'v': 'I', 'w': 179.0}, {'u': 'W', 'v': 'X', 'w': 3552.0}, {'u': 'A', 'v': 'AA', 'w': 1277.0}, {'u': 'A', 'v': 'AC', 'w': 4163.0}, {'u': 'X', 'v': 'D', 'w': 1969.0}, {'u': 'X', 'v': 'Z', 'w': 3065.0}, {'u': 'Y', 'v': 'AC', 'w': 5906.0}, {'u': 'Y', 'v': 'C', 'w': 2223.0}, {'u': 'Z', 'v': 'B', 'w': 370.0}, {'u': 'Z', 'v': 'AA', 'w': 3047.0}, {'u': 'C', 'v': 'I', 'w': 2344.0}, {'u': 'D', 'v': 'G', 'w': 1629.0}, {'u': 'E', 'v': 'F', 'w': 377298.0}, {'u': 'E', 'v': 'G', 'w': 605648.0}, {'u': 'H', 'v': 'I', 'w': 732848.0}, {'u': 'H', 'v': 'J', 'w': 672556.0}, {'u': 'J', 'v': 'L', 'w': 4246.0}, {'u': 'K', 'v': 'M', 'w': 2938.0}, {'u': 'N', 'v': 'O', 'w': 2313.0}], 'density': 0.08866995073891626, 'source_file': 'I004.stp', 'k': 9}","[['P', 'S'], ['P', 'T'], ['D', 'T'], ['G', 'U'], ['D', 'X'], ['X', 'Z'], ['B', 'Z'], ['D', 'G']]",22,markdown_table,names
KMST,KMST,"At the wildlife trust the brief is to pick exactly a set number of hides and link them with footpaths so the chosen hides make a single connected layout without any circular trails. The practical choices—selecting which hides to use and which connecting footpaths to build—are judged by summing the lengths of those paths, and the smaller that sum, the better the plan. The concrete details and distances follow below.

There are 27 hides available, 33 candidate footpaths listed, and the trust must select exactly 14 hides to form a single connected, cycle-free layout.
Candidate footpath between hide 0 and hide 8 with length 117.0.
Candidate footpath between hide 0 and hide 17 with length 995.0.
Candidate footpath between hide 0 and hide 12 with length 1854.0.
Candidate footpath between hide 8 and hide 9 with length 1056.0.
Candidate footpath between hide 8 and hide 25 with length 29080.0.
Candidate footpath between hide 9 and hide 5 with length 402.0.
Candidate footpath between hide 9 and hide 17 with length 371.0.
Candidate footpath between hide 25 and hide 24 with length 50.0.
Candidate footpath between hide 25 and hide 23 with length 19384.0.
Candidate footpath between hide 7 and hide 20 with length 814.0.
Candidate footpath between hide 7 and hide 24 with length 570.0.
Candidate footpath between hide 1 and hide 10 with length 83.0.
Candidate footpath between hide 2 and hide 11 with length 143.0.
Candidate footpath between hide 2 and hide 4 with length 520.0.
Candidate footpath between hide 2 and hide 3 with length 317.0.
Candidate footpath between hide 3 and hide 11 with length 234.0.
Candidate footpath between hide 3 and hide 12 with length 705.0.
Candidate footpath between hide 4 and hide 13 with length 811.0.
Candidate footpath between hide 5 and hide 18 with length 725.0.
Candidate footpath between hide 26 and hide 24 with length 776.0.
Candidate footpath between hide 21 and hide 22 with length 2467.0.
Candidate footpath between hide 21 and hide 23 with length 4594.0.
Candidate footpath between hide 22 and hide 23 with length 4200.0.
Candidate footpath between hide 22 and hide 19 with length 3263.0.
Candidate footpath between hide 10 and hide 11 with length 2200.0.
Candidate footpath between hide 12 and hide 15 with length 1130.0.
Candidate footpath between hide 13 and hide 14 with length 616.0.
Candidate footpath between hide 14 and hide 15 with length 741.0.
Candidate footpath between hide 14 and hide 6 with length 707.0.
Candidate footpath between hide 15 and hide 16 with length 258.0.
Candidate footpath between hide 16 and hide 18 with length 1669.0.
Candidate footpath between hide 16 and hide 6 with length 800.0.
Candidate footpath between hide 17 and hide 18 with length 133.0.
Plans are scored by the total length of chosen footpaths; select 14 hides that yield the minimal sum.

Also, when you send back your choice of paths, please use this simple JSON layout so it's easy to read:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of the footpaths you'd build; each inner pair like [u1, v1] represents a single path connecting two hides (use the hide identifiers exactly as given). This block is just a sketch of the shape I expect — not the final answer itself, just the format to follow.

Please be sure to use the exact identifiers from the instance input, with no renaming and no extra 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”.","{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 33, 'edges': [{'u': 1, 'v': 9, 'w': 117.0}, {'u': 1, 'v': 18, 'w': 995.0}, {'u': 1, 'v': 13, 'w': 1854.0}, {'u': 9, 'v': 10, 'w': 1056.0}, {'u': 9, 'v': 26, 'w': 29080.0}, {'u': 10, 'v': 6, 'w': 402.0}, {'u': 10, 'v': 18, 'w': 371.0}, {'u': 26, 'v': 25, 'w': 50.0}, {'u': 26, 'v': 24, 'w': 19384.0}, {'u': 8, 'v': 21, 'w': 814.0}, {'u': 8, 'v': 25, 'w': 570.0}, {'u': 2, 'v': 11, 'w': 83.0}, {'u': 3, 'v': 12, 'w': 143.0}, {'u': 3, 'v': 5, 'w': 520.0}, {'u': 3, 'v': 4, 'w': 317.0}, {'u': 4, 'v': 12, 'w': 234.0}, {'u': 4, 'v': 13, 'w': 705.0}, {'u': 5, 'v': 14, 'w': 811.0}, {'u': 6, 'v': 19, 'w': 725.0}, {'u': 27, 'v': 25, 'w': 776.0}, {'u': 22, 'v': 23, 'w': 2467.0}, {'u': 22, 'v': 24, 'w': 4594.0}, {'u': 23, 'v': 24, 'w': 4200.0}, {'u': 23, 'v': 20, 'w': 3263.0}, {'u': 11, 'v': 12, 'w': 2200.0}, {'u': 13, 'v': 16, 'w': 1130.0}, {'u': 14, 'v': 15, 'w': 616.0}, {'u': 15, 'v': 16, 'w': 741.0}, {'u': 15, 'v': 7, 'w': 707.0}, {'u': 16, 'v': 17, 'w': 258.0}, {'u': 17, 'v': 19, 'w': 1669.0}, {'u': 17, 'v': 7, 'w': 800.0}, {'u': 18, 'v': 19, 'w': 133.0}], 'k': 14, 'source_file': 'I010.stp', 'density': 0.09401709401709402}","[[1, 9], [1, 18], [6, 10], [10, 18], [3, 12], [3, 5], [4, 12], [5, 14], [14, 15], [15, 16], [16, 17], [17, 19], [18, 19]]",7010.0,"{'problem_type': 'KMST', 'num_nodes': 27, 'num_edges': 33, 'edges': [{'u': 0, 'v': 8, 'w': 117.0}, {'u': 0, 'v': 17, 'w': 995.0}, {'u': 0, 'v': 12, 'w': 1854.0}, {'u': 8, 'v': 9, 'w': 1056.0}, {'u': 8, 'v': 25, 'w': 29080.0}, {'u': 9, 'v': 5, 'w': 402.0}, {'u': 9, 'v': 17, 'w': 371.0}, {'u': 25, 'v': 24, 'w': 50.0}, {'u': 25, 'v': 23, 'w': 19384.0}, {'u': 7, 'v': 20, 'w': 814.0}, {'u': 7, 'v': 24, 'w': 570.0}, {'u': 1, 'v': 10, 'w': 83.0}, {'u': 2, 'v': 11, 'w': 143.0}, {'u': 2, 'v': 4, 'w': 520.0}, {'u': 2, 'v': 3, 'w': 317.0}, {'u': 3, 'v': 11, 'w': 234.0}, {'u': 3, 'v': 12, 'w': 705.0}, {'u': 4, 'v': 13, 'w': 811.0}, {'u': 5, 'v': 18, 'w': 725.0}, {'u': 26, 'v': 24, 'w': 776.0}, {'u': 21, 'v': 22, 'w': 2467.0}, {'u': 21, 'v': 23, 'w': 4594.0}, {'u': 22, 'v': 23, 'w': 4200.0}, {'u': 22, 'v': 19, 'w': 3263.0}, {'u': 10, 'v': 11, 'w': 2200.0}, {'u': 12, 'v': 15, 'w': 1130.0}, {'u': 13, 'v': 14, 'w': 616.0}, {'u': 14, 'v': 15, 'w': 741.0}, {'u': 14, 'v': 6, 'w': 707.0}, {'u': 15, 'v': 16, 'w': 258.0}, {'u': 16, 'v': 18, 'w': 1669.0}, {'u': 16, 'v': 6, 'w': 800.0}, {'u': 17, 'v': 18, 'w': 133.0}], 'density': 0.09401709401709402, 'source_file': 'I010.stp', 'k': 14}","[[0, 8], [0, 17], [5, 9], [9, 17], [2, 11], [2, 4], [3, 11], [4, 13], [13, 14], [14, 15], [15, 16], [16, 18], [17, 18]]",23,markdown_table,0
KMST,KMST,"In town the sewer team needs to select a set number of access points to service and string pipes between them so they become one connected system without any circular detours. Plans are judged by how little pipe they require in total — found by summing all the individual pipe segment lengths — and the team must include exactly the required number of points, connect them all, and avoid creating any loops. The specific nodes and distances will be shown below.

There are 30 candidate access points, 37 candidate pipe segments, and the team must choose exactly 15 points to connect.
Candidate pipe between access points 28 and 24 with length 1038.0.
Candidate pipe between access points 28 and 12 with length 2849.0.
Candidate pipe between access points 28 and 22 with length 3295.0.
Candidate pipe between access points 19 and 29 with length 541.0.
Candidate pipe between access points 19 and 30 with length 285.0.
Candidate pipe between access points 19 and 15 with length 1437.0.
Candidate pipe between access points 20 and 10 with length 924.0.
Candidate pipe between access points 20 and 29 with length 613.0.
Candidate pipe between access points 20 and 13 with length 2655.0.
Candidate pipe between access points 2 and 3 with length 1566.0.
Candidate pipe between access points 2 and 25 with length 2150.0.
Candidate pipe between access points 3 and 16 with length 597.0.
Candidate pipe between access points 3 and 17 with length 2.0.
Candidate pipe between access points 18 and 12 with length 96.0.
Candidate pipe between access points 18 and 11 with length 275.0.
Candidate pipe between access points 18 and 8 with length 1591.0.
Candidate pipe between access points 12 and 13 with length 1907.0.
Candidate pipe between access points 13 and 1 with length 4718.0.
Candidate pipe between access points 14 and 1 with length 3307.0.
Candidate pipe between access points 10 and 7 with length 5531.0.
Candidate pipe between access points 10 and 11 with length 2415.0.
Candidate pipe between access points 11 and 26 with length 1058.0.
Candidate pipe between access points 8 and 22 with length 1098.0.
Candidate pipe between access points 9 and 4 with length 352162.0.
Candidate pipe between access points 9 and 7 with length 351928.0.
Candidate pipe between access points 22 and 23 with length 47.0.
Candidate pipe between access points 23 and 26 with length 799.0.
Candidate pipe between access points 23 and 25 with length 1584.0.
Candidate pipe between access points 29 and 30 with length 787.0.
Candidate pipe between access points 30 and 27 with length 3813.0.
Candidate pipe between access points 25 and 26 with length 1170.0.
Candidate pipe between access points 27 and 6 with length 3832.0.
Candidate pipe between access points 21 and 17 with length 222.0.
Candidate pipe between access points 21 and 16 with length 702.0.
Candidate pipe between access points 16 and 7 with length 943.0.
Candidate pipe between access points 4 and 5 with length 1246.0.
Candidate pipe between access points 4 and 6 with length 706.0.
The team must include exactly 15 access points, connect them into one loop-free system, and minimize the sum of all listed pipe lengths.

When you're ready to hand over the chosen pipe segments, just return them in a little JSON sketch like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of pipe pieces to lay down; each inner pair [uX, vX] is just the two access points that get connected by that pipe. Think of it like filling out a simple form: each line says ""connect this point to that point."" This block is only a template showing the shape I expect, not the actual answer.

Please make 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”.""","{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 37, 'edges': [{'u': 28, 'v': 24, 'w': 1038.0}, {'u': 28, 'v': 12, 'w': 2849.0}, {'u': 28, 'v': 22, 'w': 3295.0}, {'u': 19, 'v': 29, 'w': 541.0}, {'u': 19, 'v': 30, 'w': 285.0}, {'u': 19, 'v': 15, 'w': 1437.0}, {'u': 20, 'v': 10, 'w': 924.0}, {'u': 20, 'v': 29, 'w': 613.0}, {'u': 20, 'v': 13, 'w': 2655.0}, {'u': 2, 'v': 3, 'w': 1566.0}, {'u': 2, 'v': 25, 'w': 2150.0}, {'u': 3, 'v': 16, 'w': 597.0}, {'u': 3, 'v': 17, 'w': 2.0}, {'u': 18, 'v': 12, 'w': 96.0}, {'u': 18, 'v': 11, 'w': 275.0}, {'u': 18, 'v': 8, 'w': 1591.0}, {'u': 12, 'v': 13, 'w': 1907.0}, {'u': 13, 'v': 1, 'w': 4718.0}, {'u': 14, 'v': 1, 'w': 3307.0}, {'u': 10, 'v': 7, 'w': 5531.0}, {'u': 10, 'v': 11, 'w': 2415.0}, {'u': 11, 'v': 26, 'w': 1058.0}, {'u': 8, 'v': 22, 'w': 1098.0}, {'u': 9, 'v': 4, 'w': 352162.0}, {'u': 9, 'v': 7, 'w': 351928.0}, {'u': 22, 'v': 23, 'w': 47.0}, {'u': 23, 'v': 26, 'w': 799.0}, {'u': 23, 'v': 25, 'w': 1584.0}, {'u': 29, 'v': 30, 'w': 787.0}, {'u': 30, 'v': 27, 'w': 3813.0}, {'u': 25, 'v': 26, 'w': 1170.0}, {'u': 27, 'v': 6, 'w': 3832.0}, {'u': 21, 'v': 17, 'w': 222.0}, {'u': 21, 'v': 16, 'w': 702.0}, {'u': 16, 'v': 7, 'w': 943.0}, {'u': 4, 'v': 5, 'w': 1246.0}, {'u': 4, 'v': 6, 'w': 706.0}], 'k': 15, 'source_file': 'I014.stp', 'density': 0.08505747126436781}","[[19, 29], [10, 20], [20, 29], [2, 3], [2, 25], [3, 17], [12, 18], [11, 18], [10, 11], [11, 26], [22, 23], [23, 26], [25, 26], [17, 21]]",11878.0,"{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 37, 'edges': [{'u': 28, 'v': 24, 'w': 1038.0}, {'u': 28, 'v': 12, 'w': 2849.0}, {'u': 28, 'v': 22, 'w': 3295.0}, {'u': 19, 'v': 29, 'w': 541.0}, {'u': 19, 'v': 30, 'w': 285.0}, {'u': 19, 'v': 15, 'w': 1437.0}, {'u': 20, 'v': 10, 'w': 924.0}, {'u': 20, 'v': 29, 'w': 613.0}, {'u': 20, 'v': 13, 'w': 2655.0}, {'u': 2, 'v': 3, 'w': 1566.0}, {'u': 2, 'v': 25, 'w': 2150.0}, {'u': 3, 'v': 16, 'w': 597.0}, {'u': 3, 'v': 17, 'w': 2.0}, {'u': 18, 'v': 12, 'w': 96.0}, {'u': 18, 'v': 11, 'w': 275.0}, {'u': 18, 'v': 8, 'w': 1591.0}, {'u': 12, 'v': 13, 'w': 1907.0}, {'u': 13, 'v': 1, 'w': 4718.0}, {'u': 14, 'v': 1, 'w': 3307.0}, {'u': 10, 'v': 7, 'w': 5531.0}, {'u': 10, 'v': 11, 'w': 2415.0}, {'u': 11, 'v': 26, 'w': 1058.0}, {'u': 8, 'v': 22, 'w': 1098.0}, {'u': 9, 'v': 4, 'w': 352162.0}, {'u': 9, 'v': 7, 'w': 351928.0}, {'u': 22, 'v': 23, 'w': 47.0}, {'u': 23, 'v': 26, 'w': 799.0}, {'u': 23, 'v': 25, 'w': 1584.0}, {'u': 29, 'v': 30, 'w': 787.0}, {'u': 30, 'v': 27, 'w': 3813.0}, {'u': 25, 'v': 26, 'w': 1170.0}, {'u': 27, 'v': 6, 'w': 3832.0}, {'u': 21, 'v': 17, 'w': 222.0}, {'u': 21, 'v': 16, 'w': 702.0}, {'u': 16, 'v': 7, 'w': 943.0}, {'u': 4, 'v': 5, 'w': 1246.0}, {'u': 4, 'v': 6, 'w': 706.0}], 'density': 0.08505747126436781, 'source_file': 'I014.stp', 'k': 15}","[[19, 29], [10, 20], [20, 29], [2, 3], [2, 25], [3, 17], [12, 18], [11, 18], [10, 11], [11, 26], [22, 23], [23, 26], [25, 26], [17, 21]]",24,nl,1
KMST,KMST,"Back at the control room the brief was simple: choose a predetermined number of sensor sites and connect them so they form one connected, cycle-free network — nothing duplicated, nothing left hanging. The job is to pick which sites and which links to install; a better plan is the one that keeps the sum of all link costs as low as possible (just total up each chosen link’s cost). The full instance details and cost table appear below.

Instance: 30 potential sensor sites, 41 candidate links; select exactly 15 sites and the links that join them so they form one connected, cycle-free network.
Candidate link joining site 19 and site 20 with cost 403.0.
Candidate link joining site 19 and site 23 with cost 427.0.
Candidate link joining site 20 and site 21 with cost 502.0.
Candidate link joining site 20 and site 12 with cost 805.0.
Candidate link joining site 27 and site 22 with cost 2954.0.
Candidate link joining site 27 and site 23 with cost 523.0.
Candidate link joining site 27 and site 29 with cost 1751.0.
Candidate link joining site 28 and site 4 with cost 286.0.
Candidate link joining site 28 and site 9 with cost 616.0.
Candidate link joining site 28 and site 26 with cost 1474.0.
Candidate link joining site 29 and site 12 with cost 448.0.
Candidate link joining site 29 and site 26 with cost 1279.0.
Candidate link joining site 21 and site 24 with cost 1659.0.
Candidate link joining site 10 and site 6 with cost 5943.0.
Candidate link joining site 10 and site 14 with cost 5520.0.
Candidate link joining site 10 and site 18 with cost 673.0.
Candidate link joining site 24 and site 11 with cost 1041.0.
Candidate link joining site 25 and site 11 with cost 524.0.
Candidate link joining site 25 and site 13 with cost 1031.0.
Candidate link joining site 11 and site 12 with cost 1411.0.
Candidate link joining site 13 and site 8 with cost 3235.0.
Candidate link joining site 13 and site 15 with cost 2241.0.
Candidate link joining site 2 and site 9 with cost 1238.0.
Candidate link joining site 2 and site 22 with cost 718.0.
Candidate link joining site 2 and site 6 with cost 96.0.
Candidate link joining site 3 and site 7 with cost 1551.0.
Candidate link joining site 3 and site 1 with cost 1626.0.
Candidate link joining site 3 and site 16 with cost 2420.0.
Candidate link joining site 14 and site 7 with cost 1350.0.
Candidate link joining site 14 and site 17 with cost 1289.0.
Candidate link joining site 0 and site 4 with cost 294127.0.
Candidate link joining site 0 and site 5 with cost 294127.0.
Candidate link joining site 1 and site 16 with cost 2572.0.
Candidate link joining site 7 and site 8 with cost 2035.0.
Candidate link joining site 8 and site 26 with cost 1619.0.
Candidate link joining site 8 and site 9 with cost 274.0.
Candidate link joining site 15 and site 16 with cost 319.0.
Candidate link joining site 15 and site 17 with cost 2862.0.
Candidate link joining site 4 and site 5 with cost 632.0.
Candidate link joining site 22 and site 5 with cost 319.0.
Candidate link joining site 17 and site 18 with cost 5446.0.
Keep the sum of chosen link costs as low as possible while connecting exactly 15 sites into a single tree.

You can just return the selected links in a tiny JSON snippet like this — nice and simple:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of it like a short checklist: ""solution"" holds a list of links, and each [uX, vX] pair is one chosen connection between two sites. It's just the shape we expect, not the actual plan — fill those pairs with the real site identifiers from the instance when you send the answer.

Please make sure to use the identifiers exactly as they appear in the instance input — no renaming and no 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”.""","{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 41, 'edges': [{'u': 20, 'v': 21, 'w': 403.0}, {'u': 20, 'v': 24, 'w': 427.0}, {'u': 21, 'v': 22, 'w': 502.0}, {'u': 21, 'v': 13, 'w': 805.0}, {'u': 28, 'v': 23, 'w': 2954.0}, {'u': 28, 'v': 24, 'w': 523.0}, {'u': 28, 'v': 30, 'w': 1751.0}, {'u': 29, 'v': 5, 'w': 286.0}, {'u': 29, 'v': 10, 'w': 616.0}, {'u': 29, 'v': 27, 'w': 1474.0}, {'u': 30, 'v': 13, 'w': 448.0}, {'u': 30, 'v': 27, 'w': 1279.0}, {'u': 22, 'v': 25, 'w': 1659.0}, {'u': 11, 'v': 7, 'w': 5943.0}, {'u': 11, 'v': 15, 'w': 5520.0}, {'u': 11, 'v': 19, 'w': 673.0}, {'u': 25, 'v': 12, 'w': 1041.0}, {'u': 26, 'v': 12, 'w': 524.0}, {'u': 26, 'v': 14, 'w': 1031.0}, {'u': 12, 'v': 13, 'w': 1411.0}, {'u': 14, 'v': 9, 'w': 3235.0}, {'u': 14, 'v': 16, 'w': 2241.0}, {'u': 3, 'v': 10, 'w': 1238.0}, {'u': 3, 'v': 23, 'w': 718.0}, {'u': 3, 'v': 7, 'w': 96.0}, {'u': 4, 'v': 8, 'w': 1551.0}, {'u': 4, 'v': 2, 'w': 1626.0}, {'u': 4, 'v': 17, 'w': 2420.0}, {'u': 15, 'v': 8, 'w': 1350.0}, {'u': 15, 'v': 18, 'w': 1289.0}, {'u': 1, 'v': 5, 'w': 294127.0}, {'u': 1, 'v': 6, 'w': 294127.0}, {'u': 2, 'v': 17, 'w': 2572.0}, {'u': 8, 'v': 9, 'w': 2035.0}, {'u': 9, 'v': 27, 'w': 1619.0}, {'u': 9, 'v': 10, 'w': 274.0}, {'u': 16, 'v': 17, 'w': 319.0}, {'u': 16, 'v': 18, 'w': 2862.0}, {'u': 5, 'v': 6, 'w': 632.0}, {'u': 23, 'v': 6, 'w': 319.0}, {'u': 18, 'v': 19, 'w': 5446.0}], 'k': 15, 'source_file': 'I067.stp', 'density': 0.09425287356321839}","[[20, 21], [20, 24], [21, 22], [13, 21], [5, 29], [10, 29], [27, 29], [13, 30], [27, 30], [3, 23], [3, 7], [9, 10], [5, 6], [6, 23]]",8279.0,"{'problem_type': 'KMST', 'num_nodes': 30, 'num_edges': 41, 'edges': [{'u': 19, 'v': 20, 'w': 403.0}, {'u': 19, 'v': 23, 'w': 427.0}, {'u': 20, 'v': 21, 'w': 502.0}, {'u': 20, 'v': 12, 'w': 805.0}, {'u': 27, 'v': 22, 'w': 2954.0}, {'u': 27, 'v': 23, 'w': 523.0}, {'u': 27, 'v': 29, 'w': 1751.0}, {'u': 28, 'v': 4, 'w': 286.0}, {'u': 28, 'v': 9, 'w': 616.0}, {'u': 28, 'v': 26, 'w': 1474.0}, {'u': 29, 'v': 12, 'w': 448.0}, {'u': 29, 'v': 26, 'w': 1279.0}, {'u': 21, 'v': 24, 'w': 1659.0}, {'u': 10, 'v': 6, 'w': 5943.0}, {'u': 10, 'v': 14, 'w': 5520.0}, {'u': 10, 'v': 18, 'w': 673.0}, {'u': 24, 'v': 11, 'w': 1041.0}, {'u': 25, 'v': 11, 'w': 524.0}, {'u': 25, 'v': 13, 'w': 1031.0}, {'u': 11, 'v': 12, 'w': 1411.0}, {'u': 13, 'v': 8, 'w': 3235.0}, {'u': 13, 'v': 15, 'w': 2241.0}, {'u': 2, 'v': 9, 'w': 1238.0}, {'u': 2, 'v': 22, 'w': 718.0}, {'u': 2, 'v': 6, 'w': 96.0}, {'u': 3, 'v': 7, 'w': 1551.0}, {'u': 3, 'v': 1, 'w': 1626.0}, {'u': 3, 'v': 16, 'w': 2420.0}, {'u': 14, 'v': 7, 'w': 1350.0}, {'u': 14, 'v': 17, 'w': 1289.0}, {'u': 0, 'v': 4, 'w': 294127.0}, {'u': 0, 'v': 5, 'w': 294127.0}, {'u': 1, 'v': 16, 'w': 2572.0}, {'u': 7, 'v': 8, 'w': 2035.0}, {'u': 8, 'v': 26, 'w': 1619.0}, {'u': 8, 'v': 9, 'w': 274.0}, {'u': 15, 'v': 16, 'w': 319.0}, {'u': 15, 'v': 17, 'w': 2862.0}, {'u': 4, 'v': 5, 'w': 632.0}, {'u': 22, 'v': 5, 'w': 319.0}, {'u': 17, 'v': 18, 'w': 5446.0}], 'density': 0.09425287356321839, 'source_file': 'I067.stp', 'k': 15}","[[19, 20], [19, 23], [20, 21], [12, 20], [4, 28], [9, 28], [26, 28], [12, 29], [26, 29], [2, 22], [2, 6], [8, 9], [4, 5], [5, 22]]",25,nl,0
KMST,KMST,"At the office they handed over a map and asked for a tight, loop-free connection among a fixed number of stations, and the consultant must decide the layout. The practical decision is picking exactly that many stations and the connecting links that make them one connected set with no circular tracks. The preferred layout is the one with the lowest total length of new track — calculate that by summing all chosen segment lengths, and the plan with the smallest sum wins. All chosen stations have to be included, cycles are not permitted, and segments are counted once; the concrete instance follows below.

The map shows 22 stations and 28 candidate segments; the consultant must pick exactly 11 stations and the connecting links to form a single, loop-free network.
Candidate segment connecting stations 16 and 0 with length 9616.0.
Candidate segment connecting stations 16 and 6 with length 399.0.
Candidate segment connecting stations 16 and 19 with length 12310.0.
Candidate segment connecting stations 7 and 8 with length 4645.0.
Candidate segment connecting stations 7 and 13 with length 3849.0.
Candidate segment connecting stations 7 and 19 with length 5078.0.
Candidate segment connecting stations 8 and 9 with length 1961.0.
Candidate segment connecting stations 8 and 13 with length 1007.0.
Candidate segment connecting stations 14 and 18 with length 384.0.
Candidate segment connecting stations 14 and 17 with length 8411.0.
Candidate segment connecting stations 15 and 11 with length 2174.0.
Candidate segment connecting stations 12 and 11 with length 4095.0.
Candidate segment connecting stations 19 and 17 with length 4903.0.
Candidate segment connecting stations 9 and 20 with length 1674.0.
Candidate segment connecting stations 10 and 3 with length 7694.0.
Candidate segment connecting stations 0 and 1 with length 808.0.
Candidate segment connecting stations 0 and 2 with length 5164.0.
Candidate segment connecting stations 1 and 6 with length 9829.0.
Candidate segment connecting stations 1 and 2 with length 4963.0.
Candidate segment connecting stations 2 and 4 with length 17874.0.
Candidate segment connecting stations 3 and 4 with length 687.0.
Candidate segment connecting stations 3 and 21 with length 23114.0.
Candidate segment connecting stations 4 and 11 with length 11008.0.
Candidate segment connecting stations 13 and 20 with length 2304.0.
Candidate segment connecting stations 5 and 6 with length 2051.0.
Candidate segment connecting stations 5 and 21 with length 13116.0.
Candidate segment connecting stations 21 and 20 with length 386.0.
Candidate segment connecting stations 17 and 18 with length 8508.0.
The consultant must select 11 stations and their links so all chosen stations are included, no cycles occur, and the sum of chosen segment lengths is minimal.

When you’re ready to hand back the exact layout, just use this tidy little JSON shape so I can read it automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This just means: ""solution"" is a list of the track segments you want to build. Each inner pair [u, v] names the two stations that the segment connects — think of each pair as one straight line between two stops. It’s just a sketch of the shape I expect, not the final plan itself.

Please use the station identifiers exactly as they appear in the instance — 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”.""","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 17, 'v': 1, 'w': 9616.0}, {'u': 17, 'v': 7, 'w': 399.0}, {'u': 17, 'v': 20, 'w': 12310.0}, {'u': 8, 'v': 9, 'w': 4645.0}, {'u': 8, 'v': 14, 'w': 3849.0}, {'u': 8, 'v': 20, 'w': 5078.0}, {'u': 9, 'v': 10, 'w': 1961.0}, {'u': 9, 'v': 14, 'w': 1007.0}, {'u': 15, 'v': 19, 'w': 384.0}, {'u': 15, 'v': 18, 'w': 8411.0}, {'u': 16, 'v': 12, 'w': 2174.0}, {'u': 13, 'v': 12, 'w': 4095.0}, {'u': 20, 'v': 18, 'w': 4903.0}, {'u': 10, 'v': 21, 'w': 1674.0}, {'u': 11, 'v': 4, 'w': 7694.0}, {'u': 1, 'v': 2, 'w': 808.0}, {'u': 1, 'v': 3, 'w': 5164.0}, {'u': 2, 'v': 7, 'w': 9829.0}, {'u': 2, 'v': 3, 'w': 4963.0}, {'u': 3, 'v': 5, 'w': 17874.0}, {'u': 4, 'v': 5, 'w': 687.0}, {'u': 4, 'v': 22, 'w': 23114.0}, {'u': 5, 'v': 12, 'w': 11008.0}, {'u': 14, 'v': 21, 'w': 2304.0}, {'u': 6, 'v': 7, 'w': 2051.0}, {'u': 6, 'v': 22, 'w': 13116.0}, {'u': 22, 'v': 21, 'w': 386.0}, {'u': 18, 'v': 19, 'w': 8508.0}], 'k': 11, 'source_file': 'I012.stp', 'density': 0.12121212121212122}","[[7, 17], [17, 20], [8, 14], [8, 20], [9, 10], [9, 14], [18, 20], [10, 21], [6, 7], [21, 22]]",33618.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 16, 'v': 0, 'w': 9616.0}, {'u': 16, 'v': 6, 'w': 399.0}, {'u': 16, 'v': 19, 'w': 12310.0}, {'u': 7, 'v': 8, 'w': 4645.0}, {'u': 7, 'v': 13, 'w': 3849.0}, {'u': 7, 'v': 19, 'w': 5078.0}, {'u': 8, 'v': 9, 'w': 1961.0}, {'u': 8, 'v': 13, 'w': 1007.0}, {'u': 14, 'v': 18, 'w': 384.0}, {'u': 14, 'v': 17, 'w': 8411.0}, {'u': 15, 'v': 11, 'w': 2174.0}, {'u': 12, 'v': 11, 'w': 4095.0}, {'u': 19, 'v': 17, 'w': 4903.0}, {'u': 9, 'v': 20, 'w': 1674.0}, {'u': 10, 'v': 3, 'w': 7694.0}, {'u': 0, 'v': 1, 'w': 808.0}, {'u': 0, 'v': 2, 'w': 5164.0}, {'u': 1, 'v': 6, 'w': 9829.0}, {'u': 1, 'v': 2, 'w': 4963.0}, {'u': 2, 'v': 4, 'w': 17874.0}, {'u': 3, 'v': 4, 'w': 687.0}, {'u': 3, 'v': 21, 'w': 23114.0}, {'u': 4, 'v': 11, 'w': 11008.0}, {'u': 13, 'v': 20, 'w': 2304.0}, {'u': 5, 'v': 6, 'w': 2051.0}, {'u': 5, 'v': 21, 'w': 13116.0}, {'u': 21, 'v': 20, 'w': 386.0}, {'u': 17, 'v': 18, 'w': 8508.0}], 'density': 0.12121212121212122, 'source_file': 'I012.stp', 'k': 11}","[[6, 16], [16, 19], [7, 13], [7, 19], [8, 9], [8, 13], [17, 19], [9, 20], [5, 6], [20, 21]]",26,nl,0
KMST,KMST,"We have a mountain range full of potential watch points and a set number of slots to fill. The decision is which specific spots to use and which straight connections to make so the selected spots become one connected, loop-free network. Plans are judged by adding up the lengths of the paths added — the smaller that sum, the better — and the rules are that exactly the given number of distinct lookouts must be chosen and no closed loops are allowed. The concrete map and distances follow below.

There are 24 potential watchpoints and 32 candidate straight paths; we must select exactly 12 lookouts so they form one connected, loop-free network.
Path between watchpoint 1 and watchpoint 3 with length 246.0.
Path between watchpoint 1 and watchpoint 16 with length 380.0.
Path between watchpoint 1 and watchpoint 19 with length 710.0.
Path between watchpoint 1 and watchpoint 2 with length 398.0.
Path between watchpoint 6 and watchpoint 7 with length 726.0.
Path between watchpoint 6 and watchpoint 8 with length 279.0.
Path between watchpoint 7 and watchpoint 22 with length 285.0.
Path between watchpoint 7 and watchpoint 11 with length 354.0.
Path between watchpoint 8 and watchpoint 22 with length 728.0.
Path between watchpoint 8 and watchpoint 2 with length 1688.0.
Path between watchpoint 21 and watchpoint 10 with length 471.0.
Path between watchpoint 22 and watchpoint 13 with length 1233.0.
Path between watchpoint 23 and watchpoint 13 with length 284.0.
Path between watchpoint 23 and watchpoint 24 with length 586.0.
Path between watchpoint 23 and watchpoint 17 with length 235.0.
Path between watchpoint 24 and watchpoint 18 with length 92.0.
Path between watchpoint 9 and watchpoint 10 with length 1024.0.
Path between watchpoint 9 and watchpoint 15 with length 226735.0.
Path between watchpoint 10 and watchpoint 11 with length 273.0.
Path between watchpoint 11 and watchpoint 15 with length 227051.0.
Path between watchpoint 12 and watchpoint 13 with length 303.0.
Path between watchpoint 12 and watchpoint 15 with length 226178.0.
Path between watchpoint 12 and watchpoint 17 with length 292.0.
Path between watchpoint 14 and watchpoint 15 with length 226239.0.
Path between watchpoint 14 and watchpoint 17 with length 263.0.
Path between watchpoint 16 and watchpoint 2 with length 20.0.
Path between watchpoint 16 and watchpoint 20 with length 710.0.
Path between watchpoint 3 and watchpoint 4 with length 710.0.
Path between watchpoint 4 and watchpoint 19 with length 247.0.
Path between watchpoint 17 and watchpoint 18 with length 625.0.
Path between watchpoint 19 and watchpoint 5 with length 304.0.
Path between watchpoint 20 and watchpoint 5 with length 75.0.
We will use the map below to pick 12 lookouts and the connecting paths that minimize the total path length.

Quick note on how I'd like the answer formatted — keep it simple and JSON-y, like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as just a list of the straight connections you'll make. Each inner pair is one edge (which two lookout IDs get linked). It's just a sketch of the shape I expect you to follow, not the real final plan.

Please use the exact node identifiers from 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”, or a capital letter followed by digits like “A1” or “X7”.","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 32, 'edges': [{'u': 1, 'v': 3, 'w': 246.0}, {'u': 1, 'v': 16, 'w': 380.0}, {'u': 1, 'v': 19, 'w': 710.0}, {'u': 1, 'v': 2, 'w': 398.0}, {'u': 6, 'v': 7, 'w': 726.0}, {'u': 6, 'v': 8, 'w': 279.0}, {'u': 7, 'v': 22, 'w': 285.0}, {'u': 7, 'v': 11, 'w': 354.0}, {'u': 8, 'v': 22, 'w': 728.0}, {'u': 8, 'v': 2, 'w': 1688.0}, {'u': 21, 'v': 10, 'w': 471.0}, {'u': 22, 'v': 13, 'w': 1233.0}, {'u': 23, 'v': 13, 'w': 284.0}, {'u': 23, 'v': 24, 'w': 586.0}, {'u': 23, 'v': 17, 'w': 235.0}, {'u': 24, 'v': 18, 'w': 92.0}, {'u': 9, 'v': 10, 'w': 1024.0}, {'u': 9, 'v': 15, 'w': 226735.0}, {'u': 10, 'v': 11, 'w': 273.0}, {'u': 11, 'v': 15, 'w': 227051.0}, {'u': 12, 'v': 13, 'w': 303.0}, {'u': 12, 'v': 15, 'w': 226178.0}, {'u': 12, 'v': 17, 'w': 292.0}, {'u': 14, 'v': 15, 'w': 226239.0}, {'u': 14, 'v': 17, 'w': 263.0}, {'u': 16, 'v': 2, 'w': 20.0}, {'u': 16, 'v': 20, 'w': 710.0}, {'u': 3, 'v': 4, 'w': 710.0}, {'u': 4, 'v': 19, 'w': 247.0}, {'u': 17, 'v': 18, 'w': 625.0}, {'u': 19, 'v': 5, 'w': 304.0}, {'u': 20, 'v': 5, 'w': 75.0}], 'k': 12, 'source_file': 'I042.stp', 'density': 0.11594202898550725}","[[7, 22], [7, 11], [10, 21], [13, 22], [13, 23], [23, 24], [17, 23], [18, 24], [10, 11], [12, 17], [14, 17]]",4368.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 32, 'edges': [{'u': 1, 'v': 3, 'w': 246.0}, {'u': 1, 'v': 16, 'w': 380.0}, {'u': 1, 'v': 19, 'w': 710.0}, {'u': 1, 'v': 2, 'w': 398.0}, {'u': 6, 'v': 7, 'w': 726.0}, {'u': 6, 'v': 8, 'w': 279.0}, {'u': 7, 'v': 22, 'w': 285.0}, {'u': 7, 'v': 11, 'w': 354.0}, {'u': 8, 'v': 22, 'w': 728.0}, {'u': 8, 'v': 2, 'w': 1688.0}, {'u': 21, 'v': 10, 'w': 471.0}, {'u': 22, 'v': 13, 'w': 1233.0}, {'u': 23, 'v': 13, 'w': 284.0}, {'u': 23, 'v': 24, 'w': 586.0}, {'u': 23, 'v': 17, 'w': 235.0}, {'u': 24, 'v': 18, 'w': 92.0}, {'u': 9, 'v': 10, 'w': 1024.0}, {'u': 9, 'v': 15, 'w': 226735.0}, {'u': 10, 'v': 11, 'w': 273.0}, {'u': 11, 'v': 15, 'w': 227051.0}, {'u': 12, 'v': 13, 'w': 303.0}, {'u': 12, 'v': 15, 'w': 226178.0}, {'u': 12, 'v': 17, 'w': 292.0}, {'u': 14, 'v': 15, 'w': 226239.0}, {'u': 14, 'v': 17, 'w': 263.0}, {'u': 16, 'v': 2, 'w': 20.0}, {'u': 16, 'v': 20, 'w': 710.0}, {'u': 3, 'v': 4, 'w': 710.0}, {'u': 4, 'v': 19, 'w': 247.0}, {'u': 17, 'v': 18, 'w': 625.0}, {'u': 19, 'v': 5, 'w': 304.0}, {'u': 20, 'v': 5, 'w': 75.0}], 'density': 0.11594202898550725, 'source_file': 'I042.stp', 'k': 12}","[[7, 22], [7, 11], [10, 21], [13, 22], [13, 23], [23, 24], [17, 23], [18, 24], [10, 11], [12, 17], [14, 17]]",27,nl,1
KMST,KMST,"Recently the farm manager had to pick exactly k barns and stitch together sections from the stock of fence parts so the chosen barns are all joined together in one enclosure, without forming any cycles and without selecting a barn more than once. The plan that’s better is simply the one that needs less total fence, which is found by summing the lengths of the pieces used. The concrete layout and pieces are shown below.

There are 22 barns, 28 available fence pieces, and the manager must enclose exactly 11 barns.
Fence piece connecting barn O and barn N of length 6711.0.
Fence piece connecting barn O and barn E of length 9951.0.
Fence piece connecting barn O and barn I of length 2435.0.
Fence piece connecting barn M and barn P of length 338.0.
Fence piece connecting barn R and barn U of length 5212.0.
Fence piece connecting barn R and barn V of length 996.0.
Fence piece connecting barn R and barn D of length 3703.0.
Fence piece connecting barn R and barn B of length 1227.0.
Fence piece connecting barn H and barn I of length 1216.0.
Fence piece connecting barn H and barn P of length 126.0.
Fence piece connecting barn H and barn Q of length 3857.0.
Fence piece connecting barn I and barn J of length 388.0.
Fence piece connecting barn J and barn N of length 4488.0.
Fence piece connecting barn A and barn B of length 274.0.
Fence piece connecting barn B and barn C of length 9930.0.
Fence piece connecting barn S and barn G of length 1540.0.
Fence piece connecting barn S and barn T of length 494.0.
Fence piece connecting barn T and barn K of length 928.0.
Fence piece connecting barn T and barn L of length 3449.0.
Fence piece connecting barn T and barn U of length 10959.0.
Fence piece connecting barn C and barn P of length 1896.0.
Fence piece connecting barn D and barn V of length 3365.0.
Fence piece connecting barn U and barn Q of length 6087.0.
Fence piece connecting barn E and barn F of length 1444.0.
Fence piece connecting barn F and barn K of length 375.0.
Fence piece connecting barn F and barn L of length 2926.0.
Fence piece connecting barn Q and barn L of length 5312.0.
Fence piece connecting barn G and barn K of length 1351.0.
The manager seeks a selection of 11 barns joined without cycles that uses the least total fence length.

I'll show the output in a tiny, friendly JSON sketch so it's clear what shape the answer should take.

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as a list of fence pieces — each pair [u, v] is a chosen connection joining barn u to barn v. This block is just the expected shape, not the actual fenced plan.

Please use the exact identifiers from the instance input — do not rename them or invent new ones. 

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”.","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 15, 'v': 14, 'w': 6711.0}, {'u': 15, 'v': 5, 'w': 9951.0}, {'u': 15, 'v': 9, 'w': 2435.0}, {'u': 13, 'v': 16, 'w': 338.0}, {'u': 18, 'v': 21, 'w': 5212.0}, {'u': 18, 'v': 22, 'w': 996.0}, {'u': 18, 'v': 4, 'w': 3703.0}, {'u': 18, 'v': 2, 'w': 1227.0}, {'u': 8, 'v': 9, 'w': 1216.0}, {'u': 8, 'v': 16, 'w': 126.0}, {'u': 8, 'v': 17, 'w': 3857.0}, {'u': 9, 'v': 10, 'w': 388.0}, {'u': 10, 'v': 14, 'w': 4488.0}, {'u': 1, 'v': 2, 'w': 274.0}, {'u': 2, 'v': 3, 'w': 9930.0}, {'u': 19, 'v': 7, 'w': 1540.0}, {'u': 19, 'v': 20, 'w': 494.0}, {'u': 20, 'v': 11, 'w': 928.0}, {'u': 20, 'v': 12, 'w': 3449.0}, {'u': 20, 'v': 21, 'w': 10959.0}, {'u': 3, 'v': 16, 'w': 1896.0}, {'u': 4, 'v': 22, 'w': 3365.0}, {'u': 21, 'v': 17, 'w': 6087.0}, {'u': 5, 'v': 6, 'w': 1444.0}, {'u': 6, 'v': 11, 'w': 375.0}, {'u': 6, 'v': 12, 'w': 2926.0}, {'u': 17, 'v': 12, 'w': 5312.0}, {'u': 7, 'v': 11, 'w': 1351.0}], 'k': 11, 'source_file': 'I037.stp', 'density': 0.12121212121212122}","[[13, 16], [8, 9], [8, 16], [8, 17], [9, 10], [19, 20], [11, 20], [6, 11], [6, 12], [12, 17]]",15960.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 'O', 'v': 'N', 'w': 6711.0}, {'u': 'O', 'v': 'E', 'w': 9951.0}, {'u': 'O', 'v': 'I', 'w': 2435.0}, {'u': 'M', 'v': 'P', 'w': 338.0}, {'u': 'R', 'v': 'U', 'w': 5212.0}, {'u': 'R', 'v': 'V', 'w': 996.0}, {'u': 'R', 'v': 'D', 'w': 3703.0}, {'u': 'R', 'v': 'B', 'w': 1227.0}, {'u': 'H', 'v': 'I', 'w': 1216.0}, {'u': 'H', 'v': 'P', 'w': 126.0}, {'u': 'H', 'v': 'Q', 'w': 3857.0}, {'u': 'I', 'v': 'J', 'w': 388.0}, {'u': 'J', 'v': 'N', 'w': 4488.0}, {'u': 'A', 'v': 'B', 'w': 274.0}, {'u': 'B', 'v': 'C', 'w': 9930.0}, {'u': 'S', 'v': 'G', 'w': 1540.0}, {'u': 'S', 'v': 'T', 'w': 494.0}, {'u': 'T', 'v': 'K', 'w': 928.0}, {'u': 'T', 'v': 'L', 'w': 3449.0}, {'u': 'T', 'v': 'U', 'w': 10959.0}, {'u': 'C', 'v': 'P', 'w': 1896.0}, {'u': 'D', 'v': 'V', 'w': 3365.0}, {'u': 'U', 'v': 'Q', 'w': 6087.0}, {'u': 'E', 'v': 'F', 'w': 1444.0}, {'u': 'F', 'v': 'K', 'w': 375.0}, {'u': 'F', 'v': 'L', 'w': 2926.0}, {'u': 'Q', 'v': 'L', 'w': 5312.0}, {'u': 'G', 'v': 'K', 'w': 1351.0}], 'density': 0.12121212121212122, 'source_file': 'I037.stp', 'k': 11}","[['M', 'P'], ['H', 'I'], ['H', 'P'], ['H', 'Q'], ['I', 'J'], ['S', 'T'], ['K', 'T'], ['F', 'K'], ['F', 'L'], ['L', 'Q']]",28,nl,names
KMST,KMST,"There’s a field job where the crew must choose exactly k towers from a set of candidates, then select which microwave connections to build so every chosen tower is reachable from the others, avoiding any redundant circular connections, and judging plans by the sum of the link costs — the smaller that sum, the better. The concrete details are shown below.

# total_candidate_towers=22
# total_candidate_links=28
# required_selected_towers=11
endpoint_u_site,endpoint_v_site,link_cost
20,14,251.0
20,18,1400.0
0,1,364.0
0,2,448.0
0,9,395.0
1,10,389.0
3,4,378.0
3,5,1056.0
3,9,356.0
4,15,351.0
4,13,1175.0
5,13,275.0
5,12,827.0
6,7,260.0
6,8,679.0
6,11,508.0
7,16,681.0
8,15,85.0
8,16,162.0
12,19,255.0
13,17,116.0
21,18,897.0
9,10,297.0
9,15,318.0
10,16,271.0
14,17,1371.0
18,19,1229.0
18,17,248.0

Also, when you send back the chosen links, please use this simple JSON layout so it's easy to parse:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as a list of the microwave links you'll build; each inner pair like [u1, v1] is one connection between two selected towers. This is just a sketch of the expected shape — not the actual answer — so fill it with the exact edge pairs you pick.

Please don't rename any identifiers or invent new labels; use the node names exactly as they appear in the instance input — no tweaks.  
- 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”.""","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 21, 'v': 15, 'w': 251.0}, {'u': 21, 'v': 19, 'w': 1400.0}, {'u': 1, 'v': 2, 'w': 364.0}, {'u': 1, 'v': 3, 'w': 448.0}, {'u': 1, 'v': 10, 'w': 395.0}, {'u': 2, 'v': 11, 'w': 389.0}, {'u': 4, 'v': 5, 'w': 378.0}, {'u': 4, 'v': 6, 'w': 1056.0}, {'u': 4, 'v': 10, 'w': 356.0}, {'u': 5, 'v': 16, 'w': 351.0}, {'u': 5, 'v': 14, 'w': 1175.0}, {'u': 6, 'v': 14, 'w': 275.0}, {'u': 6, 'v': 13, 'w': 827.0}, {'u': 7, 'v': 8, 'w': 260.0}, {'u': 7, 'v': 9, 'w': 679.0}, {'u': 7, 'v': 12, 'w': 508.0}, {'u': 8, 'v': 17, 'w': 681.0}, {'u': 9, 'v': 16, 'w': 85.0}, {'u': 9, 'v': 17, 'w': 162.0}, {'u': 13, 'v': 20, 'w': 255.0}, {'u': 14, 'v': 18, 'w': 116.0}, {'u': 22, 'v': 19, 'w': 897.0}, {'u': 10, 'v': 11, 'w': 297.0}, {'u': 10, 'v': 16, 'w': 318.0}, {'u': 11, 'v': 17, 'w': 271.0}, {'u': 15, 'v': 18, 'w': 1371.0}, {'u': 19, 'v': 20, 'w': 1229.0}, {'u': 19, 'v': 18, 'w': 248.0}], 'k': 11, 'source_file': 'I040.stp', 'density': 0.12121212121212122}","[[1, 2], [2, 11], [4, 10], [5, 16], [7, 8], [7, 9], [9, 16], [9, 17], [10, 11], [11, 17]]",3214.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 28, 'edges': [{'u': 20, 'v': 14, 'w': 251.0}, {'u': 20, 'v': 18, 'w': 1400.0}, {'u': 0, 'v': 1, 'w': 364.0}, {'u': 0, 'v': 2, 'w': 448.0}, {'u': 0, 'v': 9, 'w': 395.0}, {'u': 1, 'v': 10, 'w': 389.0}, {'u': 3, 'v': 4, 'w': 378.0}, {'u': 3, 'v': 5, 'w': 1056.0}, {'u': 3, 'v': 9, 'w': 356.0}, {'u': 4, 'v': 15, 'w': 351.0}, {'u': 4, 'v': 13, 'w': 1175.0}, {'u': 5, 'v': 13, 'w': 275.0}, {'u': 5, 'v': 12, 'w': 827.0}, {'u': 6, 'v': 7, 'w': 260.0}, {'u': 6, 'v': 8, 'w': 679.0}, {'u': 6, 'v': 11, 'w': 508.0}, {'u': 7, 'v': 16, 'w': 681.0}, {'u': 8, 'v': 15, 'w': 85.0}, {'u': 8, 'v': 16, 'w': 162.0}, {'u': 12, 'v': 19, 'w': 255.0}, {'u': 13, 'v': 17, 'w': 116.0}, {'u': 21, 'v': 18, 'w': 897.0}, {'u': 9, 'v': 10, 'w': 297.0}, {'u': 9, 'v': 15, 'w': 318.0}, {'u': 10, 'v': 16, 'w': 271.0}, {'u': 14, 'v': 17, 'w': 1371.0}, {'u': 18, 'v': 19, 'w': 1229.0}, {'u': 18, 'v': 17, 'w': 248.0}], 'density': 0.12121212121212122, 'source_file': 'I040.stp', 'k': 11}","[[0, 1], [1, 10], [3, 9], [4, 15], [6, 7], [6, 8], [8, 15], [8, 16], [9, 10], [10, 16]]",29,csv,0
KMST,KMST,"There’s a curator’s puzzle on the table: choose exactly k items from the gallery and link them together using permitted passageways so the group is all connected, but don’t let those passages form a circle. The way to judge a plan is simple — add up the lengths of the selected corridors and pick the plan with the smallest total. Every chosen exhibit must be included once, nothing extra, and the concrete map and distances appear below.

The gallery shows 25 exhibits and 32 permitted corridors; select exactly 8 exhibits.
Permitted corridor between exhibits 15 and 12 with length 5413.0.
Permitted corridor between exhibits 1 and 2 with length 531.0.
Permitted corridor between exhibits 1 and 3 with length 532.0.
Permitted corridor between exhibits 1 and 20 with length 3974.0.
Permitted corridor between exhibits 2 and 3 with length 56.0.
Permitted corridor between exhibits 2 and 5 with length 6624.0.
Permitted corridor between exhibits 4 and 5 with length 540.0.
Permitted corridor between exhibits 4 and 12 with length 659.0.
Permitted corridor between exhibits 4 and 13 with length 3953.0.
Permitted corridor between exhibits 4 and 20 with length 11657.0.
Permitted corridor between exhibits 5 and 6 with length 7632.0.
Permitted corridor between exhibits 6 and 7 with length 534.0.
Permitted corridor between exhibits 6 and 8 with length 533.0.
Permitted corridor between exhibits 6 and 23 with length 3107.0.
Permitted corridor between exhibits 7 and 8 with length 25.0.
Permitted corridor between exhibits 7 and 19 with length 2819.0.
Permitted corridor between exhibits 8 and 24 with length 2861.0.
Permitted corridor between exhibits 12 and 11 with length 5483.0.
Permitted corridor between exhibits 12 and 13 with length 3739.0.
Permitted corridor between exhibits 13 and 19 with length 946.0.
Permitted corridor between exhibits 0 and 10 with length 1005.0.
Permitted corridor between exhibits 10 and 23 with length 226.0.
Permitted corridor between exhibits 10 and 9 with length 581.0.
Permitted corridor between exhibits 16 and 17 with length 2013.0.
Permitted corridor between exhibits 16 and 24 with length 95.0.
Permitted corridor between exhibits 17 and 21 with length 2645.0.
Permitted corridor between exhibits 17 and 18 with length 1848.0.
Permitted corridor between exhibits 18 and 19 with length 1952.0.
Permitted corridor between exhibits 18 and 22 with length 1405.0.
Permitted corridor between exhibits 21 and 22 with length 366.0.
Permitted corridor between exhibits 22 and 14 with length 7728.0.
Permitted corridor between exhibits 23 and 24 with length 667.0.
Pick a connected, acyclic selection of exactly 8 exhibits that minimizes the sum of chosen corridor lengths.

You can just hand me the chosen corridors in a tiny JSON snip — nice and simple. Something like this will do:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This ""solution"" array is just a list of the passageways you pick, each pair [u, v] meaning ""connect exhibit u to exhibit v"" in the curator’s plan. Think of it like filling in a form: list the corridor pairs you want. The block above is only a sketch of the shape I expect, not the actual answer — replace those placeholders with the real labels from the instance.

Please use the identifiers exactly as they appear in the instance input — don’t rename them and don’t 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”.""","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 32, 'edges': [{'u': 16, 'v': 13, 'w': 5413.0}, {'u': 2, 'v': 3, 'w': 531.0}, {'u': 2, 'v': 4, 'w': 532.0}, {'u': 2, 'v': 21, 'w': 3974.0}, {'u': 3, 'v': 4, 'w': 56.0}, {'u': 3, 'v': 6, 'w': 6624.0}, {'u': 5, 'v': 6, 'w': 540.0}, {'u': 5, 'v': 13, 'w': 659.0}, {'u': 5, 'v': 14, 'w': 3953.0}, {'u': 5, 'v': 21, 'w': 11657.0}, {'u': 6, 'v': 7, 'w': 7632.0}, {'u': 7, 'v': 8, 'w': 534.0}, {'u': 7, 'v': 9, 'w': 533.0}, {'u': 7, 'v': 24, 'w': 3107.0}, {'u': 8, 'v': 9, 'w': 25.0}, {'u': 8, 'v': 20, 'w': 2819.0}, {'u': 9, 'v': 25, 'w': 2861.0}, {'u': 13, 'v': 12, 'w': 5483.0}, {'u': 13, 'v': 14, 'w': 3739.0}, {'u': 14, 'v': 20, 'w': 946.0}, {'u': 1, 'v': 11, 'w': 1005.0}, {'u': 11, 'v': 24, 'w': 226.0}, {'u': 11, 'v': 10, 'w': 581.0}, {'u': 17, 'v': 18, 'w': 2013.0}, {'u': 17, 'v': 25, 'w': 95.0}, {'u': 18, 'v': 22, 'w': 2645.0}, {'u': 18, 'v': 19, 'w': 1848.0}, {'u': 19, 'v': 20, 'w': 1952.0}, {'u': 19, 'v': 23, 'w': 1405.0}, {'u': 22, 'v': 23, 'w': 366.0}, {'u': 23, 'v': 15, 'w': 7728.0}, {'u': 24, 'v': 25, 'w': 667.0}], 'k': 8, 'source_file': 'I049.stp', 'density': 0.10666666666666667}","[[7, 9], [8, 9], [9, 25], [11, 24], [10, 11], [17, 25], [24, 25]]",4988.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 32, 'edges': [{'u': 15, 'v': 12, 'w': 5413.0}, {'u': 1, 'v': 2, 'w': 531.0}, {'u': 1, 'v': 3, 'w': 532.0}, {'u': 1, 'v': 20, 'w': 3974.0}, {'u': 2, 'v': 3, 'w': 56.0}, {'u': 2, 'v': 5, 'w': 6624.0}, {'u': 4, 'v': 5, 'w': 540.0}, {'u': 4, 'v': 12, 'w': 659.0}, {'u': 4, 'v': 13, 'w': 3953.0}, {'u': 4, 'v': 20, 'w': 11657.0}, {'u': 5, 'v': 6, 'w': 7632.0}, {'u': 6, 'v': 7, 'w': 534.0}, {'u': 6, 'v': 8, 'w': 533.0}, {'u': 6, 'v': 23, 'w': 3107.0}, {'u': 7, 'v': 8, 'w': 25.0}, {'u': 7, 'v': 19, 'w': 2819.0}, {'u': 8, 'v': 24, 'w': 2861.0}, {'u': 12, 'v': 11, 'w': 5483.0}, {'u': 12, 'v': 13, 'w': 3739.0}, {'u': 13, 'v': 19, 'w': 946.0}, {'u': 0, 'v': 10, 'w': 1005.0}, {'u': 10, 'v': 23, 'w': 226.0}, {'u': 10, 'v': 9, 'w': 581.0}, {'u': 16, 'v': 17, 'w': 2013.0}, {'u': 16, 'v': 24, 'w': 95.0}, {'u': 17, 'v': 21, 'w': 2645.0}, {'u': 17, 'v': 18, 'w': 1848.0}, {'u': 18, 'v': 19, 'w': 1952.0}, {'u': 18, 'v': 22, 'w': 1405.0}, {'u': 21, 'v': 22, 'w': 366.0}, {'u': 22, 'v': 14, 'w': 7728.0}, {'u': 23, 'v': 24, 'w': 667.0}], 'density': 0.10666666666666667, 'source_file': 'I049.stp', 'k': 8}","[[6, 8], [7, 8], [8, 24], [10, 23], [9, 10], [16, 24], [23, 24]]",30,nl,0
KMST,KMST,"Many people imagine wiring is just about running wire from A to B, but this job was different: only k homes should be picked to interconnect, and the electrician must choose which homes and which available segments make up the network so the selected homes are all connected, without forming any loops or repeating segments. The best choice is the one with the lowest total installation cost, obtained by adding up the costs of the installed segments. The candidate segments, house list, and prices are listed below.

# total_houses_available=26
# available_line_segments=31
# homes_to_connect=10
house_endpoint_u,house_endpoint_v,installation_cost
9,10,562.0
9,7,3256.0
9,16,829.0
10,24,1128.0
10,11,10.0
8,12,3503.0
8,11,499.0
8,16,281.0
11,18,2753.0
21,16,1147.0
21,14,59.0
21,22,2584.0
22,15,1419.0
22,23,693.0
12,3,822.0
12,2,110.0
23,5,2880.0
20,19,3371.0
20,3,2322.0
13,4,70.0
13,17,4542.0
14,5,457.0
14,17,3186.0
0,7,9281.0
6,7,469.0
6,25,1594.0
24,25,664.0
1,2,817.0
1,3,134.0
2,4,299.0
18,19,3553.0

When you give the final answer, just use this simple JSON layout so it's easy to check automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of the chosen wire segments. Each inner pair [u1, v1] is one installed segment connecting two homes (use the exact home identifiers from the instance). Think of it like filling out a short list of which connections you picked — no need for anything else in the file.

This JSON is just a sketch of the shape I expect, not the actual answer — replace the placeholders with the real edges from the instance.

Please make sure all identifiers are used 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”.","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 31, 'edges': [{'u': 10, 'v': 11, 'w': 562.0}, {'u': 10, 'v': 8, 'w': 3256.0}, {'u': 10, 'v': 17, 'w': 829.0}, {'u': 11, 'v': 25, 'w': 1128.0}, {'u': 11, 'v': 12, 'w': 10.0}, {'u': 9, 'v': 13, 'w': 3503.0}, {'u': 9, 'v': 12, 'w': 499.0}, {'u': 9, 'v': 17, 'w': 281.0}, {'u': 12, 'v': 19, 'w': 2753.0}, {'u': 22, 'v': 17, 'w': 1147.0}, {'u': 22, 'v': 15, 'w': 59.0}, {'u': 22, 'v': 23, 'w': 2584.0}, {'u': 23, 'v': 16, 'w': 1419.0}, {'u': 23, 'v': 24, 'w': 693.0}, {'u': 13, 'v': 4, 'w': 822.0}, {'u': 13, 'v': 3, 'w': 110.0}, {'u': 24, 'v': 6, 'w': 2880.0}, {'u': 21, 'v': 20, 'w': 3371.0}, {'u': 21, 'v': 4, 'w': 2322.0}, {'u': 14, 'v': 5, 'w': 70.0}, {'u': 14, 'v': 18, 'w': 4542.0}, {'u': 15, 'v': 6, 'w': 457.0}, {'u': 15, 'v': 18, 'w': 3186.0}, {'u': 1, 'v': 8, 'w': 9281.0}, {'u': 7, 'v': 8, 'w': 469.0}, {'u': 7, 'v': 26, 'w': 1594.0}, {'u': 25, 'v': 26, 'w': 664.0}, {'u': 2, 'v': 3, 'w': 817.0}, {'u': 2, 'v': 4, 'w': 134.0}, {'u': 3, 'v': 5, 'w': 299.0}, {'u': 19, 'v': 20, 'w': 3553.0}], 'k': 10, 'source_file': 'I019.stp', 'density': 0.09538461538461539}","[[10, 11], [11, 25], [11, 12], [9, 12], [9, 17], [17, 22], [15, 22], [6, 15], [25, 26]]",4807.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 31, 'edges': [{'u': 9, 'v': 10, 'w': 562.0}, {'u': 9, 'v': 7, 'w': 3256.0}, {'u': 9, 'v': 16, 'w': 829.0}, {'u': 10, 'v': 24, 'w': 1128.0}, {'u': 10, 'v': 11, 'w': 10.0}, {'u': 8, 'v': 12, 'w': 3503.0}, {'u': 8, 'v': 11, 'w': 499.0}, {'u': 8, 'v': 16, 'w': 281.0}, {'u': 11, 'v': 18, 'w': 2753.0}, {'u': 21, 'v': 16, 'w': 1147.0}, {'u': 21, 'v': 14, 'w': 59.0}, {'u': 21, 'v': 22, 'w': 2584.0}, {'u': 22, 'v': 15, 'w': 1419.0}, {'u': 22, 'v': 23, 'w': 693.0}, {'u': 12, 'v': 3, 'w': 822.0}, {'u': 12, 'v': 2, 'w': 110.0}, {'u': 23, 'v': 5, 'w': 2880.0}, {'u': 20, 'v': 19, 'w': 3371.0}, {'u': 20, 'v': 3, 'w': 2322.0}, {'u': 13, 'v': 4, 'w': 70.0}, {'u': 13, 'v': 17, 'w': 4542.0}, {'u': 14, 'v': 5, 'w': 457.0}, {'u': 14, 'v': 17, 'w': 3186.0}, {'u': 0, 'v': 7, 'w': 9281.0}, {'u': 6, 'v': 7, 'w': 469.0}, {'u': 6, 'v': 25, 'w': 1594.0}, {'u': 24, 'v': 25, 'w': 664.0}, {'u': 1, 'v': 2, 'w': 817.0}, {'u': 1, 'v': 3, 'w': 134.0}, {'u': 2, 'v': 4, 'w': 299.0}, {'u': 18, 'v': 19, 'w': 3553.0}], 'density': 0.09538461538461539, 'source_file': 'I019.stp', 'k': 10}","[[9, 10], [10, 24], [10, 11], [8, 11], [8, 16], [16, 21], [14, 21], [5, 14], [24, 25]]",31,csv,0
KMST,KMST,"We’ve got to set up a compact aid network: decide on exactly k places to serve as aid stations and pick the roads that tie those spots together so anyone can get from one chosen station to another using only those roads, with no circular routes allowed. The preferred setup is the one whose roads add up to the smallest possible travel time — calculated by adding the travel time of each chosen road. It’s important that exactly k stations are selected and each road is included only as part of that connecting system. The specific stations and road times are listed below.

There are 26 possible locations, 35 candidate roads, and we must pick exactly 13 stations.
We list a road connecting 1 and 13 with travel time 107.0.
We list a road connecting 4 and 19 with travel time 12166.0.
We list a road connecting 4 and 18 with travel time 10018.0.
We list a road connecting 19 and 18 with travel time 6764.0.
We list a road connecting 5 and 12 with travel time 7142.0.
We list a road connecting 5 and 25 with travel time 6534.0.
We list a road connecting 16 and 17 with travel time 6291.0.
We list a road connecting 16 and 23 with travel time 181.0.
We list a road connecting 16 and 18 with travel time 2044.0.
We list a road connecting 17 and 11 with travel time 5097.0.
We list a road connecting 17 and 21 with travel time 1776.0.
We list a road connecting 24 and 23 with travel time 496.0.
We list a road connecting 24 and 10 with travel time 1195.0.
We list a road connecting 24 and 6 with travel time 122.0.
We list a road connecting 22 and 10 with travel time 258.0.
We list a road connecting 22 and 23 with travel time 1365.0.
We list a road connecting 22 and 14 with travel time 6723.0.
We list a road connecting 7 and 6 with travel time 831.0.
We list a road connecting 7 and 2 with travel time 7640.0.
We list a road connecting 7 and 9 with travel time 35.0.
We list a road connecting 8 and 9 with travel time 1331.0.
We list a road connecting 8 and 10 with travel time 442.0.
We list a road connecting 8 and 15 with travel time 5959.0.
We list a road connecting 9 and 20 with travel time 5751.0.
We list a road connecting 26 and 14 with travel time 1901.0.
We list a road connecting 26 and 13 with travel time 2551.0.
We list a road connecting 21 and 12 with travel time 5949.0.
We list a road connecting 21 and 25 with travel time 6706.0.
We list a road connecting 2 and 3 with travel time 396.0.
We list a road connecting 2 and 20 with travel time 4355.0.
We list a road connecting 3 and 11 with travel time 67.0.
We list a road connecting 3 and 12 with travel time 1779.0.
We list a road connecting 11 and 6 with travel time 7786.0.
We list a road connecting 13 and 15 with travel time 2419.0.
We list a road connecting 14 and 15 with travel time 1986.0.
We’ll use these entries to choose the 13-station tree with minimum total travel time.

Just send the chosen tree as a small JSON snippet so it's easy to check automatically. Something like this works fine:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is the list of roads you'll pick for the aid network. Each pair like [u1, v1] is one road connecting station u1 to station v1. Think of it as a simple form: one pair per chosen road, and together the pairs should connect exactly k stations without any loops.

This JSON is only a sketch of the shape I expect — it's not the actual answer. Please make sure to use the exact identifiers from the instance input, with 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”.""","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 35, 'edges': [{'u': 1, 'v': 13, 'w': 107.0}, {'u': 4, 'v': 19, 'w': 12166.0}, {'u': 4, 'v': 18, 'w': 10018.0}, {'u': 19, 'v': 18, 'w': 6764.0}, {'u': 5, 'v': 12, 'w': 7142.0}, {'u': 5, 'v': 25, 'w': 6534.0}, {'u': 16, 'v': 17, 'w': 6291.0}, {'u': 16, 'v': 23, 'w': 181.0}, {'u': 16, 'v': 18, 'w': 2044.0}, {'u': 17, 'v': 11, 'w': 5097.0}, {'u': 17, 'v': 21, 'w': 1776.0}, {'u': 24, 'v': 23, 'w': 496.0}, {'u': 24, 'v': 10, 'w': 1195.0}, {'u': 24, 'v': 6, 'w': 122.0}, {'u': 22, 'v': 10, 'w': 258.0}, {'u': 22, 'v': 23, 'w': 1365.0}, {'u': 22, 'v': 14, 'w': 6723.0}, {'u': 7, 'v': 6, 'w': 831.0}, {'u': 7, 'v': 2, 'w': 7640.0}, {'u': 7, 'v': 9, 'w': 35.0}, {'u': 8, 'v': 9, 'w': 1331.0}, {'u': 8, 'v': 10, 'w': 442.0}, {'u': 8, 'v': 15, 'w': 5959.0}, {'u': 9, 'v': 20, 'w': 5751.0}, {'u': 26, 'v': 14, 'w': 1901.0}, {'u': 26, 'v': 13, 'w': 2551.0}, {'u': 21, 'v': 12, 'w': 5949.0}, {'u': 21, 'v': 25, 'w': 6706.0}, {'u': 2, 'v': 3, 'w': 396.0}, {'u': 2, 'v': 20, 'w': 4355.0}, {'u': 3, 'v': 11, 'w': 67.0}, {'u': 3, 'v': 12, 'w': 1779.0}, {'u': 11, 'v': 6, 'w': 7786.0}, {'u': 13, 'v': 15, 'w': 2419.0}, {'u': 14, 'v': 15, 'w': 1986.0}], 'k': 13, 'source_file': 'I082.stp', 'density': 0.1076923076923077}","[[16, 23], [23, 24], [10, 24], [6, 24], [10, 22], [6, 7], [2, 7], [7, 9], [8, 10], [2, 3], [3, 11], [3, 12]]",13442.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 35, 'edges': [{'u': 1, 'v': 13, 'w': 107.0}, {'u': 4, 'v': 19, 'w': 12166.0}, {'u': 4, 'v': 18, 'w': 10018.0}, {'u': 19, 'v': 18, 'w': 6764.0}, {'u': 5, 'v': 12, 'w': 7142.0}, {'u': 5, 'v': 25, 'w': 6534.0}, {'u': 16, 'v': 17, 'w': 6291.0}, {'u': 16, 'v': 23, 'w': 181.0}, {'u': 16, 'v': 18, 'w': 2044.0}, {'u': 17, 'v': 11, 'w': 5097.0}, {'u': 17, 'v': 21, 'w': 1776.0}, {'u': 24, 'v': 23, 'w': 496.0}, {'u': 24, 'v': 10, 'w': 1195.0}, {'u': 24, 'v': 6, 'w': 122.0}, {'u': 22, 'v': 10, 'w': 258.0}, {'u': 22, 'v': 23, 'w': 1365.0}, {'u': 22, 'v': 14, 'w': 6723.0}, {'u': 7, 'v': 6, 'w': 831.0}, {'u': 7, 'v': 2, 'w': 7640.0}, {'u': 7, 'v': 9, 'w': 35.0}, {'u': 8, 'v': 9, 'w': 1331.0}, {'u': 8, 'v': 10, 'w': 442.0}, {'u': 8, 'v': 15, 'w': 5959.0}, {'u': 9, 'v': 20, 'w': 5751.0}, {'u': 26, 'v': 14, 'w': 1901.0}, {'u': 26, 'v': 13, 'w': 2551.0}, {'u': 21, 'v': 12, 'w': 5949.0}, {'u': 21, 'v': 25, 'w': 6706.0}, {'u': 2, 'v': 3, 'w': 396.0}, {'u': 2, 'v': 20, 'w': 4355.0}, {'u': 3, 'v': 11, 'w': 67.0}, {'u': 3, 'v': 12, 'w': 1779.0}, {'u': 11, 'v': 6, 'w': 7786.0}, {'u': 13, 'v': 15, 'w': 2419.0}, {'u': 14, 'v': 15, 'w': 1986.0}], 'density': 0.1076923076923077, 'source_file': 'I082.stp', 'k': 13}","[[16, 23], [23, 24], [10, 24], [6, 24], [10, 22], [6, 7], [2, 7], [7, 9], [8, 10], [2, 3], [3, 11], [3, 12]]",32,nl,1
KMST,KMST,"We’re trying to build a tight little leadership circle of exactly k local leaders. That means choosing the k leaders first, then arranging specific pairwise introductions so that all chosen leaders are linked together into a single connected group, while avoiding any redundant, loop-forming introductions. Every introduction has an effort score; add those scores for the introductions that are scheduled to get the total effort, and a better choice is the one with a lower total. The actual people, possible introductions, and their effort values are listed below.

# total_local_leaders_available=24
# total_possible_introductions=28
# target_leader_count=7
leader_u,leader_v,introduction_effort
18,4,228.0
18,3,559.0
18,10,1360.0
19,22,1079.0
19,4,1578.0
20,22,1261.0
20,2,325.0
21,6,895.0
10,11,1261.0
10,24,248.0
11,23,203.0
11,9,2476.0
5,23,415.0
12,13,475.0
12,15,150.0
23,14,1243.0
13,16,149.0
13,7,973.0
6,7,939.0
6,17,881.0
7,9,94.0
3,1,229.0
3,8,275.0
2,1,495.0
2,8,321.0
1,4,559.0
15,16,475.0
8,9,1307.0

Also, when you send back the scheduled introductions, please use this simple JSON shape so it's easy to check:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as a list of the pairwise intros we'll schedule; each [u, v] is one introduction linking leader u with leader v. This snippet is just a sketch of the shape I expect — not the actual answer.

Please make sure to 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 28, 'edges': [{'u': 18, 'v': 4, 'w': 228.0}, {'u': 18, 'v': 3, 'w': 559.0}, {'u': 18, 'v': 10, 'w': 1360.0}, {'u': 19, 'v': 22, 'w': 1079.0}, {'u': 19, 'v': 4, 'w': 1578.0}, {'u': 20, 'v': 22, 'w': 1261.0}, {'u': 20, 'v': 2, 'w': 325.0}, {'u': 21, 'v': 6, 'w': 895.0}, {'u': 10, 'v': 11, 'w': 1261.0}, {'u': 10, 'v': 24, 'w': 248.0}, {'u': 11, 'v': 23, 'w': 203.0}, {'u': 11, 'v': 9, 'w': 2476.0}, {'u': 5, 'v': 23, 'w': 415.0}, {'u': 12, 'v': 13, 'w': 475.0}, {'u': 12, 'v': 15, 'w': 150.0}, {'u': 23, 'v': 14, 'w': 1243.0}, {'u': 13, 'v': 16, 'w': 149.0}, {'u': 13, 'v': 7, 'w': 973.0}, {'u': 6, 'v': 7, 'w': 939.0}, {'u': 6, 'v': 17, 'w': 881.0}, {'u': 7, 'v': 9, 'w': 94.0}, {'u': 3, 'v': 1, 'w': 229.0}, {'u': 3, 'v': 8, 'w': 275.0}, {'u': 2, 'v': 1, 'w': 495.0}, {'u': 2, 'v': 8, 'w': 321.0}, {'u': 1, 'v': 4, 'w': 559.0}, {'u': 15, 'v': 16, 'w': 475.0}, {'u': 8, 'v': 9, 'w': 1307.0}], 'k': 7, 'source_file': 'I020.stp', 'density': 0.10144927536231885}","[[4, 18], [2, 20], [1, 3], [3, 8], [2, 8], [1, 4]]",1937.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 28, 'edges': [{'u': 18, 'v': 4, 'w': 228.0}, {'u': 18, 'v': 3, 'w': 559.0}, {'u': 18, 'v': 10, 'w': 1360.0}, {'u': 19, 'v': 22, 'w': 1079.0}, {'u': 19, 'v': 4, 'w': 1578.0}, {'u': 20, 'v': 22, 'w': 1261.0}, {'u': 20, 'v': 2, 'w': 325.0}, {'u': 21, 'v': 6, 'w': 895.0}, {'u': 10, 'v': 11, 'w': 1261.0}, {'u': 10, 'v': 24, 'w': 248.0}, {'u': 11, 'v': 23, 'w': 203.0}, {'u': 11, 'v': 9, 'w': 2476.0}, {'u': 5, 'v': 23, 'w': 415.0}, {'u': 12, 'v': 13, 'w': 475.0}, {'u': 12, 'v': 15, 'w': 150.0}, {'u': 23, 'v': 14, 'w': 1243.0}, {'u': 13, 'v': 16, 'w': 149.0}, {'u': 13, 'v': 7, 'w': 973.0}, {'u': 6, 'v': 7, 'w': 939.0}, {'u': 6, 'v': 17, 'w': 881.0}, {'u': 7, 'v': 9, 'w': 94.0}, {'u': 3, 'v': 1, 'w': 229.0}, {'u': 3, 'v': 8, 'w': 275.0}, {'u': 2, 'v': 1, 'w': 495.0}, {'u': 2, 'v': 8, 'w': 321.0}, {'u': 1, 'v': 4, 'w': 559.0}, {'u': 15, 'v': 16, 'w': 475.0}, {'u': 8, 'v': 9, 'w': 1307.0}], 'density': 0.10144927536231885, 'source_file': 'I020.stp', 'k': 7}","[[4, 18], [2, 20], [1, 3], [3, 8], [2, 8], [1, 4]]",33,csv,1
KMST,KMST,"Back when the team reviewed the garden project, the brief was clear: pick exactly k ponds to showcase and use the pipe segments on hand to link them into a single, loop-free water system — no extra ponds, no duplicated connections, and every chosen pond must be part of that one network. Plans are compared by totaling the lengths of the pipes used, and the plan with the smallest total length is preferred; the concrete layout and segment lengths follow below.

There are 22 ponds and 27 pipe segments available; pick exactly 11 ponds to join into a single, loop-free water system.
Pipe between pond 18 and pond 2 with length 228.0.
Pipe between pond 18 and pond 3 with length 1400.0.
Pipe between pond 18 and pond 20 with length 423.0.
Pipe between pond 1 and pond 2 with length 1401.0.
Pipe between pond 1 and pond 3 with length 232.0.
Pipe between pond 1 and pond 8 with length 742.0.
Pipe between pond 2 and pond 6 with length 528.0.
Pipe between pond 3 and pond 9 with length 742.0.
Pipe between pond 4 and pond 15 with length 662.0.
Pipe between pond 4 and pond 5 with length 1777.0.
Pipe between pond 5 and pond 15 with length 1117.0.
Pipe between pond 5 and pond 6 with length 19.0.
Pipe between pond 19 and pond 17 with length 168.0.
Pipe between pond 7 and pond 21 with length 2721.0.
Pipe between pond 20 and pond 21 with length 657.0.
Pipe between pond 20 and pond 10 with length 759.0.
Pipe between pond 21 and pond 22 with length 610.0.
Pipe between pond 22 and pond 11 with length 679.0.
Pipe between pond 8 and pond 9 with length 224.0.
Pipe between pond 8 and pond 16 with length 150.0.
Pipe between pond 9 and pond 17 with length 148.0.
Pipe between pond 14 and pond 16 with length 1674.0.
Pipe between pond 16 and pond 17 with length 223.0.
Pipe between pond 10 and pond 11 with length 1222.0.
Pipe between pond 10 and pond 12 with length 367.0.
Pipe between pond 11 and pond 13 with length 369.0.
Pipe between pond 12 and pond 13 with length 1198.0.
Use the list below to assemble the minimal-total-length, loop-free layout that connects exactly 11 ponds.

Also, when you send your plan back, keep it in this simple JSON shape so I can read it easily:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

""solution"" is just a list of pipe segments: each inner pair [u, v] means ""connect pond u to pond v"" in the final loop-free layout. Think of it like filling out a short form — one line per pipe. This is only a sketch of the shape I expect, not the actual answer.

Please use the exact 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”.","{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 27, 'edges': [{'u': 18, 'v': 2, 'w': 228.0}, {'u': 18, 'v': 3, 'w': 1400.0}, {'u': 18, 'v': 20, 'w': 423.0}, {'u': 1, 'v': 2, 'w': 1401.0}, {'u': 1, 'v': 3, 'w': 232.0}, {'u': 1, 'v': 8, 'w': 742.0}, {'u': 2, 'v': 6, 'w': 528.0}, {'u': 3, 'v': 9, 'w': 742.0}, {'u': 4, 'v': 15, 'w': 662.0}, {'u': 4, 'v': 5, 'w': 1777.0}, {'u': 5, 'v': 15, 'w': 1117.0}, {'u': 5, 'v': 6, 'w': 19.0}, {'u': 19, 'v': 17, 'w': 168.0}, {'u': 7, 'v': 21, 'w': 2721.0}, {'u': 20, 'v': 21, 'w': 657.0}, {'u': 20, 'v': 10, 'w': 759.0}, {'u': 21, 'v': 22, 'w': 610.0}, {'u': 22, 'v': 11, 'w': 679.0}, {'u': 8, 'v': 9, 'w': 224.0}, {'u': 8, 'v': 16, 'w': 150.0}, {'u': 9, 'v': 17, 'w': 148.0}, {'u': 14, 'v': 16, 'w': 1674.0}, {'u': 16, 'v': 17, 'w': 223.0}, {'u': 10, 'v': 11, 'w': 1222.0}, {'u': 10, 'v': 12, 'w': 367.0}, {'u': 11, 'v': 13, 'w': 369.0}, {'u': 12, 'v': 13, 'w': 1198.0}], 'k': 11, 'source_file': 'I050.stp', 'density': 0.11688311688311688}","[[2, 18], [3, 18], [1, 3], [1, 8], [2, 6], [5, 6], [17, 19], [8, 16], [9, 17], [16, 17]]",3838.0,"{'problem_type': 'KMST', 'num_nodes': 22, 'num_edges': 27, 'edges': [{'u': 18, 'v': 2, 'w': 228.0}, {'u': 18, 'v': 3, 'w': 1400.0}, {'u': 18, 'v': 20, 'w': 423.0}, {'u': 1, 'v': 2, 'w': 1401.0}, {'u': 1, 'v': 3, 'w': 232.0}, {'u': 1, 'v': 8, 'w': 742.0}, {'u': 2, 'v': 6, 'w': 528.0}, {'u': 3, 'v': 9, 'w': 742.0}, {'u': 4, 'v': 15, 'w': 662.0}, {'u': 4, 'v': 5, 'w': 1777.0}, {'u': 5, 'v': 15, 'w': 1117.0}, {'u': 5, 'v': 6, 'w': 19.0}, {'u': 19, 'v': 17, 'w': 168.0}, {'u': 7, 'v': 21, 'w': 2721.0}, {'u': 20, 'v': 21, 'w': 657.0}, {'u': 20, 'v': 10, 'w': 759.0}, {'u': 21, 'v': 22, 'w': 610.0}, {'u': 22, 'v': 11, 'w': 679.0}, {'u': 8, 'v': 9, 'w': 224.0}, {'u': 8, 'v': 16, 'w': 150.0}, {'u': 9, 'v': 17, 'w': 148.0}, {'u': 14, 'v': 16, 'w': 1674.0}, {'u': 16, 'v': 17, 'w': 223.0}, {'u': 10, 'v': 11, 'w': 1222.0}, {'u': 10, 'v': 12, 'w': 367.0}, {'u': 11, 'v': 13, 'w': 369.0}, {'u': 12, 'v': 13, 'w': 1198.0}], 'density': 0.11688311688311688, 'source_file': 'I050.stp', 'k': 11}","[[2, 18], [3, 18], [1, 3], [1, 8], [2, 6], [5, 6], [17, 19], [8, 16], [9, 17], [16, 17]]",34,nl,1
KMST,KMST,"On a typical planning shift the duty is to choose exactly k landing pads from the available sites, assign allowed corridors between them so the selected pads form one connected system with no circular flight loops, and try to keep the sum of all corridor lengths as small as it can be. The sum of the corridor lengths is how the plan’s cost is measured. The full map and numbers are shown below.

{
  ""total_landing_pads"": 23,
  ""total_aerial_corridors"": 25,
  ""edges"": [
    {
      ""pad_u"": 17,
      ""pad_v"": 18,
      ""corridor_length"": 1065.0
    },
    {
      ""pad_u"": 17,
      ""pad_v"": 19,
      ""corridor_length"": 313.0
    },
    {
      ""pad_u"": 17,
      ""pad_v"": 22,
      ""corridor_length"": 707.0
    },
    {
      ""pad_u"": 18,
      ""pad_v"": 15,
      ""corridor_length"": 728.0
    },
    {
      ""pad_u"": 0,
      ""pad_v"": 9,
      ""corridor_length"": 1117.0
    },
    {
      ""pad_u"": 5,
      ""pad_v"": 3,
      ""corridor_length"": 433.0
    },
    {
      ""pad_u"": 6,
      ""pad_v"": 11,
      ""corridor_length"": 1919.0
    },
    {
      ""pad_u"": 6,
      ""pad_v"": 12,
      ""corridor_length"": 616.0
    },
    {
      ""pad_u"": 7,
      ""pad_v"": 11,
      ""corridor_length"": 657.0
    },
    {
      ""pad_u"": 7,
      ""pad_v"": 12,
      ""corridor_length"": 1662.0
    },
    {
      ""pad_u"": 13,
      ""pad_v"": 2,
      ""corridor_length"": 223.0
    },
    {
      ""pad_u"": 13,
      ""pad_v"": 16,
      ""corridor_length"": 1116.0
    },
    {
      ""pad_u"": 14,
      ""pad_v"": 4,
      ""corridor_length"": 537.0
    },
    {
      ""pad_u"": 14,
      ""pad_v"": 3,
      ""corridor_length"": 805.0
    },
    {
      ""pad_u"": 14,
      ""pad_v"": 20,
      ""corridor_length"": 1077.0
    },
    {
      ""pad_u"": 19,
      ""pad_v"": 20,
      ""corridor_length"": 217.0
    },
    {
      ""pad_u"": 19,
      ""pad_v"": 12,
      ""corridor_length"": 2484.0
    },
    {
      ""pad_u"": 20,
      ""pad_v"": 21,
      ""corridor_length"": 595.0
    },
    {
      ""pad_u"": 21,
      ""pad_v"": 9,
      ""corridor_length"": 997.0
    },
    {
      ""pad_u"": 21,
      ""pad_v"": 16,
      ""corridor_length"": 331.0
    },
    {
      ""pad_u"": 8,
      ""pad_v"": 9,
      ""corridor_length"": 1040.0
    },
    {
      ""pad_u"": 16,
      ""pad_v"": 10,
      ""corridor_length"": 564.0
    },
    {
      ""pad_u"": 1,
      ""pad_v"": 2,
      ""corridor_length"": 958.0
    },
    {
      ""pad_u"": 2,
      ""pad_v"": 4,
      ""corridor_length"": 271.0
    },
    {
      ""pad_u"": 3,
      ""pad_v"": 4,
      ""corridor_length"": 1019.0
    }
  ],
  ""target_pads_to_select"": 12
}

When you send the plan back, please stick to this simple JSON layout so I can read it automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This shows a list of corridor pairs — each pair is an edge between two chosen pads (so [u1, v1] means a corridor connecting pad u1 and pad v1). Think of it like a little form: the ""solution"" field holds all the chosen corridors that make up your connected, loop-free system. This JSON is just a sketch of the shape I need, not the actual answer — replace those placeholders with the real pad identifiers from the instance.

Please be careful to 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”.""","{'problem_type': 'KMST', 'num_nodes': 23, 'num_edges': 25, 'edges': [{'u': 18, 'v': 19, 'w': 1065.0}, {'u': 18, 'v': 20, 'w': 313.0}, {'u': 18, 'v': 23, 'w': 707.0}, {'u': 19, 'v': 16, 'w': 728.0}, {'u': 1, 'v': 10, 'w': 1117.0}, {'u': 6, 'v': 4, 'w': 433.0}, {'u': 7, 'v': 12, 'w': 1919.0}, {'u': 7, 'v': 13, 'w': 616.0}, {'u': 8, 'v': 12, 'w': 657.0}, {'u': 8, 'v': 13, 'w': 1662.0}, {'u': 14, 'v': 3, 'w': 223.0}, {'u': 14, 'v': 17, 'w': 1116.0}, {'u': 15, 'v': 5, 'w': 537.0}, {'u': 15, 'v': 4, 'w': 805.0}, {'u': 15, 'v': 21, 'w': 1077.0}, {'u': 20, 'v': 21, 'w': 217.0}, {'u': 20, 'v': 13, 'w': 2484.0}, {'u': 21, 'v': 22, 'w': 595.0}, {'u': 22, 'v': 10, 'w': 997.0}, {'u': 22, 'v': 17, 'w': 331.0}, {'u': 9, 'v': 10, 'w': 1040.0}, {'u': 17, 'v': 11, 'w': 564.0}, {'u': 2, 'v': 3, 'w': 958.0}, {'u': 3, 'v': 5, 'w': 271.0}, {'u': 4, 'v': 5, 'w': 1019.0}], 'k': 12, 'source_file': 'I006.stp', 'density': 0.09881422924901186}","[[18, 20], [4, 6], [3, 14], [5, 15], [4, 15], [15, 21], [20, 21], [21, 22], [17, 22], [11, 17], [3, 5]]",5366.0,"{'problem_type': 'KMST', 'num_nodes': 23, 'num_edges': 25, 'edges': [{'u': 17, 'v': 18, 'w': 1065.0}, {'u': 17, 'v': 19, 'w': 313.0}, {'u': 17, 'v': 22, 'w': 707.0}, {'u': 18, 'v': 15, 'w': 728.0}, {'u': 0, 'v': 9, 'w': 1117.0}, {'u': 5, 'v': 3, 'w': 433.0}, {'u': 6, 'v': 11, 'w': 1919.0}, {'u': 6, 'v': 12, 'w': 616.0}, {'u': 7, 'v': 11, 'w': 657.0}, {'u': 7, 'v': 12, 'w': 1662.0}, {'u': 13, 'v': 2, 'w': 223.0}, {'u': 13, 'v': 16, 'w': 1116.0}, {'u': 14, 'v': 4, 'w': 537.0}, {'u': 14, 'v': 3, 'w': 805.0}, {'u': 14, 'v': 20, 'w': 1077.0}, {'u': 19, 'v': 20, 'w': 217.0}, {'u': 19, 'v': 12, 'w': 2484.0}, {'u': 20, 'v': 21, 'w': 595.0}, {'u': 21, 'v': 9, 'w': 997.0}, {'u': 21, 'v': 16, 'w': 331.0}, {'u': 8, 'v': 9, 'w': 1040.0}, {'u': 16, 'v': 10, 'w': 564.0}, {'u': 1, 'v': 2, 'w': 958.0}, {'u': 2, 'v': 4, 'w': 271.0}, {'u': 3, 'v': 4, 'w': 1019.0}], 'density': 0.09881422924901186, 'source_file': 'I006.stp', 'k': 12}","[[17, 19], [3, 5], [2, 13], [4, 14], [3, 14], [14, 20], [19, 20], [20, 21], [16, 21], [10, 16], [2, 4]]",35,json,0
KMST,KMST,"Many people on campus want faster links, so the task is to select exactly k buildings to interconnect with new conduit using only the available routes, ensure those chosen buildings form a single connected group, and avoid any redundant circular runs. A plan is better if the sum of its conduit segments is smaller — total length is the straightforward sum of the chosen route lengths. The specific instance information is shown below.

# total_buildings=24
# total_available_routes=28
# target_buildings_to_connect=12
building_endpoint_u,building_endpoint_v,route_length
G,O,508.0
T,W,389.0
U,V,2441.0
U,N,280.0
U,I,1957.0
V,S,221.0
V,Q,898.0
W,S,850.0
W,X,1106.0
K,L,1217.0
K,P,4256.0
H,A,2309.0
H,F,2378.0
L,M,143.0
L,E,1095.0
M,B,654.0
M,A,2050.0
O,D,95.0
O,E,693.0
P,Q,542.0
Q,R,1896.0
R,S,1074.0
R,X,778.0
J,C,221365.0
J,B,220965.0
B,F,325.0
C,D,155.0
C,E,633.0

Also, when you send back the actual plan, please follow this little JSON layout so it's easy to check automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as a short list of conduit runs to lay down. Each inner pair like [u1, v1] is one route between two chosen buildings (use the building IDs from the instance). This block is just a sketch of the shape I expect you to return — not the actual wiring plan.

Please be sure to use the exact identifiers from the instance input — don't rename them and don't 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”.","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 28, 'edges': [{'u': 7, 'v': 15, 'w': 508.0}, {'u': 20, 'v': 23, 'w': 389.0}, {'u': 21, 'v': 22, 'w': 2441.0}, {'u': 21, 'v': 14, 'w': 280.0}, {'u': 21, 'v': 9, 'w': 1957.0}, {'u': 22, 'v': 19, 'w': 221.0}, {'u': 22, 'v': 17, 'w': 898.0}, {'u': 23, 'v': 19, 'w': 850.0}, {'u': 23, 'v': 24, 'w': 1106.0}, {'u': 11, 'v': 12, 'w': 1217.0}, {'u': 11, 'v': 16, 'w': 4256.0}, {'u': 8, 'v': 1, 'w': 2309.0}, {'u': 8, 'v': 6, 'w': 2378.0}, {'u': 12, 'v': 13, 'w': 143.0}, {'u': 12, 'v': 5, 'w': 1095.0}, {'u': 13, 'v': 2, 'w': 654.0}, {'u': 13, 'v': 1, 'w': 2050.0}, {'u': 15, 'v': 4, 'w': 95.0}, {'u': 15, 'v': 5, 'w': 693.0}, {'u': 16, 'v': 17, 'w': 542.0}, {'u': 17, 'v': 18, 'w': 1896.0}, {'u': 18, 'v': 19, 'w': 1074.0}, {'u': 18, 'v': 24, 'w': 778.0}, {'u': 10, 'v': 3, 'w': 221365.0}, {'u': 10, 'v': 2, 'w': 220965.0}, {'u': 2, 'v': 6, 'w': 325.0}, {'u': 3, 'v': 4, 'w': 155.0}, {'u': 3, 'v': 5, 'w': 633.0}], 'k': 12, 'source_file': 'I019.stp', 'density': 0.10144927536231885}","[[7, 15], [11, 12], [1, 8], [12, 13], [5, 12], [2, 13], [1, 13], [4, 15], [2, 6], [3, 4], [3, 5]]",9184.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 28, 'edges': [{'u': 'G', 'v': 'O', 'w': 508.0}, {'u': 'T', 'v': 'W', 'w': 389.0}, {'u': 'U', 'v': 'V', 'w': 2441.0}, {'u': 'U', 'v': 'N', 'w': 280.0}, {'u': 'U', 'v': 'I', 'w': 1957.0}, {'u': 'V', 'v': 'S', 'w': 221.0}, {'u': 'V', 'v': 'Q', 'w': 898.0}, {'u': 'W', 'v': 'S', 'w': 850.0}, {'u': 'W', 'v': 'X', 'w': 1106.0}, {'u': 'K', 'v': 'L', 'w': 1217.0}, {'u': 'K', 'v': 'P', 'w': 4256.0}, {'u': 'H', 'v': 'A', 'w': 2309.0}, {'u': 'H', 'v': 'F', 'w': 2378.0}, {'u': 'L', 'v': 'M', 'w': 143.0}, {'u': 'L', 'v': 'E', 'w': 1095.0}, {'u': 'M', 'v': 'B', 'w': 654.0}, {'u': 'M', 'v': 'A', 'w': 2050.0}, {'u': 'O', 'v': 'D', 'w': 95.0}, {'u': 'O', 'v': 'E', 'w': 693.0}, {'u': 'P', 'v': 'Q', 'w': 542.0}, {'u': 'Q', 'v': 'R', 'w': 1896.0}, {'u': 'R', 'v': 'S', 'w': 1074.0}, {'u': 'R', 'v': 'X', 'w': 778.0}, {'u': 'J', 'v': 'C', 'w': 221365.0}, {'u': 'J', 'v': 'B', 'w': 220965.0}, {'u': 'B', 'v': 'F', 'w': 325.0}, {'u': 'C', 'v': 'D', 'w': 155.0}, {'u': 'C', 'v': 'E', 'w': 633.0}], 'density': 0.10144927536231885, 'source_file': 'I019.stp', 'k': 12}","[['G', 'O'], ['K', 'L'], ['A', 'H'], ['L', 'M'], ['E', 'L'], ['B', 'M'], ['A', 'M'], ['D', 'O'], ['B', 'F'], ['C', 'D'], ['C', 'E']]",36,csv,names
KMST,KMST,"Backstage, the coordinator has to decide which exact k sets will be active and which approved walkway pieces to install so the chosen sets form one connected layout with no circular paths. The choices must be k distinct sets, only approved segments may be used, and the way to compare layouts is to sum the costs of the chosen segments — the lower that sum, the better the setup. The concrete details will be shown below.

# total_available_sets=28
# total_approved_walkways=36
# sets_to_activate=14
set_endpoint_u,set_endpoint_v,walkway_installation_cost
6,11,256.0
6,12,68.0
0,23,3015.0
0,13,2432.0
25,21,7280.0
25,23,7649.0
8,7,2095.0
8,9,313.0
8,18,1209.0
9,3,780.0
9,16,706.0
10,4,1447.0
10,15,187.0
13,18,1817.0
13,19,4961.0
14,15,1906.0
14,7,709.0
15,16,174.0
11,17,2543.0
12,17,2650.0
24,21,181.0
18,27,4685.0
19,27,1941.0
19,22,2807.0
17,20,162.0
1,2,767.0
1,3,798.0
1,5,746.0
1,16,947.0
2,3,99.0
2,26,3841.0
20,22,3865.0
20,26,2463.0
26,27,1442.0
4,5,1156.0
21,22,2667.0

If you want to give me the chosen layout, just drop it in this simple JSON shape so it's easy to check programmatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is just a list of the approved walkway pieces you're going to install; each inner pair [u, v] means ""connect set u to set v"". Super informal: it's just a list of edges to make the final connected, loop-free layout. The block above is only a sketch of the shape I expect, not the actual answer.

Please make sure to use the exact 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”. ""","{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 36, 'edges': [{'u': 7, 'v': 12, 'w': 256.0}, {'u': 7, 'v': 13, 'w': 68.0}, {'u': 1, 'v': 24, 'w': 3015.0}, {'u': 1, 'v': 14, 'w': 2432.0}, {'u': 26, 'v': 22, 'w': 7280.0}, {'u': 26, 'v': 24, 'w': 7649.0}, {'u': 9, 'v': 8, 'w': 2095.0}, {'u': 9, 'v': 10, 'w': 313.0}, {'u': 9, 'v': 19, 'w': 1209.0}, {'u': 10, 'v': 4, 'w': 780.0}, {'u': 10, 'v': 17, 'w': 706.0}, {'u': 11, 'v': 5, 'w': 1447.0}, {'u': 11, 'v': 16, 'w': 187.0}, {'u': 14, 'v': 19, 'w': 1817.0}, {'u': 14, 'v': 20, 'w': 4961.0}, {'u': 15, 'v': 16, 'w': 1906.0}, {'u': 15, 'v': 8, 'w': 709.0}, {'u': 16, 'v': 17, 'w': 174.0}, {'u': 12, 'v': 18, 'w': 2543.0}, {'u': 13, 'v': 18, 'w': 2650.0}, {'u': 25, 'v': 22, 'w': 181.0}, {'u': 19, 'v': 28, 'w': 4685.0}, {'u': 20, 'v': 28, 'w': 1941.0}, {'u': 20, 'v': 23, 'w': 2807.0}, {'u': 18, 'v': 21, 'w': 162.0}, {'u': 2, 'v': 3, 'w': 767.0}, {'u': 2, 'v': 4, 'w': 798.0}, {'u': 2, 'v': 6, 'w': 746.0}, {'u': 2, 'v': 17, 'w': 947.0}, {'u': 3, 'v': 4, 'w': 99.0}, {'u': 3, 'v': 27, 'w': 3841.0}, {'u': 21, 'v': 23, 'w': 3865.0}, {'u': 21, 'v': 27, 'w': 2463.0}, {'u': 27, 'v': 28, 'w': 1442.0}, {'u': 5, 'v': 6, 'w': 1156.0}, {'u': 22, 'v': 23, 'w': 2667.0}], 'k': 14, 'source_file': 'I040.stp', 'density': 0.09523809523809523}","[[9, 10], [9, 19], [4, 10], [10, 17], [11, 16], [14, 19], [15, 16], [8, 15], [16, 17], [2, 3], [2, 6], [3, 4], [5, 6]]",10569.0,"{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 36, 'edges': [{'u': 6, 'v': 11, 'w': 256.0}, {'u': 6, 'v': 12, 'w': 68.0}, {'u': 0, 'v': 23, 'w': 3015.0}, {'u': 0, 'v': 13, 'w': 2432.0}, {'u': 25, 'v': 21, 'w': 7280.0}, {'u': 25, 'v': 23, 'w': 7649.0}, {'u': 8, 'v': 7, 'w': 2095.0}, {'u': 8, 'v': 9, 'w': 313.0}, {'u': 8, 'v': 18, 'w': 1209.0}, {'u': 9, 'v': 3, 'w': 780.0}, {'u': 9, 'v': 16, 'w': 706.0}, {'u': 10, 'v': 4, 'w': 1447.0}, {'u': 10, 'v': 15, 'w': 187.0}, {'u': 13, 'v': 18, 'w': 1817.0}, {'u': 13, 'v': 19, 'w': 4961.0}, {'u': 14, 'v': 15, 'w': 1906.0}, {'u': 14, 'v': 7, 'w': 709.0}, {'u': 15, 'v': 16, 'w': 174.0}, {'u': 11, 'v': 17, 'w': 2543.0}, {'u': 12, 'v': 17, 'w': 2650.0}, {'u': 24, 'v': 21, 'w': 181.0}, {'u': 18, 'v': 27, 'w': 4685.0}, {'u': 19, 'v': 27, 'w': 1941.0}, {'u': 19, 'v': 22, 'w': 2807.0}, {'u': 17, 'v': 20, 'w': 162.0}, {'u': 1, 'v': 2, 'w': 767.0}, {'u': 1, 'v': 3, 'w': 798.0}, {'u': 1, 'v': 5, 'w': 746.0}, {'u': 1, 'v': 16, 'w': 947.0}, {'u': 2, 'v': 3, 'w': 99.0}, {'u': 2, 'v': 26, 'w': 3841.0}, {'u': 20, 'v': 22, 'w': 3865.0}, {'u': 20, 'v': 26, 'w': 2463.0}, {'u': 26, 'v': 27, 'w': 1442.0}, {'u': 4, 'v': 5, 'w': 1156.0}, {'u': 21, 'v': 22, 'w': 2667.0}], 'density': 0.09523809523809523, 'source_file': 'I040.stp', 'k': 14}","[[8, 9], [8, 18], [3, 9], [9, 16], [10, 15], [13, 18], [14, 15], [7, 14], [15, 16], [1, 2], [1, 5], [2, 3], [4, 5]]",37,csv,0
KMST,KMST,"On a busy morning the coordinator needs to lock in exactly k supplier locations and route deliveries along certain roads so the chosen locations become a single, non-repeating network. Plans are judged by total route length — add up the distances of the roads chosen and pick the layout with the least total. There can’t be duplicate stops and every one of the k must be connected without any circular detours. The concrete map and distances are provided below.

There are 25 potential supplier locations and 34 candidate roads; the coordinator must lock in exactly 8 locations and connect them into a single, loop-free delivery network.
Candidate road connecting supplier 3 and supplier 4, distance 600.0.
Candidate road connecting supplier 3 and supplier 1, distance 333.0.
Candidate road connecting supplier 3 and supplier 8, distance 33555.0.
Candidate road connecting supplier 4 and supplier 9, distance 33534.0.
Candidate road connecting supplier 4 and supplier 16, distance 619.0.
Candidate road connecting supplier 0 and supplier 13, distance 33616.0.
Candidate road connecting supplier 1 and supplier 6, distance 33582.0.
Candidate road connecting supplier 13 and supplier 6, distance 223.0.
Candidate road connecting supplier 14 and supplier 7, distance 592.0.
Candidate road connecting supplier 14 and supplier 22, distance 33464.0.
Candidate road connecting supplier 14 and supplier 19, distance 589.0.
Candidate road connecting supplier 15 and supplier 20, distance 2112.0.
Candidate road connecting supplier 15 and supplier 18, distance 374.0.
Candidate road connecting supplier 15 and supplier 23, distance 2282.0.
Candidate road connecting supplier 5 and supplier 16, distance 33505.0.
Candidate road connecting supplier 5 and supplier 9, distance 540.0.
Candidate road connecting supplier 5 and supplier 7, distance 612.0.
Candidate road connecting supplier 7 and supplier 17, distance 33477.0.
Candidate road connecting supplier 11 and supplier 12, distance 669.0.
Candidate road connecting supplier 11 and supplier 19, distance 33437.0.
Candidate road connecting supplier 11 and supplier 22, distance 643.0.
Candidate road connecting supplier 12 and supplier 21, distance 33395.0.
Candidate road connecting supplier 12 and supplier 24, distance 1339.0.
Candidate road connecting supplier 20 and supplier 10, distance 29398.0.
Candidate road connecting supplier 20 and supplier 2, distance 30506.0.
Candidate road connecting supplier 10 and supplier 2, distance 1289.0.
Candidate road connecting supplier 19 and supplier 21, distance 519.0.
Candidate road connecting supplier 21 and supplier 23, distance 1150.0.
Candidate road connecting supplier 24 and supplier 23, distance 33328.0.
Candidate road connecting supplier 24 and supplier 2, distance 1205.0.
Candidate road connecting supplier 22 and supplier 17, distance 565.0.
Candidate road connecting supplier 16 and supplier 17, distance 650.0.
Candidate road connecting supplier 8 and supplier 6, distance 222.0.
Candidate road connecting supplier 8 and supplier 9, distance 590.0.
The coordinator will choose the layout that minimizes the total distance across chosen roads while covering exactly 8 locations.

When you send back the chosen roads, please put them in a simple JSON shape like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Each pair [u1, v1] is just one road connecting two supplier locations in the final locked-in network — list every road you’re using so that the k locations become one connected, non-repeating layout. Think of the JSON as a quick form: ""solution"" holds a list of edges (each edge is a two-item list).

This JSON is only a sketch of the expected shape, not the actual answer — replace the placeholders with the real node identifiers from the instance input. Please use those 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”.""","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 34, 'edges': [{'u': 4, 'v': 5, 'w': 600.0}, {'u': 4, 'v': 2, 'w': 333.0}, {'u': 4, 'v': 9, 'w': 33555.0}, {'u': 5, 'v': 10, 'w': 33534.0}, {'u': 5, 'v': 17, 'w': 619.0}, {'u': 1, 'v': 14, 'w': 33616.0}, {'u': 2, 'v': 7, 'w': 33582.0}, {'u': 14, 'v': 7, 'w': 223.0}, {'u': 15, 'v': 8, 'w': 592.0}, {'u': 15, 'v': 23, 'w': 33464.0}, {'u': 15, 'v': 20, 'w': 589.0}, {'u': 16, 'v': 21, 'w': 2112.0}, {'u': 16, 'v': 19, 'w': 374.0}, {'u': 16, 'v': 24, 'w': 2282.0}, {'u': 6, 'v': 17, 'w': 33505.0}, {'u': 6, 'v': 10, 'w': 540.0}, {'u': 6, 'v': 8, 'w': 612.0}, {'u': 8, 'v': 18, 'w': 33477.0}, {'u': 12, 'v': 13, 'w': 669.0}, {'u': 12, 'v': 20, 'w': 33437.0}, {'u': 12, 'v': 23, 'w': 643.0}, {'u': 13, 'v': 22, 'w': 33395.0}, {'u': 13, 'v': 25, 'w': 1339.0}, {'u': 21, 'v': 11, 'w': 29398.0}, {'u': 21, 'v': 3, 'w': 30506.0}, {'u': 11, 'v': 3, 'w': 1289.0}, {'u': 20, 'v': 22, 'w': 519.0}, {'u': 22, 'v': 24, 'w': 1150.0}, {'u': 25, 'v': 24, 'w': 33328.0}, {'u': 25, 'v': 3, 'w': 1205.0}, {'u': 23, 'v': 18, 'w': 565.0}, {'u': 17, 'v': 18, 'w': 650.0}, {'u': 9, 'v': 7, 'w': 222.0}, {'u': 9, 'v': 10, 'w': 590.0}], 'k': 8, 'source_file': 'I002.stp', 'density': 0.11333333333333333}","[[7, 14], [8, 15], [15, 20], [6, 10], [6, 8], [7, 9], [9, 10]]",3368.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 34, 'edges': [{'u': 3, 'v': 4, 'w': 600.0}, {'u': 3, 'v': 1, 'w': 333.0}, {'u': 3, 'v': 8, 'w': 33555.0}, {'u': 4, 'v': 9, 'w': 33534.0}, {'u': 4, 'v': 16, 'w': 619.0}, {'u': 0, 'v': 13, 'w': 33616.0}, {'u': 1, 'v': 6, 'w': 33582.0}, {'u': 13, 'v': 6, 'w': 223.0}, {'u': 14, 'v': 7, 'w': 592.0}, {'u': 14, 'v': 22, 'w': 33464.0}, {'u': 14, 'v': 19, 'w': 589.0}, {'u': 15, 'v': 20, 'w': 2112.0}, {'u': 15, 'v': 18, 'w': 374.0}, {'u': 15, 'v': 23, 'w': 2282.0}, {'u': 5, 'v': 16, 'w': 33505.0}, {'u': 5, 'v': 9, 'w': 540.0}, {'u': 5, 'v': 7, 'w': 612.0}, {'u': 7, 'v': 17, 'w': 33477.0}, {'u': 11, 'v': 12, 'w': 669.0}, {'u': 11, 'v': 19, 'w': 33437.0}, {'u': 11, 'v': 22, 'w': 643.0}, {'u': 12, 'v': 21, 'w': 33395.0}, {'u': 12, 'v': 24, 'w': 1339.0}, {'u': 20, 'v': 10, 'w': 29398.0}, {'u': 20, 'v': 2, 'w': 30506.0}, {'u': 10, 'v': 2, 'w': 1289.0}, {'u': 19, 'v': 21, 'w': 519.0}, {'u': 21, 'v': 23, 'w': 1150.0}, {'u': 24, 'v': 23, 'w': 33328.0}, {'u': 24, 'v': 2, 'w': 1205.0}, {'u': 22, 'v': 17, 'w': 565.0}, {'u': 16, 'v': 17, 'w': 650.0}, {'u': 8, 'v': 6, 'w': 222.0}, {'u': 8, 'v': 9, 'w': 590.0}], 'density': 0.11333333333333333, 'source_file': 'I002.stp', 'k': 8}","[[6, 13], [7, 14], [14, 19], [5, 9], [5, 7], [6, 8], [8, 9]]",38,markdown_table,0
KMST,KMST,"We’ve been handed a floor plan and told to choose exactly k hubs to link up, picking from the available fiber options so the chosen hubs form a single, loop-free network; the better layouts are simply the ones with the lowest total bill, calculated by summing the cost of the cables used. The specific instance and costs are listed below.

# total_server_hubs_available=29
# available_fiber_options_count=36
# hubs_to_select_count=9
hub_endpoint_a,hub_endpoint_b,fiber_install_cost
9,7,2565.0
9,14,284.0
9,15,1348.0
11,5,149375.0
11,10,149802.0
10,18,18.0
10,16,2031.0
16,27,4150.0
16,6,2232.0
17,8,1608.0
17,1,3156.0
17,15,290.0
22,18,4381.0
22,21,2563.0
18,28,1609.0
19,4,1664.0
19,27,8139.0
19,26,6946.0
14,13,2347.0
14,12,2476.0
3,26,2632.0
28,8,10290.0
28,29,3629.0
7,8,2579.0
7,12,298.0
15,2,3076.0
20,24,7524.0
20,23,11654.0
1,2,968.0
12,5,682.0
26,27,4382.0
21,29,873.0
24,25,2750.0
24,13,6890.0
13,6,6770.0
5,6,3098.0

When you send the chosen cabling back, just drop it into this simple JSON shape so I can read it easily:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This is just a sketch of the shape I expect: ""solution"" is a list of the cables you picked, and each inner pair like [u1, v1] is an edge connecting hub u1 to hub v1. Think of each pair as one cable between two hubs — nothing fancy, just the list.

Please make sure to use the exact 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”.""","{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 9, 'v': 7, 'w': 2565.0}, {'u': 9, 'v': 14, 'w': 284.0}, {'u': 9, 'v': 15, 'w': 1348.0}, {'u': 11, 'v': 5, 'w': 149375.0}, {'u': 11, 'v': 10, 'w': 149802.0}, {'u': 10, 'v': 18, 'w': 18.0}, {'u': 10, 'v': 16, 'w': 2031.0}, {'u': 16, 'v': 27, 'w': 4150.0}, {'u': 16, 'v': 6, 'w': 2232.0}, {'u': 17, 'v': 8, 'w': 1608.0}, {'u': 17, 'v': 1, 'w': 3156.0}, {'u': 17, 'v': 15, 'w': 290.0}, {'u': 22, 'v': 18, 'w': 4381.0}, {'u': 22, 'v': 21, 'w': 2563.0}, {'u': 18, 'v': 28, 'w': 1609.0}, {'u': 19, 'v': 4, 'w': 1664.0}, {'u': 19, 'v': 27, 'w': 8139.0}, {'u': 19, 'v': 26, 'w': 6946.0}, {'u': 14, 'v': 13, 'w': 2347.0}, {'u': 14, 'v': 12, 'w': 2476.0}, {'u': 3, 'v': 26, 'w': 2632.0}, {'u': 28, 'v': 8, 'w': 10290.0}, {'u': 28, 'v': 29, 'w': 3629.0}, {'u': 7, 'v': 8, 'w': 2579.0}, {'u': 7, 'v': 12, 'w': 298.0}, {'u': 15, 'v': 2, 'w': 3076.0}, {'u': 20, 'v': 24, 'w': 7524.0}, {'u': 20, 'v': 23, 'w': 11654.0}, {'u': 1, 'v': 2, 'w': 968.0}, {'u': 12, 'v': 5, 'w': 682.0}, {'u': 26, 'v': 27, 'w': 4382.0}, {'u': 21, 'v': 29, 'w': 873.0}, {'u': 24, 'v': 25, 'w': 2750.0}, {'u': 24, 'v': 13, 'w': 6890.0}, {'u': 13, 'v': 6, 'w': 6770.0}, {'u': 5, 'v': 6, 'w': 3098.0}], 'k': 9, 'source_file': 'I025.stp', 'density': 0.08866995073891626}","[[9, 14], [9, 15], [8, 17], [15, 17], [13, 14], [12, 14], [7, 12], [5, 12]]",9333.0,"{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 36, 'edges': [{'u': 9, 'v': 7, 'w': 2565.0}, {'u': 9, 'v': 14, 'w': 284.0}, {'u': 9, 'v': 15, 'w': 1348.0}, {'u': 11, 'v': 5, 'w': 149375.0}, {'u': 11, 'v': 10, 'w': 149802.0}, {'u': 10, 'v': 18, 'w': 18.0}, {'u': 10, 'v': 16, 'w': 2031.0}, {'u': 16, 'v': 27, 'w': 4150.0}, {'u': 16, 'v': 6, 'w': 2232.0}, {'u': 17, 'v': 8, 'w': 1608.0}, {'u': 17, 'v': 1, 'w': 3156.0}, {'u': 17, 'v': 15, 'w': 290.0}, {'u': 22, 'v': 18, 'w': 4381.0}, {'u': 22, 'v': 21, 'w': 2563.0}, {'u': 18, 'v': 28, 'w': 1609.0}, {'u': 19, 'v': 4, 'w': 1664.0}, {'u': 19, 'v': 27, 'w': 8139.0}, {'u': 19, 'v': 26, 'w': 6946.0}, {'u': 14, 'v': 13, 'w': 2347.0}, {'u': 14, 'v': 12, 'w': 2476.0}, {'u': 3, 'v': 26, 'w': 2632.0}, {'u': 28, 'v': 8, 'w': 10290.0}, {'u': 28, 'v': 29, 'w': 3629.0}, {'u': 7, 'v': 8, 'w': 2579.0}, {'u': 7, 'v': 12, 'w': 298.0}, {'u': 15, 'v': 2, 'w': 3076.0}, {'u': 20, 'v': 24, 'w': 7524.0}, {'u': 20, 'v': 23, 'w': 11654.0}, {'u': 1, 'v': 2, 'w': 968.0}, {'u': 12, 'v': 5, 'w': 682.0}, {'u': 26, 'v': 27, 'w': 4382.0}, {'u': 21, 'v': 29, 'w': 873.0}, {'u': 24, 'v': 25, 'w': 2750.0}, {'u': 24, 'v': 13, 'w': 6890.0}, {'u': 13, 'v': 6, 'w': 6770.0}, {'u': 5, 'v': 6, 'w': 3098.0}], 'density': 0.08866995073891626, 'source_file': 'I025.stp', 'k': 9}","[[9, 14], [9, 15], [8, 17], [15, 17], [13, 14], [12, 14], [7, 12], [5, 12]]",39,csv,1
KMST,KMST,"Many folks assume wiring is just plug-and-play, but this time the task was to select exactly k vendor stalls and link them with approved trunk lines so they form a single connected setup without any circular circuits — a straightforward branching feed. What makes one selection better than another is simply the total length of trunk wiring required: add up every chosen trunk segment and pick the setup with the smallest total. No extra stalls, no duplicate feeds, and no loops are allowed. The concrete stall list and trunk measurements appear below.

# total_vendor_stalls=26
# total_trunk_segments=33
# target_stalls_to_power=10
trunk_endpoint_stall_u,trunk_endpoint_stall_v,trunk_length_meters
K,V,895.0
A,B,172.0
A,E,384.0
B,G,723.0
B,H,383.0
L,M,2768.0
L,X,1982.0
E,F,338.0
E,H,136.0
F,I,105.0
F,J,2020.0
G,N,1899.0
H,I,327.0
I,R,1540.0
I,Q,1392.0
J,W,1266.0
J,C,1053.0
T,U,828.0
T,P,1878.0
T,D,1746.0
U,Y,1304.0
U,Z,297.0
X,Z,1072.0
Z,S,1777.0
V,D,185.0
V,W,1933.0
W,P,1663.0
R,O,1549.0
R,S,1481.0
S,Q,1269.0
P,Q,442.0
N,O,334.0
O,M,1064.0

If you want to hand back the chosen wiring, just pop it into this tiny JSON shape so I can read it easily:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of trunk segments to be used. Each inner pair like [u1, v1] is one approved trunk connecting stall u1 to stall v1. Think of it like filling out a simple form: each line is a single connection you picked.

This JSON is just a sketch of the shape I expect — not the actual answer. Please make sure every stall identifier you use matches the instance input exactly — no renaming, no inventing 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”.""","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 33, 'edges': [{'u': 11, 'v': 22, 'w': 895.0}, {'u': 1, 'v': 2, 'w': 172.0}, {'u': 1, 'v': 5, 'w': 384.0}, {'u': 2, 'v': 7, 'w': 723.0}, {'u': 2, 'v': 8, 'w': 383.0}, {'u': 12, 'v': 13, 'w': 2768.0}, {'u': 12, 'v': 24, 'w': 1982.0}, {'u': 5, 'v': 6, 'w': 338.0}, {'u': 5, 'v': 8, 'w': 136.0}, {'u': 6, 'v': 9, 'w': 105.0}, {'u': 6, 'v': 10, 'w': 2020.0}, {'u': 7, 'v': 14, 'w': 1899.0}, {'u': 8, 'v': 9, 'w': 327.0}, {'u': 9, 'v': 18, 'w': 1540.0}, {'u': 9, 'v': 17, 'w': 1392.0}, {'u': 10, 'v': 23, 'w': 1266.0}, {'u': 10, 'v': 3, 'w': 1053.0}, {'u': 20, 'v': 21, 'w': 828.0}, {'u': 20, 'v': 16, 'w': 1878.0}, {'u': 20, 'v': 4, 'w': 1746.0}, {'u': 21, 'v': 25, 'w': 1304.0}, {'u': 21, 'v': 26, 'w': 297.0}, {'u': 24, 'v': 26, 'w': 1072.0}, {'u': 26, 'v': 19, 'w': 1777.0}, {'u': 22, 'v': 4, 'w': 185.0}, {'u': 22, 'v': 23, 'w': 1933.0}, {'u': 23, 'v': 16, 'w': 1663.0}, {'u': 18, 'v': 15, 'w': 1549.0}, {'u': 18, 'v': 19, 'w': 1481.0}, {'u': 19, 'v': 17, 'w': 1269.0}, {'u': 16, 'v': 17, 'w': 442.0}, {'u': 14, 'v': 15, 'w': 334.0}, {'u': 15, 'v': 13, 'w': 1064.0}], 'k': 10, 'source_file': 'I060.stp', 'density': 0.10153846153846154}","[[1, 2], [2, 7], [2, 8], [5, 8], [6, 9], [8, 9], [9, 17], [17, 19], [16, 17]]",4949.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 33, 'edges': [{'u': 'K', 'v': 'V', 'w': 895.0}, {'u': 'A', 'v': 'B', 'w': 172.0}, {'u': 'A', 'v': 'E', 'w': 384.0}, {'u': 'B', 'v': 'G', 'w': 723.0}, {'u': 'B', 'v': 'H', 'w': 383.0}, {'u': 'L', 'v': 'M', 'w': 2768.0}, {'u': 'L', 'v': 'X', 'w': 1982.0}, {'u': 'E', 'v': 'F', 'w': 338.0}, {'u': 'E', 'v': 'H', 'w': 136.0}, {'u': 'F', 'v': 'I', 'w': 105.0}, {'u': 'F', 'v': 'J', 'w': 2020.0}, {'u': 'G', 'v': 'N', 'w': 1899.0}, {'u': 'H', 'v': 'I', 'w': 327.0}, {'u': 'I', 'v': 'R', 'w': 1540.0}, {'u': 'I', 'v': 'Q', 'w': 1392.0}, {'u': 'J', 'v': 'W', 'w': 1266.0}, {'u': 'J', 'v': 'C', 'w': 1053.0}, {'u': 'T', 'v': 'U', 'w': 828.0}, {'u': 'T', 'v': 'P', 'w': 1878.0}, {'u': 'T', 'v': 'D', 'w': 1746.0}, {'u': 'U', 'v': 'Y', 'w': 1304.0}, {'u': 'U', 'v': 'Z', 'w': 297.0}, {'u': 'X', 'v': 'Z', 'w': 1072.0}, {'u': 'Z', 'v': 'S', 'w': 1777.0}, {'u': 'V', 'v': 'D', 'w': 185.0}, {'u': 'V', 'v': 'W', 'w': 1933.0}, {'u': 'W', 'v': 'P', 'w': 1663.0}, {'u': 'R', 'v': 'O', 'w': 1549.0}, {'u': 'R', 'v': 'S', 'w': 1481.0}, {'u': 'S', 'v': 'Q', 'w': 1269.0}, {'u': 'P', 'v': 'Q', 'w': 442.0}, {'u': 'N', 'v': 'O', 'w': 334.0}, {'u': 'O', 'v': 'M', 'w': 1064.0}], 'density': 0.10153846153846154, 'source_file': 'I060.stp', 'k': 10}","[['A', 'B'], ['B', 'G'], ['B', 'H'], ['E', 'H'], ['F', 'I'], ['H', 'I'], ['I', 'Q'], ['Q', 'S'], ['P', 'Q']]",40,csv,names
KMST,KMST,"Many people on the field crew have been debating where to put a fixed number of sensor stations and which tracks to use so everything ties into one connected route without any loops. The smarter choice is the one with the lowest total distance traveled — you get that by summing the distances of the tracks that get opened. Requirements: pick exactly the given number of distinct sites, make sure they are all connected in a single route, and avoid any closed circuits or repeating sites. The particular site coordinates and distances follow below.

{
  ""total_sites"": 24,
  ""total_candidate_tracks"": 32,
  ""edges"": [
    {
      ""site_a"": 3,
      ""site_b"": 2,
      ""track_distance"": 766.0
    },
    {
      ""site_a"": 3,
      ""site_b"": 7,
      ""track_distance"": 1533.0
    },
    {
      ""site_a"": 3,
      ""site_b"": 8,
      ""track_distance"": 100.0
    },
    {
      ""site_a"": 4,
      ""site_b"": 2,
      ""track_distance"": 781.0
    },
    {
      ""site_a"": 4,
      ""site_b"": 8,
      ""track_distance"": 53.0
    },
    {
      ""site_a"": 5,
      ""site_b"": 6,
      ""track_distance"": 603.0
    },
    {
      ""site_a"": 5,
      ""site_b"": 14,
      ""track_distance"": 1899.0
    },
    {
      ""site_a"": 5,
      ""site_b"": 20,
      ""track_distance"": 1406.0
    },
    {
      ""site_a"": 5,
      ""site_b"": 16,
      ""track_distance"": 7318.0
    },
    {
      ""site_a"": 6,
      ""site_b"": 10,
      ""track_distance"": 6587.0
    },
    {
      ""site_a"": 6,
      ""site_b"": 17,
      ""track_distance"": 6769.0
    },
    {
      ""site_a"": 24,
      ""site_b"": 13,
      ""track_distance"": 794.0
    },
    {
      ""site_a"": 1,
      ""site_b"": 9,
      ""track_distance"": 1697.0
    },
    {
      ""site_a"": 1,
      ""site_b"": 13,
      ""track_distance"": 1512.0
    },
    {
      ""site_a"": 1,
      ""site_b"": 7,
      ""track_distance"": 4859.0
    },
    {
      ""site_a"": 22,
      ""site_b"": 14,
      ""track_distance"": 3212.0
    },
    {
      ""site_a"": 22,
      ""site_b"": 23,
      ""track_distance"": 5863.0
    },
    {
      ""site_a"": 22,
      ""site_b"": 12,
      ""track_distance"": 1667.0
    },
    {
      ""site_a"": 23,
      ""site_b"": 15,
      ""track_distance"": 3496.0
    },
    {
      ""site_a"": 23,
      ""site_b"": 9,
      ""track_distance"": 1501.0
    },
    {
      ""site_a"": 12,
      ""site_b"": 7,
      ""track_distance"": 1636.0
    },
    {
      ""site_a"": 12,
      ""site_b"": 9,
      ""track_distance"": 5561.0
    },
    {
      ""site_a"": 8,
      ""site_b"": 13,
      ""track_distance"": 4351.0
    },
    {
      ""site_a"": 18,
      ""site_b"": 19,
      ""track_distance"": 7284.0
    },
    {
      ""site_a"": 18,
      ""site_b"": 20,
      ""track_distance"": 1622.0
    },
    {
      ""site_a"": 18,
      ""site_b"": 11,
      ""track_distance"": 2983.0
    },
    {
      ""site_a"": 19,
      ""site_b"": 21,
      ""track_distance"": 1401.0
    },
    {
      ""site_a"": 20,
      ""site_b"": 21,
      ""track_distance"": 7271.0
    },
    {
      ""site_a"": 21,
      ""site_b"": 16,
      ""track_distance"": 1189.0
    },
    {
      ""site_a"": 10,
      ""site_b"": 11,
      ""track_distance"": 483.0
    },
    {
      ""site_a"": 14,
      ""site_b"": 15,
      ""track_distance"": 7268.0
    },
    {
      ""site_a"": 15,
      ""site_b"": 16,
      ""track_distance"": 1550.0
    }
  ],
  ""target_sites"": 12
}

Also, when you send back the chosen tracks, just stick to this simple JSON shape so I can read it easily:

{
  ""solution"": [[""u1"", ""v1""], [""u2"", ""v2""], ...]
}

Think of ""solution"" as the list of tracks we're opening; each inner pair [uX, vX] is one track between two sites (the order in the pair doesn't matter — it's just saying those two sites are connected). This block is only a sketch of the shape I need, not the final answer itself.

Please make sure to use the exact 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 32, 'edges': [{'u': 3, 'v': 2, 'w': 766.0}, {'u': 3, 'v': 7, 'w': 1533.0}, {'u': 3, 'v': 8, 'w': 100.0}, {'u': 4, 'v': 2, 'w': 781.0}, {'u': 4, 'v': 8, 'w': 53.0}, {'u': 5, 'v': 6, 'w': 603.0}, {'u': 5, 'v': 14, 'w': 1899.0}, {'u': 5, 'v': 20, 'w': 1406.0}, {'u': 5, 'v': 16, 'w': 7318.0}, {'u': 6, 'v': 10, 'w': 6587.0}, {'u': 6, 'v': 17, 'w': 6769.0}, {'u': 24, 'v': 13, 'w': 794.0}, {'u': 1, 'v': 9, 'w': 1697.0}, {'u': 1, 'v': 13, 'w': 1512.0}, {'u': 1, 'v': 7, 'w': 4859.0}, {'u': 22, 'v': 14, 'w': 3212.0}, {'u': 22, 'v': 23, 'w': 5863.0}, {'u': 22, 'v': 12, 'w': 1667.0}, {'u': 23, 'v': 15, 'w': 3496.0}, {'u': 23, 'v': 9, 'w': 1501.0}, {'u': 12, 'v': 7, 'w': 1636.0}, {'u': 12, 'v': 9, 'w': 5561.0}, {'u': 8, 'v': 13, 'w': 4351.0}, {'u': 18, 'v': 19, 'w': 7284.0}, {'u': 18, 'v': 20, 'w': 1622.0}, {'u': 18, 'v': 11, 'w': 2983.0}, {'u': 19, 'v': 21, 'w': 1401.0}, {'u': 20, 'v': 21, 'w': 7271.0}, {'u': 21, 'v': 16, 'w': 1189.0}, {'u': 10, 'v': 11, 'w': 483.0}, {'u': 14, 'v': 15, 'w': 7268.0}, {'u': 15, 'v': 16, 'w': 1550.0}], 'k': 12, 'source_file': 'I031.stp', 'density': 0.11594202898550725}","[[2, 3], [3, 7], [3, 8], [4, 8], [5, 6], [5, 14], [5, 20], [14, 22], [12, 22], [7, 12], [18, 20]]",14497.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 32, 'edges': [{'u': 3, 'v': 2, 'w': 766.0}, {'u': 3, 'v': 7, 'w': 1533.0}, {'u': 3, 'v': 8, 'w': 100.0}, {'u': 4, 'v': 2, 'w': 781.0}, {'u': 4, 'v': 8, 'w': 53.0}, {'u': 5, 'v': 6, 'w': 603.0}, {'u': 5, 'v': 14, 'w': 1899.0}, {'u': 5, 'v': 20, 'w': 1406.0}, {'u': 5, 'v': 16, 'w': 7318.0}, {'u': 6, 'v': 10, 'w': 6587.0}, {'u': 6, 'v': 17, 'w': 6769.0}, {'u': 24, 'v': 13, 'w': 794.0}, {'u': 1, 'v': 9, 'w': 1697.0}, {'u': 1, 'v': 13, 'w': 1512.0}, {'u': 1, 'v': 7, 'w': 4859.0}, {'u': 22, 'v': 14, 'w': 3212.0}, {'u': 22, 'v': 23, 'w': 5863.0}, {'u': 22, 'v': 12, 'w': 1667.0}, {'u': 23, 'v': 15, 'w': 3496.0}, {'u': 23, 'v': 9, 'w': 1501.0}, {'u': 12, 'v': 7, 'w': 1636.0}, {'u': 12, 'v': 9, 'w': 5561.0}, {'u': 8, 'v': 13, 'w': 4351.0}, {'u': 18, 'v': 19, 'w': 7284.0}, {'u': 18, 'v': 20, 'w': 1622.0}, {'u': 18, 'v': 11, 'w': 2983.0}, {'u': 19, 'v': 21, 'w': 1401.0}, {'u': 20, 'v': 21, 'w': 7271.0}, {'u': 21, 'v': 16, 'w': 1189.0}, {'u': 10, 'v': 11, 'w': 483.0}, {'u': 14, 'v': 15, 'w': 7268.0}, {'u': 15, 'v': 16, 'w': 1550.0}], 'density': 0.11594202898550725, 'source_file': 'I031.stp', 'k': 12}","[[2, 3], [3, 7], [3, 8], [4, 8], [5, 6], [5, 14], [5, 20], [14, 22], [12, 22], [7, 12], [18, 20]]",41,json,1
KMST,KMST,"Once the planning team fixes how many community centers will be served, the next step is picking the exact streets that will connect those centers into one continuous route without any unnecessary loops or doubles. The plan that’s preferred is the one with the lowest total distance, found by summing the lengths of the chosen roads, and the specific centers and road measurements appear below.

# total_locations=26
# total_road_segments=32
# centers_to_connect=8
endpoint_location_u,endpoint_location_v,road_length
3,4,1598.0
3,19,979.0
3,20,1954.0
4,26,702.0
4,22,959.0
1,2,3.0
1,5,1349.0
1,7,445.0
21,8,2170.0
21,13,795.0
5,8,1221.0
26,25,1602.0
26,16,2815.0
15,16,1350.0
16,17,515.0
17,11,583.0
17,12,913.0
24,25,2411.0
10,14,2528.0
10,20,2351.0
14,18,3726.0
18,19,2535.0
19,25,166.0
20,23,493.0
9,6,1912.0
9,22,587.0
9,12,2047.0
6,7,1245.0
6,8,62.0
22,23,1329.0
23,7,1607.0
12,13,472.0

When you send back the chosen streets, a simple JSON layout like this works great — keep it relaxed and just list the edges you picked.

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of ""solution"" as the form field where you list each road to keep. Each pair like [u1, v1] is one street connecting two centers (use the exact node identifiers from the instance). This JSON is just a sketch of the shape I expect, not the actual answer—fill in the real pairs when you submit.

Please 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”.""","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 32, 'edges': [{'u': 3, 'v': 4, 'w': 1598.0}, {'u': 3, 'v': 19, 'w': 979.0}, {'u': 3, 'v': 20, 'w': 1954.0}, {'u': 4, 'v': 26, 'w': 702.0}, {'u': 4, 'v': 22, 'w': 959.0}, {'u': 1, 'v': 2, 'w': 3.0}, {'u': 1, 'v': 5, 'w': 1349.0}, {'u': 1, 'v': 7, 'w': 445.0}, {'u': 21, 'v': 8, 'w': 2170.0}, {'u': 21, 'v': 13, 'w': 795.0}, {'u': 5, 'v': 8, 'w': 1221.0}, {'u': 26, 'v': 25, 'w': 1602.0}, {'u': 26, 'v': 16, 'w': 2815.0}, {'u': 15, 'v': 16, 'w': 1350.0}, {'u': 16, 'v': 17, 'w': 515.0}, {'u': 17, 'v': 11, 'w': 583.0}, {'u': 17, 'v': 12, 'w': 913.0}, {'u': 24, 'v': 25, 'w': 2411.0}, {'u': 10, 'v': 14, 'w': 2528.0}, {'u': 10, 'v': 20, 'w': 2351.0}, {'u': 14, 'v': 18, 'w': 3726.0}, {'u': 18, 'v': 19, 'w': 2535.0}, {'u': 19, 'v': 25, 'w': 166.0}, {'u': 20, 'v': 23, 'w': 493.0}, {'u': 9, 'v': 6, 'w': 1912.0}, {'u': 9, 'v': 22, 'w': 587.0}, {'u': 9, 'v': 12, 'w': 2047.0}, {'u': 6, 'v': 7, 'w': 1245.0}, {'u': 6, 'v': 8, 'w': 62.0}, {'u': 22, 'v': 23, 'w': 1329.0}, {'u': 23, 'v': 7, 'w': 1607.0}, {'u': 12, 'v': 13, 'w': 472.0}], 'k': 8, 'source_file': 'I080.stp', 'density': 0.09846153846153846}","[[1, 2], [1, 7], [5, 8], [20, 23], [6, 7], [6, 8], [7, 23]]",5076.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 32, 'edges': [{'u': 3, 'v': 4, 'w': 1598.0}, {'u': 3, 'v': 19, 'w': 979.0}, {'u': 3, 'v': 20, 'w': 1954.0}, {'u': 4, 'v': 26, 'w': 702.0}, {'u': 4, 'v': 22, 'w': 959.0}, {'u': 1, 'v': 2, 'w': 3.0}, {'u': 1, 'v': 5, 'w': 1349.0}, {'u': 1, 'v': 7, 'w': 445.0}, {'u': 21, 'v': 8, 'w': 2170.0}, {'u': 21, 'v': 13, 'w': 795.0}, {'u': 5, 'v': 8, 'w': 1221.0}, {'u': 26, 'v': 25, 'w': 1602.0}, {'u': 26, 'v': 16, 'w': 2815.0}, {'u': 15, 'v': 16, 'w': 1350.0}, {'u': 16, 'v': 17, 'w': 515.0}, {'u': 17, 'v': 11, 'w': 583.0}, {'u': 17, 'v': 12, 'w': 913.0}, {'u': 24, 'v': 25, 'w': 2411.0}, {'u': 10, 'v': 14, 'w': 2528.0}, {'u': 10, 'v': 20, 'w': 2351.0}, {'u': 14, 'v': 18, 'w': 3726.0}, {'u': 18, 'v': 19, 'w': 2535.0}, {'u': 19, 'v': 25, 'w': 166.0}, {'u': 20, 'v': 23, 'w': 493.0}, {'u': 9, 'v': 6, 'w': 1912.0}, {'u': 9, 'v': 22, 'w': 587.0}, {'u': 9, 'v': 12, 'w': 2047.0}, {'u': 6, 'v': 7, 'w': 1245.0}, {'u': 6, 'v': 8, 'w': 62.0}, {'u': 22, 'v': 23, 'w': 1329.0}, {'u': 23, 'v': 7, 'w': 1607.0}, {'u': 12, 'v': 13, 'w': 472.0}], 'density': 0.09846153846153846, 'source_file': 'I080.stp', 'k': 8}","[[1, 2], [1, 7], [5, 8], [20, 23], [6, 7], [6, 8], [7, 23]]",42,csv,1
KMST,KMST,"Someone on the logistics floor has to pick a handful of hubs and schedule one-way or two-way transfer lanes so those hubs form a single, loop-free network. The choice is about which hubs make the cut and which direct lanes to open; the way to tell which choice is better is to add up all the lane distances — the smaller that total, the better the plan. Practical ground rules: include exactly the required number of hubs, ensure each chosen hub can reach the others through the lanes, and avoid creating circular routes or repeating hubs. The concrete details are shown below.

From 25 hubs and 30 candidate lanes, they must choose exactly 10 hubs and open lanes so those hubs form a single, loop-free connected network.
Candidate lane between hub 20 and hub 1 with distance 10.0.
Candidate lane between hub 20 and hub 21 with distance 1086.0.
Candidate lane between hub 20 and hub 3 with distance 692.0.
Candidate lane between hub 1 and hub 2 with distance 2740.0.
Candidate lane between hub 1 and hub 4 with distance 1552.0.
Candidate lane between hub 17 and hub 2 with distance 759.0.
Candidate lane between hub 17 and hub 16 with distance 212769.0.
Candidate lane between hub 2 and hub 16 with distance 212307.0.
Candidate lane between hub 23 and hub 3 with distance 510.0.
Candidate lane between hub 23 and hub 10 with distance 432.0.
Candidate lane between hub 23 and hub 11 with distance 1118.0.
Candidate lane between hub 24 and hub 22 with distance 764.0.
Candidate lane between hub 24 and hub 25 with distance 1265.0.
Candidate lane between hub 3 and hub 15 with distance 252791.0.
Candidate lane between hub 4 and hub 5 with distance 476.0.
Candidate lane between hub 4 and hub 15 with distance 253130.0.
Candidate lane between hub 5 and hub 10 with distance 465.0.
Candidate lane between hub 5 and hub 9 with distance 1228.0.
Candidate lane between hub 22 and hub 12 with distance 111.0.
Candidate lane between hub 22 and hub 9 with distance 208.0.
Candidate lane between hub 14 and hub 6 with distance 276624.0.
Candidate lane between hub 14 and hub 12 with distance 276365.0.
Candidate lane between hub 6 and hub 7 with distance 202.0.
Candidate lane between hub 7 and hub 11 with distance 313.0.
Candidate lane between hub 8 and hub 9 with distance 483.0.
Candidate lane between hub 8 and hub 10 with distance 1147.0.
Candidate lane between hub 8 and hub 11 with distance 501.0.
Candidate lane between hub 12 and hub 19 with distance 578.0.
Candidate lane between hub 18 and hub 19 with distance 91.0.
Candidate lane between hub 19 and hub 13 with distance 888.0.
They must include exactly 10 hubs, ensure every chosen hub can reach the others, avoid cycles, and minimize the sum of lane distances.

If you want to send the plan back, just pop it into a tiny JSON snippet like this — I find it easiest to think of it as ""a list of lanes, each lane is a pair of hubs.""

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

In plain terms: ""solution"" is the list, and each [u, v] pair is a lane from hub u to hub v. Think of it like filling out a simple form: one line per lane, with the two hubs that the lane connects. This JSON is just a sketch of the shape I expect — you'll replace the placeholders with the actual hubs from the instance.

Please use the identifiers exactly 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”, or a capital letter followed by digits like “A1” or “X7”.","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 30, 'edges': [{'u': 20, 'v': 1, 'w': 10.0}, {'u': 20, 'v': 21, 'w': 1086.0}, {'u': 20, 'v': 3, 'w': 692.0}, {'u': 1, 'v': 2, 'w': 2740.0}, {'u': 1, 'v': 4, 'w': 1552.0}, {'u': 17, 'v': 2, 'w': 759.0}, {'u': 17, 'v': 16, 'w': 212769.0}, {'u': 2, 'v': 16, 'w': 212307.0}, {'u': 23, 'v': 3, 'w': 510.0}, {'u': 23, 'v': 10, 'w': 432.0}, {'u': 23, 'v': 11, 'w': 1118.0}, {'u': 24, 'v': 22, 'w': 764.0}, {'u': 24, 'v': 25, 'w': 1265.0}, {'u': 3, 'v': 15, 'w': 252791.0}, {'u': 4, 'v': 5, 'w': 476.0}, {'u': 4, 'v': 15, 'w': 253130.0}, {'u': 5, 'v': 10, 'w': 465.0}, {'u': 5, 'v': 9, 'w': 1228.0}, {'u': 22, 'v': 12, 'w': 111.0}, {'u': 22, 'v': 9, 'w': 208.0}, {'u': 14, 'v': 6, 'w': 276624.0}, {'u': 14, 'v': 12, 'w': 276365.0}, {'u': 6, 'v': 7, 'w': 202.0}, {'u': 7, 'v': 11, 'w': 313.0}, {'u': 8, 'v': 9, 'w': 483.0}, {'u': 8, 'v': 10, 'w': 1147.0}, {'u': 8, 'v': 11, 'w': 501.0}, {'u': 12, 'v': 19, 'w': 578.0}, {'u': 18, 'v': 19, 'w': 91.0}, {'u': 19, 'v': 13, 'w': 888.0}], 'k': 10, 'source_file': 'I032.stp', 'density': 0.1}","[[22, 24], [12, 22], [9, 22], [6, 7], [7, 11], [8, 9], [8, 11], [12, 19], [18, 19]]",3251.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 30, 'edges': [{'u': 20, 'v': 1, 'w': 10.0}, {'u': 20, 'v': 21, 'w': 1086.0}, {'u': 20, 'v': 3, 'w': 692.0}, {'u': 1, 'v': 2, 'w': 2740.0}, {'u': 1, 'v': 4, 'w': 1552.0}, {'u': 17, 'v': 2, 'w': 759.0}, {'u': 17, 'v': 16, 'w': 212769.0}, {'u': 2, 'v': 16, 'w': 212307.0}, {'u': 23, 'v': 3, 'w': 510.0}, {'u': 23, 'v': 10, 'w': 432.0}, {'u': 23, 'v': 11, 'w': 1118.0}, {'u': 24, 'v': 22, 'w': 764.0}, {'u': 24, 'v': 25, 'w': 1265.0}, {'u': 3, 'v': 15, 'w': 252791.0}, {'u': 4, 'v': 5, 'w': 476.0}, {'u': 4, 'v': 15, 'w': 253130.0}, {'u': 5, 'v': 10, 'w': 465.0}, {'u': 5, 'v': 9, 'w': 1228.0}, {'u': 22, 'v': 12, 'w': 111.0}, {'u': 22, 'v': 9, 'w': 208.0}, {'u': 14, 'v': 6, 'w': 276624.0}, {'u': 14, 'v': 12, 'w': 276365.0}, {'u': 6, 'v': 7, 'w': 202.0}, {'u': 7, 'v': 11, 'w': 313.0}, {'u': 8, 'v': 9, 'w': 483.0}, {'u': 8, 'v': 10, 'w': 1147.0}, {'u': 8, 'v': 11, 'w': 501.0}, {'u': 12, 'v': 19, 'w': 578.0}, {'u': 18, 'v': 19, 'w': 91.0}, {'u': 19, 'v': 13, 'w': 888.0}], 'density': 0.1, 'source_file': 'I032.stp', 'k': 10}","[[22, 24], [12, 22], [9, 22], [6, 7], [7, 11], [8, 9], [8, 11], [12, 19], [18, 19]]",43,nl,1
KMST,KMST,"Recently the crew got instructions to wire a precise number of lamps along a neighborhood and make them one cohesive circuit. The plan must pick exactly that many different lights, join them using the available conduit paths so they’re all connected, and avoid creating any closed loops; the cost of a plan is simply the sum of the conduit run costs used, and the aim is to keep that sum as low as possible. No duplicates or missing lights are allowed — each selected fixture is part of the single, loop-free network. The specific layout and numbers are shown below.

{
  ""total_fixtures"": 24,
  ""available_conduit_runs"": 27,
  ""edges"": [
    {
      ""fixture_endpoint_a"": 5,
      ""fixture_endpoint_b"": 6,
      ""conduit_cost"": 888.0
    },
    {
      ""fixture_endpoint_a"": 5,
      ""fixture_endpoint_b"": 7,
      ""conduit_cost"": 290.0
    },
    {
      ""fixture_endpoint_a"": 6,
      ""fixture_endpoint_b"": 1,
      ""conduit_cost"": 31.0
    },
    {
      ""fixture_endpoint_a"": 6,
      ""fixture_endpoint_b"": 17,
      ""conduit_cost"": 4324.0
    },
    {
      ""fixture_endpoint_a"": 7,
      ""fixture_endpoint_b"": 1,
      ""conduit_cost"": 841.0
    },
    {
      ""fixture_endpoint_a"": 19,
      ""fixture_endpoint_b"": 10,
      ""conduit_cost"": 1467.0
    },
    {
      ""fixture_endpoint_a"": 19,
      ""fixture_endpoint_b"": 18,
      ""conduit_cost"": 4469.0
    },
    {
      ""fixture_endpoint_a"": 19,
      ""fixture_endpoint_b"": 22,
      ""conduit_cost"": 4708.0
    },
    {
      ""fixture_endpoint_a"": 22,
      ""fixture_endpoint_b"": 14,
      ""conduit_cost"": 4898.0
    },
    {
      ""fixture_endpoint_a"": 14,
      ""fixture_endpoint_b"": 15,
      ""conduit_cost"": 369.0
    },
    {
      ""fixture_endpoint_a"": 8,
      ""fixture_endpoint_b"": 9,
      ""conduit_cost"": 1303.0
    },
    {
      ""fixture_endpoint_a"": 8,
      ""fixture_endpoint_b"": 10,
      ""conduit_cost"": 1391.0
    },
    {
      ""fixture_endpoint_a"": 9,
      ""fixture_endpoint_b"": 13,
      ""conduit_cost"": 334.0
    },
    {
      ""fixture_endpoint_a"": 13,
      ""fixture_endpoint_b"": 10,
      ""conduit_cost"": 804.0
    },
    {
      ""fixture_endpoint_a"": 15,
      ""fixture_endpoint_b"": 24,
      ""conduit_cost"": 3821.0
    },
    {
      ""fixture_endpoint_a"": 23,
      ""fixture_endpoint_b"": 18,
      ""conduit_cost"": 4990.0
    },
    {
      ""fixture_endpoint_a"": 23,
      ""fixture_endpoint_b"": 24,
      ""conduit_cost"": 3583.0
    },
    {
      ""fixture_endpoint_a"": 23,
      ""fixture_endpoint_b"": 3,
      ""conduit_cost"": 4824.0
    },
    {
      ""fixture_endpoint_a"": 24,
      ""fixture_endpoint_b"": 11,
      ""conduit_cost"": 6539.0
    },
    {
      ""fixture_endpoint_a"": 16,
      ""fixture_endpoint_b"": 20,
      ""conduit_cost"": 4348.0
    },
    {
      ""fixture_endpoint_a"": 21,
      ""fixture_endpoint_b"": 20,
      ""conduit_cost"": 3506.0
    },
    {
      ""fixture_endpoint_a"": 1,
      ""fixture_endpoint_b"": 12,
      ""conduit_cost"": 2380.0
    },
    {
      ""fixture_endpoint_a"": 20,
      ""fixture_endpoint_b"": 17,
      ""conduit_cost"": 1611.0
    },
    {
      ""fixture_endpoint_a"": 3,
      ""fixture_endpoint_b"": 2,
      ""conduit_cost"": 407.0
    },
    {
      ""fixture_endpoint_a"": 3,
      ""fixture_endpoint_b"": 12,
      ""conduit_cost"": 3108.0
    },
    {
      ""fixture_endpoint_a"": 4,
      ""fixture_endpoint_b"": 12,
      ""conduit_cost"": 1074.0
    },
    {
      ""fixture_endpoint_a"": 17,
      ""fixture_endpoint_b"": 18,
      ""conduit_cost"": 602.0
    }
  ],
  ""target_fixtures"": 10
}

Oh, and when you send back your wiring plan, please stick to this little JSON layout so it’s easy to read and check:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is just the list of conduit runs you picked — each inner pair [u1, v1] is one connection joining two lamps. Think of it like filling out a form: give a list of the edges you want in the final loop-free circuit. This JSON is only a sketch of the shape I need, not the actual answer.

Please make sure you use the exact identifiers 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 27, 'edges': [{'u': 5, 'v': 6, 'w': 888.0}, {'u': 5, 'v': 7, 'w': 290.0}, {'u': 6, 'v': 1, 'w': 31.0}, {'u': 6, 'v': 17, 'w': 4324.0}, {'u': 7, 'v': 1, 'w': 841.0}, {'u': 19, 'v': 10, 'w': 1467.0}, {'u': 19, 'v': 18, 'w': 4469.0}, {'u': 19, 'v': 22, 'w': 4708.0}, {'u': 22, 'v': 14, 'w': 4898.0}, {'u': 14, 'v': 15, 'w': 369.0}, {'u': 8, 'v': 9, 'w': 1303.0}, {'u': 8, 'v': 10, 'w': 1391.0}, {'u': 9, 'v': 13, 'w': 334.0}, {'u': 13, 'v': 10, 'w': 804.0}, {'u': 15, 'v': 24, 'w': 3821.0}, {'u': 23, 'v': 18, 'w': 4990.0}, {'u': 23, 'v': 24, 'w': 3583.0}, {'u': 23, 'v': 3, 'w': 4824.0}, {'u': 24, 'v': 11, 'w': 6539.0}, {'u': 16, 'v': 20, 'w': 4348.0}, {'u': 21, 'v': 20, 'w': 3506.0}, {'u': 1, 'v': 12, 'w': 2380.0}, {'u': 20, 'v': 17, 'w': 1611.0}, {'u': 3, 'v': 2, 'w': 407.0}, {'u': 3, 'v': 12, 'w': 3108.0}, {'u': 4, 'v': 12, 'w': 1074.0}, {'u': 17, 'v': 18, 'w': 602.0}], 'k': 10, 'source_file': 'I027.stp', 'density': 0.09782608695652174}","[[5, 7], [1, 6], [6, 17], [1, 7], [1, 12], [2, 3], [3, 12], [4, 12], [17, 18]]",13057.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 27, 'edges': [{'u': 5, 'v': 6, 'w': 888.0}, {'u': 5, 'v': 7, 'w': 290.0}, {'u': 6, 'v': 1, 'w': 31.0}, {'u': 6, 'v': 17, 'w': 4324.0}, {'u': 7, 'v': 1, 'w': 841.0}, {'u': 19, 'v': 10, 'w': 1467.0}, {'u': 19, 'v': 18, 'w': 4469.0}, {'u': 19, 'v': 22, 'w': 4708.0}, {'u': 22, 'v': 14, 'w': 4898.0}, {'u': 14, 'v': 15, 'w': 369.0}, {'u': 8, 'v': 9, 'w': 1303.0}, {'u': 8, 'v': 10, 'w': 1391.0}, {'u': 9, 'v': 13, 'w': 334.0}, {'u': 13, 'v': 10, 'w': 804.0}, {'u': 15, 'v': 24, 'w': 3821.0}, {'u': 23, 'v': 18, 'w': 4990.0}, {'u': 23, 'v': 24, 'w': 3583.0}, {'u': 23, 'v': 3, 'w': 4824.0}, {'u': 24, 'v': 11, 'w': 6539.0}, {'u': 16, 'v': 20, 'w': 4348.0}, {'u': 21, 'v': 20, 'w': 3506.0}, {'u': 1, 'v': 12, 'w': 2380.0}, {'u': 20, 'v': 17, 'w': 1611.0}, {'u': 3, 'v': 2, 'w': 407.0}, {'u': 3, 'v': 12, 'w': 3108.0}, {'u': 4, 'v': 12, 'w': 1074.0}, {'u': 17, 'v': 18, 'w': 602.0}], 'density': 0.09782608695652174, 'source_file': 'I027.stp', 'k': 10}","[[5, 7], [1, 6], [6, 17], [1, 7], [1, 12], [2, 3], [3, 12], [4, 12], [17, 18]]",44,json,1
KMST,KMST,"Recently the municipality asked for a compact pump layout: settle on a target number of pump stations and select the pipe segments that join them into one connected, cycle-free structure. The plan that uses the smallest total pipe length wins — the total is just the sum of the lengths of the pipes chosen. Practically, the design must include exactly that many stations, keep every chosen station connected, avoid any closed loops, and not repeat segments. Concrete instance information appears below.

# total_candidate_sites=26
# total_candidate_pipes=32
# target_pump_stations=13
endpoint_site_a,endpoint_site_b,pipe_length
C,D,337.0
C,E,419.0
D,J,297.0
D,K,1416.0
E,J,172.0
E,L,3187.0
F,G,570.0
I,A,1859.0
G,P,1045.0
G,A,1361.0
J,S,254.0
K,N,177.0
K,L,2514.0
L,U,495.0
M,A,1722.0
N,B,192.0
N,X,3101.0
O,B,2434.0
O,P,794.0
O,Y,275.0
S,R,1257.0
S,T,3160.0
X,U,66.0
X,Q,1463.0
Y,H,2245.0
W,Q,730.0
R,V,2585.0
T,V,1243.0
T,Z,1764.0
U,Z,1259.0
Q,Z,2217.0
A,B,807.0

When you’re ready to hand in the chosen pipe segments, please use a simple JSON shape so it’s easy to read and validate. Here’s the little sketch I’m expecting:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of this as a form: the ""solution"" field is a list of the pipe segments you picked, and each [u1, v1] pair is one segment connecting two station identifiers. Super casual — just a list of the edges that make up the final connected, loop-free layout. This is just the shape I want you to follow, not the actual answer.

Please make sure every identifier you use matches the instance input exactly — don’t rename stations 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”.""","{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 32, 'edges': [{'u': 3, 'v': 4, 'w': 337.0}, {'u': 3, 'v': 5, 'w': 419.0}, {'u': 4, 'v': 10, 'w': 297.0}, {'u': 4, 'v': 11, 'w': 1416.0}, {'u': 5, 'v': 10, 'w': 172.0}, {'u': 5, 'v': 12, 'w': 3187.0}, {'u': 6, 'v': 7, 'w': 570.0}, {'u': 9, 'v': 1, 'w': 1859.0}, {'u': 7, 'v': 16, 'w': 1045.0}, {'u': 7, 'v': 1, 'w': 1361.0}, {'u': 10, 'v': 19, 'w': 254.0}, {'u': 11, 'v': 14, 'w': 177.0}, {'u': 11, 'v': 12, 'w': 2514.0}, {'u': 12, 'v': 21, 'w': 495.0}, {'u': 13, 'v': 1, 'w': 1722.0}, {'u': 14, 'v': 2, 'w': 192.0}, {'u': 14, 'v': 24, 'w': 3101.0}, {'u': 15, 'v': 2, 'w': 2434.0}, {'u': 15, 'v': 16, 'w': 794.0}, {'u': 15, 'v': 25, 'w': 275.0}, {'u': 19, 'v': 18, 'w': 1257.0}, {'u': 19, 'v': 20, 'w': 3160.0}, {'u': 24, 'v': 21, 'w': 66.0}, {'u': 24, 'v': 17, 'w': 1463.0}, {'u': 25, 'v': 8, 'w': 2245.0}, {'u': 23, 'v': 17, 'w': 730.0}, {'u': 18, 'v': 22, 'w': 2585.0}, {'u': 20, 'v': 22, 'w': 1243.0}, {'u': 20, 'v': 26, 'w': 1764.0}, {'u': 21, 'v': 26, 'w': 1259.0}, {'u': 17, 'v': 26, 'w': 2217.0}, {'u': 1, 'v': 2, 'w': 807.0}], 'k': 13, 'source_file': 'I035.stp', 'density': 0.09846153846153846}","[[3, 4], [4, 10], [4, 11], [5, 10], [7, 16], [1, 7], [10, 19], [11, 14], [2, 14], [15, 16], [15, 25], [1, 2]]",7127.0,"{'problem_type': 'KMST', 'num_nodes': 26, 'num_edges': 32, 'edges': [{'u': 'C', 'v': 'D', 'w': 337.0}, {'u': 'C', 'v': 'E', 'w': 419.0}, {'u': 'D', 'v': 'J', 'w': 297.0}, {'u': 'D', 'v': 'K', 'w': 1416.0}, {'u': 'E', 'v': 'J', 'w': 172.0}, {'u': 'E', 'v': 'L', 'w': 3187.0}, {'u': 'F', 'v': 'G', 'w': 570.0}, {'u': 'I', 'v': 'A', 'w': 1859.0}, {'u': 'G', 'v': 'P', 'w': 1045.0}, {'u': 'G', 'v': 'A', 'w': 1361.0}, {'u': 'J', 'v': 'S', 'w': 254.0}, {'u': 'K', 'v': 'N', 'w': 177.0}, {'u': 'K', 'v': 'L', 'w': 2514.0}, {'u': 'L', 'v': 'U', 'w': 495.0}, {'u': 'M', 'v': 'A', 'w': 1722.0}, {'u': 'N', 'v': 'B', 'w': 192.0}, {'u': 'N', 'v': 'X', 'w': 3101.0}, {'u': 'O', 'v': 'B', 'w': 2434.0}, {'u': 'O', 'v': 'P', 'w': 794.0}, {'u': 'O', 'v': 'Y', 'w': 275.0}, {'u': 'S', 'v': 'R', 'w': 1257.0}, {'u': 'S', 'v': 'T', 'w': 3160.0}, {'u': 'X', 'v': 'U', 'w': 66.0}, {'u': 'X', 'v': 'Q', 'w': 1463.0}, {'u': 'Y', 'v': 'H', 'w': 2245.0}, {'u': 'W', 'v': 'Q', 'w': 730.0}, {'u': 'R', 'v': 'V', 'w': 2585.0}, {'u': 'T', 'v': 'V', 'w': 1243.0}, {'u': 'T', 'v': 'Z', 'w': 1764.0}, {'u': 'U', 'v': 'Z', 'w': 1259.0}, {'u': 'Q', 'v': 'Z', 'w': 2217.0}, {'u': 'A', 'v': 'B', 'w': 807.0}], 'density': 0.09846153846153846, 'source_file': 'I035.stp', 'k': 13}","[['C', 'D'], ['D', 'J'], ['D', 'K'], ['E', 'J'], ['G', 'P'], ['A', 'G'], ['J', 'S'], ['K', 'N'], ['B', 'N'], ['O', 'P'], ['O', 'Y'], ['A', 'B']]",45,csv,names
KMST,KMST,"I’m planning a shoot and need to pick a fixed number of locations for different scenes, then lay down service roads so every chosen site can be driven between without any breaks. The choice is which exact spots to include and which roads to build so that all the picked sites are connected in one continuous layout with no loops or redundant backtracking. A better choice is the one that uses the fewest road miles overall — count the length of each service road you include and add them up, and the sum should be as small as possible. The rules are strict: pick exactly the given number of sites, don’t duplicate sites, make sure every chosen site is reachable from any other via the roads, and avoid creating circular routes. The concrete details are shown below.

There are 28 candidate filming sites, 36 potential direct roads, and I must pick exactly 14 sites.
A possible service road between site 13 and site 12 is 214.0 miles long.
A possible service road between site 13 and site 22 is 1066.0 miles long.
A possible service road between site 13 and site 11 is 1980.0 miles long.
A possible service road between site 22 and site 1 is 731.0 miles long.
A possible service road between site 22 and site 0 is 49.0 miles long.
A possible service road between site 23 and site 3 is 73.0 miles long.
A possible service road between site 24 and site 10 is 228.0 miles long.
A possible service road between site 24 and site 5 is 706.0 miles long.
A possible service road between site 24 and site 3 is 863.0 miles long.
A possible service road between site 27 and site 21 is 27.0 miles long.
A possible service road between site 27 and site 5 is 1482.0 miles long.
A possible service road between site 27 and site 11 is 385.0 miles long.
A possible service road between site 25 and site 18 is 233.0 miles long.
A possible service road between site 25 and site 26 is 949.0 miles long.
A possible service road between site 25 and site 2 is 1051.0 miles long.
A possible service road between site 26 and site 16 is 647.0 miles long.
A possible service road between site 26 and site 2 is 251.0 miles long.
A possible service road between site 6 and site 12 is 2240.0 miles long.
A possible service road between site 6 and site 11 is 1896.0 miles long.
A possible service road between site 2 and site 3 is 681.0 miles long.
A possible service road between site 4 and site 17 is 1617.0 miles long.
A possible service road between site 4 and site 18 is 483.0 miles long.
A possible service road between site 4 and site 5 is 1641.0 miles long.
A possible service road between site 7 and site 8 is 227.0 miles long.
A possible service road between site 7 and site 14 is 293.0 miles long.
A possible service road between site 7 and site 20 is 1528.0 miles long.
A possible service road between site 8 and site 9 is 1853.0 miles long.
A possible service road between site 19 and site 20 is 254.0 miles long.
A possible service road between site 20 and site 21 is 1591.0 miles long.
A possible service road between site 21 and site 17 is 389.0 miles long.
A possible service road between site 17 and site 14 is 683.0 miles long.
A possible service road between site 18 and site 15 is 778.0 miles long.
A possible service road between site 14 and site 15 is 2280.0 miles long.
A possible service road between site 15 and site 16 is 627.0 miles long.
A possible service road between site 10 and site 11 is 1845.0 miles long.
A possible service road between site 10 and site 12 is 789.0 miles long.
I'll use these entries to pick the exact 14 sites and build the minimum-mileage layout that connects them without loops.

Also, a quick format note — when you send back the roads you pick, it'd be great if you put them in a little JSON snippet like this:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

This just means ""solution"" is the list of roads you'll build. Each pair like [u1, v1] is a road connecting the two chosen sites. Think of it like filling out a short form: one line per road, listing the two endpoints. It's only a sketch of the shape I want, not the actual answer you should compute.

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"".","{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 36, 'edges': [{'u': 14, 'v': 13, 'w': 214.0}, {'u': 14, 'v': 23, 'w': 1066.0}, {'u': 14, 'v': 12, 'w': 1980.0}, {'u': 23, 'v': 2, 'w': 731.0}, {'u': 23, 'v': 1, 'w': 49.0}, {'u': 24, 'v': 4, 'w': 73.0}, {'u': 25, 'v': 11, 'w': 228.0}, {'u': 25, 'v': 6, 'w': 706.0}, {'u': 25, 'v': 4, 'w': 863.0}, {'u': 28, 'v': 22, 'w': 27.0}, {'u': 28, 'v': 6, 'w': 1482.0}, {'u': 28, 'v': 12, 'w': 385.0}, {'u': 26, 'v': 19, 'w': 233.0}, {'u': 26, 'v': 27, 'w': 949.0}, {'u': 26, 'v': 3, 'w': 1051.0}, {'u': 27, 'v': 17, 'w': 647.0}, {'u': 27, 'v': 3, 'w': 251.0}, {'u': 7, 'v': 13, 'w': 2240.0}, {'u': 7, 'v': 12, 'w': 1896.0}, {'u': 3, 'v': 4, 'w': 681.0}, {'u': 5, 'v': 18, 'w': 1617.0}, {'u': 5, 'v': 19, 'w': 483.0}, {'u': 5, 'v': 6, 'w': 1641.0}, {'u': 8, 'v': 9, 'w': 227.0}, {'u': 8, 'v': 15, 'w': 293.0}, {'u': 8, 'v': 21, 'w': 1528.0}, {'u': 9, 'v': 10, 'w': 1853.0}, {'u': 20, 'v': 21, 'w': 254.0}, {'u': 21, 'v': 22, 'w': 1591.0}, {'u': 22, 'v': 18, 'w': 389.0}, {'u': 18, 'v': 15, 'w': 683.0}, {'u': 19, 'v': 16, 'w': 778.0}, {'u': 15, 'v': 16, 'w': 2280.0}, {'u': 16, 'v': 17, 'w': 627.0}, {'u': 11, 'v': 12, 'w': 1845.0}, {'u': 11, 'v': 13, 'w': 789.0}], 'k': 14, 'source_file': 'I084.stp', 'density': 0.09523809523809523}","[[4, 24], [11, 25], [6, 25], [4, 25], [22, 28], [6, 28], [12, 28], [3, 27], [3, 4], [8, 9], [8, 15], [18, 22], [15, 18]]",6288.0,"{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 36, 'edges': [{'u': 13, 'v': 12, 'w': 214.0}, {'u': 13, 'v': 22, 'w': 1066.0}, {'u': 13, 'v': 11, 'w': 1980.0}, {'u': 22, 'v': 1, 'w': 731.0}, {'u': 22, 'v': 0, 'w': 49.0}, {'u': 23, 'v': 3, 'w': 73.0}, {'u': 24, 'v': 10, 'w': 228.0}, {'u': 24, 'v': 5, 'w': 706.0}, {'u': 24, 'v': 3, 'w': 863.0}, {'u': 27, 'v': 21, 'w': 27.0}, {'u': 27, 'v': 5, 'w': 1482.0}, {'u': 27, 'v': 11, 'w': 385.0}, {'u': 25, 'v': 18, 'w': 233.0}, {'u': 25, 'v': 26, 'w': 949.0}, {'u': 25, 'v': 2, 'w': 1051.0}, {'u': 26, 'v': 16, 'w': 647.0}, {'u': 26, 'v': 2, 'w': 251.0}, {'u': 6, 'v': 12, 'w': 2240.0}, {'u': 6, 'v': 11, 'w': 1896.0}, {'u': 2, 'v': 3, 'w': 681.0}, {'u': 4, 'v': 17, 'w': 1617.0}, {'u': 4, 'v': 18, 'w': 483.0}, {'u': 4, 'v': 5, 'w': 1641.0}, {'u': 7, 'v': 8, 'w': 227.0}, {'u': 7, 'v': 14, 'w': 293.0}, {'u': 7, 'v': 20, 'w': 1528.0}, {'u': 8, 'v': 9, 'w': 1853.0}, {'u': 19, 'v': 20, 'w': 254.0}, {'u': 20, 'v': 21, 'w': 1591.0}, {'u': 21, 'v': 17, 'w': 389.0}, {'u': 17, 'v': 14, 'w': 683.0}, {'u': 18, 'v': 15, 'w': 778.0}, {'u': 14, 'v': 15, 'w': 2280.0}, {'u': 15, 'v': 16, 'w': 627.0}, {'u': 10, 'v': 11, 'w': 1845.0}, {'u': 10, 'v': 12, 'w': 789.0}], 'density': 0.09523809523809523, 'source_file': 'I084.stp', 'k': 14}","[[3, 23], [10, 24], [5, 24], [3, 24], [21, 27], [5, 27], [11, 27], [2, 26], [2, 3], [7, 8], [7, 14], [17, 21], [14, 17]]",46,markdown_table,0
KMST,KMST,"Recently the cable company got a brief to wire up a handful of junctions: they must choose an exact number of those junctions and link them with coax so the chosen set is all connected together, with no closed loops. Plans are judged by how little cable they require — simply total the lengths of all the links you’d place. The practical constraints are straightforward: exactly that many junctions, each included only once, everything connected, and no looped paths. The specific data is given below.

{
  ""total_junctions"": 28,
  ""total_possible_links"": 34,
  ""edges"": [
    {
      ""junction_a_id"": ""AB"",
      ""junction_b_id"": ""X"",
      ""cable_length_meters"": 727.0
    },
    {
      ""junction_a_id"": ""AB"",
      ""junction_b_id"": ""P"",
      ""cable_length_meters"": 347.0
    },
    {
      ""junction_a_id"": ""AB"",
      ""junction_b_id"": ""AA"",
      ""cable_length_meters"": 784.0
    },
    {
      ""junction_a_id"": ""Z"",
      ""junction_b_id"": ""Y"",
      ""cable_length_meters"": 576.0
    },
    {
      ""junction_a_id"": ""Z"",
      ""junction_b_id"": ""J"",
      ""cable_length_meters"": 1248.0
    },
    {
      ""junction_a_id"": ""Z"",
      ""junction_b_id"": ""S"",
      ""cable_length_meters"": 1475.0
    },
    {
      ""junction_a_id"": ""A"",
      ""junction_b_id"": ""Q"",
      ""cable_length_meters"": 614.0
    },
    {
      ""junction_a_id"": ""A"",
      ""junction_b_id"": ""O"",
      ""cable_length_meters"": 1063.0
    },
    {
      ""junction_a_id"": ""B"",
      ""junction_b_id"": ""C"",
      ""cable_length_meters"": 769.0
    },
    {
      ""junction_a_id"": ""B"",
      ""junction_b_id"": ""G"",
      ""cable_length_meters"": 392.0
    },
    {
      ""junction_a_id"": ""C"",
      ""junction_b_id"": ""F"",
      ""cable_length_meters"": 315.0
    },
    {
      ""junction_a_id"": ""C"",
      ""junction_b_id"": ""I"",
      ""cable_length_meters"": 190.0
    },
    {
      ""junction_a_id"": ""K"",
      ""junction_b_id"": ""R"",
      ""cable_length_meters"": 1085.0
    },
    {
      ""junction_a_id"": ""N"",
      ""junction_b_id"": ""O"",
      ""cable_length_meters"": 265.0
    },
    {
      ""junction_a_id"": ""N"",
      ""junction_b_id"": ""P"",
      ""cable_length_meters"": 917.0
    },
    {
      ""junction_a_id"": ""N"",
      ""junction_b_id"": ""Q"",
      ""cable_length_meters"": 414.0
    },
    {
      ""junction_a_id"": ""O"",
      ""junction_b_id"": ""J"",
      ""cable_length_meters"": 7.0
    },
    {
      ""junction_a_id"": ""H"",
      ""junction_b_id"": ""M"",
      ""cable_length_meters"": 152.0
    },
    {
      ""junction_a_id"": ""H"",
      ""junction_b_id"": ""X"",
      ""cable_length_meters"": 1000.0
    },
    {
      ""junction_a_id"": ""H"",
      ""junction_b_id"": ""I"",
      ""cable_length_meters"": 685.0
    },
    {
      ""junction_a_id"": ""P"",
      ""junction_b_id"": ""T"",
      ""cable_length_meters"": 838.0
    },
    {
      ""junction_a_id"": ""Q"",
      ""junction_b_id"": ""X"",
      ""cable_length_meters"": 187.0
    },
    {
      ""junction_a_id"": ""I"",
      ""junction_b_id"": ""J"",
      ""cable_length_meters"": 1676.0
    },
    {
      ""junction_a_id"": ""D"",
      ""junction_b_id"": ""E"",
      ""cable_length_meters"": 1259.0
    },
    {
      ""junction_a_id"": ""D"",
      ""junction_b_id"": ""M"",
      ""cable_length_meters"": 1649.0
    },
    {
      ""junction_a_id"": ""V"",
      ""junction_b_id"": ""W"",
      ""cable_length_meters"": 177.0
    },
    {
      ""junction_a_id"": ""V"",
      ""junction_b_id"": ""AA"",
      ""cable_length_meters"": 1948.0
    },
    {
      ""junction_a_id"": ""F"",
      ""junction_b_id"": ""G"",
      ""cable_length_meters"": 798.0
    },
    {
      ""junction_a_id"": ""F"",
      ""junction_b_id"": ""L"",
      ""cable_length_meters"": 292.0
    },
    {
      ""junction_a_id"": ""M"",
      ""junction_b_id"": ""L"",
      ""cable_length_meters"": 182.0
    },
    {
      ""junction_a_id"": ""R"",
      ""junction_b_id"": ""S"",
      ""cable_length_meters"": 221.0
    },
    {
      ""junction_a_id"": ""R"",
      ""junction_b_id"": ""U"",
      ""cable_length_meters"": 635.0
    },
    {
      ""junction_a_id"": ""S"",
      ""junction_b_id"": ""T"",
      ""cable_length_meters"": 1988.0
    },
    {
      ""junction_a_id"": ""T"",
      ""junction_b_id"": ""AA"",
      ""cable_length_meters"": 86.0
    }
  ],
  ""required_junctions_to_connect"": 8
}

Oh, and when you send back the plan, please follow this little JSON layout so I can read it automatically:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Think of that as a simple form: ""solution"" is the list of coax runs you propose, and each [u, v] pair is a single cable connecting junction u to junction v. It's just the shape I need — a sketch of the format, not your final answer.

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”.""","{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 34, 'edges': [{'u': 28, 'v': 24, 'w': 727.0}, {'u': 28, 'v': 16, 'w': 347.0}, {'u': 28, 'v': 27, 'w': 784.0}, {'u': 26, 'v': 25, 'w': 576.0}, {'u': 26, 'v': 10, 'w': 1248.0}, {'u': 26, 'v': 19, 'w': 1475.0}, {'u': 1, 'v': 17, 'w': 614.0}, {'u': 1, 'v': 15, 'w': 1063.0}, {'u': 2, 'v': 3, 'w': 769.0}, {'u': 2, 'v': 7, 'w': 392.0}, {'u': 3, 'v': 6, 'w': 315.0}, {'u': 3, 'v': 9, 'w': 190.0}, {'u': 11, 'v': 18, 'w': 1085.0}, {'u': 14, 'v': 15, 'w': 265.0}, {'u': 14, 'v': 16, 'w': 917.0}, {'u': 14, 'v': 17, 'w': 414.0}, {'u': 15, 'v': 10, 'w': 7.0}, {'u': 8, 'v': 13, 'w': 152.0}, {'u': 8, 'v': 24, 'w': 1000.0}, {'u': 8, 'v': 9, 'w': 685.0}, {'u': 16, 'v': 20, 'w': 838.0}, {'u': 17, 'v': 24, 'w': 187.0}, {'u': 9, 'v': 10, 'w': 1676.0}, {'u': 4, 'v': 5, 'w': 1259.0}, {'u': 4, 'v': 13, 'w': 1649.0}, {'u': 22, 'v': 23, 'w': 177.0}, {'u': 22, 'v': 27, 'w': 1948.0}, {'u': 6, 'v': 7, 'w': 798.0}, {'u': 6, 'v': 12, 'w': 292.0}, {'u': 13, 'v': 12, 'w': 182.0}, {'u': 18, 'v': 19, 'w': 221.0}, {'u': 18, 'v': 21, 'w': 635.0}, {'u': 19, 'v': 20, 'w': 1988.0}, {'u': 20, 'v': 27, 'w': 86.0}], 'k': 8, 'source_file': 'I046.stp', 'density': 0.08994708994708994}","[[14, 15], [14, 17], [10, 15], [8, 13], [8, 24], [17, 24], [12, 13]]",2207.0,"{'problem_type': 'KMST', 'num_nodes': 28, 'num_edges': 34, 'edges': [{'u': 'AB', 'v': 'X', 'w': 727.0}, {'u': 'AB', 'v': 'P', 'w': 347.0}, {'u': 'AB', 'v': 'AA', 'w': 784.0}, {'u': 'Z', 'v': 'Y', 'w': 576.0}, {'u': 'Z', 'v': 'J', 'w': 1248.0}, {'u': 'Z', 'v': 'S', 'w': 1475.0}, {'u': 'A', 'v': 'Q', 'w': 614.0}, {'u': 'A', 'v': 'O', 'w': 1063.0}, {'u': 'B', 'v': 'C', 'w': 769.0}, {'u': 'B', 'v': 'G', 'w': 392.0}, {'u': 'C', 'v': 'F', 'w': 315.0}, {'u': 'C', 'v': 'I', 'w': 190.0}, {'u': 'K', 'v': 'R', 'w': 1085.0}, {'u': 'N', 'v': 'O', 'w': 265.0}, {'u': 'N', 'v': 'P', 'w': 917.0}, {'u': 'N', 'v': 'Q', 'w': 414.0}, {'u': 'O', 'v': 'J', 'w': 7.0}, {'u': 'H', 'v': 'M', 'w': 152.0}, {'u': 'H', 'v': 'X', 'w': 1000.0}, {'u': 'H', 'v': 'I', 'w': 685.0}, {'u': 'P', 'v': 'T', 'w': 838.0}, {'u': 'Q', 'v': 'X', 'w': 187.0}, {'u': 'I', 'v': 'J', 'w': 1676.0}, {'u': 'D', 'v': 'E', 'w': 1259.0}, {'u': 'D', 'v': 'M', 'w': 1649.0}, {'u': 'V', 'v': 'W', 'w': 177.0}, {'u': 'V', 'v': 'AA', 'w': 1948.0}, {'u': 'F', 'v': 'G', 'w': 798.0}, {'u': 'F', 'v': 'L', 'w': 292.0}, {'u': 'M', 'v': 'L', 'w': 182.0}, {'u': 'R', 'v': 'S', 'w': 221.0}, {'u': 'R', 'v': 'U', 'w': 635.0}, {'u': 'S', 'v': 'T', 'w': 1988.0}, {'u': 'T', 'v': 'AA', 'w': 86.0}], 'density': 0.08994708994708994, 'source_file': 'I046.stp', 'k': 8}","[['N', 'O'], ['N', 'Q'], ['J', 'O'], ['H', 'M'], ['H', 'X'], ['Q', 'X'], ['L', 'M']]",47,json,names
KMST,KMST,"I run the watering schedule at our community garden, and I need to pick a specific number of raised beds to hook up to the shared water line. The job is to decide which beds to include and which hoses to lay so all those chosen beds are joined together in a single network with no closed loops, and the plan is better the less hose it uses — you figure that by adding up the lengths of the hoses you’d need. The exact layout and hose lengths for the current case are shown below.

There are 25 raised beds and 31 candidate hose segments; I must connect exactly 12 beds into a single loop-free watering network.
Between bed 17 and bed 1 I can lay a hose of length 27798.0.
Between bed 17 and bed 22 I can lay a hose of length 7013.0.
Between bed 22 and bed 1 I can lay a hose of length 23468.0.
Between bed 0 and bed 6 I can lay a hose of length 4799.0.
Between bed 0 and bed 9 I can lay a hose of length 1485.0.
Between bed 0 and bed 24 I can lay a hose of length 6913.0.
Between bed 15 and bed 8 I can lay a hose of length 2213.0.
Between bed 15 and bed 3 I can lay a hose of length 1623.0.
Between bed 9 and bed 21 I can lay a hose of length 6191.0.
Between bed 16 and bed 12 I can lay a hose of length 480.0.
Between bed 16 and bed 4 I can lay a hose of length 1486.0.
Between bed 16 and bed 13 I can lay a hose of length 2593.0.
Between bed 3 and bed 8 I can lay a hose of length 2904.0.
Between bed 4 and bed 20 I can lay a hose of length 1778.0.
Between bed 14 and bed 7 I can lay a hose of length 1133.0.
Between bed 14 and bed 18 I can lay a hose of length 2232.0.
Between bed 14 and bed 20 I can lay a hose of length 2110.0.
Between bed 1 and bed 2 I can lay a hose of length 805.0.
Between bed 1 and bed 11 I can lay a hose of length 1344.0.
Between bed 2 and bed 11 I can lay a hose of length 840.0.
Between bed 2 and bed 10 I can lay a hose of length 23632.0.
Between bed 5 and bed 20 I can lay a hose of length 2016.0.
Between bed 6 and bed 10 I can lay a hose of length 177.0.
Between bed 12 and bed 13 I can lay a hose of length 2196.0.
Between bed 12 and bed 7 I can lay a hose of length 2768.0.
Between bed 13 and bed 19 I can lay a hose of length 2385.0.
Between bed 24 and bed 21 I can lay a hose of length 510.0.
Between bed 24 and bed 19 I can lay a hose of length 38621.0.
Between bed 7 and bed 8 I can lay a hose of length 3010.0.
Between bed 11 and bed 19 I can lay a hose of length 29430.0.
Between bed 21 and bed 23 I can lay a hose of length 10690.0.
I'll choose the 12 beds and the connecting hoses that minimize the total hose length.

Also, when you send the plan back, please use this simple JSON layout so it's easy to read and feed into the garden map:

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is a list of hose runs; each inner pair [u, v] means run a hose between bed u and bed v. It's just a quick form of saying which beds get connected to which — nothing fancy, just a list of connections.

This JSON is only a sketch of the expected shape, not the actual answer.

Please make sure all identifiers in your final answer match exactly what's 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”.","{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 31, 'edges': [{'u': 18, 'v': 2, 'w': 27798.0}, {'u': 18, 'v': 23, 'w': 7013.0}, {'u': 23, 'v': 2, 'w': 23468.0}, {'u': 1, 'v': 7, 'w': 4799.0}, {'u': 1, 'v': 10, 'w': 1485.0}, {'u': 1, 'v': 25, 'w': 6913.0}, {'u': 16, 'v': 9, 'w': 2213.0}, {'u': 16, 'v': 4, 'w': 1623.0}, {'u': 10, 'v': 22, 'w': 6191.0}, {'u': 17, 'v': 13, 'w': 480.0}, {'u': 17, 'v': 5, 'w': 1486.0}, {'u': 17, 'v': 14, 'w': 2593.0}, {'u': 4, 'v': 9, 'w': 2904.0}, {'u': 5, 'v': 21, 'w': 1778.0}, {'u': 15, 'v': 8, 'w': 1133.0}, {'u': 15, 'v': 19, 'w': 2232.0}, {'u': 15, 'v': 21, 'w': 2110.0}, {'u': 2, 'v': 3, 'w': 805.0}, {'u': 2, 'v': 12, 'w': 1344.0}, {'u': 3, 'v': 12, 'w': 840.0}, {'u': 3, 'v': 11, 'w': 23632.0}, {'u': 6, 'v': 21, 'w': 2016.0}, {'u': 7, 'v': 11, 'w': 177.0}, {'u': 13, 'v': 14, 'w': 2196.0}, {'u': 13, 'v': 8, 'w': 2768.0}, {'u': 14, 'v': 20, 'w': 2385.0}, {'u': 25, 'v': 22, 'w': 510.0}, {'u': 25, 'v': 20, 'w': 38621.0}, {'u': 8, 'v': 9, 'w': 3010.0}, {'u': 12, 'v': 20, 'w': 29430.0}, {'u': 22, 'v': 24, 'w': 10690.0}], 'k': 12, 'source_file': 'I011.stp', 'density': 0.10333333333333333}","[[9, 16], [4, 16], [13, 17], [5, 17], [5, 21], [8, 15], [15, 19], [15, 21], [6, 21], [13, 14], [8, 9]]",20277.0,"{'problem_type': 'KMST', 'num_nodes': 25, 'num_edges': 31, 'edges': [{'u': 17, 'v': 1, 'w': 27798.0}, {'u': 17, 'v': 22, 'w': 7013.0}, {'u': 22, 'v': 1, 'w': 23468.0}, {'u': 0, 'v': 6, 'w': 4799.0}, {'u': 0, 'v': 9, 'w': 1485.0}, {'u': 0, 'v': 24, 'w': 6913.0}, {'u': 15, 'v': 8, 'w': 2213.0}, {'u': 15, 'v': 3, 'w': 1623.0}, {'u': 9, 'v': 21, 'w': 6191.0}, {'u': 16, 'v': 12, 'w': 480.0}, {'u': 16, 'v': 4, 'w': 1486.0}, {'u': 16, 'v': 13, 'w': 2593.0}, {'u': 3, 'v': 8, 'w': 2904.0}, {'u': 4, 'v': 20, 'w': 1778.0}, {'u': 14, 'v': 7, 'w': 1133.0}, {'u': 14, 'v': 18, 'w': 2232.0}, {'u': 14, 'v': 20, 'w': 2110.0}, {'u': 1, 'v': 2, 'w': 805.0}, {'u': 1, 'v': 11, 'w': 1344.0}, {'u': 2, 'v': 11, 'w': 840.0}, {'u': 2, 'v': 10, 'w': 23632.0}, {'u': 5, 'v': 20, 'w': 2016.0}, {'u': 6, 'v': 10, 'w': 177.0}, {'u': 12, 'v': 13, 'w': 2196.0}, {'u': 12, 'v': 7, 'w': 2768.0}, {'u': 13, 'v': 19, 'w': 2385.0}, {'u': 24, 'v': 21, 'w': 510.0}, {'u': 24, 'v': 19, 'w': 38621.0}, {'u': 7, 'v': 8, 'w': 3010.0}, {'u': 11, 'v': 19, 'w': 29430.0}, {'u': 21, 'v': 23, 'w': 10690.0}], 'density': 0.10333333333333333, 'source_file': 'I011.stp', 'k': 12}","[[8, 15], [3, 15], [12, 16], [4, 16], [4, 20], [7, 14], [14, 18], [14, 20], [5, 20], [12, 13], [7, 8]]",48,nl,0
KMST,KMST,"Heading into the next round of surveys, the responsibility is to select a specified count of plots and pick links that tie those plots into a single connected, loopless measurement structure. The plan that wins is the one with the smallest combined link distance — just total the lengths of all the links chosen. Every selected plot must be included once, everything must be connected together, and there can’t be any loops or repeated plot selections. The concrete details for the instance are shown below.

{
  ""total_plots"": 24,
  ""available_links_count"": 30,
  ""edges"": [
    {
      ""plot_u"": 4,
      ""plot_v"": 3,
      ""link_distance"": 1297.0
    },
    {
      ""plot_u"": 4,
      ""plot_v"": 17,
      ""link_distance"": 1522.0
    },
    {
      ""plot_u"": 4,
      ""plot_v"": 24,
      ""link_distance"": 272.0
    },
    {
      ""plot_u"": 18,
      ""plot_v"": 19,
      ""link_distance"": 523.0
    },
    {
      ""plot_u"": 18,
      ""plot_v"": 23,
      ""link_distance"": 1425.0
    },
    {
      ""plot_u"": 19,
      ""plot_v"": 7,
      ""link_distance"": 2090.0
    },
    {
      ""plot_u"": 19,
      ""plot_v"": 11,
      ""link_distance"": 804.0
    },
    {
      ""plot_u"": 7,
      ""plot_v"": 8,
      ""link_distance"": 1304.0
    },
    {
      ""plot_u"": 8,
      ""plot_v"": 3,
      ""link_distance"": 2487.0
    },
    {
      ""plot_u"": 8,
      ""plot_v"": 9,
      ""link_distance"": 1434.0
    },
    {
      ""plot_u"": 9,
      ""plot_v"": 21,
      ""link_distance"": 4211.0
    },
    {
      ""plot_u"": 24,
      ""plot_v"": 10,
      ""link_distance"": 827.0
    },
    {
      ""plot_u"": 24,
      ""plot_v"": 13,
      ""link_distance"": 2537.0
    },
    {
      ""plot_u"": 1,
      ""plot_v"": 2,
      ""link_distance"": 1130.0
    },
    {
      ""plot_u"": 2,
      ""plot_v"": 10,
      ""link_distance"": 953.0
    },
    {
      ""plot_u"": 20,
      ""plot_v"": 10,
      ""link_distance"": 301.0
    },
    {
      ""plot_u"": 20,
      ""plot_v"": 14,
      ""link_distance"": 1468.0
    },
    {
      ""plot_u"": 23,
      ""plot_v"": 12,
      ""link_distance"": 1489.0
    },
    {
      ""plot_u"": 5,
      ""plot_v"": 6,
      ""link_distance"": 722.0
    },
    {
      ""plot_u"": 5,
      ""plot_v"": 22,
      ""link_distance"": 190.0
    },
    {
      ""plot_u"": 5,
      ""plot_v"": 15,
      ""link_distance"": 1108.0
    },
    {
      ""plot_u"": 13,
      ""plot_v"": 17,
      ""link_distance"": 1362.0
    },
    {
      ""plot_u"": 13,
      ""plot_v"": 12,
      ""link_distance"": 1457.0
    },
    {
      ""plot_u"": 6,
      ""plot_v"": 16,
      ""link_distance"": 986.0
    },
    {
      ""plot_u"": 15,
      ""plot_v"": 3,
      ""link_distance"": 335.0
    },
    {
      ""plot_u"": 15,
      ""plot_v"": 16,
      ""link_distance"": 1051.0
    },
    {
      ""plot_u"": 16,
      ""plot_v"": 14,
      ""link_distance"": 94.0
    },
    {
      ""plot_u"": 11,
      ""plot_v"": 12,
      ""link_distance"": 1460.0
    },
    {
      ""plot_u"": 11,
      ""plot_v"": 17,
      ""link_distance"": 1483.0
    },
    {
      ""plot_u"": 21,
      ""plot_v"": 22,
      ""link_distance"": 1082.0
    }
  ],
  ""plots_to_select"": 12
}

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

{
  ""solution"": [[u1, v1], [u2, v2], ...]
}

Here ""solution"" is just a list of the links you want to include; each inner pair [u, v] is a single link connecting plot u to plot v. Think of it like filling in a short form: list the chosen connections one pair at a time. This block is just a sketch of the shape I expect, not the actual answer.

Please make sure to use the exact identifiers from the instance input — don't rename them and don't 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”.""","{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 30, 'edges': [{'u': 4, 'v': 3, 'w': 1297.0}, {'u': 4, 'v': 17, 'w': 1522.0}, {'u': 4, 'v': 24, 'w': 272.0}, {'u': 18, 'v': 19, 'w': 523.0}, {'u': 18, 'v': 23, 'w': 1425.0}, {'u': 19, 'v': 7, 'w': 2090.0}, {'u': 19, 'v': 11, 'w': 804.0}, {'u': 7, 'v': 8, 'w': 1304.0}, {'u': 8, 'v': 3, 'w': 2487.0}, {'u': 8, 'v': 9, 'w': 1434.0}, {'u': 9, 'v': 21, 'w': 4211.0}, {'u': 24, 'v': 10, 'w': 827.0}, {'u': 24, 'v': 13, 'w': 2537.0}, {'u': 1, 'v': 2, 'w': 1130.0}, {'u': 2, 'v': 10, 'w': 953.0}, {'u': 20, 'v': 10, 'w': 301.0}, {'u': 20, 'v': 14, 'w': 1468.0}, {'u': 23, 'v': 12, 'w': 1489.0}, {'u': 5, 'v': 6, 'w': 722.0}, {'u': 5, 'v': 22, 'w': 190.0}, {'u': 5, 'v': 15, 'w': 1108.0}, {'u': 13, 'v': 17, 'w': 1362.0}, {'u': 13, 'v': 12, 'w': 1457.0}, {'u': 6, 'v': 16, 'w': 986.0}, {'u': 15, 'v': 3, 'w': 335.0}, {'u': 15, 'v': 16, 'w': 1051.0}, {'u': 16, 'v': 14, 'w': 94.0}, {'u': 11, 'v': 12, 'w': 1460.0}, {'u': 11, 'v': 17, 'w': 1483.0}, {'u': 21, 'v': 22, 'w': 1082.0}], 'k': 12, 'source_file': 'I061.stp', 'density': 0.10869565217391304}","[[3, 4], [4, 24], [10, 24], [2, 10], [10, 20], [5, 6], [5, 22], [6, 16], [3, 15], [15, 16], [14, 16]]",7028.0,"{'problem_type': 'KMST', 'num_nodes': 24, 'num_edges': 30, 'edges': [{'u': 4, 'v': 3, 'w': 1297.0}, {'u': 4, 'v': 17, 'w': 1522.0}, {'u': 4, 'v': 24, 'w': 272.0}, {'u': 18, 'v': 19, 'w': 523.0}, {'u': 18, 'v': 23, 'w': 1425.0}, {'u': 19, 'v': 7, 'w': 2090.0}, {'u': 19, 'v': 11, 'w': 804.0}, {'u': 7, 'v': 8, 'w': 1304.0}, {'u': 8, 'v': 3, 'w': 2487.0}, {'u': 8, 'v': 9, 'w': 1434.0}, {'u': 9, 'v': 21, 'w': 4211.0}, {'u': 24, 'v': 10, 'w': 827.0}, {'u': 24, 'v': 13, 'w': 2537.0}, {'u': 1, 'v': 2, 'w': 1130.0}, {'u': 2, 'v': 10, 'w': 953.0}, {'u': 20, 'v': 10, 'w': 301.0}, {'u': 20, 'v': 14, 'w': 1468.0}, {'u': 23, 'v': 12, 'w': 1489.0}, {'u': 5, 'v': 6, 'w': 722.0}, {'u': 5, 'v': 22, 'w': 190.0}, {'u': 5, 'v': 15, 'w': 1108.0}, {'u': 13, 'v': 17, 'w': 1362.0}, {'u': 13, 'v': 12, 'w': 1457.0}, {'u': 6, 'v': 16, 'w': 986.0}, {'u': 15, 'v': 3, 'w': 335.0}, {'u': 15, 'v': 16, 'w': 1051.0}, {'u': 16, 'v': 14, 'w': 94.0}, {'u': 11, 'v': 12, 'w': 1460.0}, {'u': 11, 'v': 17, 'w': 1483.0}, {'u': 21, 'v': 22, 'w': 1082.0}], 'density': 0.10869565217391304, 'source_file': 'I061.stp', 'k': 12}","[[3, 4], [4, 24], [10, 24], [2, 10], [10, 20], [5, 6], [5, 22], [6, 16], [3, 15], [15, 16], [14, 16]]",49,json,1
KMST,KMST,"Someone from network operations has to choose a handful of small cells — exactly k — and set up backhaul so the chosen cells form a single connected layout with no loops or redundant paths. The goal is simply to keep the total backhaul expense as low as possible, measured by adding the cost of each link used. The detailed layout and costs are listed below.

There are 29 small-cell sites and 34 candidate links; exactly 12 of the sites must be activated and connected.
Candidate link between small-cell 15 and small-cell 25 with backhaul cost 517.0.
Candidate link between small-cell 15 and small-cell 26 with backhaul cost 596.0.
Candidate link between small-cell 23 and small-cell 13 with backhaul cost 3743.0.
Candidate link between small-cell 16 and small-cell 29 with backhaul cost 267.0.
Candidate link between small-cell 16 and small-cell 27 with backhaul cost 1394.0.
Candidate link between small-cell 4 and small-cell 26 with backhaul cost 2559.0.
Candidate link between small-cell 4 and small-cell 17 with backhaul cost 2707.0.
Candidate link between small-cell 17 and small-cell 29 with backhaul cost 1128.0.
Candidate link between small-cell 18 and small-cell 7 with backhaul cost 32.0.
Candidate link between small-cell 18 and small-cell 8 with backhaul cost 2584.0.
Candidate link between small-cell 18 and small-cell 19 with backhaul cost 1475.0.
Candidate link between small-cell 24 and small-cell 25 with backhaul cost 329.0.
Candidate link between small-cell 24 and small-cell 20 with backhaul cost 1073.0.
Candidate link between small-cell 24 and small-cell 28 with backhaul cost 203.0.
Candidate link between small-cell 25 and small-cell 14 with backhaul cost 1333.0.
Candidate link between small-cell 26 and small-cell 29 with backhaul cost 1335.0.
Candidate link between small-cell 27 and small-cell 28 with backhaul cost 1628.0.
Candidate link between small-cell 27 and small-cell 5 with backhaul cost 2381.0.
Candidate link between small-cell 28 and small-cell 5 with backhaul cost 2078.0.
Candidate link between small-cell 5 and small-cell 12 with backhaul cost 1121.0.
Candidate link between small-cell 5 and small-cell 8 with backhaul cost 1672.0.
Candidate link between small-cell 10 and small-cell 22 with backhaul cost 2534.0.
Candidate link between small-cell 6 and small-cell 12 with backhaul cost 983.0.
Candidate link between small-cell 6 and small-cell 22 with backhaul cost 603.0.
Candidate link between small-cell 1 and small-cell 2 with backhaul cost 1136.0.
Candidate link between small-cell 1 and small-cell 3 with backhaul cost 433.0.
Candidate link between small-cell 2 and small-cell 11 with backhaul cost 439.0.
Candidate link between small-cell 2 and small-cell 22 with backhaul cost 1978.0.
Candidate link between small-cell 21 and small-cell 9 with backhaul cost 4377.0.
Candidate link between small-cell 3 and small-cell 20 with backhaul cost 376.0.
Candidate link between small-cell 20 and small-cell 11 with backhaul cost 829.0.
Candidate link between small-cell 11 and small-cell 12 with backhaul cost 911.0.
Candidate link between small-cell 13 and small-cell 9 with backhaul cost 1128.0.
Candidate link between small-cell 8 and small-cell 9 with backhaul cost 2376.0.
Select links so the activated 12 sites form a connected, acyclic layout with minimum total backhaul cost.

If you want to send back the chosen links, just use this simple JSON shape — a list of the selected edges under ""solution"". For example:

{
  ""solution"": [[""u1"", ""v1""], [""u2"", ""v2""], ...]
}

This is just a sketch of the shape I expect: ""solution"" holds a list of pairs, and each pair is an edge between two small-cell identifiers (the two ends of a backhaul link). Keep it light and use the same identifiers the instance uses — this block isn't the final answer, just the format I'll read.

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”.""","{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 34, 'edges': [{'u': 15, 'v': 25, 'w': 517.0}, {'u': 15, 'v': 26, 'w': 596.0}, {'u': 23, 'v': 13, 'w': 3743.0}, {'u': 16, 'v': 29, 'w': 267.0}, {'u': 16, 'v': 27, 'w': 1394.0}, {'u': 4, 'v': 26, 'w': 2559.0}, {'u': 4, 'v': 17, 'w': 2707.0}, {'u': 17, 'v': 29, 'w': 1128.0}, {'u': 18, 'v': 7, 'w': 32.0}, {'u': 18, 'v': 8, 'w': 2584.0}, {'u': 18, 'v': 19, 'w': 1475.0}, {'u': 24, 'v': 25, 'w': 329.0}, {'u': 24, 'v': 20, 'w': 1073.0}, {'u': 24, 'v': 28, 'w': 203.0}, {'u': 25, 'v': 14, 'w': 1333.0}, {'u': 26, 'v': 29, 'w': 1335.0}, {'u': 27, 'v': 28, 'w': 1628.0}, {'u': 27, 'v': 5, 'w': 2381.0}, {'u': 28, 'v': 5, 'w': 2078.0}, {'u': 5, 'v': 12, 'w': 1121.0}, {'u': 5, 'v': 8, 'w': 1672.0}, {'u': 10, 'v': 22, 'w': 2534.0}, {'u': 6, 'v': 12, 'w': 983.0}, {'u': 6, 'v': 22, 'w': 603.0}, {'u': 1, 'v': 2, 'w': 1136.0}, {'u': 1, 'v': 3, 'w': 433.0}, {'u': 2, 'v': 11, 'w': 439.0}, {'u': 2, 'v': 22, 'w': 1978.0}, {'u': 21, 'v': 9, 'w': 4377.0}, {'u': 3, 'v': 20, 'w': 376.0}, {'u': 20, 'v': 11, 'w': 829.0}, {'u': 11, 'v': 12, 'w': 911.0}, {'u': 13, 'v': 9, 'w': 1128.0}, {'u': 8, 'v': 9, 'w': 2376.0}], 'k': 12, 'source_file': 'I073.stp', 'density': 0.08374384236453201}","[[15, 25], [15, 26], [16, 29], [24, 25], [20, 24], [24, 28], [26, 29], [1, 3], [2, 11], [3, 20], [11, 20]]",6397.0,"{'problem_type': 'KMST', 'num_nodes': 29, 'num_edges': 34, 'edges': [{'u': 15, 'v': 25, 'w': 517.0}, {'u': 15, 'v': 26, 'w': 596.0}, {'u': 23, 'v': 13, 'w': 3743.0}, {'u': 16, 'v': 29, 'w': 267.0}, {'u': 16, 'v': 27, 'w': 1394.0}, {'u': 4, 'v': 26, 'w': 2559.0}, {'u': 4, 'v': 17, 'w': 2707.0}, {'u': 17, 'v': 29, 'w': 1128.0}, {'u': 18, 'v': 7, 'w': 32.0}, {'u': 18, 'v': 8, 'w': 2584.0}, {'u': 18, 'v': 19, 'w': 1475.0}, {'u': 24, 'v': 25, 'w': 329.0}, {'u': 24, 'v': 20, 'w': 1073.0}, {'u': 24, 'v': 28, 'w': 203.0}, {'u': 25, 'v': 14, 'w': 1333.0}, {'u': 26, 'v': 29, 'w': 1335.0}, {'u': 27, 'v': 28, 'w': 1628.0}, {'u': 27, 'v': 5, 'w': 2381.0}, {'u': 28, 'v': 5, 'w': 2078.0}, {'u': 5, 'v': 12, 'w': 1121.0}, {'u': 5, 'v': 8, 'w': 1672.0}, {'u': 10, 'v': 22, 'w': 2534.0}, {'u': 6, 'v': 12, 'w': 983.0}, {'u': 6, 'v': 22, 'w': 603.0}, {'u': 1, 'v': 2, 'w': 1136.0}, {'u': 1, 'v': 3, 'w': 433.0}, {'u': 2, 'v': 11, 'w': 439.0}, {'u': 2, 'v': 22, 'w': 1978.0}, {'u': 21, 'v': 9, 'w': 4377.0}, {'u': 3, 'v': 20, 'w': 376.0}, {'u': 20, 'v': 11, 'w': 829.0}, {'u': 11, 'v': 12, 'w': 911.0}, {'u': 13, 'v': 9, 'w': 1128.0}, {'u': 8, 'v': 9, 'w': 2376.0}], 'density': 0.08374384236453201, 'source_file': 'I073.stp', 'k': 12}","[[15, 25], [15, 26], [16, 29], [24, 25], [20, 24], [24, 28], [26, 29], [1, 3], [2, 11], [3, 20], [11, 20]]",50,nl,1