Datasets:

HaidarJomaa
/

Convex_Flip_Distance

split stringclasses 1 value	n int64 12 30	pair_name stringlengths 21 21	flip_distance int64 3 23	flip_sequence stringlengths 11 120	mis_sequence stringlengths 86 2.36k	mis_start stringlengths 18 105	mis_target stringlengths 18 105	triangulation_edges_start stringlengths 36 150	triangulation_edges_target stringlengths 36 151
train	12	train_n12_pair_000000	8	2-8 2-11 2-5 2-4 0-2 9-11 8-11 5-11	0 18 19 22 25 40 44 52 53\|0 18 19 25 40 43 44 52 53\|0 3 18 19 40 43 44 52 53\|0 2 3 18 40 43 44 52 53\|0 1 2 3 40 43 44 52 53\|1 2 3 9 40 43 44 52 53\|1 2 3 9 40 43 44 51 52\|1 2 3 9 40 42 43 44 51\|1 2 3 8 9 40 42 44 51	0 18 19 22 25 40 44 52 53	1 2 3 8 9 40 42 44 51	0-2 2-4 2-5 2-8 2-11 5-8 6-8 8-11 9-11	0-3 0-4 0-5 0-10 1-3 5-8 5-10 6-8 8-10
train	12	train_n12_pair_000001	6	0-5 0-6 0-10 0-8 3-5 8-10	0 1 3 4 6 8 26 44 51\|0 1 4 6 8 26 27 44 51\|0 1 6 8 26 27 29 44 51\|0 1 6 26 27 29 44 51 52\|0 1 26 27 29 32 44 51 52\|0 1 27 29 32 33 44 51 52\|0 1 27 29 32 33 44 52 53	0 1 3 4 6 8 26 44 51	0 1 27 29 32 33 44 52 53	0-2 0-3 0-5 0-6 0-8 0-10 3-5 6-8 8-10	0-2 0-3 3-6 3-8 3-11 4-6 6-8 8-11 9-11
train	12	train_n12_pair_000002	5	0-4 0-3 0-2 4-7 7-11	0 1 2 5 34 39 48 49 50\|0 1 5 28 34 39 48 49 50\|0 5 21 28 34 39 48 49 50\|5 13 21 28 34 39 48 49 50\|5 13 21 26 28 39 48 49 50\|5 8 13 21 26 28 39 48 49	0 1 2 5 34 39 48 49 50	5 8 13 21 26 28 39 48 49	0-2 0-3 0-4 0-7 4-7 5-7 7-9 7-10 7-11	0-7 0-10 1-7 2-7 3-5 3-7 5-7 7-9 7-10
train	12	train_n12_pair_000003	3	0-9 0-8 2-4	0 6 7 18 20 21 22 33 53\|0 6 18 20 21 22 33 52 53\|0 18 20 21 22 25 33 52 53\|0 20 21 22 25 27 33 52 53	0 6 7 18 20 21 22 33 53	0 20 21 22 25 27 33 52 53	0-2 0-8 0-9 2-4 2-6 2-7 2-8 4-6 9-11	0-2 2-6 2-7 2-8 2-11 3-6 4-6 8-11 9-11
train	12	train_n12_pair_000004	7	3-10 0-3 0-10 4-6 3-6 7-9 6-9	1 8 9 27 31 33 45 46 48\|1 4 8 9 27 33 45 46 48\|4 8 9 12 27 33 45 46 48\|4 9 12 27 33 45 46 47 48\|4 9 12 26 27 45 46 47 48\|4 9 11 12 26 45 46 47 48\|4 9 11 12 26 44 45 46 47\|4 9 11 12 26 44 46 47 51	1 8 9 27 31 33 45 46 48	4 9 11 12 26 44 46 47 51	0-3 0-10 1-3 3-6 3-10 4-6 6-9 6-10 7-9	0-6 1-3 1-5 1-6 3-5 6-8 6-10 6-11 8-10
train	12	train_n12_pair_000005	5	1-6 8-11 8-10 0-8 1-8	6 12 13 14 18 20 33 51 52\|6 13 14 18 20 21 33 51 52\|6 8 13 14 18 20 21 33 51\|6 7 8 13 14 18 20 21 33\|7 8 13 14 15 18 20 21 33\|7 8 13 15 18 20 21 33 48	6 12 13 14 18 20 33 51 52	7 8 13 15 18 20 21 33 48	0-8 1-6 1-7 1-8 2-4 2-6 4-6 8-10 8-11	0-9 0-10 1-7 1-9 2-4 2-6 2-7 4-6 7-9
train	12	train_n12_pair_000006	9	0-5 0-6 0-4 2-4 6-8 6-9 6-11 4-6 4-11	0 2 3 4 18 44 45 46 47\|0 2 4 18 33 44 45 46 47\|0 2 18 33 38 44 45 46 47\|0 18 25 33 38 44 45 46 47\|0 25 32 33 38 44 45 46 47\|0 25 32 33 38 45 46 47 48\|0 25 32 33 38 46 47 48 49\|0 25 32 33 37 38 46 48 49\|0 25 32 37 38 42 46 48 49\|0 25 31 32 37 42 46 48 49	0 2 3 4 18 44 45 46 47	0 25 31 32 37 42 46 48 49	0-2 0-4 0-5 0-6 2-4 6-8 6-9 6-10 6-11	0-2 2-11 3-10 3-11 4-10 5-10 6-10 7-9 7-10
train	12	train_n12_pair_000007	9	1-9 1-11 4-9 4-8 4-10 4-7 1-4 2-4 5-7	10 15 16 17 18 34 35 36 39\|10 16 17 18 34 35 36 37 39\|8 10 16 18 34 35 36 37 39\|8 10 16 18 34 35 37 39 51\|8 10 16 18 34 37 39 49 51\|8 10 13 16 18 34 39 49 51\|8 10 11 13 16 18 39 49 51\|8 11 13 16 18 19 39 49 51\|8 11 13 16 19 26 39 49 51\|8 11 12 13 16 19 26 49 51	10 15 16 17 18 34 35 36 39	8 11 12 13 16 19 26 49 51	1-4 1-9 1-10 1-11 2-4 4-7 4-8 4-9 5-7	0-10 1-5 1-6 1-7 1-10 2-5 3-5 7-10 8-10
train	12	train_n12_pair_000008	6	3-11 0-3 0-2 4-10 5-9 7-9	0 1 32 36 37 38 41 45 48\|0 1 2 36 37 38 41 45 48\|0 2 18 36 37 38 41 45 48\|2 10 18 36 37 38 41 45 48\|2 10 18 36 38 41 45 48 53\|2 10 18 33 36 38 45 48 53\|2 10 18 33 36 38 44 45 53	0 1 32 36 37 38 41 45 48	2 10 18 33 36 38 44 45 53	0-2 0-3 3-11 4-9 4-10 4-11 5-9 6-9 7-9	0-4 1-4 2-4 4-6 4-9 4-11 6-8 6-9 9-11
train	12	train_n12_pair_000009	5	0-2 4-9 0-9 7-9 9-11	0 2 7 18 36 41 45 48 53\|2 7 10 18 36 41 45 48 53\|2 3 7 10 18 41 45 48 53\|2 3 10 18 41 43 45 48 53\|2 3 10 18 41 43 44 45 53\|2 3 10 18 41 42 43 44 45	0 2 7 18 36 41 45 48 53	2 3 10 18 41 42 43 44 45	0-2 0-4 0-9 2-4 4-9 5-9 6-9 7-9 9-11	0-4 0-5 1-4 2-4 5-9 5-10 5-11 6-8 6-9
train	12	train_n12_pair_000010	6	2-4 6-11 4-6 6-8 8-10 8-11	0 18 25 33 38 44 47 51 52\|0 25 32 33 38 44 47 51 52\|0 25 32 33 35 38 44 51 52\|0 25 32 35 38 40 44 51 52\|0 25 32 35 38 39 40 51 52\|0 25 32 35 38 39 40 52 53\|0 25 32 35 36 38 39 40 53	0 18 25 33 38 44 47 51 52	0 25 32 35 36 38 39 40 53	0-2 2-4 2-11 4-6 4-11 6-8 6-11 8-10 8-11	0-2 2-11 3-11 4-8 4-9 4-11 5-7 5-8 9-11
train	12	train_n12_pair_000011	7	1-3 3-6 0-6 0-8 0-9 0-5 6-8	1 4 6 7 9 26 27 44 53\|0 1 4 6 7 26 27 44 53\|0 1 3 4 6 7 26 44 53\|0 1 3 6 7 26 40 44 53\|0 1 3 7 26 40 41 44 53\|0 1 3 26 40 41 43 44 53\|0 1 26 32 40 41 43 44 53\|0 1 26 32 39 40 41 43 53	1 4 6 7 9 26 27 44 53	0 1 26 32 39 40 41 43 53	0-3 0-6 0-8 0-9 1-3 3-5 3-6 6-8 9-11	0-2 0-3 3-5 3-11 5-7 5-8 5-9 5-11 9-11
train	12	train_n12_pair_000012	6	0-9 0-8 0-10 2-7 3-7 3-6	0 5 6 7 8 21 27 28 33\|0 5 6 8 21 27 28 33 51\|0 5 8 21 27 28 33 49 51\|0 5 21 27 28 33 49 50 51\|0 1 5 27 28 33 49 50 51\|0 1 4 5 27 33 49 50 51\|0 1 2 4 5 33 49 50 51	0 5 6 7 8 21 27 28 33	0 1 2 4 5 33 49 50 51	0-2 0-7 0-8 0-9 0-10 2-7 3-6 3-7 4-6	0-2 0-3 0-4 0-6 0-7 4-6 7-10 7-11 8-10
train	12	train_n12_pair_000013	6	1-6 2-6 0-6 4-6 7-10 7-11	4 5 12 20 27 33 48 49 50\|0 4 5 20 27 33 48 49 50\|0 1 4 5 27 33 48 49 50\|0 1 5 27 28 33 48 49 50\|0 1 5 26 27 28 48 49 50\|0 1 5 26 27 28 48 50 53\|0 1 5 7 26 27 28 48 53	4 5 12 20 27 33 48 49 50	0 1 5 7 26 27 28 48 53	0-6 0-7 1-6 2-6 3-6 4-6 7-9 7-10 7-11	0-2 0-3 0-7 0-9 3-5 3-6 3-7 7-9 9-11
train	12	train_n12_pair_000014	6	0-2 0-6 3-6 6-9 6-8 6-10	0 4 20 26 27 44 45 46 47\|4 12 20 26 27 44 45 46 47\|12 17 20 26 27 44 45 46 47\|12 17 19 20 26 44 45 46 47\|12 17 19 20 26 44 46 47 51\|12 17 19 20 26 46 47 49 51\|12 17 19 20 26 47 49 50 51	0 4 20 26 27 44 45 46 47	12 17 19 20 26 47 49 50 51	0-2 0-6 2-6 3-5 3-6 6-8 6-9 6-10 6-11	1-6 1-11 2-5 2-6 3-5 6-11 7-10 7-11 8-10
train	12	train_n12_pair_000015	9	0-3 0-2 3-11 5-7 5-8 5-10 4-10 4-11 5-9	0 1 32 37 38 39 40 41 42\|0 25 32 37 38 39 40 41 42\|17 25 32 37 38 39 40 41 42\|17 18 25 37 38 39 40 41 42\|17 18 25 37 38 40 41 42 44\|17 18 25 37 38 41 42 44 45\|17 18 25 36 37 38 41 44 45\|17 18 25 36 38 41 44 45 53\|17 18 23 25 36 41 44 45 53\|17 18 23 25 33 36 44 45 53	0 1 32 37 38 39 40 41 42	17 18 23 25 33 36 44 45 53	0-2 0-3 3-11 4-10 4-11 5-7 5-8 5-9 5-10	1-11 2-4 2-9 2-11 4-6 4-9 6-8 6-9 9-11
train	12	train_n12_pair_000016	7	0-2 3-11 4-11 7-9 6-9 6-11 9-11	0 25 32 33 38 45 47 48 53\|17 25 32 33 38 45 47 48 53\|17 18 25 33 38 45 47 48 53\|17 18 20 25 33 45 47 48 53\|17 18 20 25 33 44 45 47 53\|17 18 20 25 33 44 47 52 53\|17 18 20 22 25 33 44 52 53\|17 18 20 22 25 33 44 51 52	0 25 32 33 38 45 47 48 53	17 18 20 22 25 33 44 51 52	0-2 2-11 3-11 4-6 4-11 6-9 6-11 7-9 9-11	1-11 2-4 2-6 2-8 2-11 4-6 6-8 8-10 8-11
train	12	train_n12_pair_000017	9	1-6 1-11 2-4 2-5 6-11 7-9 7-11 5-11 9-11	11 12 17 18 19 47 48 50 53\|11 17 18 19 43 47 48 50 53\|3 11 18 19 43 47 48 50 53\|3 11 19 26 43 47 48 50 53\|3 9 11 26 43 47 48 50 53\|3 9 11 26 39 43 48 50 53\|3 9 11 26 39 43 50 52 53\|3 9 11 26 39 40 43 52 53\|3 6 9 11 26 39 40 52 53\|3 6 9 11 26 39 40 51 52	11 12 17 18 19 47 48 50 53	3 6 9 11 26 39 40 51 52	1-5 1-6 1-11 2-4 2-5 6-11 7-9 7-11 9-11	0-5 0-8 1-3 1-5 3-5 5-7 5-8 8-10 8-11
train	12	train_n12_pair_000018	6	0-9 0-10 1-3 0-3 6-9 4-6	1 2 7 8 9 33 36 45 48\|1 2 8 9 33 36 37 45 48\|1 2 9 33 36 37 38 45 48\|0 1 2 33 36 37 38 45 48\|0 2 18 33 36 37 38 45 48\|0 2 18 33 34 36 37 38 48\|0 2 18 34 36 37 38 39 48	1 2 7 8 9 33 36 45 48	0 2 18 34 36 37 38 39 48	0-3 0-4 0-9 0-10 1-3 4-6 4-9 6-9 7-9	0-2 0-4 2-4 4-7 4-9 4-10 4-11 5-7 7-9
train	12	train_n12_pair_000019	5	0-7 0-8 1-3 3-5 5-7	3 5 6 9 11 26 39 51 52\|3 6 9 11 26 39 40 51 52\|3 9 11 26 39 40 43 51 52\|3 11 19 26 39 40 43 51 52\|3 11 18 19 39 40 43 51 52\|3 11 18 19 40 43 44 51 52	3 5 6 9 11 26 39 51 52	3 11 18 19 40 43 44 51 52	0-5 0-7 0-8 1-3 1-5 3-5 5-7 8-10 8-11	0-5 1-5 2-4 2-5 5-8 5-11 6-8 8-10 8-11
train	12	train_n12_pair_000020	6	2-4 5-11 0-5 5-10 6-9 7-9	3 11 18 19 41 42 43 45 48\|3 11 19 26 41 42 43 45 48\|3 8 11 19 26 41 42 45 48\|8 11 16 19 26 41 42 45 48\|8 11 15 16 19 26 41 45 48\|8 11 15 16 19 26 39 41 48\|8 11 15 16 19 26 39 40 41	3 11 18 19 41 42 43 45 48	8 11 15 16 19 26 39 40 41	0-5 1-5 2-4 2-5 5-9 5-10 5-11 6-9 7-9	0-10 1-5 1-9 1-10 2-5 3-5 5-7 5-8 5-9
train	12	train_n12_pair_000021	5	0-5 0-9 1-3 0-3 9-11	1 2 3 7 9 39 40 41 53\|1 2 7 9 36 39 40 41 53\|1 2 9 36 38 39 40 41 53\|0 1 2 36 38 39 40 41 53\|0 2 18 36 38 39 40 41 53\|0 2 18 36 37 38 39 40 41	1 2 3 7 9 39 40 41 53	0 2 18 36 37 38 39 40 41	0-3 0-4 0-5 0-9 1-3 5-7 5-8 5-9 9-11	0-2 0-4 2-4 4-9 4-10 4-11 5-7 5-8 5-9
train	12	train_n12_pair_000022	8	1-11 2-7 2-6 2-11 3-6 4-6 9-11 7-11	17 20 21 25 27 33 48 50 53\|0 20 21 25 27 33 48 50 53\|0 20 25 27 33 47 48 50 53\|0 25 27 32 33 47 48 50 53\|0 1 27 32 33 47 48 50 53\|0 1 32 33 38 47 48 50 53\|0 1 32 38 43 47 48 50 53\|0 1 32 38 43 47 48 49 50\|0 1 32 38 43 46 47 48 49	17 20 21 25 27 33 48 50 53	0 1 32 38 43 46 47 48 49	1-11 2-6 2-7 2-11 3-6 4-6 7-9 7-11 9-11	0-2 0-3 3-11 4-11 5-11 6-10 6-11 7-9 7-10
train	12	train_n12_pair_000023	7	1-11 1-3 4-7 5-7 7-11 7-9 9-11	9 17 28 32 34 39 48 50 53\|1 9 28 32 34 39 48 50 53\|0 1 28 32 34 39 48 50 53\|0 1 26 28 32 39 48 50 53\|0 1 26 27 28 32 48 50 53\|0 1 26 27 28 30 32 48 53\|0 1 26 27 28 29 30 32 53\|0 1 26 27 28 29 30 31 32	9 17 28 32 34 39 48 50 53	0 1 26 27 28 29 30 31 32	1-3 1-11 3-7 3-11 4-7 5-7 7-9 7-11 9-11	0-2 0-3 3-5 3-6 3-7 3-8 3-9 3-10 3-11
train	12	train_n12_pair_000024	6	0-2 0-7 2-4 2-7 1-7 5-7	0 5 18 19 21 39 50 51 52\|5 13 18 19 21 39 50 51 52\|13 17 18 19 21 39 50 51 52\|13 17 19 21 26 39 50 51 52\|11 13 17 19 26 39 50 51 52\|11 17 19 26 39 43 50 51 52\|11 17 19 26 43 47 50 51 52	0 5 18 19 21 39 50 51 52	11 17 19 26 43 47 50 51 52	0-2 0-7 2-4 2-5 2-7 5-7 7-11 8-10 8-11	1-5 1-11 2-5 3-5 5-11 6-11 7-11 8-10 8-11
train	12	train_n12_pair_000025	6	0-7 0-5 0-4 1-4 2-4 8-10	2 3 5 10 18 39 50 51 52\|2 3 10 18 39 43 50 51 52\|2 10 18 38 39 43 50 51 52\|10 17 18 38 39 43 50 51 52\|17 18 25 38 39 43 50 51 52\|17 25 32 38 39 43 50 51 52\|17 25 32 38 39 43 50 52 53	2 3 5 10 18 39 50 51 52	17 25 32 38 39 43 50 52 53	0-4 0-5 0-7 1-4 2-4 5-7 7-11 8-10 8-11	1-11 2-11 3-11 4-11 5-7 5-11 7-11 8-11 9-11
train	12	train_n12_pair_000026	8	0-3 1-3 5-11 6-8 6-10 5-10 0-5 6-9	1 3 9 26 42 43 44 45 46\|3 9 11 26 42 43 44 45 46\|3 11 19 26 42 43 44 45 46\|3 8 11 19 26 42 44 45 46\|3 8 11 19 26 42 45 46 48\|3 8 11 19 26 41 42 45 48\|3 7 8 11 19 26 41 45 48\|7 8 11 15 19 26 41 45 48\|7 8 11 15 19 26 39 41 48	1 3 9 26 42 43 44 45 46	7 8 11 15 19 26 39 41 48	0-3 0-5 1-3 3-5 5-10 5-11 6-8 6-9 6-10	0-9 0-10 1-5 1-9 2-5 3-5 5-7 5-9 7-9
train	12	train_n12_pair_000027	9	1-3 1-11 1-6 1-5 6-10 6-11 7-10 7-11 8-10	9 11 12 17 26 46 47 49 51\|11 12 17 19 26 46 47 49 51\|4 11 12 19 26 46 47 49 51\|3 4 11 19 26 46 47 49 51\|0 3 4 19 26 46 47 49 51\|0 3 4 19 26 47 49 50 51\|0 3 4 5 19 26 49 50 51\|0 3 4 5 19 26 50 51 52\|0 3 4 5 6 19 26 51 52\|0 3 4 5 6 19 26 52 53	9 11 12 17 26 46 47 49 51	0 3 4 5 6 19 26 52 53	1-3 1-5 1-6 1-11 3-5 6-10 6-11 7-10 8-10	0-2 0-5 0-6 0-7 0-8 2-5 3-5 8-11 9-11
train	12	train_n12_pair_000028	7	0-2 2-8 3-7 3-8 4-6 3-6 1-3	0 6 7 22 27 28 29 33 53\|6 7 14 22 27 28 29 33 53\|6 7 9 14 27 28 29 33 53\|6 7 9 14 27 29 33 44 53\|6 7 9 12 14 27 33 44 53\|6 7 9 12 14 26 27 44 53\|6 7 9 11 12 14 26 44 53\|6 7 11 12 14 19 26 44 53	0 6 7 22 27 28 29 33 53	6 7 11 12 14 19 26 44 53	0-2 0-8 0-9 2-8 3-6 3-7 3-8 4-6 9-11	0-8 0-9 1-5 1-6 1-8 2-5 3-5 6-8 9-11
train	12	train_n12_pair_000029	6	1-3 8-10 4-10 3-10 0-3 0-10	1 8 9 31 35 37 39 40 51\|0 1 8 31 35 37 39 40 51\|0 1 8 31 35 36 37 39 40\|0 1 8 30 31 35 36 39 40\|0 1 7 8 30 35 36 39 40\|0 7 8 23 30 35 36 39 40\|0 7 23 30 35 36 39 40 53	1 8 9 31 35 37 39 40 51	0 7 23 30 35 36 39 40 53	0-3 0-10 1-3 3-10 4-8 4-10 5-7 5-8 8-10	0-2 0-9 2-9 3-9 4-8 4-9 5-7 5-8 9-11
train	12	train_n12_pair_000030	8	2-7 0-2 3-5 2-5 5-7 0-7 7-9 7-10	0 5 8 19 21 26 39 48 49\|0 3 5 8 19 26 39 48 49\|3 5 8 11 19 26 39 48 49\|3 5 8 11 18 19 39 48 49\|3 5 8 10 11 18 39 48 49\|3 4 5 8 10 11 18 48 49\|3 4 8 10 11 18 46 48 49\|3 4 8 10 11 18 46 49 51\|3 4 8 10 11 18 44 46 51	0 5 8 19 21 26 39 48 49	3 4 8 10 11 18 44 46 51	0-2 0-7 0-10 2-5 2-7 3-5 5-7 7-9 7-10	0-5 0-6 0-10 1-4 1-5 2-4 6-8 6-10 8-10
train	12	train_n12_pair_000031	7	3-11 4-11 2-11 1-11 4-10 2-4 8-10	17 25 32 33 34 37 38 49 51\|17 18 25 33 34 37 38 49 51\|17 18 24 25 33 34 37 49 51\|16 17 18 24 33 34 37 49 51\|8 16 18 24 33 34 37 49 51\|8 16 18 21 24 33 34 49 51\|8 16 21 24 28 33 34 49 51\|8 16 21 24 28 33 34 48 49	17 25 32 33 34 37 38 49 51	8 16 21 24 28 33 34 48 49	1-11 2-11 3-11 4-6 4-7 4-10 4-11 7-10 8-10	0-10 1-10 2-7 2-10 3-7 4-6 4-7 7-9 7-10
train	12	train_n12_pair_000032	5	0-7 1-3 1-6 8-11 0-8	5 6 9 10 12 13 33 51 52\|6 9 10 12 13 14 33 51 52\|6 10 12 13 14 18 33 51 52\|6 10 13 14 18 33 34 51 52\|6 8 10 13 14 18 33 34 51\|8 10 13 14 16 18 33 34 51	5 6 9 10 12 13 33 51 52	8 10 13 14 16 18 33 34 51	0-7 0-8 1-3 1-4 1-6 1-7 4-6 8-10 8-11	0-10 1-4 1-7 1-8 1-10 2-4 4-6 4-7 8-10
train	12	train_n12_pair_000033	7	0-9 1-8 1-6 3-6 6-8 0-8 0-10	6 7 8 12 14 20 27 33 44\|6 8 12 14 20 27 33 44 51\|4 6 8 12 20 27 33 44 51\|0 4 6 8 20 27 33 44 51\|0 4 6 8 18 20 33 44 51\|0 4 5 6 8 18 20 33 51\|0 4 5 8 18 20 33 49 51\|0 4 5 18 20 33 49 50 51	6 7 8 12 14 20 27 33 44	0 4 5 18 20 33 49 50 51	0-8 0-9 0-10 1-6 1-8 2-6 3-6 4-6 6-8	0-2 0-6 0-7 2-4 2-6 4-6 7-10 7-11 8-10
train	12	train_n12_pair_000034	8	5-10 3-10 3-11 0-3 0-2 7-9 7-10 6-10	0 1 26 31 32 42 46 48 49\|0 1 26 27 31 32 46 48 49\|0 1 26 27 32 46 47 48 49\|0 1 4 26 27 46 47 48 49\|0 4 20 26 27 46 47 48 49\|4 12 20 26 27 46 47 48 49\|4 12 20 26 27 46 47 49 51\|4 12 20 26 27 44 46 47 51\|4 12 20 26 27 44 47 51 52	0 1 26 31 32 42 46 48 49	4 12 20 26 27 44 47 51 52	0-2 0-3 3-5 3-10 3-11 5-10 6-10 7-9 7-10	0-6 1-6 2-6 3-5 3-6 6-8 6-11 8-10 8-11
train	12	train_n12_pair_000035	7	0-4 0-9 1-4 1-3 5-9 6-9 9-11	2 7 9 10 36 41 44 45 53\|7 9 10 15 36 41 44 45 53\|9 10 15 17 36 41 44 45 53\|9 15 17 30 36 41 44 45 53\|15 17 23 30 36 41 44 45 53\|15 17 23 30 33 36 44 45 53\|15 17 23 30 33 35 36 44 53\|15 16 17 23 30 33 35 36 44	2 7 9 10 36 41 44 45 53	15 16 17 23 30 33 35 36 44	0-4 0-9 1-3 1-4 4-9 5-9 6-8 6-9 9-11	1-9 1-10 1-11 2-9 3-9 4-6 4-8 4-9 6-8
train	12	train_n12_pair_000036	8	1-6 2-5 2-6 0-6 6-8 6-11 8-10 8-11	4 12 18 19 20 44 47 51 52\|0 4 18 19 20 44 47 51 52\|0 4 18 20 33 44 47 51 52\|0 2 4 18 33 44 47 51 52\|0 2 18 33 38 44 47 51 52\|0 2 18 33 38 47 50 51 52\|0 2 18 33 34 38 50 51 52\|0 2 18 33 34 38 50 52 53\|0 2 18 33 34 38 48 50 53	4 12 18 19 20 44 47 51 52	0 2 18 33 34 38 48 50 53	0-6 1-6 2-4 2-5 2-6 6-8 6-11 8-10 8-11	0-2 0-4 2-4 4-6 4-7 4-11 7-9 7-11 9-11
train	12	train_n12_pair_000037	8	1-5 1-11 2-5 6-8 6-10 5-10 8-10 7-10	11 17 18 19 42 43 44 46 51\|17 18 19 25 42 43 44 46 51\|0 18 19 25 42 43 44 46 51\|0 18 25 38 42 43 44 46 51\|0 18 25 38 42 43 46 49 51\|0 18 25 38 39 42 43 49 51\|0 18 25 38 39 43 49 50 51\|0 18 25 38 39 43 48 49 50\|0 18 25 38 39 43 48 50 53	11 17 18 19 42 43 44 46 51	0 18 25 38 39 43 48 50 53	1-5 1-11 2-4 2-5 5-10 5-11 6-8 6-10 8-10	0-2 2-4 2-11 4-11 5-7 5-11 7-9 7-11 9-11
train	12	train_n12_pair_000038	8	0-9 1-9 2-9 4-9 4-8 5-7 4-7 9-11	7 15 23 30 34 35 36 39 53\|15 17 23 30 34 35 36 39 53\|17 23 25 30 34 35 36 39 53\|17 25 30 32 34 35 36 39 53\|17 25 29 30 32 34 35 39 53\|17 25 28 29 30 32 34 39 53\|17 25 28 29 30 32 33 34 53\|17 25 27 28 29 30 32 33 53\|17 25 27 28 29 30 31 32 33	7 15 23 30 34 35 36 39 53	17 25 27 28 29 30 31 32 33	0-9 1-9 2-9 3-9 4-7 4-8 4-9 5-7 9-11	1-11 2-11 3-6 3-7 3-8 3-9 3-10 3-11 4-6
train	12	train_n12_pair_000039	5	2-5 1-5 3-5 5-7 7-11	3 5 11 19 26 39 48 50 53\|3 5 9 11 26 39 48 50 53\|1 3 5 9 26 39 48 50 53\|1 2 3 5 9 39 48 50 53\|1 2 3 4 5 9 48 50 53\|1 2 3 4 5 7 9 48 53	3 5 11 19 26 39 48 50 53	1 2 3 4 5 7 9 48 53	0-5 0-7 1-5 2-5 3-5 5-7 7-9 7-11 9-11	0-3 0-4 0-5 0-6 0-7 0-9 1-3 7-9 9-11
train	12	train_n12_pair_000040	6	3-10 3-11 0-3 6-8 6-9 6-10	1 9 27 31 32 33 44 45 46\|1 9 27 32 33 44 45 46 47\|1 4 9 27 33 44 45 46 47\|4 9 12 27 33 44 45 46 47\|4 9 12 27 33 45 46 47 48\|4 9 12 27 33 46 47 48 49\|4 9 12 27 33 47 48 49 50	1 9 27 31 32 33 44 45 46	4 9 12 27 33 47 48 49 50	0-3 1-3 3-6 3-10 3-11 4-6 6-8 6-9 6-10	0-6 1-3 1-6 3-6 4-6 6-11 7-9 7-10 7-11
train	12	train_n12_pair_000041	8	0-7 0-9 0-10 2-4 4-7 4-6 7-9 1-7	5 7 8 10 13 18 33 34 48\|7 8 10 13 15 18 33 34 48\|8 10 13 15 16 18 33 34 48\|10 13 15 16 17 18 33 34 48\|9 10 13 15 16 17 33 34 48\|9 10 12 13 15 16 17 33 48\|9 10 11 12 13 15 16 17 48\|9 10 11 12 13 14 15 16 17\|9 10 11 12 14 15 16 17 44	5 7 8 10 13 18 33 34 48	9 10 11 12 14 15 16 17 44	0-7 0-9 0-10 1-4 1-7 2-4 4-6 4-7 7-9	1-3 1-4 1-5 1-6 1-8 1-9 1-10 1-11 6-8
train	12	train_n12_pair_000042	7	1-11 3-10 5-7 5-10 4-10 7-10 6-10	16 17 24 31 37 39 42 48 49\|8 16 24 31 37 39 42 48 49\|8 16 18 24 37 39 42 48 49\|8 16 18 24 37 42 46 48 49\|8 16 18 24 33 37 46 48 49\|8 16 18 20 24 33 46 48 49\|8 16 18 20 24 33 45 46 48\|8 16 18 20 23 24 33 45 48	16 17 24 31 37 39 42 48 49	8 16 18 20 23 24 33 45 48	1-10 1-11 2-10 3-10 4-10 5-7 5-10 7-9 7-10	0-10 1-10 2-4 2-6 2-9 2-10 4-6 6-9 7-9
train	12	train_n12_pair_000043	6	2-7 2-4 0-2 4-7 5-7 7-10	0 5 8 18 21 34 39 48 49\|0 2 5 8 18 34 39 48 49\|0 1 2 5 8 34 39 48 49\|1 2 5 8 9 34 39 48 49\|1 2 3 5 8 9 39 48 49\|1 2 3 4 5 8 9 48 49\|1 2 3 4 5 7 8 9 48	0 5 8 18 21 34 39 48 49	1 2 3 4 5 7 8 9 48	0-2 0-7 0-10 2-4 2-7 4-7 5-7 7-9 7-10	0-3 0-4 0-5 0-6 0-7 0-9 0-10 1-3 7-9
train	12	train_n12_pair_000044	8	1-6 3-6 4-6 7-10 7-11 0-7 8-10 8-11	5 12 13 20 27 33 49 50 51\|5 13 20 21 27 33 49 50 51\|5 13 18 20 21 33 49 50 51\|5 13 18 19 20 21 49 50 51\|5 13 18 19 20 21 50 51 52\|5 6 13 18 19 20 21 51 52\|6 13 14 18 19 20 21 51 52\|6 13 14 18 19 20 21 52 53\|6 7 13 14 18 19 20 21 53	5 12 13 20 27 33 49 50 51	6 7 13 14 18 19 20 21 53	0-7 1-6 1-7 2-6 3-6 4-6 7-10 7-11 8-10	0-8 0-9 1-7 1-8 2-4 2-5 2-6 2-7 9-11
train	12	train_n12_pair_000045	8	2-11 0-2 3-5 5-11 6-11 4-11 3-11 6-9	0 25 26 32 43 45 47 48 53\|0 1 26 32 43 45 47 48 53\|1 9 26 32 43 45 47 48 53\|1 9 32 38 43 45 47 48 53\|1 9 32 33 38 45 47 48 53\|1 9 32 33 36 38 45 48 53\|1 9 30 32 33 36 45 48 53\|1 7 9 30 33 36 45 48 53\|1 7 9 30 33 34 36 48 53	0 25 26 32 43 45 47 48 53	1 7 9 30 33 34 36 48 53	0-2 2-11 3-5 3-11 5-11 6-9 6-11 7-9 9-11	0-3 0-9 1-3 3-9 4-6 4-7 4-9 7-9 9-11
train	12	train_n12_pair_000046	6	1-9 1-4 4-9 0-4 2-4 9-11	7 10 15 18 36 41 45 48 53\|2 7 10 18 36 41 45 48 53\|0 2 7 18 36 41 45 48 53\|0 2 3 7 18 41 45 48 53\|0 3 7 18 19 41 45 48 53\|0 3 7 19 26 41 45 48 53\|0 3 7 8 19 26 41 45 48	7 10 15 18 36 41 45 48 53	0 3 7 8 19 26 41 45 48	0-9 1-4 1-9 2-4 4-9 5-9 6-9 7-9 9-11	0-2 0-5 0-9 0-10 2-5 3-5 5-9 6-9 7-9
train	12	train_n12_pair_000047	10	0-2 0-3 3-8 4-8 1-8 0-8 9-11 8-11 5-8 5-7	0 1 6 29 35 39 40 52 53\|1 6 9 29 35 39 40 52 53\|6 9 14 29 35 39 40 52 53\|6 9 10 14 35 39 40 52 53\|6 9 10 11 14 39 40 52 53\|3 6 9 10 11 39 40 52 53\|3 9 10 11 39 40 43 52 53\|3 9 10 11 39 40 43 51 52\|3 9 10 11 39 40 42 43 51\|3 9 10 11 39 42 43 49 51\|3 9 10 11 42 43 46 49 51	0 1 6 29 35 39 40 52 53	3 9 10 11 42 43 46 49 51	0-2 0-3 0-8 3-8 4-8 5-7 5-8 8-11 9-11	0-5 1-3 1-4 1-5 5-10 5-11 6-10 7-10 8-10
train	12	train_n12_pair_000048	7	1-10 1-11 2-5 2-6 1-6 2-4 6-8	12 15 16 17 18 19 20 44 45\|12 15 17 18 19 20 44 45 53\|7 12 15 18 19 20 44 45 53\|7 12 15 18 20 33 44 45 53\|7 10 12 15 18 33 44 45 53\|7 10 15 18 33 36 44 45 53\|7 9 10 15 33 36 44 45 53\|7 9 10 15 33 36 45 48 53	12 15 16 17 18 19 20 44 45	7 9 10 15 33 36 45 48 53	1-6 1-9 1-10 1-11 2-4 2-5 2-6 6-8 6-9	0-9 1-3 1-4 1-9 4-6 4-9 6-9 7-9 9-11
train	12	train_n12_pair_000049	7	1-4 1-11 1-10 5-9 7-9 6-9 1-9	10 11 15 16 17 18 41 45 48\|11 15 16 17 18 19 41 45 48\|8 11 15 16 18 19 41 45 48\|7 8 11 15 18 19 41 45 48\|7 8 11 12 15 18 19 45 48\|7 8 11 12 15 18 19 44 45\|7 8 11 12 14 15 18 19 44\|6 7 8 11 12 14 18 19 44	10 11 15 16 17 18 41 45 48	6 7 8 11 12 14 18 19 44	1-4 1-5 1-9 1-10 1-11 2-4 5-9 6-9 7-9	0-8 0-9 0-10 1-5 1-6 1-8 2-4 2-5 6-8
train	12	train_n12_pair_000050	8	2-11 4-6 7-11 6-11 8-11 5-11 9-11 4-11	17 25 32 33 38 47 50 52 53\|9 17 32 33 38 47 50 52 53\|9 17 32 38 43 47 50 52 53\|9 17 32 38 43 44 47 52 53\|9 17 32 38 40 43 44 52 53\|9 17 32 38 40 41 43 44 53\|9 17 32 36 38 40 41 44 53\|9 17 32 36 37 38 40 41 44\|9 17 31 32 36 37 40 41 44	17 25 32 33 38 47 50 52 53	9 17 31 32 36 37 40 41 44	1-11 2-11 3-11 4-6 4-11 6-11 7-11 8-11 9-11	1-3 1-11 3-10 3-11 4-9 4-10 5-8 5-9 6-8
train	12	train_n12_pair_000051	7	2-7 1-7 0-7 3-5 7-11 5-7 9-11	5 13 19 21 26 39 50 52 53\|5 11 13 19 26 39 50 52 53\|3 5 11 19 26 39 50 52 53\|3 11 19 26 39 43 50 52 53\|3 11 18 19 39 43 50 52 53\|3 11 18 19 39 40 43 52 53\|3 11 18 19 40 43 44 52 53\|3 11 18 19 40 43 44 51 52	5 13 19 21 26 39 50 52 53	3 11 18 19 40 43 44 51 52	0-7 1-7 2-5 2-7 3-5 5-7 7-11 8-11 9-11	0-5 1-5 2-4 2-5 5-8 5-11 6-8 8-10 8-11
train	12	train_n12_pair_000052	7	2-6 2-4 6-11 0-6 1-6 4-6 9-11	4 12 18 20 33 47 48 50 53\|4 10 12 18 33 47 48 50 53\|4 9 10 12 33 47 48 50 53\|4 5 9 10 12 33 48 50 53\|5 9 10 12 13 33 48 50 53\|5 9 10 13 33 34 48 50 53\|5 9 10 13 34 39 48 50 53\|5 9 10 13 34 39 48 49 50	4 12 18 20 33 47 48 50 53	5 9 10 13 34 39 48 49 50	0-6 1-6 2-4 2-6 4-6 6-11 7-9 7-11 9-11	0-7 1-3 1-4 1-7 4-7 5-7 7-9 7-10 7-11
train	12	train_n12_pair_000053	3	3-10 6-9 5-9	17 24 25 26 31 41 42 45 48\|17 19 24 25 26 41 42 45 48\|17 19 24 25 26 39 41 42 48\|17 19 24 25 26 39 42 48 49	17 24 25 26 31 41 42 45 48	17 19 24 25 26 39 42 48 49	1-11 2-10 2-11 3-5 3-10 5-9 5-10 6-9 7-9	1-11 2-5 2-10 2-11 3-5 5-7 5-10 7-9 7-10
train	12	train_n12_pair_000054	6	1-11 2-9 1-9 2-8 3-5 5-7	15 17 22 23 26 28 29 39 53\|7 15 22 23 26 28 29 39 53\|7 14 15 22 26 28 29 39 53\|6 7 14 22 26 28 29 39 53\|6 7 9 14 26 28 29 39 53\|6 7 9 14 28 29 34 39 53\|6 7 9 14 28 29 33 34 53	15 17 22 23 26 28 29 39 53	6 7 9 14 28 29 33 34 53	1-9 1-11 2-8 2-9 3-5 3-7 3-8 5-7 9-11	0-8 0-9 1-3 1-8 3-7 3-8 4-6 4-7 9-11
train	12	train_n12_pair_000055	6	1-11 1-10 4-6 2-4 2-6 6-9	16 17 18 20 24 33 45 46 48\|8 16 18 20 24 33 45 46 48\|0 8 18 20 24 33 45 46 48\|0 8 18 19 20 24 45 46 48\|0 8 19 20 24 26 45 46 48\|0 8 19 24 26 42 45 46 48\|0 8 19 24 26 42 46 48 49	16 17 18 20 24 33 45 46 48	0 8 19 24 26 42 46 48 49	1-10 1-11 2-4 2-6 2-10 4-6 6-9 6-10 7-9	0-2 0-10 2-5 2-10 3-5 5-10 6-10 7-9 7-10
train	12	train_n12_pair_000056	7	3-11 0-3 4-6 4-10 4-8 4-11 8-10	0 1 32 33 34 35 37 38 51\|0 1 2 33 34 35 37 38 51\|0 2 18 33 34 35 37 38 51\|0 2 18 34 35 37 38 39 51\|0 2 18 34 35 38 39 51 52\|0 2 18 34 38 39 50 51 52\|0 2 5 18 34 39 50 51 52\|0 2 5 18 34 39 50 52 53	0 1 32 33 34 35 37 38 51	0 2 5 18 34 39 50 52 53	0-2 0-3 3-11 4-6 4-7 4-8 4-10 4-11 8-10	0-2 0-4 0-7 2-4 4-7 5-7 7-11 8-11 9-11
train	12	train_n12_pair_000057	7	2-5 2-9 1-9 1-10 3-5 7-9 5-7	15 16 17 19 23 26 39 41 48\|15 16 17 23 26 30 39 41 48\|9 15 16 17 26 30 39 41 48\|9 16 17 26 30 31 39 41 48\|9 17 26 30 31 32 39 41 48\|9 17 30 31 32 36 39 41 48\|9 17 30 31 32 36 39 40 41\|9 17 30 31 32 36 40 41 44	15 16 17 19 23 26 39 41 48	9 17 30 31 32 36 40 41 44	1-9 1-10 1-11 2-5 2-9 3-5 5-7 5-9 7-9	1-3 1-11 3-9 3-10 3-11 4-9 5-8 5-9 6-8
train	12	train_n12_pair_000058	7	1-11 1-3 3-11 6-11 5-11 8-11 7-11	9 17 32 38 43 47 50 52 53\|1 9 32 38 43 47 50 52 53\|0 1 32 38 43 47 50 52 53\|0 1 2 38 43 47 50 52 53\|0 1 2 38 39 43 50 52 53\|0 1 2 34 38 39 50 52 53\|0 1 2 34 38 39 48 50 53\|0 1 2 34 36 38 39 48 53	9 17 32 38 43 47 50 52 53	0 1 2 34 36 38 39 48 53	1-3 1-11 3-11 4-11 5-11 6-11 7-11 8-11 9-11	0-2 0-3 0-4 4-7 4-9 4-11 5-7 7-9 9-11
train	12	train_n12_pair_000059	7	0-2 0-3 0-9 5-9 6-9 7-9 9-11	0 1 2 7 36 41 45 48 53\|1 2 7 9 36 41 45 48 53\|2 7 9 10 36 41 45 48 53\|2 9 10 36 38 41 45 48 53\|2 9 10 33 36 38 45 48 53\|2 9 10 33 34 36 38 48 53\|2 9 10 33 34 35 36 38 53\|2 9 10 33 34 35 36 37 38	0 1 2 7 36 41 45 48 53	2 9 10 33 34 35 36 37 38	0-2 0-3 0-4 0-9 4-9 5-9 6-9 7-9 9-11	0-4 1-3 1-4 4-6 4-7 4-8 4-9 4-10 4-11
train	12	train_n12_pair_000060	7	0-7 3-5 2-5 1-5 5-7 7-11 9-11	3 5 11 19 26 39 48 50 53\|3 11 19 26 39 43 48 50 53\|3 11 18 19 39 43 48 50 53\|3 10 11 18 39 43 48 50 53\|2 3 10 18 39 43 48 50 53\|2 3 10 18 43 47 48 50 53\|2 3 10 18 43 45 47 48 53\|2 3 10 18 43 45 46 47 48	3 5 11 19 26 39 48 50 53	2 3 10 18 43 45 46 47 48	0-5 0-7 1-5 2-5 3-5 5-7 7-9 7-11 9-11	0-4 0-5 1-4 2-4 5-11 6-9 6-10 6-11 7-9
train	12	train_n12_pair_000061	8	2-9 2-10 1-10 3-5 3-7 5-7 4-7 7-9	8 16 23 24 26 28 30 39 48\|8 16 24 26 28 30 31 39 48\|8 9 16 26 28 30 31 39 48\|1 8 9 26 28 30 31 39 48\|1 8 9 28 30 31 34 39 48\|1 8 9 30 31 34 36 39 48\|1 8 9 30 31 33 34 36 48\|1 8 9 30 31 33 36 45 48\|1 8 9 30 31 33 36 44 45	8 16 23 24 26 28 30 39 48	1 8 9 30 31 33 36 44 45	0-10 1-10 2-9 2-10 3-5 3-7 3-9 5-7 7-9	0-3 0-10 1-3 3-9 3-10 4-6 4-9 6-8 6-9
train	12	train_n12_pair_000062	7	1-11 3-11 4-10 3-10 7-10 5-7 8-10	9 17 31 32 37 39 42 49 51\|1 9 31 32 37 39 42 49 51\|1 8 9 31 37 39 42 49 51\|1 8 9 26 31 39 42 49 51\|1 3 8 9 26 39 42 49 51\|1 3 8 9 26 39 40 42 51\|1 3 8 9 26 40 42 44 51\|1 3 8 9 26 40 41 42 44	9 17 31 32 37 39 42 49 51	1 3 8 9 26 40 41 42 44	1-3 1-11 3-10 3-11 4-10 5-7 5-10 7-10 8-10	0-3 0-5 0-10 1-3 3-5 5-8 5-9 5-10 6-8
train	12	train_n12_pair_000063	8	0-2 0-3 3-11 4-6 7-11 8-11 8-10 6-8	0 1 27 32 33 47 50 51 52\|1 9 27 32 33 47 50 51 52\|9 17 27 32 33 47 50 51 52\|9 12 17 27 33 47 50 51 52\|9 12 17 26 27 47 50 51 52\|9 12 17 26 27 44 47 51 52\|9 12 17 26 27 44 46 47 51\|9 12 17 26 27 44 45 46 47\|9 12 17 26 27 45 46 47 48	0 1 27 32 33 47 50 51 52	9 12 17 26 27 45 46 47 48	0-2 0-3 3-6 3-11 4-6 6-11 7-11 8-10 8-11	1-3 1-6 1-11 3-5 3-6 6-9 6-10 6-11 7-9
train	12	train_n12_pair_000064	7	2-6 3-5 3-6 8-10 0-8 1-8 6-8	6 8 12 14 20 26 27 44 51\|6 8 9 12 14 26 27 44 51\|6 8 9 12 14 27 33 44 51\|6 8 9 10 12 14 33 44 51\|6 7 8 9 10 12 14 33 44\|7 8 9 10 12 14 15 33 44\|7 8 9 10 12 15 33 44 45\|7 8 9 10 12 15 33 45 48	6 8 12 14 20 26 27 44 51	7 8 9 10 12 15 33 45 48	0-8 0-10 1-6 1-8 2-6 3-5 3-6 6-8 8-10	0-9 0-10 1-3 1-4 1-6 1-9 4-6 6-9 7-9
train	12	train_n12_pair_000065	6	0-7 0-10 2-5 7-10 1-7 8-10	5 8 12 13 18 19 20 49 51\|8 12 13 16 18 19 20 49 51\|12 13 16 17 18 19 20 49 51\|12 13 16 17 18 20 33 49 51\|12 13 14 16 17 18 20 33 51\|12 14 16 17 18 20 33 44 51\|12 14 15 16 17 18 20 33 44	5 8 12 13 18 19 20 49 51	12 14 15 16 17 18 20 33 44	0-7 0-10 1-6 1-7 2-4 2-5 2-6 7-10 8-10	1-6 1-8 1-9 1-10 1-11 2-4 2-6 4-6 6-8
train	12	train_n12_pair_000066	7	2-6 2-7 4-6 3-6 7-9 1-7 3-7	7 13 15 20 21 27 33 48 53\|7 13 15 21 27 28 33 48 53\|7 9 13 15 27 28 33 48 53\|7 9 13 15 26 27 28 48 53\|7 9 13 15 26 28 39 48 53\|7 9 13 14 15 26 28 39 53\|7 9 14 15 26 28 29 39 53\|7 9 14 15 26 29 39 40 53	7 13 15 20 21 27 33 48 53	7 9 14 15 26 29 39 40 53	0-9 1-7 1-9 2-6 2-7 3-6 4-6 7-9 9-11	0-9 1-3 1-8 1-9 3-5 3-8 5-7 5-8 9-11
train	12	train_n12_pair_000067	7	2-10 0-10 4-9 2-4 2-9 5-9 5-7	0 8 18 23 24 36 39 41 48\|0 7 8 18 23 36 39 41 48\|0 7 18 23 36 39 41 48 53\|0 7 18 19 23 39 41 48 53\|0 7 19 23 26 39 41 48 53\|0 3 7 19 26 39 41 48 53\|0 3 5 7 19 26 39 48 53\|0 3 4 5 7 19 26 48 53	0 8 18 23 24 36 39 41 48	0 3 4 5 7 19 26 48 53	0-2 0-10 2-4 2-9 2-10 4-9 5-7 5-9 7-9	0-2 0-5 0-6 0-7 0-9 2-5 3-5 7-9 9-11
train	12	train_n12_pair_000068	8	1-4 1-5 2-4 2-5 7-9 5-9 5-10 0-10	3 8 10 11 18 39 41 42 48\|3 8 11 18 19 39 41 42 48\|0 3 8 18 19 39 41 42 48\|0 3 8 19 26 39 41 42 48\|0 1 3 8 26 39 41 42 48\|0 1 3 8 26 39 40 41 42\|0 1 3 8 26 39 40 42 51\|0 1 3 6 8 26 39 40 51\|0 1 3 6 26 39 40 51 52	3 8 10 11 18 39 41 42 48	0 1 3 6 26 39 40 51 52	0-5 0-10 1-4 1-5 2-4 5-7 5-9 5-10 7-9	0-2 0-3 0-5 0-8 3-5 5-7 5-8 8-10 8-11
train	12	train_n12_pair_000069	7	1-7 5-7 3-5 3-7 8-11 0-8 8-10	5 6 13 21 26 28 39 51 52\|0 5 6 21 26 28 39 51 52\|0 5 6 21 26 27 28 51 52\|0 5 6 21 27 28 33 51 52\|0 5 6 20 21 27 33 51 52\|0 5 6 8 20 21 27 33 51\|0 5 8 20 21 27 33 49 51\|0 5 8 20 21 27 33 48 49	5 6 13 21 26 28 39 51 52	0 5 8 20 21 27 33 48 49	0-7 0-8 1-7 2-7 3-5 3-7 5-7 8-10 8-11	0-2 0-7 0-10 2-6 2-7 3-6 4-6 7-9 7-10
train	12	train_n12_pair_000070	7	2-6 2-7 3-5 8-11 2-8 2-11 9-11	17 19 20 21 22 25 26 52 53\|17 19 21 22 25 26 39 52 53\|17 19 22 25 26 39 40 52 53\|17 18 19 22 25 39 40 52 53\|17 18 19 22 23 25 39 40 53\|17 18 19 23 25 39 40 41 53\|15 17 18 19 23 39 40 41 53\|15 16 17 18 19 23 39 40 41	17 19 20 21 22 25 26 52 53	15 16 17 18 19 23 39 40 41	1-11 2-5 2-6 2-7 2-8 2-11 3-5 8-11 9-11	1-9 1-10 1-11 2-4 2-5 2-9 5-7 5-8 5-9
train	12	train_n12_pair_000071	5	4-11 2-4 2-11 6-11 5-11	17 18 25 38 43 44 47 52 53\|17 18 19 25 43 44 47 52 53\|17 19 25 26 43 44 47 52 53\|11 17 19 26 43 44 47 52 53\|11 17 19 26 40 43 44 52 53\|11 14 17 19 26 40 44 52 53	17 18 25 38 43 44 47 52 53	11 14 17 19 26 40 44 52 53	1-11 2-4 2-11 4-11 5-11 6-8 6-11 8-11 9-11	1-5 1-8 1-11 2-5 3-5 5-8 6-8 8-11 9-11
train	12	train_n12_pair_000072	6	1-4 2-4 5-7 5-8 9-11 0-9	2 7 10 18 36 39 40 41 53\|0 2 7 18 36 39 40 41 53\|0 1 2 7 36 39 40 41 53\|0 1 2 7 36 40 41 44 53\|0 1 2 7 36 41 44 45 53\|0 1 2 7 8 36 41 44 45\|0 1 2 8 36 37 41 44 45	2 7 10 18 36 39 40 41 53	0 1 2 8 36 37 41 44 45	0-4 0-9 1-4 2-4 4-9 5-7 5-8 5-9 9-11	0-2 0-3 0-4 0-10 4-9 4-10 5-9 6-8 6-9
train	12	train_n12_pair_000073	7	0-8 0-9 1-7 4-6 4-7 3-7 9-11	6 7 13 14 21 28 33 34 53\|7 13 14 15 21 28 33 34 53\|13 14 15 17 21 28 33 34 53\|14 15 17 21 22 28 33 34 53\|14 15 17 21 22 28 34 39 53\|14 15 17 21 22 26 28 39 53\|14 15 17 19 21 22 26 39 53\|14 15 16 17 19 21 22 26 39	6 7 13 14 21 28 33 34 53	14 15 16 17 19 21 22 26 39	0-8 0-9 1-7 1-8 2-7 3-7 4-6 4-7 9-11	1-8 1-9 1-10 1-11 2-5 2-7 2-8 3-5 5-7
train	12	train_n12_pair_000074	7	0-6 1-3 4-6 6-8 8-11 8-10 0-8	4 6 9 10 12 33 44 51 52\|6 9 10 12 14 33 44 51 52\|6 10 12 14 18 33 44 51 52\|6 10 11 12 14 18 44 51 52\|6 10 11 12 13 14 18 51 52\|6 8 10 11 12 13 14 18 51\|6 7 8 10 11 12 13 14 18\|7 8 10 11 12 13 14 15 18	4 6 9 10 12 33 44 51 52	7 8 10 11 12 13 14 15 18	0-6 0-8 1-3 1-4 1-6 4-6 6-8 8-10 8-11	0-9 0-10 1-4 1-5 1-6 1-7 1-8 1-9 2-4
train	12	train_n12_pair_000075	7	0-5 1-5 6-11 7-11 7-9 5-7 9-11	3 11 19 26 43 47 48 50 53\|11 17 19 26 43 47 48 50 53\|17 19 25 26 43 47 48 50 53\|17 19 25 26 39 43 48 50 53\|17 19 25 26 39 41 43 48 53\|17 19 25 26 39 40 41 43 53\|17 19 25 26 40 41 43 44 53\|17 19 25 26 40 41 42 43 44	3 11 19 26 43 47 48 50 53	17 19 25 26 40 41 42 43 44	0-5 1-5 2-5 3-5 5-11 6-11 7-9 7-11 9-11	1-11 2-5 2-11 3-5 5-8 5-9 5-10 5-11 6-8
train	12	train_n12_pair_000076	7	0-2 2-11 6-11 5-11 1-11 8-10 6-8	0 19 25 26 43 44 46 47 51\|17 19 25 26 43 44 46 47 51\|11 17 19 26 43 44 46 47 51\|11 17 19 26 42 43 44 46 51\|11 16 17 19 26 42 44 46 51\|8 11 16 19 26 42 44 46 51\|8 11 16 19 26 42 44 45 46\|8 11 16 19 26 42 45 46 48	0 19 25 26 43 44 46 47 51	8 11 16 19 26 42 45 46 48	0-2 2-5 2-11 3-5 5-11 6-8 6-10 6-11 8-10	0-10 1-5 1-10 2-5 3-5 5-10 6-9 6-10 7-9
train	12	train_n12_pair_000077	8	0-3 1-3 3-5 8-11 7-11 5-11 9-11 4-11	1 9 26 32 39 43 50 52 53\|9 17 26 32 39 43 50 52 53\|17 25 26 32 39 43 50 52 53\|17 25 32 38 39 43 50 52 53\|17 25 32 38 39 43 48 50 53\|17 25 32 38 39 41 43 48 53\|17 25 32 36 38 39 41 48 53\|17 25 32 36 37 38 39 41 48\|17 25 31 32 36 37 39 41 48	1 9 26 32 39 43 50 52 53	17 25 31 32 36 37 39 41 48	0-3 1-3 3-5 3-11 5-7 5-11 7-11 8-11 9-11	1-11 2-11 3-10 3-11 4-9 4-10 5-7 5-9 7-9
train	12	train_n12_pair_000078	7	5-11 4-11 2-4 2-11 6-8 6-10 5-10	0 18 25 38 42 43 44 45 46\|0 18 25 37 38 42 44 45 46\|0 18 24 25 37 42 44 45 46\|0 24 25 31 37 42 44 45 46\|0 8 24 31 37 42 44 45 46\|0 8 24 31 37 42 45 46 48\|0 8 24 31 37 41 42 45 48\|0 8 24 31 36 37 41 45 48	0 18 25 38 42 43 44 45 46	0 8 24 31 36 37 41 45 48	0-2 2-4 2-11 4-11 5-10 5-11 6-8 6-9 6-10	0-2 0-10 2-10 3-10 4-9 4-10 5-9 6-9 7-9
train	12	train_n12_pair_000079	8	1-8 1-10 1-3 4-8 3-8 5-8 5-7 5-10	9 14 16 17 29 35 39 40 51\|9 16 17 29 31 35 39 40 51\|9 17 29 31 32 35 39 40 51\|17 25 29 31 32 35 39 40 51\|17 25 26 29 31 32 39 40 51\|17 25 26 31 32 39 40 42 51\|17 25 26 31 32 39 42 49 51\|17 25 26 31 32 42 46 49 51\|17 25 26 27 31 32 46 49 51	9 14 16 17 29 35 39 40 51	17 25 26 27 31 32 46 49 51	1-3 1-8 1-10 1-11 3-8 4-8 5-7 5-8 8-10	1-11 2-11 3-5 3-6 3-10 3-11 6-10 7-10 8-10
train	12	train_n12_pair_000080	9	1-4 0-4 5-11 6-10 6-11 8-10 7-10 7-11 4-11	2 10 18 38 43 46 47 49 51\|0 2 18 38 43 46 47 49 51\|0 18 25 38 43 46 47 49 51\|0 18 25 33 38 46 47 49 51\|0 18 25 33 38 47 49 50 51\|0 18 25 33 34 38 49 50 51\|0 18 25 33 34 38 48 49 50\|0 18 25 33 34 38 48 50 53\|0 18 25 33 34 36 38 48 53\|0 18 23 25 33 34 36 48 53	2 10 18 38 43 46 47 49 51	0 18 23 25 33 34 36 48 53	0-4 1-4 2-4 4-11 5-11 6-10 6-11 7-10 8-10	0-2 2-4 2-9 2-11 4-6 4-7 4-9 7-9 9-11
train	12	train_n12_pair_000081	5	0-8 0-10 1-7 1-8 3-6	6 7 8 13 14 20 21 26 27\|7 8 13 14 15 20 21 26 27\|7 13 14 15 20 21 26 27 53\|7 14 15 20 21 22 26 27 53\|7 15 20 21 22 23 26 27 53\|7 15 19 20 21 22 23 26 53	6 7 8 13 14 20 21 26 27	7 15 19 20 21 22 23 26 53	0-8 0-9 0-10 1-7 1-8 2-6 2-7 3-5 3-6	0-9 1-9 2-5 2-6 2-7 2-8 2-9 3-5 9-11
train	12	train_n12_pair_000082	7	5-11 6-10 5-10 0-5 3-5 5-9 6-9	0 1 3 26 42 43 45 46 48\|0 1 3 8 26 42 45 46 48\|0 1 3 8 26 41 42 45 48\|0 1 3 7 8 26 41 45 48\|0 1 7 8 26 30 41 45 48\|0 1 7 8 30 36 41 45 48\|0 1 7 8 30 33 36 45 48\|0 1 7 8 30 33 34 36 48	0 1 3 26 42 43 45 46 48	0 1 7 8 30 33 34 36 48	0-2 0-3 0-5 3-5 5-10 5-11 6-9 6-10 7-9	0-2 0-3 0-9 0-10 3-9 4-6 4-7 4-9 7-9
train	12	train_n12_pair_000083	7	0-9 0-8 1-6 1-5 2-4 6-8 9-11	6 7 11 12 14 18 19 44 53\|6 11 12 14 18 19 44 52 53\|11 12 14 17 18 19 44 52 53\|11 14 17 18 19 40 44 52 53\|14 17 18 19 22 40 44 52 53\|14 17 19 22 26 40 44 52 53\|14 17 19 22 26 39 40 52 53\|14 17 19 22 26 39 40 51 52	6 7 11 12 14 18 19 44 53	14 17 19 22 26 39 40 51 52	0-8 0-9 1-5 1-6 1-8 2-4 2-5 6-8 9-11	1-8 1-11 2-5 2-8 3-5 5-7 5-8 8-10 8-11
train	12	train_n12_pair_000084	7	1-8 2-7 2-6 2-8 4-6 9-11 0-9	7 14 15 18 20 21 22 33 53\|7 15 18 20 21 22 23 33 53\|7 15 18 20 22 23 33 44 53\|7 15 18 22 23 33 35 44 53\|7 15 18 23 33 35 36 44 53\|7 15 18 23 35 36 40 44 53\|7 8 15 18 23 35 36 40 44\|8 15 16 18 23 35 36 40 44	7 14 15 18 20 21 22 33 53	8 15 16 18 23 35 36 40 44	0-9 1-8 1-9 2-4 2-6 2-7 2-8 4-6 9-11	0-10 1-9 1-10 2-4 2-9 4-8 4-9 5-8 6-8
train	12	train_n12_pair_000085	6	0-2 0-8 4-7 5-7 9-11 8-11	0 1 2 5 6 34 39 52 53\|1 2 5 6 9 34 39 52 53\|1 2 5 9 34 39 50 52 53\|1 2 3 5 9 39 50 52 53\|1 2 3 4 5 9 50 52 53\|1 2 3 4 5 9 50 51 52\|1 2 3 4 5 9 49 50 51	0 1 2 5 6 34 39 52 53	1 2 3 4 5 9 49 50 51	0-2 0-3 0-4 0-7 0-8 4-7 5-7 8-11 9-11	0-3 0-4 0-5 0-6 0-7 1-3 7-10 7-11 8-10
train	12	train_n12_pair_000086	7	0-9 3-8 1-3 1-8 4-8 5-7 9-11	7 9 14 15 29 35 39 40 53\|9 14 15 17 29 35 39 40 53\|9 10 14 15 17 35 39 40 53\|10 14 15 17 18 35 39 40 53\|10 15 17 18 35 36 39 40 53\|10 15 17 18 36 39 40 41 53\|10 15 17 18 36 40 41 44 53\|10 15 16 17 18 36 40 41 44	7 9 14 15 29 35 39 40 53	10 15 16 17 18 36 40 41 44	0-9 1-3 1-8 1-9 3-8 4-8 5-7 5-8 9-11	1-4 1-9 1-10 1-11 2-4 4-9 5-8 5-9 6-8
train	12	train_n12_pair_000087	9	1-11 3-6 3-10 3-11 2-11 6-10 6-9 4-6 6-8	17 25 27 31 32 33 44 45 46\|0 25 27 31 32 33 44 45 46\|0 25 31 32 33 37 44 45 46\|0 25 32 33 37 38 44 45 46\|0 18 25 33 37 38 44 45 46\|0 2 18 33 37 38 44 45 46\|0 2 18 33 36 37 38 44 45\|0 2 18 33 35 36 37 38 44\|0 2 18 35 36 37 38 40 44\|0 2 18 35 36 37 38 39 40	17 25 27 31 32 33 44 45 46	0 2 18 35 36 37 38 39 40	1-11 2-11 3-6 3-10 3-11 4-6 6-8 6-9 6-10	0-2 0-4 2-4 4-8 4-9 4-10 4-11 5-7 5-8
train	12	train_n12_pair_000088	6	2-4 2-11 4-6 6-11 7-9 6-9	0 18 25 33 38 45 46 47 48\|0 25 32 33 38 45 46 47 48\|0 1 32 33 38 45 46 47 48\|0 1 32 38 43 45 46 47 48\|0 1 32 38 42 43 45 46 48\|0 1 32 38 42 43 44 45 46\|0 1 32 38 42 43 44 46 51	0 18 25 33 38 45 46 47 48	0 1 32 38 42 43 44 46 51	0-2 2-4 2-11 4-6 4-11 6-9 6-10 6-11 7-9	0-2 0-3 3-11 4-11 5-10 5-11 6-8 6-10 8-10
train	12	train_n12_pair_000089	11	1-10 0-10 2-8 2-10 2-9 2-11 3-7 3-8 4-7 4-8 5-7	8 16 22 23 24 28 29 34 39\|0 8 22 23 24 28 29 34 39\|0 22 23 24 25 28 29 34 39\|0 23 24 25 28 29 30 34 39\|0 23 25 28 29 30 34 39 53\|0 25 28 29 30 32 34 39 53\|0 1 28 29 30 32 34 39 53\|0 1 29 30 32 34 35 39 53\|0 1 30 32 34 35 36 39 53\|0 1 30 32 35 36 39 40 53\|0 1 30 32 36 39 40 41 53\|0 1 30 32 36 40 41 44 53	8 16 22 23 24 28 29 34 39	0 1 30 32 36 40 41 44 53	0-10 1-10 2-8 2-9 2-10 3-7 3-8 4-7 5-7	0-2 0-3 3-9 3-11 4-9 5-8 5-9 6-8 9-11
train	12	train_n12_pair_000090	7	0-9 2-8 2-9 1-9 5-8 9-11 3-9	7 15 22 23 26 29 39 40 53\|15 17 22 23 26 29 39 40 53\|15 17 23 26 29 30 39 40 53\|9 15 17 26 29 30 39 40 53\|9 17 26 29 30 32 39 40 53\|9 17 26 28 29 30 32 39 53\|9 17 26 28 29 30 31 32 39\|9 17 26 28 29 31 32 39 51	7 15 22 23 26 29 39 40 53	9 17 26 28 29 31 32 39 51	0-9 1-9 2-8 2-9 3-5 3-8 5-7 5-8 9-11	1-3 1-11 3-5 3-7 3-8 3-10 3-11 5-7 8-10
train	12	train_n12_pair_000091	5	0-3 4-6 4-10 4-7 7-10	0 1 2 33 34 37 38 49 51\|0 2 18 33 34 37 38 49 51\|0 2 18 34 37 38 39 49 51\|0 2 18 34 38 39 49 50 51\|0 2 18 38 39 43 49 50 51\|0 2 18 38 39 43 50 51 52	0 1 2 33 34 37 38 49 51	0 2 18 38 39 43 50 51 52	0-2 0-3 0-4 4-6 4-7 4-10 4-11 7-10 8-10	0-2 0-4 2-4 4-11 5-7 5-11 7-11 8-10 8-11
train	12	train_n12_pair_000092	8	0-3 0-10 0-8 0-7 0-2 3-5 5-7 8-10	0 1 5 6 8 26 28 39 51\|0 5 6 8 21 26 28 39 51\|0 5 6 21 26 28 39 51 52\|0 5 21 26 28 39 50 51 52\|0 21 25 26 28 39 50 51 52\|17 21 25 26 28 39 50 51 52\|17 21 25 28 34 39 50 51 52\|17 21 25 28 33 34 50 51 52\|17 21 25 28 33 34 50 52 53	0 1 5 6 8 26 28 39 51	17 21 25 28 33 34 50 52 53	0-2 0-3 0-7 0-8 0-10 3-5 3-7 5-7 8-10	1-11 2-7 2-11 3-7 4-6 4-7 7-11 8-11 9-11
train	12	train_n12_pair_000093	7	0-7 1-3 0-3 4-7 3-7 8-10 8-11	1 5 6 9 28 33 34 51 52\|1 6 9 28 29 33 34 51 52\|0 1 6 28 29 33 34 51 52\|0 6 22 28 29 33 34 51 52\|0 6 22 27 28 29 33 51 52\|0 6 22 27 29 33 44 51 52\|0 6 22 27 29 33 44 52 53\|0 6 7 22 27 29 33 44 53	1 5 6 9 28 33 34 51 52	0 6 7 22 27 29 33 44 53	0-3 0-7 0-8 1-3 3-7 4-6 4-7 8-10 8-11	0-2 0-8 0-9 2-8 3-6 3-8 4-6 6-8 9-11
train	12	train_n12_pair_000094	8	0-2 0-4 4-11 5-11 1-11 5-9 5-7 1-5	0 2 18 38 39 41 43 48 53\|2 10 18 38 39 41 43 48 53\|10 17 18 38 39 41 43 48 53\|10 11 17 18 39 41 43 48 53\|10 11 15 17 18 39 41 48 53\|7 10 11 15 18 39 41 48 53\|7 10 11 13 15 18 39 48 53\|7 10 11 12 13 15 18 48 53\|7 10 12 13 15 18 33 48 53	0 2 18 38 39 41 43 48 53	7 10 12 13 15 18 33 48 53	0-2 0-4 2-4 4-11 5-7 5-9 5-11 7-9 9-11	0-9 1-4 1-6 1-7 1-9 2-4 4-6 7-9 9-11
train	12	train_n12_pair_000095	6	1-3 4-6 6-10 6-11 7-10 7-11	2 4 9 10 33 46 47 49 51\|2 4 10 18 33 46 47 49 51\|2 3 4 10 18 46 47 49 51\|2 3 4 10 18 47 49 50 51\|2 3 4 5 10 18 49 50 51\|2 3 4 5 10 18 50 51 52\|2 3 4 5 6 10 18 51 52	2 4 9 10 33 46 47 49 51	2 3 4 5 6 10 18 51 52	0-4 0-6 1-3 1-4 4-6 6-10 6-11 7-10 8-10	0-4 0-5 0-6 0-7 0-8 1-4 2-4 8-10 8-11
train	12	train_n12_pair_000096	6	0-9 0-10 1-9 1-6 1-10 4-6	7 8 9 12 15 27 33 45 48\|8 9 12 15 16 27 33 45 48\|9 12 15 16 17 27 33 45 48\|9 12 16 17 27 33 45 46 48\|9 16 17 27 31 33 45 46 48\|9 17 27 31 32 33 45 46 48\|9 17 26 27 31 32 45 46 48	7 8 9 12 15 27 33 45 48	9 17 26 27 31 32 45 46 48	0-9 0-10 1-3 1-6 1-9 3-6 4-6 6-9 7-9	1-3 1-11 3-5 3-6 3-10 3-11 6-9 6-10 7-9
train	12	train_n12_pair_000097	9	3-5 1-3 5-9 5-7 5-11 0-5 5-10 1-5 7-9	3 9 11 26 39 41 42 43 48\|3 9 10 11 39 41 42 43 48\|3 10 11 18 39 41 42 43 48\|3 10 11 18 39 42 43 48 49\|3 10 11 18 42 43 46 48 49\|3 8 10 11 18 42 46 48 49\|8 10 11 16 18 42 46 48 49\|8 10 11 12 16 18 46 48 49\|8 10 12 16 18 33 46 48 49\|8 10 12 16 18 33 46 49 51	3 9 11 26 39 41 42 43 48	8 10 12 16 18 33 46 49 51	0-5 1-3 1-5 3-5 5-7 5-9 5-10 5-11 7-9	0-10 1-4 1-6 1-10 2-4 4-6 6-10 7-10 8-10
train	12	train_n12_pair_000098	8	1-6 2-5 2-4 8-11 7-11 1-7 1-11 8-10	12 13 17 18 19 20 50 51 52\|13 17 18 19 20 21 50 51 52\|13 17 18 20 21 33 50 51 52\|13 17 20 21 27 33 50 51 52\|13 17 20 21 27 33 49 50 51\|13 16 17 20 21 27 33 49 51\|16 17 20 21 24 27 33 49 51\|8 16 20 21 24 27 33 49 51\|8 16 20 21 24 27 33 48 49	12 13 17 18 19 20 50 51 52	8 16 20 21 24 27 33 48 49	1-6 1-7 1-11 2-4 2-5 2-6 7-11 8-10 8-11	0-10 1-10 2-6 2-7 2-10 3-6 4-6 7-9 7-10
train	12	train_n12_pair_000099	7	0-2 0-4 2-4 5-8 5-7 5-9 0-9	0 2 3 7 18 39 40 41 53\|2 3 7 10 18 39 40 41 53\|3 7 10 11 18 39 40 41 53\|3 7 9 10 11 39 40 41 53\|3 7 9 10 11 39 41 48 53\|3 7 9 10 11 41 45 48 53\|3 4 7 9 10 11 45 48 53\|3 4 9 10 11 45 47 48 53	0 2 3 7 18 39 40 41 53	3 4 9 10 11 45 47 48 53	0-2 0-4 0-5 0-9 2-4 5-7 5-8 5-9 9-11	0-5 0-6 1-3 1-4 1-5 6-9 6-11 7-9 9-11

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Convex Flip Distance Dataset

This repository contains paired convex polygon triangulations for studying (optimal) convex flip distance with GNNs + RL.

Each row describes a source triangulation and a destination triangulation on the same number of vertices n, together with a precomputed optimal flip distance and an optimal flip sequence from source → destination. We also include MIS-based representations used in our experiments.

What’s in each row

Every example corresponds to a single pair (T_src, T_dst) with:

n: number of polygon vertices (nodes).
triangulation_edges_start: diagonals of the source triangulation.
triangulation_edges_target: diagonals of the destination triangulation.
flip_distance: precomputed optimal number of flips from source to target.
flip_sequence: the optimal flip sequence realizing flip_distance.
MIS representations:
- mis_start, mis_target
- mis_sequence

Diagonal / flip encoding

Diagonals are represented as space-separated strings of i-j with 0 ≤ i < j < n (e.g., 0-4 1-4 2-6 ...).

flip_sequence is represented as a space-separated list of diagonals (the diagonal flipped at each step) from source → target.

MIS fields

We additionally store MIS encodings that we used in our pipeline:

mis_start: MIS representation for the source triangulation
mis_target: MIS representation for the target triangulation
mis_sequence: MIS representations along the flip trajectory (step-by-step), using | as the step delimiter

Training usage

Optional rollout into sub-states (recommended for imitation learning)

A single row can be expanded into multiple sub-states along the optimal trajectory:

State s_t: current triangulation after applying the first t flips
Target stays fixed: T_dst
Label at t: the next flip action in flip_sequence
Value target at t: remaining flips until completion (flip_distance - t)

This is exactly the “rollout each row into multiple substates” approach used during our pretraining stage.

Generalization across polygon sizes

The dataset includes multiple polygon sizes (multiple n values) in both train and validation to test generalization across graph sizes.

In particular, the provided validation CSV includes an n = 50 subset, which we found convenient for evaluating cross-size generalization behavior.

Graph representations (`Graphs/` folder)

We also provide precomputed graph representations for convenience, in case you want to use the same graph encoding as our implementation.

Inside Graphs/, you’ll find two versions of the graph representation:

a .npy version (dense matrix format)
a .csv version (same content in CSV form)

These are meant as plug-and-play inputs for reproducing our representation choices (e.g., adjacency/structure matrices used in our preprocessing).

File format summary

Typical columns:

split
n
pair_name
flip_distance
flip_sequence
mis_sequence
mis_start
mis_target
triangulation_edges_start
triangulation_edges_target

Notes

All triangulations in a row share the same n.
The flip sequence is provided from source → destination, and is aligned with flip_distance.
The dataset is suitable for:
- supervised imitation learning (policy/value)
- RL fine-tuning (rollouts from triangulation_edges_start toward triangulation_edges_target)

Downloads last month: 17

Size of downloaded dataset files:

43.8 MB

Size of the auto-converted Parquet files:

13.9 MB

Number of rows:

38,092