{"id":"761.1.6.a","row":1217,"stored":{"file":"master_catalog.json","row":1217,"construction":null,"columns_sha256":null},"parameters":{"n":761,"k":1,"d":6,"N":195,"r":194,"level":3},"gate":{"string":"0","human":"T0","monomials":[[0]],"sk_key":[[0]],"sk_fingerprint":"bc179efd84e614ba","sk_canonical_frame":true,"relabelled_into_canonical_frame":false},"circuit":{"columns":[[0,1,4,5,8,11,12,14,15,19,20,22,26,27,30,31,32,34,35,36,38,39,42,44,46,48],[0,3,4,6,11,12,15,16,17,18,20,21,22,23,29,31,32,33,34,35,38,40,45,46,47],[0,1,7,8,11,13,14,15,16,17,18,20,21,23,24,26,27,31,33,38,41,42,44,47],[0,2,4,8,10,12,13,17,20,22,24,25,28,29,30,31,33,34,36,38,39,42,44,48,49,50],[0,2,9,10,13,15,16,17,18,19,20,22,23,25,26,28,29,33,35,40,43,44,46,49],[0,3,10,11,14,16,17,18,19,20,21,23,24,26,27,29,30,34,36,41,44,45,47,50],[0,4,11,12,15,17,18,19,20,21,22,24,25,27,28,30,31,35,37,42,45,46,48],[0,1,2,3,4,5,8,10,13,17,18,19,20,22,23,25,27,29,31,32,33,35,37,42,43,45,46,47,48,49,50],[0,1,4,5,6,8,11,12,13,15,17,21,23,24,29,31,33,34,35,36,37,38,42,46,47,50],[0,3,4,6,7,11,12,14,16,17,24,25,27,28,29,30,32,35,46,47,48,49],[0,2,3,4,7,8,10,11,12,13,14,16,18,19,20,21,22,25,26,29,32,34,36,37,39,44,45,46,47,48,49],[0,1,2,5,9,10,11,13,14,15,16,19,20,22,23,28,30,36,40,42,46,47,49],[0,1,6,8,9,10,11,13,16,18,19,21,23,24,26,28,30,32,35,41,42,44,47,49,50],[0,1,2,5,7,8,13,14,16,17,18,19,20,21,24,25,26,27,31,34,35,36,39,46,49],[0,1,2,3,5,6,10,11,12,13,14,15,16,17,19,20,25,27,28,29,32,33,34,36,37,39,40,42,43,45,46,47,48,49],[0,5,6,7,9,12,14,15,16,20,21,22,26,27,30,33,35,36,39,40,41,44,47,48,50],[0,1,4,5,6,7,10,11,12,13,14,16,17,19,20,21,23,26,28,30,32,35,37,38,39,40,41,44,45,46,49],[0,1,3,5,6,7,9,11,19,21,22,24,26,27,28,30,32,33,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50],[0,1,2,4,5,6,7,9,11,13,16,18,20,21,23,25,26,27,28,31,35,36,37,38,40,41,43,44,47],[0,1,2,3,6,7,9,11,13,14,16,17,18,19,24,27,28,32,33,34,35,36,37,38,41,43,44,46,49,50],[0,5,7,8,9,10,11,12,13,14,15,19,20,22,25,27,33,35,42,43,44,45,46,47,49,50],[0,2,3,5,6,8,9,12,13,17,19,22,23,26,30,31,32,33,36,37,39,43,47,48],[0,3,4,6,7,9,10,13,14,18,20,23,24,27,31,32,33,34,37,38,40,44,48,49],[0,4,5,7,8,10,11,14,15,19,21,24,25,28,32,33,34,35,38,39,41,45,49,50],[0,5,6,8,9,11,12,15,16,20,22,25,26,29,33,34,35,36,39,40,42,46,50],[0,1,2,3,4,6,7,8,9,13,23,28,30,33,34,38,40,41,42,43,45,47,48,50],[0,2,3,5,7,8,13,15,16,18,19,20,21,24,27,30,32,33,34,35,36,38,39,41,42,45,46,48,50],[0,1,3,5,6,9,11,12,15,16,17,21,25,26,27,28,30,32,33,37,38,40,43,44,47,48,49],[0,1,3,4,6,7,8,9,10,14,15,16,19,20,22,27,30,32,33,34,35,37,38,39,41,42,43,45,50],[0,1,2,4,7,12,13,15,17,18,20,22,23,26,28,29,31,36,38,40,44,45,48,49,50],[0,1,2,3,9,10,11,12,14,19,22,23,24,26,27,30,32,33,34,35,37,41,42,43,48],[0,1,2,3,4,5,8,9,15,16,18,20,21,22,23,24,25,26,27,28,29,31,36,38,39,44,45,46,48,50],[0,6,10,11,13,16,18,19,21,23,24,25,26,30,32,34,36,38,40,43,45,47],[0,2,3,5,7,10,12,15,16,21,24,25,26,27,28,30,32,34,35,41,45,48,50],[0,1,2,6,10,11,12,13,21,22,25,29,31,37,38,45,46,48,49,50],[0,2,3,4,7,9,10,11,12,15,16,18,19,20,21,22,23,26,27,29,31,33,36,39,43,44,45,46,47],[0,1,3,10,13,14,15,16,17,21,23,24,26,28,31,35,36,37,38,39,40,42,45,47],[0,2,9,10,11,13,17,19,20,21,22,24,25,30,31,33,37,39,40,41,44,45,46,48,49,50],[0,2,5,12,15,16,17,18,19,23,25,26,28,30,33,37,38,39,40,41,42,44,47,49],[0,3,6,13,16,17,18,19,20,24,26,27,29,31,34,38,39,40,41,42,43,45,48,50],[0,4,7,14,17,18,19,20,21,25,27,28,30,32,35,39,40,41,42,43,44,46,49],[0,1,2,3,4,5,10,12,15,16,17,18,19,20,22,27,29,31,35,37,38,40,41,43,44,47,48],[0,1,4,5,6,8,9,11,12,14,15,16,21,23,26,29,31,35,36,37,38,39,41,43,45],[0,1,2,6,7,8,11,15,17,18,21,24,26,27,29,30,32,33,34,35,36,37,38,40,43,44,45,48,49,50],[0,4,5,7,8,11,12,13,16,17,19,25,29,30,31,33,35,41,43,44,45,50],[0,2,3,6,8,9,10,11,12,13,15,16,18,19,21,22,26,28,33,36,37,39,42,50],[0,3,4,7,9,10,11,12,13,14,16,17,19,20,22,23,27,29,34,37,38,40,43],[0,1,2,3,5,11,13,14,15,16,18,20,23,24,26,27,30,33,36,37,39,41,42,44,45,48,50],[0,1,4,6,8,9,13,16,18,20,21,24,25,26,27,29,30,32,34,35,38,40,44,45,46,48],[0,3,4,7,10,11,13,14,18,19,21,25,26,29,30,31,33,34,35,37,38,41,43,45,47],[0,1],[0,2,4,9,10,13,14,15,16,18,19,20,21,27,29,30,31,32,33,36,38,43,44,45,49,50],[0,2],[0,3],[0,4],[0,5],[0,6],[0,7],[0,8],[0,9],[0,10],[0,11],[0,12],[0,13],[0,14],[0,15],[0,16],[0,17],[0,18],[0,19],[0,20],[0,21],[0,22],[0,23],[0,24],[0,25],[0,26],[0,27],[0,28],[0,29],[0,30],[0,31],[0,32],[0,33],[0,34],[0,35],[0,36],[0,37],[0,38],[0,39],[0,40],[0,41],[0,42],[0,43],[0,44],[0,45],[0,46],[0,47],[0,48],[0,49],[0,50],[0,1,4,5,8,11,12,14,15,19,20,22,26,27,30,31,32,34,35,36,38,39,42,44,46,48,194],[0,3,4,6,11,12,15,16,17,18,20,21,22,23,29,31,32,33,34,35,38,40,45,46,47,194],[0,1,7,8,11,13,14,15,16,17,18,20,21,23,24,26,27,31,33,38,41,42,44,47,194],[0,2,4,8,10,12,13,17,20,22,24,25,28,29,30,31,33,34,36,38,39,42,44,48,49,50,194],[0,2,9,10,13,15,16,17,18,19,20,22,23,25,26,28,29,33,35,40,43,44,46,49,194],[0,3,10,11,14,16,17,18,19,20,21,23,24,26,27,29,30,34,36,41,44,45,47,50,194],[0,4,11,12,15,17,18,19,20,21,22,24,25,27,28,30,31,35,37,42,45,46,48,194],[0,1,2,3,4,5,8,10,13,17,18,19,20,22,23,25,27,29,31,32,33,35,37,42,43,45,46,47,48,49,50,194],[0,1,4,5,6,8,11,12,13,15,17,21,23,24,29,31,33,34,35,36,37,38,42,46,47,50,194],[0,3,4,6,7,11,12,14,16,17,24,25,27,28,29,30,32,35,46,47,48,49,194],[0,2,3,4,7,8,10,11,12,13,14,16,18,19,20,21,22,25,26,29,32,34,36,37,39,44,45,46,47,48,49,194],[0,1,2,5,9,10,11,13,14,15,16,19,20,22,23,28,30,36,40,42,46,47,49,194],[0,1,6,8,9,10,11,13,16,18,19,21,23,24,26,28,30,32,35,41,42,44,47,49,50,194],[0,1,2,5,7,8,13,14,16,17,18,19,20,21,24,25,26,27,31,34,35,36,39,46,49,194],[0,1,2,3,5,6,10,11,12,13,14,15,16,17,19,20,25,27,28,29,32,33,34,36,37,39,40,42,43,45,46,47,48,49,194],[0,5,6,7,9,12,14,15,16,20,21,22,26,27,30,33,35,36,39,40,41,44,47,48,50,194],[0,1,4,5,6,7,10,11,12,13,14,16,17,19,20,21,23,26,28,30,32,35,37,38,39,40,41,44,45,46,49,194],[0,1,3,5,6,7,9,11,19,21,22,24,26,27,28,30,32,33,35,36,37,38,39,40,41,43,44,45,46,47,48,49,50,194],[0,1,2,4,5,6,7,9,11,13,16,18,20,21,23,25,26,27,28,31,35,36,37,38,40,41,43,44,47,194],[0,1,2,3,6,7,9,11,13,14,16,17,18,19,24,27,28,32,33,34,35,36,37,38,41,43,44,46,49,50,194],[0,5,7,8,9,10,11,12,13,14,15,19,20,22,25,27,33,35,42,43,44,45,46,47,49,50,194],[0,2,3,5,6,8,9,12,13,17,19,22,23,26,30,31,32,33,36,37,39,43,47,48,194],[0,3,4,6,7,9,10,13,14,18,20,23,24,27,31,32,33,34,37,38,40,44,48,49,194],[0,4,5,7,8,10,11,14,15,19,21,24,25,28,32,33,34,35,38,39,41,45,49,50,194],[0,5,6,8,9,11,12,15,16,20,22,25,26,29,33,34,35,36,39,40,42,46,50,194],[0,1,2,3,4,6,7,8,9,13,23,28,30,33,34,38,40,41,42,43,45,47,48,50,194],[0,2,3,5,7,8,13,15,16,18,19,20,21,24,27,30,32,33,34,35,36,38,39,41,42,45,46,48,50,194],[0,1,3,5,6,9,11,12,15,16,17,21,25,26,27,28,30,32,33,37,38,40,43,44,47,48,49,194],[0,1,3,4,6,7,8,9,10,14,15,16,19,20,22,27,30,32,33,34,35,37,38,39,41,42,43,45,50,194],[0,1,2,4,7,12,13,15,17,18,20,22,23,26,28,29,31,36,38,40,44,45,48,49,50,194],[0,1,2,3,9,10,11,12,14,19,22,23,24,26,27,30,32,33,34,35,37,41,42,43,48,194],[0,1,2,3,4,5,8,9,15,16,18,20,21,22,23,24,25,26,27,28,29,31,36,38,39,44,45,46,48,50,194],[0,6,10,11,13,16,18,19,21,23,24,25,26,30,32,34,36,38,40,43,45,47,194],[0,2,3,5,7,10,12,15,16,21,24,25,26,27,28,30,32,34,35,41,45,48,50,194],[0,1,2,6,10,11,12,13,21,22,25,29,31,37,38,45,46,48,49,50,194],[0,2,3,4,7,9,10,11,12,15,16,18,19,20,21,22,23,26,27,29,31,33,36,39,43,44,45,46,47,194],[0,1,3,10,13,14,15,16,17,21,23,24,26,28,31,35,36,37,38,39,40,42,45,47,194],[0,2,9,10,11,13,17,19,20,21,22,24,25,30,31,33,37,39,40,41,44,45,46,48,49,50,194],[0,2,5,12,15,16,17,18,19,23,25,26,28,30,33,37,38,39,40,41,42,44,47,49,194],[0,3,6,13,16,17,18,19,20,24,26,27,29,31,34,38,39,40,41,42,43,45,48,50,194],[0,4,7,14,17,18,19,20,21,25,27,28,30,32,35,39,40,41,42,43,44,46,49,194],[0,1,2,3,4,5,10,12,15,16,17,18,19,20,22,27,29,31,35,37,38,40,41,43,44,47,48,194],[0,1,4,5,6,8,9,11,12,14,15,16,21,23,26,29,31,35,36,37,38,39,41,43,45,194],[0,1,2,6,7,8,11,15,17,18,21,24,26,27,29,30,32,33,34,35,36,37,38,40,43,44,45,48,49,50,194],[0,4,5,7,8,11,12,13,16,17,19,25,29,30,31,33,35,41,43,44,45,50,194],[0,2,3,6,8,9,10,11,12,13,15,16,18,19,21,22,26,28,33,36,37,39,42,50,194],[0,3,4,7,9,10,11,12,13,14,16,17,19,20,22,23,27,29,34,37,38,40,43,194],[0,1,2,3,5,11,13,14,15,16,18,20,23,24,26,27,30,33,36,37,39,41,42,44,45,48,50,194],[0,1,4,6,8,9,13,16,18,20,21,24,25,26,27,29,30,32,34,35,38,40,44,45,46,48,194],[0,3,4,7,10,11,13,14,18,19,21,25,26,29,30,31,33,34,35,37,38,41,43,45,47,194],[0,1,194],[0,2,4,9,10,13,14,15,16,18,19,20,21,27,29,30,31,32,33,36,38,43,44,45,49,50,194],[0,2,194],[0,3,194],[0,4,194],[0,5,194],[0,6,194],[0,7,194],[0,8,194],[0,9,194],[0,10,194],[0,11,194],[0,12,194],[0,13,194],[0,14,194],[0,15,194],[0,16,194],[0,17,194],[0,18,194],[0,19,194],[0,20,194],[0,21,194],[0,22,194],[0,23,194],[0,24,194],[0,25,194],[0,26,194],[0,27,194],[0,28,194],[0,29,194],[0,30,194],[0,31,194],[0,32,194],[0,33,194],[0,34,194],[0,35,194],[0,36,194],[0,37,194],[0,38,194],[0,39,194],[0,40,194],[0,41,194],[0,42,194],[0,43,194],[0,44,194],[0,45,194],[0,46,194],[0,47,194],[0,48,194],[0,49,194],[0,50,194],[0,51,52,53,55,56,62,64,65,67,69,70,71,72,75,76,77,78,80,81,82,86,87,194],[0,52,53,54,56,57,63,65,66,68,70,71,72,73,76,77,78,79,81,82,83,87,88,194],[0,53,54,55,57,58,64,66,67,69,71,72,73,74,77,78,79,80,82,83,84,88,89,194],[0,51,52,53,54,58,59,62,64,68,69,71,73,74,76,77,79,82,83,84,85,86,87,89,194],[0,51,54,56,59,60,62,63,64,67,71,74,76,81,82,83,84,85,88,194],[0,52,55,57,60,61,63,64,65,68,72,75,77,82,83,84,85,86,89,194],[0,51,52,55,58,61,66,67,70,71,72,73,75,77,80,81,82,83,84,85,194],[0,52,53,56,59,62,67,68,71,72,73,74,76,78,81,82,83,84,85,86,194],[0,53,54,57,60,63,68,69,72,73,74,75,77,79,82,83,84,85,86,87,194],[0,54,55,58,61,64,69,70,73,74,75,76,78,80,83,84,85,86,87,88,194],[0,55,56,59,62,65,70,71,74,75,76,77,79,81,84,85,86,87,88,89,194],[0,51,52,53,55,57,60,62,63,64,65,66,67,69,70,81,85,88,89,194],[0,51,54,55,58,61,62,63,66,68,69,72,75,76,77,78,80,81,87,89,194],[0,51,53,59,63,65,71,72,73,75,79,80,86,87,88,194],[0,52,54,60,64,66,72,73,74,76,80,81,87,88,89,194],[0,51,52,56,61,62,64,69,70,71,72,73,74,76,78,80,86,87,88,89,194],[0,51,55,56,57,63,64,67,69,73,74,76,78,79,80,82,86,88,89,194],[0,51,53,55,57,58,62,67,68,69,71,72,74,76,78,79,82,83,86,89,194],[0,51,53,54,55,58,59,62,63,64,65,67,68,71,73,76,78,79,81,82,83,84,86,194],[0,52,54,55,56,59,60,63,64,65,66,68,69,72,74,77,79,80,82,83,84,85,87,194],[0,53,55,56,57,60,61,64,65,66,67,69,70,73,75,78,80,81,83,84,85,86,88,194],[0,54,56,57,58,61,62,65,66,67,68,70,71,74,76,79,81,82,84,85,86,87,89,194],[0,51,52,53,56,57,58,59,63,64,65,66,68,70,76,78,81,83,85,88,194],[0,52,53,54,57,58,59,60,64,65,66,67,69,71,77,79,82,84,86,89,194],[0,51,52,54,56,58,59,60,61,62,64,66,68,69,71,75,76,77,81,82,83,85,86,194],[0,52,53,55,57,59,60,61,62,63,65,67,69,70,72,76,77,78,82,83,84,86,87,194],[0,53,54,56,58,60,61,62,63,64,66,68,70,71,73,77,78,79,83,84,85,87,88,194],[0,54,55,57,59,61,62,63,64,65,67,69,71,72,74,78,79,80,84,85,86,88,89,194],[0,51,52,53,58,60,63,66,67,68,69,71,73,76,77,78,79,82,85,89,194],[0,51,54,55,56,59,61,62,65,68,71,74,75,76,79,81,82,83,87,194],[0,52,55,56,57,60,62,63,66,69,72,75,76,77,80,82,83,84,88,194],[0,53,56,57,58,61,63,64,67,70,73,76,77,78,81,83,84,85,89,194],[0,51,52,53,54,55,56,57,58,59,67,68,69,70,72,74,75,76,79,80,81,84,85,87,194],[0,52,53,54,55,56,57,58,59,60,68,69,70,71,73,75,76,77,80,81,82,85,86,88,194],[0,53,54,55,56,57,58,59,60,61,69,70,71,72,74,76,77,78,81,82,83,86,87,89,194],[0,51,52,53,54,57,58,59,60,61,64,65,67,69,73,76,79,80,81,83,84,86,88,194],[0,52,53,54,55,58,59,60,61,62,65,66,68,70,74,77,80,81,82,84,85,87,89,194],[0,51,52,54,59,60,61,63,64,65,66,70,72,76,77,80,83,85,87,88,194],[0,52,53,55,60,61,62,64,65,66,67,71,73,77,78,81,84,86,88,89,194],[0,51,52,54,55,61,63,64,66,68,69,70,71,74,75,76,77,79,80,81,85,86,89,194],[0,51,194],[0,52,194],[0,53,194],[0,54,194],[0,55,194],[0,56,194],[0,57,194],[0,58,194],[0,59,194],[0,60,194],[0,61,194],[0,62,194],[0,63,194],[0,64,194],[0,65,194],[0,66,194],[0,67,194],[0,68,194],[0,69,194],[0,70,194],[0,71,194],[0,72,194],[0,73,194],[0,74,194],[0,75,194],[0,76,194],[0,77,194],[0,78,194],[0,79,194],[0,80,194],[0,81,194],[0,82,194],[0,83,194],[0,84,194],[0,85,194],[0,86,194],[0,87,194],[0,88,194],[0,89,194],[0,51,52,53,55,56,62,64,65,67,69,70,71,72,75,76,77,78,80,81,82,86,87,193,194],[0,52,53,54,56,57,63,65,66,68,70,71,72,73,76,77,78,79,81,82,83,87,88,193,194],[0,53,54,55,57,58,64,66,67,69,71,72,73,74,77,78,79,80,82,83,84,88,89,193,194],[0,51,52,53,54,58,59,62,64,68,69,71,73,74,76,77,79,82,83,84,85,86,87,89,193,194],[0,51,54,56,59,60,62,63,64,67,71,74,76,81,82,83,84,85,88,193,194],[0,52,55,57,60,61,63,64,65,68,72,75,77,82,83,84,85,86,89,193,194],[0,51,52,55,58,61,66,67,70,71,72,73,75,77,80,81,82,83,84,85,193,194],[0,52,53,56,59,62,67,68,71,72,73,74,76,78,81,82,83,84,85,86,193,194],[0,53,54,57,60,63,68,69,72,73,74,75,77,79,82,83,84,85,86,87,193,194],[0,54,55,58,61,64,69,70,73,74,75,76,78,80,83,84,85,86,87,88,193,194],[0,55,56,59,62,65,70,71,74,75,76,77,79,81,84,85,86,87,88,89,193,194],[0,51,52,53,55,57,60,62,63,64,65,66,67,69,70,81,85,88,89,193,194],[0,51,54,55,58,61,62,63,66,68,69,72,75,76,77,78,80,81,87,89,193,194],[0,51,53,59,63,65,71,72,73,75,79,80,86,87,88,193,194],[0,52,54,60,64,66,72,73,74,76,80,81,87,88,89,193,194],[0,51,52,56,61,62,64,69,70,71,72,73,74,76,78,80,86,87,88,89,193,194],[0,51,55,56,57,63,64,67,69,73,74,76,78,79,80,82,86,88,89,193,194],[0,51,53,55,57,58,62,67,68,69,71,72,74,76,78,79,82,83,86,89,193,194],[0,51,53,54,55,58,59,62,63,64,65,67,68,71,73,76,78,79,81,82,83,84,86,193,194],[0,52,54,55,56,59,60,63,64,65,66,68,69,72,74,77,79,80,82,83,84,85,87,193,194],[0,53,55,56,57,60,61,64,65,66,67,69,70,73,75,78,80,81,83,84,85,86,88,193,194],[0,54,56,57,58,61,62,65,66,67,68,70,71,74,76,79,81,82,84,85,86,87,89,193,194],[0,51,52,53,56,57,58,59,63,64,65,66,68,70,76,78,81,83,85,88,193,194],[0,52,53,54,57,58,59,60,64,65,66,67,69,71,77,79,82,84,86,89,193,194],[0,51,52,54,56,58,59,60,61,62,64,66,68,69,71,75,76,77,81,82,83,85,86,193,194],[0,52,53,55,57,59,60,61,62,63,65,67,69,70,72,76,77,78,82,83,84,86,87,193,194],[0,53,54,56,58,60,61,62,63,64,66,68,70,71,73,77,78,79,83,84,85,87,88,193,194],[0,54,55,57,59,61,62,63,64,65,67,69,71,72,74,78,79,80,84,85,86,88,89,193,194],[0,51,52,53,58,60,63,66,67,68,69,71,73,76,77,78,79,82,85,89,193,194],[0,51,54,55,56,59,61,62,65,68,71,74,75,76,79,81,82,83,87,193,194],[0,52,55,56,57,60,62,63,66,69,72,75,76,77,80,82,83,84,88,193,194],[0,53,56,57,58,61,63,64,67,70,73,76,77,78,81,83,84,85,89,193,194],[0,51,52,53,54,55,56,57,58,59,67,68,69,70,72,74,75,76,79,80,81,84,85,87,193,194],[0,52,53,54,55,56,57,58,59,60,68,69,70,71,73,75,76,77,80,81,82,85,86,88,193,194],[0,53,54,55,56,57,58,59,60,61,69,70,71,72,74,76,77,78,81,82,83,86,87,89,193,194],[0,51,52,53,54,57,58,59,60,61,64,65,67,69,73,76,79,80,81,83,84,86,88,193,194],[0,52,53,54,55,58,59,60,61,62,65,66,68,70,74,77,80,81,82,84,85,87,89,193,194],[0,51,52,54,59,60,61,63,64,65,66,70,72,76,77,80,83,85,87,88,193,194],[0,52,53,55,60,61,62,64,65,66,67,71,73,77,78,81,84,86,88,89,193,194],[0,51,52,54,55,61,63,64,66,68,69,70,71,74,75,76,77,79,80,81,85,86,89,193,194],[0,51,193,194],[0,52,193,194],[0,53,193,194],[0,54,193,194],[0,55,193,194],[0,56,193,194],[0,57,193,194],[0,58,193,194],[0,59,193,194],[0,60,193,194],[0,61,193,194],[0,62,193,194],[0,63,193,194],[0,64,193,194],[0,65,193,194],[0,66,193,194],[0,67,193,194],[0,68,193,194],[0,69,193,194],[0,70,193,194],[0,71,193,194],[0,72,193,194],[0,73,193,194],[0,74,193,194],[0,75,193,194],[0,76,193,194],[0,77,193,194],[0,78,193,194],[0,79,193,194],[0,80,193,194],[0,81,193,194],[0,82,193,194],[0,83,193,194],[0,84,193,194],[0,85,193,194],[0,86,193,194],[0,87,193,194],[0,88,193,194],[0,89,193,194],[0,90,193,194],[0,91,193,194],[0,92,121,193,194],[0,93,193,194],[0,94,121,193,194],[0,95,193,194],[0,96,193,194],[0,97,121,193,194],[0,98,193,194],[0,99,193,194],[0,100,193,194],[0,101,121,193,194],[0,102,121,193,194],[0,103,121,193,194],[0,104,193,194],[0,105,121,193,194],[0,106,121,193,194],[0,107,121,193,194],[0,108,193,194],[0,109,193,194],[0,110,193,194],[0,111,121,193,194],[0,112,193,194],[0,113,193,194],[0,114,121,193,194],[0,115,121,193,194],[0,116,121,193,194],[0,117,121,193,194],[0,118,121,193,194],[0,119,193,194],[0,120,193,194],[0,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,193,194],[0,91,94,95,97,98,99,100,101,103,106,107,109,110,112,115,116,118,193,194],[0,92,95,96,98,99,100,101,102,104,107,108,110,111,113,116,117,119,193,194],[0,93,96,97,99,100,101,102,103,105,108,109,111,112,114,117,118,120,193,194],[0,94,97,98,100,101,102,103,104,106,109,110,112,113,115,118,119,193,194],[0,90,91,92,93,94,96,97,100,106,108,109,112,115,117,118,121,193,194],[0,90,96,99,100,102,103,104,105,106,108,111,112,114,115,117,120,193,194],[0,90,92,93,94,95,96,98,99,102,108,110,111,114,117,119,120,121,193,194],[0,91,93,94,95,96,97,99,100,103,109,111,112,115,118,120,193,194],[0,90,91,93,99,102,103,105,106,107,108,109,111,114,115,117,118,120,121,193,194],[0,91,92,94,100,103,104,106,107,108,109,110,112,115,116,118,119,193,194],[0,90,91,94,96,97,98,99,100,102,103,106,112,114,115,118,193,194],[0,90,93,94,96,102,105,106,108,109,110,111,112,114,117,118,120,193,194],[0,90,92,93,96,98,99,100,101,102,104,105,108,114,116,117,120,193,194],[0,91,93,94,97,99,100,101,102,103,105,106,109,115,117,118,193,194],[0,90,91,93,96,97,99,105,108,109,111,112,113,114,115,117,120,193,194],[0,90,93,95,96,99,101,102,103,104,105,107,108,111,117,119,120,193,194],[0,91,94,96,97,100,102,103,104,105,106,108,109,112,118,120,121,193,194],[0,90,91,93,94,96,99,100,102,108,111,112,114,115,116,117,118,120,121,193,194],[0,91,92,94,95,97,100,101,103,109,112,113,115,116,117,118,119,121,193,194],[0,90,91,94,97,99,100,103,105,106,107,108,109,111,112,115,193,194],[0,90,93,94,96,97,99,102,103,105,111,114,115,117,118,119,120,193,194],[0,90,92,93,96,99,101,102,105,107,108,109,110,111,113,114,117,121,193,194],[0,91,93,94,97,100,102,103,106,108,109,110,111,112,114,115,118,193,194],[0,92,94,95,98,101,103,104,107,109,110,111,112,113,115,116,119,121,193,194],[0,93,95,96,99,102,104,105,108,110,111,112,113,114,116,117,120,121,193,194],[0,94,96,97,100,103,105,106,109,111,112,113,114,115,117,118,193,194],[0,90,91,92,93,94,96,99,100,102,103,105,108,109,111,117,120,121,193,194],[0,90,96,98,99,102,105,107,108,111,113,114,115,116,117,119,120,121,193,194],[0,91,97,99,100,103,106,108,109,112,114,115,116,117,118,120,193,194],[0,90,91,93,94,95,96,97,99,102,103,105,106,108,111,112,114,120,121,193,194],[0,91,92,94,95,96,97,98,100,103,104,106,107,109,112,113,115,121,193,194],[0,90,91,94,100,102,103,106,109,111,112,115,117,118,119,120,193,194],[0,90,93,94,96,97,98,99,100,102,105,106,108,109,111,114,115,117,193,194],[0,90,192,193,194],[0,91,192,193,194],[0,92,121,192,193,194],[0,93,192,193,194],[0,94,121,192,193,194],[0,95,192,193,194],[0,96,192,193,194],[0,97,121,192,193,194],[0,98,192,193,194],[0,99,192,193,194],[0,100,192,193,194],[0,101,121,192,193,194],[0,102,121,192,193,194],[0,103,121,192,193,194],[0,104,192,193,194],[0,105,121,192,193,194],[0,106,121,192,193,194],[0,107,121,192,193,194],[0,108,192,193,194],[0,109,192,193,194],[0,110,192,193,194],[0,111,121,192,193,194],[0,112,192,193,194],[0,113,192,193,194],[0,114,121,192,193,194],[0,115,121,192,193,194],[0,116,121,192,193,194],[0,117,121,192,193,194],[0,118,121,192,193,194],[0,119,192,193,194],[0,120,192,193,194],[0,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,192,193,194],[0,91,94,95,97,98,99,100,101,103,106,107,109,110,112,115,116,118,192,193,194],[0,92,95,96,98,99,100,101,102,104,107,108,110,111,113,116,117,119,192,193,194],[0,93,96,97,99,100,101,102,103,105,108,109,111,112,114,117,118,120,192,193,194],[0,94,97,98,100,101,102,103,104,106,109,110,112,113,115,118,119,192,193,194],[0,90,91,92,93,94,96,97,100,106,108,109,112,115,117,118,121,192,193,194],[0,90,96,99,100,102,103,104,105,106,108,111,112,114,115,117,120,192,193,194],[0,90,92,93,94,95,96,98,99,102,108,110,111,114,117,119,120,121,192,193,194],[0,91,93,94,95,96,97,99,100,103,109,111,112,115,118,120,192,193,194],[0,90,91,93,99,102,103,105,106,107,108,109,111,114,115,117,118,120,121,192,193,194],[0,91,92,94,100,103,104,106,107,108,109,110,112,115,116,118,119,192,193,194],[0,90,91,94,96,97,98,99,100,102,103,106,112,114,115,118,192,193,194],[0,90,93,94,96,102,105,106,108,109,110,111,112,114,117,118,120,192,193,194],[0,90,92,93,96,98,99,100,101,102,104,105,108,114,116,117,120,192,193,194],[0,91,93,94,97,99,100,101,102,103,105,106,109,115,117,118,192,193,194],[0,90,91,93,96,97,99,105,108,109,111,112,113,114,115,117,120,192,193,194],[0,90,93,95,96,99,101,102,103,104,105,107,108,111,117,119,120,192,193,194],[0,91,94,96,97,100,102,103,104,105,106,108,109,112,118,120,121,192,193,194],[0,90,91,93,94,96,99,100,102,108,111,112,114,115,116,117,118,120,121,192,193,194],[0,91,92,94,95,97,100,101,103,109,112,113,115,116,117,118,119,121,192,193,194],[0,90,91,94,97,99,100,103,105,106,107,108,109,111,112,115,192,193,194],[0,90,93,94,96,97,99,102,103,105,111,114,115,117,118,119,120,192,193,194],[0,90,92,93,96,99,101,102,105,107,108,109,110,111,113,114,117,121,192,193,194],[0,91,93,94,97,100,102,103,106,108,109,110,111,112,114,115,118,192,193,194],[0,92,94,95,98,101,103,104,107,109,110,111,112,113,115,116,119,121,192,193,194],[0,93,95,96,99,102,104,105,108,110,111,112,113,114,116,117,120,121,192,193,194],[0,94,96,97,100,103,105,106,109,111,112,113,114,115,117,118,192,193,194],[0,90,91,92,93,94,96,99,100,102,103,105,108,109,111,117,120,121,192,193,194],[0,90,96,98,99,102,105,107,108,111,113,114,115,116,117,119,120,121,192,193,194],[0,91,97,99,100,103,106,108,109,112,114,115,116,117,118,120,192,193,194],[0,90,91,93,94,95,96,97,99,102,103,105,106,108,111,112,114,120,121,192,193,194],[0,91,92,94,95,96,97,98,100,103,104,106,107,109,112,113,115,121,192,193,194],[0,90,91,94,100,102,103,106,109,111,112,115,117,118,119,120,192,193,194],[0,90,93,94,96,97,98,99,100,102,105,106,108,109,111,114,115,117,192,193,194],[0,122,123,124,125,127,128,129,131,132,134,135,136,140,141,192,193,194],[0,123,124,125,126,128,129,130,132,133,135,136,137,141,142,192,193,194],[0,124,125,126,127,129,130,131,133,134,136,137,138,142,143,192,193,194],[0,125,126,127,128,130,131,132,134,135,137,138,139,143,144,192,193,194],[0,122,123,124,125,126,133,134,138,139,141,144,192,193,194],[0,122,126,128,129,131,132,136,139,141,142,192,193,194],[0,123,127,129,130,132,133,137,140,142,143,192,193,194],[0,124,128,130,131,133,134,138,141,143,144,192,193,194],[0,122,123,124,127,128,136,139,140,141,142,144,192,193,194],[0,122,127,131,132,134,135,136,137,142,143,192,193,194],[0,123,128,132,133,135,136,137,138,143,144,192,193,194],[0,122,123,125,127,128,131,132,133,135,137,138,139,140,141,144,192,193,194],[0,122,125,126,127,131,133,135,138,139,142,192,193,194],[0,123,126,127,128,132,134,136,139,140,143,192,193,194],[0,124,127,128,129,133,135,137,140,141,144,192,193,194],[0,122,123,124,127,130,131,132,135,138,140,142,192,193,194],[0,123,124,125,128,131,132,133,136,139,141,143,192,193,194],[0,124,125,126,129,132,133,134,137,140,142,144,192,193,194],[0,122,123,124,126,128,129,130,131,132,133,136,138,140,143,192,193,194],[0,123,124,125,127,129,130,131,132,133,134,137,139,141,144,192,193,194],[0,122,123,126,127,129,130,133,136,138,141,142,192,193,194],[0,123,124,127,128,130,131,134,137,139,142,143,192,193,194],[0,124,125,128,129,131,132,135,138,140,143,144,192,193,194],[0,122,123,124,126,127,128,130,131,133,134,135,139,140,144,192,193,194],[0,122,192,193,194],[0,123,192,193,194],[0,124,192,193,194],[0,125,192,193,194],[0,126,192,193,194],[0,127,192,193,194],[0,128,192,193,194],[0,129,192,193,194],[0,130,192,193,194],[0,131,192,193,194],[0,132,192,193,194],[0,133,192,193,194],[0,134,192,193,194],[0,135,192,193,194],[0,136,192,193,194],[0,137,192,193,194],[0,138,192,193,194],[0,139,192,193,194],[0,140,192,193,194],[0,141,192,193,194],[0,142,192,193,194],[0,143,192,193,194],[0,144,192,193,194],[0,122,123,124,125,127,128,129,131,132,134,135,136,140,141,191,192,193,194],[0,123,124,125,126,128,129,130,132,133,135,136,137,141,142,191,192,193,194],[0,124,125,126,127,129,130,131,133,134,136,137,138,142,143,191,192,193,194],[0,125,126,127,128,130,131,132,134,135,137,138,139,143,144,191,192,193,194],[0,122,123,124,125,126,133,134,138,139,141,144,191,192,193,194],[0,122,126,128,129,131,132,136,139,141,142,191,192,193,194],[0,123,127,129,130,132,133,137,140,142,143,191,192,193,194],[0,124,128,130,131,133,134,138,141,143,144,191,192,193,194],[0,122,123,124,127,128,136,139,140,141,142,144,191,192,193,194],[0,122,127,131,132,134,135,136,137,142,143,191,192,193,194],[0,123,128,132,133,135,136,137,138,143,144,191,192,193,194],[0,122,123,125,127,128,131,132,133,135,137,138,139,140,141,144,191,192,193,194],[0,122,125,126,127,131,133,135,138,139,142,191,192,193,194],[0,123,126,127,128,132,134,136,139,140,143,191,192,193,194],[0,124,127,128,129,133,135,137,140,141,144,191,192,193,194],[0,122,123,124,127,130,131,132,135,138,140,142,191,192,193,194],[0,123,124,125,128,131,132,133,136,139,141,143,191,192,193,194],[0,124,125,126,129,132,133,134,137,140,142,144,191,192,193,194],[0,122,123,124,126,128,129,130,131,132,133,136,138,140,143,191,192,193,194],[0,123,124,125,127,129,130,131,132,133,134,137,139,141,144,191,192,193,194],[0,122,123,126,127,129,130,133,136,138,141,142,191,192,193,194],[0,123,124,127,128,130,131,134,137,139,142,143,191,192,193,194],[0,124,125,128,129,131,132,135,138,140,143,144,191,192,193,194],[0,122,123,124,126,127,128,130,131,133,134,135,139,140,144,191,192,193,194],[0,122,191,192,193,194],[0,123,191,192,193,194],[0,124,191,192,193,194],[0,125,191,192,193,194],[0,126,191,192,193,194],[0,127,191,192,193,194],[0,128,191,192,193,194],[0,129,191,192,193,194],[0,130,191,192,193,194],[0,131,191,192,193,194],[0,132,191,192,193,194],[0,133,191,192,193,194],[0,134,191,192,193,194],[0,135,191,192,193,194],[0,136,191,192,193,194],[0,137,191,192,193,194],[0,138,191,192,193,194],[0,139,191,192,193,194],[0,140,191,192,193,194],[0,141,191,192,193,194],[0,142,191,192,193,194],[0,143,191,192,193,194],[0,144,191,192,193,194],[0,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,191,192,193,194],[0,145,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,191,192,193,194],[0,146,191,192,193,194],[0,147,191,192,193,194],[0,148,191,192,193,194],[0,146,147,148,149,150,151,153,154,156,157,158,159,160,161,162,163,191,192,193,194],[0,150,191,192,193,194],[0,151,191,192,193,194],[0,146,147,148,150,151,152,153,154,156,157,158,159,160,161,162,163,191,192,193,194],[0,153,191,192,193,194],[0,154,191,192,193,194],[0,146,147,148,150,151,153,154,155,156,157,158,159,160,161,162,163,191,192,193,194],[0,156,191,192,193,194],[0,157,191,192,193,194],[0,158,191,192,193,194],[0,159,191,192,193,194],[0,160,191,192,193,194],[0,161,191,192,193,194],[0,162,191,192,193,194],[0,163,191,192,193,194],[0,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,164,191,192,193,194],[0,145,147,149,152,153,154,156,157,158,159,160,161,162,163,191,192,193,194],[0,145,146,149,151,156,157,158,159,160,161,162,163,191,192,193,194],[0,145,146,147,149,151,153,154,155,158,159,160,161,162,163,191,192,193,194],[0,145,147,148,149,150,151,152,156,157,158,160,161,162,163,191,192,193,194],[0,146,150,155,156,157,158,159,161,162,163,191,192,193,194],[0,145,149,150,152,153,154,155,156,157,159,160,163,191,192,193,194],[0,145,148,150,151,153,154,157,159,161,162,163,164,191,192,193,194],[0,148,152,153,154,155,159,161,162,163,164,191,192,193,194],[0,146,147,149,150,152,153,154,156,157,159,160,162,163,164,191,192,193,194],[0,148,152,153,154,156,158,159,160,161,162,191,192,193,194],[0,147,151,152,155,156,158,159,160,163,164,191,192,193,194],[0,145,146,148,149,150,152,153,155,157,159,160,161,191,192,193,194],[0,149,150,151,152,154,155,157,159,160,161,191,192,193,194],[0,145,146,150,152,154,158,160,161,163,164,191,192,193,194],[0,145,147,148,149,152,154,157,158,160,161,163,164,191,192,193,194],[0,145,147,148,149,152,154,155,158,191,192,193,194],[0,146,147,152,153,154,155,157,158,191,192,193,194],[0,146,147,148,149,151,155,157,158,191,192,193,194],[0,148,150,151,152,154,155,157,158,191,192,193,194],[0,145,146,151,152,156,159,160,161,163,164,191,192,193,194],[0,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,145,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,146,190,191,192,193,194],[0,147,190,191,192,193,194],[0,148,190,191,192,193,194],[0,146,147,148,149,150,151,153,154,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,150,190,191,192,193,194],[0,151,190,191,192,193,194],[0,146,147,148,150,151,152,153,154,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,153,190,191,192,193,194],[0,154,190,191,192,193,194],[0,146,147,148,150,151,153,154,155,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,156,190,191,192,193,194],[0,157,190,191,192,193,194],[0,158,190,191,192,193,194],[0,159,190,191,192,193,194],[0,160,190,191,192,193,194],[0,161,190,191,192,193,194],[0,162,190,191,192,193,194],[0,163,190,191,192,193,194],[0,146,147,148,150,151,153,154,156,157,158,159,160,161,162,163,164,190,191,192,193,194],[0,145,147,149,152,153,154,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,145,146,149,151,156,157,158,159,160,161,162,163,190,191,192,193,194],[0,145,146,147,149,151,153,154,155,158,159,160,161,162,163,190,191,192,193,194],[0,145,147,148,149,150,151,152,156,157,158,160,161,162,163,190,191,192,193,194],[0,146,150,155,156,157,158,159,161,162,163,190,191,192,193,194],[0,145,149,150,152,153,154,155,156,157,159,160,163,190,191,192,193,194],[0,145,148,150,151,153,154,157,159,161,162,163,164,190,191,192,193,194],[0,148,152,153,154,155,159,161,162,163,164,190,191,192,193,194],[0,146,147,149,150,152,153,154,156,157,159,160,162,163,164,190,191,192,193,194],[0,148,152,153,154,156,158,159,160,161,162,190,191,192,193,194],[0,147,151,152,155,156,158,159,160,163,164,190,191,192,193,194],[0,145,146,148,149,150,152,153,155,157,159,160,161,190,191,192,193,194],[0,149,150,151,152,154,155,157,159,160,161,190,191,192,193,194],[0,145,146,150,152,154,158,160,161,163,164,190,191,192,193,194],[0,145,147,148,149,152,154,157,158,160,161,163,164,190,191,192,193,194],[0,145,147,148,149,152,154,155,158,190,191,192,193,194],[0,146,147,152,153,154,155,157,158,190,191,192,193,194],[0,146,147,148,149,151,155,157,158,190,191,192,193,194],[0,148,150,151,152,154,155,157,158,190,191,192,193,194],[0,145,146,151,152,156,159,160,161,163,164,190,191,192,193,194],[0,165,166,170,171,172,174,190,191,192,193,194],[0,166,167,171,172,173,175,190,191,192,193,194],[0,165,166,167,168,170,171,173,190,191,192,193,194],[0,166,167,168,169,171,172,174,190,191,192,193,194],[0,167,168,169,170,172,173,175,190,191,192,193,194],[0,165,166,168,169,172,173,190,191,192,193,194],[0,166,167,169,170,173,174,190,191,192,193,194],[0,167,168,170,171,174,175,190,191,192,193,194],[0,165,166,168,169,170,174,175,190,191,192,193,194],[0,165,167,169,172,174,175,190,191,192,193,194],[0,165,168,171,172,173,174,175,190,191,192,193,194],[0,165,169,170,171,173,175,190,191,192,193,194],[0,165,190,191,192,193,194],[0,166,190,191,192,193,194],[0,167,190,191,192,193,194],[0,168,190,191,192,193,194],[0,169,190,191,192,193,194],[0,170,190,191,192,193,194],[0,171,190,191,192,193,194],[0,172,190,191,192,193,194],[0,173,190,191,192,193,194],[0,174,190,191,192,193,194],[0,175,190,191,192,193,194],[0,165,166,170,171,172,174,189,190,191,192,193,194],[0,166,167,171,172,173,175,189,190,191,192,193,194],[0,165,166,167,168,170,171,173,189,190,191,192,193,194],[0,166,167,168,169,171,172,174,189,190,191,192,193,194],[0,167,168,169,170,172,173,175,189,190,191,192,193,194],[0,165,166,168,169,172,173,189,190,191,192,193,194],[0,166,167,169,170,173,174,189,190,191,192,193,194],[0,167,168,170,171,174,175,189,190,191,192,193,194],[0,165,166,168,169,170,174,175,189,190,191,192,193,194],[0,165,167,169,172,174,175,189,190,191,192,193,194],[0,165,168,171,172,173,174,175,189,190,191,192,193,194],[0,165,169,170,171,173,175,189,190,191,192,193,194],[0,165,189,190,191,192,193,194],[0,166,189,190,191,192,193,194],[0,167,189,190,191,192,193,194],[0,168,189,190,191,192,193,194],[0,169,189,190,191,192,193,194],[0,170,189,190,191,192,193,194],[0,171,189,190,191,192,193,194],[0,172,189,190,191,192,193,194],[0,173,189,190,191,192,193,194],[0,174,189,190,191,192,193,194],[0,175,189,190,191,192,193,194],[0,177,183,189,190,191,192,193,194],[0,176,182,183,189,190,191,192,193,194],[0,176,182,189,190,191,192,193,194],[0,181,183,189,190,191,192,193,194],[0,177,178,180,189,190,191,192,193,194],[0,181,182,189,190,191,192,193,194],[0,179,183,189,190,191,192,193,194],[0,176,179,183,189,190,191,192,193,194],[0,176,179,189,190,191,192,193,194],[0,178,180,189,190,191,192,193,194],[0,178,189,190,191,192,193,194],[0,181,189,190,191,192,193,194],[0,181,182,183,189,190,191,192,193,194],[0,177,178,189,190,191,192,193,194],[0,179,189,190,191,192,193,194],[0,180,183,189,190,191,192,193,194],[0,177,180,183,189,190,191,192,193,194],[0,177,183,188,189,190,191,192,193,194],[0,176,182,183,188,189,190,191,192,193,194],[0,176,182,188,189,190,191,192,193,194],[0,181,183,188,189,190,191,192,193,194],[0,177,178,180,188,189,190,191,192,193,194],[0,181,182,188,189,190,191,192,193,194],[0,179,183,188,189,190,191,192,193,194],[0,176,179,183,188,189,190,191,192,193,194],[0,176,179,188,189,190,191,192,193,194],[0,178,180,188,189,190,191,192,193,194],[0,178,188,189,190,191,192,193,194],[0,181,188,189,190,191,192,193,194],[0,181,182,183,188,189,190,191,192,193,194],[0,177,178,188,189,190,191,192,193,194],[0,179,188,189,190,191,192,193,194],[0,180,183,188,189,190,191,192,193,194],[0,177,180,183,188,189,190,191,192,193,194],[0,184,185,188,189,190,191,192,193,194],[0,185,186,188,189,190,191,192,193,194],[0,184,185,186,188,189,190,191,192,193,194],[0,184,186,188,189,190,191,192,193,194],[0,184,188,189,190,191,192,193,194],[0,185,188,189,190,191,192,193,194],[0,186,188,189,190,191,192,193,194],[0,184,185,187,188,189,190,191,192,193,194],[0,185,186,187,188,189,190,191,192,193,194],[0,184,185,186,187,188,189,190,191,192,193,194],[0,184,186,187,188,189,190,191,192,193,194],[0,184,187,188,189,190,191,192,193,194],[0,185,187,188,189,190,191,192,193,194],[0,186,187,188,189,190,191,192,193,194],[0,187,188,189,190,191,192,193,194]]},"distance":{"d":6,"is_exact":false,"upper":17,"witness":[0,101,202,281,360,425,490,537,584,625,666,689,712,729,746,753,760],"A_d":null,"certified":{"d":17,"is_exact":false,"met":true,"source":"built here by the doubling of Jain and Albert (arXiv:2408.12752) from A. Gong's [[559,1,15]] (github.com/gongaa/RM127, triply-even/): [[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[559,1,15]]; their doubling theorem (Sec. III) gives d >= min(d_sd, d_tri + 2) = 17, with d_sd at least the classical distance less one (their Lemma 2.4) and the distances of Gong's self-dual [[41,1,9]] and [[65,1,13]] codes proved here by enumerating every word of their stabiliser spaces"}},"clifford":{"kind":"powers","correction":{"S":[[1,2],[2,2],[3,2],[4,2],[8,2],[10,2],[12,2],[16,2],[17,2],[21,2],[26,2],[27,2],[28,2],[33,2],[35,2],[36,2],[37,2],[38,2],[42,2],[45,2],[48,2],[50,2],[194,2]],"CZ":[[1,194],[2,194],[3,194],[4,194],[8,194],[10,194],[12,194],[16,194],[17,194],[21,194],[26,194],[27,194],[28,194],[33,194],[35,194],[36,194],[37,194],[38,194],[42,194],[45,194],[48,194],[50,194]]},"rotation_powers":[[0,3],[3,3],[6,3],[7,3],[8,3],[9,3],[10,3],[11,3],[14,3],[16,3],[19,3],[20,3],[24,3],[27,3],[31,3],[32,3],[33,3],[37,3],[40,3],[41,3],[43,3],[44,3],[46,3],[47,3],[48,3],[51,3],[101,3],[104,3],[107,3],[108,3],[109,3],[110,3],[111,3],[112,3],[115,3],[117,3],[120,3],[121,3],[125,3],[128,3],[132,3],[133,3],[134,3],[138,3],[141,3],[142,3],[144,3],[145,3],[147,3],[148,3],[149,3],[152,3]]},"metrics":{"gamma":3.702859380293991,"gamma_t":3.702859380293991,"gamma_rho":3.702859380293991,"gamma_claim":2.3417344732547054,"gamma_t_claim":2.3417344732547054,"gamma_rho_claim":2.3417344732547054,"v_ex":1,"rate":0.001314060446780552,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling of Gong's codes"],"discovery":"pre-existing","strongest_claim":"a code built here by the doubling method of Jain and Albert (arXiv:2408.12752) from the codes in A. Gong's repository (github.com/gongaa/RM127, triply-even/): her [[559,1,15]] doubled with the self-dual CSS codes of the paper's Table I from distance 17 on (transversal_t_codes/); a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling of Gong's codes","file":"transversal_t_codes/factories.json","label":"GJ-761","N":195,"d":6,"d_is_exact":false,"origin":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance\", IEEE J. Sel. Areas Inf. Theory 6, 127 (2025), arXiv:2408.12752; A. Gong, \"On some K=1 codes admitting strongly transversal T\", note in github.com/gongaa/RM127, triply-even/ (2025)","provenance":"[[101,1,17]] code of the self-dual [102,51,18] code sub(XQ103) doubled onto [[559,1,15]]: the doubling method of Jain and Albert (arXiv:2408.12752) applied to the codes in A. Gong's repository (github.com/gongaa/RM127)"}]},"references":[{"key":"jain2025transversal","short":"Jain & Albert (2025)","full":"S. P. Jain and V. V. Albert, \"Transversal Clifford and T-gate codes of short length and high distance,\" IEEE J. Sel. Areas Inf. Theory 6, 127-137 (2025); arXiv:2408.12752.","url":"https://doi.org/10.1109/JSAIT.2025.3570832","date":"2025-05-16"},{"key":"gong2025triply","short":"Gong (2025)","full":"A. Gong, \"On some K=1 codes admitting strongly transversal T,\" note in the RM127 repository, triply-even/ (2025).","url":"https://github.com/gongaa/RM127/tree/main/triply-even","date":"2025-04-10"}]}