{"id":"805.1.6.a","row":1231,"stored":{"file":"master_catalog.json","row":1231,"construction":null,"columns_sha256":null},"parameters":{"n":805,"k":1,"d":6,"N":206,"r":205,"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":[[0,1,2,4,9,10,13,14,15,16,18,19,20,21,27,29,30,31,32,33,36,38,43,44,45,49,50],[0,2,3,5,10,11,14,15,16,17,19,20,21,22,28,30,31,32,33,34,37,39,44,45,46,50,51],[0,1,2,3,6,9,10,11,12,13,14,17,19,22,23,27,30,34,35,36,40,43,44,46,47,49,50,51],[0,1,3,7,9,11,12,16,19,21,23,24,27,28,29,30,32,33,35,37,38,41,43,47,48,49,51],[0,1,8,9,12,14,15,16,17,18,19,21,22,24,25,27,28,32,34,39,42,43,45,48],[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],[0,4,11,12,15,17,18,19,20,21,22,24,25,27,28,30,31,35,37,42,45,46,48,51],[0,1,2,4,5,9,10,12,14,15,22,23,25,26,27,28,30,33,44,45,46,47,50],[0,2,3,5,6,10,11,13,15,16,23,24,26,27,28,29,31,34,45,46,47,48,51],[0,1,2,3,6,7,9,10,11,12,13,15,17,18,19,20,21,24,25,28,31,33,35,36,38,43,44,45,46,47,48,50],[0,2,3,4,7,8,10,11,12,13,14,16,18,19,20,21,22,25,26,29,32,34,36,37,39,44,45,46,47,48,49,51],[0,1,2,3,5,8,10,11,12,16,17,18,22,23,26,29,31,32,35,36,37,40,43,44,46,47,48],[0,2,3,4,6,9,11,12,13,17,18,19,23,24,27,30,32,33,36,37,38,41,44,45,47,48,49],[0,3,4,5,7,10,12,13,14,18,19,20,24,25,28,31,33,34,37,38,39,42,45,46,48,49,50],[0,4,5,6,8,11,13,14,15,19,20,21,25,26,29,32,34,35,38,39,40,43,46,47,49,50,51],[0,1,2,4,5,6,7,10,12,13,18,19,22,26,29,31,32,35,38,39,40,41,43,45,47,48,49,51],[0,1,3,4,5,6,7,8,9,10,11,15,16,18,21,23,29,31,38,39,40,41,42,43,45,46,48],[0,2,4,5,6,7,8,9,10,11,12,16,17,19,22,24,30,32,39,40,41,42,43,44,46,47,49],[0,3,5,6,7,8,9,10,11,12,13,17,18,20,23,25,31,33,40,41,42,43,44,45,47,48,50],[0,4,6,7,8,9,10,11,12,13,14,18,19,21,24,26,32,34,41,42,43,44,45,46,48,49,51],[0,1,2,4,5,7,8,11,12,16,18,21,22,25,29,30,31,32,35,36,38,42,46,47],[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],[0,5,6,8,9,11,12,15,16,20,22,25,26,29,33,34,35,36,39,40,42,46,50,51],[0,1,2,4,6,7,12,14,15,17,18,19,20,23,26,29,31,32,33,34,35,37,38,40,41,44,45,47,49,50,51],[0,1,3,4,5,7,8,9,10,14,24,29,31,34,35,39,41,42,43,44,46,48,49,51],[0,1,5,6,8,11,13,14,16,18,19,20,21,25,27,29,31,33,35,38,40,42,47],[0,2,6,7,9,12,14,15,17,19,20,21,22,26,28,30,32,34,36,39,41,43,48],[0,3,7,8,10,13,15,16,18,20,21,22,23,27,29,31,33,35,37,40,42,44,49],[0,4,8,9,11,14,16,17,19,21,22,23,24,28,30,32,34,36,38,41,43,45,50],[0,5,9,10,12,15,17,18,20,22,23,24,25,29,31,33,35,37,39,42,44,46,51],[0,1,2,4,6,9,11,14,15,20,23,24,25,26,27,29,31,33,34,40,44,47,49,50],[0,2,3,5,7,10,12,15,16,21,24,25,26,27,28,30,32,34,35,41,45,48,50,51],[0,1,2,3,6,8,9,10,11,14,15,17,18,19,20,21,22,25,26,28,30,32,35,38,42,43,44,45,46,50,51],[0,1,3,7,11,12,13,14,22,23,26,30,32,38,39,46,47,49,50,51],[0,1,8,9,10,12,16,18,19,20,21,23,24,29,30,32,36,38,39,40,43,44,45,47,48,49,51],[0,1,4,11,14,15,16,17,18,22,24,25,27,29,32,36,37,38,39,40,41,43,46,48],[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],[0,4,7,14,17,18,19,20,21,25,27,28,30,32,35,39,40,41,42,43,44,46,49,51],[0,1,2,4,5,8,9,10,13,14,16,22,26,27,28,30,32,38,40,41,42,47,49],[0,2,3,5,6,9,10,11,14,15,17,23,27,28,29,31,33,39,41,42,43,48,50],[0,3,4,6,7,10,11,12,15,16,18,24,28,29,30,32,34,40,42,43,44,49,51],[0,1,2,5,7,8,9,10,11,12,14,15,17,18,20,21,25,27,32,35,36,38,41,49],[0,2,3,6,8,9,10,11,12,13,15,16,18,19,21,22,26,28,33,36,37,39,42,50],[0,3,4,7,9,10,11,12,13,14,16,17,19,20,22,23,27,29,34,37,38,40,43,51],[0,1,2,5,8,9,11,12,16,17,19,23,24,27,28,29,31,32,33,35,36,39,41,43,45,49,50],[0,2,3,6,9,10,12,13,17,18,20,24,25,28,29,30,32,33,34,36,37,40,42,44,46,50,51],[0,1,2,3,7,9,11,15,16,20,25,26,27,32,34,35,36,37,41,44,47,49,50,51],[0,1,3,8,9,12,13,14,15,17,18,19,20,26,28,29,30,31,32,35,37,42,43,44,48,49,51],[0,1],[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],[0,51],[0,1,2,4,9,10,13,14,15,16,18,19,20,21,27,29,30,31,32,33,36,38,43,44,45,49,50,205],[0,2,3,5,10,11,14,15,16,17,19,20,21,22,28,30,31,32,33,34,37,39,44,45,46,50,51,205],[0,1,2,3,6,9,10,11,12,13,14,17,19,22,23,27,30,34,35,36,40,43,44,46,47,49,50,51,205],[0,1,3,7,9,11,12,16,19,21,23,24,27,28,29,30,32,33,35,37,38,41,43,47,48,49,51,205],[0,1,8,9,12,14,15,16,17,18,19,21,22,24,25,27,28,32,34,39,42,43,45,48,205],[0,2,9,10,13,15,16,17,18,19,20,22,23,25,26,28,29,33,35,40,43,44,46,49,205],[0,3,10,11,14,16,17,18,19,20,21,23,24,26,27,29,30,34,36,41,44,45,47,50,205],[0,4,11,12,15,17,18,19,20,21,22,24,25,27,28,30,31,35,37,42,45,46,48,51,205],[0,1,2,4,5,9,10,12,14,15,22,23,25,26,27,28,30,33,44,45,46,47,50,205],[0,2,3,5,6,10,11,13,15,16,23,24,26,27,28,29,31,34,45,46,47,48,51,205],[0,1,2,3,6,7,9,10,11,12,13,15,17,18,19,20,21,24,25,28,31,33,35,36,38,43,44,45,46,47,48,50,205],[0,2,3,4,7,8,10,11,12,13,14,16,18,19,20,21,22,25,26,29,32,34,36,37,39,44,45,46,47,48,49,51,205],[0,1,2,3,5,8,10,11,12,16,17,18,22,23,26,29,31,32,35,36,37,40,43,44,46,47,48,205],[0,2,3,4,6,9,11,12,13,17,18,19,23,24,27,30,32,33,36,37,38,41,44,45,47,48,49,205],[0,3,4,5,7,10,12,13,14,18,19,20,24,25,28,31,33,34,37,38,39,42,45,46,48,49,50,205],[0,4,5,6,8,11,13,14,15,19,20,21,25,26,29,32,34,35,38,39,40,43,46,47,49,50,51,205],[0,1,2,4,5,6,7,10,12,13,18,19,22,26,29,31,32,35,38,39,40,41,43,45,47,48,49,51,205],[0,1,3,4,5,6,7,8,9,10,11,15,16,18,21,23,29,31,38,39,40,41,42,43,45,46,48,205],[0,2,4,5,6,7,8,9,10,11,12,16,17,19,22,24,30,32,39,40,41,42,43,44,46,47,49,205],[0,3,5,6,7,8,9,10,11,12,13,17,18,20,23,25,31,33,40,41,42,43,44,45,47,48,50,205],[0,4,6,7,8,9,10,11,12,13,14,18,19,21,24,26,32,34,41,42,43,44,45,46,48,49,51,205],[0,1,2,4,5,7,8,11,12,16,18,21,22,25,29,30,31,32,35,36,38,42,46,47,205],[0,2,3,5,6,8,9,12,13,17,19,22,23,26,30,31,32,33,36,37,39,43,47,48,205],[0,3,4,6,7,9,10,13,14,18,20,23,24,27,31,32,33,34,37,38,40,44,48,49,205],[0,4,5,7,8,10,11,14,15,19,21,24,25,28,32,33,34,35,38,39,41,45,49,50,205],[0,5,6,8,9,11,12,15,16,20,22,25,26,29,33,34,35,36,39,40,42,46,50,51,205],[0,1,2,4,6,7,12,14,15,17,18,19,20,23,26,29,31,32,33,34,35,37,38,40,41,44,45,47,49,50,51,205],[0,1,3,4,5,7,8,9,10,14,24,29,31,34,35,39,41,42,43,44,46,48,49,51,205],[0,1,5,6,8,11,13,14,16,18,19,20,21,25,27,29,31,33,35,38,40,42,47,205],[0,2,6,7,9,12,14,15,17,19,20,21,22,26,28,30,32,34,36,39,41,43,48,205],[0,3,7,8,10,13,15,16,18,20,21,22,23,27,29,31,33,35,37,40,42,44,49,205],[0,4,8,9,11,14,16,17,19,21,22,23,24,28,30,32,34,36,38,41,43,45,50,205],[0,5,9,10,12,15,17,18,20,22,23,24,25,29,31,33,35,37,39,42,44,46,51,205],[0,1,2,4,6,9,11,14,15,20,23,24,25,26,27,29,31,33,34,40,44,47,49,50,205],[0,2,3,5,7,10,12,15,16,21,24,25,26,27,28,30,32,34,35,41,45,48,50,51,205],[0,1,2,3,6,8,9,10,11,14,15,17,18,19,20,21,22,25,26,28,30,32,35,38,42,43,44,45,46,50,51,205],[0,1,3,7,11,12,13,14,22,23,26,30,32,38,39,46,47,49,50,51,205],[0,1,8,9,10,12,16,18,19,20,21,23,24,29,30,32,36,38,39,40,43,44,45,47,48,49,51,205],[0,1,4,11,14,15,16,17,18,22,24,25,27,29,32,36,37,38,39,40,41,43,46,48,205],[0,2,5,12,15,16,17,18,19,23,25,26,28,30,33,37,38,39,40,41,42,44,47,49,205],[0,3,6,13,16,17,18,19,20,24,26,27,29,31,34,38,39,40,41,42,43,45,48,50,205],[0,4,7,14,17,18,19,20,21,25,27,28,30,32,35,39,40,41,42,43,44,46,49,51,205],[0,1,2,4,5,8,9,10,13,14,16,22,26,27,28,30,32,38,40,41,42,47,49,205],[0,2,3,5,6,9,10,11,14,15,17,23,27,28,29,31,33,39,41,42,43,48,50,205],[0,3,4,6,7,10,11,12,15,16,18,24,28,29,30,32,34,40,42,43,44,49,51,205],[0,1,2,5,7,8,9,10,11,12,14,15,17,18,20,21,25,27,32,35,36,38,41,49,205],[0,2,3,6,8,9,10,11,12,13,15,16,18,19,21,22,26,28,33,36,37,39,42,50,205],[0,3,4,7,9,10,11,12,13,14,16,17,19,20,22,23,27,29,34,37,38,40,43,51,205],[0,1,2,5,8,9,11,12,16,17,19,23,24,27,28,29,31,32,33,35,36,39,41,43,45,49,50,205],[0,2,3,6,9,10,12,13,17,18,20,24,25,28,29,30,32,33,34,36,37,40,42,44,46,50,51,205],[0,1,2,3,7,9,11,15,16,20,25,26,27,32,34,35,36,37,41,44,47,49,50,51,205],[0,1,3,8,9,12,13,14,15,17,18,19,20,26,28,29,30,31,32,35,37,42,43,44,48,49,51,205],[0,1,205],[0,2,205],[0,3,205],[0,4,205],[0,5,205],[0,6,205],[0,7,205],[0,8,205],[0,9,205],[0,10,205],[0,11,205],[0,12,205],[0,13,205],[0,14,205],[0,15,205],[0,16,205],[0,17,205],[0,18,205],[0,19,205],[0,20,205],[0,21,205],[0,22,205],[0,23,205],[0,24,205],[0,25,205],[0,26,205],[0,27,205],[0,28,205],[0,29,205],[0,30,205],[0,31,205],[0,32,205],[0,33,205],[0,34,205],[0,35,205],[0,36,205],[0,37,205],[0,38,205],[0,39,205],[0,40,205],[0,41,205],[0,42,205],[0,43,205],[0,44,205],[0,45,205],[0,46,205],[0,47,205],[0,48,205],[0,49,205],[0,50,205],[0,51,205],[0,52,53,54,56,57,63,65,66,68,70,71,72,73,76,77,78,79,81,82,83,87,88,205],[0,53,54,55,57,58,64,66,67,69,71,72,73,74,77,78,79,80,82,83,84,88,89,205],[0,54,55,56,58,59,65,67,68,70,72,73,74,75,78,79,80,81,83,84,85,89,90,205],[0,52,53,54,55,59,60,63,65,69,70,72,74,75,77,78,80,83,84,85,86,87,88,90,205],[0,52,55,57,60,61,63,64,65,68,72,75,77,82,83,84,85,86,89,205],[0,53,56,58,61,62,64,65,66,69,73,76,78,83,84,85,86,87,90,205],[0,52,53,56,59,62,67,68,71,72,73,74,76,78,81,82,83,84,85,86,205],[0,53,54,57,60,63,68,69,72,73,74,75,77,79,82,83,84,85,86,87,205],[0,54,55,58,61,64,69,70,73,74,75,76,78,80,83,84,85,86,87,88,205],[0,55,56,59,62,65,70,71,74,75,76,77,79,81,84,85,86,87,88,89,205],[0,56,57,60,63,66,71,72,75,76,77,78,80,82,85,86,87,88,89,90,205],[0,52,53,54,56,58,61,63,64,65,66,67,68,70,71,82,86,89,90,205],[0,52,55,56,59,62,63,64,67,69,70,73,76,77,78,79,81,82,88,90,205],[0,52,54,60,64,66,72,73,74,76,80,81,87,88,89,205],[0,53,55,61,65,67,73,74,75,77,81,82,88,89,90,205],[0,52,53,57,62,63,65,70,71,72,73,74,75,77,79,81,87,88,89,90,205],[0,52,56,57,58,64,65,68,70,74,75,77,79,80,81,83,87,89,90,205],[0,52,54,56,58,59,63,68,69,70,72,73,75,77,79,80,83,84,87,90,205],[0,52,54,55,56,59,60,63,64,65,66,68,69,72,74,77,79,80,82,83,84,85,87,205],[0,53,55,56,57,60,61,64,65,66,67,69,70,73,75,78,80,81,83,84,85,86,88,205],[0,54,56,57,58,61,62,65,66,67,68,70,71,74,76,79,81,82,84,85,86,87,89,205],[0,55,57,58,59,62,63,66,67,68,69,71,72,75,77,80,82,83,85,86,87,88,90,205],[0,52,53,54,57,58,59,60,64,65,66,67,69,71,77,79,82,84,86,89,205],[0,53,54,55,58,59,60,61,65,66,67,68,70,72,78,80,83,85,87,90,205],[0,52,53,55,57,59,60,61,62,63,65,67,69,70,72,76,77,78,82,83,84,86,87,205],[0,53,54,56,58,60,61,62,63,64,66,68,70,71,73,77,78,79,83,84,85,87,88,205],[0,54,55,57,59,61,62,63,64,65,67,69,71,72,74,78,79,80,84,85,86,88,89,205],[0,55,56,58,60,62,63,64,65,66,68,70,72,73,75,79,80,81,85,86,87,89,90,205],[0,52,53,54,59,61,64,67,68,69,70,72,74,77,78,79,80,83,86,90,205],[0,52,55,56,57,60,62,63,66,69,72,75,76,77,80,82,83,84,88,205],[0,53,56,57,58,61,63,64,67,70,73,76,77,78,81,83,84,85,89,205],[0,54,57,58,59,62,64,65,68,71,74,77,78,79,82,84,85,86,90,205],[0,52,53,54,55,56,57,58,59,60,68,69,70,71,73,75,76,77,80,81,82,85,86,88,205],[0,53,54,55,56,57,58,59,60,61,69,70,71,72,74,76,77,78,81,82,83,86,87,89,205],[0,54,55,56,57,58,59,60,61,62,70,71,72,73,75,77,78,79,82,83,84,87,88,90,205],[0,52,53,54,55,58,59,60,61,62,65,66,68,70,74,77,80,81,82,84,85,87,89,205],[0,53,54,55,56,59,60,61,62,63,66,67,69,71,75,78,81,82,83,85,86,88,90,205],[0,52,53,55,60,61,62,64,65,66,67,71,73,77,78,81,84,86,88,89,205],[0,53,54,56,61,62,63,65,66,67,68,72,74,78,79,82,85,87,89,90,205],[0,52,53,55,56,62,64,65,67,69,70,71,72,75,76,77,78,80,81,82,86,87,90,205],[0,52,205],[0,53,205],[0,54,205],[0,55,205],[0,56,205],[0,57,205],[0,58,205],[0,59,205],[0,60,205],[0,61,205],[0,62,205],[0,63,205],[0,64,205],[0,65,205],[0,66,205],[0,67,205],[0,68,205],[0,69,205],[0,70,205],[0,71,205],[0,72,205],[0,73,205],[0,74,205],[0,75,205],[0,76,205],[0,77,205],[0,78,205],[0,79,205],[0,80,205],[0,81,205],[0,82,205],[0,83,205],[0,84,205],[0,85,205],[0,86,205],[0,87,205],[0,88,205],[0,89,205],[0,90,205],[0,52,53,54,56,57,63,65,66,68,70,71,72,73,76,77,78,79,81,82,83,87,88,204,205],[0,53,54,55,57,58,64,66,67,69,71,72,73,74,77,78,79,80,82,83,84,88,89,204,205],[0,54,55,56,58,59,65,67,68,70,72,73,74,75,78,79,80,81,83,84,85,89,90,204,205],[0,52,53,54,55,59,60,63,65,69,70,72,74,75,77,78,80,83,84,85,86,87,88,90,204,205],[0,52,55,57,60,61,63,64,65,68,72,75,77,82,83,84,85,86,89,204,205],[0,53,56,58,61,62,64,65,66,69,73,76,78,83,84,85,86,87,90,204,205],[0,52,53,56,59,62,67,68,71,72,73,74,76,78,81,82,83,84,85,86,204,205],[0,53,54,57,60,63,68,69,72,73,74,75,77,79,82,83,84,85,86,87,204,205],[0,54,55,58,61,64,69,70,73,74,75,76,78,80,83,84,85,86,87,88,204,205],[0,55,56,59,62,65,70,71,74,75,76,77,79,81,84,85,86,87,88,89,204,205],[0,56,57,60,63,66,71,72,75,76,77,78,80,82,85,86,87,88,89,90,204,205],[0,52,53,54,56,58,61,63,64,65,66,67,68,70,71,82,86,89,90,204,205],[0,52,55,56,59,62,63,64,67,69,70,73,76,77,78,79,81,82,88,90,204,205],[0,52,54,60,64,66,72,73,74,76,80,81,87,88,89,204,205],[0,53,55,61,65,67,73,74,75,77,81,82,88,89,90,204,205],[0,52,53,57,62,63,65,70,71,72,73,74,75,77,79,81,87,88,89,90,204,205],[0,52,56,57,58,64,65,68,70,74,75,77,79,80,81,83,87,89,90,204,205],[0,52,54,56,58,59,63,68,69,70,72,73,75,77,79,80,83,84,87,90,204,205],[0,52,54,55,56,59,60,63,64,65,66,68,69,72,74,77,79,80,82,83,84,85,87,204,205],[0,53,55,56,57,60,61,64,65,66,67,69,70,73,75,78,80,81,83,84,85,86,88,204,205],[0,54,56,57,58,61,62,65,66,67,68,70,71,74,76,79,81,82,84,85,86,87,89,204,205],[0,55,57,58,59,62,63,66,67,68,69,71,72,75,77,80,82,83,85,86,87,88,90,204,205],[0,52,53,54,57,58,59,60,64,65,66,67,69,71,77,79,82,84,86,89,204,205],[0,53,54,55,58,59,60,61,65,66,67,68,70,72,78,80,83,85,87,90,204,205],[0,52,53,55,57,59,60,61,62,63,65,67,69,70,72,76,77,78,82,83,84,86,87,204,205],[0,53,54,56,58,60,61,62,63,64,66,68,70,71,73,77,78,79,83,84,85,87,88,204,205],[0,54,55,57,59,61,62,63,64,65,67,69,71,72,74,78,79,80,84,85,86,88,89,204,205],[0,55,56,58,60,62,63,64,65,66,68,70,72,73,75,79,80,81,85,86,87,89,90,204,205],[0,52,53,54,59,61,64,67,68,69,70,72,74,77,78,79,80,83,86,90,204,205],[0,52,55,56,57,60,62,63,66,69,72,75,76,77,80,82,83,84,88,204,205],[0,53,56,57,58,61,63,64,67,70,73,76,77,78,81,83,84,85,89,204,205],[0,54,57,58,59,62,64,65,68,71,74,77,78,79,82,84,85,86,90,204,205],[0,52,53,54,55,56,57,58,59,60,68,69,70,71,73,75,76,77,80,81,82,85,86,88,204,205],[0,53,54,55,56,57,58,59,60,61,69,70,71,72,74,76,77,78,81,82,83,86,87,89,204,205],[0,54,55,56,57,58,59,60,61,62,70,71,72,73,75,77,78,79,82,83,84,87,88,90,204,205],[0,52,53,54,55,58,59,60,61,62,65,66,68,70,74,77,80,81,82,84,85,87,89,204,205],[0,53,54,55,56,59,60,61,62,63,66,67,69,71,75,78,81,82,83,85,86,88,90,204,205],[0,52,53,55,60,61,62,64,65,66,67,71,73,77,78,81,84,86,88,89,204,205],[0,53,54,56,61,62,63,65,66,67,68,72,74,78,79,82,85,87,89,90,204,205],[0,52,53,55,56,62,64,65,67,69,70,71,72,75,76,77,78,80,81,82,86,87,90,204,205],[0,52,204,205],[0,53,204,205],[0,54,204,205],[0,55,204,205],[0,56,204,205],[0,57,204,205],[0,58,204,205],[0,59,204,205],[0,60,204,205],[0,61,204,205],[0,62,204,205],[0,63,204,205],[0,64,204,205],[0,65,204,205],[0,66,204,205],[0,67,204,205],[0,68,204,205],[0,69,204,205],[0,70,204,205],[0,71,204,205],[0,72,204,205],[0,73,204,205],[0,74,204,205],[0,75,204,205],[0,76,204,205],[0,77,204,205],[0,78,204,205],[0,79,204,205],[0,80,204,205],[0,81,204,205],[0,82,204,205],[0,83,204,205],[0,84,204,205],[0,85,204,205],[0,86,204,205],[0,87,204,205],[0,88,204,205],[0,89,204,205],[0,90,204,205],[0,91,92,93,95,96,102,104,105,107,109,110,111,112,115,116,117,118,120,121,122,126,127,204,205],[0,92,93,94,96,97,103,105,106,108,110,111,112,113,116,117,118,119,121,122,123,127,128,204,205],[0,93,94,95,97,98,104,106,107,109,111,112,113,114,117,118,119,120,122,123,124,128,129,204,205],[0,91,92,93,94,98,99,102,104,108,109,111,113,114,116,117,119,122,123,124,125,126,127,129,204,205],[0,91,94,96,99,100,102,103,104,107,111,114,116,121,122,123,124,125,128,204,205],[0,92,95,97,100,101,103,104,105,108,112,115,117,122,123,124,125,126,129,204,205],[0,91,92,95,98,101,106,107,110,111,112,113,115,117,120,121,122,123,124,125,204,205],[0,92,93,96,99,102,107,108,111,112,113,114,116,118,121,122,123,124,125,126,204,205],[0,93,94,97,100,103,108,109,112,113,114,115,117,119,122,123,124,125,126,127,204,205],[0,94,95,98,101,104,109,110,113,114,115,116,118,120,123,124,125,126,127,128,204,205],[0,95,96,99,102,105,110,111,114,115,116,117,119,121,124,125,126,127,128,129,204,205],[0,91,92,93,95,97,100,102,103,104,105,106,107,109,110,121,125,128,129,204,205],[0,91,94,95,98,101,102,103,106,108,109,112,115,116,117,118,120,121,127,129,204,205],[0,91,93,99,103,105,111,112,113,115,119,120,126,127,128,204,205],[0,92,94,100,104,106,112,113,114,116,120,121,127,128,129,204,205],[0,91,92,96,101,102,104,109,110,111,112,113,114,116,118,120,126,127,128,129,204,205],[0,91,95,96,97,103,104,107,109,113,114,116,118,119,120,122,126,128,129,204,205],[0,91,93,95,97,98,102,107,108,109,111,112,114,116,118,119,122,123,126,129,204,205],[0,91,93,94,95,98,99,102,103,104,105,107,108,111,113,116,118,119,121,122,123,124,126,204,205],[0,92,94,95,96,99,100,103,104,105,106,108,109,112,114,117,119,120,122,123,124,125,127,204,205],[0,93,95,96,97,100,101,104,105,106,107,109,110,113,115,118,120,121,123,124,125,126,128,204,205],[0,94,96,97,98,101,102,105,106,107,108,110,111,114,116,119,121,122,124,125,126,127,129,204,205],[0,91,92,93,96,97,98,99,103,104,105,106,108,110,116,118,121,123,125,128,204,205],[0,92,93,94,97,98,99,100,104,105,106,107,109,111,117,119,122,124,126,129,204,205],[0,91,92,94,96,98,99,100,101,102,104,106,108,109,111,115,116,117,121,122,123,125,126,204,205],[0,92,93,95,97,99,100,101,102,103,105,107,109,110,112,116,117,118,122,123,124,126,127,204,205],[0,93,94,96,98,100,101,102,103,104,106,108,110,111,113,117,118,119,123,124,125,127,128,204,205],[0,94,95,97,99,101,102,103,104,105,107,109,111,112,114,118,119,120,124,125,126,128,129,204,205],[0,91,92,93,98,100,103,106,107,108,109,111,113,116,117,118,119,122,125,129,204,205],[0,91,94,95,96,99,101,102,105,108,111,114,115,116,119,121,122,123,127,204,205],[0,92,95,96,97,100,102,103,106,109,112,115,116,117,120,122,123,124,128,204,205],[0,93,96,97,98,101,103,104,107,110,113,116,117,118,121,123,124,125,129,204,205],[0,91,92,93,94,95,96,97,98,99,107,108,109,110,112,114,115,116,119,120,121,124,125,127,204,205],[0,92,93,94,95,96,97,98,99,100,108,109,110,111,113,115,116,117,120,121,122,125,126,128,204,205],[0,93,94,95,96,97,98,99,100,101,109,110,111,112,114,116,117,118,121,122,123,126,127,129,204,205],[0,91,92,93,94,97,98,99,100,101,104,105,107,109,113,116,119,120,121,123,124,126,128,204,205],[0,92,93,94,95,98,99,100,101,102,105,106,108,110,114,117,120,121,122,124,125,127,129,204,205],[0,91,92,94,99,100,101,103,104,105,106,110,112,116,117,120,123,125,127,128,204,205],[0,92,93,95,100,101,102,104,105,106,107,111,113,117,118,121,124,126,128,129,204,205],[0,91,92,94,95,101,103,104,106,108,109,110,111,114,115,116,117,119,120,121,125,126,129,204,205],[0,91,204,205],[0,92,204,205],[0,93,204,205],[0,94,204,205],[0,95,204,205],[0,96,204,205],[0,97,204,205],[0,98,204,205],[0,99,204,205],[0,100,204,205],[0,101,204,205],[0,102,204,205],[0,103,204,205],[0,104,204,205],[0,105,204,205],[0,106,204,205],[0,107,204,205],[0,108,204,205],[0,109,204,205],[0,110,204,205],[0,111,204,205],[0,112,204,205],[0,113,204,205],[0,114,204,205],[0,115,204,205],[0,116,204,205],[0,117,204,205],[0,118,204,205],[0,119,204,205],[0,120,204,205],[0,121,204,205],[0,122,204,205],[0,123,204,205],[0,124,204,205],[0,125,204,205],[0,126,204,205],[0,127,204,205],[0,128,204,205],[0,129,204,205],[0,91,92,93,95,96,102,104,105,107,109,110,111,112,115,116,117,118,120,121,122,126,127,203,204,205],[0,92,93,94,96,97,103,105,106,108,110,111,112,113,116,117,118,119,121,122,123,127,128,203,204,205],[0,93,94,95,97,98,104,106,107,109,111,112,113,114,117,118,119,120,122,123,124,128,129,203,204,205],[0,91,92,93,94,98,99,102,104,108,109,111,113,114,116,117,119,122,123,124,125,126,127,129,203,204,205],[0,91,94,96,99,100,102,103,104,107,111,114,116,121,122,123,124,125,128,203,204,205],[0,92,95,97,100,101,103,104,105,108,112,115,117,122,123,124,125,126,129,203,204,205],[0,91,92,95,98,101,106,107,110,111,112,113,115,117,120,121,122,123,124,125,203,204,205],[0,92,93,96,99,102,107,108,111,112,113,114,116,118,121,122,123,124,125,126,203,204,205],[0,93,94,97,100,103,108,109,112,113,114,115,117,119,122,123,124,125,126,127,203,204,205],[0,94,95,98,101,104,109,110,113,114,115,116,118,120,123,124,125,126,127,128,203,204,205],[0,95,96,99,102,105,110,111,114,115,116,117,119,121,124,125,126,127,128,129,203,204,205],[0,91,92,93,95,97,100,102,103,104,105,106,107,109,110,121,125,128,129,203,204,205],[0,91,94,95,98,101,102,103,106,108,109,112,115,116,117,118,120,121,127,129,203,204,205],[0,91,93,99,103,105,111,112,113,115,119,120,126,127,128,203,204,205],[0,92,94,100,104,106,112,113,114,116,120,121,127,128,129,203,204,205],[0,91,92,96,101,102,104,109,110,111,112,113,114,116,118,120,126,127,128,129,203,204,205],[0,91,95,96,97,103,104,107,109,113,114,116,118,119,120,122,126,128,129,203,204,205],[0,91,93,95,97,98,102,107,108,109,111,112,114,116,118,119,122,123,126,129,203,204,205],[0,91,93,94,95,98,99,102,103,104,105,107,108,111,113,116,118,119,121,122,123,124,126,203,204,205],[0,92,94,95,96,99,100,103,104,105,106,108,109,112,114,117,119,120,122,123,124,125,127,203,204,205],[0,93,95,96,97,100,101,104,105,106,107,109,110,113,115,118,120,121,123,124,125,126,128,203,204,205],[0,94,96,97,98,101,102,105,106,107,108,110,111,114,116,119,121,122,124,125,126,127,129,203,204,205],[0,91,92,93,96,97,98,99,103,104,105,106,108,110,116,118,121,123,125,128,203,204,205],[0,92,93,94,97,98,99,100,104,105,106,107,109,111,117,119,122,124,126,129,203,204,205],[0,91,92,94,96,98,99,100,101,102,104,106,108,109,111,115,116,117,121,122,123,125,126,203,204,205],[0,92,93,95,97,99,100,101,102,103,105,107,109,110,112,116,117,118,122,123,124,126,127,203,204,205],[0,93,94,96,98,100,101,102,103,104,106,108,110,111,113,117,118,119,123,124,125,127,128,203,204,205],[0,94,95,97,99,101,102,103,104,105,107,109,111,112,114,118,119,120,124,125,126,128,129,203,204,205],[0,91,92,93,98,100,103,106,107,108,109,111,113,116,117,118,119,122,125,129,203,204,205],[0,91,94,95,96,99,101,102,105,108,111,114,115,116,119,121,122,123,127,203,204,205],[0,92,95,96,97,100,102,103,106,109,112,115,116,117,120,122,123,124,128,203,204,205],[0,93,96,97,98,101,103,104,107,110,113,116,117,118,121,123,124,125,129,203,204,205],[0,91,92,93,94,95,96,97,98,99,107,108,109,110,112,114,115,116,119,120,121,124,125,127,203,204,205],[0,92,93,94,95,96,97,98,99,100,108,109,110,111,113,115,116,117,120,121,122,125,126,128,203,204,205],[0,93,94,95,96,97,98,99,100,101,109,110,111,112,114,116,117,118,121,122,123,126,127,129,203,204,205],[0,91,92,93,94,97,98,99,100,101,104,105,107,109,113,116,119,120,121,123,124,126,128,203,204,205],[0,92,93,94,95,98,99,100,101,102,105,106,108,110,114,117,120,121,122,124,125,127,129,203,204,205],[0,91,92,94,99,100,101,103,104,105,106,110,112,116,117,120,123,125,127,128,203,204,205],[0,92,93,95,100,101,102,104,105,106,107,111,113,117,118,121,124,126,128,129,203,204,205],[0,91,92,94,95,101,103,104,106,108,109,110,111,114,115,116,117,119,120,121,125,126,129,203,204,205],[0,91,203,204,205],[0,92,203,204,205],[0,93,203,204,205],[0,94,203,204,205],[0,95,203,204,205],[0,96,203,204,205],[0,97,203,204,205],[0,98,203,204,205],[0,99,203,204,205],[0,100,203,204,205],[0,101,203,204,205],[0,102,203,204,205],[0,103,203,204,205],[0,104,203,204,205],[0,105,203,204,205],[0,106,203,204,205],[0,107,203,204,205],[0,108,203,204,205],[0,109,203,204,205],[0,110,203,204,205],[0,111,203,204,205],[0,112,203,204,205],[0,113,203,204,205],[0,114,203,204,205],[0,115,203,204,205],[0,116,203,204,205],[0,117,203,204,205],[0,118,203,204,205],[0,119,203,204,205],[0,120,203,204,205],[0,121,203,204,205],[0,122,203,204,205],[0,123,203,204,205],[0,124,203,204,205],[0,125,203,204,205],[0,126,203,204,205],[0,127,203,204,205],[0,128,203,204,205],[0,129,203,204,205],[0,130,131,132,133,135,136,137,139,140,142,143,144,148,149,203,204,205],[0,131,132,133,134,136,137,138,140,141,143,144,145,149,150,203,204,205],[0,132,133,134,135,137,138,139,141,142,144,145,146,150,151,203,204,205],[0,133,134,135,136,138,139,140,142,143,145,146,147,151,152,203,204,205],[0,130,131,132,133,134,141,142,146,147,149,152,203,204,205],[0,130,134,136,137,139,140,144,147,149,150,203,204,205],[0,131,135,137,138,140,141,145,148,150,151,203,204,205],[0,132,136,138,139,141,142,146,149,151,152,203,204,205],[0,130,131,132,135,136,144,147,148,149,150,152,203,204,205],[0,130,135,139,140,142,143,144,145,150,151,203,204,205],[0,131,136,140,141,143,144,145,146,151,152,203,204,205],[0,130,131,133,135,136,139,140,141,143,145,146,147,148,149,152,203,204,205],[0,130,133,134,135,139,141,143,146,147,150,203,204,205],[0,131,134,135,136,140,142,144,147,148,151,203,204,205],[0,132,135,136,137,141,143,145,148,149,152,203,204,205],[0,130,131,132,135,138,139,140,143,146,148,150,203,204,205],[0,131,132,133,136,139,140,141,144,147,149,151,203,204,205],[0,132,133,134,137,140,141,142,145,148,150,152,203,204,205],[0,130,131,132,134,136,137,138,139,140,141,144,146,148,151,203,204,205],[0,131,132,133,135,137,138,139,140,141,142,145,147,149,152,203,204,205],[0,130,131,134,135,137,138,141,144,146,149,150,203,204,205],[0,131,132,135,136,138,139,142,145,147,150,151,203,204,205],[0,132,133,136,137,139,140,143,146,148,151,152,203,204,205],[0,130,131,132,134,135,136,138,139,141,142,143,147,148,152,203,204,205],[0,130,203,204,205],[0,131,203,204,205],[0,132,203,204,205],[0,133,203,204,205],[0,134,203,204,205],[0,135,203,204,205],[0,136,203,204,205],[0,137,203,204,205],[0,138,203,204,205],[0,139,203,204,205],[0,140,203,204,205],[0,141,203,204,205],[0,142,203,204,205],[0,143,203,204,205],[0,144,203,204,205],[0,145,203,204,205],[0,146,203,204,205],[0,147,203,204,205],[0,148,203,204,205],[0,149,203,204,205],[0,150,203,204,205],[0,151,203,204,205],[0,152,203,204,205],[0,130,131,132,133,135,136,137,139,140,142,143,144,148,149,202,203,204,205],[0,131,132,133,134,136,137,138,140,141,143,144,145,149,150,202,203,204,205],[0,132,133,134,135,137,138,139,141,142,144,145,146,150,151,202,203,204,205],[0,133,134,135,136,138,139,140,142,143,145,146,147,151,152,202,203,204,205],[0,130,131,132,133,134,141,142,146,147,149,152,202,203,204,205],[0,130,134,136,137,139,140,144,147,149,150,202,203,204,205],[0,131,135,137,138,140,141,145,148,150,151,202,203,204,205],[0,132,136,138,139,141,142,146,149,151,152,202,203,204,205],[0,130,131,132,135,136,144,147,148,149,150,152,202,203,204,205],[0,130,135,139,140,142,143,144,145,150,151,202,203,204,205],[0,131,136,140,141,143,144,145,146,151,152,202,203,204,205],[0,130,131,133,135,136,139,140,141,143,145,146,147,148,149,152,202,203,204,205],[0,130,133,134,135,139,141,143,146,147,150,202,203,204,205],[0,131,134,135,136,140,142,144,147,148,151,202,203,204,205],[0,132,135,136,137,141,143,145,148,149,152,202,203,204,205],[0,130,131,132,135,138,139,140,143,146,148,150,202,203,204,205],[0,131,132,133,136,139,140,141,144,147,149,151,202,203,204,205],[0,132,133,134,137,140,141,142,145,148,150,152,202,203,204,205],[0,130,131,132,134,136,137,138,139,140,141,144,146,148,151,202,203,204,205],[0,131,132,133,135,137,138,139,140,141,142,145,147,149,152,202,203,204,205],[0,130,131,134,135,137,138,141,144,146,149,150,202,203,204,205],[0,131,132,135,136,138,139,142,145,147,150,151,202,203,204,205],[0,132,133,136,137,139,140,143,146,148,151,152,202,203,204,205],[0,130,131,132,134,135,136,138,139,141,142,143,147,148,152,202,203,204,205],[0,130,202,203,204,205],[0,131,202,203,204,205],[0,132,202,203,204,205],[0,133,202,203,204,205],[0,134,202,203,204,205],[0,135,202,203,204,205],[0,136,202,203,204,205],[0,137,202,203,204,205],[0,138,202,203,204,205],[0,139,202,203,204,205],[0,140,202,203,204,205],[0,141,202,203,204,205],[0,142,202,203,204,205],[0,143,202,203,204,205],[0,144,202,203,204,205],[0,145,202,203,204,205],[0,146,202,203,204,205],[0,147,202,203,204,205],[0,148,202,203,204,205],[0,149,202,203,204,205],[0,150,202,203,204,205],[0,151,202,203,204,205],[0,152,202,203,204,205],[0,153,154,155,156,158,159,160,162,163,165,166,167,171,172,202,203,204,205],[0,154,155,156,157,159,160,161,163,164,166,167,168,172,173,202,203,204,205],[0,155,156,157,158,160,161,162,164,165,167,168,169,173,174,202,203,204,205],[0,156,157,158,159,161,162,163,165,166,168,169,170,174,175,202,203,204,205],[0,153,154,155,156,157,164,165,169,170,172,175,202,203,204,205],[0,153,157,159,160,162,163,167,170,172,173,202,203,204,205],[0,154,158,160,161,163,164,168,171,173,174,202,203,204,205],[0,155,159,161,162,164,165,169,172,174,175,202,203,204,205],[0,153,154,155,158,159,167,170,171,172,173,175,202,203,204,205],[0,153,158,162,163,165,166,167,168,173,174,202,203,204,205],[0,154,159,163,164,166,167,168,169,174,175,202,203,204,205],[0,153,154,156,158,159,162,163,164,166,168,169,170,171,172,175,202,203,204,205],[0,153,156,157,158,162,164,166,169,170,173,202,203,204,205],[0,154,157,158,159,163,165,167,170,171,174,202,203,204,205],[0,155,158,159,160,164,166,168,171,172,175,202,203,204,205],[0,153,154,155,158,161,162,163,166,169,171,173,202,203,204,205],[0,154,155,156,159,162,163,164,167,170,172,174,202,203,204,205],[0,155,156,157,160,163,164,165,168,171,173,175,202,203,204,205],[0,153,154,155,157,159,160,161,162,163,164,167,169,171,174,202,203,204,205],[0,154,155,156,158,160,161,162,163,164,165,168,170,172,175,202,203,204,205],[0,153,154,157,158,160,161,164,167,169,172,173,202,203,204,205],[0,154,155,158,159,161,162,165,168,170,173,174,202,203,204,205],[0,155,156,159,160,162,163,166,169,171,174,175,202,203,204,205],[0,153,154,155,157,158,159,161,162,164,165,166,170,171,175,202,203,204,205],[0,153,202,203,204,205],[0,154,202,203,204,205],[0,155,202,203,204,205],[0,156,202,203,204,205],[0,157,202,203,204,205],[0,158,202,203,204,205],[0,159,202,203,204,205],[0,160,202,203,204,205],[0,161,202,203,204,205],[0,162,202,203,204,205],[0,163,202,203,204,205],[0,164,202,203,204,205],[0,165,202,203,204,205],[0,166,202,203,204,205],[0,167,202,203,204,205],[0,168,202,203,204,205],[0,169,202,203,204,205],[0,170,202,203,204,205],[0,171,202,203,204,205],[0,172,202,203,204,205],[0,173,202,203,204,205],[0,174,202,203,204,205],[0,175,202,203,204,205],[0,153,154,155,156,158,159,160,162,163,165,166,167,171,172,201,202,203,204,205],[0,154,155,156,157,159,160,161,163,164,166,167,168,172,173,201,202,203,204,205],[0,155,156,157,158,160,161,162,164,165,167,168,169,173,174,201,202,203,204,205],[0,156,157,158,159,161,162,163,165,166,168,169,170,174,175,201,202,203,204,205],[0,153,154,155,156,157,164,165,169,170,172,175,201,202,203,204,205],[0,153,157,159,160,162,163,167,170,172,173,201,202,203,204,205],[0,154,158,160,161,163,164,168,171,173,174,201,202,203,204,205],[0,155,159,161,162,164,165,169,172,174,175,201,202,203,204,205],[0,153,154,155,158,159,167,170,171,172,173,175,201,202,203,204,205],[0,153,158,162,163,165,166,167,168,173,174,201,202,203,204,205],[0,154,159,163,164,166,167,168,169,174,175,201,202,203,204,205],[0,153,154,156,158,159,162,163,164,166,168,169,170,171,172,175,201,202,203,204,205],[0,153,156,157,158,162,164,166,169,170,173,201,202,203,204,205],[0,154,157,158,159,163,165,167,170,171,174,201,202,203,204,205],[0,155,158,159,160,164,166,168,171,172,175,201,202,203,204,205],[0,153,154,155,158,161,162,163,166,169,171,173,201,202,203,204,205],[0,154,155,156,159,162,163,164,167,170,172,174,201,202,203,204,205],[0,155,156,157,160,163,164,165,168,171,173,175,201,202,203,204,205],[0,153,154,155,157,159,160,161,162,163,164,167,169,171,174,201,202,203,204,205],[0,154,155,156,158,160,161,162,163,164,165,168,170,172,175,201,202,203,204,205],[0,153,154,157,158,160,161,164,167,169,172,173,201,202,203,204,205],[0,154,155,158,159,161,162,165,168,170,173,174,201,202,203,204,205],[0,155,156,159,160,162,163,166,169,171,174,175,201,202,203,204,205],[0,153,154,155,157,158,159,161,162,164,165,166,170,171,175,201,202,203,204,205],[0,153,201,202,203,204,205],[0,154,201,202,203,204,205],[0,155,201,202,203,204,205],[0,156,201,202,203,204,205],[0,157,201,202,203,204,205],[0,158,201,202,203,204,205],[0,159,201,202,203,204,205],[0,160,201,202,203,204,205],[0,161,201,202,203,204,205],[0,162,201,202,203,204,205],[0,163,201,202,203,204,205],[0,164,201,202,203,204,205],[0,165,201,202,203,204,205],[0,166,201,202,203,204,205],[0,167,201,202,203,204,205],[0,168,201,202,203,204,205],[0,169,201,202,203,204,205],[0,170,201,202,203,204,205],[0,171,201,202,203,204,205],[0,172,201,202,203,204,205],[0,173,201,202,203,204,205],[0,174,201,202,203,204,205],[0,175,201,202,203,204,205],[0,176,177,181,182,183,185,201,202,203,204,205],[0,177,178,182,183,184,186,201,202,203,204,205],[0,176,177,178,179,181,182,184,201,202,203,204,205],[0,177,178,179,180,182,183,185,201,202,203,204,205],[0,178,179,180,181,183,184,186,201,202,203,204,205],[0,176,177,179,180,183,184,201,202,203,204,205],[0,177,178,180,181,184,185,201,202,203,204,205],[0,178,179,181,182,185,186,201,202,203,204,205],[0,176,177,179,180,181,185,186,201,202,203,204,205],[0,176,178,180,183,185,186,201,202,203,204,205],[0,176,179,182,183,184,185,186,201,202,203,204,205],[0,176,180,181,182,184,186,201,202,203,204,205],[0,176,201,202,203,204,205],[0,177,201,202,203,204,205],[0,178,201,202,203,204,205],[0,179,201,202,203,204,205],[0,180,201,202,203,204,205],[0,181,201,202,203,204,205],[0,182,201,202,203,204,205],[0,183,201,202,203,204,205],[0,184,201,202,203,204,205],[0,185,201,202,203,204,205],[0,186,201,202,203,204,205],[0,176,177,181,182,183,185,200,201,202,203,204,205],[0,177,178,182,183,184,186,200,201,202,203,204,205],[0,176,177,178,179,181,182,184,200,201,202,203,204,205],[0,177,178,179,180,182,183,185,200,201,202,203,204,205],[0,178,179,180,181,183,184,186,200,201,202,203,204,205],[0,176,177,179,180,183,184,200,201,202,203,204,205],[0,177,178,180,181,184,185,200,201,202,203,204,205],[0,178,179,181,182,185,186,200,201,202,203,204,205],[0,176,177,179,180,181,185,186,200,201,202,203,204,205],[0,176,178,180,183,185,186,200,201,202,203,204,205],[0,176,179,182,183,184,185,186,200,201,202,203,204,205],[0,176,180,181,182,184,186,200,201,202,203,204,205],[0,176,200,201,202,203,204,205],[0,177,200,201,202,203,204,205],[0,178,200,201,202,203,204,205],[0,179,200,201,202,203,204,205],[0,180,200,201,202,203,204,205],[0,181,200,201,202,203,204,205],[0,182,200,201,202,203,204,205],[0,183,200,201,202,203,204,205],[0,184,200,201,202,203,204,205],[0,185,200,201,202,203,204,205],[0,186,200,201,202,203,204,205],[0,188,194,200,201,202,203,204,205],[0,187,193,194,200,201,202,203,204,205],[0,187,193,200,201,202,203,204,205],[0,192,194,200,201,202,203,204,205],[0,188,189,191,200,201,202,203,204,205],[0,192,193,200,201,202,203,204,205],[0,190,194,200,201,202,203,204,205],[0,187,190,194,200,201,202,203,204,205],[0,187,190,200,201,202,203,204,205],[0,189,191,200,201,202,203,204,205],[0,189,200,201,202,203,204,205],[0,192,200,201,202,203,204,205],[0,192,193,194,200,201,202,203,204,205],[0,188,189,200,201,202,203,204,205],[0,190,200,201,202,203,204,205],[0,191,194,200,201,202,203,204,205],[0,188,191,194,200,201,202,203,204,205],[0,188,194,199,200,201,202,203,204,205],[0,187,193,194,199,200,201,202,203,204,205],[0,187,193,199,200,201,202,203,204,205],[0,192,194,199,200,201,202,203,204,205],[0,188,189,191,199,200,201,202,203,204,205],[0,192,193,199,200,201,202,203,204,205],[0,190,194,199,200,201,202,203,204,205],[0,187,190,194,199,200,201,202,203,204,205],[0,187,190,199,200,201,202,203,204,205],[0,189,191,199,200,201,202,203,204,205],[0,189,199,200,201,202,203,204,205],[0,192,199,200,201,202,203,204,205],[0,192,193,194,199,200,201,202,203,204,205],[0,188,189,199,200,201,202,203,204,205],[0,190,199,200,201,202,203,204,205],[0,191,194,199,200,201,202,203,204,205],[0,188,191,194,199,200,201,202,203,204,205],[0,195,196,199,200,201,202,203,204,205],[0,196,197,199,200,201,202,203,204,205],[0,195,196,197,199,200,201,202,203,204,205],[0,195,197,199,200,201,202,203,204,205],[0,195,199,200,201,202,203,204,205],[0,196,199,200,201,202,203,204,205],[0,197,199,200,201,202,203,204,205],[0,195,196,198,199,200,201,202,203,204,205],[0,196,197,198,199,200,201,202,203,204,205],[0,195,196,197,198,199,200,201,202,203,204,205],[0,195,197,198,199,200,201,202,203,204,205],[0,195,198,199,200,201,202,203,204,205],[0,196,198,199,200,201,202,203,204,205],[0,197,198,199,200,201,202,203,204,205],[0,198,199,200,201,202,203,204,205]]},"distance":{"d":6,"is_exact":false,"upper":17,"witness":[0,103,206,285,364,443,522,569,616,663,710,733,756,773,790,797,804],"A_d":null,"certified":{"d":17,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table II: [[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[599,1,15]]; the doubling theorem of their 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)"}},"clifford":{"kind":"powers","correction":{"S":[[0,2],[201,1],[202,2],[203,3],[205,1]],"CZ":[[0,201],[0,203],[0,205],[201,202],[201,203],[201,204],[201,205],[203,204],[203,205]]},"rotation_powers":[[0,7],[1,7],[2,7],[3,7],[4,7],[5,7],[6,7],[7,7],[8,7],[9,7],[10,7],[11,7],[12,7],[13,7],[14,7],[15,7],[16,7],[17,7],[18,7],[19,7],[20,7],[21,7],[22,7],[23,7],[24,7],[25,7],[26,7],[27,7],[28,7],[29,7],[30,7],[31,7],[32,7],[33,7],[34,7],[35,7],[36,7],[37,7],[38,7],[39,7],[40,7],[41,7],[42,7],[43,7],[44,7],[45,7],[46,7],[47,7],[48,7],[49,7],[50,7],[51,7],[52,7],[53,7],[54,7],[55,7],[56,7],[57,7],[58,7],[59,7],[60,7],[61,7],[62,7],[63,7],[64,7],[65,7],[66,7],[67,7],[68,7],[69,7],[70,7],[71,7],[72,7],[73,7],[74,7],[75,7],[76,7],[77,7],[78,7],[79,7],[80,7],[81,7],[82,7],[83,7],[84,7],[85,7],[86,7],[87,7],[88,7],[89,7],[90,7],[91,7],[92,7],[93,7],[94,7],[95,7],[96,7],[97,7],[98,7],[99,7],[100,7],[101,7],[102,7],[103,7],[104,7],[105,7],[106,7],[107,7],[108,7],[109,7],[110,7],[111,7],[112,7],[113,7],[114,7],[115,7],[116,7],[117,7],[118,7],[119,7],[120,7],[121,7],[122,7],[123,7],[124,7],[125,7],[126,7],[127,7],[128,7],[129,7],[130,7],[131,7],[132,7],[133,7],[134,7],[135,7],[136,7],[137,7],[138,7],[139,7],[140,7],[141,7],[142,7],[143,7],[144,7],[145,7],[146,7],[147,7],[148,7],[149,7],[150,7],[151,7],[152,7],[153,7],[154,7],[155,7],[156,7],[157,7],[158,7],[159,7],[160,7],[161,7],[162,7],[163,7],[164,7],[165,7],[166,7],[167,7],[168,7],[169,7],[170,7],[171,7],[172,7],[173,7],[174,7],[175,7],[176,7],[177,7],[178,7],[179,7],[180,7],[181,7],[182,7],[183,7],[184,7],[185,7],[186,7],[187,7],[188,7],[189,7],[190,7],[191,7],[192,7],[193,7],[194,7],[195,7],[196,7],[197,7],[198,7],[199,7],[200,7],[201,7],[202,7],[203,7],[204,7],[205,7],[364,7],[365,7],[366,7],[367,7],[368,7],[369,7],[370,7],[371,7],[372,7],[373,7],[374,7],[375,7],[376,7],[377,7],[378,7],[379,7],[380,7],[381,7],[382,7],[383,7],[384,7],[385,7],[386,7],[387,7],[388,7],[389,7],[390,7],[391,7],[392,7],[393,7],[394,7],[395,7],[396,7],[397,7],[398,7],[399,7],[400,7],[401,7],[402,7],[403,7],[404,7],[405,7],[406,7],[407,7],[408,7],[409,7],[410,7],[411,7],[412,7],[413,7],[414,7],[415,7],[416,7],[417,7],[418,7],[419,7],[420,7],[421,7],[422,7],[423,7],[424,7],[425,7],[426,7],[427,7],[428,7],[429,7],[430,7],[431,7],[432,7],[433,7],[434,7],[435,7],[436,7],[437,7],[438,7],[439,7],[440,7],[441,7],[442,7],[443,7],[444,7],[445,7],[446,7],[447,7],[448,7],[449,7],[450,7],[451,7],[452,7],[453,7],[454,7],[455,7],[456,7],[457,7],[458,7],[459,7],[460,7],[461,7],[462,7],[463,7],[464,7],[465,7],[466,7],[467,7],[468,7],[469,7],[470,7],[471,7],[472,7],[473,7],[474,7],[475,7],[476,7],[477,7],[478,7],[479,7],[480,7],[481,7],[482,7],[483,7],[484,7],[485,7],[486,7],[487,7],[488,7],[489,7],[490,7],[491,7],[492,7],[493,7],[494,7],[495,7],[496,7],[497,7],[498,7],[499,7],[500,7],[501,7],[502,7],[503,7],[504,7],[505,7],[506,7],[507,7],[508,7],[509,7],[510,7],[511,7],[512,7],[513,7],[514,7],[515,7],[516,7],[517,7],[518,7],[519,7],[520,7],[521,7],[616,7],[617,7],[618,7],[619,7],[620,7],[621,7],[622,7],[623,7],[624,7],[625,7],[626,7],[627,7],[628,7],[629,7],[630,7],[631,7],[632,7],[633,7],[634,7],[635,7],[636,7],[637,7],[638,7],[639,7],[640,7],[641,7],[642,7],[643,7],[644,7],[645,7],[646,7],[647,7],[648,7],[649,7],[650,7],[651,7],[652,7],[653,7],[654,7],[655,7],[656,7],[657,7],[658,7],[659,7],[660,7],[661,7],[662,7],[663,7],[664,7],[665,7],[666,7],[667,7],[668,7],[669,7],[670,7],[671,7],[672,7],[673,7],[674,7],[675,7],[676,7],[677,7],[678,7],[679,7],[680,7],[681,7],[682,7],[683,7],[684,7],[685,7],[686,7],[687,7],[688,7],[689,7],[690,7],[691,7],[692,7],[693,7],[694,7],[695,7],[696,7],[697,7],[698,7],[699,7],[700,7],[701,7],[702,7],[703,7],[704,7],[705,7],[706,7],[707,7],[708,7],[709,7]]},"metrics":{"gamma":3.734230175605649,"gamma_t":3.734230175605649,"gamma_rho":3.734230175605649,"gamma_claim":2.361573755628127,"gamma_t_claim":2.361573755628127,"gamma_rho_claim":2.361573755628127,"v_ex":1,"rate":0.0012422360248447205,"t_count":1,"poly_degree":1,"effective_width":1},"provenance":{"regimes":["Jain-Albert doubling: weak triply even family"],"discovery":"pre-existing","strongest_claim":"a code of the weak triply even family of Jain and Albert (arXiv:2408.12752, Table II; transversal_t_codes/): quadratic-residue CSS codes doubled onto [[95,1,7]], rebuilt here from the paper's construction, where T on some qubits and T-dagger on the rest is a logical T; a verified witness, not a maximum","sources":[{"regime":"Jain-Albert doubling: weak triply even family","file":"transversal_t_codes/factories.json","label":"JA-805","N":206,"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","provenance":"[[103,1,19]] quantum QR code (extended QR [104,52,20]) doubled onto [[599,1,15]] (Table II)"}]},"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"}]}