{"id":"1345.1.3.a","row":1376,"stored":{"file":"master_catalog.json","row":1376,"construction":null,"columns_sha256":null},"parameters":{"n":1345,"k":1,"d":3,"N":342,"r":341,"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":[[0,1,2,5,7,9,11,13,14,18,20,24,25,26,27,28,30,32,33,34,36,37,41,43,46,47,48,50,51,53,54,57,60,61,63,65,68,71,72,74,77,79,82],[0,2,3,6,8,10,12,14,15,19,21,25,26,27,28,29,31,33,34,35,37,38,42,44,47,48,49,51,52,54,55,58,61,62,64,66,69,72,73,75,78,80,83],[0,1,2,3,4,5,14,15,16,18,22,24,25,29,33,35,37,38,39,41,45,46,47,49,51,52,54,55,56,57,59,60,61,62,67,68,70,71,72,73,76,77,81,82],[0,2,3,4,5,6,15,16,17,19,23,25,26,30,34,36,38,39,40,42,46,47,48,50,52,53,55,56,57,58,60,61,62,63,68,69,71,72,73,74,77,78,82,83],[0,1,2,3,4,6,9,11,13,14,16,17,25,28,30,31,32,33,34,35,36,39,40,46,49,50,56,58,59,60,62,64,65,68,69,70,71,73,75,77,78,82,83],[0,1,3,4,9,10,11,12,13,15,17,20,24,25,27,28,29,30,31,35,40,43,46,48,53,54,59,66,68,69,70,76,77,78,82,83],[0,1,4,7,9,10,12,16,20,21,24,27,29,31,33,34,37,43,44,46,48,49,50,51,53,55,57,61,63,65,67,68,69,70,72,74,78,82,83],[0,1,7,8,9,10,14,17,18,20,21,22,24,26,27,33,35,36,37,38,41,43,44,45,46,48,49,52,53,56,57,58,60,61,62,63,64,65,66,69,70,72,73,74,75,77,82,83],[0,1,5,7,8,10,13,14,15,19,20,21,22,23,24,26,30,32,33,38,39,41,42,43,44,45,48,49,51,58,59,60,62,64,66,67,68,70,72,73,75,76,77,78,79,82,83],[0,1,5,6,7,8,13,15,16,18,21,22,23,26,28,30,31,32,36,37,39,40,41,42,44,45,47,48,49,51,52,53,54,57,59,67,69,72,73,76,78,80,82,83],[0,1,5,6,8,11,13,16,17,18,19,20,22,23,25,26,28,29,30,31,34,36,38,40,42,45,47,49,51,52,55,57,58,61,63,65,70,71,72,73,81,82,83],[0,1,5,6,11,12,13,17,19,21,23,25,28,29,31,33,34,35,36,39,47,51,52,54,56,57,58,59,60,61,62,63,64,65,66,68,73,77,79,83],[0,1,5,6,9,11,12,22,25,27,28,29,33,35,40,41,43,46,47,50,51,52,54,55,58,59,62,64,66,67,68,69,71,72,77,78,79,80,82],[0,2,6,7,10,12,13,23,26,28,29,30,34,36,41,42,44,47,48,51,52,53,55,56,59,60,63,65,67,68,69,70,72,73,78,79,80,81,83],[0,1,2,3,5,8,9,18,20,25,26,28,29,31,32,33,34,35,36,41,42,45,46,47,49,50,51,52,56,63,64,65,66,69,70,72,73,77,80,81],[0,2,3,4,6,9,10,19,21,26,27,29,30,32,33,34,35,36,37,42,43,46,47,48,50,51,52,53,57,64,65,66,67,70,71,73,74,78,81,82],[0,3,4,5,7,10,11,20,22,27,28,30,31,33,34,35,36,37,38,43,44,47,48,49,51,52,53,54,58,65,66,67,68,71,72,74,75,79,82,83],[0,1,2,4,6,7,8,9,12,13,14,18,20,21,23,24,25,26,27,29,30,31,33,35,38,39,41,43,44,45,46,47,49,51,52,55,57,59,60,61,63,65,66,67,69,71,73,74,75,76,77,79,80,82,83],[0,1,3,8,10,11,15,18,19,20,21,22,31,33,37,39,40,41,42,43,44,45,51,52,54,56,57,58,62,63,64,65,66,67,70,71,75,76,78,79,80,81,82,83],[0,1,4,5,7,12,13,14,16,18,19,21,22,23,24,25,26,27,28,30,33,36,37,38,40,42,44,45,47,48,50,51,52,54,55,58,59,60,61,64,66,67,74,76,80,81,83],[0,1,6,7,8,9,11,15,17,18,19,22,23,29,30,31,32,33,36,38,39,45,47,49,50,52,54,55,56,57,59,62,63,67,71,72,74,75,79,81],[0,2,7,8,9,10,12,16,18,19,20,23,24,30,31,32,33,34,37,39,40,46,48,50,51,53,55,56,57,58,60,63,64,68,72,73,75,76,80,82],[0,3,8,9,10,11,13,17,19,20,21,24,25,31,32,33,34,35,38,40,41,47,49,51,52,54,56,57,58,59,61,64,65,69,73,74,76,77,81,83],[0,1,2,4,5,7,10,12,13,21,22,24,27,28,30,35,37,39,42,43,46,47,51,52,54,55,58,59,61,62,63,66,68,70,71,72,75,78,79],[0,2,3,5,6,8,11,13,14,22,23,25,28,29,31,36,38,40,43,44,47,48,52,53,55,56,59,60,62,63,64,67,69,71,72,73,76,79,80],[0,3,4,6,7,9,12,14,15,23,24,26,29,30,32,37,39,41,44,45,48,49,53,54,56,57,60,61,63,64,65,68,70,72,73,74,77,80,81],[0,4,5,7,8,10,13,15,16,24,25,27,30,31,33,38,40,42,45,46,49,50,54,55,57,58,61,62,64,65,66,69,71,73,74,75,78,81,82],[0,5,6,8,9,11,14,16,17,25,26,28,31,32,34,39,41,43,46,47,50,51,55,56,58,59,62,63,65,66,67,70,72,74,75,76,79,82,83],[0,1,2,5,6,10,11,12,13,14,15,17,20,24,25,28,29,30,34,35,36,37,40,41,42,43,44,46,50,52,53,54,56,59,61,64,65,66,67,72,73,74,75,76,79,80,82,83],[0,1,3,5,6,9,12,15,16,20,21,24,27,28,29,31,32,33,34,35,38,42,44,45,46,48,50,55,61,62,63,66,67,71,72,73,75,76,79,80,81,82,83],[0,1,4,5,6,9,10,11,14,16,17,18,20,21,22,24,26,27,29,35,37,39,41,45,48,49,50,53,54,56,57,60,61,62,64,65,67,71,73,76,79,80,81,83],[0,1,6,9,10,12,13,14,15,17,19,20,21,22,23,24,26,32,33,34,37,38,40,41,42,43,47,48,49,53,55,58,60,62,66,71,79,80,81],[0,2,7,10,11,13,14,15,16,18,20,21,22,23,24,25,27,33,34,35,38,39,41,42,43,44,48,49,50,54,56,59,61,63,67,72,80,81,82],[0,3,8,11,12,14,15,16,17,19,21,22,23,24,25,26,28,34,35,36,39,40,42,43,44,45,49,50,51,55,57,60,62,64,68,73,81,82,83],[0,1,2,4,5,7,11,12,14,15,16,17,22,23,28,29,30,32,33,34,35,40,44,45,47,48,52,53,54,56,57,58,60,68,69,71,72,77,79,83],[0,1,3,6,7,8,9,11,12,14,15,16,17,20,23,25,26,27,28,29,31,32,35,37,43,45,47,49,50,51,55,58,59,60,63,65,68,69,70,71,73,74,77,78,79,80,82],[0,2,4,7,8,9,10,12,13,15,16,17,18,21,24,26,27,28,29,30,32,33,36,38,44,46,48,50,51,52,56,59,60,61,64,66,69,70,71,72,74,75,78,79,80,81,83],[0,1,2,3,7,8,10,16,17,19,20,22,24,26,29,31,32,36,39,41,43,45,46,48,49,50,52,54,62,63,67,68,70,73,74,75,76,77,80,81],[0,2,3,4,8,9,11,17,18,20,21,23,25,27,30,32,33,37,40,42,44,46,47,49,50,51,53,55,63,64,68,69,71,74,75,76,77,78,81,82],[0,3,4,5,9,10,12,18,19,21,22,24,26,28,31,33,34,38,41,43,45,47,48,50,51,52,54,56,64,65,69,70,72,75,76,77,78,79,82,83],[0,1,2,4,6,7,9,10,14,18,19,22,23,24,26,28,29,30,33,35,36,37,39,41,42,43,44,47,49,50,52,54,55,60,61,63,66,68,70,72,73,74,76,78,80,82,83],[0,1,3,8,9,10,13,14,15,18,19,23,26,28,29,31,32,33,38,40,41,42,44,45,46,47,54,55,56,57,60,62,63,64,65,67,68,69,72,73,75,81,82,83],[0,1,4,5,7,10,13,15,16,18,19,25,26,28,29,36,37,39,42,45,50,51,53,54,55,56,58,60,64,66,69,70,71,72,73,76,77,79,83],[0,1,6,7,8,9,13,16,17,18,19,24,25,28,29,32,33,34,36,38,40,41,47,48,50,52,53,55,56,59,60,63,67,68,70,73,78,79,80,82],[0,2,7,8,9,10,14,17,18,19,20,25,26,29,30,33,34,35,37,39,41,42,48,49,51,53,54,56,57,60,61,64,68,69,71,74,79,80,81,83],[0,1,2,3,5,7,8,10,13,14,15,19,21,24,25,28,31,32,33,35,37,38,40,41,42,46,47,48,49,51,52,53,55,58,60,62,63,68,69,70,71,74,75,77,79,80,81],[0,2,3,4,6,8,9,11,14,15,16,20,22,25,26,29,32,33,34,36,38,39,41,42,43,47,48,49,50,52,53,54,56,59,61,63,64,69,70,71,72,75,76,78,80,81,82],[0,3,4,5,7,9,10,12,15,16,17,21,23,26,27,30,33,34,35,37,39,40,42,43,44,48,49,50,51,53,54,55,57,60,62,64,65,70,71,72,73,76,77,79,81,82,83],[0,1,2,4,6,7,8,9,10,14,16,17,20,22,25,26,30,31,32,33,35,37,38,40,44,45,46,47,48,49,52,53,55,56,57,58,60,66,68,73,78,79,80,83],[0,1,3,8,10,13,14,15,17,20,21,23,24,25,28,30,31,37,38,39,43,45,49,51,56,58,59,60,63,65,67,68,69,71,72,77,80,81,82],[0,2,4,9,11,14,15,16,18,21,22,24,25,26,29,31,32,38,39,40,44,46,50,52,57,59,60,61,64,66,68,69,70,72,73,78,81,82,83],[0,1,2,3,7,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,28,34,36,37,39,40,43,45,46,48,50,54,57,58,62,63,67,68,69,70,72,73,77,83],[0,1,3,4,5,7,8,9,10,12,15,16,17,19,21,23,26,27,28,29,30,32,33,34,35,36,38,40,43,44,48,49,50,53,54,55,57,58,59,60,61,64,65,69,70,72,73,77,78,79,82],[0,2,4,5,6,8,9,10,11,13,16,17,18,20,22,24,27,28,29,30,31,33,34,35,36,37,39,41,44,45,49,50,51,54,55,56,58,59,60,61,62,65,66,70,71,73,74,78,79,80,83],[0,1,2,3,6,10,12,13,17,19,20,21,23,24,26,27,29,31,33,35,38,40,41,42,43,45,47,48,52,53,54,55,56,59,62,65,66,67,68,75,77,80,81,82],[0,2,3,4,7,11,13,14,18,20,21,22,24,25,27,28,30,32,34,36,39,41,42,43,44,46,48,49,53,54,55,56,57,60,63,66,67,68,69,76,78,81,82,83],[0,1,2,3,4,7,8,9,11,12,13,15,18,19,20,21,22,23,24,27,29,30,31,32,34,35,36,40,41,42,44,45,46,48,49,51,53,55,56,58,60,63,64,65,67,69,70,71,72,74,83],[0,1,3,4,7,8,10,11,12,16,18,19,21,22,23,26,27,31,34,35,42,45,48,49,51,52,53,56,59,60,63,64,66,70,73,74,75,77,79,82],[0,2,4,5,8,9,11,12,13,17,19,20,22,23,24,27,28,32,35,36,43,46,49,50,52,53,54,57,60,61,64,65,67,71,74,75,76,78,80,83],[0,1,2,3,6,7,10,11,12,21,23,26,27,29,30,32,34,41,43,44,46,48,55,57,58,60,62,63,66,71,74,75,76,81,82],[0,2,3,4,7,8,11,12,13,22,24,27,28,30,31,33,35,42,44,45,47,49,56,58,59,61,63,64,67,72,75,76,77,82,83],[0,1,2,3,4,7,8,11,12,18,20,23,24,26,27,29,30,31,33,37,41,45,47,51,53,54,59,61,62,63,64,71,72,73,74,76,78,79,82,83],[0,1,3,4,7,8,11,12,14,18,19,20,21,26,31,33,36,37,38,41,42,43,47,50,51,52,53,55,57,61,62,64,68,71,73,75,80,82,83],[0,1,4,7,8,11,12,14,15,18,19,21,22,24,25,26,28,30,33,36,38,39,41,42,44,46,47,50,52,56,57,58,60,61,62,68,69,71,76,77,79,81,82,83],[0,1,7,8,11,12,14,15,16,18,19,22,23,24,28,29,30,31,32,33,36,39,40,41,42,45,46,50,54,58,59,60,62,65,68,69,70,71,74,78,79,80,83],[0,1,5,7,8,11,12,14,15,16,17,18,19,23,26,27,28,29,31,36,40,42,48,50,53,54,55,57,59,65,66,68,69,70,74,75,77,80,81,82],[0,2,6,8,9,12,13,15,16,17,18,19,20,24,27,28,29,30,32,37,41,43,49,51,54,55,56,58,60,66,67,69,70,71,75,76,78,81,82,83],[0,1,2,3,5,10,11,16,17,19,21,24,26,27,29,31,32,34,36,37,38,41,42,43,44,46,47,48,51,52,53,54,55,56,59,60,63,65,67,70,74,76,83],[0,1,3,4,5,6,7,9,12,13,14,17,22,24,26,34,35,36,38,39,41,42,44,45,46,49,50,51,52,55,56,63,64,65,66,72,74,75,79,82],[0,2,4,5,6,7,8,10,13,14,15,18,23,25,27,35,36,37,39,40,42,43,45,46,47,50,51,52,53,56,57,64,65,66,67,73,75,76,80,83],[0,1,2,3,6,8,13,15,16,18,19,20,25,27,30,32,33,34,38,40,44,50,52,58,60,61,63,66,67,71,72,76,79,81,82],[0,2,3,4,7,9,14,16,17,19,20,21,26,28,31,33,34,35,39,41,45,51,53,59,61,62,64,67,68,72,73,77,80,82,83],[0,1,2,3,4,7,8,9,10,11,13,14,15,17,21,22,24,25,26,28,29,30,33,35,37,40,41,42,43,47,48,50,51,52,53,57,61,62,69,71,72,73,77,78,79,81,82,83],[0,1,3,4,7,8,10,12,13,15,16,20,22,23,24,28,29,31,32,33,37,38,42,44,46,47,49,50,52,57,58,60,61,62,65,68,70,71,73,77,78,80,83],[0,1,4,7,8,16,17,18,20,21,23,26,27,28,29,36,37,38,39,41,45,46,54,57,58,59,60,62,65,66,68,69,77,78,81,82],[0,2,5,8,9,17,18,19,21,22,24,27,28,29,30,37,38,39,40,42,46,47,55,58,59,60,61,63,66,67,69,70,78,79,82,83],[0,1,2,3,5,6,7,10,11,13,14,19,22,23,24,26,27,29,31,32,33,34,36,37,38,39,40,46,50,51,53,54,56,57,59,62,63,64,65,67,70,72,74,77,80,82,83],[0,1,3,4,5,6,8,9,12,13,15,18,23,26,35,36,38,39,40,43,46,48,50,52,53,55,58,61,64,66,72,73,74,75,77,78,79,81,82,83],[0,1,4,6,10,11,16,18,19,20,25,26,28,30,32,33,34,39,40,43,44,46,48,49,50,56,57,59,60,61,62,63,67,68,71,72,73,75,76,77,78,80,83],[0,1,9,12,13,14,17,18,19,21,24,25,28,29,30,31,32,35,36,37,40,43,44,45,46,48,49,53,54,58,62,64,65,69,71,73,76,78,81,82],[0,2,10,13,14,15,18,19,20,22,25,26,29,30,31,32,33,36,37,38,41,44,45,46,47,49,50,54,55,59,63,65,66,70,72,74,77,79,82,83],[0,1,2,3,5,7,9,13,15,16,18,19,21,23,24,25,28,31,36,38,39,41,42,43,45,53,54,55,56,57,61,63,64,65,66,67,68,72,73,74,75,77,78,79,80,82,83],[0,1,3,4,5,6,7,8,9,10,11,13,16,17,18,19,22,27,28,29,30,33,34,36,39,40,41,42,44,47,48,50,51,53,55,56,58,60,61,62,63,64,66,67,69,71,72,73,75,76,77,78,80,81,82,83],[0,1,4,6,8,10,12,13,17,19,23,24,25,26,27,29,31,32,33,35,36,40,42,45,46,47,49,50,52,53,56,59,60,62,64,67,70,71,73,76,78,81,83],[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],[0,52],[0,53],[0,54],[0,55],[0,56],[0,57],[0,58],[0,59],[0,60],[0,61],[0,62],[0,63],[0,64],[0,65],[0,66],[0,67],[0,68],[0,69],[0,70],[0,71],[0,72],[0,73],[0,74],[0,75],[0,76],[0,77],[0,78],[0,79],[0,80],[0,81],[0,82],[0,83],[0,1,2,5,7,9,11,13,14,18,20,24,25,26,27,28,30,32,33,34,36,37,41,43,46,47,48,50,51,53,54,57,60,61,63,65,68,71,72,74,77,79,82,341],[0,2,3,6,8,10,12,14,15,19,21,25,26,27,28,29,31,33,34,35,37,38,42,44,47,48,49,51,52,54,55,58,61,62,64,66,69,72,73,75,78,80,83,341],[0,1,2,3,4,5,14,15,16,18,22,24,25,29,33,35,37,38,39,41,45,46,47,49,51,52,54,55,56,57,59,60,61,62,67,68,70,71,72,73,76,77,81,82,341],[0,2,3,4,5,6,15,16,17,19,23,25,26,30,34,36,38,39,40,42,46,47,48,50,52,53,55,56,57,58,60,61,62,63,68,69,71,72,73,74,77,78,82,83,341],[0,1,2,3,4,6,9,11,13,14,16,17,25,28,30,31,32,33,34,35,36,39,40,46,49,50,56,58,59,60,62,64,65,68,69,70,71,73,75,77,78,82,83,341],[0,1,3,4,9,10,11,12,13,15,17,20,24,25,27,28,29,30,31,35,40,43,46,48,53,54,59,66,68,69,70,76,77,78,82,83,341],[0,1,4,7,9,10,12,16,20,21,24,27,29,31,33,34,37,43,44,46,48,49,50,51,53,55,57,61,63,65,67,68,69,70,72,74,78,82,83,341],[0,1,7,8,9,10,14,17,18,20,21,22,24,26,27,33,35,36,37,38,41,43,44,45,46,48,49,52,53,56,57,58,60,61,62,63,64,65,66,69,70,72,73,74,75,77,82,83,341],[0,1,5,7,8,10,13,14,15,19,20,21,22,23,24,26,30,32,33,38,39,41,42,43,44,45,48,49,51,58,59,60,62,64,66,67,68,70,72,73,75,76,77,78,79,82,83,341],[0,1,5,6,7,8,13,15,16,18,21,22,23,26,28,30,31,32,36,37,39,40,41,42,44,45,47,48,49,51,52,53,54,57,59,67,69,72,73,76,78,80,82,83,341],[0,1,5,6,8,11,13,16,17,18,19,20,22,23,25,26,28,29,30,31,34,36,38,40,42,45,47,49,51,52,55,57,58,61,63,65,70,71,72,73,81,82,83,341],[0,1,5,6,11,12,13,17,19,21,23,25,28,29,31,33,34,35,36,39,47,51,52,54,56,57,58,59,60,61,62,63,64,65,66,68,73,77,79,83,341],[0,1,5,6,9,11,12,22,25,27,28,29,33,35,40,41,43,46,47,50,51,52,54,55,58,59,62,64,66,67,68,69,71,72,77,78,79,80,82,341],[0,2,6,7,10,12,13,23,26,28,29,30,34,36,41,42,44,47,48,51,52,53,55,56,59,60,63,65,67,68,69,70,72,73,78,79,80,81,83,341],[0,1,2,3,5,8,9,18,20,25,26,28,29,31,32,33,34,35,36,41,42,45,46,47,49,50,51,52,56,63,64,65,66,69,70,72,73,77,80,81,341],[0,2,3,4,6,9,10,19,21,26,27,29,30,32,33,34,35,36,37,42,43,46,47,48,50,51,52,53,57,64,65,66,67,70,71,73,74,78,81,82,341],[0,3,4,5,7,10,11,20,22,27,28,30,31,33,34,35,36,37,38,43,44,47,48,49,51,52,53,54,58,65,66,67,68,71,72,74,75,79,82,83,341],[0,1,2,4,6,7,8,9,12,13,14,18,20,21,23,24,25,26,27,29,30,31,33,35,38,39,41,43,44,45,46,47,49,51,52,55,57,59,60,61,63,65,66,67,69,71,73,74,75,76,77,79,80,82,83,341],[0,1,3,8,10,11,15,18,19,20,21,22,31,33,37,39,40,41,42,43,44,45,51,52,54,56,57,58,62,63,64,65,66,67,70,71,75,76,78,79,80,81,82,83,341],[0,1,4,5,7,12,13,14,16,18,19,21,22,23,24,25,26,27,28,30,33,36,37,38,40,42,44,45,47,48,50,51,52,54,55,58,59,60,61,64,66,67,74,76,80,81,83,341],[0,1,6,7,8,9,11,15,17,18,19,22,23,29,30,31,32,33,36,38,39,45,47,49,50,52,54,55,56,57,59,62,63,67,71,72,74,75,79,81,341],[0,2,7,8,9,10,12,16,18,19,20,23,24,30,31,32,33,34,37,39,40,46,48,50,51,53,55,56,57,58,60,63,64,68,72,73,75,76,80,82,341],[0,3,8,9,10,11,13,17,19,20,21,24,25,31,32,33,34,35,38,40,41,47,49,51,52,54,56,57,58,59,61,64,65,69,73,74,76,77,81,83,341],[0,1,2,4,5,7,10,12,13,21,22,24,27,28,30,35,37,39,42,43,46,47,51,52,54,55,58,59,61,62,63,66,68,70,71,72,75,78,79,341],[0,2,3,5,6,8,11,13,14,22,23,25,28,29,31,36,38,40,43,44,47,48,52,53,55,56,59,60,62,63,64,67,69,71,72,73,76,79,80,341],[0,3,4,6,7,9,12,14,15,23,24,26,29,30,32,37,39,41,44,45,48,49,53,54,56,57,60,61,63,64,65,68,70,72,73,74,77,80,81,341],[0,4,5,7,8,10,13,15,16,24,25,27,30,31,33,38,40,42,45,46,49,50,54,55,57,58,61,62,64,65,66,69,71,73,74,75,78,81,82,341],[0,5,6,8,9,11,14,16,17,25,26,28,31,32,34,39,41,43,46,47,50,51,55,56,58,59,62,63,65,66,67,70,72,74,75,76,79,82,83,341],[0,1,2,5,6,10,11,12,13,14,15,17,20,24,25,28,29,30,34,35,36,37,40,41,42,43,44,46,50,52,53,54,56,59,61,64,65,66,67,72,73,74,75,76,79,80,82,83,341],[0,1,3,5,6,9,12,15,16,20,21,24,27,28,29,31,32,33,34,35,38,42,44,45,46,48,50,55,61,62,63,66,67,71,72,73,75,76,79,80,81,82,83,341],[0,1,4,5,6,9,10,11,14,16,17,18,20,21,22,24,26,27,29,35,37,39,41,45,48,49,50,53,54,56,57,60,61,62,64,65,67,71,73,76,79,80,81,83,341],[0,1,6,9,10,12,13,14,15,17,19,20,21,22,23,24,26,32,33,34,37,38,40,41,42,43,47,48,49,53,55,58,60,62,66,71,79,80,81,341],[0,2,7,10,11,13,14,15,16,18,20,21,22,23,24,25,27,33,34,35,38,39,41,42,43,44,48,49,50,54,56,59,61,63,67,72,80,81,82,341],[0,3,8,11,12,14,15,16,17,19,21,22,23,24,25,26,28,34,35,36,39,40,42,43,44,45,49,50,51,55,57,60,62,64,68,73,81,82,83,341],[0,1,2,4,5,7,11,12,14,15,16,17,22,23,28,29,30,32,33,34,35,40,44,45,47,48,52,53,54,56,57,58,60,68,69,71,72,77,79,83,341],[0,1,3,6,7,8,9,11,12,14,15,16,17,20,23,25,26,27,28,29,31,32,35,37,43,45,47,49,50,51,55,58,59,60,63,65,68,69,70,71,73,74,77,78,79,80,82,341],[0,2,4,7,8,9,10,12,13,15,16,17,18,21,24,26,27,28,29,30,32,33,36,38,44,46,48,50,51,52,56,59,60,61,64,66,69,70,71,72,74,75,78,79,80,81,83,341],[0,1,2,3,7,8,10,16,17,19,20,22,24,26,29,31,32,36,39,41,43,45,46,48,49,50,52,54,62,63,67,68,70,73,74,75,76,77,80,81,341],[0,2,3,4,8,9,11,17,18,20,21,23,25,27,30,32,33,37,40,42,44,46,47,49,50,51,53,55,63,64,68,69,71,74,75,76,77,78,81,82,341],[0,3,4,5,9,10,12,18,19,21,22,24,26,28,31,33,34,38,41,43,45,47,48,50,51,52,54,56,64,65,69,70,72,75,76,77,78,79,82,83,341],[0,1,2,4,6,7,9,10,14,18,19,22,23,24,26,28,29,30,33,35,36,37,39,41,42,43,44,47,49,50,52,54,55,60,61,63,66,68,70,72,73,74,76,78,80,82,83,341],[0,1,3,8,9,10,13,14,15,18,19,23,26,28,29,31,32,33,38,40,41,42,44,45,46,47,54,55,56,57,60,62,63,64,65,67,68,69,72,73,75,81,82,83,341],[0,1,4,5,7,10,13,15,16,18,19,25,26,28,29,36,37,39,42,45,50,51,53,54,55,56,58,60,64,66,69,70,71,72,73,76,77,79,83,341],[0,1,6,7,8,9,13,16,17,18,19,24,25,28,29,32,33,34,36,38,40,41,47,48,50,52,53,55,56,59,60,63,67,68,70,73,78,79,80,82,341],[0,2,7,8,9,10,14,17,18,19,20,25,26,29,30,33,34,35,37,39,41,42,48,49,51,53,54,56,57,60,61,64,68,69,71,74,79,80,81,83,341],[0,1,2,3,5,7,8,10,13,14,15,19,21,24,25,28,31,32,33,35,37,38,40,41,42,46,47,48,49,51,52,53,55,58,60,62,63,68,69,70,71,74,75,77,79,80,81,341],[0,2,3,4,6,8,9,11,14,15,16,20,22,25,26,29,32,33,34,36,38,39,41,42,43,47,48,49,50,52,53,54,56,59,61,63,64,69,70,71,72,75,76,78,80,81,82,341],[0,3,4,5,7,9,10,12,15,16,17,21,23,26,27,30,33,34,35,37,39,40,42,43,44,48,49,50,51,53,54,55,57,60,62,64,65,70,71,72,73,76,77,79,81,82,83,341],[0,1,2,4,6,7,8,9,10,14,16,17,20,22,25,26,30,31,32,33,35,37,38,40,44,45,46,47,48,49,52,53,55,56,57,58,60,66,68,73,78,79,80,83,341],[0,1,3,8,10,13,14,15,17,20,21,23,24,25,28,30,31,37,38,39,43,45,49,51,56,58,59,60,63,65,67,68,69,71,72,77,80,81,82,341],[0,2,4,9,11,14,15,16,18,21,22,24,25,26,29,31,32,38,39,40,44,46,50,52,57,59,60,61,64,66,68,69,70,72,73,78,81,82,83,341],[0,1,2,3,7,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,28,34,36,37,39,40,43,45,46,48,50,54,57,58,62,63,67,68,69,70,72,73,77,83,341],[0,1,3,4,5,7,8,9,10,12,15,16,17,19,21,23,26,27,28,29,30,32,33,34,35,36,38,40,43,44,48,49,50,53,54,55,57,58,59,60,61,64,65,69,70,72,73,77,78,79,82,341],[0,2,4,5,6,8,9,10,11,13,16,17,18,20,22,24,27,28,29,30,31,33,34,35,36,37,39,41,44,45,49,50,51,54,55,56,58,59,60,61,62,65,66,70,71,73,74,78,79,80,83,341],[0,1,2,3,6,10,12,13,17,19,20,21,23,24,26,27,29,31,33,35,38,40,41,42,43,45,47,48,52,53,54,55,56,59,62,65,66,67,68,75,77,80,81,82,341],[0,2,3,4,7,11,13,14,18,20,21,22,24,25,27,28,30,32,34,36,39,41,42,43,44,46,48,49,53,54,55,56,57,60,63,66,67,68,69,76,78,81,82,83,341],[0,1,2,3,4,7,8,9,11,12,13,15,18,19,20,21,22,23,24,27,29,30,31,32,34,35,36,40,41,42,44,45,46,48,49,51,53,55,56,58,60,63,64,65,67,69,70,71,72,74,83,341],[0,1,3,4,7,8,10,11,12,16,18,19,21,22,23,26,27,31,34,35,42,45,48,49,51,52,53,56,59,60,63,64,66,70,73,74,75,77,79,82,341],[0,2,4,5,8,9,11,12,13,17,19,20,22,23,24,27,28,32,35,36,43,46,49,50,52,53,54,57,60,61,64,65,67,71,74,75,76,78,80,83,341],[0,1,2,3,6,7,10,11,12,21,23,26,27,29,30,32,34,41,43,44,46,48,55,57,58,60,62,63,66,71,74,75,76,81,82,341],[0,2,3,4,7,8,11,12,13,22,24,27,28,30,31,33,35,42,44,45,47,49,56,58,59,61,63,64,67,72,75,76,77,82,83,341],[0,1,2,3,4,7,8,11,12,18,20,23,24,26,27,29,30,31,33,37,41,45,47,51,53,54,59,61,62,63,64,71,72,73,74,76,78,79,82,83,341],[0,1,3,4,7,8,11,12,14,18,19,20,21,26,31,33,36,37,38,41,42,43,47,50,51,52,53,55,57,61,62,64,68,71,73,75,80,82,83,341],[0,1,4,7,8,11,12,14,15,18,19,21,22,24,25,26,28,30,33,36,38,39,41,42,44,46,47,50,52,56,57,58,60,61,62,68,69,71,76,77,79,81,82,83,341],[0,1,7,8,11,12,14,15,16,18,19,22,23,24,28,29,30,31,32,33,36,39,40,41,42,45,46,50,54,58,59,60,62,65,68,69,70,71,74,78,79,80,83,341],[0,1,5,7,8,11,12,14,15,16,17,18,19,23,26,27,28,29,31,36,40,42,48,50,53,54,55,57,59,65,66,68,69,70,74,75,77,80,81,82,341],[0,2,6,8,9,12,13,15,16,17,18,19,20,24,27,28,29,30,32,37,41,43,49,51,54,55,56,58,60,66,67,69,70,71,75,76,78,81,82,83,341],[0,1,2,3,5,10,11,16,17,19,21,24,26,27,29,31,32,34,36,37,38,41,42,43,44,46,47,48,51,52,53,54,55,56,59,60,63,65,67,70,74,76,83,341],[0,1,3,4,5,6,7,9,12,13,14,17,22,24,26,34,35,36,38,39,41,42,44,45,46,49,50,51,52,55,56,63,64,65,66,72,74,75,79,82,341],[0,2,4,5,6,7,8,10,13,14,15,18,23,25,27,35,36,37,39,40,42,43,45,46,47,50,51,52,53,56,57,64,65,66,67,73,75,76,80,83,341],[0,1,2,3,6,8,13,15,16,18,19,20,25,27,30,32,33,34,38,40,44,50,52,58,60,61,63,66,67,71,72,76,79,81,82,341],[0,2,3,4,7,9,14,16,17,19,20,21,26,28,31,33,34,35,39,41,45,51,53,59,61,62,64,67,68,72,73,77,80,82,83,341],[0,1,2,3,4,7,8,9,10,11,13,14,15,17,21,22,24,25,26,28,29,30,33,35,37,40,41,42,43,47,48,50,51,52,53,57,61,62,69,71,72,73,77,78,79,81,82,83,341],[0,1,3,4,7,8,10,12,13,15,16,20,22,23,24,28,29,31,32,33,37,38,42,44,46,47,49,50,52,57,58,60,61,62,65,68,70,71,73,77,78,80,83,341],[0,1,4,7,8,16,17,18,20,21,23,26,27,28,29,36,37,38,39,41,45,46,54,57,58,59,60,62,65,66,68,69,77,78,81,82,341],[0,2,5,8,9,17,18,19,21,22,24,27,28,29,30,37,38,39,40,42,46,47,55,58,59,60,61,63,66,67,69,70,78,79,82,83,341],[0,1,2,3,5,6,7,10,11,13,14,19,22,23,24,26,27,29,31,32,33,34,36,37,38,39,40,46,50,51,53,54,56,57,59,62,63,64,65,67,70,72,74,77,80,82,83,341],[0,1,3,4,5,6,8,9,12,13,15,18,23,26,35,36,38,39,40,43,46,48,50,52,53,55,58,61,64,66,72,73,74,75,77,78,79,81,82,83,341],[0,1,4,6,10,11,16,18,19,20,25,26,28,30,32,33,34,39,40,43,44,46,48,49,50,56,57,59,60,61,62,63,67,68,71,72,73,75,76,77,78,80,83,341],[0,1,9,12,13,14,17,18,19,21,24,25,28,29,30,31,32,35,36,37,40,43,44,45,46,48,49,53,54,58,62,64,65,69,71,73,76,78,81,82,341],[0,2,10,13,14,15,18,19,20,22,25,26,29,30,31,32,33,36,37,38,41,44,45,46,47,49,50,54,55,59,63,65,66,70,72,74,77,79,82,83,341],[0,1,2,3,5,7,9,13,15,16,18,19,21,23,24,25,28,31,36,38,39,41,42,43,45,53,54,55,56,57,61,63,64,65,66,67,68,72,73,74,75,77,78,79,80,82,83,341],[0,1,3,4,5,6,7,8,9,10,11,13,16,17,18,19,22,27,28,29,30,33,34,36,39,40,41,42,44,47,48,50,51,53,55,56,58,60,61,62,63,64,66,67,69,71,72,73,75,76,77,78,80,81,82,83,341],[0,1,4,6,8,10,12,13,17,19,23,24,25,26,27,29,31,32,33,35,36,40,42,45,46,47,49,50,52,53,56,59,60,62,64,67,70,71,73,76,78,81,83,341],[0,1,341],[0,2,341],[0,3,341],[0,4,341],[0,5,341],[0,6,341],[0,7,341],[0,8,341],[0,9,341],[0,10,341],[0,11,341],[0,12,341],[0,13,341],[0,14,341],[0,15,341],[0,16,341],[0,17,341],[0,18,341],[0,19,341],[0,20,341],[0,21,341],[0,22,341],[0,23,341],[0,24,341],[0,25,341],[0,26,341],[0,27,341],[0,28,341],[0,29,341],[0,30,341],[0,31,341],[0,32,341],[0,33,341],[0,34,341],[0,35,341],[0,36,341],[0,37,341],[0,38,341],[0,39,341],[0,40,341],[0,41,341],[0,42,341],[0,43,341],[0,44,341],[0,45,341],[0,46,341],[0,47,341],[0,48,341],[0,49,341],[0,50,341],[0,51,341],[0,52,341],[0,53,341],[0,54,341],[0,55,341],[0,56,341],[0,57,341],[0,58,341],[0,59,341],[0,60,341],[0,61,341],[0,62,341],[0,63,341],[0,64,341],[0,65,341],[0,66,341],[0,67,341],[0,68,341],[0,69,341],[0,70,341],[0,71,341],[0,72,341],[0,73,341],[0,74,341],[0,75,341],[0,76,341],[0,77,341],[0,78,341],[0,79,341],[0,80,341],[0,81,341],[0,82,341],[0,83,341],[0,84,85,87,92,93,96,97,98,99,101,102,103,104,110,112,113,114,115,116,119,121,126,127,128,132,133,341],[0,85,86,88,93,94,97,98,99,100,102,103,104,105,111,113,114,115,116,117,120,122,127,128,129,133,134,341],[0,84,85,86,89,92,93,94,95,96,97,100,102,105,106,110,113,117,118,119,123,126,127,129,130,132,133,134,341],[0,84,86,90,92,94,95,99,102,104,106,107,110,111,112,113,115,116,118,120,121,124,126,130,131,132,134,341],[0,84,91,92,95,97,98,99,100,101,102,104,105,107,108,110,111,115,117,122,125,126,128,131,341],[0,85,92,93,96,98,99,100,101,102,103,105,106,108,109,111,112,116,118,123,126,127,129,132,341],[0,86,93,94,97,99,100,101,102,103,104,106,107,109,110,112,113,117,119,124,127,128,130,133,341],[0,87,94,95,98,100,101,102,103,104,105,107,108,110,111,113,114,118,120,125,128,129,131,134,341],[0,84,85,87,88,92,93,95,97,98,105,106,108,109,110,111,113,116,127,128,129,130,133,341],[0,85,86,88,89,93,94,96,98,99,106,107,109,110,111,112,114,117,128,129,130,131,134,341],[0,84,85,86,89,90,92,93,94,95,96,98,100,101,102,103,104,107,108,111,114,116,118,119,121,126,127,128,129,130,131,133,341],[0,85,86,87,90,91,93,94,95,96,97,99,101,102,103,104,105,108,109,112,115,117,119,120,122,127,128,129,130,131,132,134,341],[0,84,85,86,88,91,93,94,95,99,100,101,105,106,109,112,114,115,118,119,120,123,126,127,129,130,131,341],[0,85,86,87,89,92,94,95,96,100,101,102,106,107,110,113,115,116,119,120,121,124,127,128,130,131,132,341],[0,86,87,88,90,93,95,96,97,101,102,103,107,108,111,114,116,117,120,121,122,125,128,129,131,132,133,341],[0,87,88,89,91,94,96,97,98,102,103,104,108,109,112,115,117,118,121,122,123,126,129,130,132,133,134,341],[0,84,85,87,88,89,90,93,95,96,101,102,105,109,112,114,115,118,121,122,123,124,126,128,130,131,132,134,341],[0,84,86,87,88,89,90,91,92,93,94,98,99,101,104,106,112,114,121,122,123,124,125,126,128,129,131,341],[0,85,87,88,89,90,91,92,93,94,95,99,100,102,105,107,113,115,122,123,124,125,126,127,129,130,132,341],[0,86,88,89,90,91,92,93,94,95,96,100,101,103,106,108,114,116,123,124,125,126,127,128,130,131,133,341],[0,87,89,90,91,92,93,94,95,96,97,101,102,104,107,109,115,117,124,125,126,127,128,129,131,132,134,341],[0,84,85,87,88,90,91,94,95,99,101,104,105,108,112,113,114,115,118,119,121,125,129,130,341],[0,85,86,88,89,91,92,95,96,100,102,105,106,109,113,114,115,116,119,120,122,126,130,131,341],[0,86,87,89,90,92,93,96,97,101,103,106,107,110,114,115,116,117,120,121,123,127,131,132,341],[0,87,88,90,91,93,94,97,98,102,104,107,108,111,115,116,117,118,121,122,124,128,132,133,341],[0,88,89,91,92,94,95,98,99,103,105,108,109,112,116,117,118,119,122,123,125,129,133,134,341],[0,84,85,87,89,90,95,97,98,100,101,102,103,106,109,112,114,115,116,117,118,120,121,123,124,127,128,130,132,133,134,341],[0,84,86,87,88,90,91,92,93,97,107,112,114,117,118,122,124,125,126,127,129,131,132,134,341],[0,84,88,89,91,94,96,97,99,101,102,103,104,108,110,112,114,116,118,121,123,125,130,341],[0,85,89,90,92,95,97,98,100,102,103,104,105,109,111,113,115,117,119,122,124,126,131,341],[0,86,90,91,93,96,98,99,101,103,104,105,106,110,112,114,116,118,120,123,125,127,132,341],[0,87,91,92,94,97,99,100,102,104,105,106,107,111,113,115,117,119,121,124,126,128,133,341],[0,88,92,93,95,98,100,101,103,105,106,107,108,112,114,116,118,120,122,125,127,129,134,341],[0,84,85,87,89,92,94,97,98,103,106,107,108,109,110,112,114,116,117,123,127,130,132,133,341],[0,85,86,88,90,93,95,98,99,104,107,108,109,110,111,113,115,117,118,124,128,131,133,134,341],[0,84,85,86,89,91,92,93,94,97,98,100,101,102,103,104,105,108,109,111,113,115,118,121,125,126,127,128,129,133,134,341],[0,84,86,90,94,95,96,97,105,106,109,113,115,121,122,129,130,132,133,134,341],[0,84,91,92,93,95,99,101,102,103,104,106,107,112,113,115,119,121,122,123,126,127,128,130,131,132,134,341],[0,84,87,94,97,98,99,100,101,105,107,108,110,112,115,119,120,121,122,123,124,126,129,131,341],[0,85,88,95,98,99,100,101,102,106,108,109,111,113,116,120,121,122,123,124,125,127,130,132,341],[0,86,89,96,99,100,101,102,103,107,109,110,112,114,117,121,122,123,124,125,126,128,131,133,341],[0,87,90,97,100,101,102,103,104,108,110,111,113,115,118,122,123,124,125,126,127,129,132,134,341],[0,84,85,87,88,91,92,93,96,97,99,105,109,110,111,113,115,121,123,124,125,130,132,341],[0,85,86,88,89,92,93,94,97,98,100,106,110,111,112,114,116,122,124,125,126,131,133,341],[0,86,87,89,90,93,94,95,98,99,101,107,111,112,113,115,117,123,125,126,127,132,134,341],[0,84,85,88,90,91,92,93,94,95,97,98,100,101,103,104,108,110,115,118,119,121,124,132,341],[0,85,86,89,91,92,93,94,95,96,98,99,101,102,104,105,109,111,116,119,120,122,125,133,341],[0,86,87,90,92,93,94,95,96,97,99,100,102,103,105,106,110,112,117,120,121,123,126,134,341],[0,84,85,88,91,92,94,95,99,100,102,106,107,110,111,112,114,115,116,118,119,122,124,126,128,132,133,341],[0,85,86,89,92,93,95,96,100,101,103,107,108,111,112,113,115,116,117,119,120,123,125,127,129,133,134,341],[0,84,85,86,90,92,94,98,99,103,108,109,110,115,117,118,119,120,124,127,130,132,133,134,341],[0,84,86,91,92,95,96,97,98,100,101,102,103,109,111,112,113,114,115,118,120,125,126,127,131,132,134,341],[0,84,341],[0,85,341],[0,86,341],[0,87,341],[0,88,341],[0,89,341],[0,90,341],[0,91,341],[0,92,341],[0,93,341],[0,94,341],[0,95,341],[0,96,341],[0,97,341],[0,98,341],[0,99,341],[0,100,341],[0,101,341],[0,102,341],[0,103,341],[0,104,341],[0,105,341],[0,106,341],[0,107,341],[0,108,341],[0,109,341],[0,110,341],[0,111,341],[0,112,341],[0,113,341],[0,114,341],[0,115,341],[0,116,341],[0,117,341],[0,118,341],[0,119,341],[0,120,341],[0,121,341],[0,122,341],[0,123,341],[0,124,341],[0,125,341],[0,126,341],[0,127,341],[0,128,341],[0,129,341],[0,130,341],[0,131,341],[0,132,341],[0,133,341],[0,134,341],[0,84,85,87,92,93,96,97,98,99,101,102,103,104,110,112,113,114,115,116,119,121,126,127,128,132,133,340,341],[0,85,86,88,93,94,97,98,99,100,102,103,104,105,111,113,114,115,116,117,120,122,127,128,129,133,134,340,341],[0,84,85,86,89,92,93,94,95,96,97,100,102,105,106,110,113,117,118,119,123,126,127,129,130,132,133,134,340,341],[0,84,86,90,92,94,95,99,102,104,106,107,110,111,112,113,115,116,118,120,121,124,126,130,131,132,134,340,341],[0,84,91,92,95,97,98,99,100,101,102,104,105,107,108,110,111,115,117,122,125,126,128,131,340,341],[0,85,92,93,96,98,99,100,101,102,103,105,106,108,109,111,112,116,118,123,126,127,129,132,340,341],[0,86,93,94,97,99,100,101,102,103,104,106,107,109,110,112,113,117,119,124,127,128,130,133,340,341],[0,87,94,95,98,100,101,102,103,104,105,107,108,110,111,113,114,118,120,125,128,129,131,134,340,341],[0,84,85,87,88,92,93,95,97,98,105,106,108,109,110,111,113,116,127,128,129,130,133,340,341],[0,85,86,88,89,93,94,96,98,99,106,107,109,110,111,112,114,117,128,129,130,131,134,340,341],[0,84,85,86,89,90,92,93,94,95,96,98,100,101,102,103,104,107,108,111,114,116,118,119,121,126,127,128,129,130,131,133,340,341],[0,85,86,87,90,91,93,94,95,96,97,99,101,102,103,104,105,108,109,112,115,117,119,120,122,127,128,129,130,131,132,134,340,341],[0,84,85,86,88,91,93,94,95,99,100,101,105,106,109,112,114,115,118,119,120,123,126,127,129,130,131,340,341],[0,85,86,87,89,92,94,95,96,100,101,102,106,107,110,113,115,116,119,120,121,124,127,128,130,131,132,340,341],[0,86,87,88,90,93,95,96,97,101,102,103,107,108,111,114,116,117,120,121,122,125,128,129,131,132,133,340,341],[0,87,88,89,91,94,96,97,98,102,103,104,108,109,112,115,117,118,121,122,123,126,129,130,132,133,134,340,341],[0,84,85,87,88,89,90,93,95,96,101,102,105,109,112,114,115,118,121,122,123,124,126,128,130,131,132,134,340,341],[0,84,86,87,88,89,90,91,92,93,94,98,99,101,104,106,112,114,121,122,123,124,125,126,128,129,131,340,341],[0,85,87,88,89,90,91,92,93,94,95,99,100,102,105,107,113,115,122,123,124,125,126,127,129,130,132,340,341],[0,86,88,89,90,91,92,93,94,95,96,100,101,103,106,108,114,116,123,124,125,126,127,128,130,131,133,340,341],[0,87,89,90,91,92,93,94,95,96,97,101,102,104,107,109,115,117,124,125,126,127,128,129,131,132,134,340,341],[0,84,85,87,88,90,91,94,95,99,101,104,105,108,112,113,114,115,118,119,121,125,129,130,340,341],[0,85,86,88,89,91,92,95,96,100,102,105,106,109,113,114,115,116,119,120,122,126,130,131,340,341],[0,86,87,89,90,92,93,96,97,101,103,106,107,110,114,115,116,117,120,121,123,127,131,132,340,341],[0,87,88,90,91,93,94,97,98,102,104,107,108,111,115,116,117,118,121,122,124,128,132,133,340,341],[0,88,89,91,92,94,95,98,99,103,105,108,109,112,116,117,118,119,122,123,125,129,133,134,340,341],[0,84,85,87,89,90,95,97,98,100,101,102,103,106,109,112,114,115,116,117,118,120,121,123,124,127,128,130,132,133,134,340,341],[0,84,86,87,88,90,91,92,93,97,107,112,114,117,118,122,124,125,126,127,129,131,132,134,340,341],[0,84,88,89,91,94,96,97,99,101,102,103,104,108,110,112,114,116,118,121,123,125,130,340,341],[0,85,89,90,92,95,97,98,100,102,103,104,105,109,111,113,115,117,119,122,124,126,131,340,341],[0,86,90,91,93,96,98,99,101,103,104,105,106,110,112,114,116,118,120,123,125,127,132,340,341],[0,87,91,92,94,97,99,100,102,104,105,106,107,111,113,115,117,119,121,124,126,128,133,340,341],[0,88,92,93,95,98,100,101,103,105,106,107,108,112,114,116,118,120,122,125,127,129,134,340,341],[0,84,85,87,89,92,94,97,98,103,106,107,108,109,110,112,114,116,117,123,127,130,132,133,340,341],[0,85,86,88,90,93,95,98,99,104,107,108,109,110,111,113,115,117,118,124,128,131,133,134,340,341],[0,84,85,86,89,91,92,93,94,97,98,100,101,102,103,104,105,108,109,111,113,115,118,121,125,126,127,128,129,133,134,340,341],[0,84,86,90,94,95,96,97,105,106,109,113,115,121,122,129,130,132,133,134,340,341],[0,84,91,92,93,95,99,101,102,103,104,106,107,112,113,115,119,121,122,123,126,127,128,130,131,132,134,340,341],[0,84,87,94,97,98,99,100,101,105,107,108,110,112,115,119,120,121,122,123,124,126,129,131,340,341],[0,85,88,95,98,99,100,101,102,106,108,109,111,113,116,120,121,122,123,124,125,127,130,132,340,341],[0,86,89,96,99,100,101,102,103,107,109,110,112,114,117,121,122,123,124,125,126,128,131,133,340,341],[0,87,90,97,100,101,102,103,104,108,110,111,113,115,118,122,123,124,125,126,127,129,132,134,340,341],[0,84,85,87,88,91,92,93,96,97,99,105,109,110,111,113,115,121,123,124,125,130,132,340,341],[0,85,86,88,89,92,93,94,97,98,100,106,110,111,112,114,116,122,124,125,126,131,133,340,341],[0,86,87,89,90,93,94,95,98,99,101,107,111,112,113,115,117,123,125,126,127,132,134,340,341],[0,84,85,88,90,91,92,93,94,95,97,98,100,101,103,104,108,110,115,118,119,121,124,132,340,341],[0,85,86,89,91,92,93,94,95,96,98,99,101,102,104,105,109,111,116,119,120,122,125,133,340,341],[0,86,87,90,92,93,94,95,96,97,99,100,102,103,105,106,110,112,117,120,121,123,126,134,340,341],[0,84,85,88,91,92,94,95,99,100,102,106,107,110,111,112,114,115,116,118,119,122,124,126,128,132,133,340,341],[0,85,86,89,92,93,95,96,100,101,103,107,108,111,112,113,115,116,117,119,120,123,125,127,129,133,134,340,341],[0,84,85,86,90,92,94,98,99,103,108,109,110,115,117,118,119,120,124,127,130,132,133,134,340,341],[0,84,86,91,92,95,96,97,98,100,101,102,103,109,111,112,113,114,115,118,120,125,126,127,131,132,134,340,341],[0,84,340,341],[0,85,340,341],[0,86,340,341],[0,87,340,341],[0,88,340,341],[0,89,340,341],[0,90,340,341],[0,91,340,341],[0,92,340,341],[0,93,340,341],[0,94,340,341],[0,95,340,341],[0,96,340,341],[0,97,340,341],[0,98,340,341],[0,99,340,341],[0,100,340,341],[0,101,340,341],[0,102,340,341],[0,103,340,341],[0,104,340,341],[0,105,340,341],[0,106,340,341],[0,107,340,341],[0,108,340,341],[0,109,340,341],[0,110,340,341],[0,111,340,341],[0,112,340,341],[0,113,340,341],[0,114,340,341],[0,115,340,341],[0,116,340,341],[0,117,340,341],[0,118,340,341],[0,119,340,341],[0,120,340,341],[0,121,340,341],[0,122,340,341],[0,123,340,341],[0,124,340,341],[0,125,340,341],[0,126,340,341],[0,127,340,341],[0,128,340,341],[0,129,340,341],[0,130,340,341],[0,131,340,341],[0,132,340,341],[0,133,340,341],[0,134,340,341],[0,135,136,138,143,144,147,148,149,150,152,153,154,155,161,163,164,165,166,167,170,172,177,178,179,183,184,340,341],[0,136,137,139,144,145,148,149,150,151,153,154,155,156,162,164,165,166,167,168,171,173,178,179,180,184,185,340,341],[0,135,136,137,140,143,144,145,146,147,148,151,153,156,157,161,164,168,169,170,174,177,178,180,181,183,184,185,340,341],[0,135,137,141,143,145,146,150,153,155,157,158,161,162,163,164,166,167,169,171,172,175,177,181,182,183,185,340,341],[0,135,142,143,146,148,149,150,151,152,153,155,156,158,159,161,162,166,168,173,176,177,179,182,340,341],[0,136,143,144,147,149,150,151,152,153,154,156,157,159,160,162,163,167,169,174,177,178,180,183,340,341],[0,137,144,145,148,150,151,152,153,154,155,157,158,160,161,163,164,168,170,175,178,179,181,184,340,341],[0,138,145,146,149,151,152,153,154,155,156,158,159,161,162,164,165,169,171,176,179,180,182,185,340,341],[0,135,136,138,139,143,144,146,148,149,156,157,159,160,161,162,164,167,178,179,180,181,184,340,341],[0,136,137,139,140,144,145,147,149,150,157,158,160,161,162,163,165,168,179,180,181,182,185,340,341],[0,135,136,137,140,141,143,144,145,146,147,149,151,152,153,154,155,158,159,162,165,167,169,170,172,177,178,179,180,181,182,184,340,341],[0,136,137,138,141,142,144,145,146,147,148,150,152,153,154,155,156,159,160,163,166,168,170,171,173,178,179,180,181,182,183,185,340,341],[0,135,136,137,139,142,144,145,146,150,151,152,156,157,160,163,165,166,169,170,171,174,177,178,180,181,182,340,341],[0,136,137,138,140,143,145,146,147,151,152,153,157,158,161,164,166,167,170,171,172,175,178,179,181,182,183,340,341],[0,137,138,139,141,144,146,147,148,152,153,154,158,159,162,165,167,168,171,172,173,176,179,180,182,183,184,340,341],[0,138,139,140,142,145,147,148,149,153,154,155,159,160,163,166,168,169,172,173,174,177,180,181,183,184,185,340,341],[0,135,136,138,139,140,141,144,146,147,152,153,156,160,163,165,166,169,172,173,174,175,177,179,181,182,183,185,340,341],[0,135,137,138,139,140,141,142,143,144,145,149,150,152,155,157,163,165,172,173,174,175,176,177,179,180,182,340,341],[0,136,138,139,140,141,142,143,144,145,146,150,151,153,156,158,164,166,173,174,175,176,177,178,180,181,183,340,341],[0,137,139,140,141,142,143,144,145,146,147,151,152,154,157,159,165,167,174,175,176,177,178,179,181,182,184,340,341],[0,138,140,141,142,143,144,145,146,147,148,152,153,155,158,160,166,168,175,176,177,178,179,180,182,183,185,340,341],[0,135,136,138,139,141,142,145,146,150,152,155,156,159,163,164,165,166,169,170,172,176,180,181,340,341],[0,136,137,139,140,142,143,146,147,151,153,156,157,160,164,165,166,167,170,171,173,177,181,182,340,341],[0,137,138,140,141,143,144,147,148,152,154,157,158,161,165,166,167,168,171,172,174,178,182,183,340,341],[0,138,139,141,142,144,145,148,149,153,155,158,159,162,166,167,168,169,172,173,175,179,183,184,340,341],[0,139,140,142,143,145,146,149,150,154,156,159,160,163,167,168,169,170,173,174,176,180,184,185,340,341],[0,135,136,138,140,141,146,148,149,151,152,153,154,157,160,163,165,166,167,168,169,171,172,174,175,178,179,181,183,184,185,340,341],[0,135,137,138,139,141,142,143,144,148,158,163,165,168,169,173,175,176,177,178,180,182,183,185,340,341],[0,135,139,140,142,145,147,148,150,152,153,154,155,159,161,163,165,167,169,172,174,176,181,340,341],[0,136,140,141,143,146,148,149,151,153,154,155,156,160,162,164,166,168,170,173,175,177,182,340,341],[0,137,141,142,144,147,149,150,152,154,155,156,157,161,163,165,167,169,171,174,176,178,183,340,341],[0,138,142,143,145,148,150,151,153,155,156,157,158,162,164,166,168,170,172,175,177,179,184,340,341],[0,139,143,144,146,149,151,152,154,156,157,158,159,163,165,167,169,171,173,176,178,180,185,340,341],[0,135,136,138,140,143,145,148,149,154,157,158,159,160,161,163,165,167,168,174,178,181,183,184,340,341],[0,136,137,139,141,144,146,149,150,155,158,159,160,161,162,164,166,168,169,175,179,182,184,185,340,341],[0,135,136,137,140,142,143,144,145,148,149,151,152,153,154,155,156,159,160,162,164,166,169,172,176,177,178,179,180,184,185,340,341],[0,135,137,141,145,146,147,148,156,157,160,164,166,172,173,180,181,183,184,185,340,341],[0,135,142,143,144,146,150,152,153,154,155,157,158,163,164,166,170,172,173,174,177,178,179,181,182,183,185,340,341],[0,135,138,145,148,149,150,151,152,156,158,159,161,163,166,170,171,172,173,174,175,177,180,182,340,341],[0,136,139,146,149,150,151,152,153,157,159,160,162,164,167,171,172,173,174,175,176,178,181,183,340,341],[0,137,140,147,150,151,152,153,154,158,160,161,163,165,168,172,173,174,175,176,177,179,182,184,340,341],[0,138,141,148,151,152,153,154,155,159,161,162,164,166,169,173,174,175,176,177,178,180,183,185,340,341],[0,135,136,138,139,142,143,144,147,148,150,156,160,161,162,164,166,172,174,175,176,181,183,340,341],[0,136,137,139,140,143,144,145,148,149,151,157,161,162,163,165,167,173,175,176,177,182,184,340,341],[0,137,138,140,141,144,145,146,149,150,152,158,162,163,164,166,168,174,176,177,178,183,185,340,341],[0,135,136,139,141,142,143,144,145,146,148,149,151,152,154,155,159,161,166,169,170,172,175,183,340,341],[0,136,137,140,142,143,144,145,146,147,149,150,152,153,155,156,160,162,167,170,171,173,176,184,340,341],[0,137,138,141,143,144,145,146,147,148,150,151,153,154,156,157,161,163,168,171,172,174,177,185,340,341],[0,135,136,139,142,143,145,146,150,151,153,157,158,161,162,163,165,166,167,169,170,173,175,177,179,183,184,340,341],[0,136,137,140,143,144,146,147,151,152,154,158,159,162,163,164,166,167,168,170,171,174,176,178,180,184,185,340,341],[0,135,136,137,141,143,145,149,150,154,159,160,161,166,168,169,170,171,175,178,181,183,184,185,340,341],[0,135,137,142,143,146,147,148,149,151,152,153,154,160,162,163,164,165,166,169,171,176,177,178,182,183,185,340,341],[0,135,340,341],[0,136,340,341],[0,137,340,341],[0,138,340,341],[0,139,340,341],[0,140,340,341],[0,141,340,341],[0,142,340,341],[0,143,340,341],[0,144,340,341],[0,145,340,341],[0,146,340,341],[0,147,340,341],[0,148,340,341],[0,149,340,341],[0,150,340,341],[0,151,340,341],[0,152,340,341],[0,153,340,341],[0,154,340,341],[0,155,340,341],[0,156,340,341],[0,157,340,341],[0,158,340,341],[0,159,340,341],[0,160,340,341],[0,161,340,341],[0,162,340,341],[0,163,340,341],[0,164,340,341],[0,165,340,341],[0,166,340,341],[0,167,340,341],[0,168,340,341],[0,169,340,341],[0,170,340,341],[0,171,340,341],[0,172,340,341],[0,173,340,341],[0,174,340,341],[0,175,340,341],[0,176,340,341],[0,177,340,341],[0,178,340,341],[0,179,340,341],[0,180,340,341],[0,181,340,341],[0,182,340,341],[0,183,340,341],[0,184,340,341],[0,185,340,341],[0,135,136,138,143,144,147,148,149,150,152,153,154,155,161,163,164,165,166,167,170,172,177,178,179,183,184,339,340,341],[0,136,137,139,144,145,148,149,150,151,153,154,155,156,162,164,165,166,167,168,171,173,178,179,180,184,185,339,340,341],[0,135,136,137,140,143,144,145,146,147,148,151,153,156,157,161,164,168,169,170,174,177,178,180,181,183,184,185,339,340,341],[0,135,137,141,143,145,146,150,153,155,157,158,161,162,163,164,166,167,169,171,172,175,177,181,182,183,185,339,340,341],[0,135,142,143,146,148,149,150,151,152,153,155,156,158,159,161,162,166,168,173,176,177,179,182,339,340,341],[0,136,143,144,147,149,150,151,152,153,154,156,157,159,160,162,163,167,169,174,177,178,180,183,339,340,341],[0,137,144,145,148,150,151,152,153,154,155,157,158,160,161,163,164,168,170,175,178,179,181,184,339,340,341],[0,138,145,146,149,151,152,153,154,155,156,158,159,161,162,164,165,169,171,176,179,180,182,185,339,340,341],[0,135,136,138,139,143,144,146,148,149,156,157,159,160,161,162,164,167,178,179,180,181,184,339,340,341],[0,136,137,139,140,144,145,147,149,150,157,158,160,161,162,163,165,168,179,180,181,182,185,339,340,341],[0,135,136,137,140,141,143,144,145,146,147,149,151,152,153,154,155,158,159,162,165,167,169,170,172,177,178,179,180,181,182,184,339,340,341],[0,136,137,138,141,142,144,145,146,147,148,150,152,153,154,155,156,159,160,163,166,168,170,171,173,178,179,180,181,182,183,185,339,340,341],[0,135,136,137,139,142,144,145,146,150,151,152,156,157,160,163,165,166,169,170,171,174,177,178,180,181,182,339,340,341],[0,136,137,138,140,143,145,146,147,151,152,153,157,158,161,164,166,167,170,171,172,175,178,179,181,182,183,339,340,341],[0,137,138,139,141,144,146,147,148,152,153,154,158,159,162,165,167,168,171,172,173,176,179,180,182,183,184,339,340,341],[0,138,139,140,142,145,147,148,149,153,154,155,159,160,163,166,168,169,172,173,174,177,180,181,183,184,185,339,340,341],[0,135,136,138,139,140,141,144,146,147,152,153,156,160,163,165,166,169,172,173,174,175,177,179,181,182,183,185,339,340,341],[0,135,137,138,139,140,141,142,143,144,145,149,150,152,155,157,163,165,172,173,174,175,176,177,179,180,182,339,340,341],[0,136,138,139,140,141,142,143,144,145,146,150,151,153,156,158,164,166,173,174,175,176,177,178,180,181,183,339,340,341],[0,137,139,140,141,142,143,144,145,146,147,151,152,154,157,159,165,167,174,175,176,177,178,179,181,182,184,339,340,341],[0,138,140,141,142,143,144,145,146,147,148,152,153,155,158,160,166,168,175,176,177,178,179,180,182,183,185,339,340,341],[0,135,136,138,139,141,142,145,146,150,152,155,156,159,163,164,165,166,169,170,172,176,180,181,339,340,341],[0,136,137,139,140,142,143,146,147,151,153,156,157,160,164,165,166,167,170,171,173,177,181,182,339,340,341],[0,137,138,140,141,143,144,147,148,152,154,157,158,161,165,166,167,168,171,172,174,178,182,183,339,340,341],[0,138,139,141,142,144,145,148,149,153,155,158,159,162,166,167,168,169,172,173,175,179,183,184,339,340,341],[0,139,140,142,143,145,146,149,150,154,156,159,160,163,167,168,169,170,173,174,176,180,184,185,339,340,341],[0,135,136,138,140,141,146,148,149,151,152,153,154,157,160,163,165,166,167,168,169,171,172,174,175,178,179,181,183,184,185,339,340,341],[0,135,137,138,139,141,142,143,144,148,158,163,165,168,169,173,175,176,177,178,180,182,183,185,339,340,341],[0,135,139,140,142,145,147,148,150,152,153,154,155,159,161,163,165,167,169,172,174,176,181,339,340,341],[0,136,140,141,143,146,148,149,151,153,154,155,156,160,162,164,166,168,170,173,175,177,182,339,340,341],[0,137,141,142,144,147,149,150,152,154,155,156,157,161,163,165,167,169,171,174,176,178,183,339,340,341],[0,138,142,143,145,148,150,151,153,155,156,157,158,162,164,166,168,170,172,175,177,179,184,339,340,341],[0,139,143,144,146,149,151,152,154,156,157,158,159,163,165,167,169,171,173,176,178,180,185,339,340,341],[0,135,136,138,140,143,145,148,149,154,157,158,159,160,161,163,165,167,168,174,178,181,183,184,339,340,341],[0,136,137,139,141,144,146,149,150,155,158,159,160,161,162,164,166,168,169,175,179,182,184,185,339,340,341],[0,135,136,137,140,142,143,144,145,148,149,151,152,153,154,155,156,159,160,162,164,166,169,172,176,177,178,179,180,184,185,339,340,341],[0,135,137,141,145,146,147,148,156,157,160,164,166,172,173,180,181,183,184,185,339,340,341],[0,135,142,143,144,146,150,152,153,154,155,157,158,163,164,166,170,172,173,174,177,178,179,181,182,183,185,339,340,341],[0,135,138,145,148,149,150,151,152,156,158,159,161,163,166,170,171,172,173,174,175,177,180,182,339,340,341],[0,136,139,146,149,150,151,152,153,157,159,160,162,164,167,171,172,173,174,175,176,178,181,183,339,340,341],[0,137,140,147,150,151,152,153,154,158,160,161,163,165,168,172,173,174,175,176,177,179,182,184,339,340,341],[0,138,141,148,151,152,153,154,155,159,161,162,164,166,169,173,174,175,176,177,178,180,183,185,339,340,341],[0,135,136,138,139,142,143,144,147,148,150,156,160,161,162,164,166,172,174,175,176,181,183,339,340,341],[0,136,137,139,140,143,144,145,148,149,151,157,161,162,163,165,167,173,175,176,177,182,184,339,340,341],[0,137,138,140,141,144,145,146,149,150,152,158,162,163,164,166,168,174,176,177,178,183,185,339,340,341],[0,135,136,139,141,142,143,144,145,146,148,149,151,152,154,155,159,161,166,169,170,172,175,183,339,340,341],[0,136,137,140,142,143,144,145,146,147,149,150,152,153,155,156,160,162,167,170,171,173,176,184,339,340,341],[0,137,138,141,143,144,145,146,147,148,150,151,153,154,156,157,161,163,168,171,172,174,177,185,339,340,341],[0,135,136,139,142,143,145,146,150,151,153,157,158,161,162,163,165,166,167,169,170,173,175,177,179,183,184,339,340,341],[0,136,137,140,143,144,146,147,151,152,154,158,159,162,163,164,166,167,168,170,171,174,176,178,180,184,185,339,340,341],[0,135,136,137,141,143,145,149,150,154,159,160,161,166,168,169,170,171,175,178,181,183,184,185,339,340,341],[0,135,137,142,143,146,147,148,149,151,152,153,154,160,162,163,164,165,166,169,171,176,177,178,182,183,185,339,340,341],[0,135,339,340,341],[0,136,339,340,341],[0,137,339,340,341],[0,138,339,340,341],[0,139,339,340,341],[0,140,339,340,341],[0,141,339,340,341],[0,142,339,340,341],[0,143,339,340,341],[0,144,339,340,341],[0,145,339,340,341],[0,146,339,340,341],[0,147,339,340,341],[0,148,339,340,341],[0,149,339,340,341],[0,150,339,340,341],[0,151,339,340,341],[0,152,339,340,341],[0,153,339,340,341],[0,154,339,340,341],[0,155,339,340,341],[0,156,339,340,341],[0,157,339,340,341],[0,158,339,340,341],[0,159,339,340,341],[0,160,339,340,341],[0,161,339,340,341],[0,162,339,340,341],[0,163,339,340,341],[0,164,339,340,341],[0,165,339,340,341],[0,166,339,340,341],[0,167,339,340,341],[0,168,339,340,341],[0,169,339,340,341],[0,170,339,340,341],[0,171,339,340,341],[0,172,339,340,341],[0,173,339,340,341],[0,174,339,340,341],[0,175,339,340,341],[0,176,339,340,341],[0,177,339,340,341],[0,178,339,340,341],[0,179,339,340,341],[0,180,339,340,341],[0,181,339,340,341],[0,182,339,340,341],[0,183,339,340,341],[0,184,339,340,341],[0,185,339,340,341],[0,186,187,188,190,191,197,199,200,202,204,205,206,207,210,211,212,213,215,216,217,221,222,339,340,341],[0,187,188,189,191,192,198,200,201,203,205,206,207,208,211,212,213,214,216,217,218,222,223,339,340,341],[0,188,189,190,192,193,199,201,202,204,206,207,208,209,212,213,214,215,217,218,219,223,224,339,340,341],[0,186,187,188,189,193,194,197,199,203,204,206,208,209,211,212,214,217,218,219,220,221,222,224,339,340,341],[0,186,189,191,194,195,197,198,199,202,206,209,211,216,217,218,219,220,223,339,340,341],[0,187,190,192,195,196,198,199,200,203,207,210,212,217,218,219,220,221,224,339,340,341],[0,186,187,190,193,196,201,202,205,206,207,208,210,212,215,216,217,218,219,220,339,340,341],[0,187,188,191,194,197,202,203,206,207,208,209,211,213,216,217,218,219,220,221,339,340,341],[0,188,189,192,195,198,203,204,207,208,209,210,212,214,217,218,219,220,221,222,339,340,341],[0,189,190,193,196,199,204,205,208,209,210,211,213,215,218,219,220,221,222,223,339,340,341],[0,190,191,194,197,200,205,206,209,210,211,212,214,216,219,220,221,222,223,224,339,340,341],[0,186,187,188,190,192,195,197,198,199,200,201,202,204,205,216,220,223,224,339,340,341],[0,186,189,190,193,196,197,198,201,203,204,207,210,211,212,213,215,216,222,224,339,340,341],[0,186,188,194,198,200,206,207,208,210,214,215,221,222,223,339,340,341],[0,187,189,195,199,201,207,208,209,211,215,216,222,223,224,339,340,341],[0,186,187,191,196,197,199,204,205,206,207,208,209,211,213,215,221,222,223,224,339,340,341],[0,186,190,191,192,198,199,202,204,208,209,211,213,214,215,217,221,223,224,339,340,341],[0,186,188,190,192,193,197,202,203,204,206,207,209,211,213,214,217,218,221,224,339,340,341],[0,186,188,189,190,193,194,197,198,199,200,202,203,206,208,211,213,214,216,217,218,219,221,339,340,341],[0,187,189,190,191,194,195,198,199,200,201,203,204,207,209,212,214,215,217,218,219,220,222,339,340,341],[0,188,190,191,192,195,196,199,200,201,202,204,205,208,210,213,215,216,218,219,220,221,223,339,340,341],[0,189,191,192,193,196,197,200,201,202,203,205,206,209,211,214,216,217,219,220,221,222,224,339,340,341],[0,186,187,188,191,192,193,194,198,199,200,201,203,205,211,213,216,218,220,223,339,340,341],[0,187,188,189,192,193,194,195,199,200,201,202,204,206,212,214,217,219,221,224,339,340,341],[0,186,187,189,191,193,194,195,196,197,199,201,203,204,206,210,211,212,216,217,218,220,221,339,340,341],[0,187,188,190,192,194,195,196,197,198,200,202,204,205,207,211,212,213,217,218,219,221,222,339,340,341],[0,188,189,191,193,195,196,197,198,199,201,203,205,206,208,212,213,214,218,219,220,222,223,339,340,341],[0,189,190,192,194,196,197,198,199,200,202,204,206,207,209,213,214,215,219,220,221,223,224,339,340,341],[0,186,187,188,193,195,198,201,202,203,204,206,208,211,212,213,214,217,220,224,339,340,341],[0,186,189,190,191,194,196,197,200,203,206,209,210,211,214,216,217,218,222,339,340,341],[0,187,190,191,192,195,197,198,201,204,207,210,211,212,215,217,218,219,223,339,340,341],[0,188,191,192,193,196,198,199,202,205,208,211,212,213,216,218,219,220,224,339,340,341],[0,186,187,188,189,190,191,192,193,194,202,203,204,205,207,209,210,211,214,215,216,219,220,222,339,340,341],[0,187,188,189,190,191,192,193,194,195,203,204,205,206,208,210,211,212,215,216,217,220,221,223,339,340,341],[0,188,189,190,191,192,193,194,195,196,204,205,206,207,209,211,212,213,216,217,218,221,222,224,339,340,341],[0,186,187,188,189,192,193,194,195,196,199,200,202,204,208,211,214,215,216,218,219,221,223,339,340,341],[0,187,188,189,190,193,194,195,196,197,200,201,203,205,209,212,215,216,217,219,220,222,224,339,340,341],[0,186,187,189,194,195,196,198,199,200,201,205,207,211,212,215,218,220,222,223,339,340,341],[0,187,188,190,195,196,197,199,200,201,202,206,208,212,213,216,219,221,223,224,339,340,341],[0,186,187,189,190,196,198,199,201,203,204,205,206,209,210,211,212,214,215,216,220,221,224,339,340,341],[0,186,339,340,341],[0,187,339,340,341],[0,188,339,340,341],[0,189,339,340,341],[0,190,339,340,341],[0,191,339,340,341],[0,192,339,340,341],[0,193,339,340,341],[0,194,339,340,341],[0,195,339,340,341],[0,196,339,340,341],[0,197,339,340,341],[0,198,339,340,341],[0,199,339,340,341],[0,200,339,340,341],[0,201,339,340,341],[0,202,339,340,341],[0,203,339,340,341],[0,204,339,340,341],[0,205,339,340,341],[0,206,339,340,341],[0,207,339,340,341],[0,208,339,340,341],[0,209,339,340,341],[0,210,339,340,341],[0,211,339,340,341],[0,212,339,340,341],[0,213,339,340,341],[0,214,339,340,341],[0,215,339,340,341],[0,216,339,340,341],[0,217,339,340,341],[0,218,339,340,341],[0,219,339,340,341],[0,220,339,340,341],[0,221,339,340,341],[0,222,339,340,341],[0,223,339,340,341],[0,224,339,340,341],[0,186,187,188,190,191,197,199,200,202,204,205,206,207,210,211,212,213,215,216,217,221,222,338,339,340,341],[0,187,188,189,191,192,198,200,201,203,205,206,207,208,211,212,213,214,216,217,218,222,223,338,339,340,341],[0,188,189,190,192,193,199,201,202,204,206,207,208,209,212,213,214,215,217,218,219,223,224,338,339,340,341],[0,186,187,188,189,193,194,197,199,203,204,206,208,209,211,212,214,217,218,219,220,221,222,224,338,339,340,341],[0,186,189,191,194,195,197,198,199,202,206,209,211,216,217,218,219,220,223,338,339,340,341],[0,187,190,192,195,196,198,199,200,203,207,210,212,217,218,219,220,221,224,338,339,340,341],[0,186,187,190,193,196,201,202,205,206,207,208,210,212,215,216,217,218,219,220,338,339,340,341],[0,187,188,191,194,197,202,203,206,207,208,209,211,213,216,217,218,219,220,221,338,339,340,341],[0,188,189,192,195,198,203,204,207,208,209,210,212,214,217,218,219,220,221,222,338,339,340,341],[0,189,190,193,196,199,204,205,208,209,210,211,213,215,218,219,220,221,222,223,338,339,340,341],[0,190,191,194,197,200,205,206,209,210,211,212,214,216,219,220,221,222,223,224,338,339,340,341],[0,186,187,188,190,192,195,197,198,199,200,201,202,204,205,216,220,223,224,338,339,340,341],[0,186,189,190,193,196,197,198,201,203,204,207,210,211,212,213,215,216,222,224,338,339,340,341],[0,186,188,194,198,200,206,207,208,210,214,215,221,222,223,338,339,340,341],[0,187,189,195,199,201,207,208,209,211,215,216,222,223,224,338,339,340,341],[0,186,187,191,196,197,199,204,205,206,207,208,209,211,213,215,221,222,223,224,338,339,340,341],[0,186,190,191,192,198,199,202,204,208,209,211,213,214,215,217,221,223,224,338,339,340,341],[0,186,188,190,192,193,197,202,203,204,206,207,209,211,213,214,217,218,221,224,338,339,340,341],[0,186,188,189,190,193,194,197,198,199,200,202,203,206,208,211,213,214,216,217,218,219,221,338,339,340,341],[0,187,189,190,191,194,195,198,199,200,201,203,204,207,209,212,214,215,217,218,219,220,222,338,339,340,341],[0,188,190,191,192,195,196,199,200,201,202,204,205,208,210,213,215,216,218,219,220,221,223,338,339,340,341],[0,189,191,192,193,196,197,200,201,202,203,205,206,209,211,214,216,217,219,220,221,222,224,338,339,340,341],[0,186,187,188,191,192,193,194,198,199,200,201,203,205,211,213,216,218,220,223,338,339,340,341],[0,187,188,189,192,193,194,195,199,200,201,202,204,206,212,214,217,219,221,224,338,339,340,341],[0,186,187,189,191,193,194,195,196,197,199,201,203,204,206,210,211,212,216,217,218,220,221,338,339,340,341],[0,187,188,190,192,194,195,196,197,198,200,202,204,205,207,211,212,213,217,218,219,221,222,338,339,340,341],[0,188,189,191,193,195,196,197,198,199,201,203,205,206,208,212,213,214,218,219,220,222,223,338,339,340,341],[0,189,190,192,194,196,197,198,199,200,202,204,206,207,209,213,214,215,219,220,221,223,224,338,339,340,341],[0,186,187,188,193,195,198,201,202,203,204,206,208,211,212,213,214,217,220,224,338,339,340,341],[0,186,189,190,191,194,196,197,200,203,206,209,210,211,214,216,217,218,222,338,339,340,341],[0,187,190,191,192,195,197,198,201,204,207,210,211,212,215,217,218,219,223,338,339,340,341],[0,188,191,192,193,196,198,199,202,205,208,211,212,213,216,218,219,220,224,338,339,340,341],[0,186,187,188,189,190,191,192,193,194,202,203,204,205,207,209,210,211,214,215,216,219,220,222,338,339,340,341],[0,187,188,189,190,191,192,193,194,195,203,204,205,206,208,210,211,212,215,216,217,220,221,223,338,339,340,341],[0,188,189,190,191,192,193,194,195,196,204,205,206,207,209,211,212,213,216,217,218,221,222,224,338,339,340,341],[0,186,187,188,189,192,193,194,195,196,199,200,202,204,208,211,214,215,216,218,219,221,223,338,339,340,341],[0,187,188,189,190,193,194,195,196,197,200,201,203,205,209,212,215,216,217,219,220,222,224,338,339,340,341],[0,186,187,189,194,195,196,198,199,200,201,205,207,211,212,215,218,220,222,223,338,339,340,341],[0,187,188,190,195,196,197,199,200,201,202,206,208,212,213,216,219,221,223,224,338,339,340,341],[0,186,187,189,190,196,198,199,201,203,204,205,206,209,210,211,212,214,215,216,220,221,224,338,339,340,341],[0,186,338,339,340,341],[0,187,338,339,340,341],[0,188,338,339,340,341],[0,189,338,339,340,341],[0,190,338,339,340,341],[0,191,338,339,340,341],[0,192,338,339,340,341],[0,193,338,339,340,341],[0,194,338,339,340,341],[0,195,338,339,340,341],[0,196,338,339,340,341],[0,197,338,339,340,341],[0,198,338,339,340,341],[0,199,338,339,340,341],[0,200,338,339,340,341],[0,201,338,339,340,341],[0,202,338,339,340,341],[0,203,338,339,340,341],[0,204,338,339,340,341],[0,205,338,339,340,341],[0,206,338,339,340,341],[0,207,338,339,340,341],[0,208,338,339,340,341],[0,209,338,339,340,341],[0,210,338,339,340,341],[0,211,338,339,340,341],[0,212,338,339,340,341],[0,213,338,339,340,341],[0,214,338,339,340,341],[0,215,338,339,340,341],[0,216,338,339,340,341],[0,217,338,339,340,341],[0,218,338,339,340,341],[0,219,338,339,340,341],[0,220,338,339,340,341],[0,221,338,339,340,341],[0,222,338,339,340,341],[0,223,338,339,340,341],[0,224,338,339,340,341],[0,225,226,227,229,230,236,238,239,241,243,244,245,246,249,250,251,252,254,255,256,260,261,338,339,340,341],[0,226,227,228,230,231,237,239,240,242,244,245,246,247,250,251,252,253,255,256,257,261,262,338,339,340,341],[0,227,228,229,231,232,238,240,241,243,245,246,247,248,251,252,253,254,256,257,258,262,263,338,339,340,341],[0,225,226,227,228,232,233,236,238,242,243,245,247,248,250,251,253,256,257,258,259,260,261,263,338,339,340,341],[0,225,228,230,233,234,236,237,238,241,245,248,250,255,256,257,258,259,262,338,339,340,341],[0,226,229,231,234,235,237,238,239,242,246,249,251,256,257,258,259,260,263,338,339,340,341],[0,225,226,229,232,235,240,241,244,245,246,247,249,251,254,255,256,257,258,259,338,339,340,341],[0,226,227,230,233,236,241,242,245,246,247,248,250,252,255,256,257,258,259,260,338,339,340,341],[0,227,228,231,234,237,242,243,246,247,248,249,251,253,256,257,258,259,260,261,338,339,340,341],[0,228,229,232,235,238,243,244,247,248,249,250,252,254,257,258,259,260,261,262,338,339,340,341],[0,229,230,233,236,239,244,245,248,249,250,251,253,255,258,259,260,261,262,263,338,339,340,341],[0,225,226,227,229,231,234,236,237,238,239,240,241,243,244,255,259,262,263,338,339,340,341],[0,225,228,229,232,235,236,237,240,242,243,246,249,250,251,252,254,255,261,263,338,339,340,341],[0,225,227,233,237,239,245,246,247,249,253,254,260,261,262,338,339,340,341],[0,226,228,234,238,240,246,247,248,250,254,255,261,262,263,338,339,340,341],[0,225,226,230,235,236,238,243,244,245,246,247,248,250,252,254,260,261,262,263,338,339,340,341],[0,225,229,230,231,237,238,241,243,247,248,250,252,253,254,256,260,262,263,338,339,340,341],[0,225,227,229,231,232,236,241,242,243,245,246,248,250,252,253,256,257,260,263,338,339,340,341],[0,225,227,228,229,232,233,236,237,238,239,241,242,245,247,250,252,253,255,256,257,258,260,338,339,340,341],[0,226,228,229,230,233,234,237,238,239,240,242,243,246,248,251,253,254,256,257,258,259,261,338,339,340,341],[0,227,229,230,231,234,235,238,239,240,241,243,244,247,249,252,254,255,257,258,259,260,262,338,339,340,341],[0,228,230,231,232,235,236,239,240,241,242,244,245,248,250,253,255,256,258,259,260,261,263,338,339,340,341],[0,225,226,227,230,231,232,233,237,238,239,240,242,244,250,252,255,257,259,262,338,339,340,341],[0,226,227,228,231,232,233,234,238,239,240,241,243,245,251,253,256,258,260,263,338,339,340,341],[0,225,226,228,230,232,233,234,235,236,238,240,242,243,245,249,250,251,255,256,257,259,260,338,339,340,341],[0,226,227,229,231,233,234,235,236,237,239,241,243,244,246,250,251,252,256,257,258,260,261,338,339,340,341],[0,227,228,230,232,234,235,236,237,238,240,242,244,245,247,251,252,253,257,258,259,261,262,338,339,340,341],[0,228,229,231,233,235,236,237,238,239,241,243,245,246,248,252,253,254,258,259,260,262,263,338,339,340,341],[0,225,226,227,232,234,237,240,241,242,243,245,247,250,251,252,253,256,259,263,338,339,340,341],[0,225,228,229,230,233,235,236,239,242,245,248,249,250,253,255,256,257,261,338,339,340,341],[0,226,229,230,231,234,236,237,240,243,246,249,250,251,254,256,257,258,262,338,339,340,341],[0,227,230,231,232,235,237,238,241,244,247,250,251,252,255,257,258,259,263,338,339,340,341],[0,225,226,227,228,229,230,231,232,233,241,242,243,244,246,248,249,250,253,254,255,258,259,261,338,339,340,341],[0,226,227,228,229,230,231,232,233,234,242,243,244,245,247,249,250,251,254,255,256,259,260,262,338,339,340,341],[0,227,228,229,230,231,232,233,234,235,243,244,245,246,248,250,251,252,255,256,257,260,261,263,338,339,340,341],[0,225,226,227,228,231,232,233,234,235,238,239,241,243,247,250,253,254,255,257,258,260,262,338,339,340,341],[0,226,227,228,229,232,233,234,235,236,239,240,242,244,248,251,254,255,256,258,259,261,263,338,339,340,341],[0,225,226,228,233,234,235,237,238,239,240,244,246,250,251,254,257,259,261,262,338,339,340,341],[0,226,227,229,234,235,236,238,239,240,241,245,247,251,252,255,258,260,262,263,338,339,340,341],[0,225,226,228,229,235,237,238,240,242,243,244,245,248,249,250,251,253,254,255,259,260,263,338,339,340,341],[0,225,338,339,340,341],[0,226,338,339,340,341],[0,227,338,339,340,341],[0,228,338,339,340,341],[0,229,338,339,340,341],[0,230,338,339,340,341],[0,231,338,339,340,341],[0,232,338,339,340,341],[0,233,338,339,340,341],[0,234,338,339,340,341],[0,235,338,339,340,341],[0,236,338,339,340,341],[0,237,338,339,340,341],[0,238,338,339,340,341],[0,239,338,339,340,341],[0,240,338,339,340,341],[0,241,338,339,340,341],[0,242,338,339,340,341],[0,243,338,339,340,341],[0,244,338,339,340,341],[0,245,338,339,340,341],[0,246,338,339,340,341],[0,247,338,339,340,341],[0,248,338,339,340,341],[0,249,338,339,340,341],[0,250,338,339,340,341],[0,251,338,339,340,341],[0,252,338,339,340,341],[0,253,338,339,340,341],[0,254,338,339,340,341],[0,255,338,339,340,341],[0,256,338,339,340,341],[0,257,338,339,340,341],[0,258,338,339,340,341],[0,259,338,339,340,341],[0,260,338,339,340,341],[0,261,338,339,340,341],[0,262,338,339,340,341],[0,263,338,339,340,341],[0,225,226,227,229,230,236,238,239,241,243,244,245,246,249,250,251,252,254,255,256,260,261,337,338,339,340,341],[0,226,227,228,230,231,237,239,240,242,244,245,246,247,250,251,252,253,255,256,257,261,262,337,338,339,340,341],[0,227,228,229,231,232,238,240,241,243,245,246,247,248,251,252,253,254,256,257,258,262,263,337,338,339,340,341],[0,225,226,227,228,232,233,236,238,242,243,245,247,248,250,251,253,256,257,258,259,260,261,263,337,338,339,340,341],[0,225,228,230,233,234,236,237,238,241,245,248,250,255,256,257,258,259,262,337,338,339,340,341],[0,226,229,231,234,235,237,238,239,242,246,249,251,256,257,258,259,260,263,337,338,339,340,341],[0,225,226,229,232,235,240,241,244,245,246,247,249,251,254,255,256,257,258,259,337,338,339,340,341],[0,226,227,230,233,236,241,242,245,246,247,248,250,252,255,256,257,258,259,260,337,338,339,340,341],[0,227,228,231,234,237,242,243,246,247,248,249,251,253,256,257,258,259,260,261,337,338,339,340,341],[0,228,229,232,235,238,243,244,247,248,249,250,252,254,257,258,259,260,261,262,337,338,339,340,341],[0,229,230,233,236,239,244,245,248,249,250,251,253,255,258,259,260,261,262,263,337,338,339,340,341],[0,225,226,227,229,231,234,236,237,238,239,240,241,243,244,255,259,262,263,337,338,339,340,341],[0,225,228,229,232,235,236,237,240,242,243,246,249,250,251,252,254,255,261,263,337,338,339,340,341],[0,225,227,233,237,239,245,246,247,249,253,254,260,261,262,337,338,339,340,341],[0,226,228,234,238,240,246,247,248,250,254,255,261,262,263,337,338,339,340,341],[0,225,226,230,235,236,238,243,244,245,246,247,248,250,252,254,260,261,262,263,337,338,339,340,341],[0,225,229,230,231,237,238,241,243,247,248,250,252,253,254,256,260,262,263,337,338,339,340,341],[0,225,227,229,231,232,236,241,242,243,245,246,248,250,252,253,256,257,260,263,337,338,339,340,341],[0,225,227,228,229,232,233,236,237,238,239,241,242,245,247,250,252,253,255,256,257,258,260,337,338,339,340,341],[0,226,228,229,230,233,234,237,238,239,240,242,243,246,248,251,253,254,256,257,258,259,261,337,338,339,340,341],[0,227,229,230,231,234,235,238,239,240,241,243,244,247,249,252,254,255,257,258,259,260,262,337,338,339,340,341],[0,228,230,231,232,235,236,239,240,241,242,244,245,248,250,253,255,256,258,259,260,261,263,337,338,339,340,341],[0,225,226,227,230,231,232,233,237,238,239,240,242,244,250,252,255,257,259,262,337,338,339,340,341],[0,226,227,228,231,232,233,234,238,239,240,241,243,245,251,253,256,258,260,263,337,338,339,340,341],[0,225,226,228,230,232,233,234,235,236,238,240,242,243,245,249,250,251,255,256,257,259,260,337,338,339,340,341],[0,226,227,229,231,233,234,235,236,237,239,241,243,244,246,250,251,252,256,257,258,260,261,337,338,339,340,341],[0,227,228,230,232,234,235,236,237,238,240,242,244,245,247,251,252,253,257,258,259,261,262,337,338,339,340,341],[0,228,229,231,233,235,236,237,238,239,241,243,245,246,248,252,253,254,258,259,260,262,263,337,338,339,340,341],[0,225,226,227,232,234,237,240,241,242,243,245,247,250,251,252,253,256,259,263,337,338,339,340,341],[0,225,228,229,230,233,235,236,239,242,245,248,249,250,253,255,256,257,261,337,338,339,340,341],[0,226,229,230,231,234,236,237,240,243,246,249,250,251,254,256,257,258,262,337,338,339,340,341],[0,227,230,231,232,235,237,238,241,244,247,250,251,252,255,257,258,259,263,337,338,339,340,341],[0,225,226,227,228,229,230,231,232,233,241,242,243,244,246,248,249,250,253,254,255,258,259,261,337,338,339,340,341],[0,226,227,228,229,230,231,232,233,234,242,243,244,245,247,249,250,251,254,255,256,259,260,262,337,338,339,340,341],[0,227,228,229,230,231,232,233,234,235,243,244,245,246,248,250,251,252,255,256,257,260,261,263,337,338,339,340,341],[0,225,226,227,228,231,232,233,234,235,238,239,241,243,247,250,253,254,255,257,258,260,262,337,338,339,340,341],[0,226,227,228,229,232,233,234,235,236,239,240,242,244,248,251,254,255,256,258,259,261,263,337,338,339,340,341],[0,225,226,228,233,234,235,237,238,239,240,244,246,250,251,254,257,259,261,262,337,338,339,340,341],[0,226,227,229,234,235,236,238,239,240,241,245,247,251,252,255,258,260,262,263,337,338,339,340,341],[0,225,226,228,229,235,237,238,240,242,243,244,245,248,249,250,251,253,254,255,259,260,263,337,338,339,340,341],[0,225,337,338,339,340,341],[0,226,337,338,339,340,341],[0,227,337,338,339,340,341],[0,228,337,338,339,340,341],[0,229,337,338,339,340,341],[0,230,337,338,339,340,341],[0,231,337,338,339,340,341],[0,232,337,338,339,340,341],[0,233,337,338,339,340,341],[0,234,337,338,339,340,341],[0,235,337,338,339,340,341],[0,236,337,338,339,340,341],[0,237,337,338,339,340,341],[0,238,337,338,339,340,341],[0,239,337,338,339,340,341],[0,240,337,338,339,340,341],[0,241,337,338,339,340,341],[0,242,337,338,339,340,341],[0,243,337,338,339,340,341],[0,244,337,338,339,340,341],[0,245,337,338,339,340,341],[0,246,337,338,339,340,341],[0,247,337,338,339,340,341],[0,248,337,338,339,340,341],[0,249,337,338,339,340,341],[0,250,337,338,339,340,341],[0,251,337,338,339,340,341],[0,252,337,338,339,340,341],[0,253,337,338,339,340,341],[0,254,337,338,339,340,341],[0,255,337,338,339,340,341],[0,256,337,338,339,340,341],[0,257,337,338,339,340,341],[0,258,337,338,339,340,341],[0,259,337,338,339,340,341],[0,260,337,338,339,340,341],[0,261,337,338,339,340,341],[0,262,337,338,339,340,341],[0,263,337,338,339,340,341],[0,264,265,266,267,269,270,271,273,274,276,277,278,282,283,337,338,339,340,341],[0,265,266,267,268,270,271,272,274,275,277,278,279,283,284,337,338,339,340,341],[0,266,267,268,269,271,272,273,275,276,278,279,280,284,285,337,338,339,340,341],[0,267,268,269,270,272,273,274,276,277,279,280,281,285,286,337,338,339,340,341],[0,264,265,266,267,268,275,276,280,281,283,286,337,338,339,340,341],[0,264,268,270,271,273,274,278,281,283,284,337,338,339,340,341],[0,265,269,271,272,274,275,279,282,284,285,337,338,339,340,341],[0,266,270,272,273,275,276,280,283,285,286,337,338,339,340,341],[0,264,265,266,269,270,278,281,282,283,284,286,337,338,339,340,341],[0,264,269,273,274,276,277,278,279,284,285,337,338,339,340,341],[0,265,270,274,275,277,278,279,280,285,286,337,338,339,340,341],[0,264,265,267,269,270,273,274,275,277,279,280,281,282,283,286,337,338,339,340,341],[0,264,267,268,269,273,275,277,280,281,284,337,338,339,340,341],[0,265,268,269,270,274,276,278,281,282,285,337,338,339,340,341],[0,266,269,270,271,275,277,279,282,283,286,337,338,339,340,341],[0,264,265,266,269,272,273,274,277,280,282,284,337,338,339,340,341],[0,265,266,267,270,273,274,275,278,281,283,285,337,338,339,340,341],[0,266,267,268,271,274,275,276,279,282,284,286,337,338,339,340,341],[0,264,265,266,268,270,271,272,273,274,275,278,280,282,285,337,338,339,340,341],[0,265,266,267,269,271,272,273,274,275,276,279,281,283,286,337,338,339,340,341],[0,264,265,268,269,271,272,275,278,280,283,284,337,338,339,340,341],[0,265,266,269,270,272,273,276,279,281,284,285,337,338,339,340,341],[0,266,267,270,271,273,274,277,280,282,285,286,337,338,339,340,341],[0,264,265,266,268,269,270,272,273,275,276,277,281,282,286,337,338,339,340,341],[0,264,337,338,339,340,341],[0,265,337,338,339,340,341],[0,266,337,338,339,340,341],[0,267,337,338,339,340,341],[0,268,337,338,339,340,341],[0,269,337,338,339,340,341],[0,270,337,338,339,340,341],[0,271,337,338,339,340,341],[0,272,337,338,339,340,341],[0,273,337,338,339,340,341],[0,274,337,338,339,340,341],[0,275,337,338,339,340,341],[0,276,337,338,339,340,341],[0,277,337,338,339,340,341],[0,278,337,338,339,340,341],[0,279,337,338,339,340,341],[0,280,337,338,339,340,341],[0,281,337,338,339,340,341],[0,282,337,338,339,340,341],[0,283,337,338,339,340,341],[0,284,337,338,339,340,341],[0,285,337,338,339,340,341],[0,286,337,338,339,340,341],[0,264,265,266,267,269,270,271,273,274,276,277,278,282,283,336,337,338,339,340,341],[0,265,266,267,268,270,271,272,274,275,277,278,279,283,284,336,337,338,339,340,341],[0,266,267,268,269,271,272,273,275,276,278,279,280,284,285,336,337,338,339,340,341],[0,267,268,269,270,272,273,274,276,277,279,280,281,285,286,336,337,338,339,340,341],[0,264,265,266,267,268,275,276,280,281,283,286,336,337,338,339,340,341],[0,264,268,270,271,273,274,278,281,283,284,336,337,338,339,340,341],[0,265,269,271,272,274,275,279,282,284,285,336,337,338,339,340,341],[0,266,270,272,273,275,276,280,283,285,286,336,337,338,339,340,341],[0,264,265,266,269,270,278,281,282,283,284,286,336,337,338,339,340,341],[0,264,269,273,274,276,277,278,279,284,285,336,337,338,339,340,341],[0,265,270,274,275,277,278,279,280,285,286,336,337,338,339,340,341],[0,264,265,267,269,270,273,274,275,277,279,280,281,282,283,286,336,337,338,339,340,341],[0,264,267,268,269,273,275,277,280,281,284,336,337,338,339,340,341],[0,265,268,269,270,274,276,278,281,282,285,336,337,338,339,340,341],[0,266,269,270,271,275,277,279,282,283,286,336,337,338,339,340,341],[0,264,265,266,269,272,273,274,277,280,282,284,336,337,338,339,340,341],[0,265,266,267,270,273,274,275,278,281,283,285,336,337,338,339,340,341],[0,266,267,268,271,274,275,276,279,282,284,286,336,337,338,339,340,341],[0,264,265,266,268,270,271,272,273,274,275,278,280,282,285,336,337,338,339,340,341],[0,265,266,267,269,271,272,273,274,275,276,279,281,283,286,336,337,338,339,340,341],[0,264,265,268,269,271,272,275,278,280,283,284,336,337,338,339,340,341],[0,265,266,269,270,272,273,276,279,281,284,285,336,337,338,339,340,341],[0,266,267,270,271,273,274,277,280,282,285,286,336,337,338,339,340,341],[0,264,265,266,268,269,270,272,273,275,276,277,281,282,286,336,337,338,339,340,341],[0,264,336,337,338,339,340,341],[0,265,336,337,338,339,340,341],[0,266,336,337,338,339,340,341],[0,267,336,337,338,339,340,341],[0,268,336,337,338,339,340,341],[0,269,336,337,338,339,340,341],[0,270,336,337,338,339,340,341],[0,271,336,337,338,339,340,341],[0,272,336,337,338,339,340,341],[0,273,336,337,338,339,340,341],[0,274,336,337,338,339,340,341],[0,275,336,337,338,339,340,341],[0,276,336,337,338,339,340,341],[0,277,336,337,338,339,340,341],[0,278,336,337,338,339,340,341],[0,279,336,337,338,339,340,341],[0,280,336,337,338,339,340,341],[0,281,336,337,338,339,340,341],[0,282,336,337,338,339,340,341],[0,283,336,337,338,339,340,341],[0,284,336,337,338,339,340,341],[0,285,336,337,338,339,340,341],[0,286,336,337,338,339,340,341],[0,287,288,289,290,292,293,294,296,297,299,300,301,305,306,336,337,338,339,340,341],[0,288,289,290,291,293,294,295,297,298,300,301,302,306,307,336,337,338,339,340,341],[0,289,290,291,292,294,295,296,298,299,301,302,303,307,308,336,337,338,339,340,341],[0,290,291,292,293,295,296,297,299,300,302,303,304,308,309,336,337,338,339,340,341],[0,287,288,289,290,291,298,299,303,304,306,309,336,337,338,339,340,341],[0,287,291,293,294,296,297,301,304,306,307,336,337,338,339,340,341],[0,288,292,294,295,297,298,302,305,307,308,336,337,338,339,340,341],[0,289,293,295,296,298,299,303,306,308,309,336,337,338,339,340,341],[0,287,288,289,292,293,301,304,305,306,307,309,336,337,338,339,340,341],[0,287,292,296,297,299,300,301,302,307,308,336,337,338,339,340,341],[0,288,293,297,298,300,301,302,303,308,309,336,337,338,339,340,341],[0,287,288,290,292,293,296,297,298,300,302,303,304,305,306,309,336,337,338,339,340,341],[0,287,290,291,292,296,298,300,303,304,307,336,337,338,339,340,341],[0,288,291,292,293,297,299,301,304,305,308,336,337,338,339,340,341],[0,289,292,293,294,298,300,302,305,306,309,336,337,338,339,340,341],[0,287,288,289,292,295,296,297,300,303,305,307,336,337,338,339,340,341],[0,288,289,290,293,296,297,298,301,304,306,308,336,337,338,339,340,341],[0,289,290,291,294,297,298,299,302,305,307,309,336,337,338,339,340,341],[0,287,288,289,291,293,294,295,296,297,298,301,303,305,308,336,337,338,339,340,341],[0,288,289,290,292,294,295,296,297,298,299,302,304,306,309,336,337,338,339,340,341],[0,287,288,291,292,294,295,298,301,303,306,307,336,337,338,339,340,341],[0,288,289,292,293,295,296,299,302,304,307,308,336,337,338,339,340,341],[0,289,290,293,294,296,297,300,303,305,308,309,336,337,338,339,340,341],[0,287,288,289,291,292,293,295,296,298,299,300,304,305,309,336,337,338,339,340,341],[0,287,336,337,338,339,340,341],[0,288,336,337,338,339,340,341],[0,289,336,337,338,339,340,341],[0,290,336,337,338,339,340,341],[0,291,336,337,338,339,340,341],[0,292,336,337,338,339,340,341],[0,293,336,337,338,339,340,341],[0,294,336,337,338,339,340,341],[0,295,336,337,338,339,340,341],[0,296,336,337,338,339,340,341],[0,297,336,337,338,339,340,341],[0,298,336,337,338,339,340,341],[0,299,336,337,338,339,340,341],[0,300,336,337,338,339,340,341],[0,301,336,337,338,339,340,341],[0,302,336,337,338,339,340,341],[0,303,336,337,338,339,340,341],[0,304,336,337,338,339,340,341],[0,305,336,337,338,339,340,341],[0,306,336,337,338,339,340,341],[0,307,336,337,338,339,340,341],[0,308,336,337,338,339,340,341],[0,309,336,337,338,339,340,341],[0,287,288,289,290,292,293,294,296,297,299,300,301,305,306,335,336,337,338,339,340,341],[0,288,289,290,291,293,294,295,297,298,300,301,302,306,307,335,336,337,338,339,340,341],[0,289,290,291,292,294,295,296,298,299,301,302,303,307,308,335,336,337,338,339,340,341],[0,290,291,292,293,295,296,297,299,300,302,303,304,308,309,335,336,337,338,339,340,341],[0,287,288,289,290,291,298,299,303,304,306,309,335,336,337,338,339,340,341],[0,287,291,293,294,296,297,301,304,306,307,335,336,337,338,339,340,341],[0,288,292,294,295,297,298,302,305,307,308,335,336,337,338,339,340,341],[0,289,293,295,296,298,299,303,306,308,309,335,336,337,338,339,340,341],[0,287,288,289,292,293,301,304,305,306,307,309,335,336,337,338,339,340,341],[0,287,292,296,297,299,300,301,302,307,308,335,336,337,338,339,340,341],[0,288,293,297,298,300,301,302,303,308,309,335,336,337,338,339,340,341],[0,287,288,290,292,293,296,297,298,300,302,303,304,305,306,309,335,336,337,338,339,340,341],[0,287,290,291,292,296,298,300,303,304,307,335,336,337,338,339,340,341],[0,288,291,292,293,297,299,301,304,305,308,335,336,337,338,339,340,341],[0,289,292,293,294,298,300,302,305,306,309,335,336,337,338,339,340,341],[0,287,288,289,292,295,296,297,300,303,305,307,335,336,337,338,339,340,341],[0,288,289,290,293,296,297,298,301,304,306,308,335,336,337,338,339,340,341],[0,289,290,291,294,297,298,299,302,305,307,309,335,336,337,338,339,340,341],[0,287,288,289,291,293,294,295,296,297,298,301,303,305,308,335,336,337,338,339,340,341],[0,288,289,290,292,294,295,296,297,298,299,302,304,306,309,335,336,337,338,339,340,341],[0,287,288,291,292,294,295,298,301,303,306,307,335,336,337,338,339,340,341],[0,288,289,292,293,295,296,299,302,304,307,308,335,336,337,338,339,340,341],[0,289,290,293,294,296,297,300,303,305,308,309,335,336,337,338,339,340,341],[0,287,288,289,291,292,293,295,296,298,299,300,304,305,309,335,336,337,338,339,340,341],[0,287,335,336,337,338,339,340,341],[0,288,335,336,337,338,339,340,341],[0,289,335,336,337,338,339,340,341],[0,290,335,336,337,338,339,340,341],[0,291,335,336,337,338,339,340,341],[0,292,335,336,337,338,339,340,341],[0,293,335,336,337,338,339,340,341],[0,294,335,336,337,338,339,340,341],[0,295,335,336,337,338,339,340,341],[0,296,335,336,337,338,339,340,341],[0,297,335,336,337,338,339,340,341],[0,298,335,336,337,338,339,340,341],[0,299,335,336,337,338,339,340,341],[0,300,335,336,337,338,339,340,341],[0,301,335,336,337,338,339,340,341],[0,302,335,336,337,338,339,340,341],[0,303,335,336,337,338,339,340,341],[0,304,335,336,337,338,339,340,341],[0,305,335,336,337,338,339,340,341],[0,306,335,336,337,338,339,340,341],[0,307,335,336,337,338,339,340,341],[0,308,335,336,337,338,339,340,341],[0,309,335,336,337,338,339,340,341],[0,310,311,315,316,317,319,335,336,337,338,339,340,341],[0,311,312,316,317,318,320,335,336,337,338,339,340,341],[0,310,311,312,313,315,316,318,335,336,337,338,339,340,341],[0,311,312,313,314,316,317,319,335,336,337,338,339,340,341],[0,312,313,314,315,317,318,320,335,336,337,338,339,340,341],[0,310,311,313,314,317,318,335,336,337,338,339,340,341],[0,311,312,314,315,318,319,335,336,337,338,339,340,341],[0,312,313,315,316,319,320,335,336,337,338,339,340,341],[0,310,311,313,314,315,319,320,335,336,337,338,339,340,341],[0,310,312,314,317,319,320,335,336,337,338,339,340,341],[0,310,313,316,317,318,319,320,335,336,337,338,339,340,341],[0,310,314,315,316,318,320,335,336,337,338,339,340,341],[0,310,335,336,337,338,339,340,341],[0,311,335,336,337,338,339,340,341],[0,312,335,336,337,338,339,340,341],[0,313,335,336,337,338,339,340,341],[0,314,335,336,337,338,339,340,341],[0,315,335,336,337,338,339,340,341],[0,316,335,336,337,338,339,340,341],[0,317,335,336,337,338,339,340,341],[0,318,335,336,337,338,339,340,341],[0,319,335,336,337,338,339,340,341],[0,320,335,336,337,338,339,340,341],[0,310,311,315,316,317,319,334,335,336,337,338,339,340,341],[0,311,312,316,317,318,320,334,335,336,337,338,339,340,341],[0,310,311,312,313,315,316,318,334,335,336,337,338,339,340,341],[0,311,312,313,314,316,317,319,334,335,336,337,338,339,340,341],[0,312,313,314,315,317,318,320,334,335,336,337,338,339,340,341],[0,310,311,313,314,317,318,334,335,336,337,338,339,340,341],[0,311,312,314,315,318,319,334,335,336,337,338,339,340,341],[0,312,313,315,316,319,320,334,335,336,337,338,339,340,341],[0,310,311,313,314,315,319,320,334,335,336,337,338,339,340,341],[0,310,312,314,317,319,320,334,335,336,337,338,339,340,341],[0,310,313,316,317,318,319,320,334,335,336,337,338,339,340,341],[0,310,314,315,316,318,320,334,335,336,337,338,339,340,341],[0,310,334,335,336,337,338,339,340,341],[0,311,334,335,336,337,338,339,340,341],[0,312,334,335,336,337,338,339,340,341],[0,313,334,335,336,337,338,339,340,341],[0,314,334,335,336,337,338,339,340,341],[0,315,334,335,336,337,338,339,340,341],[0,316,334,335,336,337,338,339,340,341],[0,317,334,335,336,337,338,339,340,341],[0,318,334,335,336,337,338,339,340,341],[0,319,334,335,336,337,338,339,340,341],[0,320,334,335,336,337,338,339,340,341],[0,322,328,334,335,336,337,338,339,340,341],[0,321,327,328,334,335,336,337,338,339,340,341],[0,321,327,334,335,336,337,338,339,340,341],[0,326,328,334,335,336,337,338,339,340,341],[0,322,323,325,334,335,336,337,338,339,340,341],[0,326,327,334,335,336,337,338,339,340,341],[0,324,328,334,335,336,337,338,339,340,341],[0,321,324,328,334,335,336,337,338,339,340,341],[0,321,324,334,335,336,337,338,339,340,341],[0,323,325,334,335,336,337,338,339,340,341],[0,323,334,335,336,337,338,339,340,341],[0,326,334,335,336,337,338,339,340,341],[0,326,327,328,334,335,336,337,338,339,340,341],[0,322,323,334,335,336,337,338,339,340,341],[0,324,334,335,336,337,338,339,340,341],[0,325,328,334,335,336,337,338,339,340,341],[0,322,325,328,334,335,336,337,338,339,340,341],[0,322,328,333,334,335,336,337,338,339,340,341],[0,321,327,328,333,334,335,336,337,338,339,340,341],[0,321,327,333,334,335,336,337,338,339,340,341],[0,326,328,333,334,335,336,337,338,339,340,341],[0,322,323,325,333,334,335,336,337,338,339,340,341],[0,326,327,333,334,335,336,337,338,339,340,341],[0,324,328,333,334,335,336,337,338,339,340,341],[0,321,324,328,333,334,335,336,337,338,339,340,341],[0,321,324,333,334,335,336,337,338,339,340,341],[0,323,325,333,334,335,336,337,338,339,340,341],[0,323,333,334,335,336,337,338,339,340,341],[0,326,333,334,335,336,337,338,339,340,341],[0,326,327,328,333,334,335,336,337,338,339,340,341],[0,322,323,333,334,335,336,337,338,339,340,341],[0,324,333,334,335,336,337,338,339,340,341],[0,325,328,333,334,335,336,337,338,339,340,341],[0,322,325,328,333,334,335,336,337,338,339,340,341],[0,329,330,333,334,335,336,337,338,339,340,341],[0,330,331,333,334,335,336,337,338,339,340,341],[0,329,330,331,333,334,335,336,337,338,339,340,341],[0,329,331,333,334,335,336,337,338,339,340,341],[0,329,333,334,335,336,337,338,339,340,341],[0,330,333,334,335,336,337,338,339,340,341],[0,331,333,334,335,336,337,338,339,340,341],[0,329,330,332,333,334,335,336,337,338,339,340,341],[0,330,331,332,333,334,335,336,337,338,339,340,341],[0,329,330,331,332,333,334,335,336,337,338,339,340,341],[0,329,331,332,333,334,335,336,337,338,339,340,341],[0,329,332,333,334,335,336,337,338,339,340,341],[0,330,332,333,334,335,336,337,338,339,340,341],[0,331,332,333,334,335,336,337,338,339,340,341],[0,332,333,334,335,336,337,338,339,340,341]]},"distance":{"d":3,"is_exact":false,"upper":21,"witness":[0,167,334,437,540,643,746,825,904,983,1062,1109,1156,1203,1250,1273,1296,1313,1330,1337,1344],"A_d":null,"certified":{"d":21,"is_exact":false,"met":true,"source":"Jain and Albert (arXiv:2408.12752), Table II: [[167,1,23]] quantum QR code (extended QR [168,84,24]) doubled onto [[1011,1,19]]; the doubling theorem of their Sec. III gives d >= min(d_sd, d_tri + 2) = 21, with d_sd at least the classical distance less one (their Lemma 2.4)"}},"clifford":{"kind":"powers","correction":{"S":[[335,1],[336,2],[337,3],[339,1],[340,2],[341,3]],"CZ":[[0,335],[0,337],[0,339],[0,341],[335,336],[335,337],[335,338],[335,339],[335,340],[335,341],[337,338],[337,339],[337,340],[337,341],[339,340],[339,341]]},"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],[206,7],[207,7],[208,7],[209,7],[210,7],[211,7],[212,7],[213,7],[214,7],[215,7],[216,7],[217,7],[218,7],[219,7],[220,7],[221,7],[222,7],[223,7],[224,7],[225,7],[226,7],[227,7],[228,7],[229,7],[230,7],[231,7],[232,7],[233,7],[234,7],[235,7],[236,7],[237,7],[238,7],[239,7],[240,7],[241,7],[242,7],[243,7],[244,7],[245,7],[246,7],[247,7],[248,7],[249,7],[250,7],[251,7],[252,7],[253,7],[254,7],[255,7],[256,7],[257,7],[258,7],[259,7],[260,7],[261,7],[262,7],[263,7],[264,7],[265,7],[266,7],[267,7],[268,7],[269,7],[270,7],[271,7],[272,7],[273,7],[274,7],[275,7],[276,7],[277,7],[278,7],[279,7],[280,7],[281,7],[282,7],[283,7],[284,7],[285,7],[286,7],[287,7],[288,7],[289,7],[290,7],[291,7],[292,7],[293,7],[294,7],[295,7],[296,7],[297,7],[298,7],[299,7],[300,7],[301,7],[302,7],[303,7],[304,7],[305,7],[306,7],[307,7],[308,7],[309,7],[310,7],[311,7],[312,7],[313,7],[314,7],[315,7],[316,7],[317,7],[318,7],[319,7],[320,7],[321,7],[322,7],[323,7],[324,7],[325,7],[326,7],[327,7],[328,7],[329,7],[330,7],[331,7],[332,7],[333,7],[540,7],[541,7],[542,7],[543,7],[544,7],[545,7],[546,7],[547,7],[548,7],[549,7],[550,7],[551,7],[552,7],[553,7],[554,7],[555,7],[556,7],[557,7],[558,7],[559,7],[560,7],[561,7],[562,7],[563,7],[564,7],[565,7],[566,7],[567,7],[568,7],[569,7],[570,7],[571,7],[572,7],[573,7],[574,7],[575,7],[576,7],[577,7],[578,7],[579,7],[580,7],[581,7],[582,7],[583,7],[584,7],[585,7],[586,7],[587,7],[588,7],[589,7],[590,7],[591,7],[592,7],[593,7],[594,7],[595,7],[596,7],[597,7],[598,7],[599,7],[600,7],[601,7],[602,7],[603,7],[604,7],[605,7],[606,7],[607,7],[608,7],[609,7],[610,7],[611,7],[612,7],[613,7],[614,7],[615,7],[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],[710,7],[711,7],[712,7],[713,7],[714,7],[715,7],[716,7],[717,7],[718,7],[719,7],[720,7],[721,7],[722,7],[723,7],[724,7],[725,7],[726,7],[727,7],[728,7],[729,7],[730,7],[731,7],[732,7],[733,7],[734,7],[735,7],[736,7],[737,7],[738,7],[739,7],[740,7],[741,7],[742,7],[743,7],[744,7],[745,7],[904,7],[905,7],[906,7],[907,7],[908,7],[909,7],[910,7],[911,7],[912,7],[913,7],[914,7],[915,7],[916,7],[917,7],[918,7],[919,7],[920,7],[921,7],[922,7],[923,7],[924,7],[925,7],[926,7],[927,7],[928,7],[929,7],[930,7],[931,7],[932,7],[933,7],[934,7],[935,7],[936,7],[937,7],[938,7],[939,7],[940,7],[941,7],[942,7],[943,7],[944,7],[945,7],[946,7],[947,7],[948,7],[949,7],[950,7],[951,7],[952,7],[953,7],[954,7],[955,7],[956,7],[957,7],[958,7],[959,7],[960,7],[961,7],[962,7],[963,7],[964,7],[965,7],[966,7],[967,7],[968,7],[969,7],[970,7],[971,7],[972,7],[973,7],[974,7],[975,7],[976,7],[977,7],[978,7],[979,7],[980,7],[981,7],[982,7],[983,7],[984,7],[985,7],[986,7],[987,7],[988,7],[989,7],[990,7],[991,7],[992,7],[993,7],[994,7],[995,7],[996,7],[997,7],[998,7],[999,7],[1000,7],[1001,7],[1002,7],[1003,7],[1004,7],[1005,7],[1006,7],[1007,7],[1008,7],[1009,7],[1010,7],[1011,7],[1012,7],[1013,7],[1014,7],[1015,7],[1016,7],[1017,7],[1018,7],[1019,7],[1020,7],[1021,7],[1022,7],[1023,7],[1024,7],[1025,7],[1026,7],[1027,7],[1028,7],[1029,7],[1030,7],[1031,7],[1032,7],[1033,7],[1034,7],[1035,7],[1036,7],[1037,7],[1038,7],[1039,7],[1040,7],[1041,7],[1042,7],[1043,7],[1044,7],[1045,7],[1046,7],[1047,7],[1048,7],[1049,7],[1050,7],[1051,7],[1052,7],[1053,7],[1054,7],[1055,7],[1056,7],[1057,7],[1058,7],[1059,7],[1060,7],[1061,7],[1156,7],[1157,7],[1158,7],[1159,7],[1160,7],[1161,7],[1162,7],[1163,7],[1164,7],[1165,7],[1166,7],[1167,7],[1168,7],[1169,7],[1170,7],[1171,7],[1172,7],[1173,7],[1174,7],[1175,7],[1176,7],[1177,7],[1178,7],[1179,7],[1180,7],[1181,7],[1182,7],[1183,7],[1184,7],[1185,7],[1186,7],[1187,7],[1188,7],[1189,7],[1190,7],[1191,7],[1192,7],[1193,7],[1194,7],[1195,7],[1196,7],[1197,7],[1198,7],[1199,7],[1200,7],[1201,7],[1202,7],[1203,7],[1204,7],[1205,7],[1206,7],[1207,7],[1208,7],[1209,7],[1210,7],[1211,7],[1212,7],[1213,7],[1214,7],[1215,7],[1216,7],[1217,7],[1218,7],[1219,7],[1220,7],[1221,7],[1222,7],[1223,7],[1224,7],[1225,7],[1226,7],[1227,7],[1228,7],[1229,7],[1230,7],[1231,7],[1232,7],[1233,7],[1234,7],[1235,7],[1236,7],[1237,7],[1238,7],[1239,7],[1240,7],[1241,7],[1242,7],[1243,7],[1244,7],[1245,7],[1246,7],[1247,7],[1248,7],[1249,7]]},"metrics":{"gamma":6.557499280087071,"gamma_t":6.557499280087071,"gamma_rho":6.557499280087071,"gamma_claim":2.3662657902508104,"gamma_t_claim":2.3662657902508104,"gamma_rho_claim":2.3662657902508104,"v_ex":1,"rate":0.0007434944237918215,"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-1345","N":342,"d":3,"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":"[[167,1,23]] quantum QR code (extended QR [168,84,24]) doubled onto [[1011,1,19]] (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"}]}