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2,3,6,3,4,6,3,4,6,2,3,6,3,4,6,2,3,6,2,3,6,4,4,6,4,4,6,3,3,6,4,4,6,3,3,6,3,3,6,5,4,6,5,4,6,4,3,6,5,4,6,4,3,6,4,3,6,5,3,6,6,4,6,6,3,6,5,4,6,6,4,6,5,3,7,6,3,7,7,4,7,7,3,7,6,4,7,7,4,7,6,3,6,6,3,6,7,3,7,7,3,6,6,3,7,7,3,7,6,4,6,6,3,6,6,3,7,6,4,6,6,3,7,6,4,7,6,3,7,7,3,7,8,4,7,8,3,7,7,4,7,8,4,7,7,3,6,7,3,6,8,3,7,8,3,6,7,3,7,8,3,7,7,3,6,8,4,6,8,4,7,8,3,6,8,4,7,8,3,7,8,4,6,9,4,6,8,3,6,8,4,6,9,3,6,8,3,6,9,3,6,10,4,6,10,4,6,9,3,6,10,4,6,9,3,6,9,3,6,11,4,6,11,4,6,10,3,6,11,4,6,10,3,6,10,4,6,11,3,6,11,3,6,12,4,6,11,3,6,12,4,6,12,3,6,13,4,6,13,4,6,12,3,6,13,4,6,12,3,6,12,4,6,14,4,6,13,3,6,13,4,6,14,3,6,13,3,6,14,3,6,14,3,6,15,4,6,15,3,6,14,4,6,15,4,6,14,3,6,16,4,6,16,4,6,15,3,6,16,4,6,15,3,6,15,4,6,17,4,6,16,3,6,16,4,6,17,3,6,16,3,6,17,4,6,17,3,6,17,3,6,18,4,6,17,3,6,18,4,6,18,3,5,18,4,5,18,4,6,18,3,5,18,4,6,18,3,6,18,4,5,18,3,5,18,3,5,19,4,5,18,3,5,19,4,5,19,4,5,19,3,5,19,3,5,20,4,5,19,3,5,20,4,5,20,4,5,21,4,5,20,3,5,20,4,5,21,3,5,20,3,5,21,3,5,22,4,5,22,4,5,21,3,5,22,4,5,21,3,5,21,4,5,23,4,5,22,3,5,22,4,5,23,3,5,22,3,5,23,4,5,23,3,5,23,3,5,24,4,5,23,3,5,24,4,5,24,4,5,24,3,5,24,3,5,25,4,5,24,3,5,25,4,5,25,3,5,25,3,5,26,4,5,26,3,5,25,4,5,26,4,5,25,3,4,26,4,4,26,4,5,26,3,4,26,4,5,26,3,5,26,3,4,27,4,4,27,4,4,26,3,4,27,4,4,26,3,4,26,4,4,27,3,4,27,3,4,28,4,4,27,3,4,28,4,4,28,4,4,29,4,4,28,3,4,28,4,4,29,3,4,28,3,4,29,3,4,29,3,4,30,4,4,30,3,4,29,4,4,30,4,4,29,4,4,31,4,4,30,3,4,30,4,4,31,3,4,30,3,4,31,3,4,32,4,4,32,4,4,31,3,4,32,4,4,31,3,4,31,4,6,1,5,6,1,5,6,0,4,6,1,5,6,0,4,6,0,5,6,1,4,6,1,4,6,2,5,6,1,4,6,2,5,6,2,5,6,2,4,6,2,4,6,3,5,6,2,4,6,3,5,6,3,5,6,4,5,6,3,4,6,3,5,6,4,4,6,3,4,6,4,5,6,4,4,6,4,4,6,5,5,6,4,4,6,5,5,6,5,5,7,6,5,7,5,4,7,5,5,7,6,4,7,5,4,7,6,4,6,5,4,6,6,4,7,6,4,6,5,4,7,6,4,7,5,5,6,5,4,6,5,4,7,5,5,6,5,4,7,5,5,7,5,4,7,7,5,7,7,5,7,6,4,7,7,5,7,6,4,7,6,4,7,7,4,7,8,5,7,8,4,7,7,5,7,8,5,7,7,4,7,9,5,7,9,5,7,8,4,7,9,5,7,8,4,7,8,4,6,8,4,6,9,4,7,9,4,6,8,4,7,9,4,7,8,5,7,10,5,7,9,4,7,9,5,7,10,4,7,9,4,7,10,4,6,9,4,6,10,4,7,10,4,6,9,4,7,10,4,7,9,5,7,10,4,7,10,4,7,11,5,7,10,4,7,11,5,7,11,4,6,11,5,6,11,5,7,11,4,6,11,5,7,11,4,7,11,4,6,10,4,6,11,4,7,11,4,6,10,4,7,11,4,7,10,5,6,11,4,6,11,4,6,12,5,6,11,4,6,12,5,6,12,5,6,13,5,6,12,4,6,12,5,6,13,4,6,12,4,6,13,4,6,13,4,6,14,5,6,14,4,6,13,5,6,14,5,6,13,4,6,14,4,6,15,5,6,15,4,6,14,5,6,15,5,6,14,5,6,15,4,6,15,4,6,16,5,6,15,4,6,16,5,6,16,4,6,17,5,6,17,5,6,16,4,6,17,5,6,16,4,6,16,5,6,18,5,6,17,4,6,17,5,6,18,4,6,17,4,6,18,4,5,18,5,5,18,5,6,18,4,5,18,5,6,18,4,6,18,4,5,18,4,5,19,5,5,19,4,5,18,5,5,19,5,5,18,4,5,20,5,5,20,5,5,19,4,5,20,5,5,19,4,5,19,5,5,20,4,5,20,4,5,21,5,5,20,4,5,21,5,5,21,5,5,21,4,5,21,4,5,22,5,5,21,4,5,22,5,5,22,5,5,23,5,5,22,4,5,22,5,5,23,4,5,22,4,5,23,4,5,24,5,5,24,5,5,23,4,5,24,5,5,23,4,5,23,4,5,25,5,5,25,5,5,24,4,5,25,5,5,24,4,5,24,4,5,26,5,5,26,5,5,25,4,5,26,5,5,25,4,5,25,4,4,26,5,4,26,5,5,26,4,4,26,5,5,26,4,5,26,5,4,27,5,4,26,4,4,26,5,4,27,4,4,26,4,4,27,5,4,28,5,4,27,4,4,27,5,4,28,4,4,27,4,4,28,5,4,28,4,4,28,4,4,29,5,4,28,4,4,29,5,4,29,5,4,29,4,4,29,4,4,30,5,4,29,4,4,30,5,4,30,4,4,30,4,4,31,5,4,31,4,4,30,5,4,31,5,4,30,4,4,32,5,4,32,5,4,31,4,4,32,5,4,31,4,4,31,5,6,0,5,6,1,6,6,1,5,6,0,6,6,1,6,6,0,5,6,1,5,6,2,6,6,2,5,6,1,6,6,2,6,6,1,6,6,2,5,6,2,5,6,3,6,6,2,5,6,3,6,6,3,6,7,4,6,7,3,5,7,3,6,7,4,5,7,3,5,7,4,5,6,3,5,6,4,5,7,4,5,6,3,5,7,4,5,7,3,6,6,3,5,6,3,5,7,3,6,6,3,5,7,3,6,7,3,6,7,4,5,7,4,5,7,5,6,7,4,5,7,5,6,7,5,5,6,4,5,6,5,5,7,5,5,6,4,5,7,5,5,7,4,5,7,6,6,7,6,6,7,5,5,7,6,6,7,5,5,7,5,6,7,6,5,7,6,5,7,7,6,7,6,5,7,7,6,7,7,6,7,7,5,7,7,5,7,8,6,7,7,5,7,8,6,7,8,5,7,9,6,7,9,6,7,8,5,7,9,6,7,8,5,7,8,6,7,10,6,7,9,5,7,9,6,7,10,5,7,9,5,7,10,6,7,10,5,7,10,5,7,11,6,7,10,5,7,11,6,7,11,5,6,11,6,6,11,6,7,11,5,6,11,6,7,11,5,7,11,6,6,11,5,6,11,5,6,12,6,6,11,5,6,12,6,6,12,5,6,12,5,6,13,6,6,13,5,6,12,6,6,13,6,6,12,6,6,13,5,6,13,5,6,14,6,6,13,5,6,14,6,6,14,5,6,15,6,6,15,6,6,14,5,6,15,6,6,14,5,6,14,5,6,16,6,6,16,6,6,15,5,6,16,6,6,15,5,6,15,5,6,17,6,6,17,6,6,16,5,6,17,6,6,16,5,6,16,5,6,18,6,6,18,6,6,17,5,6,18,6,6,17,5,6,17,5,5,18,6,5,18,6,6,18,5,5,18,6,6,18,5,6,18,5,5,19,6,5,19,6,5,18,5,5,19,6,5,18,5,5,18,5,5,19,5,5,20,6,5,20,5,5,19,6,5,20,6,5,19,6,5,20,5,5,20,5,5,21,6,5,20,5,5,21,6,5,21,5,5,21,5,5,22,6,5,22,5,5,21,6,5,22,6,5,21,5,5,22,5,5,23,6,5,23,5,5,22,6,5,23,6,5,22,6,5,23,5,5,23,5,5,24,6,5,23,5,5,24,6,5,24,6,5,25,6,5,24,5,5,24,6,5,25,5,5,24,5,5,25,6,5,25,5,5,25,5,5,26,6,5,25,5,5,26,6,5,26,5,4,26,6,4,26,6,5,26,5,4,26,6,5,26,5,5,26,6,4,26,6,4,25,6,5,25,6,4,26,6,5,25,6,5,26,5,4,26,5,4,27,6,4,27,5,4,26,6,4,27,6,4,26,6,4,28,6,4,27,5,4,27,6,4,28,5,4,27,5,4,28,6,4,29,6,4,28,5,4,28,6,4,29,5,4,28,5,4,29,6,4,30,6,4,29,5,4,29,6,4,30,5,4,29,5,4,30,6,4,30,5,4,30,5,4,31,6,4,30,5,4,31,6,4,31,6,4,32,6,4,31,5,4,31,6,4,32,5,4,31,5,4,32,7,6,0,6,6,0,6,6,1,7,6,0,6,6,1,7,6,1,7,7,2,7,7,1,6,7,1,7,7,2,6,7,1,6,7,2,6,6,1,6,6,2,6,7,2,6,6,1,6,7,2,6,7,1,7,6,1,6,6,1,6,7,1,7,6,1,6,7,1,7,7,1,7,7,3,7,7,2,6,7,2,7,7,3,6,7,2,6,7,3,6,6,2,6,6,3,6,7,3,6,6,2,6,7,3,6,7,2,6,7,3,6,7,4,7,7,4,6,7,3,7,7,4,7,7,3,7,7,5,7,7,4,6,7,4,7,7,5,6,7,4,6,7,5,7,7,5,6,7,5,6,7,6,7,7,5,6,7,6,7,7,6,6,7,6,6,7,7,7,7,7,6,7,6,7,7,7,7,7,6,7,7,8,7,7,7,6,7,7,7,7,8,6,7,7,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