2,0,0,0,0,2,0,0,0,7,2,0,0,0,8,2,0,1,0,5,2,0,1,0,6,5,0,1,0,7,2,0,1,0,8,31,1,1,0,9,31,1,1,0,10,31,1,1,0,11,31,1,2,0,3,2,0,2,0,4,2,0,2,0,5,2,0,2,0,6,53,1,2,0,7,2,0,2,0,8,31,1,2,0,10,31,1,3,0,2,2,0,3,0,4,2,0,3,0,6,2,0,3,0,7,2,0,3,0,8,2,0,3,0,9,31,1,4,0,1,2,0,4,0,3,2,0,4,0,6,2,0,4,0,7,2,0,5,0,1,2,0,5,0,4,40,0,5,0,6,40,0,5,0,7,2,0,6,0,0,2,0,6,0,1,40,0,6,0,5,63,1,6,0,12,65,4,6,0,13,2,0,7,0,0,5,0,7,0,1,53,3,7,0,2,40,0,7,0,5,53,2,7,0,12,5,0,7,0,13,65,3,7,0,14,2,0,8,0,1,2,0,8,0,13,31,1,9,0,1,31,1,9,0,3,2,0,9,0,4,31,1,10,0,4,31,1,10,0,5,31,1,10,0,14,31,1,11,0,2,2,0,11,0,3,31,1,11,0,4,2,0,11,0,5,2,0,11,0,6,2,0,11,0,7,31,1,12,0,3,2,0,12,0,5,2,0,12,0,6,53,0,12,0,7,2,0,12,0,8,2,0,12,0,9,31,1,12,0,10,2,0,13,0,6,5,0,13,0,7,2,0,13,0,8,31,1,13,0,9,2,0,14,0,7,31,1,14,0,9,31,1,14,0,10,53,0,1,1,7,5,0,2,1,7,31,1,2,1,8,40,0,4,1,7,31,1,7,1,0,53,2,7,1,1,5,0,7,1,2,5,0,7,1,12,53,3,7,1,13,31,1,8,1,1,31,1,8,1,13,31,1,11,1,5,5,0,12,1,7,53,1,13,1,7,53,0,2,2,7,44,2,3,2,5,44,2,3,2,6,17,3,3,2,7,44,2,3,2,8,44,2,3,2,9,44,2,4,2,4,44,2,4,2,10,44,2,5,2,3,44,2,5,2,11,44,2,6,2,3,44,2,6,2,11,53,2,7,2,2,17,3,7,2,3,17,3,7,2,11,53,3,7,2,12,44,2,8,2,3,44,2,8,2,11,44,2,9,2,3,44,2,9,2,11,44,2,10,2,4,44,2,10,2,10,44,2,11,2,5,44,2,11,2,6,17,3,11,2,7,44,2,11,2,8,44,2,11,2,9,53,1,12,2,7,53,0,3,3,7,5,0,4,3,7,53,2,7,3,3,5,0,7,3,4,5,0,7,3,10,53,3,7,3,11,5,0,10,3,7,53,1,11,3,7,53,0,4,4,7,5,0,5,4,7,44,10,6,4,7,53,2,7,4,4,5,0,7,4,5,44,10,7,4,6,44,10,7,4,8,5,0,7,4,9,53,3,7,4,10,44,10,8,4,7,5,0,9,4,7,53,1,10,4,7,44,2,5,5,7,5,0,6,5,7,44,2,7,5,5,5,0,7,5,6,44,10,7,5,7,5,0,7,5,8,44,2,7,5,9,5,0,8,5,7,44,2,9,5,7,121,0,6,6,6,67,4,6,6,7,121,0,6,6,8,67,6,7,6,6,7,0,7,6,7,4,0,7,6,8,65,3,7,6,9,35,0,8,6,3,121,0,8,6,6,67,5,8,6,7,121,0,8,6,8,35,0,10,6,4,44,11,5,7,5,98,2,5,7,6,98,2,5,7,8,44,11,5,7,9,98,2,6,7,5,43,3,6,7,6,98,1,6,7,7,43,3,6,7,8,98,2,6,7,9,44,10,6,7,11,98,1,7,7,6,67,2,7,7,8,44,10,7,7,10,44,10,7,7,11,98,2,8,7,5,43,3,8,7,6,98,1,8,7,7,43,3,8,7,8,98,2,8,7,9,44,10,8,7,11,35,0,9,7,3,44,11,9,7,5,98,2,9,7,6,98,2,9,7,8,44,11,9,7,9,35,0,10,7,3,35,0,11,7,3,35,0,12,7,2,35,14,13,7,2,35,14,0,8,2,85,0,1,8,2,44,2,4,8,5,44,2,4,8,6,53,0,4,8,7,44,2,4,8,8,44,2,4,8,9,44,2,5,8,4,4,0,5,8,5,98,2,5,8,6,5,0,5,8,7,98,2,5,8,8,4,0,5,8,9,44,2,5,8,10,44,2,6,8,4,98,2,6,8,5,44,2,6,8,7,45,0,6,8,9,44,2,6,8,10,53,2,7,8,4,5,0,7,8,5,44,2,7,8,6,96,3,7,8,9,35,0,8,8,3,44,2,8,8,4,98,2,8,8,5,44,2,8,8,7,45,0,8,8,9,44,2,8,8,10,35,0,9,8,3,44,2,9,8,4,4,0,9,8,5,98,2,9,8,6,5,0,9,8,7,98,2,9,8,8,4,0,9,8,9,44,2,9,8,10,35,0,10,8,2,44,2,10,8,5,44,2,10,8,6,53,1,10,8,7,44,2,10,8,8,44,2,10,8,9,35,0,11,8,2,35,14,12,8,2,85,0,13,8,2,35,0,0,9,2,35,14,1,9,2,85,0,2,9,2,4,0,5,9,5,45,0,5,9,6,45,0,5,9,7,108,2,5,9,8,4,0,5,9,9,45,0,6,9,5,65,2,6,9,8,45,0,6,9,9,45,0,7,9,5,35,8,7,9,7,35,0,8,9,2,45,0,8,9,5,45,0,8,9,9,35,0,9,9,3,4,0,9,9,5,45,0,9,9,6,108,1,9,9,7,45,0,9,9,8,4,0,9,9,9,35,0,10,9,2,35,14,11,9,2,85,0,12,9,2,35,0,0,10,2,35,0,1,10,2,35,14,2,10,2,85,0,3,10,2,4,0,5,10,5,45,0,5,10,6,102,0,5,10,7,45,0,5,10,8,4,0,5,10,9,45,0,6,10,5,65,2,6,10,8,45,0,6,10,9,102,0,7,10,5,17,1,7,10,7,35,0,8,10,2,108,4,8,10,5,45,0,8,10,9,35,0,9,10,2,4,0,9,10,5,45,0,9,10,6,102,0,9,10,7,108,5,9,10,8,4,0,9,10,9,35,14,10,10,2,85,0,11,10,2,35,0,0,11,3,35,0,2,11,2,35,14,3,11,2,85,0,4,11,2,44,2,4,11,7,4,0,5,11,5,45,0,5,11,6,45,0,5,11,7,45,0,5,11,8,4,0,5,11,9,45,0,6,11,5,65,2,6,11,8,45,0,6,11,9,96,0,7,11,4,45,0,7,11,5,17,1,7,11,7,53,7,7,11,9,35,0,8,11,2,45,0,8,11,5,45,0,8,11,9,35,14,9,11,2,4,0,9,11,5,45,0,9,11,6,45,0,9,11,7,45,0,9,11,8,4,0,9,11,9,85,0,10,11,2,44,2,10,11,7,35,0,0,12,3,35,0,1,12,3,35,0,2,12,3,35,0,3,12,2,35,14,4,12,2,44,2,4,12,5,44,2,4,12,6,44,2,4,12,7,44,2,4,12,8,44,2,4,12,9,85,0,5,12,2,44,2,5,12,4,4,0,5,12,5,45,0,5,12,6,45,0,5,12,7,45,0,5,12,8,4,0,5,12,9,44,2,5,12,10,44,2,6,12,4,45,0,6,12,5,44,8,6,12,7,65,2,6,12,8,45,0,6,12,9,44,2,6,12,10,44,2,7,12,4,45,0,7,12,5,44,8,7,12,6,17,1,7,12,7,44,8,7,12,8,45,0,7,12,9,44,2,7,12,10,35,14,8,12,2,44,2,8,12,4,45,0,8,12,5,44,8,8,12,7,45,0,8,12,9,44,2,8,12,10,85,0,9,12,2,44,2,9,12,4,4,0,9,12,5,45,0,9,12,6,45,0,9,12,7,45,0,9,12,8,4,0,9,12,9,44,2,9,12,10,44,2,10,12,5,44,2,10,12,6,44,2,10,12,7,44,2,10,12,8,44,2,10,12,9,35,0,1,13,3,35,0,2,13,2,35,0,3,13,2,35,0,4,13,2,35,14,5,13,2,4,0,5,13,5,108,4,5,13,6,108,0,5,13,7,45,0,5,13,8,4,0,5,13,9,114,5,6,13,2,45,0,6,13,5,65,2,6,13,8,45,0,6,13,9,35,8,7,13,2,35,4,7,13,4,45,0,7,13,5,114,5,7,13,6,35,8,7,13,7,102,0,7,13,9,114,1,8,13,2,45,0,8,13,5,45,0,8,13,9,4,0,9,13,5,45,0,9,13,6,108,5,9,13,7,108,2,9,13,8,4,0,9,13,9,35,0,0,14,4,35,0,3,14,3,44,10,4,14,4,44,10,4,14,10,4,0,5,14,5,45,0,5,14,6,45,0,5,14,7,45,0,5,14,8,4,0,5,14,9,35,8,6,14,2,35,4,6,14,4,45,0,6,14,5,114,4,6,14,6,65,2,6,14,8,45,0,6,14,9,23,3,7,14,1,34,2,7,14,3,33,10,7,14,4,76,5,7,14,5,35,8,7,14,6,77,3,7,14,7,45,0,7,14,9,44,2,7,14,10,35,8,8,14,2,35,4,8,14,4,45,0,8,14,5,114,1,8,14,6,45,0,8,14,9,4,0,9,14,5,108,5,9,14,6,108,7,9,14,7,45,0,9,14,8,4,0,9,14,9,44,10,10,14,4,44,10,10,14,10,53,0,4,15,5,53,0,4,15,6,53,0,4,15,7,53,0,4,15,8,53,0,4,15,9,53,5,5,15,4,4,0,5,15,5,45,0,5,15,6,45,0,5,15,7,45,0,5,15,8,4,0,5,15,9,53,5,5,15,10,114,4,6,15,2,45,0,6,15,5,45,0,6,15,9,35,8,7,15,2,35,4,7,15,4,45,0,7,15,5,114,0,7,15,6,45,0,7,15,9,114,0,8,15,2,45,0,8,15,5,45,0,8,15,9,35,14,9,15,2,53,4,9,15,4,4,0,9,15,5,45,0,9,15,6,45,0,9,15,7,45,0,9,15,8,4,0,9,15,9,53,4,9,15,10,35,0,10,15,2,53,1,10,15,5,53,1,10,15,6,53,1,10,15,7,53,1,10,15,8,53,1,10,15,9,35,0,11,15,2,35,0,12,15,2,35,0,13,15,3,85,0,5,16,2,53,0,5,16,5,53,0,5,16,6,53,0,5,16,7,53,0,5,16,8,53,0,5,16,9,35,14,6,16,2,53,5,6,16,4,4,0,6,16,5,4,0,6,16,9,53,5,6,16,10,45,0,7,16,5,45,0,7,16,9,53,4,8,16,4,4,0,8,16,5,4,0,8,16,9,53,4,8,16,10,85,0,9,16,2,53,1,9,16,5,53,1,9,16,6,53,1,9,16,7,53,1,9,16,8,53,1,9,16,9,35,14,10,16,2,35,0,11,16,2,35,0,12,16,3,35,0,13,16,3,35,0,14,16,3,85,0,4,17,2,35,14,5,17,2,35,0,6,17,2,44,2,6,17,5,53,0,6,17,6,53,0,6,17,7,53,0,6,17,8,44,2,6,17,9,44,2,7,17,4,43,2,7,17,5,5,0,7,17,6,5,0,7,17,7,5,0,7,17,8,43,2,7,17,9,44,2,7,17,10,44,2,8,17,5,53,1,8,17,6,53,1,8,17,7,53,1,8,17,8,44,2,8,17,9,85,0,10,17,2,35,14,11,17,2,35,0,12,17,2,35,0,13,17,2,35,0,14,17,3,85,0,3,18,2,35,14,4,18,2,35,0,5,18,2,35,0,6,18,2,44,2,7,18,6,44,2,7,18,7,44,2,7,18,8,85,0,11,18,2,35,14,12,18,2,35,0,13,18,2,35,0,14,18,3,85,0,2,19,2,35,14,3,19,2,35,0,4,19,2,35,0,5,19,3,35,0,6,19,2,85,0,12,19,2,35,14,13,19,2,35,0,14,19,2,85,0,1,20,2,35,14,2,20,2,35,0,3,20,2,35,0,4,20,2,35,0,5,20,3,35,0,6,20,3,85,0,13,20,2,35,14,14,20,2,35,14,1,21,2,35,0,2,21,2,35,0,3,21,3,35,0,4,21,3,35,0,5,21,3,35,0,6,22,4