=>

[[1]]=>[1]=>[1]=> [[1,2]]=>[1,2]=>[1,2]=>0 [[1],[2]]=>[2,1]=>[2,1]=>1 [[1,2,3]]=>[1,2,3]=>[1,2,3]=>00 [[1,3],[2]]=>[2,1,3]=>[2,1,3]=>10 [[1,2],[3]]=>[3,1,2]=>[2,3,1]=>01 [[1],[2],[3]]=>[3,2,1]=>[3,2,1]=>11 [[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>000 [[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>100 [[1,2,4],[3]]=>[3,1,2,4]=>[2,3,1,4]=>010 [[1,2,3],[4]]=>[4,1,2,3]=>[2,3,4,1]=>001 [[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>101 [[1,2],[3,4]]=>[3,4,1,2]=>[3,4,1,2]=>010 [[1,4],[2],[3]]=>[3,2,1,4]=>[3,2,1,4]=>110 [[1,3],[2],[4]]=>[4,2,1,3]=>[3,2,4,1]=>101 [[1,2],[3],[4]]=>[4,3,1,2]=>[3,4,2,1]=>011 [[1],[2],[3],[4]]=>[4,3,2,1]=>[4,3,2,1]=>111 [[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000 [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000 [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[2,3,1,4,5]=>0100 [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,3,4,1,5]=>0010 [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>0001 [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[3,1,4,2,5]=>1010 [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[3,4,1,2,5]=>0100 [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[3,1,4,5,2]=>1001 [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[3,4,1,5,2]=>0101 [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[3,4,5,1,2]=>0010 [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100 [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,2,4,1,5]=>1010 [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,4,2,1,5]=>0110 [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[3,2,4,5,1]=>1001 [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,4,2,5,1]=>0101 [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,4,5,2,1]=>0011 [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,2,1,5,3]=>1101 [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[4,2,5,1,3]=>1010 [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[4,5,2,1,3]=>0110 [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,2,5,3,1]=>1011 [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,5,2,3,1]=>0101 [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110 [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,3,2,5,1]=>1101 [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[4,3,5,2,1]=>1011 [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[4,5,3,2,1]=>0111 [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111 [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000 [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000 [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>01000 [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>00100 [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>00010 [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>00001 [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[3,1,4,2,5,6]=>10100 [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>01000 [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[3,1,4,5,2,6]=>10010 [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[3,4,1,5,2,6]=>01010 [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6]=>00100 [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[3,1,4,5,6,2]=>10001 [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[3,4,1,5,6,2]=>01001 [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[3,4,5,1,6,2]=>00101 [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>00010 [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000 [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>10100 [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>01100 [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>10010 [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>01010 [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>00110 [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>10001 [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>01001 [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>00101 [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>00011 [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[4,1,5,2,6,3]=>10101 [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[4,5,1,2,6,3]=>01001 [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[4,1,5,6,2,3]=>10010 [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,5,1,6,2,3]=>01010 [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>00100 [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,2,1,5,3,6]=>11010 [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[4,2,5,1,3,6]=>10100 [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6]=>01100 [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,2,5,3,1,6]=>10110 [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6]=>01010 [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,2,1,5,6,3]=>11001 [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[4,2,5,1,6,3]=>10101 [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[4,5,2,1,6,3]=>01101 [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[4,2,5,6,1,3]=>10010 [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[4,5,2,6,1,3]=>01010 [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[4,5,6,2,1,3]=>00110 [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,2,5,3,6,1]=>10101 [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>01001 [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[4,2,5,6,3,1]=>10011 [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[4,5,2,6,3,1]=>01011 [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1]=>00101 [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100 [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>11010 [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>10110 [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>01110 [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>11001 [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>10101 [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>01101 [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>10011 [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>01011 [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>00111 [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,3,1,6,4,2]=>11011 [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,3,6,1,4,2]=>10101 [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,6,3,1,4,2]=>01101 [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[5,3,6,4,1,2]=>10110 [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>01010 [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,3,2,1,6,4]=>11101 [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>11010 [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[5,3,6,2,1,4]=>10110 [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[5,6,3,2,1,4]=>01110 [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[5,3,2,6,4,1]=>11011 [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,3,6,2,4,1]=>10101 [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,6,3,2,4,1]=>01101 [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[5,3,6,4,2,1]=>10111 [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1]=>01011 [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110 [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>11101 [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>11011 [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>10111 [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>01111 [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111 [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000 [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000 [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>010000 [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>001000 [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>000100 [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>000010 [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>000001 [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000 [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7]=>010000 [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>100100 [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[3,4,1,5,2,6,7]=>010100 [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7]=>001000 [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>100010 [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[3,4,1,5,6,2,7]=>010010 [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[3,4,5,1,6,2,7]=>001010 [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7]=>000100 [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>100001 [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[3,4,1,5,6,7,2]=>010001 [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[3,4,5,1,6,7,2]=>001001 [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[3,4,5,6,1,7,2]=>000101 [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2]=>000010 [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000 [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>101000 [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>011000 [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>100100 [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>010100 [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>001100 [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>100010 [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>010010 [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>001010 [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>000110 [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>100001 [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>010001 [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>001001 [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>000101 [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>000011 [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010 [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[4,5,1,2,6,3,7]=>010010 [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[4,1,5,6,2,3,7]=>100100 [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[4,5,1,6,2,3,7]=>010100 [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7]=>001000 [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[4,1,5,2,6,7,3]=>101001 [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[4,5,1,2,6,7,3]=>010001 [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[4,1,5,6,2,7,3]=>100101 [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[4,5,1,6,2,7,3]=>010101 [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[4,5,6,1,2,7,3]=>001001 [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[4,1,5,6,7,2,3]=>100010 [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[4,5,1,6,7,2,3]=>010010 [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[4,5,6,1,7,2,3]=>001010 [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3]=>000100 [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,2,1,5,3,6,7]=>110100 [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[4,2,5,1,3,6,7]=>101000 [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7]=>011000 [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[4,2,5,3,1,6,7]=>101100 [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7]=>010100 [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[4,2,1,5,6,3,7]=>110010 [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[4,2,5,1,6,3,7]=>101010 [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[4,5,2,1,6,3,7]=>011010 [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[4,2,5,6,1,3,7]=>100100 [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[4,5,2,6,1,3,7]=>010100 [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7]=>001100 [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[4,2,5,3,6,1,7]=>101010 [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7]=>010010 [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[4,2,5,6,3,1,7]=>100110 [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[4,5,2,6,3,1,7]=>010110 [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7]=>001010 [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[4,2,1,5,6,7,3]=>110001 [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[4,2,5,1,6,7,3]=>101001 [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[4,5,2,1,6,7,3]=>011001 [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[4,2,5,6,1,7,3]=>100101 [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[4,5,2,6,1,7,3]=>010101 [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[4,5,6,2,1,7,3]=>001101 [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[4,2,5,6,7,1,3]=>100010 [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[4,5,2,6,7,1,3]=>010010 [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[4,5,6,2,7,1,3]=>001010 [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[4,5,6,7,2,1,3]=>000110 [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[4,2,5,3,6,7,1]=>101001 [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>010001 [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[4,2,5,6,3,7,1]=>100101 [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[4,5,2,6,3,7,1]=>010101 [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[4,5,6,2,3,7,1]=>001001 [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[4,2,5,6,7,3,1]=>100011 [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[4,5,2,6,7,3,1]=>010011 [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[4,5,6,2,7,3,1]=>001011 [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1]=>000101 [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000 [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>110100 [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>101100 [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>011100 [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>110010 [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>101010 [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>011010 [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>100110 [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>010110 [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>001110 [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>110001 [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>101001 [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>011001 [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>100101 [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>010101 [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>001101 [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>100011 [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>010011 [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>001011 [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>000111 [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[5,2,1,6,3,7,4]=>110101 [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[5,2,6,1,3,7,4]=>101001 [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[5,6,2,1,3,7,4]=>011001 [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[5,2,6,3,1,7,4]=>101101 [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[5,6,2,3,1,7,4]=>010101 [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[5,2,1,6,7,3,4]=>110010 [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[5,2,6,1,7,3,4]=>101010 [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[5,6,2,1,7,3,4]=>011010 [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[5,2,6,7,1,3,4]=>100100 [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[5,6,2,7,1,3,4]=>010100 [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[5,6,7,2,1,3,4]=>001100 [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[5,2,6,3,7,1,4]=>101010 [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[5,6,2,3,7,1,4]=>010010 [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[5,2,6,7,3,1,4]=>100110 [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[5,6,2,7,3,1,4]=>010110 [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[5,6,7,2,3,1,4]=>001010 [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[5,2,6,3,7,4,1]=>101011 [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[5,6,2,3,7,4,1]=>010011 [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[5,2,6,7,3,4,1]=>100101 [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[5,6,2,7,3,4,1]=>010101 [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1]=>001001 [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[5,3,1,6,4,2,7]=>110110 [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[5,3,6,1,4,2,7]=>101010 [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[5,6,3,1,4,2,7]=>011010 [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[5,3,6,4,1,2,7]=>101100 [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>010100 [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[5,3,1,6,4,7,2]=>110101 [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[5,3,6,1,4,7,2]=>101001 [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[5,6,3,1,4,7,2]=>011001 [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[5,3,6,4,1,7,2]=>101101 [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[5,6,3,4,1,7,2]=>010101 [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,3,1,6,7,4,2]=>110011 [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[5,3,6,1,7,4,2]=>101011 [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[5,6,3,1,7,4,2]=>011011 [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[5,3,6,7,1,4,2]=>100101 [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[5,6,3,7,1,4,2]=>010101 [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[5,6,7,3,1,4,2]=>001101 [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[5,3,6,4,7,1,2]=>101010 [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[5,6,3,4,7,1,2]=>010010 [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[5,3,6,7,4,1,2]=>100110 [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[5,6,3,7,4,1,2]=>010110 [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2]=>001010 [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[5,3,2,1,6,4,7]=>111010 [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[5,3,2,6,1,4,7]=>110100 [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[5,3,6,2,1,4,7]=>101100 [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7]=>011100 [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[5,3,2,6,4,1,7]=>110110 [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[5,3,6,2,4,1,7]=>101010 [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7]=>011010 [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[5,3,6,4,2,1,7]=>101110 [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7]=>010110 [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,3,2,1,6,7,4]=>111001 [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[5,3,2,6,1,7,4]=>110101 [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[5,3,6,2,1,7,4]=>101101 [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[5,6,3,2,1,7,4]=>011101 [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[5,3,2,6,7,1,4]=>110010 [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[5,3,6,2,7,1,4]=>101010 [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[5,6,3,2,7,1,4]=>011010 [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[5,3,6,7,2,1,4]=>100110 [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[5,6,3,7,2,1,4]=>010110 [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[5,6,7,3,2,1,4]=>001110 [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[5,3,2,6,4,7,1]=>110101 [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[5,3,6,2,4,7,1]=>101001 [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[5,6,3,2,4,7,1]=>011001 [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[5,3,6,4,2,7,1]=>101101 [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[5,6,3,4,2,7,1]=>010101 [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[5,3,2,6,7,4,1]=>110011 [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[5,3,6,2,7,4,1]=>101011 [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[5,6,3,2,7,4,1]=>011011 [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[5,3,6,7,2,4,1]=>100101 [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[5,6,3,7,2,4,1]=>010101 [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[5,6,7,3,2,4,1]=>001101 [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[5,3,6,4,7,2,1]=>101011 [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[5,6,3,4,7,2,1]=>010011 [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[5,3,6,7,4,2,1]=>100111 [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[5,6,3,7,4,2,1]=>010111 [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>001011 [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100 [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>111010 [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>110110 [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>101110 [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>011110 [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>111001 [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>110101 [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>101101 [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>011101 [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>110011 [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>101011 [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>011011 [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>100111 [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>010111 [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>001111 [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[6,4,2,1,7,5,3]=>111011 [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[6,4,2,7,1,5,3]=>110101 [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[6,4,7,2,1,5,3]=>101101 [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[6,7,4,2,1,5,3]=>011101 [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[6,4,2,7,5,1,3]=>110110 [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>101010 [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[6,7,4,2,5,1,3]=>011010 [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[6,4,7,5,2,1,3]=>101110 [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[6,7,4,5,2,1,3]=>010110 [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[6,4,2,7,5,3,1]=>110111 [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[6,4,7,2,5,3,1]=>101011 [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[6,7,4,2,5,3,1]=>011011 [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[6,4,7,5,2,3,1]=>101101 [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1]=>010101 [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,4,3,2,1,7,5]=>111101 [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>111010 [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[6,4,3,7,2,1,5]=>110110 [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[6,4,7,3,2,1,5]=>101110 [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[6,7,4,3,2,1,5]=>011110 [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[6,4,3,2,7,5,1]=>111011 [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[6,4,3,7,2,5,1]=>110101 [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[6,4,7,3,2,5,1]=>101101 [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[6,7,4,3,2,5,1]=>011101 [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[6,4,3,7,5,2,1]=>110111 [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[6,4,7,3,5,2,1]=>101011 [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[6,7,4,3,5,2,1]=>011011 [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[6,4,7,5,3,2,1]=>101111 [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1]=>010111 [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110 [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>111101 [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>111011 [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>110111 [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>101111 [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>011111 [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000 [[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000 [[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>0100000 [[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000 [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000 [[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>0000100 [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>0000010 [[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>0000001 [[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000 [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>0100000 [[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[3,1,4,5,2,6,7,8]=>1001000 [[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[3,4,1,5,2,6,7,8]=>0101000 [[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[3,4,5,1,2,6,7,8]=>0010000 [[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[3,1,4,5,6,2,7,8]=>1000100 [[1,2,4,5,7,8],[3,6]]=>[3,6,1,2,4,5,7,8]=>[3,4,1,5,6,2,7,8]=>0100100 [[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[3,4,5,1,6,2,7,8]=>0010100 [[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[3,4,5,6,1,2,7,8]=>0001000 [[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[3,1,4,5,6,7,2,8]=>1000010 [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[3,4,1,5,6,7,2,8]=>0100010 [[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[3,4,5,1,6,7,2,8]=>0010010 [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[3,4,5,6,1,7,2,8]=>0001010 [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8]=>0000100 [[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[3,1,4,5,6,7,8,2]=>1000001 [[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[3,4,1,5,6,7,8,2]=>0100001 [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[3,4,5,1,6,7,8,2]=>0010001 [[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[3,4,5,6,1,7,8,2]=>0001001 [[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[3,4,5,6,7,1,8,2]=>0000101 [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2]=>0000010 [[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000 [[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>1010000 [[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>0110000 [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>1001000 [[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>0101000 [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>0011000 [[1,3,4,5,7,8],[2],[6]]=>[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>1000100 [[1,2,4,5,7,8],[3],[6]]=>[6,3,1,2,4,5,7,8]=>[3,4,2,5,6,1,7,8]=>0100100 [[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>0010100 [[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>0001100 [[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>1000010 [[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>0100010 [[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>0010010 [[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>0001010 [[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>0000110 [[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>1000001 [[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>0100001 [[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>0010001 [[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>0001001 [[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>0000101 [[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>0000011 [[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100 [[1,3,4,7,8],[2,5,6]]=>[2,5,6,1,3,4,7,8]=>[4,1,5,6,2,3,7,8]=>1001000 [[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[4,5,1,6,2,3,7,8]=>0101000 [[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7,8]=>0010000 [[1,2,5,6,8],[3,4,7]]=>[3,4,7,1,2,5,6,8]=>[4,5,1,2,6,7,3,8]=>0100010 [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[4,5,1,6,2,7,3,8]=>0101010 [[1,2,3,6,8],[4,5,7]]=>[4,5,7,1,2,3,6,8]=>[4,5,6,1,2,7,3,8]=>0010010 [[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[4,1,5,6,7,2,3,8]=>1000100 [[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>[4,5,1,6,7,2,3,8]=>0100100 [[1,2,3,5,8],[4,6,7]]=>[4,6,7,1,2,3,5,8]=>[4,5,6,1,7,2,3,8]=>0010100 [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8]=>0001000 [[1,3,5,6,7],[2,4,8]]=>[2,4,8,1,3,5,6,7]=>[4,1,5,2,6,7,8,3]=>1010001 [[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[4,5,1,2,6,7,8,3]=>0100001 [[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[4,5,1,6,2,7,8,3]=>0101001 [[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[4,5,6,1,2,7,8,3]=>0010001 [[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[4,1,5,6,7,2,8,3]=>1000101 [[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[4,5,1,6,7,2,8,3]=>0100101 [[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[4,5,6,1,7,2,8,3]=>0010101 [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[4,5,6,7,1,2,8,3]=>0001001 [[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[4,1,5,6,7,8,2,3]=>1000010 [[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[4,5,1,6,7,8,2,3]=>0100010 [[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[4,5,6,1,7,8,2,3]=>0010010 [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[4,5,6,7,1,8,2,3]=>0001010 [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>0000100 [[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[4,2,1,5,3,6,7,8]=>1101000 [[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>1010000 [[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[4,5,2,1,3,6,7,8]=>0110000 [[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[4,2,5,3,1,6,7,8]=>1011000 [[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[4,5,2,3,1,6,7,8]=>0101000 [[1,4,5,7,8],[2,6],[3]]=>[3,2,6,1,4,5,7,8]=>[4,2,1,5,6,3,7,8]=>1100100 [[1,3,5,7,8],[2,6],[4]]=>[4,2,6,1,3,5,7,8]=>[4,2,5,1,6,3,7,8]=>1010100 [[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[4,5,2,6,1,3,7,8]=>0101000 [[1,2,3,7,8],[4,6],[5]]=>[5,4,6,1,2,3,7,8]=>[4,5,6,2,1,3,7,8]=>0011000 [[1,3,5,7,8],[2,4],[6]]=>[6,2,4,1,3,5,7,8]=>[4,2,5,3,6,1,7,8]=>1010100 [[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[4,5,2,6,3,1,7,8]=>0101100 [[1,4,5,6,8],[2,7],[3]]=>[3,2,7,1,4,5,6,8]=>[4,2,1,5,6,7,3,8]=>1100010 [[1,2,5,6,8],[3,7],[4]]=>[4,3,7,1,2,5,6,8]=>[4,5,2,1,6,7,3,8]=>0110010 [[1,3,4,6,8],[2,7],[5]]=>[5,2,7,1,3,4,6,8]=>[4,2,5,6,1,7,3,8]=>1001010 [[1,2,4,6,8],[3,7],[5]]=>[5,3,7,1,2,4,6,8]=>[4,5,2,6,1,7,3,8]=>0101010 [[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[4,5,6,2,1,7,3,8]=>0011010 [[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[4,2,5,6,7,1,3,8]=>1000100 [[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[4,5,2,6,7,1,3,8]=>0100100 [[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[4,5,6,2,7,1,3,8]=>0010100 [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[4,5,6,7,2,1,3,8]=>0001100 [[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[4,5,2,3,6,7,1,8]=>0100010 [[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[4,5,2,6,3,7,1,8]=>0101010 [[1,2,4,5,8],[3,6],[7]]=>[7,3,6,1,2,4,5,8]=>[4,5,2,6,7,3,1,8]=>0100110 [[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[4,5,6,2,7,3,1,8]=>0010110 [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[4,5,6,7,2,3,1,8]=>0001010 [[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[4,2,1,5,6,7,8,3]=>1100001 [[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[4,2,5,1,6,7,8,3]=>1010001 [[1,2,5,6,7],[3,8],[4]]=>[4,3,8,1,2,5,6,7]=>[4,5,2,1,6,7,8,3]=>0110001 [[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[4,2,5,6,1,7,8,3]=>1001001 [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[4,5,6,2,1,7,8,3]=>0011001 [[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[4,2,5,6,7,1,8,3]=>1000101 [[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[4,5,2,6,7,1,8,3]=>0100101 [[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[4,5,6,2,7,1,8,3]=>0010101 [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[4,5,6,7,2,1,8,3]=>0001101 [[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[4,2,5,6,7,8,1,3]=>1000010 [[1,2,4,5,6],[3,8],[7]]=>[7,3,8,1,2,4,5,6]=>[4,5,2,6,7,8,1,3]=>0100010 [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[4,5,6,7,2,8,1,3]=>0001010 [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,8,2,1,3]=>0000110 [[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[4,2,5,3,6,7,8,1]=>1010001 [[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[4,5,2,3,6,7,8,1]=>0100001 [[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[4,5,2,6,3,7,8,1]=>0101001 [[1,2,3,6,7],[4,5],[8]]=>[8,4,5,1,2,3,6,7]=>[4,5,6,2,3,7,8,1]=>0010001 [[1,3,4,5,7],[2,6],[8]]=>[8,2,6,1,3,4,5,7]=>[4,2,5,6,7,3,8,1]=>1000101 [[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[4,5,2,6,7,3,8,1]=>0100101 [[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[4,5,6,2,7,3,8,1]=>0010101 [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[4,5,6,7,2,3,8,1]=>0001001 [[1,3,4,5,6],[2,7],[8]]=>[8,2,7,1,3,4,5,6]=>[4,2,5,6,7,8,3,1]=>1000011 [[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[4,5,2,6,7,8,3,1]=>0100011 [[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[4,5,6,2,7,8,3,1]=>0010011 [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[4,5,6,7,2,8,3,1]=>0001011 [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1]=>0000101 [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000 [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>1101000 [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>1011000 [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>0111000 [[1,4,5,7,8],[2],[3],[6]]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>1100100 [[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>1010100 [[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>0110100 [[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>0011100 [[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>1100010 [[1,3,4,6,8],[2],[5],[7]]=>[7,5,2,1,3,4,6,8]=>[4,3,5,6,2,7,1,8]=>1001010 [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>0101010 [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>0001110 [[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>1100001 [[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>1010001 [[1,2,5,6,7],[3],[4],[8]]=>[8,4,3,1,2,5,6,7]=>[4,5,3,2,6,7,8,1]=>0110001 [[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>1001001 [[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>0011001 [[1,3,4,5,7],[2],[6],[8]]=>[8,6,2,1,3,4,5,7]=>[4,3,5,6,7,2,8,1]=>1000101 [[1,2,4,5,7],[3],[6],[8]]=>[8,6,3,1,2,4,5,7]=>[4,5,3,6,7,2,8,1]=>0100101 [[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>0010101 [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>0001101 [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>1000011 [[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>0010011 [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>0001011 [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>0000111 [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101 [[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[5,6,1,2,7,3,8,4]=>0100101 [[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[5,1,6,7,2,3,8,4]=>1001001 [[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[5,6,1,7,2,3,8,4]=>0101001 [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[5,6,7,1,2,3,8,4]=>0010001 [[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[5,6,1,2,7,8,3,4]=>0100010 [[1,3,4,6],[2,5,7,8]]=>[2,5,7,8,1,3,4,6]=>[5,1,6,7,2,8,3,4]=>1001010 [[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[5,6,7,1,2,8,3,4]=>0010010 [[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[5,1,6,7,8,2,3,4]=>1000100 [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[5,6,1,7,8,2,3,4]=>0100100 [[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[5,6,7,1,8,2,3,4]=>0010100 [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>0001000 [[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[5,2,1,6,3,7,4,8]=>1101010 [[1,3,6,8],[2,5,7],[4]]=>[4,2,5,7,1,3,6,8]=>[5,2,6,1,3,7,4,8]=>1010010 [[1,2,6,8],[3,5,7],[4]]=>[4,3,5,7,1,2,6,8]=>[5,6,2,1,3,7,4,8]=>0110010 [[1,3,6,8],[2,4,7],[5]]=>[5,2,4,7,1,3,6,8]=>[5,2,6,3,1,7,4,8]=>1011010 [[1,2,6,8],[3,4,7],[5]]=>[5,3,4,7,1,2,6,8]=>[5,6,2,3,1,7,4,8]=>0101010 [[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[5,2,6,1,7,3,4,8]=>1010100 [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[5,2,6,7,1,3,4,8]=>1001000 [[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[5,6,2,7,1,3,4,8]=>0101000 [[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[5,6,7,2,1,3,4,8]=>0011000 [[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[5,2,6,7,3,1,4,8]=>1001100 [[1,2,4,8],[3,5,7],[6]]=>[6,3,5,7,1,2,4,8]=>[5,6,2,7,3,1,4,8]=>0101100 [[1,2,3,8],[4,5,7],[6]]=>[6,4,5,7,1,2,3,8]=>[5,6,7,2,3,1,4,8]=>0010100 [[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[5,2,6,3,7,4,1,8]=>1010110 [[1,2,5,8],[3,4,6],[7]]=>[7,3,4,6,1,2,5,8]=>[5,6,2,3,7,4,1,8]=>0100110 [[1,2,4,8],[3,5,6],[7]]=>[7,3,5,6,1,2,4,8]=>[5,6,2,7,3,4,1,8]=>0101010 [[1,2,3,8],[4,5,6],[7]]=>[7,4,5,6,1,2,3,8]=>[5,6,7,2,3,4,1,8]=>0010010 [[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[5,2,6,1,3,7,8,4]=>1010001 [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[5,2,6,3,1,7,8,4]=>1011001 [[1,2,6,7],[3,4,8],[5]]=>[5,3,4,8,1,2,6,7]=>[5,6,2,3,1,7,8,4]=>0101001 [[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[5,2,6,1,7,3,8,4]=>1010101 [[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[5,6,2,1,7,3,8,4]=>0110101 [[1,2,4,7],[3,6,8],[5]]=>[5,3,6,8,1,2,4,7]=>[5,6,2,7,1,3,8,4]=>0101001 [[1,2,3,7],[4,6,8],[5]]=>[5,4,6,8,1,2,3,7]=>[5,6,7,2,1,3,8,4]=>0011001 [[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[5,2,6,3,7,1,8,4]=>1010101 [[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[5,6,2,7,3,1,8,4]=>0101101 [[1,2,3,7],[4,5,8],[6]]=>[6,4,5,8,1,2,3,7]=>[5,6,7,2,3,1,8,4]=>0010101 [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[5,2,1,6,7,8,3,4]=>1100010 [[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>[5,6,2,1,7,8,3,4]=>0110010 [[1,2,4,6],[3,7,8],[5]]=>[5,3,7,8,1,2,4,6]=>[5,6,2,7,1,8,3,4]=>0101010 [[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[5,6,7,2,1,8,3,4]=>0011010 [[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[5,2,6,7,8,1,3,4]=>1000100 [[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[5,6,7,2,8,1,3,4]=>0010100 [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[5,6,7,8,2,1,3,4]=>0001100 [[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[5,6,2,3,7,8,1,4]=>0100010 [[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[5,6,2,7,3,8,1,4]=>0101010 [[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[5,6,7,2,3,8,1,4]=>0010010 [[1,3,4,5],[2,6,8],[7]]=>[7,2,6,8,1,3,4,5]=>[5,2,6,7,8,3,1,4]=>1000110 [[1,2,4,5],[3,6,8],[7]]=>[7,3,6,8,1,2,4,5]=>[5,6,2,7,8,3,1,4]=>0100110 [[1,2,3,5],[4,6,8],[7]]=>[7,4,6,8,1,2,3,5]=>[5,6,7,2,8,3,1,4]=>0010110 [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[5,6,7,8,2,3,1,4]=>0001010 [[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[5,2,6,3,7,4,8,1]=>1010101 [[1,3,4,7],[2,5,6],[8]]=>[8,2,5,6,1,3,4,7]=>[5,2,6,7,3,4,8,1]=>1001001 [[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[5,6,2,7,3,4,8,1]=>0101001 [[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[5,6,7,2,3,4,8,1]=>0010001 [[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[5,2,6,3,7,8,4,1]=>1010011 [[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[5,6,2,7,3,8,4,1]=>0101011 [[1,2,3,6],[4,5,7],[8]]=>[8,4,5,7,1,2,3,6]=>[5,6,7,2,3,8,4,1]=>0010011 [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[5,2,6,7,8,3,4,1]=>1000101 [[1,2,4,5],[3,6,7],[8]]=>[8,3,6,7,1,2,4,5]=>[5,6,2,7,8,3,4,1]=>0100101 [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1]=>0001001 [[1,4,7,8],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8]=>[5,3,1,6,4,2,7,8]=>1101100 [[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[5,3,6,1,4,2,7,8]=>1010100 [[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[5,6,3,1,4,2,7,8]=>0110100 [[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[5,3,6,4,1,2,7,8]=>1011000 [[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>0101000 [[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[5,3,1,6,4,7,2,8]=>1101010 [[1,3,6,8],[2,5],[4,7]]=>[4,7,2,5,1,3,6,8]=>[5,3,6,1,4,7,2,8]=>1010010 [[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[5,3,6,4,1,7,2,8]=>1011010 [[1,2,6,8],[3,4],[5,7]]=>[5,7,3,4,1,2,6,8]=>[5,6,3,4,1,7,2,8]=>0101010 [[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[5,6,3,1,7,4,2,8]=>0110110 [[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[5,3,6,7,1,4,2,8]=>1001010 [[1,2,4,8],[3,6],[5,7]]=>[5,7,3,6,1,2,4,8]=>[5,6,3,7,1,4,2,8]=>0101010 [[1,2,5,8],[3,4],[6,7]]=>[6,7,3,4,1,2,5,8]=>[5,6,3,4,7,1,2,8]=>0100100 [[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[5,3,6,1,4,7,8,2]=>1010001 [[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[5,6,3,4,1,7,8,2]=>0101001 [[1,4,5,7],[2,6],[3,8]]=>[3,8,2,6,1,4,5,7]=>[5,3,1,6,7,4,8,2]=>1100101 [[1,3,5,7],[2,6],[4,8]]=>[4,8,2,6,1,3,5,7]=>[5,3,6,1,7,4,8,2]=>1010101 [[1,2,5,7],[3,6],[4,8]]=>[4,8,3,6,1,2,5,7]=>[5,6,3,1,7,4,8,2]=>0110101 [[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[5,6,3,7,1,4,8,2]=>0101001 [[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[5,6,7,3,1,4,8,2]=>0011001 [[1,3,5,7],[2,4],[6,8]]=>[6,8,2,4,1,3,5,7]=>[5,3,6,4,7,1,8,2]=>1010101 [[1,2,5,7],[3,4],[6,8]]=>[6,8,3,4,1,2,5,7]=>[5,6,3,4,7,1,8,2]=>0100101 [[1,3,4,7],[2,5],[6,8]]=>[6,8,2,5,1,3,4,7]=>[5,3,6,7,4,1,8,2]=>1001101 [[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[5,6,3,7,4,1,8,2]=>0101101 [[1,2,3,7],[4,5],[6,8]]=>[6,8,4,5,1,2,3,7]=>[5,6,7,3,4,1,8,2]=>0010101 [[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[5,3,1,6,7,8,4,2]=>1100011 [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[5,3,6,1,7,8,4,2]=>1010011 [[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[5,6,3,1,7,8,4,2]=>0110011 [[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[5,3,6,7,1,8,4,2]=>1001011 [[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[5,6,3,7,1,8,4,2]=>0101011 [[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[5,6,7,3,1,8,4,2]=>0011011 [[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[5,3,6,7,8,1,4,2]=>1000101 [[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[5,6,3,7,8,1,4,2]=>0100101 [[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[5,6,7,8,3,1,4,2]=>0001101 [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[5,3,6,4,7,8,1,2]=>1010010 [[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[5,6,3,4,7,8,1,2]=>0100010 [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[5,3,6,7,4,8,1,2]=>1001010 [[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[5,6,3,7,4,8,1,2]=>0101010 [[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[5,6,7,3,4,8,1,2]=>0010010 [[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[5,6,7,3,8,4,1,2]=>0010110 [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2]=>0001010 [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[5,3,2,1,6,4,7,8]=>1110100 [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[5,3,2,6,1,4,7,8]=>1101000 [[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[5,6,3,2,1,4,7,8]=>0111000 [[1,4,7,8],[2,5],[3],[6]]=>[6,3,2,5,1,4,7,8]=>[5,3,2,6,4,1,7,8]=>1101100 [[1,3,7,8],[2,5],[4],[6]]=>[6,4,2,5,1,3,7,8]=>[5,3,6,2,4,1,7,8]=>1010100 [[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[5,6,3,2,4,1,7,8]=>0110100 [[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[5,3,6,4,2,1,7,8]=>1011100 [[1,2,7,8],[3,4],[5],[6]]=>[6,5,3,4,1,2,7,8]=>[5,6,3,4,2,1,7,8]=>0101100 [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[5,3,2,6,1,7,4,8]=>1101010 [[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[5,3,2,6,7,1,4,8]=>1100100 [[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[5,3,6,2,7,1,4,8]=>1010100 [[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[5,6,3,2,7,1,4,8]=>0110100 [[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[5,6,3,7,2,1,4,8]=>0101100 [[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[5,3,2,6,4,7,1,8]=>1101010 [[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[5,3,6,2,4,7,1,8]=>1010010 [[1,3,6,8],[2,4],[5],[7]]=>[7,5,2,4,1,3,6,8]=>[5,3,6,4,2,7,1,8]=>1011010 [[1,2,6,8],[3,4],[5],[7]]=>[7,5,3,4,1,2,6,8]=>[5,6,3,4,2,7,1,8]=>0101010 [[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[5,3,2,6,7,4,1,8]=>1100110 [[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[5,3,6,2,7,4,1,8]=>1010110 [[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[5,6,3,2,7,4,1,8]=>0110110 [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[5,6,3,7,2,4,1,8]=>0101010 [[1,2,3,8],[4,6],[5],[7]]=>[7,5,4,6,1,2,3,8]=>[5,6,7,3,2,4,1,8]=>0011010 [[1,3,5,8],[2,4],[6],[7]]=>[7,6,2,4,1,3,5,8]=>[5,3,6,4,7,2,1,8]=>1010110 [[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[5,6,3,7,4,2,1,8]=>0101110 [[1,2,3,8],[4,5],[6],[7]]=>[7,6,4,5,1,2,3,8]=>[5,6,7,3,4,2,1,8]=>0010110 [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[5,3,2,1,6,7,8,4]=>1110001 [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[5,3,2,6,1,7,8,4]=>1101001 [[1,2,6,7],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>[5,6,3,2,1,7,8,4]=>0111001 [[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[5,3,2,6,7,1,8,4]=>1100101 [[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[5,3,6,2,7,1,8,4]=>1010101 [[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[5,6,3,2,7,1,8,4]=>0110101 [[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[5,3,6,7,2,1,8,4]=>1001101 [[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[5,6,3,7,2,1,8,4]=>0101101 [[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[5,6,7,3,2,1,8,4]=>0011101 [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[5,3,6,2,7,8,1,4]=>1010010 [[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[5,6,3,2,7,8,1,4]=>0110010 [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[5,6,3,7,2,8,1,4]=>0101010 [[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[5,6,7,3,2,8,1,4]=>0011010 [[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>[5,3,6,7,8,2,1,4]=>1000110 [[1,2,4,5],[3,8],[6],[7]]=>[7,6,3,8,1,2,4,5]=>[5,6,3,7,8,2,1,4]=>0100110 [[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[5,6,7,3,8,2,1,4]=>0010110 [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[5,6,7,8,3,2,1,4]=>0001110 [[1,4,6,7],[2,5],[3],[8]]=>[8,3,2,5,1,4,6,7]=>[5,3,2,6,4,7,8,1]=>1101001 [[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[5,3,6,2,4,7,8,1]=>1010001 [[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[5,3,2,6,7,4,8,1]=>1100101 [[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[5,3,6,2,7,4,8,1]=>1010101 [[1,3,4,7],[2,6],[5],[8]]=>[8,5,2,6,1,3,4,7]=>[5,3,6,7,2,4,8,1]=>1001001 [[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[5,6,3,7,2,4,8,1]=>0101001 [[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[5,3,6,4,7,2,8,1]=>1010101 [[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[5,6,3,4,7,2,8,1]=>0100101 [[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[5,3,6,7,4,2,8,1]=>1001101 [[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[5,6,7,3,4,2,8,1]=>0010101 [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[5,3,6,2,7,8,4,1]=>1010011 [[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[5,6,3,2,7,8,4,1]=>0110011 [[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[5,3,6,7,2,8,4,1]=>1001011 [[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[5,6,3,7,2,8,4,1]=>0101011 [[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[5,6,7,3,2,8,4,1]=>0011011 [[1,3,4,5],[2,7],[6],[8]]=>[8,6,2,7,1,3,4,5]=>[5,3,6,7,8,2,4,1]=>1000101 [[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[5,6,3,7,8,2,4,1]=>0100101 [[1,2,3,5],[4,7],[6],[8]]=>[8,6,4,7,1,2,3,5]=>[5,6,7,3,8,2,4,1]=>0010101 [[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[5,6,7,8,3,2,4,1]=>0001101 [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[5,3,6,7,4,8,2,1]=>1001011 [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[5,6,3,7,4,8,2,1]=>0101011 [[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[5,3,6,7,8,4,2,1]=>1000111 [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[5,6,3,7,8,4,2,1]=>0100111 [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[5,6,7,3,8,4,2,1]=>0010111 [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1]=>0001011 [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000 [[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>1110100 [[1,4,7,8],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>1101100 [[1,3,7,8],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>1011100 [[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>0111100 [[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>1110010 [[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>1101010 [[1,3,6,8],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6,8]=>[5,4,6,3,2,7,1,8]=>1011010 [[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>1100110 [[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>1010110 [[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>0110110 [[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>1001110 [[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[5,6,4,7,3,2,1,8]=>0101110 [[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>0011110 [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>1110001 [[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>1101001 [[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>1011001 [[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[5,4,3,6,7,2,8,1]=>1100101 [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>1010101 [[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>0011101 [[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>1100011 [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>1001011 [[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>0011011 [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>1000111 [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>0100111 [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>0010111 [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>0001111 [[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[6,3,1,7,4,2,8,5]=>1101101 [[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[6,3,7,1,4,2,8,5]=>1010101 [[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[6,7,3,1,4,2,8,5]=>0110101 [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[6,3,7,4,1,2,8,5]=>1011001 [[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[6,3,7,1,4,8,2,5]=>1010010 [[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[6,7,3,1,4,8,2,5]=>0110010 [[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[6,3,7,4,1,8,2,5]=>1011010 [[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[6,7,3,4,1,8,2,5]=>0101010 [[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[6,3,1,7,8,4,2,5]=>1100110 [[1,3,5],[2,6,8],[4,7]]=>[4,7,2,6,8,1,3,5]=>[6,3,7,1,8,4,2,5]=>1010110 [[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[6,7,3,1,8,4,2,5]=>0110110 [[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[6,7,8,3,1,4,2,5]=>0011010 [[1,3,5],[2,4,8],[6,7]]=>[6,7,2,4,8,1,3,5]=>[6,3,7,4,8,1,2,5]=>1010100 [[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[6,7,3,4,8,1,2,5]=>0100100 [[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[6,7,3,8,4,1,2,5]=>0101100 [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,3,4,1,2,5]=>0010100 [[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[6,3,1,7,4,8,5,2]=>1101011 [[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[6,3,7,1,4,8,5,2]=>1010011 [[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[6,7,3,1,4,8,5,2]=>0110011 [[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[6,3,7,4,1,8,5,2]=>1011011 [[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[6,3,1,7,8,4,5,2]=>1100101 [[1,3,5],[2,6,7],[4,8]]=>[4,8,2,6,7,1,3,5]=>[6,3,7,1,8,4,5,2]=>1010101 [[1,2,5],[3,6,7],[4,8]]=>[4,8,3,6,7,1,2,5]=>[6,7,3,1,8,4,5,2]=>0110101 [[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[6,3,7,8,1,4,5,2]=>1001001 [[1,2,3],[4,6,7],[5,8]]=>[5,8,4,6,7,1,2,3]=>[6,7,8,3,1,4,5,2]=>0011001 [[1,3,5],[2,4,7],[6,8]]=>[6,8,2,4,7,1,3,5]=>[6,3,7,4,8,1,5,2]=>1010101 [[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[6,3,7,8,4,1,5,2]=>1001101 [[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[6,7,3,8,4,1,5,2]=>0101101 [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[6,3,7,4,8,5,1,2]=>1010110 [[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[6,7,3,4,8,5,1,2]=>0100110 [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[6,7,3,8,4,5,1,2]=>0101010 [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[6,3,2,1,7,4,8,5]=>1110101 [[1,4,7],[2,6,8],[3],[5]]=>[5,3,2,6,8,1,4,7]=>[6,3,2,7,1,4,8,5]=>1101001 [[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[6,3,7,2,1,4,8,5]=>1011001 [[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[6,7,3,2,1,4,8,5]=>0111001 [[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[6,3,2,7,4,1,8,5]=>1101101 [[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[6,7,3,2,4,1,8,5]=>0110101 [[1,2,7],[3,4,8],[5],[6]]=>[6,5,3,4,8,1,2,7]=>[6,7,3,4,2,1,8,5]=>0101101 [[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[6,3,2,1,7,8,4,5]=>1110010 [[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[6,3,2,7,1,8,4,5]=>1101010 [[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[6,3,7,2,1,8,4,5]=>1011010 [[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[6,7,3,2,1,8,4,5]=>0111010 [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[6,3,2,7,8,1,4,5]=>1100100 [[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[6,3,7,2,8,1,4,5]=>1010100 [[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[6,7,3,2,8,1,4,5]=>0110100 [[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[6,3,7,8,2,1,4,5]=>1001100 [[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[6,7,3,8,2,1,4,5]=>0101100 [[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,3,2,1,4,5]=>0011100 [[1,4,6],[2,5,8],[3],[7]]=>[7,3,2,5,8,1,4,6]=>[6,3,2,7,4,8,1,5]=>1101010 [[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[6,3,7,2,4,8,1,5]=>1010010 [[1,2,6],[3,5,8],[4],[7]]=>[7,4,3,5,8,1,2,6]=>[6,7,3,2,4,8,1,5]=>0110010 [[1,2,6],[3,4,8],[5],[7]]=>[7,5,3,4,8,1,2,6]=>[6,7,3,4,2,8,1,5]=>0101010 [[1,4,5],[2,6,8],[3],[7]]=>[7,3,2,6,8,1,4,5]=>[6,3,2,7,8,4,1,5]=>1100110 [[1,3,5],[2,6,8],[4],[7]]=>[7,4,2,6,8,1,3,5]=>[6,3,7,2,8,4,1,5]=>1010110 [[1,2,5],[3,6,8],[4],[7]]=>[7,4,3,6,8,1,2,5]=>[6,7,3,2,8,4,1,5]=>0110110 [[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[6,3,7,8,2,4,1,5]=>1001010 [[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[6,7,3,8,2,4,1,5]=>0101010 [[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[6,7,8,3,2,4,1,5]=>0011010 [[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[6,3,7,4,8,2,1,5]=>1010110 [[1,3,4],[2,5,8],[6],[7]]=>[7,6,2,5,8,1,3,4]=>[6,3,7,8,4,2,1,5]=>1001110 [[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[6,7,3,8,4,2,1,5]=>0101110 [[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[6,7,8,3,4,2,1,5]=>0010110 [[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[6,3,7,2,4,8,5,1]=>1010011 [[1,2,6],[3,5,7],[4],[8]]=>[8,4,3,5,7,1,2,6]=>[6,7,3,2,4,8,5,1]=>0110011 [[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[6,3,7,4,2,8,5,1]=>1011011 [[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[6,3,2,7,8,4,5,1]=>1100101 [[1,3,5],[2,6,7],[4],[8]]=>[8,4,2,6,7,1,3,5]=>[6,3,7,2,8,4,5,1]=>1010101 [[1,2,5],[3,6,7],[4],[8]]=>[8,4,3,6,7,1,2,5]=>[6,7,3,2,8,4,5,1]=>0110101 [[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[6,3,7,8,2,4,5,1]=>1001001 [[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[6,7,3,8,2,4,5,1]=>0101001 [[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[6,7,8,3,2,4,5,1]=>0011001 [[1,3,5],[2,4,7],[6],[8]]=>[8,6,2,4,7,1,3,5]=>[6,3,7,4,8,2,5,1]=>1010101 [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[6,7,3,8,4,2,5,1]=>0101101 [[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[6,7,8,3,4,2,5,1]=>0010101 [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[6,3,7,4,8,5,2,1]=>1010111 [[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[6,7,3,4,8,5,2,1]=>0100111 [[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[6,3,7,8,4,5,2,1]=>1001011 [[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[6,7,3,8,4,5,2,1]=>0101011 [[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>0010011 [[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[6,4,2,1,7,5,3,8]=>1110110 [[1,4,8],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4,8]=>[6,4,2,7,1,5,3,8]=>1101010 [[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[6,4,7,2,1,5,3,8]=>1011010 [[1,2,8],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2,8]=>[6,7,4,2,1,5,3,8]=>0111010 [[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[6,4,2,7,5,1,3,8]=>1101100 [[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[6,4,7,2,5,1,3,8]=>1010100 [[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[6,7,4,2,5,1,3,8]=>0110100 [[1,3,8],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3,8]=>[6,4,7,5,2,1,3,8]=>1011100 [[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[6,4,2,7,5,3,1,8]=>1101110 [[1,3,8],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3,8]=>[6,4,7,2,5,3,1,8]=>1010110 [[1,2,8],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2,8]=>[6,7,4,2,5,3,1,8]=>0110110 [[1,3,8],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3,8]=>[6,4,7,5,2,3,1,8]=>1011010 [[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[6,7,4,5,2,3,1,8]=>0101010 [[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[6,4,2,1,7,5,8,3]=>1110101 [[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[6,4,2,7,1,5,8,3]=>1101001 [[1,2,7],[3,6],[4,8],[5]]=>[5,4,8,3,6,1,2,7]=>[6,7,4,2,1,5,8,3]=>0111001 [[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[6,4,7,2,5,1,8,3]=>1010101 [[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[6,7,4,2,5,1,8,3]=>0110101 [[1,3,7],[2,4],[5,8],[6]]=>[6,5,8,2,4,1,3,7]=>[6,4,7,5,2,1,8,3]=>1011101 [[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[6,7,4,5,2,1,8,3]=>0101101 [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[6,4,2,1,7,8,5,3]=>1110011 [[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[6,7,4,2,1,8,5,3]=>0111011 [[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[6,4,7,2,8,1,5,3]=>1010101 [[1,2,5],[3,7],[4,8],[6]]=>[6,4,8,3,7,1,2,5]=>[6,7,4,2,8,1,5,3]=>0110101 [[1,3,4],[2,7],[5,8],[6]]=>[6,5,8,2,7,1,3,4]=>[6,4,7,8,2,1,5,3]=>1001101 [[1,2,4],[3,7],[5,8],[6]]=>[6,5,8,3,7,1,2,4]=>[6,7,4,8,2,1,5,3]=>0101101 [[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[6,4,2,7,5,8,1,3]=>1101010 [[1,3,6],[2,5],[4,8],[7]]=>[7,4,8,2,5,1,3,6]=>[6,4,7,2,5,8,1,3]=>1010010 [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[6,4,7,5,2,8,1,3]=>1011010 [[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[6,7,4,5,2,8,1,3]=>0101010 [[1,4,5],[2,6],[3,8],[7]]=>[7,3,8,2,6,1,4,5]=>[6,4,2,7,8,5,1,3]=>1100110 [[1,3,5],[2,6],[4,8],[7]]=>[7,4,8,2,6,1,3,5]=>[6,4,7,2,8,5,1,3]=>1010110 [[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[6,7,4,8,2,5,1,3]=>0101010 [[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[6,7,8,4,2,5,1,3]=>0011010 [[1,3,5],[2,4],[6,8],[7]]=>[7,6,8,2,4,1,3,5]=>[6,4,7,5,8,2,1,3]=>1010110 [[1,3,4],[2,5],[6,8],[7]]=>[7,6,8,2,5,1,3,4]=>[6,4,7,8,5,2,1,3]=>1001110 [[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[6,4,2,7,5,3,8,1]=>1101101 [[1,3,7],[2,4],[5,6],[8]]=>[8,5,6,2,4,1,3,7]=>[6,4,7,5,2,3,8,1]=>1011001 [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[6,7,4,5,2,3,8,1]=>0101001 [[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[6,4,2,7,5,8,3,1]=>1101011 [[1,3,6],[2,5],[4,7],[8]]=>[8,4,7,2,5,1,3,6]=>[6,4,7,2,5,8,3,1]=>1010011 [[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[6,7,4,2,5,8,3,1]=>0110011 [[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[6,4,7,5,2,8,3,1]=>1011011 [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[6,4,2,7,8,5,3,1]=>1100111 [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[6,4,7,2,8,5,3,1]=>1010111 [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[6,7,4,2,8,5,3,1]=>0110111 [[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[6,4,7,8,2,5,3,1]=>1001011 [[1,2,4],[3,6],[5,7],[8]]=>[8,5,7,3,6,1,2,4]=>[6,7,4,8,2,5,3,1]=>0101011 [[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[6,4,7,5,8,2,3,1]=>1010101 [[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[6,7,4,5,8,2,3,1]=>0100101 [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[6,4,7,8,5,2,3,1]=>1001101 [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[6,4,3,2,1,7,5,8]=>1111010 [[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,7,1,5,8]=>1110100 [[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[6,4,3,7,2,1,5,8]=>1101100 [[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[6,7,4,3,2,1,5,8]=>0111100 [[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[6,4,3,7,2,5,1,8]=>1101010 [[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[6,4,7,3,2,5,1,8]=>1011010 [[1,2,8],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2,8]=>[6,7,4,3,2,5,1,8]=>0111010 [[1,4,8],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4,8]=>[6,4,3,7,5,2,1,8]=>1101110 [[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[6,4,7,3,5,2,1,8]=>1010110 [[1,2,8],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2,8]=>[6,7,4,3,5,2,1,8]=>0110110 [[1,3,8],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3,8]=>[6,4,7,5,3,2,1,8]=>1011110 [[1,2,8],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2,8]=>[6,7,4,5,3,2,1,8]=>0101110 [[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[6,4,3,2,1,7,8,5]=>1111001 [[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[6,4,3,7,2,1,8,5]=>1101101 [[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[6,4,7,3,2,1,8,5]=>1011101 [[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[6,7,4,3,2,1,8,5]=>0111101 [[1,5,6],[2,8],[3],[4],[7]]=>[7,4,3,2,8,1,5,6]=>[6,4,3,2,7,8,1,5]=>1110010 [[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[6,4,3,7,2,8,1,5]=>1101010 [[1,3,5],[2,8],[4],[6],[7]]=>[7,6,4,2,8,1,3,5]=>[6,4,7,3,8,2,1,5]=>1010110 [[1,3,4],[2,8],[5],[6],[7]]=>[7,6,5,2,8,1,3,4]=>[6,4,7,8,3,2,1,5]=>1001110 [[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[6,7,4,8,3,2,1,5]=>0101110 [[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[6,7,8,4,3,2,1,5]=>0011110 [[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[6,4,3,7,2,5,8,1]=>1101001 [[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[6,4,7,3,2,5,8,1]=>1011001 [[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[6,7,4,3,2,5,8,1]=>0111001 [[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[6,4,7,3,5,2,8,1]=>1010101 [[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[6,4,7,5,3,2,8,1]=>1011101 [[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[6,7,4,5,3,2,8,1]=>0101101 [[1,5,6],[2,7],[3],[4],[8]]=>[8,4,3,2,7,1,5,6]=>[6,4,3,2,7,8,5,1]=>1110011 [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[6,4,3,7,2,8,5,1]=>1101011 [[1,3,6],[2,7],[4],[5],[8]]=>[8,5,4,2,7,1,3,6]=>[6,4,7,3,2,8,5,1]=>1011011 [[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[6,4,3,7,8,2,5,1]=>1100101 [[1,3,5],[2,7],[4],[6],[8]]=>[8,6,4,2,7,1,3,5]=>[6,4,7,3,8,2,5,1]=>1010101 [[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[6,7,4,3,8,2,5,1]=>0110101 [[1,3,4],[2,7],[5],[6],[8]]=>[8,6,5,2,7,1,3,4]=>[6,4,7,8,3,2,5,1]=>1001101 [[1,2,4],[3,7],[5],[6],[8]]=>[8,6,5,3,7,1,2,4]=>[6,7,4,8,3,2,5,1]=>0101101 [[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[6,7,8,4,3,2,5,1]=>0011101 [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[6,7,4,5,3,8,2,1]=>0101011 [[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[6,4,3,7,8,5,2,1]=>1100111 [[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[6,4,7,3,8,5,2,1]=>1010111 [[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[6,7,4,3,8,5,2,1]=>0110111 [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[6,4,7,8,3,5,2,1]=>1001011 [[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[6,7,4,8,3,5,2,1]=>0101011 [[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[6,7,8,4,3,5,2,1]=>0011011 [[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[6,4,7,5,8,3,2,1]=>1010111 [[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[6,7,4,5,8,3,2,1]=>0100111 [[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[6,4,7,8,5,3,2,1]=>1001111 [[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[6,7,4,8,5,3,2,1]=>0101111 [[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100 [[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>1111010 [[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>1110110 [[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>1101110 [[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>1011110 [[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>0111110 [[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>1111001 [[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>1110101 [[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>1101101 [[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>1011101 [[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>0111101 [[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>1110011 [[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>1101011 [[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[6,5,7,4,3,8,2,1]=>1011011 [[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>0111011 [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>1100111 [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>1010111 [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>0110111 [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>1001111 [[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>0101111 [[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>0011111 [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[7,5,3,1,8,6,4,2]=>1110111 [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[7,5,3,8,1,6,4,2]=>1101011 [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[7,5,8,3,1,6,4,2]=>1011011 [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[7,8,5,3,1,6,4,2]=>0111011 [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[7,5,3,8,6,1,4,2]=>1101101 [[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[7,5,8,3,6,1,4,2]=>1010101 [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[7,8,5,3,6,1,4,2]=>0110101 [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[7,5,8,6,3,1,4,2]=>1011101 [[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[7,8,5,6,3,1,4,2]=>0101101 [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[7,5,3,8,6,4,1,2]=>1101110 [[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[7,5,8,3,6,4,1,2]=>1010110 [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[7,8,5,3,6,4,1,2]=>0110110 [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[7,5,8,6,3,4,1,2]=>1011010 [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>0101010 [[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[7,5,3,2,1,8,6,4]=>1111011 [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[7,5,3,2,8,1,6,4]=>1110101 [[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[7,5,3,8,2,1,6,4]=>1101101 [[1,3],[2,7],[4,8],[5],[6]]=>[6,5,4,8,2,7,1,3]=>[7,5,8,3,2,1,6,4]=>1011101 [[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[7,8,5,3,2,1,6,4]=>0111101 [[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[7,5,3,2,8,6,1,4]=>1110110 [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>1101010 [[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[7,5,8,3,2,6,1,4]=>1011010 [[1,2],[3,6],[4,8],[5],[7]]=>[7,5,4,8,3,6,1,2]=>[7,8,5,3,2,6,1,4]=>0111010 [[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[7,5,3,8,6,2,1,4]=>1101110 [[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[7,5,8,3,6,2,1,4]=>1010110 [[1,2],[3,5],[4,8],[6],[7]]=>[7,6,4,8,3,5,1,2]=>[7,8,5,3,6,2,1,4]=>0110110 [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[7,5,8,6,3,2,1,4]=>1011110 [[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[7,8,5,6,3,2,1,4]=>0101110 [[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[7,5,3,2,8,6,4,1]=>1110111 [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[7,5,3,8,2,6,4,1]=>1101011 [[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[7,8,5,3,2,6,4,1]=>0111011 [[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[7,5,3,8,6,2,4,1]=>1101101 [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[7,5,8,3,6,2,4,1]=>1010101 [[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[7,8,5,3,6,2,4,1]=>0110101 [[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[7,5,8,6,3,2,4,1]=>1011101 [[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[7,5,3,8,6,4,2,1]=>1101111 [[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[7,5,8,3,6,4,2,1]=>1010111 [[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[7,8,5,3,6,4,2,1]=>0110111 [[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[7,5,8,6,3,4,2,1]=>1011011 [[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1]=>0101011 [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[7,5,4,3,2,1,8,6]=>1111101 [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>1111010 [[1,5],[2,8],[3],[4],[6],[7]]=>[7,6,4,3,2,8,1,5]=>[7,5,4,3,8,2,1,6]=>1110110 [[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[7,5,8,4,3,2,1,6]=>1011110 [[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[7,8,5,4,3,2,1,6]=>0111110 [[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[7,5,4,3,2,8,6,1]=>1111011 [[1,5],[2,7],[3],[4],[6],[8]]=>[8,6,4,3,2,7,1,5]=>[7,5,4,3,8,2,6,1]=>1110101 [[1,4],[2,7],[3],[5],[6],[8]]=>[8,6,5,3,2,7,1,4]=>[7,5,4,8,3,2,6,1]=>1101101 [[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[7,5,8,4,3,2,6,1]=>1011101 [[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[7,8,5,4,3,2,6,1]=>0111101 [[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[7,5,4,3,8,6,2,1]=>1110111 [[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[7,5,4,8,3,6,2,1]=>1101011 [[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[7,5,8,4,3,6,2,1]=>1011011 [[1,2],[3,6],[4],[5],[7],[8]]=>[8,7,5,4,3,6,1,2]=>[7,8,5,4,3,6,2,1]=>0111011 [[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[7,5,4,8,6,3,2,1]=>1101111 [[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[7,5,8,4,6,3,2,1]=>1010111 [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[7,5,8,6,4,3,2,1]=>1011111 [[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1]=>0101111 [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110 [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>1111101 [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>1111011 [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>1110111 [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>1101111 [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>1011111 [[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>0111111 [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101 [[1,3,4,5,6],[2,7,8,9,10]]=>[2,7,8,9,10,1,3,4,5,6]=>[6,1,7,8,9,10,2,3,4,5]=>100001000 [[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5]=>000010000 [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101 [[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>00000100000 [[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000 [[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>00000001 [[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2]=>00000010 [[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>00000011 [[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,1,2,3]=>00000100 [[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,3,1]=>00000101 [[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>00000111 [[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[5,6,7,8,9,1,2,3,4]=>00001000 [[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>00001111 [[1,2,3,4],[5,6,7,8],[9]]=>[9,5,6,7,8,1,2,3,4]=>[6,7,8,9,2,3,4,5,1]=>00010001 [[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>00011111 [[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[7,8,9,4,5,6,1,2,3]=>00100100 [[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>00111111 [[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[8,9,6,7,4,5,2,3,1]=>01010101 [[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[8,9,6,7,5,4,3,2,1]=>01011111 [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>01111111 [[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>000000001 [[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,1,2]=>000000010 [[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>000000011 [[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,1,2,3]=>000000100 [[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,2,3,1]=>000000101 [[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>000000111 [[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,1,2,3,4]=>000001000 [[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[5,6,7,8,9,10,3,4,1,2]=>000001010 [[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>000001111 [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>000011111 [[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[7,8,9,10,3,4,5,6,1,2]=>000100010 [[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[7,8,9,10,4,5,6,2,3,1]=>000100101 [[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[7,8,9,10,5,6,3,4,1,2]=>000101010 [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>000111111 [[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[8,9,10,5,6,7,2,3,4,1]=>001001001 [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>001111111 [[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>010101010 [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>011111111 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111 [[1,2,3,4,5,6,7,8,9,10,11,12]]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000 [[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[11,12,7,8,9,10,1,2,3,4,5,6]=>[7,8,9,10,11,12,3,4,5,6,1,2]=>00000100010 [[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[11,12,9,10,5,6,7,8,1,2,3,4]=>[9,10,11,12,5,6,7,8,3,4,1,2]=>00010001010 [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,1,2,3,4]=>[9,10,11,12,7,8,5,6,3,4,1,2]=>00010101010 [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111 [[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000 [[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>01000000 [[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000 [[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>00100000 [[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[4,2,5,1,3,6,7,8,9]=>10100000 [[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000 [[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[5,6,7,8,1,2,3,4,9]=>00010000 [[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[5,2,6,7,1,3,4,8,9]=>10010000 [[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>01010000 [[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[5,3,2,6,1,4,7,8,9]=>11010000 [[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000 [[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[6,2,7,8,9,1,3,4,5]=>10001000 [[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[6,7,3,4,8,1,2,5,9]=>01001000 [[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[6,3,2,7,8,1,4,5,9]=>11001000 [[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[6,4,7,2,5,1,3,8,9]=>10101000 [[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[6,4,3,2,7,1,5,8,9]=>11101000 [[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000 [[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[7,4,8,2,5,9,1,3,6]=>10100100 [[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[7,4,3,2,8,9,1,5,6]=>11100100 [[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[7,8,5,6,3,4,1,2,9]=>01010100 [[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[7,5,3,8,2,6,1,4,9]=>11010100 [[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[7,5,4,3,2,8,1,6,9]=>11110100 [[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100 [[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[8,6,9,4,7,2,5,1,3]=>10101010 [[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[8,6,4,3,9,2,7,1,5]=>11101010 [[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[8,6,5,4,3,2,9,1,7]=>11111010 [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110 [[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000 [[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>010000000 [[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000 [[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10]=>001000000 [[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[4,2,5,1,3,6,7,8,9,10]=>101000000 [[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000 [[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[5,6,7,8,1,2,3,4,9,10]=>000100000 [[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[5,2,6,7,1,3,4,8,9,10]=>100100000 [[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[5,6,3,4,1,2,7,8,9,10]=>010100000 [[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[5,3,2,6,1,4,7,8,9,10]=>110100000 [[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000 [[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[6,2,7,8,9,1,3,4,5,10]=>100010000 [[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[6,7,3,4,8,1,2,5,9,10]=>010010000 [[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[6,3,2,7,8,1,4,5,9,10]=>110010000 [[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[6,4,7,2,5,1,3,8,9,10]=>101010000 [[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[6,4,3,2,7,1,5,8,9,10]=>111010000 [[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000 [[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[7,8,3,4,9,10,1,2,5,6]=>010001000 [[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[7,3,2,8,9,10,1,4,5,6]=>110001000 [[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[7,8,9,4,5,6,1,2,3,10]=>001001000 [[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[7,4,8,2,5,9,1,3,6,10]=>101001000 [[1,5,6,10],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10]=>[7,4,3,2,8,9,1,5,6,10]=>111001000 [[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[7,8,5,6,3,4,1,2,9,10]=>010101000 [[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[7,5,3,8,2,6,1,4,9,10]=>110101000 [[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9,10]=>[7,5,4,3,2,8,1,6,9,10]=>111101000 [[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000 [[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[8,5,9,10,2,6,7,1,3,4]=>100100100 [[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[8,9,5,6,3,4,10,1,2,7]=>010100100 [[1,4,7],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7]=>[8,5,3,9,2,6,10,1,4,7]=>110100100 [[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[8,5,4,3,2,9,10,1,6,7]=>[8,5,4,3,2,9,10,1,6,7]=>111100100 [[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[8,6,9,4,7,2,5,1,3,10]=>101010100 [[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5,10]=>[8,6,4,3,9,2,7,1,5,10]=>111010100 [[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7,10]=>[8,6,5,4,3,2,9,1,7,10]=>111110100 [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100 [[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[9,7,5,10,3,8,2,6,1,4]=>110101010 [[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[9,7,5,4,3,10,2,8,1,6]=>[9,7,5,4,3,10,2,8,1,6]=>111101010 [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>111111010 [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110 [[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[8,6,5,4,3,2,1,9,7]=>11111101 [[1,7],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7]=>[8,6,4,3,2,1,9,7,5]=>11111011 [[1,7,9],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9]=>[7,5,4,3,2,1,8,6,9]=>11111010 [[1,6],[2,7],[3,8],[4,9],[5]]=>[5,4,9,3,8,2,7,1,6]=>[8,6,4,2,1,9,7,5,3]=>11110111 [[1,6,9],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6,9]=>[7,5,3,2,1,8,6,4,9]=>11110110 [[1,6,8],[2,7,9],[3],[4],[5]]=>[5,4,3,2,7,9,1,6,8]=>[7,4,3,2,1,8,5,9,6]=>11110101 [[1,6,8,9],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8,9]=>[6,4,3,2,1,7,5,8,9]=>11110100 [[1,5,9],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5,9]=>[7,5,3,1,8,6,4,2,9]=>11101110 [[1,5,8],[2,6,9],[3,7],[4]]=>[4,3,7,2,6,9,1,5,8]=>[7,4,2,1,8,5,3,9,6]=>11101101 [[1,5,8,9],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8,9]=>[6,4,2,1,7,5,3,8,9]=>11101100 [[1,5,7,9],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7,9]=>[6,3,2,1,7,4,8,5,9]=>11101010 [[1,5,7,8,9],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8,9]=>[5,3,2,1,6,4,7,8,9]=>11101000 [[1,4,7],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7]=>[7,4,1,8,5,2,9,6,3]=>11011011 [[1,4,7,9],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7,9]=>[6,3,1,7,4,2,8,5,9]=>11011010 [[1,4,7,8,9],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8,9]=>[5,3,1,6,4,2,7,8,9]=>11011000 [[1,4,6,8],[2,5,7,9],[3]]=>[3,2,5,7,9,1,4,6,8]=>[6,2,1,7,3,8,4,9,5]=>11010101 [[1,4,6,8,9],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8,9]=>[5,2,1,6,3,7,4,8,9]=>11010100 [[1,4,6,7,8,9],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9]=>[4,2,1,5,3,6,7,8,9]=>11010000 [[1,3,5,7,9],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9]=>[5,1,6,2,7,3,8,4,9]=>10101010 [[1,3,5,7,8,9],[2,4,6]]=>[2,4,6,1,3,5,7,8,9]=>[4,1,5,2,6,3,7,8,9]=>10101000 [[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>10100000 [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[9,7,6,5,4,3,2,1,10,8]=>111111101 [[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>[7,6,5,4,3,10,2,9,1,8]=>[9,7,5,4,3,2,1,10,8,6]=>111111011 [[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8,10]=>[8,6,5,4,3,2,1,9,7,10]=>111111010 [[1,7],[2,8],[3,9],[4,10],[5],[6]]=>[6,5,4,10,3,9,2,8,1,7]=>[9,7,5,3,2,1,10,8,6,4]=>111110111 [[1,7,10],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7,10]=>[8,6,4,3,2,1,9,7,5,10]=>111110110 [[1,7,9],[2,8,10],[3],[4],[5],[6]]=>[6,5,4,3,2,8,10,1,7,9]=>[8,5,4,3,2,1,9,6,10,7]=>111110101 [[1,7,9,10],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9,10]=>[7,5,4,3,2,1,8,6,9,10]=>111110100 [[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,10,4,9,3,8,2,7,1,6]=>[9,7,5,3,1,10,8,6,4,2]=>111101111 [[1,6,10],[2,7],[3,8],[4,9],[5]]=>[5,4,9,3,8,2,7,1,6,10]=>[8,6,4,2,1,9,7,5,3,10]=>111101110 [[1,6,9],[2,7,10],[3,8],[4],[5]]=>[5,4,3,8,2,7,10,1,6,9]=>[8,5,3,2,1,9,6,4,10,7]=>111101101 [[1,6,9,10],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6,9,10]=>[7,5,3,2,1,8,6,4,9,10]=>111101100 [[1,6,8,10],[2,7,9],[3],[4],[5]]=>[5,4,3,2,7,9,1,6,8,10]=>[7,4,3,2,1,8,5,9,6,10]=>111101010 [[1,6,8,9,10],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8,9,10]=>[6,4,3,2,1,7,5,8,9,10]=>111101000 [[1,5,9],[2,6,10],[3,7],[4,8]]=>[4,8,3,7,2,6,10,1,5,9]=>[8,5,3,1,9,6,4,2,10,7]=>111011101 [[1,5,9,10],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5,9,10]=>[7,5,3,1,8,6,4,2,9,10]=>111011100 [[1,5,8],[2,6,9],[3,7,10],[4]]=>[4,3,7,10,2,6,9,1,5,8]=>[8,5,2,1,9,6,3,10,7,4]=>111011011 [[1,5,8,10],[2,6,9],[3,7],[4]]=>[4,3,7,2,6,9,1,5,8,10]=>[7,4,2,1,8,5,3,9,6,10]=>111011010 [[1,5,8,9,10],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8,9,10]=>[6,4,2,1,7,5,3,8,9,10]=>111011000 [[1,5,7,9],[2,6,8,10],[3],[4]]=>[4,3,2,6,8,10,1,5,7,9]=>[7,3,2,1,8,4,9,5,10,6]=>111010101 [[1,5,7,9,10],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7,9,10]=>[6,3,2,1,7,4,8,5,9,10]=>111010100 [[1,5,7,8,9,10],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8,9,10]=>[5,3,2,1,6,4,7,8,9,10]=>111010000 [[1,4,7,10],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7,10]=>[7,4,1,8,5,2,9,6,3,10]=>110110110 [[1,4,7,9],[2,5,8,10],[3,6]]=>[3,6,2,5,8,10,1,4,7,9]=>[7,3,1,8,4,2,9,5,10,6]=>110110101 [[1,4,7,9,10],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7,9,10]=>[6,3,1,7,4,2,8,5,9,10]=>110110100 [[1,4,7,8,9,10],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8,9,10]=>[5,3,1,6,4,2,7,8,9,10]=>110110000 [[1,4,6,8,10],[2,5,7,9],[3]]=>[3,2,5,7,9,1,4,6,8,10]=>[6,2,1,7,3,8,4,9,5,10]=>110101010 [[1,4,6,8,9,10],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8,9,10]=>[5,2,1,6,3,7,4,8,9,10]=>110101000 [[1,4,6,7,8,9,10],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9,10]=>[4,2,1,5,3,6,7,8,9,10]=>110100000 [[1,3,5,7,9,10],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9,10]=>[5,1,6,2,7,3,8,4,9,10]=>101010100 [[1,3,5,7,8,9,10],[2,4,6]]=>[2,4,6,1,3,5,7,8,9,10]=>[4,1,5,2,6,3,7,8,9,10]=>101010000 [[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[3,1,4,2,5,6,7,8,9,10]=>101000000 [[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[8,6,9,7,5,4,3,2,1]=>10111111 [[1,4],[2,5],[3,6],[7],[8],[9]]=>[9,8,7,3,6,2,5,1,4]=>[8,6,4,9,7,5,3,2,1]=>11011111 [[1,2,4],[3,5],[6],[7],[8],[9]]=>[9,8,7,6,3,5,1,2,4]=>[7,8,5,9,6,4,3,2,1]=>01011111 [[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[8,6,4,2,9,7,5,3,1]=>11101111 [[1,2,5],[3,6],[4,7],[8],[9]]=>[9,8,4,7,3,6,1,2,5]=>[7,8,5,3,9,6,4,2,1]=>01101111 [[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[7,4,8,5,9,6,3,2,1]=>10101111 [[1,2,3,5],[4,6],[7],[8],[9]]=>[9,8,7,4,6,1,2,3,5]=>[6,7,8,4,9,5,3,2,1]=>00101111 [[1,2,6],[3,7],[4,8],[5,9]]=>[5,9,4,8,3,7,1,2,6]=>[7,8,5,3,1,9,6,4,2]=>01110111 [[1,3,6],[2,4,7],[5,8],[9]]=>[9,5,8,2,4,7,1,3,6]=>[7,4,8,5,2,9,6,3,1]=>10110111 [[1,2,3,6],[4,7],[5,8],[9]]=>[9,5,8,4,7,1,2,3,6]=>[6,7,8,4,2,9,5,3,1]=>00110111 [[1,2,4,6],[3,5,7],[8],[9]]=>[9,8,3,5,7,1,2,4,6]=>[6,7,3,8,4,9,5,2,1]=>01010111 [[1,2,3,4,6],[5,7],[8],[9]]=>[9,8,5,7,1,2,3,4,6]=>[5,6,7,8,3,9,4,2,1]=>00010111 [[1,2,4,7],[3,5,8],[6,9]]=>[6,9,3,5,8,1,2,4,7]=>[6,7,3,8,4,1,9,5,2]=>01011011 [[1,2,3,4,7],[5,8],[6,9]]=>[6,9,5,8,1,2,3,4,7]=>[5,6,7,8,3,1,9,4,2]=>00011011 [[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[6,2,7,3,8,4,9,5,1]=>10101011 [[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[5,6,7,2,8,3,9,4,1]=>00101011 [[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,9,3,1]=>00001011 [[1,2,4,6,8],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8]=>[5,6,1,7,2,8,3,9,4]=>01010101 [[1,2,3,4,6,8],[5,7,9]]=>[5,7,9,1,2,3,4,6,8]=>[4,5,6,7,1,8,2,9,3]=>00010101 [[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,1,9,2]=>00000101 [[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,4,1,3]=>[9,7,10,8,6,5,4,3,2,1]=>101111111 [[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[10,9,8,7,3,6,2,5,1,4]=>[9,7,5,10,8,6,4,3,2,1]=>110111111 [[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,3,5,1,2,4]=>[8,9,6,10,7,5,4,3,2,1]=>010111111 [[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[10,9,4,8,3,7,2,6,1,5]=>[9,7,5,3,10,8,6,4,2,1]=>111011111 [[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[10,9,8,4,7,3,6,1,2,5]=>[8,9,6,4,10,7,5,3,2,1]=>011011111 [[1,3,5],[2,4,6],[7],[8],[9],[10]]=>[10,9,8,7,2,4,6,1,3,5]=>[8,5,9,6,10,7,4,3,2,1]=>101011111 [[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[10,9,8,7,4,6,1,2,3,5]=>[7,8,9,5,10,6,4,3,2,1]=>001011111 [[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[8,9,6,4,2,10,7,5,3,1]=>011101111 [[1,3,6],[2,4,7],[5,8],[9],[10]]=>[10,9,5,8,2,4,7,1,3,6]=>[8,5,9,6,3,10,7,4,2,1]=>101101111 [[1,2,3,6],[4,7],[5,8],[9],[10]]=>[10,9,5,8,4,7,1,2,3,6]=>[7,8,9,5,3,10,6,4,2,1]=>001101111 [[1,2,4,6],[3,5,7],[8],[9],[10]]=>[10,9,8,3,5,7,1,2,4,6]=>[7,8,4,9,5,10,6,3,2,1]=>010101111 [[1,2,3,4,6],[5,7],[8],[9],[10]]=>[10,9,8,5,7,1,2,3,4,6]=>[6,7,8,9,4,10,5,3,2,1]=>000101111 [[1,3,7],[2,4,8],[5,9],[6,10]]=>[6,10,5,9,2,4,8,1,3,7]=>[8,5,9,6,3,1,10,7,4,2]=>101110111 [[1,2,3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,1,2,3,7]=>[7,8,9,5,3,1,10,6,4,2]=>001110111 [[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[8,5,2,9,6,3,10,7,4,1]=>110110111 [[1,2,4,7],[3,5,8],[6,9],[10]]=>[10,6,9,3,5,8,1,2,4,7]=>[7,8,4,9,5,2,10,6,3,1]=>010110111 [[1,2,3,4,7],[5,8],[6,9],[10]]=>[10,6,9,5,8,1,2,3,4,7]=>[6,7,8,9,4,2,10,5,3,1]=>000110111 [[1,3,5,7],[2,4,6,8],[9],[10]]=>[10,9,2,4,6,8,1,3,5,7]=>[7,3,8,4,9,5,10,6,2,1]=>101010111 [[1,2,3,5,7],[4,6,8],[9],[10]]=>[10,9,4,6,8,1,2,3,5,7]=>[6,7,8,3,9,4,10,5,2,1]=>001010111 [[1,2,3,4,5,7],[6,8],[9],[10]]=>[10,9,6,8,1,2,3,4,5,7]=>[5,6,7,8,9,3,10,4,2,1]=>000010111 [[1,2,5,8],[3,6,9],[4,7,10]]=>[4,7,10,3,6,9,1,2,5,8]=>[7,8,4,1,9,5,2,10,6,3]=>011011011 [[1,3,5,8],[2,4,6,9],[7,10]]=>[7,10,2,4,6,9,1,3,5,8]=>[7,3,8,4,9,5,1,10,6,2]=>101011011 [[1,2,3,5,8],[4,6,9],[7,10]]=>[7,10,4,6,9,1,2,3,5,8]=>[6,7,8,3,9,4,1,10,5,2]=>001011011 [[1,2,3,4,5,8],[6,9],[7,10]]=>[7,10,6,9,1,2,3,4,5,8]=>[5,6,7,8,9,3,1,10,4,2]=>000011011 [[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[6,7,2,8,3,9,4,10,5,1]=>010101011 [[1,2,3,4,6,8],[5,7,9],[10]]=>[10,5,7,9,1,2,3,4,6,8]=>[5,6,7,8,2,9,3,10,4,1]=>000101011 [[1,2,3,4,5,6,8],[7,9],[10]]=>[10,7,9,1,2,3,4,5,6,8]=>[4,5,6,7,8,9,2,10,3,1]=>000001011 [[1,2,3,5,7,9],[4,6,8,10]]=>[4,6,8,10,1,2,3,5,7,9]=>[5,6,7,1,8,2,9,3,10,4]=>001010101 [[1,2,3,4,5,7,9],[6,8,10]]=>[6,8,10,1,2,3,4,5,7,9]=>[4,5,6,7,8,1,9,2,10,3]=>000010101 [[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,9,1,10,2]=>000000101 [[1,2],[3,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,1,4,2]=>010101101 [[1,2],[3,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,3,4,1,2]=>[9,10,7,8,5,3,6,1,4,2]=>010110101 [[1,2],[3,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,3,5,1,2]=>[9,10,7,5,8,3,6,1,4,2]=>011010101 [[1,3],[2,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,2,4,1,3]=>[9,7,10,8,5,6,3,4,1,2]=>101101010 [[1,3],[2,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,2,5,1,3]=>[9,7,10,5,8,6,3,4,1,2]=>101011010 [[1,3],[2,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,2,5,1,3]=>[9,7,10,5,8,3,6,4,1,2]=>101010110 [[1,3],[2,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,2,5,1,3]=>[9,7,10,5,8,3,6,1,4,2]=>101010101 [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>11111011111 [[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>00000010 [[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[3,4,5,6,7,8,1,2,9]=>00000100 [[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[3,4,5,6,7,8,2,1,9]=>00000110 [[1,2,3,4,5,9],[6,7,8]]=>[6,7,8,1,2,3,4,5,9]=>[4,5,6,7,8,1,2,3,9]=>00001000 [[1,2,3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>00111110 [[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>01111110 [[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010 [[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[3,4,5,6,7,8,9,1,2,10]=>000000100 [[1,2,3,4,5,10],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5,10]=>[5,6,7,8,9,1,2,3,4,10]=>000010000 [[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3,10]=>[7,8,9,6,5,4,3,2,1,10]=>001111110 [[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>011111110 [[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000 [[1,3,5,6,7,8,9],[2],[4]]=>[4,2,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>10100000 [[1,2,4,7,8,9],[3,5],[6]]=>[6,3,5,1,2,4,7,8,9]=>[4,5,2,6,3,1,7,8,9]=>01011000 [[1,4,6,7,8,9],[2],[3],[5]]=>[5,3,2,1,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>11010000 [[1,5,7,8,9],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8,9]=>[5,4,3,2,6,1,7,8,9]=>11101000 [[1,6,8,9],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8,9]=>[6,5,4,3,2,7,1,8,9]=>11110100 [[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>11111010 [[1,4],[2,6],[3,8],[5],[7],[9]]=>[9,7,5,3,8,2,6,1,4]=>[8,6,4,9,3,7,2,5,1]=>11010101 [[1,6],[2,8],[3],[4],[5],[7],[9]]=>[9,7,5,4,3,2,8,1,6]=>[8,6,5,4,3,9,2,7,1]=>11110101 [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>11111101 [[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>010000000 [[1,3,5,6,7,8,9,10],[2],[4]]=>[4,2,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>101000000 [[1,2,4,7,8,9,10],[3,5],[6]]=>[6,3,5,1,2,4,7,8,9,10]=>[4,5,2,6,3,1,7,8,9,10]=>010110000 [[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>111111010 [[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[10,8,6,9,4,7,2,5,1,3]=>[9,7,10,5,8,3,6,2,4,1]=>101010101 [[1,5],[2,7],[3,9],[4],[6],[8],[10]]=>[10,8,6,4,3,9,2,7,1,5]=>[9,7,5,4,10,3,8,2,6,1]=>111010101 [[1,7],[2,9],[3],[4],[5],[6],[8],[10]]=>[10,8,6,5,4,3,2,9,1,7]=>[9,7,6,5,4,3,10,2,8,1]=>111110101 [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>111111101 [[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[3,1,4,5,6,7,8,9,2]=>10000001 [[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>10000001 [[1,3,4,5,6,7],[2,8,9]]=>[2,8,9,1,3,4,5,6,7]=>[4,1,5,6,7,8,9,2,3]=>10000010 [[1,3,4,5,6,7],[2,9],[8]]=>[8,2,9,1,3,4,5,6,7]=>[4,2,5,6,7,8,9,1,3]=>10000010 [[1,3,4,5,6],[2,7,8,9]]=>[2,7,8,9,1,3,4,5,6]=>[5,1,6,7,8,9,2,3,4]=>10000100 [[1,3,4,5,6],[2],[7],[8],[9]]=>[9,8,7,2,1,3,4,5,6]=>[5,4,6,7,8,9,3,2,1]=>10000111 [[1,3,4,5],[2],[6],[7],[8],[9]]=>[9,8,7,6,2,1,3,4,5]=>[6,5,7,8,9,4,3,2,1]=>10001111 [[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[7,6,8,9,5,4,3,2,1]=>10011111 [[1,3],[2,5],[4,7],[6],[8],[9]]=>[9,8,6,4,7,2,5,1,3]=>[8,6,9,4,7,3,5,2,1]=>10101011 [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>10111111 [[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[3,1,4,5,6,7,8,9,10,2]=>100000001 [[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>100000001 [[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[4,1,5,6,7,8,9,10,2,3]=>100000010 [[1,3,4,5,6,7,8],[2,10],[9]]=>[9,2,10,1,3,4,5,6,7,8]=>[4,2,5,6,7,8,9,10,1,3]=>100000010 [[1,3,4,5,6,7],[2,8,9,10]]=>[2,8,9,10,1,3,4,5,6,7]=>[5,1,6,7,8,9,10,2,3,4]=>100000100 [[1,3,4,5,6,7],[2,9,10],[8]]=>[8,2,9,10,1,3,4,5,6,7]=>[5,2,6,7,8,9,10,1,3,4]=>100000100 [[1,3,4,5,6,7],[2],[8],[9],[10]]=>[10,9,8,2,1,3,4,5,6,7]=>[5,4,6,7,8,9,10,3,2,1]=>100000111 [[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[10,9,8,7,2,1,3,4,5,6]=>[6,5,7,8,9,10,4,3,2,1]=>100001111 [[1,3,4,5],[2,7,8,9],[6],[10]]=>[10,6,2,7,8,9,1,3,4,5]=>[7,3,8,9,10,2,4,5,6,1]=>100010001 [[1,3,4,5],[2,7,8],[6,10],[9]]=>[9,6,10,2,7,8,1,3,4,5]=>[7,4,8,9,10,2,5,6,1,3]=>100010010 [[1,3,4,5],[2,7],[6],[8],[9],[10]]=>[10,9,8,6,2,7,1,3,4,5]=>[7,5,8,9,10,4,6,3,2,1]=>100010111 [[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,1,3,4]=>[8,7,9,10,6,5,4,3,2,1]=>100111111 [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>101111111 [[1,2,3,4,6,8,10],[5,7,9]]=>[5,7,9,1,2,3,4,6,8,10]=>[4,5,6,7,1,8,2,9,3,10]=>000101010 [[1,2,3,5,7,8,9,10],[4,6]]=>[4,6,1,2,3,5,7,8,9,10]=>[3,4,5,1,6,2,7,8,9,10]=>001010000 [[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>001000000 [[1,2,3,4,5,6,9,10],[7,8]]=>[7,8,1,2,3,4,5,6,9,10]=>[3,4,5,6,7,8,1,2,9,10]=>000001000 [[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>000100000 [[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>000000100 [[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>000001000 [[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>000010000 [[1,2,5,6,7,8],[3,4,9]]=>[3,4,9,1,2,5,6,7,8]=>[4,5,1,2,6,7,8,9,3]=>01000001 [[1,2,5,6,7,8],[3,4],[9]]=>[9,3,4,1,2,5,6,7,8]=>[4,5,2,3,6,7,8,9,1]=>01000001 [[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,9,1]=>11000001 [[1,2,3,7,8],[4,5,6],[9]]=>[9,4,5,6,1,2,3,7,8]=>[5,6,7,2,3,4,8,9,1]=>00100001 [[1,3,6,7,8],[2,5],[4],[9]]=>[9,4,2,5,1,3,6,7,8]=>[5,3,6,2,4,7,8,9,1]=>10100001 [[1,5,6,7,8],[2],[3],[4],[9]]=>[9,4,3,2,1,5,6,7,8]=>[5,4,3,2,6,7,8,9,1]=>11100001 [[1,3,4,8],[2,6,7],[5],[9]]=>[9,5,2,6,7,1,3,4,8]=>[6,3,7,8,2,4,5,9,1]=>10010001 [[1,2,7,8],[3,4],[5,6],[9]]=>[9,5,6,3,4,1,2,7,8]=>[6,7,4,5,2,3,8,9,1]=>01010001 [[1,4,7,8],[2,6],[3],[5],[9]]=>[9,5,3,2,6,1,4,7,8]=>[6,4,3,7,2,5,8,9,1]=>11010001 [[1,6,7,8],[2],[3],[4],[5],[9]]=>[9,5,4,3,2,1,6,7,8]=>[6,5,4,3,2,7,8,9,1]=>11110001 [[1,2,5],[3,4,8],[6,7],[9]]=>[9,6,7,3,4,8,1,2,5]=>[7,8,4,5,9,2,3,6,1]=>01001001 [[1,4,5],[2,7,8],[3],[6],[9]]=>[9,6,3,2,7,8,1,4,5]=>[7,4,3,8,9,2,5,6,1]=>11001001 [[1,3,8],[2,5],[4,7],[6],[9]]=>[9,6,4,7,2,5,1,3,8]=>[7,5,8,3,6,2,4,9,1]=>10101001 [[1,5,8],[2,7],[3],[4],[6],[9]]=>[9,6,4,3,2,7,1,5,8]=>[7,5,4,3,8,2,6,9,1]=>11101001 [[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,9,1]=>11111001 [[1,2,5,6,7,8,9],[3,4],[10]]=>[10,3,4,1,2,5,6,7,8,9]=>[4,5,2,3,6,7,8,9,10,1]=>010000001 [[1,4,5,6,7,8,9],[2],[3],[10]]=>[10,3,2,1,4,5,6,7,8,9]=>[4,3,2,5,6,7,8,9,10,1]=>110000001 [[1,2,3,7,8,9],[4,5,6],[10]]=>[10,4,5,6,1,2,3,7,8,9]=>[5,6,7,2,3,4,8,9,10,1]=>001000001 [[1,3,6,7,8,9],[2,5],[4],[10]]=>[10,4,2,5,1,3,6,7,8,9]=>[5,3,6,2,4,7,8,9,10,1]=>101000001 [[1,5,6,7,8,9],[2],[3],[4],[10]]=>[10,4,3,2,1,5,6,7,8,9]=>[5,4,3,2,6,7,8,9,10,1]=>111000001 [[1,2,3,4,9],[5,6,7,8],[10]]=>[10,5,6,7,8,1,2,3,4,9]=>[6,7,8,9,2,3,4,5,10,1]=>000100001 [[1,3,4,8,9],[2,6,7],[5],[10]]=>[10,5,2,6,7,1,3,4,8,9]=>[6,3,7,8,2,4,5,9,10,1]=>100100001 [[1,2,7,8,9],[3,4],[5,6],[10]]=>[10,5,6,3,4,1,2,7,8,9]=>[6,7,4,5,2,3,8,9,10,1]=>010100001 [[1,4,7,8,9],[2,6],[3],[5],[10]]=>[10,5,3,2,6,1,4,7,8,9]=>[6,4,3,7,2,5,8,9,10,1]=>110100001 [[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[10,5,4,3,2,1,6,7,8,9]=>[6,5,4,3,2,7,8,9,10,1]=>111100001 [[1,2,5,9],[3,4,8],[6,7],[10]]=>[10,6,7,3,4,8,1,2,5,9]=>[7,8,4,5,9,2,3,6,10,1]=>010010001 [[1,4,5,9],[2,7,8],[3],[6],[10]]=>[10,6,3,2,7,8,1,4,5,9]=>[7,4,3,8,9,2,5,6,10,1]=>110010001 [[1,3,8,9],[2,5],[4,7],[6],[10]]=>[10,6,4,7,2,5,1,3,8,9]=>[7,5,8,3,6,2,4,9,10,1]=>101010001 [[1,5,8,9],[2,7],[3],[4],[6],[10]]=>[10,6,4,3,2,7,1,5,8,9]=>[7,5,4,3,8,2,6,9,10,1]=>111010001 [[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[10,6,5,4,3,2,1,7,8,9]=>[7,6,5,4,3,2,8,9,10,1]=>111110001 [[1,3,6],[2,5,9],[4,8],[7],[10]]=>[10,7,4,8,2,5,9,1,3,6]=>[8,5,9,3,6,10,2,4,7,1]=>101001001 [[1,5,6],[2,8,9],[3],[4],[7],[10]]=>[10,7,4,3,2,8,9,1,5,6]=>[8,5,4,3,9,10,2,6,7,1]=>111001001 [[1,2,9],[3,4],[5,6],[7,8],[10]]=>[10,7,8,5,6,3,4,1,2,9]=>[8,9,6,7,4,5,2,3,10,1]=>010101001 [[1,4,9],[2,6],[3,8],[5],[7],[10]]=>[10,7,5,3,8,2,6,1,4,9]=>[8,6,4,9,3,7,2,5,10,1]=>110101001 [[1,6,9],[2,8],[3],[4],[5],[7],[10]]=>[10,7,5,4,3,2,8,1,6,9]=>[8,6,5,4,3,9,2,7,10,1]=>111101001 [[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,10,1]=>111111001 [[1,2,3,6,7,8,9],[4,5]]=>[4,5,1,2,3,6,7,8,9]=>[3,4,5,1,2,6,7,8,9]=>00100000 [[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>01100000 [[1,2,6,7,8,9],[3],[4],[5]]=>[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>01110000 [[1,2,7,8,9],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>01111000 [[1,2,8,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8,9]=>[6,7,5,4,3,2,1,8,9]=>01111100 [[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[3,4,2,1,5,6,7,8,9,10]=>011000000 [[1,2,7,8,9,10],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,4,3,2,1,7,8,9,10]=>011110000 [[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8,9,10]=>[6,7,5,4,3,2,1,8,9,10]=>011111000 [[1,2,4,7],[3,6,10],[5,9],[8]]=>[8,5,9,3,6,10,1,2,4,7]=>[7,8,4,9,2,5,10,1,3,6]=>010100100 [[1,2,3],[4,5,8],[6,7],[9,10]]=>[9,10,6,7,4,5,8,1,2,3]=>[8,9,10,5,6,3,4,7,1,2]=>001010010 [[1,2,3,4,7,8,9],[5,6]]=>[5,6,1,2,3,4,7,8,9]=>[3,4,5,6,1,2,7,8,9]=>00010000 [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>110111111 [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>111011111 [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>111111011 [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>111110111 [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>111101111 [[1,2],[3,4],[5,6],[7,9],[8]]=>[8,7,9,5,6,3,4,1,2]=>[8,9,6,7,4,5,2,1,3]=>01010110 [[1,2,3,4],[5,6,7,9],[8]]=>[8,5,6,7,9,1,2,3,4]=>[6,7,8,9,2,3,4,1,5]=>00010010 [[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>00000101 [[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[3,4,5,6,7,1,8,2,9]=>00001010 [[1,2,3,4,5,6,7,9],[8],[10]]=>[10,8,1,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,9,2,10,1]=>000000101 [[1,3,4,9],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4,9]=>[6,5,7,8,4,3,2,1,9]=>10011110 [[1,3,10],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3,10]=>[8,7,9,6,5,4,3,2,1,10]=>101111110 [[1,7],[2,8],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,8,1,7]=>[8,6,5,4,3,2,9,7,1]=>11111011 [[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[3,4,1,5,6,7,8,9,2]=>01000001 [[1,2,4,5,6,7,8,9],[3,10]]=>[3,10,1,2,4,5,6,7,8,9]=>[3,4,1,5,6,7,8,9,10,2]=>010000001 [[1,2],[3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,9,1,2]=>[8,9,6,5,4,3,2,1,7]=>01111110 [[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,10,1,2]=>[9,10,7,6,5,4,3,2,1,8]=>011111110 [[1,2,3],[4,9],[5],[6],[7],[8]]=>[8,7,6,5,4,9,1,2,3]=>[7,8,9,5,4,3,2,1,6]=>00111110 [[1,2,3,4],[5,9],[6],[7],[8]]=>[8,7,6,5,9,1,2,3,4]=>[6,7,8,9,4,3,2,1,5]=>00011110 [[1,2,3,4,5],[6,9],[7],[8]]=>[8,7,6,9,1,2,3,4,5]=>[5,6,7,8,9,3,2,1,4]=>00001110 [[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,1,3]=>00000110 [[1,2,3,4,5,7],[6,8,9]]=>[6,8,9,1,2,3,4,5,7]=>[4,5,6,7,8,1,9,2,3]=>00001010 [[1,2,3],[4,10],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,10,1,2,3]=>[8,9,10,6,5,4,3,2,1,7]=>001111110 [[1,2,3,4],[5,10],[6],[7],[8],[9]]=>[9,8,7,6,5,10,1,2,3,4]=>[7,8,9,10,5,4,3,2,1,6]=>000111110 [[1,2,3,4,5],[6,10],[7],[8],[9]]=>[9,8,7,6,10,1,2,3,4,5]=>[6,7,8,9,10,4,3,2,1,5]=>000011110 [[1,2,3,4,5,6],[7,10],[8],[9]]=>[9,8,7,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,3,2,1,4]=>000001110 [[1,2,3,4,5,6,7],[8,10],[9]]=>[9,8,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,2,1,3]=>000000110 [[1,2,3,4,5,6,8],[7,9,10]]=>[7,9,10,1,2,3,4,5,6,8]=>[4,5,6,7,8,9,1,10,2,3]=>000001010 [[1,3],[2,4],[5,9],[6],[7],[8]]=>[8,7,6,5,9,2,4,1,3]=>[8,6,9,7,4,3,2,1,5]=>10111110 [[1,4],[2,5],[3,6],[7,9],[8]]=>[8,7,9,3,6,2,5,1,4]=>[8,6,4,9,7,5,2,1,3]=>11011110 [[1,3],[2,4],[5,10],[6],[7],[8],[9]]=>[9,8,7,6,5,10,2,4,1,3]=>[9,7,10,8,5,4,3,2,1,6]=>101111110 [[1,4],[2,5],[3,6],[7,10],[8],[9]]=>[9,8,7,10,3,6,2,5,1,4]=>[9,7,5,10,8,6,3,2,1,4]=>110111110 [[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[3,1,4,5,6,7,8,2,9]=>10000010 [[1,3,4,5,7,9],[2,8,10],[6]]=>[6,2,8,10,1,3,4,5,7,9]=>[5,2,6,7,8,1,9,3,10,4]=>100010101 [[1,2,3,4,5,8,9],[6,7]]=>[6,7,1,2,3,4,5,8,9]=>[3,4,5,6,7,1,2,8,9]=>00001000 [[1,2,3,4,5,6,8,9],[7,10]]=>[7,10,1,2,3,4,5,6,8,9]=>[3,4,5,6,7,8,1,9,10,2]=>000001001 [[1,2,3,4,6],[5,7,8,9]]=>[5,7,8,9,1,2,3,4,6]=>[5,6,7,8,1,9,2,3,4]=>00010100 [[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[3,4,5,6,7,1,8,9,2]=>00001001 [[1,3,6,7],[2,5,10],[4,9],[8]]=>[8,4,9,2,5,10,1,3,6,7]=>[7,4,8,2,5,9,10,1,3,6]=>101000100