=>

[1]=>[[1]]=> [1,2]=>[[1,2]]=>0 [2,1]=>[[1],[2]]=>1 [1,2,3]=>[[1,2,3]]=>00 [1,3,2]=>[[1,2],[3]]=>01 [2,1,3]=>[[1,3],[2]]=>10 [2,3,1]=>[[1,3],[2]]=>10 [3,1,2]=>[[1,2],[3]]=>01 [3,2,1]=>[[1],[2],[3]]=>11 [1,2,3,4]=>[[1,2,3,4]]=>000 [1,2,4,3]=>[[1,2,3],[4]]=>001 [1,3,2,4]=>[[1,2,4],[3]]=>010 [1,3,4,2]=>[[1,2,4],[3]]=>010 [1,4,2,3]=>[[1,2,3],[4]]=>001 [1,4,3,2]=>[[1,2],[3],[4]]=>011 [2,1,3,4]=>[[1,3,4],[2]]=>100 [2,1,4,3]=>[[1,3],[2,4]]=>101 [2,3,1,4]=>[[1,3,4],[2]]=>100 [2,3,4,1]=>[[1,3,4],[2]]=>100 [2,4,1,3]=>[[1,3],[2,4]]=>101 [2,4,3,1]=>[[1,3],[2],[4]]=>101 [3,1,2,4]=>[[1,2,4],[3]]=>010 [3,1,4,2]=>[[1,2],[3,4]]=>010 [3,2,1,4]=>[[1,4],[2],[3]]=>110 [3,2,4,1]=>[[1,4],[2],[3]]=>110 [3,4,1,2]=>[[1,2],[3,4]]=>010 [3,4,2,1]=>[[1,4],[2],[3]]=>110 [4,1,2,3]=>[[1,2,3],[4]]=>001 [4,1,3,2]=>[[1,2],[3],[4]]=>011 [4,2,1,3]=>[[1,3],[2],[4]]=>101 [4,2,3,1]=>[[1,3],[2],[4]]=>101 [4,3,1,2]=>[[1,2],[3],[4]]=>011 [4,3,2,1]=>[[1],[2],[3],[4]]=>111 [1,2,3,4,5]=>[[1,2,3,4,5]]=>0000 [1,2,3,5,4]=>[[1,2,3,4],[5]]=>0001 [1,2,4,3,5]=>[[1,2,3,5],[4]]=>0010 [1,2,4,5,3]=>[[1,2,3,5],[4]]=>0010 [1,2,5,3,4]=>[[1,2,3,4],[5]]=>0001 [1,2,5,4,3]=>[[1,2,3],[4],[5]]=>0011 [1,3,2,4,5]=>[[1,2,4,5],[3]]=>0100 [1,3,2,5,4]=>[[1,2,4],[3,5]]=>0101 [1,3,4,2,5]=>[[1,2,4,5],[3]]=>0100 [1,3,4,5,2]=>[[1,2,4,5],[3]]=>0100 [1,3,5,2,4]=>[[1,2,4],[3,5]]=>0101 [1,3,5,4,2]=>[[1,2,4],[3],[5]]=>0101 [1,4,2,3,5]=>[[1,2,3,5],[4]]=>0010 [1,4,2,5,3]=>[[1,2,3],[4,5]]=>0010 [1,4,3,2,5]=>[[1,2,5],[3],[4]]=>0110 [1,4,3,5,2]=>[[1,2,5],[3],[4]]=>0110 [1,4,5,2,3]=>[[1,2,3],[4,5]]=>0010 [1,4,5,3,2]=>[[1,2,5],[3],[4]]=>0110 [1,5,2,3,4]=>[[1,2,3,4],[5]]=>0001 [1,5,2,4,3]=>[[1,2,3],[4],[5]]=>0011 [1,5,3,2,4]=>[[1,2,4],[3],[5]]=>0101 [1,5,3,4,2]=>[[1,2,4],[3],[5]]=>0101 [1,5,4,2,3]=>[[1,2,3],[4],[5]]=>0011 [1,5,4,3,2]=>[[1,2],[3],[4],[5]]=>0111 [2,1,3,4,5]=>[[1,3,4,5],[2]]=>1000 [2,1,3,5,4]=>[[1,3,4],[2,5]]=>1001 [2,1,4,3,5]=>[[1,3,5],[2,4]]=>1010 [2,1,4,5,3]=>[[1,3,5],[2,4]]=>1010 [2,1,5,3,4]=>[[1,3,4],[2,5]]=>1001 [2,1,5,4,3]=>[[1,3],[2,4],[5]]=>1011 [2,3,1,4,5]=>[[1,3,4,5],[2]]=>1000 [2,3,1,5,4]=>[[1,3,4],[2,5]]=>1001 [2,3,4,1,5]=>[[1,3,4,5],[2]]=>1000 [2,3,4,5,1]=>[[1,3,4,5],[2]]=>1000 [2,3,5,1,4]=>[[1,3,4],[2,5]]=>1001 [2,3,5,4,1]=>[[1,3,4],[2],[5]]=>1001 [2,4,1,3,5]=>[[1,3,5],[2,4]]=>1010 [2,4,1,5,3]=>[[1,3,5],[2,4]]=>1010 [2,4,3,1,5]=>[[1,3,5],[2],[4]]=>1010 [2,4,3,5,1]=>[[1,3,5],[2],[4]]=>1010 [2,4,5,1,3]=>[[1,3,5],[2,4]]=>1010 [2,4,5,3,1]=>[[1,3,5],[2],[4]]=>1010 [2,5,1,3,4]=>[[1,3,4],[2,5]]=>1001 [2,5,1,4,3]=>[[1,3],[2,4],[5]]=>1011 [2,5,3,1,4]=>[[1,3,4],[2],[5]]=>1001 [2,5,3,4,1]=>[[1,3,4],[2],[5]]=>1001 [2,5,4,1,3]=>[[1,3],[2,4],[5]]=>1011 [2,5,4,3,1]=>[[1,3],[2],[4],[5]]=>1011 [3,1,2,4,5]=>[[1,2,4,5],[3]]=>0100 [3,1,2,5,4]=>[[1,2,4],[3,5]]=>0101 [3,1,4,2,5]=>[[1,2,5],[3,4]]=>0100 [3,1,4,5,2]=>[[1,2,5],[3,4]]=>0100 [3,1,5,2,4]=>[[1,2,4],[3,5]]=>0101 [3,1,5,4,2]=>[[1,2],[3,4],[5]]=>0101 [3,2,1,4,5]=>[[1,4,5],[2],[3]]=>1100 [3,2,1,5,4]=>[[1,4],[2,5],[3]]=>1101 [3,2,4,1,5]=>[[1,4,5],[2],[3]]=>1100 [3,2,4,5,1]=>[[1,4,5],[2],[3]]=>1100 [3,2,5,1,4]=>[[1,4],[2,5],[3]]=>1101 [3,2,5,4,1]=>[[1,4],[2,5],[3]]=>1101 [3,4,1,2,5]=>[[1,2,5],[3,4]]=>0100 [3,4,1,5,2]=>[[1,2,5],[3,4]]=>0100 [3,4,2,1,5]=>[[1,4,5],[2],[3]]=>1100 [3,4,2,5,1]=>[[1,4,5],[2],[3]]=>1100 [3,4,5,1,2]=>[[1,2,5],[3,4]]=>0100 [3,4,5,2,1]=>[[1,4,5],[2],[3]]=>1100 [3,5,1,2,4]=>[[1,2,4],[3,5]]=>0101 [3,5,1,4,2]=>[[1,2],[3,4],[5]]=>0101 [3,5,2,1,4]=>[[1,4],[2,5],[3]]=>1101 [3,5,2,4,1]=>[[1,4],[2,5],[3]]=>1101 [3,5,4,1,2]=>[[1,2],[3,4],[5]]=>0101 [3,5,4,2,1]=>[[1,4],[2],[3],[5]]=>1101 [4,1,2,3,5]=>[[1,2,3,5],[4]]=>0010 [4,1,2,5,3]=>[[1,2,3],[4,5]]=>0010 [4,1,3,2,5]=>[[1,2,5],[3],[4]]=>0110 [4,1,3,5,2]=>[[1,2,5],[3],[4]]=>0110 [4,1,5,2,3]=>[[1,2,3],[4,5]]=>0010 [4,1,5,3,2]=>[[1,2],[3,5],[4]]=>0110 [4,2,1,3,5]=>[[1,3,5],[2],[4]]=>1010 [4,2,1,5,3]=>[[1,3],[2,5],[4]]=>1010 [4,2,3,1,5]=>[[1,3,5],[2],[4]]=>1010 [4,2,3,5,1]=>[[1,3,5],[2],[4]]=>1010 [4,2,5,1,3]=>[[1,3],[2,5],[4]]=>1010 [4,2,5,3,1]=>[[1,3],[2,5],[4]]=>1010 [4,3,1,2,5]=>[[1,2,5],[3],[4]]=>0110 [4,3,1,5,2]=>[[1,2],[3,5],[4]]=>0110 [4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>1110 [4,3,2,5,1]=>[[1,5],[2],[3],[4]]=>1110 [4,3,5,1,2]=>[[1,2],[3,5],[4]]=>0110 [4,3,5,2,1]=>[[1,5],[2],[3],[4]]=>1110 [4,5,1,2,3]=>[[1,2,3],[4,5]]=>0010 [4,5,1,3,2]=>[[1,2],[3,5],[4]]=>0110 [4,5,2,1,3]=>[[1,3],[2,5],[4]]=>1010 [4,5,2,3,1]=>[[1,3],[2,5],[4]]=>1010 [4,5,3,1,2]=>[[1,2],[3,5],[4]]=>0110 [4,5,3,2,1]=>[[1,5],[2],[3],[4]]=>1110 [5,1,2,3,4]=>[[1,2,3,4],[5]]=>0001 [5,1,2,4,3]=>[[1,2,3],[4],[5]]=>0011 [5,1,3,2,4]=>[[1,2,4],[3],[5]]=>0101 [5,1,3,4,2]=>[[1,2,4],[3],[5]]=>0101 [5,1,4,2,3]=>[[1,2,3],[4],[5]]=>0011 [5,1,4,3,2]=>[[1,2],[3],[4],[5]]=>0111 [5,2,1,3,4]=>[[1,3,4],[2],[5]]=>1001 [5,2,1,4,3]=>[[1,3],[2,4],[5]]=>1011 [5,2,3,1,4]=>[[1,3,4],[2],[5]]=>1001 [5,2,3,4,1]=>[[1,3,4],[2],[5]]=>1001 [5,2,4,1,3]=>[[1,3],[2,4],[5]]=>1011 [5,2,4,3,1]=>[[1,3],[2],[4],[5]]=>1011 [5,3,1,2,4]=>[[1,2,4],[3],[5]]=>0101 [5,3,1,4,2]=>[[1,2],[3,4],[5]]=>0101 [5,3,2,1,4]=>[[1,4],[2],[3],[5]]=>1101 [5,3,2,4,1]=>[[1,4],[2],[3],[5]]=>1101 [5,3,4,1,2]=>[[1,2],[3,4],[5]]=>0101 [5,3,4,2,1]=>[[1,4],[2],[3],[5]]=>1101 [5,4,1,2,3]=>[[1,2,3],[4],[5]]=>0011 [5,4,1,3,2]=>[[1,2],[3],[4],[5]]=>0111 [5,4,2,1,3]=>[[1,3],[2],[4],[5]]=>1011 [5,4,2,3,1]=>[[1,3],[2],[4],[5]]=>1011 [5,4,3,1,2]=>[[1,2],[3],[4],[5]]=>0111 [5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>1111 [1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>00000 [1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]=>00001 [1,2,3,5,4,6]=>[[1,2,3,4,6],[5]]=>00010 [1,2,3,5,6,4]=>[[1,2,3,4,6],[5]]=>00010 [1,2,3,6,4,5]=>[[1,2,3,4,5],[6]]=>00001 [1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,2,4,3,5,6]=>[[1,2,3,5,6],[4]]=>00100 [1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]=>00101 [1,2,4,5,3,6]=>[[1,2,3,5,6],[4]]=>00100 [1,2,4,5,6,3]=>[[1,2,3,5,6],[4]]=>00100 [1,2,4,6,3,5]=>[[1,2,3,5],[4,6]]=>00101 [1,2,4,6,5,3]=>[[1,2,3,5],[4],[6]]=>00101 [1,2,5,3,4,6]=>[[1,2,3,4,6],[5]]=>00010 [1,2,5,3,6,4]=>[[1,2,3,4],[5,6]]=>00010 [1,2,5,4,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [1,2,5,4,6,3]=>[[1,2,3,6],[4],[5]]=>00110 [1,2,5,6,3,4]=>[[1,2,3,4],[5,6]]=>00010 [1,2,5,6,4,3]=>[[1,2,3,6],[4],[5]]=>00110 [1,2,6,3,4,5]=>[[1,2,3,4,5],[6]]=>00001 [1,2,6,3,5,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,2,6,4,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [1,2,6,4,5,3]=>[[1,2,3,5],[4],[6]]=>00101 [1,2,6,5,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [1,3,2,4,5,6]=>[[1,2,4,5,6],[3]]=>01000 [1,3,2,4,6,5]=>[[1,2,4,5],[3,6]]=>01001 [1,3,2,5,4,6]=>[[1,2,4,6],[3,5]]=>01010 [1,3,2,5,6,4]=>[[1,2,4,6],[3,5]]=>01010 [1,3,2,6,4,5]=>[[1,2,4,5],[3,6]]=>01001 [1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [1,3,4,2,5,6]=>[[1,2,4,5,6],[3]]=>01000 [1,3,4,2,6,5]=>[[1,2,4,5],[3,6]]=>01001 [1,3,4,5,2,6]=>[[1,2,4,5,6],[3]]=>01000 [1,3,4,5,6,2]=>[[1,2,4,5,6],[3]]=>01000 [1,3,4,6,2,5]=>[[1,2,4,5],[3,6]]=>01001 [1,3,4,6,5,2]=>[[1,2,4,5],[3],[6]]=>01001 [1,3,5,2,4,6]=>[[1,2,4,6],[3,5]]=>01010 [1,3,5,2,6,4]=>[[1,2,4,6],[3,5]]=>01010 [1,3,5,4,2,6]=>[[1,2,4,6],[3],[5]]=>01010 [1,3,5,4,6,2]=>[[1,2,4,6],[3],[5]]=>01010 [1,3,5,6,2,4]=>[[1,2,4,6],[3,5]]=>01010 [1,3,5,6,4,2]=>[[1,2,4,6],[3],[5]]=>01010 [1,3,6,2,4,5]=>[[1,2,4,5],[3,6]]=>01001 [1,3,6,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [1,3,6,4,2,5]=>[[1,2,4,5],[3],[6]]=>01001 [1,3,6,4,5,2]=>[[1,2,4,5],[3],[6]]=>01001 [1,3,6,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [1,3,6,5,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [1,4,2,3,5,6]=>[[1,2,3,5,6],[4]]=>00100 [1,4,2,3,6,5]=>[[1,2,3,5],[4,6]]=>00101 [1,4,2,5,3,6]=>[[1,2,3,6],[4,5]]=>00100 [1,4,2,5,6,3]=>[[1,2,3,6],[4,5]]=>00100 [1,4,2,6,3,5]=>[[1,2,3,5],[4,6]]=>00101 [1,4,2,6,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [1,4,3,2,5,6]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,3,2,6,5]=>[[1,2,5],[3,6],[4]]=>01101 [1,4,3,5,2,6]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,3,5,6,2]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,3,6,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [1,4,3,6,5,2]=>[[1,2,5],[3,6],[4]]=>01101 [1,4,5,2,3,6]=>[[1,2,3,6],[4,5]]=>00100 [1,4,5,2,6,3]=>[[1,2,3,6],[4,5]]=>00100 [1,4,5,3,2,6]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,5,3,6,2]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,5,6,2,3]=>[[1,2,3,6],[4,5]]=>00100 [1,4,5,6,3,2]=>[[1,2,5,6],[3],[4]]=>01100 [1,4,6,2,3,5]=>[[1,2,3,5],[4,6]]=>00101 [1,4,6,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [1,4,6,3,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [1,4,6,3,5,2]=>[[1,2,5],[3,6],[4]]=>01101 [1,4,6,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [1,4,6,5,3,2]=>[[1,2,5],[3],[4],[6]]=>01101 [1,5,2,3,4,6]=>[[1,2,3,4,6],[5]]=>00010 [1,5,2,3,6,4]=>[[1,2,3,4],[5,6]]=>00010 [1,5,2,4,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [1,5,2,4,6,3]=>[[1,2,3,6],[4],[5]]=>00110 [1,5,2,6,3,4]=>[[1,2,3,4],[5,6]]=>00010 [1,5,2,6,4,3]=>[[1,2,3],[4,6],[5]]=>00110 [1,5,3,2,4,6]=>[[1,2,4,6],[3],[5]]=>01010 [1,5,3,2,6,4]=>[[1,2,4],[3,6],[5]]=>01010 [1,5,3,4,2,6]=>[[1,2,4,6],[3],[5]]=>01010 [1,5,3,4,6,2]=>[[1,2,4,6],[3],[5]]=>01010 [1,5,3,6,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [1,5,3,6,4,2]=>[[1,2,4],[3,6],[5]]=>01010 [1,5,4,2,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [1,5,4,2,6,3]=>[[1,2,3],[4,6],[5]]=>00110 [1,5,4,3,2,6]=>[[1,2,6],[3],[4],[5]]=>01110 [1,5,4,3,6,2]=>[[1,2,6],[3],[4],[5]]=>01110 [1,5,4,6,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [1,5,4,6,3,2]=>[[1,2,6],[3],[4],[5]]=>01110 [1,5,6,2,3,4]=>[[1,2,3,4],[5,6]]=>00010 [1,5,6,2,4,3]=>[[1,2,3],[4,6],[5]]=>00110 [1,5,6,3,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [1,5,6,3,4,2]=>[[1,2,4],[3,6],[5]]=>01010 [1,5,6,4,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [1,5,6,4,3,2]=>[[1,2,6],[3],[4],[5]]=>01110 [1,6,2,3,4,5]=>[[1,2,3,4,5],[6]]=>00001 [1,6,2,3,5,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,6,2,4,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [1,6,2,4,5,3]=>[[1,2,3,5],[4],[6]]=>00101 [1,6,2,5,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,6,2,5,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [1,6,3,2,4,5]=>[[1,2,4,5],[3],[6]]=>01001 [1,6,3,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [1,6,3,4,2,5]=>[[1,2,4,5],[3],[6]]=>01001 [1,6,3,4,5,2]=>[[1,2,4,5],[3],[6]]=>01001 [1,6,3,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [1,6,3,5,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [1,6,4,2,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [1,6,4,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [1,6,4,3,2,5]=>[[1,2,5],[3],[4],[6]]=>01101 [1,6,4,3,5,2]=>[[1,2,5],[3],[4],[6]]=>01101 [1,6,4,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [1,6,4,5,3,2]=>[[1,2,5],[3],[4],[6]]=>01101 [1,6,5,2,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [1,6,5,2,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [1,6,5,3,2,4]=>[[1,2,4],[3],[5],[6]]=>01011 [1,6,5,3,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [1,6,5,4,2,3]=>[[1,2,3],[4],[5],[6]]=>00111 [1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]=>01111 [2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>10000 [2,1,3,4,6,5]=>[[1,3,4,5],[2,6]]=>10001 [2,1,3,5,4,6]=>[[1,3,4,6],[2,5]]=>10010 [2,1,3,5,6,4]=>[[1,3,4,6],[2,5]]=>10010 [2,1,3,6,4,5]=>[[1,3,4,5],[2,6]]=>10001 [2,1,3,6,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,1,4,3,5,6]=>[[1,3,5,6],[2,4]]=>10100 [2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]=>10101 [2,1,4,5,3,6]=>[[1,3,5,6],[2,4]]=>10100 [2,1,4,5,6,3]=>[[1,3,5,6],[2,4]]=>10100 [2,1,4,6,3,5]=>[[1,3,5],[2,4,6]]=>10101 [2,1,4,6,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,1,5,3,4,6]=>[[1,3,4,6],[2,5]]=>10010 [2,1,5,3,6,4]=>[[1,3,4],[2,5,6]]=>10010 [2,1,5,4,3,6]=>[[1,3,6],[2,4],[5]]=>10110 [2,1,5,4,6,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,1,5,6,3,4]=>[[1,3,4],[2,5,6]]=>10010 [2,1,5,6,4,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,1,6,3,4,5]=>[[1,3,4,5],[2,6]]=>10001 [2,1,6,3,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,1,6,4,3,5]=>[[1,3,5],[2,4],[6]]=>10101 [2,1,6,4,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,1,6,5,3,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [2,3,1,4,5,6]=>[[1,3,4,5,6],[2]]=>10000 [2,3,1,4,6,5]=>[[1,3,4,5],[2,6]]=>10001 [2,3,1,5,4,6]=>[[1,3,4,6],[2,5]]=>10010 [2,3,1,5,6,4]=>[[1,3,4,6],[2,5]]=>10010 [2,3,1,6,4,5]=>[[1,3,4,5],[2,6]]=>10001 [2,3,1,6,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,3,4,1,5,6]=>[[1,3,4,5,6],[2]]=>10000 [2,3,4,1,6,5]=>[[1,3,4,5],[2,6]]=>10001 [2,3,4,5,1,6]=>[[1,3,4,5,6],[2]]=>10000 [2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]=>10000 [2,3,4,6,1,5]=>[[1,3,4,5],[2,6]]=>10001 [2,3,4,6,5,1]=>[[1,3,4,5],[2],[6]]=>10001 [2,3,5,1,4,6]=>[[1,3,4,6],[2,5]]=>10010 [2,3,5,1,6,4]=>[[1,3,4,6],[2,5]]=>10010 [2,3,5,4,1,6]=>[[1,3,4,6],[2],[5]]=>10010 [2,3,5,4,6,1]=>[[1,3,4,6],[2],[5]]=>10010 [2,3,5,6,1,4]=>[[1,3,4,6],[2,5]]=>10010 [2,3,5,6,4,1]=>[[1,3,4,6],[2],[5]]=>10010 [2,3,6,1,4,5]=>[[1,3,4,5],[2,6]]=>10001 [2,3,6,1,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,3,6,4,1,5]=>[[1,3,4,5],[2],[6]]=>10001 [2,3,6,4,5,1]=>[[1,3,4,5],[2],[6]]=>10001 [2,3,6,5,1,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [2,4,1,3,5,6]=>[[1,3,5,6],[2,4]]=>10100 [2,4,1,3,6,5]=>[[1,3,5],[2,4,6]]=>10101 [2,4,1,5,3,6]=>[[1,3,5,6],[2,4]]=>10100 [2,4,1,5,6,3]=>[[1,3,5,6],[2,4]]=>10100 [2,4,1,6,3,5]=>[[1,3,5],[2,4,6]]=>10101 [2,4,1,6,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,4,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,3,1,6,5]=>[[1,3,5],[2,6],[4]]=>10101 [2,4,3,5,1,6]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,3,5,6,1]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,3,6,1,5]=>[[1,3,5],[2,6],[4]]=>10101 [2,4,3,6,5,1]=>[[1,3,5],[2,6],[4]]=>10101 [2,4,5,1,3,6]=>[[1,3,5,6],[2,4]]=>10100 [2,4,5,1,6,3]=>[[1,3,5,6],[2,4]]=>10100 [2,4,5,3,1,6]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,5,3,6,1]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,5,6,1,3]=>[[1,3,5,6],[2,4]]=>10100 [2,4,5,6,3,1]=>[[1,3,5,6],[2],[4]]=>10100 [2,4,6,1,3,5]=>[[1,3,5],[2,4,6]]=>10101 [2,4,6,1,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,4,6,3,1,5]=>[[1,3,5],[2,6],[4]]=>10101 [2,4,6,3,5,1]=>[[1,3,5],[2,6],[4]]=>10101 [2,4,6,5,1,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,4,6,5,3,1]=>[[1,3,5],[2],[4],[6]]=>10101 [2,5,1,3,4,6]=>[[1,3,4,6],[2,5]]=>10010 [2,5,1,3,6,4]=>[[1,3,4],[2,5,6]]=>10010 [2,5,1,4,3,6]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,1,4,6,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,1,6,3,4]=>[[1,3,4],[2,5,6]]=>10010 [2,5,1,6,4,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,3,1,4,6]=>[[1,3,4,6],[2],[5]]=>10010 [2,5,3,1,6,4]=>[[1,3,4],[2,6],[5]]=>10010 [2,5,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>10010 [2,5,3,4,6,1]=>[[1,3,4,6],[2],[5]]=>10010 [2,5,3,6,1,4]=>[[1,3,4],[2,6],[5]]=>10010 [2,5,3,6,4,1]=>[[1,3,4],[2,6],[5]]=>10010 [2,5,4,1,3,6]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,4,1,6,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,4,3,1,6]=>[[1,3,6],[2],[4],[5]]=>10110 [2,5,4,3,6,1]=>[[1,3,6],[2],[4],[5]]=>10110 [2,5,4,6,1,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,4,6,3,1]=>[[1,3,6],[2],[4],[5]]=>10110 [2,5,6,1,3,4]=>[[1,3,4],[2,5,6]]=>10010 [2,5,6,1,4,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,6,3,1,4]=>[[1,3,4],[2,6],[5]]=>10010 [2,5,6,3,4,1]=>[[1,3,4],[2,6],[5]]=>10010 [2,5,6,4,1,3]=>[[1,3,6],[2,4],[5]]=>10110 [2,5,6,4,3,1]=>[[1,3,6],[2],[4],[5]]=>10110 [2,6,1,3,4,5]=>[[1,3,4,5],[2,6]]=>10001 [2,6,1,3,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,6,1,4,3,5]=>[[1,3,5],[2,4],[6]]=>10101 [2,6,1,4,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,6,1,5,3,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,6,1,5,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [2,6,3,1,4,5]=>[[1,3,4,5],[2],[6]]=>10001 [2,6,3,1,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,6,3,4,1,5]=>[[1,3,4,5],[2],[6]]=>10001 [2,6,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>10001 [2,6,3,5,1,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,6,3,5,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [2,6,4,1,3,5]=>[[1,3,5],[2,4],[6]]=>10101 [2,6,4,1,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,6,4,3,1,5]=>[[1,3,5],[2],[4],[6]]=>10101 [2,6,4,3,5,1]=>[[1,3,5],[2],[4],[6]]=>10101 [2,6,4,5,1,3]=>[[1,3,5],[2,4],[6]]=>10101 [2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6]]=>10101 [2,6,5,1,3,4]=>[[1,3,4],[2,5],[6]]=>10011 [2,6,5,1,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [2,6,5,3,1,4]=>[[1,3,4],[2],[5],[6]]=>10011 [2,6,5,3,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [2,6,5,4,1,3]=>[[1,3],[2,4],[5],[6]]=>10111 [2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]=>10111 [3,1,2,4,5,6]=>[[1,2,4,5,6],[3]]=>01000 [3,1,2,4,6,5]=>[[1,2,4,5],[3,6]]=>01001 [3,1,2,5,4,6]=>[[1,2,4,6],[3,5]]=>01010 [3,1,2,5,6,4]=>[[1,2,4,6],[3,5]]=>01010 [3,1,2,6,4,5]=>[[1,2,4,5],[3,6]]=>01001 [3,1,2,6,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,1,4,2,5,6]=>[[1,2,5,6],[3,4]]=>01000 [3,1,4,2,6,5]=>[[1,2,5],[3,4,6]]=>01001 [3,1,4,5,2,6]=>[[1,2,5,6],[3,4]]=>01000 [3,1,4,5,6,2]=>[[1,2,5,6],[3,4]]=>01000 [3,1,4,6,2,5]=>[[1,2,5],[3,4,6]]=>01001 [3,1,4,6,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,1,5,2,4,6]=>[[1,2,4,6],[3,5]]=>01010 [3,1,5,2,6,4]=>[[1,2,4],[3,5,6]]=>01010 [3,1,5,4,2,6]=>[[1,2,6],[3,4],[5]]=>01010 [3,1,5,4,6,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,1,5,6,2,4]=>[[1,2,4],[3,5,6]]=>01010 [3,1,5,6,4,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,1,6,2,4,5]=>[[1,2,4,5],[3,6]]=>01001 [3,1,6,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,1,6,4,2,5]=>[[1,2,5],[3,4],[6]]=>01001 [3,1,6,4,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,1,6,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,1,6,5,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,2,1,4,6,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,1,5,4,6]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,1,5,6,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,1,6,4,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]=>11011 [3,2,4,1,5,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,2,4,1,6,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,4,5,1,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,2,4,5,6,1]=>[[1,4,5,6],[2],[3]]=>11000 [3,2,4,6,1,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,4,6,5,1]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,5,1,4,6]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,5,1,6,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,5,4,1,6]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,5,4,6,1]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,5,6,1,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,5,6,4,1]=>[[1,4,6],[2,5],[3]]=>11010 [3,2,6,1,4,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,6,1,5,4]=>[[1,4],[2,5],[3,6]]=>11011 [3,2,6,4,1,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,6,4,5,1]=>[[1,4,5],[2,6],[3]]=>11001 [3,2,6,5,1,4]=>[[1,4],[2,5],[3,6]]=>11011 [3,2,6,5,4,1]=>[[1,4],[2,5],[3],[6]]=>11011 [3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>01000 [3,4,1,2,6,5]=>[[1,2,5],[3,4,6]]=>01001 [3,4,1,5,2,6]=>[[1,2,5,6],[3,4]]=>01000 [3,4,1,5,6,2]=>[[1,2,5,6],[3,4]]=>01000 [3,4,1,6,2,5]=>[[1,2,5],[3,4,6]]=>01001 [3,4,1,6,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,4,2,1,5,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,2,1,6,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,4,2,5,1,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,2,5,6,1]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,2,6,1,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,4,2,6,5,1]=>[[1,4,5],[2,6],[3]]=>11001 [3,4,5,1,2,6]=>[[1,2,5,6],[3,4]]=>01000 [3,4,5,1,6,2]=>[[1,2,5,6],[3,4]]=>01000 [3,4,5,2,1,6]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,5,2,6,1]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,5,6,1,2]=>[[1,2,5,6],[3,4]]=>01000 [3,4,5,6,2,1]=>[[1,4,5,6],[2],[3]]=>11000 [3,4,6,1,2,5]=>[[1,2,5],[3,4,6]]=>01001 [3,4,6,1,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,4,6,2,1,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,4,6,2,5,1]=>[[1,4,5],[2,6],[3]]=>11001 [3,4,6,5,1,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6]]=>11001 [3,5,1,2,4,6]=>[[1,2,4,6],[3,5]]=>01010 [3,5,1,2,6,4]=>[[1,2,4],[3,5,6]]=>01010 [3,5,1,4,2,6]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,1,4,6,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,1,6,2,4]=>[[1,2,4],[3,5,6]]=>01010 [3,5,1,6,4,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,2,1,4,6]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,2,1,6,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,2,4,1,6]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,2,4,6,1]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,2,6,1,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,2,6,4,1]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,4,1,2,6]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,4,1,6,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,4,2,1,6]=>[[1,4,6],[2],[3],[5]]=>11010 [3,5,4,2,6,1]=>[[1,4,6],[2],[3],[5]]=>11010 [3,5,4,6,1,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5]]=>11010 [3,5,6,1,2,4]=>[[1,2,4],[3,5,6]]=>01010 [3,5,6,1,4,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,6,2,1,4]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,6,2,4,1]=>[[1,4,6],[2,5],[3]]=>11010 [3,5,6,4,1,2]=>[[1,2,6],[3,4],[5]]=>01010 [3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5]]=>11010 [3,6,1,2,4,5]=>[[1,2,4,5],[3,6]]=>01001 [3,6,1,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,6,1,4,2,5]=>[[1,2,5],[3,4],[6]]=>01001 [3,6,1,4,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,6,1,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,6,1,5,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [3,6,2,1,4,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,6,2,1,5,4]=>[[1,4],[2,5],[3,6]]=>11011 [3,6,2,4,1,5]=>[[1,4,5],[2,6],[3]]=>11001 [3,6,2,4,5,1]=>[[1,4,5],[2,6],[3]]=>11001 [3,6,2,5,1,4]=>[[1,4],[2,5],[3,6]]=>11011 [3,6,2,5,4,1]=>[[1,4],[2,5],[3],[6]]=>11011 [3,6,4,1,2,5]=>[[1,2,5],[3,4],[6]]=>01001 [3,6,4,1,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,6,4,2,1,5]=>[[1,4,5],[2],[3],[6]]=>11001 [3,6,4,2,5,1]=>[[1,4,5],[2],[3],[6]]=>11001 [3,6,4,5,1,2]=>[[1,2,5],[3,4],[6]]=>01001 [3,6,4,5,2,1]=>[[1,4,5],[2],[3],[6]]=>11001 [3,6,5,1,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [3,6,5,1,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [3,6,5,2,1,4]=>[[1,4],[2,5],[3],[6]]=>11011 [3,6,5,2,4,1]=>[[1,4],[2,5],[3],[6]]=>11011 [3,6,5,4,1,2]=>[[1,2],[3,4],[5],[6]]=>01011 [3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>11011 [4,1,2,3,5,6]=>[[1,2,3,5,6],[4]]=>00100 [4,1,2,3,6,5]=>[[1,2,3,5],[4,6]]=>00101 [4,1,2,5,3,6]=>[[1,2,3,6],[4,5]]=>00100 [4,1,2,5,6,3]=>[[1,2,3,6],[4,5]]=>00100 [4,1,2,6,3,5]=>[[1,2,3,5],[4,6]]=>00101 [4,1,2,6,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,1,3,2,5,6]=>[[1,2,5,6],[3],[4]]=>01100 [4,1,3,2,6,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,1,3,5,2,6]=>[[1,2,5,6],[3],[4]]=>01100 [4,1,3,5,6,2]=>[[1,2,5,6],[3],[4]]=>01100 [4,1,3,6,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,1,3,6,5,2]=>[[1,2,5],[3,6],[4]]=>01101 [4,1,5,2,3,6]=>[[1,2,3,6],[4,5]]=>00100 [4,1,5,2,6,3]=>[[1,2,3],[4,5,6]]=>00100 [4,1,5,3,2,6]=>[[1,2,6],[3,5],[4]]=>01100 [4,1,5,3,6,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,1,5,6,2,3]=>[[1,2,3],[4,5,6]]=>00100 [4,1,5,6,3,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,1,6,2,3,5]=>[[1,2,3,5],[4,6]]=>00101 [4,1,6,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,1,6,3,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,1,6,3,5,2]=>[[1,2,5],[3,6],[4]]=>01101 [4,1,6,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,1,6,5,3,2]=>[[1,2],[3,5],[4],[6]]=>01101 [4,2,1,3,5,6]=>[[1,3,5,6],[2],[4]]=>10100 [4,2,1,3,6,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,1,5,3,6]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,1,5,6,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,1,6,3,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,1,6,5,3]=>[[1,3],[2,5],[4,6]]=>10101 [4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>10100 [4,2,3,1,6,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,3,5,1,6]=>[[1,3,5,6],[2],[4]]=>10100 [4,2,3,5,6,1]=>[[1,3,5,6],[2],[4]]=>10100 [4,2,3,6,1,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,3,6,5,1]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,5,1,3,6]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,5,1,6,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,5,3,1,6]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,5,3,6,1]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,5,6,1,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,5,6,3,1]=>[[1,3,6],[2,5],[4]]=>10100 [4,2,6,1,3,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,6,1,5,3]=>[[1,3],[2,5],[4,6]]=>10101 [4,2,6,3,1,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,6,3,5,1]=>[[1,3,5],[2,6],[4]]=>10101 [4,2,6,5,1,3]=>[[1,3],[2,5],[4,6]]=>10101 [4,2,6,5,3,1]=>[[1,3],[2,5],[4],[6]]=>10101 [4,3,1,2,5,6]=>[[1,2,5,6],[3],[4]]=>01100 [4,3,1,2,6,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,3,1,5,2,6]=>[[1,2,6],[3,5],[4]]=>01100 [4,3,1,5,6,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,3,1,6,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,3,1,6,5,2]=>[[1,2],[3,5],[4,6]]=>01101 [4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4]]=>11101 [4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,2,6,1,5]=>[[1,5],[2,6],[3],[4]]=>11101 [4,3,2,6,5,1]=>[[1,5],[2,6],[3],[4]]=>11101 [4,3,5,1,2,6]=>[[1,2,6],[3,5],[4]]=>01100 [4,3,5,1,6,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,5,6,1,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,3,6,1,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,3,6,1,5,2]=>[[1,2],[3,5],[4,6]]=>01101 [4,3,6,2,1,5]=>[[1,5],[2,6],[3],[4]]=>11101 [4,3,6,2,5,1]=>[[1,5],[2,6],[3],[4]]=>11101 [4,3,6,5,1,2]=>[[1,2],[3,5],[4,6]]=>01101 [4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4]]=>11101 [4,5,1,2,3,6]=>[[1,2,3,6],[4,5]]=>00100 [4,5,1,2,6,3]=>[[1,2,3],[4,5,6]]=>00100 [4,5,1,3,2,6]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,1,3,6,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,1,6,2,3]=>[[1,2,3],[4,5,6]]=>00100 [4,5,1,6,3,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,2,1,3,6]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,2,1,6,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,2,3,1,6]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,2,3,6,1]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,2,6,1,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,2,6,3,1]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,3,1,2,6]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,3,1,6,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4]]=>11100 [4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,5,3,6,1,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>00100 [4,5,6,1,3,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,6,2,1,3]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,6,2,3,1]=>[[1,3,6],[2,5],[4]]=>10100 [4,5,6,3,1,2]=>[[1,2,6],[3,5],[4]]=>01100 [4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4]]=>11100 [4,6,1,2,3,5]=>[[1,2,3,5],[4,6]]=>00101 [4,6,1,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,6,1,3,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,6,1,3,5,2]=>[[1,2,5],[3,6],[4]]=>01101 [4,6,1,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,6,1,5,3,2]=>[[1,2],[3,5],[4],[6]]=>01101 [4,6,2,1,3,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,6,2,1,5,3]=>[[1,3],[2,5],[4,6]]=>10101 [4,6,2,3,1,5]=>[[1,3,5],[2,6],[4]]=>10101 [4,6,2,3,5,1]=>[[1,3,5],[2,6],[4]]=>10101 [4,6,2,5,1,3]=>[[1,3],[2,5],[4,6]]=>10101 [4,6,2,5,3,1]=>[[1,3],[2,5],[4],[6]]=>10101 [4,6,3,1,2,5]=>[[1,2,5],[3,6],[4]]=>01101 [4,6,3,1,5,2]=>[[1,2],[3,5],[4,6]]=>01101 [4,6,3,2,1,5]=>[[1,5],[2,6],[3],[4]]=>11101 [4,6,3,2,5,1]=>[[1,5],[2,6],[3],[4]]=>11101 [4,6,3,5,1,2]=>[[1,2],[3,5],[4,6]]=>01101 [4,6,3,5,2,1]=>[[1,5],[2,6],[3],[4]]=>11101 [4,6,5,1,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [4,6,5,1,3,2]=>[[1,2],[3,5],[4],[6]]=>01101 [4,6,5,2,1,3]=>[[1,3],[2,5],[4],[6]]=>10101 [4,6,5,2,3,1]=>[[1,3],[2,5],[4],[6]]=>10101 [4,6,5,3,1,2]=>[[1,2],[3,5],[4],[6]]=>01101 [4,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]=>11101 [5,1,2,3,4,6]=>[[1,2,3,4,6],[5]]=>00010 [5,1,2,3,6,4]=>[[1,2,3,4],[5,6]]=>00010 [5,1,2,4,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [5,1,2,4,6,3]=>[[1,2,3,6],[4],[5]]=>00110 [5,1,2,6,3,4]=>[[1,2,3,4],[5,6]]=>00010 [5,1,2,6,4,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,1,3,2,4,6]=>[[1,2,4,6],[3],[5]]=>01010 [5,1,3,2,6,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,1,3,4,2,6]=>[[1,2,4,6],[3],[5]]=>01010 [5,1,3,4,6,2]=>[[1,2,4,6],[3],[5]]=>01010 [5,1,3,6,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,1,3,6,4,2]=>[[1,2,4],[3,6],[5]]=>01010 [5,1,4,2,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [5,1,4,2,6,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,1,4,3,2,6]=>[[1,2,6],[3],[4],[5]]=>01110 [5,1,4,3,6,2]=>[[1,2,6],[3],[4],[5]]=>01110 [5,1,4,6,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,1,4,6,3,2]=>[[1,2,6],[3],[4],[5]]=>01110 [5,1,6,2,3,4]=>[[1,2,3,4],[5,6]]=>00010 [5,1,6,2,4,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,1,6,3,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,1,6,3,4,2]=>[[1,2,4],[3,6],[5]]=>01010 [5,1,6,4,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,1,6,4,3,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,2,1,3,4,6]=>[[1,3,4,6],[2],[5]]=>10010 [5,2,1,3,6,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,1,4,3,6]=>[[1,3,6],[2,4],[5]]=>10110 [5,2,1,4,6,3]=>[[1,3,6],[2,4],[5]]=>10110 [5,2,1,6,3,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,1,6,4,3]=>[[1,3],[2,4],[5,6]]=>10110 [5,2,3,1,4,6]=>[[1,3,4,6],[2],[5]]=>10010 [5,2,3,1,6,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>10010 [5,2,3,4,6,1]=>[[1,3,4,6],[2],[5]]=>10010 [5,2,3,6,1,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,3,6,4,1]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,4,1,3,6]=>[[1,3,6],[2,4],[5]]=>10110 [5,2,4,1,6,3]=>[[1,3,6],[2,4],[5]]=>10110 [5,2,4,3,1,6]=>[[1,3,6],[2],[4],[5]]=>10110 [5,2,4,3,6,1]=>[[1,3,6],[2],[4],[5]]=>10110 [5,2,4,6,1,3]=>[[1,3,6],[2,4],[5]]=>10110 [5,2,4,6,3,1]=>[[1,3,6],[2],[4],[5]]=>10110 [5,2,6,1,3,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,6,1,4,3]=>[[1,3],[2,4],[5,6]]=>10110 [5,2,6,3,1,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,6,3,4,1]=>[[1,3,4],[2,6],[5]]=>10010 [5,2,6,4,1,3]=>[[1,3],[2,4],[5,6]]=>10110 [5,2,6,4,3,1]=>[[1,3],[2,6],[4],[5]]=>10110 [5,3,1,2,4,6]=>[[1,2,4,6],[3],[5]]=>01010 [5,3,1,2,6,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,3,1,4,2,6]=>[[1,2,6],[3,4],[5]]=>01010 [5,3,1,4,6,2]=>[[1,2,6],[3,4],[5]]=>01010 [5,3,1,6,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,3,1,6,4,2]=>[[1,2],[3,4],[5,6]]=>01010 [5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5]]=>11010 [5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,2,6,1,4]=>[[1,4],[2,6],[3],[5]]=>11010 [5,3,2,6,4,1]=>[[1,4],[2,6],[3],[5]]=>11010 [5,3,4,1,2,6]=>[[1,2,6],[3,4],[5]]=>01010 [5,3,4,1,6,2]=>[[1,2,6],[3,4],[5]]=>01010 [5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,4,6,1,2]=>[[1,2,6],[3,4],[5]]=>01010 [5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5]]=>11010 [5,3,6,1,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,3,6,1,4,2]=>[[1,2],[3,4],[5,6]]=>01010 [5,3,6,2,1,4]=>[[1,4],[2,6],[3],[5]]=>11010 [5,3,6,2,4,1]=>[[1,4],[2,6],[3],[5]]=>11010 [5,3,6,4,1,2]=>[[1,2],[3,4],[5,6]]=>01010 [5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5]]=>11010 [5,4,1,2,3,6]=>[[1,2,3,6],[4],[5]]=>00110 [5,4,1,2,6,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,4,1,3,2,6]=>[[1,2,6],[3],[4],[5]]=>01110 [5,4,1,3,6,2]=>[[1,2,6],[3],[4],[5]]=>01110 [5,4,1,6,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,4,1,6,3,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5]]=>10110 [5,4,2,1,6,3]=>[[1,3],[2,6],[4],[5]]=>10110 [5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5]]=>10110 [5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5]]=>10110 [5,4,2,6,1,3]=>[[1,3],[2,6],[4],[5]]=>10110 [5,4,2,6,3,1]=>[[1,3],[2,6],[4],[5]]=>10110 [5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5]]=>01110 [5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>11110 [5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5]]=>11110 [5,4,3,6,1,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5]]=>11110 [5,4,6,1,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,4,6,1,3,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5]]=>10110 [5,4,6,2,3,1]=>[[1,3],[2,6],[4],[5]]=>10110 [5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>11110 [5,6,1,2,3,4]=>[[1,2,3,4],[5,6]]=>00010 [5,6,1,2,4,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,6,1,3,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,6,1,3,4,2]=>[[1,2,4],[3,6],[5]]=>01010 [5,6,1,4,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,6,1,4,3,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,6,2,1,3,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,6,2,1,4,3]=>[[1,3],[2,4],[5,6]]=>10110 [5,6,2,3,1,4]=>[[1,3,4],[2,6],[5]]=>10010 [5,6,2,3,4,1]=>[[1,3,4],[2,6],[5]]=>10010 [5,6,2,4,1,3]=>[[1,3],[2,4],[5,6]]=>10110 [5,6,2,4,3,1]=>[[1,3],[2,6],[4],[5]]=>10110 [5,6,3,1,2,4]=>[[1,2,4],[3,6],[5]]=>01010 [5,6,3,1,4,2]=>[[1,2],[3,4],[5,6]]=>01010 [5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5]]=>11010 [5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5]]=>11010 [5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]]=>01010 [5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5]]=>11010 [5,6,4,1,2,3]=>[[1,2,3],[4,6],[5]]=>00110 [5,6,4,1,3,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5]]=>10110 [5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5]]=>10110 [5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5]]=>01110 [5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>11110 [6,1,2,3,4,5]=>[[1,2,3,4,5],[6]]=>00001 [6,1,2,3,5,4]=>[[1,2,3,4],[5],[6]]=>00011 [6,1,2,4,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [6,1,2,4,5,3]=>[[1,2,3,5],[4],[6]]=>00101 [6,1,2,5,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [6,1,2,5,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,1,3,2,4,5]=>[[1,2,4,5],[3],[6]]=>01001 [6,1,3,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [6,1,3,4,2,5]=>[[1,2,4,5],[3],[6]]=>01001 [6,1,3,4,5,2]=>[[1,2,4,5],[3],[6]]=>01001 [6,1,3,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [6,1,3,5,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [6,1,4,2,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [6,1,4,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [6,1,4,3,2,5]=>[[1,2,5],[3],[4],[6]]=>01101 [6,1,4,3,5,2]=>[[1,2,5],[3],[4],[6]]=>01101 [6,1,4,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [6,1,4,5,3,2]=>[[1,2,5],[3],[4],[6]]=>01101 [6,1,5,2,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [6,1,5,2,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,1,5,3,2,4]=>[[1,2,4],[3],[5],[6]]=>01011 [6,1,5,3,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [6,1,5,4,2,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,1,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]=>01111 [6,2,1,3,4,5]=>[[1,3,4,5],[2],[6]]=>10001 [6,2,1,3,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [6,2,1,4,3,5]=>[[1,3,5],[2,4],[6]]=>10101 [6,2,1,4,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [6,2,1,5,3,4]=>[[1,3,4],[2,5],[6]]=>10011 [6,2,1,5,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [6,2,3,1,4,5]=>[[1,3,4,5],[2],[6]]=>10001 [6,2,3,1,5,4]=>[[1,3,4],[2,5],[6]]=>10011 [6,2,3,4,1,5]=>[[1,3,4,5],[2],[6]]=>10001 [6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>10001 [6,2,3,5,1,4]=>[[1,3,4],[2,5],[6]]=>10011 [6,2,3,5,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [6,2,4,1,3,5]=>[[1,3,5],[2,4],[6]]=>10101 [6,2,4,1,5,3]=>[[1,3,5],[2,4],[6]]=>10101 [6,2,4,3,1,5]=>[[1,3,5],[2],[4],[6]]=>10101 [6,2,4,3,5,1]=>[[1,3,5],[2],[4],[6]]=>10101 [6,2,4,5,1,3]=>[[1,3,5],[2,4],[6]]=>10101 [6,2,4,5,3,1]=>[[1,3,5],[2],[4],[6]]=>10101 [6,2,5,1,3,4]=>[[1,3,4],[2,5],[6]]=>10011 [6,2,5,1,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [6,2,5,3,1,4]=>[[1,3,4],[2],[5],[6]]=>10011 [6,2,5,3,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [6,2,5,4,1,3]=>[[1,3],[2,4],[5],[6]]=>10111 [6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]=>10111 [6,3,1,2,4,5]=>[[1,2,4,5],[3],[6]]=>01001 [6,3,1,2,5,4]=>[[1,2,4],[3,5],[6]]=>01011 [6,3,1,4,2,5]=>[[1,2,5],[3,4],[6]]=>01001 [6,3,1,4,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [6,3,1,5,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [6,3,1,5,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,2,1,5,4]=>[[1,4],[2,5],[3],[6]]=>11011 [6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,2,5,1,4]=>[[1,4],[2,5],[3],[6]]=>11011 [6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6]]=>11011 [6,3,4,1,2,5]=>[[1,2,5],[3,4],[6]]=>01001 [6,3,4,1,5,2]=>[[1,2,5],[3,4],[6]]=>01001 [6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,4,5,1,2]=>[[1,2,5],[3,4],[6]]=>01001 [6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6]]=>11001 [6,3,5,1,2,4]=>[[1,2,4],[3,5],[6]]=>01011 [6,3,5,1,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [6,3,5,2,1,4]=>[[1,4],[2,5],[3],[6]]=>11011 [6,3,5,2,4,1]=>[[1,4],[2,5],[3],[6]]=>11011 [6,3,5,4,1,2]=>[[1,2],[3,4],[5],[6]]=>01011 [6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>11011 [6,4,1,2,3,5]=>[[1,2,3,5],[4],[6]]=>00101 [6,4,1,2,5,3]=>[[1,2,3],[4,5],[6]]=>00101 [6,4,1,3,2,5]=>[[1,2,5],[3],[4],[6]]=>01101 [6,4,1,3,5,2]=>[[1,2,5],[3],[4],[6]]=>01101 [6,4,1,5,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [6,4,1,5,3,2]=>[[1,2],[3,5],[4],[6]]=>01101 [6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6]]=>10101 [6,4,2,1,5,3]=>[[1,3],[2,5],[4],[6]]=>10101 [6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6]]=>10101 [6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6]]=>10101 [6,4,2,5,1,3]=>[[1,3],[2,5],[4],[6]]=>10101 [6,4,2,5,3,1]=>[[1,3],[2,5],[4],[6]]=>10101 [6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6]]=>01101 [6,4,3,1,5,2]=>[[1,2],[3,5],[4],[6]]=>01101 [6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6]]=>11101 [6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]=>11101 [6,4,3,5,1,2]=>[[1,2],[3,5],[4],[6]]=>01101 [6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6]]=>11101 [6,4,5,1,2,3]=>[[1,2,3],[4,5],[6]]=>00101 [6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6]]=>01101 [6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6]]=>10101 [6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6]]=>10101 [6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6]]=>01101 [6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]=>11101 [6,5,1,2,3,4]=>[[1,2,3,4],[5],[6]]=>00011 [6,5,1,2,4,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,5,1,3,2,4]=>[[1,2,4],[3],[5],[6]]=>01011 [6,5,1,3,4,2]=>[[1,2,4],[3],[5],[6]]=>01011 [6,5,1,4,2,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,5,1,4,3,2]=>[[1,2],[3],[4],[5],[6]]=>01111 [6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6]]=>10011 [6,5,2,1,4,3]=>[[1,3],[2,4],[5],[6]]=>10111 [6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6]]=>10011 [6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6]]=>10011 [6,5,2,4,1,3]=>[[1,3],[2,4],[5],[6]]=>10111 [6,5,2,4,3,1]=>[[1,3],[2],[4],[5],[6]]=>10111 [6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6]]=>01011 [6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6]]=>01011 [6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6]]=>11011 [6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6]]=>11011 [6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6]]=>01011 [6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>11011 [6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6]]=>00111 [6,5,4,1,3,2]=>[[1,2],[3],[4],[5],[6]]=>01111 [6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6]]=>10111 [6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6]]=>10111 [6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6]]=>01111 [6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]=>11111 [1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>000000 [1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]=>000001 [1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6]]=>000010 [1,2,3,4,6,7,5]=>[[1,2,3,4,5,7],[6]]=>000010 [1,2,3,4,7,5,6]=>[[1,2,3,4,5,6],[7]]=>000001 [1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5]]=>000100 [1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,2,3,5,6,4,7]=>[[1,2,3,4,6,7],[5]]=>000100 [1,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5]]=>000100 [1,2,3,5,7,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,2,3,5,7,6,4]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,3,6,4,5,7]=>[[1,2,3,4,5,7],[6]]=>000010 [1,2,3,6,4,7,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,3,6,5,7,4]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,2,3,6,7,5,4]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,3,7,4,5,6]=>[[1,2,3,4,5,6],[7]]=>000001 [1,2,3,7,4,6,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,3,7,5,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,3,7,6,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>001000 [1,2,4,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [1,2,4,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>001010 [1,2,4,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,2,4,5,3,6,7]=>[[1,2,3,5,6,7],[4]]=>001000 [1,2,4,5,3,7,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,2,4,5,6,3,7]=>[[1,2,3,5,6,7],[4]]=>001000 [1,2,4,5,6,7,3]=>[[1,2,3,5,6,7],[4]]=>001000 [1,2,4,5,7,3,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,2,4,5,7,6,3]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,4,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [1,2,4,6,3,7,5]=>[[1,2,3,5,7],[4,6]]=>001010 [1,2,4,6,5,3,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,4,6,5,7,3]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,4,6,7,3,5]=>[[1,2,3,5,7],[4,6]]=>001010 [1,2,4,6,7,5,3]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,4,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,2,4,7,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,2,4,7,5,3,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,4,7,5,6,3]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,4,7,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,2,4,7,6,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,2,5,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>000100 [1,2,5,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,2,5,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [1,2,5,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>000100 [1,2,5,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,2,5,3,7,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,2,5,4,6,3,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,4,6,7,3]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,4,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,2,5,4,7,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [1,2,5,6,3,7,4]=>[[1,2,3,4,7],[5,6]]=>000100 [1,2,5,6,4,3,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,6,4,7,3]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,6,7,3,4]=>[[1,2,3,4,7],[5,6]]=>000100 [1,2,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,2,5,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,2,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,2,5,7,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,2,5,7,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,2,5,7,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,2,5,7,6,4,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,2,6,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>000010 [1,2,6,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,2,6,3,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,6,3,5,7,4]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,6,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,2,6,3,7,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,2,6,4,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,6,4,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,2,6,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,6,4,5,7,3]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,2,6,4,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,2,6,4,7,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,2,6,5,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,2,6,5,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,2,6,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,2,6,5,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,2,6,5,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,2,6,5,7,4,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,2,6,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,2,6,7,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,2,6,7,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,2,6,7,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,2,6,7,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,2,6,7,5,4,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,2,7,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>000001 [1,2,7,3,4,6,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,7,3,5,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,7,3,5,6,4]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,7,3,6,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,7,3,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,2,7,4,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,7,4,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,2,7,4,5,3,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,2,7,4,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,2,7,4,6,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,2,7,5,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,2,7,5,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,2,7,5,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,2,7,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,2,7,5,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,2,7,5,6,4,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,2,7,6,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,2,7,6,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,2,7,6,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,2,7,6,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,2,7,6,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>010000 [1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,2,4,6,7,5]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,2,4,7,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>010101 [1,3,2,5,6,4,7]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,2,5,6,7,4]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,2,5,7,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [1,3,2,5,7,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,2,6,4,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,2,6,4,7,5]=>[[1,2,4,5],[3,6,7]]=>010010 [1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,2,6,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [1,3,2,6,7,5,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,2,7,4,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,2,7,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,2,7,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,2,7,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,3,4,2,5,6,7]=>[[1,2,4,5,6,7],[3]]=>010000 [1,3,4,2,5,7,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,4,2,6,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,4,2,6,7,5]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,4,2,7,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,4,2,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,4,5,2,6,7]=>[[1,2,4,5,6,7],[3]]=>010000 [1,3,4,5,2,7,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,4,5,6,2,7]=>[[1,2,4,5,6,7],[3]]=>010000 [1,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3]]=>010000 [1,3,4,5,7,2,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,4,5,7,6,2]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,4,6,2,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,4,6,2,7,5]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,4,6,5,2,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,4,6,5,7,2]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,4,6,7,2,5]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,4,6,7,5,2]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,4,7,2,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,4,7,2,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,4,7,5,2,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,4,7,5,6,2]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,4,7,6,2,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,4,7,6,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,3,5,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>010101 [1,3,5,2,6,4,7]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,2,6,7,4]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [1,3,5,2,7,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,5,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,3,5,4,6,2,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,4,6,7,2]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,4,7,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,3,5,4,7,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,3,5,6,2,4,7]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,6,2,7,4]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,6,4,2,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,6,4,7,2]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,6,7,2,4]=>[[1,2,4,6,7],[3,5]]=>010100 [1,3,5,6,7,4,2]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,3,5,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [1,3,5,7,2,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,5,7,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,3,5,7,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,3,5,7,6,2,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,5,7,6,4,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,3,6,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [1,3,6,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>010010 [1,3,6,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [1,3,6,2,7,5,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,4,2,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,6,4,2,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,3,6,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,6,4,5,7,2]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,3,6,4,7,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,3,6,4,7,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,3,6,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,5,2,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,5,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,3,6,5,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,3,6,5,7,2,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,5,7,4,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,3,6,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [1,3,6,7,2,5,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,7,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,3,6,7,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,3,6,7,5,2,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,3,6,7,5,4,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,3,7,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [1,3,7,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,7,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,7,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,7,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,7,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,3,7,4,2,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,7,4,2,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,7,4,5,2,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,7,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,3,7,4,6,2,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,7,4,6,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,3,7,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,7,5,2,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,7,5,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,3,7,5,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,3,7,5,6,2,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,3,7,5,6,4,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,3,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,3,7,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,3,7,6,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,3,7,6,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,3,7,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,3,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [1,4,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>001000 [1,4,2,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,4,2,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [1,4,2,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>001010 [1,4,2,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,4,2,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,2,5,3,7,6]=>[[1,2,3,6],[4,5,7]]=>001001 [1,4,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,2,5,7,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [1,4,2,5,7,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,2,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [1,4,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]=>001010 [1,4,2,6,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,2,6,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,2,6,7,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [1,4,2,6,7,5,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,2,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,4,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,2,7,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,2,7,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,2,7,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,2,7,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,2,6,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,2,7,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [1,4,3,5,2,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,3,5,2,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,5,6,2,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,3,5,7,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,6,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,6,2,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,6,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,6,7,2,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,6,7,5,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,3,7,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [1,4,3,7,5,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,7,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,3,7,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [1,4,3,7,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>001001 [1,4,5,2,6,3,7]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,2,6,7,3]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [1,4,5,2,7,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,5,3,2,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,3,2,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,5,3,6,2,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,3,6,7,2]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,3,7,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,5,3,7,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,5,6,2,3,7]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,6,2,7,3]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,6,3,2,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,6,3,7,2]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,6,7,2,3]=>[[1,2,3,6,7],[4,5]]=>001000 [1,4,5,6,7,3,2]=>[[1,2,5,6,7],[3],[4]]=>011000 [1,4,5,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [1,4,5,7,2,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,5,7,3,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,5,7,3,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,5,7,6,2,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,5,7,6,3,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,4,6,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [1,4,6,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>001010 [1,4,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [1,4,6,2,7,5,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,3,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,3,2,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,3,7,2,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,3,7,5,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,5,2,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,5,3,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,4,6,5,3,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,4,6,5,7,2,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,5,7,3,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,4,6,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [1,4,6,7,2,5,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,7,3,2,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,7,3,5,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [1,4,6,7,5,2,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,4,6,7,5,3,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,4,7,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [1,4,7,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,7,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,7,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,4,7,3,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,7,3,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [1,4,7,3,5,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,7,3,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [1,4,7,3,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [1,4,7,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,4,7,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,7,5,2,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,7,5,3,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,4,7,5,3,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,4,7,5,6,2,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,4,7,5,6,3,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,4,7,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,4,7,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,4,7,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,4,7,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,4,7,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,4,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [1,5,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>000100 [1,5,2,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,5,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [1,5,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>000100 [1,5,2,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,5,2,3,7,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,2,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,5,2,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,2,4,6,3,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,5,2,4,6,7,3]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,5,2,4,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,2,4,7,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,2,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [1,5,2,6,3,7,4]=>[[1,2,3,4],[5,6,7]]=>000100 [1,5,2,6,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,2,6,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,2,6,7,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [1,5,2,6,7,4,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,2,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,5,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,2,7,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,2,7,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,2,7,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,2,7,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,5,3,2,4,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,5,3,2,4,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,2,6,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,2,6,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,2,7,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,2,7,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [1,5,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,5,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,4,6,2,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,5,3,4,6,7,2]=>[[1,2,4,6,7],[3],[5]]=>010100 [1,5,3,4,7,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,4,7,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,6,2,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,6,4,2,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,6,4,7,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,6,7,2,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,6,7,4,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,3,7,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [1,5,3,7,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,3,7,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [1,5,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,5,4,2,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [1,5,4,2,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,4,2,6,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,4,2,6,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,4,2,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,4,2,7,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [1,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,4,3,6,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,3,7,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,4,3,7,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,4,6,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,4,6,2,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,4,6,3,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,6,3,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,6,7,2,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,4,6,7,3,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,4,7,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,4,7,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [1,5,4,7,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,4,7,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,4,7,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [1,5,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,6,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [1,5,6,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>000100 [1,5,6,2,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,2,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [1,5,6,2,7,4,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,3,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,3,2,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,3,4,2,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,3,7,2,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,3,7,4,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,4,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,4,2,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,4,3,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,6,4,3,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,6,4,7,2,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,4,7,3,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [1,5,6,7,2,4,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,7,3,2,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,7,3,4,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [1,5,6,7,4,2,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [1,5,6,7,4,3,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [1,5,7,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [1,5,7,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,7,2,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,5,7,3,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,7,3,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [1,5,7,3,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,7,3,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [1,5,7,3,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [1,5,7,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,5,7,4,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [1,5,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [1,5,7,4,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,7,4,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,7,4,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [1,5,7,4,6,3,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [1,5,7,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,5,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,5,7,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,5,7,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,5,7,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,5,7,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [1,6,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>000010 [1,6,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,6,2,3,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,6,2,3,5,7,4]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,6,2,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,6,2,3,7,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,2,4,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,6,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,2,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,6,2,4,5,7,3]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,6,2,4,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,2,4,7,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,2,5,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,6,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,2,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,2,5,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,2,5,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,2,5,7,4,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,2,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,6,2,7,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,2,7,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,2,7,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,2,7,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,2,7,5,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,3,2,4,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,6,3,2,4,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,6,3,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,6,3,2,7,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,2,7,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [1,6,3,4,2,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,6,3,4,2,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,6,3,4,5,7,2]=>[[1,2,4,5,7],[3],[6]]=>010010 [1,6,3,4,7,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,4,7,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,6,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,6,3,5,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,3,5,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,3,5,7,2,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [1,6,3,5,7,4,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,7,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [1,6,3,7,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,7,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [1,6,3,7,5,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,4,2,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [1,6,4,2,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,4,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,6,4,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,6,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,4,2,7,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [1,6,4,3,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,3,2,7,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,4,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,3,5,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,3,7,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,4,3,7,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,4,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,6,4,5,2,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,6,4,5,3,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,5,3,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,5,7,2,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [1,6,4,5,7,3,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [1,6,4,7,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [1,6,4,7,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,4,7,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,4,7,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [1,6,4,7,5,3,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,5,2,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [1,6,5,2,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,5,2,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,5,2,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,5,2,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,5,2,7,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,5,3,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,5,3,2,7,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,5,3,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,5,3,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [1,6,5,3,7,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,5,3,7,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,5,4,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [1,6,5,4,2,7,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [1,6,5,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [1,6,5,4,7,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,5,4,7,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [1,6,5,7,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,5,7,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,5,7,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,5,7,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,5,7,4,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [1,6,7,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [1,6,7,2,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,7,2,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,7,2,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,7,2,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,7,2,5,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,7,3,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,7,3,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [1,6,7,3,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,7,3,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [1,6,7,3,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [1,6,7,3,5,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [1,6,7,4,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [1,6,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,7,4,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [1,6,7,4,5,3,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [1,6,7,5,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [1,6,7,5,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,7,5,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,7,5,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [1,6,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [1,6,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [1,7,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>000001 [1,7,2,3,4,6,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,7,2,3,5,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,7,2,3,5,6,4]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,7,2,3,6,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,7,2,3,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,2,4,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,7,2,4,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,7,2,4,5,3,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,7,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,7,2,4,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,7,2,4,6,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,2,5,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,7,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,7,2,5,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,7,2,5,6,4,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,2,6,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,7,2,6,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,2,6,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,2,6,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,2,6,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [1,7,3,2,4,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,7,3,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,7,3,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,7,3,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,7,3,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,7,3,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,7,3,4,2,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,7,3,4,2,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,7,3,4,5,2,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]=>010001 [1,7,3,4,6,2,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,7,3,4,6,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,3,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,7,3,5,2,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,7,3,5,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,3,5,6,2,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [1,7,3,5,6,4,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,3,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [1,7,3,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,7,3,6,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,3,6,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,3,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,7,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [1,7,4,2,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [1,7,4,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,7,4,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,7,4,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,7,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,7,4,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,7,4,3,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,3,2,6,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,7,4,3,5,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,3,6,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,7,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,7,4,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,7,4,5,2,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,7,4,5,3,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,5,3,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,5,6,2,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [1,7,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [1,7,4,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [1,7,4,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,7,4,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,7,4,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [1,7,4,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,7,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [1,7,5,2,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [1,7,5,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,7,5,2,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,5,2,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,5,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,7,5,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,7,5,3,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,5,3,2,6,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,7,5,3,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,5,3,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [1,7,5,3,6,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,7,5,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,7,5,4,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [1,7,5,4,2,6,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,7,5,4,3,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [1,7,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [1,7,5,4,6,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,7,5,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [1,7,5,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [1,7,5,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,7,5,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,7,5,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [1,7,5,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [1,7,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [1,7,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [1,7,6,2,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,6,2,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,6,2,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,6,2,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,6,2,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [1,7,6,3,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,6,3,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,7,6,3,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,6,3,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [1,7,6,3,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [1,7,6,3,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [1,7,6,4,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [1,7,6,4,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,7,6,4,3,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [1,7,6,4,3,5,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [1,7,6,4,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [1,7,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [1,7,6,5,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [1,7,6,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [1,7,6,5,3,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [1,7,6,5,3,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [1,7,6,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>100000 [2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,1,3,4,6,7,5]=>[[1,3,4,5,7],[2,6]]=>100010 [2,1,3,4,7,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,1,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,3,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,1,3,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,1,3,5,6,4,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,1,3,5,6,7,4]=>[[1,3,4,6,7],[2,5]]=>100100 [2,1,3,5,7,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,1,3,5,7,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,3,6,4,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,1,3,6,4,7,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,3,6,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,1,3,6,7,5,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,3,7,4,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,1,3,7,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,3,7,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,3,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,3,7,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,1,4,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>101010 [2,1,4,3,6,7,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,1,4,3,7,5,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,1,4,5,3,6,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,1,4,5,3,7,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,1,4,5,6,3,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,1,4,5,6,7,3]=>[[1,3,5,6,7],[2,4]]=>101000 [2,1,4,5,7,3,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,1,4,5,7,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,4,6,3,5,7]=>[[1,3,5,7],[2,4,6]]=>101010 [2,1,4,6,3,7,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,1,4,6,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,4,6,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,4,6,7,3,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,1,4,6,7,5,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,4,7,3,5,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,1,4,7,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,1,4,7,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,4,7,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,4,7,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,1,4,7,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,1,5,3,4,6,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,1,5,3,4,7,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,1,5,3,6,4,7]=>[[1,3,4,7],[2,5,6]]=>100100 [2,1,5,3,6,7,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,1,5,3,7,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,1,5,3,7,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,1,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,1,5,4,6,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,4,7,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,1,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>100100 [2,1,5,6,3,7,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,1,5,6,4,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,6,4,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,6,7,3,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,1,5,6,7,4,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,1,5,7,3,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,1,5,7,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,1,5,7,4,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,1,5,7,4,6,3]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,1,5,7,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,1,5,7,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,1,6,3,4,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,1,6,3,4,7,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,1,6,3,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,6,3,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,6,3,7,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,1,6,3,7,5,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,1,6,4,3,5,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,6,4,3,7,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,1,6,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,6,4,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,1,6,4,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,1,6,4,7,5,3]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,1,6,5,3,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,1,6,5,3,7,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,1,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,1,6,5,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,1,6,5,7,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,1,6,5,7,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,1,6,7,3,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,1,6,7,3,5,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,1,6,7,4,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,1,6,7,4,5,3]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,1,6,7,5,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,1,6,7,5,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,1,7,3,4,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,1,7,3,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,7,3,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,7,3,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,7,3,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,7,3,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,1,7,4,3,5,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,7,4,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,1,7,4,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,7,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,1,7,4,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,1,7,4,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,1,7,5,3,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,1,7,5,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,1,7,5,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,1,7,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,1,7,5,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,1,7,5,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,1,7,6,3,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,1,7,6,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,1,7,6,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,1,7,6,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,1,7,6,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>100000 [2,3,1,4,5,7,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,1,4,6,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,1,4,6,7,5]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,1,4,7,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,1,4,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,1,5,4,6,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,1,5,4,7,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,3,1,5,6,4,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,1,5,6,7,4]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,1,5,7,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,3,1,5,7,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,1,6,4,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,1,6,4,7,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,3,1,6,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,1,6,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,1,6,7,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,3,1,6,7,5,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,1,7,4,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,1,7,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,1,7,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,1,7,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,1,7,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2]]=>100000 [2,3,4,1,5,7,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,4,1,6,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,4,1,6,7,5]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,4,1,7,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,4,1,7,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2]]=>100000 [2,3,4,5,1,7,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2]]=>100000 [2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]=>100000 [2,3,4,5,7,1,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,4,6,1,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,4,6,1,7,5]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,4,6,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,4,6,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,4,6,7,1,5]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,4,6,7,5,1]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,4,7,1,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,4,7,1,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,4,7,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,4,7,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,4,7,6,1,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,4,7,6,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,3,5,1,4,6,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,1,4,7,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,3,5,1,6,4,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,1,6,7,4]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,1,7,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,3,5,1,7,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,5,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,3,5,4,6,1,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,4,6,7,1]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,4,7,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,3,5,4,7,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,3,5,6,1,4,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,6,1,7,4]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,6,4,1,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,6,4,7,1]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,6,7,1,4]=>[[1,3,4,6,7],[2,5]]=>100100 [2,3,5,6,7,4,1]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,3,5,7,1,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,3,5,7,1,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,5,7,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,3,5,7,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,3,5,7,6,1,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,3,6,1,4,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,3,6,1,4,7,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,3,6,1,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,1,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,1,7,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,3,6,1,7,5,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,4,1,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,6,4,1,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,3,6,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,6,4,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,3,6,4,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,3,6,4,7,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,3,6,5,1,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,5,1,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,3,6,5,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,3,6,5,7,1,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,5,7,4,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,3,6,7,1,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,3,6,7,1,5,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,7,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,3,6,7,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,3,6,7,5,1,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,3,6,7,5,4,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,3,7,1,4,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,3,7,1,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,7,1,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,7,1,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,7,1,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,7,1,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,3,7,4,1,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,7,4,1,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,7,4,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,7,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,3,7,4,6,1,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,7,4,6,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,3,7,5,1,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,7,5,1,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,7,5,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,3,7,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,3,7,5,6,1,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,3,7,6,1,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,3,7,6,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,3,7,6,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,3,7,6,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,3,7,6,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,3,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [2,4,1,3,5,6,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,1,3,5,7,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,1,3,6,5,7]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,1,3,6,7,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,1,3,7,5,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,1,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,1,5,3,6,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,1,5,3,7,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,1,5,6,3,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,1,5,7,3,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,1,5,7,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,1,6,3,5,7]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,1,6,3,7,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,1,6,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,1,6,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,1,6,7,3,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,1,6,7,5,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,1,7,3,5,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,1,7,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,1,7,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,1,7,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,1,7,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,1,7,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,4,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,1,6,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,1,7,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [2,4,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,3,5,1,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,5,6,1,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,3,5,7,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,5,7,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,6,5,1,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,6,7,1,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,6,7,5,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,3,7,1,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,7,1,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [2,4,3,7,5,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,7,5,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,3,7,6,1,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [2,4,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,4,5,1,3,6,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,1,3,7,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,5,1,6,3,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,1,6,7,3]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,1,7,3,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,5,1,7,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,5,3,1,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,3,1,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,5,3,6,1,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,3,6,7,1]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,3,7,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,5,3,7,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,5,6,1,3,7]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,6,1,7,3]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,6,3,1,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,6,3,7,1]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,6,7,1,3]=>[[1,3,5,6,7],[2,4]]=>101000 [2,4,5,6,7,3,1]=>[[1,3,5,6,7],[2],[4]]=>101000 [2,4,5,7,1,3,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,5,7,1,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,5,7,3,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,5,7,3,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,5,7,6,1,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,5,7,6,3,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,4,6,1,3,5,7]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,6,1,3,7,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,6,1,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,1,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,1,7,3,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,6,1,7,5,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,3,1,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,3,1,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,3,5,1,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,3,5,7,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,3,7,1,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,3,7,5,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,5,1,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,5,1,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,5,3,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,4,6,5,3,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,4,6,5,7,1,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,5,7,3,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,4,6,7,1,3,5]=>[[1,3,5,7],[2,4,6]]=>101010 [2,4,6,7,1,5,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,7,3,1,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,7,3,5,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [2,4,6,7,5,1,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,4,6,7,5,3,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,4,7,1,3,5,6]=>[[1,3,5,6],[2,4,7]]=>101001 [2,4,7,1,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,7,1,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,7,1,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,7,1,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,7,1,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,4,7,3,1,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,7,3,1,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [2,4,7,3,5,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [2,4,7,3,6,1,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [2,4,7,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,4,7,5,1,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,7,5,1,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,7,5,3,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,4,7,5,3,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,4,7,5,6,1,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,4,7,5,6,3,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,4,7,6,1,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,4,7,6,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,4,7,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,4,7,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,4,7,6,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,4,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [2,5,1,3,4,6,7]=>[[1,3,4,6,7],[2,5]]=>100100 [2,5,1,3,4,7,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,5,1,3,6,4,7]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,1,3,6,7,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,1,3,7,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,5,1,3,7,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,1,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,1,4,6,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,4,6,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,4,7,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,1,4,7,6,3]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,1,6,3,4,7]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,1,6,3,7,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,1,6,4,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,6,4,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,6,7,3,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,1,6,7,4,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,1,7,3,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,5,1,7,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,1,7,4,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,1,7,4,6,3]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,1,7,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,1,7,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,5,3,1,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,5,3,1,4,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,1,6,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,1,6,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,1,7,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,1,7,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [2,5,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,5,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,5,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5]]=>100100 [2,5,3,4,7,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,4,7,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,6,1,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,6,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,6,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,6,7,1,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,3,7,1,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [2,5,3,7,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,7,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,3,7,6,1,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [2,5,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,5,4,1,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,1,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,4,1,6,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,1,7,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [2,5,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,3,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,4,3,6,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,3,7,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,4,6,1,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,6,1,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,6,3,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,6,3,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,6,7,1,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,4,6,7,3,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,4,7,1,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,4,7,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [2,5,4,7,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,4,7,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,4,7,6,1,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [2,5,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,6,1,3,4,7]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,6,1,3,7,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,6,1,4,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,1,4,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,1,7,3,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,6,1,7,4,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,3,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,3,1,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,3,7,1,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,3,7,4,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,4,1,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,4,1,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,4,3,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,6,4,3,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,6,4,7,1,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,4,7,3,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,6,7,1,3,4]=>[[1,3,4,7],[2,5,6]]=>100100 [2,5,6,7,1,4,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,7,3,1,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,7,3,4,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [2,5,6,7,4,1,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [2,5,6,7,4,3,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [2,5,7,1,3,4,6]=>[[1,3,4,6],[2,5,7]]=>100101 [2,5,7,1,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,7,1,4,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,7,1,4,6,3]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,7,1,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,7,1,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,5,7,3,1,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,7,3,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [2,5,7,3,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,7,3,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [2,5,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [2,5,7,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,5,7,4,1,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [2,5,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [2,5,7,4,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,7,4,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [2,5,7,4,6,3,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [2,5,7,6,1,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,5,7,6,1,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,5,7,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,5,7,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,5,7,6,4,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,5,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [2,6,1,3,4,5,7]=>[[1,3,4,5,7],[2,6]]=>100010 [2,6,1,3,4,7,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,6,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,1,3,7,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,6,1,3,7,5,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,1,4,3,7,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,1,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,1,4,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,1,4,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,1,4,7,5,3]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,1,5,3,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,1,5,3,7,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,1,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,1,5,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,1,5,7,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,1,5,7,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,1,7,3,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,6,1,7,3,5,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,1,7,4,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,1,7,4,5,3]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,1,7,5,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,1,7,5,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,3,1,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,6,3,1,4,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,1,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,3,1,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,3,1,7,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,1,7,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [2,6,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,6,3,4,1,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,6,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>100010 [2,6,3,4,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,4,7,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,5,1,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,3,5,1,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,3,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,3,5,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,3,5,7,1,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,3,5,7,4,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,3,7,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [2,6,3,7,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,7,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,3,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [2,6,3,7,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,4,1,3,5,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,1,3,7,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,4,1,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,1,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,1,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,4,1,7,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [2,6,4,3,1,5,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,3,1,7,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,3,5,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,3,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,4,3,7,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,4,5,1,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,5,1,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,5,3,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,5,7,1,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [2,6,4,5,7,3,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [2,6,4,7,1,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [2,6,4,7,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,4,7,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [2,6,4,7,5,3,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,5,1,3,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [2,6,5,1,3,7,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,5,1,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,1,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,1,7,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,5,1,7,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,3,1,4,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,5,3,1,7,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,5,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,5,3,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [2,6,5,3,7,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,5,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,5,4,1,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,4,1,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [2,6,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [2,6,5,4,7,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,4,7,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [2,6,5,7,1,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,5,7,1,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,7,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,5,7,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,5,7,4,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,5,7,4,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [2,6,7,1,3,4,5]=>[[1,3,4,5],[2,6,7]]=>100010 [2,6,7,1,3,5,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,7,1,4,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,7,1,4,5,3]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,7,1,5,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,7,1,5,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,7,3,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,7,3,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [2,6,7,3,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,7,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [2,6,7,3,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [2,6,7,3,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,7,4,1,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [2,6,7,4,1,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [2,6,7,4,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,7,4,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [2,6,7,4,5,3,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [2,6,7,5,1,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [2,6,7,5,1,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,7,5,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,7,5,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [2,6,7,5,4,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [2,6,7,5,4,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [2,7,1,3,4,5,6]=>[[1,3,4,5,6],[2,7]]=>100001 [2,7,1,3,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,1,3,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,1,3,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,1,3,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,1,3,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,1,4,3,5,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,1,4,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,7,1,4,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,1,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,1,4,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,7,1,4,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,1,5,3,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,1,5,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,7,1,5,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,1,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,1,5,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,7,1,5,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,1,6,3,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,1,6,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,1,6,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,1,6,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,1,6,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [2,7,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,7,3,1,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,3,1,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,3,1,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,3,1,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,3,1,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,7,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,7,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>100001 [2,7,3,4,6,1,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,3,4,6,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,3,5,1,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,3,5,1,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,3,5,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,3,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,3,5,6,1,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,3,5,6,4,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,3,6,1,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,3,6,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,3,6,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,3,6,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,3,6,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,3,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [2,7,4,1,3,5,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,1,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,7,4,1,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,1,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,1,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,7,4,1,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,4,3,1,5,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,3,1,6,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,7,4,3,5,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,3,6,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,7,4,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,7,4,5,1,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,5,1,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,5,3,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,5,3,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [2,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [2,7,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [2,7,4,6,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,4,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,7,4,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [2,7,4,6,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [2,7,5,1,3,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [2,7,5,1,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,7,5,1,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,1,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,1,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,7,5,1,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,3,1,4,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,5,3,1,6,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,7,5,3,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,5,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [2,7,5,3,6,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,7,5,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,7,5,4,1,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,4,1,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,4,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [2,7,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [2,7,5,4,6,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [2,7,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [2,7,5,6,1,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,7,5,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [2,7,5,6,4,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [2,7,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [2,7,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [2,7,6,1,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,6,1,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,6,1,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,6,1,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,6,1,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [2,7,6,3,1,4,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,6,3,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,6,3,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,6,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [2,7,6,3,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,6,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [2,7,6,4,1,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,6,4,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,6,4,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [2,7,6,4,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [2,7,6,4,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [2,7,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [2,7,6,5,1,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [2,7,6,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [2,7,6,5,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [2,7,6,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [2,7,6,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>010000 [3,1,2,4,5,7,6]=>[[1,2,4,5,6],[3,7]]=>010001 [3,1,2,4,6,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [3,1,2,4,6,7,5]=>[[1,2,4,5,7],[3,6]]=>010010 [3,1,2,4,7,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [3,1,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,2,5,4,6,7]=>[[1,2,4,6,7],[3,5]]=>010100 [3,1,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,1,2,5,6,4,7]=>[[1,2,4,6,7],[3,5]]=>010100 [3,1,2,5,6,7,4]=>[[1,2,4,6,7],[3,5]]=>010100 [3,1,2,5,7,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,1,2,5,7,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,2,6,4,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [3,1,2,6,4,7,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,1,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,2,6,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,2,6,7,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,1,2,6,7,5,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,2,7,4,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [3,1,2,7,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,2,7,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,2,7,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,1,4,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,1,4,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,1,4,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>010010 [3,1,4,2,6,7,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,1,4,2,7,5,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,1,4,2,7,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,1,4,5,2,6,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,1,4,5,2,7,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,1,4,5,6,2,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4]]=>010000 [3,1,4,5,7,2,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,1,4,5,7,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,4,6,2,5,7]=>[[1,2,5,7],[3,4,6]]=>010010 [3,1,4,6,2,7,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,1,4,6,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,4,6,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,4,6,7,2,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,1,4,6,7,5,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,4,7,2,5,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,1,4,7,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,1,4,7,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,4,7,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,4,7,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,1,4,7,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,1,5,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>010100 [3,1,5,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,1,5,2,6,4,7]=>[[1,2,4,7],[3,5,6]]=>010100 [3,1,5,2,6,7,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,1,5,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,1,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,1,5,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,4,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,1,5,4,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,4,7,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,1,5,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>010100 [3,1,5,6,2,7,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,1,5,6,4,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,6,4,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,6,7,2,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,1,5,6,7,4,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,1,5,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,1,5,7,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,1,5,7,4,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,1,5,7,4,6,2]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,1,5,7,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,1,5,7,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,1,6,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [3,1,6,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,1,6,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,6,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,6,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,1,6,2,7,5,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,1,6,4,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,6,4,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,1,6,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,6,4,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,1,6,4,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,1,6,4,7,5,2]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,1,6,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,1,6,5,2,7,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,1,6,5,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,1,6,5,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,1,6,5,7,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,1,6,5,7,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,1,6,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,1,6,7,2,5,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,1,6,7,4,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,1,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,1,6,7,5,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,1,6,7,5,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,1,7,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [3,1,7,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,7,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,7,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,7,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,7,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,1,7,4,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,7,4,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,1,7,4,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,7,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,1,7,4,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,1,7,4,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,1,7,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,1,7,5,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,1,7,5,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,1,7,5,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,1,7,5,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,1,7,5,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,1,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,1,7,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,1,7,6,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,1,7,6,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,1,7,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,1,4,6,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,1,4,7,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,1,5,6,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,1,5,6,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,1,5,7,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,1,5,7,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,1,6,4,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,1,6,4,7,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,1,6,5,7,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,1,6,7,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,1,6,7,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,1,7,4,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,1,7,4,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,1,7,5,4,6]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,1,7,5,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,1,7,6,4,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,2,4,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,2,4,1,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,1,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,1,6,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,1,7,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,1,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,4,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,2,4,5,1,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,2,4,5,7,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,5,7,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,6,1,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,6,1,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,6,5,1,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,6,5,7,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,6,7,1,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,6,7,5,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,4,7,1,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,7,1,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,4,7,5,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,7,5,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,4,7,6,1,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,4,7,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,2,5,1,4,6,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,1,4,7,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,1,6,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,1,6,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,1,7,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,1,7,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,5,4,1,6,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,4,1,7,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,4,6,1,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,4,6,7,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,4,7,1,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,6,1,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,6,1,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,6,4,1,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,6,4,7,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,6,7,1,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,6,7,4,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,2,5,7,1,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,7,1,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,5,7,4,1,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,7,4,6,1]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,2,5,7,6,1,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,5,7,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,2,6,1,4,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,6,1,4,7,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,1,5,4,7]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,1,5,7,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,1,7,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,1,7,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,4,1,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,6,4,1,7,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,4,5,1,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,6,4,5,7,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,2,6,4,7,1,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,4,7,5,1]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,5,1,4,7]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,5,1,7,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,2,6,5,4,7,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,2,6,5,7,1,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,5,7,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,2,6,7,1,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,7,1,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,7,4,1,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,7,4,5,1]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,2,6,7,5,1,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,2,6,7,5,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,2,7,1,4,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,7,1,4,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,7,1,5,4,6]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,7,1,5,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,7,1,6,4,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,7,1,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,2,7,4,1,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,7,4,1,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,7,4,5,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,7,4,5,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,2,7,4,6,1,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,7,4,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,2,7,5,1,4,6]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,7,5,1,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,7,5,4,1,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,2,7,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,2,7,5,6,1,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,2,7,5,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,2,7,6,1,4,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,2,7,6,1,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,2,7,6,4,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,2,7,6,4,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,2,7,6,5,1,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,1,2,6,5,7]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,1,2,6,7,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,1,2,7,5,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,1,2,7,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,1,5,2,6,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,1,5,2,7,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,1,5,6,2,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,1,5,6,7,2]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,1,5,7,2,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,1,5,7,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,1,6,2,5,7]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,1,6,2,7,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,1,6,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,1,6,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,1,6,7,2,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,1,6,7,5,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,1,7,2,5,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,1,7,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,1,7,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,1,7,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,1,7,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,1,7,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,2,1,5,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,1,6,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,1,6,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,1,7,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,1,7,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,4,2,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,2,5,1,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,2,5,7,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,5,7,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,6,1,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,6,1,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,6,5,1,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,6,5,7,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,6,7,1,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,6,7,5,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,2,7,1,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,7,1,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,4,2,7,5,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,7,5,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,2,7,6,1,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,4,2,7,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,4,5,1,2,6,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,1,2,7,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,5,1,6,2,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,1,6,7,2]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,1,7,2,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,5,1,7,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,2,1,7,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,5,2,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,2,7,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,5,2,7,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,6,1,7,2]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,6,2,1,7]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,6,2,7,1]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4]]=>010000 [3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3]]=>110000 [3,4,5,7,1,2,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,5,7,1,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,5,7,2,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,5,7,2,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,5,7,6,1,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,5,7,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,4,6,1,2,5,7]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,6,1,2,7,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,6,1,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,1,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,1,7,2,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,6,1,7,5,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,2,1,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,2,1,7,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,2,5,1,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,2,5,7,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,2,7,1,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,2,7,5,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,5,1,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,5,1,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,4,6,5,2,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,4,6,5,7,1,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,4,6,7,1,2,5]=>[[1,2,5,7],[3,4,6]]=>010010 [3,4,6,7,1,5,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,7,2,1,5]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,7,2,5,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,4,6,7,5,1,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,4,6,7,5,2,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,4,7,1,2,5,6]=>[[1,2,5,6],[3,4,7]]=>010001 [3,4,7,1,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,7,1,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,7,1,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,7,1,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,7,1,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,4,7,2,1,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,7,2,1,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,4,7,2,5,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,7,2,5,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,4,7,2,6,1,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,4,7,2,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,4,7,5,1,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,7,5,1,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,7,5,2,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,4,7,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,4,7,5,6,1,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,4,7,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,4,7,6,1,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,4,7,6,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,4,7,6,2,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,4,7,6,2,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,4,7,6,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,4,7,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [3,5,1,2,4,6,7]=>[[1,2,4,6,7],[3,5]]=>010100 [3,5,1,2,4,7,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,5,1,2,6,4,7]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,1,2,6,7,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,1,2,7,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,5,1,2,7,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,1,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,4,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,1,4,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,4,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,4,7,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,1,4,7,6,2]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,1,6,2,7,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,1,6,4,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,6,4,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,6,7,2,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,1,6,7,4,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,1,7,2,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,5,1,7,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,1,7,4,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,1,7,4,6,2]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,1,7,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,1,7,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,5,2,1,4,6,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,1,4,7,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,1,6,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,1,6,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,1,7,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,1,7,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,5,2,4,1,6,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,4,1,7,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,4,6,1,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,4,6,7,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,4,7,1,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,4,7,6,1]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,6,1,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,6,1,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,6,4,1,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,6,4,7,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,6,7,1,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,6,7,4,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,2,7,1,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,7,1,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,5,2,7,4,1,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,7,4,6,1]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,2,7,6,1,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,5,2,7,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,5,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,1,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,4,1,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,1,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,1,7,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,4,1,7,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [3,5,4,2,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,2,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,4,2,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,2,7,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,4,6,1,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,6,1,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,6,2,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,4,7,1,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,4,7,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [3,5,4,7,2,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,4,7,2,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,4,7,6,1,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [3,5,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,6,1,2,4,7]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,6,1,2,7,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,6,1,4,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,1,4,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,1,7,2,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,6,1,7,4,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,2,1,4,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,2,1,7,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,2,4,1,7]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,2,4,7,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,2,7,1,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,2,7,4,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,4,1,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,4,1,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,4,2,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,6,4,2,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,6,4,7,1,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,4,7,2,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,6,7,1,2,4]=>[[1,2,4,7],[3,5,6]]=>010100 [3,5,6,7,1,4,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,7,2,1,4]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,7,2,4,1]=>[[1,4,6,7],[2,5],[3]]=>110100 [3,5,6,7,4,1,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [3,5,6,7,4,2,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [3,5,7,1,2,4,6]=>[[1,2,4,6],[3,5,7]]=>010101 [3,5,7,1,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,7,1,4,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,7,1,4,6,2]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,7,1,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,7,1,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,5,7,2,1,4,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,7,2,1,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,5,7,2,4,1,6]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,7,2,4,6,1]=>[[1,4,6],[2,5,7],[3]]=>110101 [3,5,7,2,6,1,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,5,7,2,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,5,7,4,1,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [3,5,7,4,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [3,5,7,4,2,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,7,4,2,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,7,4,6,1,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [3,5,7,4,6,2,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [3,5,7,6,1,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,5,7,6,1,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,5,7,6,2,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,5,7,6,2,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,5,7,6,4,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,5,7,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [3,6,1,2,4,5,7]=>[[1,2,4,5,7],[3,6]]=>010010 [3,6,1,2,4,7,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,6,1,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,6,1,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,6,1,2,7,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,6,1,2,7,5,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,1,4,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,1,4,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,1,4,7,5,2]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,1,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,6,1,5,2,7,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,1,5,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,1,5,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,1,5,7,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,1,5,7,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,1,7,2,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,6,1,7,2,5,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,1,7,4,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,1,7,4,5,2]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,1,7,5,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,1,7,5,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,2,1,4,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,6,2,1,4,7,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,1,5,4,7]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,1,5,7,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,1,7,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,1,7,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,4,1,5,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,6,2,4,1,7,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,4,5,1,7]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,6,2,4,5,7,1]=>[[1,4,5,7],[2,6],[3]]=>110010 [3,6,2,4,7,1,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,4,7,5,1]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,5,1,4,7]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,5,1,7,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,2,5,4,7,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,2,5,7,1,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,5,7,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,2,7,1,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,7,1,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,7,4,1,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,7,4,5,1]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,2,7,5,1,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,2,7,5,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,4,1,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,1,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,4,1,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,1,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,1,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,4,1,7,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [3,6,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,2,1,7,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,4,2,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,2,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,2,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,4,2,7,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,4,5,1,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,5,7,1,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [3,6,4,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [3,6,4,7,1,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,4,7,1,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [3,6,4,7,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,4,7,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,4,7,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [3,6,4,7,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,5,1,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [3,6,5,1,2,7,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,5,1,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,1,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,1,7,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,5,1,7,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,2,1,4,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,2,1,7,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,2,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,2,4,7,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,2,7,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,2,7,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,4,1,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,4,1,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [3,6,5,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [3,6,5,4,7,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [3,6,5,7,1,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,5,7,1,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,7,2,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,7,2,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,5,7,4,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,5,7,4,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [3,6,7,1,2,4,5]=>[[1,2,4,5],[3,6,7]]=>010010 [3,6,7,1,2,5,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,7,1,4,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,7,1,4,5,2]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,7,1,5,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,7,1,5,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,7,2,1,4,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,7,2,1,5,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,7,2,4,1,5]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,7,2,4,5,1]=>[[1,4,5],[2,6,7],[3]]=>110010 [3,6,7,2,5,1,4]=>[[1,4,7],[2,5],[3,6]]=>110110 [3,6,7,2,5,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,7,4,1,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [3,6,7,4,1,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [3,6,7,4,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,7,4,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,7,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [3,6,7,4,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [3,6,7,5,1,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [3,6,7,5,1,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,7,5,2,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,7,5,2,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [3,6,7,5,4,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [3,6,7,5,4,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [3,7,1,2,4,5,6]=>[[1,2,4,5,6],[3,7]]=>010001 [3,7,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,7,1,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,7,1,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,7,1,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,7,1,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,7,1,4,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,7,1,4,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,1,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,7,1,5,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,7,1,5,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,1,5,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,1,5,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,7,1,5,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,1,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,7,1,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,1,6,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,1,6,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,1,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [3,7,2,1,4,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,7,2,1,4,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,7,2,1,5,4,6]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,7,2,1,5,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,7,2,1,6,4,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,7,2,1,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,7,2,4,1,5,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,7,2,4,1,6,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,7,2,4,5,1,6]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,7,2,4,5,6,1]=>[[1,4,5,6],[2,7],[3]]=>110001 [3,7,2,4,6,1,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,7,2,4,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,2,5,1,4,6]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,7,2,5,1,6,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,7,2,5,4,1,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,2,5,6,1,4]=>[[1,4,6],[2,5],[3,7]]=>110101 [3,7,2,5,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,2,6,1,4,5]=>[[1,4,5],[2,6],[3,7]]=>110011 [3,7,2,6,1,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,7,2,6,4,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,2,6,4,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,2,6,5,1,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,7,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [3,7,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,1,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,7,4,1,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,1,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,1,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,7,4,1,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,2,1,6,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,2,6,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,4,2,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [3,7,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [3,7,4,6,1,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [3,7,4,6,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,4,6,2,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,4,6,2,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,4,6,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [3,7,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [3,7,5,1,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,7,5,1,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,1,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,1,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,7,5,1,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,2,1,4,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,2,1,6,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,2,4,1,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,2,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,2,6,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,2,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,4,1,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,4,1,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [3,7,5,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [3,7,5,4,6,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [3,7,5,6,1,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [3,7,5,6,1,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,6,2,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,6,2,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [3,7,5,6,4,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [3,7,5,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [3,7,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [3,7,6,1,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,6,1,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,6,1,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,6,1,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,6,1,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [3,7,6,2,1,4,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,6,2,1,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,7,6,2,4,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,6,2,4,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [3,7,6,2,5,1,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [3,7,6,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [3,7,6,4,1,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,6,4,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,6,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [3,7,6,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [3,7,6,4,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [3,7,6,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [3,7,6,5,1,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [3,7,6,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [3,7,6,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [3,7,6,5,2,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [3,7,6,5,4,1,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [3,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>001000 [4,1,2,3,5,7,6]=>[[1,2,3,5,6],[4,7]]=>001001 [4,1,2,3,6,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [4,1,2,3,6,7,5]=>[[1,2,3,5,7],[4,6]]=>001010 [4,1,2,3,7,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [4,1,2,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]=>001000 [4,1,2,5,3,7,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]=>001000 [4,1,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]=>001000 [4,1,2,5,7,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,1,2,5,7,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,2,6,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [4,1,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,1,2,6,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,2,6,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,2,6,7,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,1,2,6,7,5,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,2,7,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [4,1,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,2,7,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,2,7,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,2,7,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,2,7,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,1,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [4,1,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,2,6,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,2,7,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,1,3,5,2,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [4,1,3,5,2,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,5,6,2,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [4,1,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4]]=>011000 [4,1,3,5,7,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,6,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,6,2,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,6,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,6,7,2,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,6,7,5,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,3,7,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,1,3,7,5,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,7,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,3,7,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,1,3,7,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,1,5,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>001000 [4,1,5,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,1,5,2,6,3,7]=>[[1,2,3,7],[4,5,6]]=>001000 [4,1,5,2,6,7,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,1,5,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,1,5,2,7,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,1,5,3,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,3,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,1,5,3,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,3,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,3,7,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,1,5,3,7,6,2]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,1,5,6,2,3,7]=>[[1,2,3,7],[4,5,6]]=>001000 [4,1,5,6,2,7,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,1,5,6,3,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,6,3,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,6,7,2,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,1,5,6,7,3,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,1,5,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,1,5,7,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,1,5,7,3,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,1,5,7,3,6,2]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,1,5,7,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,1,5,7,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,1,6,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [4,1,6,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,1,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,6,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,6,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,1,6,2,7,5,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,1,6,3,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,6,3,2,7,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,1,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,1,6,3,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,1,6,3,7,5,2]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,1,6,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,1,6,5,2,7,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,1,6,5,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,1,6,5,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,1,6,5,7,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,1,6,5,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,1,6,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,1,6,7,2,5,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,1,6,7,3,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,1,6,7,3,5,2]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,1,6,7,5,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,1,6,7,5,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,1,7,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [4,1,7,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,7,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,7,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,1,7,3,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,7,3,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,1,7,3,5,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,7,3,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,1,7,3,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,1,7,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,1,7,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,1,7,5,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,1,7,5,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,1,7,5,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,1,7,5,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,1,7,5,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,1,7,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,1,7,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,1,7,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,1,7,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,1,7,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,1,7,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [4,2,1,3,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,1,3,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,1,3,6,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,1,3,7,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,1,3,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,1,5,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,1,5,3,7,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,1,5,7,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,1,5,7,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,1,6,3,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,1,6,3,7,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,1,6,5,3,7]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,1,6,5,7,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,1,6,7,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,1,6,7,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,1,7,3,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,1,7,3,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,1,7,5,3,6]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,1,7,5,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,1,7,6,3,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,1,7,6,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [4,2,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,1,6,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,1,7,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [4,2,3,5,1,7,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,5,6,1,7]=>[[1,3,5,6,7],[2],[4]]=>101000 [4,2,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4]]=>101000 [4,2,3,5,7,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,5,7,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,6,5,1,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,6,7,1,5]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,6,7,5,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,3,7,1,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,7,1,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,3,7,5,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,7,5,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,3,7,6,1,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,2,5,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,1,3,7,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,1,6,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,1,6,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,1,7,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,1,7,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,5,3,1,6,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,3,1,7,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,3,6,1,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,3,6,7,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,3,7,1,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,3,7,6,1]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,6,1,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,6,1,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,6,3,1,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,6,3,7,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,6,7,1,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,6,7,3,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,2,5,7,1,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,7,1,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,5,7,3,1,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,7,3,6,1]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,2,5,7,6,1,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,5,7,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,2,6,1,3,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,6,1,3,7,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,1,5,7,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,1,7,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,1,7,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,3,1,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,6,3,1,7,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,3,5,1,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,6,3,5,7,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,2,6,3,7,1,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,3,7,5,1]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,5,1,3,7]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,5,1,7,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,5,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,2,6,5,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,2,6,5,7,1,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,5,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,2,6,7,1,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,7,1,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,7,3,1,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,7,3,5,1]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,2,6,7,5,1,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,2,6,7,5,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,2,7,1,3,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,7,1,3,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,7,1,5,3,6]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,7,1,5,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,7,1,6,3,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,7,1,6,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,2,7,3,1,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,7,3,1,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,7,3,5,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,2,7,3,6,1,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,7,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,2,7,5,1,3,6]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,7,5,1,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,7,5,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,2,7,5,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,2,7,5,6,1,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,2,7,5,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,2,7,6,1,3,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,2,7,6,1,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,2,7,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,2,7,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,2,7,6,5,1,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,2,7,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [4,3,1,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>011000 [4,3,1,2,5,7,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,3,1,2,6,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,3,1,2,6,7,5]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,3,1,2,7,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,3,1,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,1,5,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,1,5,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,3,1,5,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,1,5,7,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,3,1,5,7,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,1,6,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,3,1,6,2,7,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,3,1,6,5,2,7]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,1,6,5,7,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,1,6,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,3,1,6,7,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,1,7,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,3,1,7,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,1,7,5,2,6]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,1,7,5,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,1,7,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,1,7,6,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,2,1,5,7,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,1,6,7,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,1,7,5,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,1,7,6,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,2,5,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,2,5,1,7,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,5,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,2,5,7,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,5,7,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,6,1,5,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,6,1,7,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,6,5,1,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,6,5,7,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,6,7,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,6,7,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,2,7,1,5,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,7,1,6,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,2,7,5,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,7,5,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,2,7,6,1,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,5,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,1,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,3,5,1,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,1,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,1,7,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,3,5,1,7,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,2,1,7,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,2,7,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,5,2,7,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,5,6,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,6,1,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,6,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,3,5,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,3,5,7,1,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,3,5,7,1,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,5,7,2,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,5,7,2,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,5,7,6,1,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,5,7,6,2,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,6,1,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,3,6,1,2,7,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,3,6,1,5,2,7]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,1,5,7,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,1,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,3,6,1,7,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,2,1,5,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,2,1,7,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,2,5,1,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,2,5,7,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,2,7,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,2,7,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,5,1,2,7]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,5,1,7,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,5,2,1,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,5,2,7,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,5,7,1,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,5,7,2,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,7,1,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,3,6,7,1,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,7,2,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,7,2,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,6,7,5,1,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,3,6,7,5,2,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,3,7,1,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,3,7,1,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,7,1,5,2,6]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,7,1,5,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,7,1,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,7,1,6,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,3,7,2,1,5,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,2,1,6,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,7,2,5,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,2,5,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,2,6,1,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,7,2,6,5,1]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,7,5,1,2,6]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,7,5,1,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,7,5,2,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,5,2,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,5,6,1,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,3,7,5,6,2,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,3,7,6,1,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,3,7,6,1,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,3,7,6,2,1,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,7,6,2,5,1]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,3,7,6,5,1,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,3,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [4,5,1,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>001000 [4,5,1,2,3,7,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,5,1,2,6,3,7]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,1,2,6,7,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,1,2,7,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,5,1,2,7,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,1,3,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,3,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,1,3,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,3,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,3,7,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,1,3,7,6,2]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,1,6,2,3,7]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,1,6,2,7,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,1,6,3,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,6,3,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,6,7,2,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,1,6,7,3,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,1,7,2,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,5,1,7,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,1,7,3,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,1,7,3,6,2]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,1,7,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,1,7,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,5,2,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,1,3,7,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,1,6,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,1,6,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,1,7,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,1,7,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,5,2,3,1,6,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,3,1,7,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,3,6,1,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,3,6,7,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,3,7,1,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,3,7,6,1]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,6,1,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,6,1,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,6,3,1,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,6,3,7,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,6,7,1,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,6,7,3,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,2,7,1,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,7,1,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,5,2,7,3,1,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,7,3,6,1]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,2,7,6,1,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,5,2,7,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,5,3,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,1,2,7,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,3,1,6,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,1,6,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,1,7,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,3,1,7,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,2,1,7,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,3,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,2,7,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,3,2,7,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,3,6,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,6,1,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,6,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,3,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,3,7,1,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,3,7,1,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,5,3,7,2,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,3,7,2,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,3,7,6,1,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,5,3,7,6,2,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,6,1,2,7,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,6,1,3,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,1,3,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,1,7,2,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,6,1,7,3,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,2,1,3,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,2,1,7,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,2,3,1,7]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,2,3,7,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,2,7,1,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,2,7,3,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,3,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,3,1,7,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,6,3,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,6,3,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,3,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,6,7,1,2,3]=>[[1,2,3,7],[4,5,6]]=>001000 [4,5,6,7,1,3,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,7,2,1,3]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,7,2,3,1]=>[[1,3,6,7],[2,5],[4]]=>101000 [4,5,6,7,3,1,2]=>[[1,2,6,7],[3,5],[4]]=>011000 [4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4]]=>111000 [4,5,7,1,2,3,6]=>[[1,2,3,6],[4,5,7]]=>001001 [4,5,7,1,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,7,1,3,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,7,1,3,6,2]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,7,1,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,7,1,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,5,7,2,1,3,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,7,2,1,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,5,7,2,3,1,6]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,7,2,3,6,1]=>[[1,3,6],[2,5,7],[4]]=>101001 [4,5,7,2,6,1,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,5,7,2,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,5,7,3,1,2,6]=>[[1,2,6],[3,5,7],[4]]=>011001 [4,5,7,3,1,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,5,7,3,2,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,7,3,2,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,7,3,6,1,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,5,7,3,6,2,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,5,7,6,1,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,5,7,6,1,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,5,7,6,2,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,5,7,6,2,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,5,7,6,3,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,5,7,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [4,6,1,2,3,5,7]=>[[1,2,3,5,7],[4,6]]=>001010 [4,6,1,2,3,7,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,6,1,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,6,1,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,6,1,2,7,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,6,1,2,7,5,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,1,3,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,6,1,3,2,7,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,1,3,5,2,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,6,1,3,5,7,2]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,6,1,3,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,1,3,7,5,2]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,1,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,6,1,5,2,7,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,1,5,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,1,5,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,1,5,7,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,1,5,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,1,7,2,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,6,1,7,2,5,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,1,7,3,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,1,7,3,5,2]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,1,7,5,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,1,7,5,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,2,1,3,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,6,2,1,3,7,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,1,5,3,7]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,1,5,7,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,1,7,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,1,7,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,3,1,5,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,6,2,3,1,7,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,3,5,1,7]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,6,2,3,5,7,1]=>[[1,3,5,7],[2,6],[4]]=>101010 [4,6,2,3,7,1,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,3,7,5,1]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,5,1,3,7]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,5,1,7,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,5,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,2,5,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,2,5,7,1,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,5,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,2,7,1,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,7,1,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,7,3,1,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,7,3,5,1]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,2,7,5,1,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,2,7,5,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,3,1,2,5,7]=>[[1,2,5,7],[3,6],[4]]=>011010 [4,6,3,1,2,7,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,3,1,5,2,7]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,1,5,7,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,1,7,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,3,1,7,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,2,1,5,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,2,1,7,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,2,5,1,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,2,5,7,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,2,7,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,2,7,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,5,1,2,7]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,5,1,7,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,5,2,1,7]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,5,2,7,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,5,7,1,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,5,7,2,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,7,1,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,3,7,1,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,7,2,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,7,2,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,3,7,5,1,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,5,1,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [4,6,5,1,2,7,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,5,1,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,1,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,1,7,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,5,1,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,2,1,3,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,2,1,7,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,2,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,2,7,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,2,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,3,1,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,3,1,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [4,6,5,3,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [4,6,5,3,7,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,3,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [4,6,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,5,7,1,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,7,2,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,7,2,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,5,7,3,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [4,6,7,1,2,3,5]=>[[1,2,3,5],[4,6,7]]=>001010 [4,6,7,1,2,5,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,7,1,3,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,7,1,3,5,2]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,7,1,5,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,7,1,5,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,7,2,1,3,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,7,2,1,5,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,7,2,3,1,5]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,7,2,3,5,1]=>[[1,3,5],[2,6,7],[4]]=>101010 [4,6,7,2,5,1,3]=>[[1,3,7],[2,5],[4,6]]=>101010 [4,6,7,2,5,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,7,3,1,2,5]=>[[1,2,5],[3,6,7],[4]]=>011010 [4,6,7,3,1,5,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,7,3,2,1,5]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,7,3,2,5,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,7,3,5,1,2]=>[[1,2,7],[3,5],[4,6]]=>011010 [4,6,7,3,5,2,1]=>[[1,5,7],[2,6],[3],[4]]=>111010 [4,6,7,5,1,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [4,6,7,5,1,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,7,5,2,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,7,5,2,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [4,6,7,5,3,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [4,6,7,5,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [4,7,1,2,3,5,6]=>[[1,2,3,5,6],[4,7]]=>001001 [4,7,1,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,7,1,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,7,1,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,7,1,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,7,1,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,1,3,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,7,1,3,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,7,1,3,5,2,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,7,1,3,5,6,2]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,7,1,3,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,7,1,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,1,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,7,1,5,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,7,1,5,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,1,5,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,1,5,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,7,1,5,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,7,1,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,1,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,1,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,1,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [4,7,2,1,3,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,7,2,1,3,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,7,2,1,5,3,6]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,7,2,1,5,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,7,2,1,6,3,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,7,2,1,6,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,7,2,3,1,5,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,7,2,3,1,6,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,7,2,3,5,1,6]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,7,2,3,5,6,1]=>[[1,3,5,6],[2,7],[4]]=>101001 [4,7,2,3,6,1,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,7,2,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,2,5,1,3,6]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,7,2,5,1,6,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,7,2,5,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,2,5,6,1,3]=>[[1,3,6],[2,5],[4,7]]=>101001 [4,7,2,5,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,2,6,1,3,5]=>[[1,3,5],[2,6],[4,7]]=>101011 [4,7,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,7,2,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,7,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [4,7,3,1,2,5,6]=>[[1,2,5,6],[3,7],[4]]=>011001 [4,7,3,1,2,6,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,7,3,1,5,2,6]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,7,3,1,5,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,7,3,1,6,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,7,3,1,6,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,7,3,2,1,5,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,2,1,6,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,7,3,2,5,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,2,5,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,2,6,1,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,7,3,2,6,5,1]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,7,3,5,1,2,6]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,7,3,5,1,6,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,7,3,5,2,1,6]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,5,2,6,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,5,6,1,2]=>[[1,2,6],[3,5],[4,7]]=>011001 [4,7,3,5,6,2,1]=>[[1,5,6],[2,7],[3],[4]]=>111001 [4,7,3,6,1,2,5]=>[[1,2,5],[3,6],[4,7]]=>011011 [4,7,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,7,3,6,2,1,5]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,7,3,6,2,5,1]=>[[1,5],[2,6],[3,7],[4]]=>111011 [4,7,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,7,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [4,7,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [4,7,5,1,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,7,5,1,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,1,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,7,5,1,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,2,1,3,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,2,1,6,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,2,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,2,6,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,2,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,3,1,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,3,1,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [4,7,5,3,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [4,7,5,3,6,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,3,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [4,7,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [4,7,5,6,1,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,6,2,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [4,7,5,6,3,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [4,7,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [4,7,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [4,7,6,1,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,6,1,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,6,1,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,6,1,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,6,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [4,7,6,2,1,3,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,6,2,1,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,7,6,2,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,6,2,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [4,7,6,2,5,1,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [4,7,6,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [4,7,6,3,1,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [4,7,6,3,1,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,7,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [4,7,6,3,2,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [4,7,6,3,5,1,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [4,7,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [4,7,6,5,1,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [4,7,6,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [4,7,6,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [4,7,6,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [4,7,6,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [4,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>000100 [5,1,2,3,4,7,6]=>[[1,2,3,4,6],[5,7]]=>000101 [5,1,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [5,1,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]=>000100 [5,1,2,3,7,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [5,1,2,3,7,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,2,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [5,1,2,4,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,2,4,6,3,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [5,1,2,4,6,7,3]=>[[1,2,3,6,7],[4],[5]]=>001100 [5,1,2,4,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,2,4,7,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,2,6,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [5,1,2,6,3,7,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,1,2,6,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,2,6,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,2,6,7,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,1,2,6,7,4,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,2,7,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [5,1,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,2,7,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,2,7,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,2,7,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,2,7,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,1,3,2,4,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [5,1,3,2,4,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,2,6,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,2,6,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,2,7,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,2,7,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,1,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [5,1,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,4,6,2,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [5,1,3,4,6,7,2]=>[[1,2,4,6,7],[3],[5]]=>010100 [5,1,3,4,7,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,4,7,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,6,2,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,6,4,2,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,6,4,7,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,6,7,2,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,6,7,4,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,3,7,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,1,3,7,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,3,7,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,1,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,1,4,2,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [5,1,4,2,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,4,2,6,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,4,2,6,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,4,2,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,4,2,7,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,1,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,4,3,6,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,3,7,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,4,3,7,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,4,6,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,4,6,2,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,4,6,3,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,6,3,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,6,7,2,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,4,6,7,3,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,1,4,7,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,4,7,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,1,4,7,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,4,7,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,4,7,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,1,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,6,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [5,1,6,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,1,6,2,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,6,2,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,6,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,1,6,2,7,4,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,1,6,3,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,6,3,2,7,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,1,6,3,4,2,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,1,6,3,7,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,1,6,3,7,4,2]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,1,6,4,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,1,6,4,2,7,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,1,6,4,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,1,6,4,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,1,6,4,7,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,1,6,4,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,1,6,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,1,6,7,2,4,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,1,6,7,3,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,1,6,7,3,4,2]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,1,6,7,4,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,1,6,7,4,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,1,7,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [5,1,7,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,7,2,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,1,7,3,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,7,3,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,1,7,3,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,7,3,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,1,7,3,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,1,7,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,1,7,4,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,1,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,1,7,4,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,7,4,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,7,4,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,1,7,4,6,3,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,1,7,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,1,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,1,7,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,1,7,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,1,7,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,1,7,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [5,2,1,3,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [5,2,1,3,4,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,1,3,6,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,1,3,6,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,1,3,7,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,1,3,7,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,1,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,1,4,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [5,2,1,4,6,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,1,4,6,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,1,4,7,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [5,2,1,4,7,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,1,6,3,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,1,6,3,7,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,1,6,4,3,7]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,1,6,4,7,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,1,6,7,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,1,6,7,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,1,7,3,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,1,7,3,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,1,7,4,3,6]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,1,7,4,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,1,7,6,3,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,1,7,6,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,2,3,1,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [5,2,3,1,4,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,1,6,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,1,6,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,1,7,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,1,7,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [5,2,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5]]=>100100 [5,2,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5]]=>100100 [5,2,3,4,7,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,4,7,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,6,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,6,1,7,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,6,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,6,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,6,7,1,4]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,3,7,1,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,3,7,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,7,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,3,7,6,1,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,2,4,1,3,6,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,1,3,7,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [5,2,4,1,6,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,1,7,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [5,2,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,3,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,4,3,6,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,3,7,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,4,6,1,3,7]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,6,1,7,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,6,3,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,6,3,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,6,7,1,3]=>[[1,3,6,7],[2,4],[5]]=>101100 [5,2,4,6,7,3,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,2,4,7,1,3,6]=>[[1,3,6],[2,4,7],[5]]=>101101 [5,2,4,7,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,4,7,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,4,7,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,4,7,6,1,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,6,1,3,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,6,1,3,7,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,1,4,3,7]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,1,4,7,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,1,7,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,1,7,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,3,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,6,3,1,7,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,6,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,2,6,3,7,1,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,3,7,4,1]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,4,1,3,7]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,4,1,7,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,4,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,2,6,4,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,2,6,4,7,1,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,4,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,7,1,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,7,3,1,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,7,3,4,1]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,2,6,7,4,1,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,2,6,7,4,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,2,7,1,3,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,7,1,3,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,7,1,4,3,6]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,7,1,4,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,7,1,6,3,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,7,1,6,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,2,7,3,1,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,7,3,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,7,3,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,7,3,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,2,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,7,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,2,7,4,1,3,6]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,7,4,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,7,4,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,2,7,4,6,3,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,2,7,6,1,3,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,2,7,6,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,2,7,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,2,7,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,2,7,6,4,1,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,2,7,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [5,3,1,2,4,6,7]=>[[1,2,4,6,7],[3],[5]]=>010100 [5,3,1,2,4,7,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,3,1,2,6,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,3,1,2,6,7,4]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,3,1,2,7,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,3,1,2,7,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,1,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,1,4,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [5,3,1,4,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,1,4,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,1,4,7,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [5,3,1,4,7,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,1,6,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,3,1,6,2,7,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,3,1,6,4,2,7]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,1,6,4,7,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,1,6,7,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,3,1,6,7,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,1,7,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,3,1,7,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,1,7,4,2,6]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,1,7,4,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,1,7,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,1,7,6,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,2,1,4,7,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,1,6,4,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,1,6,7,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,1,7,4,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,1,7,6,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,2,4,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,4,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,2,4,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,2,4,7,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,4,7,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,6,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,6,1,7,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,6,4,1,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,6,4,7,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,6,7,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,6,7,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,2,7,1,4,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,7,1,6,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,2,7,4,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,7,4,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,2,7,6,1,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,2,7,6,4,1]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,1,2,7,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [5,3,4,1,6,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,1,6,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,1,7,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [5,3,4,1,7,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,4,2,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,2,1,7,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,4,2,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,2,7,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,4,6,1,2,7]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,6,1,7,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,6,2,7,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5]]=>010100 [5,3,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5]]=>110100 [5,3,4,7,1,2,6]=>[[1,2,6],[3,4,7],[5]]=>010101 [5,3,4,7,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,4,7,2,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,4,7,2,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,4,7,6,1,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,6,1,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,3,6,1,2,7,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,3,6,1,4,2,7]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,1,4,7,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,1,7,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,3,6,1,7,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,2,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,2,1,7,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,2,4,1,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,2,4,7,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,2,7,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,2,7,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,4,1,7,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,4,2,1,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,4,2,7,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,4,7,1,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,4,7,2,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,7,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,3,6,7,1,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,7,2,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,7,2,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,6,7,4,1,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,3,6,7,4,2,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,3,7,1,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,3,7,1,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,7,1,4,2,6]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,7,1,4,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,7,1,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,7,1,6,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,3,7,2,1,4,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,2,1,6,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,7,2,4,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,2,4,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,2,6,1,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,7,2,6,4,1]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,7,4,1,2,6]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,7,4,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,7,4,2,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,4,2,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,4,6,1,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,3,7,4,6,2,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,3,7,6,1,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,3,7,6,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,3,7,6,2,1,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,7,6,2,4,1]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,3,7,6,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,3,7,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [5,4,1,2,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>001100 [5,4,1,2,3,7,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,4,1,2,6,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,4,1,2,6,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,4,1,2,7,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,4,1,2,7,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,1,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,4,1,3,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,1,3,6,2,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,4,1,3,6,7,2]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,4,1,3,7,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,1,3,7,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,1,6,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,4,1,6,2,7,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,4,1,6,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,1,6,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,1,6,7,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,4,1,6,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,1,7,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,4,1,7,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,1,7,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,1,7,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,1,7,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,1,7,6,3,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,4,2,1,3,7,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,1,6,3,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,1,6,7,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,1,7,3,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,1,7,6,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,2,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,4,2,3,1,7,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,3,6,1,7]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5]]=>101100 [5,4,2,3,7,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,3,7,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,6,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,6,1,7,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,6,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,6,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,6,7,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,6,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,2,7,1,3,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,7,1,6,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,2,7,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,7,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,2,7,6,1,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,2,7,6,3,1]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,3,1,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>011100 [5,4,3,1,2,7,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,3,1,6,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,3,1,6,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,3,1,7,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,3,1,7,6,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,3,2,6,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,2,7,1,6]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,3,2,7,6,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,3,6,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,3,6,1,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,3,6,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,6,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,6,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,3,6,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,3,7,1,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,3,7,1,6,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,3,7,2,1,6]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,3,7,2,6,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,3,7,6,1,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,3,7,6,2,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,6,1,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,4,6,1,2,7,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,4,6,1,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,1,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,1,7,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,4,6,1,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,2,1,7,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,2,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,2,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,2,7,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,2,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,3,1,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,6,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,6,3,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,6,7,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,4,6,7,1,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,7,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,7,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,4,6,7,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,4,6,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,4,7,1,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,4,7,1,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,7,1,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,7,1,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,7,1,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,7,1,6,3,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,7,2,1,3,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,7,2,1,6,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,7,2,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,7,2,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,4,7,2,6,1,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,7,2,6,3,1]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,7,3,1,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,4,7,3,1,6,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,7,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,7,3,2,6,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,7,3,6,1,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,7,3,6,2,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,4,7,6,1,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,4,7,6,1,3,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,7,6,2,1,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,7,6,2,3,1]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,4,7,6,3,1,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,4,7,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>000100 [5,6,1,2,3,7,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,6,1,2,4,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,6,1,2,4,7,3]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,6,1,2,7,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,6,1,2,7,4,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,1,3,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,6,1,3,2,7,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,1,3,4,2,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,6,1,3,4,7,2]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,6,1,3,7,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,1,3,7,4,2]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,1,4,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,6,1,4,2,7,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,1,4,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,1,4,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,1,4,7,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,1,4,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,1,7,2,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,6,1,7,2,4,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,1,7,3,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,1,7,3,4,2]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,1,7,4,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,1,7,4,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,2,1,3,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,6,2,1,3,7,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,1,4,3,7]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,1,4,7,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,1,7,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,1,7,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,3,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,6,2,3,1,7,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,6,2,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>100100 [5,6,2,3,7,1,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,3,7,4,1]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,4,1,3,7]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,4,1,7,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,4,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,2,4,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,2,4,7,1,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,4,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,2,7,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,7,1,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,7,3,1,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,7,3,4,1]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,2,7,4,1,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,2,7,4,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,3,1,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>010100 [5,6,3,1,2,7,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,3,1,4,2,7]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,1,4,7,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,1,7,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,3,1,7,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,2,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,2,1,7,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,2,4,1,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,2,4,7,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,2,7,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,2,7,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,4,1,7,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,4,2,1,7]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,4,2,7,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,4,7,1,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,4,7,2,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,7,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,3,7,1,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,7,2,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,7,2,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,3,7,4,1,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,3,7,4,2,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,4,1,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>001100 [5,6,4,1,2,7,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,4,1,3,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,1,3,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,1,7,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,4,1,7,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,2,1,7,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,2,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,2,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,2,7,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,2,7,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,3,1,7,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,6,4,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,6,4,3,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,6,4,7,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,4,7,1,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,7,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,7,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,4,7,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,4,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7]]=>000100 [5,6,7,1,2,4,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,7,1,3,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,7,1,3,4,2]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,7,1,4,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,7,2,1,4,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,7,2,3,1,4]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5]]=>100100 [5,6,7,2,4,1,3]=>[[1,3,7],[2,4],[5,6]]=>101100 [5,6,7,2,4,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,7,3,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>010100 [5,6,7,3,1,4,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,7,3,2,4,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6]]=>010100 [5,6,7,3,4,2,1]=>[[1,4,7],[2,6],[3],[5]]=>110100 [5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>001100 [5,6,7,4,1,3,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,7,4,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,7,4,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>101100 [5,6,7,4,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>011100 [5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>111100 [5,7,1,2,3,4,6]=>[[1,2,3,4,6],[5,7]]=>000101 [5,7,1,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,7,1,2,4,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,7,1,2,4,6,3]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,7,1,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,7,1,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,1,3,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,7,1,3,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,7,1,3,4,2,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,7,1,3,4,6,2]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,7,1,3,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,7,1,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,1,4,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,7,1,4,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,7,1,4,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,1,4,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,1,4,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,7,1,4,6,3,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,1,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,7,1,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,1,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,1,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,1,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,1,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [5,7,2,1,3,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,7,2,1,3,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,7,2,1,4,3,6]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,7,2,1,4,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,7,2,1,6,3,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,7,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,7,2,3,1,4,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,7,2,3,1,6,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,7,2,3,4,1,6]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,7,2,3,4,6,1]=>[[1,3,4,6],[2,7],[5]]=>100101 [5,7,2,3,6,1,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,7,2,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,2,4,1,3,6]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,7,2,4,1,6,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,7,2,4,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,2,4,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,2,4,6,1,3]=>[[1,3,6],[2,4],[5,7]]=>101101 [5,7,2,4,6,3,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,2,6,1,3,4]=>[[1,3,4],[2,6],[5,7]]=>100101 [5,7,2,6,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,7,2,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,2,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,2,6,4,1,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,7,2,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [5,7,3,1,2,4,6]=>[[1,2,4,6],[3,7],[5]]=>010101 [5,7,3,1,2,6,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,7,3,1,4,2,6]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,7,3,1,4,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,7,3,1,6,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,7,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,7,3,2,1,4,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,2,1,6,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,7,3,2,4,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,2,4,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,2,6,1,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,7,3,2,6,4,1]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,7,3,4,1,2,6]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,7,3,4,1,6,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,7,3,4,2,1,6]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,4,2,6,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,4,6,1,2]=>[[1,2,6],[3,4],[5,7]]=>010101 [5,7,3,4,6,2,1]=>[[1,4,6],[2,7],[3],[5]]=>110101 [5,7,3,6,1,2,4]=>[[1,2,4],[3,6],[5,7]]=>010101 [5,7,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,7,3,6,2,1,4]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,7,3,6,2,4,1]=>[[1,4],[2,6],[3,7],[5]]=>110101 [5,7,3,6,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,7,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [5,7,4,1,2,3,6]=>[[1,2,3,6],[4,7],[5]]=>001101 [5,7,4,1,2,6,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,7,4,1,3,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,4,1,3,6,2]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,4,1,6,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,7,4,1,6,3,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,7,4,2,1,3,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,4,2,1,6,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,7,4,2,3,1,6]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,4,2,3,6,1]=>[[1,3,6],[2,7],[4],[5]]=>101101 [5,7,4,2,6,1,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,7,4,2,6,3,1]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,7,4,3,1,2,6]=>[[1,2,6],[3,7],[4],[5]]=>011101 [5,7,4,3,1,6,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,7,4,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,7,4,3,2,6,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,7,4,3,6,1,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,7,4,3,6,2,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,7,4,6,1,2,3]=>[[1,2,3],[4,6],[5,7]]=>001101 [5,7,4,6,1,3,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,7,4,6,2,1,3]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,7,4,6,2,3,1]=>[[1,3],[2,6],[4,7],[5]]=>101101 [5,7,4,6,3,1,2]=>[[1,2],[3,6],[4,7],[5]]=>011101 [5,7,4,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5]]=>111101 [5,7,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [5,7,6,1,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,6,1,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,6,1,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,6,1,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [5,7,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,7,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [5,7,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [5,7,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [5,7,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [5,7,6,3,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,7,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [5,7,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [5,7,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [5,7,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [5,7,6,4,1,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [5,7,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [5,7,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [5,7,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [5,7,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [5,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>000010 [6,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]=>000010 [6,1,2,3,5,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [6,1,2,3,5,7,4]=>[[1,2,3,4,7],[5],[6]]=>000110 [6,1,2,3,7,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [6,1,2,3,7,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,2,4,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [6,1,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,2,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [6,1,2,4,5,7,3]=>[[1,2,3,5,7],[4],[6]]=>001010 [6,1,2,4,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,2,4,7,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,2,5,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [6,1,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,2,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,2,5,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,2,5,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,2,5,7,4,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,2,7,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [6,1,2,7,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,2,7,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,2,7,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,2,7,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,2,7,5,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,3,2,4,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [6,1,3,2,4,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,1,3,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,1,3,2,7,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,2,7,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,1,3,4,2,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [6,1,3,4,2,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [6,1,3,4,5,7,2]=>[[1,2,4,5,7],[3],[6]]=>010010 [6,1,3,4,7,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,4,7,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,1,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,1,3,5,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,3,5,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,3,5,7,2,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,1,3,5,7,4,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,7,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,1,3,7,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,7,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,1,3,7,5,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,4,2,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [6,1,4,2,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,4,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,1,4,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,1,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,4,2,7,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,1,4,3,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,3,2,7,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,4,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,3,5,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,3,7,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,4,3,7,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,4,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,1,4,5,2,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,1,4,5,3,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,5,3,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,5,7,2,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,1,4,5,7,3,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,1,4,7,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,1,4,7,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,4,7,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,4,7,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,1,4,7,5,3,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,5,2,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [6,1,5,2,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,5,2,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,5,2,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,5,2,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,5,2,7,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,5,3,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,5,3,2,7,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,5,3,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,5,3,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,1,5,3,7,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,5,3,7,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,5,4,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,1,5,4,2,7,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,1,5,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,1,5,4,7,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,5,4,7,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,1,5,7,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,5,7,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,5,7,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,5,7,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,5,7,4,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,1,7,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [6,1,7,2,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,7,2,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,7,2,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,7,2,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,7,2,5,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,7,3,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,7,3,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,1,7,3,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,7,3,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,1,7,3,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,1,7,3,5,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,1,7,4,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,1,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,7,4,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,1,7,4,5,3,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,1,7,5,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,1,7,5,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,7,5,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,7,5,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,1,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,1,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,2,1,3,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [6,2,1,3,4,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,1,3,7,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,1,3,7,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,1,4,3,7,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [6,2,1,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,1,4,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,1,4,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [6,2,1,4,7,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,1,5,3,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,1,5,3,7,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [6,2,1,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,1,5,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,1,5,7,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [6,2,1,5,7,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,1,7,3,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,1,7,3,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,1,7,4,3,5]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,1,7,4,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,1,7,5,3,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,1,7,5,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,2,3,1,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [6,2,3,1,4,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,1,5,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,3,1,5,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,3,1,7,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,1,7,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [6,2,3,4,1,7,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>100010 [6,2,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>100010 [6,2,3,4,7,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,4,7,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,5,1,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,3,5,1,7,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,3,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,3,5,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,3,5,7,1,4]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,3,5,7,4,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,3,7,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,3,7,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,7,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,3,7,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,3,7,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,4,1,3,5,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,1,3,7,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [6,2,4,1,5,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,1,5,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,1,7,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [6,2,4,1,7,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,4,3,1,5,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,3,1,7,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,3,5,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,3,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,4,3,7,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,4,5,1,3,7]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,5,1,7,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,5,3,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,5,7,1,3]=>[[1,3,5,7],[2,4],[6]]=>101010 [6,2,4,5,7,3,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,2,4,7,1,3,5]=>[[1,3,5],[2,4,7],[6]]=>101010 [6,2,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,4,7,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,4,7,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,4,7,5,3,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,5,1,3,4,7]=>[[1,3,4,7],[2,5],[6]]=>100110 [6,2,5,1,3,7,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [6,2,5,1,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,1,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,1,7,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [6,2,5,1,7,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,3,1,4,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,5,3,1,7,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,5,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,5,3,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,2,5,3,7,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,5,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,5,4,1,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,4,1,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,2,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,2,5,4,7,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,4,7,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,2,5,7,1,3,4]=>[[1,3,4],[2,5,7],[6]]=>100110 [6,2,5,7,1,4,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,7,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,5,7,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,5,7,4,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,2,5,7,4,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,2,7,1,3,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,7,1,3,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,7,1,4,3,5]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,7,1,4,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,7,1,5,3,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,7,1,5,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,2,7,3,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,7,3,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,7,3,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,7,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,2,7,3,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,7,3,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,7,4,1,3,5]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,7,4,1,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,7,4,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,7,4,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,2,7,4,5,3,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,2,7,5,1,3,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,2,7,5,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,2,7,5,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,7,5,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,2,7,5,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,2,7,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,3,1,2,4,5,7]=>[[1,2,4,5,7],[3],[6]]=>010010 [6,3,1,2,4,7,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,3,1,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,3,1,2,5,7,4]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,3,1,2,7,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,3,1,2,7,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,1,4,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [6,3,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,1,4,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [6,3,1,4,7,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,1,5,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,3,1,5,2,7,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [6,3,1,5,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,1,5,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,1,5,7,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [6,3,1,5,7,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,1,7,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,3,1,7,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,1,7,4,2,5]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,1,7,4,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,1,7,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,1,7,5,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,2,1,4,7,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,1,5,4,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,1,5,7,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,1,7,4,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,1,7,5,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,2,4,1,7,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,2,4,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,2,4,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,4,7,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,5,1,4,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,5,1,7,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,5,4,7,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,5,7,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,5,7,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,2,7,1,4,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,7,1,5,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,2,7,4,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,7,4,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,2,7,5,1,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,2,7,5,4,1]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,4,1,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,1,2,7,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [6,3,4,1,5,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,1,5,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,1,7,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [6,3,4,1,7,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,2,1,7,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,4,2,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,2,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,2,7,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,4,2,7,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,4,5,1,2,7]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,5,7,1,2]=>[[1,2,5,7],[3,4],[6]]=>010010 [6,3,4,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]=>110010 [6,3,4,7,1,2,5]=>[[1,2,5],[3,4,7],[6]]=>010010 [6,3,4,7,1,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,4,7,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,4,7,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,4,7,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,4,7,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,5,1,2,4,7]=>[[1,2,4,7],[3,5],[6]]=>010110 [6,3,5,1,2,7,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [6,3,5,1,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,1,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,1,7,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [6,3,5,1,7,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,2,1,4,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,2,1,7,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,2,4,1,7]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,2,4,7,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,2,7,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,2,7,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,4,1,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,4,1,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,3,5,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,3,5,4,7,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,3,5,7,1,2,4]=>[[1,2,4],[3,5,7],[6]]=>010110 [6,3,5,7,1,4,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,7,2,1,4]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,7,2,4,1]=>[[1,4,7],[2,5],[3],[6]]=>110110 [6,3,5,7,4,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,3,5,7,4,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,3,7,1,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,3,7,1,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,7,1,4,2,5]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,7,1,4,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,7,1,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,7,1,5,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,3,7,2,1,4,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,2,1,5,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,7,2,4,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,2,4,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,2,5,1,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,7,2,5,4,1]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,7,4,1,2,5]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,7,4,1,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,7,4,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,4,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,3,7,4,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,3,7,5,1,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,3,7,5,1,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,3,7,5,2,1,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,7,5,2,4,1]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,3,7,5,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,3,7,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>001010 [6,4,1,2,3,7,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,4,1,2,5,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,4,1,2,5,7,3]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,4,1,2,7,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,4,1,2,7,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,1,3,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,4,1,3,2,7,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,1,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,4,1,3,5,7,2]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,4,1,3,7,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,1,3,7,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,1,5,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,4,1,5,2,7,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [6,4,1,5,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,1,5,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,1,5,7,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [6,4,1,5,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,1,7,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,4,1,7,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,1,7,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,1,7,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,1,7,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,1,7,5,3,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,4,2,1,3,7,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,1,5,3,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,1,5,7,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,1,7,3,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,1,7,5,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,4,2,3,1,7,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6]]=>101010 [6,4,2,3,7,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,3,7,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,5,1,3,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,5,1,7,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,5,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,5,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,5,7,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,5,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,2,7,1,3,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,7,1,5,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,2,7,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,7,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,2,7,5,1,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,2,7,5,3,1]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,3,1,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>011010 [6,4,3,1,2,7,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,3,1,5,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,3,1,5,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,3,1,7,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,3,1,7,5,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,2,1,7,5]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,2,5,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,2,7,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,3,2,7,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,3,5,1,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,3,5,1,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,3,5,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,5,7,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,3,5,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,3,7,1,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,3,7,1,5,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,3,7,2,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,3,7,2,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,3,7,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,3,7,5,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,5,1,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>001010 [6,4,5,1,2,7,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [6,4,5,1,3,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,1,3,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,1,7,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [6,4,5,1,7,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,2,1,3,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,2,1,7,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,2,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,2,7,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,2,7,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,3,1,2,7]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,3,1,7,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,5,3,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,5,3,7,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,3,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6]]=>001010 [6,4,5,7,1,3,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,7,2,1,3]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,7,2,3,1]=>[[1,3,7],[2,5],[4],[6]]=>101010 [6,4,5,7,3,1,2]=>[[1,2,7],[3,5],[4],[6]]=>011010 [6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>111010 [6,4,7,1,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,4,7,1,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,7,1,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,7,1,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,7,1,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,7,1,5,3,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,7,2,1,3,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,7,2,1,5,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,7,2,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,7,2,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,7,2,5,3,1]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,7,3,1,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,4,7,3,1,5,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,7,3,2,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,7,3,2,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,7,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,7,3,5,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,4,7,5,1,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,4,7,5,1,3,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,7,5,2,1,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,7,5,2,3,1]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,4,7,5,3,1,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,4,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>000110 [6,5,1,2,3,7,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,5,1,2,4,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,5,1,2,4,7,3]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,5,1,2,7,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,5,1,2,7,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,1,3,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,5,1,3,2,7,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,1,3,4,2,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,5,1,3,4,7,2]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,5,1,3,7,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,1,3,7,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,1,4,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,5,1,4,2,7,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,1,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,1,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,1,4,7,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,1,4,7,3,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,1,7,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,5,1,7,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,1,7,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,1,7,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,1,7,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,1,7,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,5,2,1,3,7,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,1,4,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,5,2,1,4,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,5,2,1,7,3,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,1,7,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,5,2,3,1,7,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,5,2,3,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>100110 [6,5,2,3,7,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,4,1,3,7]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,5,2,4,1,7,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,5,2,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,2,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,2,4,7,1,3]=>[[1,3,7],[2,4],[5],[6]]=>101110 [6,5,2,4,7,3,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,2,7,1,3,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,7,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,5,2,7,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,7,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,2,7,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,5,2,7,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,3,1,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>010110 [6,5,3,1,2,7,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,3,1,4,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,5,3,1,4,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,5,3,1,7,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,3,1,7,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,2,1,7,4]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,3,2,4,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,2,4,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,2,7,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,3,2,7,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,3,4,1,2,7]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,5,3,4,1,7,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,4,7,1,2]=>[[1,2,7],[3,4],[5],[6]]=>010110 [6,5,3,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>110110 [6,5,3,7,1,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,3,7,1,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,5,3,7,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,3,7,2,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,3,7,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,5,3,7,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,4,1,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>001110 [6,5,4,1,2,7,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,4,1,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,4,1,3,7,2]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,4,1,7,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,4,1,7,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,4,2,1,7,3]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,4,2,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>101110 [6,5,4,2,7,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,4,2,7,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,4,3,1,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>011110 [6,5,4,3,1,7,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [6,5,4,3,7,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,4,3,7,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [6,5,4,7,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,4,7,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,4,7,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,4,7,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,4,7,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,4,7,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [6,5,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,5,7,1,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,7,1,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,7,1,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,7,1,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,7,1,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,7,2,1,3,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,5,7,2,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,7,2,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,5,7,2,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,5,7,2,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,7,3,1,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,5,7,3,1,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,5,7,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,5,7,3,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,5,7,4,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,5,7,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,7,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,7,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,5,7,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [6,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>000010 [6,7,1,2,3,5,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,7,1,2,4,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,7,1,2,4,5,3]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,7,1,2,5,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,7,1,2,5,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,1,3,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,7,1,3,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,7,1,3,4,2,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,7,1,3,4,5,2]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,7,1,3,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,7,1,3,5,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,1,4,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,7,1,4,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,7,1,4,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,1,4,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,1,4,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,7,1,4,5,3,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,1,5,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,7,1,5,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,1,5,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,1,5,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,1,5,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,1,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,7,2,1,3,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,7,2,1,3,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,7,2,1,4,3,5]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,7,2,1,4,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,7,2,1,5,3,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,7,2,1,5,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,7,2,3,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,7,2,3,1,5,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,7,2,3,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,7,2,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>100010 [6,7,2,3,5,1,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,7,2,3,5,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,2,4,1,3,5]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,7,2,4,1,5,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,7,2,4,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,2,4,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,2,4,5,1,3]=>[[1,3,5],[2,4],[6,7]]=>101010 [6,7,2,4,5,3,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,2,5,1,3,4]=>[[1,3,4],[2,5],[6,7]]=>100110 [6,7,2,5,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,7,2,5,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,2,5,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,2,5,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,7,2,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,7,3,1,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>010010 [6,7,3,1,2,5,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,7,3,1,4,2,5]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,7,3,1,4,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,7,3,1,5,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,7,3,1,5,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,7,3,2,1,4,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,2,1,5,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,7,3,2,4,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,2,4,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,2,5,1,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,7,3,2,5,4,1]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,7,3,4,1,2,5]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,7,3,4,1,5,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,7,3,4,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,4,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>010010 [6,7,3,4,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>110010 [6,7,3,5,1,2,4]=>[[1,2,4],[3,5],[6,7]]=>010110 [6,7,3,5,1,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,7,3,5,2,1,4]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,7,3,5,2,4,1]=>[[1,4],[2,5],[3,7],[6]]=>110110 [6,7,3,5,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,7,3,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,7,4,1,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>001010 [6,7,4,1,2,5,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,7,4,1,3,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,4,1,3,5,2]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,4,1,5,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,7,4,1,5,3,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,7,4,2,1,3,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,4,2,1,5,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,7,4,2,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,4,2,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>101010 [6,7,4,2,5,1,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,7,4,2,5,3,1]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,7,4,3,1,2,5]=>[[1,2,5],[3,7],[4],[6]]=>011010 [6,7,4,3,1,5,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,7,4,3,2,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,7,4,3,2,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,7,4,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,7,4,3,5,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,7,4,5,1,2,3]=>[[1,2,3],[4,5],[6,7]]=>001010 [6,7,4,5,1,3,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,7,4,5,2,1,3]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6]]=>101010 [6,7,4,5,3,1,2]=>[[1,2],[3,5],[4,7],[6]]=>011010 [6,7,4,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>111010 [6,7,5,1,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>000110 [6,7,5,1,2,4,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,5,1,3,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,5,1,3,4,2]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,5,1,4,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,5,1,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,7,5,2,1,3,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,5,2,1,4,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,7,5,2,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,5,2,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>100110 [6,7,5,2,4,1,3]=>[[1,3],[2,4],[5,7],[6]]=>101110 [6,7,5,2,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,7,5,3,1,2,4]=>[[1,2,4],[3,7],[5],[6]]=>010110 [6,7,5,3,1,4,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,7,5,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,7,5,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,7,5,3,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>010110 [6,7,5,3,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>110110 [6,7,5,4,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>001110 [6,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,7,5,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>101110 [6,7,5,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>011110 [6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>111110 [7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>000001 [7,1,2,3,4,6,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [7,1,2,3,5,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [7,1,2,3,5,6,4]=>[[1,2,3,4,6],[5],[7]]=>000101 [7,1,2,3,6,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [7,1,2,3,6,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,2,4,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [7,1,2,4,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,1,2,4,5,3,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [7,1,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]=>001001 [7,1,2,4,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,1,2,4,6,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,2,5,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [7,1,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,1,2,5,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,1,2,5,6,4,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,2,6,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [7,1,2,6,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,2,6,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,2,6,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,2,6,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,1,3,2,4,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [7,1,3,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,1,3,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,1,3,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,1,3,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,1,3,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,1,3,4,2,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [7,1,3,4,2,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,1,3,4,5,2,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [7,1,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]=>010001 [7,1,3,4,6,2,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,1,3,4,6,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,3,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,1,3,5,2,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,1,3,5,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,3,5,6,2,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,1,3,5,6,4,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,3,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,1,3,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,1,3,6,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,3,6,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,3,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,1,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,1,4,2,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [7,1,4,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,1,4,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,1,4,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,1,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,1,4,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,1,4,3,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,3,2,6,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,1,4,3,5,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,3,6,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,1,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,1,4,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,1,4,5,2,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,1,4,5,3,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,5,3,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,5,6,2,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,1,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,1,4,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,1,4,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,1,4,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,1,4,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,1,4,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,1,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,1,5,2,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [7,1,5,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,1,5,2,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,5,2,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,5,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,1,5,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,1,5,3,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,5,3,2,6,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,1,5,3,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,5,3,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,1,5,3,6,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,1,5,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,1,5,4,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,1,5,4,2,6,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,1,5,4,3,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,1,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,1,5,4,6,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,1,5,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,1,5,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,1,5,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,1,5,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,1,5,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,1,5,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,1,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,1,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [7,1,6,2,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,6,2,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,6,2,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,6,2,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,6,2,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,1,6,3,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,6,3,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,1,6,3,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,6,3,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,1,6,3,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,1,6,3,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,1,6,4,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,1,6,4,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,1,6,4,3,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,1,6,4,3,5,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,1,6,4,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,1,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,1,6,5,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,1,6,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,1,6,5,3,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,1,6,5,3,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,1,6,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [7,2,1,3,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [7,2,1,3,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,1,3,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,1,3,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,1,3,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,1,3,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,1,4,3,5,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,1,4,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [7,2,1,4,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,1,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,1,4,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [7,2,1,4,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,1,5,3,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,1,5,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [7,2,1,5,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,1,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,1,5,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [7,2,1,5,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,1,6,3,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,1,6,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,1,6,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,1,6,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,1,6,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,2,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [7,2,3,1,4,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,3,1,5,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,3,1,5,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,3,1,6,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,3,1,6,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [7,2,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>100001 [7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>100001 [7,2,3,4,6,1,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,3,4,6,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,3,5,1,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,3,5,1,6,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,3,5,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,3,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,3,5,6,1,4]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,3,5,6,4,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,3,6,1,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,3,6,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,3,6,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,3,6,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,3,6,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,2,4,1,3,5,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,1,3,6,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [7,2,4,1,5,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,1,5,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,1,6,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [7,2,4,1,6,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,4,3,1,5,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,3,1,6,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,2,4,3,5,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,3,6,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,2,4,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,2,4,5,1,3,6]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,5,1,6,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,5,3,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,5,3,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7]]=>101001 [7,2,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,2,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7]]=>101011 [7,2,4,6,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,4,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,2,4,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,2,4,6,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,2,5,1,3,4,6]=>[[1,3,4,6],[2,5],[7]]=>100101 [7,2,5,1,3,6,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [7,2,5,1,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,1,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,1,6,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [7,2,5,1,6,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,3,1,4,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,5,3,1,6,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,2,5,3,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,5,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,2,5,3,6,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,2,5,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,2,5,4,1,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,4,1,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,4,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,2,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,2,5,4,6,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,2,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7]]=>100101 [7,2,5,6,1,4,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,2,5,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,2,5,6,4,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,2,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,2,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7]]=>100011 [7,2,6,1,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,6,1,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,6,1,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,6,1,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,6,1,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,2,6,3,1,4,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,6,3,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,6,3,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,6,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,2,6,3,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,6,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,2,6,4,1,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,6,4,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,6,4,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,2,6,4,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,2,6,4,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,2,6,5,1,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,2,6,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,2,6,5,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,2,6,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,2,6,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [7,3,1,2,4,5,6]=>[[1,2,4,5,6],[3],[7]]=>010001 [7,3,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,3,1,2,5,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,3,1,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,3,1,2,6,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,3,1,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [7,3,1,4,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [7,3,1,4,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,1,5,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,3,1,5,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [7,3,1,5,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,1,5,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,1,5,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [7,3,1,5,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,1,6,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,3,1,6,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,1,6,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,1,6,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,1,6,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,2,1,4,6,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,1,5,4,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,1,5,6,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,1,6,4,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,1,6,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,2,4,1,6,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,4,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,2,4,6,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,4,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,5,1,4,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,5,1,6,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,5,4,1,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,5,6,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,5,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,2,6,1,4,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,6,1,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [7,3,2,6,4,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,6,4,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,2,6,5,1,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [7,3,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,1,2,6,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [7,3,4,1,5,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,1,5,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,1,6,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [7,3,4,1,6,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,2,1,6,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,2,6,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,4,2,6,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7]]=>010001 [7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>110001 [7,3,4,6,1,2,5]=>[[1,2,5],[3,4,6],[7]]=>010011 [7,3,4,6,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,4,6,2,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,4,6,2,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,4,6,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,3,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7]]=>010101 [7,3,5,1,2,6,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [7,3,5,1,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,1,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,1,6,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [7,3,5,1,6,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,2,1,4,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,2,1,6,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,2,4,1,6]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,2,4,6,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,2,6,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,2,6,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,4,1,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,4,1,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,3,5,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,3,5,4,6,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,3,5,6,1,2,4]=>[[1,2,4],[3,5,6],[7]]=>010101 [7,3,5,6,1,4,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,6,2,1,4]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,6,2,4,1]=>[[1,4,6],[2,5],[3],[7]]=>110101 [7,3,5,6,4,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,3,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7]]=>010011 [7,3,6,1,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,6,1,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,6,1,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,6,1,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,6,1,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,3,6,2,1,4,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,6,2,1,5,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [7,3,6,2,4,1,5]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,6,2,4,5,1]=>[[1,4,5],[2,6],[3],[7]]=>110011 [7,3,6,2,5,1,4]=>[[1,4],[2,5],[3,6],[7]]=>110111 [7,3,6,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,3,6,4,1,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,6,4,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,6,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,3,6,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,3,6,4,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,3,6,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,3,6,5,1,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,3,6,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,3,6,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,3,6,5,2,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,3,6,5,4,1,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [7,4,1,2,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>001001 [7,4,1,2,3,6,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,4,1,2,5,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,4,1,2,5,6,3]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,4,1,2,6,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,4,1,2,6,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,1,3,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,4,1,3,2,6,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,1,3,5,2,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,4,1,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,4,1,3,6,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,1,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,1,5,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,4,1,5,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [7,4,1,5,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,1,5,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,1,5,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [7,4,1,5,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,4,1,6,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,1,6,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,1,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,1,6,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,4,2,1,3,5,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,4,2,1,3,6,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,1,5,3,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,1,5,6,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,1,6,3,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,1,6,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [7,4,2,3,1,5,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,4,2,3,1,6,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,3,5,1,6]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,4,2,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>101001 [7,4,2,3,6,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,5,1,3,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,5,1,6,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,5,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,5,6,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,5,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,2,6,1,3,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [7,4,2,6,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [7,4,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,4,3,1,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>011001 [7,4,3,1,2,6,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,3,1,5,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,3,1,5,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,3,1,6,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,3,1,6,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,2,6,1,5]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,3,2,6,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,3,5,1,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,3,5,1,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,3,6,1,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [7,4,3,6,2,1,5]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,3,6,2,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [7,4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>001001 [7,4,5,1,2,6,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [7,4,5,1,3,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,1,3,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [7,4,5,1,6,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,2,1,3,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,2,1,6,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,2,6,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,2,6,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,3,1,2,6]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,3,1,6,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7]]=>001001 [7,4,5,6,1,3,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,6,2,1,3]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7]]=>101001 [7,4,5,6,3,1,2]=>[[1,2,6],[3,5],[4],[7]]=>011001 [7,4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>111001 [7,4,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7]]=>001011 [7,4,6,1,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,6,1,3,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,6,1,3,5,2]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,6,1,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,6,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,4,6,2,1,3,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,6,2,1,5,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [7,4,6,2,3,1,5]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,6,2,3,5,1]=>[[1,3,5],[2,6],[4],[7]]=>101011 [7,4,6,2,5,1,3]=>[[1,3],[2,5],[4,6],[7]]=>101011 [7,4,6,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,4,6,3,1,2,5]=>[[1,2,5],[3,6],[4],[7]]=>011011 [7,4,6,3,1,5,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [7,4,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,6,3,2,5,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,6,3,5,1,2]=>[[1,2],[3,5],[4,6],[7]]=>011011 [7,4,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]=>111011 [7,4,6,5,1,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,4,6,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,4,6,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,4,6,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,4,6,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,4,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>000101 [7,5,1,2,3,6,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,5,1,2,4,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,5,1,2,4,6,3]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,5,1,2,6,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,5,1,2,6,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,1,3,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,5,1,3,2,6,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,1,3,4,2,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,5,1,3,4,6,2]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,5,1,3,6,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,1,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,1,4,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,5,1,4,2,6,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,1,4,3,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,1,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,1,4,6,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,1,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,1,6,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,5,1,6,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,1,6,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,1,6,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,1,6,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,1,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,5,2,1,3,6,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,1,4,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,5,2,1,4,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,5,2,1,6,3,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [7,5,2,3,1,4,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,5,2,3,1,6,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,3,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,5,2,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>100101 [7,5,2,3,6,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,4,1,3,6]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,5,2,4,1,6,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,5,2,4,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,2,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,2,4,6,1,3]=>[[1,3,6],[2,4],[5],[7]]=>101101 [7,5,2,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,2,6,1,3,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,6,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [7,5,2,6,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,6,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,2,6,4,1,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [7,5,2,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>010101 [7,5,3,1,2,6,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,3,1,4,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,5,3,1,4,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,5,3,1,6,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,2,6,1,4]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,3,2,6,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,3,4,1,2,6]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,5,3,4,1,6,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,4,6,1,2]=>[[1,2,6],[3,4],[5],[7]]=>010101 [7,5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>110101 [7,5,3,6,1,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [7,5,3,6,2,1,4]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,3,6,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,3,6,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [7,5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,4,1,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>001101 [7,5,4,1,2,6,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,4,1,3,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,4,1,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,4,1,6,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,4,1,6,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,4,2,1,6,3]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>101101 [7,5,4,2,6,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,4,2,6,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>011101 [7,5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [7,5,4,3,6,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [7,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,4,6,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,4,6,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [7,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>000101 [7,5,6,1,2,4,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,6,1,3,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,6,1,3,4,2]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,6,1,4,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [7,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>100101 [7,5,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7]]=>101101 [7,5,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7]]=>010101 [7,5,6,3,1,4,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [7,5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>010101 [7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>110101 [7,5,6,4,1,2,3]=>[[1,2,3],[4,6],[5],[7]]=>001101 [7,5,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>101101 [7,5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>011101 [7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>111101 [7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>000011 [7,6,1,2,3,5,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,6,1,2,4,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,6,1,2,4,5,3]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,6,1,2,5,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,6,1,2,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,1,3,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,6,1,3,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,6,1,3,4,2,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,6,1,3,4,5,2]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,6,1,3,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,6,1,3,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,1,4,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,6,1,4,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,6,1,4,3,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,1,4,3,5,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,1,4,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,6,1,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,1,5,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,6,1,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,1,5,3,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,1,5,3,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,1,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,1,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,6,2,1,3,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,6,2,1,4,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,6,2,1,4,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,6,2,1,5,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,6,2,1,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,6,2,3,1,5,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>100011 [7,6,2,3,5,1,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,6,2,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,2,4,1,3,5]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,6,2,4,1,5,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,6,2,4,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,2,4,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,2,4,5,1,3]=>[[1,3,5],[2,4],[6],[7]]=>101011 [7,6,2,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,2,5,1,3,4]=>[[1,3,4],[2,5],[6],[7]]=>100111 [7,6,2,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,6,2,5,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,2,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,2,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>010011 [7,6,3,1,2,5,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,6,3,1,4,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,6,3,1,4,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,6,3,1,5,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,6,3,1,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,2,1,5,4]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,2,5,1,4]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,6,3,4,1,5,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,4,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>010011 [7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>110011 [7,6,3,5,1,2,4]=>[[1,2,4],[3,5],[6],[7]]=>010111 [7,6,3,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,6,3,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,6,3,5,2,4,1]=>[[1,4],[2,5],[3],[6],[7]]=>110111 [7,6,3,5,4,1,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>001011 [7,6,4,1,2,5,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,6,4,1,3,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,4,1,3,5,2]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,4,1,5,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,6,4,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,4,2,1,5,3]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>101011 [7,6,4,2,5,1,3]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,6,4,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>011011 [7,6,4,3,1,5,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [7,6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [7,6,4,3,5,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [7,6,4,5,1,2,3]=>[[1,2,3],[4,5],[6],[7]]=>001011 [7,6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>101011 [7,6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>011011 [7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>111011 [7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>000111 [7,6,5,1,2,4,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,5,1,3,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,5,1,3,4,2]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,5,1,4,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,5,1,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,5,2,1,4,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>100111 [7,6,5,2,4,1,3]=>[[1,3],[2,4],[5],[6],[7]]=>101111 [7,6,5,2,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>010111 [7,6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [7,6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6],[7]]=>010111 [7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>110111 [7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>001111 [7,6,5,4,1,3,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>101111 [7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7]]=>011111 [7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>111111 [8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>1111111 [7,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [8,6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [7,6,8,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [8,7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [7,8,5,6,4,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [8,6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [8,5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [7,6,5,8,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,5,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [7,5,6,8,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,7,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,7,8,4,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [7,8,6,4,5,3,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [8,6,7,4,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [8,7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [8,7,4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [8,5,6,4,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [8,6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [7,6,5,4,8,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,5,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [7,5,6,4,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,7,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,7,4,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [7,6,4,5,8,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [6,7,4,5,8,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,5,4,6,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,6,8,3,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [6,5,4,7,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,4,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [6,4,5,7,8,3,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [5,4,6,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,6,7,8,3,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [8,7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [7,8,6,5,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [7,6,8,5,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [8,7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [7,8,5,6,3,4,2,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [8,5,6,7,3,4,2,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [7,6,5,8,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,7,5,8,3,4,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,5,7,8,3,4,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,7,8,3,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [8,7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [7,8,6,4,3,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [7,6,8,4,3,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [6,7,8,4,3,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [8,7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,8,6,3,4,5,2,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [8,6,7,3,4,5,2,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,6,8,3,4,5,2,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,7,8,3,4,5,2,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [7,8,5,4,3,6,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [8,7,5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [7,8,5,3,4,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [8,7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [8,7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,4,5,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,6,5,4,3,7,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [8,6,4,3,5,7,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,5,3,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,4,3,5,6,7,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [7,6,5,4,3,8,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,5,4,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [7,5,6,4,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,7,4,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,7,4,3,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [6,7,4,5,3,8,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,5,4,6,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,6,3,8,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [6,5,4,7,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [6,4,5,7,3,8,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [5,4,6,7,3,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,6,7,3,8,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [7,6,5,3,4,8,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [7,6,4,3,5,8,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [7,6,3,4,5,8,2,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [7,5,4,3,6,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,5,3,4,6,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,3,4,5,6,8,2,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [6,5,4,3,7,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [6,5,3,4,7,8,2,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,3,4,5,7,8,2,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,4,3,6,7,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,3,4,6,7,8,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,5,6,7,8,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,6,7,8,2,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [8,7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [7,8,6,5,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [8,6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [7,6,8,5,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [8,7,5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,6,5,7,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [8,5,6,7,4,2,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [7,6,5,8,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [6,7,5,8,4,2,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,5,6,8,4,2,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,6,7,8,4,2,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [8,7,6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [8,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [7,6,8,4,5,2,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [8,7,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [7,8,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [8,5,6,4,7,2,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,6,4,5,7,2,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [8,4,5,6,7,2,3,1]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [7,5,6,4,8,2,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,5,7,4,8,2,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [6,7,4,5,8,2,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [4,5,6,7,8,2,3,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [8,7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [7,8,6,5,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [8,6,7,5,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [7,6,8,5,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,7,8,5,3,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [8,7,5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [8,6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [8,5,6,7,3,2,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [7,6,5,8,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,7,5,8,3,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,7,8,3,2,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [8,7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [8,6,7,5,2,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [7,6,8,5,2,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,8,5,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,7,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [7,8,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [8,6,5,7,2,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [7,6,5,8,2,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,5,8,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [6,5,7,8,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,6,7,8,2,3,4,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [8,7,6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [8,7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,8,6,3,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [8,6,7,3,4,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,6,8,3,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,7,8,3,4,2,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,7,8,4,2,3,5,1]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [8,7,6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,8,6,3,2,4,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [8,6,7,3,2,4,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [6,7,8,3,2,4,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [7,8,6,2,3,4,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,6,7,2,3,4,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,6,8,2,3,4,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [6,7,8,2,3,4,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,8,5,4,3,2,6,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [8,7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [7,8,5,3,4,2,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [8,7,5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [7,8,4,3,2,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [7,8,3,4,2,5,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,8,4,2,3,5,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,8,3,2,4,5,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,8,2,3,4,5,6,1]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [8,6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [8,5,6,3,4,2,7,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,4,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,4,3,5,6,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,6,5,4,2,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [8,5,6,4,2,3,7,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,6,5,3,2,4,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,6,2,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [8,5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [8,4,5,3,2,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,3,4,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [8,4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,4,2,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [7,6,5,4,3,2,8,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,5,4,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [6,5,7,4,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,7,4,3,2,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [7,6,4,5,3,2,8,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [6,7,4,5,3,2,8,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,4,5,6,3,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [6,5,4,7,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [6,4,5,7,3,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [4,5,6,7,3,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [7,5,6,3,4,2,8,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [6,5,7,3,4,2,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [7,6,4,3,5,2,8,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [7,6,3,4,5,2,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [7,5,4,3,6,2,8,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,3,6,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,5,3,4,6,2,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,3,4,5,6,2,8,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [6,5,4,3,7,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [6,4,5,3,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [5,4,6,3,7,2,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,6,3,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [6,5,3,4,7,2,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [5,6,3,4,7,2,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,4,3,5,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [6,3,4,5,7,2,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [4,5,3,6,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [4,3,5,6,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,6,7,2,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [7,6,5,4,2,3,8,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [6,7,5,4,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,5,6,4,2,3,8,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,5,7,4,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,7,4,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [7,6,4,5,2,3,8,1]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [6,7,4,5,2,3,8,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [7,4,5,6,2,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [6,5,4,7,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,4,7,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,6,7,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [4,5,6,7,2,3,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [7,6,5,3,2,4,8,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [6,7,5,3,2,4,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,5,7,3,2,4,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [7,6,5,2,3,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [7,5,6,2,3,4,8,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [5,6,7,2,3,4,8,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [6,7,4,3,2,5,8,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,6,4,2,3,5,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,6,3,2,4,5,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [6,7,3,2,4,5,8,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,2,3,4,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [6,7,2,3,4,5,8,1]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [7,5,4,3,2,6,8,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,3,5,2,6,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,5,4,2,3,6,8,1]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [7,4,5,2,3,6,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [7,5,3,2,4,6,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,5,2,3,4,6,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [7,4,3,2,5,6,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,3,2,4,5,6,8,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [7,2,3,4,5,6,8,1]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [6,5,4,3,2,7,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [4,5,6,3,2,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [6,5,3,4,2,7,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,3,4,5,2,7,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,4,3,6,2,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,3,5,6,2,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,6,2,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [6,5,4,2,3,7,8,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [6,4,5,2,3,7,8,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,5,6,2,3,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [6,5,3,2,4,7,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,5,2,3,4,7,8,1]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [6,2,3,4,5,7,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [5,4,3,2,6,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,3,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [5,3,4,2,6,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,5,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,2,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [5,4,2,3,6,7,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [4,5,2,3,6,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,3,2,4,6,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [5,2,3,4,6,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,5,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,2,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,2,3,5,6,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,4,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [7,8,6,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [8,6,7,5,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,6,8,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [6,7,8,5,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [8,7,5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [7,8,5,6,4,3,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [8,6,5,7,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,6,5,8,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [6,7,5,8,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,5,6,8,4,3,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,5,7,8,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,6,7,8,4,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [8,7,6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [7,8,6,4,5,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [8,6,7,4,5,3,1,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [6,7,8,4,5,3,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [8,7,5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [8,5,6,4,7,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [8,6,4,5,7,3,1,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [8,5,4,6,7,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [7,6,5,4,8,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [7,5,6,4,8,3,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,5,7,4,8,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,6,4,5,8,3,1,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [6,7,4,5,8,3,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,5,4,7,8,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,6,4,7,8,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,4,6,7,8,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,5,6,7,8,3,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [8,7,6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [7,8,6,5,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [7,6,8,5,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [6,7,8,5,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [8,7,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [8,6,5,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [8,5,6,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [7,6,5,8,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [6,7,5,8,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [7,5,6,8,3,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [6,5,7,8,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [5,6,7,8,3,4,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [6,7,8,4,3,5,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [8,7,6,3,4,5,1,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [7,8,5,4,3,6,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [8,7,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [7,8,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [7,8,5,3,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [8,7,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [7,8,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [8,7,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [7,8,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [8,5,4,3,6,7,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [8,5,3,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [8,4,3,5,6,7,1,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [8,3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [7,6,5,4,3,8,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [7,5,6,4,3,8,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [5,6,7,4,3,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [6,7,4,5,3,8,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [5,6,4,7,3,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,5,6,7,3,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [7,6,5,3,4,8,1,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [7,6,4,3,5,8,1,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [7,6,3,4,5,8,1,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [7,5,4,3,6,8,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [7,5,3,4,6,8,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,3,4,5,6,8,1,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [6,5,4,3,7,8,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,6,4,3,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,4,6,3,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,5,6,3,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [5,6,3,4,7,8,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [6,4,3,5,7,8,1,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [6,3,4,5,7,8,1,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [5,4,3,6,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,5,3,6,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [5,3,4,6,7,8,1,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [4,3,5,6,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [7,8,6,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [8,6,7,5,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [7,6,8,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [6,7,8,5,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [8,7,5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [7,8,5,6,4,2,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [7,6,5,8,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [6,7,5,8,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,5,6,8,4,2,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,5,7,8,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,7,8,4,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [8,7,6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [7,6,8,4,5,2,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [8,4,5,6,7,2,1,3]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [7,6,5,4,8,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [6,7,5,4,8,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [6,5,7,4,8,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,7,4,8,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [7,6,4,5,8,2,1,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [7,4,5,6,8,2,1,3]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [5,4,6,7,8,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [4,5,6,7,8,2,1,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,8,6,5,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,6,8,5,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [6,7,8,5,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,8,5,6,4,1,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [8,6,5,7,4,1,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [7,6,5,8,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [6,7,5,8,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,5,6,8,4,1,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,5,7,8,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,6,7,8,4,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [8,6,7,4,5,1,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [6,7,8,4,5,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [8,7,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [7,8,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [8,7,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,5,6,4,7,1,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [8,6,4,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [8,4,5,6,7,1,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [7,6,5,4,8,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [6,7,5,4,8,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,6,7,4,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [6,7,4,5,8,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [7,5,4,6,8,1,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,5,4,7,8,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,6,4,7,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,4,6,7,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,5,6,7,8,1,2,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [8,7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [7,8,6,5,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [8,6,7,5,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [7,6,8,5,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,7,8,5,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [8,7,5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [7,8,5,6,3,2,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [8,6,5,7,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [8,5,6,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [7,6,5,8,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,7,5,8,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [7,5,6,8,3,2,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [6,5,7,8,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,7,8,3,2,1,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [8,7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [7,8,6,5,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [8,6,7,5,2,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [7,6,8,5,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,8,5,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,7,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [7,8,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [8,6,5,7,2,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,5,6,7,2,3,1,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [7,6,5,8,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,5,8,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [7,5,6,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [6,5,7,8,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,6,7,8,2,3,1,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [8,7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [7,8,6,5,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [8,6,7,5,3,1,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [7,6,8,5,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [8,7,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [7,8,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,6,5,8,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [6,7,5,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [7,5,6,8,3,1,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [6,5,7,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [5,6,7,8,3,1,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [8,7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [7,8,6,5,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [7,6,8,5,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,8,5,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,7,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [7,8,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [8,6,5,7,2,1,3,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,5,6,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [7,6,5,8,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,7,5,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [7,5,6,8,2,1,3,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [6,5,7,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,6,7,8,2,1,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [7,8,6,5,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [8,6,7,5,1,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [7,6,8,5,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,7,8,5,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [8,7,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [7,8,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [8,6,5,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [7,6,5,8,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,7,5,8,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [7,5,6,8,1,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [6,5,7,8,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [8,7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [7,8,6,4,3,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [8,6,7,4,3,2,1,5]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [7,6,8,4,3,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [6,7,8,4,3,2,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [8,7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,8,6,3,4,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,7,8,3,4,2,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [6,7,8,4,2,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [8,7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [8,6,7,3,2,4,1,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [6,7,8,3,2,4,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [8,6,7,2,3,4,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,6,8,2,3,4,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [6,7,8,2,3,4,1,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [8,7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [6,7,8,4,3,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [8,7,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [7,8,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [8,6,7,3,4,1,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,7,8,3,4,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [8,7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [7,8,6,4,2,1,3,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [8,6,7,4,2,1,3,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [6,7,8,4,2,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [8,7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [7,8,6,4,1,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,6,8,4,1,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [6,7,8,4,1,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [8,7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,8,6,3,2,1,4,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [8,6,7,3,2,1,4,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,6,8,3,2,1,4,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,7,8,3,2,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [7,8,6,2,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,6,7,2,3,1,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,6,8,2,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [6,7,8,2,3,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [8,7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [7,8,6,3,1,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [8,6,7,3,1,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,6,8,3,1,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,7,8,3,1,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [8,7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [7,8,6,2,1,3,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,6,7,2,1,3,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [6,7,8,2,1,3,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [7,8,6,1,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [8,6,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [7,6,8,1,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [6,7,8,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [8,7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [7,8,5,4,3,2,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [8,7,4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [7,8,4,5,3,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [8,7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,7,3,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,4,5,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,7,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [7,8,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [8,7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [7,8,5,2,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [8,7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [7,8,4,3,2,5,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [8,7,3,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,4,2,5,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,7,2,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,8,2,3,4,5,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [8,7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [7,8,5,4,3,1,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [8,7,5,3,4,1,2,6]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [8,7,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [7,8,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,8,5,4,2,1,3,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [8,7,5,4,1,2,3,6]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [7,8,5,4,1,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,8,4,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [8,7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [7,8,5,3,2,1,4,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [8,7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [7,8,5,3,1,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [8,7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [7,8,5,2,1,3,4,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [8,7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [7,8,5,1,2,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [7,8,4,3,2,1,5,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [8,7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,4,2,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,8,4,2,3,1,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [8,7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,2,4,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,7,2,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,8,2,3,4,1,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,8,4,3,1,2,5,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [8,7,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [7,8,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [8,7,4,2,1,3,5,6]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [7,8,4,2,1,3,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [8,7,4,1,2,3,5,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [8,7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [7,8,3,2,1,4,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [8,7,2,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,8,2,3,1,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,8,3,1,2,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [8,7,2,1,3,4,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,8,2,1,3,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [7,8,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [8,6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [8,5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [8,6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,5,6,3,4,2,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,4,3,5,6,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,3,4,5,6,2,1,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [8,5,6,4,2,3,1,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,4,5,6,2,3,1,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,6,5,3,2,4,1,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [8,5,6,2,3,4,1,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [8,6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,5,4,3,2,6,1,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [8,4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,5,4,2,3,6,1,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [8,4,5,2,3,6,1,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,5,3,2,4,6,1,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,5,2,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [8,3,2,4,5,6,1,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [8,6,5,4,3,1,2,7]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [8,6,4,5,3,1,2,7]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [8,6,5,3,4,1,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [8,5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [8,5,4,3,6,1,2,7]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [8,5,3,4,6,1,2,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [8,4,3,5,6,1,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [8,3,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [8,6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [8,5,6,4,2,1,3,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,4,5,6,2,1,3,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,6,5,4,1,2,3,7]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [8,5,6,4,1,2,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [8,6,4,5,1,2,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [8,4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [8,6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,5,6,3,2,1,4,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [8,5,6,2,3,1,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [8,5,6,3,1,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [8,6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [8,5,6,2,1,3,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [8,6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [8,5,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [8,6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,6,2,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [8,6,4,3,1,2,5,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,6,3,4,1,2,5,7]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [8,6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [8,6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [8,5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [8,4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,3,4,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,4,5,2,3,1,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [8,4,2,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [8,5,3,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [8,3,4,5,1,2,6,7]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [8,5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [8,5,4,1,2,3,6,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [8,4,5,1,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [8,5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,5,3,1,2,4,6,7]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [8,5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [8,4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [8,3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [8,3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [8,4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [8,3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [8,3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [8,2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110 [6,7,5,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [7,5,6,4,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,7,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,7,4,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [7,6,4,5,3,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [6,7,4,5,3,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,5,4,6,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,6,3,2,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [6,5,4,7,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,4,7,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,4,6,7,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,6,7,3,2,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [7,6,5,3,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [6,7,5,3,4,2,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [7,5,6,3,4,2,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [6,5,7,3,4,2,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,7,3,4,2,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [7,6,4,3,5,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [6,7,4,3,5,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [7,5,4,3,6,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,4,3,7,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,4,3,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,4,6,3,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,4,3,6,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [3,4,5,6,7,2,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [7,6,5,4,2,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [6,7,5,4,2,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,5,6,4,2,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,6,7,4,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [7,6,4,5,2,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [6,7,4,5,2,3,1,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [7,5,4,6,2,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,5,4,7,2,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,4,7,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,6,7,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [4,5,6,7,2,3,1,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [7,6,5,3,2,4,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [6,5,7,3,2,4,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,7,3,2,4,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [7,6,5,2,3,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [6,7,5,2,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [7,5,6,2,3,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [6,5,7,2,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,6,7,2,3,4,1,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [6,7,4,3,2,5,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,7,3,4,2,5,1,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,4,2,3,5,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [6,7,4,2,3,5,1,8]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [7,6,3,2,4,5,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [6,7,3,2,4,5,1,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,2,3,4,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [6,7,2,3,4,5,1,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [7,5,4,3,2,6,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,3,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,4,3,5,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,5,3,2,4,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,4,2,3,5,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [7,2,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [6,5,4,3,2,7,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,4,3,2,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,6,3,4,2,7,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,3,4,5,2,7,1,8]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,4,3,6,2,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,3,6,2,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [5,3,4,6,2,7,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,5,6,2,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,6,2,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [5,4,6,2,3,7,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [6,5,3,2,4,7,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,4,2,3,5,7,1,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [5,4,3,2,6,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [3,4,5,2,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,5,2,3,6,7,1,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,2,3,4,6,7,1,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,5,6,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,2,5,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,2,3,5,6,7,1,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,4,5,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,4,5,6,7,1,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [7,6,5,4,3,1,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [6,7,5,4,3,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,5,6,4,3,1,2,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [7,6,4,5,3,1,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [5,4,6,7,3,1,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,5,6,7,3,1,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [7,6,5,3,4,1,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [6,7,3,4,5,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [6,5,4,3,7,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,6,3,4,7,1,2,8]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [6,3,4,5,7,1,2,8]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,3,5,6,7,1,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,4,5,6,7,1,2,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [7,6,5,4,2,1,3,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [6,5,7,4,2,1,3,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,6,4,5,2,1,3,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [7,5,4,6,2,1,3,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,4,6,7,2,1,3,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [4,5,6,7,2,1,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [7,6,5,4,1,2,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [5,6,7,4,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [7,4,5,6,1,2,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [5,4,6,7,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,5,6,7,1,2,3,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [7,6,5,3,2,1,4,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [7,6,5,2,3,1,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [6,7,5,2,3,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [7,5,6,2,3,1,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [6,5,7,2,3,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,6,7,2,3,1,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [7,6,5,2,1,3,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [7,5,6,2,1,3,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [5,6,7,2,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [7,6,5,1,2,3,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [6,7,5,1,2,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [7,5,6,1,2,3,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [6,5,7,1,2,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [5,6,7,1,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [7,6,4,3,2,1,5,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [6,7,4,3,2,1,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,6,3,4,2,1,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [6,7,3,4,2,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,4,2,3,1,5,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,6,3,2,4,1,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [7,6,2,3,4,1,5,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [6,7,2,3,4,1,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [7,6,4,3,1,2,5,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [7,6,4,2,1,3,5,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,6,3,2,1,4,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [6,7,3,2,1,4,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,2,3,1,4,5,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [6,7,2,3,1,4,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [6,7,3,1,2,4,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [7,6,1,2,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [6,7,1,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [7,5,4,3,2,1,6,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [7,4,5,3,2,1,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,4,3,5,2,1,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,3,4,5,2,1,6,8]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [7,5,4,2,3,1,6,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [7,5,3,2,4,1,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,5,2,3,4,1,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [7,4,2,3,5,1,6,8]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [7,2,3,4,5,1,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [7,5,4,3,1,2,6,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [7,4,5,1,2,3,6,8]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [7,5,3,2,1,4,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,5,2,3,1,4,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [7,5,3,1,2,4,6,8]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [7,5,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [7,4,3,2,1,5,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [7,2,3,4,1,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [7,4,3,1,2,5,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [7,3,4,1,2,5,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [7,4,1,2,3,5,6,8]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [7,3,2,1,4,5,6,8]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [7,2,3,1,4,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [7,3,1,2,4,5,6,8]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [7,2,1,3,4,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>1111100 [5,6,4,3,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [5,4,6,3,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,6,3,2,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [5,6,3,4,2,1,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,4,3,6,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [3,4,5,6,2,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [5,4,6,2,3,1,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,6,3,2,4,1,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,5,2,3,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [5,6,2,3,4,1,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [6,4,3,2,5,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [6,2,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [5,4,3,2,6,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,3,2,6,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [4,3,5,2,6,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,2,6,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [5,2,3,4,6,1,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,5,6,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,2,5,6,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,2,3,5,6,1,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,4,5,6,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,4,5,6,1,7,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [6,5,4,3,1,2,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [5,4,6,3,1,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,4,3,6,1,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [4,3,5,6,1,2,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,4,5,6,1,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [6,5,4,2,1,3,7,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [6,4,5,2,1,3,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,5,6,2,1,3,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [5,6,3,2,1,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,2,1,3,4,7,8]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [6,4,3,2,1,5,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [6,3,4,2,1,5,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [6,4,3,1,2,5,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [6,4,2,1,3,5,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [6,4,1,2,3,5,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [6,2,3,1,4,5,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [6,3,1,2,4,5,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [6,1,2,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>1111000 [4,5,3,2,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [5,3,4,2,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,5,2,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,5,2,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [5,4,2,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [4,5,2,3,1,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,5,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,2,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,2,3,5,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,4,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [5,4,3,1,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [4,3,5,1,2,6,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,4,5,1,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [5,4,2,1,3,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [4,5,2,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,5,1,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [5,3,2,1,4,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [5,2,3,1,4,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [5,3,1,2,4,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [5,1,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>1110000 [3,4,2,1,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,4,1,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,4,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [4,3,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [4,2,1,3,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [4,1,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>1100000 [2,3,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [3,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>1000000 [1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>0000000 [6,8,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101 [5,8,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [5,7,8,6,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [6,5,8,7,4,3,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [5,6,8,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [5,7,6,8,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [4,8,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [4,7,8,6,5,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [4,6,8,7,5,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [4,7,6,8,5,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [5,4,7,8,6,3,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,8,7,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [5,6,4,8,7,3,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,6,5,8,7,3,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [4,5,6,8,7,3,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [5,7,6,4,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [4,7,6,5,8,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [4,6,7,5,8,3,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [5,4,7,6,8,3,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,7,6,8,3,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [4,6,5,7,8,3,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [3,8,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [3,7,8,6,5,4,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [3,6,8,7,5,4,2,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [3,7,6,8,5,4,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [3,5,8,7,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [3,5,7,8,6,4,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [3,5,6,8,7,4,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [3,7,6,5,8,4,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [3,5,7,6,8,4,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [3,5,6,7,8,4,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,8,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [4,3,7,8,6,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [4,3,6,7,8,5,2,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,6,7,8,5,2,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,4,3,8,7,6,2,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [5,4,3,7,8,6,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,4,7,8,6,2,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,4,5,7,8,6,2,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [6,5,4,3,8,7,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [5,6,4,3,8,7,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,6,3,8,7,2,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,6,5,4,8,7,2,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [4,3,6,5,8,7,2,1]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [5,4,3,6,8,7,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,3,6,8,7,2,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,5,6,8,7,2,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [5,7,6,4,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [5,4,7,6,3,8,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,7,6,5,4,8,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [3,5,7,6,4,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [3,5,6,7,4,8,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,7,6,5,8,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [3,4,7,6,5,8,2,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [3,4,6,7,5,8,2,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,5,4,7,6,8,2,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,4,5,7,6,8,2,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [3,6,5,4,7,8,2,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [3,5,6,4,7,8,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,6,5,7,8,2,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,6,5,7,8,2,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,5,4,6,7,8,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [2,7,8,6,5,4,3,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [2,6,8,7,5,4,3,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [2,7,6,8,5,4,3,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [2,6,7,8,5,4,3,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,8,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [2,6,7,5,8,4,3,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,6,7,8,4,3,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,8,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [2,4,7,8,6,5,3,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [2,4,6,8,7,5,3,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [2,4,6,7,8,5,3,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,5,4,8,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [2,5,4,7,8,6,3,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [2,4,5,7,8,6,3,1]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [2,6,5,4,8,7,3,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [2,5,6,4,8,7,3,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,4,6,5,8,7,3,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,4,5,6,8,7,3,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,7,6,5,4,8,3,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [2,5,6,7,4,8,3,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,6,7,5,8,3,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,5,4,7,6,8,3,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [2,6,5,4,7,8,3,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,6,4,7,8,3,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,6,5,7,8,3,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,5,4,6,7,8,3,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,5,6,7,8,3,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,8,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [3,2,7,8,6,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,2,6,8,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [3,2,5,7,8,6,4,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,5,7,6,8,4,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,5,6,7,8,4,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,8,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [2,3,6,7,8,5,4,1]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [2,3,5,7,8,6,4,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,6,5,8,7,4,1]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,3,5,6,8,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,3,7,6,5,8,4,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [2,3,5,7,6,8,4,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,5,6,7,8,4,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,8,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,3,2,7,8,6,5,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [3,4,2,8,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [3,4,2,7,8,6,5,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [2,4,3,8,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [2,4,3,6,8,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,4,3,6,7,8,5,1]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [3,2,4,8,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [2,3,4,8,7,6,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [2,3,4,7,8,6,5,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,3,4,6,8,7,5,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,3,4,7,6,8,5,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,3,4,6,7,8,5,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [5,4,3,2,8,7,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [5,4,3,2,7,8,6,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,4,2,7,8,6,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,4,5,2,7,8,6,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,5,4,3,8,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [2,5,4,3,7,8,6,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [2,4,5,3,7,8,6,1]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [3,2,5,4,7,8,6,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,3,5,4,7,8,6,1]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [4,3,2,5,8,7,6,1]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,2,5,7,8,6,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,2,5,8,7,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [3,4,2,5,7,8,6,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,4,5,7,8,6,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,4,5,8,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [2,3,4,5,7,8,6,1]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [6,5,4,3,2,8,7,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [4,6,5,3,2,8,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,4,6,3,2,8,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [3,5,6,4,2,8,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,3,6,5,2,8,7,1]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [5,4,3,6,2,8,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,3,6,2,8,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,5,6,2,8,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,6,5,4,3,8,7,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [2,4,6,5,3,8,7,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,4,5,6,3,8,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,6,5,4,8,7,1]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [2,3,5,6,4,8,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [4,3,2,6,5,8,7,1]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [2,4,3,6,5,8,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [3,2,4,6,5,8,7,1]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,3,4,6,5,8,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [5,4,3,2,6,8,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [2,4,5,3,6,8,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,5,4,6,8,7,1]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,3,2,5,6,8,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,2,5,6,8,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,4,3,5,6,8,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,4,5,6,8,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,3,4,5,6,8,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [5,7,6,4,3,2,8,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [4,7,6,5,3,2,8,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [4,6,7,5,3,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [4,6,5,7,3,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [3,5,7,6,4,2,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [3,5,6,7,4,2,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,7,6,5,2,8,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [3,4,7,6,5,2,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [3,4,6,7,5,2,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,4,3,7,6,2,8,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,4,7,6,2,8,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,4,5,7,6,2,8,1]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [4,6,5,3,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [3,6,5,4,7,2,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [3,5,6,4,7,2,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,6,5,7,2,8,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,6,5,7,2,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,5,4,6,7,2,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,7,6,5,4,3,8,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [2,6,5,7,4,3,8,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,6,7,4,3,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,6,7,5,3,8,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,4,6,5,7,3,8,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,5,4,6,7,3,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,5,6,7,3,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,7,6,5,4,8,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,2,6,7,5,4,8,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,5,7,6,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,6,5,7,4,8,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,5,6,7,4,8,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,7,6,5,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [2,3,5,7,6,4,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,5,6,7,4,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,7,6,5,8,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,2,6,7,5,8,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,2,7,6,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,4,2,6,7,5,8,1]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,4,3,7,6,5,8,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [2,4,3,6,7,5,8,1]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [3,2,4,7,6,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [2,3,4,7,6,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,3,4,6,7,5,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [5,4,3,2,7,6,8,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,4,2,7,6,8,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,3,5,2,7,6,8,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,5,2,7,6,8,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,5,4,7,6,8,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,3,5,4,7,6,8,1]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [4,3,2,5,7,6,8,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,2,5,7,6,8,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,4,5,7,6,8,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,4,5,7,6,8,1]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [3,5,6,4,2,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [3,4,6,5,2,7,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,5,4,6,2,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,6,5,4,3,7,8,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,6,4,3,7,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,6,5,3,7,8,1]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,4,5,6,3,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,5,6,4,7,8,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,6,5,4,7,8,1]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [2,3,5,6,4,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,6,5,7,8,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,2,6,5,7,8,1]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,4,3,6,5,7,8,1]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [2,3,4,6,5,7,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [3,5,4,2,6,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,4,5,3,6,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,5,4,6,7,8,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,5,4,6,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [2,4,3,5,6,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [1,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [1,7,8,6,5,4,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,6,8,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [1,7,6,8,5,4,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,6,7,8,5,4,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,8,7,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [1,6,5,8,7,4,3,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [1,7,6,5,8,4,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,6,7,5,8,4,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,7,6,8,4,3,2]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [1,6,5,7,8,4,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,6,7,8,4,3,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,8,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [1,4,7,8,6,5,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [1,4,6,8,7,5,3,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [1,4,6,7,8,5,3,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,5,4,7,8,6,3,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [1,4,5,8,7,6,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [1,4,6,5,8,7,3,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,7,6,5,4,8,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,4,7,6,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [1,4,6,7,5,8,3,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,6,5,4,7,8,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,6,4,7,8,3,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,5,4,6,7,8,3,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,6,7,8,3,2]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,8,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [1,3,7,8,6,5,4,2]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [1,3,6,8,7,5,4,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [1,3,6,7,8,5,4,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,5,8,7,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,3,5,7,8,6,4,2]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [1,3,5,6,8,7,4,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,3,6,7,5,8,4,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,6,5,7,8,4,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,5,6,7,8,4,2]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,4,3,8,7,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [1,4,3,7,8,6,5,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [1,4,3,6,8,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,4,3,7,6,8,5,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [1,4,3,6,7,8,5,2]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,3,4,8,7,6,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [1,3,4,7,6,8,5,2]=>[[1,2,4,5,8],[3],[6],[7]]=>0100110 [1,3,4,6,7,8,5,2]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,5,4,3,8,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [1,4,5,3,8,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,4,5,3,7,8,6,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,5,4,8,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,4,3,5,7,8,6,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,4,5,8,7,6,2]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011 [1,3,4,5,7,8,6,2]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,6,5,4,3,8,7,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [1,5,6,4,3,8,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,4,6,5,3,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,4,5,6,3,8,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,4,3,6,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,5,4,3,6,8,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,4,5,3,6,8,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,3,4,5,6,8,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,7,6,5,4,3,8,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,6,7,5,4,3,8,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,6,5,7,4,3,8,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,6,7,4,3,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,6,7,5,3,8,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,5,6,4,7,3,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,6,5,7,3,8,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,5,4,6,7,3,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,6,7,3,8,2]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,6,5,7,4,8,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,5,6,7,4,8,2]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,3,4,6,7,5,8,2]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,3,5,4,7,6,8,2]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [1,3,4,5,7,6,8,2]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,5,4,6,3,7,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,3,6,5,7,8,2]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,3,4,6,5,7,8,2]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,5,4,3,6,7,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,3,6,7,8,2]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,4,3,5,6,7,8,2]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,4,5,6,7,8,2]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [2,1,7,8,6,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,1,6,8,7,5,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [2,1,7,6,8,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,1,6,7,8,5,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,8,7,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,1,5,7,8,6,4,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [2,1,6,5,8,7,4,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,1,5,6,8,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,1,7,6,5,8,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,1,6,7,5,8,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,7,6,8,4,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [2,1,6,5,7,8,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,6,7,8,4,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,8,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,1,4,7,8,6,5,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,1,4,6,8,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,1,4,6,7,8,5,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,1,5,4,8,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [2,1,5,4,7,8,6,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,1,4,5,8,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,1,4,5,7,8,6,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [2,1,6,5,4,8,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,1,5,6,4,8,7,3]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,4,6,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,5,4,6,8,7,3]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,4,5,6,8,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,1,7,6,5,4,8,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,1,6,7,5,4,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,7,6,4,8,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [2,1,6,5,7,4,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,6,7,4,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,7,6,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,1,4,6,7,5,8,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,1,5,4,7,6,8,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,1,5,6,4,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,5,4,6,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [1,2,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [1,2,7,8,6,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,2,7,6,8,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,2,6,7,8,5,4,3]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,2,5,8,7,6,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [1,2,6,5,8,7,4,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,2,5,6,8,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,2,7,6,5,8,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,2,5,7,6,8,4,3]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [1,2,6,5,7,8,4,3]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,2,5,6,7,8,4,3]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,4,8,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [1,2,4,7,8,6,5,3]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [1,2,4,6,8,7,5,3]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [1,2,4,6,7,8,5,3]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [1,2,5,4,8,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,2,4,5,8,7,6,3]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,2,4,5,7,8,6,3]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [1,2,5,4,6,8,7,3]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,2,4,5,6,8,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,2,7,6,5,4,8,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,2,5,7,6,4,8,3]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [1,2,5,6,7,4,8,3]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,4,7,6,5,8,3]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [1,2,5,4,7,6,8,3]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [1,2,6,5,4,7,8,3]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,2,5,6,4,7,8,3]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,5,4,6,7,8,3]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,4,5,6,7,8,3]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [3,2,1,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [3,2,1,7,8,6,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,2,1,6,8,7,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,2,1,7,6,8,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,2,1,6,7,8,5,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,2,1,5,8,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,2,1,5,7,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,1,6,5,8,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [3,2,1,5,6,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,7,6,5,8,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,2,1,6,7,5,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,2,1,5,7,6,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,1,6,5,7,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,2,1,5,6,7,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,1,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [2,3,1,7,8,6,5,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,3,1,6,8,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,3,1,7,6,8,5,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,3,1,6,7,8,5,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,3,1,5,7,8,6,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,3,1,6,5,8,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,3,1,7,6,5,8,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,3,1,6,7,5,8,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,3,1,5,7,6,8,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,3,1,5,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [1,3,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,3,2,6,8,7,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,3,2,7,6,8,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,3,2,6,7,8,5,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,3,2,5,8,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [1,3,2,5,7,8,6,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,2,6,5,8,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,3,2,5,6,8,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [1,3,2,7,6,5,8,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,3,2,6,7,5,8,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,3,2,6,5,7,8,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,3,2,5,6,7,8,4]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [2,1,3,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [2,1,3,7,8,6,5,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,1,3,6,8,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,1,3,6,7,8,5,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,1,3,6,5,8,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,1,3,5,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [1,2,3,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [1,2,3,7,8,6,5,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [1,2,3,6,8,7,5,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,2,3,7,6,8,5,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [1,2,3,6,7,8,5,4]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,8,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,2,3,5,7,8,6,4]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,2,3,6,5,8,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,2,3,5,6,8,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,2,3,7,6,5,8,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [1,2,3,6,7,5,8,4]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,7,6,8,4]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,2,3,6,5,7,8,4]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,6,7,8,4]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [4,3,2,1,7,8,6,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,2,1,6,8,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,2,1,7,6,8,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,2,1,6,7,8,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,2,1,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,4,2,1,7,8,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,4,2,1,6,8,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,4,2,1,7,6,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,4,2,1,6,7,8,5]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,4,3,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,4,3,1,7,8,6,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [2,4,3,1,6,8,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,4,3,1,7,6,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [2,4,3,1,6,7,8,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [3,2,4,1,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,4,1,7,8,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,4,1,6,8,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,4,1,7,6,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,4,1,6,7,8,5]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,3,4,1,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,4,1,7,8,6,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,4,1,6,8,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,1,7,6,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,4,1,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,4,3,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [1,4,3,2,6,8,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [1,4,3,2,7,6,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [1,4,3,2,6,7,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,3,4,2,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,3,4,2,7,8,6,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,3,4,2,6,8,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,3,4,2,7,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,3,4,2,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,1,4,3,7,8,6,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,1,4,3,6,8,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,1,4,3,7,6,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,1,4,3,6,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [1,2,4,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,2,4,3,7,8,6,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,2,4,3,7,6,8,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,2,4,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [3,2,1,4,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,1,4,7,8,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,1,4,6,8,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,1,4,7,6,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,1,4,6,7,8,5]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,3,1,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,1,4,7,8,6,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,1,4,7,6,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,1,4,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,3,2,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,3,2,4,6,8,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,3,2,4,7,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,3,2,4,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [2,1,3,4,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,1,3,4,7,8,6,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,1,3,4,7,6,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,1,3,4,6,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,2,3,4,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,2,3,4,7,8,6,5]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,2,3,4,6,8,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,2,3,4,7,6,8,5]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [5,4,3,2,1,8,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [5,4,3,2,1,7,8,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,3,2,1,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,5,4,2,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [3,5,4,2,1,7,8,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,3,5,2,1,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,4,5,2,1,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [2,5,4,3,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [2,4,5,3,1,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [2,4,5,3,1,7,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [3,2,5,4,1,8,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [3,2,5,4,1,7,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,3,5,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [4,3,2,5,1,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,2,5,1,7,8,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,2,5,1,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,4,2,5,1,7,8,6]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,4,3,5,1,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [2,4,3,5,1,7,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [3,2,4,5,1,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [2,3,4,5,1,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,4,5,1,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,5,4,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [1,5,4,3,2,7,8,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [1,4,5,3,2,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [1,4,5,3,2,7,8,6]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,5,4,2,7,8,6]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [1,3,4,5,2,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,3,4,5,2,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [2,1,4,5,3,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,2,5,4,3,7,8,6]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [1,2,4,5,3,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,2,4,5,3,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,3,2,5,4,7,8,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [2,1,3,5,4,8,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,1,3,5,4,7,8,6]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,3,5,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [4,3,2,1,5,8,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,2,1,5,7,8,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [2,4,3,1,5,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [3,2,4,1,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,4,1,5,7,8,6]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,4,1,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,4,1,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,4,3,2,5,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [1,4,3,2,5,7,8,6]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,4,2,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [2,1,4,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,1,4,3,5,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [1,2,4,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,2,4,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [3,2,1,4,5,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,1,4,5,7,8,6]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,1,4,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,3,2,4,5,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,3,2,4,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [2,1,3,4,5,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,1,3,4,5,7,8,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [5,6,4,3,2,1,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,6,5,3,2,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,4,6,3,2,1,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,6,3,2,1,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,6,5,4,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [3,5,6,4,2,1,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,3,6,5,2,1,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [3,4,6,5,2,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,4,3,6,2,1,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,3,6,2,1,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,3,5,6,2,1,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,5,6,2,1,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,6,5,4,3,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [2,5,6,4,3,1,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,4,6,5,3,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,2,6,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [3,2,5,6,4,1,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [2,3,6,5,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,3,5,6,4,1,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [4,3,2,6,5,1,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [3,4,2,6,5,1,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,4,3,6,5,1,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,4,3,2,6,1,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,3,5,2,6,1,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,5,2,6,1,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,5,4,3,6,1,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,4,5,3,6,1,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,5,4,6,1,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,3,2,5,6,1,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,2,5,6,1,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,4,3,5,6,1,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [2,3,4,5,6,1,8,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [1,6,5,4,3,2,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [1,5,6,4,3,2,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,5,4,6,3,2,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,3,6,5,4,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [1,3,4,5,6,2,8,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [2,1,6,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,1,5,6,4,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,4,6,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,5,4,6,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,4,5,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [1,2,4,5,6,3,8,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [2,3,1,6,5,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [1,3,2,6,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,3,2,5,6,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [2,1,3,5,6,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [1,2,3,6,5,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,2,3,5,6,4,8,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [4,3,2,1,6,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [3,4,2,1,6,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,4,3,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [3,2,4,1,6,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,3,4,1,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [1,3,4,2,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [2,3,1,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [1,3,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [2,1,3,4,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [5,4,3,2,1,6,8,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [4,5,3,2,1,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,5,4,2,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,3,5,2,1,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,4,5,2,1,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,5,4,3,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,4,5,3,1,6,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,5,4,1,6,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [2,3,5,4,1,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [2,3,4,5,1,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [1,4,5,3,2,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,3,5,4,2,6,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [2,1,4,5,3,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [1,2,5,4,3,6,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,2,3,5,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [4,3,2,1,5,6,8,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,2,4,1,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,3,4,1,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [1,4,3,2,5,6,8,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,3,4,2,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [2,1,4,3,5,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [1,2,4,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [3,2,1,4,5,6,8,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,3,1,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [1,3,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [2,1,3,4,5,6,8,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [5,7,6,4,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>1111010 [4,7,6,5,3,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [5,4,7,6,3,2,1,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,7,6,3,2,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [4,6,5,7,3,2,1,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>1110100 [3,5,7,6,4,2,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [3,5,6,7,4,2,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,7,6,5,2,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [3,4,7,6,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [5,4,3,7,6,2,1,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,4,7,6,2,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,6,5,4,7,2,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [3,5,6,4,7,2,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [4,3,6,5,7,2,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [2,7,6,5,4,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [2,6,7,5,4,3,1,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [2,5,7,6,4,3,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [2,5,6,7,4,3,1,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,6,7,5,3,1,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,5,6,4,7,3,1,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,5,4,6,7,3,1,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,5,6,7,3,1,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,7,6,5,4,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,2,6,7,5,4,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,5,7,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,6,5,7,4,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,5,6,7,4,1,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,7,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [2,3,6,7,5,4,1,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [2,3,5,7,6,4,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,6,5,7,4,1,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [2,3,5,6,7,4,1,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,6,7,5,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,2,6,7,5,1,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,2,4,6,7,5,1,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,3,4,7,6,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,3,4,6,7,5,1,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [5,4,3,2,7,6,1,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,3,2,7,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,5,4,2,7,6,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,3,5,2,7,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,5,2,7,6,1,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,5,4,7,6,1,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,3,2,5,7,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,4,2,5,7,6,1,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,4,5,7,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [3,5,6,4,2,7,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [3,4,6,5,2,7,1,8]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,5,4,6,2,7,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,5,4,6,3,7,1,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [3,2,6,5,4,7,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [2,3,5,6,4,7,1,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [2,4,3,6,5,7,1,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [2,3,4,6,5,7,1,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [2,3,5,4,6,7,1,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [1,7,6,5,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,6,7,5,4,3,2,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,6,5,7,4,3,2,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,6,7,4,3,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,7,6,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [1,4,6,7,5,3,2,8]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,5,6,4,7,3,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,5,4,6,7,3,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,6,7,3,2,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,6,7,5,4,2,8]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,5,7,6,4,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [1,3,6,5,7,4,2,8]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,3,5,6,7,4,2,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,3,4,6,7,5,2,8]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,3,5,4,7,6,2,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [1,4,3,5,7,6,2,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,4,5,7,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,5,4,6,3,7,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,3,6,5,4,7,2,8]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,5,4,3,6,7,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,3,6,7,2,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,4,5,6,7,2,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,7,6,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,1,6,7,5,4,3,8]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,6,7,4,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,5,6,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [1,2,7,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,2,6,7,5,4,3,8]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,2,5,7,6,4,3,8]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [1,2,5,6,7,4,3,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,4,6,7,5,3,8]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [1,2,5,6,4,7,3,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,5,4,6,7,3,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,2,4,5,6,7,3,8]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [3,2,1,7,6,5,4,8]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,2,1,5,7,6,4,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [2,3,1,6,7,5,4,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,3,1,5,6,7,4,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [1,3,2,7,6,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,3,2,6,7,5,4,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,3,2,5,7,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,2,5,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [2,1,3,6,7,5,4,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [1,2,3,7,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [1,2,3,6,7,5,4,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,7,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,2,3,6,5,7,4,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,6,7,4,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [4,3,2,1,7,6,5,8]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,2,1,6,7,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,2,4,1,7,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,4,1,6,7,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,3,4,1,7,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,4,1,6,7,5,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,4,3,2,7,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [1,4,3,2,6,7,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,3,4,2,6,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,2,4,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [3,2,1,4,7,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [2,3,1,4,6,7,5,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,3,2,4,7,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,2,3,4,7,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,2,3,4,6,7,5,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [5,4,3,2,1,7,6,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,5,3,2,1,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,5,4,2,1,7,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,4,5,2,1,7,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,4,5,3,1,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [3,2,5,4,1,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,3,4,5,1,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,5,4,3,2,7,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [1,4,5,3,2,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,5,4,2,7,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [1,3,4,5,2,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [2,1,5,4,3,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [1,2,4,5,3,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [3,2,1,5,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,3,1,5,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [1,3,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,2,3,5,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [4,3,2,1,5,7,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,2,4,1,5,7,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [2,3,4,1,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,4,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,4,2,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,2,4,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [2,3,1,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,3,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [2,1,3,4,5,7,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [1,2,3,4,5,7,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [3,6,5,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [4,3,6,5,2,1,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [2,4,6,5,3,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,4,5,6,3,1,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [2,3,6,5,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [2,3,5,6,4,1,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [4,3,2,6,5,1,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [2,4,3,6,5,1,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [2,3,4,6,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [3,5,4,2,6,1,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [1,6,5,4,3,2,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,6,4,3,2,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,6,5,3,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,5,4,6,3,2,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,6,3,2,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,5,6,4,2,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,4,3,6,5,2,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,5,4,3,6,2,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,3,6,2,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,4,3,5,6,2,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,4,5,6,2,7,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,5,6,4,3,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,6,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [1,2,6,5,4,3,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,2,4,6,5,3,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [1,2,4,5,6,3,7,8]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [3,2,1,5,6,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,1,6,5,4,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,3,1,5,6,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [1,3,2,6,5,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,3,2,5,6,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,2,3,6,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,2,3,5,6,4,7,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [4,3,2,1,6,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [2,4,3,1,6,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [3,2,4,1,6,5,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [2,3,4,1,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,1,4,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [1,2,4,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,3,2,4,6,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [2,1,3,4,6,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [1,2,3,4,6,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [3,5,4,2,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>1101000 [2,5,4,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [2,4,5,3,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [3,2,5,4,1,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,3,5,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [2,4,3,5,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [1,5,4,3,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [1,4,5,3,2,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,4,5,2,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,5,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,1,4,5,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [1,2,5,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [2,3,1,5,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [1,3,2,5,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,2,3,5,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [2,4,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>1010000 [1,4,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [1,3,4,2,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [2,1,4,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [1,2,4,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [1,3,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>0100000 [1,2,3,4,8,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,2,3,5,8,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,2,3,7,5,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,2,3,7,5,6,8,4]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,2,3,8,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,2,3,8,5,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,2,3,8,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,2,3,8,6,7,5,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,2,4,5,8,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,2,4,7,5,6,8,3]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [1,2,4,8,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,2,4,8,6,5,7,3]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [1,2,6,4,5,7,8,3]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [1,2,7,4,5,6,8,3]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [1,2,8,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,2,8,4,6,7,5,3]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [1,2,8,4,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [1,2,7,5,4,6,3,8]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [1,2,7,5,4,6,8,3]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [1,2,8,5,4,6,7,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,2,8,5,6,4,7,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,2,8,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,2,8,6,5,4,7,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [1,2,8,6,5,7,4,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [1,2,8,7,5,6,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [1,3,2,7,5,6,8,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,2,8,5,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [1,3,2,8,6,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,3,2,8,6,7,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,3,4,2,8,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,3,4,5,8,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,3,4,8,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,3,6,4,5,2,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [1,3,6,4,5,7,8,2]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,3,7,4,5,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,3,7,4,5,6,8,2]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,3,8,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,3,8,4,6,5,7,2]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [1,3,8,5,4,6,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,3,8,5,4,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,3,8,5,6,7,4,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,3,8,5,7,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,3,8,6,5,7,4,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [1,3,8,7,5,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,4,3,5,8,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,4,3,8,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,4,3,8,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,4,3,8,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,4,3,8,6,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,5,3,4,2,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,5,3,4,2,7,8,6]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [1,5,3,4,2,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [1,5,3,4,6,2,8,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [1,5,3,4,6,7,2,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,5,3,4,6,7,8,2]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [1,6,3,4,5,2,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,6,3,4,5,8,7,2]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [1,7,3,4,5,6,2,8]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,7,3,4,5,6,8,2]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,8,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,8,3,4,6,7,5,2]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [1,6,3,5,4,2,7,8]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [1,6,3,5,4,8,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [1,7,3,5,4,6,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [1,8,3,5,4,6,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,8,3,5,4,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,8,3,5,6,4,7,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,8,3,5,6,7,4,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [1,8,3,5,7,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,7,3,6,5,4,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [1,7,3,6,5,4,8,2]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [1,8,3,6,5,4,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [1,8,3,7,5,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,8,3,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [1,6,4,3,5,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,6,4,3,5,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,8,4,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,8,4,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,7,4,3,6,5,8,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [1,8,4,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,8,4,3,6,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,6,4,5,3,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [1,6,4,5,3,2,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,6,4,5,3,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,7,4,5,3,6,8,2]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [1,8,4,5,3,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,7,4,5,6,3,8,2]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [1,8,4,5,6,3,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,8,4,5,6,7,3,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,7,4,6,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [1,8,4,6,5,3,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [1,8,4,6,5,7,3,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [1,8,4,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [1,7,5,4,3,6,8,2]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [1,8,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [1,8,5,4,3,7,6,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,8,5,4,6,3,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [1,8,5,4,6,7,3,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [1,8,5,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,7,6,4,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [1,8,6,4,5,3,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [1,8,6,4,5,7,3,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [1,8,7,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [1,8,7,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [1,8,6,5,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [1,8,6,5,4,7,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [1,8,7,5,4,6,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [1,8,7,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [2,1,3,4,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,1,3,5,8,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,1,3,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,1,3,8,5,7,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [2,1,3,8,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,1,3,8,6,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,1,4,3,8,6,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,1,4,5,8,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,1,4,8,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,1,4,8,5,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,1,4,8,6,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,1,4,8,6,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,1,5,4,8,6,7,3]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,6,4,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,6,4,5,7,8,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,1,6,4,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,8,4,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,1,8,4,5,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,1,7,4,6,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,1,8,4,6,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,1,8,4,6,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,1,8,4,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,1,8,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,1,8,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [2,1,7,5,6,4,8,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [2,1,8,5,6,4,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,1,8,5,6,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,1,8,5,7,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,1,8,6,5,4,7,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [2,1,8,6,5,7,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [2,1,8,7,5,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,3,1,7,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,3,1,8,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,3,1,8,6,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,3,4,1,8,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,5,8,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,4,7,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [2,3,4,7,5,6,8,1]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [2,3,4,8,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,4,8,5,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [2,3,4,8,6,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,3,4,8,6,7,5,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,3,5,4,8,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [2,3,6,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [2,3,6,4,5,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,3,6,4,5,7,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [2,3,6,4,5,8,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,3,7,4,5,6,8,1]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [2,3,8,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,7,4,6,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,3,8,4,6,7,5,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,3,7,5,4,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,7,5,4,6,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,8,5,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,3,7,5,6,4,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,7,5,6,4,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,3,8,5,6,4,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,3,8,5,6,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,3,8,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [2,3,8,6,5,4,7,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [2,4,3,5,8,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [2,4,3,7,5,6,8,1]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [2,4,3,8,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [2,4,3,8,5,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,4,3,8,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,5,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [2,5,3,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [2,5,3,4,6,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>1001000 [2,5,3,4,6,8,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [2,5,3,4,7,6,8,1]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [2,5,3,4,8,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [2,6,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [2,6,3,4,5,7,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>1000100 [2,6,3,4,5,8,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,7,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [2,8,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,8,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [2,6,3,5,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,6,3,5,4,8,7,1]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,7,3,5,4,6,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,8,3,5,4,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,7,3,5,6,4,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [2,8,3,5,6,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,8,3,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [2,7,3,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [2,8,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [2,8,3,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [2,5,4,3,8,6,7,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,6,4,3,5,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,4,3,5,8,7,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,7,4,3,5,6,8,1]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [2,8,4,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,8,4,3,5,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,7,4,3,6,5,8,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [2,8,4,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,8,4,3,6,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,8,4,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [2,6,4,5,3,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [2,8,4,5,3,6,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,7,4,5,6,3,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [2,7,4,5,6,3,8,1]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [2,8,4,5,6,3,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,8,4,5,6,7,3,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,7,4,6,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [2,7,4,6,5,3,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [2,8,4,6,5,3,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [2,8,4,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [2,7,5,4,3,6,8,1]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [2,8,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [2,8,5,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [2,7,5,4,6,3,8,1]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [2,8,5,4,6,7,3,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [2,8,5,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [2,7,6,4,5,3,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [2,8,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [2,8,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [2,8,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [2,8,7,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [3,2,1,4,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,1,5,8,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,7,5,6,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,1,8,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,8,5,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,2,1,8,6,5,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,2,1,8,6,7,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,2,4,1,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,4,5,8,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,2,4,7,5,6,8,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,4,8,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,2,4,8,6,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,2,5,4,8,6,7,1]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,2,6,4,5,1,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,2,7,4,5,6,1,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,8,4,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,2,7,4,6,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,2,7,4,6,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,2,8,4,6,5,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,2,7,5,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,8,5,4,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [3,2,8,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [3,2,7,5,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,7,5,6,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,2,8,5,6,4,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [3,2,8,5,7,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [3,2,8,6,5,7,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [3,2,8,7,5,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [4,2,3,1,5,7,6,8]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [4,2,3,1,5,7,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [4,2,3,1,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,3,1,6,7,8,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [4,2,3,1,6,8,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,2,3,1,7,6,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [4,2,3,1,8,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,2,3,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [4,2,3,5,1,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [4,2,3,5,6,1,8,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,3,5,6,8,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,3,5,8,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [4,2,3,6,5,8,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,3,7,5,6,8,1]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [4,2,3,8,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,3,8,5,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [4,2,3,7,6,5,8,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [4,2,3,8,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [5,2,3,4,1,6,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [5,2,3,4,1,7,8,6]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [5,2,3,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [5,2,3,4,6,1,8,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [5,2,3,4,7,6,1,8]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [5,2,3,4,8,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [6,2,3,4,5,1,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [6,2,3,4,5,8,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [8,2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,2,3,4,6,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [8,2,3,4,7,6,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [6,2,3,5,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [6,2,3,5,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [6,2,3,5,4,7,1,8]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [6,2,3,5,4,7,8,1]=>[[1,3,4,7,8],[2],[5],[6]]=>1001100 [7,2,3,5,4,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [8,2,3,5,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [8,2,3,5,4,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [7,2,3,5,6,4,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [8,2,3,5,6,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [8,2,3,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [7,2,3,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [8,2,3,6,5,4,7,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [8,2,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [8,2,3,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [5,2,4,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [5,2,4,3,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,2,4,3,1,7,6,8]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,2,4,3,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [5,2,4,3,6,1,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,2,4,3,6,7,1,8]=>[[1,3,6,7,8],[2],[4],[5]]=>1011000 [5,2,4,3,7,6,1,8]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,2,4,3,7,6,8,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,2,4,3,8,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,2,4,3,5,1,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [7,2,4,3,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [7,2,4,3,6,5,8,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [8,2,4,3,6,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [8,2,4,3,6,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [8,2,4,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [6,2,4,5,3,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [7,2,4,5,3,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [7,2,4,5,3,6,8,1]=>[[1,3,5,6,8],[2],[4],[7]]=>1010010 [8,2,4,5,3,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,2,4,5,6,7,3,1]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,2,4,5,7,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [7,2,4,6,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,2,4,6,5,3,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [8,2,4,7,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [8,2,4,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [6,2,5,4,3,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,2,5,4,3,7,1,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [6,2,5,4,3,7,8,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [7,2,5,4,3,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [8,2,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [8,2,5,4,3,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [7,2,5,4,6,3,8,1]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [8,2,5,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [7,2,6,4,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,2,6,4,5,3,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [8,2,6,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,2,6,4,5,7,3,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,2,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [8,2,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [7,2,6,5,4,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [7,2,6,5,4,3,8,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [8,2,6,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [8,2,6,5,4,7,3,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [8,2,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [8,2,7,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [8,2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [4,3,2,1,8,6,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,2,7,5,6,8,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,3,2,8,5,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,3,2,8,5,7,6,1]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,2,8,6,7,5,1]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [5,3,2,4,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [5,3,2,4,1,7,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,2,4,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [5,3,2,4,7,6,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [8,3,2,4,6,5,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,3,2,4,6,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,3,2,4,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [6,3,2,5,4,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,3,2,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [6,3,2,5,4,7,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,3,2,5,4,7,8,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,3,2,5,4,8,7,1]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [7,3,2,5,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [8,3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [7,3,2,5,6,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [8,3,2,5,6,4,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,3,2,5,6,7,4,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,3,2,5,7,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,3,2,6,5,7,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [8,3,2,7,5,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [5,3,4,2,1,6,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [5,3,4,2,1,7,8,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,4,2,1,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [5,3,4,2,6,1,8,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [5,3,4,2,7,6,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,4,2,7,6,8,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,4,2,8,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [6,3,4,2,5,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,3,4,2,6,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [7,3,4,2,6,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [8,3,4,2,6,5,7,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [6,3,4,5,2,1,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [6,3,4,5,2,8,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [8,3,4,5,2,7,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [8,3,4,5,7,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [8,3,4,7,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [6,3,5,4,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [6,3,5,4,2,7,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,3,5,4,2,7,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,3,5,4,2,8,7,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,3,5,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [8,3,5,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,3,5,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [7,3,5,4,6,2,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,3,5,4,6,2,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [8,3,5,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [8,3,5,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [7,3,6,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [7,3,6,4,5,2,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [8,3,6,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [8,3,7,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [8,3,7,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,3,6,5,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [7,3,6,5,4,2,8,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [8,3,6,5,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,3,7,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,3,7,5,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,3,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [5,4,3,2,8,6,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [6,4,3,2,5,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,3,2,5,8,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [8,4,3,2,5,7,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [7,4,3,2,6,5,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [7,4,3,2,6,5,8,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [8,4,3,2,6,5,7,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [8,4,3,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [6,4,3,5,2,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [8,4,3,5,2,7,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [8,4,3,5,7,6,2,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [7,4,3,6,5,2,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [7,4,3,6,5,2,8,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [8,4,3,7,5,6,2,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [8,4,3,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [6,5,3,4,2,1,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [8,5,3,4,2,7,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [8,5,3,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [8,7,3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [7,6,3,5,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [7,6,3,5,4,2,8,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>1101110 [8,6,3,5,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,6,3,5,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>1101101 [8,7,3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,7,3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>1101011 [8,7,3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [8,5,4,3,2,7,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,5,4,3,7,6,2,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,7,4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,7,4,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [2,4,1,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,1,4,6,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,1,6,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,6,1,3,5,8,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,1,4,3,6,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,1,3,6,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,1,4,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,1,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,6,1,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,1,4,6,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,1,6,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,6,1,8,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,6,8,1,3,5,7]=>[[1,3,5,7],[2,4,6,8]]=>1010101 [2,4,1,3,6,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,6,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,6,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,1,3,5,7,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,6,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,6,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,1,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,7,1,3,5,8]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,3,6,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,6,3,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,6,3,7,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,6,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,6,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,1,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,7,1,3,8,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,6,7,8,3,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,1,6,7,8,3,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,4,6,7,8,1,3,5]=>[[1,3,5,7,8],[2,4,6]]=>1010100 [2,1,4,3,7,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,3,7,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,1,4,7,3,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,7,3,5,8,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,1,4,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,3,7,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,7,3,8,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,1,4,7,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,7,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,7,1,8,3,5,6]=>[[1,3,5,6],[2,4,7,8]]=>1010010 [2,4,1,5,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,1,3,7,6,8]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,1,7,3,6,8]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,1,3,5,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,1,5,3,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,1,3,7,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,1,4,5,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,1,5,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,1,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,1,7,8,3,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,4,5,7,8,1,3,6]=>[[1,3,5,6,8],[2,4,7]]=>1010010 [2,1,4,3,8,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,3,8,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,1,4,8,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,8,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,8,1,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,1,4,3,5,8,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,5,3,8,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,1,4,5,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,5,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,1,8,3,6,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,5,3,6,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,5,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,1,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,6,1,3,8,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,1,4,5,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,5,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,1,6,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,6,1,8,3,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,5,6,8,1,3,7]=>[[1,3,5,6,7],[2,4,8]]=>1010001 [2,4,1,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,1,5,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,1,3,6,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,1,5,6,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,1,6,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,1,3,7,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,1,5,6,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,1,7,3,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,7,1,3,8]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,1,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,1,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,1,7,8,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,7,1,8,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,4,5,6,7,8,1,3]=>[[1,3,5,6,7,8],[2,4]]=>1010000 [2,1,5,3,6,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,1,3,6,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,1,5,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,1,6,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,6,1,3,4,8,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,1,5,3,6,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,1,3,6,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,6,1,3,8,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,1,5,6,8,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,1,6,8,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,6,8,1,3,4,7]=>[[1,3,4,7],[2,5,6,8]]=>1001001 [2,5,1,3,6,4,7,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,3,6,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,6,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,6,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,1,3,7,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,6,7,3,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,6,7,3,4,8]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,3,6,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,3,6,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,6,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,6,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,1,3,7,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,6,7,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,6,7,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,7,1,3,8,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,6,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,1,6,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,1,7,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,7,1,8,3,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,5,6,7,8,1,3,4]=>[[1,3,4,7,8],[2,5,6]]=>1001000 [2,1,5,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,1,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,1,5,7,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,1,7,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,7,1,3,4,8,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,1,5,3,7,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,1,3,7,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,1,5,7,3,8,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,1,5,7,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,1,7,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,7,1,8,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,5,7,8,1,3,4,6]=>[[1,3,4,6],[2,5,7,8]]=>1001010 [2,1,5,7,3,4,6,8]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,3,5,1,4,7,6,8]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,3,5,7,1,4,6,8]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,3,5,1,7,4,8,6]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,3,1,5,7,8,4,6]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,3,5,7,8,1,4,6]=>[[1,3,4,6,8],[2,5,7]]=>1001010 [2,1,5,3,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,5,1,3,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,1,5,8,3,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,5,1,8,3,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,1,4,8,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,1,3,5,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,1,8,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,8,1,4,6,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,1,5,3,4,6,8,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,1,6,4,8,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,1,3,5,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,1,5,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,1,6,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,6,1,8,4,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,3,5,6,8,1,4,7]=>[[1,3,4,6,7],[2,5,8]]=>1001001 [2,1,5,3,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,5,1,3,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,1,4,6,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,6,1,4,7,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,6,7,1,4,8]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,1,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,6,1,7,8,4]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,3,5,6,7,8,1,4]=>[[1,3,4,6,7,8],[2,5]]=>1001000 [2,1,6,3,7,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,3,7,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,1,6,7,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,7,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,7,1,3,4,8,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,1,6,3,7,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,3,7,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,7,3,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,7,1,3,8,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,1,6,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,7,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,7,1,8,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,7,8,1,3,4,5]=>[[1,3,4,5],[2,6,7,8]]=>1000100 [2,6,1,7,3,4,5,8]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,6,1,3,4,7,5,8]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,1,6,4,7,5,8]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,1,6,3,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,6,1,3,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,6,1,4,7,8,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,1,3,6,7,4,8,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,1,3,6,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,1,6,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,6,1,7,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,6,7,1,8,4,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,3,6,7,8,1,4,5]=>[[1,3,4,5,8],[2,6,7]]=>1000100 [2,1,6,3,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,1,3,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,1,6,8,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,1,8,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,8,1,3,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,1,6,3,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,1,3,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,1,6,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,6,1,4,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,1,6,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,6,1,8,4,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,1,6,3,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,1,3,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,1,3,6,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,6,1,4,5,8,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,4,1,6,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,4,6,1,8,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,3,4,6,8,1,5,7]=>[[1,3,4,5,7],[2,6,8]]=>1000101 [2,6,1,3,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,1,3,6,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,1,6,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,6,1,4,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,4,6,1,5,7,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,4,6,7,1,5,8]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,4,6,1,7,8,5]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,3,4,6,7,8,1,5]=>[[1,3,4,5,7,8],[2,6]]=>1000100 [2,1,7,3,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,7,1,3,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,7,8,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,7,1,8,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,7,8,1,3,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,7,3,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,3,7,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,1,7,4,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,3,7,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,1,7,8,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,7,8,1,4,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,7,3,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,7,1,3,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,1,7,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,7,1,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,3,4,7,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,4,1,7,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,4,7,1,5,8,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,3,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,1,4,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,4,1,7,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,4,7,1,8,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,3,4,7,8,1,5,6]=>[[1,3,4,5,6],[2,7,8]]=>1000010 [2,1,7,3,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,7,1,3,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,7,1,4,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,1,3,4,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,1,4,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,4,1,7,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,4,7,1,5,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,4,5,7,1,6,8]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,4,5,7,1,8,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,3,4,5,7,8,1,6]=>[[1,3,4,5,6,8],[2,7]]=>1000010 [2,1,8,3,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,8,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,1,3,8,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,1,8,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,8,1,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,1,3,4,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,1,4,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,1,8,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,8,1,5,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,1,3,4,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,1,4,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,1,5,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,5,1,8,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,5,8,1,6,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [2,3,4,5,6,8,1,7]=>[[1,3,4,5,6,7],[2,8]]=>1000001 [3,1,4,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,1,4,6,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,6,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,6,1,2,5,8,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,1,4,2,6,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,2,6,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,1,4,6,2,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,6,2,8,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,1,4,6,8,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,6,8,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,6,8,1,2,5,7]=>[[1,2,5,7],[3,4,6,8]]=>0100101 [3,4,1,2,6,5,7,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,2,6,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,2,6,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,6,2,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,1,2,7,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,6,7,2,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,7,1,2,5,8]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,2,6,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,2,6,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,6,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,6,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,1,2,7,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,6,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,6,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,1,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,7,1,2,8,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,6,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,1,6,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,1,7,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,7,1,8,2,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,4,6,7,8,1,2,5]=>[[1,2,5,7,8],[3,4,6]]=>0100100 [3,1,4,2,7,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,4,1,2,7,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,1,4,7,2,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,4,7,1,2,5,8,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,1,4,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,4,1,2,7,8,5,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,4,7,1,8,2,5,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,4,7,8,1,2,5,6]=>[[1,2,5,6],[3,4,7,8]]=>0100010 [3,1,4,2,7,5,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,2,7,5,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,2,5,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,5,2,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,5,2,7,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,5,7,2,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,5,7,1,2,6,8]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,2,5,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,2,5,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,5,2,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,5,1,2,7,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,5,7,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,5,7,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,5,7,1,2,8,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,5,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,1,5,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,5,1,7,8,2,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,4,5,7,8,1,2,6]=>[[1,2,5,6,8],[3,4,7]]=>0100010 [3,1,4,2,8,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,2,8,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,8,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,8,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,8,1,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,2,5,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,2,5,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,5,2,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,1,2,8,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,5,8,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,5,8,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,8,1,2,6,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,2,5,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,1,2,6,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,5,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,5,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,1,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,6,1,2,8,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,5,6,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,1,5,6,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,6,1,8,2,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,4,5,6,8,1,2,7]=>[[1,2,5,6,7],[3,4,8]]=>0100001 [3,1,4,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,1,4,5,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,1,5,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,1,5,6,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,1,6,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,1,4,5,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,1,5,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,1,6,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,6,1,7,2,8]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,1,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,1,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,6,1,7,8,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,4,5,6,7,1,8,2]=>[[1,2,5,6,7,8],[3,4]]=>0100000 [3,1,5,2,6,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,1,2,6,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,1,5,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,1,6,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,6,1,2,4,8,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,1,5,2,6,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,1,2,6,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,1,5,6,2,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,6,1,2,8,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,1,5,6,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,1,6,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,6,1,8,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,5,6,8,1,2,4,7]=>[[1,2,4,7],[3,5,6,8]]=>0101001 [3,1,5,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,2,4,7,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,2,6,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,2,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,2,7,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,7,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,7,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,7,1,2,4,8]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,1,5,2,6,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,2,6,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,1,5,6,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,2,7,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,1,5,6,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,7,1,2,8,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,1,5,6,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,1,6,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,1,7,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,7,1,8,2,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,5,6,7,8,1,2,4]=>[[1,2,4,7,8],[3,5,6]]=>0101000 [3,1,5,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,1,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,1,5,7,2,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,7,1,2,4,8,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,1,5,2,7,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,1,2,7,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,1,5,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,1,7,2,8,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,1,5,7,8,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,1,7,8,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,5,7,8,1,2,4,6]=>[[1,2,4,6],[3,5,7,8]]=>0101010 [3,1,5,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,5,1,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,5,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,5,1,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,5,7,1,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,5,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,5,1,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,2,5,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,2,4,7,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,2,5,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,2,5,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,7,2,4,6,8]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,5,1,2,4,7,8,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,2,5,7,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,2,7,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,7,2,4,8,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,2,5,7,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,2,7,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,7,2,8,4,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [1,3,5,7,8,2,4,6]=>[[1,2,4,6,8],[3,5,7]]=>0101010 [3,1,5,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,5,1,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,1,5,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,5,1,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,1,5,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,5,1,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,2,5,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,2,4,8,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,1,2,5,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,2,5,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,8,2,4,6,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,5,1,2,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,1,2,5,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,2,4,6,8,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,6,2,4,8,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,1,2,5,6,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,2,6,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,6,2,8,4,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [1,3,5,6,8,2,4,7]=>[[1,2,4,6,7],[3,5,8]]=>0101001 [3,5,1,2,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,2,4,6,7,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,6,2,4,7,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [3,1,2,5,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,2,6,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,6,2,7,4,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,6,7,2,4,8]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [3,1,2,5,6,7,8,4]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,6,7,2,8,4]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [1,3,5,6,7,8,2,4]=>[[1,2,4,6,7,8],[3,5]]=>0101000 [3,1,6,2,7,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,1,2,7,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,1,7,2,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,7,1,2,4,8,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,1,2,7,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,1,6,7,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,1,7,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,7,1,2,8,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,1,7,8,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,6,7,8,1,2,4,5]=>[[1,2,4,5],[3,6,7,8]]=>0100100 [3,1,6,7,2,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,6,1,2,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,1,2,6,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,2,6,4,7,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,2,6,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,6,2,7,4,5,8]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,1,6,2,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,6,1,2,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,1,2,6,4,7,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,1,2,6,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,2,6,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,6,2,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,1,2,6,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,2,6,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,6,2,7,8,4,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [1,3,6,7,8,2,4,5]=>[[1,2,4,5,8],[3,6,7]]=>0100100 [3,6,1,2,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,6,8,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,6,1,8,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,6,8,1,2,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,6,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,6,1,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,2,6,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,6,2,4,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,2,6,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,2,6,8,4,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,6,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,6,1,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,2,6,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,6,2,4,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,1,2,4,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,4,6,2,5,8,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,2,4,6,8,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [1,3,4,6,8,2,5,7]=>[[1,2,4,5,7],[3,6,8]]=>0100101 [3,6,1,2,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,2,6,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,6,2,4,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,4,6,2,5,7,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [3,1,2,4,6,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,4,6,2,7,5,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,4,6,7,2,5,8]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [3,1,2,4,6,7,8,5]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [1,3,4,6,7,2,8,5]=>[[1,2,4,5,7,8],[3,6]]=>0100100 [3,1,7,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,7,1,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,7,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,7,1,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,7,8,1,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,7,1,2,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,2,7,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,2,7,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,7,2,4,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,2,7,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,7,2,8,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,7,8,2,4,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,7,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,7,1,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,7,2,4,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,2,4,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,2,4,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,4,2,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,2,4,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,4,2,7,8,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [1,3,4,7,8,2,5,6]=>[[1,2,4,5,6],[3,7,8]]=>0100010 [3,1,7,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,7,1,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,1,2,7,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,3,2,7,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,3,7,2,4,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,1,2,4,7,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,3,4,7,2,5,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,1,2,4,5,7,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,3,4,5,7,2,6,8]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,1,2,4,5,7,8,6]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [1,3,4,5,7,8,2,6]=>[[1,2,4,5,6,8],[3,7]]=>0100010 [3,1,8,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [3,8,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [3,1,2,8,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,2,8,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,8,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [3,1,2,4,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,2,4,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,2,8,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,8,2,5,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [3,1,2,4,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,2,4,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,2,5,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,5,2,8,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,5,8,2,6,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [3,1,2,4,5,6,8,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [1,3,4,5,6,8,2,7]=>[[1,2,4,5,6,7],[3,8]]=>0100001 [4,1,5,2,6,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,1,2,6,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,1,5,6,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,1,6,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,6,1,2,3,8,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,1,5,2,6,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,1,2,6,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,1,5,6,2,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,6,1,2,8,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,1,5,6,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,1,6,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,6,1,8,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,5,6,8,1,2,3,7]=>[[1,2,3,7],[4,5,6,8]]=>0010001 [4,1,5,2,6,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,1,5,6,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,6,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,2,6,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,6,2,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,1,2,7,3,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,1,7,2,3,8]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,1,5,2,6,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,2,6,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,6,2,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,1,2,7,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,1,5,6,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,6,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,1,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,7,1,2,8,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,1,5,6,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,1,6,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,1,7,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,5,6,7,1,8,2,3]=>[[1,2,3,7,8],[4,5,6]]=>0010000 [4,1,5,2,7,3,8,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,1,7,2,3,8,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,1,5,2,7,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,1,2,7,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,1,5,7,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,1,7,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,7,1,2,8,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,1,7,8,2,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,5,7,8,1,2,3,6]=>[[1,2,3,6],[4,5,7,8]]=>0010010 [4,1,5,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,5,1,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,5,1,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,2,5,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,2,5,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,2,3,7,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,2,5,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,2,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,7,2,3,6,8]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,5,2,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,2,5,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,2,3,7,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,2,5,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,2,5,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,2,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,7,2,3,8,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,2,5,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,2,5,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,2,7,8,3,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [1,4,5,7,8,2,3,6]=>[[1,2,3,6,8],[4,5,7]]=>0010010 [4,1,5,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,5,1,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,5,1,8,2,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,5,8,1,2,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,5,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,5,1,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,2,5,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,2,5,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,5,2,3,8,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,2,5,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,2,5,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,5,2,8,3,6,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,2,5,3,6,8,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,2,5,6,3,8,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,5,2,6,3,8,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,2,5,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,2,5,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,5,2,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [1,4,5,6,8,2,3,7]=>[[1,2,3,6,7],[4,5,8]]=>0010001 [4,1,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [4,1,2,5,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,2,5,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [4,1,2,5,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,2,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,2,3,7,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [4,1,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,2,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,2,7,3,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,7,2,3,8]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [4,1,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,2,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,2,7,8,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,7,2,8,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [1,4,5,6,7,8,2,3]=>[[1,2,3,6,7,8],[4,5]]=>0010000 [4,1,6,2,7,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,1,6,7,2,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,7,1,2,3,8,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,1,2,7,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,1,7,2,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,7,1,2,8,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,1,6,7,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,1,7,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,7,1,8,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,6,7,8,1,2,3,5]=>[[1,2,3,5],[4,6,7,8]]=>0010100 [4,1,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,6,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,6,1,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,6,7,1,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,6,2,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,2,6,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,2,6,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,2,6,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,2,6,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,2,7,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,7,2,3,5,8]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,6,2,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,2,6,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,2,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,2,6,7,3,8,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,2,7,3,8,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,2,6,7,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,2,7,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,7,2,8,3,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [1,4,6,7,8,2,3,5]=>[[1,2,3,5,8],[4,6,7]]=>0010100 [4,1,6,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,6,1,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,6,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,6,1,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,6,8,1,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,6,2,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,2,6,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,2,6,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,6,2,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,2,6,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,6,2,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,6,8,2,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,6,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,6,1,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,2,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,2,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,6,2,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,2,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,4,2,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,2,4,6,3,5,8,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,2,3,6,8,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [1,2,4,6,8,3,5,7]=>[[1,2,3,5,7],[4,6,8]]=>0010101 [4,1,6,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [4,6,1,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,4,2,6,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,4,6,2,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [4,1,2,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,4,2,3,6,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,2,4,6,3,5,7,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [4,1,2,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,4,2,3,6,7,5,8]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [4,1,2,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [1,4,2,3,6,7,8,5]=>[[1,2,3,5,7,8],[4,6]]=>0010100 [4,1,7,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,7,1,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,7,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,7,1,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,7,8,1,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,7,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,7,1,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,2,7,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,7,2,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,2,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,2,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,7,2,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,7,8,2,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,7,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,7,1,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,2,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,2,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,7,2,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,2,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,2,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,2,4,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,2,4,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,2,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,4,2,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,2,4,3,7,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,2,4,7,3,8,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [1,2,4,7,8,3,5,6]=>[[1,2,3,5,6],[4,7,8]]=>0010010 [4,1,7,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,7,1,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,1,2,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,4,2,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,4,7,2,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,1,2,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,4,2,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,2,4,3,7,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,2,4,7,3,5,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,1,2,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,4,2,3,5,7,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,2,4,5,7,3,6,8]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,1,2,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,4,2,3,5,7,8,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,2,4,5,7,3,8,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [1,2,4,5,7,8,3,6]=>[[1,2,3,5,6,8],[4,7]]=>0010010 [4,1,8,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [4,8,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [4,1,2,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,2,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,8,2,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [4,1,2,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,2,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,3,8,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [4,1,2,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,2,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,3,5,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,5,3,8,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,5,8,3,6,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [4,1,2,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,2,3,5,6,8,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,2,4,5,6,8,3,7]=>[[1,2,3,5,6,7],[4,8]]=>0010001 [1,4,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>0010000 [5,1,6,2,7,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,1,2,7,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,1,6,7,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,1,7,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,7,1,2,3,8,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,1,2,7,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,1,6,7,2,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,7,1,2,8,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,1,6,7,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,1,7,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,6,7,1,8,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>0001000 [5,1,6,2,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,6,1,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,6,2,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,2,6,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,2,6,3,7,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,2,6,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,2,6,7,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,7,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,6,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,6,1,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,2,6,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,2,6,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,2,3,7,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,2,6,7,3,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,7,2,3,8,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,2,6,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,2,6,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,2,7,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,7,2,8,3,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [1,5,6,7,8,2,3,4]=>[[1,2,3,4,8],[5,6,7]]=>0001000 [5,1,6,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,6,1,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,6,1,8,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,6,8,1,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,6,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,6,1,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,2,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,2,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,6,2,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,2,6,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,2,6,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,6,2,8,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,6,8,2,3,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,6,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,6,1,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,2,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,2,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,6,2,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,2,3,6,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,2,5,3,6,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,2,5,6,3,4,8,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,2,3,6,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,5,2,3,6,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [1,2,5,6,3,8,4,7]=>[[1,2,3,4,7],[5,6,8]]=>0001001 [5,1,6,2,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [5,1,2,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,5,2,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,5,6,2,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [5,1,2,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,5,2,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,3,6,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [5,1,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,5,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,6,3,7,4,8]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [5,1,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,5,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,6,3,7,8,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,6,7,3,8,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [1,2,5,6,7,8,3,4]=>[[1,2,3,4,7,8],[5,6]]=>0001000 [5,1,7,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,7,1,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,7,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,7,1,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,7,8,1,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,7,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,7,1,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,2,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,2,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,7,2,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,2,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,2,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,7,2,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,7,8,2,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,7,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,7,1,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,2,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,2,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,7,2,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,2,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,2,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,2,5,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,2,5,7,3,4,8,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,2,3,7,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,5,2,3,7,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,2,5,7,3,8,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [1,2,5,7,8,3,4,6]=>[[1,2,3,4,6],[5,7,8]]=>0001010 [5,1,7,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [5,7,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [5,1,2,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,5,2,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,5,2,3,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,5,3,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,5,7,3,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,5,2,3,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,5,3,4,7,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,3,5,7,4,6,8]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [5,1,2,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,5,2,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,5,3,4,7,8,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,3,5,7,4,8,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [1,2,3,5,7,8,4,6]=>[[1,2,3,4,6,8],[5,7]]=>0001010 [5,1,8,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [5,8,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [5,1,2,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,2,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,8,2,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [5,1,2,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,2,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,5,3,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,5,8,3,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [5,1,2,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,2,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,5,3,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,3,5,4,8,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,3,5,8,4,6,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [5,1,2,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,2,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,5,3,4,6,8,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,2,3,5,6,8,4,7]=>[[1,2,3,4,6,7],[5,8]]=>0001001 [1,5,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [1,2,5,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>0001000 [6,1,7,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,7,1,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,7,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,7,1,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,7,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,7,1,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,2,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,2,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,7,2,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,2,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,2,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,7,2,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,7,8,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,7,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,7,1,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,2,7,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,2,7,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,7,2,3,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,2,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,2,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,2,6,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,2,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,6,2,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,2,6,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,2,6,7,3,8,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [1,2,6,7,8,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>0000100 [6,1,7,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [6,1,2,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,6,2,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,6,7,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [6,1,2,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,6,2,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,6,3,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,6,7,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [6,1,2,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,6,2,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,6,3,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,3,6,4,7,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,3,6,7,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [6,1,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,6,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,6,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,3,6,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [1,2,3,6,7,8,4,5]=>[[1,2,3,4,5,8],[6,7]]=>0000100 [6,1,8,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [6,8,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [6,1,2,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,2,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,8,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [6,1,2,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,2,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,6,3,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,6,8,3,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [6,1,2,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,2,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,6,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,3,6,4,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,3,6,8,4,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [6,1,2,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,2,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,6,3,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,3,6,4,5,8,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,2,3,4,6,8,5,7]=>[[1,2,3,4,5,7],[6,8]]=>0000101 [1,6,2,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [1,2,6,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [1,2,3,6,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>0000100 [7,1,8,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [7,1,2,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,2,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,8,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [7,1,2,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,2,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,7,3,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,7,8,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [7,1,2,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,2,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,7,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,3,7,4,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,3,7,8,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [7,1,2,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,2,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,7,3,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,3,7,4,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,3,4,7,5,8,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8]]=>0000010 [1,7,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [1,2,7,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [1,2,3,7,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>0000010 [1,8,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [1,2,8,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [1,2,3,8,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,7],[8]]=>0000001 [5,3,2,6,1,4,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [7,3,2,5,4,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [8,4,5,2,3,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [7,4,5,2,3,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [6,4,5,2,3,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [5,4,6,2,1,3,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [3,6,1,5,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [4,6,5,1,3,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,6,4,3,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [7,5,4,3,2,8,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [8,6,4,3,7,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [7,6,4,3,8,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [6,7,4,3,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [5,7,4,3,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [4,7,5,1,3,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [3,7,1,5,4,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [2,1,7,5,4,8,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [3,8,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [4,8,5,1,3,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [5,8,4,3,1,7,6,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [6,8,4,3,7,1,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [7,8,4,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110 [6,8,5,7,3,1,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [5,8,6,7,1,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [4,8,6,1,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [3,8,1,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [2,1,8,6,7,4,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,1,7,6,8,4,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [3,7,1,6,8,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [4,7,6,1,8,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [5,7,6,8,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [5,4,7,2,1,8,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [6,4,7,2,8,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [7,4,6,2,8,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [8,4,6,2,7,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [8,3,2,6,7,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [7,3,2,6,8,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [6,3,2,7,8,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [5,3,2,7,1,8,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [4,3,2,1,7,8,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [3,4,1,2,8,7,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [5,3,2,8,1,7,6,4]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011 [6,3,2,8,7,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [7,3,2,8,6,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [8,4,7,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [7,4,8,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [6,4,8,2,7,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [5,4,8,2,1,7,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [4,5,8,1,2,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [3,5,1,8,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [2,1,5,8,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,1,6,8,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [3,6,1,8,7,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [4,6,8,1,7,2,5,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [5,6,8,7,1,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [6,5,8,7,2,1,4,3]=>[[1,3],[2,4],[5,7],[6,8]]=>1011101 [7,5,8,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [8,5,7,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [5,7,8,6,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [4,7,8,1,6,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [3,7,1,8,6,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [2,1,7,8,6,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [3,8,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [4,8,7,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [5,8,7,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [6,8,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [3,4,1,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>010010101 [4,3,2,1,6,5,8,7,10,9]=>[[1,5,7,9],[2,6,8,10],[3],[4]]=>111010101 [10,3,2,5,4,7,6,9,8,1]=>[[1,4,6,8],[2,5,7,9],[3],[10]]=>110101011 [4,5,6,1,2,3,8,7,10,9]=>[[1,2,3,7,9],[4,5,6,8,10]]=>001000101 [3,5,1,6,2,4,8,7,10,9]=>[[1,2,4,7,9],[3,5,6,8,10]]=>010100101 [2,1,5,6,3,4,8,7,10,9]=>[[1,3,4,7,9],[2,5,6,8,10]]=>100100101 [6,5,4,3,2,1,8,7,10,9]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>111110101 [10,5,4,3,2,7,6,9,8,1]=>[[1,6,8],[2,7,9],[3],[4],[5],[10]]=>111101011 [8,7,4,3,6,5,2,1,10,9]=>[[1,5,9],[2,6,10],[3],[4],[7],[8]]=>111011101 [10,9,4,3,6,5,8,7,2,1]=>[[1,5,7],[2,6,8],[3],[4],[9],[10]]=>111010111 [5,6,7,8,1,2,3,4,10,9]=>[[1,2,3,4,9],[5,6,7,8,10]]=>000100001 [4,6,7,1,8,2,3,5,10,9]=>[[1,2,3,5,9],[4,6,7,8,10]]=>001010001 [3,6,1,7,8,2,4,5,10,9]=>[[1,2,4,5,9],[3,6,7,8,10]]=>010010001 [2,1,6,7,8,3,4,5,10,9]=>[[1,3,4,5,9],[2,6,7,8,10]]=>100010001 [2,1,5,7,3,8,4,6,10,9]=>[[1,3,4,6,9],[2,5,7,8,10]]=>100101001 [3,5,1,7,2,8,4,6,10,9]=>[[1,2,4,6,9],[3,5,7,8,10]]=>010101001 [4,5,7,1,2,8,3,6,10,9]=>[[1,2,3,6,9],[4,5,7,8,10]]=>001001001 [3,4,1,2,7,8,5,6,10,9]=>[[1,2,5,6,9],[3,4,7,8,10]]=>010001001 [2,1,4,3,7,8,5,6,10,9]=>[[1,3,5,6,9],[2,4,7,8,10]]=>101001001 [4,3,2,1,8,7,6,5,10,9]=>[[1,5,9],[2,6,10],[3,7],[4,8]]=>111011101 [8,7,6,5,4,3,2,1,10,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>111111101 [10,7,6,5,4,3,2,9,8,1]=>[[1,8],[2,9],[3],[4],[5],[6],[7],[10]]=>111111011 [10,9,6,5,4,3,8,7,2,1]=>[[1,7],[2,8],[3],[4],[5],[6],[9],[10]]=>111110111 [10,9,8,5,4,7,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5],[8],[9],[10]]=>111101111 [10,8,9,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>101010101 [2,1,7,8,9,10,3,4,5,6]=>[[1,3,4,5,6],[2,7,8,9,10]]=>100001000 [3,7,1,8,9,10,2,4,5,6]=>[[1,2,4,5,6],[3,7,8,9,10]]=>010001000 [4,7,8,1,9,10,2,3,5,6]=>[[1,2,3,5,6],[4,7,8,9,10]]=>001001000 [5,7,8,9,1,10,2,3,4,6]=>[[1,2,3,4,6],[5,7,8,9,10]]=>000101000 [6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000 [5,6,8,9,1,2,10,3,4,7]=>[[1,2,3,4,7],[5,6,8,9,10]]=>000100100 [4,6,8,1,9,2,10,3,5,7]=>[[1,2,3,5,7],[4,6,8,9,10]]=>001010100 [3,6,1,8,9,2,10,4,5,7]=>[[1,2,4,5,7],[3,6,8,9,10]]=>010010100 [2,1,6,8,9,3,10,4,5,7]=>[[1,3,4,5,7],[2,6,8,9,10]]=>100010100 [2,1,5,8,3,9,10,4,6,7]=>[[1,3,4,6,7],[2,5,8,9,10]]=>100100100 [3,5,1,8,2,9,10,4,6,7]=>[[1,2,4,6,7],[3,5,8,9,10]]=>010100100 [4,5,8,1,2,9,10,3,6,7]=>[[1,2,3,6,7],[4,5,8,9,10]]=>001000100 [3,4,1,2,8,9,10,5,6,7]=>[[1,2,5,6,7],[3,4,8,9,10]]=>010000100 [2,1,4,3,8,9,10,5,6,7]=>[[1,3,5,6,7],[2,4,8,9,10]]=>101000100 [2,1,4,3,7,9,5,10,6,8]=>[[1,3,5,6,8],[2,4,7,9,10]]=>101001010 [3,4,1,2,7,9,5,10,6,8]=>[[1,2,5,6,8],[3,4,7,9,10]]=>010001010 [4,5,7,1,2,9,3,10,6,8]=>[[1,2,3,6,8],[4,5,7,9,10]]=>001001010 [3,5,1,7,2,9,4,10,6,8]=>[[1,2,4,6,8],[3,5,7,9,10]]=>010101010 [2,1,5,7,3,9,4,10,6,8]=>[[1,3,4,6,8],[2,5,7,9,10]]=>100101010 [2,1,6,7,9,3,4,10,5,8]=>[[1,3,4,5,8],[2,6,7,9,10]]=>100010010 [3,6,1,7,9,2,4,10,5,8]=>[[1,2,4,5,8],[3,6,7,9,10]]=>010010010 [4,6,7,1,9,2,3,10,5,8]=>[[1,2,3,5,8],[4,6,7,9,10]]=>001010010 [5,6,7,9,1,2,3,10,4,8]=>[[1,2,3,4,8],[5,6,7,9,10]]=>000100010 [2,1,5,6,3,4,9,10,7,8]=>[[1,3,4,7,8],[2,5,6,9,10]]=>100100010 [3,5,1,6,2,4,9,10,7,8]=>[[1,2,4,7,8],[3,5,6,9,10]]=>010100010 [4,5,6,1,2,3,9,10,7,8]=>[[1,2,3,7,8],[4,5,6,9,10]]=>001000010 [3,4,1,2,6,5,9,10,7,8]=>[[1,2,5,7,8],[3,4,6,9,10]]=>010010010 [2,1,4,3,6,5,9,10,7,8]=>[[1,3,5,7,8],[2,4,6,9,10]]=>101010010 [2,1,4,3,6,5,10,9,8,7]=>[[1,3,5,7],[2,4,6,8],[9],[10]]=>101010111 [10,3,2,5,4,9,8,7,6,1]=>[[1,4,6],[2,5,7],[3],[8],[9],[10]]=>110101111 [2,1,6,5,4,3,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10]]=>101110111 [6,5,4,3,2,1,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>111110111 [10,5,4,3,2,9,8,7,6,1]=>[[1,6],[2,7],[3,8],[4,9],[5],[10]]=>111101111 [10,9,4,3,8,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8],[9],[10]]=>111011111 [2,1,4,3,10,9,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>101011111 [4,3,2,1,10,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>111011111 [10,3,2,9,8,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8],[9],[10]]=>110111111 [2,1,10,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>101111111 [9,10,8,7,6,5,4,3,1,2]=>[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>011111110 [10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111 [4,2,5,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,2,6,1,3,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [5,3,6,1,2,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [6,2,4,1,3,5,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [6,3,5,1,2,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [5,3,7,1,2,4,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [5,4,7,1,2,3,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [6,2,7,1,3,4,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [6,3,7,1,2,4,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [6,4,7,1,2,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [7,3,5,1,2,4,6,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [7,3,6,1,2,4,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [7,4,6,1,2,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [3,2,8,1,4,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [4,2,8,1,3,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [5,4,8,1,2,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [6,2,8,1,3,4,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [6,3,8,1,2,4,5,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [6,4,8,1,2,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [6,5,8,1,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [7,2,8,1,3,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,3,8,1,2,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,4,8,1,2,3,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [7,5,8,1,2,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,2,4,1,3,5,6,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [8,3,5,1,2,4,6,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [8,3,6,1,2,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [8,3,7,1,2,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [8,4,7,1,2,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [8,5,7,1,2,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [3,2,5,7,1,4,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,2,5,7,1,3,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [5,2,4,7,1,3,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [4,2,6,7,1,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [5,2,6,7,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [6,2,5,7,1,3,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,2,5,8,1,4,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,2,5,8,1,3,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,3,5,8,1,2,6,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [5,2,4,8,1,3,6,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [3,2,6,8,1,4,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [4,2,6,8,1,3,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,2,6,8,1,3,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [6,2,4,8,1,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [6,3,4,8,1,2,5,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [6,2,5,8,1,3,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [6,3,5,8,1,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [6,4,5,8,1,2,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [3,2,7,8,1,4,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [5,3,7,8,1,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,4,7,8,1,2,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [6,2,7,8,1,3,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [6,3,7,8,1,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,4,7,8,1,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [7,2,4,8,1,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,3,4,8,1,2,5,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [7,3,5,8,1,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [7,4,5,8,1,2,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,4,6,8,1,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,3,4,6,1,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,3,5,6,1,2,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,2,4,7,1,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,2,5,7,1,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [8,3,5,7,1,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [8,2,6,7,1,3,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [8,4,6,7,1,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [4,6,2,5,1,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,6,3,5,1,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [3,7,2,5,1,4,6,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [4,7,3,5,1,2,6,8]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [3,7,2,6,1,4,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [4,7,3,6,1,2,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,7,2,6,1,3,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [6,7,2,5,1,3,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [4,8,2,5,1,3,6,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,8,2,4,1,3,6,7]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [5,8,3,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [5,8,3,6,1,2,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,8,4,6,1,2,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [6,8,3,5,1,2,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [3,8,2,7,1,4,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [4,8,2,7,1,3,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [4,8,3,7,1,2,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [5,8,2,7,1,3,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [5,8,3,7,1,2,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [6,8,2,7,1,3,4,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [6,8,3,7,1,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,8,5,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [7,8,2,4,1,3,5,6]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,8,2,5,1,3,4,6]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [7,8,3,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,8,4,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [4,3,2,6,1,5,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [5,3,2,6,1,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,3,2,5,1,4,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,5,2,4,1,3,7,8]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [4,3,2,7,1,5,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [5,3,2,7,1,4,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [6,3,2,7,1,4,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [6,4,2,7,1,3,5,8]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [6,4,3,7,1,2,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [6,5,2,7,1,3,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [6,5,3,7,1,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [7,3,2,5,1,4,6,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,4,2,5,1,3,6,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [7,3,2,6,1,4,5,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [7,4,2,6,1,3,5,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [7,4,3,6,1,2,5,8]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [7,5,2,6,1,3,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [7,5,3,6,1,2,4,8]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [4,3,2,8,1,5,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [5,3,2,8,1,4,6,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [6,3,2,8,1,4,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [6,4,2,8,1,3,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [6,4,3,8,1,2,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,5,2,8,1,3,4,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [6,5,3,8,1,2,4,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [7,3,2,8,1,4,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,4,2,8,1,3,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,4,3,8,1,2,5,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,5,3,8,1,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,5,4,8,1,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,6,2,8,1,3,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,3,2,5,1,4,6,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,4,2,5,1,3,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,3,2,6,1,4,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,4,2,6,1,3,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [8,5,3,6,1,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [8,6,2,4,1,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [8,6,2,5,1,3,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,3,2,7,1,4,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [8,4,2,7,1,3,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,4,3,7,1,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [8,5,2,7,1,3,4,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [8,5,3,7,1,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,6,3,7,1,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,7,2,4,1,3,5,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,7,2,5,1,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,7,3,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,7,2,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,7,3,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,7,4,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [4,6,3,5,8,1,2,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [5,6,2,4,8,1,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [4,7,2,5,8,1,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,7,3,5,8,1,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [5,7,2,4,8,1,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [5,7,3,4,8,1,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [4,7,3,6,8,1,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [5,7,2,6,8,1,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,7,4,6,8,1,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [6,7,3,4,8,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,7,3,5,8,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [3,8,2,5,7,1,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [4,8,3,5,7,1,2,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [5,8,2,4,7,1,3,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [3,8,2,6,7,1,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [5,8,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [5,8,3,6,7,1,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [6,8,2,5,7,1,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [7,8,2,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [7,8,2,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [7,8,3,5,6,1,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [4,3,2,6,8,1,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [5,3,2,6,8,1,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,4,2,6,8,1,3,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,4,3,6,8,1,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [6,3,2,5,8,1,4,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [6,4,3,5,8,1,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [6,5,2,4,8,1,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [4,3,2,7,8,1,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [5,3,2,7,8,1,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,4,2,7,8,1,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [5,4,3,7,8,1,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [6,4,2,7,8,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,4,3,7,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,4,2,5,8,1,3,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [7,4,3,5,8,1,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [7,5,2,6,8,1,3,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [7,5,3,6,8,1,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,6,2,4,8,1,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [8,4,2,5,7,1,3,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [8,5,2,4,7,1,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [8,3,2,6,7,1,4,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [8,5,2,6,7,1,3,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [8,5,3,6,7,1,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [8,6,2,4,7,1,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [8,7,2,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,7,3,4,6,1,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [8,7,2,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [4,3,7,2,6,1,5,8]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [5,4,7,2,6,1,3,8]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [6,3,7,2,5,1,4,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,4,7,2,5,1,3,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,4,7,3,5,1,2,8]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [4,3,8,2,6,1,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [5,3,8,2,6,1,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,4,8,2,6,1,3,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,4,8,3,6,1,2,7]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [6,4,8,2,5,1,3,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [6,4,8,3,5,1,2,7]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [6,5,8,2,4,1,3,7]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [6,5,8,3,4,1,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [4,3,8,2,7,1,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,3,8,2,7,1,4,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [5,4,8,2,7,1,3,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [5,4,8,3,7,1,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,3,8,2,7,1,4,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [6,4,8,2,7,1,3,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,3,8,2,5,1,4,6]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,4,8,3,5,1,2,6]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [7,5,8,2,4,1,3,6]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [7,5,8,2,6,1,3,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [7,5,8,4,6,1,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,6,8,2,5,1,3,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,6,8,3,5,1,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [8,5,6,2,4,1,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [8,4,7,3,5,1,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,5,7,2,4,1,3,6]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,3,7,2,6,1,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,4,7,2,6,1,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,4,7,3,6,1,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [8,5,7,2,6,1,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,6,7,2,4,1,3,5]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [8,6,7,2,5,1,3,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [8,6,7,3,5,1,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [5,4,3,2,7,1,6,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [6,4,3,2,7,1,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,5,3,2,7,1,4,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,5,4,2,7,1,3,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [7,5,3,2,6,1,4,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [7,5,4,2,6,1,3,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,4,3,2,8,1,6,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [6,5,3,2,8,1,4,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [6,5,4,3,8,1,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [7,5,3,2,8,1,4,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,5,4,2,8,1,3,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [7,6,3,2,8,1,4,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [7,6,4,3,8,1,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [7,6,5,2,8,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [8,5,3,2,6,1,4,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,5,4,2,6,1,3,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,6,5,2,4,1,3,7]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [8,5,3,2,7,1,4,6]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [8,6,3,2,7,1,4,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [8,6,4,3,7,1,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,7,3,2,6,1,4,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [8,7,4,2,6,1,3,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,7,4,3,6,1,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,7,5,2,6,1,3,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [8,7,6,2,4,1,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,7,6,2,5,1,3,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,7,6,3,5,1,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [4,8,3,7,2,6,1,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [5,8,3,7,2,6,1,4]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011 [5,8,4,7,2,6,1,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [5,8,4,7,3,6,1,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [6,8,3,7,2,5,1,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [6,8,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [6,8,4,7,3,5,1,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [6,8,5,7,2,4,1,3]=>[[1,3],[2,4],[5,7],[6,8]]=>1011101 [6,8,5,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [7,8,3,6,2,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [7,8,4,6,2,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [7,8,4,6,3,5,1,2]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110 [7,8,5,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [5,4,3,8,2,7,1,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,4,3,8,2,7,1,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,5,3,8,2,7,1,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [6,5,4,8,3,7,1,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [7,4,3,8,2,6,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,5,3,8,2,6,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [7,5,4,8,2,6,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [7,6,3,8,2,5,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [7,6,4,8,2,5,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [7,6,5,8,2,4,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [8,4,3,7,2,6,1,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [8,5,3,7,2,6,1,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [8,5,4,7,2,6,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [8,5,4,7,3,6,1,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [8,6,3,7,2,5,1,4]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [8,6,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [8,6,4,7,3,5,1,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [8,6,5,7,2,4,1,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [8,7,3,6,2,5,1,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [8,7,4,6,2,5,1,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [8,7,4,6,3,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [8,7,5,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [6,5,4,3,2,8,1,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [7,6,5,4,2,8,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [8,5,4,3,2,7,1,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,7,4,3,2,6,1,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,7,5,3,2,6,1,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [8,7,5,4,2,6,1,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,7,6,3,2,5,1,4]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [8,7,6,4,2,5,1,3]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [8,7,6,5,2,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,1,2,3,4,7,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [8,1,2,3,6,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [8,1,2,3,7,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [7,1,2,3,6,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [5,1,2,3,8,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,1,2,3,6,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [4,1,2,8,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [8,1,2,5,3,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [7,1,2,5,3,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,1,2,6,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [7,1,2,6,3,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [6,1,2,5,3,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [8,1,2,5,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,1,2,6,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [6,1,2,5,3,7,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [4,1,2,8,6,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,1,2,8,7,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [4,1,2,7,6,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,1,2,5,6,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [8,1,2,5,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,1,2,7,6,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [7,1,2,5,6,3,8,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [4,1,2,5,8,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,1,2,8,6,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,1,2,5,6,7,3,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [3,1,8,2,4,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,1,8,2,6,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,8,2,7,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,1,7,2,6,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [3,1,5,2,8,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,1,8,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [8,1,4,2,3,5,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [7,1,4,2,3,5,8,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [6,1,4,2,3,8,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,1,4,2,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [6,1,4,2,3,7,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [8,1,5,2,3,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [7,1,5,2,3,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,1,7,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [6,1,5,2,3,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [8,1,5,2,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [6,1,8,2,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [6,1,5,2,3,7,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [5,1,4,2,8,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,1,4,2,7,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [8,1,4,2,6,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [8,1,4,2,7,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [7,1,4,2,6,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,1,5,2,6,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [8,1,5,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [7,1,8,2,6,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [7,1,5,2,6,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,1,4,2,6,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,1,4,2,8,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [8,1,4,2,6,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,1,5,2,6,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [5,1,4,2,6,7,8,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [3,1,4,8,2,7,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,1,8,5,2,4,6,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [3,1,7,5,2,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [3,1,8,6,2,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,7,6,2,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [3,1,6,5,2,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,1,8,5,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,1,8,6,2,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [3,1,6,5,2,7,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [8,1,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [7,1,4,5,2,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [8,1,4,6,2,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [7,1,4,8,2,3,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [7,1,4,6,2,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,1,6,5,2,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [7,1,8,5,2,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [7,1,8,6,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [7,1,6,5,2,3,8,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,1,4,5,2,8,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [8,1,4,5,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,1,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,1,6,5,2,7,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,1,4,5,2,7,8,3]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [3,1,4,8,6,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,1,4,8,7,2,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,1,4,7,6,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,1,8,5,6,2,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [3,1,8,5,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,1,8,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,1,7,5,6,2,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [8,1,4,5,6,2,3,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [8,1,4,5,7,2,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,1,4,7,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,1,7,5,6,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [7,1,4,5,6,2,8,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [3,1,4,5,8,7,2,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,1,4,8,6,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,1,8,5,6,7,2,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,1,4,5,6,7,2,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [2,8,1,3,4,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,8,1,3,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,8,1,3,7,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,7,1,3,6,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,5,1,3,8,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,8,1,3,6,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,4,1,8,3,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,8,1,5,3,4,6,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,7,1,5,3,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,8,1,6,3,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,7,1,6,3,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,6,1,5,3,8,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,8,1,5,3,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,6,1,5,3,7,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,4,1,8,6,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,1,8,7,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,4,1,7,6,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,8,1,5,6,3,4,7]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,8,1,5,7,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,8,1,7,6,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,7,1,5,6,3,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,4,1,5,8,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,4,1,8,6,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,1,5,6,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [7,3,1,2,4,5,8,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [6,3,1,2,4,8,5,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [8,3,1,2,4,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [6,3,1,2,4,7,8,5]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [5,3,1,2,8,4,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [5,3,1,2,7,4,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [8,3,1,2,6,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [8,3,1,2,7,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [7,3,1,2,6,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [5,3,1,2,6,8,4,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [5,3,1,2,8,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [8,3,1,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [5,3,1,2,6,7,8,4]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [7,4,1,2,3,5,8,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [6,4,1,2,3,8,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,4,1,2,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [6,4,1,2,3,7,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [7,6,1,2,3,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [5,8,1,2,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,6,1,2,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [5,4,1,2,8,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,4,1,2,7,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [8,4,1,2,6,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [8,4,1,2,7,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [7,4,1,2,6,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,8,1,2,6,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [5,8,1,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,7,1,2,6,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [5,7,1,2,6,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,4,1,2,6,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,4,1,2,8,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [8,4,1,2,6,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [5,8,1,2,6,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [5,4,1,2,6,7,8,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [4,3,1,8,2,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [4,3,1,7,2,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [4,3,1,6,2,8,5,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,3,1,8,2,7,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [4,3,1,6,2,7,8,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [8,3,1,5,2,4,6,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [7,3,1,5,2,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,3,1,6,2,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [7,3,1,8,2,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,3,1,6,2,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [6,3,1,5,2,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [8,3,1,5,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [8,3,1,6,2,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [6,3,1,5,2,7,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [8,4,1,5,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [7,4,1,5,2,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [8,4,1,6,2,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [7,4,1,8,2,3,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [7,4,1,6,2,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [6,8,1,5,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [8,7,1,5,2,3,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [8,7,1,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [6,7,1,5,2,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,4,1,5,2,8,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [8,4,1,5,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,4,1,6,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [6,8,1,5,2,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,4,1,5,2,7,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [4,3,1,5,8,2,6,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,3,1,5,7,2,8,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,3,1,8,6,2,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [4,3,1,8,7,2,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [4,3,1,7,6,2,8,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [8,3,1,5,6,2,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,3,1,5,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [8,3,1,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [7,3,1,5,6,2,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [8,4,1,5,6,2,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [8,4,1,5,7,2,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,4,1,7,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [7,8,1,5,6,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,4,1,5,6,2,8,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,3,1,5,6,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,3,1,5,8,7,2,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [4,3,1,8,6,7,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [8,3,1,5,6,7,2,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,4,1,5,6,7,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [4,3,1,5,6,7,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [2,3,8,1,4,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,8,1,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,8,1,7,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,7,1,6,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,3,5,1,8,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,3,8,1,6,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,8,4,1,3,5,6,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,7,4,1,3,5,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,6,4,1,3,8,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,8,4,1,3,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,6,4,1,3,7,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,8,5,1,3,4,6,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,7,5,1,3,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,8,7,1,3,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,6,5,1,3,8,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,8,5,1,3,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,6,8,1,3,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,6,5,1,3,7,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,5,4,1,8,3,6,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,5,4,1,7,3,8,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,8,4,1,6,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,4,1,7,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,7,4,1,6,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,8,5,1,6,3,4,7]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,8,5,1,7,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,7,8,1,6,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,7,5,1,6,3,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,5,4,1,6,8,3,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,5,4,1,8,7,3,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [2,8,4,1,6,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,5,1,6,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,5,4,1,6,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [7,3,4,1,2,5,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [6,3,4,1,2,8,5,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [8,3,4,1,2,7,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [6,3,4,1,2,7,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [7,3,5,1,2,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [6,3,7,1,2,4,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,3,5,1,2,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [8,3,5,1,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [6,3,8,1,2,7,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,3,5,1,2,7,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [7,5,4,1,2,3,8,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [6,8,4,1,2,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [6,7,4,1,2,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,8,5,1,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,7,5,1,2,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,5,4,1,2,8,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [8,5,4,1,2,7,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [6,8,4,1,2,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,8,5,1,2,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,5,4,1,2,7,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [5,3,4,1,8,2,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [5,3,4,1,7,2,8,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [8,3,4,1,6,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,3,4,1,7,2,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [7,3,4,1,6,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [8,3,5,1,6,2,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,3,5,1,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [7,3,8,1,6,2,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,3,5,1,6,2,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [8,5,4,1,6,2,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [8,5,4,1,7,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [7,8,4,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,8,5,1,6,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,5,4,1,6,2,8,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [5,3,4,1,6,8,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [5,3,4,1,8,7,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [8,3,4,1,6,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,3,5,1,6,7,2,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,5,4,1,6,7,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [5,3,4,1,6,7,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [2,3,4,8,1,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,8,5,1,4,6,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,3,7,5,1,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,3,8,6,1,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,7,6,1,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,3,6,5,1,8,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,3,8,5,1,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,3,8,6,1,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,3,6,5,1,7,8,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,8,4,5,1,3,6,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,7,4,5,1,3,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,8,4,6,1,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,7,4,8,1,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,7,4,6,1,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,8,6,5,1,3,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,7,8,5,1,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,7,8,6,1,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,7,6,5,1,3,8,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,6,4,5,1,8,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,8,4,5,1,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,8,4,6,1,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,6,5,1,7,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,6,4,5,1,7,8,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [7,3,4,5,1,2,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [7,3,4,6,1,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [8,3,6,5,1,2,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [7,3,8,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,3,8,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,3,6,5,1,2,8,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [7,6,4,5,1,2,8,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [6,3,4,5,1,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [8,3,4,5,1,7,2,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [8,3,4,6,1,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,3,6,5,1,7,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [8,6,4,5,1,7,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [6,3,4,5,1,7,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [2,3,4,8,6,1,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,8,7,1,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,4,7,6,1,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,8,5,6,1,4,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,3,8,5,7,1,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,3,8,7,6,1,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,7,5,6,1,8,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,8,4,5,6,1,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,8,4,5,7,1,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,8,4,7,6,1,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,8,7,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,7,4,5,6,1,8,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [8,3,4,5,7,1,2,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [8,3,4,7,6,1,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [8,3,7,5,6,1,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [7,3,4,5,6,1,8,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [2,3,4,5,8,7,1,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,3,4,8,6,7,1,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,8,5,6,7,1,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,8,4,5,6,7,1,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [9,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [8,1,2,3,4,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [7,1,2,3,4,5,9,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>00000101 [9,1,2,3,4,5,8,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [7,1,2,3,4,5,8,9,6]=>[[1,2,3,4,5,6,9],[7,8]]=>00000100 [6,1,2,3,4,8,5,9,7]=>[[1,2,3,4,5,7],[6,8,9]]=>00001010 [9,1,2,3,4,7,5,6,8]=>[[1,2,3,4,5,6,8],[7],[9]]=>00000101 [9,1,2,3,4,8,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [8,1,2,3,4,7,5,9,6]=>[[1,2,3,4,5,6],[7,9],[8]]=>00000110 [6,1,2,3,4,9,8,5,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>00001011 [9,1,2,3,4,7,8,5,6]=>[[1,2,3,4,5,6],[7,8],[9]]=>00000101 [8,1,2,3,9,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [9,1,2,3,6,8,4,5,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>00001011 [5,1,2,3,6,7,8,9,4]=>[[1,2,3,4,7,8,9],[5,6]]=>00010000 [9,1,2,8,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [7,1,2,8,3,4,5,9,6]=>[[1,2,3,4,5,6],[7,8,9]]=>00000100 [8,1,2,9,6,3,4,5,7]=>[[1,2,3,4,5,7],[6,9],[8]]=>00001010 [9,1,2,8,6,7,3,4,5]=>[[1,2,3,4,5],[6,7],[8],[9]]=>00001011 [9,1,2,5,6,7,8,3,4]=>[[1,2,3,4,7,8],[5,6],[9]]=>00010001 [4,1,2,5,6,7,8,9,3]=>[[1,2,3,6,7,8,9],[4,5]]=>00100000 [3,1,9,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3,9]]=>01000001 [3,1,8,2,4,5,6,9,7]=>[[1,2,4,5,6,7],[3,8,9]]=>01000010 [9,1,8,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [8,1,7,2,3,4,5,9,6]=>[[1,2,3,4,5,6],[7,9],[8]]=>00000110 [3,1,4,9,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4,9]]=>01000001 [3,1,4,9,2,5,8,6,7]=>[[1,2,5,6,7],[3,4,8],[9]]=>01000011 [7,1,9,6,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,9],[7]]=>00001101 [9,1,8,6,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8],[9]]=>00001011 [7,1,8,9,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>00000100 [8,1,9,7,6,2,3,4,5]=>[[1,2,3,4,5],[6,9],[7],[8]]=>00001110 [3,1,4,5,6,9,2,7,8]=>[[1,2,5,6,7,8],[3,4,9]]=>01000001 [9,1,8,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7],[8],[9]]=>00010011 [3,1,4,5,6,7,9,2,8]=>[[1,2,5,6,7,8],[3,4,9]]=>01000001 [3,1,4,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [2,9,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,8,1,3,4,5,6,9,7]=>[[1,3,4,5,6,7],[2,8,9]]=>10000010 [2,8,1,3,9,4,5,6,7]=>[[1,3,4,5,6,7],[2,8,9]]=>10000010 [2,4,1,6,3,8,5,9,7]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,5,6,7,8,9,3]=>[[1,3,5,6,7,8,9],[2,4]]=>10100000 [8,3,1,2,4,5,6,9,7]=>[[1,2,4,5,6,7],[3,9],[8]]=>01000010 [6,3,1,2,4,7,8,9,5]=>[[1,2,4,5,8,9],[3,7],[6]]=>01001000 [5,3,1,2,6,7,8,9,4]=>[[1,2,4,7,8,9],[3,6],[5]]=>01010000 [8,6,1,2,3,4,5,9,7]=>[[1,2,3,4,5,7],[6,9],[8]]=>00001010 [9,7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7],[9]]=>00000101 [8,9,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [8,7,1,2,3,4,5,9,6]=>[[1,2,3,4,5,6],[7,9],[8]]=>00000110 [7,6,1,2,3,4,9,5,8]=>[[1,2,3,4,5,8],[6,9],[7]]=>00001101 [9,6,1,2,3,4,8,5,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>00001011 [9,7,1,2,3,4,8,5,6]=>[[1,2,3,4,5,6],[7,8],[9]]=>00000101 [9,8,1,2,3,7,4,5,6]=>[[1,2,3,4,5,6],[7],[8],[9]]=>00000111 [9,6,1,2,3,7,8,4,5]=>[[1,2,3,4,5],[6,7,8],[9]]=>00001001 [5,6,1,2,3,7,8,9,4]=>[[1,2,3,4,8,9],[5,6,7]]=>00010000 [5,9,1,2,6,3,4,7,8]=>[[1,2,3,4,7,8],[5,6],[9]]=>00010001 [9,8,1,2,6,7,3,4,5]=>[[1,2,3,4,5],[6,7],[8],[9]]=>00001011 [8,7,1,9,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,9],[8]]=>00000110 [8,7,1,6,2,3,4,9,5]=>[[1,2,3,4,5],[6,9],[7],[8]]=>00001110 [9,8,1,6,2,7,3,4,5]=>[[1,2,3,4,5],[6,7],[8],[9]]=>00001011 [9,8,1,7,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>00001111 [8,9,1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7],[8,9]]=>00010010 [9,4,1,5,6,7,8,2,3]=>[[1,2,3,7,8],[4,5,6],[9]]=>00100001 [2,3,9,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,3,8,1,4,5,6,9,7]=>[[1,3,4,5,6,7],[2,8,9]]=>10000010 [2,3,5,1,6,7,8,9,4]=>[[1,3,4,6,7,8,9],[2,5]]=>10010000 [2,9,4,1,3,5,6,7,8]=>[[1,3,5,6,7,8],[2,4],[9]]=>10100001 [2,9,4,1,6,3,5,7,8]=>[[1,3,5,7,8],[2,4,6],[9]]=>10101001 [2,9,4,1,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8],[9]]=>10101011 [9,3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4],[9]]=>01000001 [6,9,8,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>00001011 [9,7,8,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8],[9]]=>00000101 [6,7,8,1,2,3,4,9,5]=>[[1,2,3,4,5],[6,7,8,9]]=>00001000 [2,3,4,9,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,9,4,5,1,3,6,7,8]=>[[1,3,5,6,7,8],[2,4],[9]]=>10100001 [2,7,8,9,1,3,4,5,6]=>[[1,3,4,5,6],[2,7,8,9]]=>10000100 [9,3,4,8,1,2,5,6,7]=>[[1,2,5,6,7],[3,4,8],[9]]=>01000011 [7,3,4,8,1,2,5,9,6]=>[[1,2,5,6],[3,4,8,9],[7]]=>01000100 [2,3,4,5,9,1,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,3,4,5,8,1,6,9,7]=>[[1,3,4,5,6,7],[2,8,9]]=>10000010 [8,7,4,5,6,1,2,9,3]=>[[1,2,3,9],[4,5,6],[7],[8]]=>00100110 [9,3,4,5,6,1,8,2,7]=>[[1,2,5,6,7],[3,4,8],[9]]=>01000011 [2,3,4,5,6,9,1,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,3,4,5,6,8,1,9,7]=>[[1,3,4,5,6,7,9],[2,8]]=>10000010 [2,9,4,5,6,7,1,3,8]=>[[1,3,5,6,7,8],[2,4],[9]]=>10100001 [9,3,4,5,6,7,1,2,8]=>[[1,2,5,6,7,8],[3,4],[9]]=>01000001 [9,3,4,5,6,8,1,2,7]=>[[1,2,5,6,7],[3,4,8],[9]]=>01000011 [2,3,4,5,6,7,9,1,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,9,4,5,6,7,8,1,3]=>[[1,3,5,6,7,8],[2,4],[9]]=>10100001 [9,3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4],[9]]=>01000001 [2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 []=>[]=> [3,5,2,6,1,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,2,6,4,1,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,2,7,4,8,1,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,2,7,4,8,6,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,5,7,2,3,8,6,1]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,5,7,2,3,8,1,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,5,6,2,3,1,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,5,6,2,1,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [3,5,1,6,4,2,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [4,5,6,1,3,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,5,6,3,1,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,5,7,3,2,8,1,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,5,7,3,2,8,6,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,6,7,3,8,2,5,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,7,3,8,2,1,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,7,3,8,1,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,5,7,3,1,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,5,7,1,3,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [3,5,1,7,4,8,2,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [2,1,5,7,4,8,3,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,1,5,7,4,8,6,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [3,5,1,7,4,8,6,2]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [4,5,7,1,3,8,6,2]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,5,7,3,1,8,6,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,6,7,3,8,1,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,6,7,3,8,5,1,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,6,7,3,8,5,2,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [5,6,7,8,3,1,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [5,6,7,8,1,3,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [4,6,7,1,8,3,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [3,6,1,7,8,4,5,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [2,1,6,7,8,4,5,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,1,6,7,8,4,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,6,1,7,8,4,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [4,6,7,1,8,3,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [5,6,7,8,1,3,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [4,5,7,2,1,8,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,6,7,2,8,1,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,6,7,2,8,3,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,6,7,2,8,3,5,1]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,6,2,7,8,4,5,1]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,2,7,8,4,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,2,7,8,1,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,5,2,7,1,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,4,2,1,7,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,4,1,2,7,8,6,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,5,2,7,1,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,6,2,7,8,1,5,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,6,2,7,8,5,1,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,6,2,7,8,5,4,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [4,6,7,2,8,5,3,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,6,7,2,8,5,1,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,6,7,2,8,1,5,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,5,7,2,1,8,6,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [4,5,7,1,2,8,6,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [3,5,1,7,2,8,6,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [2,1,5,7,3,8,6,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,1,6,7,8,3,5,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,6,1,7,8,2,5,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [4,6,7,1,8,2,5,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [5,6,7,8,1,2,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,6,7,8,2,1,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,7,8,2,4,1,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,7,8,2,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,6,7,8,1,4,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,6,7,1,8,5,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [3,6,1,7,8,5,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [2,1,6,7,8,5,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,6,1,7,8,5,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [4,6,7,1,8,5,3,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [5,6,7,8,1,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,6,7,8,4,1,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [3,5,2,7,4,9,6,10,8,1]=>[[1,4,6,8,10],[2,5,7,9],[3]]=>110101010 [4,6,8,3,9,5,10,7,2,1]=>[[1,5,7,9,10],[2,6,8],[3],[4]]=>111010100 [5,6,7,8,4,3,2,1,10,9]=>[[1,6,7,8,9],[2,10],[3],[4],[5]]=>111100001 [5,7,8,9,4,10,6,3,2,1]=>[[1,6,8,9,10],[2,7],[3],[4],[5]]=>111101000 [6,7,8,9,10,4,3,2,1,5]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000 [6,7,8,9,10,3,4,1,2,5]=>[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000 [6,7,8,9,10,3,4,2,1,5]=>[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000 [6,7,8,9,10,2,3,4,1,5]=>[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000 [2,1,4,3,6,5,9,10,8,7]=>[[1,3,5,7,10],[2,4,6,8],[9]]=>101010110 [6,7,8,9,10,5,4,3,2,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000 [6,5,8,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [3,6,7,4,5,8,1,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [2,6,7,4,5,1,8,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [1,6,7,4,5,2,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,5,4,7,6,2,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [2,5,4,7,6,1,8,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [3,5,4,7,6,8,1,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [4,5,3,7,8,6,1,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [5,4,3,8,7,6,1,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [6,4,8,3,7,5,1,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [6,3,8,4,5,7,1,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [5,3,4,8,6,7,1,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [4,3,5,6,8,7,1,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [3,2,5,6,1,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [4,2,5,6,8,1,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,2,4,8,6,1,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [6,2,8,4,5,1,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [7,8,2,4,5,1,6,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,8,1,4,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [6,1,8,4,5,2,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [5,1,4,8,6,2,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [4,1,3,2,8,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [5,1,3,8,2,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [6,1,8,3,2,5,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [7,8,1,3,2,5,4,6]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,8,2,3,1,5,6,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [6,2,8,3,1,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [5,2,3,8,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [6,3,8,2,1,7,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [7,8,3,2,1,6,5,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [7,8,4,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [5,4,2,8,7,1,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [4,5,2,7,8,1,6,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [2,5,3,7,1,6,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [1,5,3,7,2,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [1,6,7,3,2,5,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [2,6,7,3,1,5,8,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [3,6,7,2,1,8,5,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [7,8,5,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [6,5,8,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [5,4,1,8,7,2,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [6,4,8,1,7,2,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [7,8,3,1,2,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [5,3,1,8,2,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [4,3,1,2,8,7,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [4,2,1,3,8,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [5,2,1,8,3,4,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [6,2,8,1,3,4,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [7,8,2,1,3,4,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [4,3,1,2,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [5,3,1,6,2,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [6,3,1,5,2,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [7,3,1,5,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,4,5,1,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,4,5,1,2,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [6,4,5,1,2,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,4,6,1,2,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [2,1,6,5,3,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [3,6,1,5,2,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [4,6,5,1,2,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,6,4,1,2,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [6,5,4,1,2,3,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,5,4,1,2,8,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [8,6,4,1,7,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,6,4,1,8,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [6,7,4,1,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [5,7,4,1,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [4,7,5,1,2,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,7,1,5,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [2,1,7,5,3,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,1,8,5,3,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [3,8,1,5,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,8,5,1,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [5,8,4,1,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [6,8,4,1,7,2,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [8,7,4,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [5,8,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [4,8,6,1,7,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,8,1,6,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,1,8,6,7,3,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,1,7,6,8,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [3,7,1,6,8,2,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [4,7,6,1,8,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,7,6,8,1,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,4,7,1,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [6,4,7,1,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [7,4,6,1,8,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,4,6,1,7,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,3,1,6,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [7,3,1,6,8,2,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [6,3,1,7,8,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [5,3,1,7,2,8,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [4,3,1,2,7,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [2,1,4,3,8,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,4,1,2,8,7,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [6,3,1,8,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [7,3,1,8,6,2,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [8,4,7,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [7,4,8,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [5,4,8,1,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [4,5,8,1,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [3,5,1,8,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,1,5,8,3,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,1,6,8,7,3,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [3,6,1,8,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [4,6,8,1,7,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [5,6,8,7,1,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [7,5,8,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [8,5,7,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,7,8,6,1,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [4,7,8,1,6,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [3,7,1,8,6,2,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,1,7,8,6,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,1,8,7,6,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [3,8,1,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [4,8,7,1,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [5,8,7,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,8,7,5,1,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,4,7,3,8,5,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,7,3,5,8,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,7,2,5,1,8,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [5,4,2,7,6,1,3,8]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,4,2,7,6,1,8,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,4,3,7,6,8,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,4,3,7,8,6,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [6,4,8,3,5,7,1,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [5,4,3,8,6,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,4,3,6,8,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,4,2,6,7,1,8,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,2,6,7,1,3,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,3,2,6,1,7,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,3,2,6,1,7,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,3,2,6,1,8,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,4,2,6,8,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,4,2,8,6,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [6,4,8,2,5,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [7,8,4,2,5,1,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,8,4,2,5,1,3,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [5,4,2,8,6,1,3,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,3,2,6,1,8,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,3,2,1,6,8,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,3,2,1,8,6,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [5,3,2,8,1,6,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [6,3,8,2,1,5,4,7]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,8,3,2,1,5,4,6]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,8,3,2,1,5,6,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [6,3,8,2,1,5,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [5,3,2,8,1,6,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,4,2,7,8,1,6,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,3,2,7,1,8,6,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,3,2,7,1,6,8,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,3,2,7,1,6,4,8]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,3,7,2,1,5,4,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,7,2,1,5,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,7,2,1,8,5,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,4,7,2,8,1,5,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,5,7,8,2,1,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,5,8,7,2,1,3,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,3,7,2,1,8,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,3,7,2,1,4,8,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,3,7,2,1,4,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [5,3,2,7,1,4,8,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,4,2,8,7,1,3,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [7,8,4,2,6,1,3,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [7,8,3,2,1,6,4,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,3,8,2,1,7,4,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [5,3,2,8,1,7,4,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,3,2,1,8,7,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,2,1,7,5,8,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [4,3,2,1,7,5,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,3,2,1,8,5,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,3,2,8,1,4,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [6,3,8,2,1,4,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [7,8,3,2,1,4,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,3,8,2,1,4,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [4,3,2,1,8,5,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,3,2,1,5,8,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [7,8,5,6,1,2,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,8,4,1,6,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,8,1,4,6,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [6,1,8,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [1,6,8,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [7,8,1,3,2,6,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,8,3,4,6,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [7,8,2,4,6,1,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,8,2,1,3,6,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,8,1,2,3,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,1,8,2,3,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,6,8,2,3,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,2,8,1,3,7,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [6,2,8,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [6,3,8,4,7,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [3,6,8,4,7,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [2,6,8,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [2,6,8,3,1,7,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [2,6,8,1,3,7,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [1,2,5,8,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [2,4,1,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,5,3,8,1,7,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [3,5,4,8,7,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [5,3,4,8,7,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [4,2,1,3,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [4,1,2,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [4,3,1,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [6,3,8,1,2,7,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [5,1,3,8,2,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [1,5,4,8,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [6,4,8,1,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [6,5,8,7,1,2,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [5,6,8,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [5,6,8,7,2,1,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [4,5,1,8,7,2,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [1,4,5,8,7,2,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [4,6,8,2,7,1,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,6,8,3,7,5,1,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,5,3,8,7,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [4,5,2,8,7,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [3,5,2,8,1,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,1,2,4,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [4,3,5,8,7,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [3,4,5,8,7,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [4,1,3,2,6,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [5,1,3,2,6,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [6,1,3,2,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [7,1,3,2,5,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [8,1,4,2,5,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,1,4,2,5,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [6,1,4,2,5,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,1,4,2,6,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [2,1,6,3,5,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [3,1,6,2,5,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [4,1,6,2,5,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [6,2,5,1,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [5,2,6,1,4,3,8,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,2,7,1,4,3,8,6]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [5,2,8,1,4,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [6,2,8,1,4,3,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [6,2,7,1,4,3,8,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [7,2,6,1,4,3,8,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [7,2,5,1,4,3,8,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [4,1,7,2,5,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,1,7,2,5,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [2,1,7,3,5,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,1,8,3,5,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [3,1,8,2,5,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,1,8,2,5,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,2,5,1,4,3,7,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [8,2,6,1,4,3,7,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [7,1,4,3,8,2,6,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [8,1,4,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [8,1,5,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [7,1,5,3,8,2,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [8,2,6,1,5,3,7,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [5,1,8,2,6,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [4,1,8,2,6,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,1,8,2,6,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,1,8,3,6,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,1,7,3,6,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [4,1,7,2,6,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,1,7,2,6,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [7,2,6,1,5,3,8,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [6,2,7,1,5,3,8,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,2,8,1,5,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [8,1,5,2,6,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [6,1,5,2,7,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,4,2,7,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [8,1,4,2,6,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,1,3,2,6,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [7,1,3,2,6,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [6,1,3,2,7,4,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [5,1,3,2,7,4,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [4,1,3,2,7,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [2,1,4,3,8,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,1,4,2,8,5,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [4,1,3,2,8,5,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [5,1,3,2,8,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [6,1,3,2,8,4,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [8,4,7,1,3,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [7,4,8,1,3,2,6,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [7,3,8,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [8,3,7,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [6,1,4,2,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [5,1,4,2,8,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [4,1,5,2,8,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [3,1,5,2,8,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,1,5,3,8,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,1,6,3,8,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [3,1,6,2,8,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [4,1,6,2,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [5,1,6,2,8,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [6,1,5,2,8,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [8,3,7,1,5,2,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [7,3,8,1,5,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [6,2,7,3,8,1,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,2,8,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [8,3,7,2,6,1,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [5,1,8,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [4,1,8,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,1,8,4,7,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [2,1,8,4,7,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,1,7,4,8,3,6,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [3,1,7,4,8,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [4,1,7,3,8,2,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [5,1,7,3,8,2,6,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [7,3,8,2,6,1,5,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [8,2,6,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [7,2,6,3,8,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [3,4,2,6,8,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [5,3,6,2,8,1,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,3,6,2,4,8,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,7,3,8,2,4,1,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,7,3,8,2,4,6,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [7,4,2,5,8,3,6,1]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [7,4,2,5,8,3,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [4,5,2,6,3,8,1,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,5,2,1,6,8,3,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [5,3,1,6,8,2,4,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [5,6,2,8,1,3,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [3,5,6,1,4,8,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [4,1,5,6,3,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,5,1,6,3,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,5,6,3,2,8,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [7,4,5,3,8,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [7,4,5,3,8,2,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,7,4,8,3,2,5,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,7,4,8,3,2,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,7,4,1,8,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,4,5,3,1,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [4,7,1,5,8,3,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [5,3,7,8,1,4,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [7,5,8,2,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [7,3,5,8,1,4,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [4,5,1,7,8,3,6,2]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [7,4,1,5,8,3,6,2]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [6,7,4,3,8,1,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,7,4,8,3,1,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,7,4,8,3,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [5,6,7,3,8,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,7,3,1,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [5,6,1,7,3,8,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,1,6,7,3,8,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [6,4,7,1,8,3,5,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,7,8,3,1,4,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,7,2,8,4,5,1,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,7,2,8,4,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,1,7,4,8,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [5,1,6,7,3,2,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,1,7,3,2,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,7,3,2,1,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,7,3,2,8,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,2,7,3,8,4,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,6,2,7,3,1,8,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,6,2,1,7,3,8,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [6,1,7,4,2,8,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,2,1,8,3,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,5,8,2,1,3,4,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [5,7,3,1,8,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [4,7,1,5,2,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,4,2,5,1,8,3,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [6,7,4,2,1,8,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,7,4,2,8,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,7,4,2,8,3,5,1]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [3,6,7,2,8,4,5,1]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,7,2,8,4,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,7,2,1,8,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [5,7,3,8,2,1,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [3,4,7,8,2,1,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,7,8,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [3,4,7,8,2,6,1,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,7,3,8,2,6,1,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [3,6,7,2,8,5,1,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,6,7,8,5,2,1,4]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,6,7,8,5,2,4,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,4,7,8,2,5,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,4,7,8,2,1,5,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [4,1,5,7,8,2,6,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [5,3,7,8,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [6,7,2,8,5,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,4,1,7,8,2,5,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [5,1,6,2,7,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,6,2,1,7,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,2,7,1,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,2,7,8,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,6,7,2,8,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,6,7,2,1,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,1,7,2,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,1,6,7,2,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [6,4,7,1,8,2,5,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [3,6,7,1,8,5,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [6,7,8,5,2,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,8,3,5,1,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [4,6,7,8,1,5,3,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [5,1,6,7,8,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,6,1,7,8,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,6,7,1,8,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [8,6,1,3,4,2,5,7]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [8,3,2,5,1,6,4,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,5,3,6,2,4,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [5,3,2,7,4,1,8,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [7,5,3,8,2,4,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,2,4,5,8,3,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [2,4,5,3,7,1,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [8,2,4,5,6,3,1,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [8,2,4,5,6,1,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [8,1,2,4,5,6,3,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [8,2,5,1,3,6,4,7]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [8,5,6,2,1,4,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [8,5,3,6,4,1,2,7]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [8,4,1,5,6,3,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [8,1,4,5,6,3,2,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [4,5,3,7,2,1,8,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [7,4,5,8,3,2,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [4,3,6,7,2,8,5,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,6,7,2,8,1,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [1,4,3,6,7,2,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [4,5,3,7,1,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,1,5,3,7,2,8,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [5,3,4,7,1,2,8,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [7,5,8,2,1,4,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [7,5,3,8,4,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,4,5,8,3,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [4,3,6,7,8,1,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [1,6,4,7,8,3,5,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [6,4,7,8,3,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [3,5,6,7,8,4,1,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [3,1,5,6,7,8,4,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [4,6,1,7,8,3,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [3,6,7,1,4,8,5,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [6,2,4,1,7,8,5,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [2,6,7,1,4,8,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [4,3,6,7,8,1,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [1,5,3,6,7,8,2,4]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [3,5,6,7,8,2,1,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,6,7,8,2,4,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [5,2,7,1,3,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,3,1,7,8,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [4,5,2,7,8,1,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,2,6,7,8,3,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,6,7,8,3,5,1]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,6,2,7,4,8,5,1]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,2,7,4,8,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,2,1,6,4,7,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,7,4,2,1,5,8,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [1,7,3,4,2,5,8,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [4,7,2,1,3,5,8,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [7,8,4,2,1,3,6,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [7,8,1,3,4,2,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,8,3,4,2,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,3,2,7,1,8,5,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [3,6,2,7,1,8,5,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [6,7,3,8,2,5,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,4,7,8,5,2,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [2,6,4,7,8,1,5,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [4,6,2,7,8,1,5,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [7,4,5,8,6,2,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,4,1,5,8,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [7,5,3,8,6,1,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,8,2,1,6,3,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [6,2,7,1,3,8,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,3,1,7,8,2,5,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [4,6,1,7,8,5,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [5,1,2,6,7,8,4,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [5,2,6,7,8,4,1,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,2,6,7,8,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [2,5,6,7,8,4,1,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [1,5,2,6,7,8,4,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [1,6,4,7,8,5,2,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [2,6,7,1,3,8,5,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,7,8,2,1,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,3,8,5,1,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,4,7,8,5,3,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [4,5,2,3,7,6,1,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [6,4,3,7,2,5,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [8,4,3,6,5,1,2,7]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [1,5,6,3,4,8,7,2]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [4,6,2,7,3,5,1,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,2,6,7,4,5,1,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [4,7,2,6,5,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [5,7,6,2,4,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [1,7,5,4,8,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [8,7,5,4,1,3,2,6]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [6,8,5,4,2,1,3,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [5,8,6,2,4,1,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [4,8,2,6,5,1,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [3,2,8,6,5,1,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [4,1,2,6,5,8,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,1,6,2,4,8,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [6,1,5,4,2,8,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [7,1,5,4,8,2,6,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [8,1,5,4,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [1,8,6,7,4,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,1,6,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [7,1,6,8,4,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [6,1,7,8,2,4,5,3]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [5,1,7,2,8,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [4,1,2,7,8,5,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,2,1,7,8,5,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,8,7,1,5,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [4,8,2,7,1,5,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [5,8,7,2,1,4,3,6]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [6,8,7,1,2,4,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,8,6,1,4,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [8,7,6,1,4,3,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [1,7,6,8,4,3,5,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [1,6,7,8,3,4,5,2]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [8,6,7,1,3,4,2,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,6,8,1,3,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [5,7,8,2,1,3,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [4,7,2,8,1,3,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [3,2,6,8,4,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [4,6,2,8,3,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,6,8,2,3,1,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [6,5,8,3,2,1,4,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,5,8,3,1,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [8,5,7,3,1,4,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [1,5,7,3,8,4,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,4,3,7,8,5,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [8,4,3,7,1,5,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [6,4,3,8,2,1,5,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [4,5,2,3,8,1,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [3,2,5,4,8,1,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,5,2,3,1,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [6,4,3,1,2,8,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [7,4,3,1,8,2,6,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [8,4,3,1,7,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [1,5,8,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [8,5,1,3,7,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [7,5,1,3,8,2,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [6,5,1,3,2,8,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [5,6,1,2,3,8,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [4,6,2,1,3,8,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [3,2,6,1,4,8,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [3,2,7,1,8,4,6,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [4,7,2,1,8,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [5,7,1,2,8,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [6,7,1,8,2,3,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [7,6,1,8,3,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [8,6,1,7,3,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [1,6,8,7,3,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [1,7,8,6,5,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [8,7,1,6,5,3,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [7,8,1,6,5,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,8,1,7,2,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [5,8,1,2,7,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [4,8,2,1,7,6,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [3,2,8,1,7,6,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [4,1,2,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [5,1,8,2,7,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [6,1,8,7,2,5,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [7,1,8,6,5,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [8,1,7,6,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [3,1,2,6,5,8,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,1,6,2,4,8,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [3,1,5,2,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,5,1,2,3,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,6,1,2,3,8,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,6,5,3,4,8,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [6,1,5,2,4,8,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [6,5,1,2,3,8,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,4,1,2,3,8,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [5,4,1,2,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [5,4,1,2,7,3,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [6,4,1,7,2,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [6,4,1,8,2,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [7,4,1,2,8,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,5,1,2,8,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,1,5,2,8,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,7,5,3,8,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [1,8,5,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,1,5,2,7,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [8,5,1,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [8,4,1,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,4,1,7,2,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [7,4,1,6,2,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [8,6,1,7,2,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,1,6,7,2,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,8,6,7,3,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,7,6,8,3,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,1,6,8,2,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,6,1,8,2,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [4,7,1,2,8,3,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [3,1,7,2,8,4,6,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [3,1,2,7,8,5,6,4]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,4,3,8,7,5,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,1,2,8,7,5,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [3,1,2,8,7,5,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,1,8,2,7,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,1,8,7,2,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,1,7,6,2,4,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [4,7,1,6,2,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [4,8,1,6,2,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,8,1,7,2,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [4,8,1,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [5,8,1,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,1,8,2,7,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,5,8,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,6,8,7,3,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [6,1,8,7,2,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [6,8,1,7,2,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,8,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [5,8,7,1,2,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [5,8,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [5,7,6,1,2,3,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [7,8,1,6,2,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,8,6,2,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,7,8,6,3,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,8,7,6,3,4,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [8,1,7,6,2,4,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,7,1,6,2,3,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [3,2,5,1,6,4,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,2,5,4,7,1,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,2,5,3,7,6,8,1]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,2,5,3,7,1,8,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,2,5,3,6,1,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,2,5,1,6,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [3,1,5,4,6,2,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [4,1,5,3,6,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,3,5,1,6,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,3,5,2,7,1,8,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,3,6,2,7,5,8,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,6,2,7,1,8,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,6,1,7,2,8,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,3,5,1,7,2,8,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [3,1,5,4,7,2,8,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [2,1,5,4,7,3,8,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [3,1,5,4,7,6,8,2]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [4,1,5,3,7,6,8,2]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,3,5,1,7,6,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,3,6,1,7,5,8,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,3,6,5,7,1,8,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [5,3,6,4,7,2,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,3,6,4,7,1,8,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [5,3,6,1,7,4,8,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [5,1,6,3,7,4,8,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [4,1,6,3,7,5,8,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [3,1,6,4,7,5,8,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [2,1,6,4,7,5,8,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,1,6,4,7,3,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,1,6,4,7,2,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [4,1,6,3,7,2,8,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [5,1,6,3,7,2,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,3,6,1,7,2,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,3,6,2,7,1,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,3,6,2,7,4,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,2,6,3,7,4,8,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,2,6,3,7,1,8,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,2,6,1,7,3,8,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [4,2,5,1,7,3,8,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,2,6,1,7,3,8,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,6,3,7,1,8,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,6,3,7,5,8,1]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,2,6,4,7,5,8,1]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,2,6,4,7,1,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,2,6,1,7,4,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,2,5,1,7,4,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,2,4,1,7,5,8,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,1,4,2,7,6,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,2,5,1,7,6,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,6,1,7,5,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,2,6,5,7,1,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [4,2,6,5,7,3,8,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,2,6,5,7,1,8,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,2,6,1,7,5,8,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,2,5,1,7,6,8,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [4,1,5,2,7,6,8,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [3,1,5,2,7,6,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [2,1,5,3,7,6,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,1,6,3,7,5,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,1,6,2,7,5,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [4,1,6,2,7,5,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [5,1,6,2,7,4,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,2,6,1,7,4,8,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,2,6,4,7,1,8,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,2,6,4,7,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,6,2,7,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,6,2,7,1,8,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,6,1,7,2,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,1,6,4,7,2,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,1,6,5,7,2,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [3,1,6,5,7,2,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [2,1,6,5,7,3,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,1,6,5,7,4,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [4,1,6,5,7,3,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [5,1,6,4,7,3,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,4,6,1,7,3,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,4,6,3,7,1,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [8,3,5,2,1,6,4,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,6,3,5,2,4,1,7]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [3,7,5,2,4,1,8,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [8,3,7,5,2,4,6,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,2,4,5,7,3,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,4,5,7,3,1,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [8,2,4,6,5,3,1,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [8,2,5,4,6,1,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [8,6,3,5,1,4,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [8,6,1,4,5,3,2,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,1,5,6,4,3,2,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [5,7,4,3,2,1,8,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [8,5,7,4,3,2,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [4,6,8,3,2,7,5,1]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,7,6,3,2,8,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [1,4,6,7,3,2,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [5,4,7,3,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [1,7,4,5,3,2,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [3,7,5,1,4,2,8,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [5,7,4,2,1,3,8,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [8,5,7,4,2,1,6,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [8,3,7,5,1,4,6,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [8,4,1,7,5,3,6,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [4,6,3,8,7,1,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [1,7,4,8,6,3,5,2]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [8,4,7,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [3,6,5,8,7,4,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [3,1,5,8,6,7,4,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [4,8,1,6,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [3,6,4,1,8,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [8,2,6,1,4,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,7,6,8,1,4,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [3,7,1,6,4,8,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [1,7,3,5,6,8,2,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,6,7,5,8,2,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [3,7,6,5,8,2,1,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,6,8,5,7,2,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [2,3,5,7,6,8,1,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,1,6,5,7,8,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [4,2,7,6,8,3,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [4,2,6,8,7,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [3,8,2,4,6,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,7,2,6,4,8,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [3,2,6,1,4,7,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [5,3,7,2,1,8,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [4,7,3,2,1,5,8,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [8,7,6,1,3,4,2,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [8,5,7,3,2,1,6,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [8,3,6,7,2,1,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,7,8,6,2,1,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [8,7,6,3,5,2,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [2,7,4,8,1,6,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [4,6,8,2,1,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [8,4,1,5,7,2,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,5,3,7,1,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,5,7,2,1,3,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,2,6,7,1,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [8,3,6,1,7,5,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [4,6,1,8,7,2,5,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [8,1,2,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [8,2,6,5,7,4,1,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [2,1,7,8,5,6,4,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [8,2,5,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [2,7,6,8,5,4,1,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [1,7,2,5,8,6,4,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,7,4,8,2,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [3,7,8,1,6,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [2,7,8,6,1,3,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [8,7,6,3,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,4,7,6,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,7,1,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [8,1,6,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [6,5,3,1,2,4,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [4,6,3,5,1,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [8,5,3,7,2,1,4,6]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [6,8,1,4,5,7,3,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [8,7,2,4,5,1,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [3,6,2,4,5,1,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,6,1,4,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [6,1,2,4,5,3,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,6,3,2,1,4,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,4,3,6,1,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [6,3,1,4,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [3,1,6,4,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [8,3,7,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [5,8,7,4,2,6,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [2,8,7,4,1,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,1,7,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,7,8,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [2,1,8,7,5,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [2,1,6,8,5,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [5,6,3,8,1,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [7,6,1,4,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [3,7,6,4,5,8,2,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [8,5,7,4,1,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [5,1,8,4,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [2,5,8,4,7,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [2,4,8,3,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,1,8,3,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [3,8,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [8,4,1,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,5,8,4,3,6,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [6,5,3,8,4,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [2,1,5,8,4,6,7,3]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [2,1,4,8,3,6,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [6,4,3,8,2,1,7,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [7,3,8,4,2,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [8,3,1,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [3,1,8,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [2,3,8,1,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [4,3,8,2,5,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,8,2,3,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,8,2,1,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [2,8,1,3,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [8,1,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [7,8,2,4,3,6,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [6,8,3,2,4,1,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [2,1,8,3,4,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,1,7,8,5,4,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [5,7,3,8,1,4,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [7,1,8,4,5,3,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [2,7,8,4,5,3,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [8,7,1,4,3,6,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [3,8,7,4,2,6,1,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [5,7,8,4,3,6,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,6,3,8,4,2,7,1]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,8,3,6,2,1,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [8,6,3,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [7,5,3,8,2,4,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [2,4,3,1,8,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [4,1,3,2,6,8,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [7,5,3,6,2,8,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [8,6,3,5,1,2,7,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [5,8,3,2,6,1,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [4,5,3,8,6,2,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,5,8,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [5,8,2,4,7,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,7,5,4,1,6,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [2,7,6,4,5,8,1,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [7,1,6,4,5,8,2,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [5,7,3,6,1,8,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [2,1,7,6,5,8,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,1,8,5,3,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [6,8,3,5,2,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,8,5,4,2,6,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [8,1,4,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [2,8,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,8,1,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [3,4,8,1,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [3,4,2,8,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,4,1,8,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,1,2,8,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [8,4,2,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [7,5,2,4,8,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,5,3,2,8,1,7,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [2,1,5,3,8,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [6,4,3,5,8,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [7,3,5,4,8,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [8,3,4,1,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,3,1,8,5,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [3,1,4,8,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [6,5,3,7,2,8,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,3,7,4,5,8,2,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [6,7,2,4,5,8,3,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [5,1,7,4,8,6,3,2]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [2,5,7,4,8,6,3,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,6,3,7,1,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [3,8,7,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [3,7,5,4,8,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [5,7,1,4,8,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,6,3,1,8,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [4,6,3,5,8,2,7,1]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,6,3,8,1,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [3,7,8,4,1,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [3,2,5,1,6,8,4,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,6,2,5,4,8,1,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [3,5,2,4,7,1,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,8,2,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [4,2,5,8,3,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [4,2,6,5,3,8,1,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [5,4,2,1,6,8,3,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [6,3,5,1,4,8,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [4,6,1,5,3,8,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,1,6,4,3,8,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [5,4,3,2,7,1,8,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,3,8,2,7,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [4,3,6,2,8,7,5,1]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,7,6,2,1,8,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [6,4,3,1,7,2,8,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,5,4,3,1,8,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [1,4,7,5,8,3,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,1,3,5,8,4,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,2,5,8,4,1,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [2,8,5,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [3,5,8,7,1,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [1,4,5,8,7,3,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,5,4,8,7,3,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,4,3,8,1,7,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [4,3,7,1,8,6,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [4,8,3,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [5,3,8,7,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [7,5,3,1,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [1,8,6,5,3,7,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [1,5,8,6,3,7,4,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [4,6,1,8,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [6,8,7,3,1,4,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,2,8,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [7,6,2,8,4,1,3,5]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,3,1,6,8,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [1,7,6,4,8,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [5,7,1,6,3,2,8,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [6,1,7,5,3,2,8,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [7,6,5,3,2,1,8,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>1101110 [6,5,3,2,8,7,4,1]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [5,2,6,3,8,7,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [5,2,7,6,3,1,8,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [6,5,2,1,7,3,8,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,2,7,4,1,8,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [4,7,2,6,3,1,8,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [2,4,8,6,3,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,8,6,2,4,7,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [7,3,6,2,4,1,8,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [3,6,7,2,1,4,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [4,3,7,8,2,1,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [8,3,7,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,8,2,5,7,1,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,3,6,2,7,1,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,8,3,6,2,1,5,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [8,7,3,6,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [4,7,8,2,1,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [4,2,6,8,1,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [5,4,8,2,7,1,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [4,8,1,5,7,2,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [5,8,3,7,1,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,8,7,2,6,1,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,6,2,7,5,1,3,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [3,6,8,1,7,5,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [5,1,6,8,2,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [6,5,2,8,1,7,4,3]=>[[1,3],[2,4],[5,7],[6,8]]=>1011101 [5,2,7,1,8,6,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [5,8,2,7,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [6,2,8,7,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [7,6,2,1,8,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [6,1,7,2,8,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,5,1,8,2,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [4,7,1,8,6,2,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [7,8,3,1,6,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [8,7,4,6,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,5,7,1,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [6,8,1,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,1,8,6,5,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [5,4,2,3,7,6,1,8]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [6,4,2,7,3,5,1,8]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [7,4,2,6,3,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [8,4,2,6,3,1,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,2,7,6,4,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,7,2,6,3,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [5,7,6,2,3,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [1,6,5,2,3,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,7,5,2,8,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,8,5,2,3,1,4,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [5,8,6,2,3,1,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,8,2,6,3,1,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,2,8,6,4,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,2,1,6,4,8,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [7,1,5,2,8,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,8,5,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,8,6,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [8,1,6,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [7,1,6,8,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [3,2,1,7,8,4,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,2,8,7,1,4,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [5,8,7,2,1,3,4,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [1,7,6,8,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [6,5,8,2,3,1,4,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [8,5,7,2,1,3,4,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [6,4,2,8,3,1,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [5,4,2,3,8,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [3,2,5,4,1,8,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,5,2,3,1,8,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [5,4,2,3,1,8,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [6,4,2,1,3,8,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [7,4,2,1,8,3,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [8,4,2,1,7,3,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [1,4,2,8,7,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,5,8,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,5,1,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [7,5,1,2,8,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,5,1,2,3,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [4,6,2,1,3,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [3,2,6,1,4,8,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,2,7,1,8,4,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [4,7,2,1,8,3,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [7,6,1,8,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [8,6,1,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,6,8,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,7,8,6,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [7,8,1,6,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [6,8,1,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [4,8,2,1,7,3,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [3,2,8,1,7,4,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,1,8,7,4,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [5,1,8,2,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [6,1,8,7,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [8,1,7,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,8,7,6,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [6,3,5,1,2,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [4,3,5,6,1,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [8,3,7,5,2,1,4,6]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [6,3,7,5,1,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,5,2,7,1,8,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,5,2,7,4,1,3,6]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [2,6,1,5,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,4,3,5,1,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,3,1,4,6,2,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,1,4,6,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [5,7,4,6,2,8,3,1]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [8,1,4,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,4,7,8,5,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [2,1,8,5,7,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [8,6,3,5,1,7,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [5,8,2,4,6,7,3,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [3,4,8,6,5,7,1,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [7,5,4,8,1,6,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [5,1,4,6,8,2,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [2,5,4,6,7,1,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,4,6,3,7,5,8,1]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [4,1,6,3,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [3,7,4,2,8,6,5,1]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [7,4,1,3,5,8,6,2]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [6,5,8,4,1,7,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [8,5,3,7,4,1,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [2,1,4,8,3,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [7,4,3,8,2,1,6,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [6,3,7,4,1,8,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [8,3,1,2,5,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,1,8,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [2,3,8,1,6,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [4,3,7,2,6,8,5,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,7,2,3,8,5,6,1]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [3,8,2,1,7,5,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [2,8,1,3,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,7,8,5,4,3,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [8,7,1,6,3,4,2,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [3,8,6,7,2,4,1,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [5,3,8,7,4,2,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [4,3,8,7,2,1,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [8,3,6,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [7,3,5,8,2,4,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [2,3,4,1,8,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [4,1,3,2,6,7,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [8,3,5,6,2,7,1,4]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [5,3,6,1,8,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [5,6,2,8,7,4,1,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [7,8,5,6,1,4,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [2,8,6,5,4,7,1,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [8,1,6,4,5,7,2,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [5,8,3,6,1,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [2,1,8,6,5,7,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,1,7,5,3,6,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [6,7,3,5,2,1,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [7,1,4,2,5,6,8,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [2,7,4,1,6,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [4,6,1,2,8,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [2,4,1,5,8,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [4,1,2,5,8,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [6,4,2,1,5,8,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [8,5,2,4,6,1,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [7,5,3,2,6,8,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [2,1,5,3,6,8,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [7,3,5,4,6,1,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [6,3,4,1,5,7,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,3,1,5,7,6,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [3,1,4,5,6,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,5,2,6,3,1,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [6,5,2,1,4,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,5,2,7,4,8,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [8,5,2,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,3,7,5,2,1,6,4]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [6,3,7,5,2,8,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [3,1,6,5,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [5,6,3,2,4,1,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [3,6,2,4,1,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,6,1,3,5,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [6,7,2,3,4,8,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [8,7,2,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [5,1,7,3,8,4,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [2,5,7,3,8,6,4,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [7,6,1,3,5,8,4,2]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [3,6,7,4,1,8,5,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [5,6,3,7,4,8,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [2,1,6,7,4,8,5,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,1,8,7,4,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [5,8,3,7,4,2,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [3,8,7,4,1,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [7,8,1,3,5,2,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [5,8,7,3,2,6,1,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [2,8,6,3,1,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,1,6,3,2,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [2,8,4,1,6,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,8,1,2,7,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,8,4,2,5,7,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [6,8,3,5,2,7,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [2,1,5,3,8,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [6,5,3,2,8,7,1,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [7,5,2,4,8,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [3,4,2,8,5,7,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [2,4,1,8,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,4,2,1,7,5,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,3,1,8,6,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [3,1,4,8,6,5,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [7,1,6,5,4,8,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [3,7,5,6,8,4,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [5,7,1,6,8,2,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [8,6,2,5,1,7,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [5,6,2,1,8,7,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [4,6,2,5,8,3,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [7,5,2,6,3,8,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [4,1,2,3,6,8,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [2,4,3,1,8,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [7,5,2,8,3,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [5,6,2,8,4,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [4,7,2,8,1,5,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [8,7,2,1,4,5,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [3,6,8,7,1,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [5,7,8,6,3,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,1,8,5,4,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [2,7,8,4,5,3,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [5,7,3,8,1,4,6,2]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [2,1,7,8,5,4,6,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [2,1,5,8,4,6,3,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [6,5,3,8,4,1,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,5,8,4,3,6,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [2,4,8,3,5,6,1,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,1,8,3,6,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [3,4,8,1,7,2,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [8,4,1,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,1,8,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [2,3,8,1,4,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [4,3,8,2,5,1,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [6,3,8,4,2,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,4,3,8,2,5,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [2,1,4,8,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [6,8,2,4,3,5,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [4,8,2,3,5,1,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,8,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [2,8,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,8,4,1,6,5,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,8,4,1,6,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,8,7,6,1,4,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,8,5,6,7,4,3,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [7,5,8,6,1,4,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [3,5,7,6,1,4,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,5,7,2,4,1,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [7,5,8,2,4,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [2,8,5,3,4,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,8,5,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,8,5,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,8,7,6,1,4,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,8,5,3,6,1,7,4]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [2,8,5,6,7,4,1,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,8,5,3,4,7,1,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,8,5,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,8,5,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [3,5,7,2,4,6,1,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [6,5,2,7,3,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [6,5,2,8,3,1,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,5,2,8,3,1,4,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [7,5,8,2,4,6,3,1]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [7,5,8,6,1,4,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [6,5,8,2,1,3,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [3,5,6,2,1,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,5,7,6,1,4,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,5,7,2,4,1,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,7,2,4,6,8,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [6,5,2,7,3,1,8,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [4,5,2,6,3,1,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,1,2,3,7,6,8,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [6,5,2,7,3,4,8,1]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,1,6,7,4,3,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,1,2,6,4,8,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,1,2,8,6,4,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [5,1,6,8,7,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [6,5,2,8,3,7,4,1]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [4,1,2,3,8,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [4,1,2,3,8,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,1,2,3,8,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,1,2,3,7,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [4,1,2,3,8,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [7,1,6,8,4,3,5,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [6,1,2,8,4,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,6,8,2,3,1,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [6,5,8,2,4,3,1,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,5,8,2,4,3,7,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [7,5,2,8,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [6,5,2,8,3,7,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,5,2,7,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,1,6,7,4,3,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,1,6,8,7,3,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [7,1,6,8,4,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [5,7,8,6,3,4,2,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [4,1,8,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,1,8,3,6,2,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [3,1,4,8,6,2,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,1,4,8,6,5,2,7]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [7,1,6,5,8,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [4,1,6,7,8,3,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,1,6,5,7,3,2,8]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [4,5,2,6,3,7,1,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,5,2,7,3,8,1,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [3,5,6,2,4,8,7,1]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,6,2,4,8,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,7,5,6,8,4,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,6,5,2,8,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,1,2,5,8,4,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,1,6,5,8,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,5,2,6,3,8,4,1]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [4,1,2,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [4,1,2,3,7,8,6,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [4,5,2,7,3,8,6,1]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,1,6,7,8,3,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,1,2,6,8,5,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [4,1,2,5,6,8,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [4,5,2,6,3,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [7,8,5,6,1,4,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [7,8,4,2,1,5,3,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,8,2,1,6,5,3,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [6,4,1,2,5,7,3,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [2,4,8,1,5,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [4,3,8,1,7,2,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [7,8,3,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,8,3,5,4,2,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,8,3,6,5,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [7,8,2,6,4,1,3,5]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,8,1,6,5,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [2,1,8,7,5,4,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [1,3,8,2,6,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [5,3,7,1,6,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [5,3,6,2,7,4,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,1,2,5,8,7,4,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [6,3,1,8,4,2,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [6,4,2,1,5,3,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [6,4,3,7,5,8,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [4,3,8,7,5,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [2,4,7,1,5,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [1,3,7,6,4,2,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [3,7,2,8,6,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [3,8,1,7,6,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [1,8,5,7,3,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [2,7,5,8,3,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [1,5,6,8,2,4,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,6,7,3,8,4,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [4,5,6,7,2,8,1,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,5,7,6,1,8,3,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [1,5,8,6,2,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,6,5,8,3,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [4,6,5,7,1,2,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [4,7,5,6,3,1,8,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [5,1,6,3,4,2,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [5,7,6,4,3,8,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,3,4,5,8,7,1,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [6,2,4,1,8,3,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [5,1,4,2,7,6,8,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [1,6,2,4,7,8,3,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [5,7,2,4,1,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [6,7,5,8,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,8,7,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [5,8,7,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [4,8,2,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,2,7,8,1,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [2,1,8,7,6,5,3,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [4,8,6,3,5,7,1,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [3,8,6,5,2,4,1,7]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [5,3,7,8,2,1,6,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,2,8,7,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [1,6,8,7,5,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [3,6,7,8,5,1,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [3,7,8,5,1,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [4,1,8,6,2,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [3,8,7,6,5,4,1,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [2,8,7,5,1,4,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,8,6,7,5,1,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,7,8,6,5,4,1,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [6,4,2,7,1,3,8,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [7,4,2,5,1,3,8,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [8,5,3,6,1,7,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [7,3,6,2,4,8,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [4,3,7,1,2,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [5,3,6,7,1,2,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [6,3,7,4,1,2,8,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [4,7,1,5,2,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,7,5,1,2,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [7,6,4,2,3,8,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [8,6,4,2,3,7,1,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [4,7,6,3,8,1,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [5,7,4,2,3,8,1,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [3,7,6,1,4,8,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [6,4,7,5,2,8,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [7,4,8,5,2,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [5,8,2,6,3,7,1,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [3,8,6,2,4,7,1,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [4,8,6,2,7,1,3,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [2,6,5,8,1,3,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,5,7,4,8,1,3,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [5,4,6,7,2,8,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [3,5,7,1,4,8,2,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [5,3,7,2,4,8,1,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,4,7,3,8,1,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [7,4,6,3,8,1,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [8,4,6,3,7,1,2,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [8,4,1,6,7,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [7,4,1,6,8,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [6,5,3,7,1,8,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,5,1,2,7,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [5,3,6,4,7,8,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [6,3,7,4,8,5,1,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [4,7,1,5,8,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [7,5,1,2,8,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,6,1,8,5,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [8,6,1,7,5,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [5,7,2,8,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [6,3,7,8,5,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [3,6,8,2,7,1,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [2,4,8,7,1,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [4,3,8,7,1,2,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [5,3,8,7,1,2,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [8,3,7,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,4,7,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,5,8,7,1,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,5,8,7,1,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [6,8,4,7,5,1,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [5,8,7,1,6,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [2,8,7,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [3,8,7,6,1,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [4,8,7,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [5,6,3,1,4,2,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [7,5,3,8,2,1,6,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [3,8,7,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,1,7,8,5,3,6,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [5,7,3,8,1,2,6,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [8,7,1,4,5,3,2,6]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [2,7,8,4,1,6,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,1,8,4,2,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,5,1,4,8,6,3,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [6,5,3,1,8,4,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [8,6,3,1,2,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,7,1,4,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [2,3,4,5,6,7,8,1,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,4,5,6,8,9,1,7]=>[[1,3,4,5,6,7,9],[2,8]]=>10000010 [2,3,5,6,7,8,9,1,4]=>[[1,3,4,6,7,8,9],[2,5]]=>10010000 [2,4,5,6,7,8,9,1,3]=>[[1,3,5,6,7,8,9],[2,4]]=>10100000 [3,4,5,6,7,8,9,1,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,7,8,9,1,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,7,1,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,4,5,6,7,8,10,1,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>100000001 [2,3,4,5,6,1,9,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,3,4,5,6,7,9,10,1,8]=>[[1,3,4,5,6,7,8,10],[2,9]]=>100000010 [2,3,4,5,1,8,9,6,7]=>[[1,3,4,5,6,7],[2,8,9]]=>10000010 [2,3,5,6,7,8,9,10,1,4]=>[[1,3,4,6,7,8,9,10],[2,5]]=>100100000 [1,4,5,6,7,8,9,2,3]=>[[1,2,3,6,7,8,9],[4,5]]=>00100000 [2,4,5,6,7,8,9,10,1,3]=>[[1,3,5,6,7,8,9,10],[2,4]]=>101000000 [3,4,5,6,7,8,9,10,1,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,6,4,5,7,2,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [5,3,2,7,4,6,8,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [7,5,3,6,2,4,8,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [8,5,3,6,2,7,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,2,6,3,4,7,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,2,6,3,4,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [6,2,7,3,4,5,8,1]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [5,4,7,6,2,3,8,1]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [6,7,3,5,2,4,8,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [3,7,6,2,4,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [2,7,6,3,4,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [8,6,5,2,3,7,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,5,2,1,7,3,4,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [7,5,2,1,8,3,4,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [1,6,3,2,8,4,5,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [5,6,2,3,1,8,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [5,4,8,6,2,7,1,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [6,8,3,5,2,7,1,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,8,5,2,3,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [6,8,2,1,7,3,4,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [1,8,6,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,8,2,7,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [2,8,1,7,3,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [3,8,6,1,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [4,8,1,5,7,2,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,2,8,3,7,1,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [8,1,2,7,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [3,6,2,7,1,8,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [6,3,7,1,2,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [7,2,6,1,8,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [3,2,1,5,8,4,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,3,5,1,6,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [5,4,6,3,8,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [3,6,4,5,8,7,1,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [6,5,3,4,8,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [5,3,2,8,7,1,4,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [5,3,1,8,7,2,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [8,5,3,7,6,1,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [6,1,8,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,3,8,1,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [7,6,8,2,3,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [3,7,8,2,4,6,1,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [6,7,3,8,2,5,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [5,4,7,8,2,6,1,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [4,2,5,8,7,1,3,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [2,3,8,7,1,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [7,2,8,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [2,1,8,7,3,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [8,2,7,6,1,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [1,2,8,7,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,3,8,7,2,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,7,8,3,6,2,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [4,1,5,8,7,2,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [5,4,8,7,6,1,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [6,8,3,7,5,1,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [7,8,6,2,5,1,3,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [8,1,6,7,3,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [8,1,6,7,3,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,1,5,3,7,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,1,5,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [7,5,1,3,6,2,4,8]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [7,5,8,3,6,2,4,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [7,4,8,3,2,6,5,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,4,1,3,2,6,5,8]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [8,1,4,3,2,6,5,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,1,4,3,2,7,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [8,1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [8,1,5,4,6,7,2,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [8,1,5,3,6,2,7,4]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [8,1,4,3,2,6,7,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,1,4,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [8,1,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,4,1,3,2,5,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [7,4,8,3,2,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,4,3,8,2,5,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,3,1,2,5,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [7,4,1,3,2,5,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,4,1,3,2,6,8,5]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [7,5,1,3,6,2,8,4]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [7,5,1,4,6,8,2,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [7,5,8,3,6,2,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [7,4,8,3,2,6,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,4,8,3,2,5,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,4,3,8,2,5,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,3,7,2,5,8,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [5,4,3,2,8,6,1,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,4,3,2,8,7,1,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,5,3,8,7,2,1,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [6,5,4,8,7,1,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [6,5,4,1,7,8,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,5,3,1,7,2,8,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,4,3,1,2,7,8,5]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [5,4,3,2,1,8,6,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [6,5,3,1,8,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [6,5,4,1,8,7,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [7,5,1,4,8,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,4,1,3,2,8,6,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [7,4,1,3,2,8,5,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [6,4,3,1,2,8,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,4,3,1,2,7,5,8]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [6,4,3,8,2,7,5,1]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,5,3,8,7,2,4,1]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [6,5,3,1,7,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,5,3,1,8,2,4,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [7,5,1,3,8,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,6,1,8,3,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,6,1,8,4,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,6,8,1,4,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,6,8,1,3,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [6,5,3,7,8,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,4,3,7,2,8,5,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,4,3,7,2,1,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,4,8,3,2,1,5,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [7,4,8,3,2,1,6,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,5,8,3,1,2,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,8,4,1,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [6,5,4,8,1,7,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [6,5,3,8,1,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [5,4,3,2,8,1,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,4,3,7,2,1,8,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,5,3,7,1,2,8,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,5,4,7,1,8,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,5,3,7,8,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,4,3,7,2,8,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [5,4,3,2,7,8,1,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,3,2,6,8,1,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,6,2,1,3,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [7,6,1,2,5,8,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [2,1,7,8,4,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,8,1,2,5,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [8,4,1,3,7,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [6,5,2,1,8,7,4,3]=>[[1,3],[2,4],[5,7],[6,8]]=>1011101 [4,7,2,8,1,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [3,4,7,1,8,2,6,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [1,8,2,4,3,5,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,7,2,4,3,5,6,8]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [1,6,2,4,3,5,7,8]=>[[1,2,3,5,7,8],[4],[6]]=>0010100 [1,5,2,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [1,6,2,5,3,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [1,7,2,5,3,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,8,2,5,3,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,8,2,6,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,7,2,6,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,8,2,7,3,5,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,7,2,8,3,5,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,6,2,8,3,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,5,2,8,3,6,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,4,2,8,3,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [1,3,2,8,4,6,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,2,3,8,4,6,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,2,3,7,4,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,3,2,7,4,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,4,2,7,3,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,5,2,7,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,6,2,7,3,5,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,7,2,6,3,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [1,8,2,6,3,5,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,8,2,5,3,6,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,7,2,5,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,6,2,5,3,7,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,5,2,4,3,7,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [1,6,2,4,3,7,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,7,2,4,3,6,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,8,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [1,8,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,7,2,3,4,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,8,2,3,4,7,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,8,2,4,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,7,2,4,3,8,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [1,6,2,4,3,8,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,5,2,4,3,8,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,6,2,5,3,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,7,2,5,3,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,8,2,5,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,8,2,6,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,7,2,6,3,8,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,3,8,4,7,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,3,2,8,4,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,4,2,8,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,5,2,8,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,6,2,8,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,7,2,8,3,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,8,2,7,3,6,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [4,6,3,7,2,5,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,3,7,5,2,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,3,8,5,1,7,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [4,6,3,8,5,1,2,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [5,6,8,3,4,1,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [5,6,8,3,4,1,7,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [4,6,2,7,5,3,1,8]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [5,6,7,2,4,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,6,8,4,3,1,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,6,8,4,3,1,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [5,7,8,4,1,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,7,8,4,1,6,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,7,8,4,1,3,6,2]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [5,6,8,4,2,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,6,8,2,4,1,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [4,6,2,8,5,1,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [3,2,6,8,5,1,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [3,2,6,8,5,1,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [4,6,2,8,5,1,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [5,6,8,2,4,1,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,6,8,4,2,1,3,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,7,8,4,1,3,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [5,7,8,4,1,2,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,7,8,4,1,2,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [6,7,8,1,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,7,8,1,5,2,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,7,8,1,5,3,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,8,1,3,5,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [5,7,8,2,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [4,7,2,8,1,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [3,2,7,8,1,6,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,2,7,8,1,6,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [4,7,2,8,1,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [5,7,8,2,1,6,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [6,7,8,1,3,5,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,8,1,5,3,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,8,1,5,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,7,8,1,5,4,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,7,8,1,4,5,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [6,7,8,1,4,5,3,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,7,8,1,4,3,5,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,7,8,1,3,4,5,2]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [5,7,8,2,1,4,6,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [4,7,2,8,1,5,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [3,2,7,8,1,5,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,6,8,4,1,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,6,2,8,3,1,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [5,6,8,3,2,1,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,7,8,3,1,4,6,2]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [5,7,8,3,1,6,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [5,7,8,3,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [4,7,3,8,1,6,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,7,3,8,1,6,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [4,7,3,8,1,5,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,6,3,8,2,1,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,5,3,2,8,1,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,5,2,3,8,1,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [3,2,5,4,8,1,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [4,5,3,2,8,1,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,6,3,8,2,1,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,7,3,8,1,5,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,7,3,8,1,2,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,7,3,8,1,2,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [5,7,8,3,1,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,7,8,3,1,2,6,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,7,8,3,1,4,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [5,6,8,3,2,1,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [3,2,7,8,1,5,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [5,7,8,2,1,4,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [6,7,8,1,3,4,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,7,8,1,4,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,7,8,1,4,2,5,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [6,7,8,1,4,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,8,1,2,5,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,7,8,1,2,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,7,8,1,2,4,5,3]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,8,1,3,2,5,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [5,7,8,2,1,3,6,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [3,2,7,8,1,4,6,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [6,7,8,1,3,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,7,8,1,2,4,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,8,1,2,3,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [7,2,8,5,1,6,4,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [1,3,7,5,2,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,7,5,4,2,6,8]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [7,2,8,5,4,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [2,8,5,4,3,1,7,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [2,8,4,5,6,1,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [2,8,6,5,7,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [2,8,4,5,3,7,1,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,8,4,3,5,6,1,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [7,2,8,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [1,6,3,7,5,2,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [6,2,3,8,5,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [6,3,2,8,5,1,4,7]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,4,8,2,5,6,3,1]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,4,8,5,2,1,3,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [6,4,8,5,1,3,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [6,3,7,5,2,1,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [4,3,7,5,1,2,8,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,3,7,1,5,6,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [3,6,1,7,5,2,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [3,4,1,2,7,6,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,2,1,7,5,8,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,6,5,7,1,4,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [6,5,2,7,4,1,8,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [3,5,2,6,4,8,7,1]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [5,3,1,8,6,4,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [5,6,1,8,7,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [6,3,5,8,2,7,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,5,8,4,2,3,7,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,2,5,8,3,7,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [1,6,5,7,3,4,2,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [1,5,2,7,4,6,3,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [5,2,1,8,7,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [7,1,3,8,4,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [2,3,4,8,6,1,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,8,6,5,1,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,7,3,5,8,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [3,2,4,7,8,6,1,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [1,5,4,6,2,7,3,8]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [5,2,4,7,1,8,3,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [5,3,6,4,1,8,7,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [5,3,6,1,4,8,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [7,3,5,6,8,4,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [6,3,5,1,8,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [2,6,1,5,8,4,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,7,6,5,8,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [5,7,1,6,3,8,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [3,2,4,1,7,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,1,4,2,7,8,6,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [5,1,4,7,2,8,6,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [3,6,4,7,8,2,5,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,1,4,6,8,5,7,2]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [6,3,4,5,7,1,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [2,5,4,6,1,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [7,2,1,4,3,6,5,8]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [7,3,4,1,2,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [7,4,3,2,1,6,5,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [7,6,3,2,5,4,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [6,7,3,2,5,4,8,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [1,8,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,8,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,3,5,1,6,2,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [7,2,1,5,6,3,4,8]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [7,2,1,6,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,3,6,1,5,4,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [7,4,6,5,1,3,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [1,8,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,8,6,4,3,7,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [6,5,7,4,3,1,8,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,4,7,5,1,3,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,3,7,1,5,4,8,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,2,1,7,5,4,8,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [3,2,1,8,5,4,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [2,5,8,4,3,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [2,6,8,4,3,7,1,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [2,7,8,4,3,6,5,1]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [1,8,7,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [1,8,7,5,6,3,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [2,7,8,5,6,3,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [2,6,8,5,7,3,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [2,5,8,6,7,1,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,4,8,6,1,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [3,2,1,8,6,7,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [5,3,7,1,6,8,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [5,4,7,6,1,8,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [4,5,7,6,8,1,3,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [4,6,7,5,8,3,1,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [1,8,6,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [1,8,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [5,4,6,7,1,8,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,3,6,1,7,8,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,2,1,6,7,8,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [6,2,1,5,7,3,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,3,5,1,7,2,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [6,4,5,7,1,2,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [6,5,4,7,2,1,8,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,6,4,7,2,8,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [1,8,4,6,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,8,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [5,7,3,2,6,8,4,1]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,6,3,2,7,8,1,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,5,3,2,7,1,8,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [6,4,3,2,1,7,8,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,2,1,4,3,7,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [4,6,3,2,8,7,1,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,7,3,2,8,6,5,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [1,8,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,8,4,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [3,6,4,8,2,7,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [3,4,5,8,1,2,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [4,3,5,1,8,2,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [4,2,1,5,8,3,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [4,2,1,6,8,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [3,5,6,8,7,1,2,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [3,6,5,8,7,2,1,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [1,8,5,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [1,8,6,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [3,6,7,8,5,4,1,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [3,5,7,8,6,1,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,4,7,8,1,6,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [4,2,1,7,8,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [2,3,8,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [2,4,8,7,1,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>10101010101 [2,1,4,3,8,7,6,5,12,11,10,9]=>[[1,3,5,9],[2,4,6,10],[7,11],[8,12]]=>10101110111 [2,1,6,5,4,3,12,11,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10],[11],[12]]=>10111011111 [4,3,2,1,6,5,8,7,10,9,12,11]=>[[1,5,7,9,11],[2,6,8,10,12],[3],[4]]=>11101010101 [4,3,2,1,8,7,6,5,10,9,12,11]=>[[1,5,9,11],[2,6,10,12],[3,7],[4,8]]=>11101110101 [6,5,4,3,2,1,10,9,8,7,12,11]=>[[1,7,11],[2,8,12],[3,9],[4,10],[5],[6]]=>11111011101 [6,5,4,3,2,1,12,11,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>11111011111 [12,11,4,3,10,9,8,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8],[9],[10],[11],[12]]=>11101111111 [12,11,10,5,4,9,8,7,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5],[8],[9],[10],[11],[12]]=>11110111111 [12,11,8,7,6,5,4,3,10,9,2,1]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8],[11],[12]]=>11111110111 [12,11,10,7,6,5,4,9,8,3,2,1]=>[[1,8],[2,9],[3],[4],[5],[6],[7],[10],[11],[12]]=>11111101111 [12,11,10,9,6,5,8,7,4,3,2,1]=>[[1,7],[2,8],[3],[4],[5],[6],[9],[10],[11],[12]]=>11111011111 [12,11,10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>11111111111 [7,4,6,1,8,3,5,2]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [8,3,5,1,7,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [8,3,4,1,7,5,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [4,8,3,1,7,5,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [4,6,2,1,7,5,8,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [1,4,6,2,7,5,8,3]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [1,7,5,2,6,8,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [7,5,2,1,6,8,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [6,8,4,3,1,7,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [3,6,8,4,1,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [3,6,7,5,1,8,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [7,5,6,1,8,3,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [3,4,6,5,7,1,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,7,5,6,1,8,3,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [6,7,5,1,8,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,8,4,1,7,5,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [6,7,5,3,1,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [8,4,2,1,6,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [1,8,4,2,6,7,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [1,5,3,2,7,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [5,3,2,1,7,6,8,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [2,5,3,1,7,6,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [2,8,4,1,6,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,7,5,1,6,8,4,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [2,4,6,1,7,5,8,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [4,7,1,6,5,8,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [4,8,2,6,5,7,1,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,6,1,2,7,5,8,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [7,5,1,2,6,8,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [8,4,1,2,6,7,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [5,3,1,2,7,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [1,2,5,3,7,6,8,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [4,3,1,2,7,6,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [3,5,1,2,7,6,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [6,7,1,5,8,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [2,7,6,1,5,8,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,3,5,1,7,6,8,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [7,6,1,5,8,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [3,6,7,1,5,8,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [7,1,6,5,8,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,5,1,6,8,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [8,4,1,6,7,5,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [5,2,3,1,7,6,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [3,5,2,1,7,6,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [1,3,5,2,7,6,8,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,7,6,2,5,8,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,6,2,1,5,8,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [8,3,1,5,7,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [6,2,4,1,7,5,8,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [6,2,5,1,7,4,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [7,1,6,4,8,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [8,2,6,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [6,1,5,2,7,4,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [7,6,2,5,8,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [8,3,5,7,6,2,1,4]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [1,8,3,5,7,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [1,5,2,3,7,6,8,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [5,2,1,3,7,6,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [7,5,2,6,8,4,1,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [8,4,2,6,7,5,1,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [6,1,4,2,7,5,8,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [8,2,6,5,7,1,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [3,6,8,2,5,7,1,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [8,3,2,5,7,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [5,1,3,2,7,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [4,1,3,2,7,6,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [4,2,1,3,7,6,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [1,4,2,3,7,6,8,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [2,4,1,3,7,6,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,5,1,3,7,6,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,8,3,5,7,6,1,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [6,8,2,3,5,7,1,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [6,7,1,3,5,8,2,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [8,3,5,7,6,1,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [5,1,2,3,7,6,8,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [3,1,2,4,7,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [10,8,9,5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>000100101 [10,6,7,3,4,8,1,2,5,9]=>[[1,2,5,9],[3,4,8],[6,7],[10]]=>010010001 [8,5,9,3,6,10,1,2,4,7]=>[[1,2,4,7],[3,6,10],[5,9],[8]]=>010100100 [9,6,10,2,7,8,1,3,4,5]=>[[1,3,4,5],[2,7,8],[6,10],[9]]=>100010010 [8,4,9,2,5,10,1,3,6,7]=>[[1,3,6,7],[2,5,10],[4,9],[8]]=>101000100 [7,4,8,2,5,9,1,3,6,10]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000 [8,1,2,4,3,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [8,1,3,5,6,2,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [8,1,3,4,2,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [8,1,3,2,4,5,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [2,7,8,3,4,5,6,1]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [2,6,3,8,4,5,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [6,3,2,1,4,5,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,3,1,4,2,6,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [7,4,1,5,6,8,2,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,7,8,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [3,7,8,5,6,2,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [3,7,8,4,2,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [3,7,8,2,4,5,1,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,6,2,8,4,5,1,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,3,6,7,4,5,8,1]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [3,5,2,4,8,6,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,4,2,8,7,1,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,6,5,8,7,1,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [6,4,5,1,7,8,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [7,4,1,2,3,8,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [6,2,4,1,3,7,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,6,4,8,3,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [2,6,5,8,7,3,4,1]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,2,5,1,7,3,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,5,2,1,8,3,4,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,5,6,7,8,3,4,1]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [2,4,6,7,3,8,5,1]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [4,2,6,7,3,1,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,7,8,2,3,1,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [4,7,8,3,2,1,6,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [5,6,4,8,1,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,6,3,8,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [4,2,5,3,7,1,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,3,6,7,2,1,8,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,6,7,2,8,1,5]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,4,5,2,7,8,1,6]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,4,2,5,6,8,1,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [5,2,7,8,6,4,1,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [5,1,2,7,8,6,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [4,7,1,8,6,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [4,7,1,2,8,6,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [4,6,8,1,2,7,5,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [6,8,7,1,5,3,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [6,8,7,3,5,1,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [7,8,1,6,3,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,8,1,3,6,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,8,3,6,5,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [4,7,2,8,6,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [1,7,3,4,8,6,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [4,2,7,1,8,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [7,8,2,3,6,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [8,5,7,1,6,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [8,5,7,1,2,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,8,2,7,1,3,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [6,8,7,2,5,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [6,2,4,8,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [1,6,8,3,7,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,6,8,3,4,7,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [6,2,4,8,1,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [6,8,7,2,3,5,1,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [6,8,2,1,7,3,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [8,5,7,2,1,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,5,7,1,2,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [8,7,6,2,1,4,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,5,7,2,3,1,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [5,8,4,2,7,1,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [1,8,7,5,3,4,6,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [1,8,7,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [8,2,5,4,7,1,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,5,2,7,3,1,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,7,6,2,4,3,1,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>1010111 [8,7,6,1,2,4,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,7,6,1,4,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,7,6,4,1,3,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [5,8,4,7,2,1,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [1,8,7,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [1,6,8,4,3,7,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [6,8,7,3,2,5,1,4]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [6,8,1,7,3,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [8,5,7,3,1,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,5,7,1,3,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,5,7,3,1,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,8,4,7,1,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,4,1,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,4,7,1,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [8,1,2,6,5,7,4,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [8,2,5,6,7,4,1,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [4,8,5,7,1,6,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [4,8,5,7,1,2,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [4,8,5,1,7,2,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,5,3,1,7,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,5,3,7,1,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [6,8,1,3,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [4,6,2,8,1,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [1,6,4,8,3,7,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [1,8,7,4,5,3,6,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [4,8,5,7,2,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,5,3,7,2,1,6,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [8,7,6,3,1,4,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,7,6,1,3,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [8,5,3,2,7,1,6,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [4,8,5,2,7,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [1,8,7,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [1,8,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011 [8,2,4,5,7,1,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,5,2,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [6,3,1,5,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [8,3,1,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,5,4,2,1,7,3,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [8,5,4,2,1,7,6,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [6,5,4,2,1,3,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,5,4,2,3,1,8,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,3,2,5,1,4,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [6,5,4,3,1,2,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [6,5,4,1,3,2,8,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [8,5,4,1,2,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [8,7,4,1,6,3,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,7,4,1,6,3,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,7,4,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,5,4,1,3,7,6,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [8,5,4,3,1,7,6,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [8,3,2,5,1,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [2,1,8,5,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,3,2,5,1,7,4,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [8,5,4,3,1,7,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [8,5,4,1,3,7,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [8,7,4,1,6,5,2,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,7,4,1,6,2,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,7,6,5,2,1,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,7,4,3,6,2,1,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,3,2,7,6,4,1,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [2,1,8,7,6,4,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,1,8,7,6,4,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,3,2,7,6,4,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [8,7,4,3,6,2,5,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,7,6,5,2,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [8,5,4,2,3,7,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [8,7,4,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [8,7,4,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,7,4,2,6,3,1,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,3,1,7,6,4,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,3,1,7,6,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,3,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,3,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [8,3,1,5,4,7,2,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [8,3,1,7,6,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,3,1,7,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,7,4,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [8,7,4,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [8,5,4,2,3,7,1,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [8,3,2,5,4,7,1,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [2,1,8,5,4,7,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [8,3,2,7,6,5,1,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [8,7,4,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [8,7,6,5,3,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,7,6,5,1,3,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [8,7,6,5,1,3,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [8,7,6,5,1,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [8,7,6,5,4,1,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [8,7,4,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [8,3,2,7,6,1,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [2,1,8,7,6,3,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,3,2,7,6,1,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,7,6,5,1,4,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [8,7,6,5,1,2,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,3,5,1,8,4,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [7,3,4,1,8,5,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [4,5,6,2,1,8,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [1,6,5,2,7,4,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [7,4,3,1,8,6,5,2]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110 [7,6,5,1,8,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [7,6,4,1,8,5,3,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [6,4,2,1,8,7,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [1,6,4,2,7,5,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,5,3,2,7,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [5,3,2,1,8,7,6,4]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011 [2,5,3,1,7,8,6,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [2,6,4,1,7,8,5,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [2,6,5,1,7,8,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [4,5,7,1,6,8,2,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [6,5,1,2,8,4,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [6,4,1,2,8,5,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [5,3,1,2,8,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [4,3,1,2,8,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [6,1,2,5,8,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [7,1,3,4,8,2,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,1,5,6,8,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [2,6,1,5,7,8,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [7,4,1,6,8,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [5,2,3,1,8,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [3,5,2,1,6,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [1,6,2,5,7,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [6,2,1,5,8,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [7,3,1,5,8,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [6,2,4,1,8,5,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [6,2,5,1,8,4,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [7,3,1,4,8,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [6,2,1,4,8,7,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [1,6,2,4,7,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [5,2,1,3,8,7,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [7,4,1,3,8,5,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,5,1,3,8,4,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [3,6,7,1,4,8,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [7,6,1,4,8,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [4,2,1,3,8,7,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [2,6,1,4,7,8,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [7,1,4,6,8,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [7,1,3,5,8,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [6,1,2,4,8,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,2,3,1,6,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [7,4,5,2,3,1,8,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [8,6,7,3,5,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [7,3,5,2,4,1,8,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [6,3,5,2,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [5,2,4,1,6,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [4,1,6,3,5,2,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [6,3,4,1,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [5,2,6,3,4,1,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [5,2,7,3,4,1,8,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,2,8,6,7,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [6,2,8,5,7,3,4,1]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,2,7,3,4,1,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,3,4,1,5,2,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [4,1,7,3,5,2,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [3,1,7,4,5,2,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [2,1,7,4,5,3,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [3,1,8,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [4,1,8,6,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [8,6,7,3,4,1,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [8,5,7,3,4,1,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [8,5,6,2,7,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [8,4,7,3,5,1,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [5,1,8,4,7,3,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [4,1,8,5,7,3,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [3,1,8,5,7,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [2,1,8,5,7,4,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [2,1,7,4,6,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [3,1,7,4,6,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [4,1,7,3,6,2,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,1,7,3,6,2,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [6,2,7,3,5,1,8,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [6,2,8,4,7,3,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [8,4,7,3,6,2,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [7,3,6,2,5,1,8,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [6,2,5,1,7,3,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [5,2,4,1,7,3,8,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [6,2,4,1,7,3,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [8,5,7,3,6,2,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [8,5,7,4,6,2,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [7,4,6,2,3,1,8,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [6,2,3,1,7,4,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [5,2,3,1,7,4,8,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [4,2,3,1,7,5,8,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [3,1,4,2,8,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [6,2,3,1,8,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [8,5,6,2,3,1,7,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [7,4,8,5,6,2,3,1]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,3,8,5,6,2,4,1]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [8,5,6,2,4,1,7,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [5,2,4,1,8,6,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [4,1,5,2,8,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,1,5,2,8,6,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [2,1,6,3,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [3,1,6,2,8,5,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [4,1,6,2,8,5,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,1,6,2,8,4,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [8,4,6,2,5,1,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [7,3,8,4,6,2,5,1]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,2,7,3,8,4,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [8,4,5,1,6,2,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [5,1,8,4,6,2,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [4,1,8,5,6,2,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,1,8,5,6,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [2,1,8,5,6,3,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,1,7,4,8,5,6,3]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [3,1,7,4,8,5,6,2]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [4,1,7,3,8,5,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [7,3,8,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [8,4,5,1,7,3,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [7,3,6,2,8,4,5,1]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [7,8,5,6,1,3,4,2]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [1,3,8,4,7,2,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,6,1,4,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [4,6,1,2,5,7,3,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [1,4,8,2,5,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,8,2,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,8,1,5,4,6,3,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [7,8,2,1,6,3,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [7,8,4,5,3,1,6,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [1,5,8,4,3,2,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [5,6,1,4,3,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [2,6,4,8,3,7,1,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [1,4,6,8,3,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [2,4,8,5,3,1,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,5,8,1,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [3,5,8,4,7,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [1,6,2,4,7,3,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [7,5,3,6,2,4,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [5,7,3,6,1,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [5,3,6,7,2,1,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,1,7,5,2,4,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [6,3,1,2,4,5,8,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [1,4,7,2,5,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [1,6,7,5,8,2,4,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [3,5,6,7,8,1,4,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [3,6,5,7,8,2,1,4]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [5,2,7,6,1,4,3,8]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [2,1,6,8,4,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,7,1,8,5,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [3,1,8,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [4,3,7,8,1,2,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [1,7,3,8,5,2,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [5,7,8,6,3,2,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [5,7,8,6,1,3,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,6,5,8,1,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,1,3,4,8,2,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [2,6,3,4,5,8,1,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [7,2,1,4,8,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [5,6,2,7,3,1,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,7,6,4,1,8,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,7,1,5,2,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,5,2,8,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,7,5,3,8,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [7,1,5,3,4,2,8,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,5,2,4,3,1,6,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [6,8,1,3,7,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [7,4,2,6,5,1,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [7,2,3,5,4,1,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>1001010 [6,8,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [5,8,2,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [2,5,3,6,8,4,7,1]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [2,1,4,7,8,5,6,3]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,5,7,8,1,4,6,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [3,5,7,4,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [5,2,8,4,6,1,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [5,2,1,8,6,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [4,2,8,5,7,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [1,4,2,7,5,8,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [4,1,8,6,7,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [5,3,8,7,6,2,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [5,8,4,7,6,2,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [5,8,7,4,3,6,1,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [6,4,8,3,1,7,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [5,8,3,7,1,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [5,8,7,4,1,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [6,8,5,3,1,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [4,5,1,2,7,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,5,1,2,6,8,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,5,6,1,8,4,7,2]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,6,2,7,5,1,4,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [4,2,6,1,7,3,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,5,3,1,7,6,2,8]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [3,5,2,7,8,1,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,1,4,7,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [4,2,5,6,1,8,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,5,3,1,6,8,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [2,1,7,5,8,6,4,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [1,2,7,5,3,8,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [4,1,2,7,3,8,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [6,4,1,7,5,2,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [6,1,3,7,5,2,4,8]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [3,1,2,6,8,5,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,7,1,2,5,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,3,7,2,4,8,6,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,4,1,7,8,6,5,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [3,4,7,5,1,8,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [2,7,4,1,5,8,6,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [2,3,7,1,5,8,6,4]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [5,2,8,1,3,7,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [2,1,6,8,3,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,6,8,3,1,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [2,8,6,4,1,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [3,6,4,8,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [6,3,7,4,5,1,8,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [2,6,3,7,5,8,1,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [5,2,1,7,8,3,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [4,7,2,3,6,8,1,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,2,7,3,6,8,1,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [5,7,4,6,2,8,1,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,7,3,4,6,1,8,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [5,3,8,4,6,1,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [8,5,2,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [8,2,3,5,1,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [4,2,8,3,6,7,1,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,4,8,1,7,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,4,1,3,6,2,5,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,8,3,1,7,2,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [5,2,8,4,7,1,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [5,8,4,7,3,1,6,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [4,6,8,3,1,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [6,3,8,2,7,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [6,3,1,8,2,4,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [5,3,8,1,2,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,7,4,1,6,2,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [8,5,4,1,2,6,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [5,1,8,4,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,6,2,8,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,8,5,3,1,7,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [8,4,5,1,2,6,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [5,6,3,7,1,2,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [1,6,3,7,2,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,3,2,7,8,5,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [4,5,7,8,3,1,6,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,7,2,5,8,1,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [8,1,3,4,6,2,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,8,2,4,6,7,1,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,5,6,8,2,7,1,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [2,4,5,6,8,1,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,8,3,5,6,1,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [5,6,2,3,7,8,1,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,8,7,3,4,1,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [6,8,7,3,4,1,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,8,4,7,1,5,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [6,8,4,7,2,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [5,4,8,7,2,6,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [5,4,8,7,1,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [5,3,8,7,6,1,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [4,3,8,7,6,1,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [4,8,3,7,5,1,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,3,4,6,5,1,2,7]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [3,8,4,7,5,1,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [3,4,8,7,6,1,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,5,8,7,6,1,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [4,5,8,7,6,1,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [4,5,8,7,1,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [4,5,8,7,2,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [3,5,8,2,7,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [3,5,8,1,7,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [2,5,8,1,7,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,5,8,7,1,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,4,8,7,1,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,8,4,7,1,5,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,2,4,6,1,5,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [8,1,4,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [1,8,4,7,2,5,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [1,4,8,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,5,8,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,5,8,2,7,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [2,5,8,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [1,4,2,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [1,3,8,2,7,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,8,3,2,7,5,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,1,3,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,2,3,1,6,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,8,3,1,7,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [2,3,8,1,7,6,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [3,4,1,8,7,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [4,3,1,8,7,6,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [4,2,1,8,7,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [3,8,2,1,7,5,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,3,2,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [8,4,2,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,2,8,7,1,6,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [5,2,8,7,1,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [5,2,8,1,7,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [5,3,8,1,7,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [5,3,8,2,7,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [6,8,3,2,7,5,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [6,8,3,1,7,5,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [6,8,2,1,7,5,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [6,8,2,7,1,5,3,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [6,8,7,2,1,4,3,5]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [8,5,6,1,2,4,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [5,8,7,1,2,4,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [6,8,1,2,7,5,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [6,8,2,3,7,5,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [5,2,8,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [5,1,8,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [5,1,8,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [4,1,8,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [4,8,1,7,2,5,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [8,4,1,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [8,3,1,2,6,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [3,8,1,2,7,5,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,1,8,2,7,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,1,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [4,1,3,8,7,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [3,1,4,8,7,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [2,1,8,3,7,6,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,8,1,3,7,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,2,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,1,2,3,6,5,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,8,2,3,7,5,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,2,8,3,7,6,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,4,3,6,8,2,5,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [3,1,6,2,5,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,5,1,8,2,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,4,5,2,8,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,4,2,6,5,8,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [1,5,4,2,6,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [3,1,6,5,8,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,6,4,2,5,8,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [1,5,2,6,4,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [1,2,6,5,4,8,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,2,5,4,7,3,8,6]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [4,1,2,6,3,8,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [7,1,5,4,2,8,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,4,7,5,2,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,1,3,5,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [7,2,5,1,8,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [1,4,5,2,8,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,6,4,2,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,4,2,8,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,2,5,3,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,2,8,6,5,3,7,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,5,2,8,6,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,6,4,2,8,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,2,1,8,7,3,4,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [7,6,2,1,8,3,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [7,3,1,6,2,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,7,6,4,2,8,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,7,5,2,6,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,6,2,7,5,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,2,7,6,5,3,8,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,2,6,5,3,8,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [1,5,2,6,3,8,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,5,2,7,6,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,6,5,2,7,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,5,7,4,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [4,1,2,8,6,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,1,8,6,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [4,3,7,1,8,2,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [8,3,1,6,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [7,1,8,3,2,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [1,8,7,3,2,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,4,2,8,7,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,7,4,2,8,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [8,1,5,4,2,7,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,4,8,5,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,5,3,1,7,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,6,2,1,7,3,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [1,8,6,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,8,5,2,6,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,5,2,7,3,8,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,2,8,5,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,2,6,3,8,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,2,7,6,3,8,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,6,2,7,3,8,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,7,2,8,5,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,4,2,8,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,1,8,3,2,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,2,1,8,6,3,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [1,8,7,3,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,4,2,8,7,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,2,8,7,5,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,2,8,6,3,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,2,7,3,8,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [4,1,7,3,6,5,8,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [5,1,8,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,1,7,6,3,4,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [5,7,8,6,2,4,1,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [5,7,1,6,2,4,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [6,4,1,5,2,7,3,8]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [8,1,4,5,3,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [6,1,4,5,3,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,1,4,5,3,7,8,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [5,1,7,8,6,2,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,1,4,8,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [7,1,8,6,3,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,1,4,5,3,8,6,2]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,1,4,5,3,6,8,2]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [8,1,4,5,3,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,4,1,5,2,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [6,3,5,7,2,1,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,3,5,8,2,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,3,5,7,2,1,8,4]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [8,4,5,7,3,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [6,4,5,8,3,7,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,8,7,6,2,4,1,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [5,4,8,6,3,1,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,4,1,8,2,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [5,8,1,6,2,4,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [8,4,1,5,2,6,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [6,3,5,8,2,1,4,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [2,3,4,1,8,6,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [8,3,5,6,2,1,4,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [2,3,8,5,1,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,3,8,6,1,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,8,6,7,1,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [8,3,5,7,2,1,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [2,3,8,5,6,1,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [7,4,5,6,3,1,8,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [8,4,5,6,3,1,7,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [7,3,5,6,2,8,1,4]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,3,5,8,2,1,6,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,3,5,6,2,1,4,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [2,7,6,5,1,3,4,8]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,7,6,8,1,3,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,7,6,5,8,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [8,7,5,6,1,4,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [2,6,4,1,8,5,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [2,6,1,3,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,7,1,3,6,5,8,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,7,6,8,4,3,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [2,7,6,1,8,3,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,7,6,1,4,3,5,8]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [7,3,5,1,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,4,1,5,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,8,1,6,3,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,4,1,8,3,2,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [2,3,8,6,4,1,7,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [2,8,6,7,4,3,1,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,3,5,7,2,4,1,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [2,3,4,1,8,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,8,6,1,7,3,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,3,8,1,6,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,3,8,1,4,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,8,6,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [9,1,2,3,4,5,6,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>000000010 [1,8,2,3,4,5,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [7,1,2,3,4,5,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]=>00000101 [2,1,9,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9]]=>10000001 [2,8,1,3,4,5,6,7,9]=>[[1,3,4,5,6,7,9],[2,8]]=>10000010 [2,10,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>100000001 [8,4,3,6,5,1,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [8,5,6,3,4,1,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [8,6,5,4,3,1,7,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [1,7,6,5,4,2,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,8,6,5,2,7,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,7,5,4,1,6,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [7,8,5,4,1,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [6,8,5,4,2,1,7,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [5,8,6,2,4,1,7,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [4,8,2,6,5,1,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [3,2,8,6,5,1,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,2,1,7,6,4,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [4,1,3,7,6,2,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,1,7,3,6,2,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [6,1,7,5,3,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [7,1,6,5,2,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [8,1,6,5,2,3,7,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,2,7,6,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,2,8,3,7,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [8,1,7,2,6,3,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [7,1,8,2,6,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [6,1,8,2,4,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [5,1,8,3,2,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [4,1,3,8,2,7,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [3,2,1,8,4,7,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,8,7,1,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [4,8,2,7,1,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [5,8,7,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [6,8,7,1,3,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [7,8,6,1,5,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [8,7,6,1,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [1,8,7,2,6,5,3,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [1,7,8,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [8,6,7,1,4,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [7,6,8,1,4,3,5,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [6,5,8,3,2,1,7,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [7,5,8,3,1,4,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [8,5,7,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [1,6,8,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,5,4,8,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [8,4,3,7,1,6,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [7,4,3,8,1,5,6,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [6,4,3,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [7,4,3,1,2,6,5,8]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [8,4,3,1,2,5,7,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,5,4,2,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [8,5,1,4,2,3,7,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [7,5,1,4,2,6,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [6,5,1,4,3,2,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [5,6,1,3,4,2,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [4,6,2,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [3,2,6,1,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,2,7,1,4,6,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [4,7,2,1,3,6,5,8]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,7,1,3,2,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [6,7,1,2,4,5,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [7,6,1,2,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [8,6,1,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,7,2,3,6,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [8,7,1,2,3,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [7,8,1,2,3,5,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,8,1,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [5,8,1,3,2,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [4,8,2,1,3,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [3,2,8,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [4,1,3,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [5,1,2,4,3,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [6,1,2,3,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [7,1,2,3,4,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [8,1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [6,7,3,8,5,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,7,4,5,1,8,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [5,4,7,6,8,1,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,3,7,8,6,1,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [3,8,4,5,7,1,2,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,4,8,6,7,1,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [4,5,6,7,1,8,3,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,5,6,2,7,4,8,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,6,1,7,8,4,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [2,5,6,1,8,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,5,6,8,1,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [8,2,4,5,1,6,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [1,4,8,6,2,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,5,6,8,2,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,5,6,2,8,4,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [2,5,6,3,4,7,8,1]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [1,4,2,6,8,5,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [8,1,3,2,5,4,6,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [8,2,3,1,5,6,4,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,8,3,1,5,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,4,1,6,8,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [3,4,1,6,7,8,5,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,3,1,7,6,8,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [5,2,7,8,1,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,3,7,2,6,4,8,1]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,7,3,1,5,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,7,2,1,8,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,2,8,1,5,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,7,8,2,1,4,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,7,1,2,8,4,5,3]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,1,3,4,8,5,2]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [5,2,7,3,4,6,8,1]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [5,1,7,3,4,8,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,1,7,8,2,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [4,1,8,7,2,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,8,1,2,7,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [4,1,3,7,5,8,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [3,1,4,5,7,8,6,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [2,1,8,3,4,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,2,1,3,4,6,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [1,8,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,2,8,3,4,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [4,2,1,6,5,8,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [5,2,6,1,4,8,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,2,6,4,1,8,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,2,7,4,8,1,6,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [5,2,7,4,8,6,1,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [5,7,2,3,8,6,1,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,7,2,3,8,1,6,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,6,2,3,1,8,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [5,6,2,1,3,8,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [5,1,6,4,2,8,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,6,1,3,2,8,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [5,6,3,1,2,8,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [5,6,3,2,1,8,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,7,3,2,8,1,6,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,7,3,2,8,6,1,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,7,3,8,2,1,5,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,3,8,1,2,5,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [5,7,3,1,8,2,6,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,7,1,3,8,2,6,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,1,7,4,8,2,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [1,5,7,4,8,3,6,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [1,5,7,4,8,6,3,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,1,7,4,8,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,7,1,3,8,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,7,3,1,8,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [6,7,3,8,1,5,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,7,3,8,5,2,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,8,3,1,4,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,7,1,8,3,5,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,1,7,8,4,5,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [1,6,7,8,4,5,3,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [1,6,7,8,4,3,5,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [6,1,7,8,4,2,5,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [6,7,1,8,3,2,5,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [5,7,2,1,8,3,6,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [6,7,2,8,1,3,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,7,2,8,3,1,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,7,2,8,3,5,1,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,2,7,8,4,5,1,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,2,7,8,4,1,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,2,7,8,1,4,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [5,2,7,1,8,4,6,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [4,2,1,7,8,5,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,1,2,7,8,6,5,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [6,2,7,8,1,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,2,7,8,5,1,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,2,7,8,5,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,2,8,5,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,7,2,1,8,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,7,1,2,8,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,1,7,2,8,6,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [1,5,7,3,8,6,4,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [1,6,7,8,3,5,4,2]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,1,7,8,2,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,7,1,8,2,5,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,7,8,2,4,1,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,7,8,2,4,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,7,1,8,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,7,8,5,2,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [1,6,7,8,5,3,4,2]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,1,7,8,5,4,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,7,1,8,5,3,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,8,4,1,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,3,8,5,2,7,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,3,4,5,8,7,2,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,6,1,4,8,7,3,2]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [3,6,4,8,5,7,1,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [5,1,4,8,6,3,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [3,4,7,1,8,6,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [6,3,8,4,2,7,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [5,3,7,1,6,8,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [4,3,8,5,6,7,2,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,6,1,2,7,8,5,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [3,6,4,2,8,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [6,3,7,5,2,8,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,5,2,7,4,8,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [5,7,1,4,8,3,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [7,8,3,5,1,4,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [5,8,1,4,6,7,2,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [6,5,8,4,3,7,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [6,3,7,4,2,8,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,1,6,2,4,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [3,8,6,7,1,4,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [5,3,8,7,4,1,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [4,3,8,7,1,5,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,3,6,1,2,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [5,6,1,8,7,3,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [7,5,3,6,4,2,8,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [6,4,1,5,3,8,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [8,2,6,3,4,7,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,2,6,3,5,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [6,2,7,4,3,5,8,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [3,7,6,4,5,2,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>1100110 [2,7,6,5,3,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [6,5,4,3,1,8,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [8,6,5,4,2,7,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [1,6,5,3,4,8,2,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [6,5,8,4,2,7,3,1]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [5,8,2,6,4,7,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [7,8,5,3,2,6,4,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [6,8,3,1,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [1,8,6,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [8,7,5,2,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,7,1,6,2,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,8,1,6,3,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [2,8,1,7,3,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [4,8,1,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [4,2,8,5,7,3,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [5,1,7,6,8,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [6,7,3,1,8,4,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [1,7,3,8,4,5,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [1,7,2,8,5,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [7,6,1,8,4,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [8,6,1,7,4,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [8,1,2,7,3,4,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [7,1,2,8,3,5,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,2,6,1,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [4,2,1,5,8,3,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [5,4,3,1,6,8,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [4,7,5,6,8,3,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [6,5,4,8,2,7,3,1]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [6,5,1,8,7,4,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [8,6,4,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [5,1,8,3,7,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,4,8,1,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [3,6,8,2,4,7,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [4,7,2,8,6,3,5,1]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [2,3,8,7,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [7,2,8,6,4,3,5,1]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [2,1,8,7,5,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,2,7,6,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [8,1,7,6,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,1,8,6,5,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [1,2,8,7,6,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,3,8,7,4,6,2,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [6,8,7,2,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [3,8,7,6,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [2,8,7,6,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [1,8,7,6,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [5,8,6,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [4,8,6,7,3,5,1,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [3,8,6,7,4,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [2,8,6,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [1,8,6,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [1,8,5,7,4,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [3,8,5,7,4,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [4,8,5,7,3,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [7,8,3,6,4,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [6,8,3,7,4,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [5,8,3,7,4,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [3,7,4,8,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [4,7,3,8,5,6,1,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,7,2,8,5,6,1,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,7,1,8,5,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [3,7,1,8,5,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [3,7,2,8,5,6,1,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [2,7,3,8,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [2,7,4,8,5,6,1,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [5,8,2,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [6,8,2,7,4,5,1,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [7,8,2,6,4,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,8,1,6,4,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [6,8,1,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [5,8,1,7,4,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [1,7,4,8,5,6,2,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [1,7,3,8,5,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [2,8,5,6,1,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [1,8,5,6,2,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [1,7,3,8,4,6,2,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [4,8,1,7,3,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [5,8,1,7,3,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [6,8,1,7,3,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [7,8,2,6,3,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [6,8,2,7,3,5,1,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [5,8,2,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [4,8,2,7,3,6,1,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,7,3,8,4,6,1,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [3,7,2,8,4,6,1,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,7,1,8,4,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [1,8,4,7,3,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [2,8,4,7,3,6,1,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [3,8,4,7,2,6,1,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [4,8,5,7,2,6,1,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [3,8,5,7,2,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [2,8,5,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [1,8,5,7,3,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [1,8,6,7,3,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [2,8,6,7,3,5,1,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [3,8,6,7,2,5,1,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [4,8,6,7,2,5,1,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [5,8,6,7,2,4,1,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [6,8,5,7,1,4,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [5,8,6,7,1,4,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [4,8,6,7,1,5,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [3,8,6,7,1,5,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [1,5,2,8,6,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [2,5,1,8,6,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,6,1,8,5,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [1,6,2,8,5,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [3,8,5,7,1,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [6,8,4,7,1,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [7,8,4,6,1,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,8,3,6,1,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [6,8,3,7,1,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [4,8,3,7,1,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,8,4,7,1,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [1,6,2,8,4,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [2,6,1,8,4,7,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [3,7,2,6,1,8,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,7,1,6,2,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [4,8,1,6,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [5,8,1,6,2,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [7,8,1,5,2,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,8,2,5,1,6,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [6,8,2,5,1,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [5,8,2,6,1,7,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [4,8,2,6,1,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [1,7,3,6,2,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,7,3,6,1,8,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]=>00000000 [1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,9],[8]]=>00000010 [1,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3]]=>01000000 [1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]=>000000000 [1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,10],[9]]=>000000010 [1,2,3,4,5,8,7,9,6]=>[[1,2,3,4,5,6,9],[7],[8]]=>00000110 [1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,9,10],[8]]=>000000100 [1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,8,9,10],[7]]=>000001000 [1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,7,8,9,10],[6]]=>000010000 [1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,6,7,8,9,10],[5]]=>000100000 [1,4,3,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3],[4]]=>01100000 [1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,5,6,7,8,9,10],[4]]=>001000000 [3,2,4,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000 [1,3,4,5,6,7,8,9,10,2]=>[[1,2,4,5,6,7,8,9,10],[3]]=>010000000 [6,7,4,8,3,5,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,7,4,5,2,8,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [5,7,4,6,2,3,1,8]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,7,4,6,3,8,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,7,4,8,3,6,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [6,8,4,5,3,7,1,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [5,8,4,6,3,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,6,4,8,3,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,6,3,7,2,4,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,3,7,2,8,1,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,3,8,2,7,1,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,6,4,8,2,7,1,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,8,4,6,2,7,1,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [6,8,4,5,2,7,1,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [7,8,4,5,2,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [6,8,4,5,2,3,1,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [5,8,4,6,2,3,1,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,6,4,8,2,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,6,3,8,2,4,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,6,3,4,2,8,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,6,3,5,2,7,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,3,5,2,8,1,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,6,3,8,2,5,1,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,8,3,6,2,5,1,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [5,8,3,6,2,4,1,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [6,8,3,5,2,4,1,7]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,8,3,5,2,4,1,6]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,8,3,5,2,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [5,8,3,6,2,7,1,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [4,8,3,6,2,7,1,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,6,3,8,2,7,1,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,6,3,7,2,8,1,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,7,3,6,2,5,1,8]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,7,3,6,2,8,1,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,7,3,8,2,6,1,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [5,7,4,8,2,6,1,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,7,3,6,2,8,1,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,7,3,6,2,4,1,8]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,7,3,5,2,4,1,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,3,5,2,8,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,4,8,2,5,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,7,5,8,2,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,8,5,7,2,3,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,7,4,8,2,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,7,3,8,2,4,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,7,3,4,2,8,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [5,7,3,4,2,6,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,7,3,4,2,8,1,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,7,4,8,2,3,1,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [5,8,4,7,2,3,1,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,8,4,7,2,3,1,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,8,4,6,2,3,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [7,8,3,6,2,4,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,8,3,7,2,4,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [5,8,3,7,2,4,1,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,8,3,7,2,5,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,7,3,8,2,5,1,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [4,7,3,5,2,8,1,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [4,7,3,5,2,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,5,3,7,2,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,5,3,7,2,8,1,6]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,5,3,8,2,7,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,8,3,5,2,7,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,8,3,4,2,7,1,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [6,8,3,4,2,7,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [7,8,3,4,2,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,8,3,4,2,5,1,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,8,3,4,2,6,1,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,8,3,5,2,6,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,5,3,8,2,6,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,5,3,6,2,8,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,7,5,2,1,8,3,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [4,8,5,2,1,7,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,6,5,2,1,3,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [5,6,4,2,3,1,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [6,4,5,3,1,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,4,6,1,3,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [4,6,8,1,7,3,2,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [4,7,8,1,6,3,5,2]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [7,4,8,1,6,5,3,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [5,4,8,1,3,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [8,4,5,3,1,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [5,4,7,1,3,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [6,4,8,1,7,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [5,6,8,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [8,5,7,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,4,6,3,7,2,1,5]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [6,3,2,8,7,4,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [2,1,6,8,7,4,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,1,7,8,6,4,5,3]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [7,3,2,8,6,4,5,1]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [7,6,8,5,2,4,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [5,7,8,6,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [5,8,7,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [6,8,7,5,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [5,8,4,2,3,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [7,8,4,2,6,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [4,8,7,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [4,8,6,2,7,3,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [3,6,1,8,7,4,2,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [3,7,1,8,6,4,5,2]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [3,8,1,6,7,5,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [3,7,1,6,8,2,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [4,7,6,2,8,1,3,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [6,7,4,2,8,1,5,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,8,4,2,7,5,1,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [2,1,8,6,7,5,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [8,3,2,6,7,5,1,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [8,6,4,3,7,5,1,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [5,8,6,7,3,1,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [6,7,5,8,1,3,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [7,6,5,8,1,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [8,6,5,7,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,6,4,3,8,1,5,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [7,3,2,6,8,1,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [2,1,7,6,8,3,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [7,5,6,8,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,5,7,8,1,2,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [8,1,3,7,4,6,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [5,2,8,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [1,6,2,5,4,7,3,8]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [6,2,7,5,4,8,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [8,1,3,5,4,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [6,1,5,4,3,8,7,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [6,1,8,3,4,5,7,2]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [7,1,5,3,4,8,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,1,4,3,5,6,8,2]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [8,1,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,7,2,4,5,6,3,8]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [6,3,2,7,5,1,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [8,4,7,2,5,6,1,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [6,5,8,2,4,7,3,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [8,5,2,1,4,3,7,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [6,5,2,8,4,1,3,7]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [5,6,2,1,4,8,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [3,6,1,8,5,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,2,6,3,5,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [3,4,1,2,8,6,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [4,3,1,2,6,8,5,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [5,8,1,6,3,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [6,3,8,5,2,1,4,7]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [8,3,1,5,2,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,8,2,6,1,5,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,8,6,7,2,1,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [8,5,6,4,2,1,7,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [7,2,5,8,3,1,6,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [1,7,5,6,3,2,4,8]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [6,1,2,3,8,5,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [7,1,2,3,6,5,8,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [7,2,1,3,8,6,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [1,5,7,3,2,4,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [5,2,7,3,1,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,8,2,4,1,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [8,7,2,6,3,4,1,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [4,8,1,6,3,2,7,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [3,1,8,6,4,2,7,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [8,1,6,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [3,5,8,7,2,4,1,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [4,2,1,3,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [2,4,1,3,8,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,5,8,3,1,7,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [8,6,1,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [2,8,1,3,6,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [6,8,2,3,4,1,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [5,1,8,3,2,4,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>11111111 [8,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,9,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,9,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,5,9,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,5,4,9,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,5,4,3,9,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,5,4,3,2,9,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110 [9,10,8,7,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [7,8,9,6,5,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [9,8,10,7,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [8,6,7,9,5,4,3,2,1]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>11111010 [9,8,7,10,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [9,8,7,6,10,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [9,8,7,6,5,10,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [9,8,7,6,5,4,10,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [9,8,7,6,5,4,3,10,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [8,7,6,5,4,3,1,2,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>01111110 [9,8,7,6,5,4,3,2,10,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110 [1,4,2,7,8,6,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,6,2,4,8,5,3,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,6,2,4,7,5,3,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,7,3,8,5,2,4,6]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [1,7,3,2,8,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [4,2,5,7,8,6,1,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [7,2,3,1,8,5,6,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [8,2,5,1,7,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [6,2,1,8,3,4,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [6,2,8,3,5,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [6,2,4,8,5,7,1,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [1,3,6,4,8,5,7,2]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [1,3,6,4,7,5,8,2]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [6,2,4,7,5,8,1,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [6,2,1,3,7,8,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,8,2,1,4,3,5,6]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,6,4,2,3,1,8,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [5,7,2,3,1,6,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [7,5,4,2,6,8,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [1,7,5,3,4,6,8,2]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [8,2,5,4,6,7,1,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [5,2,6,3,1,8,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [8,2,6,4,3,1,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,2,7,4,1,3,5,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [1,2,8,4,3,5,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [1,7,4,2,3,5,6,8]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [6,8,4,1,3,2,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,8,7,4,3,2,5,6]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [1,6,3,8,2,4,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [5,3,8,1,2,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [5,1,8,3,2,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,7,3,1,2,6,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [1,7,5,4,2,6,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [1,5,8,2,4,6,3,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,5,8,4,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,4,6,2,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [5,3,1,6,7,2,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,3,6,1,2,8,4,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [1,6,3,2,7,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [1,7,4,5,3,8,6,2]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [6,3,4,1,2,5,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [6,3,1,4,2,7,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [1,8,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [8,6,3,2,4,1,7,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [8,5,3,2,6,7,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [4,5,2,6,8,1,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,2,5,6,7,8,1,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,2,3,6,7,1,8,4]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [6,2,3,4,1,7,8,5]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [7,2,3,1,4,5,8,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [8,6,1,4,3,2,5,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,3,1,6,5,2,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [3,7,5,1,8,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [4,1,5,2,8,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,1,2,4,6,5,3,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [8,1,2,5,4,6,3,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [8,2,6,5,1,3,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,3,1,6,2,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,1,2,6,4,5,3,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [8,1,2,5,6,4,3,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [8,1,2,6,5,4,3,7]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [1,7,5,4,2,8,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [5,1,4,8,2,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,4,6,8,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,4,7,6,2,8,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,1,4,7,2,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [1,7,4,5,2,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,7,5,1,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [5,7,2,8,1,3,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,2,8,7,1,3,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [4,1,5,8,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,4,6,2,8,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,4,2,8,6,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,1,2,6,4,8,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,1,7,6,3,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [3,1,2,7,4,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,4,7,2,6,8,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,2,3,6,8,5,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [5,1,4,2,7,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [1,4,2,7,6,8,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,4,2,6,8,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,1,2,8,4,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,2,7,6,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [5,3,7,1,8,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,7,4,3,2,5,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [4,8,7,2,1,3,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [1,8,7,3,4,2,5,6]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011 [3,1,7,8,2,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,4,2,7,8,3,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,2,8,1,3,4,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [2,1,8,6,3,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [1,4,2,6,8,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,2,3,7,8,5,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,2,3,7,5,8,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,4,2,7,3,8,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [3,1,7,2,8,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,1,7,8,3,4,6,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [1,2,3,8,7,5,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [10,1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [10,1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011 [10,1,2,3,4,5,9,6,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011 [9,1,2,3,4,10,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>000000010 [10,1,2,3,9,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011 [10,1,2,9,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011 [9,1,10,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>000000010 [10,9,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011 [8,1,2,3,4,5,6,9,10,7]=>[[1,2,3,4,5,6,7,10],[8,9]]=>000000100 [7,1,2,3,4,5,10,9,6,8]=>[[1,2,3,4,5,6,8],[7,9],[10]]=>000001011 [2,9,10,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2,9,10]]=>100000010 [4,7,8,5,6,2,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [5,7,8,4,2,6,1,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [8,6,3,7,2,1,5,4]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [7,6,3,8,2,1,5,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [6,7,8,3,2,1,5,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [4,7,8,3,2,1,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [5,7,8,3,2,1,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [8,6,3,7,2,1,4,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [2,6,4,7,3,5,8,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [8,4,3,2,1,6,5,7]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [6,4,3,2,1,7,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,4,3,2,1,8,6,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [6,4,3,2,1,8,7,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [8,5,4,2,6,7,1,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [8,5,3,2,6,1,7,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [7,5,3,2,6,1,8,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [2,6,4,7,3,8,5,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [3,5,4,2,7,8,1,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [7,4,3,2,1,5,8,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,4,3,2,1,5,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,6,3,4,1,2,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [8,5,3,7,2,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [8,5,7,4,2,6,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [7,5,8,4,2,6,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [2,1,7,8,5,6,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [6,8,3,7,5,1,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [5,7,3,8,1,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [3,2,6,4,8,5,1,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,5,2,4,1,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,2,5,8,3,1,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [3,1,5,4,2,8,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [4,1,5,8,3,2,6,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,3,8,5,2,1,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,3,6,2,5,1,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,3,2,5,1,7,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,6,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,6,3,1,5,2,7,8]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [5,3,6,4,1,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [4,3,6,1,7,2,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [6,2,4,1,3,7,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [4,6,3,1,7,2,5,8]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [5,6,2,7,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [4,5,2,7,3,1,6,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [3,2,6,1,4,7,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,5,2,7,4,6,1,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,7,2,4,8,5,1,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [7,3,1,4,6,8,2,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,2,6,1,5,7,4,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [6,3,2,1,5,7,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,4,2,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,2,6,1,5,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,2,1,7,5,3,6,8]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [7,4,1,5,6,2,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [7,3,1,5,2,6,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [6,3,5,1,2,7,4,8]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [5,2,6,4,1,3,7,8]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [3,6,5,1,2,7,4,8]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [6,5,2,1,4,7,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,3,1,8,5,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,4,1,5,8,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,4,5,1,2,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,4,5,1,8,2,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,4,5,8,2,1,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,4,5,2,8,1,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,4,6,2,1,7,8,5]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,4,6,2,1,7,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,5,6,2,7,1,4,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,6,2,7,1,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,6,2,7,8,1,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [1,8,4,6,3,7,2,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [3,4,6,8,2,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,4,6,2,8,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,5,6,2,7,8,4,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,6,2,7,4,1,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [4,5,6,7,2,8,3,1]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [3,5,6,8,7,2,4,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [2,5,8,6,7,3,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [2,5,8,6,7,3,1,4]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [3,5,6,8,7,2,1,4]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [4,5,6,7,2,1,8,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [2,3,1,8,6,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,5,1,6,7,8,4,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,5,1,6,7,4,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,5,1,6,7,4,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [3,5,6,1,7,4,2,8]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [3,5,6,1,7,4,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [3,4,6,8,1,7,5,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [2,4,8,6,1,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [3,5,6,8,7,1,4,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [4,5,6,7,8,1,3,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [4,5,6,7,1,3,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [4,5,6,7,1,3,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [4,5,6,7,3,1,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,5,6,8,7,4,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [2,5,8,6,7,4,1,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [1,8,5,6,7,4,3,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [2,5,8,6,7,4,3,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [8,2,5,3,7,1,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,2,4,3,7,1,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [5,8,2,4,3,7,1,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [4,2,5,6,1,8,3,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,2,5,6,1,7,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [6,1,5,7,3,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,1,5,8,3,2,4,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [3,8,2,4,7,1,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,6,8,2,4,7,1,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,3,5,6,7,1,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,7,1,5,6,8,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [3,7,1,5,8,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,3,2,4,6,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [7,3,2,4,6,1,5,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,2,5,1,7,4,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,2,5,1,8,4,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,2,5,1,7,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [7,8,3,2,4,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,1,5,7,8,3,2,4]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [4,2,5,6,1,7,8,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,7,6,1,8,3,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [5,8,6,1,7,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [6,1,5,8,7,3,2,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [8,7,3,2,4,6,1,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [3,2,5,1,8,7,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [3,2,5,1,6,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,2,4,1,8,7,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,5,1,6,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,8,6,5,1,7,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [3,7,6,5,1,8,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [6,5,1,7,8,4,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [3,2,5,1,6,7,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,2,4,1,8,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,2,4,1,7,5,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,4,1,6,8,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,2,4,1,8,5,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [8,3,2,4,7,6,1,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,5,1,8,4,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [3,2,5,1,6,7,4,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [6,5,1,7,4,2,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [6,5,1,8,4,2,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [8,4,2,3,7,5,1,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [4,2,6,1,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [5,2,6,1,8,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [8,4,6,1,7,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [5,2,6,1,8,4,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [7,4,2,3,8,5,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [8,5,1,6,4,2,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [7,5,1,6,4,2,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [3,2,5,1,7,6,4,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,5,1,8,6,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [7,3,2,4,8,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [8,6,1,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [4,2,6,1,8,5,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [8,5,6,1,7,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [3,6,8,5,1,7,4,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [8,5,1,6,7,4,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [3,2,5,1,8,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,4,1,8,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,4,1,5,8,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,2,5,1,7,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [7,8,5,1,6,4,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [3,8,5,1,7,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [3,7,5,1,8,6,4,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [8,7,5,1,6,4,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [3,2,5,1,8,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [6,5,7,3,1,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [4,6,3,7,1,8,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,6,3,7,5,1,8,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,2,6,1,7,5,3,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [2,5,7,4,1,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [2,5,7,4,1,6,8,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [5,4,7,3,6,1,8,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,4,7,8,3,1,6,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [4,3,7,5,1,8,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [6,4,3,8,5,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [5,8,4,3,6,1,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,4,8,3,6,1,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,4,3,6,7,1,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [2,5,4,6,1,7,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [3,2,5,8,1,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [2,5,4,6,8,1,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [5,2,8,4,1,6,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [4,6,2,1,8,5,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [2,4,1,7,5,8,6,3]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,4,1,7,5,3,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,6,4,1,8,5,3,7]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [5,4,8,2,1,6,3,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [2,5,8,4,1,6,3,7]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [3,2,5,6,1,8,4,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [4,8,3,2,6,1,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [3,5,2,8,1,6,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,6,8,5,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [3,2,7,1,5,4,8,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,7,1,5,8,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,8,2,5,1,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [4,8,3,2,6,7,1,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,8,2,6,7,1,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,2,6,7,8,1,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,2,6,7,1,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,3,7,2,6,8,1,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,7,8,2,6,1,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [2,5,7,4,8,1,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [3,2,5,7,8,1,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,5,7,1,6,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,2,5,7,1,6,4,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [6,3,2,7,1,5,4,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,2,7,1,5,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,2,7,8,1,5,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [4,2,6,1,7,8,5,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [6,5,2,1,7,8,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [2,1,7,5,3,8,6,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [6,2,1,8,5,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [6,3,2,7,1,4,8,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,3,2,1,4,7,8,5]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [6,3,2,1,4,7,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,5,2,1,7,4,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,2,1,7,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [5,8,4,2,1,7,3,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [4,6,2,1,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [2,4,1,7,3,8,6,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [3,2,7,1,4,8,6,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,5,8,2,1,7,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [4,8,3,7,2,1,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,7,2,8,1,5,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [4,3,7,2,1,5,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [4,8,3,2,7,1,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,5,2,8,1,7,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [6,3,2,8,1,4,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [3,2,1,4,7,5,8,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [5,3,2,1,8,4,6,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,8,3,2,1,5,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,3,8,2,1,5,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [1,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111 [1,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111 [6,2,3,1,5,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [8,4,5,2,3,1,7,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [8,6,7,2,5,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,2,5,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [6,2,5,3,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [6,1,5,2,4,3,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [6,4,5,1,3,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [6,1,5,3,4,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [6,3,5,1,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [8,3,5,2,4,1,7,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [8,3,7,5,6,2,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,3,7,2,4,1,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,3,5,1,4,2,7,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [8,1,5,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,4,5,1,3,2,7,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [2,1,8,4,5,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,6,7,4,5,1,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [8,6,7,1,5,3,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [8,6,7,3,5,1,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [8,3,7,5,6,1,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [8,5,7,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [8,3,7,4,6,2,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [8,3,7,4,6,1,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,3,7,1,6,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,1,7,3,6,4,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [8,1,7,5,6,3,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [8,4,7,5,6,1,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [2,1,8,4,7,5,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,1,7,3,4,2,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,1,7,3,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,3,7,1,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,3,7,2,6,4,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [8,2,7,3,6,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [8,2,7,3,6,1,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,2,7,1,6,3,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,1,7,2,4,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,1,3,2,7,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [2,1,8,3,7,4,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,1,5,2,4,3,7,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [8,2,7,1,4,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,2,7,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,2,7,5,6,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [8,4,7,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [8,4,7,2,3,1,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,2,3,1,7,4,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,2,3,1,5,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [4,2,3,1,8,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [4,1,3,2,8,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [8,6,7,2,3,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [8,2,3,1,7,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,5,7,2,6,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [8,5,7,2,6,1,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [8,2,7,5,6,1,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [8,6,7,2,5,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [8,6,7,1,5,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,6,7,1,3,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [2,1,8,6,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,1,8,3,7,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,1,3,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,1,7,5,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,1,7,2,6,4,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,2,7,1,6,4,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,2,7,4,6,1,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,2,7,4,6,3,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,4,7,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,4,7,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [8,4,7,1,6,2,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,1,7,4,6,2,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,5,7,1,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [2,1,8,5,7,3,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,5,7,4,6,1,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [8,5,7,1,6,3,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [8,1,7,4,6,3,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,4,7,1,6,3,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,4,7,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [2,4,8,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [6,5,8,1,3,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [4,5,8,6,3,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [6,5,8,7,3,1,2,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [1,5,8,7,3,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [1,7,2,8,4,6,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [6,7,2,8,4,1,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [3,6,2,8,4,5,7,1]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,6,1,8,4,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,8,4,6,1,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [6,3,1,8,4,5,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [3,1,6,8,4,5,7,2]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [2,3,6,8,4,5,7,1]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [6,3,7,8,4,1,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [1,3,7,8,4,6,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,5,7,8,2,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [5,1,7,8,2,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [3,6,7,8,4,2,5,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [7,6,1,8,4,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [5,6,8,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [2,8,3,7,1,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [5,2,8,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [7,2,1,8,4,6,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [3,2,7,8,4,6,5,1]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [5,2,7,8,1,4,6,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [1,2,7,8,5,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [4,2,1,3,8,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [7,2,5,8,3,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [6,2,8,5,4,3,1,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [2,8,3,5,4,1,6,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [2,8,4,5,3,1,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [6,4,8,5,2,3,1,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [7,3,5,8,2,4,6,1]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [4,3,1,2,8,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [3,4,2,1,8,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [2,7,6,8,4,3,5,1]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [5,7,1,8,3,4,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [3,7,5,8,1,4,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [1,7,5,8,3,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [1,6,8,5,4,3,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [4,6,8,5,1,3,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,6,8,1,4,3,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [7,5,8,6,3,4,2,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [2,4,8,3,6,5,1,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,8,4,1,5,6,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,1,8,3,5,6,2,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [5,6,8,4,1,3,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [4,6,8,1,5,3,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [1,6,8,4,5,3,2,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,7,3,8,5,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [3,7,1,8,5,4,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [2,7,3,8,4,6,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [7,1,3,8,4,6,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [5,7,8,4,3,6,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [2,8,7,4,1,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [2,8,5,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [6,5,8,4,2,3,1,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [4,1,3,2,8,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,4,3,2,8,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [7,3,2,8,5,4,6,1]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [6,4,8,2,5,3,1,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [2,8,4,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>1010001 [2,8,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [6,2,8,4,5,3,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [7,2,3,8,5,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [4,2,3,1,8,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,1,4,8,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [5,1,3,2,4,8,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [2,8,1,5,3,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [1,2,8,4,5,3,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,4,2,8,5,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [1,8,4,2,5,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [8,1,5,3,2,4,6,7]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [3,8,1,5,2,4,6,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [3,5,1,4,8,2,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [1,5,2,8,4,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,2,8,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,2,5,4,3,8,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,2,4,8,5,3,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,2,7,4,8,5,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [1,5,2,7,8,4,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [5,1,2,7,4,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [8,3,5,1,4,7,2,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [2,8,1,5,4,7,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [1,2,8,5,7,4,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,2,4,8,7,5,3,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [2,8,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [6,1,2,8,7,4,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [6,4,1,2,8,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [3,6,4,8,1,7,2,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [7,6,1,4,2,8,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,1,6,2,8,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,6,7,2,8,4,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,7,1,4,2,8,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,3,7,1,4,8,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [3,7,8,1,5,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [7,1,2,8,5,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,7,2,8,4,5,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [1,4,2,7,8,5,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [6,1,2,8,4,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,4,1,2,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [7,6,1,3,2,4,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,7,1,3,2,4,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [1,2,7,3,5,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,2,7,5,8,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [5,8,1,3,7,2,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [1,2,5,8,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,5,8,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [2,8,1,7,3,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,6,1,3,2,4,7,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [4,2,8,1,7,3,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,8,1,7,4,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [7,1,2,8,4,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,2,8,4,7,5,3,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,2,8,7,4,5,3,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [2,8,1,7,5,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,3,7,1,5,2,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,8,6,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [8,6,1,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [8,1,6,2,7,4,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,1,2,8,6,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,4,1,2,8,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [3,7,4,8,1,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [3,4,8,7,1,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [4,2,8,1,7,6,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,8,1,7,6,4,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [7,8,3,4,1,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [6,7,3,4,1,8,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [5,8,3,4,1,7,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [6,7,3,4,1,5,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [5,7,3,4,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [5,6,2,7,3,4,1,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [4,6,2,8,3,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,8,3,5,1,6,2,7]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [5,6,2,4,1,7,3,8]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [4,5,1,7,3,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,6,2,7,3,8,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [5,6,2,7,3,8,1,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,6,2,7,4,8,1,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,3,8,4,7,1,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [4,6,2,8,3,7,1,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [9,2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>10000001 [10,2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>100000001 [9,2,3,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>10000001 [4,2,3,5,6,7,8,9,1]=>[[1,3,5,6,7,8,9],[2],[4]]=>10100000 [3,4,2,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000 [3,2,4,5,6,7,8,9,10,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000 [6,5,3,2,1,4,8,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [4,6,3,5,2,1,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [8,7,3,5,2,4,1,6]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [6,8,2,4,5,7,3,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [8,7,2,4,5,3,1,6]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [3,6,1,4,5,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [8,3,7,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [6,3,8,4,5,7,2,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,8,7,4,3,6,2,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [2,8,7,4,3,6,1,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,1,7,4,3,6,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [8,7,3,5,1,4,2,6]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [2,1,6,8,5,7,4,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,8,3,5,1,7,4,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [5,1,8,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [2,5,8,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [4,3,8,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,8,1,3,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [5,8,7,4,1,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [5,8,3,6,1,4,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [4,8,3,6,1,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [3,8,7,4,1,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,8,1,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [8,7,1,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,6,3,1,2,4,7,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,1,7,4,5,2,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [2,8,7,4,5,1,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,7,2,4,1,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [5,8,3,6,2,4,7,1]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [8,6,3,2,1,4,7,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [8,7,3,5,2,1,4,6]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [5,8,3,6,2,1,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,8,7,4,2,6,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [2,6,8,4,5,7,1,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [6,1,8,4,5,7,2,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [6,8,3,5,1,7,2,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [2,1,5,8,3,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [5,8,3,6,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [4,1,8,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [2,4,8,1,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,8,2,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [3,4,8,2,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [5,8,1,4,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,3,1,6,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [4,5,3,8,6,1,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [3,4,1,8,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [2,4,6,8,10,1,3,5,7,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [2,7,8,9,10,1,3,4,5,6]=>[[1,3,4,5,6],[2,7,8,9,10]]=>100001000 [5,6,7,8,10,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8,10]]=>000100001 [2,4,6,8,10,12,1,3,5,7,9,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>10101010101 [7,8,9,10,11,12,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000 [4,5,7,6,2,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [3,5,7,2,6,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [2,5,7,3,6,4,8,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [1,5,7,3,6,8,4,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [8,4,3,7,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [6,7,2,3,5,4,8,1]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,2,7,3,6,4,8,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [8,3,4,7,6,1,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,2,4,7,1,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [3,1,4,7,6,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [4,1,3,7,6,8,5,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [5,1,7,3,6,8,4,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [6,7,1,3,5,8,4,2]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [5,8,7,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [4,8,3,7,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [3,8,4,7,6,1,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [2,8,4,7,1,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,1,4,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [2,8,3,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [3,8,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [6,7,1,2,8,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [8,2,3,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [3,4,1,7,6,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [1,4,2,7,8,6,5,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [8,4,2,7,1,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [8,5,7,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [1,5,7,2,8,6,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [2,5,7,1,8,6,4,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [3,5,7,1,6,8,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [6,7,4,5,8,1,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [5,4,7,6,8,1,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [2,5,7,8,1,6,4,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [1,5,7,8,2,6,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [8,5,7,1,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,4,1,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [1,4,8,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [3,4,8,7,6,1,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [4,3,8,7,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [5,3,7,8,6,1,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [6,7,2,8,1,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [5,2,7,8,1,6,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [4,2,8,7,1,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [3,2,8,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [1,3,8,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,3,1,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,2,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [1,2,8,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [2,1,8,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [4,1,8,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [5,1,7,8,2,6,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,7,1,8,2,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,8,7,1,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [4,8,1,7,2,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [3,8,1,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [2,8,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [1,8,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [8,1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [3,1,4,5,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [10,3,4,5,6,7,8,1,2,9]=>[[1,2,5,6,7,8,9],[3,4],[10]]=>010000001 [2,10,4,5,6,7,8,1,3,9]=>[[1,3,5,6,7,8,9],[2,4],[10]]=>101000001 [6,7,1,8,4,5,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [3,7,1,5,8,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [2,7,1,5,8,3,6,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [2,6,5,1,8,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [3,6,5,1,8,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [4,6,5,1,8,7,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [5,6,4,1,8,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [8,1,4,5,7,6,2,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [6,4,5,1,8,7,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [5,4,6,1,8,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [4,5,6,1,8,7,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,5,6,1,8,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [2,5,6,1,8,3,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,4,6,1,3,8,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [3,4,6,1,2,8,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [4,3,6,1,2,8,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [5,3,6,1,8,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [7,3,1,5,8,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [8,1,3,5,7,2,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,1,2,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [7,2,1,5,8,3,6,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [6,2,5,1,8,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [4,2,6,1,3,8,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [2,3,6,1,4,8,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [4,2,5,3,1,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [6,2,4,1,3,8,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [7,2,1,4,3,8,6,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [8,1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,1,3,4,2,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [7,3,1,4,2,8,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [6,3,4,1,2,8,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [4,6,3,1,2,8,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [3,6,4,1,2,8,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [2,6,4,1,3,8,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [2,7,1,4,3,8,6,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [3,7,1,4,2,8,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [4,7,1,3,2,8,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [8,1,6,7,2,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [4,7,1,2,3,8,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [3,7,1,2,4,8,6,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,7,1,3,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,6,3,1,4,8,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [3,6,2,1,4,8,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [5,6,2,1,8,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [6,5,2,1,8,3,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [8,1,5,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [8,1,4,2,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [7,4,1,2,3,8,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [6,4,2,1,3,8,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [5,4,2,3,1,8,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [3,5,2,4,1,8,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [6,3,2,1,4,8,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [7,3,1,2,4,8,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [8,1,3,2,4,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [7,2,1,3,4,8,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [6,2,3,1,4,8,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [2,4,3,6,1,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,3,6,5,8,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,5,8,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,5,8,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,1,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,2,6,5,3,1,8,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [4,2,6,5,1,8,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [4,2,6,5,8,1,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [4,2,6,5,8,1,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [4,2,6,5,8,3,1,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [2,4,6,1,5,8,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,1,6,5,8,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,4,6,5,8,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,1,6,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,6,1,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,4,3,8,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [2,4,6,8,1,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,6,1,8,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,1,6,8,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,4,6,8,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,4,6,8,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,1,6,8,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,6,1,8,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,6,8,1,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,4,6,8,3,5,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,8,3,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,8,3,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,1,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,8,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,8,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,6,3,8,5,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,3,6,8,5,7,1]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,3,6,8,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,3,6,8,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,3,1,6,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,4,1,3,6,8,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,3,6,1,8,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,4,3,6,8,1,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,6,5,2,8,7,1,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [2,4,6,3,8,1,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,1,4,6,8,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,1,6,8,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,6,1,8,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,6,8,1,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,6,8,3,1,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,6,2,8,5,7,1,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [6,2,4,8,7,1,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [6,4,2,8,7,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [2,6,4,8,1,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [2,6,4,1,8,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [2,6,1,4,8,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,1,6,4,8,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,6,1,4,8,7,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [6,4,2,8,7,5,1,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [1,6,4,7,3,8,2,5]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [1,3,7,4,5,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [5,2,4,7,3,6,8,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [1,7,6,3,4,8,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [8,1,6,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,1,6,3,8,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,2,7,4,8,3,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [6,1,7,3,4,8,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [2,1,7,4,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [5,1,4,7,3,8,2,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [4,3,1,7,5,8,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [2,8,6,3,7,1,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [6,8,1,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [5,8,2,1,7,3,4,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [5,7,2,1,8,3,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [6,7,1,3,8,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [5,1,2,4,8,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [4,3,6,1,5,8,2,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [2,6,1,4,5,8,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [6,5,1,3,4,8,2,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [1,6,2,4,8,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,5,1,3,7,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,5,3,2,8,4,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [6,4,2,1,5,8,3,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [2,5,3,4,1,8,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [4,3,5,2,1,8,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [2,6,4,8,7,1,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [1,6,4,8,7,2,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [2,7,8,3,6,1,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [4,3,2,8,7,1,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,2,4,8,7,1,3,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [6,2,8,3,7,1,4,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [5,1,4,8,7,2,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [4,8,2,5,1,3,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [4,7,2,5,1,3,8,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [3,7,2,1,5,4,8,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,8,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [8,3,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,3,2,1,6,4,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,4,2,5,1,6,3,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [8,3,2,1,5,6,4,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,3,2,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,8,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,7,2,1,4,5,8,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,2,7,1,4,6,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,2,8,1,4,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,8,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,8,2,1,4,7,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,8,2,1,5,7,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [4,8,2,5,1,7,3,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [4,7,2,5,1,8,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [3,7,2,1,5,8,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,7,2,1,4,8,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,2,1,7,5,8,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,7,1,6,8,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [4,2,7,6,1,8,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [4,3,7,6,8,1,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,3,8,6,7,1,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [4,2,8,6,1,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [3,2,8,1,6,7,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [3,2,1,8,7,5,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,8,2,1,7,4,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,2,8,1,7,4,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,8,1,6,4,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [3,2,7,1,6,4,8,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [4,2,7,6,1,3,8,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [4,2,8,6,1,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,2,8,7,1,3,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [5,7,8,3,4,1,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [4,2,7,8,1,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [4,2,6,8,1,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,2,6,7,1,3,8,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,2,6,1,8,4,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [3,7,2,1,8,4,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,7,2,1,8,5,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [4,7,3,8,5,1,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,3,7,8,6,1,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [3,2,7,1,8,6,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,2,1,6,8,5,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [3,2,6,1,8,7,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,2,6,8,1,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,3,6,8,7,1,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [4,2,6,7,1,8,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,2,6,1,7,8,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,4,6,8,7,5,1,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [5,3,6,4,8,7,1,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [1,4,6,2,7,8,5,3]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [3,1,8,5,4,2,6,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [1,2,7,5,4,8,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [6,3,7,5,4,8,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [7,3,8,5,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [3,8,7,5,4,6,1,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [4,3,6,7,8,5,1,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,5,6,3,8,7,1,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [3,6,8,5,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [6,8,3,5,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,6,3,5,4,8,1,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [1,6,2,5,4,8,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,1,2,5,8,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,8,2,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,2,1,5,4,8,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [4,1,6,2,8,7,5,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [7,8,1,2,4,6,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,8,3,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [4,3,6,1,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [2,3,8,5,4,1,6,7]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [4,8,1,5,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,5,1,6,4,3,2,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [5,8,1,6,4,3,2,7]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [6,1,5,7,4,3,2,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [1,5,8,6,4,3,2,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [3,4,6,1,5,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [7,8,4,1,5,3,2,6]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [7,8,5,1,6,3,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [2,6,1,5,7,3,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [1,6,8,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [6,8,1,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [5,6,1,7,4,3,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,1,7,6,4,3,2,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,1,7,8,4,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,1,8,6,4,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [1,8,7,6,4,3,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [2,1,7,5,6,3,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [3,1,6,7,5,8,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [7,8,1,6,5,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,8,2,1,4,5,6,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [2,8,1,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [7,2,1,5,4,6,8,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [1,2,8,5,6,3,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [6,1,2,5,7,3,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [4,2,1,5,6,3,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [4,3,6,1,5,7,2,8]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [5,1,6,3,7,8,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [1,3,6,8,5,7,2,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [2,4,6,3,7,1,8,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [1,3,6,4,8,7,2,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [4,1,6,7,3,8,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [5,4,6,1,3,7,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [6,4,1,5,2,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [4,1,7,5,2,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [1,2,4,5,8,3,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [7,2,3,5,4,1,8,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [2,8,3,5,4,1,7,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [4,2,6,3,8,1,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [7,8,2,3,4,1,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [7,8,1,4,6,3,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [3,1,6,4,7,8,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [1,8,5,7,4,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [7,1,5,8,4,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [5,1,8,7,4,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [6,5,1,8,4,3,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [6,5,7,1,4,3,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,5,8,1,4,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [5,8,7,1,4,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,5,7,8,4,3,2,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [2,4,7,5,1,3,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,8,4,6,1,3,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [7,8,5,4,1,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [3,5,6,4,1,8,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [2,6,4,5,1,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [1,6,5,8,4,3,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [6,8,5,1,4,3,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [7,6,5,1,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [1,2,3,4,5,6,9,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [1,2,3,4,5,8,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [1,2,3,4,7,5,8,9,6]=>[[1,2,3,4,5,6,9],[7,8]]=>00000100 [1,2,5,3,6,7,8,9,4]=>[[1,2,3,4,7,8,9],[5,6]]=>00010000 [1,4,2,5,6,7,8,9,3]=>[[1,2,3,6,7,8,9],[4,5]]=>00100000 [9,8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>00000011 [7,8,9,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>00000100 [9,8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8],[9]]=>00000111 [6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>00001000 [9,8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>00001111 [9,8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>00011111 [9,8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>00111111 [9,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>01010101 [9,8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111 [9,10,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>000000010 [8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>000000100 [10,9,8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>000000111 [7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>000001000 [10,9,8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>000001111 [10,9,8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>000011111 [10,9,8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>000111111 [10,9,8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>001111111 [9,10,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010 [10,9,8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111 [3,4,6,2,7,1,5,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,6,2,5,4,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,7,5,4,1,6,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [4,3,6,2,8,1,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [6,1,2,5,4,7,8,3]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [6,2,4,5,1,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [4,2,8,5,1,3,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [4,3,6,8,1,7,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [5,3,6,4,1,7,2,8]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [6,2,1,5,8,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [1,6,7,4,8,3,5,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [1,4,6,3,7,5,8,2]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [4,6,7,2,5,8,1,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [2,4,6,1,7,5,3,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,7,5,4,1,6,3,8]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [7,5,4,6,2,8,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [1,7,5,4,3,8,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [1,4,6,3,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,5,8,4,3,6,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [5,4,6,2,7,8,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [2,5,4,1,6,7,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [5,6,3,2,7,1,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,6,3,2,7,1,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [8,5,6,3,2,7,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [5,4,6,2,8,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [2,4,1,7,8,5,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,5,4,1,6,3,8,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [5,6,3,2,1,8,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [3,5,2,1,6,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [6,8,4,3,2,1,5,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,3,8,2,1,6,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [3,7,5,8,2,1,4,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [7,3,2,8,5,1,6,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [8,4,6,3,2,1,7,5]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [8,6,4,3,2,1,7,5]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [7,6,4,3,2,1,8,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [7,8,4,3,2,1,6,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [5,4,7,2,1,8,6,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [7,5,8,3,2,6,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [5,7,3,2,1,6,8,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,7,3,2,1,6,4,8]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,3,7,2,5,1,8,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,8,3,5,2,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,2,5,7,8,4,1,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,1,5,7,8,6,3,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [3,6,7,2,8,1,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [6,3,7,2,8,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [3,2,6,1,7,4,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,5,2,1,4,7,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [7,3,5,2,1,8,4,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [2,5,4,1,3,7,8,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,5,8,4,1,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [2,4,1,7,8,3,6,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [3,7,2,8,6,1,4,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,6,8,2,1,7,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [5,3,8,2,1,4,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,8,7,3,2,1,5,6]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [4,7,3,2,1,5,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [8,4,7,3,2,1,5,6]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [8,3,5,2,1,4,7,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [7,3,2,8,6,1,4,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [3,5,2,1,4,6,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [7,8,6,5,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [1,8,9,7,6,5,4,3,2]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>01111110 [8,9,7,6,5,4,3,2,1,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100 [7,6,8,5,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [6,8,7,5,4,3,2,1,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>11111010 [1,8,7,9,6,5,4,3,2]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>01111110 [1,9,10,8,7,6,5,4,3,2]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>011111110 [7,8,3,5,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [8,6,3,7,5,2,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [5,4,1,6,3,2,8,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [5,4,1,6,2,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,7,1,6,2,8,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,7,1,6,2,8,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [2,7,6,5,1,8,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,7,6,5,1,8,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,3,6,5,1,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,3,6,4,1,5,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,3,6,1,5,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,7,6,1,4,8,5,3]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [2,7,6,1,4,8,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [7,3,5,1,8,4,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [7,3,5,1,8,6,4,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [2,7,6,1,5,8,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,7,6,4,1,8,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [2,1,7,6,3,8,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,1,7,6,3,8,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [5,7,3,6,2,8,4,1]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [2,7,6,4,1,8,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [7,3,5,1,8,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [6,3,5,1,8,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [2,3,4,8,7,6,1,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,4,8,5,7,1,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [7,3,5,4,8,1,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [6,4,3,5,8,7,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [2,1,4,5,8,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [6,4,3,5,8,7,1,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [7,3,5,4,8,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [2,3,4,8,7,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [2,3,4,8,7,5,1,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [2,7,6,5,4,8,1,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,3,5,6,8,4,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,3,5,6,8,1,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,3,5,6,8,1,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [6,4,1,5,8,7,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [6,4,1,5,8,7,3,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [6,4,1,5,8,3,7,2]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,7,1,6,3,8,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [6,4,1,5,8,3,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [7,4,1,5,8,2,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,4,1,5,8,2,6,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [6,3,5,7,8,2,1,4]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,3,5,7,8,2,4,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [2,7,6,4,5,8,3,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [5,7,3,6,1,8,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [2,1,4,5,8,6,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [7,3,5,4,8,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [2,3,4,8,5,6,1,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,4,8,7,1,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,4,8,1,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,3,4,8,1,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,8,5,1,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [6,3,5,4,8,2,7,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,4,3,5,8,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [2,1,4,5,8,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [7,4,3,5,8,2,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,3,5,4,8,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [2,3,4,8,5,1,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,4,8,1,6,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,4,8,1,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [7,8,2,6,1,5,3,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,8,1,6,2,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,8,6,7,2,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,8,5,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,8,1,7,2,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,8,2,7,1,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [2,8,6,7,1,5,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,8,5,7,1,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,8,1,7,5,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [1,8,2,7,5,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,8,2,7,4,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [2,8,1,7,4,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,8,4,7,1,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [4,8,2,7,1,6,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [4,8,1,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,8,4,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [4,8,1,7,5,6,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [1,8,4,7,5,6,2,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [1,8,3,7,5,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,8,1,7,5,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [3,8,1,7,4,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [1,8,3,7,4,6,2,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,8,3,7,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,8,1,7,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,8,2,7,1,6,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,8,2,7,4,6,1,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,8,2,7,5,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [4,8,2,7,5,6,1,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,8,3,7,5,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [3,8,4,7,5,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,8,4,7,5,6,1,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,8,3,7,5,6,1,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [2,8,3,7,4,6,1,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,8,3,7,1,6,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [2,8,1,7,3,6,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [7,5,2,8,6,4,1,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [7,5,1,8,6,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,1,8,4,5,2,6,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [1,6,7,4,2,8,5,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,6,7,3,8,5,2,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [7,1,8,3,5,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,3,8,6,2,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [7,4,2,8,6,1,3,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [7,3,1,8,4,2,5,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [1,5,7,8,2,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [2,6,3,7,8,5,4,1]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [2,6,3,7,8,4,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [2,5,3,7,8,1,6,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [3,1,5,4,7,8,2,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [5,3,1,4,8,2,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [5,2,4,8,6,1,3,7]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [5,2,3,8,4,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [4,8,1,3,6,7,2,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [6,4,2,8,1,3,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [6,3,8,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [5,8,1,3,6,2,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [1,5,7,4,2,6,8,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [5,8,1,4,2,6,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [6,5,1,2,8,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,5,3,1,4,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [5,3,1,6,4,2,7,8]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [3,5,7,1,8,6,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [3,6,2,7,5,1,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [3,4,5,8,2,7,1,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,4,6,2,8,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,5,2,6,8,1,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [4,2,5,6,1,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [5,3,6,8,4,7,2,1]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [3,7,2,5,4,8,6,1]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [3,1,6,5,4,8,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [4,1,6,5,8,3,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,1,6,8,4,3,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [8,5,4,7,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [2,7,1,5,4,3,8,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [8,2,1,5,4,3,7,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [8,4,1,5,7,3,2,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [8,4,6,1,7,3,2,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [8,3,6,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [2,7,6,1,4,3,8,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [6,7,8,5,1,3,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,8,2,4,3,5,1]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [8,3,6,2,4,7,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [3,7,6,2,4,8,5,1]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [5,7,3,8,4,6,2,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [4,7,3,5,8,6,2,1]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [8,7,2,1,4,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,7,3,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [8,7,6,3,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [8,7,3,5,1,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,4,6,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [3,7,6,5,1,8,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [8,1,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>00000010 [1,9,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [9,1,2,3,4,5,6,7,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>000000010 [7,8,1,2,3,4,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>00000100 [1,8,9,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [1,10,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [8,9,1,2,3,4,5,6,7,10]=>[[1,2,3,4,5,6,7,10],[8,9]]=>000000100 [7,1,8,2,3,4,5,6,9]=>[[1,2,3,4,5,6,9],[7,8]]=>00000100 [6,8,1,2,3,4,5,7,9]=>[[1,2,3,4,5,7,9],[6,8]]=>00001010 [1,8,2,9,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>00000010 [1,7,9,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>00000101 [1,9,10,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>000000010 [3,6,4,8,7,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [5,6,4,3,8,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [1,6,2,4,7,8,5,3]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [3,6,2,4,8,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,4,7,2,8,1,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [1,4,7,2,5,8,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,3,8,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [3,5,6,4,8,7,1,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [4,6,8,5,3,7,1,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [6,8,5,3,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [1,6,5,4,2,8,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [1,8,5,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [4,2,7,5,1,8,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [7,8,1,4,2,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [1,3,6,4,8,2,5,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [4,1,7,5,3,2,6,8]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [6,5,1,3,4,2,8,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [4,8,5,3,1,7,2,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [7,4,5,3,2,8,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [5,8,3,6,1,4,2,7]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [2,5,8,6,4,1,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [1,4,6,2,5,8,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [3,6,2,5,8,1,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [1,6,8,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [6,1,7,8,2,4,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [7,1,8,6,3,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,2,1,4,5,6,8,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [1,2,8,3,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [6,1,3,2,7,5,8,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [1,6,3,8,5,7,2,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [2,6,4,1,7,5,8,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [7,6,5,8,1,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [5,8,6,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [1,6,4,3,7,2,8,5]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [2,6,3,4,8,7,1,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [7,1,3,4,5,2,8,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [1,8,3,5,4,2,7,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [4,1,6,3,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [7,8,2,4,6,3,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [3,2,6,4,7,8,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [2,8,5,7,4,3,1,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [7,2,5,8,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [5,3,8,7,1,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [6,5,3,8,2,1,7,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [7,5,8,4,1,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [5,8,7,4,1,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [3,5,7,8,4,1,2,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [1,4,7,5,3,8,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [2,4,6,7,3,1,8,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [7,8,4,6,3,1,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [2,6,4,5,3,8,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,6,5,8,4,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [5,6,8,4,2,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [6,8,5,4,3,1,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [6,1,4,2,8,5,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [4,8,6,5,3,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [8,6,5,1,2,4,7,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [6,7,5,8,2,1,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [1,7,5,8,2,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [1,3,8,5,7,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [6,3,8,5,7,1,2,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [8,3,1,5,6,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [6,8,5,2,1,4,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [3,8,2,5,6,1,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [2,8,1,5,6,3,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [8,1,2,5,6,3,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,8,2,5,7,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,1,8,6,2,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [2,5,8,6,1,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [8,6,1,5,7,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [3,8,6,5,7,1,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [7,6,5,8,1,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [5,1,7,6,8,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [5,1,3,7,8,6,2,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [7,2,5,8,1,6,4,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [3,2,8,5,7,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,2,1,5,7,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [5,2,8,6,1,7,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [1,2,8,6,5,7,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [4,2,1,3,6,7,8,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [8,2,5,6,3,7,1,4]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [7,2,6,5,4,1,8,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [6,1,3,5,4,7,8,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [6,1,5,3,4,7,8,2]=>[[1,2,4,7,8],[3],[5],[6]]=>0101100 [7,5,6,2,4,1,8,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [8,5,2,6,3,7,1,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [4,3,1,2,6,7,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [8,1,6,5,7,3,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [3,5,8,6,2,7,1,4]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [5,8,1,6,3,7,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [1,8,5,6,3,7,2,4]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [1,7,6,5,4,2,8,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [5,7,6,1,4,2,8,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [7,1,4,2,6,5,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [4,1,7,3,5,6,8,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [2,7,4,1,5,6,8,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [5,7,6,4,1,2,8,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [4,7,6,1,5,2,8,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [1,7,6,4,5,2,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [1,8,3,6,5,7,2,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [3,8,1,6,5,7,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [8,1,3,5,7,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [7,8,5,4,1,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [6,1,5,4,3,7,8,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [7,5,6,4,2,1,8,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [8,3,2,6,5,7,1,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,4,6,2,5,1,8,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,1,4,3,5,7,8,2]=>[[1,2,5,7,8],[3],[4],[6]]=>0110100 [6,1,3,4,5,7,8,2]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [7,2,6,4,5,1,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [8,2,3,6,5,7,1,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [5,4,7,3,6,8,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [3,4,7,8,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [3,4,7,2,5,1,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [1,4,7,2,5,8,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [3,6,2,4,7,1,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [6,8,3,4,5,7,1,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [4,3,6,7,5,8,1,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [6,3,7,5,8,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [7,3,8,6,4,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [3,2,7,6,5,1,4,8]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [1,2,7,6,5,8,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [4,8,2,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [2,3,8,6,4,1,5,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [4,3,6,2,5,1,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [7,8,3,2,5,1,4,6]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,8,1,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [4,1,6,2,5,7,3,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [6,1,2,5,8,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [2,1,8,6,4,7,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [7,1,3,6,8,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,8,3,6,7,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,1,5,8,3,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [5,1,8,7,2,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,1,5,7,4,2,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [3,1,6,4,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [2,4,7,5,1,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [6,5,7,1,4,2,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [5,6,8,1,3,2,4,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [6,8,5,1,3,4,2,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [2,8,3,4,5,1,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [6,2,4,3,1,5,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [4,2,8,3,1,7,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [1,3,7,4,8,2,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [5,3,7,4,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [2,4,7,3,6,1,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,8,7,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [7,5,6,8,1,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [2,4,7,1,6,5,3,8]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [1,2,7,8,5,4,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [6,3,1,2,8,4,5,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [4,2,1,3,6,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,8,1,4,5,6,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [7,2,1,5,4,6,3,8]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [4,2,6,1,8,5,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [7,8,2,1,4,5,3,6]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,8,4,1,5,3,6,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [3,4,6,1,5,8,7,2]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [7,5,1,6,4,3,8,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [5,8,1,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [6,5,1,8,2,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [6,8,1,7,5,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [7,6,1,8,5,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [5,6,1,7,4,8,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [3,6,1,5,7,4,2,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [2,5,6,1,7,4,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [3,1,7,5,6,4,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [5,1,7,6,4,8,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,1,7,8,5,3,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [7,1,8,6,5,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [2,6,5,7,3,4,8,1]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [1,6,4,7,5,8,2,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [8,5,3,6,2,7,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [1,3,7,4,6,8,2,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [4,7,5,6,3,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>1110010 [1,7,6,5,4,8,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [8,1,6,5,7,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [1,2,7,6,8,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [6,1,7,5,3,8,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [2,1,7,5,6,8,3,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [5,4,1,7,6,8,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [4,8,5,6,2,7,3,1]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [3,8,6,4,2,7,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,8,5,2,4,6,3,1]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [2,8,6,3,7,4,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,8,1,6,2,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [6,8,1,4,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [3,8,4,1,7,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [5,4,7,1,8,3,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [3,7,4,1,8,5,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [6,7,1,4,8,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [2,7,1,8,4,5,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [6,1,2,8,4,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [6,5,1,4,3,8,2,7]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [1,6,2,5,8,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [8,5,1,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,4,2,1,7,3,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [7,4,2,1,8,5,3,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [1,5,4,2,8,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [6,4,3,1,5,8,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [3,7,6,8,4,5,2,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [2,7,6,8,5,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [1,7,6,8,5,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [1,4,8,6,7,5,2,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [2,4,8,6,7,3,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [7,3,8,5,4,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [3,4,8,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [6,3,5,8,4,7,2,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [5,4,3,8,6,7,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,4,2,8,7,3,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,2,5,8,7,3,4,1]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [3,2,8,5,7,4,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [1,3,8,7,5,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [2,1,8,7,4,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [3,1,8,5,7,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [6,1,5,8,7,4,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [5,4,1,8,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>1111001 [4,8,7,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [4,2,1,6,3,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [6,2,1,4,3,5,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [6,2,1,4,3,8,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [8,2,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [6,2,4,1,3,5,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,6,4,3,5,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,1,4,3,5,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,4,1,3,5,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,6,2,1,3,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [6,4,2,1,3,5,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [8,4,2,1,3,6,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [8,4,2,1,6,3,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [6,4,2,1,8,3,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,1,4,3,8,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,6,4,3,8,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,8,4,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,1,4,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,8,4,1,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,8,2,1,3,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [6,8,2,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [8,6,2,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,8,1,4,6,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,6,1,4,8,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,4,1,8,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,4,8,1,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,6,2,8,1,3,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,6,1,8,3,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [6,2,4,1,8,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,2,1,6,8,3,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,1,6,3,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,1,3,6,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,1,4,3,8,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,1,3,8,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,2,1,3,8,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,2,1,8,3,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,2,1,8,6,3,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [8,2,1,6,4,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [8,2,6,1,4,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [4,2,8,1,3,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,4,8,1,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,1,8,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,1,4,8,3,6,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,1,4,8,6,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,8,1,6,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [2,4,8,6,1,3,5,7]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,2,8,6,1,3,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [8,4,6,2,1,3,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [4,6,8,2,1,3,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,6,8,4,1,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,8,1,4,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,6,1,8,4,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,6,8,4,3,5,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [2,1,8,6,4,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,8,6,4,1,3,5,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [4,8,6,2,1,3,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [6,8,4,2,1,3,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,2,6,1,5,4,8,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [5,2,4,3,8,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,2,4,1,5,3,8,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,3,6,1,5,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [4,3,5,2,8,1,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,7,2,6,5,8,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [4,3,8,2,6,1,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,3,8,1,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [4,3,8,1,5,2,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [5,1,8,3,4,2,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [5,4,8,1,3,2,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [2,1,5,4,8,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [5,1,7,6,8,3,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [4,3,7,6,8,1,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [4,3,7,1,8,5,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,3,6,5,8,1,7,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [6,3,5,4,7,2,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [6,3,5,4,8,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,1,6,3,8,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,4,6,5,8,1,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [2,1,8,4,6,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [8,4,6,1,3,2,7,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [8,1,6,3,4,2,7,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,1,6,3,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [8,3,5,1,7,2,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,3,5,2,6,1,7,4]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [7,3,5,2,6,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [8,2,6,3,5,1,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,2,7,1,5,3,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,2,4,1,5,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,2,4,1,7,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,2,4,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,2,8,4,6,1,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,8,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [3,2,7,6,8,1,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,2,7,1,8,5,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,6,5,8,1,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [6,5,7,2,4,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [6,5,8,2,4,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [7,2,4,1,8,5,6,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [7,6,8,2,4,1,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,6,8,1,5,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [2,1,7,3,8,5,6,4]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [7,1,3,2,8,5,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,1,8,5,6,2,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,1,8,2,6,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,2,8,1,5,4,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,2,7,4,5,3,8,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [5,4,7,2,6,3,8,1]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,4,8,2,6,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [6,5,8,1,7,2,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [2,1,6,5,8,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [6,5,7,4,8,1,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,5,7,1,8,3,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,1,7,4,8,3,5,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [5,4,7,1,8,3,6,2]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [5,4,6,3,8,1,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [2,8,3,1,5,4,6,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,5,3,4,7,1,8,6]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [2,4,8,3,5,7,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [4,2,5,3,1,8,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,2,1,8,5,3,6,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,4,1,3,8,2,6,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [5,1,4,8,3,2,6,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,5,8,4,3,2,6,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,8,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [1,7,4,3,8,5,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [1,5,7,3,8,4,2,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,1,4,7,8,3,2,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [4,8,1,5,7,3,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [8,1,5,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [3,8,4,7,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [1,6,8,5,3,7,4,2]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [6,8,1,7,4,3,5,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [6,4,8,1,7,3,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [6,4,8,7,1,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [7,6,4,1,3,8,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [1,7,5,6,3,2,8,4]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [4,2,1,7,8,5,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [2,7,4,6,3,1,8,5]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [2,6,8,4,3,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [6,2,4,8,3,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,2,6,3,4,1,8,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [2,6,7,3,1,4,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [2,7,1,8,3,5,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,1,7,3,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [8,7,1,3,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,2,1,7,3,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [7,8,2,6,3,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [8,7,2,6,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [1,2,8,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [8,3,7,1,5,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,6,1,2,7,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,1,6,2,7,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,8,5,2,6,7,4,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [5,2,1,8,6,7,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [2,8,5,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [1,7,8,5,2,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,8,1,6,4,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,8,6,1,5,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,3,8,6,1,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [8,7,6,1,5,3,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [8,7,1,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [8,1,7,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [1,8,6,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [6,3,5,2,1,4,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [6,3,5,7,2,8,4,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [8,5,2,7,4,3,1,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [4,5,3,6,1,2,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [3,5,1,4,6,2,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [8,3,4,5,7,2,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [5,7,4,6,3,8,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [2,8,4,6,3,7,1,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [8,1,4,7,3,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [8,3,4,7,5,1,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [8,5,1,4,7,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [8,5,3,7,1,4,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [2,1,8,5,7,4,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [6,5,3,7,1,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,5,1,4,7,8,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]=>0111100 [6,3,4,7,5,8,1,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [5,1,4,6,8,3,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [4,7,1,3,5,8,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [4,8,3,7,1,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,8,6,4,1,7,2,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [3,8,1,2,5,7,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [2,8,7,5,4,1,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [8,7,2,6,4,1,3,5]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [3,8,6,7,4,2,1,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [5,7,6,8,4,2,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,3,7,8,2,4,6,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [8,3,6,2,1,4,7,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [5,3,7,6,2,1,8,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [5,3,6,2,8,7,1,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,7,8,6,4,2,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [2,6,7,5,4,8,1,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [6,1,7,4,5,8,2,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [6,7,3,5,1,8,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [2,1,6,7,5,8,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,1,5,7,3,6,8,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [5,7,3,6,1,2,8,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [4,1,7,2,5,6,8,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [2,4,7,1,6,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [4,6,2,1,8,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [3,4,6,2,7,8,5,1]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [4,6,1,2,5,8,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [5,6,1,4,8,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,6,3,1,8,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [3,5,6,4,7,1,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [3,4,6,1,5,7,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [3,4,1,5,7,6,8,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [3,8,2,7,1,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [3,8,2,7,6,1,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [3,8,2,7,6,5,1,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [3,8,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [4,8,7,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [4,8,7,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [4,8,7,2,6,1,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [4,8,7,2,1,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [4,8,7,3,1,6,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [4,8,7,3,2,1,6,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,8,7,3,2,6,1,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,8,7,3,2,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,8,7,3,6,2,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,8,7,3,6,2,1,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [4,8,7,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [4,8,7,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [4,8,7,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [5,8,7,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [5,8,7,6,3,1,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [5,8,7,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [5,8,7,6,2,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [5,8,7,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [5,8,7,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [5,8,7,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [5,8,7,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [5,8,7,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [7,3,5,2,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,2,1,5,6,4,3,8]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [1,4,6,7,3,8,2,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [6,4,5,7,1,3,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [6,3,5,1,7,4,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [6,2,1,5,7,4,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [3,2,1,5,7,4,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,4,6,7,3,8,1,5]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [1,4,6,7,3,8,5,2]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,5,6,7,8,3,4,2]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [2,5,6,7,8,3,1,4]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [3,2,1,6,7,8,4,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [5,2,1,6,7,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,3,6,1,7,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [5,4,6,7,1,8,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [1,5,6,7,8,3,2,4]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [6,4,5,7,2,1,8,3]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [5,4,6,7,2,8,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [6,3,4,2,1,7,8,5]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [4,3,6,2,7,8,5,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [3,4,6,7,2,8,5,1]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [4,2,1,5,7,3,8,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [1,5,6,7,8,2,4,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [1,5,6,7,8,4,2,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [3,4,6,7,1,8,5,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,3,6,1,7,8,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [2,1,4,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,3,6,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,8,5,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,7,5,9,8]=>[[1,3,5,7,8],[2,4,6,9]]=>10101001 [1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101 [2,4,1,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [2,4,6,1,3,5,8,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [2,4,1,6,8,3,5,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,8,5,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [2,4,1,6,3,8,9,5,7]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [2,4,1,6,3,8,5,10,7,9]=>[[1,3,5,7,9],[2,4,6,8,10]]=>101010101 [2,4,1,6,3,7,5,8,9]=>[[1,3,5,7,8,9],[2,4,6]]=>10101000 [2,4,1,6,3,8,5,9,7,10]=>[[1,3,5,7,9,10],[2,4,6,8]]=>101010100 [2,4,1,6,3,7,5,9,8,10]=>[[1,3,5,7,8,10],[2,4,6,9]]=>101010010 [2,3,1,5,4,7,6,9,8,10]=>[[1,3,4,6,8,10],[2,5,7,9]]=>100101010 [1,3,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>010101010 [1,4,3,6,2,5,7,8]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,4,3,7,2,5,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,4,3,7,6,8,2,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [1,4,3,7,5,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [1,4,3,7,2,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [1,5,3,7,4,8,2,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,3,2,6,5,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,5,4,8,2,6,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [1,5,4,8,3,7,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [1,2,3,6,5,8,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,8,2,4,5,7,1,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [3,7,8,4,5,2,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,8,1,4,5,3,6,2]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [3,8,7,4,1,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [4,8,3,6,1,5,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [5,8,3,1,6,4,7,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [5,8,1,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [7,5,1,8,6,2,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,4,1,8,2,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,1,8,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,6,3,8,5,2,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [6,1,3,8,5,2,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [7,2,8,4,1,6,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,2,8,3,6,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,2,8,3,6,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,1,8,2,3,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,5,2,3,8,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [5,1,2,3,8,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [6,2,8,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [2,6,3,8,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [2,5,1,3,8,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [1,2,4,8,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [2,4,8,1,3,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [2,4,8,3,7,6,1,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,5,4,1,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [5,2,3,8,4,7,1,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [1,4,8,2,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [6,3,8,1,5,2,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [5,3,8,1,2,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [5,1,3,8,2,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [1,5,4,8,2,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [6,5,1,2,8,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [5,3,1,6,4,2,8,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [5,1,6,2,8,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [1,4,2,5,8,7,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [3,6,2,8,7,5,1,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [4,2,6,1,8,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,3,1,5,8,2,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [3,4,8,7,1,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,4,8,1,7,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [1,3,4,8,7,2,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [6,3,1,5,4,2,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [7,8,3,5,4,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,8,2,5,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,2,1,5,4,7,3,8]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [4,3,7,5,8,6,1,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,2,7,1,8,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [1,7,6,5,3,8,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [2,7,6,5,3,8,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [1,7,6,5,2,4,8,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [2,7,1,4,8,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [3,7,6,4,8,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [5,7,6,3,8,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [5,1,6,2,4,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [4,7,6,5,1,8,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [4,7,6,5,1,2,8,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [6,1,3,5,4,8,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [1,2,6,3,4,8,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [6,1,4,2,8,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [4,7,1,6,2,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,2,6,7,4,8,5,3]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [3,1,6,7,4,2,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [3,2,8,5,4,6,1,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [4,7,1,2,5,3,8,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [4,7,6,8,3,5,1,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [2,7,6,5,1,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [6,3,2,1,7,4,8,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [4,2,1,7,3,5,8,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [7,3,1,5,4,2,8,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [8,4,1,5,2,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,2,5,1,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [4,7,2,5,3,1,8,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [7,5,4,3,2,1,8,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [5,7,4,3,2,8,1,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [1,7,6,2,4,8,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [2,7,3,6,4,8,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [6,2,7,5,3,8,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [7,1,8,5,3,6,4,2]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [5,8,3,2,7,1,6,4]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011 [8,7,3,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,7,2,6,1,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [1,8,5,7,4,3,6,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,8,5,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [3,8,6,1,7,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [7,2,8,5,6,1,4,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,3,7,5,8,2,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [3,7,2,6,8,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [3,6,5,8,1,4,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [2,6,5,8,4,1,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,5,4,8,3,2,1,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [6,3,5,1,8,4,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [8,4,1,5,7,3,6,2]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [6,3,7,4,8,5,2,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [4,7,2,5,8,6,3,1]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [6,3,1,8,4,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,5,3,8,7,4,1,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [5,4,8,1,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,2,8,1,7,3,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [6,4,7,8,1,5,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [2,5,8,7,1,3,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [5,3,8,7,2,1,6,4]=>[[1,4],[2,6],[3,7],[5,8]]=>1101011 [8,3,7,6,1,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,2,7,6,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [4,3,8,7,6,2,1,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [2,4,8,7,6,1,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [3,5,8,7,2,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [4,7,3,8,6,5,1,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [7,5,8,6,4,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [5,8,7,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [4,8,7,6,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [3,8,7,6,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [2,8,7,6,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000 [4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000 [5,6,7,8,1,2,3,4,9]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000 [5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000 [6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>11111000 [7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [8,6,9,4,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>10101010 [3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000 [4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000 [5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>111100000 [6,4,3,2,7,1,5,8,9,10]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000 [6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000 [7,5,3,8,2,6,1,4,9,10]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]=>110101000 [7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>111111000 [8,6,9,4,7,2,5,1,3,10]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>101010100 [8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100 [3,6,5,1,2,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,7,5,8,2,4,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [3,8,5,7,2,4,1,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [5,1,7,8,4,3,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [5,1,2,6,4,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [6,1,2,5,4,3,8,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [5,1,2,4,6,3,8,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [4,1,2,6,5,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [4,1,5,7,8,3,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,1,5,8,7,3,2,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [4,7,1,8,3,6,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,1,7,8,5,2,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [5,1,7,4,8,2,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [7,5,3,8,1,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [2,1,5,8,7,3,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [5,1,8,4,7,2,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [4,1,8,7,5,2,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [4,7,1,6,3,2,8,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [6,1,2,3,7,5,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [7,1,2,3,8,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,2,3,5,8,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,8,1,4,3,7,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [8,7,3,2,4,1,6,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [2,1,7,3,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [7,8,3,2,4,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,7,1,4,3,8,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [8,1,2,3,5,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [8,1,2,3,6,7,5,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [7,1,2,3,6,8,5,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [7,1,2,3,8,5,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [8,1,2,3,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [7,1,8,5,4,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [7,8,2,6,3,4,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [6,8,2,7,3,4,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [6,7,2,8,3,4,1,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [3,8,7,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,7,8,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [3,6,8,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [3,5,7,8,2,4,1,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,6,7,1,4,2,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [7,6,2,8,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,6,2,7,3,1,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [8,1,7,5,4,3,2,6]=>[[1,2,6],[3],[4],[5],[7],[8]]=>0111011 [8,1,7,4,5,3,2,6]=>[[1,2,5,6],[3],[4],[7],[8]]=>0110011 [5,8,3,7,1,4,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [2,1,7,3,4,6,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [6,7,3,2,4,1,8,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [8,7,2,4,3,6,1,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [7,1,2,3,5,6,8,4]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [6,1,2,3,8,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [5,1,2,3,7,8,6,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [5,1,2,3,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,1,2,3,8,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [6,1,2,3,5,8,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [8,6,2,4,3,1,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [7,6,3,2,4,8,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [2,1,6,3,4,8,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [8,6,3,2,4,7,1,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,6,2,4,3,1,8,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [6,1,2,3,5,7,8,4]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [5,1,2,3,6,8,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,3,8,5,4,2,7,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [2,4,8,1,7,3,6,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [3,4,8,5,7,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [7,1,4,2,6,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [6,8,1,4,7,2,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,6,4,2,8,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,6,3,8,5,4,2,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [6,8,1,7,3,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [7,1,3,6,5,4,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [7,3,1,6,5,4,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [7,1,2,3,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [6,8,1,2,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,5,8,2,7,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,1,8,2,7,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,8,2,7,6,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [6,8,2,1,7,4,3,5]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [2,1,6,3,8,5,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,5,3,8,7,4,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,5,8,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [3,5,8,7,1,4,2,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [5,3,8,4,1,7,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [4,2,8,7,6,3,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [4,2,8,7,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [4,1,8,7,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [4,3,8,7,6,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [1,5,8,4,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,7,4,6,1,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,6,3,1,2,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [5,6,1,2,4,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [4,5,8,1,7,2,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,3,2,5,8,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,5,1,8,7,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [3,5,1,8,7,2,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [4,5,8,3,1,7,2,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [3,4,8,7,6,2,1,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [3,1,4,8,7,6,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [3,4,8,7,6,5,1,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [1,2,7,5,8,6,4,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,1,4,8,2,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [6,8,1,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [3,7,8,1,2,6,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [1,3,7,8,2,6,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [2,3,7,8,1,6,5,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,7,8,1,3,6,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [8,1,2,6,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,1,2,6,7,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,2,5,7,1,3,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,8,1,6,7,3,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,6,8,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [2,8,6,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [6,8,3,4,1,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,8,3,7,4,1,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [2,6,8,3,7,5,1,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [2,8,1,6,7,5,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [8,2,5,7,1,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,4,7,2,3,6,1,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,5,7,4,2,6,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [8,3,5,7,4,1,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [8,5,2,4,7,1,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,2,3,5,7,1,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,2,4,7,3,6,1,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,2,7,1,4,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,7,1,2,4,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,7,1,4,6,2,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,4,7,1,3,6,2,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [1,6,8,3,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [8,3,5,7,1,2,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [5,8,7,1,3,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,5,4,7,1,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [8,5,4,7,1,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [8,5,1,4,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [1,4,6,8,2,7,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [1,6,5,8,2,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [8,5,6,3,1,7,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [5,6,2,8,1,7,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [1,8,4,5,7,2,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [5,8,7,3,6,1,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [8,3,5,7,1,6,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [1,6,8,3,7,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [6,3,8,2,7,5,1,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [6,8,4,2,7,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [8,6,4,7,3,1,5,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [8,4,5,7,3,1,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,4,2,5,7,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,3,4,7,2,6,1,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,7,1,3,4,6,2,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,3,7,2,4,6,1,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [2,8,4,5,7,1,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,7,3,4,5,1,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [8,7,4,5,2,6,1,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [5,8,7,2,3,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,7,2,3,4,6,1,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,7,2,3,6,1,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [1,3,2,8,5,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,2,8,5,3,7,1,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [5,2,1,8,4,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [6,2,8,4,3,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,2,8,4,3,1,6,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [7,3,4,8,2,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,3,4,8,2,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [5,3,4,1,8,2,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [8,1,4,5,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,1,5,4,3,2,7,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [3,5,4,2,8,1,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,5,3,2,8,7,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [6,4,3,2,8,7,5,1]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,5,3,2,1,7,8,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,6,3,2,7,8,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [4,1,6,3,2,7,8,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [3,6,4,2,7,8,1,5]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [8,1,6,4,3,7,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,1,7,4,3,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [2,7,4,1,3,6,5,8]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [3,7,4,2,6,1,5,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,1,7,3,2,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,7,3,2,6,4,8,1]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,7,3,2,5,4,1,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [7,6,3,2,1,5,4,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [4,7,5,6,2,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [3,1,7,5,6,2,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [2,7,5,6,1,3,4,8]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [2,6,5,7,1,3,8,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [4,6,5,7,2,8,1,3]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [5,6,4,7,2,8,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [6,5,4,1,7,2,8,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,5,4,6,2,1,8,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,4,5,7,1,8,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [5,4,6,1,7,8,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [8,1,5,6,7,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [2,1,4,6,8,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [3,4,6,8,7,1,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [4,3,1,6,8,7,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [5,3,6,8,7,2,4,1]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [6,3,5,1,8,7,2,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [7,3,5,8,6,2,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,2,8,5,6,3,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [6,2,8,5,1,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [4,2,1,8,6,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [1,3,2,8,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,3,8,6,7,1,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [8,1,3,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,3,8,7,1,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [4,2,8,7,6,1,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [5,2,8,7,6,4,1,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [7,2,1,8,6,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [7,3,6,1,8,5,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [6,3,7,8,5,4,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,3,7,8,6,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [4,3,1,7,8,6,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [3,4,7,8,6,1,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [8,1,5,7,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [3,5,7,6,8,1,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [4,5,7,6,8,3,1,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [5,4,1,7,6,8,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [6,4,7,5,8,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,4,6,5,1,8,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [7,5,6,4,3,1,8,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [6,5,1,7,4,3,8,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [4,6,7,5,3,8,1,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [3,6,7,5,1,4,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [8,1,6,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111 [2,7,6,1,5,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [3,7,6,5,1,4,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [4,7,6,5,3,1,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [8,6,4,3,1,5,7,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [8,6,4,1,5,2,7,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [8,6,5,1,3,2,7,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [8,6,3,1,7,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,7,3,1,5,2,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [5,3,1,7,2,4,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [8,7,1,2,4,5,3,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [8,6,1,2,4,7,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [8,5,1,2,6,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [8,5,1,6,4,2,7,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [8,5,1,3,6,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [8,6,1,5,3,4,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [8,6,1,5,2,4,7,3]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [8,6,1,2,5,7,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,6,1,2,7,4,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [8,7,1,2,5,4,3,6]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [5,1,4,2,3,8,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,1,4,2,7,3,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [7,1,5,8,2,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [5,7,8,1,2,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [5,7,8,1,3,4,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,8,1,7,3,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [8,1,5,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [8,4,1,2,7,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,4,2,3,8,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,4,2,7,6,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [6,1,2,8,7,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,1,2,4,8,7,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [3,1,8,4,6,7,5,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [3,1,7,6,4,8,5,2]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [7,1,2,4,6,8,5,3]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [7,1,2,6,8,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [6,1,2,7,8,5,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,2,7,4,8,5,3]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [3,1,6,4,7,8,5,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [5,7,1,3,8,4,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [5,7,1,8,4,2,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [7,1,5,3,2,8,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,1,4,5,2,8,6,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [4,7,3,1,5,8,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,8,7,3,1,5,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,1,7,4,5,2,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [8,1,7,5,3,2,6,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [8,3,7,1,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [3,1,2,8,4,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,1,2,8,6,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,7,2,6,4,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,4,2,3,8,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [1,4,2,3,8,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [5,8,1,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [5,8,1,3,4,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [3,1,8,6,4,7,5,2]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [8,1,2,6,7,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [6,1,2,8,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,2,3,5,8,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,3,5,8,6,4,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [7,1,2,8,3,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,2,8,6,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [3,1,7,8,4,6,5,2]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [3,1,8,7,6,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,1,2,7,4,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,1,2,7,3,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [1,2,3,5,8,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,3,6,8,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [7,8,5,6,3,1,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,6,3,1,4,2,8]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,8,3,1,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,8,5,3,1,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,8,5,3,1,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,8,5,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,8,5,3,6,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,8,3,4,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,6,3,4,1,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,6,3,1,2,8,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,5,3,6,1,2,8,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,5,3,1,4,2,6,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,5,3,1,6,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,6,4,1,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,6,4,8,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,8,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,8,1,4,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,1,8,4,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,1,8,2,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,3,1,6,4,2,8]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,1,8,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,1,8,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,3,8,1,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,3,8,6,1,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,3,8,6,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,8,3,6,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,8,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,8,3,1,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,3,6,1,4,2,8]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,8,4,1,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,8,6,3,1,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,8,6,3,1,4,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,8,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>0101010 [7,5,6,8,3,1,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,4,1,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [7,5,6,3,1,8,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,5,6,3,1,8,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,6,3,8,1,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,6,3,8,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,6,1,8,4,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,3,1,6,8,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [7,5,3,1,2,8,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,5,3,1,2,8,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,5,3,1,4,8,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,4,8,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,3,4,1,6,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,5,3,1,4,6,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,6,2,5,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [3,5,2,8,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [5,4,7,3,2,8,6,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,8,3,2,7,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,4,5,3,2,1,8,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,3,2,6,4,1,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,5,8,3,2,7,6,1]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,7,6,3,8,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [4,8,6,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [4,8,5,3,2,7,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [5,8,4,3,2,7,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [5,3,2,8,4,7,6,1]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [2,1,5,8,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [5,3,2,7,4,8,6,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,7,4,3,2,8,6,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,7,5,3,2,8,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [4,7,8,3,6,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [4,6,8,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [7,6,4,3,8,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [7,3,2,6,8,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [2,1,8,6,7,5,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [8,3,2,6,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [8,6,4,3,7,5,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [8,5,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011 [8,4,5,3,2,7,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [8,4,7,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,4,6,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [7,4,6,3,8,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [3,7,2,6,8,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,8,2,6,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [3,8,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [3,7,2,8,6,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [3,6,2,8,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [6,4,7,3,8,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,4,8,3,7,5,2,1]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [7,4,8,3,6,5,2,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,4,5,3,2,8,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [7,5,4,3,2,8,6,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [7,3,2,5,4,8,6,1]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [2,1,7,5,4,8,6,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [7,3,2,8,6,5,4,1]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [7,8,4,3,6,5,2,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [6,8,5,7,4,3,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [6,8,4,3,7,5,2,1]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,3,2,8,7,5,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]=>1101101 [6,3,2,7,8,5,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,4,3,8,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [2,3,1,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,4,1,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,4,5,1,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,4,5,6,1,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>10000000 [2,3,1,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,4,3,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>10100000 [2,3,4,1,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,1,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,1,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,7,1,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,7,8,1,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>100000000 [2,3,4,5,6,7,9,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>10000001 [4,6,8,3,5,7,1,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [6,8,1,2,4,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [3,5,8,2,4,7,1,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [8,3,5,2,4,1,6,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [4,2,5,7,3,6,1,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,5,2,8,3,1,6,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,2,5,8,3,7,1,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [2,1,6,8,4,7,3,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [1,2,5,8,3,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [5,3,6,8,4,7,1,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [1,6,5,8,2,4,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [3,1,2,6,8,5,7,4]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,4,3,8,2,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [5,4,8,3,2,1,6,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,4,3,7,2,6,1,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,3,6,2,7,5,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,6,3,2,1,8,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [4,1,7,3,2,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [4,3,1,7,8,2,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [3,5,1,2,7,8,6,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [7,5,1,4,8,2,6,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [5,4,7,3,8,6,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,8,4,7,6,3,1,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [5,8,7,1,4,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [8,3,5,1,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [4,8,3,1,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [1,8,4,3,5,2,7,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,6,3,1,5,2,8,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [4,7,3,6,5,2,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [5,3,7,6,4,2,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [1,6,3,4,2,8,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [1,8,3,6,2,7,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,6,8,7,4,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [6,4,8,7,5,3,1,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [7,6,4,3,8,5,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [1,7,6,2,8,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,1,3,2,6,8,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,5,3,2,7,4,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [6,3,2,1,8,5,4,7]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,5,3,2,7,4,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,2,6,3,7,4,1,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [2,8,5,3,1,6,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [2,1,7,3,8,5,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [1,6,2,3,7,8,5,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,6,7,2,8,4,5,3]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [5,7,1,8,2,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [5,1,2,7,8,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [2,4,1,7,8,6,3,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [4,2,1,7,3,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [6,2,8,4,3,1,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [7,3,2,1,8,4,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,8,3,2,5,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,1,8,2,4,5,6,3]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [8,7,6,1,2,4,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,3,7,6,2,1,4,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [3,2,8,7,5,1,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,3,6,5,2,1,4,7]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [7,6,3,5,2,4,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [7,4,6,2,5,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [8,2,4,1,6,5,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [4,2,8,1,7,5,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,2,4,1,7,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,7,1,5,6,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,5,7,3,6,4,1,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [6,8,3,7,5,4,1,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [8,1,6,7,5,2,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,1,2,6,4,3,7,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [2,8,1,7,5,4,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [2,5,1,8,6,4,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [5,7,2,6,4,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [6,2,7,5,4,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [2,1,8,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [1,2,7,5,4,3,8,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,7,2,4,3,8,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,7,2,8,3,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,7,8,6,5,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,3,8,6,5,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [1,8,7,6,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [8,1,7,3,2,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [5,1,4,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [8,6,5,3,2,1,7,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [8,6,3,2,1,7,4,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [8,6,5,4,1,7,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,6,5,1,7,3,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [8,6,1,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [4,6,3,2,7,5,1,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [1,4,3,7,2,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [7,4,8,3,1,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [7,1,5,8,3,2,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [5,7,4,1,8,2,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,7,4,3,1,8,6,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [1,8,7,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [1,8,5,3,7,2,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [4,3,1,8,7,5,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [1,4,8,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [7,4,6,3,5,2,1,8]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [1,3,5,6,8,4,2,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [3,5,4,8,7,1,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [3,1,4,6,8,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [1,6,3,8,7,2,5,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [1,6,2,4,8,7,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [8,4,1,6,7,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [7,1,6,4,8,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,3,6,8,5,1,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [1,3,7,2,6,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [3,6,5,2,8,1,4,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [3,6,5,7,2,4,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [4,2,6,3,8,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,2,6,7,3,5,1,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,6,2,4,7,5,1,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,6,2,4,1,8,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [7,3,8,2,1,6,4,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [7,3,5,2,1,8,6,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [8,7,6,4,3,1,5,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,7,6,4,1,5,2,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [3,8,7,2,1,4,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,8,2,7,1,5,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,6,8,2,1,5,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [2,4,8,1,6,5,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [4,2,8,1,5,7,3,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [8,5,7,6,1,4,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,6,1,7,3,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [8,6,1,7,5,4,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [1,6,2,8,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,8,2,4,6,7,3,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [2,8,5,4,7,1,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [2,1,5,8,6,4,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [7,2,5,6,4,3,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>1011010 [1,2,5,7,8,4,3,6]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [1,2,7,4,8,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,2,7,8,3,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,8,6,3,5,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [1,8,7,6,3,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,8,7,4,6,3,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [7,1,5,8,3,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,1,6,4,2,3,5,8]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [8,6,2,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,6,2,4,5,7,3,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [2,7,1,4,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,1,6,4,5,2,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,1,4,5,6,8,2,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [7,1,4,6,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [7,1,2,3,8,5,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [7,1,5,4,3,8,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [7,1,3,4,2,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [7,1,5,4,6,2,8,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [7,1,5,6,4,3,8,2]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [7,1,6,5,4,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [8,6,2,5,4,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [2,5,1,7,4,3,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,5,1,4,7,8,6,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [3,5,1,4,8,6,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,6,2,4,7,8,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [5,6,2,4,8,7,1,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [6,3,8,2,4,7,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [6,5,8,7,2,3,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,5,7,8,2,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,3,4,2,8,5,1,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [3,4,7,2,5,8,1,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [4,6,8,1,3,5,2,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,3,8,1,2,7,5,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [3,6,4,1,7,2,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [2,8,3,1,5,6,4,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [3,8,7,1,5,4,2,6]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [4,3,1,7,6,8,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [3,4,1,7,5,6,8,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [3,4,1,5,7,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [3,7,4,1,6,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [8,4,7,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [4,7,8,1,2,3,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [2,8,6,1,5,3,7,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [7,6,5,1,3,8,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,6,5,1,3,4,8,2]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [7,2,6,4,1,3,8,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [6,7,5,2,1,3,8,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,4,5,3,7,2,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [4,7,5,2,8,1,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [2,6,4,3,1,5,7,8]=>[[1,3,5,7,8],[2],[4],[6]]=>1010100 [7,3,8,4,1,5,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,2,3,4,1,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [4,2,8,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [6,8,5,7,2,1,3,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [4,8,5,2,7,1,3,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [6,3,5,2,1,7,4,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [6,8,5,3,1,4,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [3,6,5,4,2,8,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [1,6,4,7,2,5,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,6,4,8,2,5,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [1,6,5,8,2,4,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,6,8,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,6,2,4,3,7,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,5,6,2,4,7,3,8]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [1,5,6,2,4,7,8,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [1,5,8,2,4,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,5,7,2,4,8,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [1,6,5,7,2,4,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [1,6,7,2,4,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [1,5,6,7,2,4,8,3]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [1,5,8,2,4,6,7,3]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,5,7,2,4,6,8,3]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [1,5,7,8,3,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,5,8,3,2,4,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [1,5,6,2,4,8,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [1,7,6,2,8,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,7,3,4,2,8,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [1,6,2,4,3,8,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,5,6,2,4,8,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [1,5,8,7,3,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,4,2,3,5,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,5,2,3,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,6,5,2,3,8,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [1,7,4,2,8,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [1,7,6,5,2,8,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [1,6,7,5,2,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,7,5,2,8,4,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,7,5,6,2,8,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,5,7,6,2,4,8,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [1,5,8,3,2,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [1,6,5,2,3,7,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,6,5,2,3,7,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,6,8,4,2,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,7,4,6,2,8,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,7,3,5,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,6,8,5,2,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [1,6,4,2,3,7,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,6,4,2,3,7,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,5,8,6,2,4,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [1,5,7,3,2,4,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,7,3,4,2,8,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [1,7,4,2,8,5,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [1,6,7,4,2,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [1,6,4,2,3,8,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,7,6,4,2,8,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [1,7,5,2,8,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [1,6,4,2,3,8,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [3,7,5,6,1,4,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,5,4,1,6,7,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [1,7,6,4,3,5,8,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [8,4,1,3,7,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,7,1,3,8,2,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [4,7,8,1,2,6,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [1,8,6,4,2,7,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [8,7,1,3,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [6,8,5,7,3,2,1,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [1,8,4,3,7,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [2,4,3,7,8,6,1,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,7,6,8,3,2,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [8,1,4,3,7,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [8,2,3,4,7,6,1,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [4,2,3,8,5,6,1,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [8,2,3,7,5,6,1,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [3,7,4,8,5,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [1,4,8,3,6,2,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [7,5,8,6,3,2,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [6,5,8,7,3,2,1,4]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [8,5,7,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [2,5,3,8,7,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [1,8,7,3,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [6,8,7,5,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [5,7,6,8,3,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [3,7,6,8,4,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [1,5,4,7,6,8,2,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [1,7,4,6,5,8,2,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [3,7,4,6,5,8,1,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [3,5,4,8,6,7,1,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [3,8,4,6,5,7,1,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [3,6,4,7,5,8,1,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [1,6,2,7,5,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,6,4,8,5,7,2,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [1,8,4,6,5,7,2,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [1,5,4,8,6,7,2,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [7,8,1,5,4,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,8,1,5,2,4,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,8,2,6,5,7,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,7,2,8,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,2,6,5,8,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,5,2,7,6,8,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,7,6,8,2,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,7,6,8,4,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [5,7,6,8,1,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [7,8,5,6,1,3,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [5,8,6,7,1,3,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [1,3,2,7,6,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,7,6,8,2,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,8,1,3,2,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,8,1,6,2,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,8,6,7,2,4,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,8,1,4,2,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,8,1,4,2,5,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [7,8,2,1,4,3,6,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [4,3,6,5,8,7,1,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [3,4,1,5,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,4,5,1,6,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,4,5,6,1,7,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,4,5,6,7,1,8,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,4,5,6,7,8,1,9,2]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,1,2,5,6,7,8,9,4]=>[[1,2,4,6,7,8,9],[3,5]]=>01010000 [3,4,1,5,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,4,5,1,6,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,4,5,6,1,7,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,4,5,6,7,1,8,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,4,5,6,7,1,2,9,8]=>[[1,2,5,6,7,8],[3,4,9]]=>01000001 [3,4,5,6,7,8,1,9,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [3,4,5,6,7,8,1,2,9]=>[[1,2,5,6,7,8,9],[3,4]]=>01000000 [3,4,5,6,7,8,9,1,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [1,6,2,3,8,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,7,4,3,2,8,6,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [1,4,7,6,2,5,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [1,2,6,5,3,7,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,2,6,5,3,7,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,3,7,5,2,6,8,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,3,7,4,2,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,2,6,4,3,7,8,5]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,2,6,4,3,7,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,4,7,3,2,5,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [1,4,3,2,5,8,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [1,5,3,2,4,8,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [1,7,5,3,2,8,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [1,5,3,2,4,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [7,6,5,4,3,1,8,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [6,8,5,4,3,2,1,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [8,7,6,5,4,3,1,9,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>01111110 [7,9,6,5,4,3,2,1,8]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]=>11111101 [9,8,7,6,5,4,3,1,10,2]=>[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>011111110 [1,7,6,5,4,3,9,8,2]=>[[1,2,8],[3,9],[4],[5],[6],[7]]=>01111101 [7,1,5,4,3,8,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [3,6,5,4,8,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [6,8,1,4,3,2,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [2,8,5,4,3,7,1,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [8,10,7,6,5,4,3,2,1,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>111111101 [1,8,7,6,5,4,3,10,9,2]=>[[1,2,9],[3,10],[4],[5],[6],[7],[8]]=>011111101 [8,1,6,5,4,3,9,7,2]=>[[1,2,7],[3,9],[4],[5],[6],[8]]=>01111010 [7,6,1,4,3,8,5,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [4,6,5,8,3,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [6,8,5,1,3,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [1,8,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [3,8,5,4,7,2,1,6]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [9,1,7,6,5,4,3,10,8,2]=>[[1,2,8],[3,10],[4],[5],[6],[7],[9]]=>011111010 [7,6,5,1,3,8,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [1,6,3,4,8,7,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,4,5,8,3,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [6,8,5,4,1,2,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [1,8,5,2,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,8,2,4,3,7,1,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [1,8,3,4,7,2,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,9,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8],[9]]=>00110111 [7,5,8,4,3,2,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [4,8,5,7,3,2,1,6]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [8,4,7,5,2,6,1,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [5,4,6,8,2,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [8,4,6,5,2,1,7,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [4,8,7,5,6,1,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [2,7,5,1,8,4,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [5,1,8,7,4,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [2,8,6,7,4,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [3,6,5,2,4,1,8,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [5,2,3,6,4,1,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [6,1,4,5,3,2,8,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [3,8,7,1,4,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [5,7,1,2,4,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [4,3,7,6,8,2,5,1]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [5,3,6,8,1,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [3,2,6,8,5,7,1,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [6,3,7,2,4,8,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [7,4,8,6,5,2,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [7,1,8,2,5,4,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [2,5,3,7,4,1,8,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [3,6,4,7,5,1,8,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [8,4,7,6,2,3,1,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [8,4,7,1,2,5,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [4,2,8,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,1,7,4,2,5,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [7,4,3,8,2,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,4,1,5,8,2,7,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [2,5,8,7,3,6,1,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [2,1,5,8,7,4,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [8,3,5,6,7,4,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [7,4,3,2,8,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [4,2,7,1,8,5,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,1,7,2,8,5,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [2,4,8,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [4,7,8,3,1,5,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [3,4,7,2,8,5,6,1]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,7,1,4,8,5,6,2]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [7,2,3,4,8,5,6,1]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [6,1,8,5,2,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [2,1,7,4,5,8,6,3]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,1,8,3,6,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,2,1,6,4,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [7,8,2,6,4,1,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [2,6,3,5,8,7,1,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [7,6,2,1,5,8,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [4,5,2,7,6,1,8,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [5,1,6,8,4,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [3,6,8,7,5,2,1,4]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [7,4,8,6,5,2,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [8,1,6,4,7,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [7,6,4,1,2,3,8,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [2,6,4,8,5,3,7,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [7,3,5,8,4,2,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [3,2,5,8,4,1,7,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [8,4,7,1,5,2,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [4,8,7,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [6,1,4,8,7,3,5,2]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [7,2,8,4,3,5,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [4,7,8,1,3,5,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [8,7,3,4,1,5,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [4,8,2,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [3,1,8,7,2,5,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,8,1,7,2,5,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,2,3,7,1,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [6,4,8,7,1,3,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [2,8,4,6,7,3,1,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [4,3,8,2,7,6,1,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [6,8,4,2,1,3,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,8,2,4,3,5,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [2,8,3,7,1,5,6,4]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [8,1,2,7,3,5,6,4]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [6,4,1,3,2,8,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [5,3,8,6,2,1,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [4,6,5,2,8,3,1,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [4,3,7,5,1,8,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [6,8,5,2,7,4,3,1]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [7,2,5,4,3,8,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [3,6,8,1,4,5,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [6,8,1,2,4,5,3,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,1,6,2,4,5,3,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [3,8,6,1,2,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [5,8,1,6,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [4,1,6,5,8,2,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [4,3,8,6,2,5,1,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [8,3,6,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [2,3,6,8,4,5,1,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,7,5,4,3,8,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [6,3,8,7,4,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [5,8,4,3,7,6,1,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [8,7,4,3,1,6,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [1,7,4,3,8,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [7,1,5,3,4,8,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [2,8,6,1,7,4,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [4,8,6,5,7,2,1,3]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [4,7,6,8,2,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,1,8,7,4,3,5,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,5,4,3,1,6,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [1,5,8,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [2,5,8,6,3,4,7,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,1,3,8,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [6,5,8,4,3,1,7,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [4,6,5,2,8,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [7,2,8,1,3,6,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [1,8,5,2,3,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,8,3,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [2,8,3,1,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [4,8,3,2,5,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [8,2,3,1,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [2,1,8,3,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [1,4,8,2,3,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [3,1,2,7,8,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [7,5,1,8,2,4,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [3,5,8,1,2,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,5,8,1,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,2,7,1,8,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [3,8,4,1,2,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [5,4,8,2,3,6,7,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,8,3,6,7,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [2,3,1,6,8,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,4,3,7,1,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [1,4,7,3,2,8,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [2,7,1,4,3,8,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,4,1,8,6,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [8,4,1,3,6,2,7,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [6,8,5,1,7,2,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [7,3,6,5,8,2,1,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [7,6,3,5,8,2,1,4]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [4,5,8,7,3,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [3,5,2,8,6,1,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [8,2,5,6,1,4,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [8,6,5,4,1,2,7,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [2,6,1,8,3,7,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [4,7,1,6,2,8,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [6,1,5,3,8,7,2,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [2,8,6,3,7,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [7,6,1,5,8,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [3,6,8,5,1,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [6,5,2,4,8,1,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [5,1,4,8,2,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [4,8,2,5,1,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [3,4,8,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [4,2,1,8,5,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [1,5,4,8,2,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [7,2,1,5,8,6,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [2,8,4,5,1,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [5,4,8,3,7,6,1,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [3,1,5,8,6,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [6,3,4,8,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [5,3,4,8,1,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [7,6,1,2,8,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,5,8,4,1,2,6,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,5,8,4,6,1,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [6,5,4,8,7,1,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [6,5,4,8,1,2,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [7,5,1,6,2,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [7,5,1,6,8,2,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,5,4,1,8,2,7,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [6,5,4,7,1,2,8,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,5,4,7,8,1,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,5,3,7,1,4,2,8]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,5,3,1,8,4,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,5,1,4,8,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [8,1,6,4,7,3,5,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [7,5,1,4,8,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [6,5,3,7,1,4,8,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,4,3,1,5,8,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [7,4,1,5,3,8,6,2]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [8,1,5,4,3,7,6,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [8,1,5,4,3,7,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [7,4,1,5,3,8,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [7,4,1,5,3,2,6,8]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [8,1,5,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [8,1,6,4,2,5,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [6,5,3,1,2,7,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,5,3,8,1,4,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,6,8,1,4,3,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [8,1,7,2,5,4,3,6]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [8,1,7,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [7,6,1,2,5,4,8,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [6,5,3,8,1,4,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [6,5,3,1,2,7,8,4]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [7,5,1,4,2,6,8,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [8,1,6,4,2,5,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [7,4,1,5,3,2,8,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [6,4,3,1,5,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [6,4,3,1,5,7,2,8]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [7,4,1,5,3,6,2,8]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [8,1,5,4,3,6,2,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [8,1,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [7,4,1,5,3,6,8,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [6,4,3,1,5,7,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [6,7,3,8,4,5,1,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,7,4,5,1,8,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [4,7,5,6,2,3,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [4,7,5,6,1,8,2,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,7,5,6,3,8,1,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [3,7,5,8,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [4,5,3,8,6,7,1,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,8,3,6,5,7,1,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [5,6,4,7,1,8,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [5,6,1,7,3,8,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,1,8,2,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [5,6,1,8,4,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [4,8,1,6,5,7,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [4,5,1,8,6,7,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [7,8,4,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [4,8,2,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [5,6,2,8,1,4,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,6,3,4,1,8,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [3,6,4,5,2,7,1,8]=>[[1,4,5,7,8],[2],[3],[6]]=>1100100 [3,6,4,5,1,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [2,6,4,8,1,5,3,7]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [2,8,3,6,1,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,8,3,4,1,6,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [7,8,2,5,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [7,8,1,5,3,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [1,5,3,8,6,7,2,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [1,8,3,6,2,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,6,4,8,2,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [2,6,4,7,3,5,1,8]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [2,7,3,6,4,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [1,7,3,6,4,8,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,7,2,8,4,6,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,7,5,8,4,6,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [1,7,5,8,2,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,5,6,3,8,2,4]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [2,7,5,6,3,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [6,7,2,5,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [6,7,1,5,3,8,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,7,5,8,1,4,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,8,6,7,2,3,1,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [6,7,2,3,1,8,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [6,7,2,8,1,4,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [3,4,2,7,5,6,1,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,4,1,7,5,8,2,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [2,7,5,8,1,4,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [2,3,1,7,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,3,1,8,4,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [7,8,2,3,1,6,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [7,8,2,6,1,4,3,5]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [2,8,6,7,1,4,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [2,8,1,4,3,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,7,2,5,4,6,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [4,5,2,7,3,6,1,8]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,5,1,8,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [3,4,1,8,2,7,5,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,4,1,8,6,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,4,2,5,1,8,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,4,2,8,1,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,8,2,5,1,6,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [4,5,2,8,1,6,3,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,5,3,6,1,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [8,6,7,1,4,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [8,6,3,7,5,1,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [7,6,1,8,3,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,6,2,8,3,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [7,6,2,3,8,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [8,6,2,7,3,1,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [8,4,2,1,7,6,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,5,7,2,1,4,3,6]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [5,8,7,3,1,4,2,6]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [5,8,7,3,1,4,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [8,5,7,2,1,4,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,4,2,1,3,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [8,4,3,1,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [8,5,1,3,2,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,2,8,6,4,1,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [8,4,7,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,4,7,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [8,3,2,6,5,1,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [4,8,6,3,5,1,2,7]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,8,7,3,1,5,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,3,2,7,1,5,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,7,3,1,4,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [8,7,3,1,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,7,3,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,3,2,1,4,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,3,2,1,7,4,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [8,3,2,7,1,5,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [8,4,7,2,1,5,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,7,2,1,6,3,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [3,6,5,4,1,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [3,8,5,6,7,4,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [4,7,5,8,6,2,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [2,5,7,8,6,3,4,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [4,8,5,7,6,3,1,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [4,6,3,2,1,5,8,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [6,2,1,5,3,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [5,8,1,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [4,7,2,3,6,1,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [3,7,4,2,8,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [4,2,6,8,5,7,3,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [6,4,2,7,3,8,5,1]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [8,1,6,7,5,3,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [2,1,5,8,7,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [2,1,4,7,6,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [6,4,7,8,5,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [4,1,3,7,6,2,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [8,5,1,6,3,2,7,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [6,3,7,1,5,2,8,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [3,2,6,8,4,7,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [8,4,6,1,3,2,5,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,2,8,6,7,3,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [7,4,3,8,2,1,5,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [4,7,5,8,1,6,3,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [6,4,3,2,7,8,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [4,2,5,1,6,7,8,3]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [2,4,8,5,7,1,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,7,1,4,6,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [7,8,2,5,6,1,4,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [2,4,3,8,7,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,6,7,3,5,1,8,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [7,6,8,4,2,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [8,5,7,1,6,3,2,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [6,5,7,2,8,4,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [3,4,8,6,5,2,1,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [2,7,6,1,4,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [6,5,8,2,1,7,3,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [7,4,3,5,1,6,8,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [4,1,6,3,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [6,2,5,8,4,3,7,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [8,6,7,1,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [2,1,6,5,8,4,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,1,6,8,5,4,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [4,1,8,5,6,2,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [2,6,4,8,7,3,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [6,2,8,4,3,5,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [4,8,2,7,6,1,3,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [3,1,8,2,7,5,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,8,1,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [5,8,4,3,2,7,1,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [7,4,8,6,3,2,5,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [5,8,4,7,2,1,3,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [2,1,8,4,3,7,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [6,3,8,2,4,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,8,4,2,3,6,1,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,8,2,4,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,8,3,1,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [8,2,1,3,4,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [1,4,8,2,6,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [1,2,7,3,5,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,2,3,8,4,5,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,2,8,3,4,5,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,3,8,2,6,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,5,7,2,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,7,2,3,5,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [1,3,8,2,4,5,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,2,3,8,4,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,8,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,7,8,2,3,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,6,7,8,2,3,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,7,8,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,8,2,4,5,3,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [1,2,8,3,6,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,8,2,3,6,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,2,8,3,5,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,2,7,8,3,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,5,2,7,8,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,3,2,8,4,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,8,2,3,4,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,7,8,2,4,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [6,7,3,1,5,2,8,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,8,3,1,5,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [6,7,4,5,1,2,8,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [6,7,5,4,1,2,8,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [6,4,7,5,1,2,8,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [6,2,1,7,5,3,8,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,3,8,1,5,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [5,6,8,4,1,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [4,6,8,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [4,5,8,6,7,1,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [5,4,8,6,1,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,3,8,1,6,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [5,2,1,7,6,8,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,4,7,6,1,8,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [4,8,6,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [4,7,5,6,8,1,2,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,6,5,7,8,1,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [5,7,4,6,1,8,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,8,4,6,1,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,8,3,1,6,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [5,7,3,1,6,8,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,6,3,1,7,8,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,8,3,1,7,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,7,4,8,1,6,2,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [5,4,6,8,1,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [4,8,6,7,5,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [5,2,1,7,8,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [5,3,8,1,7,6,2,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [5,4,8,7,1,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [4,6,8,7,5,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [4,7,8,6,5,1,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [4,8,7,6,5,1,2,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [2,5,4,7,3,6,1,8]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [2,4,6,3,7,5,1,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [4,2,7,3,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [4,2,6,3,1,5,8,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [2,5,3,1,6,4,8,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [2,5,3,7,6,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [2,6,5,3,7,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [4,2,7,6,3,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [2,7,5,3,6,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [2,6,3,7,5,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [1,7,5,2,3,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [2,1,3,7,5,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,3,1,8,6,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,5,3,1,8,6,4,7]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [4,2,8,3,1,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [8,3,2,6,4,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,6,8,2,1,4,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [1,5,2,8,3,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,6,3,8,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,8,3,6,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,7,6,3,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [2,1,3,8,7,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [1,2,3,8,6,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,3,7,4,8,6,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,7,6,3,8,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,3,6,4,8,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,3,7,6,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [2,6,3,1,8,5,4,7]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [2,1,3,8,5,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [7,1,8,4,2,3,5,6]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [2,1,8,4,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [4,2,6,3,1,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,4,2,8,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [3,5,8,2,4,1,6,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [2,5,4,8,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [4,2,1,8,3,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [1,8,7,4,2,3,5,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,5,2,8,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,2,7,3,6,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,8,6,3,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,7,3,8,6,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,3,8,4,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,2,7,3,4,8,6,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,6,3,8,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,5,2,3,8,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [4,2,1,8,3,7,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [8,3,2,1,7,4,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [1,8,4,2,7,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,2,8,6,3,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,7,3,8,4,6,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,2,3,8,7,4,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,2,3,8,7,6,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [2,5,3,8,1,6,4,7]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [3,8,5,7,2,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [3,4,8,6,1,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [2,5,7,1,4,8,6,3]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,4,8,1,5,7,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,4,3,8,1,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,4,8,1,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,5,7,6,2,4,8,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [4,8,6,7,1,2,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [3,8,5,7,1,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [3,2,8,5,6,1,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,4,8,6,2,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [5,8,6,7,3,4,2,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [5,8,6,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [5,8,6,7,2,1,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [4,3,1,7,5,2,8,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [4,3,8,5,1,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,8,6,7,1,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [5,8,6,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [4,2,3,8,5,1,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,4,8,6,1,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,5,7,6,1,4,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [4,3,8,5,2,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,8,5,7,1,4,2,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [3,8,4,7,1,5,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [3,8,4,7,2,5,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [4,1,2,6,7,5,3,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [3,4,1,7,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [4,1,7,5,2,8,6,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [4,8,6,7,2,3,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [5,8,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [5,8,6,7,4,1,3,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [5,8,6,7,3,1,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [4,8,6,7,3,1,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,1,6,7,5,3,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [5,8,6,7,4,2,1,3]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [5,8,6,7,4,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [7,3,5,8,1,4,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [3,8,7,6,1,4,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [5,1,8,3,6,7,2,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [1,4,7,8,5,6,2,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [3,4,7,1,5,8,6,2]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [3,6,1,4,7,8,5,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [1,6,8,4,7,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [6,8,1,3,5,7,2,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [7,6,1,4,3,8,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [3,8,1,6,5,4,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [4,1,3,7,5,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [6,1,7,3,8,4,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [7,1,8,6,3,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [3,1,7,6,5,8,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [8,2,7,6,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [8,4,2,6,7,5,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [4,8,1,6,7,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [7,4,1,6,8,2,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [1,3,8,6,2,7,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [6,1,3,2,7,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [1,8,6,2,5,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [4,7,2,6,8,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [8,7,3,6,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [5,7,8,6,2,1,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [2,7,4,1,6,8,3,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [3,7,2,4,5,1,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [1,8,6,4,5,2,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [2,8,4,6,5,1,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [3,4,1,7,5,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [7,5,8,6,1,2,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [5,6,8,7,3,1,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [2,5,4,3,6,8,1,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [3,8,5,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [4,8,2,1,3,7,5,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [6,4,1,2,7,5,8,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [4,1,8,3,6,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,3,7,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [4,3,7,8,5,1,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [5,4,8,2,7,6,1,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [1,2,7,3,6,5,8,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [2,8,7,6,3,4,1,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [5,8,2,6,3,4,1,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,1,7,5,8,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [5,1,7,8,4,3,6,2]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [8,2,7,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [6,3,8,1,4,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [3,8,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [1,4,3,5,7,8,2,6]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [6,5,8,7,1,3,4,2]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [3,6,7,2,4,8,1,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [1,5,2,7,4,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [2,8,5,6,4,3,1,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>1011001 [1,8,6,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [6,1,5,2,8,4,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [4,6,1,8,5,7,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [4,7,1,2,8,5,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [1,4,7,2,8,5,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [1,7,3,5,8,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,3,5,8,6,1,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [3,6,8,1,5,7,2,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [3,4,6,5,8,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [6,8,1,5,7,2,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [7,1,2,5,8,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,2,5,8,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,7,6,8,2,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,6,8,1,2,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [2,7,1,5,8,6,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [2,4,7,1,8,5,6,3]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [4,7,5,8,3,1,6,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [4,7,2,1,8,5,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [7,6,8,2,1,3,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [1,2,7,6,8,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [3,7,6,8,2,1,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [7,4,2,1,6,8,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,7,4,1,8,5,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,7,4,3,1,8,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [2,7,4,1,6,8,5,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,3,7,6,8,1,5,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [7,4,2,6,8,5,1,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [7,3,2,5,8,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [3,1,7,6,8,2,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [3,7,6,8,1,2,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [1,3,7,6,8,2,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,7,4,2,6,8,5,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,4,1,2,6,8,5,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,1,4,2,8,5,6,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [7,1,8,2,5,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,3,8,4,6,1,5,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [7,2,8,1,6,4,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,1,6,8,5,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,1,2,6,8,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,7,2,6,8,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,7,6,8,3,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,6,8,3,1,2,5,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [7,1,5,8,6,3,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [7,2,5,8,6,3,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [3,6,7,1,8,5,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [7,2,6,8,5,4,1,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,6,8,2,3,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [2,7,6,8,3,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [2,7,1,6,8,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [6,7,3,1,8,5,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [6,7,1,8,5,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,2,1,6,8,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,6,8,3,2,1,5,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [4,7,8,5,6,1,3,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [4,6,5,8,7,1,3,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [5,6,4,8,1,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [8,1,5,6,7,2,4,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [6,4,5,1,8,2,7,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [5,4,6,7,1,2,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,3,6,7,2,1,5,8]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [5,3,6,7,1,4,2,8]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [8,1,4,6,7,3,2,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,1,3,6,7,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,2,1,6,8,4,5,3]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [5,2,6,7,1,4,8,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [4,2,6,7,3,1,8,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [6,2,4,1,5,8,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [7,2,1,5,4,8,6,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [8,1,4,5,3,7,2,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [7,3,1,5,4,8,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [6,3,4,1,5,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [5,3,4,2,1,8,6,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,3,5,2,7,1,6,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [5,6,3,8,1,4,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [8,1,7,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [7,6,1,2,4,5,8,3]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [4,7,8,2,3,1,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [5,6,2,8,1,4,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [6,5,2,1,3,7,8,4]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [7,5,1,3,2,6,8,4]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [8,1,6,3,2,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [7,4,1,3,5,2,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [5,4,2,3,1,6,8,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [7,3,1,4,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [8,1,4,3,5,6,2,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [6,2,3,1,5,7,8,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [7,8,4,2,1,6,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [7,8,4,2,1,5,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,8,3,4,6,2,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [6,2,3,8,7,5,1,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [6,2,3,7,8,5,1,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [5,2,6,3,8,1,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [6,4,3,8,7,5,1,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [6,2,4,1,7,3,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [4,5,6,8,3,2,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [5,6,1,4,2,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [5,6,8,4,3,7,1,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,2,8,3,4,1,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [4,6,5,8,3,2,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,2,3,4,5,8,1,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [5,1,4,3,6,2,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [5,1,4,3,7,2,8,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,1,4,3,8,2,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [5,6,2,4,1,7,8,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,7,2,4,1,8,6,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [6,1,4,2,7,8,5,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [5,2,7,4,1,6,8,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [5,1,6,3,4,2,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [4,8,6,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>1110101 [4,8,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [5,4,7,8,3,2,1,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,8,7,3,2,1,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [4,7,6,8,3,2,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [5,7,1,3,4,2,6,8]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [5,1,8,4,2,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,1,7,4,2,3,6,8]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [5,8,1,3,4,2,6,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [4,8,7,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [4,8,2,6,3,7,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [4,3,8,1,6,2,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [4,3,8,7,2,5,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,8,4,3,7,1,6,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [6,8,1,2,4,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,8,7,1,3,4,2,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [4,8,7,6,3,1,2,5]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [4,3,8,2,7,5,6,1]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [1,4,3,8,2,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [4,3,2,8,1,6,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,1,3,8,2,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [4,1,8,3,7,5,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [3,7,8,1,5,4,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [7,3,8,1,5,4,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [3,4,8,1,6,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,4,2,1,8,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,6,7,8,4,1,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [4,1,7,8,5,3,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [3,7,6,8,4,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [3,7,8,2,6,4,5,1]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [4,2,3,8,1,6,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,3,1,8,2,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [2,6,8,4,7,3,1,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [7,6,2,8,3,5,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [3,2,4,8,1,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [2,4,8,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [7,4,1,8,5,2,6,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [1,3,2,4,8,6,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,2,4,8,6,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [3,1,4,8,2,6,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,7,4,8,5,1,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [6,7,2,8,3,5,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [2,1,3,4,8,6,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [1,2,3,4,8,6,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [4,8,3,6,2,1,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [3,5,8,2,6,1,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,6,5,8,2,4,1,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [5,3,8,7,2,4,6,1]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [2,8,4,5,7,3,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,4,5,7,3,8,1,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [6,2,4,5,8,3,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [4,8,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [8,1,3,5,2,6,4,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [5,2,1,6,3,8,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [6,2,5,1,8,4,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [3,6,1,5,8,4,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [6,1,4,5,8,3,2,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [5,6,4,8,1,3,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [6,5,4,3,8,2,1,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [5,4,3,7,2,8,1,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,8,4,3,7,2,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [4,6,8,3,7,2,5,1]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [7,4,6,3,2,8,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [1,4,3,6,2,7,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,5,4,3,7,2,8,6]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [4,7,8,5,3,1,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [5,7,3,4,1,2,8,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [8,5,4,7,6,2,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [8,5,7,4,3,6,1,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [4,3,8,1,6,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,7,8,3,6,1,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [5,3,8,6,7,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [1,3,8,6,4,7,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [8,6,2,7,4,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [7,6,2,1,4,3,8,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [7,6,1,3,4,2,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,5,7,3,2,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [1,6,7,3,2,5,8,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [3,2,6,8,5,7,4,1]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [5,8,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [7,5,2,3,1,6,8,4]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [1,6,4,7,2,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [3,1,7,5,2,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [2,5,7,4,1,8,3,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [4,2,6,1,7,8,3,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,7,6,3,8,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [6,4,8,7,2,3,5,1]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [3,2,6,8,7,4,5,1]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [3,2,7,4,1,6,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [6,3,2,1,7,8,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [3,7,1,8,4,2,5,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [4,2,1,3,7,5,8,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [8,1,3,7,4,2,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,4,3,7,6,2,1,5]=>[[1,5],[2,6],[3,7],[4],[8]]=>1110111 [8,3,5,2,7,6,1,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,6,2,8,7,1,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,3,2,8,1,6,5,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [3,8,7,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [4,2,7,8,6,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,8,2,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [5,2,1,8,7,3,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [8,2,1,6,3,7,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [6,8,3,1,7,5,2,4]=>[[1,2,4],[3,5],[6,7],[8]]=>0101101 [5,8,1,6,7,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [6,2,8,1,5,7,4,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [5,7,8,2,6,1,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [8,7,2,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [8,6,7,5,2,4,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [7,2,6,8,1,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [1,2,7,8,5,6,4,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,4,8,1,6,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [3,7,1,8,2,6,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [2,1,7,3,8,6,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [8,2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,1,4,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [8,6,7,5,1,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,8,6,5,4,1,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [5,8,4,3,2,1,6,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [6,4,7,3,2,1,8,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,5,3,7,2,1,4,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [5,8,3,6,2,1,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,3,7,6,2,1,4,8]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [3,8,7,6,2,1,4,5]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [5,8,4,2,6,1,3,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [4,8,7,2,5,1,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,8,3,2,5,1,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [4,3,7,2,5,1,8,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [6,4,2,7,5,1,3,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,2,7,8,5,1,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [5,2,7,6,8,1,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [4,2,7,6,5,1,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [2,8,7,6,5,1,3,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [6,5,4,3,1,7,8,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,4,7,3,1,5,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [5,4,7,3,1,8,6,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,4,3,6,1,8,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,3,7,6,1,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [4,3,7,6,1,5,8,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [3,8,7,6,1,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [4,8,7,2,1,5,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [5,8,3,2,1,4,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [3,8,7,2,1,4,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [5,8,2,6,1,4,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [6,4,2,7,1,5,3,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [3,2,7,6,1,4,5,8]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,8,4,1,6,7,3,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [6,4,7,1,5,8,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [4,8,7,1,5,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [4,8,3,1,5,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [5,8,2,1,6,4,3,7]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [3,8,2,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [6,2,7,1,5,4,3,8]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [5,2,7,1,6,4,3,8]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [3,2,7,1,5,4,6,8]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [2,8,7,1,5,4,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [6,4,1,7,5,8,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [5,4,1,6,7,8,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [6,3,1,7,5,4,8,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [5,3,1,6,7,4,8,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [4,3,1,6,5,7,8,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [2,8,1,6,5,4,3,7]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [6,1,7,8,5,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [4,1,7,6,5,8,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [4,5,8,1,2,6,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [1,4,5,7,2,6,3,8]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [1,7,3,5,6,2,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [8,1,3,5,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,6,8,1,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [3,4,5,6,8,1,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,5,8,2,6,7,1,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [8,2,3,5,6,7,1,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [1,7,2,3,5,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [8,1,2,3,5,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [2,7,8,1,3,5,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,7,8,3,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [2,4,5,7,8,1,6,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [4,5,8,1,7,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [4,5,8,7,2,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,7,3,5,6,2,1,4]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,7,2,1,3,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [3,6,8,7,2,1,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [8,6,4,1,7,5,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [7,6,4,3,1,8,5,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [2,3,6,7,8,1,5,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [3,6,8,1,2,5,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [1,3,6,7,2,5,4,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [7,4,1,8,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [7,1,4,2,8,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,1,8,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [8,1,7,5,4,2,3,6]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [1,7,2,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,7,6,3,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [8,6,3,1,2,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,1,7,6,3,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [8,2,5,7,6,3,1,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [3,6,8,1,7,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [8,2,6,7,5,4,1,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [2,7,8,6,3,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [2,7,8,1,6,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,3,1,8,6,5,4,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [8,7,2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,7,6,3,2,1,5,4]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [2,1,8,6,3,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [8,6,1,5,2,7,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [8,5,1,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [2,1,7,5,4,3,8,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [2,1,7,8,3,6,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,1,4,8,5,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,5,3,1,6,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [6,4,1,5,2,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [8,3,7,5,2,6,1,4]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [5,3,7,4,6,8,1,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [5,8,3,7,6,2,1,4]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [4,2,6,3,8,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,8,2,1,7,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [8,3,2,4,1,7,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [7,2,8,1,4,6,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [6,8,1,4,5,3,2,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [8,2,6,1,4,7,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [8,3,5,6,1,7,4,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [6,3,5,4,1,2,8,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [8,7,3,6,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [2,7,4,3,6,1,8,5]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [3,4,7,2,8,1,5,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [4,2,3,5,8,1,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,8,4,7,1,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [8,3,4,5,7,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [3,2,4,5,6,8,1,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [5,6,8,1,4,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [1,5,7,8,4,6,2,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [1,3,5,7,8,6,2,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [3,5,7,8,6,1,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [3,5,1,6,8,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [3,1,5,6,8,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [2,3,5,6,8,1,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [5,6,4,8,2,1,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [5,1,6,3,8,4,7,2]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [2,5,1,6,8,3,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [5,1,2,6,8,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [5,7,1,8,6,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,5,2,7,8,6,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,6,7,5,2,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,7,5,2,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [2,6,7,5,1,8,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [5,7,2,8,6,1,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [3,5,7,8,6,2,1,4]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [5,1,7,8,6,3,4,2]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [5,1,3,7,8,6,4,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [5,2,7,8,4,6,1,3]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [3,2,5,7,8,6,1,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [6,2,7,5,1,8,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [1,2,6,7,5,8,3,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [6,2,7,5,4,1,8,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,5,2,4,1,8,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,7,2,5,3,8,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [6,7,4,5,2,1,8,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [5,1,7,8,6,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [2,5,7,8,6,3,1,4]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [5,1,7,8,6,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [6,3,7,5,1,8,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [1,6,7,5,3,8,2,4]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [1,6,7,5,4,2,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [6,7,5,1,4,2,8,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [5,7,8,6,4,1,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [4,1,7,2,6,5,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [2,4,7,1,5,6,8,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [6,7,4,1,5,2,8,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [1,6,7,4,5,2,8,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,6,3,7,5,8,2,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [6,3,1,7,5,8,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [2,5,3,7,8,6,1,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [6,7,5,4,2,1,8,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [6,3,2,7,5,8,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,7,4,2,5,1,8,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,2,7,4,5,1,8,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [6,2,3,7,5,8,1,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [7,5,1,6,3,8,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [2,7,6,1,3,8,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [7,3,5,1,8,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [7,3,5,1,8,2,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [3,7,5,1,8,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [2,6,7,4,1,8,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,1,6,7,3,8,5,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,6,5,1,8,4,7,2]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [3,6,5,1,8,4,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [4,6,1,5,8,7,3,2]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [7,5,1,6,2,8,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [2,3,4,7,8,1,6,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [6,8,5,4,3,2,7,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [8,9,6,5,4,3,2,1,7]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010 [6,8,5,4,3,7,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [5,8,4,3,2,1,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,5,4,3,1,8,7,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [8,7,6,5,4,3,9,1,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>01111110 [8,7,5,4,3,1,6,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [8,3,4,6,2,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [3,5,6,2,1,8,4,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,2,6,8,4,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [7,5,3,2,8,4,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,5,3,2,8,4,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [2,4,5,7,3,8,6,1]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [4,2,5,6,8,3,1,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,2,8,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [2,5,6,1,8,4,3,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [5,3,6,8,1,4,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [4,5,6,8,1,3,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [1,4,5,6,8,3,2,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [4,5,6,3,8,2,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,5,3,7,2,8,6,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [6,4,7,3,2,8,5,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,1,4,7,3,2,8,5]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [1,7,8,4,5,3,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [5,1,7,3,8,4,2,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [2,5,1,7,4,3,8,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,5,7,4,1,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [5,3,7,1,4,8,6,2]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [6,4,3,1,7,8,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,1,7,3,8,5,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [5,6,3,7,8,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,1,6,3,7,8,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,1,3,7,8,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,1,7,8,3,4,2]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [1,6,3,7,4,8,5,2]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,7,2,4,1,8,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,7,2,1,4,3,8,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,4,7,3,1,2,8,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [5,6,3,1,2,7,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,1,3,2,7,8,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [5,6,3,2,1,7,8,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [2,5,6,3,7,8,4,1]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [2,5,6,3,1,7,8,4]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [2,6,4,7,3,1,8,5]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [6,3,7,2,8,4,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,3,7,2,8,4,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [6,3,2,7,1,8,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [7,5,3,2,1,8,4,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,3,8,4,2,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [4,7,2,1,3,8,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [1,3,7,8,6,4,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,3,8,4,6,2,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [5,7,3,8,2,1,6,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [6,3,7,8,5,2,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [4,6,2,7,8,5,3,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [4,6,2,1,7,8,5,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [7,4,5,8,1,2,6,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [2,5,1,7,3,8,6,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [6,7,2,1,3,8,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [5,1,6,7,8,2,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [6,3,7,1,8,5,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,2,1,7,3,8,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,2,7,1,8,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [6,3,1,7,8,5,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [4,1,3,6,8,2,5,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,2,3,6,8,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [5,3,2,1,8,4,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [3,6,5,8,2,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [4,5,2,1,3,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [3,2,6,4,5,8,1,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,4,6,5,8,1,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [1,6,2,4,5,8,3,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,3,2,1,6,8,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [6,2,4,5,8,1,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [1,3,4,6,5,8,2,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [1,6,3,4,5,8,2,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [3,4,1,8,5,2,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [2,8,4,1,7,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [8,1,4,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,5,3,2,8,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [8,2,1,7,5,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [1,7,6,4,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [5,8,7,4,1,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [5,8,7,4,6,2,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [3,4,2,5,8,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [4,1,3,5,6,8,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [2,4,8,6,7,1,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,3,6,2,8,1,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [3,7,4,8,2,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [2,3,5,8,6,7,1,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [3,2,5,6,8,7,1,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [2,1,8,5,6,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [1,2,8,3,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [4,2,3,7,1,8,6,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [3,2,6,4,8,1,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [8,2,1,6,7,3,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,7,8,5,4,1,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [1,7,5,3,8,4,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [4,7,5,3,1,2,8,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [7,2,4,8,5,3,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [4,8,3,1,2,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,5,2,7,4,1,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [8,4,2,3,7,1,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [2,8,4,7,1,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,2,4,6,7,1,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [4,8,2,3,6,7,1,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [3,5,2,7,6,1,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [1,6,3,2,5,8,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [5,8,3,2,1,6,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,8,7,3,4,6,2,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [5,8,2,7,4,1,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [5,1,4,2,8,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [4,7,6,5,8,2,1,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [5,3,7,1,6,2,8,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [5,2,6,8,7,1,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [6,3,2,1,8,5,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [2,7,5,4,1,8,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [4,2,5,6,8,7,1,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [1,8,4,2,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [3,8,4,1,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,2,8,5,6,7,1,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,2,4,7,1,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [5,3,4,7,1,8,6,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [8,6,4,1,3,2,5,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,1,3,6,5,2,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,1,4,3,6,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [3,6,5,2,1,8,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [8,3,2,4,6,5,1,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,4,2,1,6,5,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [8,4,1,2,6,5,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [8,6,4,2,1,5,3,7]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [8,3,6,4,1,5,2,7]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [8,2,6,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [1,3,4,8,5,7,2,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [5,8,4,7,6,2,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [1,3,4,7,5,8,2,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [1,3,5,2,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,6,5,1,3,8,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [4,7,1,6,5,8,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [5,4,8,7,6,3,1,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [2,8,5,1,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [4,3,1,5,8,6,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,1,3,5,8,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [6,5,3,8,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [5,4,2,1,6,8,7,3]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [6,8,4,3,2,7,1,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [3,4,7,8,2,1,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,1,3,2,8,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,3,1,2,8,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,2,3,1,6,8,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [5,3,2,1,8,6,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,2,1,3,6,8,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [2,4,7,3,8,1,6,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [6,3,8,2,7,4,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [8,2,1,3,6,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [3,5,1,7,8,4,2,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [2,7,4,5,8,3,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [1,8,4,3,7,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,4,8,7,2,1,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [5,4,7,8,3,6,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [6,4,3,8,7,2,1,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,3,8,7,4,1,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [3,5,7,2,4,8,1,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [8,4,7,2,3,1,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,4,7,1,3,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [8,4,7,2,1,3,5,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,6,4,2,1,3,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,6,4,1,3,2,7,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,6,4,2,3,1,7,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [3,5,7,2,6,1,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [6,1,3,8,5,7,2,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [5,8,3,2,6,7,1,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [4,8,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>1110001 [2,8,1,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [1,5,8,7,4,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [2,1,7,6,4,5,8,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [1,7,2,4,6,5,8,3]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [3,5,1,7,6,8,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [5,8,2,6,1,3,7,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [6,3,5,8,7,2,1,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [2,5,7,8,4,1,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [4,2,8,1,5,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,1,5,2,6,8,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,4,5,1,6,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,2,8,5,1,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,1,8,5,2,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [2,7,1,8,5,4,6,3]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [5,8,6,2,1,3,7,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [8,2,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,6,3,5,8,1,7,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [1,7,8,3,5,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [3,4,5,1,8,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [3,8,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [3,4,5,7,8,2,6,1]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,4,6,2,8,5,1,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,4,6,8,1,5,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [3,4,7,2,1,8,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [3,4,8,2,1,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,5,2,7,8,4,6,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,6,2,8,4,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,6,8,4,1,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,5,7,2,4,8,6,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,7,2,8,4,6,1]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [3,5,7,8,4,1,6,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [3,6,2,1,8,5,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [3,6,7,2,8,5,4,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,6,8,2,4,5,1,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,7,2,1,4,8,6,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [3,7,2,8,4,5,6,1]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [3,8,2,1,4,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [4,1,5,6,7,8,3,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [4,1,6,3,7,8,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,1,6,3,8,5,2,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,1,6,7,3,8,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,1,6,8,3,5,2,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,1,7,3,2,8,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,1,8,3,2,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [4,5,2,6,8,1,3,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [4,5,7,3,8,1,6,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,5,8,3,2,1,6,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,6,2,7,8,5,1,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,6,7,3,2,8,5,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,7,2,8,3,5,6,1]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [4,7,8,3,2,5,6,1]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [4,8,2,3,1,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [5,1,2,6,8,4,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,1,6,3,8,4,2,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [5,6,2,3,8,4,1,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [5,6,2,7,8,4,1,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,6,8,3,4,2,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,7,2,3,4,8,6,1]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,7,8,3,4,2,6,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [5,8,2,3,4,1,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [6,1,2,3,7,8,5,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [6,1,2,3,8,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,1,2,7,8,5,4,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [6,1,7,3,8,5,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,1,7,8,4,5,3,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [6,1,8,3,4,5,2,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [6,7,2,3,8,5,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [6,7,2,8,4,5,3,1]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [7,1,2,3,4,8,6,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [7,1,2,8,4,5,6,3]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [7,1,8,3,4,5,6,2]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [6,4,1,8,2,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [5,8,1,2,4,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,3,5,7,2,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [3,5,8,6,1,2,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [3,1,6,8,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [3,6,2,8,1,5,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [2,6,1,3,8,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [1,7,5,2,3,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [2,7,5,1,3,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [8,2,5,7,4,6,1,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,2,1,3,7,6,4,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [8,2,5,1,3,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [8,2,7,5,3,1,6,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [8,2,6,5,4,7,1,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [7,6,5,2,4,8,1,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,8,2,5,3,1,6,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [7,1,8,6,3,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,8,1,5,3,2,4,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [1,6,7,5,3,2,4,8]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [6,5,1,2,4,8,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,8,1,6,4,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [8,4,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [1,7,3,6,5,2,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [8,1,3,7,2,6,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [7,3,2,6,5,1,8,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [7,8,4,2,5,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [8,2,7,4,5,6,1,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,2,3,6,5,1,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [7,9,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>11111101 [2,9,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>10111111 [8,10,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>111111101 [7,10,9,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>111111011 [6,10,9,8,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>111110111 [5,10,9,8,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>111101111 [4,10,9,8,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>111011111 [1,8,7,6,5,3,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [2,8,7,6,3,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [3,10,9,8,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>110111111 [1,8,7,6,5,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [1,9,8,7,6,5,4,2,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>00111111 [2,10,9,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>101111111 [7,2,8,6,5,4,1,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [7,2,8,5,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,3,2,8,5,1,7,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [8,4,7,2,5,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [6,8,5,4,3,1,7,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [5,8,6,4,1,3,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [4,8,6,1,5,3,7,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [3,6,1,8,5,2,7,4]=>[[1,2,4],[3,5,7],[6,8]]=>0101101 [3,4,1,2,8,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [6,8,3,5,4,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,2,5,8,3,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [1,7,5,6,3,4,2,8]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [7,2,6,8,5,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [7,6,3,8,5,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [7,2,6,4,8,3,1,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [1,5,7,4,2,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [4,2,3,1,7,8,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [5,2,8,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [8,6,3,4,7,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [6,8,3,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [1,6,3,2,5,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [8,3,2,1,5,4,7,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [6,3,7,1,5,8,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [2,5,1,8,4,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [6,2,5,4,8,1,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [4,3,1,6,5,8,2,7]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [1,3,5,4,6,8,2,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [6,1,3,4,5,8,2,7]=>[[1,2,4,5,7],[3,8],[6]]=>0100101 [8,3,4,1,5,2,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [7,5,4,2,6,8,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [8,2,6,4,1,7,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [7,3,8,4,5,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,2,5,1,8,4,3,6]=>[[1,3,6],[2,4,8],[5],[7]]=>1011010 [1,7,3,2,5,4,8,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [8,7,2,1,5,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [3,6,1,5,8,7,4,2]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [8,3,6,4,5,1,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [5,4,6,8,1,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [6,4,7,2,3,5,8,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [6,8,4,1,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [3,4,7,8,6,2,5,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,1,3,5,7,8,6,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [6,5,1,8,4,7,3,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [5,3,1,8,4,7,6,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [8,2,7,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [4,7,3,2,8,1,6,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [6,3,1,4,7,2,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [8,7,3,6,1,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [7,4,3,6,8,2,5,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [2,4,7,3,8,5,6,1]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [2,8,6,1,5,7,3,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [7,8,2,5,4,3,1,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [1,8,3,4,2,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,5,3,7,4,2,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [5,7,3,2,4,1,8,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [2,8,3,4,7,1,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [4,1,3,6,7,8,2,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,7,6,3,2,5,8,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [3,8,1,5,6,2,7,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [8,2,5,6,1,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [7,1,5,2,8,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [6,5,4,8,7,2,1,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [1,8,6,4,5,2,7,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [1,8,5,3,6,2,7,4]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [3,6,2,1,7,5,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [2,5,4,1,8,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [4,7,2,6,5,8,1,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,8,1,4,2,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,3,4,7,1,8,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [3,4,7,8,2,5,6,1]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [1,8,2,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [5,2,4,1,6,8,7,3]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [3,2,5,7,6,1,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [4,3,5,6,1,8,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [5,3,4,1,7,6,8,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [3,1,4,6,5,7,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [1,4,7,3,5,6,8,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [1,3,2,7,5,8,6,4]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,2,6,4,8,7,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,3,2,7,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,3,2,8,5,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,5,2,4,8,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,2,6,4,8,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,2,7,8,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [1,3,8,2,6,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,6,7,8,2,5,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,5,7,8,2,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,5,2,7,8,4,6,3]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [1,3,6,2,4,8,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,6,7,3,4,8,5,2]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [1,5,3,7,4,8,6,2]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [2,8,4,1,5,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [1,3,8,4,2,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,2,7,4,8,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [1,2,6,4,8,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,5,2,4,8,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,8,3,5,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,3,8,6,2,7,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,2,6,8,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [1,6,7,8,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,5,7,8,6,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,4,7,6,8,2,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [2,3,8,7,4,1,6,5]=>[[1,3,4,5],[2,6],[7],[8]]=>1000111 [1,2,6,8,7,5,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [1,2,7,8,6,5,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [5,2,6,7,3,4,8,1]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,2,4,7,6,3,8,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,6,2,1,7,8,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,6,2,1,4,8,7,3]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [2,6,1,4,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [5,4,2,7,6,3,8,1]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [2,3,7,6,4,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>1000110 [2,6,1,7,5,8,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,6,1,7,4,8,5,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [5,1,2,7,8,4,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [2,6,1,7,4,8,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,6,4,1,7,8,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [5,4,6,1,3,8,7,2]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [3,6,4,1,5,8,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [2,6,1,5,4,8,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,6,1,4,7,8,5,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [5,1,2,4,8,6,7,3]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,1,2,4,8,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [5,1,2,4,8,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,2,3,8,5,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [4,3,1,2,8,5,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [2,1,5,3,8,6,4,7]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [1,2,3,8,5,6,4,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [1,2,3,8,6,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [1,2,3,8,6,5,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [1,2,3,8,5,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [2,6,1,5,4,8,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [5,1,2,4,8,6,3,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [5,1,2,4,8,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [5,6,3,1,4,8,2,7]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [2,5,4,3,1,8,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,4,6,3,1,8,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [3,6,4,5,1,8,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [3,6,5,4,1,8,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [5,2,6,1,7,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [5,1,6,2,8,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [2,1,3,7,8,6,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,1,3,7,8,5,6,4]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [5,2,4,1,7,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [4,3,1,2,8,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [5,1,4,2,8,6,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [2,1,3,6,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [1,2,3,8,6,7,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,2,3,8,7,5,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,2,3,8,7,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [1,2,3,8,5,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [2,1,3,6,8,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [5,4,1,2,8,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [3,1,6,2,8,7,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [1,2,3,4,5,9,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [1,2,3,4,9,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [1,2,3,9,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [1,2,9,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>00000001 [1,2,3,4,5,6,7,10,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [1,2,3,4,5,9,7,6,8]=>[[1,2,3,4,5,6,8],[7],[9]]=>00000101 [1,2,3,4,5,6,10,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [1,2,3,4,5,10,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [1,2,3,4,10,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [1,8,3,4,2,5,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,2,3,10,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [1,8,4,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,2,10,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>000000001 [8,4,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111 [8,4,7,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [8,5,7,4,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,7,6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111 [8,6,7,3,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [8,5,7,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [8,1,7,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [8,1,7,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [8,2,7,3,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [8,3,7,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [8,5,7,2,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,6,7,2,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [8,7,6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111 [8,4,7,1,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,3,7,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,2,7,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,1,7,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [8,7,6,2,5,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [8,1,7,6,5,3,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [8,3,7,6,5,2,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [8,4,7,6,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [8,5,7,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>1011011 [8,6,7,5,4,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [8,5,7,6,4,1,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [8,3,7,6,5,1,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [8,7,6,4,5,1,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [8,7,6,2,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,7,6,1,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [6,8,1,3,2,5,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [6,8,1,4,2,5,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [7,8,3,6,1,4,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [7,8,2,5,3,6,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [7,8,2,5,1,4,3,6]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [7,8,1,4,3,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [5,8,1,4,3,7,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,8,2,5,1,4,3,7]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [6,8,2,5,3,7,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,8,2,5,4,7,1,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [2,5,4,7,6,8,1,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [2,5,3,7,6,8,1,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [2,5,1,4,3,7,6,8]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [2,6,1,4,3,7,5,8]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [2,6,5,8,1,4,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,6,1,5,3,7,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,6,3,7,4,8,1,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [2,6,4,7,5,8,1,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [5,8,3,6,4,7,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [5,8,2,6,4,7,1,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [4,8,2,6,3,7,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [4,8,1,5,3,7,2,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [4,8,1,5,2,6,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [4,8,3,7,1,5,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [6,8,3,7,1,4,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [5,8,1,3,2,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,8,4,7,1,3,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,8,4,7,1,3,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [6,8,5,7,1,3,2,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [5,7,6,8,2,4,1,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [4,7,6,8,1,3,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [4,7,5,8,1,3,2,6]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [4,7,1,3,2,6,5,8]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [3,7,1,4,2,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,7,5,8,1,4,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [3,7,6,8,1,4,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [3,7,6,8,2,5,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [4,7,6,8,2,5,1,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [4,7,5,8,3,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [4,7,5,8,2,6,1,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [3,7,5,8,2,6,1,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [3,7,4,8,2,6,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [3,7,4,8,1,5,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [3,7,1,5,2,6,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [3,7,2,6,1,5,4,8]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,7,2,6,5,8,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [4,7,3,6,5,8,1,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [3,6,5,8,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [2,6,5,8,4,7,1,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [2,6,5,8,3,7,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [2,6,3,7,1,5,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [7,6,4,2,8,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [6,8,4,3,7,2,1,5]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [6,7,4,3,5,1,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,7,3,5,4,8,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [7,6,8,3,5,2,4,1]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [7,6,3,5,8,2,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [7,6,4,2,5,1,8,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [7,6,3,8,2,4,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,3,4,8,7,2,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [6,3,8,4,7,2,1,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [6,2,8,4,1,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [6,2,7,4,1,5,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [6,3,4,7,5,8,2,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [6,3,5,7,8,4,2,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [5,6,8,3,7,2,1,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [4,6,8,3,5,7,2,1]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [5,3,8,2,4,1,6,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,8,3,6,2,5,7,1]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [4,7,8,3,5,6,2,1]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [6,4,3,5,8,2,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,3,5,8,7,2,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [5,8,3,7,2,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [5,8,4,2,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,8,4,2,3,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,4,5,3,8,2,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,8,5,3,7,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,3,8,5,7,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,4,2,8,5,3,1,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [5,6,3,4,8,2,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [6,4,2,5,1,7,3,8]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [5,3,7,2,4,1,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,5,8,3,6,7,2,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,5,8,3,7,2,6,1]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [5,3,6,8,2,1,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,3,6,7,1,8,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [4,6,3,5,7,8,2,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [4,5,7,3,6,8,2,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [5,7,4,8,6,3,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,5,6,7,2,8,4,1]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [4,5,6,7,8,9,3,2,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>11100000 [3,2,5,4,7,6,9,8,1]=>[[1,4,6,8],[2,5,7,9],[3]]=>11010101 [3,4,5,6,7,8,9,2,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>11000000 [5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>111101111 [4,7,3,9,6,2,10,8,5,1]=>[[1,5,8,10],[2,6,9],[3,7],[4]]=>111011010 [4,5,6,7,8,9,10,3,2,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000 [3,4,5,6,7,8,9,10,2,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000 [1,6,2,5,3,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,3,8,2,4,6,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,7,2,3,6,4,8,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [1,6,8,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [1,8,2,5,3,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,8,2,3,6,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [1,3,5,2,8,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,2,7,3,5,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [1,8,2,7,3,4,6,5]=>[[1,2,3,4,5],[6],[7],[8]]=>0000111 [1,5,8,2,3,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,6,8,2,3,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [5,3,6,1,2,4,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [7,1,5,8,4,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [8,1,5,7,4,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [7,1,4,5,8,2,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [7,4,1,6,2,8,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [8,4,1,7,2,6,3,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,1,4,7,5,2,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [8,1,5,4,7,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [2,1,7,5,8,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [7,1,5,4,8,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,1,4,8,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [6,4,1,7,2,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [7,8,3,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [8,7,1,6,4,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,6,1,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,6,1,8,4,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,3,8,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [8,3,7,1,2,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [8,3,6,1,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [8,3,7,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [7,3,6,1,2,4,8,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [6,7,1,8,4,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,8,1,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,1,8,5,4,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,1,8,4,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [2,1,7,8,5,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [7,6,3,1,2,4,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,1,2,3,8,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,8,1,4,2,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,8,3,1,2,7,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,7,3,1,2,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,7,1,4,2,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [4,3,6,8,5,7,1,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [6,1,2,5,4,8,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,2,1,5,8,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [1,3,6,8,7,4,2,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,2,8,5,7,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [2,6,1,5,8,3,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [5,7,1,6,8,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [4,8,1,2,5,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [8,3,6,4,7,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [1,7,8,4,6,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [2,7,3,1,5,8,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,7,4,6,8,1,3,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,7,5,8,6,4,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [8,2,6,7,5,4,3,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>1011101 [3,4,2,7,8,1,6,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [6,5,8,7,1,4,2,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [4,1,7,3,8,5,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [3,6,1,4,5,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [1,6,7,4,5,3,8,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [6,1,7,3,5,4,8,2]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [1,4,7,2,8,5,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [5,6,8,7,2,4,1,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [6,8,5,7,1,2,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [8,2,4,3,7,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [6,8,2,1,5,7,3,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [2,7,8,1,4,6,3,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [4,8,2,5,7,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,1,6,8,5,3,7,2]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [5,2,6,4,8,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [6,7,1,3,4,5,8,2]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [1,7,3,2,4,8,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [6,3,4,2,8,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [4,3,8,7,5,2,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [6,8,7,4,2,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [3,6,4,5,2,8,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [8,6,1,3,5,4,2,7]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [5,3,8,6,1,2,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [2,5,6,3,4,8,7,1]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [2,5,3,6,8,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,8,7,3,5,2,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [3,8,7,2,6,4,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [6,3,5,4,8,7,2,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [4,3,8,6,1,5,2,7]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,7,6,2,5,3,8,1]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [7,5,2,6,8,1,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [8,5,2,7,1,4,3,6]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [1,8,5,3,6,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [5,1,7,2,4,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [1,5,3,4,8,6,2,7]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [5,4,1,3,8,6,2,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [5,1,8,6,3,4,2,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [4,5,2,8,3,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [8,2,3,7,6,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>1000111 [5,8,2,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [6,8,2,5,3,4,7,1]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [7,2,5,6,4,8,1,3]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [1,6,7,4,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [7,1,3,5,8,2,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [8,2,1,3,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [6,3,1,4,7,5,8,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [4,1,3,8,2,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [2,8,3,6,7,5,4,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [3,1,7,2,8,5,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [3,6,1,4,7,2,8,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [1,5,8,4,7,2,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [7,1,3,6,2,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [6,2,7,4,5,8,1,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [2,1,8,4,5,7,3,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [1,8,5,7,3,2,4,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [2,1,8,5,4,3,6,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,7,4,1,5,3,8,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,4,8,6,2,3,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [2,7,1,4,6,3,8,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [4,7,5,6,8,1,3,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [7,1,3,2,8,5,4,6]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [2,8,5,4,1,3,6,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [5,1,7,4,2,3,8,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [3,8,6,5,1,4,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [1,3,4,8,6,5,2,7]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [4,1,8,6,5,3,2,7]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [4,8,5,2,7,3,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [7,2,8,5,3,6,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [5,2,8,4,3,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [8,4,7,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [7,5,2,8,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [5,7,4,3,6,2,8,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [6,7,5,1,2,8,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [5,2,6,8,3,4,7,1]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [7,6,2,4,5,8,3,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [3,6,8,4,7,2,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [7,6,3,8,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [2,6,3,8,4,7,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,2,3,6,5,8,4,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [6,2,7,5,8,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [2,8,3,6,4,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,1,5,6,8,3,7,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [5,8,1,2,6,4,7,3]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [1,6,8,3,2,7,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,5,7,2,8,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [7,5,1,2,8,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [5,4,8,3,6,2,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,8,2,7,4,3,6,1]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [6,4,5,8,2,7,3,1]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [5,7,3,6,4,8,2,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [1,5,6,4,8,2,7,3]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [3,1,5,6,4,8,7,2]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,5,1,6,4,7,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [1,2,6,4,3,8,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,2,6,3,5,8,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [2,3,5,1,8,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [2,3,6,1,8,5,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [1,2,7,3,6,8,5,4]=>[[1,2,3,4,8],[5],[6],[7]]=>0001110 [2,3,6,1,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [1,2,5,8,4,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,3,6,8,5,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [1,2,6,8,5,4,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,3,5,8,2,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,4,6,8,3,2,5,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,3,7,5,6,8,2,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,2,6,7,3,8,5,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,2,5,7,3,8,6,4]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [3,1,5,7,6,8,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,5,4,6,8,2,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [2,3,6,5,8,7,1,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [1,2,7,5,6,8,4,3]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [3,1,6,7,5,8,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [4,6,2,7,5,8,3,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [3,5,7,4,8,2,6,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [2,4,7,6,8,3,5,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [1,4,6,8,3,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,3,5,8,2,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,2,5,8,4,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,2,5,8,7,4,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,3,5,8,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [5,7,1,2,8,6,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,4,5,7,2,8,1,3]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [5,3,4,7,2,8,1,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [3,2,7,4,6,8,1,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,3,6,2,7,1,4,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [2,6,3,4,7,1,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [2,7,3,4,5,8,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [3,7,4,5,6,8,1,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [2,5,7,3,6,8,1,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [4,7,6,2,3,8,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [7,3,5,2,4,8,1,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [7,6,2,4,5,8,1,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [6,5,2,3,4,8,1,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [5,3,1,2,8,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [6,5,2,3,7,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [5,2,1,7,3,4,6,8]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [5,2,1,8,3,4,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [6,3,2,8,4,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,3,1,2,8,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [6,4,1,3,8,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,2,3,1,8,4,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [8,3,5,2,7,1,4,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [8,6,2,4,7,1,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [8,5,2,3,6,1,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [8,2,1,7,3,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [8,6,3,7,2,4,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>1100101 [7,1,6,2,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [8,2,7,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [8,1,6,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [8,1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011 [8,6,1,7,2,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [8,1,5,7,2,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,7,5,8,2,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [7,2,1,8,3,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,3,8,2,4,5,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,2,8,3,4,5,6,1]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [1,7,8,3,4,5,6,2]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [1,4,5,8,3,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [2,5,7,1,8,3,6,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [6,2,7,1,8,4,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [4,7,1,3,8,5,6,2]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [1,6,2,8,4,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [4,1,3,6,8,2,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [5,3,4,6,8,2,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,6,3,8,7,1,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [6,4,5,8,7,1,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [5,3,4,8,7,1,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [3,2,8,7,1,4,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,1,8,7,2,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [5,3,7,6,1,2,4,8]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [1,8,3,7,2,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,8,1,7,2,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [6,8,2,3,5,1,4,7]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [4,7,8,2,6,1,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [6,2,8,7,1,4,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [3,8,7,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,8,6,1,3,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,7,6,1,3,4,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [1,7,6,2,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,8,6,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [2,8,7,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [3,8,7,2,4,5,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [7,8,3,6,2,4,5,1]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [1,5,8,7,2,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [8,7,6,1,3,4,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [3,6,2,4,7,1,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,4,7,2,5,1,8,6]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [2,1,6,4,8,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]=>1010101 [4,1,8,5,3,2,7,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [3,6,2,5,7,1,4,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [1,2,8,3,7,5,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [6,1,3,2,8,5,4,7]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [5,6,1,2,8,4,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [1,6,3,8,7,4,2,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [4,3,8,1,2,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [1,2,3,4,5,10,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>000001111 [11,12,9,10,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010 [3,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>01000000 [2,4,1,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>10100000 [2,3,5,1,4,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]]=>10010000 [2,3,4,5,6,8,1,7,9]=>[[1,3,4,5,6,7,9],[2,8]]=>10000010 [3,6,8,7,1,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [6,5,7,2,4,8,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [3,4,1,6,5,8,7,2]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [3,5,1,2,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [3,7,5,2,1,4,6,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,8,5,2,7,4,1,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [5,2,8,4,7,3,1,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [5,2,7,4,1,3,6,8]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [4,3,5,1,2,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [3,1,4,6,2,8,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [1,4,6,5,2,8,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [3,4,5,6,1,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [3,4,5,8,7,2,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [1,4,7,2,6,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [8,4,7,5,2,1,6,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [8,1,4,7,2,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [1,8,5,7,3,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [6,3,5,1,7,4,2,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [6,1,4,8,7,3,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [6,4,8,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6,8]]=>0010101 [5,4,8,1,6,3,2,7]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [1,4,8,6,3,7,2,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [5,4,7,6,3,8,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [4,6,3,7,5,8,1,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,1,3,5,8,6,2,7]=>[[1,2,5,6,7],[3,8],[4]]=>0110001 [5,7,4,3,8,1,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [1,4,8,3,7,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]=>0110111 [4,3,8,2,1,6,5,7]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [3,8,4,2,7,1,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [3,1,2,5,7,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,8,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [3,8,1,6,7,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [3,7,2,6,8,5,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [7,2,3,8,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [8,2,1,7,5,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [8,1,3,6,5,7,4,2]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [8,2,4,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [1,7,8,5,4,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [1,8,4,5,3,2,6,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,8,5,4,3,1,6,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [7,1,6,3,4,2,5,8]=>[[1,2,4,5,8],[3],[6],[7]]=>0100110 [6,8,7,1,4,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [3,6,1,4,2,7,5,8]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [3,4,1,8,5,7,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [3,6,5,1,2,8,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,8,5,6,7,2,1,4]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,1,7,6,2,4,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [8,5,6,1,4,2,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [8,6,5,4,7,1,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [1,6,4,5,7,2,3,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [8,3,6,1,7,2,4,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,8,6,5,7,3,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [1,7,5,3,6,8,4,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [7,4,1,6,5,8,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [4,1,5,8,7,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [1,2,5,8,6,7,3,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [4,2,1,5,8,7,3,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [5,2,4,6,1,7,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [1,5,3,6,8,7,4,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [3,5,4,6,1,8,2,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,1,5,7,6,8,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [1,4,5,6,8,7,2,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [1,4,6,3,7,2,8,5]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [1,7,3,6,5,2,8,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [8,6,2,5,4,1,7,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [3,7,2,6,5,4,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]=>1101110 [7,6,2,5,4,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>1011110 [4,7,5,2,6,3,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [3,2,6,4,7,5,1,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [6,2,3,7,5,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [1,3,4,7,6,2,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [2,8,3,6,1,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,7,2,5,1,6,4,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [3,8,2,6,5,1,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,8,2,5,4,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [4,8,5,2,6,1,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [4,5,1,3,7,2,8,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [6,1,3,7,5,2,8,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [7,1,3,6,2,8,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [8,1,3,6,2,7,5,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,2,4,7,3,8,6,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [7,1,8,2,6,5,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [3,1,8,6,2,7,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [4,1,7,8,2,6,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [5,6,1,8,2,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [4,2,7,8,1,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [3,2,8,6,1,7,5,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,2,8,1,6,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [1,8,7,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [2,8,7,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [3,8,7,1,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [4,8,7,5,1,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [6,7,8,5,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [5,6,3,8,4,1,7,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [7,3,8,5,4,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [3,4,8,6,5,1,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [8,3,7,5,1,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [1,4,8,6,2,7,5,3]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [8,4,6,7,1,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [5,6,4,7,8,1,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [3,4,6,5,1,2,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [7,3,5,1,2,8,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [1,4,6,2,3,8,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [1,3,2,7,4,8,6,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [7,2,1,6,3,8,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [2,3,1,7,6,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [4,5,2,1,7,3,8,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [5,6,7,1,2,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,7,5,1,2,8,6,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [3,7,1,6,2,8,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [7,6,1,2,8,5,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [2,7,1,3,8,6,5,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [8,6,1,2,7,5,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [1,7,2,3,8,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [8,7,1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,8,1,2,6,5,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [3,8,1,6,2,7,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [4,8,5,1,2,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [5,6,8,1,2,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [2,1,3,7,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [4,2,7,3,6,8,1,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,3,6,4,2,8,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,1,5,3,8,2,7,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [5,2,6,4,7,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [2,6,3,4,7,5,1,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [2,6,3,5,4,8,1,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,7,4,3,5,8,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,3,6,4,2,8,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [7,6,4,5,2,8,1,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [5,4,3,1,8,2,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,5,4,2,7,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [5,4,1,7,2,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [5,4,1,8,3,2,6,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [6,5,2,8,3,4,7,1]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [7,4,2,1,8,3,6,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [6,5,3,4,8,2,7,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [6,1,5,3,8,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [4,6,3,1,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [5,8,4,2,7,3,1,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [8,2,6,4,7,3,1,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,6,2,5,7,4,1,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [8,5,3,2,6,4,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [8,3,1,7,2,5,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [7,5,2,6,4,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [7,1,6,2,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [8,1,7,3,5,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [8,6,1,7,4,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [8,1,3,7,2,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,7,6,8,3,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,1,5,8,4,2,6,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,3,8,4,5,2,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,2,8,5,3,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [6,1,8,4,3,2,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,1,7,4,2,5,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [1,2,7,3,4,6,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [1,7,8,4,3,5,6,2]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [1,6,2,8,3,5,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [2,6,1,7,3,5,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [3,1,5,8,4,2,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [4,3,1,6,8,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [5,7,4,8,3,2,1,6]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,8,2,7,3,1,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [5,2,8,7,3,4,1,6]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [6,4,7,5,3,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [1,8,3,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [5,8,3,2,6,4,1,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [6,8,2,4,7,5,1,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [7,3,8,2,6,4,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [4,6,8,2,7,3,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [2,6,8,7,3,4,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,2,8,6,3,5,1,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [6,8,1,7,2,5,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [3,8,7,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,8,6,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [2,7,6,3,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>1001110 [1,7,6,5,2,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [1,8,6,5,3,2,4,7]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [3,8,7,4,6,2,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [5,8,3,7,6,2,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [7,1,8,6,5,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [8,4,7,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>1110011 [8,7,2,5,4,3,1,6]=>[[1,3,6],[2],[4],[5],[7],[8]]=>1011011 [6,8,3,2,5,4,7,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [1,5,7,8,4,3,6,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [6,3,8,1,5,4,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [6,2,1,8,5,4,7,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [2,6,5,7,4,1,3,8]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [2,5,4,7,1,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [5,2,1,8,7,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [4,8,6,7,5,3,1,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [6,5,4,8,2,1,7,3]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [5,8,4,7,2,6,3,1]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [5,8,3,2,7,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [5,2,1,4,3,6,7,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [3,5,7,4,2,6,1,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,2,1,6,5,3,7,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [4,2,1,5,7,6,3,8]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [3,5,4,7,1,6,2,8]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [3,4,5,8,6,7,1,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,3,5,1,6,8,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,3,1,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,6,8,10],[4]]=>011010101 [2,4,6,8,1,3,5,7,9]=>[[1,3,5,7,9],[2,4,6,8]]=>10101010 [8,7,6,5,4,3,2,10,1,9]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>111111101 [6,5,4,10,3,9,2,8,1,7]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>111110111 [6,5,4,3,2,8,10,1,7,9]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>111110101 [4,8,3,7,2,6,10,1,5,9]=>[[1,5,9],[2,6,10],[3,7],[4,8]]=>111011101 [4,3,2,6,8,10,1,5,7,9]=>[[1,5,7,9],[2,6,8,10],[3],[4]]=>111010101 [2,1,7,3,8,4,6,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [4,1,8,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [4,1,7,2,8,3,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [7,1,3,2,8,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,1,8,2,4,3,6,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [8,1,7,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [7,1,5,2,8,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [5,1,7,2,8,3,6,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,1,8,2,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [5,1,8,2,4,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [8,1,6,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [6,1,8,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,1,8,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [8,1,6,2,5,3,7,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [8,1,6,2,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,1,8,2,7,3,5,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,1,7,2,8,3,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,7,2,5,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,1,7,2,4,3,8,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [5,1,6,2,4,3,8,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [7,1,5,2,4,3,8,6]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [7,1,6,2,4,3,8,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [7,1,6,2,5,3,8,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,6,2,8,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,8,2,6,3,5,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [1,8,2,7,5,4,6,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [1,8,2,7,4,3,5,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,8,6,4,7,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,8,4,2,6,3,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [7,4,8,1,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [7,5,8,3,2,4,1,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [1,8,5,4,3,6,2,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [1,8,5,4,3,7,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,8,5,4,7,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [1,8,4,2,5,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [7,4,8,2,1,3,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,5,4,8,2,3,6,1]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [5,1,7,4,2,6,8,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [4,1,6,3,2,5,8,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [6,5,4,3,7,1,8,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [6,5,1,7,3,8,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [6,3,2,8,5,7,1,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [6,5,4,3,8,2,7,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [6,5,4,3,8,7,1,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [7,6,3,8,5,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [5,4,8,2,1,7,3,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,4,2,8,5,1,3,7]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [7,6,4,8,5,1,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,2,8,6,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [7,2,8,6,1,5,3,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [2,1,7,8,3,6,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [6,4,1,7,8,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [4,1,5,3,2,8,6,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [6,3,1,7,8,5,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [6,5,4,2,7,8,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [4,3,1,5,2,6,8,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [5,4,2,1,6,7,8,3]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,3,1,6,7,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [6,3,8,1,2,5,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [3,6,7,1,2,5,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [7,8,3,1,2,5,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [7,8,1,3,2,4,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,8,2,1,3,5,4,6]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [5,2,3,7,1,8,6,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [2,5,3,6,1,8,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [2,6,7,3,1,8,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [2,6,7,1,3,5,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,2,8,3,1,7,4,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [3,2,5,7,1,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [4,3,1,2,7,8,6,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,1,2,7,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [5,1,4,7,8,2,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [5,3,4,7,8,6,1,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [3,5,4,6,8,7,1,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [1,5,4,6,8,2,3,7]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [1,6,7,3,2,4,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [1,5,3,6,2,7,8,4]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [5,1,3,7,2,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [5,2,4,7,8,1,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [4,2,5,7,6,1,8,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [4,5,2,8,6,1,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,3,1,8,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [6,1,8,3,2,4,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [4,3,5,7,6,8,1,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,1,5,7,6,2,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [4,5,1,8,6,2,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [5,2,1,8,3,6,4,7]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [3,4,2,1,8,7,5,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [7,6,5,4,2,1,8,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>1011110 [7,6,5,4,8,1,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [8,7,6,5,4,2,1,9,3]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>10111110 [7,6,5,8,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [8,5,4,3,2,1,7,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,6,5,4,3,2,1,9,7]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010 [7,6,5,4,3,2,1,9,8]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]=>11111101 [7,6,5,4,1,8,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [8,7,6,5,4,9,1,3,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>01111110 [9,8,7,6,5,4,2,1,10,3]=>[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>101111110 [7,6,5,2,8,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [8,7,6,5,9,2,1,4,3]=>[[1,3],[2,4],[5,9],[6],[7],[8]]=>10111110 [7,6,5,8,4,1,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [7,6,8,5,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [7,8,6,3,2,1,5,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [8,7,4,3,2,1,6,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [9,6,5,4,3,2,1,8,7]=>[[1,7],[2,8],[3],[4],[5],[6],[9]]=>11111011 [9,7,6,5,4,3,2,1,10,8]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010 [7,8,4,5,9,2,3,6,10,1]=>[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000 [7,8,1,3,2,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,8,4,1,5,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [4,6,7,1,5,2,3,8]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [3,2,5,6,1,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,2,6,1,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,5,4,6,7,8,1,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [1,5,3,6,2,4,7,8]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [2,5,4,6,7,1,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,6,7,4,5,1,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [6,2,7,4,5,1,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [4,2,5,6,7,1,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [6,1,7,3,2,4,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [7,3,2,5,4,1,6,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,3,5,4,2,1,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [7,3,5,2,4,1,6,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,6,5,2,1,4,3,8]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [1,3,6,7,5,2,8,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [7,3,4,1,6,2,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [7,3,4,1,6,5,2,8]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [7,3,4,1,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [7,3,2,5,1,6,4,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,6,5,4,1,3,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [7,3,4,1,5,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [1,3,6,7,2,5,8,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,7,4,6,2,8,5,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [4,3,1,7,2,6,8,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,6,1,4,7,3,8,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,3,2,1,7,4,8,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [1,3,4,5,8,7,2,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [6,3,4,5,8,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [2,4,5,1,6,8,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [3,1,2,5,6,8,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [4,3,2,5,6,8,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [3,7,5,4,6,8,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,1,4,6,5,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [2,3,4,5,8,6,1,7]=>[[1,3,4,5,6,7],[2],[8]]=>1000001 [2,3,4,5,8,1,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [3,1,4,6,5,8,7,2]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [3,7,5,4,6,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [5,6,1,4,7,2,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [4,3,1,7,5,6,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,3,1,7,6,5,8,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [3,1,4,6,7,8,5,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [1,4,5,2,6,8,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [3,7,5,2,6,8,1,4]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [3,7,5,2,6,8,4,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [5,6,1,2,7,4,8,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [6,3,5,2,4,7,8,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [5,3,2,1,4,7,8,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,1,4,2,7,8,6]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [5,3,1,2,4,7,8,6]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [7,1,5,2,6,8,4,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [7,1,5,2,6,8,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [1,7,4,6,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [2,7,4,6,1,8,3,5]=>[[1,3,5,8],[2,4,6],[7]]=>1010110 [2,7,4,6,1,8,5,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,3,6,7,1,5,8,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [2,3,6,7,5,1,8,4]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [4,3,2,6,7,1,8,5]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [7,3,2,5,6,8,1,4]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,1,5,4,6,8,2,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [2,7,4,6,5,8,1,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [7,3,4,5,8,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,3,4,5,8,1,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,3,4,5,8,1,2,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [1,3,4,5,8,6,2,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,3,4,5,8,2,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [6,3,4,5,8,2,1,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [6,3,4,5,8,2,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,3,4,5,8,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [2,7,4,6,5,8,3,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [7,1,5,4,6,8,3,2]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [7,3,2,5,6,8,4,1]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [5,7,4,6,1,8,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [6,3,4,5,8,1,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [7,3,4,5,8,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,3,4,5,8,2,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [4,8,6,1,7,5,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [4,7,8,2,6,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [7,6,4,2,8,3,5,1]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [8,6,4,2,7,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [8,4,7,3,6,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [8,4,6,1,7,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [6,4,7,1,8,3,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,4,8,3,6,1,5,2]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110 [6,12,5,11,4,10,3,9,2,8,1,7]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>11111011111 [6,2,1,7,3,5,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [2,1,8,6,3,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,1,7,3,5,8,6,4]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,7,3,1,5,4,6,8]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,6,3,1,4,8,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [4,2,1,8,3,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [2,1,8,6,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [6,2,1,7,3,5,8,4]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [2,7,3,1,4,8,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [3,2,1,6,4,5,7,8]=>[[1,4,5,7,8],[2,6],[3]]=>1100100 [3,2,1,5,7,8,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,1,7,3,6,8,4,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [2,7,3,1,5,6,8,4]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,4,7,5,1,6,8,3]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [4,3,7,5,6,1,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,3,6,8,5,1,7,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [2,6,1,8,3,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,1,6,8,3,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,1,8,3,5,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [3,2,1,5,6,8,4,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,2,1,5,7,4,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,1,7,3,6,4,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,1,6,3,5,8,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [8,2,4,1,7,5,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [3,8,4,7,5,1,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [8,4,3,6,1,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [8,2,1,7,3,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [2,6,1,8,3,5,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,7,3,1,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [2,4,7,5,1,6,3,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [8,2,4,1,7,5,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [5,8,6,3,1,7,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [2,4,7,1,8,5,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [2,4,8,5,1,6,3,7]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [6,2,1,7,3,4,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [6,2,1,7,8,3,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [2,7,1,8,3,5,6,4]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [2,1,8,3,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [3,2,1,6,7,4,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [3,2,1,7,4,5,6,8]=>[[1,4,5,6,8],[2,7],[3]]=>1100010 [3,2,1,6,8,4,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,1,8,3,7,4,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [2,1,8,3,6,7,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [2,4,8,5,1,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [4,3,8,5,6,1,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [3,2,1,8,4,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [1,6,8,3,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [3,8,1,5,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [1,2,6,8,4,7,3,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [6,1,5,8,2,4,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,2,4,8,3,6,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,1,2,7,8,3,6,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [3,5,7,4,8,6,1,2]=>[[1,2,6,8],[3,4],[5,7]]=>0101010 [5,3,8,4,7,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [8,7,1,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7],[8]]=>0011011 [5,8,1,2,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,2,8,4,3,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,2,5,3,7,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [6,1,2,8,7,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [7,1,6,2,8,4,5,3]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,2,6,3,8,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,2,8,5,3,6,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,2,7,3,8,5,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [4,1,2,7,8,6,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [1,6,2,8,4,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [1,6,4,2,7,3,5,8]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [1,8,6,3,2,4,5,7]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [1,7,3,2,8,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [3,1,7,8,6,2,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,8,7,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,8,7,3,5,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [1,3,2,8,7,4,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,8,3,2,6,4,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,7,6,3,2,4,5,8]=>[[1,2,4,5,8],[3],[6],[7]]=>0100110 [1,2,8,4,3,7,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [8,5,1,7,2,4,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [5,3,8,7,4,6,1,2]=>[[1,2,6],[3,4],[5,7],[8]]=>0101011 [3,8,6,4,7,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,1,8,2,7,4,5,3]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,2,5,3,8,6,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,2,7,5,3,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,2,6,3,7,5,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,2,3,7,5,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [3,7,4,8,6,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [1,8,2,7,6,4,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]=>0010111 [2,9,8,7,6,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]=>10111111 [2,8,7,6,5,1,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [7,1,6,3,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [2,7,6,3,1,5,8,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [1,8,4,3,6,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,8,4,6,5,3,2,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [7,4,2,1,6,5,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [7,6,1,4,3,5,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [7,4,1,3,5,2,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [7,3,1,2,4,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,8,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [1,8,6,7,4,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [3,6,2,1,4,8,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,1,7,2,4,6,8,5]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [3,4,7,1,5,2,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [3,6,7,4,1,5,8,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [4,3,2,7,1,5,8,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [3,1,2,8,6,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [5,4,8,6,1,2,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [5,6,8,7,4,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [1,8,2,7,4,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [6,5,8,2,3,7,1,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [6,4,8,5,3,1,7,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [5,7,8,6,1,3,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>0101010 [2,4,8,1,6,3,7,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [3,1,2,8,6,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [5,3,2,6,4,8,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [4,1,6,3,5,8,2,7]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [2,4,5,3,8,6,1,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [1,8,5,3,2,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]=>0101011 [1,8,4,5,2,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [4,1,2,7,6,5,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [2,4,1,6,7,8,5,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [1,8,4,3,6,2,7,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [5,6,7,3,2,8,1,4]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [2,5,7,3,6,8,4,1]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [5,3,2,1,4,8,6,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [5,3,1,4,2,8,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [7,6,1,3,8,5,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [3,4,7,8,1,2,6,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,6,7,8,1,4,5,2]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [3,6,2,8,1,5,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [2,3,6,8,5,1,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [3,1,6,4,8,2,5,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [7,3,2,6,8,5,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [7,3,5,8,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,2,8,4,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [7,4,5,8,2,1,3,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [1,8,5,2,4,6,3,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [1,8,4,2,3,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [6,4,2,8,3,5,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [6,3,4,8,2,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [7,5,4,8,3,6,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [2,7,4,8,5,3,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,1,5,4,8,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [7,3,2,5,8,4,6,1]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [8,4,6,3,7,2,5,1]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [7,4,6,3,8,5,1,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [2,5,6,8,3,4,1,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [8,4,6,2,7,5,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [8,5,6,7,2,4,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [2,5,6,8,4,3,1,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [2,5,7,8,4,1,3,6]=>[[1,3,6,8],[2,4,7],[5]]=>1011010 [6,5,7,8,4,1,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,5,6,8,2,4,1,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [7,4,6,2,8,5,1,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [4,3,2,6,8,5,1,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [3,5,6,8,2,4,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [3,5,6,8,4,2,1,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [2,6,7,8,1,4,5,3]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,6,7,8,1,4,2,5]=>[[1,2,5,8],[3,4,7],[6]]=>0100100 [3,5,7,8,2,1,4,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [2,6,7,8,1,4,3,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [6,5,7,8,3,1,4,2]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [2,5,7,8,3,1,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [2,4,7,3,8,1,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [6,4,7,3,8,1,5,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,7,3,8,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,4,6,3,8,2,1,5]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [6,3,2,5,4,8,1,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [6,4,5,2,3,8,1,7]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [6,4,5,3,2,8,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,4,6,3,8,2,1,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,4,7,3,8,1,6,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [2,5,7,8,3,1,6,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [4,5,7,8,3,1,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [4,5,6,8,2,3,1,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [5,4,6,2,8,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,3,2,6,8,4,1,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,4,7,2,8,1,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [4,5,7,8,2,1,3,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,6,7,8,1,3,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,6,7,8,1,3,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [2,6,7,8,1,3,5,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [2,6,7,8,1,5,3,4]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [4,6,7,8,1,5,2,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [4,6,7,8,1,2,5,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [4,5,7,8,2,1,6,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [5,4,7,2,8,1,6,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,3,2,7,8,1,6,4]=>[[1,4,8],[2,6],[3,7],[5]]=>1101010 [4,3,2,7,8,1,6,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [3,5,7,8,2,1,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [3,6,7,8,1,2,5,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [3,6,7,8,1,5,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [3,6,7,8,1,5,4,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [2,6,7,8,1,5,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [3,4,5,6,7,8,9,1,2,10]=>[[1,2,5,6,7,8,9,10],[3,4]]=>010000000 [2,4,5,6,7,8,1,3,9]=>[[1,3,5,6,7,8,9],[2,4]]=>10100000 [1,4,5,6,7,8,2,9,3]=>[[1,2,3,6,7,8,9],[4,5]]=>00100000 [1,4,5,6,7,8,9,10,2,3]=>[[1,2,3,6,7,8,9,10],[4,5]]=>001000000 [4,2,7,1,5,3,8,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,2,8,6,1,5,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [3,2,6,7,5,1,4,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [2,7,1,3,5,4,8,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [4,7,2,1,5,8,6,3]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [7,2,1,3,5,8,6,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [2,3,6,4,7,1,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [1,3,4,8,2,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [3,1,4,8,2,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,3,1,6,2,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [4,8,6,2,1,5,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,8,3,6,5,1,7,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [6,4,7,3,5,1,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,7,5,1,8,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [3,6,1,7,5,8,2,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [7,3,5,1,6,8,2,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [4,7,3,5,6,1,8,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [3,4,6,8,5,1,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [4,6,8,2,1,5,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [6,8,2,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [1,8,2,3,5,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [2,7,3,6,1,4,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,6,1,3,5,8,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [7,3,2,5,6,1,4,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [4,7,5,2,6,1,3,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [4,6,2,8,1,5,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [8,4,1,2,7,5,3,6]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [4,5,6,2,7,1,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [8,5,1,2,6,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,6,2,7,4,8,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,2,1,7,8,5,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,7,3,8,4,1,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [2,7,8,4,1,5,6,3]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [2,7,1,8,5,6,3,4]=>[[1,3,4],[2,5,6],[7,8]]=>1001010 [8,2,5,1,6,7,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [8,2,4,5,1,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [3,8,4,5,6,1,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,5,8,3,6,7,1,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,5,8,3,7,6,1,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [4,2,8,3,7,1,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [7,2,3,4,8,1,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [7,2,3,4,8,1,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,6,3,4,8,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [7,6,3,5,8,4,1,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [7,6,3,8,4,5,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [7,2,3,8,5,1,4,6]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [7,2,3,8,5,1,6,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [2,6,4,8,1,5,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [7,2,3,8,4,1,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [7,2,3,5,8,1,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [7,8,2,3,6,1,4,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [7,8,2,3,6,1,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [4,2,6,3,7,1,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [7,2,3,5,8,1,6,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [7,2,3,8,4,1,6,5]=>[[1,3,4,5],[2,6],[7,8]]=>1000110 [2,6,4,8,1,3,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [3,6,4,8,1,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [7,6,5,1,2,3,8,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,6,5,1,4,2,8,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [2,6,4,5,1,8,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [3,5,6,4,1,2,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [7,8,5,4,1,2,6,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [3,5,6,4,1,2,8,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [7,6,5,1,4,2,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [7,6,5,1,2,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [7,6,5,1,2,4,8,3]=>[[1,2,3,8],[4],[5],[6],[7]]=>0011110 [7,6,5,1,3,2,8,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,6,5,1,3,2,4,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [7,6,5,1,3,4,2,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [7,2,3,4,5,1,8,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [2,6,4,3,1,5,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,4,3,1,8,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,4,3,1,8,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [3,5,8,4,1,2,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [3,5,8,4,1,2,6,7]=>[[1,2,6,7],[3,4,8],[5]]=>0101001 [3,5,8,4,1,6,2,7]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [4,2,8,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [3,5,8,4,1,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [2,5,8,4,1,7,3,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [3,6,4,2,1,7,8,5]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,6,4,2,1,7,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,5,6,4,1,8,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [2,6,4,5,1,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [7,6,5,1,4,3,8,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [7,6,5,1,2,8,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,6,5,1,2,8,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,6,5,1,8,2,4,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [7,6,5,1,8,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,6,5,1,8,3,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,6,5,1,4,8,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [3,6,4,5,1,7,2,8]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [2,5,6,4,1,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [7,8,5,4,1,6,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [2,5,6,4,1,7,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [3,6,4,5,1,7,8,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [7,6,5,1,4,8,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [7,6,5,1,8,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [7,6,5,1,8,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [4,1,7,6,2,8,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [7,8,6,2,1,3,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [3,7,6,1,2,8,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [2,6,5,3,1,4,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [4,6,1,5,3,2,8,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [3,6,1,4,2,5,8,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [2,6,4,5,7,8,1,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [8,7,1,6,5,2,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>0011111 [7,2,5,6,8,1,3,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [6,1,3,4,2,8,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [2,4,5,6,1,8,7,3]=>[[1,3,5,6,7],[2,4],[8]]=>1010001 [8,4,1,6,5,7,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [2,8,3,4,7,5,1,6]=>[[1,3,4,5,6],[2],[7],[8]]=>1000011 [6,8,2,7,4,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [4,7,8,5,1,6,3,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [8,2,6,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [4,8,6,1,7,3,2,5]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [8,7,3,2,1,5,4,6]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [3,8,5,1,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [6,8,7,1,3,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [2,5,1,8,7,4,6,3]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [3,7,1,8,4,5,6,2]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [6,2,3,8,4,7,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [8,6,4,3,1,7,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [8,3,7,4,6,1,2,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [7,1,3,8,6,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [2,3,5,8,6,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]=>1001001 [7,4,2,1,8,6,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [4,6,7,2,5,8,3,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [7,6,2,5,3,8,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [6,2,1,3,4,8,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [6,5,4,2,8,3,1,7]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [5,4,3,1,8,7,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,1,4,3,8,5,2,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [4,7,6,2,8,1,5,3]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [6,4,5,1,7,8,3,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [4,2,3,1,7,8,6,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [3,4,2,1,8,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [2,7,6,8,1,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [6,4,5,8,3,1,2,7]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [8,1,3,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [3,6,8,1,5,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,2,8,7,4,5,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [6,3,8,5,7,4,2,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,4,6,8,5,1,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [2,1,4,8,7,5,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [2,1,6,8,3,7,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [3,6,8,2,4,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [6,2,8,1,7,5,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [2,6,5,4,8,1,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,5,3,4,8,1,7,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [8,4,3,2,5,1,7,6]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [4,2,8,1,5,3,6,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [5,1,8,2,6,4,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [7,4,8,6,2,1,3,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [4,6,2,8,3,7,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [2,1,5,8,3,6,4,7]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,8,5,3,6,7,1,4]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [7,8,5,6,4,1,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>0111010 [5,8,4,1,6,3,7,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [4,8,1,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [3,8,1,4,5,6,2,7]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [7,6,8,3,5,1,4,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [8,9,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8]]=>10101010 [9,7,10,5,8,3,6,1,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010 [5,3,8,7,6,1,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [6,5,8,4,7,1,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [6,7,4,2,5,3,1,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [7,6,4,8,3,1,5,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [7,4,8,5,6,1,3,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [7,4,2,5,6,3,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [4,2,7,5,6,3,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [3,4,7,5,6,2,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>1100010 [4,7,3,5,6,2,1,8]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [3,7,2,5,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]=>1101010 [7,8,3,5,6,1,4,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [1,6,8,5,2,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]=>0011101 [6,2,8,5,1,7,4,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [6,7,4,8,2,1,5,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [3,2,7,8,6,1,5,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [6,8,4,1,2,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [4,1,8,5,6,3,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [1,8,2,5,6,4,3,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [6,1,8,5,3,7,4,2]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [3,8,1,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,2,1,5,3,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [1,5,2,4,6,7,8,3]=>[[1,2,3,6,7,8],[4],[5]]=>0011000 [4,1,5,3,6,7,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [8,1,6,5,3,7,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [7,1,4,6,3,2,8,5]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [3,2,6,4,1,7,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [7,6,4,3,1,2,8,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [8,6,3,5,1,7,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [4,5,3,1,6,7,8,2]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [3,5,2,1,6,7,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [5,2,3,1,6,7,8,4]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [1,5,3,2,6,7,8,4]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [8,4,6,5,1,7,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [7,5,4,6,1,2,8,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [3,2,5,6,1,7,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,2,8,7,6,1,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [6,8,4,7,2,1,3,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [3,8,7,5,6,1,2,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [8,2,7,5,6,1,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [4,8,6,5,1,7,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>0110101 [1,7,4,6,2,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [7,6,4,2,1,5,8,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [5,7,4,6,1,3,8,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [8,6,4,7,3,1,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [5,2,4,3,7,1,8,6]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [3,5,4,2,7,1,8,6]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [8,6,4,1,3,5,2,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [6,7,4,1,5,3,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [7,5,4,1,2,6,8,3]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [1,7,4,2,3,6,8,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,8,2,5,3,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,8,1,5,4,7,3,2]=>[[1,2,7],[3,8],[4],[5],[6]]=>0111101 [8,2,1,5,6,4,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [3,8,1,5,6,4,2,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [6,8,4,1,2,5,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [3,2,8,1,6,5,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [3,2,6,1,5,7,8,4]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [7,6,4,1,5,2,8,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [8,6,1,5,4,7,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [3,5,1,4,6,7,8,2]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [5,2,1,4,6,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [5,4,1,3,6,7,8,2]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [8,4,1,5,3,7,2,6]=>[[1,2,6],[3,5,7],[4],[8]]=>0110011 [7,5,4,1,3,2,8,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [3,2,5,1,4,7,8,6]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [7,1,4,3,5,2,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [8,1,3,5,4,7,2,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [5,1,3,4,6,7,8,2]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [8,3,2,6,1,4,7,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [2,6,1,3,8,7,5,4]=>[[1,3,4],[2,5,7],[6],[8]]=>1001101 [2,6,8,1,5,7,4,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [2,7,1,6,4,8,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [2,8,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [8,3,2,7,1,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [4,1,8,7,3,2,6,5]=>[[1,2,5],[3,6],[4,7],[8]]=>0110111 [3,7,1,8,6,5,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [3,6,8,5,1,4,7,2]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [7,3,5,8,2,1,4,6]=>[[1,4,6],[2,5,8],[3],[7]]=>1101010 [7,3,6,2,1,4,5,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [7,4,2,8,1,6,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [8,7,5,3,2,1,6,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [7,5,2,6,3,1,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [6,8,4,5,2,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [4,6,8,5,1,7,3,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [4,7,5,1,3,8,6,2]=>[[1,2,6],[3,5,8],[4],[7]]=>0110010 [5,1,7,6,4,2,8,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [5,1,8,7,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [8,5,2,1,7,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [8,5,2,1,6,3,7,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [5,1,8,6,3,2,7,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [8,4,2,5,7,3,1,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [5,4,8,2,7,3,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [5,4,8,7,3,6,1,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [6,3,7,2,4,8,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [5,7,4,2,8,1,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [6,5,2,7,1,3,8,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [8,6,5,4,2,1,7,3]=>[[1,3],[2,7],[4],[5],[6],[8]]=>1011101 [6,4,7,3,1,8,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,5,8,4,6,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [6,5,4,3,2,1,9,8,7]=>[[1,7],[2,8],[3,9],[4],[5],[6]]=>11111011 [5,4,3,2,1,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5]]=>11110111 [3,2,1,5,4,7,6,9,8]=>[[1,4,6,8],[2,5,7,9],[3]]=>11010101 [2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]]=>10100000 [7,6,5,4,3,2,1,10,9,8]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>111111011 [3,2,1,5,4,7,6,9,8,10]=>[[1,4,6,8,10],[2,5,7,9],[3]]=>110101010 [5,6,3,7,4,2,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [7,6,3,8,5,1,4,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [6,4,8,1,3,2,5,7]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [7,4,8,6,3,1,5,2]=>[[1,2],[3,5],[4,6],[7,8]]=>0110110 [4,2,7,6,5,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [3,7,2,4,6,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [8,1,3,4,5,2,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [1,6,8,4,2,5,3,7]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [6,2,8,4,1,5,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [6,7,4,8,5,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [3,2,7,8,5,1,6,4]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [3,2,8,1,5,4,6,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [6,1,4,8,5,3,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,4,8,5,2,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [6,1,8,4,3,7,2,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [3,7,1,4,2,5,8,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [7,2,1,4,3,5,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [4,1,5,3,6,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [6,1,8,5,3,2,7,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [7,1,4,6,3,8,5,2]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [3,2,6,4,1,8,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [7,6,4,3,1,8,2,5]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [3,5,2,1,8,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [1,5,3,2,8,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [5,4,2,1,7,8,6,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [8,2,7,6,5,1,3,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [8,6,2,7,1,4,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [1,7,3,6,2,8,5,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [7,6,3,2,1,8,5,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [8,6,3,7,4,1,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [5,2,3,4,7,1,8,6]=>[[1,3,4,6,8],[2,7],[5]]=>1001010 [8,6,3,1,4,5,7,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [6,7,3,1,5,4,2,8]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [5,8,3,1,2,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [8,1,3,2,4,5,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>0100001 [8,4,1,7,2,3,6,5]=>[[1,2,3,5],[4,6],[7],[8]]=>0010111 [8,2,1,6,5,4,7,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [3,8,1,5,6,4,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [6,8,4,1,2,5,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [3,2,8,1,6,5,7,4]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [7,6,4,1,5,2,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [8,6,1,5,4,7,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [3,5,1,4,6,7,2,8]=>[[1,2,6,7,8],[3,4],[5]]=>0101000 [5,2,1,4,7,6,3,8]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [4,5,8,2,1,3,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [5,8,2,3,1,4,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [4,2,1,3,5,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [5,4,1,3,6,2,8,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [8,5,4,1,3,6,2,7]=>[[1,2,6,7],[3],[4],[5],[8]]=>0111001 [3,2,5,1,4,6,8,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [8,1,4,3,5,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,1,3,5,4,6,2,8]=>[[1,2,4,6,8],[3],[5],[7]]=>0101010 [5,1,3,4,6,2,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>0101000 [4,1,3,2,5,7,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [3,1,5,2,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101 [3,1,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101 [3,1,4,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]=>010010101 [3,1,5,2,7,4,9,6,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>010101010 [1,3,5,2,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101 [3,1,2,5,4,7,6,9,8,10]=>[[1,2,4,6,8,10],[3,5,7,9]]=>010101010 [4,6,7,3,1,5,2,8]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [6,8,1,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [6,8,3,1,4,5,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [7,5,1,8,2,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [5,3,8,4,2,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [4,5,7,2,3,6,8,1]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [2,6,3,4,7,5,8,1]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [4,5,2,7,1,6,8,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [7,3,1,4,8,5,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [6,4,2,8,7,1,5,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [7,2,4,8,1,5,3,6]=>[[1,3,5,6],[2,4],[7,8]]=>1010010 [4,6,3,1,7,8,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [5,3,1,6,7,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [4,1,6,2,7,8,5,3]=>[[1,2,3,8],[4,5,7],[6]]=>0010100 [2,1,3,4,8,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [4,5,6,7,8,9,1,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>00100000 [4,5,6,7,8,9,2,3,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>10100000 [5,6,7,8,9,1,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>00010000 [6,7,8,9,2,3,4,5,1]=>[[1,3,4,5],[2,7,8,9],[6]]=>10001000 [8,9,6,7,5,4,3,2,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010 [4,5,6,7,8,9,10,1,2,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>001000000 [4,5,6,7,8,9,10,2,3,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000 [5,6,7,8,9,10,1,2,3,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>000100000 [8,9,10,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5,9,10],[8]]=>100100100 [4,8,3,7,6,5,1,2]=>[[1,2],[3,5],[4,6],[7],[8]]=>0110111 [6,3,8,7,5,4,1,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [5,3,8,7,6,4,1,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [2,8,7,6,1,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [5,2,8,7,6,1,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [6,2,8,7,5,1,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [7,8,2,6,5,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [6,1,8,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [3,1,8,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>0101111 [7,8,2,6,1,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [6,2,8,7,1,5,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]=>1011101 [4,2,8,1,7,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [4,8,2,7,6,1,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]=>1010111 [3,8,7,2,1,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]=>1101111 [6,5,8,7,1,4,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [4,8,1,7,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [5,4,1,8,7,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]=>0111011 [6,4,8,1,7,5,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>0110101 [7,8,4,1,6,5,3,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>0110110 [7,8,3,1,6,5,4,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>0101110 [6,3,8,1,7,5,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [5,3,1,8,7,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>0101011 [7,8,2,1,6,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [6,5,3,1,8,7,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [6,4,3,1,8,7,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [7,5,2,1,8,6,4,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [5,4,2,1,8,7,6,3]=>[[1,3],[2,6],[4,7],[5,8]]=>1011011 [7,3,2,1,8,6,5,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [6,3,2,1,8,7,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [9,7,5,3,1,10,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010 [6,1,4,2,3,5,8,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,6,1,4,2,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [6,8,1,4,2,3,5,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,1,4,2,3,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [4,1,8,2,3,6,5,7]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [8,2,3,6,1,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [6,2,3,8,1,4,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [4,6,2,3,8,1,5,7]=>[[1,3,5,7],[2,6,8],[4]]=>1010101 [4,8,2,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [8,2,3,6,4,1,5,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [8,4,3,6,2,1,5,7]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [6,2,3,8,4,1,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [8,4,2,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [6,4,2,3,8,1,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,4,3,8,1,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,8,4,3,6,1,5,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,6,3,8,4,1,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [6,3,8,4,2,1,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [2,6,3,8,1,4,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,8,3,6,1,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [8,3,6,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [2,8,3,6,4,1,5,7]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [8,3,6,2,4,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [8,3,6,2,1,4,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [6,2,1,3,8,4,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [8,2,1,3,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [6,3,8,2,4,1,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [6,2,4,3,8,1,5,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,6,4,7,8,5,1,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [1,6,4,2,7,5,8,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [3,6,4,2,7,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [1,4,7,2,5,6,8,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [6,4,8,5,3,7,1,2]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [1,6,5,4,2,7,8,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [4,2,5,3,6,1,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [7,1,5,3,6,2,8,4]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [1,6,5,2,4,8,7,3]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [1,4,6,2,8,5,7,3]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [7,8,1,4,2,5,6,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [3,4,8,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>1100001 [4,8,5,3,1,6,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [6,1,3,5,8,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [6,1,8,7,4,2,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,2,8,5,7,3,6,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [1,3,6,8,7,5,2,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,8,2,5,4,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [7,1,2,4,5,8,6,3]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [1,2,7,3,5,8,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,1,3,2,5,7,8,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [4,6,2,1,7,5,3,8]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [1,6,3,7,8,5,2,4]=>[[1,2,4,8],[3,5],[6,7]]=>0101100 [4,6,2,3,7,8,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,6,3,7,1,2,8,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [4,2,1,3,5,7,8,6]=>[[1,3,5,6,8],[2,7],[4]]=>1010010 [7,3,2,4,5,1,8,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [3,8,2,5,4,1,7,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [7,8,4,2,6,3,1,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [4,2,6,3,8,7,1,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [5,8,2,7,4,3,1,6]=>[[1,3,6],[2,7],[4],[5],[8]]=>1011011 [4,3,8,5,1,7,2,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [4,3,6,8,1,2,7,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [6,4,3,5,2,8,1,7]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [6,5,3,8,4,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [6,1,7,2,8,3,9,4,10,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000 [6,1,7,8,9,10,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>000010000 [7,1,8,2,9,3,10,4,11,5,12,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000 [3,8,1,7,5,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [8,2,5,7,3,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [1,8,6,7,5,3,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]=>0101101 [8,2,6,7,5,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [1,5,8,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [5,4,8,6,2,3,7,1]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [2,7,6,1,3,5,4,8]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [6,4,1,8,2,5,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [2,8,6,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [4,1,3,6,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [2,1,6,3,5,8,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,4,1,3,8,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,4,1,3,5,8,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,6,1,3,5,8,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [4,6,1,3,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [6,1,4,3,5,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,4,1,3,5,8,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,2,1,3,5,8,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [4,2,1,3,6,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [4,2,1,6,3,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [6,2,1,8,3,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [6,2,1,3,8,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [6,1,4,3,8,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,6,4,3,8,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [8,1,4,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,4,1,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,2,1,3,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,2,1,6,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,2,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [6,2,1,4,3,5,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [8,2,4,1,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [8,2,6,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,4,6,1,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,4,1,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,1,4,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,8,4,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,6,4,8,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,4,1,8,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,4,8,1,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,2,8,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [4,2,8,1,3,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [2,6,8,1,3,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [4,6,8,1,3,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,6,1,8,3,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,1,6,8,3,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,4,6,3,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,6,1,3,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [2,4,1,8,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,1,6,8,3,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [4,1,3,6,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [1,4,3,6,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]=>0110101 [4,1,3,8,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [2,1,8,3,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,1,6,4,3,5,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,6,1,4,3,5,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,8,1,4,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,8,1,6,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [4,8,1,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,4,8,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,4,8,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,1,8,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,8,1,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,8,6,1,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [2,8,6,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,8,4,1,3,5,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,6,4,1,3,5,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [4,6,2,1,3,5,7,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [6,8,1,4,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,1,8,4,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,6,8,4,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [1,8,6,4,3,5,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,1,6,4,3,5,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,6,1,4,3,5,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,6,4,1,3,5,7,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,6,2,1,3,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,4,2,1,3,5,7,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [7,8,6,5,2,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [5,7,4,1,8,6,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,6,4,2,8,3,7,1]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,6,4,2,7,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,7,1,4,6,3,2,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,8,1,4,6,3,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [3,6,7,4,5,8,2,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,5,7,4,6,8,2,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [6,8,4,1,7,2,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [5,4,6,1,7,8,3,2]=>[[1,2,7,8],[3,6],[4],[5]]=>0111000 [5,6,4,1,8,7,3,2]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [3,5,8,4,6,7,2,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [3,6,8,4,5,7,2,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [3,7,8,4,5,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [6,8,1,4,5,3,7,2]=>[[1,2,5,7],[3,8],[4],[6]]=>0110101 [6,7,1,4,5,3,2,8]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [3,7,1,5,4,6,2,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,8,1,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [3,7,1,5,4,6,8,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [6,7,1,4,5,3,8,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [5,7,1,4,6,3,8,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,6,4,2,7,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>1011000 [5,4,7,2,8,3,1,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [5,4,7,2,8,3,6,1]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [5,6,4,2,8,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [5,8,1,4,6,3,2,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [3,8,1,5,4,6,2,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [3,6,1,5,4,2,7,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [3,6,1,5,4,8,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [6,8,3,1,4,2,5,7]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [7,3,8,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [6,7,3,1,4,2,8,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [3,6,1,5,4,7,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [3,4,1,2,7,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,1,2,6,8,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [6,8,3,1,4,7,2,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [6,4,7,2,8,5,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [5,8,1,4,7,3,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [7,8,1,4,5,3,2,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [3,8,1,5,4,7,2,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [3,6,1,5,4,8,7,2]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [3,6,1,5,4,7,2,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [6,7,3,1,4,2,5,8]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [6,8,3,1,4,2,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [7,8,3,1,4,6,2,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [7,8,4,2,6,5,1,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [6,5,8,7,3,4,2,1]=>[[1,4],[2,7],[3,8],[5],[6]]=>1101101 [7,8,3,1,4,6,5,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [6,7,3,1,4,5,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [3,7,1,5,4,2,6,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [3,8,1,5,4,2,7,6]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [5,8,1,4,7,3,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [6,8,4,2,7,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [6,4,7,2,8,5,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,3,7,1,4,8,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,8,3,1,4,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [3,7,1,5,4,8,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [3,4,1,2,8,5,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,4,1,2,5,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [3,7,1,5,4,2,8,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [6,7,3,1,4,5,8,2]=>[[1,2,5,8],[3,4],[6,7]]=>0100100 [7,3,8,1,4,5,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [7,3,8,1,4,5,6,2]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [6,8,3,1,4,5,2,7]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [3,8,1,5,4,2,6,7]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [9,8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>10111111 [8,7,6,3,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [8,7,4,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [8,5,7,4,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [9,7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>11111101 [9,8,7,6,5,4,1,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111 [10,9,8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>101111111 [9,8,7,6,5,2,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]=>10111111 [10,9,8,7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>110111111 [9,8,7,6,3,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7],[8],[9]]=>11011111 [10,9,8,7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>111011111 [8,7,6,2,5,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8]]=>1011111 [9,8,7,4,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7],[8],[9]]=>11101111 [10,9,8,7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>111101111 [8,5,4,7,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,7,3,6,5,2,1,4]=>[[1,4],[2,5],[3],[6],[7],[8]]=>1101111 [10,9,8,6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>111110111 [6,5,8,4,3,2,1,7]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [8,4,7,6,3,2,1,5]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [9,6,8,5,4,3,2,1,7]=>[[1,7],[2,8],[3],[4],[5],[6],[9]]=>11111011 [10,9,7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>111111011 [5,8,7,4,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [10,8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>111111101 [5,8,6,2,3,4,7,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,5,2,7,3,1,8,6]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [4,8,2,6,3,5,7,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [4,1,7,2,5,8,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [1,6,2,5,8,4,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [7,3,1,6,8,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [5,2,7,1,8,6,3,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [6,5,2,8,1,7,3,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [2,8,3,5,1,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [5,4,3,8,7,1,6,2]=>[[1,2],[3,6],[4,7],[5,8]]=>0111011 [8,5,4,3,7,2,6,1]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [8,3,7,4,2,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [2,8,6,5,1,7,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [6,3,2,8,4,1,7,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [2,8,3,4,1,7,5,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [5,4,2,8,3,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [2,8,4,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,8,5,3,1,7,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [2,8,6,4,1,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [3,8,7,5,1,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [8,3,7,5,2,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,4,7,6,2,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>1010111 [4,8,7,6,1,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>0110111 [7,4,8,6,2,1,5,3]=>[[1,3],[2,5],[4,6],[7,8]]=>1010110 [7,3,8,5,2,1,6,4]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,3,8,4,2,1,6,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [7,5,4,3,8,2,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [3,7,8,4,1,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [3,7,8,5,1,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [4,7,8,6,1,2,5,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [8,7,4,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]=>1110111 [5,7,8,6,1,2,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,4,7,8,3,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [7,3,4,8,2,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [7,6,4,8,3,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>1110110 [7,5,8,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [6,5,8,7,3,1,4,2]=>[[1,2],[3,4],[5,7],[6,8]]=>0101101 [2,4,8,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]=>1010011 [6,3,2,4,8,1,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [2,3,8,4,1,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [2,3,8,5,1,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [6,4,8,7,3,1,5,2]=>[[1,2],[3,5],[4,7],[6,8]]=>0110101 [8,6,4,7,3,2,5,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>1110101 [8,3,4,7,2,5,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [3,4,8,7,1,5,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,4,8,6,1,5,7,3]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [2,5,8,6,1,4,7,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [8,3,5,7,2,4,6,1]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [8,4,6,7,2,3,5,1]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [4,6,8,7,1,3,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [2,6,8,5,1,3,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [2,6,8,4,1,3,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [2,5,8,3,1,4,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [5,6,8,7,1,3,4,2]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [7,4,6,8,2,1,3,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [2,3,5,4,1,8,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [2,3,6,4,8,1,5,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [1,8,4,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [5,4,8,6,2,1,3,7]=>[[1,3,7],[2,6],[4,8],[5]]=>1011001 [2,3,6,8,1,5,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,5,6,1,4,7,8,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [2,5,6,1,4,7,3,8]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [7,3,5,1,6,8,4,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [2,7,6,1,8,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [2,7,6,8,1,4,5,3]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [1,8,7,6,3,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,8,7,6,3,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [5,7,8,6,2,3,4,1]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [2,7,6,1,8,5,3,4]=>[[1,3,4],[2,5,8],[6],[7]]=>1001110 [6,3,5,1,7,2,4,8]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [2,3,4,7,6,1,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [7,3,5,8,4,1,2,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [1,8,4,5,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,8,4,5,2,7,6,3]=>[[1,2,3,6],[4,5],[7],[8]]=>0010011 [7,3,5,8,4,1,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [2,7,6,4,8,5,1,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [7,3,5,4,6,8,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [6,3,5,4,7,1,8,2]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [6,3,5,4,7,1,2,8]=>[[1,2,7,8],[3,4],[5],[6]]=>0101100 [3,4,1,5,6,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [3,7,1,6,8,5,2,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [2,3,1,8,6,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [1,8,4,3,6,2,5,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [2,3,1,8,6,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [3,7,1,6,8,5,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [6,3,5,4,7,2,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>1101100 [7,3,5,4,6,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>1101010 [2,7,6,4,8,5,3,1]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [1,8,4,5,2,6,3,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [6,4,8,5,3,1,2,7]=>[[1,2,7],[3,5],[4,8],[6]]=>0110101 [7,3,5,8,4,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [2,3,4,6,5,8,1,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [2,3,4,7,5,1,8,6]=>[[1,3,4,5,6],[2,8],[7]]=>1000010 [2,3,4,7,5,1,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>1000010 [2,3,4,7,1,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,4,7,1,6,8,5]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [2,3,4,6,1,8,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [6,3,5,8,4,2,7,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,4,8,5,3,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [1,8,4,5,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [7,4,8,5,3,2,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [6,3,5,8,4,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [5,2,4,6,8,3,7,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [1,5,7,4,6,3,2,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,2,8,4,6,3,7,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [3,8,5,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [6,8,3,4,5,7,2,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [2,5,7,4,6,3,8,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [5,4,1,7,8,3,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [5,4,2,7,8,3,6,1]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [5,1,4,6,8,3,2,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [5,1,8,4,6,3,2,7]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [8,1,6,4,5,3,2,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [8,1,3,5,4,6,2,7]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [8,1,6,2,4,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [8,7,1,2,4,3,5,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [1,7,6,2,4,3,5,8]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [8,7,3,2,4,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]=>1100111 [8,2,6,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [1,7,6,3,4,5,2,8]=>[[1,2,4,5,8],[3],[6],[7]]=>0100110 [1,7,2,5,4,3,6,8]=>[[1,2,3,6,8],[4],[5],[7]]=>0011010 [8,7,2,4,5,3,6,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [5,8,2,4,7,3,6,1]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [6,8,3,2,4,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [8,7,1,3,4,5,2,6]=>[[1,2,4,5,6],[3],[7],[8]]=>0100011 [8,1,6,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [8,1,2,5,4,3,6,7]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [3,4,8,7,5,2,6,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [3,2,8,6,1,5,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [8,6,1,2,4,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [8,7,3,6,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>1100111 [3,8,7,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7],[8]]=>1101011 [8,7,2,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [5,3,6,2,4,8,7,1]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [3,5,2,8,6,1,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,7,2,5,1,4,8,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [5,1,8,6,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [2,5,4,1,8,6,3,7]=>[[1,3,6,7],[2,4],[5,8]]=>1011001 [3,7,6,1,8,2,5,4]=>[[1,2,4],[3,5,8],[6],[7]]=>0101110 [7,6,3,1,8,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [8,2,3,6,1,4,7,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [1,8,2,6,3,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [8,1,3,6,4,7,2,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,1,3,6,4,8,2,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [8,2,1,3,5,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [8,2,6,3,1,4,7,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,5,4,1,3,8,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [2,7,5,8,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [7,3,8,5,4,1,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,2,3,6,1,4,8,5]=>[[1,3,4,5],[2,6,8],[7]]=>1000110 [1,3,7,2,5,8,4,6]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [1,7,2,3,5,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [7,4,8,1,3,6,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [8,1,2,3,5,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [7,1,2,3,5,8,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [8,6,1,4,7,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [2,6,3,7,1,4,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [2,6,3,8,1,4,7,5]=>[[1,3,4,5],[2,7],[6,8]]=>1000101 [7,5,4,8,1,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [8,5,4,7,1,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [2,3,1,8,5,4,6,7]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [8,6,5,1,3,4,2,7]=>[[1,2,4,7],[3],[5],[6],[8]]=>0101101 [8,5,1,7,6,3,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [3,4,7,6,1,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [3,5,2,6,7,1,8,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [3,2,8,4,7,5,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [8,4,7,5,1,3,2,6]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [3,8,1,6,5,2,7,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [6,1,2,8,3,4,7,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [6,8,3,1,7,2,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [3,7,2,5,6,1,8,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [6,8,4,2,5,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [2,7,5,3,8,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [8,3,1,4,7,2,6,5]=>[[1,2,5],[3,4,6],[7],[8]]=>0100111 [8,3,2,1,5,7,4,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [2,8,3,6,4,7,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,3,6,4,8,1,2,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [8,3,6,4,7,1,2,5]=>[[1,2,5],[3,4,7],[6],[8]]=>0100101 [1,2,8,3,5,7,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,8,3,2,5,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [6,5,1,7,4,2,8,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,3,6,4,8,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [6,1,7,3,4,2,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [7,3,8,1,6,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [8,3,7,1,6,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [5,1,7,4,2,8,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [4,2,8,6,5,1,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [6,4,2,8,5,1,7,3]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [8,6,4,7,1,5,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [3,8,7,1,6,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [4,2,3,7,8,5,1,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [5,1,6,4,2,3,7,8]=>[[1,2,3,7,8],[4,6],[5]]=>0011000 [6,4,7,8,1,5,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [5,8,7,6,1,4,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,6,5,7,1,4,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [6,7,4,8,1,5,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [8,3,2,4,7,1,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [2,5,3,7,1,6,4,8]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [8,4,6,7,1,5,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>0010101 [7,4,6,8,1,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [3,7,5,8,1,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [4,7,6,8,1,5,2,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [8,5,6,7,1,4,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [8,6,7,5,1,4,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>0011101 [5,6,8,7,1,4,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [2,4,6,7,1,5,8,3]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [6,7,8,5,1,4,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>0011100 [7,8,6,5,1,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [3,1,7,5,4,2,8,6]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [2,1,8,5,4,6,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [4,1,8,5,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [5,4,1,3,6,7,2,8]=>[[1,2,6,7,8],[3],[4],[5]]=>0111000 [8,4,1,2,6,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,2,7,1,5,3,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [3,2,7,1,5,8,4,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [6,3,7,1,5,4,2,8]=>[[1,2,8],[3,4],[5,7],[6]]=>0101100 [7,3,8,1,5,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,1,5,3,8,4,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [4,5,1,3,6,8,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [3,6,8,1,5,4,2,7]=>[[1,2,7],[3,4,8],[5],[6]]=>0101101 [6,8,3,1,5,4,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,6,3,1,5,4,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [3,6,2,1,5,8,4,7]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [8,6,2,1,5,3,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [4,8,2,1,7,5,3,6]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [2,3,8,1,5,7,4,6]=>[[1,3,4,6],[2,5,7],[8]]=>1001011 [7,1,3,2,8,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,1,6,2,8,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [4,7,1,2,6,3,8,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [2,7,8,1,5,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [6,7,2,1,5,3,4,8]=>[[1,3,4,8],[2,5],[6,7]]=>1001100 [4,7,2,1,8,5,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [8,7,2,1,4,5,3,6]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [8,7,5,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [5,7,8,6,1,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [2,7,4,1,6,5,3,8]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [3,7,1,4,5,6,8,2]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [7,1,6,4,5,8,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [3,5,1,4,7,6,8,2]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [2,6,4,1,7,5,3,8]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [5,6,8,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [6,8,5,7,1,4,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]=>0111101 [8,6,5,7,1,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [8,5,7,6,1,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [6,5,7,8,1,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [7,2,3,1,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [4,2,8,1,6,5,3,7]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [6,2,4,1,8,5,3,7]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [8,3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [5,3,1,4,8,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [7,5,1,6,3,4,8,2]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [7,1,5,8,4,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [5,8,1,6,4,3,7,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [5,3,1,8,4,6,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [8,3,1,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [8,2,6,1,4,5,3,7]=>[[1,3,5,7],[2,4],[6],[8]]=>1010101 [6,2,8,1,4,5,3,7]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [7,2,6,1,5,3,4,8]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,8,6,1,5,3,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [4,2,1,5,6,3,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [7,1,2,5,8,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [7,1,4,5,6,8,3,2]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [8,5,6,7,1,4,3,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [7,6,8,5,1,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [6,8,7,5,1,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [2,6,7,1,4,5,3,8]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,5,1,7,4,6,8,2]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [7,1,5,6,4,8,3,2]=>[[1,2,6,8],[3],[4],[5],[7]]=>0111010 [7,1,6,5,4,8,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]=>0111110 [2,7,6,1,4,5,3,8]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [5,7,6,8,1,4,3,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [7,8,6,5,1,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>0111110 [4,3,1,6,5,8,7,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [5,3,1,2,4,8,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [5,3,6,2,1,8,7,4]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,3,7,2,1,4,6,8]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [5,3,7,2,8,4,1,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [7,2,4,5,8,3,1,6]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [7,2,4,5,1,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [6,2,4,5,1,8,7,3]=>[[1,3,5,7],[2,4],[6,8]]=>1010101 [3,1,4,5,2,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [1,6,4,5,2,8,7,3]=>[[1,2,3,7],[4,5],[6,8]]=>0010101 [3,7,4,5,1,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [3,7,4,5,8,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [1,7,4,2,6,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [8,7,4,5,2,1,6,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [6,3,7,1,8,4,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [5,7,4,1,6,3,2,8]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [1,7,4,8,6,3,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [5,7,4,8,6,3,1,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [4,8,3,5,6,7,1,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [1,8,3,5,6,7,2,4]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [4,8,1,5,6,7,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [4,1,3,5,6,7,2,8]=>[[1,2,5,6,7,8],[3],[4]]=>0110000 [5,8,4,3,6,1,2,7]=>[[1,2,7],[3,6],[4,8],[5]]=>0111001 [5,3,8,4,1,7,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [1,5,8,4,6,7,3,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [1,4,8,3,6,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [4,3,8,2,1,7,5,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,8,4,2,6,1,5,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [1,8,2,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [3,8,1,5,6,7,4,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [3,8,2,5,6,7,1,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [8,2,1,5,6,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [8,1,3,5,6,7,4,2]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [7,1,4,3,6,2,5,8]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [7,8,4,3,6,2,1,5]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [4,3,1,8,5,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [4,3,1,6,8,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [6,3,1,8,2,7,4,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [6,3,5,8,2,7,1,4]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [7,5,4,8,6,2,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [7,1,4,8,6,2,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [7,5,4,1,6,2,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [7,6,4,5,8,1,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [1,6,4,5,8,2,3,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [7,3,6,1,8,2,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,7,6,5,8,3,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [1,8,5,3,6,7,4,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [8,3,5,2,1,7,4,6]=>[[1,4,6],[2,5,7],[3],[8]]=>1101011 [8,4,1,5,6,7,3,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [8,4,2,5,6,7,1,3]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [4,1,8,5,6,7,3,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [1,2,8,5,6,7,3,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [4,2,1,5,6,7,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [1,5,3,8,6,7,4,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [1,4,5,8,6,7,3,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [4,3,5,8,1,7,2,6]=>[[1,2,6],[3,5,7],[4,8]]=>0110011 [3,5,4,8,6,1,2,7]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [1,4,8,5,6,7,2,3]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [3,4,8,5,6,7,1,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [4,3,7,2,5,6,8,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [2,6,3,1,4,5,8,7]=>[[1,3,4,5,7],[2,8],[6]]=>1000101 [3,7,1,5,6,2,8,4]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [4,7,1,5,6,8,2,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [8,4,2,3,5,7,1,6]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [5,3,4,6,2,8,1,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [6,4,7,2,3,8,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [6,5,7,2,8,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>1001100 [5,3,7,2,4,8,6,1]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [8,7,6,1,4,5,2,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [8,7,6,1,3,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [8,7,4,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>0010011 [8,5,6,4,1,7,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [8,4,6,2,3,1,7,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [10,3,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>010000001 [8,10,1,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8,10]]=>000000101 [2,3,10,1,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2,10]]=>100000001 [8,7,1,2,3,4,5,10,6,9]=>[[1,2,3,4,5,6,9],[7,10],[8]]=>000001101 [8,9,1,2,3,4,5,6,10,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>000000100 [7,3,5,4,1,8,6,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [2,6,5,7,3,1,8,4]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [4,2,1,6,3,7,5,8]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,1,6,3,7,8,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,1,3,7,8,6,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,8,1,7,4,3,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [4,2,1,8,3,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,1,6,3,8,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [7,3,4,2,6,8,1,5]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,6,7,5,2,4,8,1]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,6,7,5,2,4,1,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [4,2,1,7,3,6,5,8]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [3,7,6,8,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [5,8,1,7,4,2,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [3,7,8,6,2,4,5,1]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [4,2,1,3,5,8,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,1,8,3,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]=>1010111 [2,6,1,5,4,7,8,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [4,6,3,5,8,7,1,2]=>[[1,2,7],[3,5,8],[4,6]]=>0110101 [2,7,5,1,8,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [4,7,5,2,1,3,6,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [3,5,6,2,4,1,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [2,5,6,1,4,8,3,7]=>[[1,3,6,7],[2,4,8],[5]]=>1011001 [6,7,8,4,1,5,3,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [7,1,6,8,4,5,3,2]=>[[1,2,5],[3,8],[4],[6],[7]]=>0110110 [7,4,6,5,2,8,1,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>1010110 [7,1,5,6,4,2,3,8]=>[[1,2,3,8],[4,6],[5],[7]]=>0011010 [5,7,4,6,8,1,3,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [5,7,8,1,4,6,3,2]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [8,1,5,7,4,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [1,8,4,6,7,5,3,2]=>[[1,2,5,7],[3],[4],[6],[8]]=>0110101 [6,1,8,4,7,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [4,5,8,6,1,7,3,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [4,8,5,1,6,7,3,2]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [8,1,4,5,6,7,3,2]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [5,6,7,1,4,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [8,4,2,6,1,5,7,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,8,5,2,1,6,7,3]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [5,1,8,4,2,6,3,7]=>[[1,2,3,7],[4,6],[5,8]]=>0011001 [1,8,4,6,2,5,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>0010101 [6,1,5,2,3,4,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>0001100 [8,3,1,4,6,2,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [3,1,8,2,5,6,4,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [3,5,1,8,2,6,4,7]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [3,5,1,2,8,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,3,5,8,6,1,7,4]=>[[1,3,4,6,7],[2,5],[8]]=>1001001 [8,2,4,3,6,7,1,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,2,8,5,7,1,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [3,6,2,8,5,1,7,4]=>[[1,4,7],[2,5,8],[3,6]]=>1101101 [6,2,1,8,4,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [2,8,7,1,4,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [8,2,7,1,5,4,6,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [7,2,5,3,6,8,1,4]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [7,3,1,5,6,2,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [3,7,5,1,6,2,4,8]=>[[1,2,4,8],[3,5,6],[7]]=>0101010 [2,7,3,6,5,8,1,4]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [8,7,2,4,1,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [1,8,7,2,3,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>0001111 [1,7,8,2,6,4,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,7,3,8,2,6,4,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [1,2,7,3,6,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>0000110 [7,1,5,8,3,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [1,6,2,8,4,3,7,5]=>[[1,2,3,5],[4,7],[6,8]]=>0010101 [1,3,8,7,2,4,6,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [1,8,3,7,2,5,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [8,1,4,7,3,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,7,8,1,3,2,5,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [7,1,4,2,3,5,6,8]=>[[1,2,3,5,6,8],[4],[7]]=>0010010 [8,2,1,4,7,3,5,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [2,1,3,8,4,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [1,2,3,4,8,5,7,6]=>[[1,2,3,4,5,6],[7],[8]]=>0000011 [2,4,8,7,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [2,5,3,8,4,7,6,1]=>[[1,3,4,6],[2,7],[5],[8]]=>1001011 [2,8,5,7,3,6,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [3,1,8,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]=>0101011 [2,8,6,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>1000101 [2,5,7,3,4,8,6,1]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [8,3,7,6,1,4,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [3,1,7,8,2,5,6,4]=>[[1,2,4,6],[3,5,8],[7]]=>0101010 [7,3,8,5,1,6,4,2]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [7,5,1,2,3,4,8,6]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [4,8,1,5,2,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,1,2,5,3,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,3,6,8,7,5,1,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [5,4,1,8,2,7,6,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [6,7,3,1,4,8,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [5,4,1,6,8,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [5,4,7,1,2,8,6,3]=>[[1,2,3],[4,6,8],[5,7]]=>0011010 [6,7,4,1,2,8,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [6,5,1,2,3,7,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [6,5,1,2,3,4,8,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,7,4,1,2,5,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [2,4,6,3,5,7,1,8]=>[[1,3,5,7,8],[2,6],[4]]=>1010100 [1,4,6,3,7,2,5,8]=>[[1,2,5,7,8],[3,6],[4]]=>0110100 [8,6,2,5,3,1,7,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [8,2,3,4,5,1,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [1,8,3,4,2,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [2,8,3,4,1,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [8,7,2,3,1,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]=>1001111 [3,8,2,4,6,1,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [7,8,2,4,3,1,6,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [4,5,8,2,3,1,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [5,1,4,3,7,2,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [6,1,3,5,7,2,4,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [2,1,4,7,5,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [7,1,3,6,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [8,1,3,6,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [2,1,8,3,7,5,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [7,1,8,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [6,1,5,8,2,7,3,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [4,5,2,8,1,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [6,2,5,8,1,4,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [3,2,8,5,1,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [8,2,7,1,4,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [1,3,8,2,5,7,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [2,8,7,1,6,4,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]=>1010111 [3,8,7,1,5,6,4,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [3,4,8,5,6,1,7,2]=>[[1,2,5,6,7],[3,4],[8]]=>0100001 [8,3,7,4,1,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>0100111 [1,4,8,6,2,7,3,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [8,4,5,7,1,6,3,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>0110011 [3,5,6,8,4,1,7,2]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [6,2,3,1,5,4,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [7,2,3,1,4,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]=>1000110 [8,2,3,1,4,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [8,5,1,3,2,4,7,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [7,5,1,3,2,6,4,8]=>[[1,2,4,8],[3,6],[5],[7]]=>0101010 [2,6,1,4,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [3,6,4,1,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [4,5,6,1,3,2,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>0110000 [4,5,7,1,2,6,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [3,7,4,1,2,6,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [6,7,1,4,2,5,3,8]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [2,7,1,3,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]=>1001010 [8,6,1,2,4,3,7,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [2,8,1,3,4,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [7,8,1,2,5,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [3,8,4,1,2,5,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [1,2,6,7,5,3,8,4]=>[[1,2,3,4,8],[5,7],[6]]=>0001100 [1,7,5,3,2,8,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [1,6,7,5,3,8,4,2]=>[[1,2,4,8],[3,7],[5],[6]]=>0101100 [1,6,5,7,2,3,8,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [1,3,8,2,6,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [1,2,5,7,6,3,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,3,4,8,2,5,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [1,5,7,6,2,3,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>0001010 [1,5,3,8,2,6,4,7]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [1,4,8,3,2,5,7,6]=>[[1,2,5,6],[3,7],[4,8]]=>0110011 [1,4,8,3,5,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,2,4,8,3,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,3,8,4,2,6,7,5]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [1,4,8,2,3,5,7,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [6,5,7,3,8,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [4,2,6,7,5,8,3,1]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [6,7,5,2,1,8,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [3,4,8,7,5,2,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [1,7,5,2,8,4,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [5,6,8,3,1,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [6,1,4,8,3,2,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [3,4,7,1,8,6,2,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,6,8,2,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,8,2,5,6,1,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,5,2,8,6,4,1,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [4,2,5,7,3,8,6,1]=>[[1,3,6,8],[2,5,7],[4]]=>1010010 [7,4,2,5,3,8,1,6]=>[[1,3,6],[2,5,8],[4],[7]]=>1010010 [3,1,2,8,5,6,4,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [5,2,1,6,8,3,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [5,2,6,8,4,1,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [1,5,6,8,3,4,2,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [4,5,8,1,6,3,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>0110001 [4,5,1,6,8,3,2,7]=>[[1,2,6,7],[3,5,8],[4]]=>0110001 [4,5,7,3,8,2,6,1]=>[[1,5,6,8],[2,7],[3],[4]]=>1110010 [6,4,3,7,8,2,5,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,4,3,1,7,8,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [4,5,3,1,7,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [7,1,3,5,4,8,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,5,2,8,1,4,3,6]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [5,7,3,8,4,6,1,2]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [1,4,5,7,3,8,6,2]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [4,6,3,7,8,5,2,1]=>[[1,5,7,8],[2,6],[3],[4]]=>1110100 [5,3,6,7,8,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [1,5,3,6,7,8,4,2]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [4,6,1,7,3,8,5,2]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [6,3,7,1,8,4,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [6,7,2,4,8,1,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [2,6,1,4,7,3,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [3,2,5,6,7,8,1,4]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [5,2,3,6,7,8,4,1]=>[[1,3,4,7,8],[2,6],[5]]=>1001000 [6,7,1,3,2,8,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [6,2,7,1,3,4,8,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [5,2,1,7,3,8,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [6,4,2,7,1,8,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [4,2,6,3,7,8,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [4,2,6,3,7,8,5,1]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [6,7,3,8,2,4,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [3,6,2,7,4,1,8,5]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [6,7,3,2,1,4,8,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [7,1,8,3,4,2,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,2,4,1,8,3,5,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,2,4,8,6,1,3,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [7,3,4,8,6,2,1,5]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [3,5,7,2,1,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]=>1101010 [6,7,8,3,2,5,1,4]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,7,8,2,5,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [2,6,7,4,8,5,3,1]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [6,2,4,7,1,8,5,3]=>[[1,3,5,8],[2,4],[6,7]]=>1010100 [4,6,2,7,1,8,5,3]=>[[1,3,7,8],[2,5],[4,6]]=>1010100 [1,7,4,8,5,2,6,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [1,3,7,8,5,2,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [2,5,7,8,1,6,3,4]=>[[1,3,4,8],[2,5,6],[7]]=>1001010 [6,3,7,1,8,2,5,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [1,6,4,7,8,2,5,3]=>[[1,2,3,8],[4,5],[6,7]]=>0010100 [2,5,6,1,7,8,4,3]=>[[1,3,6,7,8],[2,4],[5]]=>1011000 [5,6,1,2,7,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]=>0011000 [6,7,2,1,8,5,3,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [6,7,2,8,5,4,1,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [1,6,7,4,8,5,3,2]=>[[1,2,5,8],[3,7],[4],[6]]=>0110100 [1,8,4,5,3,6,2,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [1,8,5,3,4,7,2,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,8,2,4,6,3,7,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [1,8,2,5,4,6,7,3]=>[[1,2,3,6,7],[4],[5],[8]]=>0011001 [3,6,2,7,1,4,5,8]=>[[1,4,5,8],[2,6,7],[3]]=>1100100 [1,4,7,5,2,6,8,3]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [4,6,5,3,7,1,8,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [4,2,3,8,6,7,1,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [5,2,4,8,1,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [6,2,5,4,8,3,7,1]=>[[1,3,7],[2,8],[4],[5],[6]]=>1011101 [6,4,3,5,8,2,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,2,3,4,8,1,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [3,5,2,4,7,1,6,8]=>[[1,4,6,8],[2,5,7],[3]]=>1101010 [5,3,4,8,1,6,2,7]=>[[1,2,6,7],[3,4],[5,8]]=>0101001 [4,5,3,7,1,6,2,8]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [7,6,3,8,5,1,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [4,2,6,7,3,8,1,5]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [1,5,7,4,2,8,6,3]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [1,3,7,2,8,6,4,5]=>[[1,2,4,5],[3,6,8],[7]]=>0100110 [1,4,3,7,8,6,2,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [1,5,3,6,8,2,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [4,3,6,5,7,8,1,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,2,3,5,6,8,1,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [4,2,6,7,3,8,5,1]=>[[1,3,5,8],[2,6,7],[4]]=>1010100 [3,2,5,6,8,1,7,4]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [6,4,5,2,3,8,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [6,4,2,5,3,8,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [8,6,4,7,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [8,6,2,7,4,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [4,6,2,5,3,8,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [4,6,5,2,3,8,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [6,8,2,7,4,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [6,8,7,2,4,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [2,6,4,5,8,7,3,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [2,6,4,8,7,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [8,2,4,6,7,5,3,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>1010101 [4,2,6,5,8,7,3,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [4,2,3,6,8,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [6,4,8,7,2,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [6,4,8,7,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [8,2,6,4,7,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [4,6,8,2,7,5,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [4,6,5,8,2,7,3,1]=>[[1,3,7],[2,5],[4,8],[6]]=>1010101 [2,1,8,6,4,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [6,8,7,4,2,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [9,2,4,6,8,1,3,5,7]=>[[1,3,5,7],[2,4,6,8],[9]]=>10101011 [9,4,6,8,1,2,3,5,7]=>[[1,2,3,5,7],[4,6,8],[9]]=>00101011 [9,6,8,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6,8],[9]]=>00001011 [3,5,7,9,1,2,4,6,8]=>[[1,2,4,6,8],[3,5,7,9]]=>01010101 [5,7,9,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7,9]]=>00010101 [7,9,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9]]=>00000101 [10,9,8,7,6,5,2,4,1,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>101111111 [10,9,4,8,3,7,2,6,1,5]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>111011111 [10,9,8,7,2,4,6,1,3,5]=>[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>101011111 [6,10,5,9,2,4,8,1,3,7]=>[[1,3,7],[2,4,8],[5,9],[6,10]]=>101110111 [10,9,2,4,6,8,1,3,5,7]=>[[1,3,5,7],[2,4,6,8],[9],[10]]=>101010111 [10,3,5,7,9,1,2,4,6,8]=>[[1,2,4,6,8],[3,5,7,9],[10]]=>010101011 [10,5,7,9,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5,7,9],[10]]=>000101011 [10,7,9,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7,9],[10]]=>000001011 [4,2,5,6,3,8,1,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [6,2,5,7,4,8,3,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>1011100 [8,5,2,1,4,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [6,7,3,2,5,8,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [3,2,6,4,8,1,5,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [2,3,6,4,7,8,5,1]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [7,5,1,8,3,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [5,7,8,2,6,3,4,1]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [7,1,6,3,5,8,4,2]=>[[1,2,4,8],[3],[5],[6],[7]]=>0101110 [6,3,1,7,8,4,5,2]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [5,3,6,7,4,1,8,2]=>[[1,2,7,8],[3,4],[5,6]]=>0101000 [7,3,1,2,5,8,6,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [1,6,3,5,2,4,8,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,4,8,2,7,5,1,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [6,3,2,8,5,7,4,1]=>[[1,4,7],[2,5],[3,8],[6]]=>1101101 [3,8,4,7,2,5,6,1]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [2,4,8,1,5,3,7,6]=>[[1,3,5,6],[2,4,7],[8]]=>1010011 [3,4,8,1,6,2,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [1,8,4,6,7,3,5,2]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,1,6,3,4,5,7,2]=>[[1,2,4,5,7],[3],[6],[8]]=>0100101 [7,6,5,4,1,2,8,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [5,7,6,8,3,4,2,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [2,8,1,6,5,7,4,3]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [4,6,8,2,5,3,7,1]=>[[1,3,7],[2,5,8],[4],[6]]=>1010101 [5,2,3,7,6,1,8,4]=>[[1,3,4,8],[2,6],[5,7]]=>1001010 [8,1,2,4,6,7,3,5]=>[[1,2,3,5,7],[4,6],[8]]=>0010101 [5,2,3,7,4,8,6,1]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [5,2,6,8,4,3,1,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [7,8,1,5,4,3,6,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [7,2,4,8,5,3,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [3,7,5,1,8,4,6,2]=>[[1,2,6],[3,4,8],[5],[7]]=>0101010 [2,7,8,5,4,6,1,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [5,7,4,3,8,6,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,8,1,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,3,1,7,4,2,5,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [3,1,8,2,4,5,7,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [8,1,3,7,6,2,4,5]=>[[1,2,4,5],[3,6],[7],[8]]=>0100111 [2,3,6,8,7,1,4,5]=>[[1,3,4,5],[2,6,7],[8]]=>1000101 [4,3,2,8,5,7,1,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,6,4,2,8,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [4,7,3,2,5,1,8,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [3,2,4,7,5,8,6,1]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [4,2,3,8,6,5,1,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [2,4,3,5,1,8,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [3,2,8,1,4,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [4,7,8,3,1,2,6,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [4,7,8,2,1,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [4,1,6,8,2,3,7,5]=>[[1,2,3,5],[4,6,7],[8]]=>0010101 [4,5,1,2,8,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,6,2,8,1,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [3,6,2,8,4,7,1,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,2,6,8,3,1,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,1,2,5,8,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [5,2,4,1,3,8,7,6]=>[[1,3,6],[2,4,7],[5,8]]=>1011011 [4,2,5,3,8,1,7,6]=>[[1,3,6],[2,5,7],[4,8]]=>1010011 [3,2,5,4,8,7,1,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [5,1,4,2,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [5,4,1,3,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [5,4,3,1,2,8,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [3,5,1,4,8,7,2,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [2,5,6,8,7,3,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [3,4,5,1,8,7,2,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [4,3,6,8,2,1,7,5]=>[[1,5,7],[2,6],[3,8],[4]]=>1110101 [2,4,6,8,3,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [3,4,5,2,8,7,1,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [5,3,1,4,2,8,7,6]=>[[1,2,6],[3,4,7],[5,8]]=>0101011 [5,3,2,1,4,8,7,6]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [4,3,2,5,8,1,7,6]=>[[1,5,6],[2,7],[3,8],[4]]=>1110011 [3,2,4,5,8,7,1,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [5,2,1,3,4,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]=>1001011 [5,1,2,3,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [8,6,2,5,4,1,3,7]=>[[1,3,7],[2,4],[5],[6],[8]]=>1011101 [6,5,7,4,2,8,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>1011100 [6,7,5,3,8,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>1101100 [8,2,1,6,3,4,5,7]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [8,3,5,6,2,4,1,7]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [8,6,2,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [8,1,2,3,4,6,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>0000101 [6,2,3,7,8,4,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,5,8,2,6,3,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [7,3,1,6,5,8,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>0101110 [1,5,6,7,3,4,8,2]=>[[1,2,4,7,8],[3,6],[5]]=>0101000 [6,7,8,2,1,4,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [8,4,7,6,2,1,3,5]=>[[1,3,5],[2,6],[4],[7],[8]]=>1010111 [5,3,8,4,7,2,6,1]=>[[1,4,6],[2,7],[3,8],[5]]=>1101011 [8,1,3,7,6,4,2,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>0100111 [5,3,1,7,8,6,2,4]=>[[1,2,4],[3,6,8],[5,7]]=>0101010 [3,5,8,2,7,1,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [6,2,8,5,3,1,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [8,2,6,4,7,1,3,5]=>[[1,3,5],[2,4,7],[6],[8]]=>1010101 [3,4,2,8,5,1,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [3,8,6,5,2,1,7,4]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [8,3,7,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>1100011 [4,8,5,7,2,1,3,6]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [3,4,1,8,2,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,4,6,3,7,1,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [6,8,3,4,1,5,7,2]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [5,1,7,6,2,8,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [6,8,2,5,7,4,1,3]=>[[1,3,7],[2,4],[5,8],[6]]=>1011101 [2,8,5,6,7,1,3,4]=>[[1,3,4,7],[2,5,6],[8]]=>1001001 [2,5,7,6,3,1,8,4]=>[[1,3,4,8],[2,6],[5],[7]]=>1001010 [4,2,8,3,1,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]=>1010001 [2,5,7,3,8,4,6,1]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [4,2,7,1,8,5,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,2,1,8,7,5,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [8,3,6,7,1,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [1,3,7,5,8,6,4,2]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [5,7,8,4,3,1,6,2]=>[[1,2,8],[3,6],[4,7],[5]]=>0111010 [2,7,4,5,8,3,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>1010010 [3,5,7,1,4,8,6,2]=>[[1,2,6,8],[3,4,7],[5]]=>0101010 [7,2,8,5,1,4,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [1,6,5,3,8,4,2,7]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [5,7,4,8,3,6,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [4,8,6,1,3,5,2,7]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [1,8,3,2,4,7,5,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [8,4,3,2,5,7,1,6]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [3,6,4,8,2,5,7,1]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [4,3,7,2,5,8,1,6]=>[[1,5,6],[2,7,8],[3],[4]]=>1110010 [3,2,4,7,8,5,6,1]=>[[1,4,5,6],[2,7,8],[3]]=>1100010 [2,6,4,3,8,5,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,8,2,1,6,4,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [8,2,1,3,4,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]=>1000011 [4,6,8,3,2,1,5,7]=>[[1,5,7],[2,6,8],[3],[4]]=>1110101 [3,2,6,8,5,4,1,7]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [7,3,8,2,5,4,1,6]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [4,2,5,3,8,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]=>1010011 [4,8,2,6,5,3,1,7]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [2,6,8,5,4,1,3,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [3,1,8,6,5,4,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>0101101 [5,4,8,7,3,2,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,4,8,3,7,2,5,1]=>[[1,5],[2,7],[3,8],[4],[6]]=>1110101 [4,7,3,6,2,1,8,5]=>[[1,5,8],[2,6],[3,7],[4]]=>1110110 [5,4,3,7,1,8,2,6]=>[[1,2,6],[3,7,8],[4],[5]]=>0111010 [7,3,8,5,1,4,2,6]=>[[1,2,6],[3,4],[5,8],[7]]=>0101010 [5,4,8,7,6,2,1,3]=>[[1,3],[2,6],[4,7],[5],[8]]=>1011011 [3,8,1,5,7,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]=>0101011 [4,8,5,7,3,1,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [1,5,4,8,3,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [4,8,3,6,7,1,5,2]=>[[1,2,7],[3,5],[4,6],[8]]=>0110101 [4,7,8,3,1,6,5,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [8,7,5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>1101011 [4,6,1,3,8,7,5,2]=>[[1,2,5],[3,6,7],[4],[8]]=>0110101 [6,8,2,1,7,4,5,3]=>[[1,3,5],[2,4],[6,7],[8]]=>1010101 [3,7,1,6,4,2,8,5]=>[[1,2,5],[3,4,8],[6],[7]]=>0100110 [3,1,2,7,5,6,8,4]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [3,6,1,2,7,5,8,4]=>[[1,2,4,8],[3,5,7],[6]]=>0101100 [3,7,6,2,5,8,1,4]=>[[1,4,8],[2,5],[3,6],[7]]=>1101110 [3,6,2,5,8,7,4,1]=>[[1,4,7],[2,5,8],[3],[6]]=>1101101 [8,5,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [4,7,2,6,3,8,1,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [6,3,2,4,8,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [3,7,2,4,6,1,8,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,3,7,2,8,1,4,6]=>[[1,4,6],[2,7,8],[3],[5]]=>1101010 [6,3,2,8,7,5,1,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [7,3,8,2,6,5,1,4]=>[[1,4],[2,5],[3,6],[7,8]]=>1101110 [6,4,8,7,2,5,1,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [2,5,4,8,1,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [5,2,8,1,7,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [6,2,1,3,8,7,5,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [3,6,1,8,7,5,2,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [5,6,1,2,8,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [7,5,2,8,1,6,4,3]=>[[1,3],[2,4],[5,6],[7,8]]=>1011010 [2,7,6,8,1,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]=>1011110 [7,8,5,1,6,2,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,4,8,6,1,2,5,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [7,2,1,8,3,6,5,4]=>[[1,3,4],[2,5],[6,8],[7]]=>1001110 [5,8,7,1,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>0111011 [8,5,4,3,7,2,1,6]=>[[1,6],[2,7],[3],[4],[5],[8]]=>1111011 [6,5,4,8,3,2,7,1]=>[[1,7],[2,8],[3],[4],[5],[6]]=>1111101 [7,3,1,4,8,2,5,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [5,7,2,4,6,8,1,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [6,4,7,1,3,8,5,2]=>[[1,2,5],[3,7,8],[4],[6]]=>0110100 [4,5,1,2,7,6,8,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [5,4,6,8,3,1,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [1,3,8,4,5,7,2,6]=>[[1,2,4,5,6],[3,7],[8]]=>0100011 [2,6,7,4,5,3,1,8]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [1,3,7,4,2,8,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>0100010 [7,5,8,6,2,1,3,4]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [2,8,1,3,6,5,4,7]=>[[1,3,4,7],[2,5],[6],[8]]=>1001101 [2,8,7,3,5,4,1,6]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [7,3,8,4,1,2,6,5]=>[[1,2,5],[3,4,6],[7,8]]=>0100110 [6,8,3,2,7,1,5,4]=>[[1,4],[2,5],[3,7],[6,8]]=>1101101 [3,7,1,2,4,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [7,5,6,8,2,1,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [1,7,2,3,5,6,8,4]=>[[1,2,3,4,6,8],[5],[7]]=>0001010 [3,4,6,2,8,5,7,1]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [4,2,1,7,5,8,3,6]=>[[1,3,6],[2,5,8],[4,7]]=>1010010 [4,7,1,6,5,2,8,3]=>[[1,2,3],[4,5,8],[6],[7]]=>0010110 [4,7,3,6,5,1,8,2]=>[[1,2,8],[3,5],[4,6],[7]]=>0110110 [3,2,4,8,6,7,1,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [4,2,6,8,7,3,1,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [3,4,6,1,8,5,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [4,3,7,1,6,8,2,5]=>[[1,2,5],[3,6,8],[4,7]]=>0110110 [2,8,7,4,5,3,1,6]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [2,8,7,4,3,5,1,6]=>[[1,3,5,6],[2],[4],[7],[8]]=>1010011 [3,8,1,4,2,6,5,7]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [5,8,7,6,1,2,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [5,8,7,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [4,2,7,3,6,1,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [3,8,2,4,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]=>1100001 [3,8,2,4,1,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,8,2,5,4,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [4,2,7,5,6,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [4,2,7,5,6,1,8,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [4,2,6,7,5,3,1,8]=>[[1,3,7,8],[2,5],[4],[6]]=>1010100 [3,2,6,1,4,5,8,7]=>[[1,4,5,7],[2,6,8],[3]]=>1100101 [3,8,1,2,4,6,5,7]=>[[1,2,4,5,7],[3,6],[8]]=>0100101 [5,8,7,6,1,3,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [5,8,7,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>1001011 [2,8,7,5,3,4,1,6]=>[[1,3,4,6],[2],[5],[7],[8]]=>1001011 [5,8,7,6,1,3,2,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [5,8,7,6,4,1,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [5,4,2,3,7,6,8,1]=>[[1,3,6,8],[2,7],[4],[5]]=>1011010 [7,4,3,5,2,8,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [8,4,3,7,5,1,6,2]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [8,4,7,2,5,1,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [7,4,6,2,3,5,8,1]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [5,1,7,2,4,6,8,3]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [4,5,7,1,2,6,8,3]=>[[1,2,3,8],[4,5,6],[7]]=>0010010 [5,4,1,7,3,6,8,2]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [3,6,4,7,5,2,8,1]=>[[1,4,5,8],[2,7],[3],[6]]=>1100100 [3,4,7,6,2,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,7,5,6,1,3,8,2]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [5,7,6,4,3,1,8,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [5,7,6,3,1,4,8,2]=>[[1,2,8],[3,4],[5,6],[7]]=>0101010 [7,5,2,3,4,8,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>1001010 [8,7,5,3,4,1,6,2]=>[[1,2,6],[3,4],[5],[7],[8]]=>0101011 [6,7,1,3,8,4,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [7,6,1,3,4,8,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [3,6,5,2,7,8,1,4]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [3,2,8,6,7,1,4,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,8,3,6,5,2,1,7]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [1,8,6,5,4,2,3,7]=>[[1,2,3,7],[4],[5],[6],[8]]=>0011101 [1,8,7,2,3,5,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [1,8,7,2,5,3,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>0001011 [3,6,8,5,1,2,4,7]=>[[1,2,4,7],[3,5,8],[6]]=>0101101 [3,7,5,1,8,2,6,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [7,1,2,8,3,5,6,4]=>[[1,2,3,4,6],[5,8],[7]]=>0001010 [6,1,7,8,2,5,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,7,5,2,8,1,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [7,1,4,5,8,6,2,3]=>[[1,2,3,6],[4,5],[7,8]]=>0010010 [5,7,6,4,2,8,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [7,5,6,1,2,8,4,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [4,1,3,7,8,6,2,5]=>[[1,2,5,8],[3,6],[4,7]]=>0110110 [5,1,4,3,6,8,7,2]=>[[1,2,6,7],[3,8],[4],[5]]=>0111001 [4,5,7,6,8,2,1,3]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [5,7,6,8,4,2,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>1011010 [5,1,6,8,4,2,7,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [7,4,8,2,3,6,5,1]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [5,6,8,4,7,3,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [6,4,7,8,5,2,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [3,6,4,8,5,1,2,7]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [3,7,4,8,1,2,5,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [7,4,3,8,2,6,5,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [7,6,8,3,2,5,4,1]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [8,7,1,3,5,4,6,2]=>[[1,2,4,6],[3],[5],[7],[8]]=>0101011 [7,1,8,3,4,2,6,5]=>[[1,2,4,5],[3,6],[7,8]]=>0100110 [7,6,8,3,1,4,5,2]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [3,1,4,8,2,5,7,6]=>[[1,2,5,6],[3,4,7],[8]]=>0100011 [4,8,5,2,1,3,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [5,8,2,6,3,1,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [6,8,2,3,7,4,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [7,8,2,3,4,6,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [8,1,7,2,4,5,3,6]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [8,1,3,6,2,5,4,7]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [7,2,1,6,3,5,4,8]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,7,1,6,3,5,4,8]=>[[1,3,4,8],[2,5],[6],[7]]=>1001110 [2,7,1,5,4,3,6,8]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [7,2,1,5,4,3,6,8]=>[[1,3,6,8],[2,4],[5],[7]]=>1011010 [8,1,3,5,4,2,6,7]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [8,1,5,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5],[8]]=>0101001 [8,1,5,6,2,3,7,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [8,1,4,5,3,2,6,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [8,1,4,3,5,2,6,7]=>[[1,2,5,6,7],[3],[4],[8]]=>0110001 [7,2,1,4,5,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [2,7,1,4,5,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [2,6,3,1,5,4,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [6,3,2,1,5,4,7,8]=>[[1,4,7,8],[2,5],[3],[6]]=>1101100 [7,3,1,4,5,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [7,3,1,5,4,2,6,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [7,3,1,6,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [3,7,1,6,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [3,7,1,4,5,2,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>0100010 [3,6,2,1,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]=>1101100 [2,3,6,1,5,4,7,8]=>[[1,3,4,7,8],[2,5],[6]]=>1001100 [3,5,2,4,1,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]=>1101000 [6,3,4,1,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [6,2,4,1,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,6,4,1,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [2,6,5,1,3,7,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,2,5,1,3,7,4,8]=>[[1,3,4,8],[2,5,7],[6]]=>1001100 [6,5,2,1,3,7,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>1001100 [7,6,1,2,4,5,3,8]=>[[1,2,3,5,8],[4],[6],[7]]=>0010110 [6,7,1,2,8,3,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [6,7,1,2,5,4,3,8]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [5,6,2,1,3,7,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [5,2,6,1,3,7,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [2,4,6,1,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]=>1010100 [4,7,1,3,5,2,6,8]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [4,7,1,5,3,2,6,8]=>[[1,2,6,8],[3,5],[4],[7]]=>0110010 [5,7,1,4,2,6,3,8]=>[[1,2,3,8],[4,6],[5,7]]=>0011010 [5,7,1,6,2,3,8,4]=>[[1,2,3,4],[5,6,8],[7]]=>0001010 [5,6,3,1,2,7,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [4,2,5,3,1,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>1010000 [5,3,6,1,2,7,4,8]=>[[1,2,4,8],[3,6,7],[5]]=>0101000 [3,4,6,1,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [8,2,7,5,4,1,3,6]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [6,8,5,2,3,4,1,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [8,5,6,2,7,1,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [6,5,1,2,7,8,4,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [4,7,6,1,5,3,8,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [5,7,6,4,1,3,8,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>0111010 [7,6,2,4,5,3,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>1010110 [6,1,7,5,3,8,4,2]=>[[1,2,4],[3,7,8],[5],[6]]=>0101100 [8,6,7,5,3,1,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>0101101 [8,5,2,7,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [7,6,1,5,3,8,4,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>0101110 [5,6,2,4,7,8,1,3]=>[[1,3,7,8],[2,4],[5,6]]=>1011000 [3,4,6,1,7,8,5,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [3,4,8,6,7,1,5,2]=>[[1,2,5,7],[3,4],[6],[8]]=>0100101 [4,8,5,6,7,2,3,1]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [5,8,6,4,1,2,7,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [5,8,6,1,7,2,4,3]=>[[1,2,3],[4,6,7],[5],[8]]=>0011001 [5,8,7,3,2,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [5,8,1,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,1,5,7,2,6,4,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>0011011 [8,1,7,2,5,6,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>0001011 [6,8,7,2,5,1,3,4]=>[[1,3,4],[2,5],[6,7],[8]]=>1001101 [5,8,7,2,1,6,3,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [4,8,1,5,2,6,7,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,7,8,5,1,6,2,4]=>[[1,2,4],[3,5,6],[7,8]]=>0101010 [6,5,2,7,8,1,4,3]=>[[1,3,8],[2,4],[5,7],[6]]=>1011100 [7,1,2,8,5,6,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [8,7,2,1,5,6,3,4]=>[[1,3,4],[2,5,6],[7],[8]]=>1001011 [8,6,7,1,5,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>0001101 [6,1,7,8,5,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [7,5,6,2,1,8,4,3]=>[[1,3,8],[2,4],[5,6],[7]]=>1011010 [8,7,5,2,1,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [7,1,3,5,8,6,2,4]=>[[1,2,4,6],[3,5],[7,8]]=>0101010 [5,1,3,4,6,8,7,2]=>[[1,2,4,6,7],[3,8],[5]]=>0101001 [4,5,3,6,8,2,7,1]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [5,6,3,4,8,1,7,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [4,6,7,8,5,1,3,2]=>[[1,2,7,8],[3,5],[4],[6]]=>0110100 [8,4,3,1,2,6,7,5]=>[[1,2,5,7],[3,6],[4],[8]]=>0110101 [8,5,1,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [5,1,8,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [4,6,8,1,5,3,7,2]=>[[1,2,7],[3,5,8],[4],[6]]=>0110101 [6,4,5,8,3,2,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [3,6,4,8,7,1,5,2]=>[[1,2,5],[3,4],[6,7],[8]]=>0100101 [6,5,8,1,3,4,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [5,6,8,3,1,2,7,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [6,1,8,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [7,6,8,3,5,2,1,4]=>[[1,4],[2,5],[3,8],[6],[7]]=>1101110 [8,6,1,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,7,1,3,5,6,2,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [6,7,8,3,5,1,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [3,4,8,1,2,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [5,8,2,4,3,6,7,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,8,2,3,1,6,7,4]=>[[1,3,4,7],[2,6],[5,8]]=>1001001 [6,8,2,3,5,1,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [7,8,2,3,5,6,1,4]=>[[1,3,4,6],[2,5],[7,8]]=>1001010 [8,6,5,1,4,3,7,2]=>[[1,2,7],[3],[4],[5],[6],[8]]=>0111101 [2,6,5,4,1,3,8,7]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [4,1,7,6,3,8,2,5]=>[[1,2,5],[3,6,8],[4],[7]]=>0110110 [4,8,2,5,7,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [3,4,6,5,1,8,2,7]=>[[1,2,5,7],[3,4,8],[6]]=>0100101 [2,6,5,3,4,1,8,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [4,6,1,5,2,3,8,7]=>[[1,2,3,7],[4,5,8],[6]]=>0010101 [6,2,3,5,1,4,8,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [2,6,7,5,1,8,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [8,6,1,2,5,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>0001101 [6,2,5,1,8,3,4,7]=>[[1,3,4,7],[2,5,8],[6]]=>1001101 [7,6,5,2,8,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [2,6,3,5,1,8,7,4]=>[[1,3,4,7],[2,5],[6,8]]=>1001101 [2,4,7,6,5,8,1,3]=>[[1,3,5,8],[2,4],[6],[7]]=>1010110 [2,1,4,8,7,6,3,5]=>[[1,3,5],[2,4,6],[7],[8]]=>1010111 [7,4,6,8,5,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>1110110 [8,1,3,5,7,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [3,2,8,7,5,1,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [4,8,5,1,6,7,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>0010001 [3,8,5,1,6,7,2,4]=>[[1,2,4,7],[3,5,6],[8]]=>0101001 [7,8,6,1,3,5,2,4]=>[[1,2,4],[3,5],[6,8],[7]]=>0101110 [5,6,7,2,8,1,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>1001000 [2,5,1,8,6,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [3,5,1,8,6,7,4,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [5,2,3,8,6,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]=>1001001 [8,3,5,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>0101001 [5,1,3,8,6,7,4,2]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [3,2,5,8,6,7,4,1]=>[[1,4,6,7],[2,5],[3],[8]]=>1101001 [6,2,1,5,3,8,7,4]=>[[1,3,4],[2,5,7],[6,8]]=>1001101 [5,6,3,2,8,1,4,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [8,1,6,3,5,2,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,7,6,2,5,3,1,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>1001111 [4,7,6,8,3,2,5,1]=>[[1,5,8],[2,6],[3],[4],[7]]=>1110110 [2,7,5,8,1,3,4,6]=>[[1,3,4,6],[2,5,8],[7]]=>1001010 [7,6,2,8,5,1,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]=>1011110 [8,1,3,7,5,2,6,4]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,4,8,7,5,1,6,2]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [6,3,8,1,4,2,5,7]=>[[1,2,5,7],[3,4],[6,8]]=>0100101 [6,3,8,5,7,4,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [7,4,6,8,5,1,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>0110110 [2,1,4,8,7,5,6,3]=>[[1,3,5,6],[2,4],[7],[8]]=>1010011 [7,1,5,8,2,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [3,6,8,2,4,1,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [4,5,8,2,6,7,3,1]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [5,2,8,1,6,7,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [2,5,8,4,6,7,3,1]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [5,8,3,4,6,7,2,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [8,4,3,2,6,7,1,5]=>[[1,5,7],[2,6],[3],[4],[8]]=>1110101 [4,2,8,1,6,7,3,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [2,4,8,1,6,7,3,5]=>[[1,3,5,7],[2,4,6],[8]]=>1010101 [5,1,8,2,6,7,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>0001001 [3,4,8,7,2,1,5,6]=>[[1,4,5,6],[2,7],[3],[8]]=>1100011 [7,8,5,3,6,4,2,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>1101010 [2,8,5,7,4,1,3,6]=>[[1,3,6],[2,4,7],[5],[8]]=>1011011 [5,8,4,1,6,7,2,3]=>[[1,2,3],[4,6,7],[5,8]]=>0011001 [3,8,1,4,6,7,2,5]=>[[1,2,5,7],[3,4,6],[8]]=>0100101 [8,2,3,4,6,7,1,5]=>[[1,3,4,5,7],[2,6],[8]]=>1000101 [6,2,7,3,8,4,1,5]=>[[1,3,4,5],[2,7,8],[6]]=>1000100 [7,4,3,2,8,5,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [5,3,2,8,4,6,1,7]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [8,4,2,6,5,3,1,7]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [7,4,2,5,3,1,6,8]=>[[1,3,6,8],[2,5],[4],[7]]=>1010010 [8,3,6,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6],[8]]=>1101101 [5,4,8,3,2,6,1,7]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [3,5,8,2,4,6,1,7]=>[[1,4,6,7],[2,5,8],[3]]=>1101001 [6,4,7,8,2,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>1010100 [5,8,3,6,4,2,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [4,8,6,2,5,3,1,7]=>[[1,3,7],[2,5],[4],[6],[8]]=>1010101 [1,6,4,3,2,8,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [1,5,3,2,8,4,7,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [5,7,4,3,1,2,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [2,8,7,3,5,1,4,6]=>[[1,3,4,6],[2,5],[7],[8]]=>1001011 [7,3,8,6,4,1,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>0100110 [6,1,2,7,3,8,5,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [2,1,7,4,3,8,6,5]=>[[1,3,5],[2,4,6],[7,8]]=>1010110 [6,1,4,3,8,2,7,5]=>[[1,2,5],[3,7],[4,8],[6]]=>0110101 [5,1,3,2,8,7,4,6]=>[[1,2,4,6],[3,7],[5,8]]=>0101011 [1,8,4,2,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [1,8,3,7,2,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [5,1,4,8,3,7,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [2,1,6,8,5,4,7,3]=>[[1,3,7],[2,4,8],[5],[6]]=>1011101 [6,1,5,7,8,2,4,3]=>[[1,2,3,8],[4,7],[5],[6]]=>0011100 [8,3,1,6,7,2,5,4]=>[[1,2,4],[3,5,7],[6],[8]]=>0101101 [7,4,8,6,1,3,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [4,7,6,1,2,5,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [3,7,6,1,5,2,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,5,4,8,3,2,7,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [7,3,6,1,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [5,4,7,1,3,2,6,8]=>[[1,2,6,8],[3,7],[4],[5]]=>0111010 [5,7,4,8,2,1,3,6]=>[[1,3,6],[2,7,8],[4],[5]]=>1011010 [4,6,8,2,5,1,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [7,4,6,2,1,5,3,8]=>[[1,3,8],[2,5],[4,6],[7]]=>1010110 [1,2,6,3,8,5,7,4]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [1,5,2,6,8,4,7,3]=>[[1,2,3,7],[4,6,8],[5]]=>0011001 [5,7,2,3,8,1,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [6,4,7,5,8,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>0010100 [7,4,8,5,1,6,3,2]=>[[1,2,6],[3,5],[4,8],[7]]=>0110010 [5,8,3,6,1,7,4,2]=>[[1,2,7],[3,4],[5,6],[8]]=>0101001 [8,6,4,2,1,7,5,3]=>[[1,3],[2,5],[4,7],[6],[8]]=>1010101 [7,4,2,1,5,8,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [7,6,4,1,8,5,2,3]=>[[1,2,3],[4,5],[6,8],[7]]=>0010110 [1,6,4,8,7,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [6,3,1,2,8,4,7,5]=>[[1,2,4,5],[3,7],[6,8]]=>0100101 [7,5,1,3,2,8,6,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [4,7,1,2,5,8,6,3]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [6,8,4,1,2,7,5,3]=>[[1,2,3],[4,5],[6,7],[8]]=>0010101 [7,5,8,1,2,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]=>0011010 [7,4,8,1,6,3,5,2]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [5,8,2,1,7,3,6,4]=>[[1,3,4],[2,6],[5,7],[8]]=>1001011 [3,6,1,8,2,4,7,5]=>[[1,2,4,5],[3,6,7],[8]]=>0100101 [1,3,8,7,6,2,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [5,4,1,8,7,3,2,6]=>[[1,2,6],[3,7],[4,8],[5]]=>0111011 [3,5,1,8,7,2,4,6]=>[[1,2,4,6],[3,5,7],[8]]=>0101011 [4,6,1,8,3,7,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [4,7,1,2,8,6,3,5]=>[[1,2,3,5],[4,6,8],[7]]=>0010110 [5,8,4,1,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [7,6,8,1,5,4,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>0011110 [8,6,1,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>0111101 [7,1,5,8,6,4,3,2]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [5,1,8,7,3,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]=>0101011 [4,1,8,7,6,2,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]=>0010111 [3,1,8,7,6,5,2,4]=>[[1,2,4],[3,5],[6],[7],[8]]=>0101111 [1,6,4,5,2,3,7,8]=>[[1,2,3,7,8],[4,5],[6]]=>0010100 [1,7,4,5,2,3,6,8]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [1,7,3,5,2,4,6,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,6,3,5,2,4,7,8]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,6,3,4,2,5,7,8]=>[[1,2,4,5,7,8],[3],[6]]=>0100100 [1,7,3,4,2,5,6,8]=>[[1,2,4,5,6,8],[3],[7]]=>0100010 [1,8,6,7,3,4,2,5]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [1,8,5,7,3,4,2,6]=>[[1,2,4,6],[3,7],[5],[8]]=>0101011 [1,7,3,4,2,6,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,5,2,8,4,7,3,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,4,2,8,5,7,3,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [1,7,3,5,2,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]=>0101010 [1,8,4,7,3,5,2,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [1,7,3,6,2,5,4,8]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,7,3,6,2,4,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [1,7,4,6,2,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,8,5,6,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,8,5,6,2,4,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>0011001 [1,3,2,8,5,6,4,7]=>[[1,2,4,6,7],[3,5],[8]]=>0101001 [1,4,2,8,5,6,3,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [1,5,2,8,4,6,3,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,6,2,8,4,5,3,7]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [8,1,2,4,5,3,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>0010001 [8,6,4,7,2,1,3,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>1010101 [1,6,4,7,2,8,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>0010100 [1,4,7,3,5,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [8,4,6,2,3,5,1,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [5,4,8,2,3,6,1,7]=>[[1,3,6,7],[2,8],[4],[5]]=>1011001 [7,4,8,5,2,3,1,6]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [3,8,6,2,4,5,1,7]=>[[1,4,5,7],[2,6],[3],[8]]=>1100101 [4,8,6,2,3,5,1,7]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [1,7,5,3,4,8,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [1,7,6,4,8,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [5,8,7,4,1,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [6,8,5,3,4,1,2,7]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [6,8,3,7,2,1,4,5]=>[[1,4,5],[2,7],[3,8],[6]]=>1100101 [8,5,1,6,3,7,2,4]=>[[1,2,4],[3,6,7],[5],[8]]=>0101001 [6,1,3,7,4,8,2,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [4,1,7,3,5,8,2,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [7,1,6,4,8,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>0010110 [1,8,5,7,2,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [6,1,5,8,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [5,1,7,3,8,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [6,1,5,7,8,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>0001100 [7,4,8,6,1,2,3,5]=>[[1,2,3,5],[4,6],[7,8]]=>0010110 [3,8,7,5,1,2,4,6]=>[[1,2,4,6],[3,5],[7],[8]]=>0101011 [3,7,6,1,2,4,5,8]=>[[1,2,4,5,8],[3,6],[7]]=>0100110 [4,7,6,1,2,3,5,8]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [1,6,5,8,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [6,5,8,4,1,2,3,7]=>[[1,2,3,7],[4,8],[5],[6]]=>0011101 [8,5,7,4,1,2,3,6]=>[[1,2,3,6],[4,7],[5],[8]]=>0011011 [1,5,7,4,8,2,3,6]=>[[1,2,3,6],[4,7,8],[5]]=>0011010 [7,6,4,8,2,1,3,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>1010110 [7,6,2,3,8,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>1000110 [7,4,8,5,1,6,2,3]=>[[1,2,3],[4,5,6],[7,8]]=>0010010 [8,6,2,3,1,7,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>1000101 [8,6,4,1,2,7,3,5]=>[[1,2,3,5],[4,7],[6],[8]]=>0010101 [1,7,2,8,6,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>0000110 [7,6,1,3,8,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [7,5,8,1,3,6,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>0101010 [5,4,1,8,2,3,6,7]=>[[1,2,3,6,7],[4,8],[5]]=>0011001 [1,4,8,7,2,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [1,5,8,7,2,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [6,5,1,8,2,3,4,7]=>[[1,2,3,4,7],[5,8],[6]]=>0001101 [5,7,1,3,8,2,4,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [7,6,8,1,5,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>0001110 [7,1,5,8,6,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [6,1,8,2,7,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>0000101 [4,1,8,7,2,3,5,6]=>[[1,2,3,5,6],[4,7],[8]]=>0010011 [5,1,8,7,2,3,4,6]=>[[1,2,3,4,6],[5,7],[8]]=>0001011 [1,8,7,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]=>0110111 [1,8,7,3,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]=>0101111 [7,1,5,8,3,4,2,6]=>[[1,2,4,6],[3,8],[5],[7]]=>0101010 [7,1,4,3,2,5,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>0110010 [6,4,2,3,8,5,7,1]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [6,4,2,7,5,8,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [2,4,1,7,5,8,3,6]=>[[1,3,5,6],[2,4,8],[7]]=>1010010 [7,1,4,6,5,2,3,8]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,1,4,6,5,8,2,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,1,4,6,3,8,2,5]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [7,1,4,3,2,5,8,6]=>[[1,2,5,6],[3,8],[4],[7]]=>0110010 [7,1,4,6,5,2,8,3]=>[[1,2,3,8],[4,5],[6],[7]]=>0010110 [7,1,4,6,5,3,8,2]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [7,1,4,6,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>0110110 [6,4,2,7,5,3,8,1]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [3,4,7,2,6,8,5,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [3,4,7,1,6,8,2,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,7,1,6,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]=>0100110 [2,4,1,7,5,3,6,8]=>[[1,3,5,6,8],[2,4],[7]]=>1010010 [3,4,1,7,8,6,2,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [6,4,2,3,8,5,1,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [6,4,2,7,5,8,1,3]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [6,4,2,7,5,3,1,8]=>[[1,3,8],[2,5],[4,7],[6]]=>1010100 [3,4,7,2,6,8,1,5]=>[[1,4,5,8],[2,6],[3,7]]=>1100110 [5,4,7,3,6,8,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [3,4,7,2,6,5,1,8]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,8,3,2,5,6,1,7]=>[[1,5,6,7],[2,8],[3],[4]]=>1110001 [4,8,7,3,5,1,2,6]=>[[1,2,6],[3,5],[4,7],[8]]=>0110011 [4,8,7,1,3,5,2,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,8,3,1,2,6,5,7]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [3,4,7,1,6,2,5,8]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,7,1,6,2,8,5]=>[[1,2,5,8],[3,4,6],[7]]=>0100110 [3,4,7,2,6,5,8,1]=>[[1,4,5,8],[2,6],[3],[7]]=>1100110 [4,8,3,1,2,6,7,5]=>[[1,2,5,7],[3,6],[4,8]]=>0110101 [5,8,1,6,3,4,2,7]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [6,8,5,1,3,7,2,4]=>[[1,2,4],[3,7],[5,8],[6]]=>0101101 [6,8,5,1,3,4,7,2]=>[[1,2,4,7],[3,8],[5],[6]]=>0101101 [5,8,3,4,2,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [5,4,7,3,6,2,8,1]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [5,4,7,2,6,1,8,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [6,4,3,7,5,1,2,8]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,4,3,7,5,1,8,2]=>[[1,2,8],[3,5],[4,7],[6]]=>0110100 [6,2,4,3,1,5,8,7]=>[[1,3,5,7],[2,8],[4],[6]]=>1010101 [3,8,7,4,1,5,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>0100011 [2,4,7,3,6,1,5,8]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,8,3,2,1,6,4,7]=>[[1,4,7],[2,6],[3,8],[5]]=>1101001 [5,8,7,4,3,1,2,6]=>[[1,2,6],[3,7],[4],[5],[8]]=>0111011 [5,4,7,3,6,2,1,8]=>[[1,6,8],[2,7],[3],[4],[5]]=>1111010 [7,4,3,8,5,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [3,2,5,8,6,1,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [8,4,3,7,5,2,6,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [4,3,7,8,5,1,2,6]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [5,3,7,8,4,1,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [5,2,3,8,4,1,6,7]=>[[1,3,4,6,7],[2,8],[5]]=>1001001 [8,6,5,3,7,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>1101101 [7,5,4,3,8,2,6,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>1111010 [6,4,5,3,8,2,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [7,5,6,3,8,2,4,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>1101010 [8,5,7,3,4,2,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]=>1101011 [6,5,8,3,4,2,7,1]=>[[1,4,7],[2,8],[3],[5],[6]]=>1101101 [7,5,8,3,4,2,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [7,5,8,4,6,2,3,1]=>[[1,3],[2,6],[4,8],[5],[7]]=>1011010 [7,4,8,3,6,2,5,1]=>[[1,5],[2,6],[3,8],[4],[7]]=>1110110 [6,4,8,3,5,2,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]=>1110101 [5,4,8,3,7,2,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]=>1111011 [6,5,8,4,7,2,3,1]=>[[1,3],[2,7],[4,8],[5],[6]]=>1011101 [5,4,6,3,8,2,7,1]=>[[1,6,7],[2,8],[3],[4],[5]]=>1111001 [5,3,6,2,4,7,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,3,6,1,4,8,7,2]=>[[1,2,7],[3,4,8],[5,6]]=>0101001 [5,3,7,2,4,6,8,1]=>[[1,4,6,8],[2,7],[3],[5]]=>1101010 [4,3,1,5,6,8,7,2]=>[[1,2,6,7],[3,5],[4,8]]=>0110001 [4,2,1,5,8,6,3,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,2,1,5,8,6,7,3]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [4,2,1,5,8,7,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [4,3,1,5,7,8,6,2]=>[[1,2,6,8],[3,5],[4,7]]=>0110010 [4,3,1,7,5,8,6,2]=>[[1,2,6],[3,5,8],[4,7]]=>0110010 [6,7,3,1,4,8,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>0100100 [5,3,7,1,4,8,2,6]=>[[1,2,6],[3,4,8],[5,7]]=>0101010 [4,3,1,5,7,8,2,6]=>[[1,2,6,8],[3,5,7],[4]]=>0110010 [3,2,1,8,5,4,6,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,8,5,7,4,6]=>[[1,4,6],[2,5,7],[3,8]]=>1101011 [3,2,1,8,7,5,4,6]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [5,2,7,1,8,4,3,6]=>[[1,3,6],[2,4,8],[5,7]]=>1011010 [6,7,2,1,8,4,3,5]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [6,7,2,1,8,4,5,3]=>[[1,3,5],[2,4,8],[6,7]]=>1010100 [3,2,1,8,5,6,4,7]=>[[1,4,6,7],[2,5],[3,8]]=>1101001 [3,2,1,8,6,5,4,7]=>[[1,4,7],[2,5],[3,6],[8]]=>1101101 [4,3,1,6,7,8,5,2]=>[[1,2,7,8],[3,5],[4,6]]=>0110100 [4,2,1,6,8,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]=>1010101 [4,2,1,6,8,5,7,3]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [4,2,1,6,8,5,3,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [5,2,6,1,8,4,3,7]=>[[1,3,7],[2,4,8],[5,6]]=>1011001 [5,2,6,1,8,7,4,3]=>[[1,3,7],[2,4],[5,6],[8]]=>1011001 [5,2,6,1,8,7,3,4]=>[[1,3,4],[2,6,7],[5,8]]=>1001001 [5,2,6,1,8,3,4,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [4,2,1,6,8,3,7,5]=>[[1,3,5],[2,6,7],[4,8]]=>1010101 [4,3,1,6,7,8,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [6,7,3,1,5,8,2,4]=>[[1,2,4],[3,5,8],[6,7]]=>0101100 [4,2,1,7,8,6,3,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [3,2,1,8,7,6,4,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,1,8,6,4,7,5]=>[[1,4,5],[2,6,7],[3,8]]=>1100101 [3,2,1,8,6,4,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,1,8,4,6,5,7]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,1,8,4,6,7,5]=>[[1,4,5,7],[2,6],[3,8]]=>1100101 [3,2,1,8,4,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [3,2,1,8,7,4,6,5]=>[[1,4,5],[2,6],[3,7],[8]]=>1100111 [4,2,1,7,8,3,6,5]=>[[1,3,5],[2,6,8],[4,7]]=>1010110 [5,2,7,1,8,3,6,4]=>[[1,3,4],[2,6,8],[5,7]]=>1001010 [6,7,2,1,8,3,5,4]=>[[1,3,4],[2,5,8],[6,7]]=>1001100 [5,2,7,1,8,3,4,6]=>[[1,3,4,6],[2,7,8],[5]]=>1001010 [4,2,1,7,8,3,5,6]=>[[1,3,5,6],[2,7,8],[4]]=>1010010 [3,2,1,8,4,5,7,6]=>[[1,4,5,6],[2,7],[3,8]]=>1100011 [7,5,2,8,6,3,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>1001010 [7,4,8,6,2,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>1010110 [7,3,8,6,2,4,5,1]=>[[1,4,5],[2,6],[3,8],[7]]=>1100110 [7,3,8,5,2,4,6,1]=>[[1,4,6],[2,5],[3,8],[7]]=>1101010 [7,3,8,4,5,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>1100010 [6,3,8,2,4,5,1,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [6,3,7,8,2,4,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [5,6,7,3,8,2,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [5,4,7,2,6,8,1,3]=>[[1,3,8],[2,6],[4,7],[5]]=>1011010 [5,3,8,2,4,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]=>1101001 [6,4,8,2,7,5,1,3]=>[[1,3],[2,5],[4,7],[6,8]]=>1010101 [5,6,3,7,8,2,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [6,3,7,2,5,8,4,1]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [5,3,6,8,2,4,7,1]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [5,3,6,7,8,2,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>1101000 [3,6,4,2,1,5,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [3,5,8,6,4,2,1,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [5,8,6,3,4,2,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>1101001 [5,6,3,4,2,1,8,7]=>[[1,4,7],[2,6,8],[3],[5]]=>1101001 [6,3,4,2,1,5,8,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [5,6,4,2,1,3,8,7]=>[[1,3,7],[2,6,8],[4],[5]]=>1011001 [2,5,4,1,7,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]=>1011010 [2,7,8,5,4,1,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [2,8,5,4,1,6,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [2,6,3,8,5,4,1,7]=>[[1,3,4,7],[2,8],[5],[6]]=>1001101 [2,8,6,3,5,4,1,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>1001101 [5,8,6,4,2,1,3,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>1011001 [4,2,1,5,7,8,6,3]=>[[1,3,6,8],[2,5],[4,7]]=>1010010 [2,7,8,6,3,5,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [4,3,8,5,7,6,2,1]=>[[1,5,6],[2,7],[3],[4],[8]]=>1110011 [7,6,2,1,8,4,3,5]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [2,1,8,5,6,4,3,7]=>[[1,3,6,7],[2,4],[5],[8]]=>1011001 [4,2,1,8,5,6,3,7]=>[[1,3,6,7],[2,5],[4,8]]=>1010001 [8,4,2,1,5,6,3,7]=>[[1,3,6,7],[2,5],[4],[8]]=>1010001 [2,5,6,3,8,4,1,7]=>[[1,3,4,7],[2,6,8],[5]]=>1001001 [6,3,4,2,1,8,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [3,7,8,5,6,4,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>1101010 [3,8,5,6,4,2,1,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>1101001 [3,6,4,2,1,8,5,7]=>[[1,4,5,7],[2,8],[3],[6]]=>1100101 [3,8,6,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>1100101 [3,7,8,6,4,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>1100110 [8,5,3,7,6,2,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]=>1101011 [7,6,2,4,1,8,5,3]=>[[1,3,5],[2,4],[6,8],[7]]=>1010110 [8,5,4,1,7,6,2,3]=>[[1,2,3],[4,6],[5,7],[8]]=>0011011 [7,6,2,3,8,5,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>1001110 [2,1,7,8,6,4,3,5]=>[[1,3,5],[2,4,8],[6],[7]]=>1010110 [2,1,6,4,3,7,8,5]=>[[1,3,5,8],[2,4,7],[6]]=>1010100 [6,4,2,1,3,7,8,5]=>[[1,3,5,8],[2,7],[4],[6]]=>1010100 [6,3,7,8,4,2,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>1100100 [7,8,4,2,1,6,3,5]=>[[1,3,5],[2,6],[4,8],[7]]=>1010110 [5,7,6,2,3,8,4,1]=>[[1,3,4],[2,6,8],[5],[7]]=>1001010 [2,6,1,8,4,3,7,5]=>[[1,3,5],[2,4,7],[6,8]]=>1010101 [2,6,1,7,5,8,4,3]=>[[1,3,7,8],[2,4],[5],[6]]=>1011100 [8,4,2,3,7,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]=>1010011 [8,5,7,6,2,1,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]=>1011011 [4,8,5,7,6,2,1,3]=>[[1,3,6],[2,5],[4],[7],[8]]=>1010011 [4,7,6,2,1,3,8,5]=>[[1,3,5],[2,6,8],[4],[7]]=>1010110 [7,5,6,1,8,4,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>0011010 [2,7,5,8,4,3,6,1]=>[[1,3,6],[2,8],[4],[5],[7]]=>1011010 [2,8,4,3,6,1,7,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [6,4,7,8,3,2,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [7,6,5,8,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [7,6,5,4,3,2,8,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100 [6,4,3,7,5,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>1110100 [6,3,7,2,5,4,1,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [6,3,2,7,5,4,1,8]=>[[1,4,8],[2,5],[3,7],[6]]=>1101100 [8,4,2,6,3,1,7,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [1,5,3,7,4,2,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [1,6,7,3,4,2,8,5]=>[[1,2,4,5],[3,7,8],[6]]=>0100100 [8,6,5,2,3,1,7,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [1,7,6,3,4,2,8,5]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,8,6,3,2,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]=>0101101 [8,7,5,2,1,4,6,3]=>[[1,3,6],[2,4],[5],[7],[8]]=>1011011 [7,8,5,2,1,4,6,3]=>[[1,3,6],[2,4],[5,8],[7]]=>1011010 [6,8,5,2,3,1,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [5,8,6,2,3,1,7,4]=>[[1,3,4],[2,6,7],[5],[8]]=>1001001 [4,8,2,6,3,1,7,5]=>[[1,3,5],[2,6,7],[4],[8]]=>1010101 [3,2,8,6,4,1,7,5]=>[[1,4,5],[2,6,7],[3],[8]]=>1100101 [3,2,1,7,5,4,8,6]=>[[1,4,6],[2,5,8],[3,7]]=>1101010 [4,1,3,7,5,2,8,6]=>[[1,2,5,6],[3,7,8],[4]]=>0110010 [5,1,7,3,4,2,8,6]=>[[1,2,4,6],[3,7,8],[5]]=>0101010 [7,1,6,3,2,5,8,4]=>[[1,2,4,8],[3,5],[6],[7]]=>0101110 [1,2,7,4,3,6,8,5]=>[[1,2,3,5,8],[4,6],[7]]=>0010110 [6,1,8,2,4,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [5,1,8,3,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [3,2,8,7,1,5,6,4]=>[[1,4,6],[2,5],[3,7],[8]]=>1101011 [4,8,2,7,1,5,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [5,8,7,2,1,4,6,3]=>[[1,3,6],[2,4],[5,7],[8]]=>1011011 [6,8,7,1,3,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,8,6,1,3,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [1,7,8,2,4,5,6,3]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [8,6,7,1,3,4,5,2]=>[[1,2,4,5],[3,7],[6],[8]]=>0100101 [7,6,8,1,3,4,5,2]=>[[1,2,4,5],[3,8],[6],[7]]=>0100110 [6,5,8,2,3,1,7,4]=>[[1,3,4],[2,7],[5,8],[6]]=>1001101 [1,6,8,3,2,5,7,4]=>[[1,2,4,7],[3,5],[6,8]]=>0101101 [1,5,3,8,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [8,4,2,7,1,5,6,3]=>[[1,3,6],[2,5],[4,7],[8]]=>1010011 [7,4,2,8,1,5,6,3]=>[[1,3,6],[2,5],[4,8],[7]]=>1010010 [6,4,2,8,3,1,7,5]=>[[1,3,5],[2,7],[4,8],[6]]=>1010101 [5,4,2,3,8,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]=>1011011 [4,5,2,3,1,6,8,7]=>[[1,3,6,7],[2,5,8],[4]]=>1010001 [7,4,2,1,3,6,8,5]=>[[1,3,5,8],[2,6],[4],[7]]=>1010110 [8,4,2,1,3,6,7,5]=>[[1,3,5,7],[2,6],[4],[8]]=>1010101 [1,5,3,2,4,7,8,6]=>[[1,2,4,6,8],[3,7],[5]]=>0101010 [8,5,1,3,2,6,7,4]=>[[1,2,4,7],[3,6],[5],[8]]=>0101001 [5,6,1,3,4,2,8,7]=>[[1,2,4,7],[3,6,8],[5]]=>0101001 [4,6,2,1,5,3,8,7]=>[[1,3,7],[2,5,8],[4,6]]=>1010101 [4,7,2,1,3,6,8,5]=>[[1,3,5,8],[2,6],[4,7]]=>1010110 [5,7,1,3,2,6,8,4]=>[[1,2,4,8],[3,6],[5,7]]=>0101010 [6,7,1,2,4,5,8,3]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [8,6,1,2,4,5,7,3]=>[[1,2,3,5,7],[4],[6],[8]]=>0010101 [1,8,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]=>0001001 [8,7,1,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7],[8]]=>0010011 [7,8,1,2,4,5,6,3]=>[[1,2,3,5,6],[4,8],[7]]=>0010010 [5,8,1,3,2,6,7,4]=>[[1,2,4,7],[3,6],[5,8]]=>0101001 [4,8,2,1,3,6,7,5]=>[[1,3,5,7],[2,6],[4,8]]=>1010101 [4,1,3,2,5,7,8,6]=>[[1,2,5,6,8],[3,7],[4]]=>0110010 [5,1,2,4,3,7,8,6]=>[[1,2,3,6,8],[4,7],[5]]=>0011010 [5,4,8,1,2,3,7,6]=>[[1,2,3,6],[4,7],[5,8]]=>0011011 [1,4,7,6,3,2,5,8]=>[[1,2,5,8],[3,6],[4],[7]]=>0110110 [4,8,3,2,7,6,1,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [4,3,8,2,7,1,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [4,3,2,8,1,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]=>1110111 [4,1,8,7,3,2,5,6]=>[[1,2,5,6],[3,7],[4],[8]]=>0110011 [4,7,8,1,2,5,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [2,6,3,4,7,8,1,5]=>[[1,3,4,5,8],[2,7],[6]]=>1000100 [3,1,7,8,4,2,5,6]=>[[1,2,5,6],[3,4,8],[7]]=>0100010 [3,7,8,2,6,4,1,5]=>[[1,4,5],[2,6,8],[3],[7]]=>1100110 [3,7,2,4,8,6,1,5]=>[[1,4,5],[2,6,8],[3,7]]=>1100110 [1,3,6,4,7,2,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>0100100 [4,7,1,5,8,2,3,6]=>[[1,2,3,6],[4,5,8],[7]]=>0010010 [8,6,5,2,7,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>1001101 [7,4,8,5,6,3,2,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>1110010 [3,4,6,7,8,5,1,2]=>[[1,2,5,7,8],[3,4],[6]]=>0100100 [1,2,6,4,7,5,8,3]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [3,1,7,5,4,2,6,8]=>[[1,2,6,8],[3,4],[5],[7]]=>0101010 [6,3,8,5,4,7,1,2]=>[[1,2,7],[3,4],[5,8],[6]]=>0101101 [1,6,2,5,4,7,8,3]=>[[1,2,3,7,8],[4],[5],[6]]=>0011100 [1,8,2,5,6,3,7,4]=>[[1,2,3,4,7],[5,6],[8]]=>0001001 [1,2,6,4,8,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]=>0010101 [7,8,3,1,4,2,5,6]=>[[1,2,5,6],[3,4],[7,8]]=>0100010 [4,8,1,5,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>0010001 [7,4,1,5,2,3,6,8]=>[[1,2,3,6,8],[4,5],[7]]=>0010010 [5,6,1,8,4,3,2,7]=>[[1,2,7],[3,6,8],[4],[5]]=>0111001 [5,1,8,6,4,3,2,7]=>[[1,2,7],[3,6],[4],[5],[8]]=>0111001 [5,1,6,3,8,7,2,4]=>[[1,2,4],[3,6,7],[5,8]]=>0101001 [6,1,2,5,8,3,7,4]=>[[1,2,3,4],[5,7],[6,8]]=>0001101 [6,1,8,7,4,3,2,5]=>[[1,2,5],[3,7],[4],[6],[8]]=>0110101 [7,1,2,5,4,8,6,3]=>[[1,2,3,6],[4,8],[5],[7]]=>0011010 [1,2,7,5,8,3,6,4]=>[[1,2,3,4],[5,6],[7,8]]=>0001010 [4,1,6,3,7,5,2,8]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [1,3,6,7,8,5,2,4]=>[[1,2,4,7,8],[3,5],[6]]=>0101100 [1,2,6,4,7,8,5,3]=>[[1,2,3,5,8],[4,7],[6]]=>0010100 [4,1,6,3,7,8,2,5]=>[[1,2,5,8],[3,6,7],[4]]=>0110100 [3,1,6,4,8,2,7,5]=>[[1,2,5],[3,4,7],[6,8]]=>0100101 [7,8,4,1,6,3,2,5]=>[[1,2,5],[3,6],[4,8],[7]]=>0110110 [4,1,6,3,8,7,2,5]=>[[1,2,5],[3,6,7],[4,8]]=>0110101 [7,5,1,8,4,3,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>0111010 [6,5,1,7,4,3,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>0111100 [4,1,8,5,2,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]=>0010011 [4,1,6,8,3,7,