Identifier
Mp00134:
Standard tableaux
—descent word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
=>
Cc0007;cc-rep-0
[[1]]=>=>
[[1,2]]=>0=>0
[[1],[2]]=>1=>1
[[1,2,3]]=>00=>00
[[1,3],[2]]=>10=>01
[[1,2],[3]]=>01=>10
[[1],[2],[3]]=>11=>11
[[1,2,3,4]]=>000=>000
[[1,3,4],[2]]=>100=>001
[[1,2,4],[3]]=>010=>010
[[1,2,3],[4]]=>001=>100
[[1,3],[2,4]]=>101=>101
[[1,2],[3,4]]=>010=>010
[[1,4],[2],[3]]=>110=>011
[[1,3],[2],[4]]=>101=>101
[[1,2],[3],[4]]=>011=>110
[[1],[2],[3],[4]]=>111=>111
[[1,2,3,4,5]]=>0000=>0000
[[1,3,4,5],[2]]=>1000=>0001
[[1,2,4,5],[3]]=>0100=>0010
[[1,2,3,5],[4]]=>0010=>0100
[[1,2,3,4],[5]]=>0001=>1000
[[1,3,5],[2,4]]=>1010=>0101
[[1,2,5],[3,4]]=>0100=>0010
[[1,3,4],[2,5]]=>1001=>1001
[[1,2,4],[3,5]]=>0101=>1010
[[1,2,3],[4,5]]=>0010=>0100
[[1,4,5],[2],[3]]=>1100=>0011
[[1,3,5],[2],[4]]=>1010=>0101
[[1,2,5],[3],[4]]=>0110=>0110
[[1,3,4],[2],[5]]=>1001=>1001
[[1,2,4],[3],[5]]=>0101=>1010
[[1,2,3],[4],[5]]=>0011=>1100
[[1,4],[2,5],[3]]=>1101=>1011
[[1,3],[2,5],[4]]=>1010=>0101
[[1,2],[3,5],[4]]=>0110=>0110
[[1,3],[2,4],[5]]=>1011=>1101
[[1,2],[3,4],[5]]=>0101=>1010
[[1,5],[2],[3],[4]]=>1110=>0111
[[1,4],[2],[3],[5]]=>1101=>1011
[[1,3],[2],[4],[5]]=>1011=>1101
[[1,2],[3],[4],[5]]=>0111=>1110
[[1],[2],[3],[4],[5]]=>1111=>1111
[[1,2,3,4,5,6]]=>00000=>00000
[[1,3,4,5,6],[2]]=>10000=>00001
[[1,2,4,5,6],[3]]=>01000=>00010
[[1,2,3,5,6],[4]]=>00100=>00100
[[1,2,3,4,6],[5]]=>00010=>01000
[[1,2,3,4,5],[6]]=>00001=>10000
[[1,3,5,6],[2,4]]=>10100=>00101
[[1,2,5,6],[3,4]]=>01000=>00010
[[1,3,4,6],[2,5]]=>10010=>01001
[[1,2,4,6],[3,5]]=>01010=>01010
[[1,2,3,6],[4,5]]=>00100=>00100
[[1,3,4,5],[2,6]]=>10001=>10001
[[1,2,4,5],[3,6]]=>01001=>10010
[[1,2,3,5],[4,6]]=>00101=>10100
[[1,2,3,4],[5,6]]=>00010=>01000
[[1,4,5,6],[2],[3]]=>11000=>00011
[[1,3,5,6],[2],[4]]=>10100=>00101
[[1,2,5,6],[3],[4]]=>01100=>00110
[[1,3,4,6],[2],[5]]=>10010=>01001
[[1,2,4,6],[3],[5]]=>01010=>01010
[[1,2,3,6],[4],[5]]=>00110=>01100
[[1,3,4,5],[2],[6]]=>10001=>10001
[[1,2,4,5],[3],[6]]=>01001=>10010
[[1,2,3,5],[4],[6]]=>00101=>10100
[[1,2,3,4],[5],[6]]=>00011=>11000
[[1,3,5],[2,4,6]]=>10101=>10101
[[1,2,5],[3,4,6]]=>01001=>10010
[[1,3,4],[2,5,6]]=>10010=>01001
[[1,2,4],[3,5,6]]=>01010=>01010
[[1,2,3],[4,5,6]]=>00100=>00100
[[1,4,6],[2,5],[3]]=>11010=>01011
[[1,3,6],[2,5],[4]]=>10100=>00101
[[1,2,6],[3,5],[4]]=>01100=>00110
[[1,3,6],[2,4],[5]]=>10110=>01101
[[1,2,6],[3,4],[5]]=>01010=>01010
[[1,4,5],[2,6],[3]]=>11001=>10011
[[1,3,5],[2,6],[4]]=>10101=>10101
[[1,2,5],[3,6],[4]]=>01101=>10110
[[1,3,4],[2,6],[5]]=>10010=>01001
[[1,2,4],[3,6],[5]]=>01010=>01010
[[1,2,3],[4,6],[5]]=>00110=>01100
[[1,3,5],[2,4],[6]]=>10101=>10101
[[1,2,5],[3,4],[6]]=>01001=>10010
[[1,3,4],[2,5],[6]]=>10011=>11001
[[1,2,4],[3,5],[6]]=>01011=>11010
[[1,2,3],[4,5],[6]]=>00101=>10100
[[1,5,6],[2],[3],[4]]=>11100=>00111
[[1,4,6],[2],[3],[5]]=>11010=>01011
[[1,3,6],[2],[4],[5]]=>10110=>01101
[[1,2,6],[3],[4],[5]]=>01110=>01110
[[1,4,5],[2],[3],[6]]=>11001=>10011
[[1,3,5],[2],[4],[6]]=>10101=>10101
[[1,2,5],[3],[4],[6]]=>01101=>10110
[[1,3,4],[2],[5],[6]]=>10011=>11001
[[1,2,4],[3],[5],[6]]=>01011=>11010
[[1,2,3],[4],[5],[6]]=>00111=>11100
[[1,4],[2,5],[3,6]]=>11011=>11011
[[1,3],[2,5],[4,6]]=>10101=>10101
[[1,2],[3,5],[4,6]]=>01101=>10110
[[1,3],[2,4],[5,6]]=>10110=>01101
[[1,2],[3,4],[5,6]]=>01010=>01010
[[1,5],[2,6],[3],[4]]=>11101=>10111
[[1,4],[2,6],[3],[5]]=>11010=>01011
[[1,3],[2,6],[4],[5]]=>10110=>01101
[[1,2],[3,6],[4],[5]]=>01110=>01110
[[1,4],[2,5],[3],[6]]=>11011=>11011
[[1,3],[2,5],[4],[6]]=>10101=>10101
[[1,2],[3,5],[4],[6]]=>01101=>10110
[[1,3],[2,4],[5],[6]]=>10111=>11101
[[1,2],[3,4],[5],[6]]=>01011=>11010
[[1,6],[2],[3],[4],[5]]=>11110=>01111
[[1,5],[2],[3],[4],[6]]=>11101=>10111
[[1,4],[2],[3],[5],[6]]=>11011=>11011
[[1,3],[2],[4],[5],[6]]=>10111=>11101
[[1,2],[3],[4],[5],[6]]=>01111=>11110
[[1],[2],[3],[4],[5],[6]]=>11111=>11111
[[1,2,3,4,5,6,7]]=>000000=>000000
[[1,3,4,5,6,7],[2]]=>100000=>000001
[[1,2,4,5,6,7],[3]]=>010000=>000010
[[1,2,3,5,6,7],[4]]=>001000=>000100
[[1,2,3,4,6,7],[5]]=>000100=>001000
[[1,2,3,4,5,7],[6]]=>000010=>010000
[[1,2,3,4,5,6],[7]]=>000001=>100000
[[1,3,5,6,7],[2,4]]=>101000=>000101
[[1,2,5,6,7],[3,4]]=>010000=>000010
[[1,3,4,6,7],[2,5]]=>100100=>001001
[[1,2,4,6,7],[3,5]]=>010100=>001010
[[1,2,3,6,7],[4,5]]=>001000=>000100
[[1,3,4,5,7],[2,6]]=>100010=>010001
[[1,2,4,5,7],[3,6]]=>010010=>010010
[[1,2,3,5,7],[4,6]]=>001010=>010100
[[1,2,3,4,7],[5,6]]=>000100=>001000
[[1,3,4,5,6],[2,7]]=>100001=>100001
[[1,2,4,5,6],[3,7]]=>010001=>100010
[[1,2,3,5,6],[4,7]]=>001001=>100100
[[1,2,3,4,6],[5,7]]=>000101=>101000
[[1,2,3,4,5],[6,7]]=>000010=>010000
[[1,4,5,6,7],[2],[3]]=>110000=>000011
[[1,3,5,6,7],[2],[4]]=>101000=>000101
[[1,2,5,6,7],[3],[4]]=>011000=>000110
[[1,3,4,6,7],[2],[5]]=>100100=>001001
[[1,2,4,6,7],[3],[5]]=>010100=>001010
[[1,2,3,6,7],[4],[5]]=>001100=>001100
[[1,3,4,5,7],[2],[6]]=>100010=>010001
[[1,2,4,5,7],[3],[6]]=>010010=>010010
[[1,2,3,5,7],[4],[6]]=>001010=>010100
[[1,2,3,4,7],[5],[6]]=>000110=>011000
[[1,3,4,5,6],[2],[7]]=>100001=>100001
[[1,2,4,5,6],[3],[7]]=>010001=>100010
[[1,2,3,5,6],[4],[7]]=>001001=>100100
[[1,2,3,4,6],[5],[7]]=>000101=>101000
[[1,2,3,4,5],[6],[7]]=>000011=>110000
[[1,3,5,7],[2,4,6]]=>101010=>010101
[[1,2,5,7],[3,4,6]]=>010010=>010010
[[1,3,4,7],[2,5,6]]=>100100=>001001
[[1,2,4,7],[3,5,6]]=>010100=>001010
[[1,2,3,7],[4,5,6]]=>001000=>000100
[[1,3,5,6],[2,4,7]]=>101001=>100101
[[1,2,5,6],[3,4,7]]=>010001=>100010
[[1,3,4,6],[2,5,7]]=>100101=>101001
[[1,2,4,6],[3,5,7]]=>010101=>101010
[[1,2,3,6],[4,5,7]]=>001001=>100100
[[1,3,4,5],[2,6,7]]=>100010=>010001
[[1,2,4,5],[3,6,7]]=>010010=>010010
[[1,2,3,5],[4,6,7]]=>001010=>010100
[[1,2,3,4],[5,6,7]]=>000100=>001000
[[1,4,6,7],[2,5],[3]]=>110100=>001011
[[1,3,6,7],[2,5],[4]]=>101000=>000101
[[1,2,6,7],[3,5],[4]]=>011000=>000110
[[1,3,6,7],[2,4],[5]]=>101100=>001101
[[1,2,6,7],[3,4],[5]]=>010100=>001010
[[1,4,5,7],[2,6],[3]]=>110010=>010011
[[1,3,5,7],[2,6],[4]]=>101010=>010101
[[1,2,5,7],[3,6],[4]]=>011010=>010110
[[1,3,4,7],[2,6],[5]]=>100100=>001001
[[1,2,4,7],[3,6],[5]]=>010100=>001010
[[1,2,3,7],[4,6],[5]]=>001100=>001100
[[1,3,5,7],[2,4],[6]]=>101010=>010101
[[1,2,5,7],[3,4],[6]]=>010010=>010010
[[1,3,4,7],[2,5],[6]]=>100110=>011001
[[1,2,4,7],[3,5],[6]]=>010110=>011010
[[1,2,3,7],[4,5],[6]]=>001010=>010100
[[1,4,5,6],[2,7],[3]]=>110001=>100011
[[1,3,5,6],[2,7],[4]]=>101001=>100101
[[1,2,5,6],[3,7],[4]]=>011001=>100110
[[1,3,4,6],[2,7],[5]]=>100101=>101001
[[1,2,4,6],[3,7],[5]]=>010101=>101010
[[1,2,3,6],[4,7],[5]]=>001101=>101100
[[1,3,4,5],[2,7],[6]]=>100010=>010001
[[1,2,4,5],[3,7],[6]]=>010010=>010010
[[1,2,3,5],[4,7],[6]]=>001010=>010100
[[1,2,3,4],[5,7],[6]]=>000110=>011000
[[1,3,5,6],[2,4],[7]]=>101001=>100101
[[1,2,5,6],[3,4],[7]]=>010001=>100010
[[1,3,4,6],[2,5],[7]]=>100101=>101001
[[1,2,4,6],[3,5],[7]]=>010101=>101010
[[1,2,3,6],[4,5],[7]]=>001001=>100100
[[1,3,4,5],[2,6],[7]]=>100011=>110001
[[1,2,4,5],[3,6],[7]]=>010011=>110010
[[1,2,3,5],[4,6],[7]]=>001011=>110100
[[1,2,3,4],[5,6],[7]]=>000101=>101000
[[1,5,6,7],[2],[3],[4]]=>111000=>000111
[[1,4,6,7],[2],[3],[5]]=>110100=>001011
[[1,3,6,7],[2],[4],[5]]=>101100=>001101
[[1,2,6,7],[3],[4],[5]]=>011100=>001110
[[1,4,5,7],[2],[3],[6]]=>110010=>010011
[[1,3,5,7],[2],[4],[6]]=>101010=>010101
[[1,2,5,7],[3],[4],[6]]=>011010=>010110
[[1,3,4,7],[2],[5],[6]]=>100110=>011001
[[1,2,4,7],[3],[5],[6]]=>010110=>011010
[[1,2,3,7],[4],[5],[6]]=>001110=>011100
[[1,4,5,6],[2],[3],[7]]=>110001=>100011
[[1,3,5,6],[2],[4],[7]]=>101001=>100101
[[1,2,5,6],[3],[4],[7]]=>011001=>100110
[[1,3,4,6],[2],[5],[7]]=>100101=>101001
[[1,2,4,6],[3],[5],[7]]=>010101=>101010
[[1,2,3,6],[4],[5],[7]]=>001101=>101100
[[1,3,4,5],[2],[6],[7]]=>100011=>110001
[[1,2,4,5],[3],[6],[7]]=>010011=>110010
[[1,2,3,5],[4],[6],[7]]=>001011=>110100
[[1,2,3,4],[5],[6],[7]]=>000111=>111000
[[1,4,6],[2,5,7],[3]]=>110101=>101011
[[1,3,6],[2,5,7],[4]]=>101001=>100101
[[1,2,6],[3,5,7],[4]]=>011001=>100110
[[1,3,6],[2,4,7],[5]]=>101101=>101101
[[1,2,6],[3,4,7],[5]]=>010101=>101010
[[1,4,5],[2,6,7],[3]]=>110010=>010011
[[1,3,5],[2,6,7],[4]]=>101010=>010101
[[1,2,5],[3,6,7],[4]]=>011010=>010110
[[1,3,4],[2,6,7],[5]]=>100100=>001001
[[1,2,4],[3,6,7],[5]]=>010100=>001010
[[1,2,3],[4,6,7],[5]]=>001100=>001100
[[1,3,5],[2,4,7],[6]]=>101010=>010101
[[1,2,5],[3,4,7],[6]]=>010010=>010010
[[1,3,4],[2,5,7],[6]]=>100110=>011001
[[1,2,4],[3,5,7],[6]]=>010110=>011010
[[1,2,3],[4,5,7],[6]]=>001010=>010100
[[1,3,5],[2,4,6],[7]]=>101011=>110101
[[1,2,5],[3,4,6],[7]]=>010011=>110010
[[1,3,4],[2,5,6],[7]]=>100101=>101001
[[1,2,4],[3,5,6],[7]]=>010101=>101010
[[1,2,3],[4,5,6],[7]]=>001001=>100100
[[1,4,7],[2,5],[3,6]]=>110110=>011011
[[1,3,7],[2,5],[4,6]]=>101010=>010101
[[1,2,7],[3,5],[4,6]]=>011010=>010110
[[1,3,7],[2,4],[5,6]]=>101100=>001101
[[1,2,7],[3,4],[5,6]]=>010100=>001010
[[1,4,6],[2,5],[3,7]]=>110101=>101011
[[1,3,6],[2,5],[4,7]]=>101001=>100101
[[1,2,6],[3,5],[4,7]]=>011001=>100110
[[1,3,6],[2,4],[5,7]]=>101101=>101101
[[1,2,6],[3,4],[5,7]]=>010101=>101010
[[1,4,5],[2,6],[3,7]]=>110011=>110011
[[1,3,5],[2,6],[4,7]]=>101011=>110101
[[1,2,5],[3,6],[4,7]]=>011011=>110110
[[1,3,4],[2,6],[5,7]]=>100101=>101001
[[1,2,4],[3,6],[5,7]]=>010101=>101010
[[1,2,3],[4,6],[5,7]]=>001101=>101100
[[1,3,5],[2,4],[6,7]]=>101010=>010101
[[1,2,5],[3,4],[6,7]]=>010010=>010010
[[1,3,4],[2,5],[6,7]]=>100110=>011001
[[1,2,4],[3,5],[6,7]]=>010110=>011010
[[1,2,3],[4,5],[6,7]]=>001010=>010100
[[1,5,7],[2,6],[3],[4]]=>111010=>010111
[[1,4,7],[2,6],[3],[5]]=>110100=>001011
[[1,3,7],[2,6],[4],[5]]=>101100=>001101
[[1,2,7],[3,6],[4],[5]]=>011100=>001110
[[1,4,7],[2,5],[3],[6]]=>110110=>011011
[[1,3,7],[2,5],[4],[6]]=>101010=>010101
[[1,2,7],[3,5],[4],[6]]=>011010=>010110
[[1,3,7],[2,4],[5],[6]]=>101110=>011101
[[1,2,7],[3,4],[5],[6]]=>010110=>011010
[[1,5,6],[2,7],[3],[4]]=>111001=>100111
[[1,4,6],[2,7],[3],[5]]=>110101=>101011
[[1,3,6],[2,7],[4],[5]]=>101101=>101101
[[1,2,6],[3,7],[4],[5]]=>011101=>101110
[[1,4,5],[2,7],[3],[6]]=>110010=>010011
[[1,3,5],[2,7],[4],[6]]=>101010=>010101
[[1,2,5],[3,7],[4],[6]]=>011010=>010110
[[1,3,4],[2,7],[5],[6]]=>100110=>011001
[[1,2,4],[3,7],[5],[6]]=>010110=>011010
[[1,2,3],[4,7],[5],[6]]=>001110=>011100
[[1,4,6],[2,5],[3],[7]]=>110101=>101011
[[1,3,6],[2,5],[4],[7]]=>101001=>100101
[[1,2,6],[3,5],[4],[7]]=>011001=>100110
[[1,3,6],[2,4],[5],[7]]=>101101=>101101
[[1,2,6],[3,4],[5],[7]]=>010101=>101010
[[1,4,5],[2,6],[3],[7]]=>110011=>110011
[[1,3,5],[2,6],[4],[7]]=>101011=>110101
[[1,2,5],[3,6],[4],[7]]=>011011=>110110
[[1,3,4],[2,6],[5],[7]]=>100101=>101001
[[1,2,4],[3,6],[5],[7]]=>010101=>101010
[[1,2,3],[4,6],[5],[7]]=>001101=>101100
[[1,3,5],[2,4],[6],[7]]=>101011=>110101
[[1,2,5],[3,4],[6],[7]]=>010011=>110010
[[1,3,4],[2,5],[6],[7]]=>100111=>111001
[[1,2,4],[3,5],[6],[7]]=>010111=>111010
[[1,2,3],[4,5],[6],[7]]=>001011=>110100
[[1,6,7],[2],[3],[4],[5]]=>111100=>001111
[[1,5,7],[2],[3],[4],[6]]=>111010=>010111
[[1,4,7],[2],[3],[5],[6]]=>110110=>011011
[[1,3,7],[2],[4],[5],[6]]=>101110=>011101
[[1,2,7],[3],[4],[5],[6]]=>011110=>011110
[[1,5,6],[2],[3],[4],[7]]=>111001=>100111
[[1,4,6],[2],[3],[5],[7]]=>110101=>101011
[[1,3,6],[2],[4],[5],[7]]=>101101=>101101
[[1,2,6],[3],[4],[5],[7]]=>011101=>101110
[[1,4,5],[2],[3],[6],[7]]=>110011=>110011
[[1,3,5],[2],[4],[6],[7]]=>101011=>110101
[[1,2,5],[3],[4],[6],[7]]=>011011=>110110
[[1,3,4],[2],[5],[6],[7]]=>100111=>111001
[[1,2,4],[3],[5],[6],[7]]=>010111=>111010
[[1,2,3],[4],[5],[6],[7]]=>001111=>111100
[[1,5],[2,6],[3,7],[4]]=>111011=>110111
[[1,4],[2,6],[3,7],[5]]=>110101=>101011
[[1,3],[2,6],[4,7],[5]]=>101101=>101101
[[1,2],[3,6],[4,7],[5]]=>011101=>101110
[[1,4],[2,5],[3,7],[6]]=>110110=>011011
[[1,3],[2,5],[4,7],[6]]=>101010=>010101
[[1,2],[3,5],[4,7],[6]]=>011010=>010110
[[1,3],[2,4],[5,7],[6]]=>101110=>011101
[[1,2],[3,4],[5,7],[6]]=>010110=>011010
[[1,4],[2,5],[3,6],[7]]=>110111=>111011
[[1,3],[2,5],[4,6],[7]]=>101011=>110101
[[1,2],[3,5],[4,6],[7]]=>011011=>110110
[[1,3],[2,4],[5,6],[7]]=>101101=>101101
[[1,2],[3,4],[5,6],[7]]=>010101=>101010
[[1,6],[2,7],[3],[4],[5]]=>111101=>101111
[[1,5],[2,7],[3],[4],[6]]=>111010=>010111
[[1,4],[2,7],[3],[5],[6]]=>110110=>011011
[[1,3],[2,7],[4],[5],[6]]=>101110=>011101
[[1,2],[3,7],[4],[5],[6]]=>011110=>011110
[[1,5],[2,6],[3],[4],[7]]=>111011=>110111
[[1,4],[2,6],[3],[5],[7]]=>110101=>101011
[[1,3],[2,6],[4],[5],[7]]=>101101=>101101
[[1,2],[3,6],[4],[5],[7]]=>011101=>101110
[[1,4],[2,5],[3],[6],[7]]=>110111=>111011
[[1,3],[2,5],[4],[6],[7]]=>101011=>110101
[[1,2],[3,5],[4],[6],[7]]=>011011=>110110
[[1,3],[2,4],[5],[6],[7]]=>101111=>111101
[[1,2],[3,4],[5],[6],[7]]=>010111=>111010
[[1,7],[2],[3],[4],[5],[6]]=>111110=>011111
[[1,6],[2],[3],[4],[5],[7]]=>111101=>101111
[[1,5],[2],[3],[4],[6],[7]]=>111011=>110111
[[1,4],[2],[3],[5],[6],[7]]=>110111=>111011
[[1,3],[2],[4],[5],[6],[7]]=>101111=>111101
[[1,2],[3],[4],[5],[6],[7]]=>011111=>111110
[[1],[2],[3],[4],[5],[6],[7]]=>111111=>111111
[[1,2,3,4,5,6,7,8]]=>0000000=>0000000
[[1,3,4,5,6,7,8],[2]]=>1000000=>0000001
[[1,2,4,5,6,7,8],[3]]=>0100000=>0000010
[[1,2,3,5,6,7,8],[4]]=>0010000=>0000100
[[1,2,3,4,6,7,8],[5]]=>0001000=>0001000
[[1,2,3,4,5,7,8],[6]]=>0000100=>0010000
[[1,2,3,4,5,6,8],[7]]=>0000010=>0100000
[[1,2,3,4,5,6,7],[8]]=>0000001=>1000000
[[1,3,5,6,7,8],[2,4]]=>1010000=>0000101
[[1,2,5,6,7,8],[3,4]]=>0100000=>0000010
[[1,3,4,6,7,8],[2,5]]=>1001000=>0001001
[[1,2,4,6,7,8],[3,5]]=>0101000=>0001010
[[1,2,3,6,7,8],[4,5]]=>0010000=>0000100
[[1,3,4,5,7,8],[2,6]]=>1000100=>0010001
[[1,2,4,5,7,8],[3,6]]=>0100100=>0010010
[[1,2,3,5,7,8],[4,6]]=>0010100=>0010100
[[1,2,3,4,7,8],[5,6]]=>0001000=>0001000
[[1,3,4,5,6,8],[2,7]]=>1000010=>0100001
[[1,2,4,5,6,8],[3,7]]=>0100010=>0100010
[[1,2,3,5,6,8],[4,7]]=>0010010=>0100100
[[1,2,3,4,6,8],[5,7]]=>0001010=>0101000
[[1,2,3,4,5,8],[6,7]]=>0000100=>0010000
[[1,3,4,5,6,7],[2,8]]=>1000001=>1000001
[[1,2,4,5,6,7],[3,8]]=>0100001=>1000010
[[1,2,3,5,6,7],[4,8]]=>0010001=>1000100
[[1,2,3,4,6,7],[5,8]]=>0001001=>1001000
[[1,2,3,4,5,7],[6,8]]=>0000101=>1010000
[[1,2,3,4,5,6],[7,8]]=>0000010=>0100000
[[1,4,5,6,7,8],[2],[3]]=>1100000=>0000011
[[1,3,5,6,7,8],[2],[4]]=>1010000=>0000101
[[1,2,5,6,7,8],[3],[4]]=>0110000=>0000110
[[1,3,4,6,7,8],[2],[5]]=>1001000=>0001001
[[1,2,4,6,7,8],[3],[5]]=>0101000=>0001010
[[1,2,3,6,7,8],[4],[5]]=>0011000=>0001100
[[1,3,4,5,7,8],[2],[6]]=>1000100=>0010001
[[1,2,4,5,7,8],[3],[6]]=>0100100=>0010010
[[1,2,3,5,7,8],[4],[6]]=>0010100=>0010100
[[1,2,3,4,7,8],[5],[6]]=>0001100=>0011000
[[1,3,4,5,6,8],[2],[7]]=>1000010=>0100001
[[1,2,4,5,6,8],[3],[7]]=>0100010=>0100010
[[1,2,3,5,6,8],[4],[7]]=>0010010=>0100100
[[1,2,3,4,6,8],[5],[7]]=>0001010=>0101000
[[1,2,3,4,5,8],[6],[7]]=>0000110=>0110000
[[1,3,4,5,6,7],[2],[8]]=>1000001=>1000001
[[1,2,4,5,6,7],[3],[8]]=>0100001=>1000010
[[1,2,3,5,6,7],[4],[8]]=>0010001=>1000100
[[1,2,3,4,6,7],[5],[8]]=>0001001=>1001000
[[1,2,3,4,5,7],[6],[8]]=>0000101=>1010000
[[1,2,3,4,5,6],[7],[8]]=>0000011=>1100000
[[1,3,5,7,8],[2,4,6]]=>1010100=>0010101
[[1,2,5,7,8],[3,4,6]]=>0100100=>0010010
[[1,3,4,7,8],[2,5,6]]=>1001000=>0001001
[[1,2,4,7,8],[3,5,6]]=>0101000=>0001010
[[1,2,3,7,8],[4,5,6]]=>0010000=>0000100
[[1,3,5,6,8],[2,4,7]]=>1010010=>0100101
[[1,2,5,6,8],[3,4,7]]=>0100010=>0100010
[[1,3,4,6,8],[2,5,7]]=>1001010=>0101001
[[1,2,4,6,8],[3,5,7]]=>0101010=>0101010
[[1,2,3,6,8],[4,5,7]]=>0010010=>0100100
[[1,3,4,5,8],[2,6,7]]=>1000100=>0010001
[[1,2,4,5,8],[3,6,7]]=>0100100=>0010010
[[1,2,3,5,8],[4,6,7]]=>0010100=>0010100
[[1,2,3,4,8],[5,6,7]]=>0001000=>0001000
[[1,3,5,6,7],[2,4,8]]=>1010001=>1000101
[[1,2,5,6,7],[3,4,8]]=>0100001=>1000010
[[1,3,4,6,7],[2,5,8]]=>1001001=>1001001
[[1,2,4,6,7],[3,5,8]]=>0101001=>1001010
[[1,2,3,6,7],[4,5,8]]=>0010001=>1000100
[[1,3,4,5,7],[2,6,8]]=>1000101=>1010001
[[1,2,4,5,7],[3,6,8]]=>0100101=>1010010
[[1,2,3,5,7],[4,6,8]]=>0010101=>1010100
[[1,2,3,4,7],[5,6,8]]=>0001001=>1001000
[[1,3,4,5,6],[2,7,8]]=>1000010=>0100001
[[1,2,4,5,6],[3,7,8]]=>0100010=>0100010
[[1,2,3,5,6],[4,7,8]]=>0010010=>0100100
[[1,2,3,4,6],[5,7,8]]=>0001010=>0101000
[[1,2,3,4,5],[6,7,8]]=>0000100=>0010000
[[1,4,6,7,8],[2,5],[3]]=>1101000=>0001011
[[1,3,6,7,8],[2,5],[4]]=>1010000=>0000101
[[1,2,6,7,8],[3,5],[4]]=>0110000=>0000110
[[1,3,6,7,8],[2,4],[5]]=>1011000=>0001101
[[1,2,6,7,8],[3,4],[5]]=>0101000=>0001010
[[1,4,5,7,8],[2,6],[3]]=>1100100=>0010011
[[1,3,5,7,8],[2,6],[4]]=>1010100=>0010101
[[1,2,5,7,8],[3,6],[4]]=>0110100=>0010110
[[1,3,4,7,8],[2,6],[5]]=>1001000=>0001001
[[1,2,4,7,8],[3,6],[5]]=>0101000=>0001010
[[1,2,3,7,8],[4,6],[5]]=>0011000=>0001100
[[1,3,5,7,8],[2,4],[6]]=>1010100=>0010101
[[1,2,5,7,8],[3,4],[6]]=>0100100=>0010010
[[1,3,4,7,8],[2,5],[6]]=>1001100=>0011001
[[1,2,4,7,8],[3,5],[6]]=>0101100=>0011010
[[1,2,3,7,8],[4,5],[6]]=>0010100=>0010100
[[1,4,5,6,8],[2,7],[3]]=>1100010=>0100011
[[1,3,5,6,8],[2,7],[4]]=>1010010=>0100101
[[1,2,5,6,8],[3,7],[4]]=>0110010=>0100110
[[1,3,4,6,8],[2,7],[5]]=>1001010=>0101001
[[1,2,4,6,8],[3,7],[5]]=>0101010=>0101010
[[1,2,3,6,8],[4,7],[5]]=>0011010=>0101100
[[1,3,4,5,8],[2,7],[6]]=>1000100=>0010001
[[1,2,4,5,8],[3,7],[6]]=>0100100=>0010010
[[1,2,3,5,8],[4,7],[6]]=>0010100=>0010100
[[1,2,3,4,8],[5,7],[6]]=>0001100=>0011000
[[1,3,5,6,8],[2,4],[7]]=>1010010=>0100101
[[1,2,5,6,8],[3,4],[7]]=>0100010=>0100010
[[1,3,4,6,8],[2,5],[7]]=>1001010=>0101001
[[1,2,4,6,8],[3,5],[7]]=>0101010=>0101010
[[1,2,3,6,8],[4,5],[7]]=>0010010=>0100100
[[1,3,4,5,8],[2,6],[7]]=>1000110=>0110001
[[1,2,4,5,8],[3,6],[7]]=>0100110=>0110010
[[1,2,3,5,8],[4,6],[7]]=>0010110=>0110100
[[1,2,3,4,8],[5,6],[7]]=>0001010=>0101000
[[1,4,5,6,7],[2,8],[3]]=>1100001=>1000011
[[1,3,5,6,7],[2,8],[4]]=>1010001=>1000101
[[1,2,5,6,7],[3,8],[4]]=>0110001=>1000110
[[1,3,4,6,7],[2,8],[5]]=>1001001=>1001001
[[1,2,4,6,7],[3,8],[5]]=>0101001=>1001010
[[1,2,3,6,7],[4,8],[5]]=>0011001=>1001100
[[1,3,4,5,7],[2,8],[6]]=>1000101=>1010001
[[1,2,4,5,7],[3,8],[6]]=>0100101=>1010010
[[1,2,3,5,7],[4,8],[6]]=>0010101=>1010100
[[1,2,3,4,7],[5,8],[6]]=>0001101=>1011000
[[1,3,4,5,6],[2,8],[7]]=>1000010=>0100001
[[1,2,4,5,6],[3,8],[7]]=>0100010=>0100010
[[1,2,3,5,6],[4,8],[7]]=>0010010=>0100100
[[1,2,3,4,6],[5,8],[7]]=>0001010=>0101000
[[1,2,3,4,5],[6,8],[7]]=>0000110=>0110000
[[1,3,5,6,7],[2,4],[8]]=>1010001=>1000101
[[1,2,5,6,7],[3,4],[8]]=>0100001=>1000010
[[1,3,4,6,7],[2,5],[8]]=>1001001=>1001001
[[1,2,4,6,7],[3,5],[8]]=>0101001=>1001010
[[1,2,3,6,7],[4,5],[8]]=>0010001=>1000100
[[1,3,4,5,7],[2,6],[8]]=>1000101=>1010001
[[1,2,4,5,7],[3,6],[8]]=>0100101=>1010010
[[1,2,3,5,7],[4,6],[8]]=>0010101=>1010100
[[1,2,3,4,7],[5,6],[8]]=>0001001=>1001000
[[1,3,4,5,6],[2,7],[8]]=>1000011=>1100001
[[1,2,4,5,6],[3,7],[8]]=>0100011=>1100010
[[1,2,3,5,6],[4,7],[8]]=>0010011=>1100100
[[1,2,3,4,6],[5,7],[8]]=>0001011=>1101000
[[1,2,3,4,5],[6,7],[8]]=>0000101=>1010000
[[1,5,6,7,8],[2],[3],[4]]=>1110000=>0000111
[[1,4,6,7,8],[2],[3],[5]]=>1101000=>0001011
[[1,3,6,7,8],[2],[4],[5]]=>1011000=>0001101
[[1,2,6,7,8],[3],[4],[5]]=>0111000=>0001110
[[1,4,5,7,8],[2],[3],[6]]=>1100100=>0010011
[[1,3,5,7,8],[2],[4],[6]]=>1010100=>0010101
[[1,2,5,7,8],[3],[4],[6]]=>0110100=>0010110
[[1,3,4,7,8],[2],[5],[6]]=>1001100=>0011001
[[1,2,4,7,8],[3],[5],[6]]=>0101100=>0011010
[[1,2,3,7,8],[4],[5],[6]]=>0011100=>0011100
[[1,4,5,6,8],[2],[3],[7]]=>1100010=>0100011
[[1,3,5,6,8],[2],[4],[7]]=>1010010=>0100101
[[1,2,5,6,8],[3],[4],[7]]=>0110010=>0100110
[[1,3,4,6,8],[2],[5],[7]]=>1001010=>0101001
[[1,2,4,6,8],[3],[5],[7]]=>0101010=>0101010
[[1,2,3,6,8],[4],[5],[7]]=>0011010=>0101100
[[1,3,4,5,8],[2],[6],[7]]=>1000110=>0110001
[[1,2,4,5,8],[3],[6],[7]]=>0100110=>0110010
[[1,2,3,5,8],[4],[6],[7]]=>0010110=>0110100
[[1,2,3,4,8],[5],[6],[7]]=>0001110=>0111000
[[1,4,5,6,7],[2],[3],[8]]=>1100001=>1000011
[[1,3,5,6,7],[2],[4],[8]]=>1010001=>1000101
[[1,2,5,6,7],[3],[4],[8]]=>0110001=>1000110
[[1,3,4,6,7],[2],[5],[8]]=>1001001=>1001001
[[1,2,4,6,7],[3],[5],[8]]=>0101001=>1001010
[[1,2,3,6,7],[4],[5],[8]]=>0011001=>1001100
[[1,3,4,5,7],[2],[6],[8]]=>1000101=>1010001
[[1,2,4,5,7],[3],[6],[8]]=>0100101=>1010010
[[1,2,3,5,7],[4],[6],[8]]=>0010101=>1010100
[[1,2,3,4,7],[5],[6],[8]]=>0001101=>1011000
[[1,3,4,5,6],[2],[7],[8]]=>1000011=>1100001
[[1,2,4,5,6],[3],[7],[8]]=>0100011=>1100010
[[1,2,3,5,6],[4],[7],[8]]=>0010011=>1100100
[[1,2,3,4,6],[5],[7],[8]]=>0001011=>1101000
[[1,2,3,4,5],[6],[7],[8]]=>0000111=>1110000
[[1,3,5,7],[2,4,6,8]]=>1010101=>1010101
[[1,2,5,7],[3,4,6,8]]=>0100101=>1010010
[[1,3,4,7],[2,5,6,8]]=>1001001=>1001001
[[1,2,4,7],[3,5,6,8]]=>0101001=>1001010
[[1,2,3,7],[4,5,6,8]]=>0010001=>1000100
[[1,3,5,6],[2,4,7,8]]=>1010010=>0100101
[[1,2,5,6],[3,4,7,8]]=>0100010=>0100010
[[1,3,4,6],[2,5,7,8]]=>1001010=>0101001
[[1,2,4,6],[3,5,7,8]]=>0101010=>0101010
[[1,2,3,6],[4,5,7,8]]=>0010010=>0100100
[[1,3,4,5],[2,6,7,8]]=>1000100=>0010001
[[1,2,4,5],[3,6,7,8]]=>0100100=>0010010
[[1,2,3,5],[4,6,7,8]]=>0010100=>0010100
[[1,2,3,4],[5,6,7,8]]=>0001000=>0001000
[[1,4,6,8],[2,5,7],[3]]=>1101010=>0101011
[[1,3,6,8],[2,5,7],[4]]=>1010010=>0100101
[[1,2,6,8],[3,5,7],[4]]=>0110010=>0100110
[[1,3,6,8],[2,4,7],[5]]=>1011010=>0101101
[[1,2,6,8],[3,4,7],[5]]=>0101010=>0101010
[[1,4,5,8],[2,6,7],[3]]=>1100100=>0010011
[[1,3,5,8],[2,6,7],[4]]=>1010100=>0010101
[[1,2,5,8],[3,6,7],[4]]=>0110100=>0010110
[[1,3,4,8],[2,6,7],[5]]=>1001000=>0001001
[[1,2,4,8],[3,6,7],[5]]=>0101000=>0001010
[[1,2,3,8],[4,6,7],[5]]=>0011000=>0001100
[[1,3,5,8],[2,4,7],[6]]=>1010100=>0010101
[[1,2,5,8],[3,4,7],[6]]=>0100100=>0010010
[[1,3,4,8],[2,5,7],[6]]=>1001100=>0011001
[[1,2,4,8],[3,5,7],[6]]=>0101100=>0011010
[[1,2,3,8],[4,5,7],[6]]=>0010100=>0010100
[[1,3,5,8],[2,4,6],[7]]=>1010110=>0110101
[[1,2,5,8],[3,4,6],[7]]=>0100110=>0110010
[[1,3,4,8],[2,5,6],[7]]=>1001010=>0101001
[[1,2,4,8],[3,5,6],[7]]=>0101010=>0101010
[[1,2,3,8],[4,5,6],[7]]=>0010010=>0100100
[[1,4,6,7],[2,5,8],[3]]=>1101001=>1001011
[[1,3,6,7],[2,5,8],[4]]=>1010001=>1000101
[[1,2,6,7],[3,5,8],[4]]=>0110001=>1000110
[[1,3,6,7],[2,4,8],[5]]=>1011001=>1001101
[[1,2,6,7],[3,4,8],[5]]=>0101001=>1001010
[[1,4,5,7],[2,6,8],[3]]=>1100101=>1010011
[[1,3,5,7],[2,6,8],[4]]=>1010101=>1010101
[[1,2,5,7],[3,6,8],[4]]=>0110101=>1010110
[[1,3,4,7],[2,6,8],[5]]=>1001001=>1001001
[[1,2,4,7],[3,6,8],[5]]=>0101001=>1001010
[[1,2,3,7],[4,6,8],[5]]=>0011001=>1001100
[[1,3,5,7],[2,4,8],[6]]=>1010101=>1010101
[[1,2,5,7],[3,4,8],[6]]=>0100101=>1010010
[[1,3,4,7],[2,5,8],[6]]=>1001101=>1011001
[[1,2,4,7],[3,5,8],[6]]=>0101101=>1011010
[[1,2,3,7],[4,5,8],[6]]=>0010101=>1010100
[[1,4,5,6],[2,7,8],[3]]=>1100010=>0100011
[[1,3,5,6],[2,7,8],[4]]=>1010010=>0100101
[[1,2,5,6],[3,7,8],[4]]=>0110010=>0100110
[[1,3,4,6],[2,7,8],[5]]=>1001010=>0101001
[[1,2,4,6],[3,7,8],[5]]=>0101010=>0101010
[[1,2,3,6],[4,7,8],[5]]=>0011010=>0101100
[[1,3,4,5],[2,7,8],[6]]=>1000100=>0010001
[[1,2,4,5],[3,7,8],[6]]=>0100100=>0010010
[[1,2,3,5],[4,7,8],[6]]=>0010100=>0010100
[[1,2,3,4],[5,7,8],[6]]=>0001100=>0011000
[[1,3,5,6],[2,4,8],[7]]=>1010010=>0100101
[[1,2,5,6],[3,4,8],[7]]=>0100010=>0100010
[[1,3,4,6],[2,5,8],[7]]=>1001010=>0101001
[[1,2,4,6],[3,5,8],[7]]=>0101010=>0101010
[[1,2,3,6],[4,5,8],[7]]=>0010010=>0100100
[[1,3,4,5],[2,6,8],[7]]=>1000110=>0110001
[[1,2,4,5],[3,6,8],[7]]=>0100110=>0110010
[[1,2,3,5],[4,6,8],[7]]=>0010110=>0110100
[[1,2,3,4],[5,6,8],[7]]=>0001010=>0101000
[[1,3,5,7],[2,4,6],[8]]=>1010101=>1010101
[[1,2,5,7],[3,4,6],[8]]=>0100101=>1010010
[[1,3,4,7],[2,5,6],[8]]=>1001001=>1001001
[[1,2,4,7],[3,5,6],[8]]=>0101001=>1001010
[[1,2,3,7],[4,5,6],[8]]=>0010001=>1000100
[[1,3,5,6],[2,4,7],[8]]=>1010011=>1100101
[[1,2,5,6],[3,4,7],[8]]=>0100011=>1100010
[[1,3,4,6],[2,5,7],[8]]=>1001011=>1101001
[[1,2,4,6],[3,5,7],[8]]=>0101011=>1101010
[[1,2,3,6],[4,5,7],[8]]=>0010011=>1100100
[[1,3,4,5],[2,6,7],[8]]=>1000101=>1010001
[[1,2,4,5],[3,6,7],[8]]=>0100101=>1010010
[[1,2,3,5],[4,6,7],[8]]=>0010101=>1010100
[[1,2,3,4],[5,6,7],[8]]=>0001001=>1001000
[[1,4,7,8],[2,5],[3,6]]=>1101100=>0011011
[[1,3,7,8],[2,5],[4,6]]=>1010100=>0010101
[[1,2,7,8],[3,5],[4,6]]=>0110100=>0010110
[[1,3,7,8],[2,4],[5,6]]=>1011000=>0001101
[[1,2,7,8],[3,4],[5,6]]=>0101000=>0001010
[[1,4,6,8],[2,5],[3,7]]=>1101010=>0101011
[[1,3,6,8],[2,5],[4,7]]=>1010010=>0100101
[[1,2,6,8],[3,5],[4,7]]=>0110010=>0100110
[[1,3,6,8],[2,4],[5,7]]=>1011010=>0101101
[[1,2,6,8],[3,4],[5,7]]=>0101010=>0101010
[[1,4,5,8],[2,6],[3,7]]=>1100110=>0110011
[[1,3,5,8],[2,6],[4,7]]=>1010110=>0110101
[[1,2,5,8],[3,6],[4,7]]=>0110110=>0110110
[[1,3,4,8],[2,6],[5,7]]=>1001010=>0101001
[[1,2,4,8],[3,6],[5,7]]=>0101010=>0101010
[[1,2,3,8],[4,6],[5,7]]=>0011010=>0101100
[[1,3,5,8],[2,4],[6,7]]=>1010100=>0010101
[[1,2,5,8],[3,4],[6,7]]=>0100100=>0010010
[[1,3,4,8],[2,5],[6,7]]=>1001100=>0011001
[[1,2,4,8],[3,5],[6,7]]=>0101100=>0011010
[[1,2,3,8],[4,5],[6,7]]=>0010100=>0010100
[[1,4,6,7],[2,5],[3,8]]=>1101001=>1001011
[[1,3,6,7],[2,5],[4,8]]=>1010001=>1000101
[[1,2,6,7],[3,5],[4,8]]=>0110001=>1000110
[[1,3,6,7],[2,4],[5,8]]=>1011001=>1001101
[[1,2,6,7],[3,4],[5,8]]=>0101001=>1001010
[[1,4,5,7],[2,6],[3,8]]=>1100101=>1010011
[[1,3,5,7],[2,6],[4,8]]=>1010101=>1010101
[[1,2,5,7],[3,6],[4,8]]=>0110101=>1010110
[[1,3,4,7],[2,6],[5,8]]=>1001001=>1001001
[[1,2,4,7],[3,6],[5,8]]=>0101001=>1001010
[[1,2,3,7],[4,6],[5,8]]=>0011001=>1001100
[[1,3,5,7],[2,4],[6,8]]=>1010101=>1010101
[[1,2,5,7],[3,4],[6,8]]=>0100101=>1010010
[[1,3,4,7],[2,5],[6,8]]=>1001101=>1011001
[[1,2,4,7],[3,5],[6,8]]=>0101101=>1011010
[[1,2,3,7],[4,5],[6,8]]=>0010101=>1010100
[[1,4,5,6],[2,7],[3,8]]=>1100011=>1100011
[[1,3,5,6],[2,7],[4,8]]=>1010011=>1100101
[[1,2,5,6],[3,7],[4,8]]=>0110011=>1100110
[[1,3,4,6],[2,7],[5,8]]=>1001011=>1101001
[[1,2,4,6],[3,7],[5,8]]=>0101011=>1101010
[[1,2,3,6],[4,7],[5,8]]=>0011011=>1101100
[[1,3,4,5],[2,7],[6,8]]=>1000101=>1010001
[[1,2,4,5],[3,7],[6,8]]=>0100101=>1010010
[[1,2,3,5],[4,7],[6,8]]=>0010101=>1010100
[[1,2,3,4],[5,7],[6,8]]=>0001101=>1011000
[[1,3,5,6],[2,4],[7,8]]=>1010010=>0100101
[[1,2,5,6],[3,4],[7,8]]=>0100010=>0100010
[[1,3,4,6],[2,5],[7,8]]=>1001010=>0101001
[[1,2,4,6],[3,5],[7,8]]=>0101010=>0101010
[[1,2,3,6],[4,5],[7,8]]=>0010010=>0100100
[[1,3,4,5],[2,6],[7,8]]=>1000110=>0110001
[[1,2,4,5],[3,6],[7,8]]=>0100110=>0110010
[[1,2,3,5],[4,6],[7,8]]=>0010110=>0110100
[[1,2,3,4],[5,6],[7,8]]=>0001010=>0101000
[[1,5,7,8],[2,6],[3],[4]]=>1110100=>0010111
[[1,4,7,8],[2,6],[3],[5]]=>1101000=>0001011
[[1,3,7,8],[2,6],[4],[5]]=>1011000=>0001101
[[1,2,7,8],[3,6],[4],[5]]=>0111000=>0001110
[[1,4,7,8],[2,5],[3],[6]]=>1101100=>0011011
[[1,3,7,8],[2,5],[4],[6]]=>1010100=>0010101
[[1,2,7,8],[3,5],[4],[6]]=>0110100=>0010110
[[1,3,7,8],[2,4],[5],[6]]=>1011100=>0011101
[[1,2,7,8],[3,4],[5],[6]]=>0101100=>0011010
[[1,5,6,8],[2,7],[3],[4]]=>1110010=>0100111
[[1,4,6,8],[2,7],[3],[5]]=>1101010=>0101011
[[1,3,6,8],[2,7],[4],[5]]=>1011010=>0101101
[[1,2,6,8],[3,7],[4],[5]]=>0111010=>0101110
[[1,4,5,8],[2,7],[3],[6]]=>1100100=>0010011
[[1,3,5,8],[2,7],[4],[6]]=>1010100=>0010101
[[1,2,5,8],[3,7],[4],[6]]=>0110100=>0010110
[[1,3,4,8],[2,7],[5],[6]]=>1001100=>0011001
[[1,2,4,8],[3,7],[5],[6]]=>0101100=>0011010
[[1,2,3,8],[4,7],[5],[6]]=>0011100=>0011100
[[1,4,6,8],[2,5],[3],[7]]=>1101010=>0101011
[[1,3,6,8],[2,5],[4],[7]]=>1010010=>0100101
[[1,2,6,8],[3,5],[4],[7]]=>0110010=>0100110
[[1,3,6,8],[2,4],[5],[7]]=>1011010=>0101101
[[1,2,6,8],[3,4],[5],[7]]=>0101010=>0101010
[[1,4,5,8],[2,6],[3],[7]]=>1100110=>0110011
[[1,3,5,8],[2,6],[4],[7]]=>1010110=>0110101
[[1,2,5,8],[3,6],[4],[7]]=>0110110=>0110110
[[1,3,4,8],[2,6],[5],[7]]=>1001010=>0101001
[[1,2,4,8],[3,6],[5],[7]]=>0101010=>0101010
[[1,2,3,8],[4,6],[5],[7]]=>0011010=>0101100
[[1,3,5,8],[2,4],[6],[7]]=>1010110=>0110101
[[1,2,5,8],[3,4],[6],[7]]=>0100110=>0110010
[[1,3,4,8],[2,5],[6],[7]]=>1001110=>0111001
[[1,2,4,8],[3,5],[6],[7]]=>0101110=>0111010
[[1,2,3,8],[4,5],[6],[7]]=>0010110=>0110100
[[1,5,6,7],[2,8],[3],[4]]=>1110001=>1000111
[[1,4,6,7],[2,8],[3],[5]]=>1101001=>1001011
[[1,3,6,7],[2,8],[4],[5]]=>1011001=>1001101
[[1,2,6,7],[3,8],[4],[5]]=>0111001=>1001110
[[1,4,5,7],[2,8],[3],[6]]=>1100101=>1010011
[[1,3,5,7],[2,8],[4],[6]]=>1010101=>1010101
[[1,2,5,7],[3,8],[4],[6]]=>0110101=>1010110
[[1,3,4,7],[2,8],[5],[6]]=>1001101=>1011001
[[1,2,4,7],[3,8],[5],[6]]=>0101101=>1011010
[[1,2,3,7],[4,8],[5],[6]]=>0011101=>1011100
[[1,4,5,6],[2,8],[3],[7]]=>1100010=>0100011
[[1,3,5,6],[2,8],[4],[7]]=>1010010=>0100101
[[1,2,5,6],[3,8],[4],[7]]=>0110010=>0100110
[[1,3,4,6],[2,8],[5],[7]]=>1001010=>0101001
[[1,2,4,6],[3,8],[5],[7]]=>0101010=>0101010
[[1,2,3,6],[4,8],[5],[7]]=>0011010=>0101100
[[1,3,4,5],[2,8],[6],[7]]=>1000110=>0110001
[[1,2,4,5],[3,8],[6],[7]]=>0100110=>0110010
[[1,2,3,5],[4,8],[6],[7]]=>0010110=>0110100
[[1,2,3,4],[5,8],[6],[7]]=>0001110=>0111000
[[1,4,6,7],[2,5],[3],[8]]=>1101001=>1001011
[[1,3,6,7],[2,5],[4],[8]]=>1010001=>1000101
[[1,2,6,7],[3,5],[4],[8]]=>0110001=>1000110
[[1,3,6,7],[2,4],[5],[8]]=>1011001=>1001101
[[1,2,6,7],[3,4],[5],[8]]=>0101001=>1001010
[[1,4,5,7],[2,6],[3],[8]]=>1100101=>1010011
[[1,3,5,7],[2,6],[4],[8]]=>1010101=>1010101
[[1,2,5,7],[3,6],[4],[8]]=>0110101=>1010110
[[1,3,4,7],[2,6],[5],[8]]=>1001001=>1001001
[[1,2,4,7],[3,6],[5],[8]]=>0101001=>1001010
[[1,2,3,7],[4,6],[5],[8]]=>0011001=>1001100
[[1,3,5,7],[2,4],[6],[8]]=>1010101=>1010101
[[1,2,5,7],[3,4],[6],[8]]=>0100101=>1010010
[[1,3,4,7],[2,5],[6],[8]]=>1001101=>1011001
[[1,2,4,7],[3,5],[6],[8]]=>0101101=>1011010
[[1,2,3,7],[4,5],[6],[8]]=>0010101=>1010100
[[1,4,5,6],[2,7],[3],[8]]=>1100011=>1100011
[[1,3,5,6],[2,7],[4],[8]]=>1010011=>1100101
[[1,2,5,6],[3,7],[4],[8]]=>0110011=>1100110
[[1,3,4,6],[2,7],[5],[8]]=>1001011=>1101001
[[1,2,4,6],[3,7],[5],[8]]=>0101011=>1101010
[[1,2,3,6],[4,7],[5],[8]]=>0011011=>1101100
[[1,3,4,5],[2,7],[6],[8]]=>1000101=>1010001
[[1,2,4,5],[3,7],[6],[8]]=>0100101=>1010010
[[1,2,3,5],[4,7],[6],[8]]=>0010101=>1010100
[[1,2,3,4],[5,7],[6],[8]]=>0001101=>1011000
[[1,3,5,6],[2,4],[7],[8]]=>1010011=>1100101
[[1,2,5,6],[3,4],[7],[8]]=>0100011=>1100010
[[1,3,4,6],[2,5],[7],[8]]=>1001011=>1101001
[[1,2,4,6],[3,5],[7],[8]]=>0101011=>1101010
[[1,2,3,6],[4,5],[7],[8]]=>0010011=>1100100
[[1,3,4,5],[2,6],[7],[8]]=>1000111=>1110001
[[1,2,4,5],[3,6],[7],[8]]=>0100111=>1110010
[[1,2,3,5],[4,6],[7],[8]]=>0010111=>1110100
[[1,2,3,4],[5,6],[7],[8]]=>0001011=>1101000
[[1,6,7,8],[2],[3],[4],[5]]=>1111000=>0001111
[[1,5,7,8],[2],[3],[4],[6]]=>1110100=>0010111
[[1,4,7,8],[2],[3],[5],[6]]=>1101100=>0011011
[[1,3,7,8],[2],[4],[5],[6]]=>1011100=>0011101
[[1,2,7,8],[3],[4],[5],[6]]=>0111100=>0011110
[[1,5,6,8],[2],[3],[4],[7]]=>1110010=>0100111
[[1,4,6,8],[2],[3],[5],[7]]=>1101010=>0101011
[[1,3,6,8],[2],[4],[5],[7]]=>1011010=>0101101
[[1,2,6,8],[3],[4],[5],[7]]=>0111010=>0101110
[[1,4,5,8],[2],[3],[6],[7]]=>1100110=>0110011
[[1,3,5,8],[2],[4],[6],[7]]=>1010110=>0110101
[[1,2,5,8],[3],[4],[6],[7]]=>0110110=>0110110
[[1,3,4,8],[2],[5],[6],[7]]=>1001110=>0111001
[[1,2,4,8],[3],[5],[6],[7]]=>0101110=>0111010
[[1,2,3,8],[4],[5],[6],[7]]=>0011110=>0111100
[[1,5,6,7],[2],[3],[4],[8]]=>1110001=>1000111
[[1,4,6,7],[2],[3],[5],[8]]=>1101001=>1001011
[[1,3,6,7],[2],[4],[5],[8]]=>1011001=>1001101
[[1,2,6,7],[3],[4],[5],[8]]=>0111001=>1001110
[[1,4,5,7],[2],[3],[6],[8]]=>1100101=>1010011
[[1,3,5,7],[2],[4],[6],[8]]=>1010101=>1010101
[[1,2,5,7],[3],[4],[6],[8]]=>0110101=>1010110
[[1,3,4,7],[2],[5],[6],[8]]=>1001101=>1011001
[[1,2,4,7],[3],[5],[6],[8]]=>0101101=>1011010
[[1,2,3,7],[4],[5],[6],[8]]=>0011101=>1011100
[[1,4,5,6],[2],[3],[7],[8]]=>1100011=>1100011
[[1,3,5,6],[2],[4],[7],[8]]=>1010011=>1100101
[[1,2,5,6],[3],[4],[7],[8]]=>0110011=>1100110
[[1,3,4,6],[2],[5],[7],[8]]=>1001011=>1101001
[[1,2,4,6],[3],[5],[7],[8]]=>0101011=>1101010
[[1,2,3,6],[4],[5],[7],[8]]=>0011011=>1101100
[[1,3,4,5],[2],[6],[7],[8]]=>1000111=>1110001
[[1,2,4,5],[3],[6],[7],[8]]=>0100111=>1110010
[[1,2,3,5],[4],[6],[7],[8]]=>0010111=>1110100
[[1,2,3,4],[5],[6],[7],[8]]=>0001111=>1111000
[[1,4,7],[2,5,8],[3,6]]=>1101101=>1011011
[[1,3,7],[2,5,8],[4,6]]=>1010101=>1010101
[[1,2,7],[3,5,8],[4,6]]=>0110101=>1010110
[[1,3,7],[2,4,8],[5,6]]=>1011001=>1001101
[[1,2,7],[3,4,8],[5,6]]=>0101001=>1001010
[[1,4,6],[2,5,8],[3,7]]=>1101010=>0101011
[[1,3,6],[2,5,8],[4,7]]=>1010010=>0100101
[[1,2,6],[3,5,8],[4,7]]=>0110010=>0100110
[[1,3,6],[2,4,8],[5,7]]=>1011010=>0101101
[[1,2,6],[3,4,8],[5,7]]=>0101010=>0101010
[[1,4,5],[2,6,8],[3,7]]=>1100110=>0110011
[[1,3,5],[2,6,8],[4,7]]=>1010110=>0110101
[[1,2,5],[3,6,8],[4,7]]=>0110110=>0110110
[[1,3,4],[2,6,8],[5,7]]=>1001010=>0101001
[[1,2,4],[3,6,8],[5,7]]=>0101010=>0101010
[[1,2,3],[4,6,8],[5,7]]=>0011010=>0101100
[[1,3,5],[2,4,8],[6,7]]=>1010100=>0010101
[[1,2,5],[3,4,8],[6,7]]=>0100100=>0010010
[[1,3,4],[2,5,8],[6,7]]=>1001100=>0011001
[[1,2,4],[3,5,8],[6,7]]=>0101100=>0011010
[[1,2,3],[4,5,8],[6,7]]=>0010100=>0010100
[[1,4,6],[2,5,7],[3,8]]=>1101011=>1101011
[[1,3,6],[2,5,7],[4,8]]=>1010011=>1100101
[[1,2,6],[3,5,7],[4,8]]=>0110011=>1100110
[[1,3,6],[2,4,7],[5,8]]=>1011011=>1101101
[[1,2,6],[3,4,7],[5,8]]=>0101011=>1101010
[[1,4,5],[2,6,7],[3,8]]=>1100101=>1010011
[[1,3,5],[2,6,7],[4,8]]=>1010101=>1010101
[[1,2,5],[3,6,7],[4,8]]=>0110101=>1010110
[[1,3,4],[2,6,7],[5,8]]=>1001001=>1001001
[[1,2,4],[3,6,7],[5,8]]=>0101001=>1001010
[[1,2,3],[4,6,7],[5,8]]=>0011001=>1001100
[[1,3,5],[2,4,7],[6,8]]=>1010101=>1010101
[[1,2,5],[3,4,7],[6,8]]=>0100101=>1010010
[[1,3,4],[2,5,7],[6,8]]=>1001101=>1011001
[[1,2,4],[3,5,7],[6,8]]=>0101101=>1011010
[[1,2,3],[4,5,7],[6,8]]=>0010101=>1010100
[[1,3,5],[2,4,6],[7,8]]=>1010110=>0110101
[[1,2,5],[3,4,6],[7,8]]=>0100110=>0110010
[[1,3,4],[2,5,6],[7,8]]=>1001010=>0101001
[[1,2,4],[3,5,6],[7,8]]=>0101010=>0101010
[[1,2,3],[4,5,6],[7,8]]=>0010010=>0100100
[[1,5,7],[2,6,8],[3],[4]]=>1110101=>1010111
[[1,4,7],[2,6,8],[3],[5]]=>1101001=>1001011
[[1,3,7],[2,6,8],[4],[5]]=>1011001=>1001101
[[1,2,7],[3,6,8],[4],[5]]=>0111001=>1001110
[[1,4,7],[2,5,8],[3],[6]]=>1101101=>1011011
[[1,3,7],[2,5,8],[4],[6]]=>1010101=>1010101
[[1,2,7],[3,5,8],[4],[6]]=>0110101=>1010110
[[1,3,7],[2,4,8],[5],[6]]=>1011101=>1011101
[[1,2,7],[3,4,8],[5],[6]]=>0101101=>1011010
[[1,5,6],[2,7,8],[3],[4]]=>1110010=>0100111
[[1,4,6],[2,7,8],[3],[5]]=>1101010=>0101011
[[1,3,6],[2,7,8],[4],[5]]=>1011010=>0101101
[[1,2,6],[3,7,8],[4],[5]]=>0111010=>0101110
[[1,4,5],[2,7,8],[3],[6]]=>1100100=>0010011
[[1,3,5],[2,7,8],[4],[6]]=>1010100=>0010101
[[1,2,5],[3,7,8],[4],[6]]=>0110100=>0010110
[[1,3,4],[2,7,8],[5],[6]]=>1001100=>0011001
[[1,2,4],[3,7,8],[5],[6]]=>0101100=>0011010
[[1,2,3],[4,7,8],[5],[6]]=>0011100=>0011100
[[1,4,6],[2,5,8],[3],[7]]=>1101010=>0101011
[[1,3,6],[2,5,8],[4],[7]]=>1010010=>0100101
[[1,2,6],[3,5,8],[4],[7]]=>0110010=>0100110
[[1,3,6],[2,4,8],[5],[7]]=>1011010=>0101101
[[1,2,6],[3,4,8],[5],[7]]=>0101010=>0101010
[[1,4,5],[2,6,8],[3],[7]]=>1100110=>0110011
[[1,3,5],[2,6,8],[4],[7]]=>1010110=>0110101
[[1,2,5],[3,6,8],[4],[7]]=>0110110=>0110110
[[1,3,4],[2,6,8],[5],[7]]=>1001010=>0101001
[[1,2,4],[3,6,8],[5],[7]]=>0101010=>0101010
[[1,2,3],[4,6,8],[5],[7]]=>0011010=>0101100
[[1,3,5],[2,4,8],[6],[7]]=>1010110=>0110101
[[1,2,5],[3,4,8],[6],[7]]=>0100110=>0110010
[[1,3,4],[2,5,8],[6],[7]]=>1001110=>0111001
[[1,2,4],[3,5,8],[6],[7]]=>0101110=>0111010
[[1,2,3],[4,5,8],[6],[7]]=>0010110=>0110100
[[1,4,6],[2,5,7],[3],[8]]=>1101011=>1101011
[[1,3,6],[2,5,7],[4],[8]]=>1010011=>1100101
[[1,2,6],[3,5,7],[4],[8]]=>0110011=>1100110
[[1,3,6],[2,4,7],[5],[8]]=>1011011=>1101101
[[1,2,6],[3,4,7],[5],[8]]=>0101011=>1101010
[[1,4,5],[2,6,7],[3],[8]]=>1100101=>1010011
[[1,3,5],[2,6,7],[4],[8]]=>1010101=>1010101
[[1,2,5],[3,6,7],[4],[8]]=>0110101=>1010110
[[1,3,4],[2,6,7],[5],[8]]=>1001001=>1001001
[[1,2,4],[3,6,7],[5],[8]]=>0101001=>1001010
[[1,2,3],[4,6,7],[5],[8]]=>0011001=>1001100
[[1,3,5],[2,4,7],[6],[8]]=>1010101=>1010101
[[1,2,5],[3,4,7],[6],[8]]=>0100101=>1010010
[[1,3,4],[2,5,7],[6],[8]]=>1001101=>1011001
[[1,2,4],[3,5,7],[6],[8]]=>0101101=>1011010
[[1,2,3],[4,5,7],[6],[8]]=>0010101=>1010100
[[1,3,5],[2,4,6],[7],[8]]=>1010111=>1110101
[[1,2,5],[3,4,6],[7],[8]]=>0100111=>1110010
[[1,3,4],[2,5,6],[7],[8]]=>1001011=>1101001
[[1,2,4],[3,5,6],[7],[8]]=>0101011=>1101010
[[1,2,3],[4,5,6],[7],[8]]=>0010011=>1100100
[[1,5,8],[2,6],[3,7],[4]]=>1110110=>0110111
[[1,4,8],[2,6],[3,7],[5]]=>1101010=>0101011
[[1,3,8],[2,6],[4,7],[5]]=>1011010=>0101101
[[1,2,8],[3,6],[4,7],[5]]=>0111010=>0101110
[[1,4,8],[2,5],[3,7],[6]]=>1101100=>0011011
[[1,3,8],[2,5],[4,7],[6]]=>1010100=>0010101
[[1,2,8],[3,5],[4,7],[6]]=>0110100=>0010110
[[1,3,8],[2,4],[5,7],[6]]=>1011100=>0011101
[[1,2,8],[3,4],[5,7],[6]]=>0101100=>0011010
[[1,4,8],[2,5],[3,6],[7]]=>1101110=>0111011
[[1,3,8],[2,5],[4,6],[7]]=>1010110=>0110101
[[1,2,8],[3,5],[4,6],[7]]=>0110110=>0110110
[[1,3,8],[2,4],[5,6],[7]]=>1011010=>0101101
[[1,2,8],[3,4],[5,6],[7]]=>0101010=>0101010
[[1,5,7],[2,6],[3,8],[4]]=>1110101=>1010111
[[1,4,7],[2,6],[3,8],[5]]=>1101001=>1001011
[[1,3,7],[2,6],[4,8],[5]]=>1011001=>1001101
[[1,2,7],[3,6],[4,8],[5]]=>0111001=>1001110
[[1,4,7],[2,5],[3,8],[6]]=>1101101=>1011011
[[1,3,7],[2,5],[4,8],[6]]=>1010101=>1010101
[[1,2,7],[3,5],[4,8],[6]]=>0110101=>1010110
[[1,3,7],[2,4],[5,8],[6]]=>1011101=>1011101
[[1,2,7],[3,4],[5,8],[6]]=>0101101=>1011010
[[1,5,6],[2,7],[3,8],[4]]=>1110011=>1100111
[[1,4,6],[2,7],[3,8],[5]]=>1101011=>1101011
[[1,3,6],[2,7],[4,8],[5]]=>1011011=>1101101
[[1,2,6],[3,7],[4,8],[5]]=>0111011=>1101110
[[1,4,5],[2,7],[3,8],[6]]=>1100101=>1010011
[[1,3,5],[2,7],[4,8],[6]]=>1010101=>1010101
[[1,2,5],[3,7],[4,8],[6]]=>0110101=>1010110
[[1,3,4],[2,7],[5,8],[6]]=>1001101=>1011001
[[1,2,4],[3,7],[5,8],[6]]=>0101101=>1011010
[[1,2,3],[4,7],[5,8],[6]]=>0011101=>1011100
[[1,4,6],[2,5],[3,8],[7]]=>1101010=>0101011
[[1,3,6],[2,5],[4,8],[7]]=>1010010=>0100101
[[1,2,6],[3,5],[4,8],[7]]=>0110010=>0100110
[[1,3,6],[2,4],[5,8],[7]]=>1011010=>0101101
[[1,2,6],[3,4],[5,8],[7]]=>0101010=>0101010
[[1,4,5],[2,6],[3,8],[7]]=>1100110=>0110011
[[1,3,5],[2,6],[4,8],[7]]=>1010110=>0110101
[[1,2,5],[3,6],[4,8],[7]]=>0110110=>0110110
[[1,3,4],[2,6],[5,8],[7]]=>1001010=>0101001
[[1,2,4],[3,6],[5,8],[7]]=>0101010=>0101010
[[1,2,3],[4,6],[5,8],[7]]=>0011010=>0101100
[[1,3,5],[2,4],[6,8],[7]]=>1010110=>0110101
[[1,2,5],[3,4],[6,8],[7]]=>0100110=>0110010
[[1,3,4],[2,5],[6,8],[7]]=>1001110=>0111001
[[1,2,4],[3,5],[6,8],[7]]=>0101110=>0111010
[[1,2,3],[4,5],[6,8],[7]]=>0010110=>0110100
[[1,4,7],[2,5],[3,6],[8]]=>1101101=>1011011
[[1,3,7],[2,5],[4,6],[8]]=>1010101=>1010101
[[1,2,7],[3,5],[4,6],[8]]=>0110101=>1010110
[[1,3,7],[2,4],[5,6],[8]]=>1011001=>1001101
[[1,2,7],[3,4],[5,6],[8]]=>0101001=>1001010
[[1,4,6],[2,5],[3,7],[8]]=>1101011=>1101011
[[1,3,6],[2,5],[4,7],[8]]=>1010011=>1100101
[[1,2,6],[3,5],[4,7],[8]]=>0110011=>1100110
[[1,3,6],[2,4],[5,7],[8]]=>1011011=>1101101
[[1,2,6],[3,4],[5,7],[8]]=>0101011=>1101010
[[1,4,5],[2,6],[3,7],[8]]=>1100111=>1110011
[[1,3,5],[2,6],[4,7],[8]]=>1010111=>1110101
[[1,2,5],[3,6],[4,7],[8]]=>0110111=>1110110
[[1,3,4],[2,6],[5,7],[8]]=>1001011=>1101001
[[1,2,4],[3,6],[5,7],[8]]=>0101011=>1101010
[[1,2,3],[4,6],[5,7],[8]]=>0011011=>1101100
[[1,3,5],[2,4],[6,7],[8]]=>1010101=>1010101
[[1,2,5],[3,4],[6,7],[8]]=>0100101=>1010010
[[1,3,4],[2,5],[6,7],[8]]=>1001101=>1011001
[[1,2,4],[3,5],[6,7],[8]]=>0101101=>1011010
[[1,2,3],[4,5],[6,7],[8]]=>0010101=>1010100
[[1,6,8],[2,7],[3],[4],[5]]=>1111010=>0101111
[[1,5,8],[2,7],[3],[4],[6]]=>1110100=>0010111
[[1,4,8],[2,7],[3],[5],[6]]=>1101100=>0011011
[[1,3,8],[2,7],[4],[5],[6]]=>1011100=>0011101
[[1,2,8],[3,7],[4],[5],[6]]=>0111100=>0011110
[[1,5,8],[2,6],[3],[4],[7]]=>1110110=>0110111
[[1,4,8],[2,6],[3],[5],[7]]=>1101010=>0101011
[[1,3,8],[2,6],[4],[5],[7]]=>1011010=>0101101
[[1,2,8],[3,6],[4],[5],[7]]=>0111010=>0101110
[[1,4,8],[2,5],[3],[6],[7]]=>1101110=>0111011
[[1,3,8],[2,5],[4],[6],[7]]=>1010110=>0110101
[[1,2,8],[3,5],[4],[6],[7]]=>0110110=>0110110
[[1,3,8],[2,4],[5],[6],[7]]=>1011110=>0111101
[[1,2,8],[3,4],[5],[6],[7]]=>0101110=>0111010
[[1,6,7],[2,8],[3],[4],[5]]=>1111001=>1001111
[[1,5,7],[2,8],[3],[4],[6]]=>1110101=>1010111
[[1,4,7],[2,8],[3],[5],[6]]=>1101101=>1011011
[[1,3,7],[2,8],[4],[5],[6]]=>1011101=>1011101
[[1,2,7],[3,8],[4],[5],[6]]=>0111101=>1011110
[[1,5,6],[2,8],[3],[4],[7]]=>1110010=>0100111
[[1,4,6],[2,8],[3],[5],[7]]=>1101010=>0101011
[[1,3,6],[2,8],[4],[5],[7]]=>1011010=>0101101
[[1,2,6],[3,8],[4],[5],[7]]=>0111010=>0101110
[[1,4,5],[2,8],[3],[6],[7]]=>1100110=>0110011
[[1,3,5],[2,8],[4],[6],[7]]=>1010110=>0110101
[[1,2,5],[3,8],[4],[6],[7]]=>0110110=>0110110
[[1,3,4],[2,8],[5],[6],[7]]=>1001110=>0111001
[[1,2,4],[3,8],[5],[6],[7]]=>0101110=>0111010
[[1,2,3],[4,8],[5],[6],[7]]=>0011110=>0111100
[[1,5,7],[2,6],[3],[4],[8]]=>1110101=>1010111
[[1,4,7],[2,6],[3],[5],[8]]=>1101001=>1001011
[[1,3,7],[2,6],[4],[5],[8]]=>1011001=>1001101
[[1,2,7],[3,6],[4],[5],[8]]=>0111001=>1001110
[[1,4,7],[2,5],[3],[6],[8]]=>1101101=>1011011
[[1,3,7],[2,5],[4],[6],[8]]=>1010101=>1010101
[[1,2,7],[3,5],[4],[6],[8]]=>0110101=>1010110
[[1,3,7],[2,4],[5],[6],[8]]=>1011101=>1011101
[[1,2,7],[3,4],[5],[6],[8]]=>0101101=>1011010
[[1,5,6],[2,7],[3],[4],[8]]=>1110011=>1100111
[[1,4,6],[2,7],[3],[5],[8]]=>1101011=>1101011
[[1,3,6],[2,7],[4],[5],[8]]=>1011011=>1101101
[[1,2,6],[3,7],[4],[5],[8]]=>0111011=>1101110
[[1,4,5],[2,7],[3],[6],[8]]=>1100101=>1010011
[[1,3,5],[2,7],[4],[6],[8]]=>1010101=>1010101
[[1,2,5],[3,7],[4],[6],[8]]=>0110101=>1010110
[[1,3,4],[2,7],[5],[6],[8]]=>1001101=>1011001
[[1,2,4],[3,7],[5],[6],[8]]=>0101101=>1011010
[[1,2,3],[4,7],[5],[6],[8]]=>0011101=>1011100
[[1,4,6],[2,5],[3],[7],[8]]=>1101011=>1101011
[[1,3,6],[2,5],[4],[7],[8]]=>1010011=>1100101
[[1,2,6],[3,5],[4],[7],[8]]=>0110011=>1100110
[[1,3,6],[2,4],[5],[7],[8]]=>1011011=>1101101
[[1,2,6],[3,4],[5],[7],[8]]=>0101011=>1101010
[[1,4,5],[2,6],[3],[7],[8]]=>1100111=>1110011
[[1,3,5],[2,6],[4],[7],[8]]=>1010111=>1110101
[[1,2,5],[3,6],[4],[7],[8]]=>0110111=>1110110
[[1,3,4],[2,6],[5],[7],[8]]=>1001011=>1101001
[[1,2,4],[3,6],[5],[7],[8]]=>0101011=>1101010
[[1,2,3],[4,6],[5],[7],[8]]=>0011011=>1101100
[[1,3,5],[2,4],[6],[7],[8]]=>1010111=>1110101
[[1,2,5],[3,4],[6],[7],[8]]=>0100111=>1110010
[[1,3,4],[2,5],[6],[7],[8]]=>1001111=>1111001
[[1,2,4],[3,5],[6],[7],[8]]=>0101111=>1111010
[[1,2,3],[4,5],[6],[7],[8]]=>0010111=>1110100
[[1,7,8],[2],[3],[4],[5],[6]]=>1111100=>0011111
[[1,6,8],[2],[3],[4],[5],[7]]=>1111010=>0101111
[[1,5,8],[2],[3],[4],[6],[7]]=>1110110=>0110111
[[1,4,8],[2],[3],[5],[6],[7]]=>1101110=>0111011
[[1,3,8],[2],[4],[5],[6],[7]]=>1011110=>0111101
[[1,2,8],[3],[4],[5],[6],[7]]=>0111110=>0111110
[[1,6,7],[2],[3],[4],[5],[8]]=>1111001=>1001111
[[1,5,7],[2],[3],[4],[6],[8]]=>1110101=>1010111
[[1,4,7],[2],[3],[5],[6],[8]]=>1101101=>1011011
[[1,3,7],[2],[4],[5],[6],[8]]=>1011101=>1011101
[[1,2,7],[3],[4],[5],[6],[8]]=>0111101=>1011110
[[1,5,6],[2],[3],[4],[7],[8]]=>1110011=>1100111
[[1,4,6],[2],[3],[5],[7],[8]]=>1101011=>1101011
[[1,3,6],[2],[4],[5],[7],[8]]=>1011011=>1101101
[[1,2,6],[3],[4],[5],[7],[8]]=>0111011=>1101110
[[1,4,5],[2],[3],[6],[7],[8]]=>1100111=>1110011
[[1,3,5],[2],[4],[6],[7],[8]]=>1010111=>1110101
[[1,2,5],[3],[4],[6],[7],[8]]=>0110111=>1110110
[[1,3,4],[2],[5],[6],[7],[8]]=>1001111=>1111001
[[1,2,4],[3],[5],[6],[7],[8]]=>0101111=>1111010
[[1,2,3],[4],[5],[6],[7],[8]]=>0011111=>1111100
[[1,5],[2,6],[3,7],[4,8]]=>1110111=>1110111
[[1,4],[2,6],[3,7],[5,8]]=>1101011=>1101011
[[1,3],[2,6],[4,7],[5,8]]=>1011011=>1101101
[[1,2],[3,6],[4,7],[5,8]]=>0111011=>1101110
[[1,4],[2,5],[3,7],[6,8]]=>1101101=>1011011
[[1,3],[2,5],[4,7],[6,8]]=>1010101=>1010101
[[1,2],[3,5],[4,7],[6,8]]=>0110101=>1010110
[[1,3],[2,4],[5,7],[6,8]]=>1011101=>1011101
[[1,2],[3,4],[5,7],[6,8]]=>0101101=>1011010
[[1,4],[2,5],[3,6],[7,8]]=>1101110=>0111011
[[1,3],[2,5],[4,6],[7,8]]=>1010110=>0110101
[[1,2],[3,5],[4,6],[7,8]]=>0110110=>0110110
[[1,3],[2,4],[5,6],[7,8]]=>1011010=>0101101
[[1,2],[3,4],[5,6],[7,8]]=>0101010=>0101010
[[1,6],[2,7],[3,8],[4],[5]]=>1111011=>1101111
[[1,5],[2,7],[3,8],[4],[6]]=>1110101=>1010111
[[1,4],[2,7],[3,8],[5],[6]]=>1101101=>1011011
[[1,3],[2,7],[4,8],[5],[6]]=>1011101=>1011101
[[1,2],[3,7],[4,8],[5],[6]]=>0111101=>1011110
[[1,5],[2,6],[3,8],[4],[7]]=>1110110=>0110111
[[1,4],[2,6],[3,8],[5],[7]]=>1101010=>0101011
[[1,3],[2,6],[4,8],[5],[7]]=>1011010=>0101101
[[1,2],[3,6],[4,8],[5],[7]]=>0111010=>0101110
[[1,4],[2,5],[3,8],[6],[7]]=>1101110=>0111011
[[1,3],[2,5],[4,8],[6],[7]]=>1010110=>0110101
[[1,2],[3,5],[4,8],[6],[7]]=>0110110=>0110110
[[1,3],[2,4],[5,8],[6],[7]]=>1011110=>0111101
[[1,2],[3,4],[5,8],[6],[7]]=>0101110=>0111010
[[1,5],[2,6],[3,7],[4],[8]]=>1110111=>1110111
[[1,4],[2,6],[3,7],[5],[8]]=>1101011=>1101011
[[1,3],[2,6],[4,7],[5],[8]]=>1011011=>1101101
[[1,2],[3,6],[4,7],[5],[8]]=>0111011=>1101110
[[1,4],[2,5],[3,7],[6],[8]]=>1101101=>1011011
[[1,3],[2,5],[4,7],[6],[8]]=>1010101=>1010101
[[1,2],[3,5],[4,7],[6],[8]]=>0110101=>1010110
[[1,3],[2,4],[5,7],[6],[8]]=>1011101=>1011101
[[1,2],[3,4],[5,7],[6],[8]]=>0101101=>1011010
[[1,4],[2,5],[3,6],[7],[8]]=>1101111=>1111011
[[1,3],[2,5],[4,6],[7],[8]]=>1010111=>1110101
[[1,2],[3,5],[4,6],[7],[8]]=>0110111=>1110110
[[1,3],[2,4],[5,6],[7],[8]]=>1011011=>1101101
[[1,2],[3,4],[5,6],[7],[8]]=>0101011=>1101010
[[1,7],[2,8],[3],[4],[5],[6]]=>1111101=>1011111
[[1,6],[2,8],[3],[4],[5],[7]]=>1111010=>0101111
[[1,5],[2,8],[3],[4],[6],[7]]=>1110110=>0110111
[[1,4],[2,8],[3],[5],[6],[7]]=>1101110=>0111011
[[1,3],[2,8],[4],[5],[6],[7]]=>1011110=>0111101
[[1,2],[3,8],[4],[5],[6],[7]]=>0111110=>0111110
[[1,6],[2,7],[3],[4],[5],[8]]=>1111011=>1101111
[[1,5],[2,7],[3],[4],[6],[8]]=>1110101=>1010111
[[1,4],[2,7],[3],[5],[6],[8]]=>1101101=>1011011
[[1,3],[2,7],[4],[5],[6],[8]]=>1011101=>1011101
[[1,2],[3,7],[4],[5],[6],[8]]=>0111101=>1011110
[[1,5],[2,6],[3],[4],[7],[8]]=>1110111=>1110111
[[1,4],[2,6],[3],[5],[7],[8]]=>1101011=>1101011
[[1,3],[2,6],[4],[5],[7],[8]]=>1011011=>1101101
[[1,2],[3,6],[4],[5],[7],[8]]=>0111011=>1101110
[[1,4],[2,5],[3],[6],[7],[8]]=>1101111=>1111011
[[1,3],[2,5],[4],[6],[7],[8]]=>1010111=>1110101
[[1,2],[3,5],[4],[6],[7],[8]]=>0110111=>1110110
[[1,3],[2,4],[5],[6],[7],[8]]=>1011111=>1111101
[[1,2],[3,4],[5],[6],[7],[8]]=>0101111=>1111010
[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110=>0111111
[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101=>1011111
[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011=>1101111
[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111=>1110111
[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111=>1111011
[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111=>1111101
[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111=>1111110
[[1],[2],[3],[4],[5],[6],[7],[8]]=>1111111=>1111111
[[1,3,5,7,9],[2,4,6,8,10]]=>101010101=>101010101
[[1,3,5,7,8],[2,4,6,9,10]]=>101010010=>010010101
[[1,3,5,6,9],[2,4,7,8,10]]=>101001001=>100100101
[[1,3,5,6,8],[2,4,7,9,10]]=>101001010=>010100101
[[1,3,5,6,7],[2,4,8,9,10]]=>101000100=>001000101
[[1,3,4,7,9],[2,5,6,8,10]]=>100100101=>101001001
[[1,3,4,7,8],[2,5,6,9,10]]=>100100010=>010001001
[[1,3,4,6,9],[2,5,7,8,10]]=>100101001=>100101001
[[1,3,4,6,8],[2,5,7,9,10]]=>100101010=>010101001
[[1,3,4,6,7],[2,5,8,9,10]]=>100100100=>001001001
[[1,3,4,5,9],[2,6,7,8,10]]=>100010001=>100010001
[[1,3,4,5,8],[2,6,7,9,10]]=>100010010=>010010001
[[1,3,4,5,7],[2,6,8,9,10]]=>100010100=>001010001
[[1,3,4,5,6],[2,7,8,9,10]]=>100001000=>000100001
[[1,2,5,7,9],[3,4,6,8,10]]=>010010101=>101010010
[[1,2,5,7,8],[3,4,6,9,10]]=>010010010=>010010010
[[1,2,5,6,9],[3,4,7,8,10]]=>010001001=>100100010
[[1,2,5,6,8],[3,4,7,9,10]]=>010001010=>010100010
[[1,2,5,6,7],[3,4,8,9,10]]=>010000100=>001000010
[[1,2,4,7,9],[3,5,6,8,10]]=>010100101=>101001010
[[1,2,4,7,8],[3,5,6,9,10]]=>010100010=>010001010
[[1,2,4,6,9],[3,5,7,8,10]]=>010101001=>100101010
[[1,2,4,6,8],[3,5,7,9,10]]=>010101010=>010101010
[[1,2,4,6,7],[3,5,8,9,10]]=>010100100=>001001010
[[1,2,4,5,9],[3,6,7,8,10]]=>010010001=>100010010
[[1,2,4,5,8],[3,6,7,9,10]]=>010010010=>010010010
[[1,2,4,5,7],[3,6,8,9,10]]=>010010100=>001010010
[[1,2,4,5,6],[3,7,8,9,10]]=>010001000=>000100010
[[1,2,3,7,9],[4,5,6,8,10]]=>001000101=>101000100
[[1,2,3,7,8],[4,5,6,9,10]]=>001000010=>010000100
[[1,2,3,6,9],[4,5,7,8,10]]=>001001001=>100100100
[[1,2,3,6,8],[4,5,7,9,10]]=>001001010=>010100100
[[1,2,3,6,7],[4,5,8,9,10]]=>001000100=>001000100
[[1,2,3,5,9],[4,6,7,8,10]]=>001010001=>100010100
[[1,2,3,5,8],[4,6,7,9,10]]=>001010010=>010010100
[[1,2,3,5,7],[4,6,8,9,10]]=>001010100=>001010100
[[1,2,3,5,6],[4,7,8,9,10]]=>001001000=>000100100
[[1,2,3,4,9],[5,6,7,8,10]]=>000100001=>100001000
[[1,2,3,4,8],[5,6,7,9,10]]=>000100010=>010001000
[[1,2,3,4,7],[5,6,8,9,10]]=>000100100=>001001000
[[1,2,3,4,6],[5,7,8,9,10]]=>000101000=>000101000
[[1,2,3,4,5],[6,7,8,9,10]]=>000010000=>000010000
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>10101010101=>10101010101
[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>10101010010=>01001010101
[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>10101001001=>10010010101
[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>10101001010=>01010010101
[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>10101000100=>00100010101
[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>10100100101=>10100100101
[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>10100100010=>01000100101
[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>10100101001=>10010100101
[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>10100101010=>01010100101
[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>10100100100=>00100100101
[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>10100010001=>10001000101
[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>10100010010=>01001000101
[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>10100010100=>00101000101
[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>10100001000=>00010000101
[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>10010010101=>10101001001
[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>10010010010=>01001001001
[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>10010001001=>10010001001
[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>10010001010=>01010001001
[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>10010000100=>00100001001
[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>10010100101=>10100101001
[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>10010100010=>01000101001
[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>10010101001=>10010101001
[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>10010101010=>01010101001
[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>10010100100=>00100101001
[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>10010010001=>10001001001
[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>10010010010=>01001001001
[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>10010010100=>00101001001
[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>10010001000=>00010001001
[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>10001000101=>10100010001
[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>10001000010=>01000010001
[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>10001001001=>10010010001
[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>10001001010=>01010010001
[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>10001000100=>00100010001
[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>10001010001=>10001010001
[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>10001010010=>01001010001
[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>10001010100=>00101010001
[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>10001001000=>00010010001
[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>10000100001=>10000100001
[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>10000100010=>01000100001
[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>10000100100=>00100100001
[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>10000101000=>00010100001
[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>10000010000=>00001000001
[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>01001010101=>10101010010
[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>01001010010=>01001010010
[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>01001001001=>10010010010
[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>01001001010=>01010010010
[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>01001000100=>00100010010
[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>01000100101=>10100100010
[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>01000100010=>01000100010
[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>01000101001=>10010100010
[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>01000101010=>01010100010
[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>01000100100=>00100100010
[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>01000010001=>10001000010
[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>01000010010=>01001000010
[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>01000010100=>00101000010
[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>01000001000=>00010000010
[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>01010010101=>10101001010
[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>01010010010=>01001001010
[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>01010001001=>10010001010
[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>01010001010=>01010001010
[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>01010000100=>00100001010
[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>01010100101=>10100101010
[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>01010100010=>01000101010
[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>01010101001=>10010101010
[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>01010101010=>01010101010
[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>01010100100=>00100101010
[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>01010010001=>10001001010
[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>01010010010=>01001001010
[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>01010010100=>00101001010
[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>01010001000=>00010001010
[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>01001000101=>10100010010
[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>01001000010=>01000010010
[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>01001001001=>10010010010
[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>01001001010=>01010010010
[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>01001000100=>00100010010
[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>01001010001=>10001010010
[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>01001010010=>01001010010
[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>01001010100=>00101010010
[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>01001001000=>00010010010
[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>01000100001=>10000100010
[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>01000100010=>01000100010
[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>01000100100=>00100100010
[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>01000101000=>00010100010
[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>01000010000=>00001000010
[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>00100010101=>10101000100
[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>00100010010=>01001000100
[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>00100001001=>10010000100
[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>00100001010=>01010000100
[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>00100000100=>00100000100
[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>00100100101=>10100100100
[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>00100100010=>01000100100
[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>00100101001=>10010100100
[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>00100101010=>01010100100
[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>00100100100=>00100100100
[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>00100010001=>10001000100
[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>00100010010=>01001000100
[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>00100010100=>00101000100
[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>00100001000=>00010000100
[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>00101000101=>10100010100
[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>00101000010=>01000010100
[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>00101001001=>10010010100
[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>00101001010=>01010010100
[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>00101000100=>00100010100
[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>00101010001=>10001010100
[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>00101010010=>01001010100
[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>00101010100=>00101010100
[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>00101001000=>00010010100
[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>00100100001=>10000100100
[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>00100100010=>01000100100
[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>00100100100=>00100100100
[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>00100101000=>00010100100
[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>00100010000=>00001000100
[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>00010000101=>10100001000
[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>00010000010=>01000001000
[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>00010001001=>10010001000
[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>00010001010=>01010001000
[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>00010000100=>00100001000
[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>00010010001=>10001001000
[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>00010010010=>01001001000
[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>00010010100=>00101001000
[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>00010001000=>00010001000
[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>00010100001=>10000101000
[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>00010100010=>01000101000
[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>00010100100=>00100101000
[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>00010101000=>00010101000
[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>00010010000=>00001001000
[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>00001000001=>10000010000
[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>00001000010=>01000010000
[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>00001000100=>00100010000
[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>00001001000=>00010010000
[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>00001010000=>00001010000
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000=>00000100000
[[1,2,3,4,5,6,7,8,9]]=>00000000=>00000000
[[1,2,3,4,5,6,7,8],[9]]=>00000001=>10000000
[[1,2,3,4,5,6,7],[8,9]]=>00000010=>01000000
[[1,2,3,4,5,6,7],[8],[9]]=>00000011=>11000000
[[1,2,3,4,5,6],[7,8,9]]=>00000100=>00100000
[[1,2,3,4,5,6],[7,8],[9]]=>00000101=>10100000
[[1,2,3,4,5,6],[7],[8],[9]]=>00000111=>11100000
[[1,2,3,4,5],[6,7,8,9]]=>00001000=>00010000
[[1,2,3,4,5],[6,7,8],[9]]=>00001001=>10010000
[[1,2,3,4,5],[6,7],[8,9]]=>00001010=>01010000
[[1,2,3,4,5],[6,7],[8],[9]]=>00001011=>11010000
[[1,2,3,4,5],[6],[7],[8],[9]]=>00001111=>11110000
[[1,2,3,4],[5,6,7,8],[9]]=>00010001=>10001000
[[1,2,3,4],[5,6,7],[8,9]]=>00010010=>01001000
[[1,2,3,4],[5,6,7],[8],[9]]=>00010011=>11001000
[[1,2,3,4],[5,6],[7,8],[9]]=>00010101=>10101000
[[1,2,3,4],[5,6],[7],[8],[9]]=>00010111=>11101000
[[1,2,3,4],[5],[6],[7],[8],[9]]=>00011111=>11111000
[[1,2,3],[4,5,6],[7,8,9]]=>00100100=>00100100
[[1,2,3],[4,5,6],[7,8],[9]]=>00100101=>10100100
[[1,2,3],[4,5,6],[7],[8],[9]]=>00100111=>11100100
[[1,2,3],[4,5],[6,7],[8,9]]=>00101010=>01010100
[[1,2,3],[4,5],[6,7],[8],[9]]=>00101011=>11010100
[[1,2,3],[4,5],[6],[7],[8],[9]]=>00101111=>11110100
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>00111111=>11111100
[[1,2],[3,4],[5,6],[7,8],[9]]=>01010101=>10101010
[[1,2],[3,4],[5,6],[7],[8],[9]]=>01010111=>11101010
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>01011111=>11111010
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111=>11111110
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>11111111=>11111111
[[1,2,3,4,5,6,7,8,9,10]]=>000000000=>000000000
[[1,2,3,4,5,6,7,8,9],[10]]=>000000001=>100000000
[[1,2,3,4,5,6,7,8],[9,10]]=>000000010=>010000000
[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011=>110000000
[[1,2,3,4,5,6,7],[8,9,10]]=>000000100=>001000000
[[1,2,3,4,5,6,7],[8,9],[10]]=>000000101=>101000000
[[1,2,3,4,5,6,7],[8],[9],[10]]=>000000111=>111000000
[[1,2,3,4,5,6],[7,8,9,10]]=>000001000=>000100000
[[1,2,3,4,5,6],[7,8,9],[10]]=>000001001=>100100000
[[1,2,3,4,5,6],[7,8],[9,10]]=>000001010=>010100000
[[1,2,3,4,5,6],[7,8],[9],[10]]=>000001011=>110100000
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>000001111=>111100000
[[1,2,3,4,5],[6,7,8,9],[10]]=>000010001=>100010000
[[1,2,3,4,5],[6,7,8],[9,10]]=>000010010=>010010000
[[1,2,3,4,5],[6,7,8],[9],[10]]=>000010011=>110010000
[[1,2,3,4,5],[6,7],[8,9],[10]]=>000010101=>101010000
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>000010111=>111010000
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>000011111=>111110000
[[1,2,3,4],[5,6,7,8],[9,10]]=>000100010=>010001000
[[1,2,3,4],[5,6,7,8],[9],[10]]=>000100011=>110001000
[[1,2,3,4],[5,6,7],[8,9,10]]=>000100100=>001001000
[[1,2,3,4],[5,6,7],[8,9],[10]]=>000100101=>101001000
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>000100111=>111001000
[[1,2,3,4],[5,6],[7,8],[9,10]]=>000101010=>010101000
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>000101011=>110101000
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>000101111=>111101000
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>000111111=>111111000
[[1,2,3],[4,5,6],[7,8,9],[10]]=>001001001=>100100100
[[1,2,3],[4,5,6],[7,8],[9,10]]=>001001010=>010100100
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>001001011=>110100100
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>001001111=>111100100
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>001010101=>101010100
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>001010111=>111010100
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>001011111=>111110100
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>001111111=>111111100
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010=>010101010
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>010101011=>110101010
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>010101111=>111101010
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>010111111=>111111010
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111=>111111110
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111=>111111111
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010=>01010101010
[[1,3,4,5,6,7,8,9],[2]]=>10000000=>00000001
[[1,2,5,6,7,8,9],[3,4]]=>01000000=>00000010
[[1,4,5,6,7,8,9],[2],[3]]=>11000000=>00000011
[[1,2,3,7,8,9],[4,5,6]]=>00100000=>00000100
[[1,3,6,7,8,9],[2,5],[4]]=>10100000=>00000101
[[1,5,6,7,8,9],[2],[3],[4]]=>11100000=>00000111
[[1,2,3,4,9],[5,6,7,8]]=>00010000=>00001000
[[1,3,4,8,9],[2,6,7],[5]]=>10010000=>00001001
[[1,2,7,8,9],[3,4],[5,6]]=>01010000=>00001010
[[1,4,7,8,9],[2,6],[3],[5]]=>11010000=>00001011
[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000=>00001111
[[1,3,4,5],[2,7,8,9],[6]]=>10001000=>00010001
[[1,2,5,9],[3,4,8],[6,7]]=>01001000=>00010010
[[1,4,5,9],[2,7,8],[3],[6]]=>11001000=>00010011
[[1,3,8,9],[2,5],[4,7],[6]]=>10101000=>00010101
[[1,5,8,9],[2,7],[3],[4],[6]]=>11101000=>00010111
[[1,7,8,9],[2],[3],[4],[5],[6]]=>11111000=>00011111
[[1,3,6],[2,5,9],[4,8],[7]]=>10100100=>00100101
[[1,5,6],[2,8,9],[3],[4],[7]]=>11100100=>00100111
[[1,2,9],[3,4],[5,6],[7,8]]=>01010100=>00101010
[[1,4,9],[2,6],[3,8],[5],[7]]=>11010100=>00101011
[[1,6,9],[2,8],[3],[4],[5],[7]]=>11110100=>00101111
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100=>00111111
[[1,3],[2,5],[4,7],[6,9],[8]]=>10101010=>01010101
[[1,5],[2,7],[3,9],[4],[6],[8]]=>11101010=>01010111
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010=>01011111
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110=>01111111
[[1,3,4,5,6,7,8,9,10],[2]]=>100000000=>000000001
[[1,2,5,6,7,8,9,10],[3,4]]=>010000000=>000000010
[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000=>000000011
[[1,2,3,7,8,9,10],[4,5,6]]=>001000000=>000000100
[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000=>000000101
[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000=>000000111
[[1,2,3,4,9,10],[5,6,7,8]]=>000100000=>000001000
[[1,3,4,8,9,10],[2,6,7],[5]]=>100100000=>000001001
[[1,2,7,8,9,10],[3,4],[5,6]]=>010100000=>000001010
[[1,4,7,8,9,10],[2,6],[3],[5]]=>110100000=>000001011
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>111100000=>000001111
[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000=>000010001
[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000=>000010010
[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000=>000010011
[[1,3,8,9,10],[2,5],[4,7],[6]]=>101010000=>000010101
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000=>000010111
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000=>000011111
[[1,2,5,6],[3,4,9,10],[7,8]]=>010001000=>000100010
[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000=>000100011
[[1,2,3,10],[4,5,6],[7,8,9]]=>001001000=>000100100
[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000=>000100101
[[1,5,6,10],[2,8,9],[3],[4],[7]]=>111001000=>000100111
[[1,2,9,10],[3,4],[5,6],[7,8]]=>010101000=>000101010
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>110101000=>000101011
[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>111101000=>000101111
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>111111000=>000111111
[[1,3,4],[2,6,7],[5,9,10],[8]]=>100100100=>001001001
[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100=>001001010
[[1,4,7],[2,6,10],[3,9],[5],[8]]=>110100100=>001001011
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100=>001001111
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>101010100=>001010101
[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>111010100=>001010111
[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>111110100=>001011111
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100=>001111111
[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>110101010=>010101011
[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>111101010=>010101111
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010=>010111111
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110=>011111111
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>11111101=>10111111
[[1,7],[2,8],[3,9],[4],[5],[6]]=>11111011=>11011111
[[1,7,9],[2,8],[3],[4],[5],[6]]=>11111010=>01011111
[[1,6],[2,7],[3,8],[4,9],[5]]=>11110111=>11101111
[[1,6,9],[2,7],[3,8],[4],[5]]=>11110110=>01101111
[[1,6,8],[2,7,9],[3],[4],[5]]=>11110101=>10101111
[[1,6,8,9],[2,7],[3],[4],[5]]=>11110100=>00101111
[[1,5,9],[2,6],[3,7],[4,8]]=>11101110=>01110111
[[1,5,8],[2,6,9],[3,7],[4]]=>11101101=>10110111
[[1,5,8,9],[2,6],[3,7],[4]]=>11101100=>00110111
[[1,5,7,9],[2,6,8],[3],[4]]=>11101010=>01010111
[[1,5,7,8,9],[2,6],[3],[4]]=>11101000=>00010111
[[1,4,7],[2,5,8],[3,6,9]]=>11011011=>11011011
[[1,4,7,9],[2,5,8],[3,6]]=>11011010=>01011011
[[1,4,7,8,9],[2,5],[3,6]]=>11011000=>00011011
[[1,4,6,8],[2,5,7,9],[3]]=>11010101=>10101011
[[1,4,6,8,9],[2,5,7],[3]]=>11010100=>00101011
[[1,4,6,7,8,9],[2,5],[3]]=>11010000=>00001011
[[1,3,5,7,9],[2,4,6,8]]=>10101010=>01010101
[[1,3,5,7,8,9],[2,4,6]]=>10101000=>00010101
[[1,3,5,6,7,8,9],[2,4]]=>10100000=>00000101
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>111111101=>101111111
[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>111111011=>110111111
[[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>111111010=>010111111
[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>111110111=>111011111
[[1,7,10],[2,8],[3,9],[4],[5],[6]]=>111110110=>011011111
[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>111110101=>101011111
[[1,7,9,10],[2,8],[3],[4],[5],[6]]=>111110100=>001011111
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>111101111=>111101111
[[1,6,10],[2,7],[3,8],[4,9],[5]]=>111101110=>011101111
[[1,6,9],[2,7,10],[3,8],[4],[5]]=>111101101=>101101111
[[1,6,9,10],[2,7],[3,8],[4],[5]]=>111101100=>001101111
[[1,6,8,10],[2,7,9],[3],[4],[5]]=>111101010=>010101111
[[1,6,8,9,10],[2,7],[3],[4],[5]]=>111101000=>000101111
[[1,5,9],[2,6,10],[3,7],[4,8]]=>111011101=>101110111
[[1,5,9,10],[2,6],[3,7],[4,8]]=>111011100=>001110111
[[1,5,8],[2,6,9],[3,7,10],[4]]=>111011011=>110110111
[[1,5,8,10],[2,6,9],[3,7],[4]]=>111011010=>010110111
[[1,5,8,9,10],[2,6],[3,7],[4]]=>111011000=>000110111
[[1,5,7,9],[2,6,8,10],[3],[4]]=>111010101=>101010111
[[1,5,7,9,10],[2,6,8],[3],[4]]=>111010100=>001010111
[[1,5,7,8,9,10],[2,6],[3],[4]]=>111010000=>000010111
[[1,4,7,10],[2,5,8],[3,6,9]]=>110110110=>011011011
[[1,4,7,9],[2,5,8,10],[3,6]]=>110110101=>101011011
[[1,4,7,9,10],[2,5,8],[3,6]]=>110110100=>001011011
[[1,4,7,8,9,10],[2,5],[3,6]]=>110110000=>000011011
[[1,4,6,8,10],[2,5,7,9],[3]]=>110101010=>010101011
[[1,4,6,8,9,10],[2,5,7],[3]]=>110101000=>000101011
[[1,4,6,7,8,9,10],[2,5],[3]]=>110100000=>000001011
[[1,3,5,7,9,10],[2,4,6,8]]=>101010100=>001010101
[[1,3,5,7,8,9,10],[2,4,6]]=>101010000=>000010101
[[1,3,5,6,7,8,9,10],[2,4]]=>101000000=>000000101
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>10111111=>11111101
[[1,4],[2,5],[3,6],[7],[8],[9]]=>11011111=>11111011
[[1,2,4],[3,5],[6],[7],[8],[9]]=>01011111=>11111010
[[1,5],[2,6],[3,7],[4,8],[9]]=>11101111=>11110111
[[1,2,5],[3,6],[4,7],[8],[9]]=>01101111=>11110110
[[1,3,5],[2,4,6],[7],[8],[9]]=>10101111=>11110101
[[1,2,3,5],[4,6],[7],[8],[9]]=>00101111=>11110100
[[1,2,6],[3,7],[4,8],[5,9]]=>01110111=>11101110
[[1,3,6],[2,4,7],[5,8],[9]]=>10110111=>11101101
[[1,2,3,6],[4,7],[5,8],[9]]=>00110111=>11101100
[[1,2,4,6],[3,5,7],[8],[9]]=>01010111=>11101010
[[1,2,3,4,6],[5,7],[8],[9]]=>00010111=>11101000
[[1,2,4,7],[3,5,8],[6,9]]=>01011011=>11011010
[[1,2,3,4,7],[5,8],[6,9]]=>00011011=>11011000
[[1,3,5,7],[2,4,6,8],[9]]=>10101011=>11010101
[[1,2,3,5,7],[4,6,8],[9]]=>00101011=>11010100
[[1,2,3,4,5,7],[6,8],[9]]=>00001011=>11010000
[[1,2,4,6,8],[3,5,7,9]]=>01010101=>10101010
[[1,2,3,4,6,8],[5,7,9]]=>00010101=>10101000
[[1,2,3,4,5,6,8],[7,9]]=>00000101=>10100000
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>101111111=>111111101
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>110111111=>111111011
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>010111111=>111111010
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>111011111=>111110111
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>011011111=>111110110
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>101011111=>111110101
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>001011111=>111110100
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>011101111=>111101110
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>101101111=>111101101
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>001101111=>111101100
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>010101111=>111101010
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>000101111=>111101000
[[1,3,7],[2,4,8],[5,9],[6,10]]=>101110111=>111011101
[[1,2,3,7],[4,8],[5,9],[6,10]]=>001110111=>111011100
[[1,4,7],[2,5,8],[3,6,9],[10]]=>110110111=>111011011
[[1,2,4,7],[3,5,8],[6,9],[10]]=>010110111=>111011010
[[1,2,3,4,7],[5,8],[6,9],[10]]=>000110111=>111011000
[[1,3,5,7],[2,4,6,8],[9],[10]]=>101010111=>111010101
[[1,2,3,5,7],[4,6,8],[9],[10]]=>001010111=>111010100
[[1,2,3,4,5,7],[6,8],[9],[10]]=>000010111=>111010000
[[1,2,5,8],[3,6,9],[4,7,10]]=>011011011=>110110110
[[1,3,5,8],[2,4,6,9],[7,10]]=>101011011=>110110101
[[1,2,3,5,8],[4,6,9],[7,10]]=>001011011=>110110100
[[1,2,3,4,5,8],[6,9],[7,10]]=>000011011=>110110000
[[1,2,4,6,8],[3,5,7,9],[10]]=>010101011=>110101010
[[1,2,3,4,6,8],[5,7,9],[10]]=>000101011=>110101000
[[1,2,3,4,5,6,8],[7,9],[10]]=>000001011=>110100000
[[1,2,3,5,7,9],[4,6,8,10]]=>001010101=>101010100
[[1,2,3,4,5,7,9],[6,8,10]]=>000010101=>101010000
[[1,2,3,4,5,6,7,9],[8,10]]=>000000101=>101000000
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>010101101=>101101010
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>010110110=>011011010
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>010110101=>101011010
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>010111011=>110111010
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>011011010=>010110110
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>011011101=>101110110
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>011010110=>011010110
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>011010101=>101010110
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>011011011=>110110110
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>011101110=>011101110
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>011101101=>101101110
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>011101011=>110101110
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>011110111=>111011110
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>101101010=>010101101
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>101101101=>101101101
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>101110110=>011011101
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>101110101=>101011101
[[1,3],[2,4],[5,8],[6,9],[7,10]]=>101111011=>110111101
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>101011010=>010110101
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>101011101=>101110101
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>101010110=>011010101
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>101010101=>101010101
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>101011011=>110110101
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>101101110=>011101101
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>101101101=>101101101
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>101101011=>110101101
[[1,3],[2,7],[4,8],[5,9],[6,10]]=>101110111=>111011101
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>110111010=>010111011
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>110111101=>101111011
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>110110110=>011011011
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>110110101=>101011011
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>110111011=>110111011
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>110101110=>011101011
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>110101101=>101101011
[[1,4],[2,6],[3,8],[5,9],[7,10]]=>110101011=>110101011
[[1,4],[2,7],[3,8],[5,9],[6,10]]=>110110111=>111011011
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>111011110=>011110111
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>111011101=>101110111
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>111011011=>110110111
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>111010111=>111010111
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>01010101101=>10110101010
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>01010110101=>10101101010
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>01011010101=>10101011010
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>01101010110=>01101010110
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>01101010101=>10101010110
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>10110101010=>01010101101
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>10111101110=>01110111101
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>10101101010=>01010110101
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>10101011010=>01011010101
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>10101010110=>01101010101
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>10101010101=>10101010101
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>10111011110=>01111011101
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>11010101011=>11010101011
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
Map
reverse
Description
Return the reversal of a binary word.
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