Identifier
Mp00134:
Standard tableaux
—descent word⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
Cc0007;cc-rep-0
[[1]]=>=>[1]
[[1,2]]=>0=>[2]
[[1],[2]]=>1=>[1,1]
[[1,2,3]]=>00=>[3]
[[1,3],[2]]=>10=>[1,2]
[[1,2],[3]]=>01=>[2,1]
[[1],[2],[3]]=>11=>[1,1,1]
[[1,2,3,4]]=>000=>[4]
[[1,3,4],[2]]=>100=>[1,3]
[[1,2,4],[3]]=>010=>[2,2]
[[1,2,3],[4]]=>001=>[3,1]
[[1,3],[2,4]]=>101=>[1,2,1]
[[1,2],[3,4]]=>010=>[2,2]
[[1,4],[2],[3]]=>110=>[1,1,2]
[[1,3],[2],[4]]=>101=>[1,2,1]
[[1,2],[3],[4]]=>011=>[2,1,1]
[[1],[2],[3],[4]]=>111=>[1,1,1,1]
[[1,2,3,4,5]]=>0000=>[5]
[[1,3,4,5],[2]]=>1000=>[1,4]
[[1,2,4,5],[3]]=>0100=>[2,3]
[[1,2,3,5],[4]]=>0010=>[3,2]
[[1,2,3,4],[5]]=>0001=>[4,1]
[[1,3,5],[2,4]]=>1010=>[1,2,2]
[[1,2,5],[3,4]]=>0100=>[2,3]
[[1,3,4],[2,5]]=>1001=>[1,3,1]
[[1,2,4],[3,5]]=>0101=>[2,2,1]
[[1,2,3],[4,5]]=>0010=>[3,2]
[[1,4,5],[2],[3]]=>1100=>[1,1,3]
[[1,3,5],[2],[4]]=>1010=>[1,2,2]
[[1,2,5],[3],[4]]=>0110=>[2,1,2]
[[1,3,4],[2],[5]]=>1001=>[1,3,1]
[[1,2,4],[3],[5]]=>0101=>[2,2,1]
[[1,2,3],[4],[5]]=>0011=>[3,1,1]
[[1,4],[2,5],[3]]=>1101=>[1,1,2,1]
[[1,3],[2,5],[4]]=>1010=>[1,2,2]
[[1,2],[3,5],[4]]=>0110=>[2,1,2]
[[1,3],[2,4],[5]]=>1011=>[1,2,1,1]
[[1,2],[3,4],[5]]=>0101=>[2,2,1]
[[1,5],[2],[3],[4]]=>1110=>[1,1,1,2]
[[1,4],[2],[3],[5]]=>1101=>[1,1,2,1]
[[1,3],[2],[4],[5]]=>1011=>[1,2,1,1]
[[1,2],[3],[4],[5]]=>0111=>[2,1,1,1]
[[1],[2],[3],[4],[5]]=>1111=>[1,1,1,1,1]
[[1,2,3,4,5,6]]=>00000=>[6]
[[1,3,4,5,6],[2]]=>10000=>[1,5]
[[1,2,4,5,6],[3]]=>01000=>[2,4]
[[1,2,3,5,6],[4]]=>00100=>[3,3]
[[1,2,3,4,6],[5]]=>00010=>[4,2]
[[1,2,3,4,5],[6]]=>00001=>[5,1]
[[1,3,5,6],[2,4]]=>10100=>[1,2,3]
[[1,2,5,6],[3,4]]=>01000=>[2,4]
[[1,3,4,6],[2,5]]=>10010=>[1,3,2]
[[1,2,4,6],[3,5]]=>01010=>[2,2,2]
[[1,2,3,6],[4,5]]=>00100=>[3,3]
[[1,3,4,5],[2,6]]=>10001=>[1,4,1]
[[1,2,4,5],[3,6]]=>01001=>[2,3,1]
[[1,2,3,5],[4,6]]=>00101=>[3,2,1]
[[1,2,3,4],[5,6]]=>00010=>[4,2]
[[1,4,5,6],[2],[3]]=>11000=>[1,1,4]
[[1,3,5,6],[2],[4]]=>10100=>[1,2,3]
[[1,2,5,6],[3],[4]]=>01100=>[2,1,3]
[[1,3,4,6],[2],[5]]=>10010=>[1,3,2]
[[1,2,4,6],[3],[5]]=>01010=>[2,2,2]
[[1,2,3,6],[4],[5]]=>00110=>[3,1,2]
[[1,3,4,5],[2],[6]]=>10001=>[1,4,1]
[[1,2,4,5],[3],[6]]=>01001=>[2,3,1]
[[1,2,3,5],[4],[6]]=>00101=>[3,2,1]
[[1,2,3,4],[5],[6]]=>00011=>[4,1,1]
[[1,3,5],[2,4,6]]=>10101=>[1,2,2,1]
[[1,2,5],[3,4,6]]=>01001=>[2,3,1]
[[1,3,4],[2,5,6]]=>10010=>[1,3,2]
[[1,2,4],[3,5,6]]=>01010=>[2,2,2]
[[1,2,3],[4,5,6]]=>00100=>[3,3]
[[1,4,6],[2,5],[3]]=>11010=>[1,1,2,2]
[[1,3,6],[2,5],[4]]=>10100=>[1,2,3]
[[1,2,6],[3,5],[4]]=>01100=>[2,1,3]
[[1,3,6],[2,4],[5]]=>10110=>[1,2,1,2]
[[1,2,6],[3,4],[5]]=>01010=>[2,2,2]
[[1,4,5],[2,6],[3]]=>11001=>[1,1,3,1]
[[1,3,5],[2,6],[4]]=>10101=>[1,2,2,1]
[[1,2,5],[3,6],[4]]=>01101=>[2,1,2,1]
[[1,3,4],[2,6],[5]]=>10010=>[1,3,2]
[[1,2,4],[3,6],[5]]=>01010=>[2,2,2]
[[1,2,3],[4,6],[5]]=>00110=>[3,1,2]
[[1,3,5],[2,4],[6]]=>10101=>[1,2,2,1]
[[1,2,5],[3,4],[6]]=>01001=>[2,3,1]
[[1,3,4],[2,5],[6]]=>10011=>[1,3,1,1]
[[1,2,4],[3,5],[6]]=>01011=>[2,2,1,1]
[[1,2,3],[4,5],[6]]=>00101=>[3,2,1]
[[1,5,6],[2],[3],[4]]=>11100=>[1,1,1,3]
[[1,4,6],[2],[3],[5]]=>11010=>[1,1,2,2]
[[1,3,6],[2],[4],[5]]=>10110=>[1,2,1,2]
[[1,2,6],[3],[4],[5]]=>01110=>[2,1,1,2]
[[1,4,5],[2],[3],[6]]=>11001=>[1,1,3,1]
[[1,3,5],[2],[4],[6]]=>10101=>[1,2,2,1]
[[1,2,5],[3],[4],[6]]=>01101=>[2,1,2,1]
[[1,3,4],[2],[5],[6]]=>10011=>[1,3,1,1]
[[1,2,4],[3],[5],[6]]=>01011=>[2,2,1,1]
[[1,2,3],[4],[5],[6]]=>00111=>[3,1,1,1]
[[1,4],[2,5],[3,6]]=>11011=>[1,1,2,1,1]
[[1,3],[2,5],[4,6]]=>10101=>[1,2,2,1]
[[1,2],[3,5],[4,6]]=>01101=>[2,1,2,1]
[[1,3],[2,4],[5,6]]=>10110=>[1,2,1,2]
[[1,2],[3,4],[5,6]]=>01010=>[2,2,2]
[[1,5],[2,6],[3],[4]]=>11101=>[1,1,1,2,1]
[[1,4],[2,6],[3],[5]]=>11010=>[1,1,2,2]
[[1,3],[2,6],[4],[5]]=>10110=>[1,2,1,2]
[[1,2],[3,6],[4],[5]]=>01110=>[2,1,1,2]
[[1,4],[2,5],[3],[6]]=>11011=>[1,1,2,1,1]
[[1,3],[2,5],[4],[6]]=>10101=>[1,2,2,1]
[[1,2],[3,5],[4],[6]]=>01101=>[2,1,2,1]
[[1,3],[2,4],[5],[6]]=>10111=>[1,2,1,1,1]
[[1,2],[3,4],[5],[6]]=>01011=>[2,2,1,1]
[[1,6],[2],[3],[4],[5]]=>11110=>[1,1,1,1,2]
[[1,5],[2],[3],[4],[6]]=>11101=>[1,1,1,2,1]
[[1,4],[2],[3],[5],[6]]=>11011=>[1,1,2,1,1]
[[1,3],[2],[4],[5],[6]]=>10111=>[1,2,1,1,1]
[[1,2],[3],[4],[5],[6]]=>01111=>[2,1,1,1,1]
[[1],[2],[3],[4],[5],[6]]=>11111=>[1,1,1,1,1,1]
[[1,2,3,4,5,6,7]]=>000000=>[7]
[[1,3,4,5,6,7],[2]]=>100000=>[1,6]
[[1,2,4,5,6,7],[3]]=>010000=>[2,5]
[[1,2,3,5,6,7],[4]]=>001000=>[3,4]
[[1,2,3,4,6,7],[5]]=>000100=>[4,3]
[[1,2,3,4,5,7],[6]]=>000010=>[5,2]
[[1,2,3,4,5,6],[7]]=>000001=>[6,1]
[[1,3,5,6,7],[2,4]]=>101000=>[1,2,4]
[[1,2,5,6,7],[3,4]]=>010000=>[2,5]
[[1,3,4,6,7],[2,5]]=>100100=>[1,3,3]
[[1,2,4,6,7],[3,5]]=>010100=>[2,2,3]
[[1,2,3,6,7],[4,5]]=>001000=>[3,4]
[[1,3,4,5,7],[2,6]]=>100010=>[1,4,2]
[[1,2,4,5,7],[3,6]]=>010010=>[2,3,2]
[[1,2,3,5,7],[4,6]]=>001010=>[3,2,2]
[[1,2,3,4,7],[5,6]]=>000100=>[4,3]
[[1,3,4,5,6],[2,7]]=>100001=>[1,5,1]
[[1,2,4,5,6],[3,7]]=>010001=>[2,4,1]
[[1,2,3,5,6],[4,7]]=>001001=>[3,3,1]
[[1,2,3,4,6],[5,7]]=>000101=>[4,2,1]
[[1,2,3,4,5],[6,7]]=>000010=>[5,2]
[[1,4,5,6,7],[2],[3]]=>110000=>[1,1,5]
[[1,3,5,6,7],[2],[4]]=>101000=>[1,2,4]
[[1,2,5,6,7],[3],[4]]=>011000=>[2,1,4]
[[1,3,4,6,7],[2],[5]]=>100100=>[1,3,3]
[[1,2,4,6,7],[3],[5]]=>010100=>[2,2,3]
[[1,2,3,6,7],[4],[5]]=>001100=>[3,1,3]
[[1,3,4,5,7],[2],[6]]=>100010=>[1,4,2]
[[1,2,4,5,7],[3],[6]]=>010010=>[2,3,2]
[[1,2,3,5,7],[4],[6]]=>001010=>[3,2,2]
[[1,2,3,4,7],[5],[6]]=>000110=>[4,1,2]
[[1,3,4,5,6],[2],[7]]=>100001=>[1,5,1]
[[1,2,4,5,6],[3],[7]]=>010001=>[2,4,1]
[[1,2,3,5,6],[4],[7]]=>001001=>[3,3,1]
[[1,2,3,4,6],[5],[7]]=>000101=>[4,2,1]
[[1,2,3,4,5],[6],[7]]=>000011=>[5,1,1]
[[1,3,5,7],[2,4,6]]=>101010=>[1,2,2,2]
[[1,2,5,7],[3,4,6]]=>010010=>[2,3,2]
[[1,3,4,7],[2,5,6]]=>100100=>[1,3,3]
[[1,2,4,7],[3,5,6]]=>010100=>[2,2,3]
[[1,2,3,7],[4,5,6]]=>001000=>[3,4]
[[1,3,5,6],[2,4,7]]=>101001=>[1,2,3,1]
[[1,2,5,6],[3,4,7]]=>010001=>[2,4,1]
[[1,3,4,6],[2,5,7]]=>100101=>[1,3,2,1]
[[1,2,4,6],[3,5,7]]=>010101=>[2,2,2,1]
[[1,2,3,6],[4,5,7]]=>001001=>[3,3,1]
[[1,3,4,5],[2,6,7]]=>100010=>[1,4,2]
[[1,2,4,5],[3,6,7]]=>010010=>[2,3,2]
[[1,2,3,5],[4,6,7]]=>001010=>[3,2,2]
[[1,2,3,4],[5,6,7]]=>000100=>[4,3]
[[1,4,6,7],[2,5],[3]]=>110100=>[1,1,2,3]
[[1,3,6,7],[2,5],[4]]=>101000=>[1,2,4]
[[1,2,6,7],[3,5],[4]]=>011000=>[2,1,4]
[[1,3,6,7],[2,4],[5]]=>101100=>[1,2,1,3]
[[1,2,6,7],[3,4],[5]]=>010100=>[2,2,3]
[[1,4,5,7],[2,6],[3]]=>110010=>[1,1,3,2]
[[1,3,5,7],[2,6],[4]]=>101010=>[1,2,2,2]
[[1,2,5,7],[3,6],[4]]=>011010=>[2,1,2,2]
[[1,3,4,7],[2,6],[5]]=>100100=>[1,3,3]
[[1,2,4,7],[3,6],[5]]=>010100=>[2,2,3]
[[1,2,3,7],[4,6],[5]]=>001100=>[3,1,3]
[[1,3,5,7],[2,4],[6]]=>101010=>[1,2,2,2]
[[1,2,5,7],[3,4],[6]]=>010010=>[2,3,2]
[[1,3,4,7],[2,5],[6]]=>100110=>[1,3,1,2]
[[1,2,4,7],[3,5],[6]]=>010110=>[2,2,1,2]
[[1,2,3,7],[4,5],[6]]=>001010=>[3,2,2]
[[1,4,5,6],[2,7],[3]]=>110001=>[1,1,4,1]
[[1,3,5,6],[2,7],[4]]=>101001=>[1,2,3,1]
[[1,2,5,6],[3,7],[4]]=>011001=>[2,1,3,1]
[[1,3,4,6],[2,7],[5]]=>100101=>[1,3,2,1]
[[1,2,4,6],[3,7],[5]]=>010101=>[2,2,2,1]
[[1,2,3,6],[4,7],[5]]=>001101=>[3,1,2,1]
[[1,3,4,5],[2,7],[6]]=>100010=>[1,4,2]
[[1,2,4,5],[3,7],[6]]=>010010=>[2,3,2]
[[1,2,3,5],[4,7],[6]]=>001010=>[3,2,2]
[[1,2,3,4],[5,7],[6]]=>000110=>[4,1,2]
[[1,3,5,6],[2,4],[7]]=>101001=>[1,2,3,1]
[[1,2,5,6],[3,4],[7]]=>010001=>[2,4,1]
[[1,3,4,6],[2,5],[7]]=>100101=>[1,3,2,1]
[[1,2,4,6],[3,5],[7]]=>010101=>[2,2,2,1]
[[1,2,3,6],[4,5],[7]]=>001001=>[3,3,1]
[[1,3,4,5],[2,6],[7]]=>100011=>[1,4,1,1]
[[1,2,4,5],[3,6],[7]]=>010011=>[2,3,1,1]
[[1,2,3,5],[4,6],[7]]=>001011=>[3,2,1,1]
[[1,2,3,4],[5,6],[7]]=>000101=>[4,2,1]
[[1,5,6,7],[2],[3],[4]]=>111000=>[1,1,1,4]
[[1,4,6,7],[2],[3],[5]]=>110100=>[1,1,2,3]
[[1,3,6,7],[2],[4],[5]]=>101100=>[1,2,1,3]
[[1,2,6,7],[3],[4],[5]]=>011100=>[2,1,1,3]
[[1,4,5,7],[2],[3],[6]]=>110010=>[1,1,3,2]
[[1,3,5,7],[2],[4],[6]]=>101010=>[1,2,2,2]
[[1,2,5,7],[3],[4],[6]]=>011010=>[2,1,2,2]
[[1,3,4,7],[2],[5],[6]]=>100110=>[1,3,1,2]
[[1,2,4,7],[3],[5],[6]]=>010110=>[2,2,1,2]
[[1,2,3,7],[4],[5],[6]]=>001110=>[3,1,1,2]
[[1,4,5,6],[2],[3],[7]]=>110001=>[1,1,4,1]
[[1,3,5,6],[2],[4],[7]]=>101001=>[1,2,3,1]
[[1,2,5,6],[3],[4],[7]]=>011001=>[2,1,3,1]
[[1,3,4,6],[2],[5],[7]]=>100101=>[1,3,2,1]
[[1,2,4,6],[3],[5],[7]]=>010101=>[2,2,2,1]
[[1,2,3,6],[4],[5],[7]]=>001101=>[3,1,2,1]
[[1,3,4,5],[2],[6],[7]]=>100011=>[1,4,1,1]
[[1,2,4,5],[3],[6],[7]]=>010011=>[2,3,1,1]
[[1,2,3,5],[4],[6],[7]]=>001011=>[3,2,1,1]
[[1,2,3,4],[5],[6],[7]]=>000111=>[4,1,1,1]
[[1,4,6],[2,5,7],[3]]=>110101=>[1,1,2,2,1]
[[1,3,6],[2,5,7],[4]]=>101001=>[1,2,3,1]
[[1,2,6],[3,5,7],[4]]=>011001=>[2,1,3,1]
[[1,3,6],[2,4,7],[5]]=>101101=>[1,2,1,2,1]
[[1,2,6],[3,4,7],[5]]=>010101=>[2,2,2,1]
[[1,4,5],[2,6,7],[3]]=>110010=>[1,1,3,2]
[[1,3,5],[2,6,7],[4]]=>101010=>[1,2,2,2]
[[1,2,5],[3,6,7],[4]]=>011010=>[2,1,2,2]
[[1,3,4],[2,6,7],[5]]=>100100=>[1,3,3]
[[1,2,4],[3,6,7],[5]]=>010100=>[2,2,3]
[[1,2,3],[4,6,7],[5]]=>001100=>[3,1,3]
[[1,3,5],[2,4,7],[6]]=>101010=>[1,2,2,2]
[[1,2,5],[3,4,7],[6]]=>010010=>[2,3,2]
[[1,3,4],[2,5,7],[6]]=>100110=>[1,3,1,2]
[[1,2,4],[3,5,7],[6]]=>010110=>[2,2,1,2]
[[1,2,3],[4,5,7],[6]]=>001010=>[3,2,2]
[[1,3,5],[2,4,6],[7]]=>101011=>[1,2,2,1,1]
[[1,2,5],[3,4,6],[7]]=>010011=>[2,3,1,1]
[[1,3,4],[2,5,6],[7]]=>100101=>[1,3,2,1]
[[1,2,4],[3,5,6],[7]]=>010101=>[2,2,2,1]
[[1,2,3],[4,5,6],[7]]=>001001=>[3,3,1]
[[1,4,7],[2,5],[3,6]]=>110110=>[1,1,2,1,2]
[[1,3,7],[2,5],[4,6]]=>101010=>[1,2,2,2]
[[1,2,7],[3,5],[4,6]]=>011010=>[2,1,2,2]
[[1,3,7],[2,4],[5,6]]=>101100=>[1,2,1,3]
[[1,2,7],[3,4],[5,6]]=>010100=>[2,2,3]
[[1,4,6],[2,5],[3,7]]=>110101=>[1,1,2,2,1]
[[1,3,6],[2,5],[4,7]]=>101001=>[1,2,3,1]
[[1,2,6],[3,5],[4,7]]=>011001=>[2,1,3,1]
[[1,3,6],[2,4],[5,7]]=>101101=>[1,2,1,2,1]
[[1,2,6],[3,4],[5,7]]=>010101=>[2,2,2,1]
[[1,4,5],[2,6],[3,7]]=>110011=>[1,1,3,1,1]
[[1,3,5],[2,6],[4,7]]=>101011=>[1,2,2,1,1]
[[1,2,5],[3,6],[4,7]]=>011011=>[2,1,2,1,1]
[[1,3,4],[2,6],[5,7]]=>100101=>[1,3,2,1]
[[1,2,4],[3,6],[5,7]]=>010101=>[2,2,2,1]
[[1,2,3],[4,6],[5,7]]=>001101=>[3,1,2,1]
[[1,3,5],[2,4],[6,7]]=>101010=>[1,2,2,2]
[[1,2,5],[3,4],[6,7]]=>010010=>[2,3,2]
[[1,3,4],[2,5],[6,7]]=>100110=>[1,3,1,2]
[[1,2,4],[3,5],[6,7]]=>010110=>[2,2,1,2]
[[1,2,3],[4,5],[6,7]]=>001010=>[3,2,2]
[[1,5,7],[2,6],[3],[4]]=>111010=>[1,1,1,2,2]
[[1,4,7],[2,6],[3],[5]]=>110100=>[1,1,2,3]
[[1,3,7],[2,6],[4],[5]]=>101100=>[1,2,1,3]
[[1,2,7],[3,6],[4],[5]]=>011100=>[2,1,1,3]
[[1,4,7],[2,5],[3],[6]]=>110110=>[1,1,2,1,2]
[[1,3,7],[2,5],[4],[6]]=>101010=>[1,2,2,2]
[[1,2,7],[3,5],[4],[6]]=>011010=>[2,1,2,2]
[[1,3,7],[2,4],[5],[6]]=>101110=>[1,2,1,1,2]
[[1,2,7],[3,4],[5],[6]]=>010110=>[2,2,1,2]
[[1,5,6],[2,7],[3],[4]]=>111001=>[1,1,1,3,1]
[[1,4,6],[2,7],[3],[5]]=>110101=>[1,1,2,2,1]
[[1,3,6],[2,7],[4],[5]]=>101101=>[1,2,1,2,1]
[[1,2,6],[3,7],[4],[5]]=>011101=>[2,1,1,2,1]
[[1,4,5],[2,7],[3],[6]]=>110010=>[1,1,3,2]
[[1,3,5],[2,7],[4],[6]]=>101010=>[1,2,2,2]
[[1,2,5],[3,7],[4],[6]]=>011010=>[2,1,2,2]
[[1,3,4],[2,7],[5],[6]]=>100110=>[1,3,1,2]
[[1,2,4],[3,7],[5],[6]]=>010110=>[2,2,1,2]
[[1,2,3],[4,7],[5],[6]]=>001110=>[3,1,1,2]
[[1,4,6],[2,5],[3],[7]]=>110101=>[1,1,2,2,1]
[[1,3,6],[2,5],[4],[7]]=>101001=>[1,2,3,1]
[[1,2,6],[3,5],[4],[7]]=>011001=>[2,1,3,1]
[[1,3,6],[2,4],[5],[7]]=>101101=>[1,2,1,2,1]
[[1,2,6],[3,4],[5],[7]]=>010101=>[2,2,2,1]
[[1,4,5],[2,6],[3],[7]]=>110011=>[1,1,3,1,1]
[[1,3,5],[2,6],[4],[7]]=>101011=>[1,2,2,1,1]
[[1,2,5],[3,6],[4],[7]]=>011011=>[2,1,2,1,1]
[[1,3,4],[2,6],[5],[7]]=>100101=>[1,3,2,1]
[[1,2,4],[3,6],[5],[7]]=>010101=>[2,2,2,1]
[[1,2,3],[4,6],[5],[7]]=>001101=>[3,1,2,1]
[[1,3,5],[2,4],[6],[7]]=>101011=>[1,2,2,1,1]
[[1,2,5],[3,4],[6],[7]]=>010011=>[2,3,1,1]
[[1,3,4],[2,5],[6],[7]]=>100111=>[1,3,1,1,1]
[[1,2,4],[3,5],[6],[7]]=>010111=>[2,2,1,1,1]
[[1,2,3],[4,5],[6],[7]]=>001011=>[3,2,1,1]
[[1,6,7],[2],[3],[4],[5]]=>111100=>[1,1,1,1,3]
[[1,5,7],[2],[3],[4],[6]]=>111010=>[1,1,1,2,2]
[[1,4,7],[2],[3],[5],[6]]=>110110=>[1,1,2,1,2]
[[1,3,7],[2],[4],[5],[6]]=>101110=>[1,2,1,1,2]
[[1,2,7],[3],[4],[5],[6]]=>011110=>[2,1,1,1,2]
[[1,5,6],[2],[3],[4],[7]]=>111001=>[1,1,1,3,1]
[[1,4,6],[2],[3],[5],[7]]=>110101=>[1,1,2,2,1]
[[1,3,6],[2],[4],[5],[7]]=>101101=>[1,2,1,2,1]
[[1,2,6],[3],[4],[5],[7]]=>011101=>[2,1,1,2,1]
[[1,4,5],[2],[3],[6],[7]]=>110011=>[1,1,3,1,1]
[[1,3,5],[2],[4],[6],[7]]=>101011=>[1,2,2,1,1]
[[1,2,5],[3],[4],[6],[7]]=>011011=>[2,1,2,1,1]
[[1,3,4],[2],[5],[6],[7]]=>100111=>[1,3,1,1,1]
[[1,2,4],[3],[5],[6],[7]]=>010111=>[2,2,1,1,1]
[[1,2,3],[4],[5],[6],[7]]=>001111=>[3,1,1,1,1]
[[1,5],[2,6],[3,7],[4]]=>111011=>[1,1,1,2,1,1]
[[1,4],[2,6],[3,7],[5]]=>110101=>[1,1,2,2,1]
[[1,3],[2,6],[4,7],[5]]=>101101=>[1,2,1,2,1]
[[1,2],[3,6],[4,7],[5]]=>011101=>[2,1,1,2,1]
[[1,4],[2,5],[3,7],[6]]=>110110=>[1,1,2,1,2]
[[1,3],[2,5],[4,7],[6]]=>101010=>[1,2,2,2]
[[1,2],[3,5],[4,7],[6]]=>011010=>[2,1,2,2]
[[1,3],[2,4],[5,7],[6]]=>101110=>[1,2,1,1,2]
[[1,2],[3,4],[5,7],[6]]=>010110=>[2,2,1,2]
[[1,4],[2,5],[3,6],[7]]=>110111=>[1,1,2,1,1,1]
[[1,3],[2,5],[4,6],[7]]=>101011=>[1,2,2,1,1]
[[1,2],[3,5],[4,6],[7]]=>011011=>[2,1,2,1,1]
[[1,3],[2,4],[5,6],[7]]=>101101=>[1,2,1,2,1]
[[1,2],[3,4],[5,6],[7]]=>010101=>[2,2,2,1]
[[1,6],[2,7],[3],[4],[5]]=>111101=>[1,1,1,1,2,1]
[[1,5],[2,7],[3],[4],[6]]=>111010=>[1,1,1,2,2]
[[1,4],[2,7],[3],[5],[6]]=>110110=>[1,1,2,1,2]
[[1,3],[2,7],[4],[5],[6]]=>101110=>[1,2,1,1,2]
[[1,2],[3,7],[4],[5],[6]]=>011110=>[2,1,1,1,2]
[[1,5],[2,6],[3],[4],[7]]=>111011=>[1,1,1,2,1,1]
[[1,4],[2,6],[3],[5],[7]]=>110101=>[1,1,2,2,1]
[[1,3],[2,6],[4],[5],[7]]=>101101=>[1,2,1,2,1]
[[1,2],[3,6],[4],[5],[7]]=>011101=>[2,1,1,2,1]
[[1,4],[2,5],[3],[6],[7]]=>110111=>[1,1,2,1,1,1]
[[1,3],[2,5],[4],[6],[7]]=>101011=>[1,2,2,1,1]
[[1,2],[3,5],[4],[6],[7]]=>011011=>[2,1,2,1,1]
[[1,3],[2,4],[5],[6],[7]]=>101111=>[1,2,1,1,1,1]
[[1,2],[3,4],[5],[6],[7]]=>010111=>[2,2,1,1,1]
[[1,7],[2],[3],[4],[5],[6]]=>111110=>[1,1,1,1,1,2]
[[1,6],[2],[3],[4],[5],[7]]=>111101=>[1,1,1,1,2,1]
[[1,5],[2],[3],[4],[6],[7]]=>111011=>[1,1,1,2,1,1]
[[1,4],[2],[3],[5],[6],[7]]=>110111=>[1,1,2,1,1,1]
[[1,3],[2],[4],[5],[6],[7]]=>101111=>[1,2,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7]]=>011111=>[2,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7]]=>111111=>[1,1,1,1,1,1,1]
[[1,2,3,4,5,6,7,8]]=>0000000=>[8]
[[1,3,4,5,6,7,8],[2]]=>1000000=>[1,7]
[[1,2,4,5,6,7,8],[3]]=>0100000=>[2,6]
[[1,2,3,5,6,7,8],[4]]=>0010000=>[3,5]
[[1,2,3,4,6,7,8],[5]]=>0001000=>[4,4]
[[1,2,3,4,5,7,8],[6]]=>0000100=>[5,3]
[[1,2,3,4,5,6,8],[7]]=>0000010=>[6,2]
[[1,2,3,4,5,6,7],[8]]=>0000001=>[7,1]
[[1,3,5,6,7,8],[2,4]]=>1010000=>[1,2,5]
[[1,2,5,6,7,8],[3,4]]=>0100000=>[2,6]
[[1,3,4,6,7,8],[2,5]]=>1001000=>[1,3,4]
[[1,2,4,6,7,8],[3,5]]=>0101000=>[2,2,4]
[[1,2,3,6,7,8],[4,5]]=>0010000=>[3,5]
[[1,3,4,5,7,8],[2,6]]=>1000100=>[1,4,3]
[[1,2,4,5,7,8],[3,6]]=>0100100=>[2,3,3]
[[1,2,3,5,7,8],[4,6]]=>0010100=>[3,2,3]
[[1,2,3,4,7,8],[5,6]]=>0001000=>[4,4]
[[1,3,4,5,6,8],[2,7]]=>1000010=>[1,5,2]
[[1,2,4,5,6,8],[3,7]]=>0100010=>[2,4,2]
[[1,2,3,5,6,8],[4,7]]=>0010010=>[3,3,2]
[[1,2,3,4,6,8],[5,7]]=>0001010=>[4,2,2]
[[1,2,3,4,5,8],[6,7]]=>0000100=>[5,3]
[[1,3,4,5,6,7],[2,8]]=>1000001=>[1,6,1]
[[1,2,4,5,6,7],[3,8]]=>0100001=>[2,5,1]
[[1,2,3,5,6,7],[4,8]]=>0010001=>[3,4,1]
[[1,2,3,4,6,7],[5,8]]=>0001001=>[4,3,1]
[[1,2,3,4,5,7],[6,8]]=>0000101=>[5,2,1]
[[1,2,3,4,5,6],[7,8]]=>0000010=>[6,2]
[[1,4,5,6,7,8],[2],[3]]=>1100000=>[1,1,6]
[[1,3,5,6,7,8],[2],[4]]=>1010000=>[1,2,5]
[[1,2,5,6,7,8],[3],[4]]=>0110000=>[2,1,5]
[[1,3,4,6,7,8],[2],[5]]=>1001000=>[1,3,4]
[[1,2,4,6,7,8],[3],[5]]=>0101000=>[2,2,4]
[[1,2,3,6,7,8],[4],[5]]=>0011000=>[3,1,4]
[[1,3,4,5,7,8],[2],[6]]=>1000100=>[1,4,3]
[[1,2,4,5,7,8],[3],[6]]=>0100100=>[2,3,3]
[[1,2,3,5,7,8],[4],[6]]=>0010100=>[3,2,3]
[[1,2,3,4,7,8],[5],[6]]=>0001100=>[4,1,3]
[[1,3,4,5,6,8],[2],[7]]=>1000010=>[1,5,2]
[[1,2,4,5,6,8],[3],[7]]=>0100010=>[2,4,2]
[[1,2,3,5,6,8],[4],[7]]=>0010010=>[3,3,2]
[[1,2,3,4,6,8],[5],[7]]=>0001010=>[4,2,2]
[[1,2,3,4,5,8],[6],[7]]=>0000110=>[5,1,2]
[[1,3,4,5,6,7],[2],[8]]=>1000001=>[1,6,1]
[[1,2,4,5,6,7],[3],[8]]=>0100001=>[2,5,1]
[[1,2,3,5,6,7],[4],[8]]=>0010001=>[3,4,1]
[[1,2,3,4,6,7],[5],[8]]=>0001001=>[4,3,1]
[[1,2,3,4,5,7],[6],[8]]=>0000101=>[5,2,1]
[[1,2,3,4,5,6],[7],[8]]=>0000011=>[6,1,1]
[[1,3,5,7,8],[2,4,6]]=>1010100=>[1,2,2,3]
[[1,2,5,7,8],[3,4,6]]=>0100100=>[2,3,3]
[[1,3,4,7,8],[2,5,6]]=>1001000=>[1,3,4]
[[1,2,4,7,8],[3,5,6]]=>0101000=>[2,2,4]
[[1,2,3,7,8],[4,5,6]]=>0010000=>[3,5]
[[1,3,5,6,8],[2,4,7]]=>1010010=>[1,2,3,2]
[[1,2,5,6,8],[3,4,7]]=>0100010=>[2,4,2]
[[1,3,4,6,8],[2,5,7]]=>1001010=>[1,3,2,2]
[[1,2,4,6,8],[3,5,7]]=>0101010=>[2,2,2,2]
[[1,2,3,6,8],[4,5,7]]=>0010010=>[3,3,2]
[[1,3,4,5,8],[2,6,7]]=>1000100=>[1,4,3]
[[1,2,4,5,8],[3,6,7]]=>0100100=>[2,3,3]
[[1,2,3,5,8],[4,6,7]]=>0010100=>[3,2,3]
[[1,2,3,4,8],[5,6,7]]=>0001000=>[4,4]
[[1,3,5,6,7],[2,4,8]]=>1010001=>[1,2,4,1]
[[1,2,5,6,7],[3,4,8]]=>0100001=>[2,5,1]
[[1,3,4,6,7],[2,5,8]]=>1001001=>[1,3,3,1]
[[1,2,4,6,7],[3,5,8]]=>0101001=>[2,2,3,1]
[[1,2,3,6,7],[4,5,8]]=>0010001=>[3,4,1]
[[1,3,4,5,7],[2,6,8]]=>1000101=>[1,4,2,1]
[[1,2,4,5,7],[3,6,8]]=>0100101=>[2,3,2,1]
[[1,2,3,5,7],[4,6,8]]=>0010101=>[3,2,2,1]
[[1,2,3,4,7],[5,6,8]]=>0001001=>[4,3,1]
[[1,3,4,5,6],[2,7,8]]=>1000010=>[1,5,2]
[[1,2,4,5,6],[3,7,8]]=>0100010=>[2,4,2]
[[1,2,3,5,6],[4,7,8]]=>0010010=>[3,3,2]
[[1,2,3,4,6],[5,7,8]]=>0001010=>[4,2,2]
[[1,2,3,4,5],[6,7,8]]=>0000100=>[5,3]
[[1,4,6,7,8],[2,5],[3]]=>1101000=>[1,1,2,4]
[[1,3,6,7,8],[2,5],[4]]=>1010000=>[1,2,5]
[[1,2,6,7,8],[3,5],[4]]=>0110000=>[2,1,5]
[[1,3,6,7,8],[2,4],[5]]=>1011000=>[1,2,1,4]
[[1,2,6,7,8],[3,4],[5]]=>0101000=>[2,2,4]
[[1,4,5,7,8],[2,6],[3]]=>1100100=>[1,1,3,3]
[[1,3,5,7,8],[2,6],[4]]=>1010100=>[1,2,2,3]
[[1,2,5,7,8],[3,6],[4]]=>0110100=>[2,1,2,3]
[[1,3,4,7,8],[2,6],[5]]=>1001000=>[1,3,4]
[[1,2,4,7,8],[3,6],[5]]=>0101000=>[2,2,4]
[[1,2,3,7,8],[4,6],[5]]=>0011000=>[3,1,4]
[[1,3,5,7,8],[2,4],[6]]=>1010100=>[1,2,2,3]
[[1,2,5,7,8],[3,4],[6]]=>0100100=>[2,3,3]
[[1,3,4,7,8],[2,5],[6]]=>1001100=>[1,3,1,3]
[[1,2,4,7,8],[3,5],[6]]=>0101100=>[2,2,1,3]
[[1,2,3,7,8],[4,5],[6]]=>0010100=>[3,2,3]
[[1,4,5,6,8],[2,7],[3]]=>1100010=>[1,1,4,2]
[[1,3,5,6,8],[2,7],[4]]=>1010010=>[1,2,3,2]
[[1,2,5,6,8],[3,7],[4]]=>0110010=>[2,1,3,2]
[[1,3,4,6,8],[2,7],[5]]=>1001010=>[1,3,2,2]
[[1,2,4,6,8],[3,7],[5]]=>0101010=>[2,2,2,2]
[[1,2,3,6,8],[4,7],[5]]=>0011010=>[3,1,2,2]
[[1,3,4,5,8],[2,7],[6]]=>1000100=>[1,4,3]
[[1,2,4,5,8],[3,7],[6]]=>0100100=>[2,3,3]
[[1,2,3,5,8],[4,7],[6]]=>0010100=>[3,2,3]
[[1,2,3,4,8],[5,7],[6]]=>0001100=>[4,1,3]
[[1,3,5,6,8],[2,4],[7]]=>1010010=>[1,2,3,2]
[[1,2,5,6,8],[3,4],[7]]=>0100010=>[2,4,2]
[[1,3,4,6,8],[2,5],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,6,8],[3,5],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,6,8],[4,5],[7]]=>0010010=>[3,3,2]
[[1,3,4,5,8],[2,6],[7]]=>1000110=>[1,4,1,2]
[[1,2,4,5,8],[3,6],[7]]=>0100110=>[2,3,1,2]
[[1,2,3,5,8],[4,6],[7]]=>0010110=>[3,2,1,2]
[[1,2,3,4,8],[5,6],[7]]=>0001010=>[4,2,2]
[[1,4,5,6,7],[2,8],[3]]=>1100001=>[1,1,5,1]
[[1,3,5,6,7],[2,8],[4]]=>1010001=>[1,2,4,1]
[[1,2,5,6,7],[3,8],[4]]=>0110001=>[2,1,4,1]
[[1,3,4,6,7],[2,8],[5]]=>1001001=>[1,3,3,1]
[[1,2,4,6,7],[3,8],[5]]=>0101001=>[2,2,3,1]
[[1,2,3,6,7],[4,8],[5]]=>0011001=>[3,1,3,1]
[[1,3,4,5,7],[2,8],[6]]=>1000101=>[1,4,2,1]
[[1,2,4,5,7],[3,8],[6]]=>0100101=>[2,3,2,1]
[[1,2,3,5,7],[4,8],[6]]=>0010101=>[3,2,2,1]
[[1,2,3,4,7],[5,8],[6]]=>0001101=>[4,1,2,1]
[[1,3,4,5,6],[2,8],[7]]=>1000010=>[1,5,2]
[[1,2,4,5,6],[3,8],[7]]=>0100010=>[2,4,2]
[[1,2,3,5,6],[4,8],[7]]=>0010010=>[3,3,2]
[[1,2,3,4,6],[5,8],[7]]=>0001010=>[4,2,2]
[[1,2,3,4,5],[6,8],[7]]=>0000110=>[5,1,2]
[[1,3,5,6,7],[2,4],[8]]=>1010001=>[1,2,4,1]
[[1,2,5,6,7],[3,4],[8]]=>0100001=>[2,5,1]
[[1,3,4,6,7],[2,5],[8]]=>1001001=>[1,3,3,1]
[[1,2,4,6,7],[3,5],[8]]=>0101001=>[2,2,3,1]
[[1,2,3,6,7],[4,5],[8]]=>0010001=>[3,4,1]
[[1,3,4,5,7],[2,6],[8]]=>1000101=>[1,4,2,1]
[[1,2,4,5,7],[3,6],[8]]=>0100101=>[2,3,2,1]
[[1,2,3,5,7],[4,6],[8]]=>0010101=>[3,2,2,1]
[[1,2,3,4,7],[5,6],[8]]=>0001001=>[4,3,1]
[[1,3,4,5,6],[2,7],[8]]=>1000011=>[1,5,1,1]
[[1,2,4,5,6],[3,7],[8]]=>0100011=>[2,4,1,1]
[[1,2,3,5,6],[4,7],[8]]=>0010011=>[3,3,1,1]
[[1,2,3,4,6],[5,7],[8]]=>0001011=>[4,2,1,1]
[[1,2,3,4,5],[6,7],[8]]=>0000101=>[5,2,1]
[[1,5,6,7,8],[2],[3],[4]]=>1110000=>[1,1,1,5]
[[1,4,6,7,8],[2],[3],[5]]=>1101000=>[1,1,2,4]
[[1,3,6,7,8],[2],[4],[5]]=>1011000=>[1,2,1,4]
[[1,2,6,7,8],[3],[4],[5]]=>0111000=>[2,1,1,4]
[[1,4,5,7,8],[2],[3],[6]]=>1100100=>[1,1,3,3]
[[1,3,5,7,8],[2],[4],[6]]=>1010100=>[1,2,2,3]
[[1,2,5,7,8],[3],[4],[6]]=>0110100=>[2,1,2,3]
[[1,3,4,7,8],[2],[5],[6]]=>1001100=>[1,3,1,3]
[[1,2,4,7,8],[3],[5],[6]]=>0101100=>[2,2,1,3]
[[1,2,3,7,8],[4],[5],[6]]=>0011100=>[3,1,1,3]
[[1,4,5,6,8],[2],[3],[7]]=>1100010=>[1,1,4,2]
[[1,3,5,6,8],[2],[4],[7]]=>1010010=>[1,2,3,2]
[[1,2,5,6,8],[3],[4],[7]]=>0110010=>[2,1,3,2]
[[1,3,4,6,8],[2],[5],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,6,8],[3],[5],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,6,8],[4],[5],[7]]=>0011010=>[3,1,2,2]
[[1,3,4,5,8],[2],[6],[7]]=>1000110=>[1,4,1,2]
[[1,2,4,5,8],[3],[6],[7]]=>0100110=>[2,3,1,2]
[[1,2,3,5,8],[4],[6],[7]]=>0010110=>[3,2,1,2]
[[1,2,3,4,8],[5],[6],[7]]=>0001110=>[4,1,1,2]
[[1,4,5,6,7],[2],[3],[8]]=>1100001=>[1,1,5,1]
[[1,3,5,6,7],[2],[4],[8]]=>1010001=>[1,2,4,1]
[[1,2,5,6,7],[3],[4],[8]]=>0110001=>[2,1,4,1]
[[1,3,4,6,7],[2],[5],[8]]=>1001001=>[1,3,3,1]
[[1,2,4,6,7],[3],[5],[8]]=>0101001=>[2,2,3,1]
[[1,2,3,6,7],[4],[5],[8]]=>0011001=>[3,1,3,1]
[[1,3,4,5,7],[2],[6],[8]]=>1000101=>[1,4,2,1]
[[1,2,4,5,7],[3],[6],[8]]=>0100101=>[2,3,2,1]
[[1,2,3,5,7],[4],[6],[8]]=>0010101=>[3,2,2,1]
[[1,2,3,4,7],[5],[6],[8]]=>0001101=>[4,1,2,1]
[[1,3,4,5,6],[2],[7],[8]]=>1000011=>[1,5,1,1]
[[1,2,4,5,6],[3],[7],[8]]=>0100011=>[2,4,1,1]
[[1,2,3,5,6],[4],[7],[8]]=>0010011=>[3,3,1,1]
[[1,2,3,4,6],[5],[7],[8]]=>0001011=>[4,2,1,1]
[[1,2,3,4,5],[6],[7],[8]]=>0000111=>[5,1,1,1]
[[1,3,5,7],[2,4,6,8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,4,6,8]]=>0100101=>[2,3,2,1]
[[1,3,4,7],[2,5,6,8]]=>1001001=>[1,3,3,1]
[[1,2,4,7],[3,5,6,8]]=>0101001=>[2,2,3,1]
[[1,2,3,7],[4,5,6,8]]=>0010001=>[3,4,1]
[[1,3,5,6],[2,4,7,8]]=>1010010=>[1,2,3,2]
[[1,2,5,6],[3,4,7,8]]=>0100010=>[2,4,2]
[[1,3,4,6],[2,5,7,8]]=>1001010=>[1,3,2,2]
[[1,2,4,6],[3,5,7,8]]=>0101010=>[2,2,2,2]
[[1,2,3,6],[4,5,7,8]]=>0010010=>[3,3,2]
[[1,3,4,5],[2,6,7,8]]=>1000100=>[1,4,3]
[[1,2,4,5],[3,6,7,8]]=>0100100=>[2,3,3]
[[1,2,3,5],[4,6,7,8]]=>0010100=>[3,2,3]
[[1,2,3,4],[5,6,7,8]]=>0001000=>[4,4]
[[1,4,6,8],[2,5,7],[3]]=>1101010=>[1,1,2,2,2]
[[1,3,6,8],[2,5,7],[4]]=>1010010=>[1,2,3,2]
[[1,2,6,8],[3,5,7],[4]]=>0110010=>[2,1,3,2]
[[1,3,6,8],[2,4,7],[5]]=>1011010=>[1,2,1,2,2]
[[1,2,6,8],[3,4,7],[5]]=>0101010=>[2,2,2,2]
[[1,4,5,8],[2,6,7],[3]]=>1100100=>[1,1,3,3]
[[1,3,5,8],[2,6,7],[4]]=>1010100=>[1,2,2,3]
[[1,2,5,8],[3,6,7],[4]]=>0110100=>[2,1,2,3]
[[1,3,4,8],[2,6,7],[5]]=>1001000=>[1,3,4]
[[1,2,4,8],[3,6,7],[5]]=>0101000=>[2,2,4]
[[1,2,3,8],[4,6,7],[5]]=>0011000=>[3,1,4]
[[1,3,5,8],[2,4,7],[6]]=>1010100=>[1,2,2,3]
[[1,2,5,8],[3,4,7],[6]]=>0100100=>[2,3,3]
[[1,3,4,8],[2,5,7],[6]]=>1001100=>[1,3,1,3]
[[1,2,4,8],[3,5,7],[6]]=>0101100=>[2,2,1,3]
[[1,2,3,8],[4,5,7],[6]]=>0010100=>[3,2,3]
[[1,3,5,8],[2,4,6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5,8],[3,4,6],[7]]=>0100110=>[2,3,1,2]
[[1,3,4,8],[2,5,6],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,8],[3,5,6],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,8],[4,5,6],[7]]=>0010010=>[3,3,2]
[[1,4,6,7],[2,5,8],[3]]=>1101001=>[1,1,2,3,1]
[[1,3,6,7],[2,5,8],[4]]=>1010001=>[1,2,4,1]
[[1,2,6,7],[3,5,8],[4]]=>0110001=>[2,1,4,1]
[[1,3,6,7],[2,4,8],[5]]=>1011001=>[1,2,1,3,1]
[[1,2,6,7],[3,4,8],[5]]=>0101001=>[2,2,3,1]
[[1,4,5,7],[2,6,8],[3]]=>1100101=>[1,1,3,2,1]
[[1,3,5,7],[2,6,8],[4]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,6,8],[4]]=>0110101=>[2,1,2,2,1]
[[1,3,4,7],[2,6,8],[5]]=>1001001=>[1,3,3,1]
[[1,2,4,7],[3,6,8],[5]]=>0101001=>[2,2,3,1]
[[1,2,3,7],[4,6,8],[5]]=>0011001=>[3,1,3,1]
[[1,3,5,7],[2,4,8],[6]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,4,8],[6]]=>0100101=>[2,3,2,1]
[[1,3,4,7],[2,5,8],[6]]=>1001101=>[1,3,1,2,1]
[[1,2,4,7],[3,5,8],[6]]=>0101101=>[2,2,1,2,1]
[[1,2,3,7],[4,5,8],[6]]=>0010101=>[3,2,2,1]
[[1,4,5,6],[2,7,8],[3]]=>1100010=>[1,1,4,2]
[[1,3,5,6],[2,7,8],[4]]=>1010010=>[1,2,3,2]
[[1,2,5,6],[3,7,8],[4]]=>0110010=>[2,1,3,2]
[[1,3,4,6],[2,7,8],[5]]=>1001010=>[1,3,2,2]
[[1,2,4,6],[3,7,8],[5]]=>0101010=>[2,2,2,2]
[[1,2,3,6],[4,7,8],[5]]=>0011010=>[3,1,2,2]
[[1,3,4,5],[2,7,8],[6]]=>1000100=>[1,4,3]
[[1,2,4,5],[3,7,8],[6]]=>0100100=>[2,3,3]
[[1,2,3,5],[4,7,8],[6]]=>0010100=>[3,2,3]
[[1,2,3,4],[5,7,8],[6]]=>0001100=>[4,1,3]
[[1,3,5,6],[2,4,8],[7]]=>1010010=>[1,2,3,2]
[[1,2,5,6],[3,4,8],[7]]=>0100010=>[2,4,2]
[[1,3,4,6],[2,5,8],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,6],[3,5,8],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,6],[4,5,8],[7]]=>0010010=>[3,3,2]
[[1,3,4,5],[2,6,8],[7]]=>1000110=>[1,4,1,2]
[[1,2,4,5],[3,6,8],[7]]=>0100110=>[2,3,1,2]
[[1,2,3,5],[4,6,8],[7]]=>0010110=>[3,2,1,2]
[[1,2,3,4],[5,6,8],[7]]=>0001010=>[4,2,2]
[[1,3,5,7],[2,4,6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,4,6],[8]]=>0100101=>[2,3,2,1]
[[1,3,4,7],[2,5,6],[8]]=>1001001=>[1,3,3,1]
[[1,2,4,7],[3,5,6],[8]]=>0101001=>[2,2,3,1]
[[1,2,3,7],[4,5,6],[8]]=>0010001=>[3,4,1]
[[1,3,5,6],[2,4,7],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,5,6],[3,4,7],[8]]=>0100011=>[2,4,1,1]
[[1,3,4,6],[2,5,7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4,6],[3,5,7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3,6],[4,5,7],[8]]=>0010011=>[3,3,1,1]
[[1,3,4,5],[2,6,7],[8]]=>1000101=>[1,4,2,1]
[[1,2,4,5],[3,6,7],[8]]=>0100101=>[2,3,2,1]
[[1,2,3,5],[4,6,7],[8]]=>0010101=>[3,2,2,1]
[[1,2,3,4],[5,6,7],[8]]=>0001001=>[4,3,1]
[[1,4,7,8],[2,5],[3,6]]=>1101100=>[1,1,2,1,3]
[[1,3,7,8],[2,5],[4,6]]=>1010100=>[1,2,2,3]
[[1,2,7,8],[3,5],[4,6]]=>0110100=>[2,1,2,3]
[[1,3,7,8],[2,4],[5,6]]=>1011000=>[1,2,1,4]
[[1,2,7,8],[3,4],[5,6]]=>0101000=>[2,2,4]
[[1,4,6,8],[2,5],[3,7]]=>1101010=>[1,1,2,2,2]
[[1,3,6,8],[2,5],[4,7]]=>1010010=>[1,2,3,2]
[[1,2,6,8],[3,5],[4,7]]=>0110010=>[2,1,3,2]
[[1,3,6,8],[2,4],[5,7]]=>1011010=>[1,2,1,2,2]
[[1,2,6,8],[3,4],[5,7]]=>0101010=>[2,2,2,2]
[[1,4,5,8],[2,6],[3,7]]=>1100110=>[1,1,3,1,2]
[[1,3,5,8],[2,6],[4,7]]=>1010110=>[1,2,2,1,2]
[[1,2,5,8],[3,6],[4,7]]=>0110110=>[2,1,2,1,2]
[[1,3,4,8],[2,6],[5,7]]=>1001010=>[1,3,2,2]
[[1,2,4,8],[3,6],[5,7]]=>0101010=>[2,2,2,2]
[[1,2,3,8],[4,6],[5,7]]=>0011010=>[3,1,2,2]
[[1,3,5,8],[2,4],[6,7]]=>1010100=>[1,2,2,3]
[[1,2,5,8],[3,4],[6,7]]=>0100100=>[2,3,3]
[[1,3,4,8],[2,5],[6,7]]=>1001100=>[1,3,1,3]
[[1,2,4,8],[3,5],[6,7]]=>0101100=>[2,2,1,3]
[[1,2,3,8],[4,5],[6,7]]=>0010100=>[3,2,3]
[[1,4,6,7],[2,5],[3,8]]=>1101001=>[1,1,2,3,1]
[[1,3,6,7],[2,5],[4,8]]=>1010001=>[1,2,4,1]
[[1,2,6,7],[3,5],[4,8]]=>0110001=>[2,1,4,1]
[[1,3,6,7],[2,4],[5,8]]=>1011001=>[1,2,1,3,1]
[[1,2,6,7],[3,4],[5,8]]=>0101001=>[2,2,3,1]
[[1,4,5,7],[2,6],[3,8]]=>1100101=>[1,1,3,2,1]
[[1,3,5,7],[2,6],[4,8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,6],[4,8]]=>0110101=>[2,1,2,2,1]
[[1,3,4,7],[2,6],[5,8]]=>1001001=>[1,3,3,1]
[[1,2,4,7],[3,6],[5,8]]=>0101001=>[2,2,3,1]
[[1,2,3,7],[4,6],[5,8]]=>0011001=>[3,1,3,1]
[[1,3,5,7],[2,4],[6,8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,4],[6,8]]=>0100101=>[2,3,2,1]
[[1,3,4,7],[2,5],[6,8]]=>1001101=>[1,3,1,2,1]
[[1,2,4,7],[3,5],[6,8]]=>0101101=>[2,2,1,2,1]
[[1,2,3,7],[4,5],[6,8]]=>0010101=>[3,2,2,1]
[[1,4,5,6],[2,7],[3,8]]=>1100011=>[1,1,4,1,1]
[[1,3,5,6],[2,7],[4,8]]=>1010011=>[1,2,3,1,1]
[[1,2,5,6],[3,7],[4,8]]=>0110011=>[2,1,3,1,1]
[[1,3,4,6],[2,7],[5,8]]=>1001011=>[1,3,2,1,1]
[[1,2,4,6],[3,7],[5,8]]=>0101011=>[2,2,2,1,1]
[[1,2,3,6],[4,7],[5,8]]=>0011011=>[3,1,2,1,1]
[[1,3,4,5],[2,7],[6,8]]=>1000101=>[1,4,2,1]
[[1,2,4,5],[3,7],[6,8]]=>0100101=>[2,3,2,1]
[[1,2,3,5],[4,7],[6,8]]=>0010101=>[3,2,2,1]
[[1,2,3,4],[5,7],[6,8]]=>0001101=>[4,1,2,1]
[[1,3,5,6],[2,4],[7,8]]=>1010010=>[1,2,3,2]
[[1,2,5,6],[3,4],[7,8]]=>0100010=>[2,4,2]
[[1,3,4,6],[2,5],[7,8]]=>1001010=>[1,3,2,2]
[[1,2,4,6],[3,5],[7,8]]=>0101010=>[2,2,2,2]
[[1,2,3,6],[4,5],[7,8]]=>0010010=>[3,3,2]
[[1,3,4,5],[2,6],[7,8]]=>1000110=>[1,4,1,2]
[[1,2,4,5],[3,6],[7,8]]=>0100110=>[2,3,1,2]
[[1,2,3,5],[4,6],[7,8]]=>0010110=>[3,2,1,2]
[[1,2,3,4],[5,6],[7,8]]=>0001010=>[4,2,2]
[[1,5,7,8],[2,6],[3],[4]]=>1110100=>[1,1,1,2,3]
[[1,4,7,8],[2,6],[3],[5]]=>1101000=>[1,1,2,4]
[[1,3,7,8],[2,6],[4],[5]]=>1011000=>[1,2,1,4]
[[1,2,7,8],[3,6],[4],[5]]=>0111000=>[2,1,1,4]
[[1,4,7,8],[2,5],[3],[6]]=>1101100=>[1,1,2,1,3]
[[1,3,7,8],[2,5],[4],[6]]=>1010100=>[1,2,2,3]
[[1,2,7,8],[3,5],[4],[6]]=>0110100=>[2,1,2,3]
[[1,3,7,8],[2,4],[5],[6]]=>1011100=>[1,2,1,1,3]
[[1,2,7,8],[3,4],[5],[6]]=>0101100=>[2,2,1,3]
[[1,5,6,8],[2,7],[3],[4]]=>1110010=>[1,1,1,3,2]
[[1,4,6,8],[2,7],[3],[5]]=>1101010=>[1,1,2,2,2]
[[1,3,6,8],[2,7],[4],[5]]=>1011010=>[1,2,1,2,2]
[[1,2,6,8],[3,7],[4],[5]]=>0111010=>[2,1,1,2,2]
[[1,4,5,8],[2,7],[3],[6]]=>1100100=>[1,1,3,3]
[[1,3,5,8],[2,7],[4],[6]]=>1010100=>[1,2,2,3]
[[1,2,5,8],[3,7],[4],[6]]=>0110100=>[2,1,2,3]
[[1,3,4,8],[2,7],[5],[6]]=>1001100=>[1,3,1,3]
[[1,2,4,8],[3,7],[5],[6]]=>0101100=>[2,2,1,3]
[[1,2,3,8],[4,7],[5],[6]]=>0011100=>[3,1,1,3]
[[1,4,6,8],[2,5],[3],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,6,8],[2,5],[4],[7]]=>1010010=>[1,2,3,2]
[[1,2,6,8],[3,5],[4],[7]]=>0110010=>[2,1,3,2]
[[1,3,6,8],[2,4],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,6,8],[3,4],[5],[7]]=>0101010=>[2,2,2,2]
[[1,4,5,8],[2,6],[3],[7]]=>1100110=>[1,1,3,1,2]
[[1,3,5,8],[2,6],[4],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5,8],[3,6],[4],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,4,8],[2,6],[5],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,8],[3,6],[5],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,8],[4,6],[5],[7]]=>0011010=>[3,1,2,2]
[[1,3,5,8],[2,4],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5,8],[3,4],[6],[7]]=>0100110=>[2,3,1,2]
[[1,3,4,8],[2,5],[6],[7]]=>1001110=>[1,3,1,1,2]
[[1,2,4,8],[3,5],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,2,3,8],[4,5],[6],[7]]=>0010110=>[3,2,1,2]
[[1,5,6,7],[2,8],[3],[4]]=>1110001=>[1,1,1,4,1]
[[1,4,6,7],[2,8],[3],[5]]=>1101001=>[1,1,2,3,1]
[[1,3,6,7],[2,8],[4],[5]]=>1011001=>[1,2,1,3,1]
[[1,2,6,7],[3,8],[4],[5]]=>0111001=>[2,1,1,3,1]
[[1,4,5,7],[2,8],[3],[6]]=>1100101=>[1,1,3,2,1]
[[1,3,5,7],[2,8],[4],[6]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,8],[4],[6]]=>0110101=>[2,1,2,2,1]
[[1,3,4,7],[2,8],[5],[6]]=>1001101=>[1,3,1,2,1]
[[1,2,4,7],[3,8],[5],[6]]=>0101101=>[2,2,1,2,1]
[[1,2,3,7],[4,8],[5],[6]]=>0011101=>[3,1,1,2,1]
[[1,4,5,6],[2,8],[3],[7]]=>1100010=>[1,1,4,2]
[[1,3,5,6],[2,8],[4],[7]]=>1010010=>[1,2,3,2]
[[1,2,5,6],[3,8],[4],[7]]=>0110010=>[2,1,3,2]
[[1,3,4,6],[2,8],[5],[7]]=>1001010=>[1,3,2,2]
[[1,2,4,6],[3,8],[5],[7]]=>0101010=>[2,2,2,2]
[[1,2,3,6],[4,8],[5],[7]]=>0011010=>[3,1,2,2]
[[1,3,4,5],[2,8],[6],[7]]=>1000110=>[1,4,1,2]
[[1,2,4,5],[3,8],[6],[7]]=>0100110=>[2,3,1,2]
[[1,2,3,5],[4,8],[6],[7]]=>0010110=>[3,2,1,2]
[[1,2,3,4],[5,8],[6],[7]]=>0001110=>[4,1,1,2]
[[1,4,6,7],[2,5],[3],[8]]=>1101001=>[1,1,2,3,1]
[[1,3,6,7],[2,5],[4],[8]]=>1010001=>[1,2,4,1]
[[1,2,6,7],[3,5],[4],[8]]=>0110001=>[2,1,4,1]
[[1,3,6,7],[2,4],[5],[8]]=>1011001=>[1,2,1,3,1]
[[1,2,6,7],[3,4],[5],[8]]=>0101001=>[2,2,3,1]
[[1,4,5,7],[2,6],[3],[8]]=>1100101=>[1,1,3,2,1]
[[1,3,5,7],[2,6],[4],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,6],[4],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,4,7],[2,6],[5],[8]]=>1001001=>[1,3,3,1]
[[1,2,4,7],[3,6],[5],[8]]=>0101001=>[2,2,3,1]
[[1,2,3,7],[4,6],[5],[8]]=>0011001=>[3,1,3,1]
[[1,3,5,7],[2,4],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3,4],[6],[8]]=>0100101=>[2,3,2,1]
[[1,3,4,7],[2,5],[6],[8]]=>1001101=>[1,3,1,2,1]
[[1,2,4,7],[3,5],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,2,3,7],[4,5],[6],[8]]=>0010101=>[3,2,2,1]
[[1,4,5,6],[2,7],[3],[8]]=>1100011=>[1,1,4,1,1]
[[1,3,5,6],[2,7],[4],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,5,6],[3,7],[4],[8]]=>0110011=>[2,1,3,1,1]
[[1,3,4,6],[2,7],[5],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4,6],[3,7],[5],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3,6],[4,7],[5],[8]]=>0011011=>[3,1,2,1,1]
[[1,3,4,5],[2,7],[6],[8]]=>1000101=>[1,4,2,1]
[[1,2,4,5],[3,7],[6],[8]]=>0100101=>[2,3,2,1]
[[1,2,3,5],[4,7],[6],[8]]=>0010101=>[3,2,2,1]
[[1,2,3,4],[5,7],[6],[8]]=>0001101=>[4,1,2,1]
[[1,3,5,6],[2,4],[7],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,5,6],[3,4],[7],[8]]=>0100011=>[2,4,1,1]
[[1,3,4,6],[2,5],[7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4,6],[3,5],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3,6],[4,5],[7],[8]]=>0010011=>[3,3,1,1]
[[1,3,4,5],[2,6],[7],[8]]=>1000111=>[1,4,1,1,1]
[[1,2,4,5],[3,6],[7],[8]]=>0100111=>[2,3,1,1,1]
[[1,2,3,5],[4,6],[7],[8]]=>0010111=>[3,2,1,1,1]
[[1,2,3,4],[5,6],[7],[8]]=>0001011=>[4,2,1,1]
[[1,6,7,8],[2],[3],[4],[5]]=>1111000=>[1,1,1,1,4]
[[1,5,7,8],[2],[3],[4],[6]]=>1110100=>[1,1,1,2,3]
[[1,4,7,8],[2],[3],[5],[6]]=>1101100=>[1,1,2,1,3]
[[1,3,7,8],[2],[4],[5],[6]]=>1011100=>[1,2,1,1,3]
[[1,2,7,8],[3],[4],[5],[6]]=>0111100=>[2,1,1,1,3]
[[1,5,6,8],[2],[3],[4],[7]]=>1110010=>[1,1,1,3,2]
[[1,4,6,8],[2],[3],[5],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,6,8],[2],[4],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,6,8],[3],[4],[5],[7]]=>0111010=>[2,1,1,2,2]
[[1,4,5,8],[2],[3],[6],[7]]=>1100110=>[1,1,3,1,2]
[[1,3,5,8],[2],[4],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5,8],[3],[4],[6],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,4,8],[2],[5],[6],[7]]=>1001110=>[1,3,1,1,2]
[[1,2,4,8],[3],[5],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,2,3,8],[4],[5],[6],[7]]=>0011110=>[3,1,1,1,2]
[[1,5,6,7],[2],[3],[4],[8]]=>1110001=>[1,1,1,4,1]
[[1,4,6,7],[2],[3],[5],[8]]=>1101001=>[1,1,2,3,1]
[[1,3,6,7],[2],[4],[5],[8]]=>1011001=>[1,2,1,3,1]
[[1,2,6,7],[3],[4],[5],[8]]=>0111001=>[2,1,1,3,1]
[[1,4,5,7],[2],[3],[6],[8]]=>1100101=>[1,1,3,2,1]
[[1,3,5,7],[2],[4],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5,7],[3],[4],[6],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,4,7],[2],[5],[6],[8]]=>1001101=>[1,3,1,2,1]
[[1,2,4,7],[3],[5],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,2,3,7],[4],[5],[6],[8]]=>0011101=>[3,1,1,2,1]
[[1,4,5,6],[2],[3],[7],[8]]=>1100011=>[1,1,4,1,1]
[[1,3,5,6],[2],[4],[7],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,5,6],[3],[4],[7],[8]]=>0110011=>[2,1,3,1,1]
[[1,3,4,6],[2],[5],[7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4,6],[3],[5],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3,6],[4],[5],[7],[8]]=>0011011=>[3,1,2,1,1]
[[1,3,4,5],[2],[6],[7],[8]]=>1000111=>[1,4,1,1,1]
[[1,2,4,5],[3],[6],[7],[8]]=>0100111=>[2,3,1,1,1]
[[1,2,3,5],[4],[6],[7],[8]]=>0010111=>[3,2,1,1,1]
[[1,2,3,4],[5],[6],[7],[8]]=>0001111=>[4,1,1,1,1]
[[1,4,7],[2,5,8],[3,6]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,5,8],[4,6]]=>1010101=>[1,2,2,2,1]
[[1,2,7],[3,5,8],[4,6]]=>0110101=>[2,1,2,2,1]
[[1,3,7],[2,4,8],[5,6]]=>1011001=>[1,2,1,3,1]
[[1,2,7],[3,4,8],[5,6]]=>0101001=>[2,2,3,1]
[[1,4,6],[2,5,8],[3,7]]=>1101010=>[1,1,2,2,2]
[[1,3,6],[2,5,8],[4,7]]=>1010010=>[1,2,3,2]
[[1,2,6],[3,5,8],[4,7]]=>0110010=>[2,1,3,2]
[[1,3,6],[2,4,8],[5,7]]=>1011010=>[1,2,1,2,2]
[[1,2,6],[3,4,8],[5,7]]=>0101010=>[2,2,2,2]
[[1,4,5],[2,6,8],[3,7]]=>1100110=>[1,1,3,1,2]
[[1,3,5],[2,6,8],[4,7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,6,8],[4,7]]=>0110110=>[2,1,2,1,2]
[[1,3,4],[2,6,8],[5,7]]=>1001010=>[1,3,2,2]
[[1,2,4],[3,6,8],[5,7]]=>0101010=>[2,2,2,2]
[[1,2,3],[4,6,8],[5,7]]=>0011010=>[3,1,2,2]
[[1,3,5],[2,4,8],[6,7]]=>1010100=>[1,2,2,3]
[[1,2,5],[3,4,8],[6,7]]=>0100100=>[2,3,3]
[[1,3,4],[2,5,8],[6,7]]=>1001100=>[1,3,1,3]
[[1,2,4],[3,5,8],[6,7]]=>0101100=>[2,2,1,3]
[[1,2,3],[4,5,8],[6,7]]=>0010100=>[3,2,3]
[[1,4,6],[2,5,7],[3,8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,5,7],[4,8]]=>1010011=>[1,2,3,1,1]
[[1,2,6],[3,5,7],[4,8]]=>0110011=>[2,1,3,1,1]
[[1,3,6],[2,4,7],[5,8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,4,7],[5,8]]=>0101011=>[2,2,2,1,1]
[[1,4,5],[2,6,7],[3,8]]=>1100101=>[1,1,3,2,1]
[[1,3,5],[2,6,7],[4,8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,6,7],[4,8]]=>0110101=>[2,1,2,2,1]
[[1,3,4],[2,6,7],[5,8]]=>1001001=>[1,3,3,1]
[[1,2,4],[3,6,7],[5,8]]=>0101001=>[2,2,3,1]
[[1,2,3],[4,6,7],[5,8]]=>0011001=>[3,1,3,1]
[[1,3,5],[2,4,7],[6,8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,4,7],[6,8]]=>0100101=>[2,3,2,1]
[[1,3,4],[2,5,7],[6,8]]=>1001101=>[1,3,1,2,1]
[[1,2,4],[3,5,7],[6,8]]=>0101101=>[2,2,1,2,1]
[[1,2,3],[4,5,7],[6,8]]=>0010101=>[3,2,2,1]
[[1,3,5],[2,4,6],[7,8]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,4,6],[7,8]]=>0100110=>[2,3,1,2]
[[1,3,4],[2,5,6],[7,8]]=>1001010=>[1,3,2,2]
[[1,2,4],[3,5,6],[7,8]]=>0101010=>[2,2,2,2]
[[1,2,3],[4,5,6],[7,8]]=>0010010=>[3,3,2]
[[1,5,7],[2,6,8],[3],[4]]=>1110101=>[1,1,1,2,2,1]
[[1,4,7],[2,6,8],[3],[5]]=>1101001=>[1,1,2,3,1]
[[1,3,7],[2,6,8],[4],[5]]=>1011001=>[1,2,1,3,1]
[[1,2,7],[3,6,8],[4],[5]]=>0111001=>[2,1,1,3,1]
[[1,4,7],[2,5,8],[3],[6]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,5,8],[4],[6]]=>1010101=>[1,2,2,2,1]
[[1,2,7],[3,5,8],[4],[6]]=>0110101=>[2,1,2,2,1]
[[1,3,7],[2,4,8],[5],[6]]=>1011101=>[1,2,1,1,2,1]
[[1,2,7],[3,4,8],[5],[6]]=>0101101=>[2,2,1,2,1]
[[1,5,6],[2,7,8],[3],[4]]=>1110010=>[1,1,1,3,2]
[[1,4,6],[2,7,8],[3],[5]]=>1101010=>[1,1,2,2,2]
[[1,3,6],[2,7,8],[4],[5]]=>1011010=>[1,2,1,2,2]
[[1,2,6],[3,7,8],[4],[5]]=>0111010=>[2,1,1,2,2]
[[1,4,5],[2,7,8],[3],[6]]=>1100100=>[1,1,3,3]
[[1,3,5],[2,7,8],[4],[6]]=>1010100=>[1,2,2,3]
[[1,2,5],[3,7,8],[4],[6]]=>0110100=>[2,1,2,3]
[[1,3,4],[2,7,8],[5],[6]]=>1001100=>[1,3,1,3]
[[1,2,4],[3,7,8],[5],[6]]=>0101100=>[2,2,1,3]
[[1,2,3],[4,7,8],[5],[6]]=>0011100=>[3,1,1,3]
[[1,4,6],[2,5,8],[3],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,6],[2,5,8],[4],[7]]=>1010010=>[1,2,3,2]
[[1,2,6],[3,5,8],[4],[7]]=>0110010=>[2,1,3,2]
[[1,3,6],[2,4,8],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,6],[3,4,8],[5],[7]]=>0101010=>[2,2,2,2]
[[1,4,5],[2,6,8],[3],[7]]=>1100110=>[1,1,3,1,2]
[[1,3,5],[2,6,8],[4],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,6,8],[4],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,4],[2,6,8],[5],[7]]=>1001010=>[1,3,2,2]
[[1,2,4],[3,6,8],[5],[7]]=>0101010=>[2,2,2,2]
[[1,2,3],[4,6,8],[5],[7]]=>0011010=>[3,1,2,2]
[[1,3,5],[2,4,8],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,4,8],[6],[7]]=>0100110=>[2,3,1,2]
[[1,3,4],[2,5,8],[6],[7]]=>1001110=>[1,3,1,1,2]
[[1,2,4],[3,5,8],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,2,3],[4,5,8],[6],[7]]=>0010110=>[3,2,1,2]
[[1,4,6],[2,5,7],[3],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,5,7],[4],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,6],[3,5,7],[4],[8]]=>0110011=>[2,1,3,1,1]
[[1,3,6],[2,4,7],[5],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,4,7],[5],[8]]=>0101011=>[2,2,2,1,1]
[[1,4,5],[2,6,7],[3],[8]]=>1100101=>[1,1,3,2,1]
[[1,3,5],[2,6,7],[4],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,6,7],[4],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,4],[2,6,7],[5],[8]]=>1001001=>[1,3,3,1]
[[1,2,4],[3,6,7],[5],[8]]=>0101001=>[2,2,3,1]
[[1,2,3],[4,6,7],[5],[8]]=>0011001=>[3,1,3,1]
[[1,3,5],[2,4,7],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,4,7],[6],[8]]=>0100101=>[2,3,2,1]
[[1,3,4],[2,5,7],[6],[8]]=>1001101=>[1,3,1,2,1]
[[1,2,4],[3,5,7],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,2,3],[4,5,7],[6],[8]]=>0010101=>[3,2,2,1]
[[1,3,5],[2,4,6],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2,5],[3,4,6],[7],[8]]=>0100111=>[2,3,1,1,1]
[[1,3,4],[2,5,6],[7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4],[3,5,6],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3],[4,5,6],[7],[8]]=>0010011=>[3,3,1,1]
[[1,5,8],[2,6],[3,7],[4]]=>1110110=>[1,1,1,2,1,2]
[[1,4,8],[2,6],[3,7],[5]]=>1101010=>[1,1,2,2,2]
[[1,3,8],[2,6],[4,7],[5]]=>1011010=>[1,2,1,2,2]
[[1,2,8],[3,6],[4,7],[5]]=>0111010=>[2,1,1,2,2]
[[1,4,8],[2,5],[3,7],[6]]=>1101100=>[1,1,2,1,3]
[[1,3,8],[2,5],[4,7],[6]]=>1010100=>[1,2,2,3]
[[1,2,8],[3,5],[4,7],[6]]=>0110100=>[2,1,2,3]
[[1,3,8],[2,4],[5,7],[6]]=>1011100=>[1,2,1,1,3]
[[1,2,8],[3,4],[5,7],[6]]=>0101100=>[2,2,1,3]
[[1,4,8],[2,5],[3,6],[7]]=>1101110=>[1,1,2,1,1,2]
[[1,3,8],[2,5],[4,6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,8],[3,5],[4,6],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,8],[2,4],[5,6],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,8],[3,4],[5,6],[7]]=>0101010=>[2,2,2,2]
[[1,5,7],[2,6],[3,8],[4]]=>1110101=>[1,1,1,2,2,1]
[[1,4,7],[2,6],[3,8],[5]]=>1101001=>[1,1,2,3,1]
[[1,3,7],[2,6],[4,8],[5]]=>1011001=>[1,2,1,3,1]
[[1,2,7],[3,6],[4,8],[5]]=>0111001=>[2,1,1,3,1]
[[1,4,7],[2,5],[3,8],[6]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,5],[4,8],[6]]=>1010101=>[1,2,2,2,1]
[[1,2,7],[3,5],[4,8],[6]]=>0110101=>[2,1,2,2,1]
[[1,3,7],[2,4],[5,8],[6]]=>1011101=>[1,2,1,1,2,1]
[[1,2,7],[3,4],[5,8],[6]]=>0101101=>[2,2,1,2,1]
[[1,5,6],[2,7],[3,8],[4]]=>1110011=>[1,1,1,3,1,1]
[[1,4,6],[2,7],[3,8],[5]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,7],[4,8],[5]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,7],[4,8],[5]]=>0111011=>[2,1,1,2,1,1]
[[1,4,5],[2,7],[3,8],[6]]=>1100101=>[1,1,3,2,1]
[[1,3,5],[2,7],[4,8],[6]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,7],[4,8],[6]]=>0110101=>[2,1,2,2,1]
[[1,3,4],[2,7],[5,8],[6]]=>1001101=>[1,3,1,2,1]
[[1,2,4],[3,7],[5,8],[6]]=>0101101=>[2,2,1,2,1]
[[1,2,3],[4,7],[5,8],[6]]=>0011101=>[3,1,1,2,1]
[[1,4,6],[2,5],[3,8],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,6],[2,5],[4,8],[7]]=>1010010=>[1,2,3,2]
[[1,2,6],[3,5],[4,8],[7]]=>0110010=>[2,1,3,2]
[[1,3,6],[2,4],[5,8],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,6],[3,4],[5,8],[7]]=>0101010=>[2,2,2,2]
[[1,4,5],[2,6],[3,8],[7]]=>1100110=>[1,1,3,1,2]
[[1,3,5],[2,6],[4,8],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,6],[4,8],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,4],[2,6],[5,8],[7]]=>1001010=>[1,3,2,2]
[[1,2,4],[3,6],[5,8],[7]]=>0101010=>[2,2,2,2]
[[1,2,3],[4,6],[5,8],[7]]=>0011010=>[3,1,2,2]
[[1,3,5],[2,4],[6,8],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,4],[6,8],[7]]=>0100110=>[2,3,1,2]
[[1,3,4],[2,5],[6,8],[7]]=>1001110=>[1,3,1,1,2]
[[1,2,4],[3,5],[6,8],[7]]=>0101110=>[2,2,1,1,2]
[[1,2,3],[4,5],[6,8],[7]]=>0010110=>[3,2,1,2]
[[1,4,7],[2,5],[3,6],[8]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,5],[4,6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,7],[3,5],[4,6],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,7],[2,4],[5,6],[8]]=>1011001=>[1,2,1,3,1]
[[1,2,7],[3,4],[5,6],[8]]=>0101001=>[2,2,3,1]
[[1,4,6],[2,5],[3,7],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,5],[4,7],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,6],[3,5],[4,7],[8]]=>0110011=>[2,1,3,1,1]
[[1,3,6],[2,4],[5,7],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,4],[5,7],[8]]=>0101011=>[2,2,2,1,1]
[[1,4,5],[2,6],[3,7],[8]]=>1100111=>[1,1,3,1,1,1]
[[1,3,5],[2,6],[4,7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2,5],[3,6],[4,7],[8]]=>0110111=>[2,1,2,1,1,1]
[[1,3,4],[2,6],[5,7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4],[3,6],[5,7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3],[4,6],[5,7],[8]]=>0011011=>[3,1,2,1,1]
[[1,3,5],[2,4],[6,7],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,4],[6,7],[8]]=>0100101=>[2,3,2,1]
[[1,3,4],[2,5],[6,7],[8]]=>1001101=>[1,3,1,2,1]
[[1,2,4],[3,5],[6,7],[8]]=>0101101=>[2,2,1,2,1]
[[1,2,3],[4,5],[6,7],[8]]=>0010101=>[3,2,2,1]
[[1,6,8],[2,7],[3],[4],[5]]=>1111010=>[1,1,1,1,2,2]
[[1,5,8],[2,7],[3],[4],[6]]=>1110100=>[1,1,1,2,3]
[[1,4,8],[2,7],[3],[5],[6]]=>1101100=>[1,1,2,1,3]
[[1,3,8],[2,7],[4],[5],[6]]=>1011100=>[1,2,1,1,3]
[[1,2,8],[3,7],[4],[5],[6]]=>0111100=>[2,1,1,1,3]
[[1,5,8],[2,6],[3],[4],[7]]=>1110110=>[1,1,1,2,1,2]
[[1,4,8],[2,6],[3],[5],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,8],[2,6],[4],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,8],[3,6],[4],[5],[7]]=>0111010=>[2,1,1,2,2]
[[1,4,8],[2,5],[3],[6],[7]]=>1101110=>[1,1,2,1,1,2]
[[1,3,8],[2,5],[4],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,8],[3,5],[4],[6],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,8],[2,4],[5],[6],[7]]=>1011110=>[1,2,1,1,1,2]
[[1,2,8],[3,4],[5],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,6,7],[2,8],[3],[4],[5]]=>1111001=>[1,1,1,1,3,1]
[[1,5,7],[2,8],[3],[4],[6]]=>1110101=>[1,1,1,2,2,1]
[[1,4,7],[2,8],[3],[5],[6]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,8],[4],[5],[6]]=>1011101=>[1,2,1,1,2,1]
[[1,2,7],[3,8],[4],[5],[6]]=>0111101=>[2,1,1,1,2,1]
[[1,5,6],[2,8],[3],[4],[7]]=>1110010=>[1,1,1,3,2]
[[1,4,6],[2,8],[3],[5],[7]]=>1101010=>[1,1,2,2,2]
[[1,3,6],[2,8],[4],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2,6],[3,8],[4],[5],[7]]=>0111010=>[2,1,1,2,2]
[[1,4,5],[2,8],[3],[6],[7]]=>1100110=>[1,1,3,1,2]
[[1,3,5],[2,8],[4],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2,5],[3,8],[4],[6],[7]]=>0110110=>[2,1,2,1,2]
[[1,3,4],[2,8],[5],[6],[7]]=>1001110=>[1,3,1,1,2]
[[1,2,4],[3,8],[5],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,2,3],[4,8],[5],[6],[7]]=>0011110=>[3,1,1,1,2]
[[1,5,7],[2,6],[3],[4],[8]]=>1110101=>[1,1,1,2,2,1]
[[1,4,7],[2,6],[3],[5],[8]]=>1101001=>[1,1,2,3,1]
[[1,3,7],[2,6],[4],[5],[8]]=>1011001=>[1,2,1,3,1]
[[1,2,7],[3,6],[4],[5],[8]]=>0111001=>[2,1,1,3,1]
[[1,4,7],[2,5],[3],[6],[8]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2,5],[4],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,7],[3,5],[4],[6],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,7],[2,4],[5],[6],[8]]=>1011101=>[1,2,1,1,2,1]
[[1,2,7],[3,4],[5],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,5,6],[2,7],[3],[4],[8]]=>1110011=>[1,1,1,3,1,1]
[[1,4,6],[2,7],[3],[5],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,7],[4],[5],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,7],[4],[5],[8]]=>0111011=>[2,1,1,2,1,1]
[[1,4,5],[2,7],[3],[6],[8]]=>1100101=>[1,1,3,2,1]
[[1,3,5],[2,7],[4],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2,5],[3,7],[4],[6],[8]]=>0110101=>[2,1,2,2,1]
[[1,3,4],[2,7],[5],[6],[8]]=>1001101=>[1,3,1,2,1]
[[1,2,4],[3,7],[5],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,2,3],[4,7],[5],[6],[8]]=>0011101=>[3,1,1,2,1]
[[1,4,6],[2,5],[3],[7],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2,5],[4],[7],[8]]=>1010011=>[1,2,3,1,1]
[[1,2,6],[3,5],[4],[7],[8]]=>0110011=>[2,1,3,1,1]
[[1,3,6],[2,4],[5],[7],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3,4],[5],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,4,5],[2,6],[3],[7],[8]]=>1100111=>[1,1,3,1,1,1]
[[1,3,5],[2,6],[4],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2,5],[3,6],[4],[7],[8]]=>0110111=>[2,1,2,1,1,1]
[[1,3,4],[2,6],[5],[7],[8]]=>1001011=>[1,3,2,1,1]
[[1,2,4],[3,6],[5],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,2,3],[4,6],[5],[7],[8]]=>0011011=>[3,1,2,1,1]
[[1,3,5],[2,4],[6],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2,5],[3,4],[6],[7],[8]]=>0100111=>[2,3,1,1,1]
[[1,3,4],[2,5],[6],[7],[8]]=>1001111=>[1,3,1,1,1,1]
[[1,2,4],[3,5],[6],[7],[8]]=>0101111=>[2,2,1,1,1,1]
[[1,2,3],[4,5],[6],[7],[8]]=>0010111=>[3,2,1,1,1]
[[1,7,8],[2],[3],[4],[5],[6]]=>1111100=>[1,1,1,1,1,3]
[[1,6,8],[2],[3],[4],[5],[7]]=>1111010=>[1,1,1,1,2,2]
[[1,5,8],[2],[3],[4],[6],[7]]=>1110110=>[1,1,1,2,1,2]
[[1,4,8],[2],[3],[5],[6],[7]]=>1101110=>[1,1,2,1,1,2]
[[1,3,8],[2],[4],[5],[6],[7]]=>1011110=>[1,2,1,1,1,2]
[[1,2,8],[3],[4],[5],[6],[7]]=>0111110=>[2,1,1,1,1,2]
[[1,6,7],[2],[3],[4],[5],[8]]=>1111001=>[1,1,1,1,3,1]
[[1,5,7],[2],[3],[4],[6],[8]]=>1110101=>[1,1,1,2,2,1]
[[1,4,7],[2],[3],[5],[6],[8]]=>1101101=>[1,1,2,1,2,1]
[[1,3,7],[2],[4],[5],[6],[8]]=>1011101=>[1,2,1,1,2,1]
[[1,2,7],[3],[4],[5],[6],[8]]=>0111101=>[2,1,1,1,2,1]
[[1,5,6],[2],[3],[4],[7],[8]]=>1110011=>[1,1,1,3,1,1]
[[1,4,6],[2],[3],[5],[7],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3,6],[2],[4],[5],[7],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2,6],[3],[4],[5],[7],[8]]=>0111011=>[2,1,1,2,1,1]
[[1,4,5],[2],[3],[6],[7],[8]]=>1100111=>[1,1,3,1,1,1]
[[1,3,5],[2],[4],[6],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2,5],[3],[4],[6],[7],[8]]=>0110111=>[2,1,2,1,1,1]
[[1,3,4],[2],[5],[6],[7],[8]]=>1001111=>[1,3,1,1,1,1]
[[1,2,4],[3],[5],[6],[7],[8]]=>0101111=>[2,2,1,1,1,1]
[[1,2,3],[4],[5],[6],[7],[8]]=>0011111=>[3,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4,8]]=>1110111=>[1,1,1,2,1,1,1]
[[1,4],[2,6],[3,7],[5,8]]=>1101011=>[1,1,2,2,1,1]
[[1,3],[2,6],[4,7],[5,8]]=>1011011=>[1,2,1,2,1,1]
[[1,2],[3,6],[4,7],[5,8]]=>0111011=>[2,1,1,2,1,1]
[[1,4],[2,5],[3,7],[6,8]]=>1101101=>[1,1,2,1,2,1]
[[1,3],[2,5],[4,7],[6,8]]=>1010101=>[1,2,2,2,1]
[[1,2],[3,5],[4,7],[6,8]]=>0110101=>[2,1,2,2,1]
[[1,3],[2,4],[5,7],[6,8]]=>1011101=>[1,2,1,1,2,1]
[[1,2],[3,4],[5,7],[6,8]]=>0101101=>[2,2,1,2,1]
[[1,4],[2,5],[3,6],[7,8]]=>1101110=>[1,1,2,1,1,2]
[[1,3],[2,5],[4,6],[7,8]]=>1010110=>[1,2,2,1,2]
[[1,2],[3,5],[4,6],[7,8]]=>0110110=>[2,1,2,1,2]
[[1,3],[2,4],[5,6],[7,8]]=>1011010=>[1,2,1,2,2]
[[1,2],[3,4],[5,6],[7,8]]=>0101010=>[2,2,2,2]
[[1,6],[2,7],[3,8],[4],[5]]=>1111011=>[1,1,1,1,2,1,1]
[[1,5],[2,7],[3,8],[4],[6]]=>1110101=>[1,1,1,2,2,1]
[[1,4],[2,7],[3,8],[5],[6]]=>1101101=>[1,1,2,1,2,1]
[[1,3],[2,7],[4,8],[5],[6]]=>1011101=>[1,2,1,1,2,1]
[[1,2],[3,7],[4,8],[5],[6]]=>0111101=>[2,1,1,1,2,1]
[[1,5],[2,6],[3,8],[4],[7]]=>1110110=>[1,1,1,2,1,2]
[[1,4],[2,6],[3,8],[5],[7]]=>1101010=>[1,1,2,2,2]
[[1,3],[2,6],[4,8],[5],[7]]=>1011010=>[1,2,1,2,2]
[[1,2],[3,6],[4,8],[5],[7]]=>0111010=>[2,1,1,2,2]
[[1,4],[2,5],[3,8],[6],[7]]=>1101110=>[1,1,2,1,1,2]
[[1,3],[2,5],[4,8],[6],[7]]=>1010110=>[1,2,2,1,2]
[[1,2],[3,5],[4,8],[6],[7]]=>0110110=>[2,1,2,1,2]
[[1,3],[2,4],[5,8],[6],[7]]=>1011110=>[1,2,1,1,1,2]
[[1,2],[3,4],[5,8],[6],[7]]=>0101110=>[2,2,1,1,2]
[[1,5],[2,6],[3,7],[4],[8]]=>1110111=>[1,1,1,2,1,1,1]
[[1,4],[2,6],[3,7],[5],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3],[2,6],[4,7],[5],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2],[3,6],[4,7],[5],[8]]=>0111011=>[2,1,1,2,1,1]
[[1,4],[2,5],[3,7],[6],[8]]=>1101101=>[1,1,2,1,2,1]
[[1,3],[2,5],[4,7],[6],[8]]=>1010101=>[1,2,2,2,1]
[[1,2],[3,5],[4,7],[6],[8]]=>0110101=>[2,1,2,2,1]
[[1,3],[2,4],[5,7],[6],[8]]=>1011101=>[1,2,1,1,2,1]
[[1,2],[3,4],[5,7],[6],[8]]=>0101101=>[2,2,1,2,1]
[[1,4],[2,5],[3,6],[7],[8]]=>1101111=>[1,1,2,1,1,1,1]
[[1,3],[2,5],[4,6],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2],[3,5],[4,6],[7],[8]]=>0110111=>[2,1,2,1,1,1]
[[1,3],[2,4],[5,6],[7],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2],[3,4],[5,6],[7],[8]]=>0101011=>[2,2,2,1,1]
[[1,7],[2,8],[3],[4],[5],[6]]=>1111101=>[1,1,1,1,1,2,1]
[[1,6],[2,8],[3],[4],[5],[7]]=>1111010=>[1,1,1,1,2,2]
[[1,5],[2,8],[3],[4],[6],[7]]=>1110110=>[1,1,1,2,1,2]
[[1,4],[2,8],[3],[5],[6],[7]]=>1101110=>[1,1,2,1,1,2]
[[1,3],[2,8],[4],[5],[6],[7]]=>1011110=>[1,2,1,1,1,2]
[[1,2],[3,8],[4],[5],[6],[7]]=>0111110=>[2,1,1,1,1,2]
[[1,6],[2,7],[3],[4],[5],[8]]=>1111011=>[1,1,1,1,2,1,1]
[[1,5],[2,7],[3],[4],[6],[8]]=>1110101=>[1,1,1,2,2,1]
[[1,4],[2,7],[3],[5],[6],[8]]=>1101101=>[1,1,2,1,2,1]
[[1,3],[2,7],[4],[5],[6],[8]]=>1011101=>[1,2,1,1,2,1]
[[1,2],[3,7],[4],[5],[6],[8]]=>0111101=>[2,1,1,1,2,1]
[[1,5],[2,6],[3],[4],[7],[8]]=>1110111=>[1,1,1,2,1,1,1]
[[1,4],[2,6],[3],[5],[7],[8]]=>1101011=>[1,1,2,2,1,1]
[[1,3],[2,6],[4],[5],[7],[8]]=>1011011=>[1,2,1,2,1,1]
[[1,2],[3,6],[4],[5],[7],[8]]=>0111011=>[2,1,1,2,1,1]
[[1,4],[2,5],[3],[6],[7],[8]]=>1101111=>[1,1,2,1,1,1,1]
[[1,3],[2,5],[4],[6],[7],[8]]=>1010111=>[1,2,2,1,1,1]
[[1,2],[3,5],[4],[6],[7],[8]]=>0110111=>[2,1,2,1,1,1]
[[1,3],[2,4],[5],[6],[7],[8]]=>1011111=>[1,2,1,1,1,1,1]
[[1,2],[3,4],[5],[6],[7],[8]]=>0101111=>[2,2,1,1,1,1]
[[1,8],[2],[3],[4],[5],[6],[7]]=>1111110=>[1,1,1,1,1,1,2]
[[1,7],[2],[3],[4],[5],[6],[8]]=>1111101=>[1,1,1,1,1,2,1]
[[1,6],[2],[3],[4],[5],[7],[8]]=>1111011=>[1,1,1,1,2,1,1]
[[1,5],[2],[3],[4],[6],[7],[8]]=>1110111=>[1,1,1,2,1,1,1]
[[1,4],[2],[3],[5],[6],[7],[8]]=>1101111=>[1,1,2,1,1,1,1]
[[1,3],[2],[4],[5],[6],[7],[8]]=>1011111=>[1,2,1,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7],[8]]=>0111111=>[2,1,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>1111111=>[1,1,1,1,1,1,1,1]
[[1,3,5,7,9],[2,4,6,8,10]]=>101010101=>[1,2,2,2,2,1]
[[1,3,5,7,8],[2,4,6,9,10]]=>101010010=>[1,2,2,3,2]
[[1,3,5,6,9],[2,4,7,8,10]]=>101001001=>[1,2,3,3,1]
[[1,3,5,6,8],[2,4,7,9,10]]=>101001010=>[1,2,3,2,2]
[[1,3,5,6,7],[2,4,8,9,10]]=>101000100=>[1,2,4,3]
[[1,3,4,7,9],[2,5,6,8,10]]=>100100101=>[1,3,3,2,1]
[[1,3,4,7,8],[2,5,6,9,10]]=>100100010=>[1,3,4,2]
[[1,3,4,6,9],[2,5,7,8,10]]=>100101001=>[1,3,2,3,1]
[[1,3,4,6,8],[2,5,7,9,10]]=>100101010=>[1,3,2,2,2]
[[1,3,4,6,7],[2,5,8,9,10]]=>100100100=>[1,3,3,3]
[[1,3,4,5,9],[2,6,7,8,10]]=>100010001=>[1,4,4,1]
[[1,3,4,5,8],[2,6,7,9,10]]=>100010010=>[1,4,3,2]
[[1,3,4,5,7],[2,6,8,9,10]]=>100010100=>[1,4,2,3]
[[1,3,4,5,6],[2,7,8,9,10]]=>100001000=>[1,5,4]
[[1,2,5,7,9],[3,4,6,8,10]]=>010010101=>[2,3,2,2,1]
[[1,2,5,7,8],[3,4,6,9,10]]=>010010010=>[2,3,3,2]
[[1,2,5,6,9],[3,4,7,8,10]]=>010001001=>[2,4,3,1]
[[1,2,5,6,8],[3,4,7,9,10]]=>010001010=>[2,4,2,2]
[[1,2,5,6,7],[3,4,8,9,10]]=>010000100=>[2,5,3]
[[1,2,4,7,9],[3,5,6,8,10]]=>010100101=>[2,2,3,2,1]
[[1,2,4,7,8],[3,5,6,9,10]]=>010100010=>[2,2,4,2]
[[1,2,4,6,9],[3,5,7,8,10]]=>010101001=>[2,2,2,3,1]
[[1,2,4,6,8],[3,5,7,9,10]]=>010101010=>[2,2,2,2,2]
[[1,2,4,6,7],[3,5,8,9,10]]=>010100100=>[2,2,3,3]
[[1,2,4,5,9],[3,6,7,8,10]]=>010010001=>[2,3,4,1]
[[1,2,4,5,8],[3,6,7,9,10]]=>010010010=>[2,3,3,2]
[[1,2,4,5,7],[3,6,8,9,10]]=>010010100=>[2,3,2,3]
[[1,2,4,5,6],[3,7,8,9,10]]=>010001000=>[2,4,4]
[[1,2,3,7,9],[4,5,6,8,10]]=>001000101=>[3,4,2,1]
[[1,2,3,7,8],[4,5,6,9,10]]=>001000010=>[3,5,2]
[[1,2,3,6,9],[4,5,7,8,10]]=>001001001=>[3,3,3,1]
[[1,2,3,6,8],[4,5,7,9,10]]=>001001010=>[3,3,2,2]
[[1,2,3,6,7],[4,5,8,9,10]]=>001000100=>[3,4,3]
[[1,2,3,5,9],[4,6,7,8,10]]=>001010001=>[3,2,4,1]
[[1,2,3,5,8],[4,6,7,9,10]]=>001010010=>[3,2,3,2]
[[1,2,3,5,7],[4,6,8,9,10]]=>001010100=>[3,2,2,3]
[[1,2,3,5,6],[4,7,8,9,10]]=>001001000=>[3,3,4]
[[1,2,3,4,9],[5,6,7,8,10]]=>000100001=>[4,5,1]
[[1,2,3,4,8],[5,6,7,9,10]]=>000100010=>[4,4,2]
[[1,2,3,4,7],[5,6,8,9,10]]=>000100100=>[4,3,3]
[[1,2,3,4,6],[5,7,8,9,10]]=>000101000=>[4,2,4]
[[1,2,3,4,5],[6,7,8,9,10]]=>000010000=>[5,5]
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>10101010101=>[1,2,2,2,2,2,1]
[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>10101010010=>[1,2,2,2,3,2]
[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>10101001001=>[1,2,2,3,3,1]
[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>10101001010=>[1,2,2,3,2,2]
[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>10101000100=>[1,2,2,4,3]
[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>10100100101=>[1,2,3,3,2,1]
[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>10100100010=>[1,2,3,4,2]
[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>10100101001=>[1,2,3,2,3,1]
[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>10100101010=>[1,2,3,2,2,2]
[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>10100100100=>[1,2,3,3,3]
[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>10100010001=>[1,2,4,4,1]
[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>10100010010=>[1,2,4,3,2]
[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>10100010100=>[1,2,4,2,3]
[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>10100001000=>[1,2,5,4]
[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>10010010101=>[1,3,3,2,2,1]
[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>10010010010=>[1,3,3,3,2]
[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>10010001001=>[1,3,4,3,1]
[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>10010001010=>[1,3,4,2,2]
[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>10010000100=>[1,3,5,3]
[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>10010100101=>[1,3,2,3,2,1]
[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>10010100010=>[1,3,2,4,2]
[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>10010101001=>[1,3,2,2,3,1]
[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>10010101010=>[1,3,2,2,2,2]
[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>10010100100=>[1,3,2,3,3]
[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>10010010001=>[1,3,3,4,1]
[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>10010010010=>[1,3,3,3,2]
[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>10010010100=>[1,3,3,2,3]
[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>10010001000=>[1,3,4,4]
[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>10001000101=>[1,4,4,2,1]
[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>10001000010=>[1,4,5,2]
[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>10001001001=>[1,4,3,3,1]
[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>10001001010=>[1,4,3,2,2]
[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>10001000100=>[1,4,4,3]
[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>10001010001=>[1,4,2,4,1]
[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>10001010010=>[1,4,2,3,2]
[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>10001010100=>[1,4,2,2,3]
[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>10001001000=>[1,4,3,4]
[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>10000100001=>[1,5,5,1]
[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>10000100010=>[1,5,4,2]
[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>10000100100=>[1,5,3,3]
[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>10000101000=>[1,5,2,4]
[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>10000010000=>[1,6,5]
[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>01001010101=>[2,3,2,2,2,1]
[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>01001010010=>[2,3,2,3,2]
[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>01001001001=>[2,3,3,3,1]
[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>01001001010=>[2,3,3,2,2]
[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>01001000100=>[2,3,4,3]
[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>01000100101=>[2,4,3,2,1]
[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>01000100010=>[2,4,4,2]
[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>01000101001=>[2,4,2,3,1]
[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>01000101010=>[2,4,2,2,2]
[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>01000100100=>[2,4,3,3]
[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>01000010001=>[2,5,4,1]
[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>01000010010=>[2,5,3,2]
[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>01000010100=>[2,5,2,3]
[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>01000001000=>[2,6,4]
[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>01010010101=>[2,2,3,2,2,1]
[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>01010010010=>[2,2,3,3,2]
[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>01010001001=>[2,2,4,3,1]
[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>01010001010=>[2,2,4,2,2]
[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>01010000100=>[2,2,5,3]
[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>01010100101=>[2,2,2,3,2,1]
[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>01010100010=>[2,2,2,4,2]
[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>01010101001=>[2,2,2,2,3,1]
[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>01010101010=>[2,2,2,2,2,2]
[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>01010100100=>[2,2,2,3,3]
[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>01010010001=>[2,2,3,4,1]
[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>01010010010=>[2,2,3,3,2]
[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>01010010100=>[2,2,3,2,3]
[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>01010001000=>[2,2,4,4]
[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>01001000101=>[2,3,4,2,1]
[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>01001000010=>[2,3,5,2]
[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>01001001001=>[2,3,3,3,1]
[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>01001001010=>[2,3,3,2,2]
[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>01001000100=>[2,3,4,3]
[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>01001010001=>[2,3,2,4,1]
[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>01001010010=>[2,3,2,3,2]
[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>01001010100=>[2,3,2,2,3]
[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>01001001000=>[2,3,3,4]
[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>01000100001=>[2,4,5,1]
[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>01000100010=>[2,4,4,2]
[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>01000100100=>[2,4,3,3]
[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>01000101000=>[2,4,2,4]
[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>01000010000=>[2,5,5]
[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>00100010101=>[3,4,2,2,1]
[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>00100010010=>[3,4,3,2]
[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>00100001001=>[3,5,3,1]
[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>00100001010=>[3,5,2,2]
[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>00100000100=>[3,6,3]
[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>00100100101=>[3,3,3,2,1]
[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>00100100010=>[3,3,4,2]
[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>00100101001=>[3,3,2,3,1]
[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>00100101010=>[3,3,2,2,2]
[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>00100100100=>[3,3,3,3]
[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>00100010001=>[3,4,4,1]
[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>00100010010=>[3,4,3,2]
[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>00100010100=>[3,4,2,3]
[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>00100001000=>[3,5,4]
[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>00101000101=>[3,2,4,2,1]
[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>00101000010=>[3,2,5,2]
[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>00101001001=>[3,2,3,3,1]
[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>00101001010=>[3,2,3,2,2]
[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>00101000100=>[3,2,4,3]
[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>00101010001=>[3,2,2,4,1]
[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>00101010010=>[3,2,2,3,2]
[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>00101010100=>[3,2,2,2,3]
[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>00101001000=>[3,2,3,4]
[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>00100100001=>[3,3,5,1]
[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>00100100010=>[3,3,4,2]
[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>00100100100=>[3,3,3,3]
[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>00100101000=>[3,3,2,4]
[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>00100010000=>[3,4,5]
[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>00010000101=>[4,5,2,1]
[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>00010000010=>[4,6,2]
[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>00010001001=>[4,4,3,1]
[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>00010001010=>[4,4,2,2]
[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>00010000100=>[4,5,3]
[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>00010010001=>[4,3,4,1]
[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>00010010010=>[4,3,3,2]
[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>00010010100=>[4,3,2,3]
[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>00010001000=>[4,4,4]
[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>00010100001=>[4,2,5,1]
[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>00010100010=>[4,2,4,2]
[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>00010100100=>[4,2,3,3]
[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>00010101000=>[4,2,2,4]
[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>00010010000=>[4,3,5]
[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>00001000001=>[5,6,1]
[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>00001000010=>[5,5,2]
[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>00001000100=>[5,4,3]
[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>00001001000=>[5,3,4]
[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>00001010000=>[5,2,5]
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>00000100000=>[6,6]
[[1,2,3,4,5,6,7,8,9]]=>00000000=>[9]
[[1,2,3,4,5,6,7,8],[9]]=>00000001=>[8,1]
[[1,2,3,4,5,6,7],[8,9]]=>00000010=>[7,2]
[[1,2,3,4,5,6,7],[8],[9]]=>00000011=>[7,1,1]
[[1,2,3,4,5,6],[7,8,9]]=>00000100=>[6,3]
[[1,2,3,4,5,6],[7,8],[9]]=>00000101=>[6,2,1]
[[1,2,3,4,5,6],[7],[8],[9]]=>00000111=>[6,1,1,1]
[[1,2,3,4,5],[6,7,8,9]]=>00001000=>[5,4]
[[1,2,3,4,5],[6,7,8],[9]]=>00001001=>[5,3,1]
[[1,2,3,4,5],[6,7],[8,9]]=>00001010=>[5,2,2]
[[1,2,3,4,5],[6,7],[8],[9]]=>00001011=>[5,2,1,1]
[[1,2,3,4,5],[6],[7],[8],[9]]=>00001111=>[5,1,1,1,1]
[[1,2,3,4],[5,6,7,8],[9]]=>00010001=>[4,4,1]
[[1,2,3,4],[5,6,7],[8,9]]=>00010010=>[4,3,2]
[[1,2,3,4],[5,6,7],[8],[9]]=>00010011=>[4,3,1,1]
[[1,2,3,4],[5,6],[7,8],[9]]=>00010101=>[4,2,2,1]
[[1,2,3,4],[5,6],[7],[8],[9]]=>00010111=>[4,2,1,1,1]
[[1,2,3,4],[5],[6],[7],[8],[9]]=>00011111=>[4,1,1,1,1,1]
[[1,2,3],[4,5,6],[7,8,9]]=>00100100=>[3,3,3]
[[1,2,3],[4,5,6],[7,8],[9]]=>00100101=>[3,3,2,1]
[[1,2,3],[4,5,6],[7],[8],[9]]=>00100111=>[3,3,1,1,1]
[[1,2,3],[4,5],[6,7],[8,9]]=>00101010=>[3,2,2,2]
[[1,2,3],[4,5],[6,7],[8],[9]]=>00101011=>[3,2,2,1,1]
[[1,2,3],[4,5],[6],[7],[8],[9]]=>00101111=>[3,2,1,1,1,1]
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>00111111=>[3,1,1,1,1,1,1]
[[1,2],[3,4],[5,6],[7,8],[9]]=>01010101=>[2,2,2,2,1]
[[1,2],[3,4],[5,6],[7],[8],[9]]=>01010111=>[2,2,2,1,1,1]
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>01011111=>[2,2,1,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>01111111=>[2,1,1,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>11111111=>[1,1,1,1,1,1,1,1,1]
[[1,2,3,4,5,6,7,8,9,10]]=>000000000=>[10]
[[1,2,3,4,5,6,7,8,9],[10]]=>000000001=>[9,1]
[[1,2,3,4,5,6,7,8],[9,10]]=>000000010=>[8,2]
[[1,2,3,4,5,6,7,8],[9],[10]]=>000000011=>[8,1,1]
[[1,2,3,4,5,6,7],[8,9,10]]=>000000100=>[7,3]
[[1,2,3,4,5,6,7],[8,9],[10]]=>000000101=>[7,2,1]
[[1,2,3,4,5,6,7],[8],[9],[10]]=>000000111=>[7,1,1,1]
[[1,2,3,4,5,6],[7,8,9,10]]=>000001000=>[6,4]
[[1,2,3,4,5,6],[7,8,9],[10]]=>000001001=>[6,3,1]
[[1,2,3,4,5,6],[7,8],[9,10]]=>000001010=>[6,2,2]
[[1,2,3,4,5,6],[7,8],[9],[10]]=>000001011=>[6,2,1,1]
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>000001111=>[6,1,1,1,1]
[[1,2,3,4,5],[6,7,8,9],[10]]=>000010001=>[5,4,1]
[[1,2,3,4,5],[6,7,8],[9,10]]=>000010010=>[5,3,2]
[[1,2,3,4,5],[6,7,8],[9],[10]]=>000010011=>[5,3,1,1]
[[1,2,3,4,5],[6,7],[8,9],[10]]=>000010101=>[5,2,2,1]
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>000010111=>[5,2,1,1,1]
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>000011111=>[5,1,1,1,1,1]
[[1,2,3,4],[5,6,7,8],[9,10]]=>000100010=>[4,4,2]
[[1,2,3,4],[5,6,7,8],[9],[10]]=>000100011=>[4,4,1,1]
[[1,2,3,4],[5,6,7],[8,9,10]]=>000100100=>[4,3,3]
[[1,2,3,4],[5,6,7],[8,9],[10]]=>000100101=>[4,3,2,1]
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>000100111=>[4,3,1,1,1]
[[1,2,3,4],[5,6],[7,8],[9,10]]=>000101010=>[4,2,2,2]
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>000101011=>[4,2,2,1,1]
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>000101111=>[4,2,1,1,1,1]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>000111111=>[4,1,1,1,1,1,1]
[[1,2,3],[4,5,6],[7,8,9],[10]]=>001001001=>[3,3,3,1]
[[1,2,3],[4,5,6],[7,8],[9,10]]=>001001010=>[3,3,2,2]
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>001001011=>[3,3,2,1,1]
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>001001111=>[3,3,1,1,1,1]
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>001010101=>[3,2,2,2,1]
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>001010111=>[3,2,2,1,1,1]
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>001011111=>[3,2,1,1,1,1,1]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>001111111=>[3,1,1,1,1,1,1,1]
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>010101010=>[2,2,2,2,2]
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>010101011=>[2,2,2,2,1,1]
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>010101111=>[2,2,2,1,1,1,1]
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>010111111=>[2,2,1,1,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>011111111=>[2,1,1,1,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>111111111=>[1,1,1,1,1,1,1,1,1,1]
[[1,2,3,4,5],[6,7,8],[9,10,11]]=>0000100100=>[5,3,3]
[[1,2,3,4,5],[6,7,8],[9,10],[11]]=>0000100101=>[5,3,2,1]
[[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>0000100111=>[5,3,1,1,1]
[[1,2,3,4,5],[6,7],[8,9],[10,11]]=>0000101010=>[5,2,2,2]
[[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>0000101011=>[5,2,2,1,1]
[[1,2,3,4],[5,6,7,8],[9,10,11]]=>0001000100=>[4,4,3]
[[1,2,3,4],[5,6,7],[8,9],[10,11]]=>0001001010=>[4,3,2,2]
[[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>0001001011=>[4,3,2,1,1]
[[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>0001010101=>[4,2,2,2,1]
[[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>0010010011=>[3,3,3,1,1]
[[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>0010010101=>[3,3,2,2,1]
[[1,2,3,4,5,6,7,8,9,10,11,12]]=>00000000000=>[12]
[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>00000100010=>[6,4,2]
[[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>00001000100=>[5,4,3]
[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>00001010101=>[5,2,2,2,1]
[[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>00010001001=>[4,4,3,1]
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>00010001010=>[4,4,2,2]
[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>00010001011=>[4,4,2,1,1]
[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>00010010010=>[4,3,3,2]
[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>00010010101=>[4,3,2,2,1]
[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>00010101010=>[4,2,2,2,2]
[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>00100100101=>[3,3,3,2,1]
[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>00100101011=>[3,3,2,2,1,1]
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>01010101010=>[2,2,2,2,2,2]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>11111111111=>[1,1,1,1,1,1,1,1,1,1,1,1]
[[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>000010010011=>[5,3,3,1,1]
[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>000010010101=>[5,3,2,2,1]
[[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>000100010101=>[4,4,2,2,1]
[[1,3,4,5,6,7,8,9],[2]]=>10000000=>[1,8]
[[1,2,5,6,7,8,9],[3,4]]=>01000000=>[2,7]
[[1,4,5,6,7,8,9],[2],[3]]=>11000000=>[1,1,7]
[[1,2,3,7,8,9],[4,5,6]]=>00100000=>[3,6]
[[1,3,6,7,8,9],[2,5],[4]]=>10100000=>[1,2,6]
[[1,5,6,7,8,9],[2],[3],[4]]=>11100000=>[1,1,1,6]
[[1,2,3,4,9],[5,6,7,8]]=>00010000=>[4,5]
[[1,3,4,8,9],[2,6,7],[5]]=>10010000=>[1,3,5]
[[1,2,7,8,9],[3,4],[5,6]]=>01010000=>[2,2,5]
[[1,4,7,8,9],[2,6],[3],[5]]=>11010000=>[1,1,2,5]
[[1,6,7,8,9],[2],[3],[4],[5]]=>11110000=>[1,1,1,1,5]
[[1,3,4,5],[2,7,8,9],[6]]=>10001000=>[1,4,4]
[[1,2,5,9],[3,4,8],[6,7]]=>01001000=>[2,3,4]
[[1,4,5,9],[2,7,8],[3],[6]]=>11001000=>[1,1,3,4]
[[1,3,8,9],[2,5],[4,7],[6]]=>10101000=>[1,2,2,4]
[[1,5,8,9],[2,7],[3],[4],[6]]=>11101000=>[1,1,1,2,4]
[[1,7,8,9],[2],[3],[4],[5],[6]]=>11111000=>[1,1,1,1,1,4]
[[1,3,6],[2,5,9],[4,8],[7]]=>10100100=>[1,2,3,3]
[[1,5,6],[2,8,9],[3],[4],[7]]=>11100100=>[1,1,1,3,3]
[[1,2,9],[3,4],[5,6],[7,8]]=>01010100=>[2,2,2,3]
[[1,4,9],[2,6],[3,8],[5],[7]]=>11010100=>[1,1,2,2,3]
[[1,6,9],[2,8],[3],[4],[5],[7]]=>11110100=>[1,1,1,1,2,3]
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>11111100=>[1,1,1,1,1,1,3]
[[1,3],[2,5],[4,7],[6,9],[8]]=>10101010=>[1,2,2,2,2]
[[1,5],[2,7],[3,9],[4],[6],[8]]=>11101010=>[1,1,1,2,2,2]
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>11111010=>[1,1,1,1,1,2,2]
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>11111110=>[1,1,1,1,1,1,1,2]
[[1,3,4,5,6,7,8,9,10],[2]]=>100000000=>[1,9]
[[1,2,5,6,7,8,9,10],[3,4]]=>010000000=>[2,8]
[[1,4,5,6,7,8,9,10],[2],[3]]=>110000000=>[1,1,8]
[[1,2,3,7,8,9,10],[4,5,6]]=>001000000=>[3,7]
[[1,3,6,7,8,9,10],[2,5],[4]]=>101000000=>[1,2,7]
[[1,5,6,7,8,9,10],[2],[3],[4]]=>111000000=>[1,1,1,7]
[[1,2,3,4,9,10],[5,6,7,8]]=>000100000=>[4,6]
[[1,3,4,8,9,10],[2,6,7],[5]]=>100100000=>[1,3,6]
[[1,2,7,8,9,10],[3,4],[5,6]]=>010100000=>[2,2,6]
[[1,4,7,8,9,10],[2,6],[3],[5]]=>110100000=>[1,1,2,6]
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>111100000=>[1,1,1,1,6]
[[1,3,4,5,10],[2,7,8,9],[6]]=>100010000=>[1,4,5]
[[1,2,5,9,10],[3,4,8],[6,7]]=>010010000=>[2,3,5]
[[1,4,5,9,10],[2,7,8],[3],[6]]=>110010000=>[1,1,3,5]
[[1,3,8,9,10],[2,5],[4,7],[6]]=>101010000=>[1,2,2,5]
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>111010000=>[1,1,1,2,5]
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>111110000=>[1,1,1,1,1,5]
[[1,2,5,6],[3,4,9,10],[7,8]]=>010001000=>[2,4,4]
[[1,4,5,6],[2,8,9,10],[3],[7]]=>110001000=>[1,1,4,4]
[[1,2,3,10],[4,5,6],[7,8,9]]=>001001000=>[3,3,4]
[[1,3,6,10],[2,5,9],[4,8],[7]]=>101001000=>[1,2,3,4]
[[1,5,6,10],[2,8,9],[3],[4],[7]]=>111001000=>[1,1,1,3,4]
[[1,2,9,10],[3,4],[5,6],[7,8]]=>010101000=>[2,2,2,4]
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>110101000=>[1,1,2,2,4]
[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>111101000=>[1,1,1,1,2,4]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>111111000=>[1,1,1,1,1,1,4]
[[1,3,4],[2,6,7],[5,9,10],[8]]=>100100100=>[1,3,3,3]
[[1,2,7],[3,4,10],[5,6],[8,9]]=>010100100=>[2,2,3,3]
[[1,4,7],[2,6,10],[3,9],[5],[8]]=>110100100=>[1,1,2,3,3]
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>111100100=>[1,1,1,1,3,3]
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>101010100=>[1,2,2,2,3]
[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>111010100=>[1,1,1,2,2,3]
[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>111110100=>[1,1,1,1,1,2,3]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>111111100=>[1,1,1,1,1,1,1,3]
[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>110101010=>[1,1,2,2,2,2]
[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>111101010=>[1,1,1,1,2,2,2]
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>111111010=>[1,1,1,1,1,1,2,2]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>111111110=>[1,1,1,1,1,1,1,1,2]
[[1,2,5,6,11],[3,4,9,10],[7,8]]=>0100010000=>[2,4,5]
[[1,2,3,10,11],[4,5,6],[7,8,9]]=>0010010000=>[3,3,5]
[[1,5,6,10,11],[2,8,9],[3],[4],[7]]=>1110010000=>[1,1,1,3,5]
[[1,2,9,10,11],[3,4],[5,6],[7,8]]=>0101010000=>[2,2,2,5]
[[1,2,7,11],[3,4,10],[5,6],[8,9]]=>0101001000=>[2,2,3,4]
[[1,4,7,11],[2,6,10],[3,9],[5],[8]]=>1101001000=>[1,1,2,3,4]
[[1,3,10,11],[2,5],[4,7],[6,9],[8]]=>1010101000=>[1,2,2,2,4]
[[1,4,5],[2,7,8],[3,10,11],[6],[9]]=>1100100100=>[1,1,3,3,3]
[[1,3,8],[2,5,11],[4,7],[6,10],[9]]=>1010100100=>[1,2,2,3,3]
[[1,2,5,6,11,12],[3,4,9,10],[7,8]]=>01000100000=>[2,4,6]
[[1,2,3,7,12],[4,5,6,11],[8,9,10]]=>00100010000=>[3,4,5]
[[1,3,4,8],[2,6,7,12],[5,10,11],[9]]=>10010001000=>[1,3,4,4]
[[1,2,7,8],[3,4,11,12],[5,6],[9,10]]=>01010001000=>[2,2,4,4]
[[1,4,7,8],[2,6,11,12],[3,10],[5],[9]]=>11010001000=>[1,1,2,4,4]
[[1,2,5,12],[3,4,8],[6,7,11],[9,10]]=>01001001000=>[2,3,3,4]
[[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]=>10100100100=>[1,2,3,3,3]
[[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]]=>11010100100=>[1,1,2,2,3,3]
[[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]]=>110010010000=>[1,1,3,3,5]
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>11111101=>[1,1,1,1,1,1,2,1]
[[1,7],[2,8],[3,9],[4],[5],[6]]=>11111011=>[1,1,1,1,1,2,1,1]
[[1,7,9],[2,8],[3],[4],[5],[6]]=>11111010=>[1,1,1,1,1,2,2]
[[1,6],[2,7],[3,8],[4,9],[5]]=>11110111=>[1,1,1,1,2,1,1,1]
[[1,6,9],[2,7],[3,8],[4],[5]]=>11110110=>[1,1,1,1,2,1,2]
[[1,6,8],[2,7,9],[3],[4],[5]]=>11110101=>[1,1,1,1,2,2,1]
[[1,6,8,9],[2,7],[3],[4],[5]]=>11110100=>[1,1,1,1,2,3]
[[1,5,9],[2,6],[3,7],[4,8]]=>11101110=>[1,1,1,2,1,1,2]
[[1,5,8],[2,6,9],[3,7],[4]]=>11101101=>[1,1,1,2,1,2,1]
[[1,5,8,9],[2,6],[3,7],[4]]=>11101100=>[1,1,1,2,1,3]
[[1,5,7,9],[2,6,8],[3],[4]]=>11101010=>[1,1,1,2,2,2]
[[1,5,7,8,9],[2,6],[3],[4]]=>11101000=>[1,1,1,2,4]
[[1,4,7],[2,5,8],[3,6,9]]=>11011011=>[1,1,2,1,2,1,1]
[[1,4,7,9],[2,5,8],[3,6]]=>11011010=>[1,1,2,1,2,2]
[[1,4,7,8,9],[2,5],[3,6]]=>11011000=>[1,1,2,1,4]
[[1,4,6,8],[2,5,7,9],[3]]=>11010101=>[1,1,2,2,2,1]
[[1,4,6,8,9],[2,5,7],[3]]=>11010100=>[1,1,2,2,3]
[[1,4,6,7,8,9],[2,5],[3]]=>11010000=>[1,1,2,5]
[[1,3,5,7,9],[2,4,6,8]]=>10101010=>[1,2,2,2,2]
[[1,3,5,7,8,9],[2,4,6]]=>10101000=>[1,2,2,4]
[[1,3,5,6,7,8,9],[2,4]]=>10100000=>[1,2,6]
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>111111101=>[1,1,1,1,1,1,1,2,1]
[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>111111011=>[1,1,1,1,1,1,2,1,1]
[[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>111111010=>[1,1,1,1,1,1,2,2]
[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>111110111=>[1,1,1,1,1,2,1,1,1]
[[1,7,10],[2,8],[3,9],[4],[5],[6]]=>111110110=>[1,1,1,1,1,2,1,2]
[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>111110101=>[1,1,1,1,1,2,2,1]
[[1,7,9,10],[2,8],[3],[4],[5],[6]]=>111110100=>[1,1,1,1,1,2,3]
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>111101111=>[1,1,1,1,2,1,1,1,1]
[[1,6,10],[2,7],[3,8],[4,9],[5]]=>111101110=>[1,1,1,1,2,1,1,2]
[[1,6,9],[2,7,10],[3,8],[4],[5]]=>111101101=>[1,1,1,1,2,1,2,1]
[[1,6,9,10],[2,7],[3,8],[4],[5]]=>111101100=>[1,1,1,1,2,1,3]
[[1,6,8,10],[2,7,9],[3],[4],[5]]=>111101010=>[1,1,1,1,2,2,2]
[[1,6,8,9,10],[2,7],[3],[4],[5]]=>111101000=>[1,1,1,1,2,4]
[[1,5,9],[2,6,10],[3,7],[4,8]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,5,9,10],[2,6],[3,7],[4,8]]=>111011100=>[1,1,1,2,1,1,3]
[[1,5,8],[2,6,9],[3,7,10],[4]]=>111011011=>[1,1,1,2,1,2,1,1]
[[1,5,8,10],[2,6,9],[3,7],[4]]=>111011010=>[1,1,1,2,1,2,2]
[[1,5,8,9,10],[2,6],[3,7],[4]]=>111011000=>[1,1,1,2,1,4]
[[1,5,7,9],[2,6,8,10],[3],[4]]=>111010101=>[1,1,1,2,2,2,1]
[[1,5,7,9,10],[2,6,8],[3],[4]]=>111010100=>[1,1,1,2,2,3]
[[1,5,7,8,9,10],[2,6],[3],[4]]=>111010000=>[1,1,1,2,5]
[[1,4,7,10],[2,5,8],[3,6,9]]=>110110110=>[1,1,2,1,2,1,2]
[[1,4,7,9],[2,5,8,10],[3,6]]=>110110101=>[1,1,2,1,2,2,1]
[[1,4,7,9,10],[2,5,8],[3,6]]=>110110100=>[1,1,2,1,2,3]
[[1,4,7,8,9,10],[2,5],[3,6]]=>110110000=>[1,1,2,1,5]
[[1,4,6,8,10],[2,5,7,9],[3]]=>110101010=>[1,1,2,2,2,2]
[[1,4,6,8,9,10],[2,5,7],[3]]=>110101000=>[1,1,2,2,4]
[[1,4,6,7,8,9,10],[2,5],[3]]=>110100000=>[1,1,2,6]
[[1,3,5,7,9,10],[2,4,6,8]]=>101010100=>[1,2,2,2,3]
[[1,3,5,7,8,9,10],[2,4,6]]=>101010000=>[1,2,2,5]
[[1,3,5,6,7,8,9,10],[2,4]]=>101000000=>[1,2,7]
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>10111111=>[1,2,1,1,1,1,1,1]
[[1,4],[2,5],[3,6],[7],[8],[9]]=>11011111=>[1,1,2,1,1,1,1,1]
[[1,2,4],[3,5],[6],[7],[8],[9]]=>01011111=>[2,2,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4,8],[9]]=>11101111=>[1,1,1,2,1,1,1,1]
[[1,2,5],[3,6],[4,7],[8],[9]]=>01101111=>[2,1,2,1,1,1,1]
[[1,3,5],[2,4,6],[7],[8],[9]]=>10101111=>[1,2,2,1,1,1,1]
[[1,2,3,5],[4,6],[7],[8],[9]]=>00101111=>[3,2,1,1,1,1]
[[1,2,6],[3,7],[4,8],[5,9]]=>01110111=>[2,1,1,2,1,1,1]
[[1,3,6],[2,4,7],[5,8],[9]]=>10110111=>[1,2,1,2,1,1,1]
[[1,2,3,6],[4,7],[5,8],[9]]=>00110111=>[3,1,2,1,1,1]
[[1,2,4,6],[3,5,7],[8],[9]]=>01010111=>[2,2,2,1,1,1]
[[1,2,3,4,6],[5,7],[8],[9]]=>00010111=>[4,2,1,1,1]
[[1,2,4,7],[3,5,8],[6,9]]=>01011011=>[2,2,1,2,1,1]
[[1,2,3,4,7],[5,8],[6,9]]=>00011011=>[4,1,2,1,1]
[[1,3,5,7],[2,4,6,8],[9]]=>10101011=>[1,2,2,2,1,1]
[[1,2,3,5,7],[4,6,8],[9]]=>00101011=>[3,2,2,1,1]
[[1,2,3,4,5,7],[6,8],[9]]=>00001011=>[5,2,1,1]
[[1,2,4,6,8],[3,5,7,9]]=>01010101=>[2,2,2,2,1]
[[1,2,3,4,6,8],[5,7,9]]=>00010101=>[4,2,2,1]
[[1,2,3,4,5,6,8],[7,9]]=>00000101=>[6,2,1]
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>101111111=>[1,2,1,1,1,1,1,1,1]
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>110111111=>[1,1,2,1,1,1,1,1,1]
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>010111111=>[2,2,1,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>111011111=>[1,1,1,2,1,1,1,1,1]
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>011011111=>[2,1,2,1,1,1,1,1]
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>101011111=>[1,2,2,1,1,1,1,1]
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>001011111=>[3,2,1,1,1,1,1]
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>011101111=>[2,1,1,2,1,1,1,1]
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>101101111=>[1,2,1,2,1,1,1,1]
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>001101111=>[3,1,2,1,1,1,1]
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>010101111=>[2,2,2,1,1,1,1]
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>000101111=>[4,2,1,1,1,1]
[[1,3,7],[2,4,8],[5,9],[6,10]]=>101110111=>[1,2,1,1,2,1,1,1]
[[1,2,3,7],[4,8],[5,9],[6,10]]=>001110111=>[3,1,1,2,1,1,1]
[[1,4,7],[2,5,8],[3,6,9],[10]]=>110110111=>[1,1,2,1,2,1,1,1]
[[1,2,4,7],[3,5,8],[6,9],[10]]=>010110111=>[2,2,1,2,1,1,1]
[[1,2,3,4,7],[5,8],[6,9],[10]]=>000110111=>[4,1,2,1,1,1]
[[1,3,5,7],[2,4,6,8],[9],[10]]=>101010111=>[1,2,2,2,1,1,1]
[[1,2,3,5,7],[4,6,8],[9],[10]]=>001010111=>[3,2,2,1,1,1]
[[1,2,3,4,5,7],[6,8],[9],[10]]=>000010111=>[5,2,1,1,1]
[[1,2,5,8],[3,6,9],[4,7,10]]=>011011011=>[2,1,2,1,2,1,1]
[[1,3,5,8],[2,4,6,9],[7,10]]=>101011011=>[1,2,2,1,2,1,1]
[[1,2,3,5,8],[4,6,9],[7,10]]=>001011011=>[3,2,1,2,1,1]
[[1,2,3,4,5,8],[6,9],[7,10]]=>000011011=>[5,1,2,1,1]
[[1,2,4,6,8],[3,5,7,9],[10]]=>010101011=>[2,2,2,2,1,1]
[[1,2,3,4,6,8],[5,7,9],[10]]=>000101011=>[4,2,2,1,1]
[[1,2,3,4,5,6,8],[7,9],[10]]=>000001011=>[6,2,1,1]
[[1,2,3,5,7,9],[4,6,8,10]]=>001010101=>[3,2,2,2,1]
[[1,2,3,4,5,7,9],[6,8,10]]=>000010101=>[5,2,2,1]
[[1,2,3,4,5,6,7,9],[8,10]]=>000000101=>[7,2,1]
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>010101101=>[2,2,2,1,2,1]
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>010110110=>[2,2,1,2,1,2]
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>010110101=>[2,2,1,2,2,1]
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>010111011=>[2,2,1,1,2,1,1]
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>011011010=>[2,1,2,1,2,2]
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>011011101=>[2,1,2,1,1,2,1]
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>011010110=>[2,1,2,2,1,2]
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>011010101=>[2,1,2,2,2,1]
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>011011011=>[2,1,2,1,2,1,1]
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>011101110=>[2,1,1,2,1,1,2]
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>011101101=>[2,1,1,2,1,2,1]
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>011101011=>[2,1,1,2,2,1,1]
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>011110111=>[2,1,1,1,2,1,1,1]
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>101101010=>[1,2,1,2,2,2]
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>101101101=>[1,2,1,2,1,2,1]
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>101110110=>[1,2,1,1,2,1,2]
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>101110101=>[1,2,1,1,2,2,1]
[[1,3],[2,4],[5,8],[6,9],[7,10]]=>101111011=>[1,2,1,1,1,2,1,1]
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>101011010=>[1,2,2,1,2,2]
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>101011101=>[1,2,2,1,1,2,1]
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>101010110=>[1,2,2,2,1,2]
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>101010101=>[1,2,2,2,2,1]
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>101011011=>[1,2,2,1,2,1,1]
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>101101110=>[1,2,1,2,1,1,2]
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>101101101=>[1,2,1,2,1,2,1]
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>101101011=>[1,2,1,2,2,1,1]
[[1,3],[2,7],[4,8],[5,9],[6,10]]=>101110111=>[1,2,1,1,2,1,1,1]
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>110111010=>[1,1,2,1,1,2,2]
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>110111101=>[1,1,2,1,1,1,2,1]
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>110110110=>[1,1,2,1,2,1,2]
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>110110101=>[1,1,2,1,2,2,1]
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>110111011=>[1,1,2,1,1,2,1,1]
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>110101110=>[1,1,2,2,1,1,2]
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>110101101=>[1,1,2,2,1,2,1]
[[1,4],[2,6],[3,8],[5,9],[7,10]]=>110101011=>[1,1,2,2,2,1,1]
[[1,4],[2,7],[3,8],[5,9],[6,10]]=>110110111=>[1,1,2,1,2,1,1,1]
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>111011110=>[1,1,1,2,1,1,1,2]
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>111011011=>[1,1,1,2,1,2,1,1]
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>111010111=>[1,1,1,2,2,1,1,1]
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>01010101101=>[2,2,2,2,1,2,1]
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>01010110110=>[2,2,2,1,2,1,2]
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>01010110101=>[2,2,2,1,2,2,1]
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>01010111011=>[2,2,2,1,1,2,1,1]
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>01011011010=>[2,2,1,2,1,2,2]
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>01011011101=>[2,2,1,2,1,1,2,1]
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>01011010110=>[2,2,1,2,2,1,2]
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>01011010101=>[2,2,1,2,2,2,1]
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>01011011011=>[2,2,1,2,1,2,1,1]
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>01011101110=>[2,2,1,1,2,1,1,2]
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>01011101101=>[2,2,1,1,2,1,2,1]
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>01011101011=>[2,2,1,1,2,2,1,1]
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>01011110111=>[2,2,1,1,1,2,1,1,1]
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>01101101010=>[2,1,2,1,2,2,2]
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>01101101101=>[2,1,2,1,2,1,2,1]
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>01101110110=>[2,1,2,1,1,2,1,2]
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>01101110101=>[2,1,2,1,1,2,2,1]
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>01101111011=>[2,1,2,1,1,1,2,1,1]
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>01101011010=>[2,1,2,2,1,2,2]
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>01101011101=>[2,1,2,2,1,1,2,1]
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>01101010110=>[2,1,2,2,2,1,2]
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>01101010101=>[2,1,2,2,2,2,1]
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>01101011011=>[2,1,2,2,1,2,1,1]
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>01101101110=>[2,1,2,1,2,1,1,2]
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>01101101101=>[2,1,2,1,2,1,2,1]
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>01101101011=>[2,1,2,1,2,2,1,1]
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>01101110111=>[2,1,2,1,1,2,1,1,1]
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>01110111010=>[2,1,1,2,1,1,2,2]
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>01110111101=>[2,1,1,2,1,1,1,2,1]
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>01110110110=>[2,1,1,2,1,2,1,2]
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>01110110101=>[2,1,1,2,1,2,2,1]
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>01110111011=>[2,1,1,2,1,1,2,1,1]
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>01110101110=>[2,1,1,2,2,1,1,2]
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>01110101101=>[2,1,1,2,2,1,2,1]
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>01110101011=>[2,1,1,2,2,2,1,1]
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>01110110111=>[2,1,1,2,1,2,1,1,1]
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>01111011110=>[2,1,1,1,2,1,1,1,2]
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>01111011101=>[2,1,1,1,2,1,1,2,1]
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>01111011011=>[2,1,1,1,2,1,2,1,1]
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>01111010111=>[2,1,1,1,2,2,1,1,1]
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>01111101111=>[2,1,1,1,1,2,1,1,1,1]
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>10110101010=>[1,2,1,2,2,2,2]
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>10110101101=>[1,2,1,2,2,1,2,1]
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>10110110110=>[1,2,1,2,1,2,1,2]
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>10110110101=>[1,2,1,2,1,2,2,1]
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>10110111011=>[1,2,1,2,1,1,2,1,1]
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>10111011010=>[1,2,1,1,2,1,2,2]
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>10111011101=>[1,2,1,1,2,1,1,2,1]
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>10111010110=>[1,2,1,1,2,2,1,2]
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>10111010101=>[1,2,1,1,2,2,2,1]
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>10111011011=>[1,2,1,1,2,1,2,1,1]
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>10111101110=>[1,2,1,1,1,2,1,1,2]
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>10111101101=>[1,2,1,1,1,2,1,2,1]
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>10111101011=>[1,2,1,1,1,2,2,1,1]
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>10111110111=>[1,2,1,1,1,1,2,1,1,1]
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>10101101010=>[1,2,2,1,2,2,2]
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>10101101101=>[1,2,2,1,2,1,2,1]
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>10101110110=>[1,2,2,1,1,2,1,2]
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>10101110101=>[1,2,2,1,1,2,2,1]
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>10101111011=>[1,2,2,1,1,1,2,1,1]
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>10101011010=>[1,2,2,2,1,2,2]
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>10101011101=>[1,2,2,2,1,1,2,1]
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>10101010110=>[1,2,2,2,2,1,2]
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>10101010101=>[1,2,2,2,2,2,1]
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>10101011011=>[1,2,2,2,1,2,1,1]
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>10101101110=>[1,2,2,1,2,1,1,2]
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>10101101101=>[1,2,2,1,2,1,2,1]
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>10101101011=>[1,2,2,1,2,2,1,1]
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>10101110111=>[1,2,2,1,1,2,1,1,1]
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>10110111010=>[1,2,1,2,1,1,2,2]
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>10110111101=>[1,2,1,2,1,1,1,2,1]
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>10110110110=>[1,2,1,2,1,2,1,2]
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>10110110101=>[1,2,1,2,1,2,2,1]
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>10110111011=>[1,2,1,2,1,1,2,1,1]
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>10110101110=>[1,2,1,2,2,1,1,2]
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>10110101101=>[1,2,1,2,2,1,2,1]
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>10110101011=>[1,2,1,2,2,2,1,1]
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>10110110111=>[1,2,1,2,1,2,1,1,1]
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>10111011110=>[1,2,1,1,2,1,1,1,2]
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>10111011101=>[1,2,1,1,2,1,1,2,1]
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>10111011011=>[1,2,1,1,2,1,2,1,1]
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>10111010111=>[1,2,1,1,2,2,1,1,1]
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>10111101111=>[1,2,1,1,1,2,1,1,1,1]
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>11011101010=>[1,1,2,1,1,2,2,2]
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>11011101101=>[1,1,2,1,1,2,1,2,1]
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>11011110110=>[1,1,2,1,1,1,2,1,2]
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>11011110101=>[1,1,2,1,1,1,2,2,1]
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>11011111011=>[1,1,2,1,1,1,1,2,1,1]
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>11011011010=>[1,1,2,1,2,1,2,2]
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>11011011101=>[1,1,2,1,2,1,1,2,1]
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>11011010110=>[1,1,2,1,2,2,1,2]
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>11011010101=>[1,1,2,1,2,2,2,1]
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>11011011011=>[1,1,2,1,2,1,2,1,1]
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>11011101110=>[1,1,2,1,1,2,1,1,2]
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>11011101101=>[1,1,2,1,1,2,1,2,1]
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>11011101011=>[1,1,2,1,1,2,2,1,1]
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>11011110111=>[1,1,2,1,1,1,2,1,1,1]
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>11010111010=>[1,1,2,2,1,1,2,2]
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>11010111101=>[1,1,2,2,1,1,1,2,1]
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>11010110110=>[1,1,2,2,1,2,1,2]
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>11010110101=>[1,1,2,2,1,2,2,1]
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>11010111011=>[1,1,2,2,1,1,2,1,1]
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>11010101110=>[1,1,2,2,2,1,1,2]
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>11010101101=>[1,1,2,2,2,1,2,1]
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>11010101011=>[1,1,2,2,2,2,1,1]
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>11010110111=>[1,1,2,2,1,2,1,1,1]
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>11011011110=>[1,1,2,1,2,1,1,1,2]
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>11011011101=>[1,1,2,1,2,1,1,2,1]
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>11011011011=>[1,1,2,1,2,1,2,1,1]
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>11011010111=>[1,1,2,1,2,2,1,1,1]
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>11011101111=>[1,1,2,1,1,2,1,1,1,1]
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>11101111010=>[1,1,1,2,1,1,1,2,2]
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>11101111101=>[1,1,1,2,1,1,1,1,2,1]
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>11101110110=>[1,1,1,2,1,1,2,1,2]
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>11101110101=>[1,1,1,2,1,1,2,2,1]
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>11101111011=>[1,1,1,2,1,1,1,2,1,1]
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>11101101110=>[1,1,1,2,1,2,1,1,2]
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>11101101101=>[1,1,1,2,1,2,1,2,1]
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>11101101011=>[1,1,1,2,1,2,2,1,1]
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>11101110111=>[1,1,1,2,1,1,2,1,1,1]
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>11101011110=>[1,1,1,2,2,1,1,1,2]
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>11101011101=>[1,1,1,2,2,1,1,2,1]
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>11101011011=>[1,1,1,2,2,1,2,1,1]
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>11101010111=>[1,1,1,2,2,2,1,1,1]
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>11101101111=>[1,1,1,2,1,2,1,1,1,1]
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>11110111110=>[1,1,1,1,2,1,1,1,1,2]
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>11110111101=>[1,1,1,1,2,1,1,1,2,1]
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>11110111011=>[1,1,1,1,2,1,1,2,1,1]
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>11110110111=>[1,1,1,1,2,1,2,1,1,1]
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>11110101111=>[1,1,1,1,2,2,1,1,1,1]
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>11111011111=>[1,1,1,1,1,2,1,1,1,1,1]
[[1,2,3,4,5,6,7,9],[8]]=>00000010=>[7,2]
[[1,2,3,4,5,6,9],[7,8]]=>00000100=>[6,3]
[[1,2,3,4,5,6,9],[7],[8]]=>00000110=>[6,1,2]
[[1,2,3,4,5,9],[6,7,8]]=>00001000=>[5,4]
[[1,2,3,4,5,9],[6,7],[8]]=>00001010=>[5,2,2]
[[1,2,3,4,5,9],[6],[7],[8]]=>00001110=>[5,1,1,2]
[[1,2,3,4,9],[5,6,7],[8]]=>00010010=>[4,3,2]
[[1,2,3,4,9],[5,6],[7,8]]=>00010100=>[4,2,3]
[[1,2,3,4,9],[5,6],[7],[8]]=>00010110=>[4,2,1,2]
[[1,2,3,4,9],[5],[6],[7],[8]]=>00011110=>[4,1,1,1,2]
[[1,2,3,7],[4,5,6,9],[8]]=>00100010=>[3,4,2]
[[1,2,3,9],[4,5,6],[7,8]]=>00100100=>[3,3,3]
[[1,2,3,9],[4,5,6],[7],[8]]=>00100110=>[3,3,1,2]
[[1,2,3,9],[4,5],[6,7],[8]]=>00101010=>[3,2,2,2]
[[1,2,3,9],[4,5],[6],[7],[8]]=>00101110=>[3,2,1,1,2]
[[1,2,3,9],[4],[5],[6],[7],[8]]=>00111110=>[3,1,1,1,1,2]
[[1,2,5],[3,4,8],[6,7,9]]=>01001001=>[2,3,3,1]
[[1,2,5],[3,4,9],[6,7],[8]]=>01001010=>[2,3,2,2]
[[1,2,5],[3,4,9],[6],[7],[8]]=>01001110=>[2,3,1,1,2]
[[1,2,9],[3,4],[5,6],[7],[8]]=>01010110=>[2,2,2,1,2]
[[1,2,9],[3,4],[5],[6],[7],[8]]=>01011110=>[2,2,1,1,1,2]
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>01111110=>[2,1,1,1,1,1,2]
[[1,3],[2,5],[4,9],[6],[7],[8]]=>10101110=>[1,2,2,1,1,2]
[[1,3],[2,9],[4],[5],[6],[7],[8]]=>10111110=>[1,2,1,1,1,1,2]
[[1,2,3,4,5,6,7,8,10],[9]]=>000000010=>[8,2]
[[1,2,3,4,5,6,7,10],[8,9]]=>000000100=>[7,3]
[[1,2,3,4,5,6,7,10],[8],[9]]=>000000110=>[7,1,2]
[[1,2,3,4,5,6,10],[7,8,9]]=>000001000=>[6,4]
[[1,2,3,4,5,6,10],[7,8],[9]]=>000001010=>[6,2,2]
[[1,2,3,4,5,6,10],[7],[8],[9]]=>000001110=>[6,1,1,2]
[[1,2,3,4,5,10],[6,7,8,9]]=>000010000=>[5,5]
[[1,2,3,4,5,10],[6,7,8],[9]]=>000010010=>[5,3,2]
[[1,2,3,4,5,10],[6,7],[8,9]]=>000010100=>[5,2,3]
[[1,2,3,4,5,10],[6,7],[8],[9]]=>000010110=>[5,2,1,2]
[[1,2,3,4,5,10],[6],[7],[8],[9]]=>000011110=>[5,1,1,1,2]
[[1,2,3,4,10],[5,6,7,8],[9]]=>000100010=>[4,4,2]
[[1,2,3,4,10],[5,6,7],[8,9]]=>000100100=>[4,3,3]
[[1,2,3,4,10],[5,6,7],[8],[9]]=>000100110=>[4,3,1,2]
[[1,2,3,4,10],[5,6],[7,8],[9]]=>000101010=>[4,2,2,2]
[[1,2,3,4,10],[5,6],[7],[8],[9]]=>000101110=>[4,2,1,1,2]
[[1,2,3,4,10],[5],[6],[7],[8],[9]]=>000111110=>[4,1,1,1,1,2]
[[1,2,3,7],[4,5,6,10],[8,9]]=>001000100=>[3,4,3]
[[1,2,3,7],[4,5,6,10],[8],[9]]=>001000110=>[3,4,1,2]
[[1,2,3,10],[4,5,6],[7,8],[9]]=>001001010=>[3,3,2,2]
[[1,2,3,10],[4,5,6],[7],[8],[9]]=>001001110=>[3,3,1,1,2]
[[1,2,3,10],[4,5],[6,7],[8,9]]=>001010100=>[3,2,2,3]
[[1,2,3,10],[4,5],[6,7],[8],[9]]=>001010110=>[3,2,2,1,2]
[[1,2,3,10],[4,5],[6],[7],[8],[9]]=>001011110=>[3,2,1,1,1,2]
[[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>001111110=>[3,1,1,1,1,1,2]
[[1,2,5],[3,4,8],[6,7,10],[9]]=>010010010=>[2,3,3,2]
[[1,2,5],[3,4,10],[6,7],[8,9]]=>010010100=>[2,3,2,3]
[[1,2,5],[3,4,10],[6,7],[8],[9]]=>010010110=>[2,3,2,1,2]
[[1,2,5],[3,4,10],[6],[7],[8],[9]]=>010011110=>[2,3,1,1,1,2]
[[1,2,10],[3,4],[5,6],[7,8],[9]]=>010101010=>[2,2,2,2,2]
[[1,2,10],[3,4],[5,6],[7],[8],[9]]=>010101110=>[2,2,2,1,1,2]
[[1,2,10],[3,4],[5],[6],[7],[8],[9]]=>010111110=>[2,2,1,1,1,1,2]
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>011111110=>[2,1,1,1,1,1,1,2]
[[1,3],[2,5],[4,7],[6,10],[8],[9]]=>101010110=>[1,2,2,2,1,2]
[[1,3],[2,5],[4,10],[6],[7],[8],[9]]=>101011110=>[1,2,2,1,1,1,2]
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>101111110=>[1,2,1,1,1,1,1,2]
[]=>=>[1]
[[1,2,4,5,6,7,8,9],[3]]=>01000000=>[2,7]
[[1,3,4,6,7,8,9],[2,5]]=>10010000=>[1,3,5]
[[1,3,5,6,7,8,9],[2],[4]]=>10100000=>[1,2,6]
[[1,3,5,6,8,9],[2,4,7]]=>10100100=>[1,2,3,3]
[[1,2,4,7,8,9],[3,5],[6]]=>01011000=>[2,2,1,4]
[[1,4,6,7,8,9],[2],[3],[5]]=>11010000=>[1,1,2,5]
[[1,3,5,7,8],[2,4,6,9]]=>10101001=>[1,2,2,3,1]
[[1,2,5,7,9],[3,6,8],[4]]=>01101010=>[2,1,2,2,2]
[[1,4,6,8,9],[2,5],[3,7]]=>11010100=>[1,1,2,2,3]
[[1,3,5,8,9],[2,6],[4],[7]]=>10101100=>[1,2,2,1,3]
[[1,5,7,8,9],[2],[3],[4],[6]]=>11101000=>[1,1,1,2,4]
[[1,2,5,6],[3,7,8,9],[4]]=>01100100=>[2,1,3,3]
[[1,3,4,7],[2,6,8],[5,9]]=>10010011=>[1,3,3,1,1]
[[1,3,6,8],[2,7,9],[4],[5]]=>10110101=>[1,2,1,2,2,1]
[[1,2,6,9],[3,4],[5,7],[8]]=>01010110=>[2,2,2,1,2]
[[1,4,6,9],[2,7],[3],[5],[8]]=>11010110=>[1,1,2,2,1,2]
[[1,6,8,9],[2],[3],[4],[5],[7]]=>11110100=>[1,1,1,1,2,3]
[[1,2,4],[3,5,7],[6,8],[9]]=>01011011=>[2,2,1,2,1,1]
[[1,4,7],[2,8,9],[3],[5],[6]]=>11011010=>[1,1,2,1,2,2]
[[1,5,8],[2,6],[3,7],[4,9]]=>11101101=>[1,1,1,2,1,2,1]
[[1,3,7],[2,5],[4,8],[6],[9]]=>10101011=>[1,2,2,2,1,1]
[[1,5,7],[2,8],[3],[4],[6],[9]]=>11101011=>[1,1,1,2,2,1,1]
[[1,7,9],[2],[3],[4],[5],[6],[8]]=>11111010=>[1,1,1,1,1,2,2]
[[1,4],[2,6],[3,8],[5],[7],[9]]=>11010101=>[1,1,2,2,2,1]
[[1,6],[2,8],[3],[4],[5],[7],[9]]=>11110101=>[1,1,1,1,2,2,1]
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>11111101=>[1,1,1,1,1,1,2,1]
[[1,2,4,5,6,7,8,9,10],[3]]=>010000000=>[2,8]
[[1,3,4,6,7,8,9,10],[2,5]]=>100100000=>[1,3,6]
[[1,3,5,6,7,8,9,10],[2],[4]]=>101000000=>[1,2,7]
[[1,3,5,6,8,9,10],[2,4,7]]=>101001000=>[1,2,3,4]
[[1,2,4,7,8,9,10],[3,5],[6]]=>010110000=>[2,2,1,5]
[[1,4,6,7,8,9,10],[2],[3],[5]]=>110100000=>[1,1,2,6]
[[1,3,5,7,8,10],[2,4,6,9]]=>101010010=>[1,2,2,3,2]
[[1,2,5,7,9,10],[3,6,8],[4]]=>011010100=>[2,1,2,2,3]
[[1,4,6,8,9,10],[2,5],[3,7]]=>110101000=>[1,1,2,2,4]
[[1,3,5,8,9,10],[2,6],[4],[7]]=>101011000=>[1,2,2,1,4]
[[1,5,7,8,9,10],[2],[3],[4],[6]]=>111010000=>[1,1,1,2,5]
[[1,2,5,6,9],[3,7,8,10],[4]]=>011001001=>[2,1,3,3,1]
[[1,3,4,7,10],[2,6,8],[5,9]]=>100100110=>[1,3,3,1,2]
[[1,3,6,8,10],[2,7,9],[4],[5]]=>101101010=>[1,2,1,2,2,2]
[[1,2,6,9,10],[3,4],[5,7],[8]]=>010101100=>[2,2,2,1,3]
[[1,4,6,9,10],[2,7],[3],[5],[8]]=>110101100=>[1,1,2,2,1,3]
[[1,6,8,9,10],[2],[3],[4],[5],[7]]=>111101000=>[1,1,1,1,2,4]
[[1,3,4,8],[2,6,9,10],[5,7]]=>100101010=>[1,3,2,2,2]
[[1,3,6,7],[2,8,9,10],[4],[5]]=>101100100=>[1,2,1,3,3]
[[1,4,7,9],[2,5,8],[3,6,10]]=>110110101=>[1,1,2,1,2,2,1]
[[1,4,7,9],[2,8,10],[3],[5],[6]]=>110110101=>[1,1,2,1,2,2,1]
[[1,5,8,10],[2,6],[3,7],[4,9]]=>111011010=>[1,1,1,2,1,2,2]
[[1,3,7,10],[2,5],[4,8],[6],[9]]=>101010110=>[1,2,2,2,1,2]
[[1,5,7,10],[2,8],[3],[4],[6],[9]]=>111010110=>[1,1,1,2,2,1,2]
[[1,7,9,10],[2],[3],[4],[5],[6],[8]]=>111110100=>[1,1,1,1,1,2,3]
[[1,2,5],[3,7,8],[4,9,10],[6]]=>011010010=>[2,1,2,3,2]
[[1,4,6],[2,5,9],[3,8],[7,10]]=>110101001=>[1,1,2,2,3,1]
[[1,3,5],[2,6,8],[4,9],[7],[10]]=>101011011=>[1,2,2,1,2,1,1]
[[1,5,8],[2,9,10],[3],[4],[6],[7]]=>111011010=>[1,1,1,2,1,2,2]
[[1,2,8],[3,4],[5,6],[7,9],[10]]=>010101011=>[2,2,2,2,1,1]
[[1,4,8],[2,6],[3,9],[5],[7],[10]]=>110101011=>[1,1,2,2,2,1,1]
[[1,6,8],[2,9],[3],[4],[5],[7],[10]]=>111101011=>[1,1,1,1,2,2,1,1]
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>111111010=>[1,1,1,1,1,1,2,2]
[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>101010101=>[1,2,2,2,2,1]
[[1,5],[2,7],[3,9],[4],[6],[8],[10]]=>111010101=>[1,1,1,2,2,2,1]
[[1,7],[2,9],[3],[4],[5],[6],[8],[10]]=>111110101=>[1,1,1,1,1,2,2,1]
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>111111101=>[1,1,1,1,1,1,1,2,1]
[[1,3,4,5,6,7,8],[2,9]]=>10000001=>[1,7,1]
[[1,3,4,5,6,7,8],[2],[9]]=>10000001=>[1,7,1]
[[1,3,4,5,6,7],[2,8,9]]=>10000010=>[1,6,2]
[[1,3,4,5,6,7],[2,9],[8]]=>10000010=>[1,6,2]
[[1,3,4,5,6,7],[2],[8],[9]]=>10000011=>[1,6,1,1]
[[1,3,4,5,6],[2,7,8,9]]=>10000100=>[1,5,3]
[[1,3,4,5,6],[2,8,9],[7]]=>10000100=>[1,5,3]
[[1,3,4,5,6],[2,8],[7,9]]=>10000101=>[1,5,2,1]
[[1,3,4,5,6],[2,8],[7],[9]]=>10000101=>[1,5,2,1]
[[1,3,4,5,6],[2],[7],[8],[9]]=>10000111=>[1,5,1,1,1]
[[1,3,4,5],[2,7,8],[6,9]]=>10001001=>[1,4,3,1]
[[1,3,4,5],[2,7,8],[6],[9]]=>10001001=>[1,4,3,1]
[[1,3,4,5],[2,7],[6,9],[8]]=>10001010=>[1,4,2,2]
[[1,3,4,5],[2,7],[6],[8],[9]]=>10001011=>[1,4,2,1,1]
[[1,3,4,5],[2],[6],[7],[8],[9]]=>10001111=>[1,4,1,1,1,1]
[[1,3,4],[2,6,7],[5,8,9]]=>10010010=>[1,3,3,2]
[[1,3,4],[2,6,7],[5,9],[8]]=>10010010=>[1,3,3,2]
[[1,3,4],[2,6,7],[5],[8],[9]]=>10010011=>[1,3,3,1,1]
[[1,3,4],[2,6],[5,8],[7,9]]=>10010101=>[1,3,2,2,1]
[[1,3,4],[2,6],[5,8],[7],[9]]=>10010101=>[1,3,2,2,1]
[[1,3,4],[2,6],[5],[7],[8],[9]]=>10010111=>[1,3,2,1,1,1]
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>10011111=>[1,3,1,1,1,1,1]
[[1,3],[2,5],[4,7],[6],[8],[9]]=>10101011=>[1,2,2,2,1,1]
[[1,3],[2,5],[4],[6],[7],[8],[9]]=>10101111=>[1,2,2,1,1,1,1]
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>10111111=>[1,2,1,1,1,1,1,1]
[[1,3,4,5,6,7,8,9],[2,10]]=>100000001=>[1,8,1]
[[1,3,4,5,6,7,8,9],[2],[10]]=>100000001=>[1,8,1]
[[1,3,4,5,6,7,8],[2,9,10]]=>100000010=>[1,7,2]
[[1,3,4,5,6,7,8],[2,10],[9]]=>100000010=>[1,7,2]
[[1,3,4,5,6,7,8],[2],[9],[10]]=>100000011=>[1,7,1,1]
[[1,3,4,5,6,7],[2,8,9,10]]=>100000100=>[1,6,3]
[[1,3,4,5,6,7],[2,9,10],[8]]=>100000100=>[1,6,3]
[[1,3,4,5,6,7],[2,9],[8,10]]=>100000101=>[1,6,2,1]
[[1,3,4,5,6,7],[2,9],[8],[10]]=>100000101=>[1,6,2,1]
[[1,3,4,5,6,7],[2],[8],[9],[10]]=>100000111=>[1,6,1,1,1]
[[1,3,4,5,6],[2,8,9,10],[7]]=>100001000=>[1,5,4]
[[1,3,4,5,6],[2,8,9],[7,10]]=>100001001=>[1,5,3,1]
[[1,3,4,5,6],[2,8,9],[7],[10]]=>100001001=>[1,5,3,1]
[[1,3,4,5,6],[2,8],[7,10],[9]]=>100001010=>[1,5,2,2]
[[1,3,4,5,6],[2,8],[7],[9],[10]]=>100001011=>[1,5,2,1,1]
[[1,3,4,5,6],[2],[7],[8],[9],[10]]=>100001111=>[1,5,1,1,1,1]
[[1,3,4,5],[2,7,8,9],[6,10]]=>100010001=>[1,4,4,1]
[[1,3,4,5],[2,7,8,9],[6],[10]]=>100010001=>[1,4,4,1]
[[1,3,4,5],[2,7,8],[6,9,10]]=>100010010=>[1,4,3,2]
[[1,3,4,5],[2,7,8],[6,10],[9]]=>100010010=>[1,4,3,2]
[[1,3,4,5],[2,7,8],[6],[9],[10]]=>100010011=>[1,4,3,1,1]
[[1,3,4,5],[2,7],[6,9],[8,10]]=>100010101=>[1,4,2,2,1]
[[1,3,4,5],[2,7],[6,9],[8],[10]]=>100010101=>[1,4,2,2,1]
[[1,3,4,5],[2,7],[6],[8],[9],[10]]=>100010111=>[1,4,2,1,1,1]
[[1,3,4,5],[2],[6],[7],[8],[9],[10]]=>100011111=>[1,4,1,1,1,1,1]
[[1,3,4],[2,6,7],[5,9],[8,10]]=>100100101=>[1,3,3,2,1]
[[1,3,4],[2,6,7],[5,9],[8],[10]]=>100100101=>[1,3,3,2,1]
[[1,3,4],[2,6,7],[5],[8],[9],[10]]=>100100111=>[1,3,3,1,1,1]
[[1,3,4],[2,6],[5,8],[7,10],[9]]=>100101010=>[1,3,2,2,2]
[[1,3,4],[2,6],[5,8],[7],[9],[10]]=>100101011=>[1,3,2,2,1,1]
[[1,3,4],[2,6],[5],[7],[8],[9],[10]]=>100101111=>[1,3,2,1,1,1,1]
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>100111111=>[1,3,1,1,1,1,1,1]
[[1,3],[2,5],[4,7],[6],[8],[9],[10]]=>101010111=>[1,2,2,2,1,1,1]
[[1,3],[2,5],[4],[6],[7],[8],[9],[10]]=>101011111=>[1,2,2,1,1,1,1,1]
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>101111111=>[1,2,1,1,1,1,1,1,1]
[[1,2,4,6,8,10],[3,5,7,9]]=>010101010=>[2,2,2,2,2]
[[1,2,4,6,8,9,10],[3,5,7]]=>010101000=>[2,2,2,4]
[[1,2,4,6,7,8,10],[3,5,9]]=>010100010=>[2,2,4,2]
[[1,2,4,6,7,9,10],[3,5,8]]=>010100100=>[2,2,3,3]
[[1,2,4,6,7,8,9,10],[3,5]]=>010100000=>[2,2,6]
[[1,2,4,5,6,8,10],[3,7,9]]=>010001010=>[2,4,2,2]
[[1,2,4,5,6,9,10],[3,7,8]]=>010001000=>[2,4,4]
[[1,2,4,5,7,8,10],[3,6,9]]=>010010010=>[2,3,3,2]
[[1,2,4,5,7,9,10],[3,6,8]]=>010010100=>[2,3,2,3]
[[1,2,4,5,7,8,9,10],[3,6]]=>010010000=>[2,3,5]
[[1,2,4,5,6,7,8,10],[3,9]]=>010000010=>[2,6,2]
[[1,2,4,5,6,7,9,10],[3,8]]=>010000100=>[2,5,3]
[[1,2,4,5,6,8,9,10],[3,7]]=>010001000=>[2,4,4]
[[1,2,3,4,6,8,10],[5,7,9]]=>000101010=>[4,2,2,2]
[[1,2,3,4,6,9,10],[5,7,8]]=>000101000=>[4,2,4]
[[1,2,3,4,7,8,10],[5,6,9]]=>000100010=>[4,4,2]
[[1,2,3,4,7,9,10],[5,6,8]]=>000100100=>[4,3,3]
[[1,2,3,4,7,8,9,10],[5,6]]=>000100000=>[4,6]
[[1,2,3,5,6,8,10],[4,7,9]]=>001001010=>[3,3,2,2]
[[1,2,3,5,6,9,10],[4,7,8]]=>001001000=>[3,3,4]
[[1,2,3,5,7,8,10],[4,6,9]]=>001010010=>[3,2,3,2]
[[1,2,3,5,7,9,10],[4,6,8]]=>001010100=>[3,2,2,3]
[[1,2,3,5,7,8,9,10],[4,6]]=>001010000=>[3,2,5]
[[1,2,3,5,6,7,8,10],[4,9]]=>001000010=>[3,5,2]
[[1,2,3,5,6,7,9,10],[4,8]]=>001000100=>[3,4,3]
[[1,2,3,5,6,8,9,10],[4,7]]=>001001000=>[3,3,4]
[[1,2,3,5,6,7,8,9,10],[4]]=>001000000=>[3,7]
[[1,2,3,4,5,6,8,10],[7,9]]=>000001010=>[6,2,2]
[[1,2,3,4,5,6,9,10],[7,8]]=>000001000=>[6,4]
[[1,2,3,4,5,7,8,10],[6,9]]=>000010010=>[5,3,2]
[[1,2,3,4,5,7,9,10],[6,8]]=>000010100=>[5,2,3]
[[1,2,3,4,5,8,9,10],[6,7]]=>000010000=>[5,5]
[[1,2,3,4,6,7,8,10],[5,9]]=>000100010=>[4,4,2]
[[1,2,3,4,6,7,9,10],[5,8]]=>000100100=>[4,3,3]
[[1,2,3,4,6,8,9,10],[5,7]]=>000101000=>[4,2,4]
[[1,2,3,4,6,7,8,9,10],[5]]=>000100000=>[4,6]
[[1,2,3,4,5,6,7,9,10],[8]]=>000000100=>[7,3]
[[1,2,3,4,5,6,8,9,10],[7]]=>000001000=>[6,4]
[[1,2,3,4,5,7,8,9,10],[6]]=>000010000=>[5,5]
[[1,2,4,6,8,10,12],[3,5,7,9,11]]=>01010101010=>[2,2,2,2,2,2]
[[1,2,4,6,8,10,11,12],[3,5,7,9]]=>01010101000=>[2,2,2,2,4]
[[1,2,4,6,8,9,10,12],[3,5,7,11]]=>01010100010=>[2,2,2,4,2]
[[1,2,4,6,8,9,11,12],[3,5,7,10]]=>01010100100=>[2,2,2,3,3]
[[1,2,4,6,7,8,10,12],[3,5,9,11]]=>01010001010=>[2,2,4,2,2]
[[1,2,4,6,7,8,11,12],[3,5,9,10]]=>01010001000=>[2,2,4,4]
[[1,2,4,6,7,9,10,12],[3,5,8,11]]=>01010010010=>[2,2,3,3,2]
[[1,2,4,6,7,9,11,12],[3,5,8,10]]=>01010010100=>[2,2,3,2,3]
[[1,2,4,6,7,8,9,11,12],[3,5,10]]=>01010000100=>[2,2,5,3]
[[1,2,4,6,7,8,10,11,12],[3,5,9]]=>01010001000=>[2,2,4,4]
[[1,2,4,5,6,8,10,12],[3,7,9,11]]=>01000101010=>[2,4,2,2,2]
[[1,2,4,5,6,8,11,12],[3,7,9,10]]=>01000101000=>[2,4,2,4]
[[1,2,4,5,6,9,10,12],[3,7,8,11]]=>01000100010=>[2,4,4,2]
[[1,2,4,5,6,9,11,12],[3,7,8,10]]=>01000100100=>[2,4,3,3]
[[1,2,4,5,6,9,10,11,12],[3,7,8]]=>01000100000=>[2,4,6]
[[1,2,4,5,7,8,10,12],[3,6,9,11]]=>01001001010=>[2,3,3,2,2]
[[1,2,4,5,7,8,11,12],[3,6,9,10]]=>01001001000=>[2,3,3,4]
[[1,2,4,5,7,9,10,12],[3,6,8,11]]=>01001010010=>[2,3,2,3,2]
[[1,2,4,5,7,9,11,12],[3,6,8,10]]=>01001010100=>[2,3,2,2,3]
[[1,2,4,5,7,8,9,10,12],[3,6,11]]=>01001000010=>[2,3,5,2]
[[1,2,4,5,7,8,9,11,12],[3,6,10]]=>01001000100=>[2,3,4,3]
[[1,2,4,5,7,8,10,11,12],[3,6,9]]=>01001001000=>[2,3,3,4]
[[1,2,4,5,6,7,8,11,12],[3,9,10]]=>01000001000=>[2,6,4]
[[1,2,4,5,6,7,9,10,12],[3,8,11]]=>01000010010=>[2,5,3,2]
[[1,2,4,5,6,7,9,11,12],[3,8,10]]=>01000010100=>[2,5,2,3]
[[1,2,4,5,6,7,10,11,12],[3,8,9]]=>01000010000=>[2,5,5]
[[1,2,4,5,6,8,9,10,12],[3,7,11]]=>01000100010=>[2,4,4,2]
[[1,2,4,5,6,8,9,11,12],[3,7,10]]=>01000100100=>[2,4,3,3]
[[1,2,4,5,6,8,10,11,12],[3,7,9]]=>01000101000=>[2,4,2,4]
[[1,2,4,5,6,8,9,10,11,12],[3,7]]=>01000100000=>[2,4,6]
[[1,2,4,5,6,7,8,9,10,12],[3,11]]=>01000000010=>[2,8,2]
[[1,2,4,5,6,7,8,10,11,12],[3,9]]=>01000001000=>[2,6,4]
[[1,2,4,5,6,7,9,10,11,12],[3,8]]=>01000010000=>[2,5,5]
[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>01000000000=>[2,10]
[[1,2,3,4,6,8,10,12],[5,7,9,11]]=>00010101010=>[4,2,2,2,2]
[[1,2,3,4,6,8,11,12],[5,7,9,10]]=>00010101000=>[4,2,2,4]
[[1,2,3,4,6,9,10,12],[5,7,8,11]]=>00010100010=>[4,2,4,2]
[[1,2,3,4,6,9,11,12],[5,7,8,10]]=>00010100100=>[4,2,3,3]
[[1,2,3,4,7,8,10,12],[5,6,9,11]]=>00010001010=>[4,4,2,2]
[[1,2,3,4,7,8,11,12],[5,6,9,10]]=>00010001000=>[4,4,4]
[[1,2,3,4,7,9,10,12],[5,6,8,11]]=>00010010010=>[4,3,3,2]
[[1,2,3,4,7,9,11,12],[5,6,8,10]]=>00010010100=>[4,3,2,3]
[[1,2,3,4,7,9,10,11,12],[5,6,8]]=>00010010000=>[4,3,5]
[[1,2,3,4,7,8,9,10,12],[5,6,11]]=>00010000010=>[4,6,2]
[[1,2,3,4,7,8,9,11,12],[5,6,10]]=>00010000100=>[4,5,3]
[[1,2,3,4,7,8,10,11,12],[5,6,9]]=>00010001000=>[4,4,4]
[[1,2,3,4,7,8,9,10,11,12],[5,6]]=>00010000000=>[4,8]
[[1,2,3,5,6,8,10,12],[4,7,9,11]]=>00100101010=>[3,3,2,2,2]
[[1,2,3,5,6,8,11,12],[4,7,9,10]]=>00100101000=>[3,3,2,4]
[[1,2,3,5,6,9,10,12],[4,7,8,11]]=>00100100010=>[3,3,4,2]
[[1,2,3,5,6,9,11,12],[4,7,8,10]]=>00100100100=>[3,3,3,3]
[[1,2,3,5,7,8,10,12],[4,6,9,11]]=>00101001010=>[3,2,3,2,2]
[[1,2,3,5,7,8,11,12],[4,6,9,10]]=>00101001000=>[3,2,3,4]
[[1,2,3,5,7,9,10,12],[4,6,8,11]]=>00101010010=>[3,2,2,3,2]
[[1,2,3,5,7,9,11,12],[4,6,8,10]]=>00101010100=>[3,2,2,2,3]
[[1,2,3,5,7,8,9,10,12],[4,6,11]]=>00101000010=>[3,2,5,2]
[[1,2,3,5,7,8,9,11,12],[4,6,10]]=>00101000100=>[3,2,4,3]
[[1,2,3,5,7,8,10,11,12],[4,6,9]]=>00101001000=>[3,2,3,4]
[[1,2,3,5,6,7,8,10,12],[4,9,11]]=>00100001010=>[3,5,2,2]
[[1,2,3,5,6,7,8,11,12],[4,9,10]]=>00100001000=>[3,5,4]
[[1,2,3,5,6,7,9,10,12],[4,8,11]]=>00100010010=>[3,4,3,2]
[[1,2,3,5,6,7,9,11,12],[4,8,10]]=>00100010100=>[3,4,2,3]
[[1,2,3,5,6,7,10,11,12],[4,8,9]]=>00100010000=>[3,4,5]
[[1,2,3,5,6,8,9,10,12],[4,7,11]]=>00100100010=>[3,3,4,2]
[[1,2,3,5,6,8,9,11,12],[4,7,10]]=>00100100100=>[3,3,3,3]
[[1,2,3,5,6,8,10,11,12],[4,7,9]]=>00100101000=>[3,3,2,4]
[[1,2,3,5,6,7,8,9,11,12],[4,10]]=>00100000100=>[3,6,3]
[[1,2,3,5,6,7,8,10,11,12],[4,9]]=>00100001000=>[3,5,4]
[[1,2,3,5,6,7,9,10,11,12],[4,8]]=>00100010000=>[3,4,5]
[[1,2,3,4,5,6,9,10,12],[7,8,11]]=>00000100010=>[6,4,2]
[[1,2,3,4,5,6,10,11,12],[7,8,9]]=>00000100000=>[6,6]
[[1,2,3,4,5,7,8,11,12],[6,9,10]]=>00001001000=>[5,3,4]
[[1,2,3,4,5,7,10,11,12],[6,8,9]]=>00001010000=>[5,2,5]
[[1,2,3,4,5,8,9,10,12],[6,7,11]]=>00001000010=>[5,5,2]
[[1,2,3,4,5,8,9,11,12],[6,7,10]]=>00001000100=>[5,4,3]
[[1,2,3,4,5,8,10,11,12],[6,7,9]]=>00001001000=>[5,3,4]
[[1,2,3,4,6,7,8,10,12],[5,9,11]]=>00010001010=>[4,4,2,2]
[[1,2,3,4,6,7,8,11,12],[5,9,10]]=>00010001000=>[4,4,4]
[[1,2,3,4,6,7,9,10,12],[5,8,11]]=>00010010010=>[4,3,3,2]
[[1,2,3,4,6,7,9,11,12],[5,8,10]]=>00010010100=>[4,3,2,3]
[[1,2,3,4,6,7,10,11,12],[5,8,9]]=>00010010000=>[4,3,5]
[[1,2,3,4,6,8,9,10,12],[5,7,11]]=>00010100010=>[4,2,4,2]
[[1,2,3,4,6,8,9,11,12],[5,7,10]]=>00010100100=>[4,2,3,3]
[[1,2,3,4,6,8,10,11,12],[5,7,9]]=>00010101000=>[4,2,2,4]
[[1,2,3,4,6,7,8,9,10,12],[5,11]]=>00010000010=>[4,6,2]
[[1,2,3,4,6,7,8,9,11,12],[5,10]]=>00010000100=>[4,5,3]
[[1,2,3,4,6,7,8,10,11,12],[5,9]]=>00010001000=>[4,4,4]
[[1,2,3,4,6,7,9,10,11,12],[5,8]]=>00010010000=>[4,3,5]
[[1,2,3,4,6,7,8,9,10,11,12],[5]]=>00010000000=>[4,8]
[[1,2,3,4,5,6,7,8,11,12],[9,10]]=>00000001000=>[8,4]
[[1,2,3,4,5,6,8,9,10,12],[7,11]]=>00000100010=>[6,4,2]
[[1,2,3,4,5,6,9,10,11,12],[7,8]]=>00000100000=>[6,6]
[[1,2,3,4,5,7,8,9,10,12],[6,11]]=>00001000010=>[5,5,2]
[[1,2,3,4,5,7,8,9,11,12],[6,10]]=>00001000100=>[5,4,3]
[[1,2,3,4,5,7,8,10,11,12],[6,9]]=>00001001000=>[5,3,4]
[[1,2,3,4,5,7,9,10,11,12],[6,8]]=>00001010000=>[5,2,5]
[[1,2,3,4,5,6,7,8,9,10,12],[11]]=>00000000010=>[10,2]
[[1,2,3,4,5,6,7,8,10,11,12],[9]]=>00000001000=>[8,4]
[[1,2,3,4,5,6,8,9,10,11,12],[7]]=>00000100000=>[6,6]
[[1,2,5,6,7,8],[3,4,9]]=>01000001=>[2,6,1]
[[1,2,5,6,7,8],[3,4],[9]]=>01000001=>[2,6,1]
[[1,4,5,6,7,8],[2],[3],[9]]=>11000001=>[1,1,6,1]
[[1,2,3,7,8],[4,5,6,9]]=>00100001=>[3,5,1]
[[1,2,3,7,8],[4,5,6],[9]]=>00100001=>[3,5,1]
[[1,3,6,7,8],[2,5],[4,9]]=>10100001=>[1,2,5,1]
[[1,3,6,7,8],[2,5],[4],[9]]=>10100001=>[1,2,5,1]
[[1,5,6,7,8],[2],[3],[4],[9]]=>11100001=>[1,1,1,5,1]
[[1,3,4,8],[2,6,7],[5,9]]=>10010001=>[1,3,4,1]
[[1,3,4,8],[2,6,7],[5],[9]]=>10010001=>[1,3,4,1]
[[1,2,7,8],[3,4],[5,6],[9]]=>01010001=>[2,2,4,1]
[[1,4,7,8],[2,6],[3],[5],[9]]=>11010001=>[1,1,2,4,1]
[[1,6,7,8],[2],[3],[4],[5],[9]]=>11110001=>[1,1,1,1,4,1]
[[1,2,5],[3,4,8],[6,7],[9]]=>01001001=>[2,3,3,1]
[[1,4,5],[2,7,8],[3],[6],[9]]=>11001001=>[1,1,3,3,1]
[[1,3,8],[2,5],[4,7],[6,9]]=>10101001=>[1,2,2,3,1]
[[1,3,8],[2,5],[4,7],[6],[9]]=>10101001=>[1,2,2,3,1]
[[1,5,8],[2,7],[3],[4],[6],[9]]=>11101001=>[1,1,1,2,3,1]
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>11111001=>[1,1,1,1,1,3,1]
[[1,2,5,6,7,8,9],[3,4,10]]=>010000001=>[2,7,1]
[[1,2,5,6,7,8,9],[3,4],[10]]=>010000001=>[2,7,1]
[[1,4,5,6,7,8,9],[2],[3],[10]]=>110000001=>[1,1,7,1]
[[1,2,3,7,8,9],[4,5,6,10]]=>001000001=>[3,6,1]
[[1,2,3,7,8,9],[4,5,6],[10]]=>001000001=>[3,6,1]
[[1,3,6,7,8,9],[2,5],[4,10]]=>101000001=>[1,2,6,1]
[[1,3,6,7,8,9],[2,5],[4],[10]]=>101000001=>[1,2,6,1]
[[1,5,6,7,8,9],[2],[3],[4],[10]]=>111000001=>[1,1,1,6,1]
[[1,2,3,4,9],[5,6,7,8],[10]]=>000100001=>[4,5,1]
[[1,3,4,8,9],[2,6,7],[5,10]]=>100100001=>[1,3,5,1]
[[1,3,4,8,9],[2,6,7],[5],[10]]=>100100001=>[1,3,5,1]
[[1,2,7,8,9],[3,4],[5,6],[10]]=>010100001=>[2,2,5,1]
[[1,4,7,8,9],[2,6],[3],[5],[10]]=>110100001=>[1,1,2,5,1]
[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>111100001=>[1,1,1,1,5,1]
[[1,2,5,9],[3,4,8],[6,7,10]]=>010010001=>[2,3,4,1]
[[1,2,5,9],[3,4,8],[6,7],[10]]=>010010001=>[2,3,4,1]
[[1,4,5,9],[2,7,8],[3],[6],[10]]=>110010001=>[1,1,3,4,1]
[[1,3,8,9],[2,5],[4,7],[6,10]]=>101010001=>[1,2,2,4,1]
[[1,3,8,9],[2,5],[4,7],[6],[10]]=>101010001=>[1,2,2,4,1]
[[1,5,8,9],[2,7],[3],[4],[6],[10]]=>111010001=>[1,1,1,2,4,1]
[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>111110001=>[1,1,1,1,1,4,1]
[[1,3,6],[2,5,9],[4,8],[7,10]]=>101001001=>[1,2,3,3,1]
[[1,3,6],[2,5,9],[4,8],[7],[10]]=>101001001=>[1,2,3,3,1]
[[1,5,6],[2,8,9],[3],[4],[7],[10]]=>111001001=>[1,1,1,3,3,1]
[[1,2,9],[3,4],[5,6],[7,8],[10]]=>010101001=>[2,2,2,3,1]
[[1,4,9],[2,6],[3,8],[5],[7],[10]]=>110101001=>[1,1,2,2,3,1]
[[1,6,9],[2,8],[3],[4],[5],[7],[10]]=>111101001=>[1,1,1,1,2,3,1]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>111111001=>[1,1,1,1,1,1,3,1]
[[1,2,3,6,7,8,9],[4,5]]=>00100000=>[3,6]
[[1,2,5,6,7,8,9],[3],[4]]=>01100000=>[2,1,6]
[[1,2,3,4,8,9],[5,6,7]]=>00010000=>[4,5]
[[1,2,4,7,8,9],[3,6],[5]]=>01010000=>[2,2,5]
[[1,2,6,7,8,9],[3],[4],[5]]=>01110000=>[2,1,1,5]
[[1,2,4,5,9],[3,7,8],[6]]=>01001000=>[2,3,4]
[[1,2,3,8,9],[4,5],[6,7]]=>00101000=>[3,2,4]
[[1,2,5,8,9],[3,7],[4],[6]]=>01101000=>[2,1,2,4]
[[1,2,7,8,9],[3],[4],[5],[6]]=>01111000=>[2,1,1,1,4]
[[1,2,5,6],[3,4,8,9],[7]]=>01000100=>[2,4,3]
[[1,2,3,6],[4,5,9],[7,8]]=>00100100=>[3,3,3]
[[1,2,5,6],[3,8,9],[4],[7]]=>01100100=>[2,1,3,3]
[[1,2,4,9],[3,6],[5,8],[7]]=>01010100=>[2,2,2,3]
[[1,2,6,9],[3,8],[4],[5],[7]]=>01110100=>[2,1,1,2,3]
[[1,2,8,9],[3],[4],[5],[6],[7]]=>01111100=>[2,1,1,1,1,3]
[[1,2,4],[3,6,7],[5,9],[8]]=>01010010=>[2,2,3,2]
[[1,2,7],[3,6,9],[4],[5],[8]]=>01110010=>[2,1,1,3,2]
[[1,2,5],[3,7],[4,9],[6],[8]]=>01101010=>[2,1,2,2,2]
[[1,2,7],[3,9],[4],[5],[6],[8]]=>01111010=>[2,1,1,1,2,2]
[[1,2],[3,6],[4,8],[5],[7],[9]]=>01110101=>[2,1,1,2,2,1]
[[1,2],[3,8],[4],[5],[6],[7],[9]]=>01111101=>[2,1,1,1,1,2,1]
[[1,2,3,6,7,8,9,10],[4,5]]=>001000000=>[3,7]
[[1,2,5,6,7,8,9,10],[3],[4]]=>011000000=>[2,1,7]
[[1,2,3,4,8,9,10],[5,6,7]]=>000100000=>[4,6]
[[1,2,4,7,8,9,10],[3,6],[5]]=>010100000=>[2,2,6]
[[1,2,6,7,8,9,10],[3],[4],[5]]=>011100000=>[2,1,1,6]
[[1,2,4,5,9,10],[3,7,8],[6]]=>010010000=>[2,3,5]
[[1,2,3,8,9,10],[4,5],[6,7]]=>001010000=>[3,2,5]
[[1,2,5,8,9,10],[3,7],[4],[6]]=>011010000=>[2,1,2,5]
[[1,2,7,8,9,10],[3],[4],[5],[6]]=>011110000=>[2,1,1,1,5]
[[1,2,4,5,6],[3,8,9,10],[7]]=>010001000=>[2,4,4]
[[1,2,3,6,10],[4,5,9],[7,8]]=>001001000=>[3,3,4]
[[1,2,5,6,10],[3,8,9],[4],[7]]=>011001000=>[2,1,3,4]
[[1,2,4,9,10],[3,6],[5,8],[7]]=>010101000=>[2,2,2,4]
[[1,2,6,9,10],[3,8],[4],[5],[7]]=>011101000=>[2,1,1,2,4]
[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>011111000=>[2,1,1,1,1,4]
[[1,2,6,7],[3,5,9,10],[4],[8]]=>011000100=>[2,1,4,3]
[[1,2,4,7],[3,6,10],[5,9],[8]]=>010100100=>[2,2,3,3]
[[1,2,6,7],[3,9,10],[4],[5],[8]]=>011100100=>[2,1,1,3,3]
[[1,2,5,10],[3,7],[4,9],[6],[8]]=>011010100=>[2,1,2,2,3]
[[1,2,7,10],[3,9],[4],[5],[6],[8]]=>011110100=>[2,1,1,1,2,3]
[[1,2,9,10],[3],[4],[5],[6],[7],[8]]=>011111100=>[2,1,1,1,1,1,3]
[[1,2,3],[4,5,8],[6,7],[9,10]]=>001010010=>[3,2,3,2]
[[1,2,5],[3,7,8],[4,10],[6],[9]]=>011010010=>[2,1,2,3,2]
[[1,2,8],[3,7,10],[4],[5],[6],[9]]=>011110010=>[2,1,1,1,3,2]
[[1,2,4],[3,6],[5,8],[7,10],[9]]=>010101010=>[2,2,2,2,2]
[[1,2,6],[3,8],[4,10],[5],[7],[9]]=>011101010=>[2,1,1,2,2,2]
[[1,2,8],[3,10],[4],[5],[6],[7],[9]]=>011111010=>[2,1,1,1,1,2,2]
[[1,2],[3,5],[4,7],[6,9],[8],[10]]=>011010101=>[2,1,2,2,2,1]
[[1,2],[3,7],[4,9],[5],[6],[8],[10]]=>011110101=>[2,1,1,1,2,2,1]
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]]=>011111101=>[2,1,1,1,1,1,2,1]
[[1,2,3,4,7,8,9],[5,6]]=>00010000=>[4,5]
[[1,2,4,5,8,9],[3,7],[6]]=>01001000=>[2,3,4]
[[1,2,4,5,6,7],[3,9],[8]]=>01000010=>[2,5,2]
[[1,2,5,6,9],[3,8],[4],[7]]=>01100100=>[2,1,3,3]
[[1,2,3,4,7,8],[5,6],[9]]=>00010001=>[4,4,1]
[[1,2,5,6,7,8],[3],[4],[9]]=>01100001=>[2,1,5,1]
[[1,2,4,5],[3,7],[6,9],[8]]=>01001010=>[2,3,2,2]
[[1,2,6,7],[3,9],[4],[5],[8]]=>01110010=>[2,1,1,3,2]
[[1,2,5,6],[3,8],[4],[7],[9]]=>01100101=>[2,1,3,2,1]
[[1,2,7,8],[3],[4],[5],[6],[9]]=>01111001=>[2,1,1,1,3,1]
[[1,2,4,5,8,9,10],[3,7],[6]]=>010010000=>[2,3,5]
[[1,2,4,5,6,7],[3,9,10],[8]]=>010000100=>[2,5,3]
[[1,2,3,4,9,10],[5,6],[7,8]]=>000101000=>[4,2,4]
[[1,2,5,6,9,10],[3,8],[4],[7]]=>011001000=>[2,1,3,4]
[[1,2,4,5,6,7,8,9],[3],[10]]=>010000001=>[2,7,1]
[[1,2,3,4,7,8],[5,6],[9,10]]=>000100010=>[4,4,2]
[[1,2,5,6,7,8],[3,10],[4],[9]]=>011000010=>[2,1,5,2]
[[1,2,4,5,10],[3,7],[6,9],[8]]=>010010100=>[2,3,2,3]
[[1,2,6,7,10],[3,9],[4],[5],[8]]=>011100100=>[2,1,1,3,3]
[[1,2,4,5,8,9],[3,7],[6],[10]]=>010010001=>[2,3,4,1]
[[1,2,6,7,8,9],[3],[4],[5],[10]]=>011100001=>[2,1,1,5,1]
[[1,2,5,6],[3,8],[4,10],[7],[9]]=>011001010=>[2,1,3,2,2]
[[1,2,7,8],[3,10],[4],[5],[6],[9]]=>011110010=>[2,1,1,1,3,2]
[[1,2,4,5],[3,7],[6,9],[8],[10]]=>010010101=>[2,3,2,2,1]
[[1,2,6,7],[3,9],[4],[5],[8],[10]]=>011100101=>[2,1,1,3,2,1]
[[1,2,8,9],[3],[4],[5],[6],[7],[10]]=>011111001=>[2,1,1,1,1,3,1]
[[1,6,10],[2,7,11],[3,8],[4,9],[5]]=>1111011101=>[1,1,1,1,2,1,1,2,1]
[[1,5,9],[2,6,10],[3,7,11],[4,8]]=>1110111011=>[1,1,1,2,1,1,2,1,1]
[[1,6,10],[2,7,11],[3,8,12],[4,9],[5]]=>11110111011=>[1,1,1,1,2,1,1,2,1,1]
[[1,5,9,12],[2,6,10],[3,7,11],[4,8]]=>11101110110=>[1,1,1,2,1,1,2,1,2]
[[1,5,8,11],[2,6,9,12],[3,7,10],[4]]=>11101101101=>[1,1,1,2,1,2,1,2,1]
[[1,5,8,10],[2,6,9,11],[3,7],[4]]=>1110110101=>[1,1,1,2,1,2,2,1]
[[1,4,7,10,12],[2,5,8,11],[3,6,9]]=>11011011010=>[1,1,2,1,2,1,2,2]
[[1,5,8,10,11],[2,6,9],[3,7],[4]]=>1110110100=>[1,1,1,2,1,2,3]
[[1,4,7,9,11,12],[2,5,8,10],[3,6]]=>11011010100=>[1,1,2,1,2,2,3]
[[1,5,7,9,11],[2,6,8,10],[3],[4]]=>1110101010=>[1,1,1,2,2,2,2]
[[1,6,9,12,13],[2,7,10],[3,8,11],[4],[5]]=>111101101100=>[1,1,1,1,2,1,2,1,3]
[[1,4,7,10,11],[2,5,8],[3,6,9]]=>1101101100=>[1,1,2,1,2,1,3]
[[1,6,8,10,11],[2,7,9],[3],[4],[5]]=>1111010100=>[1,1,1,1,2,2,3]
[[1,6,10,11,12],[2,7],[3,8],[4,9],[5]]=>11110111000=>[1,1,1,1,2,1,1,4]
[[1,5,9,10,11],[2,6],[3,7],[4,8]]=>1110111000=>[1,1,1,2,1,1,4]
[[1,6,9,10,11],[2,7],[3,8],[4],[5]]=>1111011000=>[1,1,1,1,2,1,4]
[[1,5,9,11],[2,6,10,12],[3,7],[4,8]]=>11101110101=>[1,1,1,2,1,1,2,2,1]
[[1,6,8,10],[2,7,9,11],[3],[4],[5]]=>1111010101=>[1,1,1,1,2,2,2,1]
[[1,6,9],[2,7,10],[3,8,11],[4],[5]]=>1111011011=>[1,1,1,1,2,1,2,1,1]
[[1,3],[2,5],[4,9],[6],[7],[8],[10]]=>101011101=>[1,2,2,1,1,2,1]
[[1,3],[2,5],[4,8],[6],[7],[9],[10]]=>101011011=>[1,2,2,1,2,1,1]
[[1,3],[2,7],[4,9],[5],[6],[8],[10]]=>101110101=>[1,2,1,1,2,2,1]
[[1,3],[2,7],[4,8],[5],[6],[9],[10]]=>101110111=>[1,2,1,1,2,1,1,1]
[[1,3],[2,6],[4,9],[5],[7],[8],[10]]=>101101101=>[1,2,1,2,1,2,1]
[[1,3],[2,6],[4,8],[5],[7],[9],[10]]=>101101011=>[1,2,1,2,2,1,1]
[[1,3],[2,6],[4],[5],[7],[8],[9],[10]]=>101101111=>[1,2,1,2,1,1,1,1]
[[1,3],[2,9],[4],[5],[6],[7],[8],[10]]=>101111101=>[1,2,1,1,1,1,2,1]
[[1,3],[2,8],[4],[5],[6],[7],[9],[10]]=>101111011=>[1,2,1,1,1,2,1,1]
[[1,3],[2,7],[4],[5],[6],[8],[9],[10]]=>101110111=>[1,2,1,1,2,1,1,1]
[[1,5],[2,7],[3,8],[4],[6],[9],[10]]=>111010111=>[1,1,1,2,2,1,1,1]
[[1,5],[2,6],[3,9],[4],[7],[8],[10]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,5],[2,6],[3,8],[4],[7],[9],[10]]=>111011011=>[1,1,1,2,1,2,1,1]
[[1,5],[2,6],[3],[4],[7],[8],[9],[10]]=>111011111=>[1,1,1,2,1,1,1,1,1]
[[1,4],[2,7],[3,9],[5],[6],[8],[10]]=>110110101=>[1,1,2,1,2,2,1]
[[1,4],[2,7],[3,8],[5],[6],[9],[10]]=>110110111=>[1,1,2,1,2,1,1,1]
[[1,4],[2,6],[3,9],[5],[7],[8],[10]]=>110101101=>[1,1,2,2,1,2,1]
[[1,4],[2,6],[3,8],[5],[7],[9],[10]]=>110101011=>[1,1,2,2,2,1,1]
[[1,4],[2,6],[3],[5],[7],[8],[9],[10]]=>110101111=>[1,1,2,2,1,1,1,1]
[[1,4],[2,9],[3],[5],[6],[7],[8],[10]]=>110111101=>[1,1,2,1,1,1,2,1]
[[1,4],[2,8],[3],[5],[6],[7],[9],[10]]=>110111011=>[1,1,2,1,1,2,1,1]
[[1,4],[2,7],[3],[5],[6],[8],[9],[10]]=>110110111=>[1,1,2,1,2,1,1,1]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>110111111=>[1,1,2,1,1,1,1,1,1]
[[1,7],[2,8],[3],[4],[5],[6],[9],[10]]=>111110111=>[1,1,1,1,1,2,1,1,1]
[[1,6],[2,9],[3],[4],[5],[7],[8],[10]]=>111101101=>[1,1,1,1,2,1,2,1]
[[1,6],[2,8],[3],[4],[5],[7],[9],[10]]=>111101011=>[1,1,1,1,2,2,1,1]
[[1,6],[2,7],[3],[4],[5],[8],[9],[10]]=>111101111=>[1,1,1,1,2,1,1,1,1]
[[1,5],[2,9],[3],[4],[6],[7],[8],[10]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,5],[2,8],[3],[4],[6],[7],[9],[10]]=>111011011=>[1,1,1,2,1,2,1,1]
[[1,5],[2,7],[3],[4],[6],[8],[9],[10]]=>111010111=>[1,1,1,2,2,1,1,1]
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>111011111=>[1,1,1,2,1,1,1,1,1]
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>111111011=>[1,1,1,1,1,1,2,1,1]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>111110111=>[1,1,1,1,1,2,1,1,1]
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>111101111=>[1,1,1,1,2,1,1,1,1]
[[1,3],[2,5],[4,7],[6,9],[8,11],[10],[12]]=>10101010101=>[1,2,2,2,2,2,1]
[[1,3],[2,5],[4,7],[6,9],[8],[10],[11],[12]]=>10101010111=>[1,2,2,2,2,1,1,1]
[[1,3],[2,5],[4,7],[6,11],[8],[9],[10],[12]]=>10101011101=>[1,2,2,2,1,1,2,1]
[[1,3],[2,5],[4,7],[6,10],[8],[9],[11],[12]]=>10101011011=>[1,2,2,2,1,2,1,1]
[[1,3],[2,5],[4,9],[6,11],[7],[8],[10],[12]]=>10101110101=>[1,2,2,1,1,2,2,1]
[[1,3],[2,5],[4,9],[6,10],[7],[8],[11],[12]]=>10101110111=>[1,2,2,1,1,2,1,1,1]
[[1,3],[2,5],[4,8],[6,11],[7],[9],[10],[12]]=>10101101101=>[1,2,2,1,2,1,2,1]
[[1,3],[2,5],[4,8],[6,10],[7],[9],[11],[12]]=>10101101011=>[1,2,2,1,2,2,1,1]
[[1,3],[2,5],[4,10],[6],[7],[8],[9],[11],[12]]=>10101111011=>[1,2,2,1,1,1,2,1,1]
[[1,3],[2,5],[4,9],[6],[7],[8],[10],[11],[12]]=>10101110111=>[1,2,2,1,1,2,1,1,1]
[[1,3],[2,5],[4],[6],[7],[8],[9],[10],[11],[12]]=>10101111111=>[1,2,2,1,1,1,1,1,1,1]
[[1,3],[2,7],[4,9],[5,11],[6],[8],[10],[12]]=>10111010101=>[1,2,1,1,2,2,2,1]
[[1,3],[2,7],[4,9],[5,10],[6],[8],[11],[12]]=>10111010111=>[1,2,1,1,2,2,1,1,1]
[[1,3],[2,7],[4,8],[5,11],[6],[9],[10],[12]]=>10111011101=>[1,2,1,1,2,1,1,2,1]
[[1,3],[2,7],[4,8],[5,10],[6],[9],[11],[12]]=>10111011011=>[1,2,1,1,2,1,2,1,1]
[[1,3],[2,6],[4,9],[5,11],[7],[8],[10],[12]]=>10110110101=>[1,2,1,2,1,2,2,1]
[[1,3],[2,6],[4,9],[5,10],[7],[8],[11],[12]]=>10110110111=>[1,2,1,2,1,2,1,1,1]
[[1,3],[2,6],[4,8],[5,11],[7],[9],[10],[12]]=>10110101101=>[1,2,1,2,2,1,2,1]
[[1,3],[2,6],[4,8],[5,10],[7],[9],[11],[12]]=>10110101011=>[1,2,1,2,2,2,1,1]
[[1,3],[2,6],[4,11],[5],[7],[8],[9],[10],[12]]=>10110111101=>[1,2,1,2,1,1,1,2,1]
[[1,3],[2,6],[4,10],[5],[7],[8],[9],[11],[12]]=>10110111011=>[1,2,1,2,1,1,2,1,1]
[[1,3],[2,6],[4,9],[5],[7],[8],[10],[11],[12]]=>10110110111=>[1,2,1,2,1,2,1,1,1]
[[1,3],[2,9],[4,10],[5],[6],[7],[8],[11],[12]]=>10111110111=>[1,2,1,1,1,1,2,1,1,1]
[[1,3],[2,8],[4,11],[5],[6],[7],[9],[10],[12]]=>10111101101=>[1,2,1,1,1,2,1,2,1]
[[1,3],[2,8],[4,10],[5],[6],[7],[9],[11],[12]]=>10111101011=>[1,2,1,1,1,2,2,1,1]
[[1,3],[2,8],[4,9],[5],[6],[7],[10],[11],[12]]=>10111101111=>[1,2,1,1,1,2,1,1,1,1]
[[1,3],[2,7],[4,11],[5],[6],[8],[9],[10],[12]]=>10111011101=>[1,2,1,1,2,1,1,2,1]
[[1,3],[2,7],[4,10],[5],[6],[8],[9],[11],[12]]=>10111011011=>[1,2,1,1,2,1,2,1,1]
[[1,3],[2,7],[4,9],[5],[6],[8],[10],[11],[12]]=>10111010111=>[1,2,1,1,2,2,1,1,1]
[[1,3],[2,11],[4],[5],[6],[7],[8],[9],[10],[12]]=>10111111101=>[1,2,1,1,1,1,1,1,2,1]
[[1,3],[2,9],[4],[5],[6],[7],[8],[10],[11],[12]]=>10111110111=>[1,2,1,1,1,1,2,1,1,1]
[[1,3],[2,8],[4],[5],[6],[7],[9],[10],[11],[12]]=>10111101111=>[1,2,1,1,1,2,1,1,1,1]
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>10111111111=>[1,2,1,1,1,1,1,1,1,1,1]
[[1,5],[2,7],[3,9],[4,10],[6],[8],[11],[12]]=>11101010111=>[1,1,1,2,2,2,1,1,1]
[[1,5],[2,7],[3,8],[4,11],[6],[9],[10],[12]]=>11101011101=>[1,1,1,2,2,1,1,2,1]
[[1,5],[2,7],[3,8],[4,10],[6],[9],[11],[12]]=>11101011011=>[1,1,1,2,2,1,2,1,1]
[[1,5],[2,6],[3,9],[4,11],[7],[8],[10],[12]]=>11101110101=>[1,1,1,2,1,1,2,2,1]
[[1,5],[2,6],[3,9],[4,10],[7],[8],[11],[12]]=>11101110111=>[1,1,1,2,1,1,2,1,1,1]
[[1,5],[2,6],[3,8],[4,11],[7],[9],[10],[12]]=>11101101101=>[1,1,1,2,1,2,1,2,1]
[[1,5],[2,6],[3,8],[4,10],[7],[9],[11],[12]]=>11101101011=>[1,1,1,2,1,2,2,1,1]
[[1,5],[2,6],[3,8],[4],[7],[9],[10],[11],[12]]=>11101101111=>[1,1,1,2,1,2,1,1,1,1]
[[1,5],[2,6],[3,11],[4],[7],[8],[9],[10],[12]]=>11101111101=>[1,1,1,2,1,1,1,1,2,1]
[[1,5],[2,6],[3,10],[4],[7],[8],[9],[11],[12]]=>11101111011=>[1,1,1,2,1,1,1,2,1,1]
[[1,5],[2,6],[3,9],[4],[7],[8],[10],[11],[12]]=>11101110111=>[1,1,1,2,1,1,2,1,1,1]
[[1,4],[2,7],[3,9],[5,11],[6],[8],[10],[12]]=>11011010101=>[1,1,2,1,2,2,2,1]
[[1,4],[2,7],[3,9],[5,10],[6],[8],[11],[12]]=>11011010111=>[1,1,2,1,2,2,1,1,1]
[[1,4],[2,7],[3,8],[5,11],[6],[9],[10],[12]]=>11011011101=>[1,1,2,1,2,1,1,2,1]
[[1,4],[2,7],[3,8],[5,10],[6],[9],[11],[12]]=>11011011011=>[1,1,2,1,2,1,2,1,1]
[[1,4],[2,6],[3,9],[5,11],[7],[8],[10],[12]]=>11010110101=>[1,1,2,2,1,2,2,1]
[[1,4],[2,6],[3,9],[5,10],[7],[8],[11],[12]]=>11010110111=>[1,1,2,2,1,2,1,1,1]
[[1,4],[2,6],[3,8],[5,11],[7],[9],[10],[12]]=>11010101101=>[1,1,2,2,2,1,2,1]
[[1,4],[2,6],[3,8],[5,10],[7],[9],[11],[12]]=>11010101011=>[1,1,2,2,2,2,1,1]
[[1,4],[2,6],[3,11],[5],[7],[8],[9],[10],[12]]=>11010111101=>[1,1,2,2,1,1,1,2,1]
[[1,4],[2,6],[3,10],[5],[7],[8],[9],[11],[12]]=>11010111011=>[1,1,2,2,1,1,2,1,1]
[[1,4],[2,6],[3,9],[5],[7],[8],[10],[11],[12]]=>11010110111=>[1,1,2,2,1,2,1,1,1]
[[1,4],[2,9],[3,11],[5],[6],[7],[8],[10],[12]]=>11011110101=>[1,1,2,1,1,1,2,2,1]
[[1,4],[2,9],[3,10],[5],[6],[7],[8],[11],[12]]=>11011110111=>[1,1,2,1,1,1,2,1,1,1]
[[1,4],[2,8],[3,11],[5],[6],[7],[9],[10],[12]]=>11011101101=>[1,1,2,1,1,2,1,2,1]
[[1,4],[2,8],[3,10],[5],[6],[7],[9],[11],[12]]=>11011101011=>[1,1,2,1,1,2,2,1,1]
[[1,4],[2,8],[3,9],[5],[6],[7],[10],[11],[12]]=>11011101111=>[1,1,2,1,1,2,1,1,1,1]
[[1,4],[2,7],[3,11],[5],[6],[8],[9],[10],[12]]=>11011011101=>[1,1,2,1,2,1,1,2,1]
[[1,4],[2,7],[3,10],[5],[6],[8],[9],[11],[12]]=>11011011011=>[1,1,2,1,2,1,2,1,1]
[[1,4],[2,7],[3,9],[5],[6],[8],[10],[11],[12]]=>11011010111=>[1,1,2,1,2,2,1,1,1]
[[1,4],[2,10],[3],[5],[6],[7],[8],[9],[11],[12]]=>11011111011=>[1,1,2,1,1,1,1,2,1,1]
[[1,4],[2,9],[3],[5],[6],[7],[8],[10],[11],[12]]=>11011110111=>[1,1,2,1,1,1,2,1,1,1]
[[1,4],[2,8],[3],[5],[6],[7],[9],[10],[11],[12]]=>11011101111=>[1,1,2,1,1,2,1,1,1,1]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10],[11],[12]]=>11011111111=>[1,1,2,1,1,1,1,1,1,1,1]
[[1,7],[2,8],[3,9],[4],[5],[6],[10],[11],[12]]=>11111011111=>[1,1,1,1,1,2,1,1,1,1,1]
[[1,6],[2,9],[3,10],[4],[5],[7],[8],[11],[12]]=>11110110111=>[1,1,1,1,2,1,2,1,1,1]
[[1,6],[2,8],[3,9],[4],[5],[7],[10],[11],[12]]=>11110101111=>[1,1,1,1,2,2,1,1,1,1]
[[1,6],[2,7],[3,11],[4],[5],[8],[9],[10],[12]]=>11110111101=>[1,1,1,1,2,1,1,1,2,1]
[[1,6],[2,7],[3,10],[4],[5],[8],[9],[11],[12]]=>11110111011=>[1,1,1,1,2,1,1,2,1,1]
[[1,6],[2,7],[3,9],[4],[5],[8],[10],[11],[12]]=>11110110111=>[1,1,1,1,2,1,2,1,1,1]
[[1,5],[2,9],[3,11],[4],[6],[7],[8],[10],[12]]=>11101110101=>[1,1,1,2,1,1,2,2,1]
[[1,5],[2,9],[3,10],[4],[6],[7],[8],[11],[12]]=>11101110111=>[1,1,1,2,1,1,2,1,1,1]
[[1,5],[2,8],[3,11],[4],[6],[7],[9],[10],[12]]=>11101101101=>[1,1,1,2,1,2,1,2,1]
[[1,5],[2,8],[3,10],[4],[6],[7],[9],[11],[12]]=>11101101011=>[1,1,1,2,1,2,2,1,1]
[[1,5],[2,8],[3,9],[4],[6],[7],[10],[11],[12]]=>11101101111=>[1,1,1,2,1,2,1,1,1,1]
[[1,5],[2,7],[3,11],[4],[6],[8],[9],[10],[12]]=>11101011101=>[1,1,1,2,2,1,1,2,1]
[[1,5],[2,7],[3,10],[4],[6],[8],[9],[11],[12]]=>11101011011=>[1,1,1,2,2,1,2,1,1]
[[1,5],[2,7],[3,9],[4],[6],[8],[10],[11],[12]]=>11101010111=>[1,1,1,2,2,2,1,1,1]
[[1,5],[2,11],[3],[4],[6],[7],[8],[9],[10],[12]]=>11101111101=>[1,1,1,2,1,1,1,1,2,1]
[[1,5],[2,10],[3],[4],[6],[7],[8],[9],[11],[12]]=>11101111011=>[1,1,1,2,1,1,1,2,1,1]
[[1,5],[2,9],[3],[4],[6],[7],[8],[10],[11],[12]]=>11101110111=>[1,1,1,2,1,1,2,1,1,1]
[[1,5],[2,8],[3],[4],[6],[7],[9],[10],[11],[12]]=>11101101111=>[1,1,1,2,1,2,1,1,1,1]
[[1,7],[2,8],[3],[4],[5],[6],[9],[10],[11],[12]]=>11111011111=>[1,1,1,1,1,2,1,1,1,1,1]
[[1,6],[2,11],[3],[4],[5],[7],[8],[9],[10],[12]]=>11110111101=>[1,1,1,1,2,1,1,1,2,1]
[[1,6],[2,10],[3],[4],[5],[7],[8],[9],[11],[12]]=>11110111011=>[1,1,1,1,2,1,1,2,1,1]
[[1,6],[2,9],[3],[4],[5],[7],[8],[10],[11],[12]]=>11110110111=>[1,1,1,1,2,1,2,1,1,1]
[[1,6],[2,8],[3],[4],[5],[7],[9],[10],[11],[12]]=>11110101111=>[1,1,1,1,2,2,1,1,1,1]
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]]=>11111111101=>[1,1,1,1,1,1,1,1,1,2,1]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10],[11],[12]]=>11111011111=>[1,1,1,1,1,2,1,1,1,1,1]
[[1,2],[3,5],[4],[6],[7],[8],[9]]=>01101111=>[2,1,2,1,1,1,1]
[[1,2,4],[3],[5],[6],[7],[8],[9]]=>01011111=>[2,2,1,1,1,1,1]
[[1,2],[3,4],[5,7],[6],[8],[9]]=>01011011=>[2,2,1,2,1,1]
[[1,3,6],[2,5],[4],[7],[8],[9]]=>10100111=>[1,2,3,1,1,1]
[[1,2,3,5],[4],[6],[7],[8],[9]]=>00101111=>[3,2,1,1,1,1]
[[1,2],[3,4],[5,6],[7,9],[8]]=>01010110=>[2,2,2,1,2]
[[1,2,3],[4,5,7],[6],[8],[9]]=>00101011=>[3,2,2,1,1]
[[1,2,4,7],[3,6],[5],[8],[9]]=>01010011=>[2,2,3,1,1]
[[1,2,3,4,6],[5],[7],[8],[9]]=>00010111=>[4,2,1,1,1]
[[1,3,4],[2,7],[5,8],[6,9]]=>10011011=>[1,3,1,2,1,1]
[[1,2,5],[3,6,9],[4,8],[7]]=>01101100=>[2,1,2,1,3]
[[1,3,5,8],[2,4,7],[6],[9]]=>10101001=>[1,2,2,3,1]
[[1,2,3,5,8],[4,7],[6],[9]]=>00101001=>[3,2,3,1]
[[1,2,3,4,5,7],[6],[8],[9]]=>00001011=>[5,2,1,1]
[[1,3,6,9],[2,5,8],[4,7]]=>10100100=>[1,2,3,3]
[[1,2,3,5,6],[4,8],[7,9]]=>00100101=>[3,3,2,1]
[[1,2,3,4],[5,6,7,9],[8]]=>00010010=>[4,3,2]
[[1,2,4,6,9],[3,5,8],[7]]=>01010100=>[2,2,2,3]
[[1,2,3,4,6,9],[5,8],[7]]=>00010100=>[4,2,3]
[[1,2,3,4,5,6,8],[7],[9]]=>00000101=>[6,2,1]
[[1,2,3,5,7,9],[4,6,8]]=>00101010=>[3,2,2,2]
[[1,2,3,4,5,7,9],[6,8]]=>00001010=>[5,2,2]
[[1,2],[3,5],[4],[6],[7],[8],[9],[10]]=>011011111=>[2,1,2,1,1,1,1,1]
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]=>010111111=>[2,2,1,1,1,1,1,1]
[[1,2],[3,4],[5,7],[6],[8],[9],[10]]=>010110111=>[2,2,1,2,1,1,1]
[[1,3,6],[2,5],[4],[7],[8],[9],[10]]=>101001111=>[1,2,3,1,1,1,1]
[[1,2,3,5],[4],[6],[7],[8],[9],[10]]=>001011111=>[3,2,1,1,1,1,1]
[[1,2],[3,4],[5,6],[7,9],[8],[10]]=>010101101=>[2,2,2,1,2,1]
[[1,2,3],[4,5,7],[6],[8],[9],[10]]=>001010111=>[3,2,2,1,1,1]
[[1,2,4,7],[3,6],[5],[8],[9],[10]]=>010100111=>[2,2,3,1,1,1]
[[1,2,3,4,6],[5],[7],[8],[9],[10]]=>000101111=>[4,2,1,1,1,1]
[[1,3,4],[2,7],[5,8],[6,10],[9]]=>100110110=>[1,3,1,2,1,2]
[[1,2,5],[3,6,9],[4,8],[7],[10]]=>011011001=>[2,1,2,1,3,1]
[[1,3,5,8],[2,4,7],[6],[9],[10]]=>101010011=>[1,2,2,3,1,1]
[[1,2,3,5,8],[4,7],[6],[9],[10]]=>001010011=>[3,2,3,1,1]
[[1,2,3,4,5,7],[6],[8],[9],[10]]=>000010111=>[5,2,1,1,1]
[[1,2,5],[3,6,7],[4,9],[8,10]]=>011010101=>[2,1,2,2,2,1]
[[1,2,4,5],[3,8],[6,9],[7,10]]=>010011011=>[2,3,1,2,1,1]
[[1,2,3],[4,5,6],[7,8,10],[9]]=>001001010=>[3,3,2,2]
[[1,2,3,5,6],[4,8],[7,10],[9]]=>001001010=>[3,3,2,2]
[[1,2,3,4],[5,6,7,9],[8],[10]]=>000100101=>[4,3,2,1]
[[1,2,4,6,9],[3,5,8],[7],[10]]=>010101001=>[2,2,2,3,1]
[[1,2,3,4,6,9],[5,8],[7],[10]]=>000101001=>[4,2,3,1]
[[1,2,3,4,5,6,8],[7],[9],[10]]=>000001011=>[6,2,1,1]
[[1,3,4,6],[2,7,9],[5,8,10]]=>100101101=>[1,3,2,1,2,1]
[[1,2,3,7],[4,5,8,10],[6,9]]=>001010110=>[3,2,2,1,2]
[[1,2,4,7,10],[3,6,9],[5,8]]=>010100100=>[2,2,3,3]
[[1,2,3,4,6,7],[5,9],[8,10]]=>000100101=>[4,3,2,1]
[[1,3,5,7,10],[2,4,6,9],[8]]=>101010100=>[1,2,2,2,3]
[[1,2,3,5,7,10],[4,6,9],[8]]=>001010100=>[3,2,2,3]
[[1,2,3,4,5,7,10],[6,9],[8]]=>000010100=>[5,2,3]
[[1,2,3,4,5,6,7,9],[8],[10]]=>000000101=>[7,2,1]
[[1,2,8],[3,9],[4],[5],[6],[7]]=>01111101=>[2,1,1,1,1,2,1]
[[1,2,7],[3,8],[4,9],[5],[6]]=>01111011=>[2,1,1,1,2,1,1]
[[1,2,7,9],[3,8],[4],[5],[6]]=>01111010=>[2,1,1,1,2,2]
[[1,2,6,9],[3,7],[4,8],[5]]=>01110110=>[2,1,1,2,1,2]
[[1,2,6,8],[3,7,9],[4],[5]]=>01110101=>[2,1,1,2,2,1]
[[1,2,6,8,9],[3,7],[4],[5]]=>01110100=>[2,1,1,2,3]
[[1,2,5,8],[3,6,9],[4,7]]=>01101101=>[2,1,2,1,2,1]
[[1,2,5,8,9],[3,6],[4,7]]=>01101100=>[2,1,2,1,3]
[[1,2,5,7,8,9],[3,6],[4]]=>01101000=>[2,1,2,4]
[[1,2,4,6,8,9],[3,5,7]]=>01010100=>[2,2,2,3]
[[1,2,4,6,7,8,9],[3,5]]=>01010000=>[2,2,5]
[[1,2,9],[3,10],[4],[5],[6],[7],[8]]=>011111101=>[2,1,1,1,1,1,2,1]
[[1,2,8],[3,9],[4,10],[5],[6],[7]]=>011111011=>[2,1,1,1,1,2,1,1]
[[1,2,8,10],[3,9],[4],[5],[6],[7]]=>011111010=>[2,1,1,1,1,2,2]
[[1,2,7],[3,8],[4,9],[5,10],[6]]=>011110111=>[2,1,1,1,2,1,1,1]
[[1,2,7,10],[3,8],[4,9],[5],[6]]=>011110110=>[2,1,1,1,2,1,2]
[[1,2,7,9],[3,8,10],[4],[5],[6]]=>011110101=>[2,1,1,1,2,2,1]
[[1,2,7,9,10],[3,8],[4],[5],[6]]=>011110100=>[2,1,1,1,2,3]
[[1,2,6,10],[3,7],[4,8],[5,9]]=>011101110=>[2,1,1,2,1,1,2]
[[1,2,6,9],[3,7,10],[4,8],[5]]=>011101101=>[2,1,1,2,1,2,1]
[[1,2,6,9,10],[3,7],[4,8],[5]]=>011101100=>[2,1,1,2,1,3]
[[1,2,6,8,10],[3,7,9],[4],[5]]=>011101010=>[2,1,1,2,2,2]
[[1,2,6,8,9,10],[3,7],[4],[5]]=>011101000=>[2,1,1,2,4]
[[1,2,5,8,10],[3,6,9],[4,7]]=>011011010=>[2,1,2,1,2,2]
[[1,2,5,8,9,10],[3,6],[4,7]]=>011011000=>[2,1,2,1,4]
[[1,2,5,7,9],[3,6,8,10],[4]]=>011010101=>[2,1,2,2,2,1]
[[1,2,5,7,8,9,10],[3,6],[4]]=>011010000=>[2,1,2,5]
[[1,2,3,4],[5,6],[7,9],[8,10]]=>000101101=>[4,2,1,2,1]
[[1,2,3,4],[5,7],[6,8],[9,10]]=>000110110=>[4,1,2,1,2]
[[1,2,3,4],[5,7],[6,9],[8,10]]=>000110101=>[4,1,2,2,1]
[[1,2,3,4],[5,8],[6,9],[7,10]]=>000111011=>[4,1,1,2,1,1]
[[1,2,3,5],[4,6],[7,8],[9,10]]=>001011010=>[3,2,1,2,2]
[[1,2,3,5],[4,6],[7,9],[8,10]]=>001011101=>[3,2,1,1,2,1]
[[1,2,3,5],[4,7],[6,8],[9,10]]=>001010110=>[3,2,2,1,2]
[[1,2,3,5],[4,7],[6,9],[8,10]]=>001010101=>[3,2,2,2,1]
[[1,2,3,5],[4,8],[6,9],[7,10]]=>001011011=>[3,2,1,2,1,1]
[[1,2,3,6],[4,7],[5,8],[9,10]]=>001101110=>[3,1,2,1,1,2]
[[1,2,3,6],[4,7],[5,9],[8,10]]=>001101101=>[3,1,2,1,2,1]
[[1,2,3,6],[4,8],[5,9],[7,10]]=>001101011=>[3,1,2,2,1,1]
[[1,2,4,6],[3,5],[7,8],[9,10]]=>010101010=>[2,2,2,2,2]
[[1,2,4,6],[3,5],[7,9],[8,10]]=>010101101=>[2,2,2,1,2,1]
[[1,2,4,7],[3,5],[6,8],[9,10]]=>010110110=>[2,2,1,2,1,2]
[[1,2,4,7],[3,5],[6,9],[8,10]]=>010110101=>[2,2,1,2,2,1]
[[1,2,4,8],[3,5],[6,9],[7,10]]=>010111011=>[2,2,1,1,2,1,1]
[[1,2,4,5],[3,6],[7,8],[9,10]]=>010011010=>[2,3,1,2,2]
[[1,2,4,5],[3,6],[7,9],[8,10]]=>010011101=>[2,3,1,1,2,1]
[[1,2,4,5],[3,7],[6,8],[9,10]]=>010010110=>[2,3,2,1,2]
[[1,2,4,5],[3,7],[6,9],[8,10]]=>010010101=>[2,3,2,2,1]
[[1,2,4,6],[3,7],[5,8],[9,10]]=>010101110=>[2,2,2,1,1,2]
[[1,2,4,6],[3,7],[5,9],[8,10]]=>010101101=>[2,2,2,1,2,1]
[[1,2,4,6],[3,8],[5,9],[7,10]]=>010101011=>[2,2,2,2,1,1]
[[1,2,4,7],[3,8],[5,9],[6,10]]=>010110111=>[2,2,1,2,1,1,1]
[[1,2,5,8],[3,6],[4,7],[9,10]]=>011011010=>[2,1,2,1,2,2]
[[1,2,5,9],[3,6],[4,7],[8,10]]=>011011101=>[2,1,2,1,1,2,1]
[[1,2,5,7],[3,6],[4,8],[9,10]]=>011010110=>[2,1,2,2,1,2]
[[1,2,5,7],[3,6],[4,9],[8,10]]=>011010101=>[2,1,2,2,2,1]
[[1,2,5,8],[3,6],[4,9],[7,10]]=>011011011=>[2,1,2,1,2,1,1]
[[1,2,5,6],[3,7],[4,8],[9,10]]=>011001110=>[2,1,3,1,1,2]
[[1,2,5,6],[3,7],[4,9],[8,10]]=>011001101=>[2,1,3,1,2,1]
[[1,2,5,6],[3,8],[4,9],[7,10]]=>011001011=>[2,1,3,2,1,1]
[[1,2,5,7],[3,8],[4,9],[6,10]]=>011010111=>[2,1,2,2,1,1,1]
[[1,2,6,9],[3,7],[4,8],[5,10]]=>011101101=>[2,1,1,2,1,2,1]
[[1,2,6,8],[3,7],[4,9],[5,10]]=>011101011=>[2,1,1,2,2,1,1]
[[1,2,6,7],[3,8],[4,9],[5,10]]=>011100111=>[2,1,1,3,1,1,1]
[[1,2,3,4],[5,6],[7,8],[9,11],[10,12]]=>00010101101=>[4,2,2,1,2,1]
[[1,2,3,4],[5,6],[7,9],[8,11],[10,12]]=>00010110101=>[4,2,1,2,2,1]
[[1,2,3,4],[5,6],[7,10],[8,11],[9,12]]=>00010111011=>[4,2,1,1,2,1,1]
[[1,2,3,4],[5,7],[6,9],[8,11],[10,12]]=>00011010101=>[4,1,2,2,2,1]
[[1,2,3,4],[5,8],[6,9],[7,10],[11,12]]=>00011101110=>[4,1,1,2,1,1,2]
[[1,2,3,5],[4,7],[6,9],[8,11],[10,12]]=>00101010101=>[3,2,2,2,2,1]
[[1,2,3,5],[4,7],[6,10],[8,11],[9,12]]=>00101011011=>[3,2,2,1,2,1,1]
[[1,2,3,5],[4,8],[6,10],[7,11],[9,12]]=>00101101011=>[3,2,1,2,2,1,1]
[[1,2,3,6],[4,8],[5,10],[7,11],[9,12]]=>00110101011=>[3,1,2,2,2,1,1]
[[1,2,3,7],[4,8],[5,9],[6,10],[11,12]]=>00111011110=>[3,1,1,2,1,1,1,2]
[[1,2,4,6],[3,5],[7,8],[9,10],[11,12]]=>01010101010=>[2,2,2,2,2,2]
[[1,2,4,6],[3,5],[7,8],[9,11],[10,12]]=>01010101101=>[2,2,2,2,1,2,1]
[[1,2,4,6],[3,5],[7,9],[8,10],[11,12]]=>01010110110=>[2,2,2,1,2,1,2]
[[1,2,4,6],[3,5],[7,9],[8,11],[10,12]]=>01010110101=>[2,2,2,1,2,2,1]
[[1,2,4,6],[3,5],[7,10],[8,11],[9,12]]=>01010111011=>[2,2,2,1,1,2,1,1]
[[1,2,4,7],[3,5],[6,8],[9,10],[11,12]]=>01011011010=>[2,2,1,2,1,2,2]
[[1,2,4,7],[3,5],[6,8],[9,11],[10,12]]=>01011011101=>[2,2,1,2,1,1,2,1]
[[1,2,4,7],[3,5],[6,9],[8,10],[11,12]]=>01011010110=>[2,2,1,2,2,1,2]
[[1,2,4,7],[3,5],[6,9],[8,11],[10,12]]=>01011010101=>[2,2,1,2,2,2,1]
[[1,2,4,7],[3,5],[6,10],[8,11],[9,12]]=>01011011011=>[2,2,1,2,1,2,1,1]
[[1,2,4,8],[3,5],[6,9],[7,10],[11,12]]=>01011101110=>[2,2,1,1,2,1,1,2]
[[1,2,4,8],[3,5],[6,9],[7,11],[10,12]]=>01011101101=>[2,2,1,1,2,1,2,1]
[[1,2,4,8],[3,5],[6,10],[7,11],[9,12]]=>01011101011=>[2,2,1,1,2,2,1,1]
[[1,2,4,9],[3,5],[6,10],[7,11],[8,12]]=>01011110111=>[2,2,1,1,1,2,1,1,1]
[[1,2,4,5],[3,7],[6,9],[8,11],[10,12]]=>01001010101=>[2,3,2,2,2,1]
[[1,2,4,6],[3,7],[5,9],[8,10],[11,12]]=>01010110110=>[2,2,2,1,2,1,2]
[[1,2,4,6],[3,7],[5,9],[8,11],[10,12]]=>01010110101=>[2,2,2,1,2,2,1]
[[1,2,4,6],[3,7],[5,10],[8,11],[9,12]]=>01010111011=>[2,2,2,1,1,2,1,1]
[[1,2,4,6],[3,8],[5,9],[7,11],[10,12]]=>01010101101=>[2,2,2,2,1,2,1]
[[1,2,4,6],[3,8],[5,10],[7,11],[9,12]]=>01010101011=>[2,2,2,2,2,1,1]
[[1,2,4,6],[3,9],[5,10],[7,11],[8,12]]=>01010110111=>[2,2,2,1,2,1,1,1]
[[1,2,4,7],[3,8],[5,9],[6,11],[10,12]]=>01011011101=>[2,2,1,2,1,1,2,1]
[[1,2,4,7],[3,8],[5,10],[6,11],[9,12]]=>01011011011=>[2,2,1,2,1,2,1,1]
[[1,2,4,7],[3,9],[5,10],[6,11],[8,12]]=>01011010111=>[2,2,1,2,2,1,1,1]
[[1,2,5,8],[3,6],[4,7],[9,10],[11,12]]=>01101101010=>[2,1,2,1,2,2,2]
[[1,2,5,8],[3,6],[4,7],[9,11],[10,12]]=>01101101101=>[2,1,2,1,2,1,2,1]
[[1,2,5,9],[3,6],[4,7],[8,10],[11,12]]=>01101110110=>[2,1,2,1,1,2,1,2]
[[1,2,5,9],[3,6],[4,7],[8,11],[10,12]]=>01101110101=>[2,1,2,1,1,2,2,1]
[[1,2,5,10],[3,6],[4,7],[8,11],[9,12]]=>01101111011=>[2,1,2,1,1,1,2,1,1]
[[1,2,5,7],[3,6],[4,8],[9,10],[11,12]]=>01101011010=>[2,1,2,2,1,2,2]
[[1,2,5,7],[3,6],[4,8],[9,11],[10,12]]=>01101011101=>[2,1,2,2,1,1,2,1]
[[1,2,5,7],[3,6],[4,9],[8,10],[11,12]]=>01101010110=>[2,1,2,2,2,1,2]
[[1,2,5,7],[3,6],[4,9],[8,11],[10,12]]=>01101010101=>[2,1,2,2,2,2,1]
[[1,2,5,7],[3,6],[4,10],[8,11],[9,12]]=>01101011011=>[2,1,2,2,1,2,1,1]
[[1,2,5,8],[3,6],[4,9],[7,10],[11,12]]=>01101101110=>[2,1,2,1,2,1,1,2]
[[1,2,5,8],[3,6],[4,9],[7,11],[10,12]]=>01101101101=>[2,1,2,1,2,1,2,1]
[[1,2,5,8],[3,6],[4,10],[7,11],[9,12]]=>01101101011=>[2,1,2,1,2,2,1,1]
[[1,2,5,9],[3,6],[4,10],[7,11],[8,12]]=>01101110111=>[2,1,2,1,1,2,1,1,1]
[[1,2,5,7],[3,8],[4,9],[6,11],[10,12]]=>01101011101=>[2,1,2,2,1,1,2,1]
[[1,2,5,7],[3,8],[4,10],[6,11],[9,12]]=>01101011011=>[2,1,2,2,1,2,1,1]
[[1,2,5,7],[3,9],[4,10],[6,11],[8,12]]=>01101010111=>[2,1,2,2,2,1,1,1]
[[1,2,6,10],[3,7],[4,8],[5,9],[11,12]]=>01110111010=>[2,1,1,2,1,1,2,2]
[[1,2,6,11],[3,7],[4,8],[5,9],[10,12]]=>01110111101=>[2,1,1,2,1,1,1,2,1]
[[1,2,6,9],[3,7],[4,8],[5,10],[11,12]]=>01110110110=>[2,1,1,2,1,2,1,2]
[[1,2,6,9],[3,7],[4,8],[5,11],[10,12]]=>01110110101=>[2,1,1,2,1,2,2,1]
[[1,2,6,10],[3,7],[4,8],[5,11],[9,12]]=>01110111011=>[2,1,1,2,1,1,2,1,1]
[[1,2,6,8],[3,7],[4,9],[5,10],[11,12]]=>01110101110=>[2,1,1,2,2,1,1,2]
[[1,2,6,8],[3,7],[4,9],[5,11],[10,12]]=>01110101101=>[2,1,1,2,2,1,2,1]
[[1,2,6,8],[3,7],[4,10],[5,11],[9,12]]=>01110101011=>[2,1,1,2,2,2,1,1]
[[1,2,6,9],[3,7],[4,10],[5,11],[8,12]]=>01110110111=>[2,1,1,2,1,2,1,1,1]
[[1,2,7,12],[3,8],[4,9],[5,10],[6,11]]=>01111011110=>[2,1,1,1,2,1,1,1,2]
[[1,2,7,11],[3,8],[4,9],[5,10],[6,12]]=>01111011101=>[2,1,1,1,2,1,1,2,1]
[[1,2,7,10],[3,8],[4,9],[5,11],[6,12]]=>01111011011=>[2,1,1,1,2,1,2,1,1]
[[1,2,7,9],[3,8],[4,10],[5,11],[6,12]]=>01111010111=>[2,1,1,1,2,2,1,1,1]
[[1,2,8],[3,9],[4,10],[5,11],[6,12],[7]]=>01111101111=>[2,1,1,1,1,2,1,1,1,1]
[[1,5],[2,6],[3],[4],[7],[8],[9]]=>11101111=>[1,1,1,2,1,1,1,1]
[[1,3,6],[2,7],[4],[5],[8],[9]]=>10110111=>[1,2,1,2,1,1,1]
[[1,3,8],[2,9],[4],[5],[6],[7]]=>10111101=>[1,2,1,1,1,2,1]
[[1,5,7],[2,6,8],[3],[4],[9]]=>11101011=>[1,1,1,2,2,1,1]
[[1,3,4,7],[2,8],[5],[6],[9]]=>10011011=>[1,3,1,2,1,1]
[[1,5,9],[2,6],[3],[4],[7],[8]]=>11101110=>[1,1,1,2,1,1,2]
[[1,3,4,9],[2],[5],[6],[7],[8]]=>10011110=>[1,3,1,1,1,2]
[[1,3,4,5,8],[2,9],[6],[7]]=>10001101=>[1,4,1,2,1]
[[1,3,4,7,9],[2,8],[5],[6]]=>10011010=>[1,3,1,2,2]
[[1,3,4,5,6,9],[2],[7],[8]]=>10000110=>[1,5,1,2]
[[1,7],[2,8],[3,9],[4],[5],[6],[10]]=>111110111=>[1,1,1,1,1,2,1,1,1]
[[1,3,6],[2,7],[4],[5],[8],[9],[10]]=>101101111=>[1,2,1,2,1,1,1,1]
[[1,3,8],[2,9],[4,10],[5],[6],[7]]=>101111011=>[1,2,1,1,1,2,1,1]
[[1,5,7],[2,6,8],[3],[4],[9],[10]]=>111010111=>[1,1,1,2,2,1,1,1]
[[1,3,4,7],[2,8],[5],[6],[9],[10]]=>100110111=>[1,3,1,2,1,1,1]
[[1,3,10],[2],[4],[5],[6],[7],[8],[9]]=>101111110=>[1,2,1,1,1,1,1,2]
[[1,5,9],[2,6,10],[3],[4],[7],[8]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,3,4,9],[2,10],[5],[6],[7],[8]]=>100111101=>[1,3,1,1,1,2,1]
[[1,3,6,8],[2,7,9],[4],[5],[10]]=>101101011=>[1,2,1,2,2,1,1]
[[1,3,4,5,8],[2,9],[6],[7],[10]]=>100011011=>[1,4,1,2,1,1]
[[1,3,6,10],[2,7],[4],[5],[8],[9]]=>101101110=>[1,2,1,2,1,1,2]
[[1,3,4,5,10],[2],[6],[7],[8],[9]]=>100011110=>[1,4,1,1,1,2]
[[1,3,4,7,9],[2,8,10],[5],[6]]=>100110101=>[1,3,1,2,2,1]
[[1,3,4,5,6,9],[2,10],[7],[8]]=>100001101=>[1,5,1,2,1]
[[1,3,4,5,8,10],[2,9],[6],[7]]=>100011010=>[1,4,1,2,2]
[[1,3,4,5,6,7,10],[2],[8],[9]]=>100000110=>[1,6,1,2]
[[1,6],[2,8],[3,9],[4],[5],[7]]=>11110101=>[1,1,1,1,2,2,1]
[[1,6,8],[2,9],[3],[4],[5],[7]]=>11110101=>[1,1,1,1,2,2,1]
[[1,5],[2,7],[3,8],[4,9],[6]]=>11101011=>[1,1,1,2,2,1,1]
[[1,5,8],[2,7],[3,9],[4],[6]]=>11101001=>[1,1,1,2,3,1]
[[1,5,7],[2,8,9],[3],[4],[6]]=>11101010=>[1,1,1,2,2,2]
[[1,5,7,9],[2,8],[3],[4],[6]]=>11101010=>[1,1,1,2,2,2]
[[1,4,8],[2,6],[3,7],[5,9]]=>11010101=>[1,1,2,2,2,1]
[[1,4,7],[2,6,9],[3,8],[5]]=>11010010=>[1,1,2,3,2]
[[1,4,7,9],[2,6],[3,8],[5]]=>11010010=>[1,1,2,3,2]
[[1,4,6,8],[2,7,9],[3],[5]]=>11010101=>[1,1,2,2,2,1]
[[1,4,6,8,9],[2,7],[3],[5]]=>11010100=>[1,1,2,2,3]
[[1,3,6],[2,5,8],[4,7,9]]=>10100101=>[1,2,3,2,1]
[[1,3,6,8],[2,5,9],[4,7]]=>10100101=>[1,2,3,2,1]
[[1,3,6,8,9],[2,5],[4,7]]=>10100100=>[1,2,3,3]
[[1,3,5,7],[2,6,8,9],[4]]=>10101010=>[1,2,2,2,2]
[[1,3,5,7,9],[2,6,8],[4]]=>10101010=>[1,2,2,2,2]
[[1,3,5,7,8,9],[2,6],[4]]=>10101000=>[1,2,2,4]
[[1,7],[2,9],[3,10],[4],[5],[6],[8]]=>111110101=>[1,1,1,1,1,2,2,1]
[[1,7,9],[2,10],[3],[4],[5],[6],[8]]=>111110101=>[1,1,1,1,1,2,2,1]
[[1,6],[2,8],[3,9],[4,10],[5],[7]]=>111101011=>[1,1,1,1,2,2,1,1]
[[1,6,9],[2,8],[3,10],[4],[5],[7]]=>111101001=>[1,1,1,1,2,3,1]
[[1,6,8],[2,9,10],[3],[4],[5],[7]]=>111101010=>[1,1,1,1,2,2,2]
[[1,6,8,10],[2,9],[3],[4],[5],[7]]=>111101010=>[1,1,1,1,2,2,2]
[[1,5,9],[2,7],[3,8],[4,10],[6]]=>111010101=>[1,1,1,2,2,2,1]
[[1,5,8],[2,7,10],[3,9],[4],[6]]=>111010010=>[1,1,1,2,3,2]
[[1,5,8,10],[2,7],[3,9],[4],[6]]=>111010010=>[1,1,1,2,3,2]
[[1,5,7,9],[2,8,10],[3],[4],[6]]=>111010101=>[1,1,1,2,2,2,1]
[[1,5,7,9,10],[2,8],[3],[4],[6]]=>111010100=>[1,1,1,2,2,3]
[[1,4,8],[2,6,10],[3,7],[5,9]]=>110101010=>[1,1,2,2,2,2]
[[1,4,8,10],[2,6],[3,7],[5,9]]=>110101010=>[1,1,2,2,2,2]
[[1,4,7],[2,6,9],[3,8,10],[5]]=>110100101=>[1,1,2,3,2,1]
[[1,4,7,9],[2,6,10],[3,8],[5]]=>110100101=>[1,1,2,3,2,1]
[[1,4,7,9,10],[2,6],[3,8],[5]]=>110100100=>[1,1,2,3,3]
[[1,4,6,8],[2,7,9,10],[3],[5]]=>110101010=>[1,1,2,2,2,2]
[[1,4,6,8,10],[2,7,9],[3],[5]]=>110101010=>[1,1,2,2,2,2]
[[1,4,6,8,9,10],[2,7],[3],[5]]=>110101000=>[1,1,2,2,4]
[[1,3,6,9],[2,5,8],[4,7,10]]=>101001001=>[1,2,3,3,1]
[[1,3,6,8],[2,5,9,10],[4,7]]=>101001010=>[1,2,3,2,2]
[[1,3,6,8,10],[2,5,9],[4,7]]=>101001010=>[1,2,3,2,2]
[[1,3,6,8,9,10],[2,5],[4,7]]=>101001000=>[1,2,3,4]
[[1,3,5,7,9],[2,6,8,10],[4]]=>101010101=>[1,2,2,2,2,1]
[[1,3,5,7,9,10],[2,6,8],[4]]=>101010100=>[1,2,2,2,3]
[[1,3,5,7,8,9,10],[2,6],[4]]=>101010000=>[1,2,2,5]
[[1,2,3,5,7,10],[4,6,8,11],[9,12]]=>00101011011=>[3,2,2,1,2,1,1]
[[1,7],[2,8],[3],[4],[5],[6],[9]]=>11111011=>[1,1,1,1,1,2,1,1]
[[1,6],[2,7],[3,8],[4],[5],[9]]=>11110111=>[1,1,1,1,2,1,1,1]
[[1,6,8],[2,7],[3],[4],[5],[9]]=>11110101=>[1,1,1,1,2,2,1]
[[1,5,8],[2,6],[3,7],[4],[9]]=>11101101=>[1,1,1,2,1,2,1]
[[1,5,7,8],[2,6],[3],[4],[9]]=>11101001=>[1,1,1,2,3,1]
[[1,4,8],[2,5],[3,6],[7,9]]=>11011101=>[1,1,2,1,1,2,1]
[[1,4,7],[2,5,8],[3,6],[9]]=>11011011=>[1,1,2,1,2,1,1]
[[1,4,7,8],[2,5],[3,6],[9]]=>11011001=>[1,1,2,1,3,1]
[[1,4,6,8],[2,5,7],[3],[9]]=>11010101=>[1,1,2,2,2,1]
[[1,4,6,7,8],[2,5],[3],[9]]=>11010001=>[1,1,2,4,1]
[[1,3,6],[2,4,7],[5,8,9]]=>10110110=>[1,2,1,2,1,2]
[[1,3,6,8],[2,4,7],[5,9]]=>10110101=>[1,2,1,2,2,1]
[[1,3,6,7,8],[2,4],[5,9]]=>10110001=>[1,2,1,4,1]
[[1,3,5,7,8],[2,4,6],[9]]=>10101001=>[1,2,2,3,1]
[[1,3,5,6,7,8],[2,4],[9]]=>10100001=>[1,2,5,1]
[[1,2,4,6,7,8],[3,5,9]]=>01010001=>[2,2,4,1]
[[1,2,4,5,6,7,8],[3,9]]=>01000001=>[2,6,1]
[[1,8],[2,9],[3],[4],[5],[6],[7],[10]]=>111111011=>[1,1,1,1,1,1,2,1,1]
[[1,7,9],[2,8],[3],[4],[5],[6],[10]]=>111110101=>[1,1,1,1,1,2,2,1]
[[1,6],[2,7],[3,8],[4,9],[5],[10]]=>111101111=>[1,1,1,1,2,1,1,1,1]
[[1,6,9],[2,7],[3,8],[4],[5],[10]]=>111101101=>[1,1,1,1,2,1,2,1]
[[1,6,8],[2,7,9],[3],[4],[5],[10]]=>111101011=>[1,1,1,1,2,2,1,1]
[[1,6,8,9],[2,7],[3],[4],[5],[10]]=>111101001=>[1,1,1,1,2,3,1]
[[1,5,9],[2,6],[3,7],[4,8],[10]]=>111011101=>[1,1,1,2,1,1,2,1]
[[1,5,8],[2,6,9],[3,7],[4],[10]]=>111011011=>[1,1,1,2,1,2,1,1]
[[1,5,8,9],[2,6],[3,7],[4],[10]]=>111011001=>[1,1,1,2,1,3,1]
[[1,5,7,9],[2,6,8],[3],[4],[10]]=>111010101=>[1,1,1,2,2,2,1]
[[1,5,7,8,9],[2,6],[3],[4],[10]]=>111010001=>[1,1,1,2,4,1]
[[1,4,8],[2,5,9],[3,6],[7,10]]=>110111011=>[1,1,2,1,1,2,1,1]
[[1,4,8,9],[2,5],[3,6],[7,10]]=>110111001=>[1,1,2,1,1,3,1]
[[1,4,7,9],[2,5,8],[3,6],[10]]=>110110101=>[1,1,2,1,2,2,1]
[[1,4,7,8,9],[2,5],[3,6],[10]]=>110110001=>[1,1,2,1,4,1]
[[1,4,6,8],[2,5,7,9],[3],[10]]=>110101011=>[1,1,2,2,2,1,1]
[[1,4,6,8,9],[2,5,7],[3],[10]]=>110101001=>[1,1,2,2,3,1]
[[1,4,6,7,8,9],[2,5],[3],[10]]=>110100001=>[1,1,2,5,1]
[[1,3,6,9],[2,4,7],[5,8,10]]=>101101101=>[1,2,1,2,1,2,1]
[[1,3,6,8],[2,4,7,9],[5,10]]=>101101011=>[1,2,1,2,2,1,1]
[[1,3,6,8,9],[2,4,7],[5,10]]=>101101001=>[1,2,1,2,3,1]
[[1,3,6,7,8,9],[2,4],[5,10]]=>101100001=>[1,2,1,5,1]
[[1,3,5,7,9],[2,4,6,8],[10]]=>101010101=>[1,2,2,2,2,1]
[[1,3,5,7,8,9],[2,4,6],[10]]=>101010001=>[1,2,2,4,1]
[[1,3,5,6,7,8,9],[2,4],[10]]=>101000001=>[1,2,6,1]
[[1,2,4,6,8,9],[3,5,7,10]]=>010101001=>[2,2,2,3,1]
[[1,2,4,6,7,8,9],[3,5,10]]=>010100001=>[2,2,5,1]
[[1,2,4,5,6,7,8,9],[3,10]]=>010000001=>[2,7,1]
[[1,2],[3,9],[4],[5],[6],[7],[8]]=>01111110=>[2,1,1,1,1,1,2]
[[1,2],[3,8],[4,9],[5],[6],[7]]=>01111101=>[2,1,1,1,1,2,1]
[[1,2],[3,7],[4,8],[5,9],[6]]=>01111011=>[2,1,1,1,2,1,1]
[[1,2,7],[3,8,9],[4],[5],[6]]=>01111010=>[2,1,1,1,2,2]
[[1,2,6],[3,7,9],[4,8],[5]]=>01110110=>[2,1,1,2,1,2]
[[1,2,5],[3,6,8],[4,7,9]]=>01101101=>[2,1,2,1,2,1]
[[1,2,5,7],[3,6,8,9],[4]]=>01101010=>[2,1,2,2,2]
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>011111110=>[2,1,1,1,1,1,1,2]
[[1,2],[3,9],[4,10],[5],[6],[7],[8]]=>011111101=>[2,1,1,1,1,1,2,1]
[[1,2],[3,8],[4,9],[5,10],[6],[7]]=>011111011=>[2,1,1,1,1,2,1,1]
[[1,2,8],[3,9,10],[4],[5],[6],[7]]=>011111010=>[2,1,1,1,1,2,2]
[[1,2,7],[3,8,10],[4,9],[5],[6]]=>011110110=>[2,1,1,1,2,1,2]
[[1,2,6],[3,7,10],[4,8],[5,9]]=>011101110=>[2,1,1,2,1,1,2]
[[1,2,6],[3,7,9],[4,8,10],[5]]=>011101101=>[2,1,1,2,1,2,1]
[[1,2,6,8],[3,7,9,10],[4],[5]]=>011101010=>[2,1,1,2,2,2]
[[1,2,5,8],[3,6,9,10],[4,7]]=>011011010=>[2,1,2,1,2,2]
[[1,2,4,7],[3,5,8],[6,9],[10],[11]]=>0101101111=>[2,2,1,2,1,1,1,1]
[[1,2,4,8],[3,5,9],[6,10],[7,11]]=>0101110111=>[2,2,1,1,2,1,1,1]
[[1,4,8],[2,5,9],[3,6,10],[7,11]]=>1101110111=>[1,1,2,1,1,2,1,1,1]
[[1,4,8],[2,5,9],[3,6,10],[7,11],[12]]=>11011101111=>[1,1,2,1,1,2,1,1,1,1]
[[1,2,5,9],[3,6,10],[4,7,11],[8,12]]=>01101110111=>[2,1,2,1,1,2,1,1,1]
[[1,2,5,8],[3,6,9],[4,7,10],[11]]=>0110110111=>[2,1,2,1,2,1,1,1]
[[1,3,6,10],[2,4,7,11],[5,8,12],[9,13]]=>101101110111=>[1,2,1,2,1,1,2,1,1,1]
[[1,3,6,9],[2,4,7,10],[5,8,11],[12]]=>10110110111=>[1,2,1,2,1,2,1,1,1]
[[1,3,5,8],[2,4,6,9],[7,10],[11]]=>1010110111=>[1,2,2,1,2,1,1,1]
[[1,2,4,7,10],[3,5,8,11],[6,9,12]]=>01011011011=>[2,2,1,2,1,2,1,1]
[[1,2,4,6,9],[3,5,7,10],[8,11]]=>0101011011=>[2,2,2,1,2,1,1]
[[1,2,4,6,9],[3,5,7,10],[8,11],[12]]=>01010110111=>[2,2,2,1,2,1,1,1]
[[1,2,3,5,8],[4,6,9],[7,10],[11]]=>0010110111=>[3,2,1,2,1,1,1]
[[1,3],[2,8],[4,9],[5],[6],[7]]=>10111101=>[1,2,1,1,1,2,1]
[[1,2,3],[4,9],[5],[6],[7],[8]]=>00111110=>[3,1,1,1,1,2]
[[1,4],[2,7],[3,8],[5,9],[6]]=>11011011=>[1,1,2,1,2,1,1]
[[1,3,9],[2,4],[5,8],[6],[7]]=>10111100=>[1,2,1,1,1,3]
[[1,2,4],[3,8,9],[5],[6],[7]]=>01011100=>[2,2,1,1,3]
[[1,2,3,4],[5,9],[6],[7],[8]]=>00011110=>[4,1,1,1,2]
[[1,4,9],[2,5],[3,7],[6,8]]=>11011010=>[1,1,2,1,2,2]
[[1,2,5],[3,4,9],[6,8],[7]]=>01001100=>[2,3,1,3]
[[1,4,5,9],[2,7],[3,8],[6]]=>11001010=>[1,1,3,2,2]
[[1,2,3,5],[4,8,9],[6],[7]]=>00101100=>[3,2,1,3]
[[1,2,3,4,5],[6,9],[7],[8]]=>00001110=>[5,1,1,2]
[[1,4,5,6,9],[2,7],[3,8]]=>11000110=>[1,1,4,1,2]
[[1,2,4,6],[3,5,8,9],[7]]=>01010100=>[2,2,2,3]
[[1,2,3,4,6],[5,8,9],[7]]=>00010100=>[4,2,3]
[[1,2,3,4,5,6],[7,9],[8]]=>00000110=>[6,1,2]
[[1,2,3,5,7],[4,6,8,9]]=>00101010=>[3,2,2,2]
[[1,2,3,4,5,7],[6,8,9]]=>00001010=>[5,2,2]
[[1,3],[2,9],[4,10],[5],[6],[7],[8]]=>101111101=>[1,2,1,1,1,1,2,1]
[[1,2,3],[4,10],[5],[6],[7],[8],[9]]=>001111110=>[3,1,1,1,1,1,2]
[[1,4],[2,8],[3,9],[5,10],[6],[7]]=>110111011=>[1,1,2,1,1,2,1,1]
[[1,3,10],[2,4],[5,9],[6],[7],[8]]=>101111100=>[1,2,1,1,1,1,3]
[[1,2,4],[3,9,10],[5],[6],[7],[8]]=>010111100=>[2,2,1,1,1,3]
[[1,2,3,4],[5,10],[6],[7],[8],[9]]=>000111110=>[4,1,1,1,1,2]
[[1,4,10],[2,5],[3,8],[6,9],[7]]=>110111010=>[1,1,2,1,1,2,2]
[[1,2,5],[3,4,10],[6,9],[7],[8]]=>010011100=>[2,3,1,1,3]
[[1,4,5,10],[2,8],[3,9],[6],[7]]=>110011010=>[1,1,3,1,2,2]
[[1,2,3,5],[4,9,10],[6],[7],[8]]=>001011100=>[3,2,1,1,3]
[[1,2,3,4,5],[6,10],[7],[8],[9]]=>000011110=>[5,1,1,1,2]
[[1,2,9],[3,5,10],[4,6],[7,8]]=>011011001=>[2,1,2,1,3,1]
[[1,5,6,10],[2,7],[3,8],[4,9]]=>111001110=>[1,1,1,3,1,1,2]
[[1,3,6],[2,5,9],[4,8,10],[7]]=>101001001=>[1,2,3,3,1]
[[1,2,3,10],[4,5,6],[7,9],[8]]=>001001100=>[3,3,1,3]
[[1,4,5,6,10],[2,8],[3,9],[7]]=>110001010=>[1,1,4,2,2]
[[1,2,4,6],[3,5,9,10],[7],[8]]=>010101100=>[2,2,2,1,3]
[[1,2,3,4,6],[5,9,10],[7],[8]]=>000101100=>[4,2,1,3]
[[1,2,3,4,5,6],[7,10],[8],[9]]=>000001110=>[6,1,1,2]
[[1,3,6,10],[2,4,7],[5,8,9]]=>101101100=>[1,2,1,2,1,3]
[[1,2,4,7],[3,5,6,10],[8,9]]=>010100100=>[2,2,3,3]
[[1,4,5,6,7,10],[2,8],[3,9]]=>110000110=>[1,1,5,1,2]
[[1,2,3,5,7],[4,6,9,10],[8]]=>001010100=>[3,2,2,3]
[[1,2,3,4,5,7],[6,9,10],[8]]=>000010100=>[5,2,3]
[[1,2,3,4,5,6,7],[8,10],[9]]=>000000110=>[7,1,2]
[[1,2,3,4,6,8],[5,7,9,10]]=>000101010=>[4,2,2,2]
[[1,2,3,4,5,6,8],[7,9,10]]=>000001010=>[6,2,2]
[[1,3],[2,4],[5,9],[6],[7],[8]]=>10111110=>[1,2,1,1,1,1,2]
[[1,3,9],[2,4],[5],[6],[7],[8]]=>10111110=>[1,2,1,1,1,1,2]
[[1,4],[2,5],[3,6],[7,9],[8]]=>11011110=>[1,1,2,1,1,1,2]
[[1,4,9],[2,5],[3,6],[7],[8]]=>11011110=>[1,1,2,1,1,1,2]
[[1,2,4],[3,5,9],[6],[7],[8]]=>01011110=>[2,2,1,1,1,2]
[[1,2,4,9],[3,5],[6],[7],[8]]=>01011110=>[2,2,1,1,1,2]
[[1,2,5],[3,6,9],[4,7],[8]]=>01101110=>[2,1,2,1,1,2]
[[1,2,5,9],[3,6],[4,7],[8]]=>01101110=>[2,1,2,1,1,2]
[[1,3,5,9],[2,4,6],[7],[8]]=>10101110=>[1,2,2,1,1,2]
[[1,2,3,5,9],[4,6],[7],[8]]=>00101110=>[3,2,1,1,2]
[[1,3,6,9],[2,4,7],[5,8]]=>10110110=>[1,2,1,2,1,2]
[[1,2,3,6,9],[4,7],[5,8]]=>00110110=>[3,1,2,1,2]
[[1,2,4,6],[3,5,7,9],[8]]=>01010110=>[2,2,2,1,2]
[[1,2,4,6,9],[3,5,7],[8]]=>01010110=>[2,2,2,1,2]
[[1,2,3,4,6,9],[5,7],[8]]=>00010110=>[4,2,1,2]
[[1,3],[2,4],[5,10],[6],[7],[8],[9]]=>101111110=>[1,2,1,1,1,1,1,2]
[[1,3,10],[2,4],[5],[6],[7],[8],[9]]=>101111110=>[1,2,1,1,1,1,1,2]
[[1,4],[2,5],[3,6],[7,10],[8],[9]]=>110111110=>[1,1,2,1,1,1,1,2]
[[1,4,10],[2,5],[3,6],[7],[8],[9]]=>110111110=>[1,1,2,1,1,1,1,2]
[[1,2,4],[3,5,10],[6],[7],[8],[9]]=>010111110=>[2,2,1,1,1,1,2]
[[1,2,4,10],[3,5],[6],[7],[8],[9]]=>010111110=>[2,2,1,1,1,1,2]
[[1,5,10],[2,6],[3,7],[4,8],[9]]=>111011110=>[1,1,1,2,1,1,1,2]
[[1,2,5],[3,6,10],[4,7],[8],[9]]=>011011110=>[2,1,2,1,1,1,2]
[[1,2,5,10],[3,6],[4,7],[8],[9]]=>011011110=>[2,1,2,1,1,1,2]
[[1,3,5,10],[2,4,6],[7],[8],[9]]=>101011110=>[1,2,2,1,1,1,2]
[[1,2,3,5,10],[4,6],[7],[8],[9]]=>001011110=>[3,2,1,1,1,2]
[[1,3,6],[2,4,7],[5,8,10],[9]]=>101101110=>[1,2,1,2,1,1,2]
[[1,3,6,10],[2,4,7],[5,8],[9]]=>101101110=>[1,2,1,2,1,1,2]
[[1,2,3,6,10],[4,7],[5,8],[9]]=>001101110=>[3,1,2,1,1,2]
[[1,2,4,6],[3,5,7,10],[8],[9]]=>010101110=>[2,2,2,1,1,2]
[[1,2,4,6,10],[3,5,7],[8],[9]]=>010101110=>[2,2,2,1,1,2]
[[1,2,3,4,6,10],[5,7],[8],[9]]=>000101110=>[4,2,1,1,2]
[[1,2,4,7],[3,5,8,10],[6,9]]=>010110110=>[2,2,1,2,1,2]
[[1,2,4,7,10],[3,5,8],[6,9]]=>010110110=>[2,2,1,2,1,2]
[[1,2,3,4,7,10],[5,8],[6,9]]=>000110110=>[4,1,2,1,2]
[[1,3,5,7,10],[2,4,6,8],[9]]=>101010110=>[1,2,2,2,1,2]
[[1,2,3,5,7,10],[4,6,8],[9]]=>001010110=>[3,2,2,1,2]
[[1,2,3,4,5,7,10],[6,8],[9]]=>000010110=>[5,2,1,2]
[[1,2,4,6,10],[3,5,7,11],[8,12],[9,13]]=>010101110111=>[2,2,2,1,1,2,1,1,1]
[[1,2,4,6,8],[3,5,7,9],[10],[11],[12]]=>01010101111=>[2,2,2,2,1,1,1,1]
[[1,2,4,6,8],[3,5,7,9],[10],[11]]=>0101010111=>[2,2,2,2,1,1,1]
[[1,2,3,6,10],[4,7,11],[5,8,12],[9,13]]=>001101110111=>[3,1,2,1,1,2,1,1,1]
[[1,2,3,6,9],[4,7,10],[5,8,11],[12],[13]]=>001101101111=>[3,1,2,1,2,1,1,1,1]
[[1,2,3,6,9],[4,7,10],[5,8,11]]=>0011011011=>[3,1,2,1,2,1,1]
[[1,2,3,4,8],[5,9],[6,10],[7,11],[12]]=>00011101111=>[4,1,1,2,1,1,1,1]
[[1,2,3,4,8],[5,9],[6,10],[7,11]]=>0001110111=>[4,1,1,2,1,1,1]
[[1,2,3,4,7],[5,8],[6,9],[10],[11]]=>0001101111=>[4,1,2,1,1,1,1]
[[1,3,6,9],[2,4,7,10],[5,8,11],[12],[13]]=>101101101111=>[1,2,1,2,1,2,1,1,1,1]
[[1,3,5,9],[2,4,6,10],[7,11],[8,12],[13]]=>101011101111=>[1,2,2,1,1,2,1,1,1,1]
[[1,3,5,9],[2,4,6,10],[7,11],[8,12]]=>10101110111=>[1,2,2,1,1,2,1,1,1]
[[1,3,5,7],[2,4,6,8],[9],[10],[11]]=>1010101111=>[1,2,2,2,1,1,1,1]
[[1,4,7],[2,5,8],[3,6,9],[10],[11]]=>1101101111=>[1,1,2,1,2,1,1,1,1]
[[1,4],[2,5],[3],[6],[7],[8],[9]]=>11011111=>[1,1,2,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4],[8],[9]]=>11101111=>[1,1,1,2,1,1,1,1]
[[1,3,5],[2,6],[4],[7],[8],[9]]=>10101111=>[1,2,2,1,1,1,1]
[[1,3,6],[2,7],[4,8],[5],[9]]=>10110111=>[1,2,1,2,1,1,1]
[[1,4,6],[2,5,7],[3],[8],[9]]=>11010111=>[1,1,2,2,1,1,1]
[[1,3,4,6],[2,7],[5],[8],[9]]=>10010111=>[1,3,2,1,1,1]
[[1,3,7],[2,4],[5,8],[6,9]]=>10111011=>[1,2,1,1,2,1,1]
[[1,4,7],[2,5,8],[3,9],[6]]=>11011011=>[1,1,2,1,2,1,1]
[[1,3,4,7],[2,8],[5,9],[6]]=>10011011=>[1,3,1,2,1,1]
[[1,3,5,7],[2,6,8],[4],[9]]=>10101011=>[1,2,2,2,1,1]
[[1,3,4,5,7],[2,8],[6],[9]]=>10001011=>[1,4,2,1,1]
[[1,3,5,8],[2,6,9],[4,7]]=>10101101=>[1,2,2,1,2,1]
[[1,3,4,5,8],[2,6],[7,9]]=>10001101=>[1,4,1,2,1]
[[1,3,4,6,8],[2,7,9],[5]]=>10010101=>[1,3,2,2,1]
[[1,3,4,5,6,8],[2,9],[7]]=>10000101=>[1,5,2,1]
[[1,3,4,5,7,9],[2,6,8]]=>10001010=>[1,4,2,2]
[[1,3,4,5,6,7,9],[2,8]]=>10000010=>[1,6,2]
[[1,4],[2,5],[3],[6],[7],[8],[9],[10]]=>110111111=>[1,1,2,1,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4],[8],[9],[10]]=>111011111=>[1,1,1,2,1,1,1,1,1]
[[1,3,5],[2,6],[4],[7],[8],[9],[10]]=>101011111=>[1,2,2,1,1,1,1,1]
[[1,3,6],[2,7],[4,8],[5],[9],[10]]=>101101111=>[1,2,1,2,1,1,1,1]
[[1,4,6],[2,5,7],[3],[8],[9],[10]]=>110101111=>[1,1,2,2,1,1,1,1]
[[1,3,4,6],[2,7],[5],[8],[9],[10]]=>100101111=>[1,3,2,1,1,1,1]
[[1,3,7],[2,8],[4,9],[5,10],[6]]=>101110111=>[1,2,1,1,2,1,1,1]
[[1,4,7],[2,5,8],[3,9],[6],[10]]=>110110111=>[1,1,2,1,2,1,1,1]
[[1,3,4,7],[2,8],[5,9],[6],[10]]=>100110111=>[1,3,1,2,1,1,1]
[[1,3,5,7],[2,6,8],[4],[9],[10]]=>101010111=>[1,2,2,2,1,1,1]
[[1,3,4,5,7],[2,8],[6],[9],[10]]=>100010111=>[1,4,2,1,1,1]
[[1,3,4,8],[2,5],[6,9],[7,10]]=>100111011=>[1,3,1,1,2,1,1]
[[1,3,5,8],[2,6,9],[4,10],[7]]=>101011011=>[1,2,2,1,2,1,1]
[[1,3,4,5,8],[2,9],[6,10],[7]]=>100011011=>[1,4,1,2,1,1]
[[1,3,4,6,8],[2,7,9],[5],[10]]=>100101011=>[1,3,2,2,1,1]
[[1,3,4,5,6,8],[2,9],[7],[10]]=>100001011=>[1,5,2,1,1]
[[1,4,6,9],[2,5,7,10],[3,8]]=>110101101=>[1,1,2,2,1,2,1]
[[1,3,4,6,9],[2,7,10],[5,8]]=>100101101=>[1,3,2,1,2,1]
[[1,3,4,5,6,9],[2,7],[8,10]]=>100001101=>[1,5,1,2,1]
[[1,3,4,5,7,9],[2,8,10],[6]]=>100010101=>[1,4,2,2,1]
[[1,3,4,5,6,7,9],[2,10],[8]]=>100000101=>[1,6,2,1]
[[1,3,4,6,8,10],[2,5,7,9]]=>100101010=>[1,3,2,2,2]
[[1,3,4,5,6,8,10],[2,7,9]]=>100001010=>[1,5,2,2]
[[1,3,4,5,6,7,8,10],[2,9]]=>100000010=>[1,7,2]
[[1,2,3,7],[4,8],[5,9],[6]]=>00111011=>[3,1,1,2,1,1]
[[1,2,3,5,8],[4,6,9],[7]]=>00101101=>[3,2,1,2,1]
[[1,2,3,4,5,8],[6,9],[7]]=>00001101=>[5,1,2,1]
[[1,2,4,8],[3,5,9],[6,10],[7]]=>010111011=>[2,2,1,1,2,1,1]
[[1,2,3,4,8],[5,9],[6,10],[7]]=>000111011=>[4,1,1,2,1,1]
[[1,2,3,6,9],[4,7,10],[5,8]]=>001101101=>[3,1,2,1,2,1]
[[1,2,4,6,9],[3,5,7,10],[8]]=>010101101=>[2,2,2,1,2,1]
[[1,2,3,4,6,9],[5,7,10],[8]]=>000101101=>[4,2,1,2,1]
[[1,2,3,4,5,6,9],[7,10],[8]]=>000001101=>[6,1,2,1]
[[1,2,3,4,5,7],[6,9],[8]]=>00001010=>[5,2,2]
[[1,2,3,4,6],[5,7,8,9]]=>00010100=>[4,2,3]
[[1,2,3,4,6],[5,7,9],[8]]=>00010110=>[4,2,1,2]
[[1,2,3,4,6],[5,8],[7,9]]=>00010101=>[4,2,2,1]
[[1,2,3,4,6],[5,8],[7],[9]]=>00010101=>[4,2,2,1]
[[1,2,3,5],[4,6,7,9],[8]]=>00101010=>[3,2,2,2]
[[1,2,3,5],[4,6,8],[7,9]]=>00101101=>[3,2,1,2,1]
[[1,2,3,5],[4,6,8],[7],[9]]=>00101101=>[3,2,1,2,1]
[[1,2,3,5],[4,7],[6,9],[8]]=>00101010=>[3,2,2,2]
[[1,2,3,5],[4,7],[6],[8],[9]]=>00101011=>[3,2,2,1,1]
[[1,2,4],[3,5,7],[6,8,9]]=>01011010=>[2,2,1,2,2]
[[1,2,4],[3,5,7],[6,9],[8]]=>01011010=>[2,2,1,2,2]
[[1,2,4],[3,5,7],[6],[8],[9]]=>01011011=>[2,2,1,2,1,1]
[[1,2,4],[3,6],[5,8],[7,9]]=>01010101=>[2,2,2,2,1]
[[1,2,4],[3,6],[5,8],[7],[9]]=>01010101=>[2,2,2,2,1]
[[1,2,4],[3,6],[5],[7],[8],[9]]=>01010111=>[2,2,2,1,1,1]
[[1,2,3,4,5,6,8],[7,10],[9]]=>000001010=>[6,2,2]
[[1,2,3,4,5,7],[6,8,9,10]]=>000010100=>[5,2,3]
[[1,2,3,4,5,7],[6,8,10],[9]]=>000010110=>[5,2,1,2]
[[1,2,3,4,5,7],[6,9],[8,10]]=>000010101=>[5,2,2,1]
[[1,2,3,4,5,7],[6,9],[8],[10]]=>000010101=>[5,2,2,1]
[[1,2,3,4,6],[5,7,8,10],[9]]=>000101010=>[4,2,2,2]
[[1,2,3,4,6],[5,7,9],[8,10]]=>000101101=>[4,2,1,2,1]
[[1,2,3,4,6],[5,7,9],[8],[10]]=>000101101=>[4,2,1,2,1]
[[1,2,3,4,6],[5,8],[7,10],[9]]=>000101010=>[4,2,2,2]
[[1,2,3,4,6],[5,8],[7],[9],[10]]=>000101011=>[4,2,2,1,1]
[[1,2,3,5],[4,6,7,9],[8,10]]=>001010101=>[3,2,2,2,1]
[[1,2,3,5],[4,6,7,9],[8],[10]]=>001010101=>[3,2,2,2,1]
[[1,2,3,5],[4,6,8],[7,9,10]]=>001011010=>[3,2,1,2,2]
[[1,2,3,5],[4,6,8],[7,10],[9]]=>001011010=>[3,2,1,2,2]
[[1,2,3,5],[4,6,8],[7],[9],[10]]=>001011011=>[3,2,1,2,1,1]
[[1,2,3,5],[4,7],[6,9],[8],[10]]=>001010101=>[3,2,2,2,1]
[[1,2,3,5],[4,7],[6],[8],[9],[10]]=>001010111=>[3,2,2,1,1,1]
[[1,2,4],[3,5,7],[6,8,10],[9]]=>010110110=>[2,2,1,2,1,2]
[[1,2,4],[3,5,7],[6,9],[8,10]]=>010110101=>[2,2,1,2,2,1]
[[1,2,4],[3,5,7],[6,9],[8],[10]]=>010110101=>[2,2,1,2,2,1]
[[1,2,4],[3,5,7],[6],[8],[9],[10]]=>010110111=>[2,2,1,2,1,1,1]
[[1,2,4],[3,6],[5,8],[7],[9],[10]]=>010101011=>[2,2,2,2,1,1]
[[1,2,4],[3,6],[5],[7],[8],[9],[10]]=>010101111=>[2,2,2,1,1,1,1]
[[1,4,5,6],[2,8,9],[3],[7]]=>11000100=>[1,1,4,3]
[[1,4,5],[2,7,8],[3,10],[6],[9]]=>110010010=>[1,1,3,3,2]
[[1,2,4,5,6,7],[3,8,9]]=>01000010=>[2,5,2]
[[1,2,4,5,6,7,8],[3,9,10]]=>010000010=>[2,6,2]
[[1,3,8],[2,5],[4,7],[6,10],[9]]=>101010010=>[1,2,2,3,2]
[[1,4,7],[2,6],[3,9],[5],[8]]=>11010010=>[1,1,2,3,2]
[[1,6,7],[2,9],[3],[4],[5],[8]]=>11110010=>[1,1,1,1,3,2]
[[1,3,6,7],[2,5,10],[4,9],[8]]=>101000100=>[1,2,4,3]
[[1,5,6,7],[2,9,10],[3],[4],[8]]=>111000100=>[1,1,1,4,3]
[[1,5,8],[2,7],[3,10],[4],[6],[9]]=>111010010=>[1,1,1,2,3,2]
[[1,7,8],[2,10],[3],[4],[5],[6],[9]]=>111110010=>[1,1,1,1,1,3,2]
[[1,5,7,8],[2,6,9,10],[3],[4]]=>111010010=>[1,1,1,2,3,2]
[[1,5,6,9],[2,7,8,10],[3],[4]]=>111001001=>[1,1,1,3,3,1]
[[1,5,6,8],[2,7,9,10],[3],[4]]=>111001010=>[1,1,1,3,2,2]
[[1,5,6,7],[2,8,9,10],[3],[4]]=>111000100=>[1,1,1,4,3]
[[1,4,7,9],[2,6,8,10],[3],[5]]=>110100101=>[1,1,2,3,2,1]
[[1,4,7,8],[2,6,9,10],[3],[5]]=>110100010=>[1,1,2,4,2]
[[1,4,6,9],[2,7,8,10],[3],[5]]=>110101001=>[1,1,2,2,3,1]
[[1,4,6,7],[2,8,9,10],[3],[5]]=>110100100=>[1,1,2,3,3]
[[1,4,5,9],[2,7,8,10],[3],[6]]=>110010001=>[1,1,3,4,1]
[[1,4,5,8],[2,7,9,10],[3],[6]]=>110010010=>[1,1,3,3,2]
[[1,4,5,7],[2,8,9,10],[3],[6]]=>110010100=>[1,1,3,2,3]
[[1,3,7,9],[2,5,8,10],[4],[6]]=>101010101=>[1,2,2,2,2,1]
[[1,3,7,8],[2,5,9,10],[4],[6]]=>101010010=>[1,2,2,3,2]
[[1,3,6,9],[2,5,8,10],[4],[7]]=>101001001=>[1,2,3,3,1]
[[1,3,6,8],[2,5,9,10],[4],[7]]=>101001010=>[1,2,3,2,2]
[[1,3,6,7],[2,5,9,10],[4],[8]]=>101000100=>[1,2,4,3]
[[1,3,7,9],[2,6,8,10],[4],[5]]=>101100101=>[1,2,1,3,2,1]
[[1,3,7,8],[2,6,9,10],[4],[5]]=>101100010=>[1,2,1,4,2]
[[1,3,6,9],[2,7,8,10],[4],[5]]=>101101001=>[1,2,1,2,3,1]
[[1,3,6,8],[2,7,9,10],[4],[5]]=>101101010=>[1,2,1,2,2,2]
[[1,3,5,9],[2,7,8,10],[4],[6]]=>101010001=>[1,2,2,4,1]
[[1,3,5,8],[2,7,9,10],[4],[6]]=>101010010=>[1,2,2,3,2]
[[1,3,5,7],[2,8,9,10],[4],[6]]=>101010100=>[1,2,2,2,3]
[[1,3,5,6],[2,8,9,10],[4],[7]]=>101001000=>[1,2,3,4]
[[1,3,4,9],[2,6,7,10],[5],[8]]=>100100101=>[1,3,3,2,1]
[[1,3,4,8],[2,6,7,10],[5],[9]]=>100100010=>[1,3,4,2]
[[1,3,4,9],[2,6,8,10],[5],[7]]=>100101001=>[1,3,2,3,1]
[[1,3,4,8],[2,6,9,10],[5],[7]]=>100101010=>[1,3,2,2,2]
[[1,3,4,7],[2,6,9,10],[5],[8]]=>100100100=>[1,3,3,3]
[[1,3,4,9],[2,7,8,10],[5],[6]]=>100110001=>[1,3,1,4,1]
[[1,3,4,8],[2,7,9,10],[5],[6]]=>100110010=>[1,3,1,3,2]
[[1,3,4,7],[2,8,9,10],[5],[6]]=>100110100=>[1,3,1,2,3]
[[1,3,4,6],[2,8,9,10],[5],[7]]=>100101000=>[1,3,2,4]
[[1,3,4,5],[2,7,8,10],[6],[9]]=>100010010=>[1,4,3,2]
[[1,3,4,5],[2,7,9,10],[6],[8]]=>100010100=>[1,4,2,3]
[[1,3,4,5],[2,8,9,10],[6],[7]]=>100011000=>[1,4,1,4]
[[1,4,7,8,9],[2,6,10,11,12],[3],[5]]=>11010000100=>[1,1,2,5,3]
[[1,4,6,8,11],[2,7,9,10,12],[3],[5]]=>11010101001=>[1,1,2,2,2,3,1]
[[1,4,6,8,10],[2,7,9,11,12],[3],[5]]=>11010101010=>[1,1,2,2,2,2,2]
[[1,4,6,8,9],[2,7,10,11,12],[3],[5]]=>11010100100=>[1,1,2,2,3,3]
[[1,4,6,7,9],[2,8,10,11,12],[3],[5]]=>11010010100=>[1,1,2,3,2,3]
[[1,4,6,7,8],[2,9,10,11,12],[3],[5]]=>11010001000=>[1,1,2,4,4]
[[1,4,5,7,9],[2,8,10,11,12],[3],[6]]=>11001010100=>[1,1,3,2,2,3]
[[1,4,5,6,10],[2,8,9,11,12],[3],[7]]=>11000100010=>[1,1,4,4,2]
[[1,3,7,9,11],[2,5,8,10,12],[4],[6]]=>10101010101=>[1,2,2,2,2,2,1]
[[1,3,7,9,10],[2,5,8,11,12],[4],[6]]=>10101010010=>[1,2,2,2,3,2]
[[1,3,7,8,11],[2,5,9,10,12],[4],[6]]=>10101001001=>[1,2,2,3,3,1]
[[1,3,7,8,10],[2,5,9,11,12],[4],[6]]=>10101001010=>[1,2,2,3,2,2]
[[1,3,7,8,9],[2,5,10,11,12],[4],[6]]=>10101000100=>[1,2,2,4,3]
[[1,3,6,9,11],[2,5,8,10,12],[4],[7]]=>10100100101=>[1,2,3,3,2,1]
[[1,3,6,9,10],[2,5,8,11,12],[4],[7]]=>10100100010=>[1,2,3,4,2]
[[1,3,6,8,11],[2,5,9,10,12],[4],[7]]=>10100101001=>[1,2,3,2,3,1]
[[1,3,6,8,10],[2,5,9,11,12],[4],[7]]=>10100101010=>[1,2,3,2,2,2]
[[1,3,6,8,9],[2,5,10,11,12],[4],[7]]=>10100100100=>[1,2,3,3,3]
[[1,3,6,7,11],[2,5,9,10,12],[4],[8]]=>10100010001=>[1,2,4,4,1]
[[1,3,6,7,10],[2,5,9,11,12],[4],[8]]=>10100010010=>[1,2,4,3,2]
[[1,3,6,7,9],[2,5,10,11,12],[4],[8]]=>10100010100=>[1,2,4,2,3]
[[1,3,6,7,8],[2,5,10,11,12],[4],[9]]=>10100001000=>[1,2,5,4]
[[1,3,6,8,11],[2,7,9,10,12],[4],[5]]=>10110101001=>[1,2,1,2,2,3,1]
[[1,3,6,8,10],[2,7,9,11,12],[4],[5]]=>10110101010=>[1,2,1,2,2,2,2]
[[1,3,5,8,11],[2,7,9,10,12],[4],[6]]=>10101001001=>[1,2,2,3,3,1]
[[1,3,5,8,10],[2,7,9,11,12],[4],[6]]=>10101001010=>[1,2,2,3,2,2]
[[1,3,5,8,9],[2,7,10,11,12],[4],[6]]=>10101000100=>[1,2,2,4,3]
[[1,3,5,7,11],[2,8,9,10,12],[4],[6]]=>10101010001=>[1,2,2,2,4,1]
[[1,3,5,7,10],[2,8,9,11,12],[4],[6]]=>10101010010=>[1,2,2,2,3,2]
[[1,3,5,7,9],[2,8,10,11,12],[4],[6]]=>10101010100=>[1,2,2,2,2,3]
[[1,3,5,6,10],[2,8,9,11,12],[4],[7]]=>10100100010=>[1,2,3,4,2]
[[1,3,5,6,9],[2,8,10,11,12],[4],[7]]=>10100100100=>[1,2,3,3,3]
[[1,3,4,9,11],[2,6,7,10,12],[5],[8]]=>10010010101=>[1,3,3,2,2,1]
[[1,3,4,9,10],[2,6,7,11,12],[5],[8]]=>10010010010=>[1,3,3,3,2]
[[1,3,4,8,11],[2,6,7,10,12],[5],[9]]=>10010001001=>[1,3,4,3,1]
[[1,3,4,8,10],[2,6,7,11,12],[5],[9]]=>10010001010=>[1,3,4,2,2]
[[1,3,4,8,9],[2,6,7,11,12],[5],[10]]=>10010000100=>[1,3,5,3]
[[1,3,4,9,11],[2,6,8,10,12],[5],[7]]=>10010100101=>[1,3,2,3,2,1]
[[1,3,4,9,10],[2,6,8,11,12],[5],[7]]=>10010100010=>[1,3,2,4,2]
[[1,3,4,8,11],[2,6,9,10,12],[5],[7]]=>10010101001=>[1,3,2,2,3,1]
[[1,3,4,8,10],[2,6,9,11,12],[5],[7]]=>10010101010=>[1,3,2,2,2,2]
[[1,3,4,8,9],[2,6,10,11,12],[5],[7]]=>10010100100=>[1,3,2,3,3]
[[1,3,4,7,11],[2,6,9,10,12],[5],[8]]=>10010010001=>[1,3,3,4,1]
[[1,3,4,7,10],[2,6,9,11,12],[5],[8]]=>10010010010=>[1,3,3,3,2]
[[1,3,4,7,9],[2,6,10,11,12],[5],[8]]=>10010010100=>[1,3,3,2,3]
[[1,3,4,7,8],[2,6,10,11,12],[5],[9]]=>10010001000=>[1,3,4,4]
[[1,3,4,6,10],[2,8,9,11,12],[5],[7]]=>10010100010=>[1,3,2,4,2]
[[1,3,4,6,9],[2,8,10,11,12],[5],[7]]=>10010100100=>[1,3,2,3,3]
[[1,3,4,5,11],[2,7,8,9,12],[6],[10]]=>10001000101=>[1,4,4,2,1]
[[1,3,4,5,10],[2,7,8,9,12],[6],[11]]=>10001000010=>[1,4,5,2]
[[1,3,4,5,11],[2,7,8,10,12],[6],[9]]=>10001001001=>[1,4,3,3,1]
[[1,3,4,5,10],[2,7,8,11,12],[6],[9]]=>10001001010=>[1,4,3,2,2]
[[1,3,4,5,9],[2,7,8,11,12],[6],[10]]=>10001000100=>[1,4,4,3]
[[1,3,4,5,11],[2,7,9,10,12],[6],[8]]=>10001010001=>[1,4,2,4,1]
[[1,3,4,5,10],[2,7,9,11,12],[6],[8]]=>10001010010=>[1,4,2,3,2]
[[1,3,4,5,9],[2,7,10,11,12],[6],[8]]=>10001010100=>[1,4,2,2,3]
[[1,3,4,5,8],[2,7,10,11,12],[6],[9]]=>10001001000=>[1,4,3,4]
[[1,3,4,5,6],[2,8,9,10,11],[7],[12]]=>10000100001=>[1,5,5,1]
[[1,3,4,5,6],[2,8,9,10,12],[7],[11]]=>10000100010=>[1,5,4,2]
[[1,3,4,5,6],[2,8,9,11,12],[7],[10]]=>10000100100=>[1,5,3,3]
[[1,3,4,5,6],[2,8,10,11,12],[7],[9]]=>10000101000=>[1,5,2,4]
[[1,3,4,5,6,7],[2,9,10,11,12],[8]]=>10000010000=>[1,6,5]
[[1,6,7,8,9],[2,10],[3],[4],[5]]=>111100001=>[1,1,1,1,5,1]
[[1,2,3],[4,7,8],[5],[6],[9]]=>00111001=>[3,1,1,3,1]
[[1,2,3],[4,8,9],[5],[6],[7],[10]]=>001111001=>[3,1,1,1,3,1]
[[1,4,5,6,7,8],[2,9],[3]]=>11000001=>[1,1,6,1]
[[1,2,3,5,6],[4,7,8,9]]=>00100100=>[3,3,3]
[[1,2,5,6,7],[3,4,8],[9]]=>01000011=>[2,5,1,1]
[[1,3,5,6,7],[2,8],[4,9]]=>10100011=>[1,2,4,1,1]
[[1,5,6,7,8],[2,9],[3],[4]]=>11100001=>[1,1,1,5,1]
[[1,2,3,6],[4,5,7,8],[9]]=>00100101=>[3,3,2,1]
[[1,3,6,7],[2,4,8],[5,9]]=>10110011=>[1,2,1,3,1,1]
[[1,2,3,6],[4,7,8],[5],[9]]=>00110101=>[3,1,2,2,1]
[[1,4,6,7],[2,8],[3,9],[5]]=>11010011=>[1,1,2,3,1,1]
[[1,6,7,8],[2,9],[3],[4],[5]]=>11110001=>[1,1,1,1,4,1]
[[1,3,7],[2,5],[4,8],[6,9]]=>10101011=>[1,2,2,2,1,1]
[[1,5,7],[2,8],[3,9],[4],[6]]=>11101011=>[1,1,1,2,2,1,1]
[[1,7,8],[2,9],[3],[4],[5],[6]]=>11111001=>[1,1,1,1,1,3,1]
[[1,4],[2,6],[3,8],[5,9],[7]]=>11010101=>[1,1,2,2,2,1]
[[1,4,5,6,7,8,9],[2,10],[3]]=>110000001=>[1,1,7,1]
[[1,2,3,5,6,7],[4,8,9,10]]=>001000100=>[3,4,3]
[[1,2,5,6,7,8],[3,4,9],[10]]=>010000011=>[2,6,1,1]
[[1,3,5,6,7,8],[2,9],[4,10]]=>101000011=>[1,2,5,1,1]
[[1,5,6,7,8,9],[2,10],[3],[4]]=>111000001=>[1,1,1,6,1]
[[1,2,3,6,7],[4,5,8,9],[10]]=>001000101=>[3,4,2,1]
[[1,3,6,7,8],[2,4,9],[5,10]]=>101100011=>[1,2,1,4,1,1]
[[1,2,3,6,7],[4,8,9],[5],[10]]=>001100101=>[3,1,3,2,1]
[[1,4,6,7,8],[2,9],[3,10],[5]]=>110100011=>[1,1,2,4,1,1]
[[1,3,4,7],[2,5,6,8],[9,10]]=>100100110=>[1,3,3,1,2]
[[1,2,3,4],[5,7,8,9],[6],[10]]=>000110001=>[4,1,4,1]
[[1,2,4,7],[3,5,8],[6,9,10]]=>010110110=>[2,2,1,2,1,2]
[[1,4,7,8],[2,5,9],[3,6],[10]]=>110110011=>[1,1,2,1,3,1,1]
[[1,2,3,7],[4,8,9],[5],[6],[10]]=>001110101=>[3,1,1,2,2,1]
[[1,3,7,8],[2,5],[4,9],[6,10]]=>101010011=>[1,2,2,3,1,1]
[[1,5,7,8],[2,9],[3,10],[4],[6]]=>111010011=>[1,1,1,2,3,1,1]
[[1,7,8,9],[2,10],[3],[4],[5],[6]]=>111110001=>[1,1,1,1,1,4,1]
[[1,2,5],[3,4,8],[6,7,9],[10]]=>010010011=>[2,3,3,1,1]
[[1,3,8],[2,5,9],[4,6],[7,10]]=>101011011=>[1,2,2,1,2,1,1]
[[1,4,8],[2,6],[3,9],[5,10],[7]]=>110101011=>[1,1,2,2,2,1,1]
[[1,6,8],[2,9],[3,10],[4],[5],[7]]=>111101011=>[1,1,1,1,2,2,1,1]
[[1,8,9],[2,10],[3],[4],[5],[6],[7]]=>111111001=>[1,1,1,1,1,1,3,1]
[[1,5],[2,7],[3,9],[4,10],[6],[8]]=>111010101=>[1,1,1,2,2,2,1]
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
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.
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