Identifier
Mp00109:
Permutations
—descent word⟶
Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
[1,2]=>0=>[2]
[2,1]=>1=>[1,1]
[1,2,3]=>00=>[3]
[1,3,2]=>01=>[2,1]
[2,1,3]=>10=>[1,2]
[2,3,1]=>01=>[2,1]
[3,1,2]=>10=>[1,2]
[3,2,1]=>11=>[1,1,1]
[1,2,3,4]=>000=>[4]
[1,2,4,3]=>001=>[3,1]
[1,3,2,4]=>010=>[2,2]
[1,3,4,2]=>001=>[3,1]
[1,4,2,3]=>010=>[2,2]
[1,4,3,2]=>011=>[2,1,1]
[2,1,3,4]=>100=>[1,3]
[2,1,4,3]=>101=>[1,2,1]
[2,3,1,4]=>010=>[2,2]
[2,3,4,1]=>001=>[3,1]
[2,4,1,3]=>010=>[2,2]
[2,4,3,1]=>011=>[2,1,1]
[3,1,2,4]=>100=>[1,3]
[3,1,4,2]=>101=>[1,2,1]
[3,2,1,4]=>110=>[1,1,2]
[3,2,4,1]=>101=>[1,2,1]
[3,4,1,2]=>010=>[2,2]
[3,4,2,1]=>011=>[2,1,1]
[4,1,2,3]=>100=>[1,3]
[4,1,3,2]=>101=>[1,2,1]
[4,2,1,3]=>110=>[1,1,2]
[4,2,3,1]=>101=>[1,2,1]
[4,3,1,2]=>110=>[1,1,2]
[4,3,2,1]=>111=>[1,1,1,1]
[1,2,3,4,5]=>0000=>[5]
[1,2,3,5,4]=>0001=>[4,1]
[1,2,4,3,5]=>0010=>[3,2]
[1,2,4,5,3]=>0001=>[4,1]
[1,2,5,3,4]=>0010=>[3,2]
[1,2,5,4,3]=>0011=>[3,1,1]
[1,3,2,4,5]=>0100=>[2,3]
[1,3,2,5,4]=>0101=>[2,2,1]
[1,3,4,2,5]=>0010=>[3,2]
[1,3,4,5,2]=>0001=>[4,1]
[1,3,5,2,4]=>0010=>[3,2]
[1,3,5,4,2]=>0011=>[3,1,1]
[1,4,2,3,5]=>0100=>[2,3]
[1,4,2,5,3]=>0101=>[2,2,1]
[1,4,3,2,5]=>0110=>[2,1,2]
[1,4,3,5,2]=>0101=>[2,2,1]
[1,4,5,2,3]=>0010=>[3,2]
[1,4,5,3,2]=>0011=>[3,1,1]
[1,5,2,3,4]=>0100=>[2,3]
[1,5,2,4,3]=>0101=>[2,2,1]
[1,5,3,2,4]=>0110=>[2,1,2]
[1,5,3,4,2]=>0101=>[2,2,1]
[1,5,4,2,3]=>0110=>[2,1,2]
[1,5,4,3,2]=>0111=>[2,1,1,1]
[2,1,3,4,5]=>1000=>[1,4]
[2,1,3,5,4]=>1001=>[1,3,1]
[2,1,4,3,5]=>1010=>[1,2,2]
[2,1,4,5,3]=>1001=>[1,3,1]
[2,1,5,3,4]=>1010=>[1,2,2]
[2,1,5,4,3]=>1011=>[1,2,1,1]
[2,3,1,4,5]=>0100=>[2,3]
[2,3,1,5,4]=>0101=>[2,2,1]
[2,3,4,1,5]=>0010=>[3,2]
[2,3,4,5,1]=>0001=>[4,1]
[2,3,5,1,4]=>0010=>[3,2]
[2,3,5,4,1]=>0011=>[3,1,1]
[2,4,1,3,5]=>0100=>[2,3]
[2,4,1,5,3]=>0101=>[2,2,1]
[2,4,3,1,5]=>0110=>[2,1,2]
[2,4,3,5,1]=>0101=>[2,2,1]
[2,4,5,1,3]=>0010=>[3,2]
[2,4,5,3,1]=>0011=>[3,1,1]
[2,5,1,3,4]=>0100=>[2,3]
[2,5,1,4,3]=>0101=>[2,2,1]
[2,5,3,1,4]=>0110=>[2,1,2]
[2,5,3,4,1]=>0101=>[2,2,1]
[2,5,4,1,3]=>0110=>[2,1,2]
[2,5,4,3,1]=>0111=>[2,1,1,1]
[3,1,2,4,5]=>1000=>[1,4]
[3,1,2,5,4]=>1001=>[1,3,1]
[3,1,4,2,5]=>1010=>[1,2,2]
[3,1,4,5,2]=>1001=>[1,3,1]
[3,1,5,2,4]=>1010=>[1,2,2]
[3,1,5,4,2]=>1011=>[1,2,1,1]
[3,2,1,4,5]=>1100=>[1,1,3]
[3,2,1,5,4]=>1101=>[1,1,2,1]
[3,2,4,1,5]=>1010=>[1,2,2]
[3,2,4,5,1]=>1001=>[1,3,1]
[3,2,5,1,4]=>1010=>[1,2,2]
[3,2,5,4,1]=>1011=>[1,2,1,1]
[3,4,1,2,5]=>0100=>[2,3]
[3,4,1,5,2]=>0101=>[2,2,1]
[3,4,2,1,5]=>0110=>[2,1,2]
[3,4,2,5,1]=>0101=>[2,2,1]
[3,4,5,1,2]=>0010=>[3,2]
[3,4,5,2,1]=>0011=>[3,1,1]
[3,5,1,2,4]=>0100=>[2,3]
[3,5,1,4,2]=>0101=>[2,2,1]
[3,5,2,1,4]=>0110=>[2,1,2]
[3,5,2,4,1]=>0101=>[2,2,1]
[3,5,4,1,2]=>0110=>[2,1,2]
[3,5,4,2,1]=>0111=>[2,1,1,1]
[4,1,2,3,5]=>1000=>[1,4]
[4,1,2,5,3]=>1001=>[1,3,1]
[4,1,3,2,5]=>1010=>[1,2,2]
[4,1,3,5,2]=>1001=>[1,3,1]
[4,1,5,2,3]=>1010=>[1,2,2]
[4,1,5,3,2]=>1011=>[1,2,1,1]
[4,2,1,3,5]=>1100=>[1,1,3]
[4,2,1,5,3]=>1101=>[1,1,2,1]
[4,2,3,1,5]=>1010=>[1,2,2]
[4,2,3,5,1]=>1001=>[1,3,1]
[4,2,5,1,3]=>1010=>[1,2,2]
[4,2,5,3,1]=>1011=>[1,2,1,1]
[4,3,1,2,5]=>1100=>[1,1,3]
[4,3,1,5,2]=>1101=>[1,1,2,1]
[4,3,2,1,5]=>1110=>[1,1,1,2]
[4,3,2,5,1]=>1101=>[1,1,2,1]
[4,3,5,1,2]=>1010=>[1,2,2]
[4,3,5,2,1]=>1011=>[1,2,1,1]
[4,5,1,2,3]=>0100=>[2,3]
[4,5,1,3,2]=>0101=>[2,2,1]
[4,5,2,1,3]=>0110=>[2,1,2]
[4,5,2,3,1]=>0101=>[2,2,1]
[4,5,3,1,2]=>0110=>[2,1,2]
[4,5,3,2,1]=>0111=>[2,1,1,1]
[5,1,2,3,4]=>1000=>[1,4]
[5,1,2,4,3]=>1001=>[1,3,1]
[5,1,3,2,4]=>1010=>[1,2,2]
[5,1,3,4,2]=>1001=>[1,3,1]
[5,1,4,2,3]=>1010=>[1,2,2]
[5,1,4,3,2]=>1011=>[1,2,1,1]
[5,2,1,3,4]=>1100=>[1,1,3]
[5,2,1,4,3]=>1101=>[1,1,2,1]
[5,2,3,1,4]=>1010=>[1,2,2]
[5,2,3,4,1]=>1001=>[1,3,1]
[5,2,4,1,3]=>1010=>[1,2,2]
[5,2,4,3,1]=>1011=>[1,2,1,1]
[5,3,1,2,4]=>1100=>[1,1,3]
[5,3,1,4,2]=>1101=>[1,1,2,1]
[5,3,2,1,4]=>1110=>[1,1,1,2]
[5,3,2,4,1]=>1101=>[1,1,2,1]
[5,3,4,1,2]=>1010=>[1,2,2]
[5,3,4,2,1]=>1011=>[1,2,1,1]
[5,4,1,2,3]=>1100=>[1,1,3]
[5,4,1,3,2]=>1101=>[1,1,2,1]
[5,4,2,1,3]=>1110=>[1,1,1,2]
[5,4,2,3,1]=>1101=>[1,1,2,1]
[5,4,3,1,2]=>1110=>[1,1,1,2]
[5,4,3,2,1]=>1111=>[1,1,1,1,1]
[1,2,3,4,5,6]=>00000=>[6]
[1,2,3,4,6,5]=>00001=>[5,1]
[1,2,3,5,4,6]=>00010=>[4,2]
[1,2,3,5,6,4]=>00001=>[5,1]
[1,2,3,6,4,5]=>00010=>[4,2]
[1,2,3,6,5,4]=>00011=>[4,1,1]
[1,2,4,3,5,6]=>00100=>[3,3]
[1,2,4,3,6,5]=>00101=>[3,2,1]
[1,2,4,5,3,6]=>00010=>[4,2]
[1,2,4,5,6,3]=>00001=>[5,1]
[1,2,4,6,3,5]=>00010=>[4,2]
[1,2,4,6,5,3]=>00011=>[4,1,1]
[1,2,5,3,4,6]=>00100=>[3,3]
[1,2,5,3,6,4]=>00101=>[3,2,1]
[1,2,5,4,3,6]=>00110=>[3,1,2]
[1,2,5,4,6,3]=>00101=>[3,2,1]
[1,2,5,6,3,4]=>00010=>[4,2]
[1,2,5,6,4,3]=>00011=>[4,1,1]
[1,2,6,3,4,5]=>00100=>[3,3]
[1,2,6,3,5,4]=>00101=>[3,2,1]
[1,2,6,4,3,5]=>00110=>[3,1,2]
[1,2,6,4,5,3]=>00101=>[3,2,1]
[1,2,6,5,3,4]=>00110=>[3,1,2]
[1,2,6,5,4,3]=>00111=>[3,1,1,1]
[1,3,2,4,5,6]=>01000=>[2,4]
[1,3,2,4,6,5]=>01001=>[2,3,1]
[1,3,2,5,4,6]=>01010=>[2,2,2]
[1,3,2,5,6,4]=>01001=>[2,3,1]
[1,3,2,6,4,5]=>01010=>[2,2,2]
[1,3,2,6,5,4]=>01011=>[2,2,1,1]
[1,3,4,2,5,6]=>00100=>[3,3]
[1,3,4,2,6,5]=>00101=>[3,2,1]
[1,3,4,5,2,6]=>00010=>[4,2]
[1,3,4,5,6,2]=>00001=>[5,1]
[1,3,4,6,2,5]=>00010=>[4,2]
[1,3,4,6,5,2]=>00011=>[4,1,1]
[1,3,5,2,4,6]=>00100=>[3,3]
[1,3,5,2,6,4]=>00101=>[3,2,1]
[1,3,5,4,2,6]=>00110=>[3,1,2]
[1,3,5,4,6,2]=>00101=>[3,2,1]
[1,3,5,6,2,4]=>00010=>[4,2]
[1,3,5,6,4,2]=>00011=>[4,1,1]
[1,3,6,2,4,5]=>00100=>[3,3]
[1,3,6,2,5,4]=>00101=>[3,2,1]
[1,3,6,4,2,5]=>00110=>[3,1,2]
[1,3,6,4,5,2]=>00101=>[3,2,1]
[1,3,6,5,2,4]=>00110=>[3,1,2]
[1,3,6,5,4,2]=>00111=>[3,1,1,1]
[1,4,2,3,5,6]=>01000=>[2,4]
[1,4,2,3,6,5]=>01001=>[2,3,1]
[1,4,2,5,3,6]=>01010=>[2,2,2]
[1,4,2,5,6,3]=>01001=>[2,3,1]
[1,4,2,6,3,5]=>01010=>[2,2,2]
[1,4,2,6,5,3]=>01011=>[2,2,1,1]
[1,4,3,2,5,6]=>01100=>[2,1,3]
[1,4,3,2,6,5]=>01101=>[2,1,2,1]
[1,4,3,5,2,6]=>01010=>[2,2,2]
[1,4,3,5,6,2]=>01001=>[2,3,1]
[1,4,3,6,2,5]=>01010=>[2,2,2]
[1,4,3,6,5,2]=>01011=>[2,2,1,1]
[1,4,5,2,3,6]=>00100=>[3,3]
[1,4,5,2,6,3]=>00101=>[3,2,1]
[1,4,5,3,2,6]=>00110=>[3,1,2]
[1,4,5,3,6,2]=>00101=>[3,2,1]
[1,4,5,6,2,3]=>00010=>[4,2]
[1,4,5,6,3,2]=>00011=>[4,1,1]
[1,4,6,2,3,5]=>00100=>[3,3]
[1,4,6,2,5,3]=>00101=>[3,2,1]
[1,4,6,3,2,5]=>00110=>[3,1,2]
[1,4,6,3,5,2]=>00101=>[3,2,1]
[1,4,6,5,2,3]=>00110=>[3,1,2]
[1,4,6,5,3,2]=>00111=>[3,1,1,1]
[1,5,2,3,4,6]=>01000=>[2,4]
[1,5,2,3,6,4]=>01001=>[2,3,1]
[1,5,2,4,3,6]=>01010=>[2,2,2]
[1,5,2,4,6,3]=>01001=>[2,3,1]
[1,5,2,6,3,4]=>01010=>[2,2,2]
[1,5,2,6,4,3]=>01011=>[2,2,1,1]
[1,5,3,2,4,6]=>01100=>[2,1,3]
[1,5,3,2,6,4]=>01101=>[2,1,2,1]
[1,5,3,4,2,6]=>01010=>[2,2,2]
[1,5,3,4,6,2]=>01001=>[2,3,1]
[1,5,3,6,2,4]=>01010=>[2,2,2]
[1,5,3,6,4,2]=>01011=>[2,2,1,1]
[1,5,4,2,3,6]=>01100=>[2,1,3]
[1,5,4,2,6,3]=>01101=>[2,1,2,1]
[1,5,4,3,2,6]=>01110=>[2,1,1,2]
[1,5,4,3,6,2]=>01101=>[2,1,2,1]
[1,5,4,6,2,3]=>01010=>[2,2,2]
[1,5,4,6,3,2]=>01011=>[2,2,1,1]
[1,5,6,2,3,4]=>00100=>[3,3]
[1,5,6,2,4,3]=>00101=>[3,2,1]
[1,5,6,3,2,4]=>00110=>[3,1,2]
[1,5,6,3,4,2]=>00101=>[3,2,1]
[1,5,6,4,2,3]=>00110=>[3,1,2]
[1,5,6,4,3,2]=>00111=>[3,1,1,1]
[1,6,2,3,4,5]=>01000=>[2,4]
[1,6,2,3,5,4]=>01001=>[2,3,1]
[1,6,2,4,3,5]=>01010=>[2,2,2]
[1,6,2,4,5,3]=>01001=>[2,3,1]
[1,6,2,5,3,4]=>01010=>[2,2,2]
[1,6,2,5,4,3]=>01011=>[2,2,1,1]
[1,6,3,2,4,5]=>01100=>[2,1,3]
[1,6,3,2,5,4]=>01101=>[2,1,2,1]
[1,6,3,4,2,5]=>01010=>[2,2,2]
[1,6,3,4,5,2]=>01001=>[2,3,1]
[1,6,3,5,2,4]=>01010=>[2,2,2]
[1,6,3,5,4,2]=>01011=>[2,2,1,1]
[1,6,4,2,3,5]=>01100=>[2,1,3]
[1,6,4,2,5,3]=>01101=>[2,1,2,1]
[1,6,4,3,2,5]=>01110=>[2,1,1,2]
[1,6,4,3,5,2]=>01101=>[2,1,2,1]
[1,6,4,5,2,3]=>01010=>[2,2,2]
[1,6,4,5,3,2]=>01011=>[2,2,1,1]
[1,6,5,2,3,4]=>01100=>[2,1,3]
[1,6,5,2,4,3]=>01101=>[2,1,2,1]
[1,6,5,3,2,4]=>01110=>[2,1,1,2]
[1,6,5,3,4,2]=>01101=>[2,1,2,1]
[1,6,5,4,2,3]=>01110=>[2,1,1,2]
[1,6,5,4,3,2]=>01111=>[2,1,1,1,1]
[2,1,3,4,5,6]=>10000=>[1,5]
[2,1,3,4,6,5]=>10001=>[1,4,1]
[2,1,3,5,4,6]=>10010=>[1,3,2]
[2,1,3,5,6,4]=>10001=>[1,4,1]
[2,1,3,6,4,5]=>10010=>[1,3,2]
[2,1,3,6,5,4]=>10011=>[1,3,1,1]
[2,1,4,3,5,6]=>10100=>[1,2,3]
[2,1,4,3,6,5]=>10101=>[1,2,2,1]
[2,1,4,5,3,6]=>10010=>[1,3,2]
[2,1,4,5,6,3]=>10001=>[1,4,1]
[2,1,4,6,3,5]=>10010=>[1,3,2]
[2,1,4,6,5,3]=>10011=>[1,3,1,1]
[2,1,5,3,4,6]=>10100=>[1,2,3]
[2,1,5,3,6,4]=>10101=>[1,2,2,1]
[2,1,5,4,3,6]=>10110=>[1,2,1,2]
[2,1,5,4,6,3]=>10101=>[1,2,2,1]
[2,1,5,6,3,4]=>10010=>[1,3,2]
[2,1,5,6,4,3]=>10011=>[1,3,1,1]
[2,1,6,3,4,5]=>10100=>[1,2,3]
[2,1,6,3,5,4]=>10101=>[1,2,2,1]
[2,1,6,4,3,5]=>10110=>[1,2,1,2]
[2,1,6,4,5,3]=>10101=>[1,2,2,1]
[2,1,6,5,3,4]=>10110=>[1,2,1,2]
[2,1,6,5,4,3]=>10111=>[1,2,1,1,1]
[2,3,1,4,5,6]=>01000=>[2,4]
[2,3,1,4,6,5]=>01001=>[2,3,1]
[2,3,1,5,4,6]=>01010=>[2,2,2]
[2,3,1,5,6,4]=>01001=>[2,3,1]
[2,3,1,6,4,5]=>01010=>[2,2,2]
[2,3,1,6,5,4]=>01011=>[2,2,1,1]
[2,3,4,1,5,6]=>00100=>[3,3]
[2,3,4,1,6,5]=>00101=>[3,2,1]
[2,3,4,5,1,6]=>00010=>[4,2]
[2,3,4,5,6,1]=>00001=>[5,1]
[2,3,4,6,1,5]=>00010=>[4,2]
[2,3,4,6,5,1]=>00011=>[4,1,1]
[2,3,5,1,4,6]=>00100=>[3,3]
[2,3,5,1,6,4]=>00101=>[3,2,1]
[2,3,5,4,1,6]=>00110=>[3,1,2]
[2,3,5,4,6,1]=>00101=>[3,2,1]
[2,3,5,6,1,4]=>00010=>[4,2]
[2,3,5,6,4,1]=>00011=>[4,1,1]
[2,3,6,1,4,5]=>00100=>[3,3]
[2,3,6,1,5,4]=>00101=>[3,2,1]
[2,3,6,4,1,5]=>00110=>[3,1,2]
[2,3,6,4,5,1]=>00101=>[3,2,1]
[2,3,6,5,1,4]=>00110=>[3,1,2]
[2,3,6,5,4,1]=>00111=>[3,1,1,1]
[2,4,1,3,5,6]=>01000=>[2,4]
[2,4,1,3,6,5]=>01001=>[2,3,1]
[2,4,1,5,3,6]=>01010=>[2,2,2]
[2,4,1,5,6,3]=>01001=>[2,3,1]
[2,4,1,6,3,5]=>01010=>[2,2,2]
[2,4,1,6,5,3]=>01011=>[2,2,1,1]
[2,4,3,1,5,6]=>01100=>[2,1,3]
[2,4,3,1,6,5]=>01101=>[2,1,2,1]
[2,4,3,5,1,6]=>01010=>[2,2,2]
[2,4,3,5,6,1]=>01001=>[2,3,1]
[2,4,3,6,1,5]=>01010=>[2,2,2]
[2,4,3,6,5,1]=>01011=>[2,2,1,1]
[2,4,5,1,3,6]=>00100=>[3,3]
[2,4,5,1,6,3]=>00101=>[3,2,1]
[2,4,5,3,1,6]=>00110=>[3,1,2]
[2,4,5,3,6,1]=>00101=>[3,2,1]
[2,4,5,6,1,3]=>00010=>[4,2]
[2,4,5,6,3,1]=>00011=>[4,1,1]
[2,4,6,1,3,5]=>00100=>[3,3]
[2,4,6,1,5,3]=>00101=>[3,2,1]
[2,4,6,3,1,5]=>00110=>[3,1,2]
[2,4,6,3,5,1]=>00101=>[3,2,1]
[2,4,6,5,1,3]=>00110=>[3,1,2]
[2,4,6,5,3,1]=>00111=>[3,1,1,1]
[2,5,1,3,4,6]=>01000=>[2,4]
[2,5,1,3,6,4]=>01001=>[2,3,1]
[2,5,1,4,3,6]=>01010=>[2,2,2]
[2,5,1,4,6,3]=>01001=>[2,3,1]
[2,5,1,6,3,4]=>01010=>[2,2,2]
[2,5,1,6,4,3]=>01011=>[2,2,1,1]
[2,5,3,1,4,6]=>01100=>[2,1,3]
[2,5,3,1,6,4]=>01101=>[2,1,2,1]
[2,5,3,4,1,6]=>01010=>[2,2,2]
[2,5,3,4,6,1]=>01001=>[2,3,1]
[2,5,3,6,1,4]=>01010=>[2,2,2]
[2,5,3,6,4,1]=>01011=>[2,2,1,1]
[2,5,4,1,3,6]=>01100=>[2,1,3]
[2,5,4,1,6,3]=>01101=>[2,1,2,1]
[2,5,4,3,1,6]=>01110=>[2,1,1,2]
[2,5,4,3,6,1]=>01101=>[2,1,2,1]
[2,5,4,6,1,3]=>01010=>[2,2,2]
[2,5,4,6,3,1]=>01011=>[2,2,1,1]
[2,5,6,1,3,4]=>00100=>[3,3]
[2,5,6,1,4,3]=>00101=>[3,2,1]
[2,5,6,3,1,4]=>00110=>[3,1,2]
[2,5,6,3,4,1]=>00101=>[3,2,1]
[2,5,6,4,1,3]=>00110=>[3,1,2]
[2,5,6,4,3,1]=>00111=>[3,1,1,1]
[2,6,1,3,4,5]=>01000=>[2,4]
[2,6,1,3,5,4]=>01001=>[2,3,1]
[2,6,1,4,3,5]=>01010=>[2,2,2]
[2,6,1,4,5,3]=>01001=>[2,3,1]
[2,6,1,5,3,4]=>01010=>[2,2,2]
[2,6,1,5,4,3]=>01011=>[2,2,1,1]
[2,6,3,1,4,5]=>01100=>[2,1,3]
[2,6,3,1,5,4]=>01101=>[2,1,2,1]
[2,6,3,4,1,5]=>01010=>[2,2,2]
[2,6,3,4,5,1]=>01001=>[2,3,1]
[2,6,3,5,1,4]=>01010=>[2,2,2]
[2,6,3,5,4,1]=>01011=>[2,2,1,1]
[2,6,4,1,3,5]=>01100=>[2,1,3]
[2,6,4,1,5,3]=>01101=>[2,1,2,1]
[2,6,4,3,1,5]=>01110=>[2,1,1,2]
[2,6,4,3,5,1]=>01101=>[2,1,2,1]
[2,6,4,5,1,3]=>01010=>[2,2,2]
[2,6,4,5,3,1]=>01011=>[2,2,1,1]
[2,6,5,1,3,4]=>01100=>[2,1,3]
[2,6,5,1,4,3]=>01101=>[2,1,2,1]
[2,6,5,3,1,4]=>01110=>[2,1,1,2]
[2,6,5,3,4,1]=>01101=>[2,1,2,1]
[2,6,5,4,1,3]=>01110=>[2,1,1,2]
[2,6,5,4,3,1]=>01111=>[2,1,1,1,1]
[3,1,2,4,5,6]=>10000=>[1,5]
[3,1,2,4,6,5]=>10001=>[1,4,1]
[3,1,2,5,4,6]=>10010=>[1,3,2]
[3,1,2,5,6,4]=>10001=>[1,4,1]
[3,1,2,6,4,5]=>10010=>[1,3,2]
[3,1,2,6,5,4]=>10011=>[1,3,1,1]
[3,1,4,2,5,6]=>10100=>[1,2,3]
[3,1,4,2,6,5]=>10101=>[1,2,2,1]
[3,1,4,5,2,6]=>10010=>[1,3,2]
[3,1,4,5,6,2]=>10001=>[1,4,1]
[3,1,4,6,2,5]=>10010=>[1,3,2]
[3,1,4,6,5,2]=>10011=>[1,3,1,1]
[3,1,5,2,4,6]=>10100=>[1,2,3]
[3,1,5,2,6,4]=>10101=>[1,2,2,1]
[3,1,5,4,2,6]=>10110=>[1,2,1,2]
[3,1,5,4,6,2]=>10101=>[1,2,2,1]
[3,1,5,6,2,4]=>10010=>[1,3,2]
[3,1,5,6,4,2]=>10011=>[1,3,1,1]
[3,1,6,2,4,5]=>10100=>[1,2,3]
[3,1,6,2,5,4]=>10101=>[1,2,2,1]
[3,1,6,4,2,5]=>10110=>[1,2,1,2]
[3,1,6,4,5,2]=>10101=>[1,2,2,1]
[3,1,6,5,2,4]=>10110=>[1,2,1,2]
[3,1,6,5,4,2]=>10111=>[1,2,1,1,1]
[3,2,1,4,5,6]=>11000=>[1,1,4]
[3,2,1,4,6,5]=>11001=>[1,1,3,1]
[3,2,1,5,4,6]=>11010=>[1,1,2,2]
[3,2,1,5,6,4]=>11001=>[1,1,3,1]
[3,2,1,6,4,5]=>11010=>[1,1,2,2]
[3,2,1,6,5,4]=>11011=>[1,1,2,1,1]
[3,2,4,1,5,6]=>10100=>[1,2,3]
[3,2,4,1,6,5]=>10101=>[1,2,2,1]
[3,2,4,5,1,6]=>10010=>[1,3,2]
[3,2,4,5,6,1]=>10001=>[1,4,1]
[3,2,4,6,1,5]=>10010=>[1,3,2]
[3,2,4,6,5,1]=>10011=>[1,3,1,1]
[3,2,5,1,4,6]=>10100=>[1,2,3]
[3,2,5,1,6,4]=>10101=>[1,2,2,1]
[3,2,5,4,1,6]=>10110=>[1,2,1,2]
[3,2,5,4,6,1]=>10101=>[1,2,2,1]
[3,2,5,6,1,4]=>10010=>[1,3,2]
[3,2,5,6,4,1]=>10011=>[1,3,1,1]
[3,2,6,1,4,5]=>10100=>[1,2,3]
[3,2,6,1,5,4]=>10101=>[1,2,2,1]
[3,2,6,4,1,5]=>10110=>[1,2,1,2]
[3,2,6,4,5,1]=>10101=>[1,2,2,1]
[3,2,6,5,1,4]=>10110=>[1,2,1,2]
[3,2,6,5,4,1]=>10111=>[1,2,1,1,1]
[3,4,1,2,5,6]=>01000=>[2,4]
[3,4,1,2,6,5]=>01001=>[2,3,1]
[3,4,1,5,2,6]=>01010=>[2,2,2]
[3,4,1,5,6,2]=>01001=>[2,3,1]
[3,4,1,6,2,5]=>01010=>[2,2,2]
[3,4,1,6,5,2]=>01011=>[2,2,1,1]
[3,4,2,1,5,6]=>01100=>[2,1,3]
[3,4,2,1,6,5]=>01101=>[2,1,2,1]
[3,4,2,5,1,6]=>01010=>[2,2,2]
[3,4,2,5,6,1]=>01001=>[2,3,1]
[3,4,2,6,1,5]=>01010=>[2,2,2]
[3,4,2,6,5,1]=>01011=>[2,2,1,1]
[3,4,5,1,2,6]=>00100=>[3,3]
[3,4,5,1,6,2]=>00101=>[3,2,1]
[3,4,5,2,1,6]=>00110=>[3,1,2]
[3,4,5,2,6,1]=>00101=>[3,2,1]
[3,4,5,6,1,2]=>00010=>[4,2]
[3,4,5,6,2,1]=>00011=>[4,1,1]
[3,4,6,1,2,5]=>00100=>[3,3]
[3,4,6,1,5,2]=>00101=>[3,2,1]
[3,4,6,2,1,5]=>00110=>[3,1,2]
[3,4,6,2,5,1]=>00101=>[3,2,1]
[3,4,6,5,1,2]=>00110=>[3,1,2]
[3,4,6,5,2,1]=>00111=>[3,1,1,1]
[3,5,1,2,4,6]=>01000=>[2,4]
[3,5,1,2,6,4]=>01001=>[2,3,1]
[3,5,1,4,2,6]=>01010=>[2,2,2]
[3,5,1,4,6,2]=>01001=>[2,3,1]
[3,5,1,6,2,4]=>01010=>[2,2,2]
[3,5,1,6,4,2]=>01011=>[2,2,1,1]
[3,5,2,1,4,6]=>01100=>[2,1,3]
[3,5,2,1,6,4]=>01101=>[2,1,2,1]
[3,5,2,4,1,6]=>01010=>[2,2,2]
[3,5,2,4,6,1]=>01001=>[2,3,1]
[3,5,2,6,1,4]=>01010=>[2,2,2]
[3,5,2,6,4,1]=>01011=>[2,2,1,1]
[3,5,4,1,2,6]=>01100=>[2,1,3]
[3,5,4,1,6,2]=>01101=>[2,1,2,1]
[3,5,4,2,1,6]=>01110=>[2,1,1,2]
[3,5,4,2,6,1]=>01101=>[2,1,2,1]
[3,5,4,6,1,2]=>01010=>[2,2,2]
[3,5,4,6,2,1]=>01011=>[2,2,1,1]
[3,5,6,1,2,4]=>00100=>[3,3]
[3,5,6,1,4,2]=>00101=>[3,2,1]
[3,5,6,2,1,4]=>00110=>[3,1,2]
[3,5,6,2,4,1]=>00101=>[3,2,1]
[3,5,6,4,1,2]=>00110=>[3,1,2]
[3,5,6,4,2,1]=>00111=>[3,1,1,1]
[3,6,1,2,4,5]=>01000=>[2,4]
[3,6,1,2,5,4]=>01001=>[2,3,1]
[3,6,1,4,2,5]=>01010=>[2,2,2]
[3,6,1,4,5,2]=>01001=>[2,3,1]
[3,6,1,5,2,4]=>01010=>[2,2,2]
[3,6,1,5,4,2]=>01011=>[2,2,1,1]
[3,6,2,1,4,5]=>01100=>[2,1,3]
[3,6,2,1,5,4]=>01101=>[2,1,2,1]
[3,6,2,4,1,5]=>01010=>[2,2,2]
[3,6,2,4,5,1]=>01001=>[2,3,1]
[3,6,2,5,1,4]=>01010=>[2,2,2]
[3,6,2,5,4,1]=>01011=>[2,2,1,1]
[3,6,4,1,2,5]=>01100=>[2,1,3]
[3,6,4,1,5,2]=>01101=>[2,1,2,1]
[3,6,4,2,1,5]=>01110=>[2,1,1,2]
[3,6,4,2,5,1]=>01101=>[2,1,2,1]
[3,6,4,5,1,2]=>01010=>[2,2,2]
[3,6,4,5,2,1]=>01011=>[2,2,1,1]
[3,6,5,1,2,4]=>01100=>[2,1,3]
[3,6,5,1,4,2]=>01101=>[2,1,2,1]
[3,6,5,2,1,4]=>01110=>[2,1,1,2]
[3,6,5,2,4,1]=>01101=>[2,1,2,1]
[3,6,5,4,1,2]=>01110=>[2,1,1,2]
[3,6,5,4,2,1]=>01111=>[2,1,1,1,1]
[4,1,2,3,5,6]=>10000=>[1,5]
[4,1,2,3,6,5]=>10001=>[1,4,1]
[4,1,2,5,3,6]=>10010=>[1,3,2]
[4,1,2,5,6,3]=>10001=>[1,4,1]
[4,1,2,6,3,5]=>10010=>[1,3,2]
[4,1,2,6,5,3]=>10011=>[1,3,1,1]
[4,1,3,2,5,6]=>10100=>[1,2,3]
[4,1,3,2,6,5]=>10101=>[1,2,2,1]
[4,1,3,5,2,6]=>10010=>[1,3,2]
[4,1,3,5,6,2]=>10001=>[1,4,1]
[4,1,3,6,2,5]=>10010=>[1,3,2]
[4,1,3,6,5,2]=>10011=>[1,3,1,1]
[4,1,5,2,3,6]=>10100=>[1,2,3]
[4,1,5,2,6,3]=>10101=>[1,2,2,1]
[4,1,5,3,2,6]=>10110=>[1,2,1,2]
[4,1,5,3,6,2]=>10101=>[1,2,2,1]
[4,1,5,6,2,3]=>10010=>[1,3,2]
[4,1,5,6,3,2]=>10011=>[1,3,1,1]
[4,1,6,2,3,5]=>10100=>[1,2,3]
[4,1,6,2,5,3]=>10101=>[1,2,2,1]
[4,1,6,3,2,5]=>10110=>[1,2,1,2]
[4,1,6,3,5,2]=>10101=>[1,2,2,1]
[4,1,6,5,2,3]=>10110=>[1,2,1,2]
[4,1,6,5,3,2]=>10111=>[1,2,1,1,1]
[4,2,1,3,5,6]=>11000=>[1,1,4]
[4,2,1,3,6,5]=>11001=>[1,1,3,1]
[4,2,1,5,3,6]=>11010=>[1,1,2,2]
[4,2,1,5,6,3]=>11001=>[1,1,3,1]
[4,2,1,6,3,5]=>11010=>[1,1,2,2]
[4,2,1,6,5,3]=>11011=>[1,1,2,1,1]
[4,2,3,1,5,6]=>10100=>[1,2,3]
[4,2,3,1,6,5]=>10101=>[1,2,2,1]
[4,2,3,5,1,6]=>10010=>[1,3,2]
[4,2,3,5,6,1]=>10001=>[1,4,1]
[4,2,3,6,1,5]=>10010=>[1,3,2]
[4,2,3,6,5,1]=>10011=>[1,3,1,1]
[4,2,5,1,3,6]=>10100=>[1,2,3]
[4,2,5,1,6,3]=>10101=>[1,2,2,1]
[4,2,5,3,1,6]=>10110=>[1,2,1,2]
[4,2,5,3,6,1]=>10101=>[1,2,2,1]
[4,2,5,6,1,3]=>10010=>[1,3,2]
[4,2,5,6,3,1]=>10011=>[1,3,1,1]
[4,2,6,1,3,5]=>10100=>[1,2,3]
[4,2,6,1,5,3]=>10101=>[1,2,2,1]
[4,2,6,3,1,5]=>10110=>[1,2,1,2]
[4,2,6,3,5,1]=>10101=>[1,2,2,1]
[4,2,6,5,1,3]=>10110=>[1,2,1,2]
[4,2,6,5,3,1]=>10111=>[1,2,1,1,1]
[4,3,1,2,5,6]=>11000=>[1,1,4]
[4,3,1,2,6,5]=>11001=>[1,1,3,1]
[4,3,1,5,2,6]=>11010=>[1,1,2,2]
[4,3,1,5,6,2]=>11001=>[1,1,3,1]
[4,3,1,6,2,5]=>11010=>[1,1,2,2]
[4,3,1,6,5,2]=>11011=>[1,1,2,1,1]
[4,3,2,1,5,6]=>11100=>[1,1,1,3]
[4,3,2,1,6,5]=>11101=>[1,1,1,2,1]
[4,3,2,5,1,6]=>11010=>[1,1,2,2]
[4,3,2,5,6,1]=>11001=>[1,1,3,1]
[4,3,2,6,1,5]=>11010=>[1,1,2,2]
[4,3,2,6,5,1]=>11011=>[1,1,2,1,1]
[4,3,5,1,2,6]=>10100=>[1,2,3]
[4,3,5,1,6,2]=>10101=>[1,2,2,1]
[4,3,5,2,1,6]=>10110=>[1,2,1,2]
[4,3,5,2,6,1]=>10101=>[1,2,2,1]
[4,3,5,6,1,2]=>10010=>[1,3,2]
[4,3,5,6,2,1]=>10011=>[1,3,1,1]
[4,3,6,1,2,5]=>10100=>[1,2,3]
[4,3,6,1,5,2]=>10101=>[1,2,2,1]
[4,3,6,2,1,5]=>10110=>[1,2,1,2]
[4,3,6,2,5,1]=>10101=>[1,2,2,1]
[4,3,6,5,1,2]=>10110=>[1,2,1,2]
[4,3,6,5,2,1]=>10111=>[1,2,1,1,1]
[4,5,1,2,3,6]=>01000=>[2,4]
[4,5,1,2,6,3]=>01001=>[2,3,1]
[4,5,1,3,2,6]=>01010=>[2,2,2]
[4,5,1,3,6,2]=>01001=>[2,3,1]
[4,5,1,6,2,3]=>01010=>[2,2,2]
[4,5,1,6,3,2]=>01011=>[2,2,1,1]
[4,5,2,1,3,6]=>01100=>[2,1,3]
[4,5,2,1,6,3]=>01101=>[2,1,2,1]
[4,5,2,3,1,6]=>01010=>[2,2,2]
[4,5,2,3,6,1]=>01001=>[2,3,1]
[4,5,2,6,1,3]=>01010=>[2,2,2]
[4,5,2,6,3,1]=>01011=>[2,2,1,1]
[4,5,3,1,2,6]=>01100=>[2,1,3]
[4,5,3,1,6,2]=>01101=>[2,1,2,1]
[4,5,3,2,1,6]=>01110=>[2,1,1,2]
[4,5,3,2,6,1]=>01101=>[2,1,2,1]
[4,5,3,6,1,2]=>01010=>[2,2,2]
[4,5,3,6,2,1]=>01011=>[2,2,1,1]
[4,5,6,1,2,3]=>00100=>[3,3]
[4,5,6,1,3,2]=>00101=>[3,2,1]
[4,5,6,2,1,3]=>00110=>[3,1,2]
[4,5,6,2,3,1]=>00101=>[3,2,1]
[4,5,6,3,1,2]=>00110=>[3,1,2]
[4,5,6,3,2,1]=>00111=>[3,1,1,1]
[4,6,1,2,3,5]=>01000=>[2,4]
[4,6,1,2,5,3]=>01001=>[2,3,1]
[4,6,1,3,2,5]=>01010=>[2,2,2]
[4,6,1,3,5,2]=>01001=>[2,3,1]
[4,6,1,5,2,3]=>01010=>[2,2,2]
[4,6,1,5,3,2]=>01011=>[2,2,1,1]
[4,6,2,1,3,5]=>01100=>[2,1,3]
[4,6,2,1,5,3]=>01101=>[2,1,2,1]
[4,6,2,3,1,5]=>01010=>[2,2,2]
[4,6,2,3,5,1]=>01001=>[2,3,1]
[4,6,2,5,1,3]=>01010=>[2,2,2]
[4,6,2,5,3,1]=>01011=>[2,2,1,1]
[4,6,3,1,2,5]=>01100=>[2,1,3]
[4,6,3,1,5,2]=>01101=>[2,1,2,1]
[4,6,3,2,1,5]=>01110=>[2,1,1,2]
[4,6,3,2,5,1]=>01101=>[2,1,2,1]
[4,6,3,5,1,2]=>01010=>[2,2,2]
[4,6,3,5,2,1]=>01011=>[2,2,1,1]
[4,6,5,1,2,3]=>01100=>[2,1,3]
[4,6,5,1,3,2]=>01101=>[2,1,2,1]
[4,6,5,2,1,3]=>01110=>[2,1,1,2]
[4,6,5,2,3,1]=>01101=>[2,1,2,1]
[4,6,5,3,1,2]=>01110=>[2,1,1,2]
[4,6,5,3,2,1]=>01111=>[2,1,1,1,1]
[5,1,2,3,4,6]=>10000=>[1,5]
[5,1,2,3,6,4]=>10001=>[1,4,1]
[5,1,2,4,3,6]=>10010=>[1,3,2]
[5,1,2,4,6,3]=>10001=>[1,4,1]
[5,1,2,6,3,4]=>10010=>[1,3,2]
[5,1,2,6,4,3]=>10011=>[1,3,1,1]
[5,1,3,2,4,6]=>10100=>[1,2,3]
[5,1,3,2,6,4]=>10101=>[1,2,2,1]
[5,1,3,4,2,6]=>10010=>[1,3,2]
[5,1,3,4,6,2]=>10001=>[1,4,1]
[5,1,3,6,2,4]=>10010=>[1,3,2]
[5,1,3,6,4,2]=>10011=>[1,3,1,1]
[5,1,4,2,3,6]=>10100=>[1,2,3]
[5,1,4,2,6,3]=>10101=>[1,2,2,1]
[5,1,4,3,2,6]=>10110=>[1,2,1,2]
[5,1,4,3,6,2]=>10101=>[1,2,2,1]
[5,1,4,6,2,3]=>10010=>[1,3,2]
[5,1,4,6,3,2]=>10011=>[1,3,1,1]
[5,1,6,2,3,4]=>10100=>[1,2,3]
[5,1,6,2,4,3]=>10101=>[1,2,2,1]
[5,1,6,3,2,4]=>10110=>[1,2,1,2]
[5,1,6,3,4,2]=>10101=>[1,2,2,1]
[5,1,6,4,2,3]=>10110=>[1,2,1,2]
[5,1,6,4,3,2]=>10111=>[1,2,1,1,1]
[5,2,1,3,4,6]=>11000=>[1,1,4]
[5,2,1,3,6,4]=>11001=>[1,1,3,1]
[5,2,1,4,3,6]=>11010=>[1,1,2,2]
[5,2,1,4,6,3]=>11001=>[1,1,3,1]
[5,2,1,6,3,4]=>11010=>[1,1,2,2]
[5,2,1,6,4,3]=>11011=>[1,1,2,1,1]
[5,2,3,1,4,6]=>10100=>[1,2,3]
[5,2,3,1,6,4]=>10101=>[1,2,2,1]
[5,2,3,4,1,6]=>10010=>[1,3,2]
[5,2,3,4,6,1]=>10001=>[1,4,1]
[5,2,3,6,1,4]=>10010=>[1,3,2]
[5,2,3,6,4,1]=>10011=>[1,3,1,1]
[5,2,4,1,3,6]=>10100=>[1,2,3]
[5,2,4,1,6,3]=>10101=>[1,2,2,1]
[5,2,4,3,1,6]=>10110=>[1,2,1,2]
[5,2,4,3,6,1]=>10101=>[1,2,2,1]
[5,2,4,6,1,3]=>10010=>[1,3,2]
[5,2,4,6,3,1]=>10011=>[1,3,1,1]
[5,2,6,1,3,4]=>10100=>[1,2,3]
[5,2,6,1,4,3]=>10101=>[1,2,2,1]
[5,2,6,3,1,4]=>10110=>[1,2,1,2]
[5,2,6,3,4,1]=>10101=>[1,2,2,1]
[5,2,6,4,1,3]=>10110=>[1,2,1,2]
[5,2,6,4,3,1]=>10111=>[1,2,1,1,1]
[5,3,1,2,4,6]=>11000=>[1,1,4]
[5,3,1,2,6,4]=>11001=>[1,1,3,1]
[5,3,1,4,2,6]=>11010=>[1,1,2,2]
[5,3,1,4,6,2]=>11001=>[1,1,3,1]
[5,3,1,6,2,4]=>11010=>[1,1,2,2]
[5,3,1,6,4,2]=>11011=>[1,1,2,1,1]
[5,3,2,1,4,6]=>11100=>[1,1,1,3]
[5,3,2,1,6,4]=>11101=>[1,1,1,2,1]
[5,3,2,4,1,6]=>11010=>[1,1,2,2]
[5,3,2,4,6,1]=>11001=>[1,1,3,1]
[5,3,2,6,1,4]=>11010=>[1,1,2,2]
[5,3,2,6,4,1]=>11011=>[1,1,2,1,1]
[5,3,4,1,2,6]=>10100=>[1,2,3]
[5,3,4,1,6,2]=>10101=>[1,2,2,1]
[5,3,4,2,1,6]=>10110=>[1,2,1,2]
[5,3,4,2,6,1]=>10101=>[1,2,2,1]
[5,3,4,6,1,2]=>10010=>[1,3,2]
[5,3,4,6,2,1]=>10011=>[1,3,1,1]
[5,3,6,1,2,4]=>10100=>[1,2,3]
[5,3,6,1,4,2]=>10101=>[1,2,2,1]
[5,3,6,2,1,4]=>10110=>[1,2,1,2]
[5,3,6,2,4,1]=>10101=>[1,2,2,1]
[5,3,6,4,1,2]=>10110=>[1,2,1,2]
[5,3,6,4,2,1]=>10111=>[1,2,1,1,1]
[5,4,1,2,3,6]=>11000=>[1,1,4]
[5,4,1,2,6,3]=>11001=>[1,1,3,1]
[5,4,1,3,2,6]=>11010=>[1,1,2,2]
[5,4,1,3,6,2]=>11001=>[1,1,3,1]
[5,4,1,6,2,3]=>11010=>[1,1,2,2]
[5,4,1,6,3,2]=>11011=>[1,1,2,1,1]
[5,4,2,1,3,6]=>11100=>[1,1,1,3]
[5,4,2,1,6,3]=>11101=>[1,1,1,2,1]
[5,4,2,3,1,6]=>11010=>[1,1,2,2]
[5,4,2,3,6,1]=>11001=>[1,1,3,1]
[5,4,2,6,1,3]=>11010=>[1,1,2,2]
[5,4,2,6,3,1]=>11011=>[1,1,2,1,1]
[5,4,3,1,2,6]=>11100=>[1,1,1,3]
[5,4,3,1,6,2]=>11101=>[1,1,1,2,1]
[5,4,3,2,1,6]=>11110=>[1,1,1,1,2]
[5,4,3,2,6,1]=>11101=>[1,1,1,2,1]
[5,4,3,6,1,2]=>11010=>[1,1,2,2]
[5,4,3,6,2,1]=>11011=>[1,1,2,1,1]
[5,4,6,1,2,3]=>10100=>[1,2,3]
[5,4,6,1,3,2]=>10101=>[1,2,2,1]
[5,4,6,2,1,3]=>10110=>[1,2,1,2]
[5,4,6,2,3,1]=>10101=>[1,2,2,1]
[5,4,6,3,1,2]=>10110=>[1,2,1,2]
[5,4,6,3,2,1]=>10111=>[1,2,1,1,1]
[5,6,1,2,3,4]=>01000=>[2,4]
[5,6,1,2,4,3]=>01001=>[2,3,1]
[5,6,1,3,2,4]=>01010=>[2,2,2]
[5,6,1,3,4,2]=>01001=>[2,3,1]
[5,6,1,4,2,3]=>01010=>[2,2,2]
[5,6,1,4,3,2]=>01011=>[2,2,1,1]
[5,6,2,1,3,4]=>01100=>[2,1,3]
[5,6,2,1,4,3]=>01101=>[2,1,2,1]
[5,6,2,3,1,4]=>01010=>[2,2,2]
[5,6,2,3,4,1]=>01001=>[2,3,1]
[5,6,2,4,1,3]=>01010=>[2,2,2]
[5,6,2,4,3,1]=>01011=>[2,2,1,1]
[5,6,3,1,2,4]=>01100=>[2,1,3]
[5,6,3,1,4,2]=>01101=>[2,1,2,1]
[5,6,3,2,1,4]=>01110=>[2,1,1,2]
[5,6,3,2,4,1]=>01101=>[2,1,2,1]
[5,6,3,4,1,2]=>01010=>[2,2,2]
[5,6,3,4,2,1]=>01011=>[2,2,1,1]
[5,6,4,1,2,3]=>01100=>[2,1,3]
[5,6,4,1,3,2]=>01101=>[2,1,2,1]
[5,6,4,2,1,3]=>01110=>[2,1,1,2]
[5,6,4,2,3,1]=>01101=>[2,1,2,1]
[5,6,4,3,1,2]=>01110=>[2,1,1,2]
[5,6,4,3,2,1]=>01111=>[2,1,1,1,1]
[6,1,2,3,4,5]=>10000=>[1,5]
[6,1,2,3,5,4]=>10001=>[1,4,1]
[6,1,2,4,3,5]=>10010=>[1,3,2]
[6,1,2,4,5,3]=>10001=>[1,4,1]
[6,1,2,5,3,4]=>10010=>[1,3,2]
[6,1,2,5,4,3]=>10011=>[1,3,1,1]
[6,1,3,2,4,5]=>10100=>[1,2,3]
[6,1,3,2,5,4]=>10101=>[1,2,2,1]
[6,1,3,4,2,5]=>10010=>[1,3,2]
[6,1,3,4,5,2]=>10001=>[1,4,1]
[6,1,3,5,2,4]=>10010=>[1,3,2]
[6,1,3,5,4,2]=>10011=>[1,3,1,1]
[6,1,4,2,3,5]=>10100=>[1,2,3]
[6,1,4,2,5,3]=>10101=>[1,2,2,1]
[6,1,4,3,2,5]=>10110=>[1,2,1,2]
[6,1,4,3,5,2]=>10101=>[1,2,2,1]
[6,1,4,5,2,3]=>10010=>[1,3,2]
[6,1,4,5,3,2]=>10011=>[1,3,1,1]
[6,1,5,2,3,4]=>10100=>[1,2,3]
[6,1,5,2,4,3]=>10101=>[1,2,2,1]
[6,1,5,3,2,4]=>10110=>[1,2,1,2]
[6,1,5,3,4,2]=>10101=>[1,2,2,1]
[6,1,5,4,2,3]=>10110=>[1,2,1,2]
[6,1,5,4,3,2]=>10111=>[1,2,1,1,1]
[6,2,1,3,4,5]=>11000=>[1,1,4]
[6,2,1,3,5,4]=>11001=>[1,1,3,1]
[6,2,1,4,3,5]=>11010=>[1,1,2,2]
[6,2,1,4,5,3]=>11001=>[1,1,3,1]
[6,2,1,5,3,4]=>11010=>[1,1,2,2]
[6,2,1,5,4,3]=>11011=>[1,1,2,1,1]
[6,2,3,1,4,5]=>10100=>[1,2,3]
[6,2,3,1,5,4]=>10101=>[1,2,2,1]
[6,2,3,4,1,5]=>10010=>[1,3,2]
[6,2,3,4,5,1]=>10001=>[1,4,1]
[6,2,3,5,1,4]=>10010=>[1,3,2]
[6,2,3,5,4,1]=>10011=>[1,3,1,1]
[6,2,4,1,3,5]=>10100=>[1,2,3]
[6,2,4,1,5,3]=>10101=>[1,2,2,1]
[6,2,4,3,1,5]=>10110=>[1,2,1,2]
[6,2,4,3,5,1]=>10101=>[1,2,2,1]
[6,2,4,5,1,3]=>10010=>[1,3,2]
[6,2,4,5,3,1]=>10011=>[1,3,1,1]
[6,2,5,1,3,4]=>10100=>[1,2,3]
[6,2,5,1,4,3]=>10101=>[1,2,2,1]
[6,2,5,3,1,4]=>10110=>[1,2,1,2]
[6,2,5,3,4,1]=>10101=>[1,2,2,1]
[6,2,5,4,1,3]=>10110=>[1,2,1,2]
[6,2,5,4,3,1]=>10111=>[1,2,1,1,1]
[6,3,1,2,4,5]=>11000=>[1,1,4]
[6,3,1,2,5,4]=>11001=>[1,1,3,1]
[6,3,1,4,2,5]=>11010=>[1,1,2,2]
[6,3,1,4,5,2]=>11001=>[1,1,3,1]
[6,3,1,5,2,4]=>11010=>[1,1,2,2]
[6,3,1,5,4,2]=>11011=>[1,1,2,1,1]
[6,3,2,1,4,5]=>11100=>[1,1,1,3]
[6,3,2,1,5,4]=>11101=>[1,1,1,2,1]
[6,3,2,4,1,5]=>11010=>[1,1,2,2]
[6,3,2,4,5,1]=>11001=>[1,1,3,1]
[6,3,2,5,1,4]=>11010=>[1,1,2,2]
[6,3,2,5,4,1]=>11011=>[1,1,2,1,1]
[6,3,4,1,2,5]=>10100=>[1,2,3]
[6,3,4,1,5,2]=>10101=>[1,2,2,1]
[6,3,4,2,1,5]=>10110=>[1,2,1,2]
[6,3,4,2,5,1]=>10101=>[1,2,2,1]
[6,3,4,5,1,2]=>10010=>[1,3,2]
[6,3,4,5,2,1]=>10011=>[1,3,1,1]
[6,3,5,1,2,4]=>10100=>[1,2,3]
[6,3,5,1,4,2]=>10101=>[1,2,2,1]
[6,3,5,2,1,4]=>10110=>[1,2,1,2]
[6,3,5,2,4,1]=>10101=>[1,2,2,1]
[6,3,5,4,1,2]=>10110=>[1,2,1,2]
[6,3,5,4,2,1]=>10111=>[1,2,1,1,1]
[6,4,1,2,3,5]=>11000=>[1,1,4]
[6,4,1,2,5,3]=>11001=>[1,1,3,1]
[6,4,1,3,2,5]=>11010=>[1,1,2,2]
[6,4,1,3,5,2]=>11001=>[1,1,3,1]
[6,4,1,5,2,3]=>11010=>[1,1,2,2]
[6,4,1,5,3,2]=>11011=>[1,1,2,1,1]
[6,4,2,1,3,5]=>11100=>[1,1,1,3]
[6,4,2,1,5,3]=>11101=>[1,1,1,2,1]
[6,4,2,3,1,5]=>11010=>[1,1,2,2]
[6,4,2,3,5,1]=>11001=>[1,1,3,1]
[6,4,2,5,1,3]=>11010=>[1,1,2,2]
[6,4,2,5,3,1]=>11011=>[1,1,2,1,1]
[6,4,3,1,2,5]=>11100=>[1,1,1,3]
[6,4,3,1,5,2]=>11101=>[1,1,1,2,1]
[6,4,3,2,1,5]=>11110=>[1,1,1,1,2]
[6,4,3,2,5,1]=>11101=>[1,1,1,2,1]
[6,4,3,5,1,2]=>11010=>[1,1,2,2]
[6,4,3,5,2,1]=>11011=>[1,1,2,1,1]
[6,4,5,1,2,3]=>10100=>[1,2,3]
[6,4,5,1,3,2]=>10101=>[1,2,2,1]
[6,4,5,2,1,3]=>10110=>[1,2,1,2]
[6,4,5,2,3,1]=>10101=>[1,2,2,1]
[6,4,5,3,1,2]=>10110=>[1,2,1,2]
[6,4,5,3,2,1]=>10111=>[1,2,1,1,1]
[6,5,1,2,3,4]=>11000=>[1,1,4]
[6,5,1,2,4,3]=>11001=>[1,1,3,1]
[6,5,1,3,2,4]=>11010=>[1,1,2,2]
[6,5,1,3,4,2]=>11001=>[1,1,3,1]
[6,5,1,4,2,3]=>11010=>[1,1,2,2]
[6,5,1,4,3,2]=>11011=>[1,1,2,1,1]
[6,5,2,1,3,4]=>11100=>[1,1,1,3]
[6,5,2,1,4,3]=>11101=>[1,1,1,2,1]
[6,5,2,3,1,4]=>11010=>[1,1,2,2]
[6,5,2,3,4,1]=>11001=>[1,1,3,1]
[6,5,2,4,1,3]=>11010=>[1,1,2,2]
[6,5,2,4,3,1]=>11011=>[1,1,2,1,1]
[6,5,3,1,2,4]=>11100=>[1,1,1,3]
[6,5,3,1,4,2]=>11101=>[1,1,1,2,1]
[6,5,3,2,1,4]=>11110=>[1,1,1,1,2]
[6,5,3,2,4,1]=>11101=>[1,1,1,2,1]
[6,5,3,4,1,2]=>11010=>[1,1,2,2]
[6,5,3,4,2,1]=>11011=>[1,1,2,1,1]
[6,5,4,1,2,3]=>11100=>[1,1,1,3]
[6,5,4,1,3,2]=>11101=>[1,1,1,2,1]
[6,5,4,2,1,3]=>11110=>[1,1,1,1,2]
[6,5,4,2,3,1]=>11101=>[1,1,1,2,1]
[6,5,4,3,1,2]=>11110=>[1,1,1,1,2]
[6,5,4,3,2,1]=>11111=>[1,1,1,1,1,1]
[1,2,3,4,5,6,7]=>000000=>[7]
[1,2,3,4,5,7,6]=>000001=>[6,1]
[1,2,3,4,6,5,7]=>000010=>[5,2]
[1,2,3,4,6,7,5]=>000001=>[6,1]
[1,2,3,4,7,5,6]=>000010=>[5,2]
[1,2,3,4,7,6,5]=>000011=>[5,1,1]
[1,2,3,5,4,6,7]=>000100=>[4,3]
[1,2,3,5,4,7,6]=>000101=>[4,2,1]
[1,2,3,5,6,4,7]=>000010=>[5,2]
[1,2,3,5,6,7,4]=>000001=>[6,1]
[1,2,3,5,7,4,6]=>000010=>[5,2]
[1,2,3,5,7,6,4]=>000011=>[5,1,1]
[1,2,3,6,4,5,7]=>000100=>[4,3]
[1,2,3,6,4,7,5]=>000101=>[4,2,1]
[1,2,3,6,5,4,7]=>000110=>[4,1,2]
[1,2,3,6,5,7,4]=>000101=>[4,2,1]
[1,2,3,6,7,4,5]=>000010=>[5,2]
[1,2,3,6,7,5,4]=>000011=>[5,1,1]
[1,2,3,7,4,5,6]=>000100=>[4,3]
[1,2,3,7,4,6,5]=>000101=>[4,2,1]
[1,2,3,7,5,4,6]=>000110=>[4,1,2]
[1,2,3,7,5,6,4]=>000101=>[4,2,1]
[1,2,3,7,6,4,5]=>000110=>[4,1,2]
[1,2,3,7,6,5,4]=>000111=>[4,1,1,1]
[1,2,4,3,5,6,7]=>001000=>[3,4]
[1,2,4,3,5,7,6]=>001001=>[3,3,1]
[1,2,4,3,6,5,7]=>001010=>[3,2,2]
[1,2,4,3,6,7,5]=>001001=>[3,3,1]
[1,2,4,3,7,5,6]=>001010=>[3,2,2]
[1,2,4,3,7,6,5]=>001011=>[3,2,1,1]
[1,2,4,5,3,6,7]=>000100=>[4,3]
[1,2,4,5,3,7,6]=>000101=>[4,2,1]
[1,2,4,5,6,3,7]=>000010=>[5,2]
[1,2,4,5,6,7,3]=>000001=>[6,1]
[1,2,4,5,7,3,6]=>000010=>[5,2]
[1,2,4,5,7,6,3]=>000011=>[5,1,1]
[1,2,4,6,3,5,7]=>000100=>[4,3]
[1,2,4,6,3,7,5]=>000101=>[4,2,1]
[1,2,4,6,5,3,7]=>000110=>[4,1,2]
[1,2,4,6,5,7,3]=>000101=>[4,2,1]
[1,2,4,6,7,3,5]=>000010=>[5,2]
[1,2,4,6,7,5,3]=>000011=>[5,1,1]
[1,2,4,7,3,5,6]=>000100=>[4,3]
[1,2,4,7,3,6,5]=>000101=>[4,2,1]
[1,2,4,7,5,3,6]=>000110=>[4,1,2]
[1,2,4,7,5,6,3]=>000101=>[4,2,1]
[1,2,4,7,6,3,5]=>000110=>[4,1,2]
[1,2,4,7,6,5,3]=>000111=>[4,1,1,1]
[1,2,5,3,4,6,7]=>001000=>[3,4]
[1,2,5,3,4,7,6]=>001001=>[3,3,1]
[1,2,5,3,6,4,7]=>001010=>[3,2,2]
[1,2,5,3,6,7,4]=>001001=>[3,3,1]
[1,2,5,3,7,4,6]=>001010=>[3,2,2]
[1,2,5,3,7,6,4]=>001011=>[3,2,1,1]
[1,2,5,4,3,6,7]=>001100=>[3,1,3]
[1,2,5,4,3,7,6]=>001101=>[3,1,2,1]
[1,2,5,4,6,3,7]=>001010=>[3,2,2]
[1,2,5,4,6,7,3]=>001001=>[3,3,1]
[1,2,5,4,7,3,6]=>001010=>[3,2,2]
[1,2,5,4,7,6,3]=>001011=>[3,2,1,1]
[1,2,5,6,3,4,7]=>000100=>[4,3]
[1,2,5,6,3,7,4]=>000101=>[4,2,1]
[1,2,5,6,4,3,7]=>000110=>[4,1,2]
[1,2,5,6,4,7,3]=>000101=>[4,2,1]
[1,2,5,6,7,3,4]=>000010=>[5,2]
[1,2,5,6,7,4,3]=>000011=>[5,1,1]
[1,2,5,7,3,4,6]=>000100=>[4,3]
[1,2,5,7,3,6,4]=>000101=>[4,2,1]
[1,2,5,7,4,3,6]=>000110=>[4,1,2]
[1,2,5,7,4,6,3]=>000101=>[4,2,1]
[1,2,5,7,6,3,4]=>000110=>[4,1,2]
[1,2,5,7,6,4,3]=>000111=>[4,1,1,1]
[1,2,6,3,4,5,7]=>001000=>[3,4]
[1,2,6,3,4,7,5]=>001001=>[3,3,1]
[1,2,6,3,5,4,7]=>001010=>[3,2,2]
[1,2,6,3,5,7,4]=>001001=>[3,3,1]
[1,2,6,3,7,4,5]=>001010=>[3,2,2]
[1,2,6,3,7,5,4]=>001011=>[3,2,1,1]
[1,2,6,4,3,5,7]=>001100=>[3,1,3]
[1,2,6,4,3,7,5]=>001101=>[3,1,2,1]
[1,2,6,4,5,3,7]=>001010=>[3,2,2]
[1,2,6,4,5,7,3]=>001001=>[3,3,1]
[1,2,6,4,7,3,5]=>001010=>[3,2,2]
[1,2,6,4,7,5,3]=>001011=>[3,2,1,1]
[1,2,6,5,3,4,7]=>001100=>[3,1,3]
[1,2,6,5,3,7,4]=>001101=>[3,1,2,1]
[1,2,6,5,4,3,7]=>001110=>[3,1,1,2]
[1,2,6,5,4,7,3]=>001101=>[3,1,2,1]
[1,2,6,5,7,3,4]=>001010=>[3,2,2]
[1,2,6,5,7,4,3]=>001011=>[3,2,1,1]
[1,2,6,7,3,4,5]=>000100=>[4,3]
[1,2,6,7,3,5,4]=>000101=>[4,2,1]
[1,2,6,7,4,3,5]=>000110=>[4,1,2]
[1,2,6,7,4,5,3]=>000101=>[4,2,1]
[1,2,6,7,5,3,4]=>000110=>[4,1,2]
[1,2,6,7,5,4,3]=>000111=>[4,1,1,1]
[1,2,7,3,4,5,6]=>001000=>[3,4]
[1,2,7,3,4,6,5]=>001001=>[3,3,1]
[1,2,7,3,5,4,6]=>001010=>[3,2,2]
[1,2,7,3,5,6,4]=>001001=>[3,3,1]
[1,2,7,3,6,4,5]=>001010=>[3,2,2]
[1,2,7,3,6,5,4]=>001011=>[3,2,1,1]
[1,2,7,4,3,5,6]=>001100=>[3,1,3]
[1,2,7,4,3,6,5]=>001101=>[3,1,2,1]
[1,2,7,4,5,3,6]=>001010=>[3,2,2]
[1,2,7,4,5,6,3]=>001001=>[3,3,1]
[1,2,7,4,6,3,5]=>001010=>[3,2,2]
[1,2,7,4,6,5,3]=>001011=>[3,2,1,1]
[1,2,7,5,3,4,6]=>001100=>[3,1,3]
[1,2,7,5,3,6,4]=>001101=>[3,1,2,1]
[1,2,7,5,4,3,6]=>001110=>[3,1,1,2]
[1,2,7,5,4,6,3]=>001101=>[3,1,2,1]
[1,2,7,5,6,3,4]=>001010=>[3,2,2]
[1,2,7,5,6,4,3]=>001011=>[3,2,1,1]
[1,2,7,6,3,4,5]=>001100=>[3,1,3]
[1,2,7,6,3,5,4]=>001101=>[3,1,2,1]
[1,2,7,6,4,3,5]=>001110=>[3,1,1,2]
[1,2,7,6,4,5,3]=>001101=>[3,1,2,1]
[1,2,7,6,5,3,4]=>001110=>[3,1,1,2]
[1,2,7,6,5,4,3]=>001111=>[3,1,1,1,1]
[1,3,2,4,5,6,7]=>010000=>[2,5]
[1,3,2,4,5,7,6]=>010001=>[2,4,1]
[1,3,2,4,6,5,7]=>010010=>[2,3,2]
[1,3,2,4,6,7,5]=>010001=>[2,4,1]
[1,3,2,4,7,5,6]=>010010=>[2,3,2]
[1,3,2,4,7,6,5]=>010011=>[2,3,1,1]
[1,3,2,5,4,6,7]=>010100=>[2,2,3]
[1,3,2,5,4,7,6]=>010101=>[2,2,2,1]
[1,3,2,5,6,4,7]=>010010=>[2,3,2]
[1,3,2,5,6,7,4]=>010001=>[2,4,1]
[1,3,2,5,7,4,6]=>010010=>[2,3,2]
[1,3,2,5,7,6,4]=>010011=>[2,3,1,1]
[1,3,2,6,4,5,7]=>010100=>[2,2,3]
[1,3,2,6,4,7,5]=>010101=>[2,2,2,1]
[1,3,2,6,5,4,7]=>010110=>[2,2,1,2]
[1,3,2,6,5,7,4]=>010101=>[2,2,2,1]
[1,3,2,6,7,4,5]=>010010=>[2,3,2]
[1,3,2,6,7,5,4]=>010011=>[2,3,1,1]
[1,3,2,7,4,5,6]=>010100=>[2,2,3]
[1,3,2,7,4,6,5]=>010101=>[2,2,2,1]
[1,3,2,7,5,4,6]=>010110=>[2,2,1,2]
[1,3,2,7,5,6,4]=>010101=>[2,2,2,1]
[1,3,2,7,6,4,5]=>010110=>[2,2,1,2]
[1,3,2,7,6,5,4]=>010111=>[2,2,1,1,1]
[1,3,4,2,5,6,7]=>001000=>[3,4]
[1,3,4,2,5,7,6]=>001001=>[3,3,1]
[1,3,4,2,6,5,7]=>001010=>[3,2,2]
[1,3,4,2,6,7,5]=>001001=>[3,3,1]
[1,3,4,2,7,5,6]=>001010=>[3,2,2]
[1,3,4,2,7,6,5]=>001011=>[3,2,1,1]
[1,3,4,5,2,6,7]=>000100=>[4,3]
[1,3,4,5,2,7,6]=>000101=>[4,2,1]
[1,3,4,5,6,2,7]=>000010=>[5,2]
[1,3,4,5,6,7,2]=>000001=>[6,1]
[1,3,4,5,7,2,6]=>000010=>[5,2]
[1,3,4,5,7,6,2]=>000011=>[5,1,1]
[1,3,4,6,2,5,7]=>000100=>[4,3]
[1,3,4,6,2,7,5]=>000101=>[4,2,1]
[1,3,4,6,5,2,7]=>000110=>[4,1,2]
[1,3,4,6,5,7,2]=>000101=>[4,2,1]
[1,3,4,6,7,2,5]=>000010=>[5,2]
[1,3,4,6,7,5,2]=>000011=>[5,1,1]
[1,3,4,7,2,5,6]=>000100=>[4,3]
[1,3,4,7,2,6,5]=>000101=>[4,2,1]
[1,3,4,7,5,2,6]=>000110=>[4,1,2]
[1,3,4,7,5,6,2]=>000101=>[4,2,1]
[1,3,4,7,6,2,5]=>000110=>[4,1,2]
[1,3,4,7,6,5,2]=>000111=>[4,1,1,1]
[1,3,5,2,4,6,7]=>001000=>[3,4]
[1,3,5,2,4,7,6]=>001001=>[3,3,1]
[1,3,5,2,6,4,7]=>001010=>[3,2,2]
[1,3,5,2,6,7,4]=>001001=>[3,3,1]
[1,3,5,2,7,4,6]=>001010=>[3,2,2]
[1,3,5,2,7,6,4]=>001011=>[3,2,1,1]
[1,3,5,4,2,6,7]=>001100=>[3,1,3]
[1,3,5,4,2,7,6]=>001101=>[3,1,2,1]
[1,3,5,4,6,2,7]=>001010=>[3,2,2]
[1,3,5,4,6,7,2]=>001001=>[3,3,1]
[1,3,5,4,7,2,6]=>001010=>[3,2,2]
[1,3,5,4,7,6,2]=>001011=>[3,2,1,1]
[1,3,5,6,2,4,7]=>000100=>[4,3]
[1,3,5,6,2,7,4]=>000101=>[4,2,1]
[1,3,5,6,4,2,7]=>000110=>[4,1,2]
[1,3,5,6,4,7,2]=>000101=>[4,2,1]
[1,3,5,6,7,2,4]=>000010=>[5,2]
[1,3,5,6,7,4,2]=>000011=>[5,1,1]
[1,3,5,7,2,4,6]=>000100=>[4,3]
[1,3,5,7,2,6,4]=>000101=>[4,2,1]
[1,3,5,7,4,2,6]=>000110=>[4,1,2]
[1,3,5,7,4,6,2]=>000101=>[4,2,1]
[1,3,5,7,6,2,4]=>000110=>[4,1,2]
[1,3,5,7,6,4,2]=>000111=>[4,1,1,1]
[1,3,6,2,4,5,7]=>001000=>[3,4]
[1,3,6,2,4,7,5]=>001001=>[3,3,1]
[1,3,6,2,5,4,7]=>001010=>[3,2,2]
[1,3,6,2,5,7,4]=>001001=>[3,3,1]
[1,3,6,2,7,4,5]=>001010=>[3,2,2]
[1,3,6,2,7,5,4]=>001011=>[3,2,1,1]
[1,3,6,4,2,5,7]=>001100=>[3,1,3]
[1,3,6,4,2,7,5]=>001101=>[3,1,2,1]
[1,3,6,4,5,2,7]=>001010=>[3,2,2]
[1,3,6,4,5,7,2]=>001001=>[3,3,1]
[1,3,6,4,7,2,5]=>001010=>[3,2,2]
[1,3,6,4,7,5,2]=>001011=>[3,2,1,1]
[1,3,6,5,2,4,7]=>001100=>[3,1,3]
[1,3,6,5,2,7,4]=>001101=>[3,1,2,1]
[1,3,6,5,4,2,7]=>001110=>[3,1,1,2]
[1,3,6,5,4,7,2]=>001101=>[3,1,2,1]
[1,3,6,5,7,2,4]=>001010=>[3,2,2]
[1,3,6,5,7,4,2]=>001011=>[3,2,1,1]
[1,3,6,7,2,4,5]=>000100=>[4,3]
[1,3,6,7,2,5,4]=>000101=>[4,2,1]
[1,3,6,7,4,2,5]=>000110=>[4,1,2]
[1,3,6,7,4,5,2]=>000101=>[4,2,1]
[1,3,6,7,5,2,4]=>000110=>[4,1,2]
[1,3,6,7,5,4,2]=>000111=>[4,1,1,1]
[1,3,7,2,4,5,6]=>001000=>[3,4]
[1,3,7,2,4,6,5]=>001001=>[3,3,1]
[1,3,7,2,5,4,6]=>001010=>[3,2,2]
[1,3,7,2,5,6,4]=>001001=>[3,3,1]
[1,3,7,2,6,4,5]=>001010=>[3,2,2]
[1,3,7,2,6,5,4]=>001011=>[3,2,1,1]
[1,3,7,4,2,5,6]=>001100=>[3,1,3]
[1,3,7,4,2,6,5]=>001101=>[3,1,2,1]
[1,3,7,4,5,2,6]=>001010=>[3,2,2]
[1,3,7,4,5,6,2]=>001001=>[3,3,1]
[1,3,7,4,6,2,5]=>001010=>[3,2,2]
[1,3,7,4,6,5,2]=>001011=>[3,2,1,1]
[1,3,7,5,2,4,6]=>001100=>[3,1,3]
[1,3,7,5,2,6,4]=>001101=>[3,1,2,1]
[1,3,7,5,4,2,6]=>001110=>[3,1,1,2]
[1,3,7,5,4,6,2]=>001101=>[3,1,2,1]
[1,3,7,5,6,2,4]=>001010=>[3,2,2]
[1,3,7,5,6,4,2]=>001011=>[3,2,1,1]
[1,3,7,6,2,4,5]=>001100=>[3,1,3]
[1,3,7,6,2,5,4]=>001101=>[3,1,2,1]
[1,3,7,6,4,2,5]=>001110=>[3,1,1,2]
[1,3,7,6,4,5,2]=>001101=>[3,1,2,1]
[1,3,7,6,5,2,4]=>001110=>[3,1,1,2]
[1,3,7,6,5,4,2]=>001111=>[3,1,1,1,1]
[1,4,2,3,5,6,7]=>010000=>[2,5]
[1,4,2,3,5,7,6]=>010001=>[2,4,1]
[1,4,2,3,6,5,7]=>010010=>[2,3,2]
[1,4,2,3,6,7,5]=>010001=>[2,4,1]
[1,4,2,3,7,5,6]=>010010=>[2,3,2]
[1,4,2,3,7,6,5]=>010011=>[2,3,1,1]
[1,4,2,5,3,6,7]=>010100=>[2,2,3]
[1,4,2,5,3,7,6]=>010101=>[2,2,2,1]
[1,4,2,5,6,3,7]=>010010=>[2,3,2]
[1,4,2,5,6,7,3]=>010001=>[2,4,1]
[1,4,2,5,7,3,6]=>010010=>[2,3,2]
[1,4,2,5,7,6,3]=>010011=>[2,3,1,1]
[1,4,2,6,3,5,7]=>010100=>[2,2,3]
[1,4,2,6,3,7,5]=>010101=>[2,2,2,1]
[1,4,2,6,5,3,7]=>010110=>[2,2,1,2]
[1,4,2,6,5,7,3]=>010101=>[2,2,2,1]
[1,4,2,6,7,3,5]=>010010=>[2,3,2]
[1,4,2,6,7,5,3]=>010011=>[2,3,1,1]
[1,4,2,7,3,5,6]=>010100=>[2,2,3]
[1,4,2,7,3,6,5]=>010101=>[2,2,2,1]
[1,4,2,7,5,3,6]=>010110=>[2,2,1,2]
[1,4,2,7,5,6,3]=>010101=>[2,2,2,1]
[1,4,2,7,6,3,5]=>010110=>[2,2,1,2]
[1,4,2,7,6,5,3]=>010111=>[2,2,1,1,1]
[1,4,3,2,5,6,7]=>011000=>[2,1,4]
[1,4,3,2,5,7,6]=>011001=>[2,1,3,1]
[1,4,3,2,6,5,7]=>011010=>[2,1,2,2]
[1,4,3,2,6,7,5]=>011001=>[2,1,3,1]
[1,4,3,2,7,5,6]=>011010=>[2,1,2,2]
[1,4,3,2,7,6,5]=>011011=>[2,1,2,1,1]
[1,4,3,5,2,6,7]=>010100=>[2,2,3]
[1,4,3,5,2,7,6]=>010101=>[2,2,2,1]
[1,4,3,5,6,2,7]=>010010=>[2,3,2]
[1,4,3,5,6,7,2]=>010001=>[2,4,1]
[1,4,3,5,7,2,6]=>010010=>[2,3,2]
[1,4,3,5,7,6,2]=>010011=>[2,3,1,1]
[1,4,3,6,2,5,7]=>010100=>[2,2,3]
[1,4,3,6,2,7,5]=>010101=>[2,2,2,1]
[1,4,3,6,5,2,7]=>010110=>[2,2,1,2]
[1,4,3,6,5,7,2]=>010101=>[2,2,2,1]
[1,4,3,6,7,2,5]=>010010=>[2,3,2]
[1,4,3,6,7,5,2]=>010011=>[2,3,1,1]
[1,4,3,7,2,5,6]=>010100=>[2,2,3]
[1,4,3,7,2,6,5]=>010101=>[2,2,2,1]
[1,4,3,7,5,2,6]=>010110=>[2,2,1,2]
[1,4,3,7,5,6,2]=>010101=>[2,2,2,1]
[1,4,3,7,6,2,5]=>010110=>[2,2,1,2]
[1,4,3,7,6,5,2]=>010111=>[2,2,1,1,1]
[1,4,5,2,3,6,7]=>001000=>[3,4]
[1,4,5,2,3,7,6]=>001001=>[3,3,1]
[1,4,5,2,6,3,7]=>001010=>[3,2,2]
[1,4,5,2,6,7,3]=>001001=>[3,3,1]
[1,4,5,2,7,3,6]=>001010=>[3,2,2]
[1,4,5,2,7,6,3]=>001011=>[3,2,1,1]
[1,4,5,3,2,6,7]=>001100=>[3,1,3]
[1,4,5,3,2,7,6]=>001101=>[3,1,2,1]
[1,4,5,3,6,2,7]=>001010=>[3,2,2]
[1,4,5,3,6,7,2]=>001001=>[3,3,1]
[1,4,5,3,7,2,6]=>001010=>[3,2,2]
[1,4,5,3,7,6,2]=>001011=>[3,2,1,1]
[1,4,5,6,2,3,7]=>000100=>[4,3]
[1,4,5,6,2,7,3]=>000101=>[4,2,1]
[1,4,5,6,3,2,7]=>000110=>[4,1,2]
[1,4,5,6,3,7,2]=>000101=>[4,2,1]
[1,4,5,6,7,2,3]=>000010=>[5,2]
[1,4,5,6,7,3,2]=>000011=>[5,1,1]
[1,4,5,7,2,3,6]=>000100=>[4,3]
[1,4,5,7,2,6,3]=>000101=>[4,2,1]
[1,4,5,7,3,2,6]=>000110=>[4,1,2]
[1,4,5,7,3,6,2]=>000101=>[4,2,1]
[1,4,5,7,6,2,3]=>000110=>[4,1,2]
[1,4,5,7,6,3,2]=>000111=>[4,1,1,1]
[1,4,6,2,3,5,7]=>001000=>[3,4]
[1,4,6,2,3,7,5]=>001001=>[3,3,1]
[1,4,6,2,5,3,7]=>001010=>[3,2,2]
[1,4,6,2,5,7,3]=>001001=>[3,3,1]
[1,4,6,2,7,3,5]=>001010=>[3,2,2]
[1,4,6,2,7,5,3]=>001011=>[3,2,1,1]
[1,4,6,3,2,5,7]=>001100=>[3,1,3]
[1,4,6,3,2,7,5]=>001101=>[3,1,2,1]
[1,4,6,3,5,2,7]=>001010=>[3,2,2]
[1,4,6,3,5,7,2]=>001001=>[3,3,1]
[1,4,6,3,7,2,5]=>001010=>[3,2,2]
[1,4,6,3,7,5,2]=>001011=>[3,2,1,1]
[1,4,6,5,2,3,7]=>001100=>[3,1,3]
[1,4,6,5,2,7,3]=>001101=>[3,1,2,1]
[1,4,6,5,3,2,7]=>001110=>[3,1,1,2]
[1,4,6,5,3,7,2]=>001101=>[3,1,2,1]
[1,4,6,5,7,2,3]=>001010=>[3,2,2]
[1,4,6,5,7,3,2]=>001011=>[3,2,1,1]
[1,4,6,7,2,3,5]=>000100=>[4,3]
[1,4,6,7,2,5,3]=>000101=>[4,2,1]
[1,4,6,7,3,2,5]=>000110=>[4,1,2]
[1,4,6,7,3,5,2]=>000101=>[4,2,1]
[1,4,6,7,5,2,3]=>000110=>[4,1,2]
[1,4,6,7,5,3,2]=>000111=>[4,1,1,1]
[1,4,7,2,3,5,6]=>001000=>[3,4]
[1,4,7,2,3,6,5]=>001001=>[3,3,1]
[1,4,7,2,5,3,6]=>001010=>[3,2,2]
[1,4,7,2,5,6,3]=>001001=>[3,3,1]
[1,4,7,2,6,3,5]=>001010=>[3,2,2]
[1,4,7,2,6,5,3]=>001011=>[3,2,1,1]
[1,4,7,3,2,5,6]=>001100=>[3,1,3]
[1,4,7,3,2,6,5]=>001101=>[3,1,2,1]
[1,4,7,3,5,2,6]=>001010=>[3,2,2]
[1,4,7,3,5,6,2]=>001001=>[3,3,1]
[1,4,7,3,6,2,5]=>001010=>[3,2,2]
[1,4,7,3,6,5,2]=>001011=>[3,2,1,1]
[1,4,7,5,2,3,6]=>001100=>[3,1,3]
[1,4,7,5,2,6,3]=>001101=>[3,1,2,1]
[1,4,7,5,3,2,6]=>001110=>[3,1,1,2]
[1,4,7,5,3,6,2]=>001101=>[3,1,2,1]
[1,4,7,5,6,2,3]=>001010=>[3,2,2]
[1,4,7,5,6,3,2]=>001011=>[3,2,1,1]
[1,4,7,6,2,3,5]=>001100=>[3,1,3]
[1,4,7,6,2,5,3]=>001101=>[3,1,2,1]
[1,4,7,6,3,2,5]=>001110=>[3,1,1,2]
[1,4,7,6,3,5,2]=>001101=>[3,1,2,1]
[1,4,7,6,5,2,3]=>001110=>[3,1,1,2]
[1,4,7,6,5,3,2]=>001111=>[3,1,1,1,1]
[1,5,2,3,4,6,7]=>010000=>[2,5]
[1,5,2,3,4,7,6]=>010001=>[2,4,1]
[1,5,2,3,6,4,7]=>010010=>[2,3,2]
[1,5,2,3,6,7,4]=>010001=>[2,4,1]
[1,5,2,3,7,4,6]=>010010=>[2,3,2]
[1,5,2,3,7,6,4]=>010011=>[2,3,1,1]
[1,5,2,4,3,6,7]=>010100=>[2,2,3]
[1,5,2,4,3,7,6]=>010101=>[2,2,2,1]
[1,5,2,4,6,3,7]=>010010=>[2,3,2]
[1,5,2,4,6,7,3]=>010001=>[2,4,1]
[1,5,2,4,7,3,6]=>010010=>[2,3,2]
[1,5,2,4,7,6,3]=>010011=>[2,3,1,1]
[1,5,2,6,3,4,7]=>010100=>[2,2,3]
[1,5,2,6,3,7,4]=>010101=>[2,2,2,1]
[1,5,2,6,4,3,7]=>010110=>[2,2,1,2]
[1,5,2,6,4,7,3]=>010101=>[2,2,2,1]
[1,5,2,6,7,3,4]=>010010=>[2,3,2]
[1,5,2,6,7,4,3]=>010011=>[2,3,1,1]
[1,5,2,7,3,4,6]=>010100=>[2,2,3]
[1,5,2,7,3,6,4]=>010101=>[2,2,2,1]
[1,5,2,7,4,3,6]=>010110=>[2,2,1,2]
[1,5,2,7,4,6,3]=>010101=>[2,2,2,1]
[1,5,2,7,6,3,4]=>010110=>[2,2,1,2]
[1,5,2,7,6,4,3]=>010111=>[2,2,1,1,1]
[1,5,3,2,4,6,7]=>011000=>[2,1,4]
[1,5,3,2,4,7,6]=>011001=>[2,1,3,1]
[1,5,3,2,6,4,7]=>011010=>[2,1,2,2]
[1,5,3,2,6,7,4]=>011001=>[2,1,3,1]
[1,5,3,2,7,4,6]=>011010=>[2,1,2,2]
[1,5,3,2,7,6,4]=>011011=>[2,1,2,1,1]
[1,5,3,4,2,6,7]=>010100=>[2,2,3]
[1,5,3,4,2,7,6]=>010101=>[2,2,2,1]
[1,5,3,4,6,2,7]=>010010=>[2,3,2]
[1,5,3,4,6,7,2]=>010001=>[2,4,1]
[1,5,3,4,7,2,6]=>010010=>[2,3,2]
[1,5,3,4,7,6,2]=>010011=>[2,3,1,1]
[1,5,3,6,2,4,7]=>010100=>[2,2,3]
[1,5,3,6,2,7,4]=>010101=>[2,2,2,1]
[1,5,3,6,4,2,7]=>010110=>[2,2,1,2]
[1,5,3,6,4,7,2]=>010101=>[2,2,2,1]
[1,5,3,6,7,2,4]=>010010=>[2,3,2]
[1,5,3,6,7,4,2]=>010011=>[2,3,1,1]
[1,5,3,7,2,4,6]=>010100=>[2,2,3]
[1,5,3,7,2,6,4]=>010101=>[2,2,2,1]
[1,5,3,7,4,2,6]=>010110=>[2,2,1,2]
[1,5,3,7,4,6,2]=>010101=>[2,2,2,1]
[1,5,3,7,6,2,4]=>010110=>[2,2,1,2]
[1,5,3,7,6,4,2]=>010111=>[2,2,1,1,1]
[1,5,4,2,3,6,7]=>011000=>[2,1,4]
[1,5,4,2,3,7,6]=>011001=>[2,1,3,1]
[1,5,4,2,6,3,7]=>011010=>[2,1,2,2]
[1,5,4,2,6,7,3]=>011001=>[2,1,3,1]
[1,5,4,2,7,3,6]=>011010=>[2,1,2,2]
[1,5,4,2,7,6,3]=>011011=>[2,1,2,1,1]
[1,5,4,3,2,6,7]=>011100=>[2,1,1,3]
[1,5,4,3,2,7,6]=>011101=>[2,1,1,2,1]
[1,5,4,3,6,2,7]=>011010=>[2,1,2,2]
[1,5,4,3,6,7,2]=>011001=>[2,1,3,1]
[1,5,4,3,7,2,6]=>011010=>[2,1,2,2]
[1,5,4,3,7,6,2]=>011011=>[2,1,2,1,1]
[1,5,4,6,2,3,7]=>010100=>[2,2,3]
[1,5,4,6,2,7,3]=>010101=>[2,2,2,1]
[1,5,4,6,3,2,7]=>010110=>[2,2,1,2]
[1,5,4,6,3,7,2]=>010101=>[2,2,2,1]
[1,5,4,6,7,2,3]=>010010=>[2,3,2]
[1,5,4,6,7,3,2]=>010011=>[2,3,1,1]
[1,5,4,7,2,3,6]=>010100=>[2,2,3]
[1,5,4,7,2,6,3]=>010101=>[2,2,2,1]
[1,5,4,7,3,2,6]=>010110=>[2,2,1,2]
[1,5,4,7,3,6,2]=>010101=>[2,2,2,1]
[1,5,4,7,6,2,3]=>010110=>[2,2,1,2]
[1,5,4,7,6,3,2]=>010111=>[2,2,1,1,1]
[1,5,6,2,3,4,7]=>001000=>[3,4]
[1,5,6,2,3,7,4]=>001001=>[3,3,1]
[1,5,6,2,4,3,7]=>001010=>[3,2,2]
[1,5,6,2,4,7,3]=>001001=>[3,3,1]
[1,5,6,2,7,3,4]=>001010=>[3,2,2]
[1,5,6,2,7,4,3]=>001011=>[3,2,1,1]
[1,5,6,3,2,4,7]=>001100=>[3,1,3]
[1,5,6,3,2,7,4]=>001101=>[3,1,2,1]
[1,5,6,3,4,2,7]=>001010=>[3,2,2]
[1,5,6,3,4,7,2]=>001001=>[3,3,1]
[1,5,6,3,7,2,4]=>001010=>[3,2,2]
[1,5,6,3,7,4,2]=>001011=>[3,2,1,1]
[1,5,6,4,2,3,7]=>001100=>[3,1,3]
[1,5,6,4,2,7,3]=>001101=>[3,1,2,1]
[1,5,6,4,3,2,7]=>001110=>[3,1,1,2]
[1,5,6,4,3,7,2]=>001101=>[3,1,2,1]
[1,5,6,4,7,2,3]=>001010=>[3,2,2]
[1,5,6,4,7,3,2]=>001011=>[3,2,1,1]
[1,5,6,7,2,3,4]=>000100=>[4,3]
[1,5,6,7,2,4,3]=>000101=>[4,2,1]
[1,5,6,7,3,2,4]=>000110=>[4,1,2]
[1,5,6,7,3,4,2]=>000101=>[4,2,1]
[1,5,6,7,4,2,3]=>000110=>[4,1,2]
[1,5,6,7,4,3,2]=>000111=>[4,1,1,1]
[1,5,7,2,3,4,6]=>001000=>[3,4]
[1,5,7,2,3,6,4]=>001001=>[3,3,1]
[1,5,7,2,4,3,6]=>001010=>[3,2,2]
[1,5,7,2,4,6,3]=>001001=>[3,3,1]
[1,5,7,2,6,3,4]=>001010=>[3,2,2]
[1,5,7,2,6,4,3]=>001011=>[3,2,1,1]
[1,5,7,3,2,4,6]=>001100=>[3,1,3]
[1,5,7,3,2,6,4]=>001101=>[3,1,2,1]
[1,5,7,3,4,2,6]=>001010=>[3,2,2]
[1,5,7,3,4,6,2]=>001001=>[3,3,1]
[1,5,7,3,6,2,4]=>001010=>[3,2,2]
[1,5,7,3,6,4,2]=>001011=>[3,2,1,1]
[1,5,7,4,2,3,6]=>001100=>[3,1,3]
[1,5,7,4,2,6,3]=>001101=>[3,1,2,1]
[1,5,7,4,3,2,6]=>001110=>[3,1,1,2]
[1,5,7,4,3,6,2]=>001101=>[3,1,2,1]
[1,5,7,4,6,2,3]=>001010=>[3,2,2]
[1,5,7,4,6,3,2]=>001011=>[3,2,1,1]
[1,5,7,6,2,3,4]=>001100=>[3,1,3]
[1,5,7,6,2,4,3]=>001101=>[3,1,2,1]
[1,5,7,6,3,2,4]=>001110=>[3,1,1,2]
[1,5,7,6,3,4,2]=>001101=>[3,1,2,1]
[1,5,7,6,4,2,3]=>001110=>[3,1,1,2]
[1,5,7,6,4,3,2]=>001111=>[3,1,1,1,1]
[1,6,2,3,4,5,7]=>010000=>[2,5]
[1,6,2,3,4,7,5]=>010001=>[2,4,1]
[1,6,2,3,5,4,7]=>010010=>[2,3,2]
[1,6,2,3,5,7,4]=>010001=>[2,4,1]
[1,6,2,3,7,4,5]=>010010=>[2,3,2]
[1,6,2,3,7,5,4]=>010011=>[2,3,1,1]
[1,6,2,4,3,5,7]=>010100=>[2,2,3]
[1,6,2,4,3,7,5]=>010101=>[2,2,2,1]
[1,6,2,4,5,3,7]=>010010=>[2,3,2]
[1,6,2,4,5,7,3]=>010001=>[2,4,1]
[1,6,2,4,7,3,5]=>010010=>[2,3,2]
[1,6,2,4,7,5,3]=>010011=>[2,3,1,1]
[1,6,2,5,3,4,7]=>010100=>[2,2,3]
[1,6,2,5,3,7,4]=>010101=>[2,2,2,1]
[1,6,2,5,4,3,7]=>010110=>[2,2,1,2]
[1,6,2,5,4,7,3]=>010101=>[2,2,2,1]
[1,6,2,5,7,3,4]=>010010=>[2,3,2]
[1,6,2,5,7,4,3]=>010011=>[2,3,1,1]
[1,6,2,7,3,4,5]=>010100=>[2,2,3]
[1,6,2,7,3,5,4]=>010101=>[2,2,2,1]
[1,6,2,7,4,3,5]=>010110=>[2,2,1,2]
[1,6,2,7,4,5,3]=>010101=>[2,2,2,1]
[1,6,2,7,5,3,4]=>010110=>[2,2,1,2]
[1,6,2,7,5,4,3]=>010111=>[2,2,1,1,1]
[1,6,3,2,4,5,7]=>011000=>[2,1,4]
[1,6,3,2,4,7,5]=>011001=>[2,1,3,1]
[1,6,3,2,5,4,7]=>011010=>[2,1,2,2]
[1,6,3,2,5,7,4]=>011001=>[2,1,3,1]
[1,6,3,2,7,4,5]=>011010=>[2,1,2,2]
[1,6,3,2,7,5,4]=>011011=>[2,1,2,1,1]
[1,6,3,4,2,5,7]=>010100=>[2,2,3]
[1,6,3,4,2,7,5]=>010101=>[2,2,2,1]
[1,6,3,4,5,2,7]=>010010=>[2,3,2]
[1,6,3,4,5,7,2]=>010001=>[2,4,1]
[1,6,3,4,7,2,5]=>010010=>[2,3,2]
[1,6,3,4,7,5,2]=>010011=>[2,3,1,1]
[1,6,3,5,2,4,7]=>010100=>[2,2,3]
[1,6,3,5,2,7,4]=>010101=>[2,2,2,1]
[1,6,3,5,4,2,7]=>010110=>[2,2,1,2]
[1,6,3,5,4,7,2]=>010101=>[2,2,2,1]
[1,6,3,5,7,2,4]=>010010=>[2,3,2]
[1,6,3,5,7,4,2]=>010011=>[2,3,1,1]
[1,6,3,7,2,4,5]=>010100=>[2,2,3]
[1,6,3,7,2,5,4]=>010101=>[2,2,2,1]
[1,6,3,7,4,2,5]=>010110=>[2,2,1,2]
[1,6,3,7,4,5,2]=>010101=>[2,2,2,1]
[1,6,3,7,5,2,4]=>010110=>[2,2,1,2]
[1,6,3,7,5,4,2]=>010111=>[2,2,1,1,1]
[1,6,4,2,3,5,7]=>011000=>[2,1,4]
[1,6,4,2,3,7,5]=>011001=>[2,1,3,1]
[1,6,4,2,5,3,7]=>011010=>[2,1,2,2]
[1,6,4,2,5,7,3]=>011001=>[2,1,3,1]
[1,6,4,2,7,3,5]=>011010=>[2,1,2,2]
[1,6,4,2,7,5,3]=>011011=>[2,1,2,1,1]
[1,6,4,3,2,5,7]=>011100=>[2,1,1,3]
[1,6,4,3,2,7,5]=>011101=>[2,1,1,2,1]
[1,6,4,3,5,2,7]=>011010=>[2,1,2,2]
[1,6,4,3,5,7,2]=>011001=>[2,1,3,1]
[1,6,4,3,7,2,5]=>011010=>[2,1,2,2]
[1,6,4,3,7,5,2]=>011011=>[2,1,2,1,1]
[1,6,4,5,2,3,7]=>010100=>[2,2,3]
[1,6,4,5,2,7,3]=>010101=>[2,2,2,1]
[1,6,4,5,3,2,7]=>010110=>[2,2,1,2]
[1,6,4,5,3,7,2]=>010101=>[2,2,2,1]
[1,6,4,5,7,2,3]=>010010=>[2,3,2]
[1,6,4,5,7,3,2]=>010011=>[2,3,1,1]
[1,6,4,7,2,3,5]=>010100=>[2,2,3]
[1,6,4,7,2,5,3]=>010101=>[2,2,2,1]
[1,6,4,7,3,2,5]=>010110=>[2,2,1,2]
[1,6,4,7,3,5,2]=>010101=>[2,2,2,1]
[1,6,4,7,5,2,3]=>010110=>[2,2,1,2]
[1,6,4,7,5,3,2]=>010111=>[2,2,1,1,1]
[1,6,5,2,3,4,7]=>011000=>[2,1,4]
[1,6,5,2,3,7,4]=>011001=>[2,1,3,1]
[1,6,5,2,4,3,7]=>011010=>[2,1,2,2]
[1,6,5,2,4,7,3]=>011001=>[2,1,3,1]
[1,6,5,2,7,3,4]=>011010=>[2,1,2,2]
[1,6,5,2,7,4,3]=>011011=>[2,1,2,1,1]
[1,6,5,3,2,4,7]=>011100=>[2,1,1,3]
[1,6,5,3,2,7,4]=>011101=>[2,1,1,2,1]
[1,6,5,3,4,2,7]=>011010=>[2,1,2,2]
[1,6,5,3,4,7,2]=>011001=>[2,1,3,1]
[1,6,5,3,7,2,4]=>011010=>[2,1,2,2]
[1,6,5,3,7,4,2]=>011011=>[2,1,2,1,1]
[1,6,5,4,2,3,7]=>011100=>[2,1,1,3]
[1,6,5,4,2,7,3]=>011101=>[2,1,1,2,1]
[1,6,5,4,3,2,7]=>011110=>[2,1,1,1,2]
[1,6,5,4,3,7,2]=>011101=>[2,1,1,2,1]
[1,6,5,4,7,2,3]=>011010=>[2,1,2,2]
[1,6,5,4,7,3,2]=>011011=>[2,1,2,1,1]
[1,6,5,7,2,3,4]=>010100=>[2,2,3]
[1,6,5,7,2,4,3]=>010101=>[2,2,2,1]
[1,6,5,7,3,2,4]=>010110=>[2,2,1,2]
[1,6,5,7,3,4,2]=>010101=>[2,2,2,1]
[1,6,5,7,4,2,3]=>010110=>[2,2,1,2]
[1,6,5,7,4,3,2]=>010111=>[2,2,1,1,1]
[1,6,7,2,3,4,5]=>001000=>[3,4]
[1,6,7,2,3,5,4]=>001001=>[3,3,1]
[1,6,7,2,4,3,5]=>001010=>[3,2,2]
[1,6,7,2,4,5,3]=>001001=>[3,3,1]
[1,6,7,2,5,3,4]=>001010=>[3,2,2]
[1,6,7,2,5,4,3]=>001011=>[3,2,1,1]
[1,6,7,3,2,4,5]=>001100=>[3,1,3]
[1,6,7,3,2,5,4]=>001101=>[3,1,2,1]
[1,6,7,3,4,2,5]=>001010=>[3,2,2]
[1,6,7,3,4,5,2]=>001001=>[3,3,1]
[1,6,7,3,5,2,4]=>001010=>[3,2,2]
[1,6,7,3,5,4,2]=>001011=>[3,2,1,1]
[1,6,7,4,2,3,5]=>001100=>[3,1,3]
[1,6,7,4,2,5,3]=>001101=>[3,1,2,1]
[1,6,7,4,3,2,5]=>001110=>[3,1,1,2]
[1,6,7,4,3,5,2]=>001101=>[3,1,2,1]
[1,6,7,4,5,2,3]=>001010=>[3,2,2]
[1,6,7,4,5,3,2]=>001011=>[3,2,1,1]
[1,6,7,5,2,3,4]=>001100=>[3,1,3]
[1,6,7,5,2,4,3]=>001101=>[3,1,2,1]
[1,6,7,5,3,2,4]=>001110=>[3,1,1,2]
[1,6,7,5,3,4,2]=>001101=>[3,1,2,1]
[1,6,7,5,4,2,3]=>001110=>[3,1,1,2]
[1,6,7,5,4,3,2]=>001111=>[3,1,1,1,1]
[1,7,2,3,4,5,6]=>010000=>[2,5]
[1,7,2,3,4,6,5]=>010001=>[2,4,1]
[1,7,2,3,5,4,6]=>010010=>[2,3,2]
[1,7,2,3,5,6,4]=>010001=>[2,4,1]
[1,7,2,3,6,4,5]=>010010=>[2,3,2]
[1,7,2,3,6,5,4]=>010011=>[2,3,1,1]
[1,7,2,4,3,5,6]=>010100=>[2,2,3]
[1,7,2,4,3,6,5]=>010101=>[2,2,2,1]
[1,7,2,4,5,3,6]=>010010=>[2,3,2]
[1,7,2,4,5,6,3]=>010001=>[2,4,1]
[1,7,2,4,6,3,5]=>010010=>[2,3,2]
[1,7,2,4,6,5,3]=>010011=>[2,3,1,1]
[1,7,2,5,3,4,6]=>010100=>[2,2,3]
[1,7,2,5,3,6,4]=>010101=>[2,2,2,1]
[1,7,2,5,4,3,6]=>010110=>[2,2,1,2]
[1,7,2,5,4,6,3]=>010101=>[2,2,2,1]
[1,7,2,5,6,3,4]=>010010=>[2,3,2]
[1,7,2,5,6,4,3]=>010011=>[2,3,1,1]
[1,7,2,6,3,4,5]=>010100=>[2,2,3]
[1,7,2,6,3,5,4]=>010101=>[2,2,2,1]
[1,7,2,6,4,3,5]=>010110=>[2,2,1,2]
[1,7,2,6,4,5,3]=>010101=>[2,2,2,1]
[1,7,2,6,5,3,4]=>010110=>[2,2,1,2]
[1,7,2,6,5,4,3]=>010111=>[2,2,1,1,1]
[1,7,3,2,4,5,6]=>011000=>[2,1,4]
[1,7,3,2,4,6,5]=>011001=>[2,1,3,1]
[1,7,3,2,5,4,6]=>011010=>[2,1,2,2]
[1,7,3,2,5,6,4]=>011001=>[2,1,3,1]
[1,7,3,2,6,4,5]=>011010=>[2,1,2,2]
[1,7,3,2,6,5,4]=>011011=>[2,1,2,1,1]
[1,7,3,4,2,5,6]=>010100=>[2,2,3]
[1,7,3,4,2,6,5]=>010101=>[2,2,2,1]
[1,7,3,4,5,2,6]=>010010=>[2,3,2]
[1,7,3,4,5,6,2]=>010001=>[2,4,1]
[1,7,3,4,6,2,5]=>010010=>[2,3,2]
[1,7,3,4,6,5,2]=>010011=>[2,3,1,1]
[1,7,3,5,2,4,6]=>010100=>[2,2,3]
[1,7,3,5,2,6,4]=>010101=>[2,2,2,1]
[1,7,3,5,4,2,6]=>010110=>[2,2,1,2]
[1,7,3,5,4,6,2]=>010101=>[2,2,2,1]
[1,7,3,5,6,2,4]=>010010=>[2,3,2]
[1,7,3,5,6,4,2]=>010011=>[2,3,1,1]
[1,7,3,6,2,4,5]=>010100=>[2,2,3]
[1,7,3,6,2,5,4]=>010101=>[2,2,2,1]
[1,7,3,6,4,2,5]=>010110=>[2,2,1,2]
[1,7,3,6,4,5,2]=>010101=>[2,2,2,1]
[1,7,3,6,5,2,4]=>010110=>[2,2,1,2]
[1,7,3,6,5,4,2]=>010111=>[2,2,1,1,1]
[1,7,4,2,3,5,6]=>011000=>[2,1,4]
[1,7,4,2,3,6,5]=>011001=>[2,1,3,1]
[1,7,4,2,5,3,6]=>011010=>[2,1,2,2]
[1,7,4,2,5,6,3]=>011001=>[2,1,3,1]
[1,7,4,2,6,3,5]=>011010=>[2,1,2,2]
[1,7,4,2,6,5,3]=>011011=>[2,1,2,1,1]
[1,7,4,3,2,5,6]=>011100=>[2,1,1,3]
[1,7,4,3,2,6,5]=>011101=>[2,1,1,2,1]
[1,7,4,3,5,2,6]=>011010=>[2,1,2,2]
[1,7,4,3,5,6,2]=>011001=>[2,1,3,1]
[1,7,4,3,6,2,5]=>011010=>[2,1,2,2]
[1,7,4,3,6,5,2]=>011011=>[2,1,2,1,1]
[1,7,4,5,2,3,6]=>010100=>[2,2,3]
[1,7,4,5,2,6,3]=>010101=>[2,2,2,1]
[1,7,4,5,3,2,6]=>010110=>[2,2,1,2]
[1,7,4,5,3,6,2]=>010101=>[2,2,2,1]
[1,7,4,5,6,2,3]=>010010=>[2,3,2]
[1,7,4,5,6,3,2]=>010011=>[2,3,1,1]
[1,7,4,6,2,3,5]=>010100=>[2,2,3]
[1,7,4,6,2,5,3]=>010101=>[2,2,2,1]
[1,7,4,6,3,2,5]=>010110=>[2,2,1,2]
[1,7,4,6,3,5,2]=>010101=>[2,2,2,1]
[1,7,4,6,5,2,3]=>010110=>[2,2,1,2]
[1,7,4,6,5,3,2]=>010111=>[2,2,1,1,1]
[1,7,5,2,3,4,6]=>011000=>[2,1,4]
[1,7,5,2,3,6,4]=>011001=>[2,1,3,1]
[1,7,5,2,4,3,6]=>011010=>[2,1,2,2]
[1,7,5,2,4,6,3]=>011001=>[2,1,3,1]
[1,7,5,2,6,3,4]=>011010=>[2,1,2,2]
[1,7,5,2,6,4,3]=>011011=>[2,1,2,1,1]
[1,7,5,3,2,4,6]=>011100=>[2,1,1,3]
[1,7,5,3,2,6,4]=>011101=>[2,1,1,2,1]
[1,7,5,3,4,2,6]=>011010=>[2,1,2,2]
[1,7,5,3,4,6,2]=>011001=>[2,1,3,1]
[1,7,5,3,6,2,4]=>011010=>[2,1,2,2]
[1,7,5,3,6,4,2]=>011011=>[2,1,2,1,1]
[1,7,5,4,2,3,6]=>011100=>[2,1,1,3]
[1,7,5,4,2,6,3]=>011101=>[2,1,1,2,1]
[1,7,5,4,3,2,6]=>011110=>[2,1,1,1,2]
[1,7,5,4,3,6,2]=>011101=>[2,1,1,2,1]
[1,7,5,4,6,2,3]=>011010=>[2,1,2,2]
[1,7,5,4,6,3,2]=>011011=>[2,1,2,1,1]
[1,7,5,6,2,3,4]=>010100=>[2,2,3]
[1,7,5,6,2,4,3]=>010101=>[2,2,2,1]
[1,7,5,6,3,2,4]=>010110=>[2,2,1,2]
[1,7,5,6,3,4,2]=>010101=>[2,2,2,1]
[1,7,5,6,4,2,3]=>010110=>[2,2,1,2]
[1,7,5,6,4,3,2]=>010111=>[2,2,1,1,1]
[1,7,6,2,3,4,5]=>011000=>[2,1,4]
[1,7,6,2,3,5,4]=>011001=>[2,1,3,1]
[1,7,6,2,4,3,5]=>011010=>[2,1,2,2]
[1,7,6,2,4,5,3]=>011001=>[2,1,3,1]
[1,7,6,2,5,3,4]=>011010=>[2,1,2,2]
[1,7,6,2,5,4,3]=>011011=>[2,1,2,1,1]
[1,7,6,3,2,4,5]=>011100=>[2,1,1,3]
[1,7,6,3,2,5,4]=>011101=>[2,1,1,2,1]
[1,7,6,3,4,2,5]=>011010=>[2,1,2,2]
[1,7,6,3,4,5,2]=>011001=>[2,1,3,1]
[1,7,6,3,5,2,4]=>011010=>[2,1,2,2]
[1,7,6,3,5,4,2]=>011011=>[2,1,2,1,1]
[1,7,6,4,2,3,5]=>011100=>[2,1,1,3]
[1,7,6,4,2,5,3]=>011101=>[2,1,1,2,1]
[1,7,6,4,3,2,5]=>011110=>[2,1,1,1,2]
[1,7,6,4,3,5,2]=>011101=>[2,1,1,2,1]
[1,7,6,4,5,2,3]=>011010=>[2,1,2,2]
[1,7,6,4,5,3,2]=>011011=>[2,1,2,1,1]
[1,7,6,5,2,3,4]=>011100=>[2,1,1,3]
[1,7,6,5,2,4,3]=>011101=>[2,1,1,2,1]
[1,7,6,5,3,2,4]=>011110=>[2,1,1,1,2]
[1,7,6,5,3,4,2]=>011101=>[2,1,1,2,1]
[1,7,6,5,4,2,3]=>011110=>[2,1,1,1,2]
[1,7,6,5,4,3,2]=>011111=>[2,1,1,1,1,1]
[2,1,3,4,5,6,7]=>100000=>[1,6]
[2,1,3,4,5,7,6]=>100001=>[1,5,1]
[2,1,3,4,6,5,7]=>100010=>[1,4,2]
[2,1,3,4,6,7,5]=>100001=>[1,5,1]
[2,1,3,4,7,5,6]=>100010=>[1,4,2]
[2,1,3,4,7,6,5]=>100011=>[1,4,1,1]
[2,1,3,5,4,6,7]=>100100=>[1,3,3]
[2,1,3,5,4,7,6]=>100101=>[1,3,2,1]
[2,1,3,5,6,4,7]=>100010=>[1,4,2]
[2,1,3,5,6,7,4]=>100001=>[1,5,1]
[2,1,3,5,7,4,6]=>100010=>[1,4,2]
[2,1,3,5,7,6,4]=>100011=>[1,4,1,1]
[2,1,3,6,4,5,7]=>100100=>[1,3,3]
[2,1,3,6,4,7,5]=>100101=>[1,3,2,1]
[2,1,3,6,5,4,7]=>100110=>[1,3,1,2]
[2,1,3,6,5,7,4]=>100101=>[1,3,2,1]
[2,1,3,6,7,4,5]=>100010=>[1,4,2]
[2,1,3,6,7,5,4]=>100011=>[1,4,1,1]
[2,1,3,7,4,5,6]=>100100=>[1,3,3]
[2,1,3,7,4,6,5]=>100101=>[1,3,2,1]
[2,1,3,7,5,4,6]=>100110=>[1,3,1,2]
[2,1,3,7,5,6,4]=>100101=>[1,3,2,1]
[2,1,3,7,6,4,5]=>100110=>[1,3,1,2]
[2,1,3,7,6,5,4]=>100111=>[1,3,1,1,1]
[2,1,4,3,5,6,7]=>101000=>[1,2,4]
[2,1,4,3,5,7,6]=>101001=>[1,2,3,1]
[2,1,4,3,6,5,7]=>101010=>[1,2,2,2]
[2,1,4,3,6,7,5]=>101001=>[1,2,3,1]
[2,1,4,3,7,5,6]=>101010=>[1,2,2,2]
[2,1,4,3,7,6,5]=>101011=>[1,2,2,1,1]
[2,1,4,5,3,6,7]=>100100=>[1,3,3]
[2,1,4,5,3,7,6]=>100101=>[1,3,2,1]
[2,1,4,5,6,3,7]=>100010=>[1,4,2]
[2,1,4,5,6,7,3]=>100001=>[1,5,1]
[2,1,4,5,7,3,6]=>100010=>[1,4,2]
[2,1,4,5,7,6,3]=>100011=>[1,4,1,1]
[2,1,4,6,3,5,7]=>100100=>[1,3,3]
[2,1,4,6,3,7,5]=>100101=>[1,3,2,1]
[2,1,4,6,5,3,7]=>100110=>[1,3,1,2]
[2,1,4,6,5,7,3]=>100101=>[1,3,2,1]
[2,1,4,6,7,3,5]=>100010=>[1,4,2]
[2,1,4,6,7,5,3]=>100011=>[1,4,1,1]
[2,1,4,7,3,5,6]=>100100=>[1,3,3]
[2,1,4,7,3,6,5]=>100101=>[1,3,2,1]
[2,1,4,7,5,3,6]=>100110=>[1,3,1,2]
[2,1,4,7,5,6,3]=>100101=>[1,3,2,1]
[2,1,4,7,6,3,5]=>100110=>[1,3,1,2]
[2,1,4,7,6,5,3]=>100111=>[1,3,1,1,1]
[2,1,5,3,4,6,7]=>101000=>[1,2,4]
[2,1,5,3,4,7,6]=>101001=>[1,2,3,1]
[2,1,5,3,6,4,7]=>101010=>[1,2,2,2]
[2,1,5,3,6,7,4]=>101001=>[1,2,3,1]
[2,1,5,3,7,4,6]=>101010=>[1,2,2,2]
[2,1,5,3,7,6,4]=>101011=>[1,2,2,1,1]
[2,1,5,4,3,6,7]=>101100=>[1,2,1,3]
[2,1,5,4,3,7,6]=>101101=>[1,2,1,2,1]
[2,1,5,4,6,3,7]=>101010=>[1,2,2,2]
[2,1,5,4,6,7,3]=>101001=>[1,2,3,1]
[2,1,5,4,7,3,6]=>101010=>[1,2,2,2]
[2,1,5,4,7,6,3]=>101011=>[1,2,2,1,1]
[2,1,5,6,3,4,7]=>100100=>[1,3,3]
[2,1,5,6,3,7,4]=>100101=>[1,3,2,1]
[2,1,5,6,4,3,7]=>100110=>[1,3,1,2]
[2,1,5,6,4,7,3]=>100101=>[1,3,2,1]
[2,1,5,6,7,3,4]=>100010=>[1,4,2]
[2,1,5,6,7,4,3]=>100011=>[1,4,1,1]
[2,1,5,7,3,4,6]=>100100=>[1,3,3]
[2,1,5,7,3,6,4]=>100101=>[1,3,2,1]
[2,1,5,7,4,3,6]=>100110=>[1,3,1,2]
[2,1,5,7,4,6,3]=>100101=>[1,3,2,1]
[2,1,5,7,6,3,4]=>100110=>[1,3,1,2]
[2,1,5,7,6,4,3]=>100111=>[1,3,1,1,1]
[2,1,6,3,4,5,7]=>101000=>[1,2,4]
[2,1,6,3,4,7,5]=>101001=>[1,2,3,1]
[2,1,6,3,5,4,7]=>101010=>[1,2,2,2]
[2,1,6,3,5,7,4]=>101001=>[1,2,3,1]
[2,1,6,3,7,4,5]=>101010=>[1,2,2,2]
[2,1,6,3,7,5,4]=>101011=>[1,2,2,1,1]
[2,1,6,4,3,5,7]=>101100=>[1,2,1,3]
[2,1,6,4,3,7,5]=>101101=>[1,2,1,2,1]
[2,1,6,4,5,3,7]=>101010=>[1,2,2,2]
[2,1,6,4,5,7,3]=>101001=>[1,2,3,1]
[2,1,6,4,7,3,5]=>101010=>[1,2,2,2]
[2,1,6,4,7,5,3]=>101011=>[1,2,2,1,1]
[2,1,6,5,3,4,7]=>101100=>[1,2,1,3]
[2,1,6,5,3,7,4]=>101101=>[1,2,1,2,1]
[2,1,6,5,4,3,7]=>101110=>[1,2,1,1,2]
[2,1,6,5,4,7,3]=>101101=>[1,2,1,2,1]
[2,1,6,5,7,3,4]=>101010=>[1,2,2,2]
[2,1,6,5,7,4,3]=>101011=>[1,2,2,1,1]
[2,1,6,7,3,4,5]=>100100=>[1,3,3]
[2,1,6,7,3,5,4]=>100101=>[1,3,2,1]
[2,1,6,7,4,3,5]=>100110=>[1,3,1,2]
[2,1,6,7,4,5,3]=>100101=>[1,3,2,1]
[2,1,6,7,5,3,4]=>100110=>[1,3,1,2]
[2,1,6,7,5,4,3]=>100111=>[1,3,1,1,1]
[2,1,7,3,4,5,6]=>101000=>[1,2,4]
[2,1,7,3,4,6,5]=>101001=>[1,2,3,1]
[2,1,7,3,5,4,6]=>101010=>[1,2,2,2]
[2,1,7,3,5,6,4]=>101001=>[1,2,3,1]
[2,1,7,3,6,4,5]=>101010=>[1,2,2,2]
[2,1,7,3,6,5,4]=>101011=>[1,2,2,1,1]
[2,1,7,4,3,5,6]=>101100=>[1,2,1,3]
[2,1,7,4,3,6,5]=>101101=>[1,2,1,2,1]
[2,1,7,4,5,3,6]=>101010=>[1,2,2,2]
[2,1,7,4,5,6,3]=>101001=>[1,2,3,1]
[2,1,7,4,6,3,5]=>101010=>[1,2,2,2]
[2,1,7,4,6,5,3]=>101011=>[1,2,2,1,1]
[2,1,7,5,3,4,6]=>101100=>[1,2,1,3]
[2,1,7,5,3,6,4]=>101101=>[1,2,1,2,1]
[2,1,7,5,4,3,6]=>101110=>[1,2,1,1,2]
[2,1,7,5,4,6,3]=>101101=>[1,2,1,2,1]
[2,1,7,5,6,3,4]=>101010=>[1,2,2,2]
[2,1,7,5,6,4,3]=>101011=>[1,2,2,1,1]
[2,1,7,6,3,4,5]=>101100=>[1,2,1,3]
[2,1,7,6,3,5,4]=>101101=>[1,2,1,2,1]
[2,1,7,6,4,3,5]=>101110=>[1,2,1,1,2]
[2,1,7,6,4,5,3]=>101101=>[1,2,1,2,1]
[2,1,7,6,5,3,4]=>101110=>[1,2,1,1,2]
[2,1,7,6,5,4,3]=>101111=>[1,2,1,1,1,1]
[2,3,1,4,5,6,7]=>010000=>[2,5]
[2,3,1,4,5,7,6]=>010001=>[2,4,1]
[2,3,1,4,6,5,7]=>010010=>[2,3,2]
[2,3,1,4,6,7,5]=>010001=>[2,4,1]
[2,3,1,4,7,5,6]=>010010=>[2,3,2]
[2,3,1,4,7,6,5]=>010011=>[2,3,1,1]
[2,3,1,5,4,6,7]=>010100=>[2,2,3]
[2,3,1,5,4,7,6]=>010101=>[2,2,2,1]
[2,3,1,5,6,4,7]=>010010=>[2,3,2]
[2,3,1,5,6,7,4]=>010001=>[2,4,1]
[2,3,1,5,7,4,6]=>010010=>[2,3,2]
[2,3,1,5,7,6,4]=>010011=>[2,3,1,1]
[2,3,1,6,4,5,7]=>010100=>[2,2,3]
[2,3,1,6,4,7,5]=>010101=>[2,2,2,1]
[2,3,1,6,5,4,7]=>010110=>[2,2,1,2]
[2,3,1,6,5,7,4]=>010101=>[2,2,2,1]
[2,3,1,6,7,4,5]=>010010=>[2,3,2]
[2,3,1,6,7,5,4]=>010011=>[2,3,1,1]
[2,3,1,7,4,5,6]=>010100=>[2,2,3]
[2,3,1,7,4,6,5]=>010101=>[2,2,2,1]
[2,3,1,7,5,4,6]=>010110=>[2,2,1,2]
[2,3,1,7,5,6,4]=>010101=>[2,2,2,1]
[2,3,1,7,6,4,5]=>010110=>[2,2,1,2]
[2,3,1,7,6,5,4]=>010111=>[2,2,1,1,1]
[2,3,4,1,5,6,7]=>001000=>[3,4]
[2,3,4,1,5,7,6]=>001001=>[3,3,1]
[2,3,4,1,6,5,7]=>001010=>[3,2,2]
[2,3,4,1,6,7,5]=>001001=>[3,3,1]
[2,3,4,1,7,5,6]=>001010=>[3,2,2]
[2,3,4,1,7,6,5]=>001011=>[3,2,1,1]
[2,3,4,5,1,6,7]=>000100=>[4,3]
[2,3,4,5,1,7,6]=>000101=>[4,2,1]
[2,3,4,5,6,1,7]=>000010=>[5,2]
[2,3,4,5,6,7,1]=>000001=>[6,1]
[2,3,4,5,7,1,6]=>000010=>[5,2]
[2,3,4,5,7,6,1]=>000011=>[5,1,1]
[2,3,4,6,1,5,7]=>000100=>[4,3]
[2,3,4,6,1,7,5]=>000101=>[4,2,1]
[2,3,4,6,5,1,7]=>000110=>[4,1,2]
[2,3,4,6,5,7,1]=>000101=>[4,2,1]
[2,3,4,6,7,1,5]=>000010=>[5,2]
[2,3,4,6,7,5,1]=>000011=>[5,1,1]
[2,3,4,7,1,5,6]=>000100=>[4,3]
[2,3,4,7,1,6,5]=>000101=>[4,2,1]
[2,3,4,7,5,1,6]=>000110=>[4,1,2]
[2,3,4,7,5,6,1]=>000101=>[4,2,1]
[2,3,4,7,6,1,5]=>000110=>[4,1,2]
[2,3,4,7,6,5,1]=>000111=>[4,1,1,1]
[2,3,5,1,4,6,7]=>001000=>[3,4]
[2,3,5,1,4,7,6]=>001001=>[3,3,1]
[2,3,5,1,6,4,7]=>001010=>[3,2,2]
[2,3,5,1,6,7,4]=>001001=>[3,3,1]
[2,3,5,1,7,4,6]=>001010=>[3,2,2]
[2,3,5,1,7,6,4]=>001011=>[3,2,1,1]
[2,3,5,4,1,6,7]=>001100=>[3,1,3]
[2,3,5,4,1,7,6]=>001101=>[3,1,2,1]
[2,3,5,4,6,1,7]=>001010=>[3,2,2]
[2,3,5,4,6,7,1]=>001001=>[3,3,1]
[2,3,5,4,7,1,6]=>001010=>[3,2,2]
[2,3,5,4,7,6,1]=>001011=>[3,2,1,1]
[2,3,5,6,1,4,7]=>000100=>[4,3]
[2,3,5,6,1,7,4]=>000101=>[4,2,1]
[2,3,5,6,4,1,7]=>000110=>[4,1,2]
[2,3,5,6,4,7,1]=>000101=>[4,2,1]
[2,3,5,6,7,1,4]=>000010=>[5,2]
[2,3,5,6,7,4,1]=>000011=>[5,1,1]
[2,3,5,7,1,4,6]=>000100=>[4,3]
[2,3,5,7,1,6,4]=>000101=>[4,2,1]
[2,3,5,7,4,1,6]=>000110=>[4,1,2]
[2,3,5,7,4,6,1]=>000101=>[4,2,1]
[2,3,5,7,6,1,4]=>000110=>[4,1,2]
[2,3,5,7,6,4,1]=>000111=>[4,1,1,1]
[2,3,6,1,4,5,7]=>001000=>[3,4]
[2,3,6,1,4,7,5]=>001001=>[3,3,1]
[2,3,6,1,5,4,7]=>001010=>[3,2,2]
[2,3,6,1,5,7,4]=>001001=>[3,3,1]
[2,3,6,1,7,4,5]=>001010=>[3,2,2]
[2,3,6,1,7,5,4]=>001011=>[3,2,1,1]
[2,3,6,4,1,5,7]=>001100=>[3,1,3]
[2,3,6,4,1,7,5]=>001101=>[3,1,2,1]
[2,3,6,4,5,1,7]=>001010=>[3,2,2]
[2,3,6,4,5,7,1]=>001001=>[3,3,1]
[2,3,6,4,7,1,5]=>001010=>[3,2,2]
[2,3,6,4,7,5,1]=>001011=>[3,2,1,1]
[2,3,6,5,1,4,7]=>001100=>[3,1,3]
[2,3,6,5,1,7,4]=>001101=>[3,1,2,1]
[2,3,6,5,4,1,7]=>001110=>[3,1,1,2]
[2,3,6,5,4,7,1]=>001101=>[3,1,2,1]
[2,3,6,5,7,1,4]=>001010=>[3,2,2]
[2,3,6,5,7,4,1]=>001011=>[3,2,1,1]
[2,3,6,7,1,4,5]=>000100=>[4,3]
[2,3,6,7,1,5,4]=>000101=>[4,2,1]
[2,3,6,7,4,1,5]=>000110=>[4,1,2]
[2,3,6,7,4,5,1]=>000101=>[4,2,1]
[2,3,6,7,5,1,4]=>000110=>[4,1,2]
[2,3,6,7,5,4,1]=>000111=>[4,1,1,1]
[2,3,7,1,4,5,6]=>001000=>[3,4]
[2,3,7,1,4,6,5]=>001001=>[3,3,1]
[2,3,7,1,5,4,6]=>001010=>[3,2,2]
[2,3,7,1,5,6,4]=>001001=>[3,3,1]
[2,3,7,1,6,4,5]=>001010=>[3,2,2]
[2,3,7,1,6,5,4]=>001011=>[3,2,1,1]
[2,3,7,4,1,5,6]=>001100=>[3,1,3]
[2,3,7,4,1,6,5]=>001101=>[3,1,2,1]
[2,3,7,4,5,1,6]=>001010=>[3,2,2]
[2,3,7,4,5,6,1]=>001001=>[3,3,1]
[2,3,7,4,6,1,5]=>001010=>[3,2,2]
[2,3,7,4,6,5,1]=>001011=>[3,2,1,1]
[2,3,7,5,1,4,6]=>001100=>[3,1,3]
[2,3,7,5,1,6,4]=>001101=>[3,1,2,1]
[2,3,7,5,4,1,6]=>001110=>[3,1,1,2]
[2,3,7,5,4,6,1]=>001101=>[3,1,2,1]
[2,3,7,5,6,1,4]=>001010=>[3,2,2]
[2,3,7,5,6,4,1]=>001011=>[3,2,1,1]
[2,3,7,6,1,4,5]=>001100=>[3,1,3]
[2,3,7,6,1,5,4]=>001101=>[3,1,2,1]
[2,3,7,6,4,1,5]=>001110=>[3,1,1,2]
[2,3,7,6,4,5,1]=>001101=>[3,1,2,1]
[2,3,7,6,5,1,4]=>001110=>[3,1,1,2]
[2,3,7,6,5,4,1]=>001111=>[3,1,1,1,1]
[2,4,1,3,5,6,7]=>010000=>[2,5]
[2,4,1,3,5,7,6]=>010001=>[2,4,1]
[2,4,1,3,6,5,7]=>010010=>[2,3,2]
[2,4,1,3,6,7,5]=>010001=>[2,4,1]
[2,4,1,3,7,5,6]=>010010=>[2,3,2]
[2,4,1,3,7,6,5]=>010011=>[2,3,1,1]
[2,4,1,5,3,6,7]=>010100=>[2,2,3]
[2,4,1,5,3,7,6]=>010101=>[2,2,2,1]
[2,4,1,5,6,3,7]=>010010=>[2,3,2]
[2,4,1,5,6,7,3]=>010001=>[2,4,1]
[2,4,1,5,7,3,6]=>010010=>[2,3,2]
[2,4,1,5,7,6,3]=>010011=>[2,3,1,1]
[2,4,1,6,3,5,7]=>010100=>[2,2,3]
[2,4,1,6,3,7,5]=>010101=>[2,2,2,1]
[2,4,1,6,5,3,7]=>010110=>[2,2,1,2]
[2,4,1,6,5,7,3]=>010101=>[2,2,2,1]
[2,4,1,6,7,3,5]=>010010=>[2,3,2]
[2,4,1,6,7,5,3]=>010011=>[2,3,1,1]
[2,4,1,7,3,5,6]=>010100=>[2,2,3]
[2,4,1,7,3,6,5]=>010101=>[2,2,2,1]
[2,4,1,7,5,3,6]=>010110=>[2,2,1,2]
[2,4,1,7,5,6,3]=>010101=>[2,2,2,1]
[2,4,1,7,6,3,5]=>010110=>[2,2,1,2]
[2,4,1,7,6,5,3]=>010111=>[2,2,1,1,1]
[2,4,3,1,5,6,7]=>011000=>[2,1,4]
[2,4,3,1,5,7,6]=>011001=>[2,1,3,1]
[2,4,3,1,6,5,7]=>011010=>[2,1,2,2]
[2,4,3,1,6,7,5]=>011001=>[2,1,3,1]
[2,4,3,1,7,5,6]=>011010=>[2,1,2,2]
[2,4,3,1,7,6,5]=>011011=>[2,1,2,1,1]
[2,4,3,5,1,6,7]=>010100=>[2,2,3]
[2,4,3,5,1,7,6]=>010101=>[2,2,2,1]
[2,4,3,5,6,1,7]=>010010=>[2,3,2]
[2,4,3,5,6,7,1]=>010001=>[2,4,1]
[2,4,3,5,7,1,6]=>010010=>[2,3,2]
[2,4,3,5,7,6,1]=>010011=>[2,3,1,1]
[2,4,3,6,1,5,7]=>010100=>[2,2,3]
[2,4,3,6,1,7,5]=>010101=>[2,2,2,1]
[2,4,3,6,5,1,7]=>010110=>[2,2,1,2]
[2,4,3,6,5,7,1]=>010101=>[2,2,2,1]
[2,4,3,6,7,1,5]=>010010=>[2,3,2]
[2,4,3,6,7,5,1]=>010011=>[2,3,1,1]
[2,4,3,7,1,5,6]=>010100=>[2,2,3]
[2,4,3,7,1,6,5]=>010101=>[2,2,2,1]
[2,4,3,7,5,1,6]=>010110=>[2,2,1,2]
[2,4,3,7,5,6,1]=>010101=>[2,2,2,1]
[2,4,3,7,6,1,5]=>010110=>[2,2,1,2]
[2,4,3,7,6,5,1]=>010111=>[2,2,1,1,1]
[2,4,5,1,3,6,7]=>001000=>[3,4]
[2,4,5,1,3,7,6]=>001001=>[3,3,1]
[2,4,5,1,6,3,7]=>001010=>[3,2,2]
[2,4,5,1,6,7,3]=>001001=>[3,3,1]
[2,4,5,1,7,3,6]=>001010=>[3,2,2]
[2,4,5,1,7,6,3]=>001011=>[3,2,1,1]
[2,4,5,3,1,6,7]=>001100=>[3,1,3]
[2,4,5,3,1,7,6]=>001101=>[3,1,2,1]
[2,4,5,3,6,1,7]=>001010=>[3,2,2]
[2,4,5,3,6,7,1]=>001001=>[3,3,1]
[2,4,5,3,7,1,6]=>001010=>[3,2,2]
[2,4,5,3,7,6,1]=>001011=>[3,2,1,1]
[2,4,5,6,1,3,7]=>000100=>[4,3]
[2,4,5,6,1,7,3]=>000101=>[4,2,1]
[2,4,5,6,3,1,7]=>000110=>[4,1,2]
[2,4,5,6,3,7,1]=>000101=>[4,2,1]
[2,4,5,6,7,1,3]=>000010=>[5,2]
[2,4,5,6,7,3,1]=>000011=>[5,1,1]
[2,4,5,7,1,3,6]=>000100=>[4,3]
[2,4,5,7,1,6,3]=>000101=>[4,2,1]
[2,4,5,7,3,1,6]=>000110=>[4,1,2]
[2,4,5,7,3,6,1]=>000101=>[4,2,1]
[2,4,5,7,6,1,3]=>000110=>[4,1,2]
[2,4,5,7,6,3,1]=>000111=>[4,1,1,1]
[2,4,6,1,3,5,7]=>001000=>[3,4]
[2,4,6,1,3,7,5]=>001001=>[3,3,1]
[2,4,6,1,5,3,7]=>001010=>[3,2,2]
[2,4,6,1,5,7,3]=>001001=>[3,3,1]
[2,4,6,1,7,3,5]=>001010=>[3,2,2]
[2,4,6,1,7,5,3]=>001011=>[3,2,1,1]
[2,4,6,3,1,5,7]=>001100=>[3,1,3]
[2,4,6,3,1,7,5]=>001101=>[3,1,2,1]
[2,4,6,3,5,1,7]=>001010=>[3,2,2]
[2,4,6,3,5,7,1]=>001001=>[3,3,1]
[2,4,6,3,7,1,5]=>001010=>[3,2,2]
[2,4,6,3,7,5,1]=>001011=>[3,2,1,1]
[2,4,6,5,1,3,7]=>001100=>[3,1,3]
[2,4,6,5,1,7,3]=>001101=>[3,1,2,1]
[2,4,6,5,3,1,7]=>001110=>[3,1,1,2]
[2,4,6,5,3,7,1]=>001101=>[3,1,2,1]
[2,4,6,5,7,1,3]=>001010=>[3,2,2]
[2,4,6,5,7,3,1]=>001011=>[3,2,1,1]
[2,4,6,7,1,3,5]=>000100=>[4,3]
[2,4,6,7,1,5,3]=>000101=>[4,2,1]
[2,4,6,7,3,1,5]=>000110=>[4,1,2]
[2,4,6,7,3,5,1]=>000101=>[4,2,1]
[2,4,6,7,5,1,3]=>000110=>[4,1,2]
[2,4,6,7,5,3,1]=>000111=>[4,1,1,1]
[2,4,7,1,3,5,6]=>001000=>[3,4]
[2,4,7,1,3,6,5]=>001001=>[3,3,1]
[2,4,7,1,5,3,6]=>001010=>[3,2,2]
[2,4,7,1,5,6,3]=>001001=>[3,3,1]
[2,4,7,1,6,3,5]=>001010=>[3,2,2]
[2,4,7,1,6,5,3]=>001011=>[3,2,1,1]
[2,4,7,3,1,5,6]=>001100=>[3,1,3]
[2,4,7,3,1,6,5]=>001101=>[3,1,2,1]
[2,4,7,3,5,1,6]=>001010=>[3,2,2]
[2,4,7,3,5,6,1]=>001001=>[3,3,1]
[2,4,7,3,6,1,5]=>001010=>[3,2,2]
[2,4,7,3,6,5,1]=>001011=>[3,2,1,1]
[2,4,7,5,1,3,6]=>001100=>[3,1,3]
[2,4,7,5,1,6,3]=>001101=>[3,1,2,1]
[2,4,7,5,3,1,6]=>001110=>[3,1,1,2]
[2,4,7,5,3,6,1]=>001101=>[3,1,2,1]
[2,4,7,5,6,1,3]=>001010=>[3,2,2]
[2,4,7,5,6,3,1]=>001011=>[3,2,1,1]
[2,4,7,6,1,3,5]=>001100=>[3,1,3]
[2,4,7,6,1,5,3]=>001101=>[3,1,2,1]
[2,4,7,6,3,1,5]=>001110=>[3,1,1,2]
[2,4,7,6,3,5,1]=>001101=>[3,1,2,1]
[2,4,7,6,5,1,3]=>001110=>[3,1,1,2]
[2,4,7,6,5,3,1]=>001111=>[3,1,1,1,1]
[2,5,1,3,4,6,7]=>010000=>[2,5]
[2,5,1,3,4,7,6]=>010001=>[2,4,1]
[2,5,1,3,6,4,7]=>010010=>[2,3,2]
[2,5,1,3,6,7,4]=>010001=>[2,4,1]
[2,5,1,3,7,4,6]=>010010=>[2,3,2]
[2,5,1,3,7,6,4]=>010011=>[2,3,1,1]
[2,5,1,4,3,6,7]=>010100=>[2,2,3]
[2,5,1,4,3,7,6]=>010101=>[2,2,2,1]
[2,5,1,4,6,3,7]=>010010=>[2,3,2]
[2,5,1,4,6,7,3]=>010001=>[2,4,1]
[2,5,1,4,7,3,6]=>010010=>[2,3,2]
[2,5,1,4,7,6,3]=>010011=>[2,3,1,1]
[2,5,1,6,3,4,7]=>010100=>[2,2,3]
[2,5,1,6,3,7,4]=>010101=>[2,2,2,1]
[2,5,1,6,4,3,7]=>010110=>[2,2,1,2]
[2,5,1,6,4,7,3]=>010101=>[2,2,2,1]
[2,5,1,6,7,3,4]=>010010=>[2,3,2]
[2,5,1,6,7,4,3]=>010011=>[2,3,1,1]
[2,5,1,7,3,4,6]=>010100=>[2,2,3]
[2,5,1,7,3,6,4]=>010101=>[2,2,2,1]
[2,5,1,7,4,3,6]=>010110=>[2,2,1,2]
[2,5,1,7,4,6,3]=>010101=>[2,2,2,1]
[2,5,1,7,6,3,4]=>010110=>[2,2,1,2]
[2,5,1,7,6,4,3]=>010111=>[2,2,1,1,1]
[2,5,3,1,4,6,7]=>011000=>[2,1,4]
[2,5,3,1,4,7,6]=>011001=>[2,1,3,1]
[2,5,3,1,6,4,7]=>011010=>[2,1,2,2]
[2,5,3,1,6,7,4]=>011001=>[2,1,3,1]
[2,5,3,1,7,4,6]=>011010=>[2,1,2,2]
[2,5,3,1,7,6,4]=>011011=>[2,1,2,1,1]
[2,5,3,4,1,6,7]=>010100=>[2,2,3]
[2,5,3,4,1,7,6]=>010101=>[2,2,2,1]
[2,5,3,4,6,1,7]=>010010=>[2,3,2]
[2,5,3,4,6,7,1]=>010001=>[2,4,1]
[2,5,3,4,7,1,6]=>010010=>[2,3,2]
[2,5,3,4,7,6,1]=>010011=>[2,3,1,1]
[2,5,3,6,1,4,7]=>010100=>[2,2,3]
[2,5,3,6,1,7,4]=>010101=>[2,2,2,1]
[2,5,3,6,4,1,7]=>010110=>[2,2,1,2]
[2,5,3,6,4,7,1]=>010101=>[2,2,2,1]
[2,5,3,6,7,1,4]=>010010=>[2,3,2]
[2,5,3,6,7,4,1]=>010011=>[2,3,1,1]
[2,5,3,7,1,4,6]=>010100=>[2,2,3]
[2,5,3,7,1,6,4]=>010101=>[2,2,2,1]
[2,5,3,7,4,1,6]=>010110=>[2,2,1,2]
[2,5,3,7,4,6,1]=>010101=>[2,2,2,1]
[2,5,3,7,6,1,4]=>010110=>[2,2,1,2]
[2,5,3,7,6,4,1]=>010111=>[2,2,1,1,1]
[2,5,4,1,3,6,7]=>011000=>[2,1,4]
[2,5,4,1,3,7,6]=>011001=>[2,1,3,1]
[2,5,4,1,6,3,7]=>011010=>[2,1,2,2]
[2,5,4,1,6,7,3]=>011001=>[2,1,3,1]
[2,5,4,1,7,3,6]=>011010=>[2,1,2,2]
[2,5,4,1,7,6,3]=>011011=>[2,1,2,1,1]
[2,5,4,3,1,6,7]=>011100=>[2,1,1,3]
[2,5,4,3,1,7,6]=>011101=>[2,1,1,2,1]
[2,5,4,3,6,1,7]=>011010=>[2,1,2,2]
[2,5,4,3,6,7,1]=>011001=>[2,1,3,1]
[2,5,4,3,7,1,6]=>011010=>[2,1,2,2]
[2,5,4,3,7,6,1]=>011011=>[2,1,2,1,1]
[2,5,4,6,1,3,7]=>010100=>[2,2,3]
[2,5,4,6,1,7,3]=>010101=>[2,2,2,1]
[2,5,4,6,3,1,7]=>010110=>[2,2,1,2]
[2,5,4,6,3,7,1]=>010101=>[2,2,2,1]
[2,5,4,6,7,1,3]=>010010=>[2,3,2]
[2,5,4,6,7,3,1]=>010011=>[2,3,1,1]
[2,5,4,7,1,3,6]=>010100=>[2,2,3]
[2,5,4,7,1,6,3]=>010101=>[2,2,2,1]
[2,5,4,7,3,1,6]=>010110=>[2,2,1,2]
[2,5,4,7,3,6,1]=>010101=>[2,2,2,1]
[2,5,4,7,6,1,3]=>010110=>[2,2,1,2]
[2,5,4,7,6,3,1]=>010111=>[2,2,1,1,1]
[2,5,6,1,3,4,7]=>001000=>[3,4]
[2,5,6,1,3,7,4]=>001001=>[3,3,1]
[2,5,6,1,4,3,7]=>001010=>[3,2,2]
[2,5,6,1,4,7,3]=>001001=>[3,3,1]
[2,5,6,1,7,3,4]=>001010=>[3,2,2]
[2,5,6,1,7,4,3]=>001011=>[3,2,1,1]
[2,5,6,3,1,4,7]=>001100=>[3,1,3]
[2,5,6,3,1,7,4]=>001101=>[3,1,2,1]
[2,5,6,3,4,1,7]=>001010=>[3,2,2]
[2,5,6,3,4,7,1]=>001001=>[3,3,1]
[2,5,6,3,7,1,4]=>001010=>[3,2,2]
[2,5,6,3,7,4,1]=>001011=>[3,2,1,1]
[2,5,6,4,1,3,7]=>001100=>[3,1,3]
[2,5,6,4,1,7,3]=>001101=>[3,1,2,1]
[2,5,6,4,3,1,7]=>001110=>[3,1,1,2]
[2,5,6,4,3,7,1]=>001101=>[3,1,2,1]
[2,5,6,4,7,1,3]=>001010=>[3,2,2]
[2,5,6,4,7,3,1]=>001011=>[3,2,1,1]
[2,5,6,7,1,3,4]=>000100=>[4,3]
[2,5,6,7,1,4,3]=>000101=>[4,2,1]
[2,5,6,7,3,1,4]=>000110=>[4,1,2]
[2,5,6,7,3,4,1]=>000101=>[4,2,1]
[2,5,6,7,4,1,3]=>000110=>[4,1,2]
[2,5,6,7,4,3,1]=>000111=>[4,1,1,1]
[2,5,7,1,3,4,6]=>001000=>[3,4]
[2,5,7,1,3,6,4]=>001001=>[3,3,1]
[2,5,7,1,4,3,6]=>001010=>[3,2,2]
[2,5,7,1,4,6,3]=>001001=>[3,3,1]
[2,5,7,1,6,3,4]=>001010=>[3,2,2]
[2,5,7,1,6,4,3]=>001011=>[3,2,1,1]
[2,5,7,3,1,4,6]=>001100=>[3,1,3]
[2,5,7,3,1,6,4]=>001101=>[3,1,2,1]
[2,5,7,3,4,1,6]=>001010=>[3,2,2]
[2,5,7,3,4,6,1]=>001001=>[3,3,1]
[2,5,7,3,6,1,4]=>001010=>[3,2,2]
[2,5,7,3,6,4,1]=>001011=>[3,2,1,1]
[2,5,7,4,1,3,6]=>001100=>[3,1,3]
[2,5,7,4,1,6,3]=>001101=>[3,1,2,1]
[2,5,7,4,3,1,6]=>001110=>[3,1,1,2]
[2,5,7,4,3,6,1]=>001101=>[3,1,2,1]
[2,5,7,4,6,1,3]=>001010=>[3,2,2]
[2,5,7,4,6,3,1]=>001011=>[3,2,1,1]
[2,5,7,6,1,3,4]=>001100=>[3,1,3]
[2,5,7,6,1,4,3]=>001101=>[3,1,2,1]
[2,5,7,6,3,1,4]=>001110=>[3,1,1,2]
[2,5,7,6,3,4,1]=>001101=>[3,1,2,1]
[2,5,7,6,4,1,3]=>001110=>[3,1,1,2]
[2,5,7,6,4,3,1]=>001111=>[3,1,1,1,1]
[2,6,1,3,4,5,7]=>010000=>[2,5]
[2,6,1,3,4,7,5]=>010001=>[2,4,1]
[2,6,1,3,5,4,7]=>010010=>[2,3,2]
[2,6,1,3,5,7,4]=>010001=>[2,4,1]
[2,6,1,3,7,4,5]=>010010=>[2,3,2]
[2,6,1,3,7,5,4]=>010011=>[2,3,1,1]
[2,6,1,4,3,5,7]=>010100=>[2,2,3]
[2,6,1,4,3,7,5]=>010101=>[2,2,2,1]
[2,6,1,4,5,3,7]=>010010=>[2,3,2]
[2,6,1,4,5,7,3]=>010001=>[2,4,1]
[2,6,1,4,7,3,5]=>010010=>[2,3,2]
[2,6,1,4,7,5,3]=>010011=>[2,3,1,1]
[2,6,1,5,3,4,7]=>010100=>[2,2,3]
[2,6,1,5,3,7,4]=>010101=>[2,2,2,1]
[2,6,1,5,4,3,7]=>010110=>[2,2,1,2]
[2,6,1,5,4,7,3]=>010101=>[2,2,2,1]
[2,6,1,5,7,3,4]=>010010=>[2,3,2]
[2,6,1,5,7,4,3]=>010011=>[2,3,1,1]
[2,6,1,7,3,4,5]=>010100=>[2,2,3]
[2,6,1,7,3,5,4]=>010101=>[2,2,2,1]
[2,6,1,7,4,3,5]=>010110=>[2,2,1,2]
[2,6,1,7,4,5,3]=>010101=>[2,2,2,1]
[2,6,1,7,5,3,4]=>010110=>[2,2,1,2]
[2,6,1,7,5,4,3]=>010111=>[2,2,1,1,1]
[2,6,3,1,4,5,7]=>011000=>[2,1,4]
[2,6,3,1,4,7,5]=>011001=>[2,1,3,1]
[2,6,3,1,5,4,7]=>011010=>[2,1,2,2]
[2,6,3,1,5,7,4]=>011001=>[2,1,3,1]
[2,6,3,1,7,4,5]=>011010=>[2,1,2,2]
[2,6,3,1,7,5,4]=>011011=>[2,1,2,1,1]
[2,6,3,4,1,5,7]=>010100=>[2,2,3]
[2,6,3,4,1,7,5]=>010101=>[2,2,2,1]
[2,6,3,4,5,1,7]=>010010=>[2,3,2]
[2,6,3,4,5,7,1]=>010001=>[2,4,1]
[2,6,3,4,7,1,5]=>010010=>[2,3,2]
[2,6,3,4,7,5,1]=>010011=>[2,3,1,1]
[2,6,3,5,1,4,7]=>010100=>[2,2,3]
[2,6,3,5,1,7,4]=>010101=>[2,2,2,1]
[2,6,3,5,4,1,7]=>010110=>[2,2,1,2]
[2,6,3,5,4,7,1]=>010101=>[2,2,2,1]
[2,6,3,5,7,1,4]=>010010=>[2,3,2]
[2,6,3,5,7,4,1]=>010011=>[2,3,1,1]
[2,6,3,7,1,4,5]=>010100=>[2,2,3]
[2,6,3,7,1,5,4]=>010101=>[2,2,2,1]
[2,6,3,7,4,1,5]=>010110=>[2,2,1,2]
[2,6,3,7,4,5,1]=>010101=>[2,2,2,1]
[2,6,3,7,5,1,4]=>010110=>[2,2,1,2]
[2,6,3,7,5,4,1]=>010111=>[2,2,1,1,1]
[2,6,4,1,3,5,7]=>011000=>[2,1,4]
[2,6,4,1,3,7,5]=>011001=>[2,1,3,1]
[2,6,4,1,5,3,7]=>011010=>[2,1,2,2]
[2,6,4,1,5,7,3]=>011001=>[2,1,3,1]
[2,6,4,1,7,3,5]=>011010=>[2,1,2,2]
[2,6,4,1,7,5,3]=>011011=>[2,1,2,1,1]
[2,6,4,3,1,5,7]=>011100=>[2,1,1,3]
[2,6,4,3,1,7,5]=>011101=>[2,1,1,2,1]
[2,6,4,3,5,1,7]=>011010=>[2,1,2,2]
[2,6,4,3,5,7,1]=>011001=>[2,1,3,1]
[2,6,4,3,7,1,5]=>011010=>[2,1,2,2]
[2,6,4,3,7,5,1]=>011011=>[2,1,2,1,1]
[2,6,4,5,1,3,7]=>010100=>[2,2,3]
[2,6,4,5,1,7,3]=>010101=>[2,2,2,1]
[2,6,4,5,3,1,7]=>010110=>[2,2,1,2]
[2,6,4,5,3,7,1]=>010101=>[2,2,2,1]
[2,6,4,5,7,1,3]=>010010=>[2,3,2]
[2,6,4,5,7,3,1]=>010011=>[2,3,1,1]
[2,6,4,7,1,3,5]=>010100=>[2,2,3]
[2,6,4,7,1,5,3]=>010101=>[2,2,2,1]
[2,6,4,7,3,1,5]=>010110=>[2,2,1,2]
[2,6,4,7,3,5,1]=>010101=>[2,2,2,1]
[2,6,4,7,5,1,3]=>010110=>[2,2,1,2]
[2,6,4,7,5,3,1]=>010111=>[2,2,1,1,1]
[2,6,5,1,3,4,7]=>011000=>[2,1,4]
[2,6,5,1,3,7,4]=>011001=>[2,1,3,1]
[2,6,5,1,4,3,7]=>011010=>[2,1,2,2]
[2,6,5,1,4,7,3]=>011001=>[2,1,3,1]
[2,6,5,1,7,3,4]=>011010=>[2,1,2,2]
[2,6,5,1,7,4,3]=>011011=>[2,1,2,1,1]
[2,6,5,3,1,4,7]=>011100=>[2,1,1,3]
[2,6,5,3,1,7,4]=>011101=>[2,1,1,2,1]
[2,6,5,3,4,1,7]=>011010=>[2,1,2,2]
[2,6,5,3,4,7,1]=>011001=>[2,1,3,1]
[2,6,5,3,7,1,4]=>011010=>[2,1,2,2]
[2,6,5,3,7,4,1]=>011011=>[2,1,2,1,1]
[2,6,5,4,1,3,7]=>011100=>[2,1,1,3]
[2,6,5,4,1,7,3]=>011101=>[2,1,1,2,1]
[2,6,5,4,3,1,7]=>011110=>[2,1,1,1,2]
[2,6,5,4,3,7,1]=>011101=>[2,1,1,2,1]
[2,6,5,4,7,1,3]=>011010=>[2,1,2,2]
[2,6,5,4,7,3,1]=>011011=>[2,1,2,1,1]
[2,6,5,7,1,3,4]=>010100=>[2,2,3]
[2,6,5,7,1,4,3]=>010101=>[2,2,2,1]
[2,6,5,7,3,1,4]=>010110=>[2,2,1,2]
[2,6,5,7,3,4,1]=>010101=>[2,2,2,1]
[2,6,5,7,4,1,3]=>010110=>[2,2,1,2]
[2,6,5,7,4,3,1]=>010111=>[2,2,1,1,1]
[2,6,7,1,3,4,5]=>001000=>[3,4]
[2,6,7,1,3,5,4]=>001001=>[3,3,1]
[2,6,7,1,4,3,5]=>001010=>[3,2,2]
[2,6,7,1,4,5,3]=>001001=>[3,3,1]
[2,6,7,1,5,3,4]=>001010=>[3,2,2]
[2,6,7,1,5,4,3]=>001011=>[3,2,1,1]
[2,6,7,3,1,4,5]=>001100=>[3,1,3]
[2,6,7,3,1,5,4]=>001101=>[3,1,2,1]
[2,6,7,3,4,1,5]=>001010=>[3,2,2]
[2,6,7,3,4,5,1]=>001001=>[3,3,1]
[2,6,7,3,5,1,4]=>001010=>[3,2,2]
[2,6,7,3,5,4,1]=>001011=>[3,2,1,1]
[2,6,7,4,1,3,5]=>001100=>[3,1,3]
[2,6,7,4,1,5,3]=>001101=>[3,1,2,1]
[2,6,7,4,3,1,5]=>001110=>[3,1,1,2]
[2,6,7,4,3,5,1]=>001101=>[3,1,2,1]
[2,6,7,4,5,1,3]=>001010=>[3,2,2]
[2,6,7,4,5,3,1]=>001011=>[3,2,1,1]
[2,6,7,5,1,3,4]=>001100=>[3,1,3]
[2,6,7,5,1,4,3]=>001101=>[3,1,2,1]
[2,6,7,5,3,1,4]=>001110=>[3,1,1,2]
[2,6,7,5,3,4,1]=>001101=>[3,1,2,1]
[2,6,7,5,4,1,3]=>001110=>[3,1,1,2]
[2,6,7,5,4,3,1]=>001111=>[3,1,1,1,1]
[2,7,1,3,4,5,6]=>010000=>[2,5]
[2,7,1,3,4,6,5]=>010001=>[2,4,1]
[2,7,1,3,5,4,6]=>010010=>[2,3,2]
[2,7,1,3,5,6,4]=>010001=>[2,4,1]
[2,7,1,3,6,4,5]=>010010=>[2,3,2]
[2,7,1,3,6,5,4]=>010011=>[2,3,1,1]
[2,7,1,4,3,5,6]=>010100=>[2,2,3]
[2,7,1,4,3,6,5]=>010101=>[2,2,2,1]
[2,7,1,4,5,3,6]=>010010=>[2,3,2]
[2,7,1,4,5,6,3]=>010001=>[2,4,1]
[2,7,1,4,6,3,5]=>010010=>[2,3,2]
[2,7,1,4,6,5,3]=>010011=>[2,3,1,1]
[2,7,1,5,3,4,6]=>010100=>[2,2,3]
[2,7,1,5,3,6,4]=>010101=>[2,2,2,1]
[2,7,1,5,4,3,6]=>010110=>[2,2,1,2]
[2,7,1,5,4,6,3]=>010101=>[2,2,2,1]
[2,7,1,5,6,3,4]=>010010=>[2,3,2]
[2,7,1,5,6,4,3]=>010011=>[2,3,1,1]
[2,7,1,6,3,4,5]=>010100=>[2,2,3]
[2,7,1,6,3,5,4]=>010101=>[2,2,2,1]
[2,7,1,6,4,3,5]=>010110=>[2,2,1,2]
[2,7,1,6,4,5,3]=>010101=>[2,2,2,1]
[2,7,1,6,5,3,4]=>010110=>[2,2,1,2]
[2,7,1,6,5,4,3]=>010111=>[2,2,1,1,1]
[2,7,3,1,4,5,6]=>011000=>[2,1,4]
[2,7,3,1,4,6,5]=>011001=>[2,1,3,1]
[2,7,3,1,5,4,6]=>011010=>[2,1,2,2]
[2,7,3,1,5,6,4]=>011001=>[2,1,3,1]
[2,7,3,1,6,4,5]=>011010=>[2,1,2,2]
[2,7,3,1,6,5,4]=>011011=>[2,1,2,1,1]
[2,7,3,4,1,5,6]=>010100=>[2,2,3]
[2,7,3,4,1,6,5]=>010101=>[2,2,2,1]
[2,7,3,4,5,1,6]=>010010=>[2,3,2]
[2,7,3,4,5,6,1]=>010001=>[2,4,1]
[2,7,3,4,6,1,5]=>010010=>[2,3,2]
[2,7,3,4,6,5,1]=>010011=>[2,3,1,1]
[2,7,3,5,1,4,6]=>010100=>[2,2,3]
[2,7,3,5,1,6,4]=>010101=>[2,2,2,1]
[2,7,3,5,4,1,6]=>010110=>[2,2,1,2]
[2,7,3,5,4,6,1]=>010101=>[2,2,2,1]
[2,7,3,5,6,1,4]=>010010=>[2,3,2]
[2,7,3,5,6,4,1]=>010011=>[2,3,1,1]
[2,7,3,6,1,4,5]=>010100=>[2,2,3]
[2,7,3,6,1,5,4]=>010101=>[2,2,2,1]
[2,7,3,6,4,1,5]=>010110=>[2,2,1,2]
[2,7,3,6,4,5,1]=>010101=>[2,2,2,1]
[2,7,3,6,5,1,4]=>010110=>[2,2,1,2]
[2,7,3,6,5,4,1]=>010111=>[2,2,1,1,1]
[2,7,4,1,3,5,6]=>011000=>[2,1,4]
[2,7,4,1,3,6,5]=>011001=>[2,1,3,1]
[2,7,4,1,5,3,6]=>011010=>[2,1,2,2]
[2,7,4,1,5,6,3]=>011001=>[2,1,3,1]
[2,7,4,1,6,3,5]=>011010=>[2,1,2,2]
[2,7,4,1,6,5,3]=>011011=>[2,1,2,1,1]
[2,7,4,3,1,5,6]=>011100=>[2,1,1,3]
[2,7,4,3,1,6,5]=>011101=>[2,1,1,2,1]
[2,7,4,3,5,1,6]=>011010=>[2,1,2,2]
[2,7,4,3,5,6,1]=>011001=>[2,1,3,1]
[2,7,4,3,6,1,5]=>011010=>[2,1,2,2]
[2,7,4,3,6,5,1]=>011011=>[2,1,2,1,1]
[2,7,4,5,1,3,6]=>010100=>[2,2,3]
[2,7,4,5,1,6,3]=>010101=>[2,2,2,1]
[2,7,4,5,3,1,6]=>010110=>[2,2,1,2]
[2,7,4,5,3,6,1]=>010101=>[2,2,2,1]
[2,7,4,5,6,1,3]=>010010=>[2,3,2]
[2,7,4,5,6,3,1]=>010011=>[2,3,1,1]
[2,7,4,6,1,3,5]=>010100=>[2,2,3]
[2,7,4,6,1,5,3]=>010101=>[2,2,2,1]
[2,7,4,6,3,1,5]=>010110=>[2,2,1,2]
[2,7,4,6,3,5,1]=>010101=>[2,2,2,1]
[2,7,4,6,5,1,3]=>010110=>[2,2,1,2]
[2,7,4,6,5,3,1]=>010111=>[2,2,1,1,1]
[2,7,5,1,3,4,6]=>011000=>[2,1,4]
[2,7,5,1,3,6,4]=>011001=>[2,1,3,1]
[2,7,5,1,4,3,6]=>011010=>[2,1,2,2]
[2,7,5,1,4,6,3]=>011001=>[2,1,3,1]
[2,7,5,1,6,3,4]=>011010=>[2,1,2,2]
[2,7,5,1,6,4,3]=>011011=>[2,1,2,1,1]
[2,7,5,3,1,4,6]=>011100=>[2,1,1,3]
[2,7,5,3,1,6,4]=>011101=>[2,1,1,2,1]
[2,7,5,3,4,1,6]=>011010=>[2,1,2,2]
[2,7,5,3,4,6,1]=>011001=>[2,1,3,1]
[2,7,5,3,6,1,4]=>011010=>[2,1,2,2]
[2,7,5,3,6,4,1]=>011011=>[2,1,2,1,1]
[2,7,5,4,1,3,6]=>011100=>[2,1,1,3]
[2,7,5,4,1,6,3]=>011101=>[2,1,1,2,1]
[2,7,5,4,3,1,6]=>011110=>[2,1,1,1,2]
[2,7,5,4,3,6,1]=>011101=>[2,1,1,2,1]
[2,7,5,4,6,1,3]=>011010=>[2,1,2,2]
[2,7,5,4,6,3,1]=>011011=>[2,1,2,1,1]
[2,7,5,6,1,3,4]=>010100=>[2,2,3]
[2,7,5,6,1,4,3]=>010101=>[2,2,2,1]
[2,7,5,6,3,1,4]=>010110=>[2,2,1,2]
[2,7,5,6,3,4,1]=>010101=>[2,2,2,1]
[2,7,5,6,4,1,3]=>010110=>[2,2,1,2]
[2,7,5,6,4,3,1]=>010111=>[2,2,1,1,1]
[2,7,6,1,3,4,5]=>011000=>[2,1,4]
[2,7,6,1,3,5,4]=>011001=>[2,1,3,1]
[2,7,6,1,4,3,5]=>011010=>[2,1,2,2]
[2,7,6,1,4,5,3]=>011001=>[2,1,3,1]
[2,7,6,1,5,3,4]=>011010=>[2,1,2,2]
[2,7,6,1,5,4,3]=>011011=>[2,1,2,1,1]
[2,7,6,3,1,4,5]=>011100=>[2,1,1,3]
[2,7,6,3,1,5,4]=>011101=>[2,1,1,2,1]
[2,7,6,3,4,1,5]=>011010=>[2,1,2,2]
[2,7,6,3,4,5,1]=>011001=>[2,1,3,1]
[2,7,6,3,5,1,4]=>011010=>[2,1,2,2]
[2,7,6,3,5,4,1]=>011011=>[2,1,2,1,1]
[2,7,6,4,1,3,5]=>011100=>[2,1,1,3]
[2,7,6,4,1,5,3]=>011101=>[2,1,1,2,1]
[2,7,6,4,3,1,5]=>011110=>[2,1,1,1,2]
[2,7,6,4,3,5,1]=>011101=>[2,1,1,2,1]
[2,7,6,4,5,1,3]=>011010=>[2,1,2,2]
[2,7,6,4,5,3,1]=>011011=>[2,1,2,1,1]
[2,7,6,5,1,3,4]=>011100=>[2,1,1,3]
[2,7,6,5,1,4,3]=>011101=>[2,1,1,2,1]
[2,7,6,5,3,1,4]=>011110=>[2,1,1,1,2]
[2,7,6,5,3,4,1]=>011101=>[2,1,1,2,1]
[2,7,6,5,4,1,3]=>011110=>[2,1,1,1,2]
[2,7,6,5,4,3,1]=>011111=>[2,1,1,1,1,1]
[3,1,2,4,5,6,7]=>100000=>[1,6]
[3,1,2,4,5,7,6]=>100001=>[1,5,1]
[3,1,2,4,6,5,7]=>100010=>[1,4,2]
[3,1,2,4,6,7,5]=>100001=>[1,5,1]
[3,1,2,4,7,5,6]=>100010=>[1,4,2]
[3,1,2,4,7,6,5]=>100011=>[1,4,1,1]
[3,1,2,5,4,6,7]=>100100=>[1,3,3]
[3,1,2,5,4,7,6]=>100101=>[1,3,2,1]
[3,1,2,5,6,4,7]=>100010=>[1,4,2]
[3,1,2,5,6,7,4]=>100001=>[1,5,1]
[3,1,2,5,7,4,6]=>100010=>[1,4,2]
[3,1,2,5,7,6,4]=>100011=>[1,4,1,1]
[3,1,2,6,4,5,7]=>100100=>[1,3,3]
[3,1,2,6,4,7,5]=>100101=>[1,3,2,1]
[3,1,2,6,5,4,7]=>100110=>[1,3,1,2]
[3,1,2,6,5,7,4]=>100101=>[1,3,2,1]
[3,1,2,6,7,4,5]=>100010=>[1,4,2]
[3,1,2,6,7,5,4]=>100011=>[1,4,1,1]
[3,1,2,7,4,5,6]=>100100=>[1,3,3]
[3,1,2,7,4,6,5]=>100101=>[1,3,2,1]
[3,1,2,7,5,4,6]=>100110=>[1,3,1,2]
[3,1,2,7,5,6,4]=>100101=>[1,3,2,1]
[3,1,2,7,6,4,5]=>100110=>[1,3,1,2]
[3,1,2,7,6,5,4]=>100111=>[1,3,1,1,1]
[3,1,4,2,5,6,7]=>101000=>[1,2,4]
[3,1,4,2,5,7,6]=>101001=>[1,2,3,1]
[3,1,4,2,6,5,7]=>101010=>[1,2,2,2]
[3,1,4,2,6,7,5]=>101001=>[1,2,3,1]
[3,1,4,2,7,5,6]=>101010=>[1,2,2,2]
[3,1,4,2,7,6,5]=>101011=>[1,2,2,1,1]
[3,1,4,5,2,6,7]=>100100=>[1,3,3]
[3,1,4,5,2,7,6]=>100101=>[1,3,2,1]
[3,1,4,5,6,2,7]=>100010=>[1,4,2]
[3,1,4,5,6,7,2]=>100001=>[1,5,1]
[3,1,4,5,7,2,6]=>100010=>[1,4,2]
[3,1,4,5,7,6,2]=>100011=>[1,4,1,1]
[3,1,4,6,2,5,7]=>100100=>[1,3,3]
[3,1,4,6,2,7,5]=>100101=>[1,3,2,1]
[3,1,4,6,5,2,7]=>100110=>[1,3,1,2]
[3,1,4,6,5,7,2]=>100101=>[1,3,2,1]
[3,1,4,6,7,2,5]=>100010=>[1,4,2]
[3,1,4,6,7,5,2]=>100011=>[1,4,1,1]
[3,1,4,7,2,5,6]=>100100=>[1,3,3]
[3,1,4,7,2,6,5]=>100101=>[1,3,2,1]
[3,1,4,7,5,2,6]=>100110=>[1,3,1,2]
[3,1,4,7,5,6,2]=>100101=>[1,3,2,1]
[3,1,4,7,6,2,5]=>100110=>[1,3,1,2]
[3,1,4,7,6,5,2]=>100111=>[1,3,1,1,1]
[3,1,5,2,4,6,7]=>101000=>[1,2,4]
[3,1,5,2,4,7,6]=>101001=>[1,2,3,1]
[3,1,5,2,6,4,7]=>101010=>[1,2,2,2]
[3,1,5,2,6,7,4]=>101001=>[1,2,3,1]
[3,1,5,2,7,4,6]=>101010=>[1,2,2,2]
[3,1,5,2,7,6,4]=>101011=>[1,2,2,1,1]
[3,1,5,4,2,6,7]=>101100=>[1,2,1,3]
[3,1,5,4,2,7,6]=>101101=>[1,2,1,2,1]
[3,1,5,4,6,2,7]=>101010=>[1,2,2,2]
[3,1,5,4,6,7,2]=>101001=>[1,2,3,1]
[3,1,5,4,7,2,6]=>101010=>[1,2,2,2]
[3,1,5,4,7,6,2]=>101011=>[1,2,2,1,1]
[3,1,5,6,2,4,7]=>100100=>[1,3,3]
[3,1,5,6,2,7,4]=>100101=>[1,3,2,1]
[3,1,5,6,4,2,7]=>100110=>[1,3,1,2]
[3,1,5,6,4,7,2]=>100101=>[1,3,2,1]
[3,1,5,6,7,2,4]=>100010=>[1,4,2]
[3,1,5,6,7,4,2]=>100011=>[1,4,1,1]
[3,1,5,7,2,4,6]=>100100=>[1,3,3]
[3,1,5,7,2,6,4]=>100101=>[1,3,2,1]
[3,1,5,7,4,2,6]=>100110=>[1,3,1,2]
[3,1,5,7,4,6,2]=>100101=>[1,3,2,1]
[3,1,5,7,6,2,4]=>100110=>[1,3,1,2]
[3,1,5,7,6,4,2]=>100111=>[1,3,1,1,1]
[3,1,6,2,4,5,7]=>101000=>[1,2,4]
[3,1,6,2,4,7,5]=>101001=>[1,2,3,1]
[3,1,6,2,5,4,7]=>101010=>[1,2,2,2]
[3,1,6,2,5,7,4]=>101001=>[1,2,3,1]
[3,1,6,2,7,4,5]=>101010=>[1,2,2,2]
[3,1,6,2,7,5,4]=>101011=>[1,2,2,1,1]
[3,1,6,4,2,5,7]=>101100=>[1,2,1,3]
[3,1,6,4,2,7,5]=>101101=>[1,2,1,2,1]
[3,1,6,4,5,2,7]=>101010=>[1,2,2,2]
[3,1,6,4,5,7,2]=>101001=>[1,2,3,1]
[3,1,6,4,7,2,5]=>101010=>[1,2,2,2]
[3,1,6,4,7,5,2]=>101011=>[1,2,2,1,1]
[3,1,6,5,2,4,7]=>101100=>[1,2,1,3]
[3,1,6,5,2,7,4]=>101101=>[1,2,1,2,1]
[3,1,6,5,4,2,7]=>101110=>[1,2,1,1,2]
[3,1,6,5,4,7,2]=>101101=>[1,2,1,2,1]
[3,1,6,5,7,2,4]=>101010=>[1,2,2,2]
[3,1,6,5,7,4,2]=>101011=>[1,2,2,1,1]
[3,1,6,7,2,4,5]=>100100=>[1,3,3]
[3,1,6,7,2,5,4]=>100101=>[1,3,2,1]
[3,1,6,7,4,2,5]=>100110=>[1,3,1,2]
[3,1,6,7,4,5,2]=>100101=>[1,3,2,1]
[3,1,6,7,5,2,4]=>100110=>[1,3,1,2]
[3,1,6,7,5,4,2]=>100111=>[1,3,1,1,1]
[3,1,7,2,4,5,6]=>101000=>[1,2,4]
[3,1,7,2,4,6,5]=>101001=>[1,2,3,1]
[3,1,7,2,5,4,6]=>101010=>[1,2,2,2]
[3,1,7,2,5,6,4]=>101001=>[1,2,3,1]
[3,1,7,2,6,4,5]=>101010=>[1,2,2,2]
[3,1,7,2,6,5,4]=>101011=>[1,2,2,1,1]
[3,1,7,4,2,5,6]=>101100=>[1,2,1,3]
[3,1,7,4,2,6,5]=>101101=>[1,2,1,2,1]
[3,1,7,4,5,2,6]=>101010=>[1,2,2,2]
[3,1,7,4,5,6,2]=>101001=>[1,2,3,1]
[3,1,7,4,6,2,5]=>101010=>[1,2,2,2]
[3,1,7,4,6,5,2]=>101011=>[1,2,2,1,1]
[3,1,7,5,2,4,6]=>101100=>[1,2,1,3]
[3,1,7,5,2,6,4]=>101101=>[1,2,1,2,1]
[3,1,7,5,4,2,6]=>101110=>[1,2,1,1,2]
[3,1,7,5,4,6,2]=>101101=>[1,2,1,2,1]
[3,1,7,5,6,2,4]=>101010=>[1,2,2,2]
[3,1,7,5,6,4,2]=>101011=>[1,2,2,1,1]
[3,1,7,6,2,4,5]=>101100=>[1,2,1,3]
[3,1,7,6,2,5,4]=>101101=>[1,2,1,2,1]
[3,1,7,6,4,2,5]=>101110=>[1,2,1,1,2]
[3,1,7,6,4,5,2]=>101101=>[1,2,1,2,1]
[3,1,7,6,5,2,4]=>101110=>[1,2,1,1,2]
[3,1,7,6,5,4,2]=>101111=>[1,2,1,1,1,1]
[3,2,1,4,5,6,7]=>110000=>[1,1,5]
[3,2,1,4,5,7,6]=>110001=>[1,1,4,1]
[3,2,1,4,6,5,7]=>110010=>[1,1,3,2]
[3,2,1,4,6,7,5]=>110001=>[1,1,4,1]
[3,2,1,4,7,5,6]=>110010=>[1,1,3,2]
[3,2,1,4,7,6,5]=>110011=>[1,1,3,1,1]
[3,2,1,5,4,6,7]=>110100=>[1,1,2,3]
[3,2,1,5,4,7,6]=>110101=>[1,1,2,2,1]
[3,2,1,5,6,4,7]=>110010=>[1,1,3,2]
[3,2,1,5,6,7,4]=>110001=>[1,1,4,1]
[3,2,1,5,7,4,6]=>110010=>[1,1,3,2]
[3,2,1,5,7,6,4]=>110011=>[1,1,3,1,1]
[3,2,1,6,4,5,7]=>110100=>[1,1,2,3]
[3,2,1,6,4,7,5]=>110101=>[1,1,2,2,1]
[3,2,1,6,5,4,7]=>110110=>[1,1,2,1,2]
[3,2,1,6,5,7,4]=>110101=>[1,1,2,2,1]
[3,2,1,6,7,4,5]=>110010=>[1,1,3,2]
[3,2,1,6,7,5,4]=>110011=>[1,1,3,1,1]
[3,2,1,7,4,5,6]=>110100=>[1,1,2,3]
[3,2,1,7,4,6,5]=>110101=>[1,1,2,2,1]
[3,2,1,7,5,4,6]=>110110=>[1,1,2,1,2]
[3,2,1,7,5,6,4]=>110101=>[1,1,2,2,1]
[3,2,1,7,6,4,5]=>110110=>[1,1,2,1,2]
[3,2,1,7,6,5,4]=>110111=>[1,1,2,1,1,1]
[3,2,4,1,5,6,7]=>101000=>[1,2,4]
[3,2,4,1,5,7,6]=>101001=>[1,2,3,1]
[3,2,4,1,6,5,7]=>101010=>[1,2,2,2]
[3,2,4,1,6,7,5]=>101001=>[1,2,3,1]
[3,2,4,1,7,5,6]=>101010=>[1,2,2,2]
[3,2,4,1,7,6,5]=>101011=>[1,2,2,1,1]
[3,2,4,5,1,6,7]=>100100=>[1,3,3]
[3,2,4,5,1,7,6]=>100101=>[1,3,2,1]
[3,2,4,5,6,1,7]=>100010=>[1,4,2]
[3,2,4,5,6,7,1]=>100001=>[1,5,1]
[3,2,4,5,7,1,6]=>100010=>[1,4,2]
[3,2,4,5,7,6,1]=>100011=>[1,4,1,1]
[3,2,4,6,1,5,7]=>100100=>[1,3,3]
[3,2,4,6,1,7,5]=>100101=>[1,3,2,1]
[3,2,4,6,5,1,7]=>100110=>[1,3,1,2]
[3,2,4,6,5,7,1]=>100101=>[1,3,2,1]
[3,2,4,6,7,1,5]=>100010=>[1,4,2]
[3,2,4,6,7,5,1]=>100011=>[1,4,1,1]
[3,2,4,7,1,5,6]=>100100=>[1,3,3]
[3,2,4,7,1,6,5]=>100101=>[1,3,2,1]
[3,2,4,7,5,1,6]=>100110=>[1,3,1,2]
[3,2,4,7,5,6,1]=>100101=>[1,3,2,1]
[3,2,4,7,6,1,5]=>100110=>[1,3,1,2]
[3,2,4,7,6,5,1]=>100111=>[1,3,1,1,1]
[3,2,5,1,4,6,7]=>101000=>[1,2,4]
[3,2,5,1,4,7,6]=>101001=>[1,2,3,1]
[3,2,5,1,6,4,7]=>101010=>[1,2,2,2]
[3,2,5,1,6,7,4]=>101001=>[1,2,3,1]
[3,2,5,1,7,4,6]=>101010=>[1,2,2,2]
[3,2,5,1,7,6,4]=>101011=>[1,2,2,1,1]
[3,2,5,4,1,6,7]=>101100=>[1,2,1,3]
[3,2,5,4,1,7,6]=>101101=>[1,2,1,2,1]
[3,2,5,4,6,1,7]=>101010=>[1,2,2,2]
[3,2,5,4,6,7,1]=>101001=>[1,2,3,1]
[3,2,5,4,7,1,6]=>101010=>[1,2,2,2]
[3,2,5,4,7,6,1]=>101011=>[1,2,2,1,1]
[3,2,5,6,1,4,7]=>100100=>[1,3,3]
[3,2,5,6,1,7,4]=>100101=>[1,3,2,1]
[3,2,5,6,4,1,7]=>100110=>[1,3,1,2]
[3,2,5,6,4,7,1]=>100101=>[1,3,2,1]
[3,2,5,6,7,1,4]=>100010=>[1,4,2]
[3,2,5,6,7,4,1]=>100011=>[1,4,1,1]
[3,2,5,7,1,4,6]=>100100=>[1,3,3]
[3,2,5,7,1,6,4]=>100101=>[1,3,2,1]
[3,2,5,7,4,1,6]=>100110=>[1,3,1,2]
[3,2,5,7,4,6,1]=>100101=>[1,3,2,1]
[3,2,5,7,6,1,4]=>100110=>[1,3,1,2]
[3,2,5,7,6,4,1]=>100111=>[1,3,1,1,1]
[3,2,6,1,4,5,7]=>101000=>[1,2,4]
[3,2,6,1,4,7,5]=>101001=>[1,2,3,1]
[3,2,6,1,5,4,7]=>101010=>[1,2,2,2]
[3,2,6,1,5,7,4]=>101001=>[1,2,3,1]
[3,2,6,1,7,4,5]=>101010=>[1,2,2,2]
[3,2,6,1,7,5,4]=>101011=>[1,2,2,1,1]
[3,2,6,4,1,5,7]=>101100=>[1,2,1,3]
[3,2,6,4,1,7,5]=>101101=>[1,2,1,2,1]
[3,2,6,4,5,1,7]=>101010=>[1,2,2,2]
[3,2,6,4,5,7,1]=>101001=>[1,2,3,1]
[3,2,6,4,7,1,5]=>101010=>[1,2,2,2]
[3,2,6,4,7,5,1]=>101011=>[1,2,2,1,1]
[3,2,6,5,1,4,7]=>101100=>[1,2,1,3]
[3,2,6,5,1,7,4]=>101101=>[1,2,1,2,1]
[3,2,6,5,4,1,7]=>101110=>[1,2,1,1,2]
[3,2,6,5,4,7,1]=>101101=>[1,2,1,2,1]
[3,2,6,5,7,1,4]=>101010=>[1,2,2,2]
[3,2,6,5,7,4,1]=>101011=>[1,2,2,1,1]
[3,2,6,7,1,4,5]=>100100=>[1,3,3]
[3,2,6,7,1,5,4]=>100101=>[1,3,2,1]
[3,2,6,7,4,1,5]=>100110=>[1,3,1,2]
[3,2,6,7,4,5,1]=>100101=>[1,3,2,1]
[3,2,6,7,5,1,4]=>100110=>[1,3,1,2]
[3,2,6,7,5,4,1]=>100111=>[1,3,1,1,1]
[3,2,7,1,4,5,6]=>101000=>[1,2,4]
[3,2,7,1,4,6,5]=>101001=>[1,2,3,1]
[3,2,7,1,5,4,6]=>101010=>[1,2,2,2]
[3,2,7,1,5,6,4]=>101001=>[1,2,3,1]
[3,2,7,1,6,4,5]=>101010=>[1,2,2,2]
[3,2,7,1,6,5,4]=>101011=>[1,2,2,1,1]
[3,2,7,4,1,5,6]=>101100=>[1,2,1,3]
[3,2,7,4,1,6,5]=>101101=>[1,2,1,2,1]
[3,2,7,4,5,1,6]=>101010=>[1,2,2,2]
[3,2,7,4,5,6,1]=>101001=>[1,2,3,1]
[3,2,7,4,6,1,5]=>101010=>[1,2,2,2]
[3,2,7,4,6,5,1]=>101011=>[1,2,2,1,1]
[3,2,7,5,1,4,6]=>101100=>[1,2,1,3]
[3,2,7,5,1,6,4]=>101101=>[1,2,1,2,1]
[3,2,7,5,4,1,6]=>101110=>[1,2,1,1,2]
[3,2,7,5,4,6,1]=>101101=>[1,2,1,2,1]
[3,2,7,5,6,1,4]=>101010=>[1,2,2,2]
[3,2,7,5,6,4,1]=>101011=>[1,2,2,1,1]
[3,2,7,6,1,4,5]=>101100=>[1,2,1,3]
[3,2,7,6,1,5,4]=>101101=>[1,2,1,2,1]
[3,2,7,6,4,1,5]=>101110=>[1,2,1,1,2]
[3,2,7,6,4,5,1]=>101101=>[1,2,1,2,1]
[3,2,7,6,5,1,4]=>101110=>[1,2,1,1,2]
[3,2,7,6,5,4,1]=>101111=>[1,2,1,1,1,1]
[3,4,1,2,5,6,7]=>010000=>[2,5]
[3,4,1,2,5,7,6]=>010001=>[2,4,1]
[3,4,1,2,6,5,7]=>010010=>[2,3,2]
[3,4,1,2,6,7,5]=>010001=>[2,4,1]
[3,4,1,2,7,5,6]=>010010=>[2,3,2]
[3,4,1,2,7,6,5]=>010011=>[2,3,1,1]
[3,4,1,5,2,6,7]=>010100=>[2,2,3]
[3,4,1,5,2,7,6]=>010101=>[2,2,2,1]
[3,4,1,5,6,2,7]=>010010=>[2,3,2]
[3,4,1,5,6,7,2]=>010001=>[2,4,1]
[3,4,1,5,7,2,6]=>010010=>[2,3,2]
[3,4,1,5,7,6,2]=>010011=>[2,3,1,1]
[3,4,1,6,2,5,7]=>010100=>[2,2,3]
[3,4,1,6,2,7,5]=>010101=>[2,2,2,1]
[3,4,1,6,5,2,7]=>010110=>[2,2,1,2]
[3,4,1,6,5,7,2]=>010101=>[2,2,2,1]
[3,4,1,6,7,2,5]=>010010=>[2,3,2]
[3,4,1,6,7,5,2]=>010011=>[2,3,1,1]
[3,4,1,7,2,5,6]=>010100=>[2,2,3]
[3,4,1,7,2,6,5]=>010101=>[2,2,2,1]
[3,4,1,7,5,2,6]=>010110=>[2,2,1,2]
[3,4,1,7,5,6,2]=>010101=>[2,2,2,1]
[3,4,1,7,6,2,5]=>010110=>[2,2,1,2]
[3,4,1,7,6,5,2]=>010111=>[2,2,1,1,1]
[3,4,2,1,5,6,7]=>011000=>[2,1,4]
[3,4,2,1,5,7,6]=>011001=>[2,1,3,1]
[3,4,2,1,6,5,7]=>011010=>[2,1,2,2]
[3,4,2,1,6,7,5]=>011001=>[2,1,3,1]
[3,4,2,1,7,5,6]=>011010=>[2,1,2,2]
[3,4,2,1,7,6,5]=>011011=>[2,1,2,1,1]
[3,4,2,5,1,6,7]=>010100=>[2,2,3]
[3,4,2,5,1,7,6]=>010101=>[2,2,2,1]
[3,4,2,5,6,1,7]=>010010=>[2,3,2]
[3,4,2,5,6,7,1]=>010001=>[2,4,1]
[3,4,2,5,7,1,6]=>010010=>[2,3,2]
[3,4,2,5,7,6,1]=>010011=>[2,3,1,1]
[3,4,2,6,1,5,7]=>010100=>[2,2,3]
[3,4,2,6,1,7,5]=>010101=>[2,2,2,1]
[3,4,2,6,5,1,7]=>010110=>[2,2,1,2]
[3,4,2,6,5,7,1]=>010101=>[2,2,2,1]
[3,4,2,6,7,1,5]=>010010=>[2,3,2]
[3,4,2,6,7,5,1]=>010011=>[2,3,1,1]
[3,4,2,7,1,5,6]=>010100=>[2,2,3]
[3,4,2,7,1,6,5]=>010101=>[2,2,2,1]
[3,4,2,7,5,1,6]=>010110=>[2,2,1,2]
[3,4,2,7,5,6,1]=>010101=>[2,2,2,1]
[3,4,2,7,6,1,5]=>010110=>[2,2,1,2]
[3,4,2,7,6,5,1]=>010111=>[2,2,1,1,1]
[3,4,5,1,2,6,7]=>001000=>[3,4]
[3,4,5,1,2,7,6]=>001001=>[3,3,1]
[3,4,5,1,6,2,7]=>001010=>[3,2,2]
[3,4,5,1,6,7,2]=>001001=>[3,3,1]
[3,4,5,1,7,2,6]=>001010=>[3,2,2]
[3,4,5,1,7,6,2]=>001011=>[3,2,1,1]
[3,4,5,2,1,6,7]=>001100=>[3,1,3]
[3,4,5,2,1,7,6]=>001101=>[3,1,2,1]
[3,4,5,2,6,1,7]=>001010=>[3,2,2]
[3,4,5,2,6,7,1]=>001001=>[3,3,1]
[3,4,5,2,7,1,6]=>001010=>[3,2,2]
[3,4,5,2,7,6,1]=>001011=>[3,2,1,1]
[3,4,5,6,1,2,7]=>000100=>[4,3]
[3,4,5,6,1,7,2]=>000101=>[4,2,1]
[3,4,5,6,2,1,7]=>000110=>[4,1,2]
[3,4,5,6,2,7,1]=>000101=>[4,2,1]
[3,4,5,6,7,1,2]=>000010=>[5,2]
[3,4,5,6,7,2,1]=>000011=>[5,1,1]
[3,4,5,7,1,2,6]=>000100=>[4,3]
[3,4,5,7,1,6,2]=>000101=>[4,2,1]
[3,4,5,7,2,1,6]=>000110=>[4,1,2]
[3,4,5,7,2,6,1]=>000101=>[4,2,1]
[3,4,5,7,6,1,2]=>000110=>[4,1,2]
[3,4,5,7,6,2,1]=>000111=>[4,1,1,1]
[3,4,6,1,2,5,7]=>001000=>[3,4]
[3,4,6,1,2,7,5]=>001001=>[3,3,1]
[3,4,6,1,5,2,7]=>001010=>[3,2,2]
[3,4,6,1,5,7,2]=>001001=>[3,3,1]
[3,4,6,1,7,2,5]=>001010=>[3,2,2]
[3,4,6,1,7,5,2]=>001011=>[3,2,1,1]
[3,4,6,2,1,5,7]=>001100=>[3,1,3]
[3,4,6,2,1,7,5]=>001101=>[3,1,2,1]
[3,4,6,2,5,1,7]=>001010=>[3,2,2]
[3,4,6,2,5,7,1]=>001001=>[3,3,1]
[3,4,6,2,7,1,5]=>001010=>[3,2,2]
[3,4,6,2,7,5,1]=>001011=>[3,2,1,1]
[3,4,6,5,1,2,7]=>001100=>[3,1,3]
[3,4,6,5,1,7,2]=>001101=>[3,1,2,1]
[3,4,6,5,2,1,7]=>001110=>[3,1,1,2]
[3,4,6,5,2,7,1]=>001101=>[3,1,2,1]
[3,4,6,5,7,1,2]=>001010=>[3,2,2]
[3,4,6,5,7,2,1]=>001011=>[3,2,1,1]
[3,4,6,7,1,2,5]=>000100=>[4,3]
[3,4,6,7,1,5,2]=>000101=>[4,2,1]
[3,4,6,7,2,1,5]=>000110=>[4,1,2]
[3,4,6,7,2,5,1]=>000101=>[4,2,1]
[3,4,6,7,5,1,2]=>000110=>[4,1,2]
[3,4,6,7,5,2,1]=>000111=>[4,1,1,1]
[3,4,7,1,2,5,6]=>001000=>[3,4]
[3,4,7,1,2,6,5]=>001001=>[3,3,1]
[3,4,7,1,5,2,6]=>001010=>[3,2,2]
[3,4,7,1,5,6,2]=>001001=>[3,3,1]
[3,4,7,1,6,2,5]=>001010=>[3,2,2]
[3,4,7,1,6,5,2]=>001011=>[3,2,1,1]
[3,4,7,2,1,5,6]=>001100=>[3,1,3]
[3,4,7,2,1,6,5]=>001101=>[3,1,2,1]
[3,4,7,2,5,1,6]=>001010=>[3,2,2]
[3,4,7,2,5,6,1]=>001001=>[3,3,1]
[3,4,7,2,6,1,5]=>001010=>[3,2,2]
[3,4,7,2,6,5,1]=>001011=>[3,2,1,1]
[3,4,7,5,1,2,6]=>001100=>[3,1,3]
[3,4,7,5,1,6,2]=>001101=>[3,1,2,1]
[3,4,7,5,2,1,6]=>001110=>[3,1,1,2]
[3,4,7,5,2,6,1]=>001101=>[3,1,2,1]
[3,4,7,5,6,1,2]=>001010=>[3,2,2]
[3,4,7,5,6,2,1]=>001011=>[3,2,1,1]
[3,4,7,6,1,2,5]=>001100=>[3,1,3]
[3,4,7,6,1,5,2]=>001101=>[3,1,2,1]
[3,4,7,6,2,1,5]=>001110=>[3,1,1,2]
[3,4,7,6,2,5,1]=>001101=>[3,1,2,1]
[3,4,7,6,5,1,2]=>001110=>[3,1,1,2]
[3,4,7,6,5,2,1]=>001111=>[3,1,1,1,1]
[3,5,1,2,4,6,7]=>010000=>[2,5]
[3,5,1,2,4,7,6]=>010001=>[2,4,1]
[3,5,1,2,6,4,7]=>010010=>[2,3,2]
[3,5,1,2,6,7,4]=>010001=>[2,4,1]
[3,5,1,2,7,4,6]=>010010=>[2,3,2]
[3,5,1,2,7,6,4]=>010011=>[2,3,1,1]
[3,5,1,4,2,6,7]=>010100=>[2,2,3]
[3,5,1,4,2,7,6]=>010101=>[2,2,2,1]
[3,5,1,4,6,2,7]=>010010=>[2,3,2]
[3,5,1,4,6,7,2]=>010001=>[2,4,1]
[3,5,1,4,7,2,6]=>010010=>[2,3,2]
[3,5,1,4,7,6,2]=>010011=>[2,3,1,1]
[3,5,1,6,2,4,7]=>010100=>[2,2,3]
[3,5,1,6,2,7,4]=>010101=>[2,2,2,1]
[3,5,1,6,4,2,7]=>010110=>[2,2,1,2]
[3,5,1,6,4,7,2]=>010101=>[2,2,2,1]
[3,5,1,6,7,2,4]=>010010=>[2,3,2]
[3,5,1,6,7,4,2]=>010011=>[2,3,1,1]
[3,5,1,7,2,4,6]=>010100=>[2,2,3]
[3,5,1,7,2,6,4]=>010101=>[2,2,2,1]
[3,5,1,7,4,2,6]=>010110=>[2,2,1,2]
[3,5,1,7,4,6,2]=>010101=>[2,2,2,1]
[3,5,1,7,6,2,4]=>010110=>[2,2,1,2]
[3,5,1,7,6,4,2]=>010111=>[2,2,1,1,1]
[3,5,2,1,4,6,7]=>011000=>[2,1,4]
[3,5,2,1,4,7,6]=>011001=>[2,1,3,1]
[3,5,2,1,6,4,7]=>011010=>[2,1,2,2]
[3,5,2,1,6,7,4]=>011001=>[2,1,3,1]
[3,5,2,1,7,4,6]=>011010=>[2,1,2,2]
[3,5,2,1,7,6,4]=>011011=>[2,1,2,1,1]
[3,5,2,4,1,6,7]=>010100=>[2,2,3]
[3,5,2,4,1,7,6]=>010101=>[2,2,2,1]
[3,5,2,4,6,1,7]=>010010=>[2,3,2]
[3,5,2,4,6,7,1]=>010001=>[2,4,1]
[3,5,2,4,7,1,6]=>010010=>[2,3,2]
[3,5,2,4,7,6,1]=>010011=>[2,3,1,1]
[3,5,2,6,1,4,7]=>010100=>[2,2,3]
[3,5,2,6,1,7,4]=>010101=>[2,2,2,1]
[3,5,2,6,4,1,7]=>010110=>[2,2,1,2]
[3,5,2,6,4,7,1]=>010101=>[2,2,2,1]
[3,5,2,6,7,1,4]=>010010=>[2,3,2]
[3,5,2,6,7,4,1]=>010011=>[2,3,1,1]
[3,5,2,7,1,4,6]=>010100=>[2,2,3]
[3,5,2,7,1,6,4]=>010101=>[2,2,2,1]
[3,5,2,7,4,1,6]=>010110=>[2,2,1,2]
[3,5,2,7,4,6,1]=>010101=>[2,2,2,1]
[3,5,2,7,6,1,4]=>010110=>[2,2,1,2]
[3,5,2,7,6,4,1]=>010111=>[2,2,1,1,1]
[3,5,4,1,2,6,7]=>011000=>[2,1,4]
[3,5,4,1,2,7,6]=>011001=>[2,1,3,1]
[3,5,4,1,6,2,7]=>011010=>[2,1,2,2]
[3,5,4,1,6,7,2]=>011001=>[2,1,3,1]
[3,5,4,1,7,2,6]=>011010=>[2,1,2,2]
[3,5,4,1,7,6,2]=>011011=>[2,1,2,1,1]
[3,5,4,2,1,6,7]=>011100=>[2,1,1,3]
[3,5,4,2,1,7,6]=>011101=>[2,1,1,2,1]
[3,5,4,2,6,1,7]=>011010=>[2,1,2,2]
[3,5,4,2,6,7,1]=>011001=>[2,1,3,1]
[3,5,4,2,7,1,6]=>011010=>[2,1,2,2]
[3,5,4,2,7,6,1]=>011011=>[2,1,2,1,1]
[3,5,4,6,1,2,7]=>010100=>[2,2,3]
[3,5,4,6,1,7,2]=>010101=>[2,2,2,1]
[3,5,4,6,2,1,7]=>010110=>[2,2,1,2]
[3,5,4,6,2,7,1]=>010101=>[2,2,2,1]
[3,5,4,6,7,1,2]=>010010=>[2,3,2]
[3,5,4,6,7,2,1]=>010011=>[2,3,1,1]
[3,5,4,7,1,2,6]=>010100=>[2,2,3]
[3,5,4,7,1,6,2]=>010101=>[2,2,2,1]
[3,5,4,7,2,1,6]=>010110=>[2,2,1,2]
[3,5,4,7,2,6,1]=>010101=>[2,2,2,1]
[3,5,4,7,6,1,2]=>010110=>[2,2,1,2]
[3,5,4,7,6,2,1]=>010111=>[2,2,1,1,1]
[3,5,6,1,2,4,7]=>001000=>[3,4]
[3,5,6,1,2,7,4]=>001001=>[3,3,1]
[3,5,6,1,4,2,7]=>001010=>[3,2,2]
[3,5,6,1,4,7,2]=>001001=>[3,3,1]
[3,5,6,1,7,2,4]=>001010=>[3,2,2]
[3,5,6,1,7,4,2]=>001011=>[3,2,1,1]
[3,5,6,2,1,4,7]=>001100=>[3,1,3]
[3,5,6,2,1,7,4]=>001101=>[3,1,2,1]
[3,5,6,2,4,1,7]=>001010=>[3,2,2]
[3,5,6,2,4,7,1]=>001001=>[3,3,1]
[3,5,6,2,7,1,4]=>001010=>[3,2,2]
[3,5,6,2,7,4,1]=>001011=>[3,2,1,1]
[3,5,6,4,1,2,7]=>001100=>[3,1,3]
[3,5,6,4,1,7,2]=>001101=>[3,1,2,1]
[3,5,6,4,2,1,7]=>001110=>[3,1,1,2]
[3,5,6,4,2,7,1]=>001101=>[3,1,2,1]
[3,5,6,4,7,1,2]=>001010=>[3,2,2]
[3,5,6,4,7,2,1]=>001011=>[3,2,1,1]
[3,5,6,7,1,2,4]=>000100=>[4,3]
[3,5,6,7,1,4,2]=>000101=>[4,2,1]
[3,5,6,7,2,1,4]=>000110=>[4,1,2]
[3,5,6,7,2,4,1]=>000101=>[4,2,1]
[3,5,6,7,4,1,2]=>000110=>[4,1,2]
[3,5,6,7,4,2,1]=>000111=>[4,1,1,1]
[3,5,7,1,2,4,6]=>001000=>[3,4]
[3,5,7,1,2,6,4]=>001001=>[3,3,1]
[3,5,7,1,4,2,6]=>001010=>[3,2,2]
[3,5,7,1,4,6,2]=>001001=>[3,3,1]
[3,5,7,1,6,2,4]=>001010=>[3,2,2]
[3,5,7,1,6,4,2]=>001011=>[3,2,1,1]
[3,5,7,2,1,4,6]=>001100=>[3,1,3]
[3,5,7,2,1,6,4]=>001101=>[3,1,2,1]
[3,5,7,2,4,1,6]=>001010=>[3,2,2]
[3,5,7,2,4,6,1]=>001001=>[3,3,1]
[3,5,7,2,6,1,4]=>001010=>[3,2,2]
[3,5,7,2,6,4,1]=>001011=>[3,2,1,1]
[3,5,7,4,1,2,6]=>001100=>[3,1,3]
[3,5,7,4,1,6,2]=>001101=>[3,1,2,1]
[3,5,7,4,2,1,6]=>001110=>[3,1,1,2]
[3,5,7,4,2,6,1]=>001101=>[3,1,2,1]
[3,5,7,4,6,1,2]=>001010=>[3,2,2]
[3,5,7,4,6,2,1]=>001011=>[3,2,1,1]
[3,5,7,6,1,2,4]=>001100=>[3,1,3]
[3,5,7,6,1,4,2]=>001101=>[3,1,2,1]
[3,5,7,6,2,1,4]=>001110=>[3,1,1,2]
[3,5,7,6,2,4,1]=>001101=>[3,1,2,1]
[3,5,7,6,4,1,2]=>001110=>[3,1,1,2]
[3,5,7,6,4,2,1]=>001111=>[3,1,1,1,1]
[3,6,1,2,4,5,7]=>010000=>[2,5]
[3,6,1,2,4,7,5]=>010001=>[2,4,1]
[3,6,1,2,5,4,7]=>010010=>[2,3,2]
[3,6,1,2,5,7,4]=>010001=>[2,4,1]
[3,6,1,2,7,4,5]=>010010=>[2,3,2]
[3,6,1,2,7,5,4]=>010011=>[2,3,1,1]
[3,6,1,4,2,5,7]=>010100=>[2,2,3]
[3,6,1,4,2,7,5]=>010101=>[2,2,2,1]
[3,6,1,4,5,2,7]=>010010=>[2,3,2]
[3,6,1,4,5,7,2]=>010001=>[2,4,1]
[3,6,1,4,7,2,5]=>010010=>[2,3,2]
[3,6,1,4,7,5,2]=>010011=>[2,3,1,1]
[3,6,1,5,2,4,7]=>010100=>[2,2,3]
[3,6,1,5,2,7,4]=>010101=>[2,2,2,1]
[3,6,1,5,4,2,7]=>010110=>[2,2,1,2]
[3,6,1,5,4,7,2]=>010101=>[2,2,2,1]
[3,6,1,5,7,2,4]=>010010=>[2,3,2]
[3,6,1,5,7,4,2]=>010011=>[2,3,1,1]
[3,6,1,7,2,4,5]=>010100=>[2,2,3]
[3,6,1,7,2,5,4]=>010101=>[2,2,2,1]
[3,6,1,7,4,2,5]=>010110=>[2,2,1,2]
[3,6,1,7,4,5,2]=>010101=>[2,2,2,1]
[3,6,1,7,5,2,4]=>010110=>[2,2,1,2]
[3,6,1,7,5,4,2]=>010111=>[2,2,1,1,1]
[3,6,2,1,4,5,7]=>011000=>[2,1,4]
[3,6,2,1,4,7,5]=>011001=>[2,1,3,1]
[3,6,2,1,5,4,7]=>011010=>[2,1,2,2]
[3,6,2,1,5,7,4]=>011001=>[2,1,3,1]
[3,6,2,1,7,4,5]=>011010=>[2,1,2,2]
[3,6,2,1,7,5,4]=>011011=>[2,1,2,1,1]
[3,6,2,4,1,5,7]=>010100=>[2,2,3]
[3,6,2,4,1,7,5]=>010101=>[2,2,2,1]
[3,6,2,4,5,1,7]=>010010=>[2,3,2]
[3,6,2,4,5,7,1]=>010001=>[2,4,1]
[3,6,2,4,7,1,5]=>010010=>[2,3,2]
[3,6,2,4,7,5,1]=>010011=>[2,3,1,1]
[3,6,2,5,1,4,7]=>010100=>[2,2,3]
[3,6,2,5,1,7,4]=>010101=>[2,2,2,1]
[3,6,2,5,4,1,7]=>010110=>[2,2,1,2]
[3,6,2,5,4,7,1]=>010101=>[2,2,2,1]
[3,6,2,5,7,1,4]=>010010=>[2,3,2]
[3,6,2,5,7,4,1]=>010011=>[2,3,1,1]
[3,6,2,7,1,4,5]=>010100=>[2,2,3]
[3,6,2,7,1,5,4]=>010101=>[2,2,2,1]
[3,6,2,7,4,1,5]=>010110=>[2,2,1,2]
[3,6,2,7,4,5,1]=>010101=>[2,2,2,1]
[3,6,2,7,5,1,4]=>010110=>[2,2,1,2]
[3,6,2,7,5,4,1]=>010111=>[2,2,1,1,1]
[3,6,4,1,2,5,7]=>011000=>[2,1,4]
[3,6,4,1,2,7,5]=>011001=>[2,1,3,1]
[3,6,4,1,5,2,7]=>011010=>[2,1,2,2]
[3,6,4,1,5,7,2]=>011001=>[2,1,3,1]
[3,6,4,1,7,2,5]=>011010=>[2,1,2,2]
[3,6,4,1,7,5,2]=>011011=>[2,1,2,1,1]
[3,6,4,2,1,5,7]=>011100=>[2,1,1,3]
[3,6,4,2,1,7,5]=>011101=>[2,1,1,2,1]
[3,6,4,2,5,1,7]=>011010=>[2,1,2,2]
[3,6,4,2,5,7,1]=>011001=>[2,1,3,1]
[3,6,4,2,7,1,5]=>011010=>[2,1,2,2]
[3,6,4,2,7,5,1]=>011011=>[2,1,2,1,1]
[3,6,4,5,1,2,7]=>010100=>[2,2,3]
[3,6,4,5,1,7,2]=>010101=>[2,2,2,1]
[3,6,4,5,2,1,7]=>010110=>[2,2,1,2]
[3,6,4,5,2,7,1]=>010101=>[2,2,2,1]
[3,6,4,5,7,1,2]=>010010=>[2,3,2]
[3,6,4,5,7,2,1]=>010011=>[2,3,1,1]
[3,6,4,7,1,2,5]=>010100=>[2,2,3]
[3,6,4,7,1,5,2]=>010101=>[2,2,2,1]
[3,6,4,7,2,1,5]=>010110=>[2,2,1,2]
[3,6,4,7,2,5,1]=>010101=>[2,2,2,1]
[3,6,4,7,5,1,2]=>010110=>[2,2,1,2]
[3,6,4,7,5,2,1]=>010111=>[2,2,1,1,1]
[3,6,5,1,2,4,7]=>011000=>[2,1,4]
[3,6,5,1,2,7,4]=>011001=>[2,1,3,1]
[3,6,5,1,4,2,7]=>011010=>[2,1,2,2]
[3,6,5,1,4,7,2]=>011001=>[2,1,3,1]
[3,6,5,1,7,2,4]=>011010=>[2,1,2,2]
[3,6,5,1,7,4,2]=>011011=>[2,1,2,1,1]
[3,6,5,2,1,4,7]=>011100=>[2,1,1,3]
[3,6,5,2,1,7,4]=>011101=>[2,1,1,2,1]
[3,6,5,2,4,1,7]=>011010=>[2,1,2,2]
[3,6,5,2,4,7,1]=>011001=>[2,1,3,1]
[3,6,5,2,7,1,4]=>011010=>[2,1,2,2]
[3,6,5,2,7,4,1]=>011011=>[2,1,2,1,1]
[3,6,5,4,1,2,7]=>011100=>[2,1,1,3]
[3,6,5,4,1,7,2]=>011101=>[2,1,1,2,1]
[3,6,5,4,2,1,7]=>011110=>[2,1,1,1,2]
[3,6,5,4,2,7,1]=>011101=>[2,1,1,2,1]
[3,6,5,4,7,1,2]=>011010=>[2,1,2,2]
[3,6,5,4,7,2,1]=>011011=>[2,1,2,1,1]
[3,6,5,7,1,2,4]=>010100=>[2,2,3]
[3,6,5,7,1,4,2]=>010101=>[2,2,2,1]
[3,6,5,7,2,1,4]=>010110=>[2,2,1,2]
[3,6,5,7,2,4,1]=>010101=>[2,2,2,1]
[3,6,5,7,4,1,2]=>010110=>[2,2,1,2]
[3,6,5,7,4,2,1]=>010111=>[2,2,1,1,1]
[3,6,7,1,2,4,5]=>001000=>[3,4]
[3,6,7,1,2,5,4]=>001001=>[3,3,1]
[3,6,7,1,4,2,5]=>001010=>[3,2,2]
[3,6,7,1,4,5,2]=>001001=>[3,3,1]
[3,6,7,1,5,2,4]=>001010=>[3,2,2]
[3,6,7,1,5,4,2]=>001011=>[3,2,1,1]
[3,6,7,2,1,4,5]=>001100=>[3,1,3]
[3,6,7,2,1,5,4]=>001101=>[3,1,2,1]
[3,6,7,2,4,1,5]=>001010=>[3,2,2]
[3,6,7,2,4,5,1]=>001001=>[3,3,1]
[3,6,7,2,5,1,4]=>001010=>[3,2,2]
[3,6,7,2,5,4,1]=>001011=>[3,2,1,1]
[3,6,7,4,1,2,5]=>001100=>[3,1,3]
[3,6,7,4,1,5,2]=>001101=>[3,1,2,1]
[3,6,7,4,2,1,5]=>001110=>[3,1,1,2]
[3,6,7,4,2,5,1]=>001101=>[3,1,2,1]
[3,6,7,4,5,1,2]=>001010=>[3,2,2]
[3,6,7,4,5,2,1]=>001011=>[3,2,1,1]
[3,6,7,5,1,2,4]=>001100=>[3,1,3]
[3,6,7,5,1,4,2]=>001101=>[3,1,2,1]
[3,6,7,5,2,1,4]=>001110=>[3,1,1,2]
[3,6,7,5,2,4,1]=>001101=>[3,1,2,1]
[3,6,7,5,4,1,2]=>001110=>[3,1,1,2]
[3,6,7,5,4,2,1]=>001111=>[3,1,1,1,1]
[3,7,1,2,4,5,6]=>010000=>[2,5]
[3,7,1,2,4,6,5]=>010001=>[2,4,1]
[3,7,1,2,5,4,6]=>010010=>[2,3,2]
[3,7,1,2,5,6,4]=>010001=>[2,4,1]
[3,7,1,2,6,4,5]=>010010=>[2,3,2]
[3,7,1,2,6,5,4]=>010011=>[2,3,1,1]
[3,7,1,4,2,5,6]=>010100=>[2,2,3]
[3,7,1,4,2,6,5]=>010101=>[2,2,2,1]
[3,7,1,4,5,2,6]=>010010=>[2,3,2]
[3,7,1,4,5,6,2]=>010001=>[2,4,1]
[3,7,1,4,6,2,5]=>010010=>[2,3,2]
[3,7,1,4,6,5,2]=>010011=>[2,3,1,1]
[3,7,1,5,2,4,6]=>010100=>[2,2,3]
[3,7,1,5,2,6,4]=>010101=>[2,2,2,1]
[3,7,1,5,4,2,6]=>010110=>[2,2,1,2]
[3,7,1,5,4,6,2]=>010101=>[2,2,2,1]
[3,7,1,5,6,2,4]=>010010=>[2,3,2]
[3,7,1,5,6,4,2]=>010011=>[2,3,1,1]
[3,7,1,6,2,4,5]=>010100=>[2,2,3]
[3,7,1,6,2,5,4]=>010101=>[2,2,2,1]
[3,7,1,6,4,2,5]=>010110=>[2,2,1,2]
[3,7,1,6,4,5,2]=>010101=>[2,2,2,1]
[3,7,1,6,5,2,4]=>010110=>[2,2,1,2]
[3,7,1,6,5,4,2]=>010111=>[2,2,1,1,1]
[3,7,2,1,4,5,6]=>011000=>[2,1,4]
[3,7,2,1,4,6,5]=>011001=>[2,1,3,1]
[3,7,2,1,5,4,6]=>011010=>[2,1,2,2]
[3,7,2,1,5,6,4]=>011001=>[2,1,3,1]
[3,7,2,1,6,4,5]=>011010=>[2,1,2,2]
[3,7,2,1,6,5,4]=>011011=>[2,1,2,1,1]
[3,7,2,4,1,5,6]=>010100=>[2,2,3]
[3,7,2,4,1,6,5]=>010101=>[2,2,2,1]
[3,7,2,4,5,1,6]=>010010=>[2,3,2]
[3,7,2,4,5,6,1]=>010001=>[2,4,1]
[3,7,2,4,6,1,5]=>010010=>[2,3,2]
[3,7,2,4,6,5,1]=>010011=>[2,3,1,1]
[3,7,2,5,1,4,6]=>010100=>[2,2,3]
[3,7,2,5,1,6,4]=>010101=>[2,2,2,1]
[3,7,2,5,4,1,6]=>010110=>[2,2,1,2]
[3,7,2,5,4,6,1]=>010101=>[2,2,2,1]
[3,7,2,5,6,1,4]=>010010=>[2,3,2]
[3,7,2,5,6,4,1]=>010011=>[2,3,1,1]
[3,7,2,6,1,4,5]=>010100=>[2,2,3]
[3,7,2,6,1,5,4]=>010101=>[2,2,2,1]
[3,7,2,6,4,1,5]=>010110=>[2,2,1,2]
[3,7,2,6,4,5,1]=>010101=>[2,2,2,1]
[3,7,2,6,5,1,4]=>010110=>[2,2,1,2]
[3,7,2,6,5,4,1]=>010111=>[2,2,1,1,1]
[3,7,4,1,2,5,6]=>011000=>[2,1,4]
[3,7,4,1,2,6,5]=>011001=>[2,1,3,1]
[3,7,4,1,5,2,6]=>011010=>[2,1,2,2]
[3,7,4,1,5,6,2]=>011001=>[2,1,3,1]
[3,7,4,1,6,2,5]=>011010=>[2,1,2,2]
[3,7,4,1,6,5,2]=>011011=>[2,1,2,1,1]
[3,7,4,2,1,5,6]=>011100=>[2,1,1,3]
[3,7,4,2,1,6,5]=>011101=>[2,1,1,2,1]
[3,7,4,2,5,1,6]=>011010=>[2,1,2,2]
[3,7,4,2,5,6,1]=>011001=>[2,1,3,1]
[3,7,4,2,6,1,5]=>011010=>[2,1,2,2]
[3,7,4,2,6,5,1]=>011011=>[2,1,2,1,1]
[3,7,4,5,1,2,6]=>010100=>[2,2,3]
[3,7,4,5,1,6,2]=>010101=>[2,2,2,1]
[3,7,4,5,2,1,6]=>010110=>[2,2,1,2]
[3,7,4,5,2,6,1]=>010101=>[2,2,2,1]
[3,7,4,5,6,1,2]=>010010=>[2,3,2]
[3,7,4,5,6,2,1]=>010011=>[2,3,1,1]
[3,7,4,6,1,2,5]=>010100=>[2,2,3]
[3,7,4,6,1,5,2]=>010101=>[2,2,2,1]
[3,7,4,6,2,1,5]=>010110=>[2,2,1,2]
[3,7,4,6,2,5,1]=>010101=>[2,2,2,1]
[3,7,4,6,5,1,2]=>010110=>[2,2,1,2]
[3,7,4,6,5,2,1]=>010111=>[2,2,1,1,1]
[3,7,5,1,2,4,6]=>011000=>[2,1,4]
[3,7,5,1,2,6,4]=>011001=>[2,1,3,1]
[3,7,5,1,4,2,6]=>011010=>[2,1,2,2]
[3,7,5,1,4,6,2]=>011001=>[2,1,3,1]
[3,7,5,1,6,2,4]=>011010=>[2,1,2,2]
[3,7,5,1,6,4,2]=>011011=>[2,1,2,1,1]
[3,7,5,2,1,4,6]=>011100=>[2,1,1,3]
[3,7,5,2,1,6,4]=>011101=>[2,1,1,2,1]
[3,7,5,2,4,1,6]=>011010=>[2,1,2,2]
[3,7,5,2,4,6,1]=>011001=>[2,1,3,1]
[3,7,5,2,6,1,4]=>011010=>[2,1,2,2]
[3,7,5,2,6,4,1]=>011011=>[2,1,2,1,1]
[3,7,5,4,1,2,6]=>011100=>[2,1,1,3]
[3,7,5,4,1,6,2]=>011101=>[2,1,1,2,1]
[3,7,5,4,2,1,6]=>011110=>[2,1,1,1,2]
[3,7,5,4,2,6,1]=>011101=>[2,1,1,2,1]
[3,7,5,4,6,1,2]=>011010=>[2,1,2,2]
[3,7,5,4,6,2,1]=>011011=>[2,1,2,1,1]
[3,7,5,6,1,2,4]=>010100=>[2,2,3]
[3,7,5,6,1,4,2]=>010101=>[2,2,2,1]
[3,7,5,6,2,1,4]=>010110=>[2,2,1,2]
[3,7,5,6,2,4,1]=>010101=>[2,2,2,1]
[3,7,5,6,4,1,2]=>010110=>[2,2,1,2]
[3,7,5,6,4,2,1]=>010111=>[2,2,1,1,1]
[3,7,6,1,2,4,5]=>011000=>[2,1,4]
[3,7,6,1,2,5,4]=>011001=>[2,1,3,1]
[3,7,6,1,4,2,5]=>011010=>[2,1,2,2]
[3,7,6,1,4,5,2]=>011001=>[2,1,3,1]
[3,7,6,1,5,2,4]=>011010=>[2,1,2,2]
[3,7,6,1,5,4,2]=>011011=>[2,1,2,1,1]
[3,7,6,2,1,4,5]=>011100=>[2,1,1,3]
[3,7,6,2,1,5,4]=>011101=>[2,1,1,2,1]
[3,7,6,2,4,1,5]=>011010=>[2,1,2,2]
[3,7,6,2,4,5,1]=>011001=>[2,1,3,1]
[3,7,6,2,5,1,4]=>011010=>[2,1,2,2]
[3,7,6,2,5,4,1]=>011011=>[2,1,2,1,1]
[3,7,6,4,1,2,5]=>011100=>[2,1,1,3]
[3,7,6,4,1,5,2]=>011101=>[2,1,1,2,1]
[3,7,6,4,2,1,5]=>011110=>[2,1,1,1,2]
[3,7,6,4,2,5,1]=>011101=>[2,1,1,2,1]
[3,7,6,4,5,1,2]=>011010=>[2,1,2,2]
[3,7,6,4,5,2,1]=>011011=>[2,1,2,1,1]
[3,7,6,5,1,2,4]=>011100=>[2,1,1,3]
[3,7,6,5,1,4,2]=>011101=>[2,1,1,2,1]
[3,7,6,5,2,1,4]=>011110=>[2,1,1,1,2]
[3,7,6,5,2,4,1]=>011101=>[2,1,1,2,1]
[3,7,6,5,4,1,2]=>011110=>[2,1,1,1,2]
[3,7,6,5,4,2,1]=>011111=>[2,1,1,1,1,1]
[4,1,2,3,5,6,7]=>100000=>[1,6]
[4,1,2,3,5,7,6]=>100001=>[1,5,1]
[4,1,2,3,6,5,7]=>100010=>[1,4,2]
[4,1,2,3,6,7,5]=>100001=>[1,5,1]
[4,1,2,3,7,5,6]=>100010=>[1,4,2]
[4,1,2,3,7,6,5]=>100011=>[1,4,1,1]
[4,1,2,5,3,6,7]=>100100=>[1,3,3]
[4,1,2,5,3,7,6]=>100101=>[1,3,2,1]
[4,1,2,5,6,3,7]=>100010=>[1,4,2]
[4,1,2,5,6,7,3]=>100001=>[1,5,1]
[4,1,2,5,7,3,6]=>100010=>[1,4,2]
[4,1,2,5,7,6,3]=>100011=>[1,4,1,1]
[4,1,2,6,3,5,7]=>100100=>[1,3,3]
[4,1,2,6,3,7,5]=>100101=>[1,3,2,1]
[4,1,2,6,5,3,7]=>100110=>[1,3,1,2]
[4,1,2,6,5,7,3]=>100101=>[1,3,2,1]
[4,1,2,6,7,3,5]=>100010=>[1,4,2]
[4,1,2,6,7,5,3]=>100011=>[1,4,1,1]
[4,1,2,7,3,5,6]=>100100=>[1,3,3]
[4,1,2,7,3,6,5]=>100101=>[1,3,2,1]
[4,1,2,7,5,3,6]=>100110=>[1,3,1,2]
[4,1,2,7,5,6,3]=>100101=>[1,3,2,1]
[4,1,2,7,6,3,5]=>100110=>[1,3,1,2]
[4,1,2,7,6,5,3]=>100111=>[1,3,1,1,1]
[4,1,3,2,5,6,7]=>101000=>[1,2,4]
[4,1,3,2,5,7,6]=>101001=>[1,2,3,1]
[4,1,3,2,6,5,7]=>101010=>[1,2,2,2]
[4,1,3,2,6,7,5]=>101001=>[1,2,3,1]
[4,1,3,2,7,5,6]=>101010=>[1,2,2,2]
[4,1,3,2,7,6,5]=>101011=>[1,2,2,1,1]
[4,1,3,5,2,6,7]=>100100=>[1,3,3]
[4,1,3,5,2,7,6]=>100101=>[1,3,2,1]
[4,1,3,5,6,2,7]=>100010=>[1,4,2]
[4,1,3,5,6,7,2]=>100001=>[1,5,1]
[4,1,3,5,7,2,6]=>100010=>[1,4,2]
[4,1,3,5,7,6,2]=>100011=>[1,4,1,1]
[4,1,3,6,2,5,7]=>100100=>[1,3,3]
[4,1,3,6,2,7,5]=>100101=>[1,3,2,1]
[4,1,3,6,5,2,7]=>100110=>[1,3,1,2]
[4,1,3,6,5,7,2]=>100101=>[1,3,2,1]
[4,1,3,6,7,2,5]=>100010=>[1,4,2]
[4,1,3,6,7,5,2]=>100011=>[1,4,1,1]
[4,1,3,7,2,5,6]=>100100=>[1,3,3]
[4,1,3,7,2,6,5]=>100101=>[1,3,2,1]
[4,1,3,7,5,2,6]=>100110=>[1,3,1,2]
[4,1,3,7,5,6,2]=>100101=>[1,3,2,1]
[4,1,3,7,6,2,5]=>100110=>[1,3,1,2]
[4,1,3,7,6,5,2]=>100111=>[1,3,1,1,1]
[4,1,5,2,3,6,7]=>101000=>[1,2,4]
[4,1,5,2,3,7,6]=>101001=>[1,2,3,1]
[4,1,5,2,6,3,7]=>101010=>[1,2,2,2]
[4,1,5,2,6,7,3]=>101001=>[1,2,3,1]
[4,1,5,2,7,3,6]=>101010=>[1,2,2,2]
[4,1,5,2,7,6,3]=>101011=>[1,2,2,1,1]
[4,1,5,3,2,6,7]=>101100=>[1,2,1,3]
[4,1,5,3,2,7,6]=>101101=>[1,2,1,2,1]
[4,1,5,3,6,2,7]=>101010=>[1,2,2,2]
[4,1,5,3,6,7,2]=>101001=>[1,2,3,1]
[4,1,5,3,7,2,6]=>101010=>[1,2,2,2]
[4,1,5,3,7,6,2]=>101011=>[1,2,2,1,1]
[4,1,5,6,2,3,7]=>100100=>[1,3,3]
[4,1,5,6,2,7,3]=>100101=>[1,3,2,1]
[4,1,5,6,3,2,7]=>100110=>[1,3,1,2]
[4,1,5,6,3,7,2]=>100101=>[1,3,2,1]
[4,1,5,6,7,2,3]=>100010=>[1,4,2]
[4,1,5,6,7,3,2]=>100011=>[1,4,1,1]
[4,1,5,7,2,3,6]=>100100=>[1,3,3]
[4,1,5,7,2,6,3]=>100101=>[1,3,2,1]
[4,1,5,7,3,2,6]=>100110=>[1,3,1,2]
[4,1,5,7,3,6,2]=>100101=>[1,3,2,1]
[4,1,5,7,6,2,3]=>100110=>[1,3,1,2]
[4,1,5,7,6,3,2]=>100111=>[1,3,1,1,1]
[4,1,6,2,3,5,7]=>101000=>[1,2,4]
[4,1,6,2,3,7,5]=>101001=>[1,2,3,1]
[4,1,6,2,5,3,7]=>101010=>[1,2,2,2]
[4,1,6,2,5,7,3]=>101001=>[1,2,3,1]
[4,1,6,2,7,3,5]=>101010=>[1,2,2,2]
[4,1,6,2,7,5,3]=>101011=>[1,2,2,1,1]
[4,1,6,3,2,5,7]=>101100=>[1,2,1,3]
[4,1,6,3,2,7,5]=>101101=>[1,2,1,2,1]
[4,1,6,3,5,2,7]=>101010=>[1,2,2,2]
[4,1,6,3,5,7,2]=>101001=>[1,2,3,1]
[4,1,6,3,7,2,5]=>101010=>[1,2,2,2]
[4,1,6,3,7,5,2]=>101011=>[1,2,2,1,1]
[4,1,6,5,2,3,7]=>101100=>[1,2,1,3]
[4,1,6,5,2,7,3]=>101101=>[1,2,1,2,1]
[4,1,6,5,3,2,7]=>101110=>[1,2,1,1,2]
[4,1,6,5,3,7,2]=>101101=>[1,2,1,2,1]
[4,1,6,5,7,2,3]=>101010=>[1,2,2,2]
[4,1,6,5,7,3,2]=>101011=>[1,2,2,1,1]
[4,1,6,7,2,3,5]=>100100=>[1,3,3]
[4,1,6,7,2,5,3]=>100101=>[1,3,2,1]
[4,1,6,7,3,2,5]=>100110=>[1,3,1,2]
[4,1,6,7,3,5,2]=>100101=>[1,3,2,1]
[4,1,6,7,5,2,3]=>100110=>[1,3,1,2]
[4,1,6,7,5,3,2]=>100111=>[1,3,1,1,1]
[4,1,7,2,3,5,6]=>101000=>[1,2,4]
[4,1,7,2,3,6,5]=>101001=>[1,2,3,1]
[4,1,7,2,5,3,6]=>101010=>[1,2,2,2]
[4,1,7,2,5,6,3]=>101001=>[1,2,3,1]
[4,1,7,2,6,3,5]=>101010=>[1,2,2,2]
[4,1,7,2,6,5,3]=>101011=>[1,2,2,1,1]
[4,1,7,3,2,5,6]=>101100=>[1,2,1,3]
[4,1,7,3,2,6,5]=>101101=>[1,2,1,2,1]
[4,1,7,3,5,2,6]=>101010=>[1,2,2,2]
[4,1,7,3,5,6,2]=>101001=>[1,2,3,1]
[4,1,7,3,6,2,5]=>101010=>[1,2,2,2]
[4,1,7,3,6,5,2]=>101011=>[1,2,2,1,1]
[4,1,7,5,2,3,6]=>101100=>[1,2,1,3]
[4,1,7,5,2,6,3]=>101101=>[1,2,1,2,1]
[4,1,7,5,3,2,6]=>101110=>[1,2,1,1,2]
[4,1,7,5,3,6,2]=>101101=>[1,2,1,2,1]
[4,1,7,5,6,2,3]=>101010=>[1,2,2,2]
[4,1,7,5,6,3,2]=>101011=>[1,2,2,1,1]
[4,1,7,6,2,3,5]=>101100=>[1,2,1,3]
[4,1,7,6,2,5,3]=>101101=>[1,2,1,2,1]
[4,1,7,6,3,2,5]=>101110=>[1,2,1,1,2]
[4,1,7,6,3,5,2]=>101101=>[1,2,1,2,1]
[4,1,7,6,5,2,3]=>101110=>[1,2,1,1,2]
[4,1,7,6,5,3,2]=>101111=>[1,2,1,1,1,1]
[4,2,1,3,5,6,7]=>110000=>[1,1,5]
[4,2,1,3,5,7,6]=>110001=>[1,1,4,1]
[4,2,1,3,6,5,7]=>110010=>[1,1,3,2]
[4,2,1,3,6,7,5]=>110001=>[1,1,4,1]
[4,2,1,3,7,5,6]=>110010=>[1,1,3,2]
[4,2,1,3,7,6,5]=>110011=>[1,1,3,1,1]
[4,2,1,5,3,6,7]=>110100=>[1,1,2,3]
[4,2,1,5,3,7,6]=>110101=>[1,1,2,2,1]
[4,2,1,5,6,3,7]=>110010=>[1,1,3,2]
[4,2,1,5,6,7,3]=>110001=>[1,1,4,1]
[4,2,1,5,7,3,6]=>110010=>[1,1,3,2]
[4,2,1,5,7,6,3]=>110011=>[1,1,3,1,1]
[4,2,1,6,3,5,7]=>110100=>[1,1,2,3]
[4,2,1,6,3,7,5]=>110101=>[1,1,2,2,1]
[4,2,1,6,5,3,7]=>110110=>[1,1,2,1,2]
[4,2,1,6,5,7,3]=>110101=>[1,1,2,2,1]
[4,2,1,6,7,3,5]=>110010=>[1,1,3,2]
[4,2,1,6,7,5,3]=>110011=>[1,1,3,1,1]
[4,2,1,7,3,5,6]=>110100=>[1,1,2,3]
[4,2,1,7,3,6,5]=>110101=>[1,1,2,2,1]
[4,2,1,7,5,3,6]=>110110=>[1,1,2,1,2]
[4,2,1,7,5,6,3]=>110101=>[1,1,2,2,1]
[4,2,1,7,6,3,5]=>110110=>[1,1,2,1,2]
[4,2,1,7,6,5,3]=>110111=>[1,1,2,1,1,1]
[4,2,3,1,5,6,7]=>101000=>[1,2,4]
[4,2,3,1,5,7,6]=>101001=>[1,2,3,1]
[4,2,3,1,6,5,7]=>101010=>[1,2,2,2]
[4,2,3,1,6,7,5]=>101001=>[1,2,3,1]
[4,2,3,1,7,5,6]=>101010=>[1,2,2,2]
[4,2,3,1,7,6,5]=>101011=>[1,2,2,1,1]
[4,2,3,5,1,6,7]=>100100=>[1,3,3]
[4,2,3,5,1,7,6]=>100101=>[1,3,2,1]
[4,2,3,5,6,1,7]=>100010=>[1,4,2]
[4,2,3,5,6,7,1]=>100001=>[1,5,1]
[4,2,3,5,7,1,6]=>100010=>[1,4,2]
[4,2,3,5,7,6,1]=>100011=>[1,4,1,1]
[4,2,3,6,1,5,7]=>100100=>[1,3,3]
[4,2,3,6,1,7,5]=>100101=>[1,3,2,1]
[4,2,3,6,5,1,7]=>100110=>[1,3,1,2]
[4,2,3,6,5,7,1]=>100101=>[1,3,2,1]
[4,2,3,6,7,1,5]=>100010=>[1,4,2]
[4,2,3,6,7,5,1]=>100011=>[1,4,1,1]
[4,2,3,7,1,5,6]=>100100=>[1,3,3]
[4,2,3,7,1,6,5]=>100101=>[1,3,2,1]
[4,2,3,7,5,1,6]=>100110=>[1,3,1,2]
[4,2,3,7,5,6,1]=>100101=>[1,3,2,1]
[4,2,3,7,6,1,5]=>100110=>[1,3,1,2]
[4,2,3,7,6,5,1]=>100111=>[1,3,1,1,1]
[4,2,5,1,3,6,7]=>101000=>[1,2,4]
[4,2,5,1,3,7,6]=>101001=>[1,2,3,1]
[4,2,5,1,6,3,7]=>101010=>[1,2,2,2]
[4,2,5,1,6,7,3]=>101001=>[1,2,3,1]
[4,2,5,1,7,3,6]=>101010=>[1,2,2,2]
[4,2,5,1,7,6,3]=>101011=>[1,2,2,1,1]
[4,2,5,3,1,6,7]=>101100=>[1,2,1,3]
[4,2,5,3,1,7,6]=>101101=>[1,2,1,2,1]
[4,2,5,3,6,1,7]=>101010=>[1,2,2,2]
[4,2,5,3,6,7,1]=>101001=>[1,2,3,1]
[4,2,5,3,7,1,6]=>101010=>[1,2,2,2]
[4,2,5,3,7,6,1]=>101011=>[1,2,2,1,1]
[4,2,5,6,1,3,7]=>100100=>[1,3,3]
[4,2,5,6,1,7,3]=>100101=>[1,3,2,1]
[4,2,5,6,3,1,7]=>100110=>[1,3,1,2]
[4,2,5,6,3,7,1]=>100101=>[1,3,2,1]
[4,2,5,6,7,1,3]=>100010=>[1,4,2]
[4,2,5,6,7,3,1]=>100011=>[1,4,1,1]
[4,2,5,7,1,3,6]=>100100=>[1,3,3]
[4,2,5,7,1,6,3]=>100101=>[1,3,2,1]
[4,2,5,7,3,1,6]=>100110=>[1,3,1,2]
[4,2,5,7,3,6,1]=>100101=>[1,3,2,1]
[4,2,5,7,6,1,3]=>100110=>[1,3,1,2]
[4,2,5,7,6,3,1]=>100111=>[1,3,1,1,1]
[4,2,6,1,3,5,7]=>101000=>[1,2,4]
[4,2,6,1,3,7,5]=>101001=>[1,2,3,1]
[4,2,6,1,5,3,7]=>101010=>[1,2,2,2]
[4,2,6,1,5,7,3]=>101001=>[1,2,3,1]
[4,2,6,1,7,3,5]=>101010=>[1,2,2,2]
[4,2,6,1,7,5,3]=>101011=>[1,2,2,1,1]
[4,2,6,3,1,5,7]=>101100=>[1,2,1,3]
[4,2,6,3,1,7,5]=>101101=>[1,2,1,2,1]
[4,2,6,3,5,1,7]=>101010=>[1,2,2,2]
[4,2,6,3,5,7,1]=>101001=>[1,2,3,1]
[4,2,6,3,7,1,5]=>101010=>[1,2,2,2]
[4,2,6,3,7,5,1]=>101011=>[1,2,2,1,1]
[4,2,6,5,1,3,7]=>101100=>[1,2,1,3]
[4,2,6,5,1,7,3]=>101101=>[1,2,1,2,1]
[4,2,6,5,3,1,7]=>101110=>[1,2,1,1,2]
[4,2,6,5,3,7,1]=>101101=>[1,2,1,2,1]
[4,2,6,5,7,1,3]=>101010=>[1,2,2,2]
[4,2,6,5,7,3,1]=>101011=>[1,2,2,1,1]
[4,2,6,7,1,3,5]=>100100=>[1,3,3]
[4,2,6,7,1,5,3]=>100101=>[1,3,2,1]
[4,2,6,7,3,1,5]=>100110=>[1,3,1,2]
[4,2,6,7,3,5,1]=>100101=>[1,3,2,1]
[4,2,6,7,5,1,3]=>100110=>[1,3,1,2]
[4,2,6,7,5,3,1]=>100111=>[1,3,1,1,1]
[4,2,7,1,3,5,6]=>101000=>[1,2,4]
[4,2,7,1,3,6,5]=>101001=>[1,2,3,1]
[4,2,7,1,5,3,6]=>101010=>[1,2,2,2]
[4,2,7,1,5,6,3]=>101001=>[1,2,3,1]
[4,2,7,1,6,3,5]=>101010=>[1,2,2,2]
[4,2,7,1,6,5,3]=>101011=>[1,2,2,1,1]
[4,2,7,3,1,5,6]=>101100=>[1,2,1,3]
[4,2,7,3,1,6,5]=>101101=>[1,2,1,2,1]
[4,2,7,3,5,1,6]=>101010=>[1,2,2,2]
[4,2,7,3,5,6,1]=>101001=>[1,2,3,1]
[4,2,7,3,6,1,5]=>101010=>[1,2,2,2]
[4,2,7,3,6,5,1]=>101011=>[1,2,2,1,1]
[4,2,7,5,1,3,6]=>101100=>[1,2,1,3]
[4,2,7,5,1,6,3]=>101101=>[1,2,1,2,1]
[4,2,7,5,3,1,6]=>101110=>[1,2,1,1,2]
[4,2,7,5,3,6,1]=>101101=>[1,2,1,2,1]
[4,2,7,5,6,1,3]=>101010=>[1,2,2,2]
[4,2,7,5,6,3,1]=>101011=>[1,2,2,1,1]
[4,2,7,6,1,3,5]=>101100=>[1,2,1,3]
[4,2,7,6,1,5,3]=>101101=>[1,2,1,2,1]
[4,2,7,6,3,1,5]=>101110=>[1,2,1,1,2]
[4,2,7,6,3,5,1]=>101101=>[1,2,1,2,1]
[4,2,7,6,5,1,3]=>101110=>[1,2,1,1,2]
[4,2,7,6,5,3,1]=>101111=>[1,2,1,1,1,1]
[4,3,1,2,5,6,7]=>110000=>[1,1,5]
[4,3,1,2,5,7,6]=>110001=>[1,1,4,1]
[4,3,1,2,6,5,7]=>110010=>[1,1,3,2]
[4,3,1,2,6,7,5]=>110001=>[1,1,4,1]
[4,3,1,2,7,5,6]=>110010=>[1,1,3,2]
[4,3,1,2,7,6,5]=>110011=>[1,1,3,1,1]
[4,3,1,5,2,6,7]=>110100=>[1,1,2,3]
[4,3,1,5,2,7,6]=>110101=>[1,1,2,2,1]
[4,3,1,5,6,2,7]=>110010=>[1,1,3,2]
[4,3,1,5,6,7,2]=>110001=>[1,1,4,1]
[4,3,1,5,7,2,6]=>110010=>[1,1,3,2]
[4,3,1,5,7,6,2]=>110011=>[1,1,3,1,1]
[4,3,1,6,2,5,7]=>110100=>[1,1,2,3]
[4,3,1,6,2,7,5]=>110101=>[1,1,2,2,1]
[4,3,1,6,5,2,7]=>110110=>[1,1,2,1,2]
[4,3,1,6,5,7,2]=>110101=>[1,1,2,2,1]
[4,3,1,6,7,2,5]=>110010=>[1,1,3,2]
[4,3,1,6,7,5,2]=>110011=>[1,1,3,1,1]
[4,3,1,7,2,5,6]=>110100=>[1,1,2,3]
[4,3,1,7,2,6,5]=>110101=>[1,1,2,2,1]
[4,3,1,7,5,2,6]=>110110=>[1,1,2,1,2]
[4,3,1,7,5,6,2]=>110101=>[1,1,2,2,1]
[4,3,1,7,6,2,5]=>110110=>[1,1,2,1,2]
[4,3,1,7,6,5,2]=>110111=>[1,1,2,1,1,1]
[4,3,2,1,5,6,7]=>111000=>[1,1,1,4]
[4,3,2,1,5,7,6]=>111001=>[1,1,1,3,1]
[4,3,2,1,6,5,7]=>111010=>[1,1,1,2,2]
[4,3,2,1,6,7,5]=>111001=>[1,1,1,3,1]
[4,3,2,1,7,5,6]=>111010=>[1,1,1,2,2]
[4,3,2,1,7,6,5]=>111011=>[1,1,1,2,1,1]
[4,3,2,5,1,6,7]=>110100=>[1,1,2,3]
[4,3,2,5,1,7,6]=>110101=>[1,1,2,2,1]
[4,3,2,5,6,1,7]=>110010=>[1,1,3,2]
[4,3,2,5,6,7,1]=>110001=>[1,1,4,1]
[4,3,2,5,7,1,6]=>110010=>[1,1,3,2]
[4,3,2,5,7,6,1]=>110011=>[1,1,3,1,1]
[4,3,2,6,1,5,7]=>110100=>[1,1,2,3]
[4,3,2,6,1,7,5]=>110101=>[1,1,2,2,1]
[4,3,2,6,5,1,7]=>110110=>[1,1,2,1,2]
[4,3,2,6,5,7,1]=>110101=>[1,1,2,2,1]
[4,3,2,6,7,1,5]=>110010=>[1,1,3,2]
[4,3,2,6,7,5,1]=>110011=>[1,1,3,1,1]
[4,3,2,7,1,5,6]=>110100=>[1,1,2,3]
[4,3,2,7,1,6,5]=>110101=>[1,1,2,2,1]
[4,3,2,7,5,1,6]=>110110=>[1,1,2,1,2]
[4,3,2,7,5,6,1]=>110101=>[1,1,2,2,1]
[4,3,2,7,6,1,5]=>110110=>[1,1,2,1,2]
[4,3,2,7,6,5,1]=>110111=>[1,1,2,1,1,1]
[4,3,5,1,2,6,7]=>101000=>[1,2,4]
[4,3,5,1,2,7,6]=>101001=>[1,2,3,1]
[4,3,5,1,6,2,7]=>101010=>[1,2,2,2]
[4,3,5,1,6,7,2]=>101001=>[1,2,3,1]
[4,3,5,1,7,2,6]=>101010=>[1,2,2,2]
[4,3,5,1,7,6,2]=>101011=>[1,2,2,1,1]
[4,3,5,2,1,6,7]=>101100=>[1,2,1,3]
[4,3,5,2,1,7,6]=>101101=>[1,2,1,2,1]
[4,3,5,2,6,1,7]=>101010=>[1,2,2,2]
[4,3,5,2,6,7,1]=>101001=>[1,2,3,1]
[4,3,5,2,7,1,6]=>101010=>[1,2,2,2]
[4,3,5,2,7,6,1]=>101011=>[1,2,2,1,1]
[4,3,5,6,1,2,7]=>100100=>[1,3,3]
[4,3,5,6,1,7,2]=>100101=>[1,3,2,1]
[4,3,5,6,2,1,7]=>100110=>[1,3,1,2]
[4,3,5,6,2,7,1]=>100101=>[1,3,2,1]
[4,3,5,6,7,1,2]=>100010=>[1,4,2]
[4,3,5,6,7,2,1]=>100011=>[1,4,1,1]
[4,3,5,7,1,2,6]=>100100=>[1,3,3]
[4,3,5,7,1,6,2]=>100101=>[1,3,2,1]
[4,3,5,7,2,1,6]=>100110=>[1,3,1,2]
[4,3,5,7,2,6,1]=>100101=>[1,3,2,1]
[4,3,5,7,6,1,2]=>100110=>[1,3,1,2]
[4,3,5,7,6,2,1]=>100111=>[1,3,1,1,1]
[4,3,6,1,2,5,7]=>101000=>[1,2,4]
[4,3,6,1,2,7,5]=>101001=>[1,2,3,1]
[4,3,6,1,5,2,7]=>101010=>[1,2,2,2]
[4,3,6,1,5,7,2]=>101001=>[1,2,3,1]
[4,3,6,1,7,2,5]=>101010=>[1,2,2,2]
[4,3,6,1,7,5,2]=>101011=>[1,2,2,1,1]
[4,3,6,2,1,5,7]=>101100=>[1,2,1,3]
[4,3,6,2,1,7,5]=>101101=>[1,2,1,2,1]
[4,3,6,2,5,1,7]=>101010=>[1,2,2,2]
[4,3,6,2,5,7,1]=>101001=>[1,2,3,1]
[4,3,6,2,7,1,5]=>101010=>[1,2,2,2]
[4,3,6,2,7,5,1]=>101011=>[1,2,2,1,1]
[4,3,6,5,1,2,7]=>101100=>[1,2,1,3]
[4,3,6,5,1,7,2]=>101101=>[1,2,1,2,1]
[4,3,6,5,2,1,7]=>101110=>[1,2,1,1,2]
[4,3,6,5,2,7,1]=>101101=>[1,2,1,2,1]
[4,3,6,5,7,1,2]=>101010=>[1,2,2,2]
[4,3,6,5,7,2,1]=>101011=>[1,2,2,1,1]
[4,3,6,7,1,2,5]=>100100=>[1,3,3]
[4,3,6,7,1,5,2]=>100101=>[1,3,2,1]
[4,3,6,7,2,1,5]=>100110=>[1,3,1,2]
[4,3,6,7,2,5,1]=>100101=>[1,3,2,1]
[4,3,6,7,5,1,2]=>100110=>[1,3,1,2]
[4,3,6,7,5,2,1]=>100111=>[1,3,1,1,1]
[4,3,7,1,2,5,6]=>101000=>[1,2,4]
[4,3,7,1,2,6,5]=>101001=>[1,2,3,1]
[4,3,7,1,5,2,6]=>101010=>[1,2,2,2]
[4,3,7,1,5,6,2]=>101001=>[1,2,3,1]
[4,3,7,1,6,2,5]=>101010=>[1,2,2,2]
[4,3,7,1,6,5,2]=>101011=>[1,2,2,1,1]
[4,3,7,2,1,5,6]=>101100=>[1,2,1,3]
[4,3,7,2,1,6,5]=>101101=>[1,2,1,2,1]
[4,3,7,2,5,1,6]=>101010=>[1,2,2,2]
[4,3,7,2,5,6,1]=>101001=>[1,2,3,1]
[4,3,7,2,6,1,5]=>101010=>[1,2,2,2]
[4,3,7,2,6,5,1]=>101011=>[1,2,2,1,1]
[4,3,7,5,1,2,6]=>101100=>[1,2,1,3]
[4,3,7,5,1,6,2]=>101101=>[1,2,1,2,1]
[4,3,7,5,2,1,6]=>101110=>[1,2,1,1,2]
[4,3,7,5,2,6,1]=>101101=>[1,2,1,2,1]
[4,3,7,5,6,1,2]=>101010=>[1,2,2,2]
[4,3,7,5,6,2,1]=>101011=>[1,2,2,1,1]
[4,3,7,6,1,2,5]=>101100=>[1,2,1,3]
[4,3,7,6,1,5,2]=>101101=>[1,2,1,2,1]
[4,3,7,6,2,1,5]=>101110=>[1,2,1,1,2]
[4,3,7,6,2,5,1]=>101101=>[1,2,1,2,1]
[4,3,7,6,5,1,2]=>101110=>[1,2,1,1,2]
[4,3,7,6,5,2,1]=>101111=>[1,2,1,1,1,1]
[4,5,1,2,3,6,7]=>010000=>[2,5]
[4,5,1,2,3,7,6]=>010001=>[2,4,1]
[4,5,1,2,6,3,7]=>010010=>[2,3,2]
[4,5,1,2,6,7,3]=>010001=>[2,4,1]
[4,5,1,2,7,3,6]=>010010=>[2,3,2]
[4,5,1,2,7,6,3]=>010011=>[2,3,1,1]
[4,5,1,3,2,6,7]=>010100=>[2,2,3]
[4,5,1,3,2,7,6]=>010101=>[2,2,2,1]
[4,5,1,3,6,2,7]=>010010=>[2,3,2]
[4,5,1,3,6,7,2]=>010001=>[2,4,1]
[4,5,1,3,7,2,6]=>010010=>[2,3,2]
[4,5,1,3,7,6,2]=>010011=>[2,3,1,1]
[4,5,1,6,2,3,7]=>010100=>[2,2,3]
[4,5,1,6,2,7,3]=>010101=>[2,2,2,1]
[4,5,1,6,3,2,7]=>010110=>[2,2,1,2]
[4,5,1,6,3,7,2]=>010101=>[2,2,2,1]
[4,5,1,6,7,2,3]=>010010=>[2,3,2]
[4,5,1,6,7,3,2]=>010011=>[2,3,1,1]
[4,5,1,7,2,3,6]=>010100=>[2,2,3]
[4,5,1,7,2,6,3]=>010101=>[2,2,2,1]
[4,5,1,7,3,2,6]=>010110=>[2,2,1,2]
[4,5,1,7,3,6,2]=>010101=>[2,2,2,1]
[4,5,1,7,6,2,3]=>010110=>[2,2,1,2]
[4,5,1,7,6,3,2]=>010111=>[2,2,1,1,1]
[4,5,2,1,3,6,7]=>011000=>[2,1,4]
[4,5,2,1,3,7,6]=>011001=>[2,1,3,1]
[4,5,2,1,6,3,7]=>011010=>[2,1,2,2]
[4,5,2,1,6,7,3]=>011001=>[2,1,3,1]
[4,5,2,1,7,3,6]=>011010=>[2,1,2,2]
[4,5,2,1,7,6,3]=>011011=>[2,1,2,1,1]
[4,5,2,3,1,6,7]=>010100=>[2,2,3]
[4,5,2,3,1,7,6]=>010101=>[2,2,2,1]
[4,5,2,3,6,1,7]=>010010=>[2,3,2]
[4,5,2,3,6,7,1]=>010001=>[2,4,1]
[4,5,2,3,7,1,6]=>010010=>[2,3,2]
[4,5,2,3,7,6,1]=>010011=>[2,3,1,1]
[4,5,2,6,1,3,7]=>010100=>[2,2,3]
[4,5,2,6,1,7,3]=>010101=>[2,2,2,1]
[4,5,2,6,3,1,7]=>010110=>[2,2,1,2]
[4,5,2,6,3,7,1]=>010101=>[2,2,2,1]
[4,5,2,6,7,1,3]=>010010=>[2,3,2]
[4,5,2,6,7,3,1]=>010011=>[2,3,1,1]
[4,5,2,7,1,3,6]=>010100=>[2,2,3]
[4,5,2,7,1,6,3]=>010101=>[2,2,2,1]
[4,5,2,7,3,1,6]=>010110=>[2,2,1,2]
[4,5,2,7,3,6,1]=>010101=>[2,2,2,1]
[4,5,2,7,6,1,3]=>010110=>[2,2,1,2]
[4,5,2,7,6,3,1]=>010111=>[2,2,1,1,1]
[4,5,3,1,2,6,7]=>011000=>[2,1,4]
[4,5,3,1,2,7,6]=>011001=>[2,1,3,1]
[4,5,3,1,6,2,7]=>011010=>[2,1,2,2]
[4,5,3,1,6,7,2]=>011001=>[2,1,3,1]
[4,5,3,1,7,2,6]=>011010=>[2,1,2,2]
[4,5,3,1,7,6,2]=>011011=>[2,1,2,1,1]
[4,5,3,2,1,6,7]=>011100=>[2,1,1,3]
[4,5,3,2,1,7,6]=>011101=>[2,1,1,2,1]
[4,5,3,2,6,1,7]=>011010=>[2,1,2,2]
[4,5,3,2,6,7,1]=>011001=>[2,1,3,1]
[4,5,3,2,7,1,6]=>011010=>[2,1,2,2]
[4,5,3,2,7,6,1]=>011011=>[2,1,2,1,1]
[4,5,3,6,1,2,7]=>010100=>[2,2,3]
[4,5,3,6,1,7,2]=>010101=>[2,2,2,1]
[4,5,3,6,2,1,7]=>010110=>[2,2,1,2]
[4,5,3,6,2,7,1]=>010101=>[2,2,2,1]
[4,5,3,6,7,1,2]=>010010=>[2,3,2]
[4,5,3,6,7,2,1]=>010011=>[2,3,1,1]
[4,5,3,7,1,2,6]=>010100=>[2,2,3]
[4,5,3,7,1,6,2]=>010101=>[2,2,2,1]
[4,5,3,7,2,1,6]=>010110=>[2,2,1,2]
[4,5,3,7,2,6,1]=>010101=>[2,2,2,1]
[4,5,3,7,6,1,2]=>010110=>[2,2,1,2]
[4,5,3,7,6,2,1]=>010111=>[2,2,1,1,1]
[4,5,6,1,2,3,7]=>001000=>[3,4]
[4,5,6,1,2,7,3]=>001001=>[3,3,1]
[4,5,6,1,3,2,7]=>001010=>[3,2,2]
[4,5,6,1,3,7,2]=>001001=>[3,3,1]
[4,5,6,1,7,2,3]=>001010=>[3,2,2]
[4,5,6,1,7,3,2]=>001011=>[3,2,1,1]
[4,5,6,2,1,3,7]=>001100=>[3,1,3]
[4,5,6,2,1,7,3]=>001101=>[3,1,2,1]
[4,5,6,2,3,1,7]=>001010=>[3,2,2]
[4,5,6,2,3,7,1]=>001001=>[3,3,1]
[4,5,6,2,7,1,3]=>001010=>[3,2,2]
[4,5,6,2,7,3,1]=>001011=>[3,2,1,1]
[4,5,6,3,1,2,7]=>001100=>[3,1,3]
[4,5,6,3,1,7,2]=>001101=>[3,1,2,1]
[4,5,6,3,2,1,7]=>001110=>[3,1,1,2]
[4,5,6,3,2,7,1]=>001101=>[3,1,2,1]
[4,5,6,3,7,1,2]=>001010=>[3,2,2]
[4,5,6,3,7,2,1]=>001011=>[3,2,1,1]
[4,5,6,7,1,2,3]=>000100=>[4,3]
[4,5,6,7,1,3,2]=>000101=>[4,2,1]
[4,5,6,7,2,1,3]=>000110=>[4,1,2]
[4,5,6,7,2,3,1]=>000101=>[4,2,1]
[4,5,6,7,3,1,2]=>000110=>[4,1,2]
[4,5,6,7,3,2,1]=>000111=>[4,1,1,1]
[4,5,7,1,2,3,6]=>001000=>[3,4]
[4,5,7,1,2,6,3]=>001001=>[3,3,1]
[4,5,7,1,3,2,6]=>001010=>[3,2,2]
[4,5,7,1,3,6,2]=>001001=>[3,3,1]
[4,5,7,1,6,2,3]=>001010=>[3,2,2]
[4,5,7,1,6,3,2]=>001011=>[3,2,1,1]
[4,5,7,2,1,3,6]=>001100=>[3,1,3]
[4,5,7,2,1,6,3]=>001101=>[3,1,2,1]
[4,5,7,2,3,1,6]=>001010=>[3,2,2]
[4,5,7,2,3,6,1]=>001001=>[3,3,1]
[4,5,7,2,6,1,3]=>001010=>[3,2,2]
[4,5,7,2,6,3,1]=>001011=>[3,2,1,1]
[4,5,7,3,1,2,6]=>001100=>[3,1,3]
[4,5,7,3,1,6,2]=>001101=>[3,1,2,1]
[4,5,7,3,2,1,6]=>001110=>[3,1,1,2]
[4,5,7,3,2,6,1]=>001101=>[3,1,2,1]
[4,5,7,3,6,1,2]=>001010=>[3,2,2]
[4,5,7,3,6,2,1]=>001011=>[3,2,1,1]
[4,5,7,6,1,2,3]=>001100=>[3,1,3]
[4,5,7,6,1,3,2]=>001101=>[3,1,2,1]
[4,5,7,6,2,1,3]=>001110=>[3,1,1,2]
[4,5,7,6,2,3,1]=>001101=>[3,1,2,1]
[4,5,7,6,3,1,2]=>001110=>[3,1,1,2]
[4,5,7,6,3,2,1]=>001111=>[3,1,1,1,1]
[4,6,1,2,3,5,7]=>010000=>[2,5]
[4,6,1,2,3,7,5]=>010001=>[2,4,1]
[4,6,1,2,5,3,7]=>010010=>[2,3,2]
[4,6,1,2,5,7,3]=>010001=>[2,4,1]
[4,6,1,2,7,3,5]=>010010=>[2,3,2]
[4,6,1,2,7,5,3]=>010011=>[2,3,1,1]
[4,6,1,3,2,5,7]=>010100=>[2,2,3]
[4,6,1,3,2,7,5]=>010101=>[2,2,2,1]
[4,6,1,3,5,2,7]=>010010=>[2,3,2]
[4,6,1,3,5,7,2]=>010001=>[2,4,1]
[4,6,1,3,7,2,5]=>010010=>[2,3,2]
[4,6,1,3,7,5,2]=>010011=>[2,3,1,1]
[4,6,1,5,2,3,7]=>010100=>[2,2,3]
[4,6,1,5,2,7,3]=>010101=>[2,2,2,1]
[4,6,1,5,3,2,7]=>010110=>[2,2,1,2]
[4,6,1,5,3,7,2]=>010101=>[2,2,2,1]
[4,6,1,5,7,2,3]=>010010=>[2,3,2]
[4,6,1,5,7,3,2]=>010011=>[2,3,1,1]
[4,6,1,7,2,3,5]=>010100=>[2,2,3]
[4,6,1,7,2,5,3]=>010101=>[2,2,2,1]
[4,6,1,7,3,2,5]=>010110=>[2,2,1,2]
[4,6,1,7,3,5,2]=>010101=>[2,2,2,1]
[4,6,1,7,5,2,3]=>010110=>[2,2,1,2]
[4,6,1,7,5,3,2]=>010111=>[2,2,1,1,1]
[4,6,2,1,3,5,7]=>011000=>[2,1,4]
[4,6,2,1,3,7,5]=>011001=>[2,1,3,1]
[4,6,2,1,5,3,7]=>011010=>[2,1,2,2]
[4,6,2,1,5,7,3]=>011001=>[2,1,3,1]
[4,6,2,1,7,3,5]=>011010=>[2,1,2,2]
[4,6,2,1,7,5,3]=>011011=>[2,1,2,1,1]
[4,6,2,3,1,5,7]=>010100=>[2,2,3]
[4,6,2,3,1,7,5]=>010101=>[2,2,2,1]
[4,6,2,3,5,1,7]=>010010=>[2,3,2]
[4,6,2,3,5,7,1]=>010001=>[2,4,1]
[4,6,2,3,7,1,5]=>010010=>[2,3,2]
[4,6,2,3,7,5,1]=>010011=>[2,3,1,1]
[4,6,2,5,1,3,7]=>010100=>[2,2,3]
[4,6,2,5,1,7,3]=>010101=>[2,2,2,1]
[4,6,2,5,3,1,7]=>010110=>[2,2,1,2]
[4,6,2,5,3,7,1]=>010101=>[2,2,2,1]
[4,6,2,5,7,1,3]=>010010=>[2,3,2]
[4,6,2,5,7,3,1]=>010011=>[2,3,1,1]
[4,6,2,7,1,3,5]=>010100=>[2,2,3]
[4,6,2,7,1,5,3]=>010101=>[2,2,2,1]
[4,6,2,7,3,1,5]=>010110=>[2,2,1,2]
[4,6,2,7,3,5,1]=>010101=>[2,2,2,1]
[4,6,2,7,5,1,3]=>010110=>[2,2,1,2]
[4,6,2,7,5,3,1]=>010111=>[2,2,1,1,1]
[4,6,3,1,2,5,7]=>011000=>[2,1,4]
[4,6,3,1,2,7,5]=>011001=>[2,1,3,1]
[4,6,3,1,5,2,7]=>011010=>[2,1,2,2]
[4,6,3,1,5,7,2]=>011001=>[2,1,3,1]
[4,6,3,1,7,2,5]=>011010=>[2,1,2,2]
[4,6,3,1,7,5,2]=>011011=>[2,1,2,1,1]
[4,6,3,2,1,5,7]=>011100=>[2,1,1,3]
[4,6,3,2,1,7,5]=>011101=>[2,1,1,2,1]
[4,6,3,2,5,1,7]=>011010=>[2,1,2,2]
[4,6,3,2,5,7,1]=>011001=>[2,1,3,1]
[4,6,3,2,7,1,5]=>011010=>[2,1,2,2]
[4,6,3,2,7,5,1]=>011011=>[2,1,2,1,1]
[4,6,3,5,1,2,7]=>010100=>[2,2,3]
[4,6,3,5,1,7,2]=>010101=>[2,2,2,1]
[4,6,3,5,2,1,7]=>010110=>[2,2,1,2]
[4,6,3,5,2,7,1]=>010101=>[2,2,2,1]
[4,6,3,5,7,1,2]=>010010=>[2,3,2]
[4,6,3,5,7,2,1]=>010011=>[2,3,1,1]
[4,6,3,7,1,2,5]=>010100=>[2,2,3]
[4,6,3,7,1,5,2]=>010101=>[2,2,2,1]
[4,6,3,7,2,1,5]=>010110=>[2,2,1,2]
[4,6,3,7,2,5,1]=>010101=>[2,2,2,1]
[4,6,3,7,5,1,2]=>010110=>[2,2,1,2]
[4,6,3,7,5,2,1]=>010111=>[2,2,1,1,1]
[4,6,5,1,2,3,7]=>011000=>[2,1,4]
[4,6,5,1,2,7,3]=>011001=>[2,1,3,1]
[4,6,5,1,3,2,7]=>011010=>[2,1,2,2]
[4,6,5,1,3,7,2]=>011001=>[2,1,3,1]
[4,6,5,1,7,2,3]=>011010=>[2,1,2,2]
[4,6,5,1,7,3,2]=>011011=>[2,1,2,1,1]
[4,6,5,2,1,3,7]=>011100=>[2,1,1,3]
[4,6,5,2,1,7,3]=>011101=>[2,1,1,2,1]
[4,6,5,2,3,1,7]=>011010=>[2,1,2,2]
[4,6,5,2,3,7,1]=>011001=>[2,1,3,1]
[4,6,5,2,7,1,3]=>011010=>[2,1,2,2]
[4,6,5,2,7,3,1]=>011011=>[2,1,2,1,1]
[4,6,5,3,1,2,7]=>011100=>[2,1,1,3]
[4,6,5,3,1,7,2]=>011101=>[2,1,1,2,1]
[4,6,5,3,2,1,7]=>011110=>[2,1,1,1,2]
[4,6,5,3,2,7,1]=>011101=>[2,1,1,2,1]
[4,6,5,3,7,1,2]=>011010=>[2,1,2,2]
[4,6,5,3,7,2,1]=>011011=>[2,1,2,1,1]
[4,6,5,7,1,2,3]=>010100=>[2,2,3]
[4,6,5,7,1,3,2]=>010101=>[2,2,2,1]
[4,6,5,7,2,1,3]=>010110=>[2,2,1,2]
[4,6,5,7,2,3,1]=>010101=>[2,2,2,1]
[4,6,5,7,3,1,2]=>010110=>[2,2,1,2]
[4,6,5,7,3,2,1]=>010111=>[2,2,1,1,1]
[4,6,7,1,2,3,5]=>001000=>[3,4]
[4,6,7,1,2,5,3]=>001001=>[3,3,1]
[4,6,7,1,3,2,5]=>001010=>[3,2,2]
[4,6,7,1,3,5,2]=>001001=>[3,3,1]
[4,6,7,1,5,2,3]=>001010=>[3,2,2]
[4,6,7,1,5,3,2]=>001011=>[3,2,1,1]
[4,6,7,2,1,3,5]=>001100=>[3,1,3]
[4,6,7,2,1,5,3]=>001101=>[3,1,2,1]
[4,6,7,2,3,1,5]=>001010=>[3,2,2]
[4,6,7,2,3,5,1]=>001001=>[3,3,1]
[4,6,7,2,5,1,3]=>001010=>[3,2,2]
[4,6,7,2,5,3,1]=>001011=>[3,2,1,1]
[4,6,7,3,1,2,5]=>001100=>[3,1,3]
[4,6,7,3,1,5,2]=>001101=>[3,1,2,1]
[4,6,7,3,2,1,5]=>001110=>[3,1,1,2]
[4,6,7,3,2,5,1]=>001101=>[3,1,2,1]
[4,6,7,3,5,1,2]=>001010=>[3,2,2]
[4,6,7,3,5,2,1]=>001011=>[3,2,1,1]
[4,6,7,5,1,2,3]=>001100=>[3,1,3]
[4,6,7,5,1,3,2]=>001101=>[3,1,2,1]
[4,6,7,5,2,1,3]=>001110=>[3,1,1,2]
[4,6,7,5,2,3,1]=>001101=>[3,1,2,1]
[4,6,7,5,3,1,2]=>001110=>[3,1,1,2]
[4,6,7,5,3,2,1]=>001111=>[3,1,1,1,1]
[4,7,1,2,3,5,6]=>010000=>[2,5]
[4,7,1,2,3,6,5]=>010001=>[2,4,1]
[4,7,1,2,5,3,6]=>010010=>[2,3,2]
[4,7,1,2,5,6,3]=>010001=>[2,4,1]
[4,7,1,2,6,3,5]=>010010=>[2,3,2]
[4,7,1,2,6,5,3]=>010011=>[2,3,1,1]
[4,7,1,3,2,5,6]=>010100=>[2,2,3]
[4,7,1,3,2,6,5]=>010101=>[2,2,2,1]
[4,7,1,3,5,2,6]=>010010=>[2,3,2]
[4,7,1,3,5,6,2]=>010001=>[2,4,1]
[4,7,1,3,6,2,5]=>010010=>[2,3,2]
[4,7,1,3,6,5,2]=>010011=>[2,3,1,1]
[4,7,1,5,2,3,6]=>010100=>[2,2,3]
[4,7,1,5,2,6,3]=>010101=>[2,2,2,1]
[4,7,1,5,3,2,6]=>010110=>[2,2,1,2]
[4,7,1,5,3,6,2]=>010101=>[2,2,2,1]
[4,7,1,5,6,2,3]=>010010=>[2,3,2]
[4,7,1,5,6,3,2]=>010011=>[2,3,1,1]
[4,7,1,6,2,3,5]=>010100=>[2,2,3]
[4,7,1,6,2,5,3]=>010101=>[2,2,2,1]
[4,7,1,6,3,2,5]=>010110=>[2,2,1,2]
[4,7,1,6,3,5,2]=>010101=>[2,2,2,1]
[4,7,1,6,5,2,3]=>010110=>[2,2,1,2]
[4,7,1,6,5,3,2]=>010111=>[2,2,1,1,1]
[4,7,2,1,3,5,6]=>011000=>[2,1,4]
[4,7,2,1,3,6,5]=>011001=>[2,1,3,1]
[4,7,2,1,5,3,6]=>011010=>[2,1,2,2]
[4,7,2,1,5,6,3]=>011001=>[2,1,3,1]
[4,7,2,1,6,3,5]=>011010=>[2,1,2,2]
[4,7,2,1,6,5,3]=>011011=>[2,1,2,1,1]
[4,7,2,3,1,5,6]=>010100=>[2,2,3]
[4,7,2,3,1,6,5]=>010101=>[2,2,2,1]
[4,7,2,3,5,1,6]=>010010=>[2,3,2]
[4,7,2,3,5,6,1]=>010001=>[2,4,1]
[4,7,2,3,6,1,5]=>010010=>[2,3,2]
[4,7,2,3,6,5,1]=>010011=>[2,3,1,1]
[4,7,2,5,1,3,6]=>010100=>[2,2,3]
[4,7,2,5,1,6,3]=>010101=>[2,2,2,1]
[4,7,2,5,3,1,6]=>010110=>[2,2,1,2]
[4,7,2,5,3,6,1]=>010101=>[2,2,2,1]
[4,7,2,5,6,1,3]=>010010=>[2,3,2]
[4,7,2,5,6,3,1]=>010011=>[2,3,1,1]
[4,7,2,6,1,3,5]=>010100=>[2,2,3]
[4,7,2,6,1,5,3]=>010101=>[2,2,2,1]
[4,7,2,6,3,1,5]=>010110=>[2,2,1,2]
[4,7,2,6,3,5,1]=>010101=>[2,2,2,1]
[4,7,2,6,5,1,3]=>010110=>[2,2,1,2]
[4,7,2,6,5,3,1]=>010111=>[2,2,1,1,1]
[4,7,3,1,2,5,6]=>011000=>[2,1,4]
[4,7,3,1,2,6,5]=>011001=>[2,1,3,1]
[4,7,3,1,5,2,6]=>011010=>[2,1,2,2]
[4,7,3,1,5,6,2]=>011001=>[2,1,3,1]
[4,7,3,1,6,2,5]=>011010=>[2,1,2,2]
[4,7,3,1,6,5,2]=>011011=>[2,1,2,1,1]
[4,7,3,2,1,5,6]=>011100=>[2,1,1,3]
[4,7,3,2,1,6,5]=>011101=>[2,1,1,2,1]
[4,7,3,2,5,1,6]=>011010=>[2,1,2,2]
[4,7,3,2,5,6,1]=>011001=>[2,1,3,1]
[4,7,3,2,6,1,5]=>011010=>[2,1,2,2]
[4,7,3,2,6,5,1]=>011011=>[2,1,2,1,1]
[4,7,3,5,1,2,6]=>010100=>[2,2,3]
[4,7,3,5,1,6,2]=>010101=>[2,2,2,1]
[4,7,3,5,2,1,6]=>010110=>[2,2,1,2]
[4,7,3,5,2,6,1]=>010101=>[2,2,2,1]
[4,7,3,5,6,1,2]=>010010=>[2,3,2]
[4,7,3,5,6,2,1]=>010011=>[2,3,1,1]
[4,7,3,6,1,2,5]=>010100=>[2,2,3]
[4,7,3,6,1,5,2]=>010101=>[2,2,2,1]
[4,7,3,6,2,1,5]=>010110=>[2,2,1,2]
[4,7,3,6,2,5,1]=>010101=>[2,2,2,1]
[4,7,3,6,5,1,2]=>010110=>[2,2,1,2]
[4,7,3,6,5,2,1]=>010111=>[2,2,1,1,1]
[4,7,5,1,2,3,6]=>011000=>[2,1,4]
[4,7,5,1,2,6,3]=>011001=>[2,1,3,1]
[4,7,5,1,3,2,6]=>011010=>[2,1,2,2]
[4,7,5,1,3,6,2]=>011001=>[2,1,3,1]
[4,7,5,1,6,2,3]=>011010=>[2,1,2,2]
[4,7,5,1,6,3,2]=>011011=>[2,1,2,1,1]
[4,7,5,2,1,3,6]=>011100=>[2,1,1,3]
[4,7,5,2,1,6,3]=>011101=>[2,1,1,2,1]
[4,7,5,2,3,1,6]=>011010=>[2,1,2,2]
[4,7,5,2,3,6,1]=>011001=>[2,1,3,1]
[4,7,5,2,6,1,3]=>011010=>[2,1,2,2]
[4,7,5,2,6,3,1]=>011011=>[2,1,2,1,1]
[4,7,5,3,1,2,6]=>011100=>[2,1,1,3]
[4,7,5,3,1,6,2]=>011101=>[2,1,1,2,1]
[4,7,5,3,2,1,6]=>011110=>[2,1,1,1,2]
[4,7,5,3,2,6,1]=>011101=>[2,1,1,2,1]
[4,7,5,3,6,1,2]=>011010=>[2,1,2,2]
[4,7,5,3,6,2,1]=>011011=>[2,1,2,1,1]
[4,7,5,6,1,2,3]=>010100=>[2,2,3]
[4,7,5,6,1,3,2]=>010101=>[2,2,2,1]
[4,7,5,6,2,1,3]=>010110=>[2,2,1,2]
[4,7,5,6,2,3,1]=>010101=>[2,2,2,1]
[4,7,5,6,3,1,2]=>010110=>[2,2,1,2]
[4,7,5,6,3,2,1]=>010111=>[2,2,1,1,1]
[4,7,6,1,2,3,5]=>011000=>[2,1,4]
[4,7,6,1,2,5,3]=>011001=>[2,1,3,1]
[4,7,6,1,3,2,5]=>011010=>[2,1,2,2]
[4,7,6,1,3,5,2]=>011001=>[2,1,3,1]
[4,7,6,1,5,2,3]=>011010=>[2,1,2,2]
[4,7,6,1,5,3,2]=>011011=>[2,1,2,1,1]
[4,7,6,2,1,3,5]=>011100=>[2,1,1,3]
[4,7,6,2,1,5,3]=>011101=>[2,1,1,2,1]
[4,7,6,2,3,1,5]=>011010=>[2,1,2,2]
[4,7,6,2,3,5,1]=>011001=>[2,1,3,1]
[4,7,6,2,5,1,3]=>011010=>[2,1,2,2]
[4,7,6,2,5,3,1]=>011011=>[2,1,2,1,1]
[4,7,6,3,1,2,5]=>011100=>[2,1,1,3]
[4,7,6,3,1,5,2]=>011101=>[2,1,1,2,1]
[4,7,6,3,2,1,5]=>011110=>[2,1,1,1,2]
[4,7,6,3,2,5,1]=>011101=>[2,1,1,2,1]
[4,7,6,3,5,1,2]=>011010=>[2,1,2,2]
[4,7,6,3,5,2,1]=>011011=>[2,1,2,1,1]
[4,7,6,5,1,2,3]=>011100=>[2,1,1,3]
[4,7,6,5,1,3,2]=>011101=>[2,1,1,2,1]
[4,7,6,5,2,1,3]=>011110=>[2,1,1,1,2]
[4,7,6,5,2,3,1]=>011101=>[2,1,1,2,1]
[4,7,6,5,3,1,2]=>011110=>[2,1,1,1,2]
[4,7,6,5,3,2,1]=>011111=>[2,1,1,1,1,1]
[5,1,2,3,4,6,7]=>100000=>[1,6]
[5,1,2,3,4,7,6]=>100001=>[1,5,1]
[5,1,2,3,6,4,7]=>100010=>[1,4,2]
[5,1,2,3,6,7,4]=>100001=>[1,5,1]
[5,1,2,3,7,4,6]=>100010=>[1,4,2]
[5,1,2,3,7,6,4]=>100011=>[1,4,1,1]
[5,1,2,4,3,6,7]=>100100=>[1,3,3]
[5,1,2,4,3,7,6]=>100101=>[1,3,2,1]
[5,1,2,4,6,3,7]=>100010=>[1,4,2]
[5,1,2,4,6,7,3]=>100001=>[1,5,1]
[5,1,2,4,7,3,6]=>100010=>[1,4,2]
[5,1,2,4,7,6,3]=>100011=>[1,4,1,1]
[5,1,2,6,3,4,7]=>100100=>[1,3,3]
[5,1,2,6,3,7,4]=>100101=>[1,3,2,1]
[5,1,2,6,4,3,7]=>100110=>[1,3,1,2]
[5,1,2,6,4,7,3]=>100101=>[1,3,2,1]
[5,1,2,6,7,3,4]=>100010=>[1,4,2]
[5,1,2,6,7,4,3]=>100011=>[1,4,1,1]
[5,1,2,7,3,4,6]=>100100=>[1,3,3]
[5,1,2,7,3,6,4]=>100101=>[1,3,2,1]
[5,1,2,7,4,3,6]=>100110=>[1,3,1,2]
[5,1,2,7,4,6,3]=>100101=>[1,3,2,1]
[5,1,2,7,6,3,4]=>100110=>[1,3,1,2]
[5,1,2,7,6,4,3]=>100111=>[1,3,1,1,1]
[5,1,3,2,4,6,7]=>101000=>[1,2,4]
[5,1,3,2,4,7,6]=>101001=>[1,2,3,1]
[5,1,3,2,6,4,7]=>101010=>[1,2,2,2]
[5,1,3,2,6,7,4]=>101001=>[1,2,3,1]
[5,1,3,2,7,4,6]=>101010=>[1,2,2,2]
[5,1,3,2,7,6,4]=>101011=>[1,2,2,1,1]
[5,1,3,4,2,6,7]=>100100=>[1,3,3]
[5,1,3,4,2,7,6]=>100101=>[1,3,2,1]
[5,1,3,4,6,2,7]=>100010=>[1,4,2]
[5,1,3,4,6,7,2]=>100001=>[1,5,1]
[5,1,3,4,7,2,6]=>100010=>[1,4,2]
[5,1,3,4,7,6,2]=>100011=>[1,4,1,1]
[5,1,3,6,2,4,7]=>100100=>[1,3,3]
[5,1,3,6,2,7,4]=>100101=>[1,3,2,1]
[5,1,3,6,4,2,7]=>100110=>[1,3,1,2]
[5,1,3,6,4,7,2]=>100101=>[1,3,2,1]
[5,1,3,6,7,2,4]=>100010=>[1,4,2]
[5,1,3,6,7,4,2]=>100011=>[1,4,1,1]
[5,1,3,7,2,4,6]=>100100=>[1,3,3]
[5,1,3,7,2,6,4]=>100101=>[1,3,2,1]
[5,1,3,7,4,2,6]=>100110=>[1,3,1,2]
[5,1,3,7,4,6,2]=>100101=>[1,3,2,1]
[5,1,3,7,6,2,4]=>100110=>[1,3,1,2]
[5,1,3,7,6,4,2]=>100111=>[1,3,1,1,1]
[5,1,4,2,3,6,7]=>101000=>[1,2,4]
[5,1,4,2,3,7,6]=>101001=>[1,2,3,1]
[5,1,4,2,6,3,7]=>101010=>[1,2,2,2]
[5,1,4,2,6,7,3]=>101001=>[1,2,3,1]
[5,1,4,2,7,3,6]=>101010=>[1,2,2,2]
[5,1,4,2,7,6,3]=>101011=>[1,2,2,1,1]
[5,1,4,3,2,6,7]=>101100=>[1,2,1,3]
[5,1,4,3,2,7,6]=>101101=>[1,2,1,2,1]
[5,1,4,3,6,2,7]=>101010=>[1,2,2,2]
[5,1,4,3,6,7,2]=>101001=>[1,2,3,1]
[5,1,4,3,7,2,6]=>101010=>[1,2,2,2]
[5,1,4,3,7,6,2]=>101011=>[1,2,2,1,1]
[5,1,4,6,2,3,7]=>100100=>[1,3,3]
[5,1,4,6,2,7,3]=>100101=>[1,3,2,1]
[5,1,4,6,3,2,7]=>100110=>[1,3,1,2]
[5,1,4,6,3,7,2]=>100101=>[1,3,2,1]
[5,1,4,6,7,2,3]=>100010=>[1,4,2]
[5,1,4,6,7,3,2]=>100011=>[1,4,1,1]
[5,1,4,7,2,3,6]=>100100=>[1,3,3]
[5,1,4,7,2,6,3]=>100101=>[1,3,2,1]
[5,1,4,7,3,2,6]=>100110=>[1,3,1,2]
[5,1,4,7,3,6,2]=>100101=>[1,3,2,1]
[5,1,4,7,6,2,3]=>100110=>[1,3,1,2]
[5,1,4,7,6,3,2]=>100111=>[1,3,1,1,1]
[5,1,6,2,3,4,7]=>101000=>[1,2,4]
[5,1,6,2,3,7,4]=>101001=>[1,2,3,1]
[5,1,6,2,4,3,7]=>101010=>[1,2,2,2]
[5,1,6,2,4,7,3]=>101001=>[1,2,3,1]
[5,1,6,2,7,3,4]=>101010=>[1,2,2,2]
[5,1,6,2,7,4,3]=>101011=>[1,2,2,1,1]
[5,1,6,3,2,4,7]=>101100=>[1,2,1,3]
[5,1,6,3,2,7,4]=>101101=>[1,2,1,2,1]
[5,1,6,3,4,2,7]=>101010=>[1,2,2,2]
[5,1,6,3,4,7,2]=>101001=>[1,2,3,1]
[5,1,6,3,7,2,4]=>101010=>[1,2,2,2]
[5,1,6,3,7,4,2]=>101011=>[1,2,2,1,1]
[5,1,6,4,2,3,7]=>101100=>[1,2,1,3]
[5,1,6,4,2,7,3]=>101101=>[1,2,1,2,1]
[5,1,6,4,3,2,7]=>101110=>[1,2,1,1,2]
[5,1,6,4,3,7,2]=>101101=>[1,2,1,2,1]
[5,1,6,4,7,2,3]=>101010=>[1,2,2,2]
[5,1,6,4,7,3,2]=>101011=>[1,2,2,1,1]
[5,1,6,7,2,3,4]=>100100=>[1,3,3]
[5,1,6,7,2,4,3]=>100101=>[1,3,2,1]
[5,1,6,7,3,2,4]=>100110=>[1,3,1,2]
[5,1,6,7,3,4,2]=>100101=>[1,3,2,1]
[5,1,6,7,4,2,3]=>100110=>[1,3,1,2]
[5,1,6,7,4,3,2]=>100111=>[1,3,1,1,1]
[5,1,7,2,3,4,6]=>101000=>[1,2,4]
[5,1,7,2,3,6,4]=>101001=>[1,2,3,1]
[5,1,7,2,4,3,6]=>101010=>[1,2,2,2]
[5,1,7,2,4,6,3]=>101001=>[1,2,3,1]
[5,1,7,2,6,3,4]=>101010=>[1,2,2,2]
[5,1,7,2,6,4,3]=>101011=>[1,2,2,1,1]
[5,1,7,3,2,4,6]=>101100=>[1,2,1,3]
[5,1,7,3,2,6,4]=>101101=>[1,2,1,2,1]
[5,1,7,3,4,2,6]=>101010=>[1,2,2,2]
[5,1,7,3,4,6,2]=>101001=>[1,2,3,1]
[5,1,7,3,6,2,4]=>101010=>[1,2,2,2]
[5,1,7,3,6,4,2]=>101011=>[1,2,2,1,1]
[5,1,7,4,2,3,6]=>101100=>[1,2,1,3]
[5,1,7,4,2,6,3]=>101101=>[1,2,1,2,1]
[5,1,7,4,3,2,6]=>101110=>[1,2,1,1,2]
[5,1,7,4,3,6,2]=>101101=>[1,2,1,2,1]
[5,1,7,4,6,2,3]=>101010=>[1,2,2,2]
[5,1,7,4,6,3,2]=>101011=>[1,2,2,1,1]
[5,1,7,6,2,3,4]=>101100=>[1,2,1,3]
[5,1,7,6,2,4,3]=>101101=>[1,2,1,2,1]
[5,1,7,6,3,2,4]=>101110=>[1,2,1,1,2]
[5,1,7,6,3,4,2]=>101101=>[1,2,1,2,1]
[5,1,7,6,4,2,3]=>101110=>[1,2,1,1,2]
[5,1,7,6,4,3,2]=>101111=>[1,2,1,1,1,1]
[5,2,1,3,4,6,7]=>110000=>[1,1,5]
[5,2,1,3,4,7,6]=>110001=>[1,1,4,1]
[5,2,1,3,6,4,7]=>110010=>[1,1,3,2]
[5,2,1,3,6,7,4]=>110001=>[1,1,4,1]
[5,2,1,3,7,4,6]=>110010=>[1,1,3,2]
[5,2,1,3,7,6,4]=>110011=>[1,1,3,1,1]
[5,2,1,4,3,6,7]=>110100=>[1,1,2,3]
[5,2,1,4,3,7,6]=>110101=>[1,1,2,2,1]
[5,2,1,4,6,3,7]=>110010=>[1,1,3,2]
[5,2,1,4,6,7,3]=>110001=>[1,1,4,1]
[5,2,1,4,7,3,6]=>110010=>[1,1,3,2]
[5,2,1,4,7,6,3]=>110011=>[1,1,3,1,1]
[5,2,1,6,3,4,7]=>110100=>[1,1,2,3]
[5,2,1,6,3,7,4]=>110101=>[1,1,2,2,1]
[5,2,1,6,4,3,7]=>110110=>[1,1,2,1,2]
[5,2,1,6,4,7,3]=>110101=>[1,1,2,2,1]
[5,2,1,6,7,3,4]=>110010=>[1,1,3,2]
[5,2,1,6,7,4,3]=>110011=>[1,1,3,1,1]
[5,2,1,7,3,4,6]=>110100=>[1,1,2,3]
[5,2,1,7,3,6,4]=>110101=>[1,1,2,2,1]
[5,2,1,7,4,3,6]=>110110=>[1,1,2,1,2]
[5,2,1,7,4,6,3]=>110101=>[1,1,2,2,1]
[5,2,1,7,6,3,4]=>110110=>[1,1,2,1,2]
[5,2,1,7,6,4,3]=>110111=>[1,1,2,1,1,1]
[5,2,3,1,4,6,7]=>101000=>[1,2,4]
[5,2,3,1,4,7,6]=>101001=>[1,2,3,1]
[5,2,3,1,6,4,7]=>101010=>[1,2,2,2]
[5,2,3,1,6,7,4]=>101001=>[1,2,3,1]
[5,2,3,1,7,4,6]=>101010=>[1,2,2,2]
[5,2,3,1,7,6,4]=>101011=>[1,2,2,1,1]
[5,2,3,4,1,6,7]=>100100=>[1,3,3]
[5,2,3,4,1,7,6]=>100101=>[1,3,2,1]
[5,2,3,4,6,1,7]=>100010=>[1,4,2]
[5,2,3,4,6,7,1]=>100001=>[1,5,1]
[5,2,3,4,7,1,6]=>100010=>[1,4,2]
[5,2,3,4,7,6,1]=>100011=>[1,4,1,1]
[5,2,3,6,1,4,7]=>100100=>[1,3,3]
[5,2,3,6,1,7,4]=>100101=>[1,3,2,1]
[5,2,3,6,4,1,7]=>100110=>[1,3,1,2]
[5,2,3,6,4,7,1]=>100101=>[1,3,2,1]
[5,2,3,6,7,1,4]=>100010=>[1,4,2]
[5,2,3,6,7,4,1]=>100011=>[1,4,1,1]
[5,2,3,7,1,4,6]=>100100=>[1,3,3]
[5,2,3,7,1,6,4]=>100101=>[1,3,2,1]
[5,2,3,7,4,1,6]=>100110=>[1,3,1,2]
[5,2,3,7,4,6,1]=>100101=>[1,3,2,1]
[5,2,3,7,6,1,4]=>100110=>[1,3,1,2]
[5,2,3,7,6,4,1]=>100111=>[1,3,1,1,1]
[5,2,4,1,3,6,7]=>101000=>[1,2,4]
[5,2,4,1,3,7,6]=>101001=>[1,2,3,1]
[5,2,4,1,6,3,7]=>101010=>[1,2,2,2]
[5,2,4,1,6,7,3]=>101001=>[1,2,3,1]
[5,2,4,1,7,3,6]=>101010=>[1,2,2,2]
[5,2,4,1,7,6,3]=>101011=>[1,2,2,1,1]
[5,2,4,3,1,6,7]=>101100=>[1,2,1,3]
[5,2,4,3,1,7,6]=>101101=>[1,2,1,2,1]
[5,2,4,3,6,1,7]=>101010=>[1,2,2,2]
[5,2,4,3,6,7,1]=>101001=>[1,2,3,1]
[5,2,4,3,7,1,6]=>101010=>[1,2,2,2]
[5,2,4,3,7,6,1]=>101011=>[1,2,2,1,1]
[5,2,4,6,1,3,7]=>100100=>[1,3,3]
[5,2,4,6,1,7,3]=>100101=>[1,3,2,1]
[5,2,4,6,3,1,7]=>100110=>[1,3,1,2]
[5,2,4,6,3,7,1]=>100101=>[1,3,2,1]
[5,2,4,6,7,1,3]=>100010=>[1,4,2]
[5,2,4,6,7,3,1]=>100011=>[1,4,1,1]
[5,2,4,7,1,3,6]=>100100=>[1,3,3]
[5,2,4,7,1,6,3]=>100101=>[1,3,2,1]
[5,2,4,7,3,1,6]=>100110=>[1,3,1,2]
[5,2,4,7,3,6,1]=>100101=>[1,3,2,1]
[5,2,4,7,6,1,3]=>100110=>[1,3,1,2]
[5,2,4,7,6,3,1]=>100111=>[1,3,1,1,1]
[5,2,6,1,3,4,7]=>101000=>[1,2,4]
[5,2,6,1,3,7,4]=>101001=>[1,2,3,1]
[5,2,6,1,4,3,7]=>101010=>[1,2,2,2]
[5,2,6,1,4,7,3]=>101001=>[1,2,3,1]
[5,2,6,1,7,3,4]=>101010=>[1,2,2,2]
[5,2,6,1,7,4,3]=>101011=>[1,2,2,1,1]
[5,2,6,3,1,4,7]=>101100=>[1,2,1,3]
[5,2,6,3,1,7,4]=>101101=>[1,2,1,2,1]
[5,2,6,3,4,1,7]=>101010=>[1,2,2,2]
[5,2,6,3,4,7,1]=>101001=>[1,2,3,1]
[5,2,6,3,7,1,4]=>101010=>[1,2,2,2]
[5,2,6,3,7,4,1]=>101011=>[1,2,2,1,1]
[5,2,6,4,1,3,7]=>101100=>[1,2,1,3]
[5,2,6,4,1,7,3]=>101101=>[1,2,1,2,1]
[5,2,6,4,3,1,7]=>101110=>[1,2,1,1,2]
[5,2,6,4,3,7,1]=>101101=>[1,2,1,2,1]
[5,2,6,4,7,1,3]=>101010=>[1,2,2,2]
[5,2,6,4,7,3,1]=>101011=>[1,2,2,1,1]
[5,2,6,7,1,3,4]=>100100=>[1,3,3]
[5,2,6,7,1,4,3]=>100101=>[1,3,2,1]
[5,2,6,7,3,1,4]=>100110=>[1,3,1,2]
[5,2,6,7,3,4,1]=>100101=>[1,3,2,1]
[5,2,6,7,4,1,3]=>100110=>[1,3,1,2]
[5,2,6,7,4,3,1]=>100111=>[1,3,1,1,1]
[5,2,7,1,3,4,6]=>101000=>[1,2,4]
[5,2,7,1,3,6,4]=>101001=>[1,2,3,1]
[5,2,7,1,4,3,6]=>101010=>[1,2,2,2]
[5,2,7,1,4,6,3]=>101001=>[1,2,3,1]
[5,2,7,1,6,3,4]=>101010=>[1,2,2,2]
[5,2,7,1,6,4,3]=>101011=>[1,2,2,1,1]
[5,2,7,3,1,4,6]=>101100=>[1,2,1,3]
[5,2,7,3,1,6,4]=>101101=>[1,2,1,2,1]
[5,2,7,3,4,1,6]=>101010=>[1,2,2,2]
[5,2,7,3,4,6,1]=>101001=>[1,2,3,1]
[5,2,7,3,6,1,4]=>101010=>[1,2,2,2]
[5,2,7,3,6,4,1]=>101011=>[1,2,2,1,1]
[5,2,7,4,1,3,6]=>101100=>[1,2,1,3]
[5,2,7,4,1,6,3]=>101101=>[1,2,1,2,1]
[5,2,7,4,3,1,6]=>101110=>[1,2,1,1,2]
[5,2,7,4,3,6,1]=>101101=>[1,2,1,2,1]
[5,2,7,4,6,1,3]=>101010=>[1,2,2,2]
[5,2,7,4,6,3,1]=>101011=>[1,2,2,1,1]
[5,2,7,6,1,3,4]=>101100=>[1,2,1,3]
[5,2,7,6,1,4,3]=>101101=>[1,2,1,2,1]
[5,2,7,6,3,1,4]=>101110=>[1,2,1,1,2]
[5,2,7,6,3,4,1]=>101101=>[1,2,1,2,1]
[5,2,7,6,4,1,3]=>101110=>[1,2,1,1,2]
[5,2,7,6,4,3,1]=>101111=>[1,2,1,1,1,1]
[5,3,1,2,4,6,7]=>110000=>[1,1,5]
[5,3,1,2,4,7,6]=>110001=>[1,1,4,1]
[5,3,1,2,6,4,7]=>110010=>[1,1,3,2]
[5,3,1,2,6,7,4]=>110001=>[1,1,4,1]
[5,3,1,2,7,4,6]=>110010=>[1,1,3,2]
[5,3,1,2,7,6,4]=>110011=>[1,1,3,1,1]
[5,3,1,4,2,6,7]=>110100=>[1,1,2,3]
[5,3,1,4,2,7,6]=>110101=>[1,1,2,2,1]
[5,3,1,4,6,2,7]=>110010=>[1,1,3,2]
[5,3,1,4,6,7,2]=>110001=>[1,1,4,1]
[5,3,1,4,7,2,6]=>110010=>[1,1,3,2]
[5,3,1,4,7,6,2]=>110011=>[1,1,3,1,1]
[5,3,1,6,2,4,7]=>110100=>[1,1,2,3]
[5,3,1,6,2,7,4]=>110101=>[1,1,2,2,1]
[5,3,1,6,4,2,7]=>110110=>[1,1,2,1,2]
[5,3,1,6,4,7,2]=>110101=>[1,1,2,2,1]
[5,3,1,6,7,2,4]=>110010=>[1,1,3,2]
[5,3,1,6,7,4,2]=>110011=>[1,1,3,1,1]
[5,3,1,7,2,4,6]=>110100=>[1,1,2,3]
[5,3,1,7,2,6,4]=>110101=>[1,1,2,2,1]
[5,3,1,7,4,2,6]=>110110=>[1,1,2,1,2]
[5,3,1,7,4,6,2]=>110101=>[1,1,2,2,1]
[5,3,1,7,6,2,4]=>110110=>[1,1,2,1,2]
[5,3,1,7,6,4,2]=>110111=>[1,1,2,1,1,1]
[5,3,2,1,4,6,7]=>111000=>[1,1,1,4]
[5,3,2,1,4,7,6]=>111001=>[1,1,1,3,1]
[5,3,2,1,6,4,7]=>111010=>[1,1,1,2,2]
[5,3,2,1,6,7,4]=>111001=>[1,1,1,3,1]
[5,3,2,1,7,4,6]=>111010=>[1,1,1,2,2]
[5,3,2,1,7,6,4]=>111011=>[1,1,1,2,1,1]
[5,3,2,4,1,6,7]=>110100=>[1,1,2,3]
[5,3,2,4,1,7,6]=>110101=>[1,1,2,2,1]
[5,3,2,4,6,1,7]=>110010=>[1,1,3,2]
[5,3,2,4,6,7,1]=>110001=>[1,1,4,1]
[5,3,2,4,7,1,6]=>110010=>[1,1,3,2]
[5,3,2,4,7,6,1]=>110011=>[1,1,3,1,1]
[5,3,2,6,1,4,7]=>110100=>[1,1,2,3]
[5,3,2,6,1,7,4]=>110101=>[1,1,2,2,1]
[5,3,2,6,4,1,7]=>110110=>[1,1,2,1,2]
[5,3,2,6,4,7,1]=>110101=>[1,1,2,2,1]
[5,3,2,6,7,1,4]=>110010=>[1,1,3,2]
[5,3,2,6,7,4,1]=>110011=>[1,1,3,1,1]
[5,3,2,7,1,4,6]=>110100=>[1,1,2,3]
[5,3,2,7,1,6,4]=>110101=>[1,1,2,2,1]
[5,3,2,7,4,1,6]=>110110=>[1,1,2,1,2]
[5,3,2,7,4,6,1]=>110101=>[1,1,2,2,1]
[5,3,2,7,6,1,4]=>110110=>[1,1,2,1,2]
[5,3,2,7,6,4,1]=>110111=>[1,1,2,1,1,1]
[5,3,4,1,2,6,7]=>101000=>[1,2,4]
[5,3,4,1,2,7,6]=>101001=>[1,2,3,1]
[5,3,4,1,6,2,7]=>101010=>[1,2,2,2]
[5,3,4,1,6,7,2]=>101001=>[1,2,3,1]
[5,3,4,1,7,2,6]=>101010=>[1,2,2,2]
[5,3,4,1,7,6,2]=>101011=>[1,2,2,1,1]
[5,3,4,2,1,6,7]=>101100=>[1,2,1,3]
[5,3,4,2,1,7,6]=>101101=>[1,2,1,2,1]
[5,3,4,2,6,1,7]=>101010=>[1,2,2,2]
[5,3,4,2,6,7,1]=>101001=>[1,2,3,1]
[5,3,4,2,7,1,6]=>101010=>[1,2,2,2]
[5,3,4,2,7,6,1]=>101011=>[1,2,2,1,1]
[5,3,4,6,1,2,7]=>100100=>[1,3,3]
[5,3,4,6,1,7,2]=>100101=>[1,3,2,1]
[5,3,4,6,2,1,7]=>100110=>[1,3,1,2]
[5,3,4,6,2,7,1]=>100101=>[1,3,2,1]
[5,3,4,6,7,1,2]=>100010=>[1,4,2]
[5,3,4,6,7,2,1]=>100011=>[1,4,1,1]
[5,3,4,7,1,2,6]=>100100=>[1,3,3]
[5,3,4,7,1,6,2]=>100101=>[1,3,2,1]
[5,3,4,7,2,1,6]=>100110=>[1,3,1,2]
[5,3,4,7,2,6,1]=>100101=>[1,3,2,1]
[5,3,4,7,6,1,2]=>100110=>[1,3,1,2]
[5,3,4,7,6,2,1]=>100111=>[1,3,1,1,1]
[5,3,6,1,2,4,7]=>101000=>[1,2,4]
[5,3,6,1,2,7,4]=>101001=>[1,2,3,1]
[5,3,6,1,4,2,7]=>101010=>[1,2,2,2]
[5,3,6,1,4,7,2]=>101001=>[1,2,3,1]
[5,3,6,1,7,2,4]=>101010=>[1,2,2,2]
[5,3,6,1,7,4,2]=>101011=>[1,2,2,1,1]
[5,3,6,2,1,4,7]=>101100=>[1,2,1,3]
[5,3,6,2,1,7,4]=>101101=>[1,2,1,2,1]
[5,3,6,2,4,1,7]=>101010=>[1,2,2,2]
[5,3,6,2,4,7,1]=>101001=>[1,2,3,1]
[5,3,6,2,7,1,4]=>101010=>[1,2,2,2]
[5,3,6,2,7,4,1]=>101011=>[1,2,2,1,1]
[5,3,6,4,1,2,7]=>101100=>[1,2,1,3]
[5,3,6,4,1,7,2]=>101101=>[1,2,1,2,1]
[5,3,6,4,2,1,7]=>101110=>[1,2,1,1,2]
[5,3,6,4,2,7,1]=>101101=>[1,2,1,2,1]
[5,3,6,4,7,1,2]=>101010=>[1,2,2,2]
[5,3,6,4,7,2,1]=>101011=>[1,2,2,1,1]
[5,3,6,7,1,2,4]=>100100=>[1,3,3]
[5,3,6,7,1,4,2]=>100101=>[1,3,2,1]
[5,3,6,7,2,1,4]=>100110=>[1,3,1,2]
[5,3,6,7,2,4,1]=>100101=>[1,3,2,1]
[5,3,6,7,4,1,2]=>100110=>[1,3,1,2]
[5,3,6,7,4,2,1]=>100111=>[1,3,1,1,1]
[5,3,7,1,2,4,6]=>101000=>[1,2,4]
[5,3,7,1,2,6,4]=>101001=>[1,2,3,1]
[5,3,7,1,4,2,6]=>101010=>[1,2,2,2]
[5,3,7,1,4,6,2]=>101001=>[1,2,3,1]
[5,3,7,1,6,2,4]=>101010=>[1,2,2,2]
[5,3,7,1,6,4,2]=>101011=>[1,2,2,1,1]
[5,3,7,2,1,4,6]=>101100=>[1,2,1,3]
[5,3,7,2,1,6,4]=>101101=>[1,2,1,2,1]
[5,3,7,2,4,1,6]=>101010=>[1,2,2,2]
[5,3,7,2,4,6,1]=>101001=>[1,2,3,1]
[5,3,7,2,6,1,4]=>101010=>[1,2,2,2]
[5,3,7,2,6,4,1]=>101011=>[1,2,2,1,1]
[5,3,7,4,1,2,6]=>101100=>[1,2,1,3]
[5,3,7,4,1,6,2]=>101101=>[1,2,1,2,1]
[5,3,7,4,2,1,6]=>101110=>[1,2,1,1,2]
[5,3,7,4,2,6,1]=>101101=>[1,2,1,2,1]
[5,3,7,4,6,1,2]=>101010=>[1,2,2,2]
[5,3,7,4,6,2,1]=>101011=>[1,2,2,1,1]
[5,3,7,6,1,2,4]=>101100=>[1,2,1,3]
[5,3,7,6,1,4,2]=>101101=>[1,2,1,2,1]
[5,3,7,6,2,1,4]=>101110=>[1,2,1,1,2]
[5,3,7,6,2,4,1]=>101101=>[1,2,1,2,1]
[5,3,7,6,4,1,2]=>101110=>[1,2,1,1,2]
[5,3,7,6,4,2,1]=>101111=>[1,2,1,1,1,1]
[5,4,1,2,3,6,7]=>110000=>[1,1,5]
[5,4,1,2,3,7,6]=>110001=>[1,1,4,1]
[5,4,1,2,6,3,7]=>110010=>[1,1,3,2]
[5,4,1,2,6,7,3]=>110001=>[1,1,4,1]
[5,4,1,2,7,3,6]=>110010=>[1,1,3,2]
[5,4,1,2,7,6,3]=>110011=>[1,1,3,1,1]
[5,4,1,3,2,6,7]=>110100=>[1,1,2,3]
[5,4,1,3,2,7,6]=>110101=>[1,1,2,2,1]
[5,4,1,3,6,2,7]=>110010=>[1,1,3,2]
[5,4,1,3,6,7,2]=>110001=>[1,1,4,1]
[5,4,1,3,7,2,6]=>110010=>[1,1,3,2]
[5,4,1,3,7,6,2]=>110011=>[1,1,3,1,1]
[5,4,1,6,2,3,7]=>110100=>[1,1,2,3]
[5,4,1,6,2,7,3]=>110101=>[1,1,2,2,1]
[5,4,1,6,3,2,7]=>110110=>[1,1,2,1,2]
[5,4,1,6,3,7,2]=>110101=>[1,1,2,2,1]
[5,4,1,6,7,2,3]=>110010=>[1,1,3,2]
[5,4,1,6,7,3,2]=>110011=>[1,1,3,1,1]
[5,4,1,7,2,3,6]=>110100=>[1,1,2,3]
[5,4,1,7,2,6,3]=>110101=>[1,1,2,2,1]
[5,4,1,7,3,2,6]=>110110=>[1,1,2,1,2]
[5,4,1,7,3,6,2]=>110101=>[1,1,2,2,1]
[5,4,1,7,6,2,3]=>110110=>[1,1,2,1,2]
[5,4,1,7,6,3,2]=>110111=>[1,1,2,1,1,1]
[5,4,2,1,3,6,7]=>111000=>[1,1,1,4]
[5,4,2,1,3,7,6]=>111001=>[1,1,1,3,1]
[5,4,2,1,6,3,7]=>111010=>[1,1,1,2,2]
[5,4,2,1,6,7,3]=>111001=>[1,1,1,3,1]
[5,4,2,1,7,3,6]=>111010=>[1,1,1,2,2]
[5,4,2,1,7,6,3]=>111011=>[1,1,1,2,1,1]
[5,4,2,3,1,6,7]=>110100=>[1,1,2,3]
[5,4,2,3,1,7,6]=>110101=>[1,1,2,2,1]
[5,4,2,3,6,1,7]=>110010=>[1,1,3,2]
[5,4,2,3,6,7,1]=>110001=>[1,1,4,1]
[5,4,2,3,7,1,6]=>110010=>[1,1,3,2]
[5,4,2,3,7,6,1]=>110011=>[1,1,3,1,1]
[5,4,2,6,1,3,7]=>110100=>[1,1,2,3]
[5,4,2,6,1,7,3]=>110101=>[1,1,2,2,1]
[5,4,2,6,3,1,7]=>110110=>[1,1,2,1,2]
[5,4,2,6,3,7,1]=>110101=>[1,1,2,2,1]
[5,4,2,6,7,1,3]=>110010=>[1,1,3,2]
[5,4,2,6,7,3,1]=>110011=>[1,1,3,1,1]
[5,4,2,7,1,3,6]=>110100=>[1,1,2,3]
[5,4,2,7,1,6,3]=>110101=>[1,1,2,2,1]
[5,4,2,7,3,1,6]=>110110=>[1,1,2,1,2]
[5,4,2,7,3,6,1]=>110101=>[1,1,2,2,1]
[5,4,2,7,6,1,3]=>110110=>[1,1,2,1,2]
[5,4,2,7,6,3,1]=>110111=>[1,1,2,1,1,1]
[5,4,3,1,2,6,7]=>111000=>[1,1,1,4]
[5,4,3,1,2,7,6]=>111001=>[1,1,1,3,1]
[5,4,3,1,6,2,7]=>111010=>[1,1,1,2,2]
[5,4,3,1,6,7,2]=>111001=>[1,1,1,3,1]
[5,4,3,1,7,2,6]=>111010=>[1,1,1,2,2]
[5,4,3,1,7,6,2]=>111011=>[1,1,1,2,1,1]
[5,4,3,2,1,6,7]=>111100=>[1,1,1,1,3]
[5,4,3,2,1,7,6]=>111101=>[1,1,1,1,2,1]
[5,4,3,2,6,1,7]=>111010=>[1,1,1,2,2]
[5,4,3,2,6,7,1]=>111001=>[1,1,1,3,1]
[5,4,3,2,7,1,6]=>111010=>[1,1,1,2,2]
[5,4,3,2,7,6,1]=>111011=>[1,1,1,2,1,1]
[5,4,3,6,1,2,7]=>110100=>[1,1,2,3]
[5,4,3,6,1,7,2]=>110101=>[1,1,2,2,1]
[5,4,3,6,2,1,7]=>110110=>[1,1,2,1,2]
[5,4,3,6,2,7,1]=>110101=>[1,1,2,2,1]
[5,4,3,6,7,1,2]=>110010=>[1,1,3,2]
[5,4,3,6,7,2,1]=>110011=>[1,1,3,1,1]
[5,4,3,7,1,2,6]=>110100=>[1,1,2,3]
[5,4,3,7,1,6,2]=>110101=>[1,1,2,2,1]
[5,4,3,7,2,1,6]=>110110=>[1,1,2,1,2]
[5,4,3,7,2,6,1]=>110101=>[1,1,2,2,1]
[5,4,3,7,6,1,2]=>110110=>[1,1,2,1,2]
[5,4,3,7,6,2,1]=>110111=>[1,1,2,1,1,1]
[5,4,6,1,2,3,7]=>101000=>[1,2,4]
[5,4,6,1,2,7,3]=>101001=>[1,2,3,1]
[5,4,6,1,3,2,7]=>101010=>[1,2,2,2]
[5,4,6,1,3,7,2]=>101001=>[1,2,3,1]
[5,4,6,1,7,2,3]=>101010=>[1,2,2,2]
[5,4,6,1,7,3,2]=>101011=>[1,2,2,1,1]
[5,4,6,2,1,3,7]=>101100=>[1,2,1,3]
[5,4,6,2,1,7,3]=>101101=>[1,2,1,2,1]
[5,4,6,2,3,1,7]=>101010=>[1,2,2,2]
[5,4,6,2,3,7,1]=>101001=>[1,2,3,1]
[5,4,6,2,7,1,3]=>101010=>[1,2,2,2]
[5,4,6,2,7,3,1]=>101011=>[1,2,2,1,1]
[5,4,6,3,1,2,7]=>101100=>[1,2,1,3]
[5,4,6,3,1,7,2]=>101101=>[1,2,1,2,1]
[5,4,6,3,2,1,7]=>101110=>[1,2,1,1,2]
[5,4,6,3,2,7,1]=>101101=>[1,2,1,2,1]
[5,4,6,3,7,1,2]=>101010=>[1,2,2,2]
[5,4,6,3,7,2,1]=>101011=>[1,2,2,1,1]
[5,4,6,7,1,2,3]=>100100=>[1,3,3]
[5,4,6,7,1,3,2]=>100101=>[1,3,2,1]
[5,4,6,7,2,1,3]=>100110=>[1,3,1,2]
[5,4,6,7,2,3,1]=>100101=>[1,3,2,1]
[5,4,6,7,3,1,2]=>100110=>[1,3,1,2]
[5,4,6,7,3,2,1]=>100111=>[1,3,1,1,1]
[5,4,7,1,2,3,6]=>101000=>[1,2,4]
[5,4,7,1,2,6,3]=>101001=>[1,2,3,1]
[5,4,7,1,3,2,6]=>101010=>[1,2,2,2]
[5,4,7,1,3,6,2]=>101001=>[1,2,3,1]
[5,4,7,1,6,2,3]=>101010=>[1,2,2,2]
[5,4,7,1,6,3,2]=>101011=>[1,2,2,1,1]
[5,4,7,2,1,3,6]=>101100=>[1,2,1,3]
[5,4,7,2,1,6,3]=>101101=>[1,2,1,2,1]
[5,4,7,2,3,1,6]=>101010=>[1,2,2,2]
[5,4,7,2,3,6,1]=>101001=>[1,2,3,1]
[5,4,7,2,6,1,3]=>101010=>[1,2,2,2]
[5,4,7,2,6,3,1]=>101011=>[1,2,2,1,1]
[5,4,7,3,1,2,6]=>101100=>[1,2,1,3]
[5,4,7,3,1,6,2]=>101101=>[1,2,1,2,1]
[5,4,7,3,2,1,6]=>101110=>[1,2,1,1,2]
[5,4,7,3,2,6,1]=>101101=>[1,2,1,2,1]
[5,4,7,3,6,1,2]=>101010=>[1,2,2,2]
[5,4,7,3,6,2,1]=>101011=>[1,2,2,1,1]
[5,4,7,6,1,2,3]=>101100=>[1,2,1,3]
[5,4,7,6,1,3,2]=>101101=>[1,2,1,2,1]
[5,4,7,6,2,1,3]=>101110=>[1,2,1,1,2]
[5,4,7,6,2,3,1]=>101101=>[1,2,1,2,1]
[5,4,7,6,3,1,2]=>101110=>[1,2,1,1,2]
[5,4,7,6,3,2,1]=>101111=>[1,2,1,1,1,1]
[5,6,1,2,3,4,7]=>010000=>[2,5]
[5,6,1,2,3,7,4]=>010001=>[2,4,1]
[5,6,1,2,4,3,7]=>010010=>[2,3,2]
[5,6,1,2,4,7,3]=>010001=>[2,4,1]
[5,6,1,2,7,3,4]=>010010=>[2,3,2]
[5,6,1,2,7,4,3]=>010011=>[2,3,1,1]
[5,6,1,3,2,4,7]=>010100=>[2,2,3]
[5,6,1,3,2,7,4]=>010101=>[2,2,2,1]
[5,6,1,3,4,2,7]=>010010=>[2,3,2]
[5,6,1,3,4,7,2]=>010001=>[2,4,1]
[5,6,1,3,7,2,4]=>010010=>[2,3,2]
[5,6,1,3,7,4,2]=>010011=>[2,3,1,1]
[5,6,1,4,2,3,7]=>010100=>[2,2,3]
[5,6,1,4,2,7,3]=>010101=>[2,2,2,1]
[5,6,1,4,3,2,7]=>010110=>[2,2,1,2]
[5,6,1,4,3,7,2]=>010101=>[2,2,2,1]
[5,6,1,4,7,2,3]=>010010=>[2,3,2]
[5,6,1,4,7,3,2]=>010011=>[2,3,1,1]
[5,6,1,7,2,3,4]=>010100=>[2,2,3]
[5,6,1,7,2,4,3]=>010101=>[2,2,2,1]
[5,6,1,7,3,2,4]=>010110=>[2,2,1,2]
[5,6,1,7,3,4,2]=>010101=>[2,2,2,1]
[5,6,1,7,4,2,3]=>010110=>[2,2,1,2]
[5,6,1,7,4,3,2]=>010111=>[2,2,1,1,1]
[5,6,2,1,3,4,7]=>011000=>[2,1,4]
[5,6,2,1,3,7,4]=>011001=>[2,1,3,1]
[5,6,2,1,4,3,7]=>011010=>[2,1,2,2]
[5,6,2,1,4,7,3]=>011001=>[2,1,3,1]
[5,6,2,1,7,3,4]=>011010=>[2,1,2,2]
[5,6,2,1,7,4,3]=>011011=>[2,1,2,1,1]
[5,6,2,3,1,4,7]=>010100=>[2,2,3]
[5,6,2,3,1,7,4]=>010101=>[2,2,2,1]
[5,6,2,3,4,1,7]=>010010=>[2,3,2]
[5,6,2,3,4,7,1]=>010001=>[2,4,1]
[5,6,2,3,7,1,4]=>010010=>[2,3,2]
[5,6,2,3,7,4,1]=>010011=>[2,3,1,1]
[5,6,2,4,1,3,7]=>010100=>[2,2,3]
[5,6,2,4,1,7,3]=>010101=>[2,2,2,1]
[5,6,2,4,3,1,7]=>010110=>[2,2,1,2]
[5,6,2,4,3,7,1]=>010101=>[2,2,2,1]
[5,6,2,4,7,1,3]=>010010=>[2,3,2]
[5,6,2,4,7,3,1]=>010011=>[2,3,1,1]
[5,6,2,7,1,3,4]=>010100=>[2,2,3]
[5,6,2,7,1,4,3]=>010101=>[2,2,2,1]
[5,6,2,7,3,1,4]=>010110=>[2,2,1,2]
[5,6,2,7,3,4,1]=>010101=>[2,2,2,1]
[5,6,2,7,4,1,3]=>010110=>[2,2,1,2]
[5,6,2,7,4,3,1]=>010111=>[2,2,1,1,1]
[5,6,3,1,2,4,7]=>011000=>[2,1,4]
[5,6,3,1,2,7,4]=>011001=>[2,1,3,1]
[5,6,3,1,4,2,7]=>011010=>[2,1,2,2]
[5,6,3,1,4,7,2]=>011001=>[2,1,3,1]
[5,6,3,1,7,2,4]=>011010=>[2,1,2,2]
[5,6,3,1,7,4,2]=>011011=>[2,1,2,1,1]
[5,6,3,2,1,4,7]=>011100=>[2,1,1,3]
[5,6,3,2,1,7,4]=>011101=>[2,1,1,2,1]
[5,6,3,2,4,1,7]=>011010=>[2,1,2,2]
[5,6,3,2,4,7,1]=>011001=>[2,1,3,1]
[5,6,3,2,7,1,4]=>011010=>[2,1,2,2]
[5,6,3,2,7,4,1]=>011011=>[2,1,2,1,1]
[5,6,3,4,1,2,7]=>010100=>[2,2,3]
[5,6,3,4,1,7,2]=>010101=>[2,2,2,1]
[5,6,3,4,2,1,7]=>010110=>[2,2,1,2]
[5,6,3,4,2,7,1]=>010101=>[2,2,2,1]
[5,6,3,4,7,1,2]=>010010=>[2,3,2]
[5,6,3,4,7,2,1]=>010011=>[2,3,1,1]
[5,6,3,7,1,2,4]=>010100=>[2,2,3]
[5,6,3,7,1,4,2]=>010101=>[2,2,2,1]
[5,6,3,7,2,1,4]=>010110=>[2,2,1,2]
[5,6,3,7,2,4,1]=>010101=>[2,2,2,1]
[5,6,3,7,4,1,2]=>010110=>[2,2,1,2]
[5,6,3,7,4,2,1]=>010111=>[2,2,1,1,1]
[5,6,4,1,2,3,7]=>011000=>[2,1,4]
[5,6,4,1,2,7,3]=>011001=>[2,1,3,1]
[5,6,4,1,3,2,7]=>011010=>[2,1,2,2]
[5,6,4,1,3,7,2]=>011001=>[2,1,3,1]
[5,6,4,1,7,2,3]=>011010=>[2,1,2,2]
[5,6,4,1,7,3,2]=>011011=>[2,1,2,1,1]
[5,6,4,2,1,3,7]=>011100=>[2,1,1,3]
[5,6,4,2,1,7,3]=>011101=>[2,1,1,2,1]
[5,6,4,2,3,1,7]=>011010=>[2,1,2,2]
[5,6,4,2,3,7,1]=>011001=>[2,1,3,1]
[5,6,4,2,7,1,3]=>011010=>[2,1,2,2]
[5,6,4,2,7,3,1]=>011011=>[2,1,2,1,1]
[5,6,4,3,1,2,7]=>011100=>[2,1,1,3]
[5,6,4,3,1,7,2]=>011101=>[2,1,1,2,1]
[5,6,4,3,2,1,7]=>011110=>[2,1,1,1,2]
[5,6,4,3,2,7,1]=>011101=>[2,1,1,2,1]
[5,6,4,3,7,1,2]=>011010=>[2,1,2,2]
[5,6,4,3,7,2,1]=>011011=>[2,1,2,1,1]
[5,6,4,7,1,2,3]=>010100=>[2,2,3]
[5,6,4,7,1,3,2]=>010101=>[2,2,2,1]
[5,6,4,7,2,1,3]=>010110=>[2,2,1,2]
[5,6,4,7,2,3,1]=>010101=>[2,2,2,1]
[5,6,4,7,3,1,2]=>010110=>[2,2,1,2]
[5,6,4,7,3,2,1]=>010111=>[2,2,1,1,1]
[5,6,7,1,2,3,4]=>001000=>[3,4]
[5,6,7,1,2,4,3]=>001001=>[3,3,1]
[5,6,7,1,3,2,4]=>001010=>[3,2,2]
[5,6,7,1,3,4,2]=>001001=>[3,3,1]
[5,6,7,1,4,2,3]=>001010=>[3,2,2]
[5,6,7,1,4,3,2]=>001011=>[3,2,1,1]
[5,6,7,2,1,3,4]=>001100=>[3,1,3]
[5,6,7,2,1,4,3]=>001101=>[3,1,2,1]
[5,6,7,2,3,1,4]=>001010=>[3,2,2]
[5,6,7,2,3,4,1]=>001001=>[3,3,1]
[5,6,7,2,4,1,3]=>001010=>[3,2,2]
[5,6,7,2,4,3,1]=>001011=>[3,2,1,1]
[5,6,7,3,1,2,4]=>001100=>[3,1,3]
[5,6,7,3,1,4,2]=>001101=>[3,1,2,1]
[5,6,7,3,2,1,4]=>001110=>[3,1,1,2]
[5,6,7,3,2,4,1]=>001101=>[3,1,2,1]
[5,6,7,3,4,1,2]=>001010=>[3,2,2]
[5,6,7,3,4,2,1]=>001011=>[3,2,1,1]
[5,6,7,4,1,2,3]=>001100=>[3,1,3]
[5,6,7,4,1,3,2]=>001101=>[3,1,2,1]
[5,6,7,4,2,1,3]=>001110=>[3,1,1,2]
[5,6,7,4,2,3,1]=>001101=>[3,1,2,1]
[5,6,7,4,3,1,2]=>001110=>[3,1,1,2]
[5,6,7,4,3,2,1]=>001111=>[3,1,1,1,1]
[5,7,1,2,3,4,6]=>010000=>[2,5]
[5,7,1,2,3,6,4]=>010001=>[2,4,1]
[5,7,1,2,4,3,6]=>010010=>[2,3,2]
[5,7,1,2,4,6,3]=>010001=>[2,4,1]
[5,7,1,2,6,3,4]=>010010=>[2,3,2]
[5,7,1,2,6,4,3]=>010011=>[2,3,1,1]
[5,7,1,3,2,4,6]=>010100=>[2,2,3]
[5,7,1,3,2,6,4]=>010101=>[2,2,2,1]
[5,7,1,3,4,2,6]=>010010=>[2,3,2]
[5,7,1,3,4,6,2]=>010001=>[2,4,1]
[5,7,1,3,6,2,4]=>010010=>[2,3,2]
[5,7,1,3,6,4,2]=>010011=>[2,3,1,1]
[5,7,1,4,2,3,6]=>010100=>[2,2,3]
[5,7,1,4,2,6,3]=>010101=>[2,2,2,1]
[5,7,1,4,3,2,6]=>010110=>[2,2,1,2]
[5,7,1,4,3,6,2]=>010101=>[2,2,2,1]
[5,7,1,4,6,2,3]=>010010=>[2,3,2]
[5,7,1,4,6,3,2]=>010011=>[2,3,1,1]
[5,7,1,6,2,3,4]=>010100=>[2,2,3]
[5,7,1,6,2,4,3]=>010101=>[2,2,2,1]
[5,7,1,6,3,2,4]=>010110=>[2,2,1,2]
[5,7,1,6,3,4,2]=>010101=>[2,2,2,1]
[5,7,1,6,4,2,3]=>010110=>[2,2,1,2]
[5,7,1,6,4,3,2]=>010111=>[2,2,1,1,1]
[5,7,2,1,3,4,6]=>011000=>[2,1,4]
[5,7,2,1,3,6,4]=>011001=>[2,1,3,1]
[5,7,2,1,4,3,6]=>011010=>[2,1,2,2]
[5,7,2,1,4,6,3]=>011001=>[2,1,3,1]
[5,7,2,1,6,3,4]=>011010=>[2,1,2,2]
[5,7,2,1,6,4,3]=>011011=>[2,1,2,1,1]
[5,7,2,3,1,4,6]=>010100=>[2,2,3]
[5,7,2,3,1,6,4]=>010101=>[2,2,2,1]
[5,7,2,3,4,1,6]=>010010=>[2,3,2]
[5,7,2,3,4,6,1]=>010001=>[2,4,1]
[5,7,2,3,6,1,4]=>010010=>[2,3,2]
[5,7,2,3,6,4,1]=>010011=>[2,3,1,1]
[5,7,2,4,1,3,6]=>010100=>[2,2,3]
[5,7,2,4,1,6,3]=>010101=>[2,2,2,1]
[5,7,2,4,3,1,6]=>010110=>[2,2,1,2]
[5,7,2,4,3,6,1]=>010101=>[2,2,2,1]
[5,7,2,4,6,1,3]=>010010=>[2,3,2]
[5,7,2,4,6,3,1]=>010011=>[2,3,1,1]
[5,7,2,6,1,3,4]=>010100=>[2,2,3]
[5,7,2,6,1,4,3]=>010101=>[2,2,2,1]
[5,7,2,6,3,1,4]=>010110=>[2,2,1,2]
[5,7,2,6,3,4,1]=>010101=>[2,2,2,1]
[5,7,2,6,4,1,3]=>010110=>[2,2,1,2]
[5,7,2,6,4,3,1]=>010111=>[2,2,1,1,1]
[5,7,3,1,2,4,6]=>011000=>[2,1,4]
[5,7,3,1,2,6,4]=>011001=>[2,1,3,1]
[5,7,3,1,4,2,6]=>011010=>[2,1,2,2]
[5,7,3,1,4,6,2]=>011001=>[2,1,3,1]
[5,7,3,1,6,2,4]=>011010=>[2,1,2,2]
[5,7,3,1,6,4,2]=>011011=>[2,1,2,1,1]
[5,7,3,2,1,4,6]=>011100=>[2,1,1,3]
[5,7,3,2,1,6,4]=>011101=>[2,1,1,2,1]
[5,7,3,2,4,1,6]=>011010=>[2,1,2,2]
[5,7,3,2,4,6,1]=>011001=>[2,1,3,1]
[5,7,3,2,6,1,4]=>011010=>[2,1,2,2]
[5,7,3,2,6,4,1]=>011011=>[2,1,2,1,1]
[5,7,3,4,1,2,6]=>010100=>[2,2,3]
[5,7,3,4,1,6,2]=>010101=>[2,2,2,1]
[5,7,3,4,2,1,6]=>010110=>[2,2,1,2]
[5,7,3,4,2,6,1]=>010101=>[2,2,2,1]
[5,7,3,4,6,1,2]=>010010=>[2,3,2]
[5,7,3,4,6,2,1]=>010011=>[2,3,1,1]
[5,7,3,6,1,2,4]=>010100=>[2,2,3]
[5,7,3,6,1,4,2]=>010101=>[2,2,2,1]
[5,7,3,6,2,1,4]=>010110=>[2,2,1,2]
[5,7,3,6,2,4,1]=>010101=>[2,2,2,1]
[5,7,3,6,4,1,2]=>010110=>[2,2,1,2]
[5,7,3,6,4,2,1]=>010111=>[2,2,1,1,1]
[5,7,4,1,2,3,6]=>011000=>[2,1,4]
[5,7,4,1,2,6,3]=>011001=>[2,1,3,1]
[5,7,4,1,3,2,6]=>011010=>[2,1,2,2]
[5,7,4,1,3,6,2]=>011001=>[2,1,3,1]
[5,7,4,1,6,2,3]=>011010=>[2,1,2,2]
[5,7,4,1,6,3,2]=>011011=>[2,1,2,1,1]
[5,7,4,2,1,3,6]=>011100=>[2,1,1,3]
[5,7,4,2,1,6,3]=>011101=>[2,1,1,2,1]
[5,7,4,2,3,1,6]=>011010=>[2,1,2,2]
[5,7,4,2,3,6,1]=>011001=>[2,1,3,1]
[5,7,4,2,6,1,3]=>011010=>[2,1,2,2]
[5,7,4,2,6,3,1]=>011011=>[2,1,2,1,1]
[5,7,4,3,1,2,6]=>011100=>[2,1,1,3]
[5,7,4,3,1,6,2]=>011101=>[2,1,1,2,1]
[5,7,4,3,2,1,6]=>011110=>[2,1,1,1,2]
[5,7,4,3,2,6,1]=>011101=>[2,1,1,2,1]
[5,7,4,3,6,1,2]=>011010=>[2,1,2,2]
[5,7,4,3,6,2,1]=>011011=>[2,1,2,1,1]
[5,7,4,6,1,2,3]=>010100=>[2,2,3]
[5,7,4,6,1,3,2]=>010101=>[2,2,2,1]
[5,7,4,6,2,1,3]=>010110=>[2,2,1,2]
[5,7,4,6,2,3,1]=>010101=>[2,2,2,1]
[5,7,4,6,3,1,2]=>010110=>[2,2,1,2]
[5,7,4,6,3,2,1]=>010111=>[2,2,1,1,1]
[5,7,6,1,2,3,4]=>011000=>[2,1,4]
[5,7,6,1,2,4,3]=>011001=>[2,1,3,1]
[5,7,6,1,3,2,4]=>011010=>[2,1,2,2]
[5,7,6,1,3,4,2]=>011001=>[2,1,3,1]
[5,7,6,1,4,2,3]=>011010=>[2,1,2,2]
[5,7,6,1,4,3,2]=>011011=>[2,1,2,1,1]
[5,7,6,2,1,3,4]=>011100=>[2,1,1,3]
[5,7,6,2,1,4,3]=>011101=>[2,1,1,2,1]
[5,7,6,2,3,1,4]=>011010=>[2,1,2,2]
[5,7,6,2,3,4,1]=>011001=>[2,1,3,1]
[5,7,6,2,4,1,3]=>011010=>[2,1,2,2]
[5,7,6,2,4,3,1]=>011011=>[2,1,2,1,1]
[5,7,6,3,1,2,4]=>011100=>[2,1,1,3]
[5,7,6,3,1,4,2]=>011101=>[2,1,1,2,1]
[5,7,6,3,2,1,4]=>011110=>[2,1,1,1,2]
[5,7,6,3,2,4,1]=>011101=>[2,1,1,2,1]
[5,7,6,3,4,1,2]=>011010=>[2,1,2,2]
[5,7,6,3,4,2,1]=>011011=>[2,1,2,1,1]
[5,7,6,4,1,2,3]=>011100=>[2,1,1,3]
[5,7,6,4,1,3,2]=>011101=>[2,1,1,2,1]
[5,7,6,4,2,1,3]=>011110=>[2,1,1,1,2]
[5,7,6,4,2,3,1]=>011101=>[2,1,1,2,1]
[5,7,6,4,3,1,2]=>011110=>[2,1,1,1,2]
[5,7,6,4,3,2,1]=>011111=>[2,1,1,1,1,1]
[6,1,2,3,4,5,7]=>100000=>[1,6]
[6,1,2,3,4,7,5]=>100001=>[1,5,1]
[6,1,2,3,5,4,7]=>100010=>[1,4,2]
[6,1,2,3,5,7,4]=>100001=>[1,5,1]
[6,1,2,3,7,4,5]=>100010=>[1,4,2]
[6,1,2,3,7,5,4]=>100011=>[1,4,1,1]
[6,1,2,4,3,5,7]=>100100=>[1,3,3]
[6,1,2,4,3,7,5]=>100101=>[1,3,2,1]
[6,1,2,4,5,3,7]=>100010=>[1,4,2]
[6,1,2,4,5,7,3]=>100001=>[1,5,1]
[6,1,2,4,7,3,5]=>100010=>[1,4,2]
[6,1,2,4,7,5,3]=>100011=>[1,4,1,1]
[6,1,2,5,3,4,7]=>100100=>[1,3,3]
[6,1,2,5,3,7,4]=>100101=>[1,3,2,1]
[6,1,2,5,4,3,7]=>100110=>[1,3,1,2]
[6,1,2,5,4,7,3]=>100101=>[1,3,2,1]
[6,1,2,5,7,3,4]=>100010=>[1,4,2]
[6,1,2,5,7,4,3]=>100011=>[1,4,1,1]
[6,1,2,7,3,4,5]=>100100=>[1,3,3]
[6,1,2,7,3,5,4]=>100101=>[1,3,2,1]
[6,1,2,7,4,3,5]=>100110=>[1,3,1,2]
[6,1,2,7,4,5,3]=>100101=>[1,3,2,1]
[6,1,2,7,5,3,4]=>100110=>[1,3,1,2]
[6,1,2,7,5,4,3]=>100111=>[1,3,1,1,1]
[6,1,3,2,4,5,7]=>101000=>[1,2,4]
[6,1,3,2,4,7,5]=>101001=>[1,2,3,1]
[6,1,3,2,5,4,7]=>101010=>[1,2,2,2]
[6,1,3,2,5,7,4]=>101001=>[1,2,3,1]
[6,1,3,2,7,4,5]=>101010=>[1,2,2,2]
[6,1,3,2,7,5,4]=>101011=>[1,2,2,1,1]
[6,1,3,4,2,5,7]=>100100=>[1,3,3]
[6,1,3,4,2,7,5]=>100101=>[1,3,2,1]
[6,1,3,4,5,2,7]=>100010=>[1,4,2]
[6,1,3,4,5,7,2]=>100001=>[1,5,1]
[6,1,3,4,7,2,5]=>100010=>[1,4,2]
[6,1,3,4,7,5,2]=>100011=>[1,4,1,1]
[6,1,3,5,2,4,7]=>100100=>[1,3,3]
[6,1,3,5,2,7,4]=>100101=>[1,3,2,1]
[6,1,3,5,4,2,7]=>100110=>[1,3,1,2]
[6,1,3,5,4,7,2]=>100101=>[1,3,2,1]
[6,1,3,5,7,2,4]=>100010=>[1,4,2]
[6,1,3,5,7,4,2]=>100011=>[1,4,1,1]
[6,1,3,7,2,4,5]=>100100=>[1,3,3]
[6,1,3,7,2,5,4]=>100101=>[1,3,2,1]
[6,1,3,7,4,2,5]=>100110=>[1,3,1,2]
[6,1,3,7,4,5,2]=>100101=>[1,3,2,1]
[6,1,3,7,5,2,4]=>100110=>[1,3,1,2]
[6,1,3,7,5,4,2]=>100111=>[1,3,1,1,1]
[6,1,4,2,3,5,7]=>101000=>[1,2,4]
[6,1,4,2,3,7,5]=>101001=>[1,2,3,1]
[6,1,4,2,5,3,7]=>101010=>[1,2,2,2]
[6,1,4,2,5,7,3]=>101001=>[1,2,3,1]
[6,1,4,2,7,3,5]=>101010=>[1,2,2,2]
[6,1,4,2,7,5,3]=>101011=>[1,2,2,1,1]
[6,1,4,3,2,5,7]=>101100=>[1,2,1,3]
[6,1,4,3,2,7,5]=>101101=>[1,2,1,2,1]
[6,1,4,3,5,2,7]=>101010=>[1,2,2,2]
[6,1,4,3,5,7,2]=>101001=>[1,2,3,1]
[6,1,4,3,7,2,5]=>101010=>[1,2,2,2]
[6,1,4,3,7,5,2]=>101011=>[1,2,2,1,1]
[6,1,4,5,2,3,7]=>100100=>[1,3,3]
[6,1,4,5,2,7,3]=>100101=>[1,3,2,1]
[6,1,4,5,3,2,7]=>100110=>[1,3,1,2]
[6,1,4,5,3,7,2]=>100101=>[1,3,2,1]
[6,1,4,5,7,2,3]=>100010=>[1,4,2]
[6,1,4,5,7,3,2]=>100011=>[1,4,1,1]
[6,1,4,7,2,3,5]=>100100=>[1,3,3]
[6,1,4,7,2,5,3]=>100101=>[1,3,2,1]
[6,1,4,7,3,2,5]=>100110=>[1,3,1,2]
[6,1,4,7,3,5,2]=>100101=>[1,3,2,1]
[6,1,4,7,5,2,3]=>100110=>[1,3,1,2]
[6,1,4,7,5,3,2]=>100111=>[1,3,1,1,1]
[6,1,5,2,3,4,7]=>101000=>[1,2,4]
[6,1,5,2,3,7,4]=>101001=>[1,2,3,1]
[6,1,5,2,4,3,7]=>101010=>[1,2,2,2]
[6,1,5,2,4,7,3]=>101001=>[1,2,3,1]
[6,1,5,2,7,3,4]=>101010=>[1,2,2,2]
[6,1,5,2,7,4,3]=>101011=>[1,2,2,1,1]
[6,1,5,3,2,4,7]=>101100=>[1,2,1,3]
[6,1,5,3,2,7,4]=>101101=>[1,2,1,2,1]
[6,1,5,3,4,2,7]=>101010=>[1,2,2,2]
[6,1,5,3,4,7,2]=>101001=>[1,2,3,1]
[6,1,5,3,7,2,4]=>101010=>[1,2,2,2]
[6,1,5,3,7,4,2]=>101011=>[1,2,2,1,1]
[6,1,5,4,2,3,7]=>101100=>[1,2,1,3]
[6,1,5,4,2,7,3]=>101101=>[1,2,1,2,1]
[6,1,5,4,3,2,7]=>101110=>[1,2,1,1,2]
[6,1,5,4,3,7,2]=>101101=>[1,2,1,2,1]
[6,1,5,4,7,2,3]=>101010=>[1,2,2,2]
[6,1,5,4,7,3,2]=>101011=>[1,2,2,1,1]
[6,1,5,7,2,3,4]=>100100=>[1,3,3]
[6,1,5,7,2,4,3]=>100101=>[1,3,2,1]
[6,1,5,7,3,2,4]=>100110=>[1,3,1,2]
[6,1,5,7,3,4,2]=>100101=>[1,3,2,1]
[6,1,5,7,4,2,3]=>100110=>[1,3,1,2]
[6,1,5,7,4,3,2]=>100111=>[1,3,1,1,1]
[6,1,7,2,3,4,5]=>101000=>[1,2,4]
[6,1,7,2,3,5,4]=>101001=>[1,2,3,1]
[6,1,7,2,4,3,5]=>101010=>[1,2,2,2]
[6,1,7,2,4,5,3]=>101001=>[1,2,3,1]
[6,1,7,2,5,3,4]=>101010=>[1,2,2,2]
[6,1,7,2,5,4,3]=>101011=>[1,2,2,1,1]
[6,1,7,3,2,4,5]=>101100=>[1,2,1,3]
[6,1,7,3,2,5,4]=>101101=>[1,2,1,2,1]
[6,1,7,3,4,2,5]=>101010=>[1,2,2,2]
[6,1,7,3,4,5,2]=>101001=>[1,2,3,1]
[6,1,7,3,5,2,4]=>101010=>[1,2,2,2]
[6,1,7,3,5,4,2]=>101011=>[1,2,2,1,1]
[6,1,7,4,2,3,5]=>101100=>[1,2,1,3]
[6,1,7,4,2,5,3]=>101101=>[1,2,1,2,1]
[6,1,7,4,3,2,5]=>101110=>[1,2,1,1,2]
[6,1,7,4,3,5,2]=>101101=>[1,2,1,2,1]
[6,1,7,4,5,2,3]=>101010=>[1,2,2,2]
[6,1,7,4,5,3,2]=>101011=>[1,2,2,1,1]
[6,1,7,5,2,3,4]=>101100=>[1,2,1,3]
[6,1,7,5,2,4,3]=>101101=>[1,2,1,2,1]
[6,1,7,5,3,2,4]=>101110=>[1,2,1,1,2]
[6,1,7,5,3,4,2]=>101101=>[1,2,1,2,1]
[6,1,7,5,4,2,3]=>101110=>[1,2,1,1,2]
[6,1,7,5,4,3,2]=>101111=>[1,2,1,1,1,1]
[6,2,1,3,4,5,7]=>110000=>[1,1,5]
[6,2,1,3,4,7,5]=>110001=>[1,1,4,1]
[6,2,1,3,5,4,7]=>110010=>[1,1,3,2]
[6,2,1,3,5,7,4]=>110001=>[1,1,4,1]
[6,2,1,3,7,4,5]=>110010=>[1,1,3,2]
[6,2,1,3,7,5,4]=>110011=>[1,1,3,1,1]
[6,2,1,4,3,5,7]=>110100=>[1,1,2,3]
[6,2,1,4,3,7,5]=>110101=>[1,1,2,2,1]
[6,2,1,4,5,3,7]=>110010=>[1,1,3,2]
[6,2,1,4,5,7,3]=>110001=>[1,1,4,1]
[6,2,1,4,7,3,5]=>110010=>[1,1,3,2]
[6,2,1,4,7,5,3]=>110011=>[1,1,3,1,1]
[6,2,1,5,3,4,7]=>110100=>[1,1,2,3]
[6,2,1,5,3,7,4]=>110101=>[1,1,2,2,1]
[6,2,1,5,4,3,7]=>110110=>[1,1,2,1,2]
[6,2,1,5,4,7,3]=>110101=>[1,1,2,2,1]
[6,2,1,5,7,3,4]=>110010=>[1,1,3,2]
[6,2,1,5,7,4,3]=>110011=>[1,1,3,1,1]
[6,2,1,7,3,4,5]=>110100=>[1,1,2,3]
[6,2,1,7,3,5,4]=>110101=>[1,1,2,2,1]
[6,2,1,7,4,3,5]=>110110=>[1,1,2,1,2]
[6,2,1,7,4,5,3]=>110101=>[1,1,2,2,1]
[6,2,1,7,5,3,4]=>110110=>[1,1,2,1,2]
[6,2,1,7,5,4,3]=>110111=>[1,1,2,1,1,1]
[6,2,3,1,4,5,7]=>101000=>[1,2,4]
[6,2,3,1,4,7,5]=>101001=>[1,2,3,1]
[6,2,3,1,5,4,7]=>101010=>[1,2,2,2]
[6,2,3,1,5,7,4]=>101001=>[1,2,3,1]
[6,2,3,1,7,4,5]=>101010=>[1,2,2,2]
[6,2,3,1,7,5,4]=>101011=>[1,2,2,1,1]
[6,2,3,4,1,5,7]=>100100=>[1,3,3]
[6,2,3,4,1,7,5]=>100101=>[1,3,2,1]
[6,2,3,4,5,1,7]=>100010=>[1,4,2]
[6,2,3,4,5,7,1]=>100001=>[1,5,1]
[6,2,3,4,7,1,5]=>100010=>[1,4,2]
[6,2,3,4,7,5,1]=>100011=>[1,4,1,1]
[6,2,3,5,1,4,7]=>100100=>[1,3,3]
[6,2,3,5,1,7,4]=>100101=>[1,3,2,1]
[6,2,3,5,4,1,7]=>100110=>[1,3,1,2]
[6,2,3,5,4,7,1]=>100101=>[1,3,2,1]
[6,2,3,5,7,1,4]=>100010=>[1,4,2]
[6,2,3,5,7,4,1]=>100011=>[1,4,1,1]
[6,2,3,7,1,4,5]=>100100=>[1,3,3]
[6,2,3,7,1,5,4]=>100101=>[1,3,2,1]
[6,2,3,7,4,1,5]=>100110=>[1,3,1,2]
[6,2,3,7,4,5,1]=>100101=>[1,3,2,1]
[6,2,3,7,5,1,4]=>100110=>[1,3,1,2]
[6,2,3,7,5,4,1]=>100111=>[1,3,1,1,1]
[6,2,4,1,3,5,7]=>101000=>[1,2,4]
[6,2,4,1,3,7,5]=>101001=>[1,2,3,1]
[6,2,4,1,5,3,7]=>101010=>[1,2,2,2]
[6,2,4,1,5,7,3]=>101001=>[1,2,3,1]
[6,2,4,1,7,3,5]=>101010=>[1,2,2,2]
[6,2,4,1,7,5,3]=>101011=>[1,2,2,1,1]
[6,2,4,3,1,5,7]=>101100=>[1,2,1,3]
[6,2,4,3,1,7,5]=>101101=>[1,2,1,2,1]
[6,2,4,3,5,1,7]=>101010=>[1,2,2,2]
[6,2,4,3,5,7,1]=>101001=>[1,2,3,1]
[6,2,4,3,7,1,5]=>101010=>[1,2,2,2]
[6,2,4,3,7,5,1]=>101011=>[1,2,2,1,1]
[6,2,4,5,1,3,7]=>100100=>[1,3,3]
[6,2,4,5,1,7,3]=>100101=>[1,3,2,1]
[6,2,4,5,3,1,7]=>100110=>[1,3,1,2]
[6,2,4,5,3,7,1]=>100101=>[1,3,2,1]
[6,2,4,5,7,1,3]=>100010=>[1,4,2]
[6,2,4,5,7,3,1]=>100011=>[1,4,1,1]
[6,2,4,7,1,3,5]=>100100=>[1,3,3]
[6,2,4,7,1,5,3]=>100101=>[1,3,2,1]
[6,2,4,7,3,1,5]=>100110=>[1,3,1,2]
[6,2,4,7,3,5,1]=>100101=>[1,3,2,1]
[6,2,4,7,5,1,3]=>100110=>[1,3,1,2]
[6,2,4,7,5,3,1]=>100111=>[1,3,1,1,1]
[6,2,5,1,3,4,7]=>101000=>[1,2,4]
[6,2,5,1,3,7,4]=>101001=>[1,2,3,1]
[6,2,5,1,4,3,7]=>101010=>[1,2,2,2]
[6,2,5,1,4,7,3]=>101001=>[1,2,3,1]
[6,2,5,1,7,3,4]=>101010=>[1,2,2,2]
[6,2,5,1,7,4,3]=>101011=>[1,2,2,1,1]
[6,2,5,3,1,4,7]=>101100=>[1,2,1,3]
[6,2,5,3,1,7,4]=>101101=>[1,2,1,2,1]
[6,2,5,3,4,1,7]=>101010=>[1,2,2,2]
[6,2,5,3,4,7,1]=>101001=>[1,2,3,1]
[6,2,5,3,7,1,4]=>101010=>[1,2,2,2]
[6,2,5,3,7,4,1]=>101011=>[1,2,2,1,1]
[6,2,5,4,1,3,7]=>101100=>[1,2,1,3]
[6,2,5,4,1,7,3]=>101101=>[1,2,1,2,1]
[6,2,5,4,3,1,7]=>101110=>[1,2,1,1,2]
[6,2,5,4,3,7,1]=>101101=>[1,2,1,2,1]
[6,2,5,4,7,1,3]=>101010=>[1,2,2,2]
[6,2,5,4,7,3,1]=>101011=>[1,2,2,1,1]
[6,2,5,7,1,3,4]=>100100=>[1,3,3]
[6,2,5,7,1,4,3]=>100101=>[1,3,2,1]
[6,2,5,7,3,1,4]=>100110=>[1,3,1,2]
[6,2,5,7,3,4,1]=>100101=>[1,3,2,1]
[6,2,5,7,4,1,3]=>100110=>[1,3,1,2]
[6,2,5,7,4,3,1]=>100111=>[1,3,1,1,1]
[6,2,7,1,3,4,5]=>101000=>[1,2,4]
[6,2,7,1,3,5,4]=>101001=>[1,2,3,1]
[6,2,7,1,4,3,5]=>101010=>[1,2,2,2]
[6,2,7,1,4,5,3]=>101001=>[1,2,3,1]
[6,2,7,1,5,3,4]=>101010=>[1,2,2,2]
[6,2,7,1,5,4,3]=>101011=>[1,2,2,1,1]
[6,2,7,3,1,4,5]=>101100=>[1,2,1,3]
[6,2,7,3,1,5,4]=>101101=>[1,2,1,2,1]
[6,2,7,3,4,1,5]=>101010=>[1,2,2,2]
[6,2,7,3,4,5,1]=>101001=>[1,2,3,1]
[6,2,7,3,5,1,4]=>101010=>[1,2,2,2]
[6,2,7,3,5,4,1]=>101011=>[1,2,2,1,1]
[6,2,7,4,1,3,5]=>101100=>[1,2,1,3]
[6,2,7,4,1,5,3]=>101101=>[1,2,1,2,1]
[6,2,7,4,3,1,5]=>101110=>[1,2,1,1,2]
[6,2,7,4,3,5,1]=>101101=>[1,2,1,2,1]
[6,2,7,4,5,1,3]=>101010=>[1,2,2,2]
[6,2,7,4,5,3,1]=>101011=>[1,2,2,1,1]
[6,2,7,5,1,3,4]=>101100=>[1,2,1,3]
[6,2,7,5,1,4,3]=>101101=>[1,2,1,2,1]
[6,2,7,5,3,1,4]=>101110=>[1,2,1,1,2]
[6,2,7,5,3,4,1]=>101101=>[1,2,1,2,1]
[6,2,7,5,4,1,3]=>101110=>[1,2,1,1,2]
[6,2,7,5,4,3,1]=>101111=>[1,2,1,1,1,1]
[6,3,1,2,4,5,7]=>110000=>[1,1,5]
[6,3,1,2,4,7,5]=>110001=>[1,1,4,1]
[6,3,1,2,5,4,7]=>110010=>[1,1,3,2]
[6,3,1,2,5,7,4]=>110001=>[1,1,4,1]
[6,3,1,2,7,4,5]=>110010=>[1,1,3,2]
[6,3,1,2,7,5,4]=>110011=>[1,1,3,1,1]
[6,3,1,4,2,5,7]=>110100=>[1,1,2,3]
[6,3,1,4,2,7,5]=>110101=>[1,1,2,2,1]
[6,3,1,4,5,2,7]=>110010=>[1,1,3,2]
[6,3,1,4,5,7,2]=>110001=>[1,1,4,1]
[6,3,1,4,7,2,5]=>110010=>[1,1,3,2]
[6,3,1,4,7,5,2]=>110011=>[1,1,3,1,1]
[6,3,1,5,2,4,7]=>110100=>[1,1,2,3]
[6,3,1,5,2,7,4]=>110101=>[1,1,2,2,1]
[6,3,1,5,4,2,7]=>110110=>[1,1,2,1,2]
[6,3,1,5,4,7,2]=>110101=>[1,1,2,2,1]
[6,3,1,5,7,2,4]=>110010=>[1,1,3,2]
[6,3,1,5,7,4,2]=>110011=>[1,1,3,1,1]
[6,3,1,7,2,4,5]=>110100=>[1,1,2,3]
[6,3,1,7,2,5,4]=>110101=>[1,1,2,2,1]
[6,3,1,7,4,2,5]=>110110=>[1,1,2,1,2]
[6,3,1,7,4,5,2]=>110101=>[1,1,2,2,1]
[6,3,1,7,5,2,4]=>110110=>[1,1,2,1,2]
[6,3,1,7,5,4,2]=>110111=>[1,1,2,1,1,1]
[6,3,2,1,4,5,7]=>111000=>[1,1,1,4]
[6,3,2,1,4,7,5]=>111001=>[1,1,1,3,1]
[6,3,2,1,5,4,7]=>111010=>[1,1,1,2,2]
[6,3,2,1,5,7,4]=>111001=>[1,1,1,3,1]
[6,3,2,1,7,4,5]=>111010=>[1,1,1,2,2]
[6,3,2,1,7,5,4]=>111011=>[1,1,1,2,1,1]
[6,3,2,4,1,5,7]=>110100=>[1,1,2,3]
[6,3,2,4,1,7,5]=>110101=>[1,1,2,2,1]
[6,3,2,4,5,1,7]=>110010=>[1,1,3,2]
[6,3,2,4,5,7,1]=>110001=>[1,1,4,1]
[6,3,2,4,7,1,5]=>110010=>[1,1,3,2]
[6,3,2,4,7,5,1]=>110011=>[1,1,3,1,1]
[6,3,2,5,1,4,7]=>110100=>[1,1,2,3]
[6,3,2,5,1,7,4]=>110101=>[1,1,2,2,1]
[6,3,2,5,4,1,7]=>110110=>[1,1,2,1,2]
[6,3,2,5,4,7,1]=>110101=>[1,1,2,2,1]
[6,3,2,5,7,1,4]=>110010=>[1,1,3,2]
[6,3,2,5,7,4,1]=>110011=>[1,1,3,1,1]
[6,3,2,7,1,4,5]=>110100=>[1,1,2,3]
[6,3,2,7,1,5,4]=>110101=>[1,1,2,2,1]
[6,3,2,7,4,1,5]=>110110=>[1,1,2,1,2]
[6,3,2,7,4,5,1]=>110101=>[1,1,2,2,1]
[6,3,2,7,5,1,4]=>110110=>[1,1,2,1,2]
[6,3,2,7,5,4,1]=>110111=>[1,1,2,1,1,1]
[6,3,4,1,2,5,7]=>101000=>[1,2,4]
[6,3,4,1,2,7,5]=>101001=>[1,2,3,1]
[6,3,4,1,5,2,7]=>101010=>[1,2,2,2]
[6,3,4,1,5,7,2]=>101001=>[1,2,3,1]
[6,3,4,1,7,2,5]=>101010=>[1,2,2,2]
[6,3,4,1,7,5,2]=>101011=>[1,2,2,1,1]
[6,3,4,2,1,5,7]=>101100=>[1,2,1,3]
[6,3,4,2,1,7,5]=>101101=>[1,2,1,2,1]
[6,3,4,2,5,1,7]=>101010=>[1,2,2,2]
[6,3,4,2,5,7,1]=>101001=>[1,2,3,1]
[6,3,4,2,7,1,5]=>101010=>[1,2,2,2]
[6,3,4,2,7,5,1]=>101011=>[1,2,2,1,1]
[6,3,4,5,1,2,7]=>100100=>[1,3,3]
[6,3,4,5,1,7,2]=>100101=>[1,3,2,1]
[6,3,4,5,2,1,7]=>100110=>[1,3,1,2]
[6,3,4,5,2,7,1]=>100101=>[1,3,2,1]
[6,3,4,5,7,1,2]=>100010=>[1,4,2]
[6,3,4,5,7,2,1]=>100011=>[1,4,1,1]
[6,3,4,7,1,2,5]=>100100=>[1,3,3]
[6,3,4,7,1,5,2]=>100101=>[1,3,2,1]
[6,3,4,7,2,1,5]=>100110=>[1,3,1,2]
[6,3,4,7,2,5,1]=>100101=>[1,3,2,1]
[6,3,4,7,5,1,2]=>100110=>[1,3,1,2]
[6,3,4,7,5,2,1]=>100111=>[1,3,1,1,1]
[6,3,5,1,2,4,7]=>101000=>[1,2,4]
[6,3,5,1,2,7,4]=>101001=>[1,2,3,1]
[6,3,5,1,4,2,7]=>101010=>[1,2,2,2]
[6,3,5,1,4,7,2]=>101001=>[1,2,3,1]
[6,3,5,1,7,2,4]=>101010=>[1,2,2,2]
[6,3,5,1,7,4,2]=>101011=>[1,2,2,1,1]
[6,3,5,2,1,4,7]=>101100=>[1,2,1,3]
[6,3,5,2,1,7,4]=>101101=>[1,2,1,2,1]
[6,3,5,2,4,1,7]=>101010=>[1,2,2,2]
[6,3,5,2,4,7,1]=>101001=>[1,2,3,1]
[6,3,5,2,7,1,4]=>101010=>[1,2,2,2]
[6,3,5,2,7,4,1]=>101011=>[1,2,2,1,1]
[6,3,5,4,1,2,7]=>101100=>[1,2,1,3]
[6,3,5,4,1,7,2]=>101101=>[1,2,1,2,1]
[6,3,5,4,2,1,7]=>101110=>[1,2,1,1,2]
[6,3,5,4,2,7,1]=>101101=>[1,2,1,2,1]
[6,3,5,4,7,1,2]=>101010=>[1,2,2,2]
[6,3,5,4,7,2,1]=>101011=>[1,2,2,1,1]
[6,3,5,7,1,2,4]=>100100=>[1,3,3]
[6,3,5,7,1,4,2]=>100101=>[1,3,2,1]
[6,3,5,7,2,1,4]=>100110=>[1,3,1,2]
[6,3,5,7,2,4,1]=>100101=>[1,3,2,1]
[6,3,5,7,4,1,2]=>100110=>[1,3,1,2]
[6,3,5,7,4,2,1]=>100111=>[1,3,1,1,1]
[6,3,7,1,2,4,5]=>101000=>[1,2,4]
[6,3,7,1,2,5,4]=>101001=>[1,2,3,1]
[6,3,7,1,4,2,5]=>101010=>[1,2,2,2]
[6,3,7,1,4,5,2]=>101001=>[1,2,3,1]
[6,3,7,1,5,2,4]=>101010=>[1,2,2,2]
[6,3,7,1,5,4,2]=>101011=>[1,2,2,1,1]
[6,3,7,2,1,4,5]=>101100=>[1,2,1,3]
[6,3,7,2,1,5,4]=>101101=>[1,2,1,2,1]
[6,3,7,2,4,1,5]=>101010=>[1,2,2,2]
[6,3,7,2,4,5,1]=>101001=>[1,2,3,1]
[6,3,7,2,5,1,4]=>101010=>[1,2,2,2]
[6,3,7,2,5,4,1]=>101011=>[1,2,2,1,1]
[6,3,7,4,1,2,5]=>101100=>[1,2,1,3]
[6,3,7,4,1,5,2]=>101101=>[1,2,1,2,1]
[6,3,7,4,2,1,5]=>101110=>[1,2,1,1,2]
[6,3,7,4,2,5,1]=>101101=>[1,2,1,2,1]
[6,3,7,4,5,1,2]=>101010=>[1,2,2,2]
[6,3,7,4,5,2,1]=>101011=>[1,2,2,1,1]
[6,3,7,5,1,2,4]=>101100=>[1,2,1,3]
[6,3,7,5,1,4,2]=>101101=>[1,2,1,2,1]
[6,3,7,5,2,1,4]=>101110=>[1,2,1,1,2]
[6,3,7,5,2,4,1]=>101101=>[1,2,1,2,1]
[6,3,7,5,4,1,2]=>101110=>[1,2,1,1,2]
[6,3,7,5,4,2,1]=>101111=>[1,2,1,1,1,1]
[6,4,1,2,3,5,7]=>110000=>[1,1,5]
[6,4,1,2,3,7,5]=>110001=>[1,1,4,1]
[6,4,1,2,5,3,7]=>110010=>[1,1,3,2]
[6,4,1,2,5,7,3]=>110001=>[1,1,4,1]
[6,4,1,2,7,3,5]=>110010=>[1,1,3,2]
[6,4,1,2,7,5,3]=>110011=>[1,1,3,1,1]
[6,4,1,3,2,5,7]=>110100=>[1,1,2,3]
[6,4,1,3,2,7,5]=>110101=>[1,1,2,2,1]
[6,4,1,3,5,2,7]=>110010=>[1,1,3,2]
[6,4,1,3,5,7,2]=>110001=>[1,1,4,1]
[6,4,1,3,7,2,5]=>110010=>[1,1,3,2]
[6,4,1,3,7,5,2]=>110011=>[1,1,3,1,1]
[6,4,1,5,2,3,7]=>110100=>[1,1,2,3]
[6,4,1,5,2,7,3]=>110101=>[1,1,2,2,1]
[6,4,1,5,3,2,7]=>110110=>[1,1,2,1,2]
[6,4,1,5,3,7,2]=>110101=>[1,1,2,2,1]
[6,4,1,5,7,2,3]=>110010=>[1,1,3,2]
[6,4,1,5,7,3,2]=>110011=>[1,1,3,1,1]
[6,4,1,7,2,3,5]=>110100=>[1,1,2,3]
[6,4,1,7,2,5,3]=>110101=>[1,1,2,2,1]
[6,4,1,7,3,2,5]=>110110=>[1,1,2,1,2]
[6,4,1,7,3,5,2]=>110101=>[1,1,2,2,1]
[6,4,1,7,5,2,3]=>110110=>[1,1,2,1,2]
[6,4,1,7,5,3,2]=>110111=>[1,1,2,1,1,1]
[6,4,2,1,3,5,7]=>111000=>[1,1,1,4]
[6,4,2,1,3,7,5]=>111001=>[1,1,1,3,1]
[6,4,2,1,5,3,7]=>111010=>[1,1,1,2,2]
[6,4,2,1,5,7,3]=>111001=>[1,1,1,3,1]
[6,4,2,1,7,3,5]=>111010=>[1,1,1,2,2]
[6,4,2,1,7,5,3]=>111011=>[1,1,1,2,1,1]
[6,4,2,3,1,5,7]=>110100=>[1,1,2,3]
[6,4,2,3,1,7,5]=>110101=>[1,1,2,2,1]
[6,4,2,3,5,1,7]=>110010=>[1,1,3,2]
[6,4,2,3,5,7,1]=>110001=>[1,1,4,1]
[6,4,2,3,7,1,5]=>110010=>[1,1,3,2]
[6,4,2,3,7,5,1]=>110011=>[1,1,3,1,1]
[6,4,2,5,1,3,7]=>110100=>[1,1,2,3]
[6,4,2,5,1,7,3]=>110101=>[1,1,2,2,1]
[6,4,2,5,3,1,7]=>110110=>[1,1,2,1,2]
[6,4,2,5,3,7,1]=>110101=>[1,1,2,2,1]
[6,4,2,5,7,1,3]=>110010=>[1,1,3,2]
[6,4,2,5,7,3,1]=>110011=>[1,1,3,1,1]
[6,4,2,7,1,3,5]=>110100=>[1,1,2,3]
[6,4,2,7,1,5,3]=>110101=>[1,1,2,2,1]
[6,4,2,7,3,1,5]=>110110=>[1,1,2,1,2]
[6,4,2,7,3,5,1]=>110101=>[1,1,2,2,1]
[6,4,2,7,5,1,3]=>110110=>[1,1,2,1,2]
[6,4,2,7,5,3,1]=>110111=>[1,1,2,1,1,1]
[6,4,3,1,2,5,7]=>111000=>[1,1,1,4]
[6,4,3,1,2,7,5]=>111001=>[1,1,1,3,1]
[6,4,3,1,5,2,7]=>111010=>[1,1,1,2,2]
[6,4,3,1,5,7,2]=>111001=>[1,1,1,3,1]
[6,4,3,1,7,2,5]=>111010=>[1,1,1,2,2]
[6,4,3,1,7,5,2]=>111011=>[1,1,1,2,1,1]
[6,4,3,2,1,5,7]=>111100=>[1,1,1,1,3]
[6,4,3,2,1,7,5]=>111101=>[1,1,1,1,2,1]
[6,4,3,2,5,1,7]=>111010=>[1,1,1,2,2]
[6,4,3,2,5,7,1]=>111001=>[1,1,1,3,1]
[6,4,3,2,7,1,5]=>111010=>[1,1,1,2,2]
[6,4,3,2,7,5,1]=>111011=>[1,1,1,2,1,1]
[6,4,3,5,1,2,7]=>110100=>[1,1,2,3]
[6,4,3,5,1,7,2]=>110101=>[1,1,2,2,1]
[6,4,3,5,2,1,7]=>110110=>[1,1,2,1,2]
[6,4,3,5,2,7,1]=>110101=>[1,1,2,2,1]
[6,4,3,5,7,1,2]=>110010=>[1,1,3,2]
[6,4,3,5,7,2,1]=>110011=>[1,1,3,1,1]
[6,4,3,7,1,2,5]=>110100=>[1,1,2,3]
[6,4,3,7,1,5,2]=>110101=>[1,1,2,2,1]
[6,4,3,7,2,1,5]=>110110=>[1,1,2,1,2]
[6,4,3,7,2,5,1]=>110101=>[1,1,2,2,1]
[6,4,3,7,5,1,2]=>110110=>[1,1,2,1,2]
[6,4,3,7,5,2,1]=>110111=>[1,1,2,1,1,1]
[6,4,5,1,2,3,7]=>101000=>[1,2,4]
[6,4,5,1,2,7,3]=>101001=>[1,2,3,1]
[6,4,5,1,3,2,7]=>101010=>[1,2,2,2]
[6,4,5,1,3,7,2]=>101001=>[1,2,3,1]
[6,4,5,1,7,2,3]=>101010=>[1,2,2,2]
[6,4,5,1,7,3,2]=>101011=>[1,2,2,1,1]
[6,4,5,2,1,3,7]=>101100=>[1,2,1,3]
[6,4,5,2,1,7,3]=>101101=>[1,2,1,2,1]
[6,4,5,2,3,1,7]=>101010=>[1,2,2,2]
[6,4,5,2,3,7,1]=>101001=>[1,2,3,1]
[6,4,5,2,7,1,3]=>101010=>[1,2,2,2]
[6,4,5,2,7,3,1]=>101011=>[1,2,2,1,1]
[6,4,5,3,1,2,7]=>101100=>[1,2,1,3]
[6,4,5,3,1,7,2]=>101101=>[1,2,1,2,1]
[6,4,5,3,2,1,7]=>101110=>[1,2,1,1,2]
[6,4,5,3,2,7,1]=>101101=>[1,2,1,2,1]
[6,4,5,3,7,1,2]=>101010=>[1,2,2,2]
[6,4,5,3,7,2,1]=>101011=>[1,2,2,1,1]
[6,4,5,7,1,2,3]=>100100=>[1,3,3]
[6,4,5,7,1,3,2]=>100101=>[1,3,2,1]
[6,4,5,7,2,1,3]=>100110=>[1,3,1,2]
[6,4,5,7,2,3,1]=>100101=>[1,3,2,1]
[6,4,5,7,3,1,2]=>100110=>[1,3,1,2]
[6,4,5,7,3,2,1]=>100111=>[1,3,1,1,1]
[6,4,7,1,2,3,5]=>101000=>[1,2,4]
[6,4,7,1,2,5,3]=>101001=>[1,2,3,1]
[6,4,7,1,3,2,5]=>101010=>[1,2,2,2]
[6,4,7,1,3,5,2]=>101001=>[1,2,3,1]
[6,4,7,1,5,2,3]=>101010=>[1,2,2,2]
[6,4,7,1,5,3,2]=>101011=>[1,2,2,1,1]
[6,4,7,2,1,3,5]=>101100=>[1,2,1,3]
[6,4,7,2,1,5,3]=>101101=>[1,2,1,2,1]
[6,4,7,2,3,1,5]=>101010=>[1,2,2,2]
[6,4,7,2,3,5,1]=>101001=>[1,2,3,1]
[6,4,7,2,5,1,3]=>101010=>[1,2,2,2]
[6,4,7,2,5,3,1]=>101011=>[1,2,2,1,1]
[6,4,7,3,1,2,5]=>101100=>[1,2,1,3]
[6,4,7,3,1,5,2]=>101101=>[1,2,1,2,1]
[6,4,7,3,2,1,5]=>101110=>[1,2,1,1,2]
[6,4,7,3,2,5,1]=>101101=>[1,2,1,2,1]
[6,4,7,3,5,1,2]=>101010=>[1,2,2,2]
[6,4,7,3,5,2,1]=>101011=>[1,2,2,1,1]
[6,4,7,5,1,2,3]=>101100=>[1,2,1,3]
[6,4,7,5,1,3,2]=>101101=>[1,2,1,2,1]
[6,4,7,5,2,1,3]=>101110=>[1,2,1,1,2]
[6,4,7,5,2,3,1]=>101101=>[1,2,1,2,1]
[6,4,7,5,3,1,2]=>101110=>[1,2,1,1,2]
[6,4,7,5,3,2,1]=>101111=>[1,2,1,1,1,1]
[6,5,1,2,3,4,7]=>110000=>[1,1,5]
[6,5,1,2,3,7,4]=>110001=>[1,1,4,1]
[6,5,1,2,4,3,7]=>110010=>[1,1,3,2]
[6,5,1,2,4,7,3]=>110001=>[1,1,4,1]
[6,5,1,2,7,3,4]=>110010=>[1,1,3,2]
[6,5,1,2,7,4,3]=>110011=>[1,1,3,1,1]
[6,5,1,3,2,4,7]=>110100=>[1,1,2,3]
[6,5,1,3,2,7,4]=>110101=>[1,1,2,2,1]
[6,5,1,3,4,2,7]=>110010=>[1,1,3,2]
[6,5,1,3,4,7,2]=>110001=>[1,1,4,1]
[6,5,1,3,7,2,4]=>110010=>[1,1,3,2]
[6,5,1,3,7,4,2]=>110011=>[1,1,3,1,1]
[6,5,1,4,2,3,7]=>110100=>[1,1,2,3]
[6,5,1,4,2,7,3]=>110101=>[1,1,2,2,1]
[6,5,1,4,3,2,7]=>110110=>[1,1,2,1,2]
[6,5,1,4,3,7,2]=>110101=>[1,1,2,2,1]
[6,5,1,4,7,2,3]=>110010=>[1,1,3,2]
[6,5,1,4,7,3,2]=>110011=>[1,1,3,1,1]
[6,5,1,7,2,3,4]=>110100=>[1,1,2,3]
[6,5,1,7,2,4,3]=>110101=>[1,1,2,2,1]
[6,5,1,7,3,2,4]=>110110=>[1,1,2,1,2]
[6,5,1,7,3,4,2]=>110101=>[1,1,2,2,1]
[6,5,1,7,4,2,3]=>110110=>[1,1,2,1,2]
[6,5,1,7,4,3,2]=>110111=>[1,1,2,1,1,1]
[6,5,2,1,3,4,7]=>111000=>[1,1,1,4]
[6,5,2,1,3,7,4]=>111001=>[1,1,1,3,1]
[6,5,2,1,4,3,7]=>111010=>[1,1,1,2,2]
[6,5,2,1,4,7,3]=>111001=>[1,1,1,3,1]
[6,5,2,1,7,3,4]=>111010=>[1,1,1,2,2]
[6,5,2,1,7,4,3]=>111011=>[1,1,1,2,1,1]
[6,5,2,3,1,4,7]=>110100=>[1,1,2,3]
[6,5,2,3,1,7,4]=>110101=>[1,1,2,2,1]
[6,5,2,3,4,1,7]=>110010=>[1,1,3,2]
[6,5,2,3,4,7,1]=>110001=>[1,1,4,1]
[6,5,2,3,7,1,4]=>110010=>[1,1,3,2]
[6,5,2,3,7,4,1]=>110011=>[1,1,3,1,1]
[6,5,2,4,1,3,7]=>110100=>[1,1,2,3]
[6,5,2,4,1,7,3]=>110101=>[1,1,2,2,1]
[6,5,2,4,3,1,7]=>110110=>[1,1,2,1,2]
[6,5,2,4,3,7,1]=>110101=>[1,1,2,2,1]
[6,5,2,4,7,1,3]=>110010=>[1,1,3,2]
[6,5,2,4,7,3,1]=>110011=>[1,1,3,1,1]
[6,5,2,7,1,3,4]=>110100=>[1,1,2,3]
[6,5,2,7,1,4,3]=>110101=>[1,1,2,2,1]
[6,5,2,7,3,1,4]=>110110=>[1,1,2,1,2]
[6,5,2,7,3,4,1]=>110101=>[1,1,2,2,1]
[6,5,2,7,4,1,3]=>110110=>[1,1,2,1,2]
[6,5,2,7,4,3,1]=>110111=>[1,1,2,1,1,1]
[6,5,3,1,2,4,7]=>111000=>[1,1,1,4]
[6,5,3,1,2,7,4]=>111001=>[1,1,1,3,1]
[6,5,3,1,4,2,7]=>111010=>[1,1,1,2,2]
[6,5,3,1,4,7,2]=>111001=>[1,1,1,3,1]
[6,5,3,1,7,2,4]=>111010=>[1,1,1,2,2]
[6,5,3,1,7,4,2]=>111011=>[1,1,1,2,1,1]
[6,5,3,2,1,4,7]=>111100=>[1,1,1,1,3]
[6,5,3,2,1,7,4]=>111101=>[1,1,1,1,2,1]
[6,5,3,2,4,1,7]=>111010=>[1,1,1,2,2]
[6,5,3,2,4,7,1]=>111001=>[1,1,1,3,1]
[6,5,3,2,7,1,4]=>111010=>[1,1,1,2,2]
[6,5,3,2,7,4,1]=>111011=>[1,1,1,2,1,1]
[6,5,3,4,1,2,7]=>110100=>[1,1,2,3]
[6,5,3,4,1,7,2]=>110101=>[1,1,2,2,1]
[6,5,3,4,2,1,7]=>110110=>[1,1,2,1,2]
[6,5,3,4,2,7,1]=>110101=>[1,1,2,2,1]
[6,5,3,4,7,1,2]=>110010=>[1,1,3,2]
[6,5,3,4,7,2,1]=>110011=>[1,1,3,1,1]
[6,5,3,7,1,2,4]=>110100=>[1,1,2,3]
[6,5,3,7,1,4,2]=>110101=>[1,1,2,2,1]
[6,5,3,7,2,1,4]=>110110=>[1,1,2,1,2]
[6,5,3,7,2,4,1]=>110101=>[1,1,2,2,1]
[6,5,3,7,4,1,2]=>110110=>[1,1,2,1,2]
[6,5,3,7,4,2,1]=>110111=>[1,1,2,1,1,1]
[6,5,4,1,2,3,7]=>111000=>[1,1,1,4]
[6,5,4,1,2,7,3]=>111001=>[1,1,1,3,1]
[6,5,4,1,3,2,7]=>111010=>[1,1,1,2,2]
[6,5,4,1,3,7,2]=>111001=>[1,1,1,3,1]
[6,5,4,1,7,2,3]=>111010=>[1,1,1,2,2]
[6,5,4,1,7,3,2]=>111011=>[1,1,1,2,1,1]
[6,5,4,2,1,3,7]=>111100=>[1,1,1,1,3]
[6,5,4,2,1,7,3]=>111101=>[1,1,1,1,2,1]
[6,5,4,2,3,1,7]=>111010=>[1,1,1,2,2]
[6,5,4,2,3,7,1]=>111001=>[1,1,1,3,1]
[6,5,4,2,7,1,3]=>111010=>[1,1,1,2,2]
[6,5,4,2,7,3,1]=>111011=>[1,1,1,2,1,1]
[6,5,4,3,1,2,7]=>111100=>[1,1,1,1,3]
[6,5,4,3,1,7,2]=>111101=>[1,1,1,1,2,1]
[6,5,4,3,2,1,7]=>111110=>[1,1,1,1,1,2]
[6,5,4,3,2,7,1]=>111101=>[1,1,1,1,2,1]
[6,5,4,3,7,1,2]=>111010=>[1,1,1,2,2]
[6,5,4,3,7,2,1]=>111011=>[1,1,1,2,1,1]
[6,5,4,7,1,2,3]=>110100=>[1,1,2,3]
[6,5,4,7,1,3,2]=>110101=>[1,1,2,2,1]
[6,5,4,7,2,1,3]=>110110=>[1,1,2,1,2]
[6,5,4,7,2,3,1]=>110101=>[1,1,2,2,1]
[6,5,4,7,3,1,2]=>110110=>[1,1,2,1,2]
[6,5,4,7,3,2,1]=>110111=>[1,1,2,1,1,1]
[6,5,7,1,2,3,4]=>101000=>[1,2,4]
[6,5,7,1,2,4,3]=>101001=>[1,2,3,1]
[6,5,7,1,3,2,4]=>101010=>[1,2,2,2]
[6,5,7,1,3,4,2]=>101001=>[1,2,3,1]
[6,5,7,1,4,2,3]=>101010=>[1,2,2,2]
[6,5,7,1,4,3,2]=>101011=>[1,2,2,1,1]
[6,5,7,2,1,3,4]=>101100=>[1,2,1,3]
[6,5,7,2,1,4,3]=>101101=>[1,2,1,2,1]
[6,5,7,2,3,1,4]=>101010=>[1,2,2,2]
[6,5,7,2,3,4,1]=>101001=>[1,2,3,1]
[6,5,7,2,4,1,3]=>101010=>[1,2,2,2]
[6,5,7,2,4,3,1]=>101011=>[1,2,2,1,1]
[6,5,7,3,1,2,4]=>101100=>[1,2,1,3]
[6,5,7,3,1,4,2]=>101101=>[1,2,1,2,1]
[6,5,7,3,2,1,4]=>101110=>[1,2,1,1,2]
[6,5,7,3,2,4,1]=>101101=>[1,2,1,2,1]
[6,5,7,3,4,1,2]=>101010=>[1,2,2,2]
[6,5,7,3,4,2,1]=>101011=>[1,2,2,1,1]
[6,5,7,4,1,2,3]=>101100=>[1,2,1,3]
[6,5,7,4,1,3,2]=>101101=>[1,2,1,2,1]
[6,5,7,4,2,1,3]=>101110=>[1,2,1,1,2]
[6,5,7,4,2,3,1]=>101101=>[1,2,1,2,1]
[6,5,7,4,3,1,2]=>101110=>[1,2,1,1,2]
[6,5,7,4,3,2,1]=>101111=>[1,2,1,1,1,1]
[6,7,1,2,3,4,5]=>010000=>[2,5]
[6,7,1,2,3,5,4]=>010001=>[2,4,1]
[6,7,1,2,4,3,5]=>010010=>[2,3,2]
[6,7,1,2,4,5,3]=>010001=>[2,4,1]
[6,7,1,2,5,3,4]=>010010=>[2,3,2]
[6,7,1,2,5,4,3]=>010011=>[2,3,1,1]
[6,7,1,3,2,4,5]=>010100=>[2,2,3]
[6,7,1,3,2,5,4]=>010101=>[2,2,2,1]
[6,7,1,3,4,2,5]=>010010=>[2,3,2]
[6,7,1,3,4,5,2]=>010001=>[2,4,1]
[6,7,1,3,5,2,4]=>010010=>[2,3,2]
[6,7,1,3,5,4,2]=>010011=>[2,3,1,1]
[6,7,1,4,2,3,5]=>010100=>[2,2,3]
[6,7,1,4,2,5,3]=>010101=>[2,2,2,1]
[6,7,1,4,3,2,5]=>010110=>[2,2,1,2]
[6,7,1,4,3,5,2]=>010101=>[2,2,2,1]
[6,7,1,4,5,2,3]=>010010=>[2,3,2]
[6,7,1,4,5,3,2]=>010011=>[2,3,1,1]
[6,7,1,5,2,3,4]=>010100=>[2,2,3]
[6,7,1,5,2,4,3]=>010101=>[2,2,2,1]
[6,7,1,5,3,2,4]=>010110=>[2,2,1,2]
[6,7,1,5,3,4,2]=>010101=>[2,2,2,1]
[6,7,1,5,4,2,3]=>010110=>[2,2,1,2]
[6,7,1,5,4,3,2]=>010111=>[2,2,1,1,1]
[6,7,2,1,3,4,5]=>011000=>[2,1,4]
[6,7,2,1,3,5,4]=>011001=>[2,1,3,1]
[6,7,2,1,4,3,5]=>011010=>[2,1,2,2]
[6,7,2,1,4,5,3]=>011001=>[2,1,3,1]
[6,7,2,1,5,3,4]=>011010=>[2,1,2,2]
[6,7,2,1,5,4,3]=>011011=>[2,1,2,1,1]
[6,7,2,3,1,4,5]=>010100=>[2,2,3]
[6,7,2,3,1,5,4]=>010101=>[2,2,2,1]
[6,7,2,3,4,1,5]=>010010=>[2,3,2]
[6,7,2,3,4,5,1]=>010001=>[2,4,1]
[6,7,2,3,5,1,4]=>010010=>[2,3,2]
[6,7,2,3,5,4,1]=>010011=>[2,3,1,1]
[6,7,2,4,1,3,5]=>010100=>[2,2,3]
[6,7,2,4,1,5,3]=>010101=>[2,2,2,1]
[6,7,2,4,3,1,5]=>010110=>[2,2,1,2]
[6,7,2,4,3,5,1]=>010101=>[2,2,2,1]
[6,7,2,4,5,1,3]=>010010=>[2,3,2]
[6,7,2,4,5,3,1]=>010011=>[2,3,1,1]
[6,7,2,5,1,3,4]=>010100=>[2,2,3]
[6,7,2,5,1,4,3]=>010101=>[2,2,2,1]
[6,7,2,5,3,1,4]=>010110=>[2,2,1,2]
[6,7,2,5,3,4,1]=>010101=>[2,2,2,1]
[6,7,2,5,4,1,3]=>010110=>[2,2,1,2]
[6,7,2,5,4,3,1]=>010111=>[2,2,1,1,1]
[6,7,3,1,2,4,5]=>011000=>[2,1,4]
[6,7,3,1,2,5,4]=>011001=>[2,1,3,1]
[6,7,3,1,4,2,5]=>011010=>[2,1,2,2]
[6,7,3,1,4,5,2]=>011001=>[2,1,3,1]
[6,7,3,1,5,2,4]=>011010=>[2,1,2,2]
[6,7,3,1,5,4,2]=>011011=>[2,1,2,1,1]
[6,7,3,2,1,4,5]=>011100=>[2,1,1,3]
[6,7,3,2,1,5,4]=>011101=>[2,1,1,2,1]
[6,7,3,2,4,1,5]=>011010=>[2,1,2,2]
[6,7,3,2,4,5,1]=>011001=>[2,1,3,1]
[6,7,3,2,5,1,4]=>011010=>[2,1,2,2]
[6,7,3,2,5,4,1]=>011011=>[2,1,2,1,1]
[6,7,3,4,1,2,5]=>010100=>[2,2,3]
[6,7,3,4,1,5,2]=>010101=>[2,2,2,1]
[6,7,3,4,2,1,5]=>010110=>[2,2,1,2]
[6,7,3,4,2,5,1]=>010101=>[2,2,2,1]
[6,7,3,4,5,1,2]=>010010=>[2,3,2]
[6,7,3,4,5,2,1]=>010011=>[2,3,1,1]
[6,7,3,5,1,2,4]=>010100=>[2,2,3]
[6,7,3,5,1,4,2]=>010101=>[2,2,2,1]
[6,7,3,5,2,1,4]=>010110=>[2,2,1,2]
[6,7,3,5,2,4,1]=>010101=>[2,2,2,1]
[6,7,3,5,4,1,2]=>010110=>[2,2,1,2]
[6,7,3,5,4,2,1]=>010111=>[2,2,1,1,1]
[6,7,4,1,2,3,5]=>011000=>[2,1,4]
[6,7,4,1,2,5,3]=>011001=>[2,1,3,1]
[6,7,4,1,3,2,5]=>011010=>[2,1,2,2]
[6,7,4,1,3,5,2]=>011001=>[2,1,3,1]
[6,7,4,1,5,2,3]=>011010=>[2,1,2,2]
[6,7,4,1,5,3,2]=>011011=>[2,1,2,1,1]
[6,7,4,2,1,3,5]=>011100=>[2,1,1,3]
[6,7,4,2,1,5,3]=>011101=>[2,1,1,2,1]
[6,7,4,2,3,1,5]=>011010=>[2,1,2,2]
[6,7,4,2,3,5,1]=>011001=>[2,1,3,1]
[6,7,4,2,5,1,3]=>011010=>[2,1,2,2]
[6,7,4,2,5,3,1]=>011011=>[2,1,2,1,1]
[6,7,4,3,1,2,5]=>011100=>[2,1,1,3]
[6,7,4,3,1,5,2]=>011101=>[2,1,1,2,1]
[6,7,4,3,2,1,5]=>011110=>[2,1,1,1,2]
[6,7,4,3,2,5,1]=>011101=>[2,1,1,2,1]
[6,7,4,3,5,1,2]=>011010=>[2,1,2,2]
[6,7,4,3,5,2,1]=>011011=>[2,1,2,1,1]
[6,7,4,5,1,2,3]=>010100=>[2,2,3]
[6,7,4,5,1,3,2]=>010101=>[2,2,2,1]
[6,7,4,5,2,1,3]=>010110=>[2,2,1,2]
[6,7,4,5,2,3,1]=>010101=>[2,2,2,1]
[6,7,4,5,3,1,2]=>010110=>[2,2,1,2]
[6,7,4,5,3,2,1]=>010111=>[2,2,1,1,1]
[6,7,5,1,2,3,4]=>011000=>[2,1,4]
[6,7,5,1,2,4,3]=>011001=>[2,1,3,1]
[6,7,5,1,3,2,4]=>011010=>[2,1,2,2]
[6,7,5,1,3,4,2]=>011001=>[2,1,3,1]
[6,7,5,1,4,2,3]=>011010=>[2,1,2,2]
[6,7,5,1,4,3,2]=>011011=>[2,1,2,1,1]
[6,7,5,2,1,3,4]=>011100=>[2,1,1,3]
[6,7,5,2,1,4,3]=>011101=>[2,1,1,2,1]
[6,7,5,2,3,1,4]=>011010=>[2,1,2,2]
[6,7,5,2,3,4,1]=>011001=>[2,1,3,1]
[6,7,5,2,4,1,3]=>011010=>[2,1,2,2]
[6,7,5,2,4,3,1]=>011011=>[2,1,2,1,1]
[6,7,5,3,1,2,4]=>011100=>[2,1,1,3]
[6,7,5,3,1,4,2]=>011101=>[2,1,1,2,1]
[6,7,5,3,2,1,4]=>011110=>[2,1,1,1,2]
[6,7,5,3,2,4,1]=>011101=>[2,1,1,2,1]
[6,7,5,3,4,1,2]=>011010=>[2,1,2,2]
[6,7,5,3,4,2,1]=>011011=>[2,1,2,1,1]
[6,7,5,4,1,2,3]=>011100=>[2,1,1,3]
[6,7,5,4,1,3,2]=>011101=>[2,1,1,2,1]
[6,7,5,4,2,1,3]=>011110=>[2,1,1,1,2]
[6,7,5,4,2,3,1]=>011101=>[2,1,1,2,1]
[6,7,5,4,3,1,2]=>011110=>[2,1,1,1,2]
[6,7,5,4,3,2,1]=>011111=>[2,1,1,1,1,1]
[7,1,2,3,4,5,6]=>100000=>[1,6]
[7,1,2,3,4,6,5]=>100001=>[1,5,1]
[7,1,2,3,5,4,6]=>100010=>[1,4,2]
[7,1,2,3,5,6,4]=>100001=>[1,5,1]
[7,1,2,3,6,4,5]=>100010=>[1,4,2]
[7,1,2,3,6,5,4]=>100011=>[1,4,1,1]
[7,1,2,4,3,5,6]=>100100=>[1,3,3]
[7,1,2,4,3,6,5]=>100101=>[1,3,2,1]
[7,1,2,4,5,3,6]=>100010=>[1,4,2]
[7,1,2,4,5,6,3]=>100001=>[1,5,1]
[7,1,2,4,6,3,5]=>100010=>[1,4,2]
[7,1,2,4,6,5,3]=>100011=>[1,4,1,1]
[7,1,2,5,3,4,6]=>100100=>[1,3,3]
[7,1,2,5,3,6,4]=>100101=>[1,3,2,1]
[7,1,2,5,4,3,6]=>100110=>[1,3,1,2]
[7,1,2,5,4,6,3]=>100101=>[1,3,2,1]
[7,1,2,5,6,3,4]=>100010=>[1,4,2]
[7,1,2,5,6,4,3]=>100011=>[1,4,1,1]
[7,1,2,6,3,4,5]=>100100=>[1,3,3]
[7,1,2,6,3,5,4]=>100101=>[1,3,2,1]
[7,1,2,6,4,3,5]=>100110=>[1,3,1,2]
[7,1,2,6,4,5,3]=>100101=>[1,3,2,1]
[7,1,2,6,5,3,4]=>100110=>[1,3,1,2]
[7,1,2,6,5,4,3]=>100111=>[1,3,1,1,1]
[7,1,3,2,4,5,6]=>101000=>[1,2,4]
[7,1,3,2,4,6,5]=>101001=>[1,2,3,1]
[7,1,3,2,5,4,6]=>101010=>[1,2,2,2]
[7,1,3,2,5,6,4]=>101001=>[1,2,3,1]
[7,1,3,2,6,4,5]=>101010=>[1,2,2,2]
[7,1,3,2,6,5,4]=>101011=>[1,2,2,1,1]
[7,1,3,4,2,5,6]=>100100=>[1,3,3]
[7,1,3,4,2,6,5]=>100101=>[1,3,2,1]
[7,1,3,4,5,2,6]=>100010=>[1,4,2]
[7,1,3,4,5,6,2]=>100001=>[1,5,1]
[7,1,3,4,6,2,5]=>100010=>[1,4,2]
[7,1,3,4,6,5,2]=>100011=>[1,4,1,1]
[7,1,3,5,2,4,6]=>100100=>[1,3,3]
[7,1,3,5,2,6,4]=>100101=>[1,3,2,1]
[7,1,3,5,4,2,6]=>100110=>[1,3,1,2]
[7,1,3,5,4,6,2]=>100101=>[1,3,2,1]
[7,1,3,5,6,2,4]=>100010=>[1,4,2]
[7,1,3,5,6,4,2]=>100011=>[1,4,1,1]
[7,1,3,6,2,4,5]=>100100=>[1,3,3]
[7,1,3,6,2,5,4]=>100101=>[1,3,2,1]
[7,1,3,6,4,2,5]=>100110=>[1,3,1,2]
[7,1,3,6,4,5,2]=>100101=>[1,3,2,1]
[7,1,3,6,5,2,4]=>100110=>[1,3,1,2]
[7,1,3,6,5,4,2]=>100111=>[1,3,1,1,1]
[7,1,4,2,3,5,6]=>101000=>[1,2,4]
[7,1,4,2,3,6,5]=>101001=>[1,2,3,1]
[7,1,4,2,5,3,6]=>101010=>[1,2,2,2]
[7,1,4,2,5,6,3]=>101001=>[1,2,3,1]
[7,1,4,2,6,3,5]=>101010=>[1,2,2,2]
[7,1,4,2,6,5,3]=>101011=>[1,2,2,1,1]
[7,1,4,3,2,5,6]=>101100=>[1,2,1,3]
[7,1,4,3,2,6,5]=>101101=>[1,2,1,2,1]
[7,1,4,3,5,2,6]=>101010=>[1,2,2,2]
[7,1,4,3,5,6,2]=>101001=>[1,2,3,1]
[7,1,4,3,6,2,5]=>101010=>[1,2,2,2]
[7,1,4,3,6,5,2]=>101011=>[1,2,2,1,1]
[7,1,4,5,2,3,6]=>100100=>[1,3,3]
[7,1,4,5,2,6,3]=>100101=>[1,3,2,1]
[7,1,4,5,3,2,6]=>100110=>[1,3,1,2]
[7,1,4,5,3,6,2]=>100101=>[1,3,2,1]
[7,1,4,5,6,2,3]=>100010=>[1,4,2]
[7,1,4,5,6,3,2]=>100011=>[1,4,1,1]
[7,1,4,6,2,3,5]=>100100=>[1,3,3]
[7,1,4,6,2,5,3]=>100101=>[1,3,2,1]
[7,1,4,6,3,2,5]=>100110=>[1,3,1,2]
[7,1,4,6,3,5,2]=>100101=>[1,3,2,1]
[7,1,4,6,5,2,3]=>100110=>[1,3,1,2]
[7,1,4,6,5,3,2]=>100111=>[1,3,1,1,1]
[7,1,5,2,3,4,6]=>101000=>[1,2,4]
[7,1,5,2,3,6,4]=>101001=>[1,2,3,1]
[7,1,5,2,4,3,6]=>101010=>[1,2,2,2]
[7,1,5,2,4,6,3]=>101001=>[1,2,3,1]
[7,1,5,2,6,3,4]=>101010=>[1,2,2,2]
[7,1,5,2,6,4,3]=>101011=>[1,2,2,1,1]
[7,1,5,3,2,4,6]=>101100=>[1,2,1,3]
[7,1,5,3,2,6,4]=>101101=>[1,2,1,2,1]
[7,1,5,3,4,2,6]=>101010=>[1,2,2,2]
[7,1,5,3,4,6,2]=>101001=>[1,2,3,1]
[7,1,5,3,6,2,4]=>101010=>[1,2,2,2]
[7,1,5,3,6,4,2]=>101011=>[1,2,2,1,1]
[7,1,5,4,2,3,6]=>101100=>[1,2,1,3]
[7,1,5,4,2,6,3]=>101101=>[1,2,1,2,1]
[7,1,5,4,3,2,6]=>101110=>[1,2,1,1,2]
[7,1,5,4,3,6,2]=>101101=>[1,2,1,2,1]
[7,1,5,4,6,2,3]=>101010=>[1,2,2,2]
[7,1,5,4,6,3,2]=>101011=>[1,2,2,1,1]
[7,1,5,6,2,3,4]=>100100=>[1,3,3]
[7,1,5,6,2,4,3]=>100101=>[1,3,2,1]
[7,1,5,6,3,2,4]=>100110=>[1,3,1,2]
[7,1,5,6,3,4,2]=>100101=>[1,3,2,1]
[7,1,5,6,4,2,3]=>100110=>[1,3,1,2]
[7,1,5,6,4,3,2]=>100111=>[1,3,1,1,1]
[7,1,6,2,3,4,5]=>101000=>[1,2,4]
[7,1,6,2,3,5,4]=>101001=>[1,2,3,1]
[7,1,6,2,4,3,5]=>101010=>[1,2,2,2]
[7,1,6,2,4,5,3]=>101001=>[1,2,3,1]
[7,1,6,2,5,3,4]=>101010=>[1,2,2,2]
[7,1,6,2,5,4,3]=>101011=>[1,2,2,1,1]
[7,1,6,3,2,4,5]=>101100=>[1,2,1,3]
[7,1,6,3,2,5,4]=>101101=>[1,2,1,2,1]
[7,1,6,3,4,2,5]=>101010=>[1,2,2,2]
[7,1,6,3,4,5,2]=>101001=>[1,2,3,1]
[7,1,6,3,5,2,4]=>101010=>[1,2,2,2]
[7,1,6,3,5,4,2]=>101011=>[1,2,2,1,1]
[7,1,6,4,2,3,5]=>101100=>[1,2,1,3]
[7,1,6,4,2,5,3]=>101101=>[1,2,1,2,1]
[7,1,6,4,3,2,5]=>101110=>[1,2,1,1,2]
[7,1,6,4,3,5,2]=>101101=>[1,2,1,2,1]
[7,1,6,4,5,2,3]=>101010=>[1,2,2,2]
[7,1,6,4,5,3,2]=>101011=>[1,2,2,1,1]
[7,1,6,5,2,3,4]=>101100=>[1,2,1,3]
[7,1,6,5,2,4,3]=>101101=>[1,2,1,2,1]
[7,1,6,5,3,2,4]=>101110=>[1,2,1,1,2]
[7,1,6,5,3,4,2]=>101101=>[1,2,1,2,1]
[7,1,6,5,4,2,3]=>101110=>[1,2,1,1,2]
[7,1,6,5,4,3,2]=>101111=>[1,2,1,1,1,1]
[7,2,1,3,4,5,6]=>110000=>[1,1,5]
[7,2,1,3,4,6,5]=>110001=>[1,1,4,1]
[7,2,1,3,5,4,6]=>110010=>[1,1,3,2]
[7,2,1,3,5,6,4]=>110001=>[1,1,4,1]
[7,2,1,3,6,4,5]=>110010=>[1,1,3,2]
[7,2,1,3,6,5,4]=>110011=>[1,1,3,1,1]
[7,2,1,4,3,5,6]=>110100=>[1,1,2,3]
[7,2,1,4,3,6,5]=>110101=>[1,1,2,2,1]
[7,2,1,4,5,3,6]=>110010=>[1,1,3,2]
[7,2,1,4,5,6,3]=>110001=>[1,1,4,1]
[7,2,1,4,6,3,5]=>110010=>[1,1,3,2]
[7,2,1,4,6,5,3]=>110011=>[1,1,3,1,1]
[7,2,1,5,3,4,6]=>110100=>[1,1,2,3]
[7,2,1,5,3,6,4]=>110101=>[1,1,2,2,1]
[7,2,1,5,4,3,6]=>110110=>[1,1,2,1,2]
[7,2,1,5,4,6,3]=>110101=>[1,1,2,2,1]
[7,2,1,5,6,3,4]=>110010=>[1,1,3,2]
[7,2,1,5,6,4,3]=>110011=>[1,1,3,1,1]
[7,2,1,6,3,4,5]=>110100=>[1,1,2,3]
[7,2,1,6,3,5,4]=>110101=>[1,1,2,2,1]
[7,2,1,6,4,3,5]=>110110=>[1,1,2,1,2]
[7,2,1,6,4,5,3]=>110101=>[1,1,2,2,1]
[7,2,1,6,5,3,4]=>110110=>[1,1,2,1,2]
[7,2,1,6,5,4,3]=>110111=>[1,1,2,1,1,1]
[7,2,3,1,4,5,6]=>101000=>[1,2,4]
[7,2,3,1,4,6,5]=>101001=>[1,2,3,1]
[7,2,3,1,5,4,6]=>101010=>[1,2,2,2]
[7,2,3,1,5,6,4]=>101001=>[1,2,3,1]
[7,2,3,1,6,4,5]=>101010=>[1,2,2,2]
[7,2,3,1,6,5,4]=>101011=>[1,2,2,1,1]
[7,2,3,4,1,5,6]=>100100=>[1,3,3]
[7,2,3,4,1,6,5]=>100101=>[1,3,2,1]
[7,2,3,4,5,1,6]=>100010=>[1,4,2]
[7,2,3,4,5,6,1]=>100001=>[1,5,1]
[7,2,3,4,6,1,5]=>100010=>[1,4,2]
[7,2,3,4,6,5,1]=>100011=>[1,4,1,1]
[7,2,3,5,1,4,6]=>100100=>[1,3,3]
[7,2,3,5,1,6,4]=>100101=>[1,3,2,1]
[7,2,3,5,4,1,6]=>100110=>[1,3,1,2]
[7,2,3,5,4,6,1]=>100101=>[1,3,2,1]
[7,2,3,5,6,1,4]=>100010=>[1,4,2]
[7,2,3,5,6,4,1]=>100011=>[1,4,1,1]
[7,2,3,6,1,4,5]=>100100=>[1,3,3]
[7,2,3,6,1,5,4]=>100101=>[1,3,2,1]
[7,2,3,6,4,1,5]=>100110=>[1,3,1,2]
[7,2,3,6,4,5,1]=>100101=>[1,3,2,1]
[7,2,3,6,5,1,4]=>100110=>[1,3,1,2]
[7,2,3,6,5,4,1]=>100111=>[1,3,1,1,1]
[7,2,4,1,3,5,6]=>101000=>[1,2,4]
[7,2,4,1,3,6,5]=>101001=>[1,2,3,1]
[7,2,4,1,5,3,6]=>101010=>[1,2,2,2]
[7,2,4,1,5,6,3]=>101001=>[1,2,3,1]
[7,2,4,1,6,3,5]=>101010=>[1,2,2,2]
[7,2,4,1,6,5,3]=>101011=>[1,2,2,1,1]
[7,2,4,3,1,5,6]=>101100=>[1,2,1,3]
[7,2,4,3,1,6,5]=>101101=>[1,2,1,2,1]
[7,2,4,3,5,1,6]=>101010=>[1,2,2,2]
[7,2,4,3,5,6,1]=>101001=>[1,2,3,1]
[7,2,4,3,6,1,5]=>101010=>[1,2,2,2]
[7,2,4,3,6,5,1]=>101011=>[1,2,2,1,1]
[7,2,4,5,1,3,6]=>100100=>[1,3,3]
[7,2,4,5,1,6,3]=>100101=>[1,3,2,1]
[7,2,4,5,3,1,6]=>100110=>[1,3,1,2]
[7,2,4,5,3,6,1]=>100101=>[1,3,2,1]
[7,2,4,5,6,1,3]=>100010=>[1,4,2]
[7,2,4,5,6,3,1]=>100011=>[1,4,1,1]
[7,2,4,6,1,3,5]=>100100=>[1,3,3]
[7,2,4,6,1,5,3]=>100101=>[1,3,2,1]
[7,2,4,6,3,1,5]=>100110=>[1,3,1,2]
[7,2,4,6,3,5,1]=>100101=>[1,3,2,1]
[7,2,4,6,5,1,3]=>100110=>[1,3,1,2]
[7,2,4,6,5,3,1]=>100111=>[1,3,1,1,1]
[7,2,5,1,3,4,6]=>101000=>[1,2,4]
[7,2,5,1,3,6,4]=>101001=>[1,2,3,1]
[7,2,5,1,4,3,6]=>101010=>[1,2,2,2]
[7,2,5,1,4,6,3]=>101001=>[1,2,3,1]
[7,2,5,1,6,3,4]=>101010=>[1,2,2,2]
[7,2,5,1,6,4,3]=>101011=>[1,2,2,1,1]
[7,2,5,3,1,4,6]=>101100=>[1,2,1,3]
[7,2,5,3,1,6,4]=>101101=>[1,2,1,2,1]
[7,2,5,3,4,1,6]=>101010=>[1,2,2,2]
[7,2,5,3,4,6,1]=>101001=>[1,2,3,1]
[7,2,5,3,6,1,4]=>101010=>[1,2,2,2]
[7,2,5,3,6,4,1]=>101011=>[1,2,2,1,1]
[7,2,5,4,1,3,6]=>101100=>[1,2,1,3]
[7,2,5,4,1,6,3]=>101101=>[1,2,1,2,1]
[7,2,5,4,3,1,6]=>101110=>[1,2,1,1,2]
[7,2,5,4,3,6,1]=>101101=>[1,2,1,2,1]
[7,2,5,4,6,1,3]=>101010=>[1,2,2,2]
[7,2,5,4,6,3,1]=>101011=>[1,2,2,1,1]
[7,2,5,6,1,3,4]=>100100=>[1,3,3]
[7,2,5,6,1,4,3]=>100101=>[1,3,2,1]
[7,2,5,6,3,1,4]=>100110=>[1,3,1,2]
[7,2,5,6,3,4,1]=>100101=>[1,3,2,1]
[7,2,5,6,4,1,3]=>100110=>[1,3,1,2]
[7,2,5,6,4,3,1]=>100111=>[1,3,1,1,1]
[7,2,6,1,3,4,5]=>101000=>[1,2,4]
[7,2,6,1,3,5,4]=>101001=>[1,2,3,1]
[7,2,6,1,4,3,5]=>101010=>[1,2,2,2]
[7,2,6,1,4,5,3]=>101001=>[1,2,3,1]
[7,2,6,1,5,3,4]=>101010=>[1,2,2,2]
[7,2,6,1,5,4,3]=>101011=>[1,2,2,1,1]
[7,2,6,3,1,4,5]=>101100=>[1,2,1,3]
[7,2,6,3,1,5,4]=>101101=>[1,2,1,2,1]
[7,2,6,3,4,1,5]=>101010=>[1,2,2,2]
[7,2,6,3,4,5,1]=>101001=>[1,2,3,1]
[7,2,6,3,5,1,4]=>101010=>[1,2,2,2]
[7,2,6,3,5,4,1]=>101011=>[1,2,2,1,1]
[7,2,6,4,1,3,5]=>101100=>[1,2,1,3]
[7,2,6,4,1,5,3]=>101101=>[1,2,1,2,1]
[7,2,6,4,3,1,5]=>101110=>[1,2,1,1,2]
[7,2,6,4,3,5,1]=>101101=>[1,2,1,2,1]
[7,2,6,4,5,1,3]=>101010=>[1,2,2,2]
[7,2,6,4,5,3,1]=>101011=>[1,2,2,1,1]
[7,2,6,5,1,3,4]=>101100=>[1,2,1,3]
[7,2,6,5,1,4,3]=>101101=>[1,2,1,2,1]
[7,2,6,5,3,1,4]=>101110=>[1,2,1,1,2]
[7,2,6,5,3,4,1]=>101101=>[1,2,1,2,1]
[7,2,6,5,4,1,3]=>101110=>[1,2,1,1,2]
[7,2,6,5,4,3,1]=>101111=>[1,2,1,1,1,1]
[7,3,1,2,4,5,6]=>110000=>[1,1,5]
[7,3,1,2,4,6,5]=>110001=>[1,1,4,1]
[7,3,1,2,5,4,6]=>110010=>[1,1,3,2]
[7,3,1,2,5,6,4]=>110001=>[1,1,4,1]
[7,3,1,2,6,4,5]=>110010=>[1,1,3,2]
[7,3,1,2,6,5,4]=>110011=>[1,1,3,1,1]
[7,3,1,4,2,5,6]=>110100=>[1,1,2,3]
[7,3,1,4,2,6,5]=>110101=>[1,1,2,2,1]
[7,3,1,4,5,2,6]=>110010=>[1,1,3,2]
[7,3,1,4,5,6,2]=>110001=>[1,1,4,1]
[7,3,1,4,6,2,5]=>110010=>[1,1,3,2]
[7,3,1,4,6,5,2]=>110011=>[1,1,3,1,1]
[7,3,1,5,2,4,6]=>110100=>[1,1,2,3]
[7,3,1,5,2,6,4]=>110101=>[1,1,2,2,1]
[7,3,1,5,4,2,6]=>110110=>[1,1,2,1,2]
[7,3,1,5,4,6,2]=>110101=>[1,1,2,2,1]
[7,3,1,5,6,2,4]=>110010=>[1,1,3,2]
[7,3,1,5,6,4,2]=>110011=>[1,1,3,1,1]
[7,3,1,6,2,4,5]=>110100=>[1,1,2,3]
[7,3,1,6,2,5,4]=>110101=>[1,1,2,2,1]
[7,3,1,6,4,2,5]=>110110=>[1,1,2,1,2]
[7,3,1,6,4,5,2]=>110101=>[1,1,2,2,1]
[7,3,1,6,5,2,4]=>110110=>[1,1,2,1,2]
[7,3,1,6,5,4,2]=>110111=>[1,1,2,1,1,1]
[7,3,2,1,4,5,6]=>111000=>[1,1,1,4]
[7,3,2,1,4,6,5]=>111001=>[1,1,1,3,1]
[7,3,2,1,5,4,6]=>111010=>[1,1,1,2,2]
[7,3,2,1,5,6,4]=>111001=>[1,1,1,3,1]
[7,3,2,1,6,4,5]=>111010=>[1,1,1,2,2]
[7,3,2,1,6,5,4]=>111011=>[1,1,1,2,1,1]
[7,3,2,4,1,5,6]=>110100=>[1,1,2,3]
[7,3,2,4,1,6,5]=>110101=>[1,1,2,2,1]
[7,3,2,4,5,1,6]=>110010=>[1,1,3,2]
[7,3,2,4,5,6,1]=>110001=>[1,1,4,1]
[7,3,2,4,6,1,5]=>110010=>[1,1,3,2]
[7,3,2,4,6,5,1]=>110011=>[1,1,3,1,1]
[7,3,2,5,1,4,6]=>110100=>[1,1,2,3]
[7,3,2,5,1,6,4]=>110101=>[1,1,2,2,1]
[7,3,2,5,4,1,6]=>110110=>[1,1,2,1,2]
[7,3,2,5,4,6,1]=>110101=>[1,1,2,2,1]
[7,3,2,5,6,1,4]=>110010=>[1,1,3,2]
[7,3,2,5,6,4,1]=>110011=>[1,1,3,1,1]
[7,3,2,6,1,4,5]=>110100=>[1,1,2,3]
[7,3,2,6,1,5,4]=>110101=>[1,1,2,2,1]
[7,3,2,6,4,1,5]=>110110=>[1,1,2,1,2]
[7,3,2,6,4,5,1]=>110101=>[1,1,2,2,1]
[7,3,2,6,5,1,4]=>110110=>[1,1,2,1,2]
[7,3,2,6,5,4,1]=>110111=>[1,1,2,1,1,1]
[7,3,4,1,2,5,6]=>101000=>[1,2,4]
[7,3,4,1,2,6,5]=>101001=>[1,2,3,1]
[7,3,4,1,5,2,6]=>101010=>[1,2,2,2]
[7,3,4,1,5,6,2]=>101001=>[1,2,3,1]
[7,3,4,1,6,2,5]=>101010=>[1,2,2,2]
[7,3,4,1,6,5,2]=>101011=>[1,2,2,1,1]
[7,3,4,2,1,5,6]=>101100=>[1,2,1,3]
[7,3,4,2,1,6,5]=>101101=>[1,2,1,2,1]
[7,3,4,2,5,1,6]=>101010=>[1,2,2,2]
[7,3,4,2,5,6,1]=>101001=>[1,2,3,1]
[7,3,4,2,6,1,5]=>101010=>[1,2,2,2]
[7,3,4,2,6,5,1]=>101011=>[1,2,2,1,1]
[7,3,4,5,1,2,6]=>100100=>[1,3,3]
[7,3,4,5,1,6,2]=>100101=>[1,3,2,1]
[7,3,4,5,2,1,6]=>100110=>[1,3,1,2]
[7,3,4,5,2,6,1]=>100101=>[1,3,2,1]
[7,3,4,5,6,1,2]=>100010=>[1,4,2]
[7,3,4,5,6,2,1]=>100011=>[1,4,1,1]
[7,3,4,6,1,2,5]=>100100=>[1,3,3]
[7,3,4,6,1,5,2]=>100101=>[1,3,2,1]
[7,3,4,6,2,1,5]=>100110=>[1,3,1,2]
[7,3,4,6,2,5,1]=>100101=>[1,3,2,1]
[7,3,4,6,5,1,2]=>100110=>[1,3,1,2]
[7,3,4,6,5,2,1]=>100111=>[1,3,1,1,1]
[7,3,5,1,2,4,6]=>101000=>[1,2,4]
[7,3,5,1,2,6,4]=>101001=>[1,2,3,1]
[7,3,5,1,4,2,6]=>101010=>[1,2,2,2]
[7,3,5,1,4,6,2]=>101001=>[1,2,3,1]
[7,3,5,1,6,2,4]=>101010=>[1,2,2,2]
[7,3,5,1,6,4,2]=>101011=>[1,2,2,1,1]
[7,3,5,2,1,4,6]=>101100=>[1,2,1,3]
[7,3,5,2,1,6,4]=>101101=>[1,2,1,2,1]
[7,3,5,2,4,1,6]=>101010=>[1,2,2,2]
[7,3,5,2,4,6,1]=>101001=>[1,2,3,1]
[7,3,5,2,6,1,4]=>101010=>[1,2,2,2]
[7,3,5,2,6,4,1]=>101011=>[1,2,2,1,1]
[7,3,5,4,1,2,6]=>101100=>[1,2,1,3]
[7,3,5,4,1,6,2]=>101101=>[1,2,1,2,1]
[7,3,5,4,2,1,6]=>101110=>[1,2,1,1,2]
[7,3,5,4,2,6,1]=>101101=>[1,2,1,2,1]
[7,3,5,4,6,1,2]=>101010=>[1,2,2,2]
[7,3,5,4,6,2,1]=>101011=>[1,2,2,1,1]
[7,3,5,6,1,2,4]=>100100=>[1,3,3]
[7,3,5,6,1,4,2]=>100101=>[1,3,2,1]
[7,3,5,6,2,1,4]=>100110=>[1,3,1,2]
[7,3,5,6,2,4,1]=>100101=>[1,3,2,1]
[7,3,5,6,4,1,2]=>100110=>[1,3,1,2]
[7,3,5,6,4,2,1]=>100111=>[1,3,1,1,1]
[7,3,6,1,2,4,5]=>101000=>[1,2,4]
[7,3,6,1,2,5,4]=>101001=>[1,2,3,1]
[7,3,6,1,4,2,5]=>101010=>[1,2,2,2]
[7,3,6,1,4,5,2]=>101001=>[1,2,3,1]
[7,3,6,1,5,2,4]=>101010=>[1,2,2,2]
[7,3,6,1,5,4,2]=>101011=>[1,2,2,1,1]
[7,3,6,2,1,4,5]=>101100=>[1,2,1,3]
[7,3,6,2,1,5,4]=>101101=>[1,2,1,2,1]
[7,3,6,2,4,1,5]=>101010=>[1,2,2,2]
[7,3,6,2,4,5,1]=>101001=>[1,2,3,1]
[7,3,6,2,5,1,4]=>101010=>[1,2,2,2]
[7,3,6,2,5,4,1]=>101011=>[1,2,2,1,1]
[7,3,6,4,1,2,5]=>101100=>[1,2,1,3]
[7,3,6,4,1,5,2]=>101101=>[1,2,1,2,1]
[7,3,6,4,2,1,5]=>101110=>[1,2,1,1,2]
[7,3,6,4,2,5,1]=>101101=>[1,2,1,2,1]
[7,3,6,4,5,1,2]=>101010=>[1,2,2,2]
[7,3,6,4,5,2,1]=>101011=>[1,2,2,1,1]
[7,3,6,5,1,2,4]=>101100=>[1,2,1,3]
[7,3,6,5,1,4,2]=>101101=>[1,2,1,2,1]
[7,3,6,5,2,1,4]=>101110=>[1,2,1,1,2]
[7,3,6,5,2,4,1]=>101101=>[1,2,1,2,1]
[7,3,6,5,4,1,2]=>101110=>[1,2,1,1,2]
[7,3,6,5,4,2,1]=>101111=>[1,2,1,1,1,1]
[7,4,1,2,3,5,6]=>110000=>[1,1,5]
[7,4,1,2,3,6,5]=>110001=>[1,1,4,1]
[7,4,1,2,5,3,6]=>110010=>[1,1,3,2]
[7,4,1,2,5,6,3]=>110001=>[1,1,4,1]
[7,4,1,2,6,3,5]=>110010=>[1,1,3,2]
[7,4,1,2,6,5,3]=>110011=>[1,1,3,1,1]
[7,4,1,3,2,5,6]=>110100=>[1,1,2,3]
[7,4,1,3,2,6,5]=>110101=>[1,1,2,2,1]
[7,4,1,3,5,2,6]=>110010=>[1,1,3,2]
[7,4,1,3,5,6,2]=>110001=>[1,1,4,1]
[7,4,1,3,6,2,5]=>110010=>[1,1,3,2]
[7,4,1,3,6,5,2]=>110011=>[1,1,3,1,1]
[7,4,1,5,2,3,6]=>110100=>[1,1,2,3]
[7,4,1,5,2,6,3]=>110101=>[1,1,2,2,1]
[7,4,1,5,3,2,6]=>110110=>[1,1,2,1,2]
[7,4,1,5,3,6,2]=>110101=>[1,1,2,2,1]
[7,4,1,5,6,2,3]=>110010=>[1,1,3,2]
[7,4,1,5,6,3,2]=>110011=>[1,1,3,1,1]
[7,4,1,6,2,3,5]=>110100=>[1,1,2,3]
[7,4,1,6,2,5,3]=>110101=>[1,1,2,2,1]
[7,4,1,6,3,2,5]=>110110=>[1,1,2,1,2]
[7,4,1,6,3,5,2]=>110101=>[1,1,2,2,1]
[7,4,1,6,5,2,3]=>110110=>[1,1,2,1,2]
[7,4,1,6,5,3,2]=>110111=>[1,1,2,1,1,1]
[7,4,2,1,3,5,6]=>111000=>[1,1,1,4]
[7,4,2,1,3,6,5]=>111001=>[1,1,1,3,1]
[7,4,2,1,5,3,6]=>111010=>[1,1,1,2,2]
[7,4,2,1,5,6,3]=>111001=>[1,1,1,3,1]
[7,4,2,1,6,3,5]=>111010=>[1,1,1,2,2]
[7,4,2,1,6,5,3]=>111011=>[1,1,1,2,1,1]
[7,4,2,3,1,5,6]=>110100=>[1,1,2,3]
[7,4,2,3,1,6,5]=>110101=>[1,1,2,2,1]
[7,4,2,3,5,1,6]=>110010=>[1,1,3,2]
[7,4,2,3,5,6,1]=>110001=>[1,1,4,1]
[7,4,2,3,6,1,5]=>110010=>[1,1,3,2]
[7,4,2,3,6,5,1]=>110011=>[1,1,3,1,1]
[7,4,2,5,1,3,6]=>110100=>[1,1,2,3]
[7,4,2,5,1,6,3]=>110101=>[1,1,2,2,1]
[7,4,2,5,3,1,6]=>110110=>[1,1,2,1,2]
[7,4,2,5,3,6,1]=>110101=>[1,1,2,2,1]
[7,4,2,5,6,1,3]=>110010=>[1,1,3,2]
[7,4,2,5,6,3,1]=>110011=>[1,1,3,1,1]
[7,4,2,6,1,3,5]=>110100=>[1,1,2,3]
[7,4,2,6,1,5,3]=>110101=>[1,1,2,2,1]
[7,4,2,6,3,1,5]=>110110=>[1,1,2,1,2]
[7,4,2,6,3,5,1]=>110101=>[1,1,2,2,1]
[7,4,2,6,5,1,3]=>110110=>[1,1,2,1,2]
[7,4,2,6,5,3,1]=>110111=>[1,1,2,1,1,1]
[7,4,3,1,2,5,6]=>111000=>[1,1,1,4]
[7,4,3,1,2,6,5]=>111001=>[1,1,1,3,1]
[7,4,3,1,5,2,6]=>111010=>[1,1,1,2,2]
[7,4,3,1,5,6,2]=>111001=>[1,1,1,3,1]
[7,4,3,1,6,2,5]=>111010=>[1,1,1,2,2]
[7,4,3,1,6,5,2]=>111011=>[1,1,1,2,1,1]
[7,4,3,2,1,5,6]=>111100=>[1,1,1,1,3]
[7,4,3,2,1,6,5]=>111101=>[1,1,1,1,2,1]
[7,4,3,2,5,1,6]=>111010=>[1,1,1,2,2]
[7,4,3,2,5,6,1]=>111001=>[1,1,1,3,1]
[7,4,3,2,6,1,5]=>111010=>[1,1,1,2,2]
[7,4,3,2,6,5,1]=>111011=>[1,1,1,2,1,1]
[7,4,3,5,1,2,6]=>110100=>[1,1,2,3]
[7,4,3,5,1,6,2]=>110101=>[1,1,2,2,1]
[7,4,3,5,2,1,6]=>110110=>[1,1,2,1,2]
[7,4,3,5,2,6,1]=>110101=>[1,1,2,2,1]
[7,4,3,5,6,1,2]=>110010=>[1,1,3,2]
[7,4,3,5,6,2,1]=>110011=>[1,1,3,1,1]
[7,4,3,6,1,2,5]=>110100=>[1,1,2,3]
[7,4,3,6,1,5,2]=>110101=>[1,1,2,2,1]
[7,4,3,6,2,1,5]=>110110=>[1,1,2,1,2]
[7,4,3,6,2,5,1]=>110101=>[1,1,2,2,1]
[7,4,3,6,5,1,2]=>110110=>[1,1,2,1,2]
[7,4,3,6,5,2,1]=>110111=>[1,1,2,1,1,1]
[7,4,5,1,2,3,6]=>101000=>[1,2,4]
[7,4,5,1,2,6,3]=>101001=>[1,2,3,1]
[7,4,5,1,3,2,6]=>101010=>[1,2,2,2]
[7,4,5,1,3,6,2]=>101001=>[1,2,3,1]
[7,4,5,1,6,2,3]=>101010=>[1,2,2,2]
[7,4,5,1,6,3,2]=>101011=>[1,2,2,1,1]
[7,4,5,2,1,3,6]=>101100=>[1,2,1,3]
[7,4,5,2,1,6,3]=>101101=>[1,2,1,2,1]
[7,4,5,2,3,1,6]=>101010=>[1,2,2,2]
[7,4,5,2,3,6,1]=>101001=>[1,2,3,1]
[7,4,5,2,6,1,3]=>101010=>[1,2,2,2]
[7,4,5,2,6,3,1]=>101011=>[1,2,2,1,1]
[7,4,5,3,1,2,6]=>101100=>[1,2,1,3]
[7,4,5,3,1,6,2]=>101101=>[1,2,1,2,1]
[7,4,5,3,2,1,6]=>101110=>[1,2,1,1,2]
[7,4,5,3,2,6,1]=>101101=>[1,2,1,2,1]
[7,4,5,3,6,1,2]=>101010=>[1,2,2,2]
[7,4,5,3,6,2,1]=>101011=>[1,2,2,1,1]
[7,4,5,6,1,2,3]=>100100=>[1,3,3]
[7,4,5,6,1,3,2]=>100101=>[1,3,2,1]
[7,4,5,6,2,1,3]=>100110=>[1,3,1,2]
[7,4,5,6,2,3,1]=>100101=>[1,3,2,1]
[7,4,5,6,3,1,2]=>100110=>[1,3,1,2]
[7,4,5,6,3,2,1]=>100111=>[1,3,1,1,1]
[7,4,6,1,2,3,5]=>101000=>[1,2,4]
[7,4,6,1,2,5,3]=>101001=>[1,2,3,1]
[7,4,6,1,3,2,5]=>101010=>[1,2,2,2]
[7,4,6,1,3,5,2]=>101001=>[1,2,3,1]
[7,4,6,1,5,2,3]=>101010=>[1,2,2,2]
[7,4,6,1,5,3,2]=>101011=>[1,2,2,1,1]
[7,4,6,2,1,3,5]=>101100=>[1,2,1,3]
[7,4,6,2,1,5,3]=>101101=>[1,2,1,2,1]
[7,4,6,2,3,1,5]=>101010=>[1,2,2,2]
[7,4,6,2,3,5,1]=>101001=>[1,2,3,1]
[7,4,6,2,5,1,3]=>101010=>[1,2,2,2]
[7,4,6,2,5,3,1]=>101011=>[1,2,2,1,1]
[7,4,6,3,1,2,5]=>101100=>[1,2,1,3]
[7,4,6,3,1,5,2]=>101101=>[1,2,1,2,1]
[7,4,6,3,2,1,5]=>101110=>[1,2,1,1,2]
[7,4,6,3,2,5,1]=>101101=>[1,2,1,2,1]
[7,4,6,3,5,1,2]=>101010=>[1,2,2,2]
[7,4,6,3,5,2,1]=>101011=>[1,2,2,1,1]
[7,4,6,5,1,2,3]=>101100=>[1,2,1,3]
[7,4,6,5,1,3,2]=>101101=>[1,2,1,2,1]
[7,4,6,5,2,1,3]=>101110=>[1,2,1,1,2]
[7,4,6,5,2,3,1]=>101101=>[1,2,1,2,1]
[7,4,6,5,3,1,2]=>101110=>[1,2,1,1,2]
[7,4,6,5,3,2,1]=>101111=>[1,2,1,1,1,1]
[7,5,1,2,3,4,6]=>110000=>[1,1,5]
[7,5,1,2,3,6,4]=>110001=>[1,1,4,1]
[7,5,1,2,4,3,6]=>110010=>[1,1,3,2]
[7,5,1,2,4,6,3]=>110001=>[1,1,4,1]
[7,5,1,2,6,3,4]=>110010=>[1,1,3,2]
[7,5,1,2,6,4,3]=>110011=>[1,1,3,1,1]
[7,5,1,3,2,4,6]=>110100=>[1,1,2,3]
[7,5,1,3,2,6,4]=>110101=>[1,1,2,2,1]
[7,5,1,3,4,2,6]=>110010=>[1,1,3,2]
[7,5,1,3,4,6,2]=>110001=>[1,1,4,1]
[7,5,1,3,6,2,4]=>110010=>[1,1,3,2]
[7,5,1,3,6,4,2]=>110011=>[1,1,3,1,1]
[7,5,1,4,2,3,6]=>110100=>[1,1,2,3]
[7,5,1,4,2,6,3]=>110101=>[1,1,2,2,1]
[7,5,1,4,3,2,6]=>110110=>[1,1,2,1,2]
[7,5,1,4,3,6,2]=>110101=>[1,1,2,2,1]
[7,5,1,4,6,2,3]=>110010=>[1,1,3,2]
[7,5,1,4,6,3,2]=>110011=>[1,1,3,1,1]
[7,5,1,6,2,3,4]=>110100=>[1,1,2,3]
[7,5,1,6,2,4,3]=>110101=>[1,1,2,2,1]
[7,5,1,6,3,2,4]=>110110=>[1,1,2,1,2]
[7,5,1,6,3,4,2]=>110101=>[1,1,2,2,1]
[7,5,1,6,4,2,3]=>110110=>[1,1,2,1,2]
[7,5,1,6,4,3,2]=>110111=>[1,1,2,1,1,1]
[7,5,2,1,3,4,6]=>111000=>[1,1,1,4]
[7,5,2,1,3,6,4]=>111001=>[1,1,1,3,1]
[7,5,2,1,4,3,6]=>111010=>[1,1,1,2,2]
[7,5,2,1,4,6,3]=>111001=>[1,1,1,3,1]
[7,5,2,1,6,3,4]=>111010=>[1,1,1,2,2]
[7,5,2,1,6,4,3]=>111011=>[1,1,1,2,1,1]
[7,5,2,3,1,4,6]=>110100=>[1,1,2,3]
[7,5,2,3,1,6,4]=>110101=>[1,1,2,2,1]
[7,5,2,3,4,1,6]=>110010=>[1,1,3,2]
[7,5,2,3,4,6,1]=>110001=>[1,1,4,1]
[7,5,2,3,6,1,4]=>110010=>[1,1,3,2]
[7,5,2,3,6,4,1]=>110011=>[1,1,3,1,1]
[7,5,2,4,1,3,6]=>110100=>[1,1,2,3]
[7,5,2,4,1,6,3]=>110101=>[1,1,2,2,1]
[7,5,2,4,3,1,6]=>110110=>[1,1,2,1,2]
[7,5,2,4,3,6,1]=>110101=>[1,1,2,2,1]
[7,5,2,4,6,1,3]=>110010=>[1,1,3,2]
[7,5,2,4,6,3,1]=>110011=>[1,1,3,1,1]
[7,5,2,6,1,3,4]=>110100=>[1,1,2,3]
[7,5,2,6,1,4,3]=>110101=>[1,1,2,2,1]
[7,5,2,6,3,1,4]=>110110=>[1,1,2,1,2]
[7,5,2,6,3,4,1]=>110101=>[1,1,2,2,1]
[7,5,2,6,4,1,3]=>110110=>[1,1,2,1,2]
[7,5,2,6,4,3,1]=>110111=>[1,1,2,1,1,1]
[7,5,3,1,2,4,6]=>111000=>[1,1,1,4]
[7,5,3,1,2,6,4]=>111001=>[1,1,1,3,1]
[7,5,3,1,4,2,6]=>111010=>[1,1,1,2,2]
[7,5,3,1,4,6,2]=>111001=>[1,1,1,3,1]
[7,5,3,1,6,2,4]=>111010=>[1,1,1,2,2]
[7,5,3,1,6,4,2]=>111011=>[1,1,1,2,1,1]
[7,5,3,2,1,4,6]=>111100=>[1,1,1,1,3]
[7,5,3,2,1,6,4]=>111101=>[1,1,1,1,2,1]
[7,5,3,2,4,1,6]=>111010=>[1,1,1,2,2]
[7,5,3,2,4,6,1]=>111001=>[1,1,1,3,1]
[7,5,3,2,6,1,4]=>111010=>[1,1,1,2,2]
[7,5,3,2,6,4,1]=>111011=>[1,1,1,2,1,1]
[7,5,3,4,1,2,6]=>110100=>[1,1,2,3]
[7,5,3,4,1,6,2]=>110101=>[1,1,2,2,1]
[7,5,3,4,2,1,6]=>110110=>[1,1,2,1,2]
[7,5,3,4,2,6,1]=>110101=>[1,1,2,2,1]
[7,5,3,4,6,1,2]=>110010=>[1,1,3,2]
[7,5,3,4,6,2,1]=>110011=>[1,1,3,1,1]
[7,5,3,6,1,2,4]=>110100=>[1,1,2,3]
[7,5,3,6,1,4,2]=>110101=>[1,1,2,2,1]
[7,5,3,6,2,1,4]=>110110=>[1,1,2,1,2]
[7,5,3,6,2,4,1]=>110101=>[1,1,2,2,1]
[7,5,3,6,4,1,2]=>110110=>[1,1,2,1,2]
[7,5,3,6,4,2,1]=>110111=>[1,1,2,1,1,1]
[7,5,4,1,2,3,6]=>111000=>[1,1,1,4]
[7,5,4,1,2,6,3]=>111001=>[1,1,1,3,1]
[7,5,4,1,3,2,6]=>111010=>[1,1,1,2,2]
[7,5,4,1,3,6,2]=>111001=>[1,1,1,3,1]
[7,5,4,1,6,2,3]=>111010=>[1,1,1,2,2]
[7,5,4,1,6,3,2]=>111011=>[1,1,1,2,1,1]
[7,5,4,2,1,3,6]=>111100=>[1,1,1,1,3]
[7,5,4,2,1,6,3]=>111101=>[1,1,1,1,2,1]
[7,5,4,2,3,1,6]=>111010=>[1,1,1,2,2]
[7,5,4,2,3,6,1]=>111001=>[1,1,1,3,1]
[7,5,4,2,6,1,3]=>111010=>[1,1,1,2,2]
[7,5,4,2,6,3,1]=>111011=>[1,1,1,2,1,1]
[7,5,4,3,1,2,6]=>111100=>[1,1,1,1,3]
[7,5,4,3,1,6,2]=>111101=>[1,1,1,1,2,1]
[7,5,4,3,2,1,6]=>111110=>[1,1,1,1,1,2]
[7,5,4,3,2,6,1]=>111101=>[1,1,1,1,2,1]
[7,5,4,3,6,1,2]=>111010=>[1,1,1,2,2]
[7,5,4,3,6,2,1]=>111011=>[1,1,1,2,1,1]
[7,5,4,6,1,2,3]=>110100=>[1,1,2,3]
[7,5,4,6,1,3,2]=>110101=>[1,1,2,2,1]
[7,5,4,6,2,1,3]=>110110=>[1,1,2,1,2]
[7,5,4,6,2,3,1]=>110101=>[1,1,2,2,1]
[7,5,4,6,3,1,2]=>110110=>[1,1,2,1,2]
[7,5,4,6,3,2,1]=>110111=>[1,1,2,1,1,1]
[7,5,6,1,2,3,4]=>101000=>[1,2,4]
[7,5,6,1,2,4,3]=>101001=>[1,2,3,1]
[7,5,6,1,3,2,4]=>101010=>[1,2,2,2]
[7,5,6,1,3,4,2]=>101001=>[1,2,3,1]
[7,5,6,1,4,2,3]=>101010=>[1,2,2,2]
[7,5,6,1,4,3,2]=>101011=>[1,2,2,1,1]
[7,5,6,2,1,3,4]=>101100=>[1,2,1,3]
[7,5,6,2,1,4,3]=>101101=>[1,2,1,2,1]
[7,5,6,2,3,1,4]=>101010=>[1,2,2,2]
[7,5,6,2,3,4,1]=>101001=>[1,2,3,1]
[7,5,6,2,4,1,3]=>101010=>[1,2,2,2]
[7,5,6,2,4,3,1]=>101011=>[1,2,2,1,1]
[7,5,6,3,1,2,4]=>101100=>[1,2,1,3]
[7,5,6,3,1,4,2]=>101101=>[1,2,1,2,1]
[7,5,6,3,2,1,4]=>101110=>[1,2,1,1,2]
[7,5,6,3,2,4,1]=>101101=>[1,2,1,2,1]
[7,5,6,3,4,1,2]=>101010=>[1,2,2,2]
[7,5,6,3,4,2,1]=>101011=>[1,2,2,1,1]
[7,5,6,4,1,2,3]=>101100=>[1,2,1,3]
[7,5,6,4,1,3,2]=>101101=>[1,2,1,2,1]
[7,5,6,4,2,1,3]=>101110=>[1,2,1,1,2]
[7,5,6,4,2,3,1]=>101101=>[1,2,1,2,1]
[7,5,6,4,3,1,2]=>101110=>[1,2,1,1,2]
[7,5,6,4,3,2,1]=>101111=>[1,2,1,1,1,1]
[7,6,1,2,3,4,5]=>110000=>[1,1,5]
[7,6,1,2,3,5,4]=>110001=>[1,1,4,1]
[7,6,1,2,4,3,5]=>110010=>[1,1,3,2]
[7,6,1,2,4,5,3]=>110001=>[1,1,4,1]
[7,6,1,2,5,3,4]=>110010=>[1,1,3,2]
[7,6,1,2,5,4,3]=>110011=>[1,1,3,1,1]
[7,6,1,3,2,4,5]=>110100=>[1,1,2,3]
[7,6,1,3,2,5,4]=>110101=>[1,1,2,2,1]
[7,6,1,3,4,2,5]=>110010=>[1,1,3,2]
[7,6,1,3,4,5,2]=>110001=>[1,1,4,1]
[7,6,1,3,5,2,4]=>110010=>[1,1,3,2]
[7,6,1,3,5,4,2]=>110011=>[1,1,3,1,1]
[7,6,1,4,2,3,5]=>110100=>[1,1,2,3]
[7,6,1,4,2,5,3]=>110101=>[1,1,2,2,1]
[7,6,1,4,3,2,5]=>110110=>[1,1,2,1,2]
[7,6,1,4,3,5,2]=>110101=>[1,1,2,2,1]
[7,6,1,4,5,2,3]=>110010=>[1,1,3,2]
[7,6,1,4,5,3,2]=>110011=>[1,1,3,1,1]
[7,6,1,5,2,3,4]=>110100=>[1,1,2,3]
[7,6,1,5,2,4,3]=>110101=>[1,1,2,2,1]
[7,6,1,5,3,2,4]=>110110=>[1,1,2,1,2]
[7,6,1,5,3,4,2]=>110101=>[1,1,2,2,1]
[7,6,1,5,4,2,3]=>110110=>[1,1,2,1,2]
[7,6,1,5,4,3,2]=>110111=>[1,1,2,1,1,1]
[7,6,2,1,3,4,5]=>111000=>[1,1,1,4]
[7,6,2,1,3,5,4]=>111001=>[1,1,1,3,1]
[7,6,2,1,4,3,5]=>111010=>[1,1,1,2,2]
[7,6,2,1,4,5,3]=>111001=>[1,1,1,3,1]
[7,6,2,1,5,3,4]=>111010=>[1,1,1,2,2]
[7,6,2,1,5,4,3]=>111011=>[1,1,1,2,1,1]
[7,6,2,3,1,4,5]=>110100=>[1,1,2,3]
[7,6,2,3,1,5,4]=>110101=>[1,1,2,2,1]
[7,6,2,3,4,1,5]=>110010=>[1,1,3,2]
[7,6,2,3,4,5,1]=>110001=>[1,1,4,1]
[7,6,2,3,5,1,4]=>110010=>[1,1,3,2]
[7,6,2,3,5,4,1]=>110011=>[1,1,3,1,1]
[7,6,2,4,1,3,5]=>110100=>[1,1,2,3]
[7,6,2,4,1,5,3]=>110101=>[1,1,2,2,1]
[7,6,2,4,3,1,5]=>110110=>[1,1,2,1,2]
[7,6,2,4,3,5,1]=>110101=>[1,1,2,2,1]
[7,6,2,4,5,1,3]=>110010=>[1,1,3,2]
[7,6,2,4,5,3,1]=>110011=>[1,1,3,1,1]
[7,6,2,5,1,3,4]=>110100=>[1,1,2,3]
[7,6,2,5,1,4,3]=>110101=>[1,1,2,2,1]
[7,6,2,5,3,1,4]=>110110=>[1,1,2,1,2]
[7,6,2,5,3,4,1]=>110101=>[1,1,2,2,1]
[7,6,2,5,4,1,3]=>110110=>[1,1,2,1,2]
[7,6,2,5,4,3,1]=>110111=>[1,1,2,1,1,1]
[7,6,3,1,2,4,5]=>111000=>[1,1,1,4]
[7,6,3,1,2,5,4]=>111001=>[1,1,1,3,1]
[7,6,3,1,4,2,5]=>111010=>[1,1,1,2,2]
[7,6,3,1,4,5,2]=>111001=>[1,1,1,3,1]
[7,6,3,1,5,2,4]=>111010=>[1,1,1,2,2]
[7,6,3,1,5,4,2]=>111011=>[1,1,1,2,1,1]
[7,6,3,2,1,4,5]=>111100=>[1,1,1,1,3]
[7,6,3,2,1,5,4]=>111101=>[1,1,1,1,2,1]
[7,6,3,2,4,1,5]=>111010=>[1,1,1,2,2]
[7,6,3,2,4,5,1]=>111001=>[1,1,1,3,1]
[7,6,3,2,5,1,4]=>111010=>[1,1,1,2,2]
[7,6,3,2,5,4,1]=>111011=>[1,1,1,2,1,1]
[7,6,3,4,1,2,5]=>110100=>[1,1,2,3]
[7,6,3,4,1,5,2]=>110101=>[1,1,2,2,1]
[7,6,3,4,2,1,5]=>110110=>[1,1,2,1,2]
[7,6,3,4,2,5,1]=>110101=>[1,1,2,2,1]
[7,6,3,4,5,1,2]=>110010=>[1,1,3,2]
[7,6,3,4,5,2,1]=>110011=>[1,1,3,1,1]
[7,6,3,5,1,2,4]=>110100=>[1,1,2,3]
[7,6,3,5,1,4,2]=>110101=>[1,1,2,2,1]
[7,6,3,5,2,1,4]=>110110=>[1,1,2,1,2]
[7,6,3,5,2,4,1]=>110101=>[1,1,2,2,1]
[7,6,3,5,4,1,2]=>110110=>[1,1,2,1,2]
[7,6,3,5,4,2,1]=>110111=>[1,1,2,1,1,1]
[7,6,4,1,2,3,5]=>111000=>[1,1,1,4]
[7,6,4,1,2,5,3]=>111001=>[1,1,1,3,1]
[7,6,4,1,3,2,5]=>111010=>[1,1,1,2,2]
[7,6,4,1,3,5,2]=>111001=>[1,1,1,3,1]
[7,6,4,1,5,2,3]=>111010=>[1,1,1,2,2]
[7,6,4,1,5,3,2]=>111011=>[1,1,1,2,1,1]
[7,6,4,2,1,3,5]=>111100=>[1,1,1,1,3]
[7,6,4,2,1,5,3]=>111101=>[1,1,1,1,2,1]
[7,6,4,2,3,1,5]=>111010=>[1,1,1,2,2]
[7,6,4,2,3,5,1]=>111001=>[1,1,1,3,1]
[7,6,4,2,5,1,3]=>111010=>[1,1,1,2,2]
[7,6,4,2,5,3,1]=>111011=>[1,1,1,2,1,1]
[7,6,4,3,1,2,5]=>111100=>[1,1,1,1,3]
[7,6,4,3,1,5,2]=>111101=>[1,1,1,1,2,1]
[7,6,4,3,2,1,5]=>111110=>[1,1,1,1,1,2]
[7,6,4,3,2,5,1]=>111101=>[1,1,1,1,2,1]
[7,6,4,3,5,1,2]=>111010=>[1,1,1,2,2]
[7,6,4,3,5,2,1]=>111011=>[1,1,1,2,1,1]
[7,6,4,5,1,2,3]=>110100=>[1,1,2,3]
[7,6,4,5,1,3,2]=>110101=>[1,1,2,2,1]
[7,6,4,5,2,1,3]=>110110=>[1,1,2,1,2]
[7,6,4,5,2,3,1]=>110101=>[1,1,2,2,1]
[7,6,4,5,3,1,2]=>110110=>[1,1,2,1,2]
[7,6,4,5,3,2,1]=>110111=>[1,1,2,1,1,1]
[7,6,5,1,2,3,4]=>111000=>[1,1,1,4]
[7,6,5,1,2,4,3]=>111001=>[1,1,1,3,1]
[7,6,5,1,3,2,4]=>111010=>[1,1,1,2,2]
[7,6,5,1,3,4,2]=>111001=>[1,1,1,3,1]
[7,6,5,1,4,2,3]=>111010=>[1,1,1,2,2]
[7,6,5,1,4,3,2]=>111011=>[1,1,1,2,1,1]
[7,6,5,2,1,3,4]=>111100=>[1,1,1,1,3]
[7,6,5,2,1,4,3]=>111101=>[1,1,1,1,2,1]
[7,6,5,2,3,1,4]=>111010=>[1,1,1,2,2]
[7,6,5,2,3,4,1]=>111001=>[1,1,1,3,1]
[7,6,5,2,4,1,3]=>111010=>[1,1,1,2,2]
[7,6,5,2,4,3,1]=>111011=>[1,1,1,2,1,1]
[7,6,5,3,1,2,4]=>111100=>[1,1,1,1,3]
[7,6,5,3,1,4,2]=>111101=>[1,1,1,1,2,1]
[7,6,5,3,2,1,4]=>111110=>[1,1,1,1,1,2]
[7,6,5,3,2,4,1]=>111101=>[1,1,1,1,2,1]
[7,6,5,3,4,1,2]=>111010=>[1,1,1,2,2]
[7,6,5,3,4,2,1]=>111011=>[1,1,1,2,1,1]
[7,6,5,4,1,2,3]=>111100=>[1,1,1,1,3]
[7,6,5,4,1,3,2]=>111101=>[1,1,1,1,2,1]
[7,6,5,4,2,1,3]=>111110=>[1,1,1,1,1,2]
[7,6,5,4,2,3,1]=>111101=>[1,1,1,1,2,1]
[7,6,5,4,3,1,2]=>111110=>[1,1,1,1,1,2]
[7,6,5,4,3,2,1]=>111111=>[1,1,1,1,1,1,1]
[8,7,6,5,4,3,2,1]=>1111111=>[1,1,1,1,1,1,1,1]
[7,8,6,5,4,3,2,1]=>0111111=>[2,1,1,1,1,1,1]
[8,6,7,5,4,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[7,6,8,5,4,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[6,7,8,5,4,3,2,1]=>0011111=>[3,1,1,1,1,1]
[8,7,5,6,4,3,2,1]=>1101111=>[1,1,2,1,1,1,1]
[7,8,5,6,4,3,2,1]=>0101111=>[2,2,1,1,1,1]
[8,6,5,7,4,3,2,1]=>1101111=>[1,1,2,1,1,1,1]
[8,5,6,7,4,3,2,1]=>1001111=>[1,3,1,1,1,1]
[7,6,5,8,4,3,2,1]=>1101111=>[1,1,2,1,1,1,1]
[6,7,5,8,4,3,2,1]=>0101111=>[2,2,1,1,1,1]
[7,5,6,8,4,3,2,1]=>1001111=>[1,3,1,1,1,1]
[6,5,7,8,4,3,2,1]=>1001111=>[1,3,1,1,1,1]
[5,6,7,8,4,3,2,1]=>0001111=>[4,1,1,1,1]
[8,7,6,4,5,3,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,4,5,3,2,1]=>1010111=>[1,2,2,1,1,1]
[7,6,8,4,5,3,2,1]=>1010111=>[1,2,2,1,1,1]
[8,7,5,4,6,3,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,6,5,4,7,3,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,5,6,4,7,3,2,1]=>1010111=>[1,2,2,1,1,1]
[8,6,4,5,7,3,2,1]=>1100111=>[1,1,3,1,1,1]
[7,6,5,4,8,3,2,1]=>1110111=>[1,1,1,2,1,1,1]
[6,7,5,4,8,3,2,1]=>0110111=>[2,1,2,1,1,1]
[7,5,6,4,8,3,2,1]=>1010111=>[1,2,2,1,1,1]
[6,5,7,4,8,3,2,1]=>1010111=>[1,2,2,1,1,1]
[5,6,7,4,8,3,2,1]=>0010111=>[3,2,1,1,1]
[7,6,4,5,8,3,2,1]=>1100111=>[1,1,3,1,1,1]
[6,7,4,5,8,3,2,1]=>0100111=>[2,3,1,1,1]
[7,5,4,6,8,3,2,1]=>1100111=>[1,1,3,1,1,1]
[7,4,5,6,8,3,2,1]=>1000111=>[1,4,1,1,1]
[6,5,4,7,8,3,2,1]=>1100111=>[1,1,3,1,1,1]
[5,6,4,7,8,3,2,1]=>0100111=>[2,3,1,1,1]
[6,4,5,7,8,3,2,1]=>1000111=>[1,4,1,1,1]
[5,4,6,7,8,3,2,1]=>1000111=>[1,4,1,1,1]
[4,5,6,7,8,3,2,1]=>0000111=>[5,1,1,1]
[8,7,6,5,3,4,2,1]=>1111011=>[1,1,1,1,2,1,1]
[7,8,6,5,3,4,2,1]=>0111011=>[2,1,1,2,1,1]
[7,6,8,5,3,4,2,1]=>1011011=>[1,2,1,2,1,1]
[8,7,5,6,3,4,2,1]=>1101011=>[1,1,2,2,1,1]
[7,8,5,6,3,4,2,1]=>0101011=>[2,2,2,1,1]
[8,5,6,7,3,4,2,1]=>1001011=>[1,3,2,1,1]
[7,6,5,8,3,4,2,1]=>1101011=>[1,1,2,2,1,1]
[6,7,5,8,3,4,2,1]=>0101011=>[2,2,2,1,1]
[5,6,7,8,3,4,2,1]=>0001011=>[4,2,1,1]
[8,7,6,4,3,5,2,1]=>1111011=>[1,1,1,1,2,1,1]
[7,8,6,4,3,5,2,1]=>0111011=>[2,1,1,2,1,1]
[7,6,8,4,3,5,2,1]=>1011011=>[1,2,1,2,1,1]
[6,7,8,4,3,5,2,1]=>0011011=>[3,1,2,1,1]
[8,7,6,3,4,5,2,1]=>1110011=>[1,1,1,3,1,1]
[7,8,6,3,4,5,2,1]=>0110011=>[2,1,3,1,1]
[8,6,7,3,4,5,2,1]=>1010011=>[1,2,3,1,1]
[7,6,8,3,4,5,2,1]=>1010011=>[1,2,3,1,1]
[6,7,8,3,4,5,2,1]=>0010011=>[3,3,1,1]
[8,7,5,4,3,6,2,1]=>1111011=>[1,1,1,1,2,1,1]
[7,8,5,4,3,6,2,1]=>0111011=>[2,1,1,2,1,1]
[7,8,5,3,4,6,2,1]=>0110011=>[2,1,3,1,1]
[8,7,4,3,5,6,2,1]=>1110011=>[1,1,1,3,1,1]
[8,7,3,4,5,6,2,1]=>1100011=>[1,1,4,1,1]
[7,6,5,4,3,8,2,1]=>1111011=>[1,1,1,1,2,1,1]
[7,5,6,4,3,8,2,1]=>1011011=>[1,2,1,2,1,1]
[7,4,5,6,3,8,2,1]=>1001011=>[1,3,2,1,1]
[6,4,5,7,3,8,2,1]=>1001011=>[1,3,2,1,1]
[5,4,6,7,3,8,2,1]=>1001011=>[1,3,2,1,1]
[4,5,6,7,3,8,2,1]=>0001011=>[4,2,1,1]
[7,6,3,4,5,8,2,1]=>1100011=>[1,1,4,1,1]
[7,5,4,3,6,8,2,1]=>1110011=>[1,1,1,3,1,1]
[7,5,3,4,6,8,2,1]=>1100011=>[1,1,4,1,1]
[6,5,4,3,7,8,2,1]=>1110011=>[1,1,1,3,1,1]
[8,7,6,5,4,2,3,1]=>1111101=>[1,1,1,1,1,2,1]
[8,6,7,5,4,2,3,1]=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,4,2,3,1]=>1011101=>[1,2,1,1,2,1]
[8,5,6,7,4,2,3,1]=>1001101=>[1,3,1,2,1]
[7,6,5,8,4,2,3,1]=>1101101=>[1,1,2,1,2,1]
[6,7,5,8,4,2,3,1]=>0101101=>[2,2,1,2,1]
[7,5,6,8,4,2,3,1]=>1001101=>[1,3,1,2,1]
[5,6,7,8,4,2,3,1]=>0001101=>[4,1,2,1]
[8,7,6,4,5,2,3,1]=>1110101=>[1,1,1,2,2,1]
[8,6,7,4,5,2,3,1]=>1010101=>[1,2,2,2,1]
[7,6,8,4,5,2,3,1]=>1010101=>[1,2,2,2,1]
[8,7,5,4,6,2,3,1]=>1110101=>[1,1,1,2,2,1]
[8,7,4,5,6,2,3,1]=>1100101=>[1,1,3,2,1]
[8,6,5,4,7,2,3,1]=>1110101=>[1,1,1,2,2,1]
[8,5,6,4,7,2,3,1]=>1010101=>[1,2,2,2,1]
[8,6,4,5,7,2,3,1]=>1100101=>[1,1,3,2,1]
[7,5,6,4,8,2,3,1]=>1010101=>[1,2,2,2,1]
[6,5,7,4,8,2,3,1]=>1010101=>[1,2,2,2,1]
[4,5,6,7,8,2,3,1]=>0000101=>[5,2,1]
[8,7,6,5,3,2,4,1]=>1111101=>[1,1,1,1,1,2,1]
[7,8,6,5,3,2,4,1]=>0111101=>[2,1,1,1,2,1]
[8,6,7,5,3,2,4,1]=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,3,2,4,1]=>1011101=>[1,2,1,1,2,1]
[6,7,8,5,3,2,4,1]=>0011101=>[3,1,1,2,1]
[8,6,5,7,3,2,4,1]=>1101101=>[1,1,2,1,2,1]
[8,5,6,7,3,2,4,1]=>1001101=>[1,3,1,2,1]
[7,6,5,8,3,2,4,1]=>1101101=>[1,1,2,1,2,1]
[6,7,5,8,3,2,4,1]=>0101101=>[2,2,1,2,1]
[5,6,7,8,3,2,4,1]=>0001101=>[4,1,2,1]
[8,7,6,5,2,3,4,1]=>1111001=>[1,1,1,1,3,1]
[8,6,7,5,2,3,4,1]=>1011001=>[1,2,1,3,1]
[7,6,8,5,2,3,4,1]=>1011001=>[1,2,1,3,1]
[6,7,8,5,2,3,4,1]=>0011001=>[3,1,3,1]
[8,7,5,6,2,3,4,1]=>1101001=>[1,1,2,3,1]
[7,8,5,6,2,3,4,1]=>0101001=>[2,2,3,1]
[8,6,5,7,2,3,4,1]=>1101001=>[1,1,2,3,1]
[8,5,6,7,2,3,4,1]=>1001001=>[1,3,3,1]
[7,6,5,8,2,3,4,1]=>1101001=>[1,1,2,3,1]
[6,7,5,8,2,3,4,1]=>0101001=>[2,2,3,1]
[6,5,7,8,2,3,4,1]=>1001001=>[1,3,3,1]
[5,6,7,8,2,3,4,1]=>0001001=>[4,3,1]
[8,7,6,4,3,2,5,1]=>1111101=>[1,1,1,1,1,2,1]
[7,8,6,4,3,2,5,1]=>0111101=>[2,1,1,1,2,1]
[8,6,7,4,3,2,5,1]=>1011101=>[1,2,1,1,2,1]
[7,6,8,4,3,2,5,1]=>1011101=>[1,2,1,1,2,1]
[6,7,8,4,3,2,5,1]=>0011101=>[3,1,1,2,1]
[8,7,6,3,4,2,5,1]=>1110101=>[1,1,1,2,2,1]
[8,6,7,3,4,2,5,1]=>1010101=>[1,2,2,2,1]
[7,6,8,3,4,2,5,1]=>1010101=>[1,2,2,2,1]
[7,6,8,4,2,3,5,1]=>1011001=>[1,2,1,3,1]
[6,7,8,4,2,3,5,1]=>0011001=>[3,1,3,1]
[8,6,7,3,2,4,5,1]=>1011001=>[1,2,1,3,1]
[6,7,8,3,2,4,5,1]=>0011001=>[3,1,3,1]
[8,7,6,2,3,4,5,1]=>1110001=>[1,1,1,4,1]
[7,8,6,2,3,4,5,1]=>0110001=>[2,1,4,1]
[8,6,7,2,3,4,5,1]=>1010001=>[1,2,4,1]
[7,6,8,2,3,4,5,1]=>1010001=>[1,2,4,1]
[6,7,8,2,3,4,5,1]=>0010001=>[3,4,1]
[8,7,5,3,4,2,6,1]=>1110101=>[1,1,1,2,2,1]
[7,8,5,3,4,2,6,1]=>0110101=>[2,1,2,2,1]
[8,7,5,3,2,4,6,1]=>1111001=>[1,1,1,1,3,1]
[7,8,4,3,2,5,6,1]=>0111001=>[2,1,1,3,1]
[7,8,3,4,2,5,6,1]=>0101001=>[2,2,3,1]
[7,8,3,2,4,5,6,1]=>0110001=>[2,1,4,1]
[8,6,5,4,3,2,7,1]=>1111101=>[1,1,1,1,1,2,1]
[8,5,6,3,4,2,7,1]=>1010101=>[1,2,2,2,1]
[8,6,4,3,5,2,7,1]=>1110101=>[1,1,1,2,2,1]
[8,6,3,4,5,2,7,1]=>1100101=>[1,1,3,2,1]
[8,4,5,3,6,2,7,1]=>1010101=>[1,2,2,2,1]
[8,5,6,4,2,3,7,1]=>1011001=>[1,2,1,3,1]
[8,6,4,2,3,5,7,1]=>1110001=>[1,1,1,4,1]
[8,5,3,4,2,6,7,1]=>1101001=>[1,1,2,3,1]
[8,5,4,2,3,6,7,1]=>1110001=>[1,1,1,4,1]
[7,4,5,6,3,2,8,1]=>1001101=>[1,3,1,2,1]
[6,4,5,7,3,2,8,1]=>1001101=>[1,3,1,2,1]
[4,5,6,7,3,2,8,1]=>0001101=>[4,1,2,1]
[7,5,6,3,4,2,8,1]=>1010101=>[1,2,2,2,1]
[6,5,7,3,4,2,8,1]=>1010101=>[1,2,2,2,1]
[7,4,5,3,6,2,8,1]=>1010101=>[1,2,2,2,1]
[6,5,4,3,7,2,8,1]=>1110101=>[1,1,1,2,2,1]
[6,4,5,3,7,2,8,1]=>1010101=>[1,2,2,2,1]
[5,4,6,3,7,2,8,1]=>1010101=>[1,2,2,2,1]
[4,5,6,3,7,2,8,1]=>0010101=>[3,2,2,1]
[6,5,3,4,7,2,8,1]=>1100101=>[1,1,3,2,1]
[5,6,3,4,7,2,8,1]=>0100101=>[2,3,2,1]
[5,4,3,6,7,2,8,1]=>1100101=>[1,1,3,2,1]
[6,7,5,4,2,3,8,1]=>0111001=>[2,1,1,3,1]
[7,5,6,4,2,3,8,1]=>1011001=>[1,2,1,3,1]
[6,5,7,4,2,3,8,1]=>1011001=>[1,2,1,3,1]
[5,6,7,4,2,3,8,1]=>0011001=>[3,1,3,1]
[6,7,4,5,2,3,8,1]=>0101001=>[2,2,3,1]
[7,4,5,6,2,3,8,1]=>1001001=>[1,3,3,1]
[6,5,4,7,2,3,8,1]=>1101001=>[1,1,2,3,1]
[5,6,4,7,2,3,8,1]=>0101001=>[2,2,3,1]
[6,4,5,7,2,3,8,1]=>1001001=>[1,3,3,1]
[5,4,6,7,2,3,8,1]=>1001001=>[1,3,3,1]
[4,5,6,7,2,3,8,1]=>0001001=>[4,3,1]
[6,7,5,3,2,4,8,1]=>0111001=>[2,1,1,3,1]
[6,5,7,3,2,4,8,1]=>1011001=>[1,2,1,3,1]
[7,6,5,2,3,4,8,1]=>1110001=>[1,1,1,4,1]
[5,6,7,2,3,4,8,1]=>0010001=>[3,4,1]
[6,7,4,3,2,5,8,1]=>0111001=>[2,1,1,3,1]
[7,6,4,2,3,5,8,1]=>1110001=>[1,1,1,4,1]
[6,7,3,2,4,5,8,1]=>0110001=>[2,1,4,1]
[6,7,2,3,4,5,8,1]=>0100001=>[2,5,1]
[7,5,2,3,4,6,8,1]=>1100001=>[1,1,5,1]
[6,5,4,3,2,7,8,1]=>1111001=>[1,1,1,1,3,1]
[5,4,6,3,2,7,8,1]=>1011001=>[1,2,1,3,1]
[5,4,3,6,2,7,8,1]=>1101001=>[1,1,2,3,1]
[3,4,5,6,2,7,8,1]=>0001001=>[4,3,1]
[6,5,4,2,3,7,8,1]=>1110001=>[1,1,1,4,1]
[5,6,4,2,3,7,8,1]=>0110001=>[2,1,4,1]
[6,4,5,2,3,7,8,1]=>1010001=>[1,2,4,1]
[5,4,6,2,3,7,8,1]=>1010001=>[1,2,4,1]
[6,5,2,3,4,7,8,1]=>1100001=>[1,1,5,1]
[5,4,3,2,6,7,8,1]=>1110001=>[1,1,1,4,1]
[4,3,5,2,6,7,8,1]=>1010001=>[1,2,4,1]
[5,4,2,3,6,7,8,1]=>1100001=>[1,1,5,1]
[4,5,2,3,6,7,8,1]=>0100001=>[2,5,1]
[5,2,3,4,6,7,8,1]=>1000001=>[1,6,1]
[4,3,2,5,6,7,8,1]=>1100001=>[1,1,5,1]
[3,4,2,5,6,7,8,1]=>0100001=>[2,5,1]
[3,2,4,5,6,7,8,1]=>1000001=>[1,6,1]
[2,3,4,5,6,7,8,1]=>0000001=>[7,1]
[8,7,6,5,4,3,1,2]=>1111110=>[1,1,1,1,1,1,2]
[7,8,6,5,4,3,1,2]=>0111110=>[2,1,1,1,1,2]
[8,7,5,6,4,3,1,2]=>1101110=>[1,1,2,1,1,2]
[7,8,5,6,4,3,1,2]=>0101110=>[2,2,1,1,2]
[7,6,5,8,4,3,1,2]=>1101110=>[1,1,2,1,1,2]
[6,7,5,8,4,3,1,2]=>0101110=>[2,2,1,1,2]
[7,5,6,8,4,3,1,2]=>1001110=>[1,3,1,1,2]
[5,6,7,8,4,3,1,2]=>0001110=>[4,1,1,2]
[7,8,6,4,5,3,1,2]=>0110110=>[2,1,2,1,2]
[8,6,7,4,5,3,1,2]=>1010110=>[1,2,2,1,2]
[8,7,5,4,6,3,1,2]=>1110110=>[1,1,1,2,1,2]
[8,5,6,4,7,3,1,2]=>1010110=>[1,2,2,1,2]
[6,7,4,5,8,3,1,2]=>0100110=>[2,3,1,2]
[5,6,4,7,8,3,1,2]=>0100110=>[2,3,1,2]
[4,5,6,7,8,3,1,2]=>0000110=>[5,1,2]
[8,7,6,5,3,4,1,2]=>1111010=>[1,1,1,1,2,2]
[7,8,6,5,3,4,1,2]=>0111010=>[2,1,1,2,2]
[6,7,8,5,3,4,1,2]=>0011010=>[3,1,2,2]
[8,7,5,6,3,4,1,2]=>1101010=>[1,1,2,2,2]
[7,8,5,6,3,4,1,2]=>0101010=>[2,2,2,2]
[8,5,6,7,3,4,1,2]=>1001010=>[1,3,2,2]
[7,6,5,8,3,4,1,2]=>1101010=>[1,1,2,2,2]
[6,7,5,8,3,4,1,2]=>0101010=>[2,2,2,2]
[7,5,6,8,3,4,1,2]=>1001010=>[1,3,2,2]
[6,5,7,8,3,4,1,2]=>1001010=>[1,3,2,2]
[5,6,7,8,3,4,1,2]=>0001010=>[4,2,2]
[7,8,5,4,3,6,1,2]=>0111010=>[2,1,1,2,2]
[8,7,4,5,3,6,1,2]=>1101010=>[1,1,2,2,2]
[7,8,4,5,3,6,1,2]=>0101010=>[2,2,2,2]
[7,8,5,3,4,6,1,2]=>0110010=>[2,1,3,2]
[8,7,4,3,5,6,1,2]=>1110010=>[1,1,1,3,2]
[7,8,4,3,5,6,1,2]=>0110010=>[2,1,3,2]
[7,8,3,4,5,6,1,2]=>0100010=>[2,4,2]
[8,5,4,3,6,7,1,2]=>1110010=>[1,1,1,3,2]
[8,5,3,4,6,7,1,2]=>1100010=>[1,1,4,2]
[8,4,3,5,6,7,1,2]=>1100010=>[1,1,4,2]
[7,6,5,4,3,8,1,2]=>1111010=>[1,1,1,1,2,2]
[5,6,7,4,3,8,1,2]=>0011010=>[3,1,2,2]
[6,7,4,5,3,8,1,2]=>0101010=>[2,2,2,2]
[5,6,4,7,3,8,1,2]=>0101010=>[2,2,2,2]
[5,4,6,7,3,8,1,2]=>1001010=>[1,3,2,2]
[4,5,6,7,3,8,1,2]=>0001010=>[4,2,2]
[7,5,6,3,4,8,1,2]=>1010010=>[1,2,3,2]
[7,6,3,4,5,8,1,2]=>1100010=>[1,1,4,2]
[7,5,4,3,6,8,1,2]=>1110010=>[1,1,1,3,2]
[7,5,3,4,6,8,1,2]=>1100010=>[1,1,4,2]
[6,5,4,3,7,8,1,2]=>1110010=>[1,1,1,3,2]
[5,4,6,3,7,8,1,2]=>1010010=>[1,2,3,2]
[4,5,6,3,7,8,1,2]=>0010010=>[3,3,2]
[5,6,3,4,7,8,1,2]=>0100010=>[2,4,2]
[6,4,3,5,7,8,1,2]=>1100010=>[1,1,4,2]
[6,3,4,5,7,8,1,2]=>1000010=>[1,5,2]
[5,4,3,6,7,8,1,2]=>1100010=>[1,1,4,2]
[4,5,3,6,7,8,1,2]=>0100010=>[2,4,2]
[5,3,4,6,7,8,1,2]=>1000010=>[1,5,2]
[4,3,5,6,7,8,1,2]=>1000010=>[1,5,2]
[3,4,5,6,7,8,1,2]=>0000010=>[6,2]
[8,7,6,5,4,2,1,3]=>1111110=>[1,1,1,1,1,1,2]
[7,6,8,5,4,2,1,3]=>1011110=>[1,2,1,1,1,2]
[6,7,8,5,4,2,1,3]=>0011110=>[3,1,1,1,2]
[8,7,5,6,4,2,1,3]=>1101110=>[1,1,2,1,1,2]
[7,8,5,6,4,2,1,3]=>0101110=>[2,2,1,1,2]
[7,6,5,8,4,2,1,3]=>1101110=>[1,1,2,1,1,2]
[6,7,5,8,4,2,1,3]=>0101110=>[2,2,1,1,2]
[7,5,6,8,4,2,1,3]=>1001110=>[1,3,1,1,2]
[6,5,7,8,4,2,1,3]=>1001110=>[1,3,1,1,2]
[5,6,7,8,4,2,1,3]=>0001110=>[4,1,1,2]
[7,6,8,4,5,2,1,3]=>1010110=>[1,2,2,1,2]
[8,7,4,5,6,2,1,3]=>1100110=>[1,1,3,1,2]
[6,7,5,4,8,2,1,3]=>0110110=>[2,1,2,1,2]
[7,5,6,4,8,2,1,3]=>1010110=>[1,2,2,1,2]
[7,6,4,5,8,2,1,3]=>1100110=>[1,1,3,1,2]
[4,5,6,7,8,2,1,3]=>0000110=>[5,1,2]
[8,7,6,5,4,1,2,3]=>1111100=>[1,1,1,1,1,3]
[6,7,8,5,4,1,2,3]=>0011100=>[3,1,1,3]
[7,8,5,6,4,1,2,3]=>0101100=>[2,2,1,3]
[8,5,6,7,4,1,2,3]=>1001100=>[1,3,1,3]
[7,6,5,8,4,1,2,3]=>1101100=>[1,1,2,1,3]
[6,7,5,8,4,1,2,3]=>0101100=>[2,2,1,3]
[7,5,6,8,4,1,2,3]=>1001100=>[1,3,1,3]
[6,5,7,8,4,1,2,3]=>1001100=>[1,3,1,3]
[5,6,7,8,4,1,2,3]=>0001100=>[4,1,3]
[8,7,5,4,6,1,2,3]=>1110100=>[1,1,1,2,3]
[8,5,6,4,7,1,2,3]=>1010100=>[1,2,2,3]
[8,6,4,5,7,1,2,3]=>1100100=>[1,1,3,3]
[7,6,5,4,8,1,2,3]=>1110100=>[1,1,1,2,3]
[6,7,5,4,8,1,2,3]=>0110100=>[2,1,2,3]
[7,5,6,4,8,1,2,3]=>1010100=>[1,2,2,3]
[6,5,7,4,8,1,2,3]=>1010100=>[1,2,2,3]
[5,6,7,4,8,1,2,3]=>0010100=>[3,2,3]
[7,6,4,5,8,1,2,3]=>1100100=>[1,1,3,3]
[6,7,4,5,8,1,2,3]=>0100100=>[2,3,3]
[7,5,4,6,8,1,2,3]=>1100100=>[1,1,3,3]
[7,4,5,6,8,1,2,3]=>1000100=>[1,4,3]
[6,5,4,7,8,1,2,3]=>1100100=>[1,1,3,3]
[5,6,4,7,8,1,2,3]=>0100100=>[2,3,3]
[6,4,5,7,8,1,2,3]=>1000100=>[1,4,3]
[5,4,6,7,8,1,2,3]=>1000100=>[1,4,3]
[4,5,6,7,8,1,2,3]=>0000100=>[5,3]
[8,7,6,5,3,2,1,4]=>1111110=>[1,1,1,1,1,1,2]
[7,8,6,5,3,2,1,4]=>0111110=>[2,1,1,1,1,2]
[8,6,7,5,3,2,1,4]=>1011110=>[1,2,1,1,1,2]
[7,6,8,5,3,2,1,4]=>1011110=>[1,2,1,1,1,2]
[6,7,8,5,3,2,1,4]=>0011110=>[3,1,1,1,2]
[8,7,5,6,3,2,1,4]=>1101110=>[1,1,2,1,1,2]
[7,8,5,6,3,2,1,4]=>0101110=>[2,2,1,1,2]
[8,6,5,7,3,2,1,4]=>1101110=>[1,1,2,1,1,2]
[8,5,6,7,3,2,1,4]=>1001110=>[1,3,1,1,2]
[7,6,5,8,3,2,1,4]=>1101110=>[1,1,2,1,1,2]
[6,7,5,8,3,2,1,4]=>0101110=>[2,2,1,1,2]
[7,5,6,8,3,2,1,4]=>1001110=>[1,3,1,1,2]
[6,5,7,8,3,2,1,4]=>1001110=>[1,3,1,1,2]
[5,6,7,8,3,2,1,4]=>0001110=>[4,1,1,2]
[8,7,6,5,2,3,1,4]=>1111010=>[1,1,1,1,2,2]
[7,8,6,5,2,3,1,4]=>0111010=>[2,1,1,2,2]
[8,6,7,5,2,3,1,4]=>1011010=>[1,2,1,2,2]
[7,6,8,5,2,3,1,4]=>1011010=>[1,2,1,2,2]
[6,7,8,5,2,3,1,4]=>0011010=>[3,1,2,2]
[8,7,5,6,2,3,1,4]=>1101010=>[1,1,2,2,2]
[7,8,5,6,2,3,1,4]=>0101010=>[2,2,2,2]
[8,6,5,7,2,3,1,4]=>1101010=>[1,1,2,2,2]
[8,5,6,7,2,3,1,4]=>1001010=>[1,3,2,2]
[7,6,5,8,2,3,1,4]=>1101010=>[1,1,2,2,2]
[6,7,5,8,2,3,1,4]=>0101010=>[2,2,2,2]
[7,5,6,8,2,3,1,4]=>1001010=>[1,3,2,2]
[6,5,7,8,2,3,1,4]=>1001010=>[1,3,2,2]
[5,6,7,8,2,3,1,4]=>0001010=>[4,2,2]
[8,7,6,5,3,1,2,4]=>1111100=>[1,1,1,1,1,3]
[7,8,6,5,3,1,2,4]=>0111100=>[2,1,1,1,3]
[7,8,5,6,3,1,2,4]=>0101100=>[2,2,1,3]
[7,6,5,8,3,1,2,4]=>1101100=>[1,1,2,1,3]
[6,7,5,8,3,1,2,4]=>0101100=>[2,2,1,3]
[7,5,6,8,3,1,2,4]=>1001100=>[1,3,1,3]
[6,5,7,8,3,1,2,4]=>1001100=>[1,3,1,3]
[5,6,7,8,3,1,2,4]=>0001100=>[4,1,3]
[8,7,6,5,2,1,3,4]=>1111100=>[1,1,1,1,1,3]
[7,6,8,5,2,1,3,4]=>1011100=>[1,2,1,1,3]
[6,7,8,5,2,1,3,4]=>0011100=>[3,1,1,3]
[7,8,5,6,2,1,3,4]=>0101100=>[2,2,1,3]
[8,6,5,7,2,1,3,4]=>1101100=>[1,1,2,1,3]
[8,5,6,7,2,1,3,4]=>1001100=>[1,3,1,3]
[7,6,5,8,2,1,3,4]=>1101100=>[1,1,2,1,3]
[6,7,5,8,2,1,3,4]=>0101100=>[2,2,1,3]
[7,5,6,8,2,1,3,4]=>1001100=>[1,3,1,3]
[6,5,7,8,2,1,3,4]=>1001100=>[1,3,1,3]
[5,6,7,8,2,1,3,4]=>0001100=>[4,1,3]
[8,7,6,5,1,2,3,4]=>1111000=>[1,1,1,1,4]
[7,8,6,5,1,2,3,4]=>0111000=>[2,1,1,4]
[8,6,7,5,1,2,3,4]=>1011000=>[1,2,1,4]
[7,6,8,5,1,2,3,4]=>1011000=>[1,2,1,4]
[6,7,8,5,1,2,3,4]=>0011000=>[3,1,4]
[8,7,5,6,1,2,3,4]=>1101000=>[1,1,2,4]
[7,8,5,6,1,2,3,4]=>0101000=>[2,2,4]
[8,6,5,7,1,2,3,4]=>1101000=>[1,1,2,4]
[8,5,6,7,1,2,3,4]=>1001000=>[1,3,4]
[7,6,5,8,1,2,3,4]=>1101000=>[1,1,2,4]
[6,7,5,8,1,2,3,4]=>0101000=>[2,2,4]
[7,5,6,8,1,2,3,4]=>1001000=>[1,3,4]
[6,5,7,8,1,2,3,4]=>1001000=>[1,3,4]
[5,6,7,8,1,2,3,4]=>0001000=>[4,4]
[8,7,6,4,3,2,1,5]=>1111110=>[1,1,1,1,1,1,2]
[7,8,6,4,3,2,1,5]=>0111110=>[2,1,1,1,1,2]
[8,6,7,4,3,2,1,5]=>1011110=>[1,2,1,1,1,2]
[7,6,8,4,3,2,1,5]=>1011110=>[1,2,1,1,1,2]
[6,7,8,4,3,2,1,5]=>0011110=>[3,1,1,1,2]
[8,7,6,3,4,2,1,5]=>1110110=>[1,1,1,2,1,2]
[7,8,6,3,4,2,1,5]=>0110110=>[2,1,2,1,2]
[6,7,8,3,4,2,1,5]=>0010110=>[3,2,1,2]
[8,7,6,4,2,3,1,5]=>1111010=>[1,1,1,1,2,2]
[7,6,8,4,2,3,1,5]=>1011010=>[1,2,1,2,2]
[6,7,8,4,2,3,1,5]=>0011010=>[3,1,2,2]
[8,7,6,3,2,4,1,5]=>1111010=>[1,1,1,1,2,2]
[8,6,7,3,2,4,1,5]=>1011010=>[1,2,1,2,2]
[6,7,8,3,2,4,1,5]=>0011010=>[3,1,2,2]
[8,7,6,2,3,4,1,5]=>1110010=>[1,1,1,3,2]
[6,7,8,2,3,4,1,5]=>0010010=>[3,3,2]
[8,7,6,4,3,1,2,5]=>1111100=>[1,1,1,1,1,3]
[6,7,8,4,3,1,2,5]=>0011100=>[3,1,1,3]
[8,7,6,3,4,1,2,5]=>1110100=>[1,1,1,2,3]
[6,7,8,3,4,1,2,5]=>0010100=>[3,2,3]
[8,7,6,4,2,1,3,5]=>1111100=>[1,1,1,1,1,3]
[7,8,6,4,2,1,3,5]=>0111100=>[2,1,1,1,3]
[8,6,7,4,2,1,3,5]=>1011100=>[1,2,1,1,3]
[6,7,8,4,2,1,3,5]=>0011100=>[3,1,1,3]
[8,7,6,4,1,2,3,5]=>1111000=>[1,1,1,1,4]
[7,8,6,4,1,2,3,5]=>0111000=>[2,1,1,4]
[7,6,8,4,1,2,3,5]=>1011000=>[1,2,1,4]
[6,7,8,4,1,2,3,5]=>0011000=>[3,1,4]
[8,7,6,3,2,1,4,5]=>1111100=>[1,1,1,1,1,3]
[7,6,8,3,2,1,4,5]=>1011100=>[1,2,1,1,3]
[6,7,8,3,2,1,4,5]=>0011100=>[3,1,1,3]
[8,7,6,2,3,1,4,5]=>1110100=>[1,1,1,2,3]
[7,6,8,2,3,1,4,5]=>1010100=>[1,2,2,3]
[6,7,8,2,3,1,4,5]=>0010100=>[3,2,3]
[8,7,6,3,1,2,4,5]=>1111000=>[1,1,1,1,4]
[7,8,6,3,1,2,4,5]=>0111000=>[2,1,1,4]
[6,7,8,3,1,2,4,5]=>0011000=>[3,1,4]
[8,7,6,2,1,3,4,5]=>1111000=>[1,1,1,1,4]
[7,8,6,2,1,3,4,5]=>0111000=>[2,1,1,4]
[6,7,8,2,1,3,4,5]=>0011000=>[3,1,4]
[8,7,6,1,2,3,4,5]=>1110000=>[1,1,1,5]
[7,8,6,1,2,3,4,5]=>0110000=>[2,1,5]
[8,6,7,1,2,3,4,5]=>1010000=>[1,2,5]
[7,6,8,1,2,3,4,5]=>1010000=>[1,2,5]
[6,7,8,1,2,3,4,5]=>0010000=>[3,5]
[8,7,5,4,3,2,1,6]=>1111110=>[1,1,1,1,1,1,2]
[7,8,5,4,3,2,1,6]=>0111110=>[2,1,1,1,1,2]
[8,7,5,3,4,2,1,6]=>1110110=>[1,1,1,2,1,2]
[8,7,3,4,5,2,1,6]=>1100110=>[1,1,3,1,2]
[7,8,3,4,5,2,1,6]=>0100110=>[2,3,1,2]
[8,7,4,5,2,3,1,6]=>1101010=>[1,1,2,2,2]
[7,8,4,5,2,3,1,6]=>0101010=>[2,2,2,2]
[8,7,5,3,2,4,1,6]=>1111010=>[1,1,1,1,2,2]
[8,7,4,3,2,5,1,6]=>1111010=>[1,1,1,1,2,2]
[7,8,4,3,2,5,1,6]=>0111010=>[2,1,1,2,2]
[8,7,3,4,2,5,1,6]=>1101010=>[1,1,2,2,2]
[7,8,3,4,2,5,1,6]=>0101010=>[2,2,2,2]
[8,7,5,4,3,1,2,6]=>1111100=>[1,1,1,1,1,3]
[7,8,5,4,3,1,2,6]=>0111100=>[2,1,1,1,3]
[8,7,5,3,4,1,2,6]=>1110100=>[1,1,1,2,3]
[7,8,5,3,4,1,2,6]=>0110100=>[2,1,2,3]
[7,8,5,4,2,1,3,6]=>0111100=>[2,1,1,1,3]
[7,8,5,4,1,2,3,6]=>0111000=>[2,1,1,4]
[8,7,4,5,1,2,3,6]=>1101000=>[1,1,2,4]
[8,7,5,3,2,1,4,6]=>1111100=>[1,1,1,1,1,3]
[7,8,5,3,2,1,4,6]=>0111100=>[2,1,1,1,3]
[8,7,5,2,3,1,4,6]=>1110100=>[1,1,1,2,3]
[8,7,5,3,1,2,4,6]=>1111000=>[1,1,1,1,4]
[7,8,5,3,1,2,4,6]=>0111000=>[2,1,1,4]
[8,7,5,2,1,3,4,6]=>1111000=>[1,1,1,1,4]
[7,8,5,2,1,3,4,6]=>0111000=>[2,1,1,4]
[8,7,5,1,2,3,4,6]=>1110000=>[1,1,1,5]
[7,8,5,1,2,3,4,6]=>0110000=>[2,1,5]
[8,7,4,3,2,1,5,6]=>1111100=>[1,1,1,1,1,3]
[7,8,4,3,2,1,5,6]=>0111100=>[2,1,1,1,3]
[8,7,3,4,2,1,5,6]=>1101100=>[1,1,2,1,3]
[7,8,3,4,2,1,5,6]=>0101100=>[2,2,1,3]
[7,8,4,2,3,1,5,6]=>0110100=>[2,1,2,3]
[8,7,3,2,4,1,5,6]=>1110100=>[1,1,1,2,3]
[7,8,3,2,4,1,5,6]=>0110100=>[2,1,2,3]
[7,8,2,3,4,1,5,6]=>0100100=>[2,3,3]
[7,8,4,3,1,2,5,6]=>0111000=>[2,1,1,4]
[8,7,3,4,1,2,5,6]=>1101000=>[1,1,2,4]
[7,8,3,4,1,2,5,6]=>0101000=>[2,2,4]
[7,8,4,2,1,3,5,6]=>0111000=>[2,1,1,4]
[7,8,4,1,2,3,5,6]=>0110000=>[2,1,5]
[8,7,3,2,1,4,5,6]=>1111000=>[1,1,1,1,4]
[7,8,3,2,1,4,5,6]=>0111000=>[2,1,1,4]
[7,8,2,3,1,4,5,6]=>0101000=>[2,2,4]
[7,8,3,1,2,4,5,6]=>0110000=>[2,1,5]
[7,8,2,1,3,4,5,6]=>0110000=>[2,1,5]
[7,8,1,2,3,4,5,6]=>0100000=>[2,6]
[8,6,5,4,3,2,1,7]=>1111110=>[1,1,1,1,1,1,2]
[8,5,6,4,3,2,1,7]=>1011110=>[1,2,1,1,1,2]
[8,4,5,6,3,2,1,7]=>1001110=>[1,3,1,1,2]
[8,6,5,3,4,2,1,7]=>1110110=>[1,1,1,2,1,2]
[8,5,6,3,4,2,1,7]=>1010110=>[1,2,2,1,2]
[8,4,5,3,6,2,1,7]=>1010110=>[1,2,2,1,2]
[8,6,5,4,2,3,1,7]=>1111010=>[1,1,1,1,2,2]
[8,5,6,4,2,3,1,7]=>1011010=>[1,2,1,2,2]
[8,6,5,3,2,4,1,7]=>1111010=>[1,1,1,1,2,2]
[8,6,5,2,3,4,1,7]=>1110010=>[1,1,1,3,2]
[8,5,6,2,3,4,1,7]=>1010010=>[1,2,3,2]
[8,6,4,2,3,5,1,7]=>1110010=>[1,1,1,3,2]
[8,6,3,2,4,5,1,7]=>1110010=>[1,1,1,3,2]
[8,5,2,3,4,6,1,7]=>1100010=>[1,1,4,2]
[8,6,4,5,3,1,2,7]=>1101100=>[1,1,2,1,3]
[8,5,6,3,4,1,2,7]=>1010100=>[1,2,2,3]
[8,6,3,4,5,1,2,7]=>1100100=>[1,1,3,3]
[8,4,5,3,6,1,2,7]=>1010100=>[1,2,2,3]
[8,4,3,5,6,1,2,7]=>1100100=>[1,1,3,3]
[8,6,5,4,2,1,3,7]=>1111100=>[1,1,1,1,1,3]
[8,5,6,4,2,1,3,7]=>1011100=>[1,2,1,1,3]
[8,5,6,4,1,2,3,7]=>1011000=>[1,2,1,4]
[8,4,5,6,1,2,3,7]=>1001000=>[1,3,4]
[8,6,5,3,2,1,4,7]=>1111100=>[1,1,1,1,1,3]
[8,5,6,3,2,1,4,7]=>1011100=>[1,2,1,1,3]
[8,6,5,2,3,1,4,7]=>1110100=>[1,1,1,2,3]
[8,5,6,2,3,1,4,7]=>1010100=>[1,2,2,3]
[8,5,6,3,1,2,4,7]=>1011000=>[1,2,1,4]
[8,6,5,2,1,3,4,7]=>1111000=>[1,1,1,1,4]
[8,5,6,2,1,3,4,7]=>1011000=>[1,2,1,4]
[8,6,5,1,2,3,4,7]=>1110000=>[1,1,1,5]
[8,5,6,1,2,3,4,7]=>1010000=>[1,2,5]
[8,6,4,3,2,1,5,7]=>1111100=>[1,1,1,1,1,3]
[8,6,3,4,2,1,5,7]=>1101100=>[1,1,2,1,3]
[8,6,4,2,3,1,5,7]=>1110100=>[1,1,1,2,3]
[8,6,3,2,4,1,5,7]=>1110100=>[1,1,1,2,3]
[8,6,3,4,1,2,5,7]=>1101000=>[1,1,2,4]
[8,6,4,2,1,3,5,7]=>1111000=>[1,1,1,1,4]
[8,6,4,1,2,3,5,7]=>1110000=>[1,1,1,5]
[8,4,5,3,2,1,6,7]=>1011100=>[1,2,1,1,3]
[8,4,3,5,2,1,6,7]=>1101100=>[1,1,2,1,3]
[8,3,4,5,2,1,6,7]=>1001100=>[1,3,1,3]
[8,4,5,2,3,1,6,7]=>1010100=>[1,2,2,3]
[8,5,2,3,4,1,6,7]=>1100100=>[1,1,3,3]
[8,4,2,3,5,1,6,7]=>1100100=>[1,1,3,3]
[8,5,3,4,1,2,6,7]=>1101000=>[1,1,2,4]
[8,5,4,2,1,3,6,7]=>1111000=>[1,1,1,1,4]
[8,5,3,2,1,4,6,7]=>1111000=>[1,1,1,1,4]
[8,5,3,1,2,4,6,7]=>1110000=>[1,1,1,5]
[8,4,3,2,1,5,6,7]=>1111000=>[1,1,1,1,4]
[8,3,4,1,2,5,6,7]=>1010000=>[1,2,5]
[8,4,2,1,3,5,6,7]=>1110000=>[1,1,1,5]
[8,3,2,1,4,5,6,7]=>1110000=>[1,1,1,5]
[8,3,1,2,4,5,6,7]=>1100000=>[1,1,6]
[8,1,2,3,4,5,6,7]=>1000000=>[1,7]
[7,6,5,4,3,2,1,8]=>1111110=>[1,1,1,1,1,1,2]
[6,7,5,4,3,2,1,8]=>0111110=>[2,1,1,1,1,2]
[7,5,6,4,3,2,1,8]=>1011110=>[1,2,1,1,1,2]
[6,5,7,4,3,2,1,8]=>1011110=>[1,2,1,1,1,2]
[5,6,7,4,3,2,1,8]=>0011110=>[3,1,1,1,2]
[7,6,4,5,3,2,1,8]=>1101110=>[1,1,2,1,1,2]
[7,4,5,6,3,2,1,8]=>1001110=>[1,3,1,1,2]
[6,5,4,7,3,2,1,8]=>1101110=>[1,1,2,1,1,2]
[5,6,4,7,3,2,1,8]=>0101110=>[2,2,1,1,2]
[4,5,6,7,3,2,1,8]=>0001110=>[4,1,1,2]
[7,6,5,3,4,2,1,8]=>1110110=>[1,1,1,2,1,2]
[6,7,5,3,4,2,1,8]=>0110110=>[2,1,2,1,2]
[7,5,6,3,4,2,1,8]=>1010110=>[1,2,2,1,2]
[6,5,7,3,4,2,1,8]=>1010110=>[1,2,2,1,2]
[5,6,7,3,4,2,1,8]=>0010110=>[3,2,1,2]
[7,6,3,4,5,2,1,8]=>1100110=>[1,1,3,1,2]
[7,4,5,3,6,2,1,8]=>1010110=>[1,2,2,1,2]
[7,3,4,5,6,2,1,8]=>1000110=>[1,4,1,2]
[6,5,4,3,7,2,1,8]=>1110110=>[1,1,1,2,1,2]
[5,4,6,3,7,2,1,8]=>1010110=>[1,2,2,1,2]
[5,4,3,6,7,2,1,8]=>1100110=>[1,1,3,1,2]
[7,5,6,4,2,3,1,8]=>1011010=>[1,2,1,2,2]
[5,6,7,4,2,3,1,8]=>0011010=>[3,1,2,2]
[7,6,4,5,2,3,1,8]=>1101010=>[1,1,2,2,2]
[6,7,4,5,2,3,1,8]=>0101010=>[2,2,2,2]
[7,4,5,6,2,3,1,8]=>1001010=>[1,3,2,2]
[6,5,4,7,2,3,1,8]=>1101010=>[1,1,2,2,2]
[5,6,4,7,2,3,1,8]=>0101010=>[2,2,2,2]
[5,4,6,7,2,3,1,8]=>1001010=>[1,3,2,2]
[4,5,6,7,2,3,1,8]=>0001010=>[4,2,2]
[5,6,7,3,2,4,1,8]=>0011010=>[3,1,2,2]
[7,6,5,2,3,4,1,8]=>1110010=>[1,1,1,3,2]
[6,7,5,2,3,4,1,8]=>0110010=>[2,1,3,2]
[7,5,6,2,3,4,1,8]=>1010010=>[1,2,3,2]
[6,5,7,2,3,4,1,8]=>1010010=>[1,2,3,2]
[5,6,7,2,3,4,1,8]=>0010010=>[3,3,2]
[6,7,4,3,2,5,1,8]=>0111010=>[2,1,1,2,2]
[6,7,3,4,2,5,1,8]=>0101010=>[2,2,2,2]
[7,6,4,2,3,5,1,8]=>1110010=>[1,1,1,3,2]
[7,6,3,2,4,5,1,8]=>1110010=>[1,1,1,3,2]
[6,7,3,2,4,5,1,8]=>0110010=>[2,1,3,2]
[7,6,2,3,4,5,1,8]=>1100010=>[1,1,4,2]
[6,7,2,3,4,5,1,8]=>0100010=>[2,4,2]
[7,4,5,3,2,6,1,8]=>1011010=>[1,2,1,2,2]
[7,5,3,4,2,6,1,8]=>1101010=>[1,1,2,2,2]
[7,4,3,5,2,6,1,8]=>1101010=>[1,1,2,2,2]
[7,4,5,2,3,6,1,8]=>1010010=>[1,2,3,2]
[7,5,3,2,4,6,1,8]=>1110010=>[1,1,1,3,2]
[7,4,2,3,5,6,1,8]=>1100010=>[1,1,4,2]
[5,4,6,3,2,7,1,8]=>1011010=>[1,2,1,2,2]
[5,6,3,4,2,7,1,8]=>0101010=>[2,2,2,2]
[6,3,4,5,2,7,1,8]=>1001010=>[1,3,2,2]
[5,4,3,6,2,7,1,8]=>1101010=>[1,1,2,2,2]
[4,5,3,6,2,7,1,8]=>0101010=>[2,2,2,2]
[3,4,5,6,2,7,1,8]=>0001010=>[4,2,2]
[6,5,3,2,4,7,1,8]=>1110010=>[1,1,1,3,2]
[6,4,2,3,5,7,1,8]=>1100010=>[1,1,4,2]
[6,3,2,4,5,7,1,8]=>1100010=>[1,1,4,2]
[6,2,3,4,5,7,1,8]=>1000010=>[1,5,2]
[5,4,3,2,6,7,1,8]=>1110010=>[1,1,1,3,2]
[4,5,2,3,6,7,1,8]=>0100010=>[2,4,2]
[7,4,5,6,3,1,2,8]=>1001100=>[1,3,1,3]
[5,4,6,7,3,1,2,8]=>1001100=>[1,3,1,3]
[4,5,6,7,3,1,2,8]=>0001100=>[4,1,3]
[7,5,6,3,4,1,2,8]=>1010100=>[1,2,2,3]
[7,5,3,4,6,1,2,8]=>1100100=>[1,1,3,3]
[6,5,4,3,7,1,2,8]=>1110100=>[1,1,1,2,3]
[3,4,5,6,7,1,2,8]=>0000100=>[5,3]
[7,4,5,6,2,1,3,8]=>1001100=>[1,3,1,3]
[4,5,6,7,2,1,3,8]=>0001100=>[4,1,3]
[7,6,5,4,1,2,3,8]=>1111000=>[1,1,1,1,4]
[7,5,6,4,1,2,3,8]=>1011000=>[1,2,1,4]
[7,6,4,5,1,2,3,8]=>1101000=>[1,1,2,4]
[7,5,4,6,1,2,3,8]=>1101000=>[1,1,2,4]
[7,4,5,6,1,2,3,8]=>1001000=>[1,3,4]
[4,5,6,7,1,2,3,8]=>0001000=>[4,4]
[7,6,5,2,3,1,4,8]=>1110100=>[1,1,1,2,3]
[6,7,5,2,3,1,4,8]=>0110100=>[2,1,2,3]
[7,5,6,2,3,1,4,8]=>1010100=>[1,2,2,3]
[6,5,7,2,3,1,4,8]=>1010100=>[1,2,2,3]
[5,6,7,2,3,1,4,8]=>0010100=>[3,2,3]
[7,5,6,3,1,2,4,8]=>1011000=>[1,2,1,4]
[7,6,5,2,1,3,4,8]=>1111000=>[1,1,1,1,4]
[7,6,5,1,2,3,4,8]=>1110000=>[1,1,1,5]
[6,7,5,1,2,3,4,8]=>0110000=>[2,1,5]
[7,5,6,1,2,3,4,8]=>1010000=>[1,2,5]
[6,5,7,1,2,3,4,8]=>1010000=>[1,2,5]
[5,6,7,1,2,3,4,8]=>0010000=>[3,5]
[7,6,4,3,2,1,5,8]=>1111100=>[1,1,1,1,1,3]
[6,7,4,3,2,1,5,8]=>0111100=>[2,1,1,1,3]
[7,6,3,2,4,1,5,8]=>1110100=>[1,1,1,2,3]
[7,6,2,3,4,1,5,8]=>1100100=>[1,1,3,3]
[6,7,2,3,4,1,5,8]=>0100100=>[2,3,3]
[7,6,4,2,1,3,5,8]=>1111000=>[1,1,1,1,4]
[7,6,3,2,1,4,5,8]=>1111000=>[1,1,1,1,4]
[6,7,3,2,1,4,5,8]=>0111000=>[2,1,1,4]
[7,6,2,3,1,4,5,8]=>1101000=>[1,1,2,4]
[6,7,3,1,2,4,5,8]=>0110000=>[2,1,5]
[6,7,1,2,3,4,5,8]=>0100000=>[2,6]
[7,5,2,3,4,1,6,8]=>1100100=>[1,1,3,3]
[7,4,2,3,5,1,6,8]=>1100100=>[1,1,3,3]
[7,2,3,4,5,1,6,8]=>1000100=>[1,4,3]
[7,5,3,4,1,2,6,8]=>1101000=>[1,1,2,4]
[7,4,5,1,2,3,6,8]=>1010000=>[1,2,5]
[7,5,3,2,1,4,6,8]=>1111000=>[1,1,1,1,4]
[7,5,3,1,2,4,6,8]=>1110000=>[1,1,1,5]
[7,5,1,2,3,4,6,8]=>1100000=>[1,1,6]
[7,4,3,2,1,5,6,8]=>1111000=>[1,1,1,1,4]
[7,4,3,1,2,5,6,8]=>1110000=>[1,1,1,5]
[7,3,4,1,2,5,6,8]=>1010000=>[1,2,5]
[7,3,1,2,4,5,6,8]=>1100000=>[1,1,6]
[7,1,2,3,4,5,6,8]=>1000000=>[1,7]
[5,6,4,3,2,1,7,8]=>0111100=>[2,1,1,1,3]
[5,4,6,3,2,1,7,8]=>1011100=>[1,2,1,1,3]
[4,5,6,3,2,1,7,8]=>0011100=>[3,1,1,3]
[6,5,3,4,2,1,7,8]=>1101100=>[1,1,2,1,3]
[5,4,3,6,2,1,7,8]=>1101100=>[1,1,2,1,3]
[3,4,5,6,2,1,7,8]=>0001100=>[4,1,3]
[5,4,6,2,3,1,7,8]=>1010100=>[1,2,2,3]
[5,6,3,2,4,1,7,8]=>0110100=>[2,1,2,3]
[6,5,2,3,4,1,7,8]=>1100100=>[1,1,3,3]
[5,6,2,3,4,1,7,8]=>0100100=>[2,3,3]
[6,4,3,2,5,1,7,8]=>1110100=>[1,1,1,2,3]
[5,4,3,2,6,1,7,8]=>1110100=>[1,1,1,2,3]
[4,5,3,2,6,1,7,8]=>0110100=>[2,1,2,3]
[5,3,2,4,6,1,7,8]=>1100100=>[1,1,3,3]
[6,5,4,3,1,2,7,8]=>1111000=>[1,1,1,1,4]
[5,6,4,2,1,3,7,8]=>0111000=>[2,1,1,4]
[6,4,5,2,1,3,7,8]=>1011000=>[1,2,1,4]
[6,4,3,2,1,5,7,8]=>1111000=>[1,1,1,1,4]
[6,3,4,2,1,5,7,8]=>1011000=>[1,2,1,4]
[6,4,3,1,2,5,7,8]=>1110000=>[1,1,1,5]
[6,4,2,1,3,5,7,8]=>1110000=>[1,1,1,5]
[5,4,3,2,1,6,7,8]=>1111000=>[1,1,1,1,4]
[4,5,3,2,1,6,7,8]=>0111000=>[2,1,1,4]
[5,3,4,2,1,6,7,8]=>1011000=>[1,2,1,4]
[4,3,5,2,1,6,7,8]=>1011000=>[1,2,1,4]
[3,4,5,2,1,6,7,8]=>0011000=>[3,1,4]
[5,4,2,3,1,6,7,8]=>1101000=>[1,1,2,4]
[4,5,2,3,1,6,7,8]=>0101000=>[2,2,4]
[5,3,2,4,1,6,7,8]=>1101000=>[1,1,2,4]
[5,2,3,4,1,6,7,8]=>1001000=>[1,3,4]
[4,3,2,5,1,6,7,8]=>1101000=>[1,1,2,4]
[3,4,2,5,1,6,7,8]=>0101000=>[2,2,4]
[4,2,3,5,1,6,7,8]=>1001000=>[1,3,4]
[3,2,4,5,1,6,7,8]=>1001000=>[1,3,4]
[2,3,4,5,1,6,7,8]=>0001000=>[4,4]
[5,4,3,1,2,6,7,8]=>1110000=>[1,1,1,5]
[5,3,4,1,2,6,7,8]=>1010000=>[1,2,5]
[5,4,2,1,3,6,7,8]=>1110000=>[1,1,1,5]
[5,4,1,2,3,6,7,8]=>1100000=>[1,1,6]
[4,5,1,2,3,6,7,8]=>0100000=>[2,6]
[5,3,2,1,4,6,7,8]=>1110000=>[1,1,1,5]
[5,2,3,1,4,6,7,8]=>1010000=>[1,2,5]
[5,3,1,2,4,6,7,8]=>1100000=>[1,1,6]
[5,2,1,3,4,6,7,8]=>1100000=>[1,1,6]
[5,1,2,3,4,6,7,8]=>1000000=>[1,7]
[4,3,2,1,5,6,7,8]=>1110000=>[1,1,1,5]
[3,4,2,1,5,6,7,8]=>0110000=>[2,1,5]
[4,2,3,1,5,6,7,8]=>1010000=>[1,2,5]
[3,2,4,1,5,6,7,8]=>1010000=>[1,2,5]
[2,3,4,1,5,6,7,8]=>0010000=>[3,5]
[4,3,1,2,5,6,7,8]=>1100000=>[1,1,6]
[3,4,1,2,5,6,7,8]=>0100000=>[2,6]
[4,2,1,3,5,6,7,8]=>1100000=>[1,1,6]
[4,1,2,3,5,6,7,8]=>1000000=>[1,7]
[3,2,1,4,5,6,7,8]=>1100000=>[1,1,6]
[2,3,1,4,5,6,7,8]=>0100000=>[2,6]
[3,1,2,4,5,6,7,8]=>1000000=>[1,7]
[2,1,3,4,5,6,7,8]=>1000000=>[1,7]
[1,2,3,4,5,6,7,8]=>0000000=>[8]
[6,8,7,5,4,3,2,1]=>0111111=>[2,1,1,1,1,1,1]
[5,8,7,6,4,3,2,1]=>0111111=>[2,1,1,1,1,1,1]
[5,7,8,6,4,3,2,1]=>0011111=>[3,1,1,1,1,1]
[6,5,8,7,4,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[5,6,8,7,4,3,2,1]=>0011111=>[3,1,1,1,1,1]
[5,7,6,8,4,3,2,1]=>0101111=>[2,2,1,1,1,1]
[4,8,7,6,5,3,2,1]=>0111111=>[2,1,1,1,1,1,1]
[4,7,8,6,5,3,2,1]=>0011111=>[3,1,1,1,1,1]
[4,6,8,7,5,3,2,1]=>0011111=>[3,1,1,1,1,1]
[4,7,6,8,5,3,2,1]=>0101111=>[2,2,1,1,1,1]
[4,6,7,8,5,3,2,1]=>0001111=>[4,1,1,1,1]
[4,5,8,7,6,3,2,1]=>0011111=>[3,1,1,1,1,1]
[4,5,7,8,6,3,2,1]=>0001111=>[4,1,1,1,1]
[4,6,5,8,7,3,2,1]=>0101111=>[2,2,1,1,1,1]
[4,5,6,8,7,3,2,1]=>0001111=>[4,1,1,1,1]
[5,7,6,4,8,3,2,1]=>0110111=>[2,1,2,1,1,1]
[4,7,6,5,8,3,2,1]=>0110111=>[2,1,2,1,1,1]
[4,6,7,5,8,3,2,1]=>0010111=>[3,2,1,1,1]
[5,4,7,6,8,3,2,1]=>1010111=>[1,2,2,1,1,1]
[4,5,7,6,8,3,2,1]=>0010111=>[3,2,1,1,1]
[4,6,5,7,8,3,2,1]=>0100111=>[2,3,1,1,1]
[3,8,7,6,5,4,2,1]=>0111111=>[2,1,1,1,1,1,1]
[3,5,8,7,6,4,2,1]=>0011111=>[3,1,1,1,1,1]
[3,5,7,8,6,4,2,1]=>0001111=>[4,1,1,1,1]
[3,5,6,8,7,4,2,1]=>0001111=>[4,1,1,1,1]
[3,7,6,5,8,4,2,1]=>0110111=>[2,1,2,1,1,1]
[3,6,7,5,8,4,2,1]=>0010111=>[3,2,1,1,1]
[3,5,6,7,8,4,2,1]=>0000111=>[5,1,1,1]
[3,4,8,7,6,5,2,1]=>0011111=>[3,1,1,1,1,1]
[3,4,6,7,8,5,2,1]=>0000111=>[5,1,1,1]
[5,4,3,7,8,6,2,1]=>1100111=>[1,1,3,1,1,1]
[3,4,5,7,8,6,2,1]=>0000111=>[5,1,1,1]
[4,5,6,3,8,7,2,1]=>0010111=>[3,2,1,1,1]
[4,3,6,5,8,7,2,1]=>1010111=>[1,2,2,1,1,1]
[5,4,3,6,8,7,2,1]=>1100111=>[1,1,3,1,1,1]
[4,5,3,6,8,7,2,1]=>0100111=>[2,3,1,1,1]
[5,7,6,4,3,8,2,1]=>0111011=>[2,1,1,2,1,1]
[4,7,6,5,3,8,2,1]=>0111011=>[2,1,1,2,1,1]
[3,4,7,6,5,8,2,1]=>0011011=>[3,1,2,1,1]
[4,5,3,7,6,8,2,1]=>0101011=>[2,2,2,1,1]
[4,3,5,7,6,8,2,1]=>1001011=>[1,3,2,1,1]
[3,4,6,5,7,8,2,1]=>0010011=>[3,3,1,1]
[2,8,7,6,5,4,3,1]=>0111111=>[2,1,1,1,1,1,1]
[2,7,6,8,5,4,3,1]=>0101111=>[2,2,1,1,1,1]
[2,5,6,7,8,4,3,1]=>0000111=>[5,1,1,1]
[2,4,8,7,6,5,3,1]=>0011111=>[3,1,1,1,1,1]
[2,4,6,8,7,5,3,1]=>0001111=>[4,1,1,1,1]
[2,4,6,7,8,5,3,1]=>0000111=>[5,1,1,1]
[2,5,4,8,7,6,3,1]=>0101111=>[2,2,1,1,1,1]
[2,4,5,7,8,6,3,1]=>0000111=>[5,1,1,1]
[2,5,6,4,8,7,3,1]=>0010111=>[3,2,1,1,1]
[2,4,6,5,8,7,3,1]=>0010111=>[3,2,1,1,1]
[2,7,6,5,4,8,3,1]=>0111011=>[2,1,1,2,1,1]
[2,6,7,5,4,8,3,1]=>0011011=>[3,1,2,1,1]
[2,4,7,6,5,8,3,1]=>0011011=>[3,1,2,1,1]
[2,6,5,4,7,8,3,1]=>0110011=>[2,1,3,1,1]
[3,2,8,7,6,5,4,1]=>1011111=>[1,2,1,1,1,1,1]
[3,2,6,8,7,5,4,1]=>1001111=>[1,3,1,1,1,1]
[3,2,5,7,6,8,4,1]=>1001011=>[1,3,2,1,1]
[3,2,5,6,7,8,4,1]=>1000011=>[1,5,1,1]
[2,3,8,7,6,5,4,1]=>0011111=>[3,1,1,1,1,1]
[2,3,6,7,8,5,4,1]=>0000111=>[5,1,1,1]
[2,3,5,7,8,6,4,1]=>0000111=>[5,1,1,1]
[2,3,7,6,5,8,4,1]=>0011011=>[3,1,2,1,1]
[2,3,5,6,7,8,4,1]=>0000011=>[6,1,1]
[4,3,2,8,7,6,5,1]=>1101111=>[1,1,2,1,1,1,1]
[3,4,2,8,7,6,5,1]=>0101111=>[2,2,1,1,1,1]
[3,4,2,7,8,6,5,1]=>0100111=>[2,3,1,1,1]
[2,4,3,8,7,6,5,1]=>0101111=>[2,2,1,1,1,1]
[2,4,3,6,8,7,5,1]=>0100111=>[2,3,1,1,1]
[3,2,4,8,7,6,5,1]=>1001111=>[1,3,1,1,1,1]
[2,3,4,8,7,6,5,1]=>0001111=>[4,1,1,1,1]
[2,3,4,6,7,8,5,1]=>0000011=>[6,1,1]
[5,4,3,2,8,7,6,1]=>1110111=>[1,1,1,2,1,1,1]
[5,4,3,2,7,8,6,1]=>1110011=>[1,1,1,3,1,1]
[2,5,4,3,8,7,6,1]=>0110111=>[2,1,2,1,1,1]
[2,5,4,3,7,8,6,1]=>0110011=>[2,1,3,1,1]
[2,4,5,3,8,7,6,1]=>0010111=>[3,2,1,1,1]
[2,3,5,4,8,7,6,1]=>0010111=>[3,2,1,1,1]
[4,3,2,5,8,7,6,1]=>1100111=>[1,1,3,1,1,1]
[2,4,3,5,8,7,6,1]=>0100111=>[2,3,1,1,1]
[2,3,4,5,8,7,6,1]=>0000111=>[5,1,1,1]
[6,5,4,3,2,8,7,1]=>1111011=>[1,1,1,1,2,1,1]
[4,6,5,3,2,8,7,1]=>0111011=>[2,1,1,2,1,1]
[5,4,6,3,2,8,7,1]=>1011011=>[1,2,1,2,1,1]
[4,5,6,3,2,8,7,1]=>0011011=>[3,1,2,1,1]
[3,6,5,4,2,8,7,1]=>0111011=>[2,1,1,2,1,1]
[3,5,6,4,2,8,7,1]=>0011011=>[3,1,2,1,1]
[4,3,6,5,2,8,7,1]=>1011011=>[1,2,1,2,1,1]
[5,4,3,6,2,8,7,1]=>1101011=>[1,1,2,2,1,1]
[2,6,5,4,3,8,7,1]=>0111011=>[2,1,1,2,1,1]
[2,4,6,5,3,8,7,1]=>0011011=>[3,1,2,1,1]
[4,3,2,6,5,8,7,1]=>1101011=>[1,1,2,2,1,1]
[2,4,3,6,5,8,7,1]=>0101011=>[2,2,2,1,1]
[2,3,4,6,5,8,7,1]=>0001011=>[4,2,1,1]
[5,4,3,2,6,8,7,1]=>1110011=>[1,1,1,3,1,1]
[2,5,4,3,6,8,7,1]=>0110011=>[2,1,3,1,1]
[4,3,2,5,6,8,7,1]=>1100011=>[1,1,4,1,1]
[3,4,2,5,6,8,7,1]=>0100011=>[2,4,1,1]
[2,4,3,5,6,8,7,1]=>0100011=>[2,4,1,1]
[2,3,4,5,6,8,7,1]=>0000011=>[6,1,1]
[4,7,6,5,3,2,8,1]=>0111101=>[2,1,1,1,2,1]
[4,6,5,7,3,2,8,1]=>0101101=>[2,2,1,2,1]
[3,5,7,6,4,2,8,1]=>0011101=>[3,1,1,2,1]
[3,5,6,7,4,2,8,1]=>0001101=>[4,1,2,1]
[4,3,7,6,5,2,8,1]=>1011101=>[1,2,1,1,2,1]
[4,3,6,7,5,2,8,1]=>1001101=>[1,3,1,2,1]
[3,4,7,6,5,2,8,1]=>0011101=>[3,1,1,2,1]
[5,4,3,7,6,2,8,1]=>1101101=>[1,1,2,1,2,1]
[4,6,5,3,7,2,8,1]=>0110101=>[2,1,2,2,1]
[3,6,5,4,7,2,8,1]=>0110101=>[2,1,2,2,1]
[3,5,6,4,7,2,8,1]=>0010101=>[3,2,2,1]
[4,3,6,5,7,2,8,1]=>1010101=>[1,2,2,2,1]
[3,5,4,6,7,2,8,1]=>0100101=>[2,3,2,1]
[2,5,4,7,6,3,8,1]=>0101101=>[2,2,1,2,1]
[2,4,6,5,7,3,8,1]=>0010101=>[3,2,2,1]
[2,4,5,6,7,3,8,1]=>0000101=>[5,2,1]
[3,2,6,7,5,4,8,1]=>1001101=>[1,3,1,2,1]
[3,2,6,5,7,4,8,1]=>1010101=>[1,2,2,2,1]
[2,3,7,6,5,4,8,1]=>0011101=>[3,1,1,2,1]
[4,3,2,7,6,5,8,1]=>1101101=>[1,1,2,1,2,1]
[4,3,2,6,7,5,8,1]=>1100101=>[1,1,3,2,1]
[3,4,2,7,6,5,8,1]=>0101101=>[2,2,1,2,1]
[2,4,3,7,6,5,8,1]=>0101101=>[2,2,1,2,1]
[3,2,4,7,6,5,8,1]=>1001101=>[1,3,1,2,1]
[2,3,4,7,6,5,8,1]=>0001101=>[4,1,2,1]
[5,4,3,2,7,6,8,1]=>1110101=>[1,1,1,2,2,1]
[4,3,5,2,7,6,8,1]=>1010101=>[1,2,2,2,1]
[2,5,4,3,7,6,8,1]=>0110101=>[2,1,2,2,1]
[3,2,5,4,7,6,8,1]=>1010101=>[1,2,2,2,1]
[2,3,5,4,7,6,8,1]=>0010101=>[3,2,2,1]
[4,3,2,5,7,6,8,1]=>1100101=>[1,1,3,2,1]
[2,4,3,5,7,6,8,1]=>0100101=>[2,3,2,1]
[3,2,4,5,7,6,8,1]=>1000101=>[1,4,2,1]
[2,3,4,5,7,6,8,1]=>0000101=>[5,2,1]
[3,6,5,4,2,7,8,1]=>0111001=>[2,1,1,3,1]
[3,5,6,4,2,7,8,1]=>0011001=>[3,1,3,1]
[2,6,5,4,3,7,8,1]=>0111001=>[2,1,1,3,1]
[2,5,4,6,3,7,8,1]=>0101001=>[2,2,3,1]
[2,3,6,5,4,7,8,1]=>0011001=>[3,1,3,1]
[2,3,5,6,4,7,8,1]=>0001001=>[4,3,1]
[4,3,2,6,5,7,8,1]=>1101001=>[1,1,2,3,1]
[3,4,2,6,5,7,8,1]=>0101001=>[2,2,3,1]
[2,4,3,6,5,7,8,1]=>0101001=>[2,2,3,1]
[2,3,4,6,5,7,8,1]=>0001001=>[4,3,1]
[3,5,4,2,6,7,8,1]=>0110001=>[2,1,4,1]
[2,5,4,3,6,7,8,1]=>0110001=>[2,1,4,1]
[2,4,5,3,6,7,8,1]=>0010001=>[3,4,1]
[3,2,5,4,6,7,8,1]=>1010001=>[1,2,4,1]
[2,3,5,4,6,7,8,1]=>0010001=>[3,4,1]
[2,4,3,5,6,7,8,1]=>0100001=>[2,5,1]
[1,8,7,6,5,4,3,2]=>0111111=>[2,1,1,1,1,1,1]
[1,7,8,6,5,4,3,2]=>0011111=>[3,1,1,1,1,1]
[1,6,8,7,5,4,3,2]=>0011111=>[3,1,1,1,1,1]
[1,7,6,8,5,4,3,2]=>0101111=>[2,2,1,1,1,1]
[1,6,7,8,5,4,3,2]=>0001111=>[4,1,1,1,1]
[1,7,6,5,8,4,3,2]=>0110111=>[2,1,2,1,1,1]
[1,6,7,5,8,4,3,2]=>0010111=>[3,2,1,1,1]
[1,5,7,6,8,4,3,2]=>0010111=>[3,2,1,1,1]
[1,6,5,7,8,4,3,2]=>0100111=>[2,3,1,1,1]
[1,5,6,7,8,4,3,2]=>0000111=>[5,1,1,1]
[1,4,8,7,6,5,3,2]=>0011111=>[3,1,1,1,1,1]
[1,4,7,8,6,5,3,2]=>0001111=>[4,1,1,1,1]
[1,4,6,8,7,5,3,2]=>0001111=>[4,1,1,1,1]
[1,4,6,7,8,5,3,2]=>0000111=>[5,1,1,1]
[1,4,5,7,8,6,3,2]=>0000111=>[5,1,1,1]
[1,4,6,5,8,7,3,2]=>0010111=>[3,2,1,1,1]
[1,4,7,6,5,8,3,2]=>0011011=>[3,1,2,1,1]
[1,6,5,4,7,8,3,2]=>0110011=>[2,1,3,1,1]
[1,3,8,7,6,5,4,2]=>0011111=>[3,1,1,1,1,1]
[1,3,6,8,7,5,4,2]=>0001111=>[4,1,1,1,1]
[1,3,6,7,8,5,4,2]=>0000111=>[5,1,1,1]
[1,3,5,8,7,6,4,2]=>0001111=>[4,1,1,1,1]
[1,3,5,7,8,6,4,2]=>0000111=>[5,1,1,1]
[1,3,5,7,6,8,4,2]=>0001011=>[4,2,1,1]
[1,3,6,5,7,8,4,2]=>0010011=>[3,3,1,1]
[1,3,5,6,7,8,4,2]=>0000011=>[6,1,1]
[1,4,3,8,7,6,5,2]=>0101111=>[2,2,1,1,1,1]
[1,4,3,7,8,6,5,2]=>0100111=>[2,3,1,1,1]
[1,4,3,6,8,7,5,2]=>0100111=>[2,3,1,1,1]
[1,4,3,7,6,8,5,2]=>0101011=>[2,2,2,1,1]
[1,3,4,8,7,6,5,2]=>0001111=>[4,1,1,1,1]
[1,3,4,7,6,8,5,2]=>0001011=>[4,2,1,1]
[1,3,4,6,7,8,5,2]=>0000011=>[6,1,1]
[1,5,4,3,8,7,6,2]=>0110111=>[2,1,2,1,1,1]
[1,3,5,4,7,8,6,2]=>0010011=>[3,3,1,1]
[1,4,3,5,8,7,6,2]=>0100111=>[2,3,1,1,1]
[1,4,3,5,7,8,6,2]=>0100011=>[2,4,1,1]
[1,3,4,5,8,7,6,2]=>0000111=>[5,1,1,1]
[1,6,5,4,3,8,7,2]=>0111011=>[2,1,1,2,1,1]
[1,5,6,4,3,8,7,2]=>0011011=>[3,1,2,1,1]
[1,4,6,5,3,8,7,2]=>0011011=>[3,1,2,1,1]
[1,3,6,5,4,8,7,2]=>0011011=>[3,1,2,1,1]
[1,4,3,6,5,8,7,2]=>0101011=>[2,2,2,1,1]
[1,5,4,3,6,8,7,2]=>0110011=>[2,1,3,1,1]
[1,6,7,5,4,3,8,2]=>0011101=>[3,1,1,2,1]
[1,3,5,7,6,4,8,2]=>0001101=>[4,1,2,1]
[1,3,4,7,6,5,8,2]=>0001101=>[4,1,2,1]
[1,3,5,4,7,6,8,2]=>0010101=>[3,2,2,1]
[1,4,3,6,5,7,8,2]=>0101001=>[2,2,3,1]
[1,5,4,3,6,7,8,2]=>0110001=>[2,1,4,1]
[2,1,8,7,6,5,4,3]=>1011111=>[1,2,1,1,1,1,1]
[2,1,7,8,6,5,4,3]=>1001111=>[1,3,1,1,1,1]
[2,1,6,8,7,5,4,3]=>1001111=>[1,3,1,1,1,1]
[2,1,7,6,8,5,4,3]=>1010111=>[1,2,2,1,1,1]
[2,1,6,7,8,5,4,3]=>1000111=>[1,4,1,1,1]
[2,1,5,7,8,6,4,3]=>1000111=>[1,4,1,1,1]
[2,1,6,5,8,7,4,3]=>1010111=>[1,2,2,1,1,1]
[2,1,7,6,5,8,4,3]=>1011011=>[1,2,1,2,1,1]
[2,1,6,7,5,8,4,3]=>1001011=>[1,3,2,1,1]
[2,1,6,5,7,8,4,3]=>1010011=>[1,2,3,1,1]
[2,1,5,6,7,8,4,3]=>1000011=>[1,5,1,1]
[2,1,4,8,7,6,5,3]=>1001111=>[1,3,1,1,1,1]
[2,1,4,7,8,6,5,3]=>1000111=>[1,4,1,1,1]
[2,1,4,6,8,7,5,3]=>1000111=>[1,4,1,1,1]
[2,1,4,6,7,8,5,3]=>1000011=>[1,5,1,1]
[2,1,4,5,8,7,6,3]=>1000111=>[1,4,1,1,1]
[2,1,4,5,7,8,6,3]=>1000011=>[1,5,1,1]
[2,1,4,6,5,8,7,3]=>1001011=>[1,3,2,1,1]
[2,1,4,5,6,8,7,3]=>1000011=>[1,5,1,1]
[2,1,5,7,6,4,8,3]=>1001101=>[1,3,1,2,1]
[2,1,6,5,7,4,8,3]=>1010101=>[1,2,2,2,1]
[2,1,5,6,7,4,8,3]=>1000101=>[1,4,2,1]
[2,1,4,7,6,5,8,3]=>1001101=>[1,3,1,2,1]
[2,1,4,6,7,5,8,3]=>1000101=>[1,4,2,1]
[2,1,5,4,7,6,8,3]=>1010101=>[1,2,2,2,1]
[2,1,5,6,4,7,8,3]=>1001001=>[1,3,3,1]
[2,1,4,5,6,7,8,3]=>1000001=>[1,6,1]
[1,2,8,7,6,5,4,3]=>0011111=>[3,1,1,1,1,1]
[1,2,6,7,8,5,4,3]=>0000111=>[5,1,1,1]
[1,2,6,5,8,7,4,3]=>0010111=>[3,2,1,1,1]
[1,2,7,6,5,8,4,3]=>0011011=>[3,1,2,1,1]
[1,2,5,7,6,8,4,3]=>0001011=>[4,2,1,1]
[1,2,6,5,7,8,4,3]=>0010011=>[3,3,1,1]
[1,2,5,6,7,8,4,3]=>0000011=>[6,1,1]
[1,2,4,8,7,6,5,3]=>0001111=>[4,1,1,1,1]
[1,2,4,7,8,6,5,3]=>0000111=>[5,1,1,1]
[1,2,4,6,8,7,5,3]=>0000111=>[5,1,1,1]
[1,2,4,6,7,8,5,3]=>0000011=>[6,1,1]
[1,2,5,4,8,7,6,3]=>0010111=>[3,2,1,1,1]
[1,2,4,5,7,8,6,3]=>0000011=>[6,1,1]
[1,2,6,5,4,8,7,3]=>0011011=>[3,1,2,1,1]
[1,2,5,7,6,4,8,3]=>0001101=>[4,1,2,1]
[1,2,5,6,7,4,8,3]=>0000101=>[5,2,1]
[1,2,4,7,6,5,8,3]=>0001101=>[4,1,2,1]
[1,2,6,5,4,7,8,3]=>0011001=>[3,1,3,1]
[3,2,1,8,7,6,5,4]=>1101111=>[1,1,2,1,1,1,1]
[3,2,1,7,8,6,5,4]=>1100111=>[1,1,3,1,1,1]
[3,2,1,6,8,7,5,4]=>1100111=>[1,1,3,1,1,1]
[3,2,1,7,6,8,5,4]=>1101011=>[1,1,2,2,1,1]
[3,2,1,6,7,8,5,4]=>1100011=>[1,1,4,1,1]
[3,2,1,5,8,7,6,4]=>1100111=>[1,1,3,1,1,1]
[3,2,1,5,7,8,6,4]=>1100011=>[1,1,4,1,1]
[3,2,1,6,5,8,7,4]=>1101011=>[1,1,2,2,1,1]
[3,2,1,5,6,8,7,4]=>1100011=>[1,1,4,1,1]
[3,2,1,7,6,5,8,4]=>1101101=>[1,1,2,1,2,1]
[3,2,1,6,7,5,8,4]=>1100101=>[1,1,3,2,1]
[3,2,1,5,7,6,8,4]=>1100101=>[1,1,3,2,1]
[3,2,1,6,5,7,8,4]=>1101001=>[1,1,2,3,1]
[3,2,1,5,6,7,8,4]=>1100001=>[1,1,5,1]
[2,3,1,8,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[2,3,1,6,8,7,5,4]=>0100111=>[2,3,1,1,1]
[2,3,1,7,6,8,5,4]=>0101011=>[2,2,2,1,1]
[2,3,1,6,7,8,5,4]=>0100011=>[2,4,1,1]
[2,3,1,6,5,8,7,4]=>0101011=>[2,2,2,1,1]
[2,3,1,5,6,7,8,4]=>0100001=>[2,5,1]
[1,3,2,8,7,6,5,4]=>0101111=>[2,2,1,1,1,1]
[1,3,2,6,8,7,5,4]=>0100111=>[2,3,1,1,1]
[1,3,2,5,7,8,6,4]=>0100011=>[2,4,1,1]
[1,3,2,6,5,8,7,4]=>0101011=>[2,2,2,1,1]
[1,3,2,7,6,5,8,4]=>0101101=>[2,2,1,2,1]
[1,3,2,5,7,6,8,4]=>0100101=>[2,3,2,1]
[1,3,2,6,5,7,8,4]=>0101001=>[2,2,3,1]
[2,1,3,8,7,6,5,4]=>1001111=>[1,3,1,1,1,1]
[2,1,3,7,8,6,5,4]=>1000111=>[1,4,1,1,1]
[2,1,3,6,8,7,5,4]=>1000111=>[1,4,1,1,1]
[1,2,3,8,7,6,5,4]=>0001111=>[4,1,1,1,1]
[1,2,3,7,8,6,5,4]=>0000111=>[5,1,1,1]
[1,2,3,6,8,7,5,4]=>0000111=>[5,1,1,1]
[1,2,3,7,6,8,5,4]=>0001011=>[4,2,1,1]
[1,2,3,6,7,8,5,4]=>0000011=>[6,1,1]
[1,2,3,5,8,7,6,4]=>0000111=>[5,1,1,1]
[1,2,3,5,7,8,6,4]=>0000011=>[6,1,1]
[1,2,3,6,5,8,7,4]=>0001011=>[4,2,1,1]
[1,2,3,5,6,8,7,4]=>0000011=>[6,1,1]
[1,2,3,7,6,5,8,4]=>0001101=>[4,1,2,1]
[1,2,3,6,7,5,8,4]=>0000101=>[5,2,1]
[1,2,3,5,7,6,8,4]=>0000101=>[5,2,1]
[1,2,3,6,5,7,8,4]=>0001001=>[4,3,1]
[1,2,3,5,6,7,8,4]=>0000001=>[7,1]
[4,3,2,1,8,7,6,5]=>1110111=>[1,1,1,2,1,1,1]
[4,3,2,1,7,8,6,5]=>1110011=>[1,1,1,3,1,1]
[4,3,2,1,6,8,7,5]=>1110011=>[1,1,1,3,1,1]
[4,3,2,1,7,6,8,5]=>1110101=>[1,1,1,2,2,1]
[4,3,2,1,6,7,8,5]=>1110001=>[1,1,1,4,1]
[3,4,2,1,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[3,4,2,1,7,8,6,5]=>0110011=>[2,1,3,1,1]
[3,4,2,1,6,8,7,5]=>0110011=>[2,1,3,1,1]
[3,4,2,1,7,6,8,5]=>0110101=>[2,1,2,2,1]
[3,4,2,1,6,7,8,5]=>0110001=>[2,1,4,1]
[2,4,3,1,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[2,4,3,1,6,8,7,5]=>0110011=>[2,1,3,1,1]
[2,4,3,1,7,6,8,5]=>0110101=>[2,1,2,2,1]
[2,4,3,1,6,7,8,5]=>0110001=>[2,1,4,1]
[3,2,4,1,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[3,2,4,1,7,8,6,5]=>1010011=>[1,2,3,1,1]
[3,2,4,1,6,8,7,5]=>1010011=>[1,2,3,1,1]
[3,2,4,1,7,6,8,5]=>1010101=>[1,2,2,2,1]
[3,2,4,1,6,7,8,5]=>1010001=>[1,2,4,1]
[2,3,4,1,8,7,6,5]=>0010111=>[3,2,1,1,1]
[2,3,4,1,7,8,6,5]=>0010011=>[3,3,1,1]
[2,3,4,1,6,8,7,5]=>0010011=>[3,3,1,1]
[2,3,4,1,7,6,8,5]=>0010101=>[3,2,2,1]
[2,3,4,1,6,7,8,5]=>0010001=>[3,4,1]
[1,4,3,2,8,7,6,5]=>0110111=>[2,1,2,1,1,1]
[1,4,3,2,7,6,8,5]=>0110101=>[2,1,2,2,1]
[1,4,3,2,6,7,8,5]=>0110001=>[2,1,4,1]
[1,3,4,2,8,7,6,5]=>0010111=>[3,2,1,1,1]
[1,3,4,2,7,8,6,5]=>0010011=>[3,3,1,1]
[1,3,4,2,6,8,7,5]=>0010011=>[3,3,1,1]
[1,3,4,2,7,6,8,5]=>0010101=>[3,2,2,1]
[1,3,4,2,6,7,8,5]=>0010001=>[3,4,1]
[2,1,4,3,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[2,1,4,3,7,8,6,5]=>1010011=>[1,2,3,1,1]
[2,1,4,3,6,8,7,5]=>1010011=>[1,2,3,1,1]
[2,1,4,3,7,6,8,5]=>1010101=>[1,2,2,2,1]
[2,1,4,3,6,7,8,5]=>1010001=>[1,2,4,1]
[1,2,4,3,8,7,6,5]=>0010111=>[3,2,1,1,1]
[1,2,4,3,7,8,6,5]=>0010011=>[3,3,1,1]
[1,2,4,3,6,8,7,5]=>0010011=>[3,3,1,1]
[1,2,4,3,7,6,8,5]=>0010101=>[3,2,2,1]
[1,2,4,3,6,7,8,5]=>0010001=>[3,4,1]
[3,2,1,4,8,7,6,5]=>1100111=>[1,1,3,1,1,1]
[3,2,1,4,7,8,6,5]=>1100011=>[1,1,4,1,1]
[3,2,1,4,6,8,7,5]=>1100011=>[1,1,4,1,1]
[3,2,1,4,7,6,8,5]=>1100101=>[1,1,3,2,1]
[3,2,1,4,6,7,8,5]=>1100001=>[1,1,5,1]
[2,3,1,4,8,7,6,5]=>0100111=>[2,3,1,1,1]
[2,3,1,4,7,8,6,5]=>0100011=>[2,4,1,1]
[2,3,1,4,7,6,8,5]=>0100101=>[2,3,2,1]
[2,3,1,4,6,7,8,5]=>0100001=>[2,5,1]
[1,3,2,4,8,7,6,5]=>0100111=>[2,3,1,1,1]
[1,3,2,4,6,8,7,5]=>0100011=>[2,4,1,1]
[1,3,2,4,7,6,8,5]=>0100101=>[2,3,2,1]
[1,3,2,4,6,7,8,5]=>0100001=>[2,5,1]
[2,1,3,4,8,7,6,5]=>1000111=>[1,4,1,1,1]
[2,1,3,4,7,6,8,5]=>1000101=>[1,4,2,1]
[2,1,3,4,6,7,8,5]=>1000001=>[1,6,1]
[1,2,3,4,8,7,6,5]=>0000111=>[5,1,1,1]
[1,2,3,4,7,8,6,5]=>0000011=>[6,1,1]
[1,2,3,4,6,8,7,5]=>0000011=>[6,1,1]
[1,2,3,4,7,6,8,5]=>0000101=>[5,2,1]
[1,2,3,4,6,7,8,5]=>0000001=>[7,1]
[5,4,3,2,1,8,7,6]=>1111011=>[1,1,1,1,2,1,1]
[5,4,3,2,1,7,8,6]=>1111001=>[1,1,1,1,3,1]
[4,5,3,2,1,8,7,6]=>0111011=>[2,1,1,2,1,1]
[3,5,4,2,1,8,7,6]=>0111011=>[2,1,1,2,1,1]
[3,5,4,2,1,7,8,6]=>0111001=>[2,1,1,3,1]
[4,3,5,2,1,8,7,6]=>1011011=>[1,2,1,2,1,1]
[3,4,5,2,1,8,7,6]=>0011011=>[3,1,2,1,1]
[3,4,5,2,1,7,8,6]=>0011001=>[3,1,3,1]
[2,5,4,3,1,8,7,6]=>0111011=>[2,1,1,2,1,1]
[2,5,4,3,1,7,8,6]=>0111001=>[2,1,1,3,1]
[2,4,5,3,1,8,7,6]=>0011011=>[3,1,2,1,1]
[3,2,5,4,1,8,7,6]=>1011011=>[1,2,1,2,1,1]
[3,2,5,4,1,7,8,6]=>1011001=>[1,2,1,3,1]
[2,3,5,4,1,8,7,6]=>0011011=>[3,1,2,1,1]
[4,3,2,5,1,8,7,6]=>1101011=>[1,1,2,2,1,1]
[3,4,2,5,1,8,7,6]=>0101011=>[2,2,2,1,1]
[3,4,2,5,1,7,8,6]=>0101001=>[2,2,3,1]
[2,4,3,5,1,8,7,6]=>0101011=>[2,2,2,1,1]
[2,4,3,5,1,7,8,6]=>0101001=>[2,2,3,1]
[3,2,4,5,1,8,7,6]=>1001011=>[1,3,2,1,1]
[2,3,4,5,1,8,7,6]=>0001011=>[4,2,1,1]
[1,3,5,4,2,7,8,6]=>0011001=>[3,1,3,1]
[1,4,3,5,2,7,8,6]=>0101001=>[2,2,3,1]
[1,3,4,5,2,8,7,6]=>0001011=>[4,2,1,1]
[1,3,4,5,2,7,8,6]=>0001001=>[4,3,1]
[1,2,5,4,3,7,8,6]=>0011001=>[3,1,3,1]
[1,2,4,5,3,8,7,6]=>0001011=>[4,2,1,1]
[1,2,4,5,3,7,8,6]=>0001001=>[4,3,1]
[1,3,2,5,4,7,8,6]=>0101001=>[2,2,3,1]
[2,1,3,5,4,8,7,6]=>1001011=>[1,3,2,1,1]
[1,2,3,5,4,8,7,6]=>0001011=>[4,2,1,1]
[1,2,3,5,4,7,8,6]=>0001001=>[4,3,1]
[4,3,2,1,5,8,7,6]=>1110011=>[1,1,1,3,1,1]
[4,3,2,1,5,7,8,6]=>1110001=>[1,1,1,4,1]
[3,2,4,1,5,8,7,6]=>1010011=>[1,2,3,1,1]
[3,2,4,1,5,7,8,6]=>1010001=>[1,2,4,1]
[2,3,4,1,5,8,7,6]=>0010011=>[3,3,1,1]
[2,3,4,1,5,7,8,6]=>0010001=>[3,4,1]
[1,4,3,2,5,8,7,6]=>0110011=>[2,1,3,1,1]
[1,4,3,2,5,7,8,6]=>0110001=>[2,1,4,1]
[1,3,4,2,5,8,7,6]=>0010011=>[3,3,1,1]
[1,3,4,2,5,7,8,6]=>0010001=>[3,4,1]
[1,2,4,3,5,7,8,6]=>0010001=>[3,4,1]
[3,2,1,4,5,8,7,6]=>1100011=>[1,1,4,1,1]
[3,2,1,4,5,7,8,6]=>1100001=>[1,1,5,1]
[2,3,1,4,5,7,8,6]=>0100001=>[2,5,1]
[1,3,2,4,5,7,8,6]=>0100001=>[2,5,1]
[1,2,3,4,5,8,7,6]=>0000011=>[6,1,1]
[1,2,3,4,5,7,8,6]=>0000001=>[7,1]
[6,5,4,3,2,1,8,7]=>1111101=>[1,1,1,1,1,2,1]
[5,6,4,3,2,1,8,7]=>0111101=>[2,1,1,1,2,1]
[4,6,5,3,2,1,8,7]=>0111101=>[2,1,1,1,2,1]
[5,4,6,3,2,1,8,7]=>1011101=>[1,2,1,1,2,1]
[4,5,6,3,2,1,8,7]=>0011101=>[3,1,1,2,1]
[3,6,5,4,2,1,8,7]=>0111101=>[2,1,1,1,2,1]
[3,5,6,4,2,1,8,7]=>0011101=>[3,1,1,2,1]
[4,3,6,5,2,1,8,7]=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,2,1,8,7]=>1101101=>[1,1,2,1,2,1]
[4,5,3,6,2,1,8,7]=>0101101=>[2,2,1,2,1]
[3,4,5,6,2,1,8,7]=>0001101=>[4,1,2,1]
[2,6,5,4,3,1,8,7]=>0111101=>[2,1,1,1,2,1]
[2,5,6,4,3,1,8,7]=>0011101=>[3,1,1,2,1]
[2,4,6,5,3,1,8,7]=>0011101=>[3,1,1,2,1]
[2,3,6,5,4,1,8,7]=>0011101=>[3,1,1,2,1]
[2,3,5,6,4,1,8,7]=>0001101=>[4,1,2,1]
[2,4,3,6,5,1,8,7]=>0101101=>[2,2,1,2,1]
[5,4,3,2,6,1,8,7]=>1110101=>[1,1,1,2,2,1]
[4,5,3,2,6,1,8,7]=>0110101=>[2,1,2,2,1]
[3,5,4,2,6,1,8,7]=>0110101=>[2,1,2,2,1]
[4,3,5,2,6,1,8,7]=>1010101=>[1,2,2,2,1]
[3,4,5,2,6,1,8,7]=>0010101=>[3,2,2,1]
[2,5,4,3,6,1,8,7]=>0110101=>[2,1,2,2,1]
[2,4,5,3,6,1,8,7]=>0010101=>[3,2,2,1]
[3,2,5,4,6,1,8,7]=>1010101=>[1,2,2,2,1]
[3,4,2,5,6,1,8,7]=>0100101=>[2,3,2,1]
[2,3,4,5,6,1,8,7]=>0000101=>[5,2,1]
[1,5,4,6,3,2,8,7]=>0101101=>[2,2,1,2,1]
[1,3,6,5,4,2,8,7]=>0011101=>[3,1,1,2,1]
[2,1,6,5,4,3,8,7]=>1011101=>[1,2,1,1,2,1]
[2,1,5,6,4,3,8,7]=>1001101=>[1,3,1,2,1]
[2,1,4,6,5,3,8,7]=>1001101=>[1,3,1,2,1]
[2,1,5,4,6,3,8,7]=>1010101=>[1,2,2,2,1]
[2,1,4,5,6,3,8,7]=>1000101=>[1,4,2,1]
[2,3,1,6,5,4,8,7]=>0101101=>[2,2,1,2,1]
[1,2,3,6,5,4,8,7]=>0001101=>[4,1,2,1]
[1,2,3,5,6,4,8,7]=>0000101=>[5,2,1]
[4,3,2,1,6,5,8,7]=>1110101=>[1,1,1,2,2,1]
[3,4,2,1,6,5,8,7]=>0110101=>[2,1,2,2,1]
[2,4,3,1,6,5,8,7]=>0110101=>[2,1,2,2,1]
[3,2,4,1,6,5,8,7]=>1010101=>[1,2,2,2,1]
[2,3,4,1,6,5,8,7]=>0010101=>[3,2,2,1]
[2,1,4,3,6,5,8,7]=>1010101=>[1,2,2,2,1]
[1,2,4,3,6,5,8,7]=>0010101=>[3,2,2,1]
[1,3,2,4,6,5,8,7]=>0100101=>[2,3,2,1]
[2,1,3,4,6,5,8,7]=>1000101=>[1,4,2,1]
[1,2,3,4,6,5,8,7]=>0000101=>[5,2,1]
[5,4,3,2,1,6,8,7]=>1111001=>[1,1,1,1,3,1]
[4,5,3,2,1,6,8,7]=>0111001=>[2,1,1,3,1]
[3,5,4,2,1,6,8,7]=>0111001=>[2,1,1,3,1]
[2,5,4,3,1,6,8,7]=>0111001=>[2,1,1,3,1]
[2,4,5,3,1,6,8,7]=>0011001=>[3,1,3,1]
[3,2,5,4,1,6,8,7]=>1011001=>[1,2,1,3,1]
[1,3,5,4,2,6,8,7]=>0011001=>[3,1,3,1]
[1,3,4,5,2,6,8,7]=>0001001=>[4,3,1]
[2,1,4,5,3,6,8,7]=>1001001=>[1,3,3,1]
[1,2,5,4,3,6,8,7]=>0011001=>[3,1,3,1]
[2,1,3,5,4,6,8,7]=>1001001=>[1,3,3,1]
[4,3,2,1,5,6,8,7]=>1110001=>[1,1,1,4,1]
[3,2,4,1,5,6,8,7]=>1010001=>[1,2,4,1]
[2,3,4,1,5,6,8,7]=>0010001=>[3,4,1]
[1,4,3,2,5,6,8,7]=>0110001=>[2,1,4,1]
[1,3,4,2,5,6,8,7]=>0010001=>[3,4,1]
[2,1,4,3,5,6,8,7]=>1010001=>[1,2,4,1]
[1,2,4,3,5,6,8,7]=>0010001=>[3,4,1]
[2,1,3,4,5,6,8,7]=>1000001=>[1,6,1]
[1,2,3,4,5,6,8,7]=>0000001=>[7,1]
[5,7,6,4,3,2,1,8]=>0111110=>[2,1,1,1,1,2]
[4,7,6,5,3,2,1,8]=>0111110=>[2,1,1,1,1,2]
[4,6,7,5,3,2,1,8]=>0011110=>[3,1,1,1,2]
[4,5,7,6,3,2,1,8]=>0011110=>[3,1,1,1,2]
[4,6,5,7,3,2,1,8]=>0101110=>[2,2,1,1,2]
[3,5,7,6,4,2,1,8]=>0011110=>[3,1,1,1,2]
[3,5,6,7,4,2,1,8]=>0001110=>[4,1,1,2]
[3,4,7,6,5,2,1,8]=>0011110=>[3,1,1,1,2]
[4,5,3,7,6,2,1,8]=>0101110=>[2,2,1,1,2]
[3,5,4,7,6,2,1,8]=>0101110=>[2,2,1,1,2]
[4,3,5,7,6,2,1,8]=>1001110=>[1,3,1,1,2]
[2,5,6,7,4,3,1,8]=>0001110=>[4,1,1,2]
[2,4,6,7,5,3,1,8]=>0001110=>[4,1,1,2]
[3,2,7,6,5,4,1,8]=>1011110=>[1,2,1,1,1,2]
[3,2,6,7,5,4,1,8]=>1001110=>[1,3,1,1,2]
[3,2,5,7,6,4,1,8]=>1001110=>[1,3,1,1,2]
[2,3,7,6,5,4,1,8]=>0011110=>[3,1,1,1,2]
[2,3,6,7,5,4,1,8]=>0001110=>[4,1,1,2]
[2,3,5,7,6,4,1,8]=>0001110=>[4,1,1,2]
[2,3,6,5,7,4,1,8]=>0010110=>[3,2,1,2]
[2,3,5,6,7,4,1,8]=>0000110=>[5,1,2]
[3,2,4,6,7,5,1,8]=>1000110=>[1,4,1,2]
[2,3,4,7,6,5,1,8]=>0001110=>[4,1,1,2]
[5,4,3,2,7,6,1,8]=>1110110=>[1,1,1,2,1,2]
[4,5,3,2,7,6,1,8]=>0110110=>[2,1,2,1,2]
[3,5,4,2,7,6,1,8]=>0110110=>[2,1,2,1,2]
[3,2,5,4,7,6,1,8]=>1010110=>[1,2,2,1,2]
[4,3,2,5,7,6,1,8]=>1100110=>[1,1,3,1,2]
[3,6,5,4,2,7,1,8]=>0111010=>[2,1,1,2,2]
[3,4,6,5,2,7,1,8]=>0011010=>[3,1,2,2]
[3,5,4,6,2,7,1,8]=>0101010=>[2,2,2,2]
[2,5,4,6,3,7,1,8]=>0101010=>[2,2,2,2]
[3,2,6,5,4,7,1,8]=>1011010=>[1,2,1,2,2]
[3,4,2,6,5,7,1,8]=>0101010=>[2,2,2,2]
[2,4,3,6,5,7,1,8]=>0101010=>[2,2,2,2]
[3,5,4,2,6,7,1,8]=>0110010=>[2,1,3,2]
[2,5,4,3,6,7,1,8]=>0110010=>[2,1,3,2]
[1,5,6,7,4,3,2,8]=>0001110=>[4,1,1,2]
[1,4,6,5,7,3,2,8]=>0010110=>[3,2,1,2]
[1,3,5,7,6,4,2,8]=>0001110=>[4,1,1,2]
[1,3,5,6,7,4,2,8]=>0000110=>[5,1,2]
[1,3,5,4,7,6,2,8]=>0010110=>[3,2,1,2]
[1,4,3,5,7,6,2,8]=>0100110=>[2,3,1,2]
[1,5,4,6,3,7,2,8]=>0101010=>[2,2,2,2]
[1,3,6,5,4,7,2,8]=>0011010=>[3,1,2,2]
[1,4,3,6,5,7,2,8]=>0101010=>[2,2,2,2]
[1,5,4,3,6,7,2,8]=>0110010=>[2,1,3,2]
[1,3,4,5,6,7,2,8]=>0000010=>[6,2]
[2,1,4,6,7,5,3,8]=>1000110=>[1,4,1,2]
[1,2,5,7,6,4,3,8]=>0001110=>[4,1,1,2]
[1,2,5,6,7,4,3,8]=>0000110=>[5,1,2]
[1,2,5,6,4,7,3,8]=>0001010=>[4,2,2]
[1,2,5,4,6,7,3,8]=>0010010=>[3,3,2]
[3,2,1,5,7,6,4,8]=>1100110=>[1,1,3,1,2]
[3,2,1,5,6,7,4,8]=>1100010=>[1,1,4,2]
[2,3,1,6,7,5,4,8]=>0100110=>[2,3,1,2]
[2,3,1,6,5,7,4,8]=>0101010=>[2,2,2,2]
[2,3,1,5,6,7,4,8]=>0100010=>[2,4,2]
[1,3,2,5,7,6,4,8]=>0100110=>[2,3,1,2]
[1,3,2,6,5,7,4,8]=>0101010=>[2,2,2,2]
[1,3,2,5,6,7,4,8]=>0100010=>[2,4,2]
[2,1,3,6,7,5,4,8]=>1000110=>[1,4,1,2]
[1,2,3,7,6,5,4,8]=>0001110=>[4,1,1,2]
[1,2,3,6,7,5,4,8]=>0000110=>[5,1,2]
[1,2,3,5,7,6,4,8]=>0000110=>[5,1,2]
[1,2,3,6,5,7,4,8]=>0001010=>[4,2,2]
[1,2,3,5,6,7,4,8]=>0000010=>[6,2]
[4,3,2,1,7,6,5,8]=>1110110=>[1,1,1,2,1,2]
[4,3,2,1,6,7,5,8]=>1110010=>[1,1,1,3,2]
[3,2,4,1,7,6,5,8]=>1010110=>[1,2,2,1,2]
[3,2,4,1,6,7,5,8]=>1010010=>[1,2,3,2]
[2,3,4,1,7,6,5,8]=>0010110=>[3,2,1,2]
[2,3,4,1,6,7,5,8]=>0010010=>[3,3,2]
[1,4,3,2,7,6,5,8]=>0110110=>[2,1,2,1,2]
[1,4,3,2,6,7,5,8]=>0110010=>[2,1,3,2]
[1,3,4,2,6,7,5,8]=>0010010=>[3,3,2]
[1,2,4,3,6,7,5,8]=>0010010=>[3,3,2]
[2,3,1,4,6,7,5,8]=>0100010=>[2,4,2]
[1,3,2,4,7,6,5,8]=>0100110=>[2,3,1,2]
[1,2,3,4,7,6,5,8]=>0000110=>[5,1,2]
[1,2,3,4,6,7,5,8]=>0000010=>[6,2]
[5,4,3,2,1,7,6,8]=>1111010=>[1,1,1,1,2,2]
[4,5,3,2,1,7,6,8]=>0111010=>[2,1,1,2,2]
[3,5,4,2,1,7,6,8]=>0111010=>[2,1,1,2,2]
[2,5,4,3,1,7,6,8]=>0111010=>[2,1,1,2,2]
[2,4,5,3,1,7,6,8]=>0011010=>[3,1,2,2]
[3,2,5,4,1,7,6,8]=>1011010=>[1,2,1,2,2]
[3,4,2,5,1,7,6,8]=>0101010=>[2,2,2,2]
[2,4,3,5,1,7,6,8]=>0101010=>[2,2,2,2]
[1,3,5,4,2,7,6,8]=>0011010=>[3,1,2,2]
[1,4,3,5,2,7,6,8]=>0101010=>[2,2,2,2]
[1,3,4,5,2,7,6,8]=>0001010=>[4,2,2]
[2,3,1,5,4,7,6,8]=>0101010=>[2,2,2,2]
[1,3,2,5,4,7,6,8]=>0101010=>[2,2,2,2]
[1,2,3,5,4,7,6,8]=>0001010=>[4,2,2]
[4,3,2,1,5,7,6,8]=>1110010=>[1,1,1,3,2]
[3,2,4,1,5,7,6,8]=>1010010=>[1,2,3,2]
[2,3,4,1,5,7,6,8]=>0010010=>[3,3,2]
[1,4,3,2,5,7,6,8]=>0110010=>[2,1,3,2]
[1,3,4,2,5,7,6,8]=>0010010=>[3,3,2]
[1,3,2,4,5,7,6,8]=>0100010=>[2,4,2]
[1,2,3,4,5,7,6,8]=>0000010=>[6,2]
[3,6,5,4,2,1,7,8]=>0111100=>[2,1,1,1,3]
[4,3,6,5,2,1,7,8]=>1011100=>[1,2,1,1,3]
[2,4,6,5,3,1,7,8]=>0011100=>[3,1,1,3]
[2,4,5,6,3,1,7,8]=>0001100=>[4,1,3]
[4,3,2,6,5,1,7,8]=>1101100=>[1,1,2,1,3]
[3,5,4,2,6,1,7,8]=>0110100=>[2,1,2,3]
[1,5,6,4,3,2,7,8]=>0011100=>[3,1,1,3]
[1,4,6,5,3,2,7,8]=>0011100=>[3,1,1,3]
[1,5,4,6,3,2,7,8]=>0101100=>[2,2,1,3]
[1,4,5,6,3,2,7,8]=>0001100=>[4,1,3]
[1,3,5,6,4,2,7,8]=>0001100=>[4,1,3]
[1,4,3,6,5,2,7,8]=>0101100=>[2,2,1,3]
[1,5,4,3,6,2,7,8]=>0110100=>[2,1,2,3]
[2,1,5,6,4,3,7,8]=>1001100=>[1,3,1,3]
[2,1,4,6,5,3,7,8]=>1001100=>[1,3,1,3]
[1,2,6,5,4,3,7,8]=>0011100=>[3,1,1,3]
[1,2,5,6,4,3,7,8]=>0001100=>[4,1,3]
[1,2,4,5,6,3,7,8]=>0000100=>[5,3]
[3,2,1,5,6,4,7,8]=>1100100=>[1,1,3,3]
[1,3,2,5,6,4,7,8]=>0100100=>[2,3,3]
[1,2,3,5,6,4,7,8]=>0000100=>[5,3]
[4,3,2,1,6,5,7,8]=>1110100=>[1,1,1,2,3]
[3,2,4,1,6,5,7,8]=>1010100=>[1,2,2,3]
[2,3,4,1,6,5,7,8]=>0010100=>[3,2,3]
[2,1,4,3,6,5,7,8]=>1010100=>[1,2,2,3]
[1,2,4,3,6,5,7,8]=>0010100=>[3,2,3]
[1,3,2,4,6,5,7,8]=>0100100=>[2,3,3]
[2,1,3,4,6,5,7,8]=>1000100=>[1,4,3]
[1,2,3,4,6,5,7,8]=>0000100=>[5,3]
[3,5,4,2,1,6,7,8]=>0111000=>[2,1,1,4]
[2,5,4,3,1,6,7,8]=>0111000=>[2,1,1,4]
[2,4,5,3,1,6,7,8]=>0011000=>[3,1,4]
[3,2,5,4,1,6,7,8]=>1011000=>[1,2,1,4]
[2,3,5,4,1,6,7,8]=>0011000=>[3,1,4]
[2,4,3,5,1,6,7,8]=>0101000=>[2,2,4]
[1,3,5,4,2,6,7,8]=>0011000=>[3,1,4]
[1,3,4,5,2,6,7,8]=>0001000=>[4,4]
[1,3,2,5,4,6,7,8]=>0101000=>[2,2,4]
[1,2,3,5,4,6,7,8]=>0001000=>[4,4]
[2,4,3,1,5,6,7,8]=>0110000=>[2,1,5]
[1,4,3,2,5,6,7,8]=>0110000=>[2,1,5]
[1,3,4,2,5,6,7,8]=>0010000=>[3,5]
[2,1,4,3,5,6,7,8]=>1010000=>[1,2,5]
[1,2,4,3,5,6,7,8]=>0010000=>[3,5]
[1,3,2,4,5,6,7,8]=>0100000=>[2,6]
[1,2,3,4,8,6,7,5]=>0000101=>[5,2,1]
[1,2,3,5,8,6,7,4]=>0000101=>[5,2,1]
[1,2,3,7,5,6,4,8]=>0001010=>[4,2,2]
[1,2,3,7,5,6,8,4]=>0001001=>[4,3,1]
[1,2,3,8,5,6,7,4]=>0001001=>[4,3,1]
[1,2,3,8,5,7,6,4]=>0001011=>[4,2,1,1]
[1,2,3,8,6,5,7,4]=>0001101=>[4,1,2,1]
[1,2,3,8,6,7,5,4]=>0001011=>[4,2,1,1]
[1,2,4,5,8,6,7,3]=>0000101=>[5,2,1]
[1,2,4,8,5,6,7,3]=>0001001=>[4,3,1]
[1,2,4,8,6,5,7,3]=>0001101=>[4,1,2,1]
[1,2,5,4,8,6,7,3]=>0010101=>[3,2,2,1]
[1,2,6,4,5,3,7,8]=>0010100=>[3,2,3]
[1,2,6,4,5,8,7,3]=>0010011=>[3,3,1,1]
[1,2,8,4,5,6,7,3]=>0010001=>[3,4,1]
[1,2,8,4,6,7,5,3]=>0010011=>[3,3,1,1]
[1,2,8,4,7,6,5,3]=>0010111=>[3,2,1,1,1]
[1,2,7,5,4,6,8,3]=>0011001=>[3,1,3,1]
[1,2,8,5,4,6,7,3]=>0011001=>[3,1,3,1]
[1,2,8,5,4,7,6,3]=>0011011=>[3,1,2,1,1]
[1,2,8,6,5,4,7,3]=>0011101=>[3,1,1,2,1]
[1,2,8,7,5,6,4,3]=>0011011=>[3,1,2,1,1]
[1,3,2,7,5,6,8,4]=>0101001=>[2,2,3,1]
[1,3,2,8,5,7,6,4]=>0101011=>[2,2,2,1,1]
[1,3,4,5,8,6,7,2]=>0000101=>[5,2,1]
[1,3,4,8,5,6,7,2]=>0001001=>[4,3,1]
[1,3,6,4,5,2,8,7]=>0010101=>[3,2,2,1]
[1,3,6,4,5,7,2,8]=>0010010=>[3,3,2]
[1,3,6,4,5,8,7,2]=>0010011=>[3,3,1,1]
[1,3,8,4,5,6,7,2]=>0010001=>[3,4,1]
[1,3,8,4,6,5,7,2]=>0010101=>[3,2,2,1]
[1,3,8,5,4,6,7,2]=>0011001=>[3,1,3,1]
[1,3,8,5,4,7,6,2]=>0011011=>[3,1,2,1,1]
[1,3,8,5,6,7,4,2]=>0010011=>[3,3,1,1]
[1,3,8,5,7,6,4,2]=>0010111=>[3,2,1,1,1]
[1,3,8,6,5,7,4,2]=>0011011=>[3,1,2,1,1]
[1,3,8,7,5,6,4,2]=>0011011=>[3,1,2,1,1]
[1,4,3,8,5,6,7,2]=>0101001=>[2,2,3,1]
[1,4,3,8,5,7,6,2]=>0101011=>[2,2,2,1,1]
[1,4,3,8,6,7,5,2]=>0101011=>[2,2,2,1,1]
[1,5,3,4,2,7,8,6]=>0101001=>[2,2,3,1]
[1,5,3,4,6,2,7,8]=>0100100=>[2,3,3]
[1,5,3,4,6,7,2,8]=>0100010=>[2,4,2]
[1,5,3,4,7,6,2,8]=>0100110=>[2,3,1,2]
[1,5,3,4,8,6,7,2]=>0100101=>[2,3,2,1]
[1,8,3,4,6,7,5,2]=>0100011=>[2,4,1,1]
[1,6,3,5,4,2,7,8]=>0101100=>[2,2,1,3]
[1,6,3,5,4,8,7,2]=>0101011=>[2,2,2,1,1]
[1,8,3,5,4,7,6,2]=>0101011=>[2,2,2,1,1]
[1,8,3,5,6,4,7,2]=>0100101=>[2,3,2,1]
[1,8,3,5,7,6,4,2]=>0100111=>[2,3,1,1,1]
[1,8,3,6,5,4,7,2]=>0101101=>[2,2,1,2,1]
[1,8,3,7,5,6,4,2]=>0101011=>[2,2,2,1,1]
[1,8,3,7,6,5,4,2]=>0101111=>[2,2,1,1,1,1]
[1,6,4,3,5,2,7,8]=>0110100=>[2,1,2,3]
[1,8,4,3,5,6,7,2]=>0110001=>[2,1,4,1]
[1,8,4,3,5,7,6,2]=>0110011=>[2,1,3,1,1]
[1,7,4,3,6,5,8,2]=>0110101=>[2,1,2,2,1]
[1,8,4,3,6,7,5,2]=>0110011=>[2,1,3,1,1]
[1,6,4,5,3,8,7,2]=>0101011=>[2,2,2,1,1]
[1,8,4,5,6,3,7,2]=>0100101=>[2,3,2,1]
[1,8,4,5,6,7,3,2]=>0100011=>[2,4,1,1]
[1,8,4,6,5,7,3,2]=>0101011=>[2,2,2,1,1]
[1,8,4,7,6,5,3,2]=>0101111=>[2,2,1,1,1,1]
[1,7,5,4,3,6,8,2]=>0111001=>[2,1,1,3,1]
[1,8,5,4,3,6,7,2]=>0111001=>[2,1,1,3,1]
[1,8,5,4,3,7,6,2]=>0111011=>[2,1,1,2,1,1]
[1,8,5,4,6,3,7,2]=>0110101=>[2,1,2,2,1]
[1,8,5,4,6,7,3,2]=>0110011=>[2,1,3,1,1]
[1,8,5,4,7,6,3,2]=>0110111=>[2,1,2,1,1,1]
[1,8,6,4,5,7,3,2]=>0110011=>[2,1,3,1,1]
[1,8,7,4,5,6,3,2]=>0110011=>[2,1,3,1,1]
[1,8,7,4,6,5,3,2]=>0110111=>[2,1,2,1,1,1]
[1,8,6,5,4,7,3,2]=>0111011=>[2,1,1,2,1,1]
[1,8,7,5,4,6,3,2]=>0111011=>[2,1,1,2,1,1]
[1,8,7,5,6,4,3,2]=>0110111=>[2,1,2,1,1,1]
[2,1,3,4,8,6,7,5]=>1000101=>[1,4,2,1]
[2,1,4,3,8,6,7,5]=>1010101=>[1,2,2,2,1]
[2,1,4,5,8,6,7,3]=>1000101=>[1,4,2,1]
[2,1,4,8,5,6,7,3]=>1001001=>[1,3,3,1]
[2,1,4,8,5,7,6,3]=>1001011=>[1,3,2,1,1]
[2,1,4,8,6,5,7,3]=>1001101=>[1,3,1,2,1]
[2,1,4,8,6,7,5,3]=>1001011=>[1,3,2,1,1]
[2,1,5,4,8,6,7,3]=>1010101=>[1,2,2,2,1]
[2,1,6,4,5,3,8,7]=>1010101=>[1,2,2,2,1]
[2,1,6,4,5,7,8,3]=>1010001=>[1,2,4,1]
[2,1,6,4,5,8,7,3]=>1010011=>[1,2,3,1,1]
[2,1,8,4,5,6,7,3]=>1010001=>[1,2,4,1]
[2,1,8,4,5,7,6,3]=>1010011=>[1,2,3,1,1]
[2,1,8,4,6,5,7,3]=>1010101=>[1,2,2,2,1]
[2,1,8,4,6,7,5,3]=>1010011=>[1,2,3,1,1]
[2,1,8,4,7,6,5,3]=>1010111=>[1,2,2,1,1,1]
[2,1,7,5,4,6,8,3]=>1011001=>[1,2,1,3,1]
[2,1,8,5,4,6,7,3]=>1011001=>[1,2,1,3,1]
[2,1,8,5,4,7,6,3]=>1011011=>[1,2,1,2,1,1]
[2,1,7,5,6,4,8,3]=>1010101=>[1,2,2,2,1]
[2,1,8,5,6,4,7,3]=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,6,4,3]=>1010111=>[1,2,2,1,1,1]
[2,1,8,7,5,6,4,3]=>1011011=>[1,2,1,2,1,1]
[2,3,1,8,5,6,7,4]=>0101001=>[2,2,3,1]
[2,3,1,8,6,7,5,4]=>0101011=>[2,2,2,1,1]
[2,3,4,1,8,6,7,5]=>0010101=>[3,2,2,1]
[2,3,4,5,8,6,7,1]=>0000101=>[5,2,1]
[2,3,4,7,5,6,1,8]=>0001010=>[4,2,2]
[2,3,4,7,5,6,8,1]=>0001001=>[4,3,1]
[2,3,4,8,5,6,7,1]=>0001001=>[4,3,1]
[2,3,4,8,5,7,6,1]=>0001011=>[4,2,1,1]
[2,3,4,8,6,5,7,1]=>0001101=>[4,1,2,1]
[2,3,4,8,6,7,5,1]=>0001011=>[4,2,1,1]
[2,3,6,4,5,1,8,7]=>0010101=>[3,2,2,1]
[2,3,6,4,5,7,8,1]=>0010001=>[3,4,1]
[2,3,7,4,5,6,8,1]=>0010001=>[3,4,1]
[2,3,8,4,5,6,7,1]=>0010001=>[3,4,1]
[2,3,7,4,6,5,8,1]=>0010101=>[3,2,2,1]
[2,3,7,5,4,6,1,8]=>0011010=>[3,1,2,2]
[2,3,7,5,4,6,8,1]=>0011001=>[3,1,3,1]
[2,3,7,5,6,4,1,8]=>0010110=>[3,2,1,2]
[2,3,7,5,6,4,8,1]=>0010101=>[3,2,2,1]
[2,3,8,5,7,6,4,1]=>0010111=>[3,2,1,1,1]
[2,4,3,1,8,6,7,5]=>0110101=>[2,1,2,2,1]
[2,4,3,5,8,6,7,1]=>0100101=>[2,3,2,1]
[2,4,3,8,5,6,7,1]=>0101001=>[2,2,3,1]
[2,4,3,8,6,7,5,1]=>0101011=>[2,2,2,1,1]
[2,5,3,4,1,6,7,8]=>0101000=>[2,2,4]
[2,5,3,4,1,8,7,6]=>0101011=>[2,2,2,1,1]
[2,5,3,4,6,7,1,8]=>0100010=>[2,4,2]
[2,5,3,4,8,7,6,1]=>0100111=>[2,3,1,1,1]
[2,6,3,4,5,7,8,1]=>0100001=>[2,5,1]
[2,6,3,4,5,8,7,1]=>0100011=>[2,4,1,1]
[2,6,3,5,4,1,7,8]=>0101100=>[2,2,1,3]
[2,6,3,5,4,1,8,7]=>0101101=>[2,2,1,2,1]
[2,6,3,5,4,7,8,1]=>0101001=>[2,2,3,1]
[2,7,3,5,4,6,8,1]=>0101001=>[2,2,3,1]
[2,7,3,5,6,4,8,1]=>0100101=>[2,3,2,1]
[2,8,3,5,7,6,4,1]=>0100111=>[2,3,1,1,1]
[2,7,3,6,5,4,1,8]=>0101110=>[2,2,1,1,2]
[2,8,3,7,5,6,4,1]=>0101011=>[2,2,2,1,1]
[2,5,4,3,8,6,7,1]=>0110101=>[2,1,2,2,1]
[2,6,4,3,5,7,8,1]=>0110001=>[2,1,4,1]
[2,8,4,3,7,6,5,1]=>0110111=>[2,1,2,1,1,1]
[2,6,4,5,3,1,7,8]=>0101100=>[2,2,1,3]
[2,6,4,5,3,1,8,7]=>0101101=>[2,2,1,2,1]
[2,6,4,5,3,7,8,1]=>0101001=>[2,2,3,1]
[2,6,4,5,3,8,7,1]=>0101011=>[2,2,2,1,1]
[2,7,4,5,6,3,1,8]=>0100110=>[2,3,1,2]
[2,7,4,5,6,3,8,1]=>0100101=>[2,3,2,1]
[2,7,5,4,3,6,8,1]=>0111001=>[2,1,1,3,1]
[2,8,5,4,3,6,7,1]=>0111001=>[2,1,1,3,1]
[2,8,5,4,3,7,6,1]=>0111011=>[2,1,1,2,1,1]
[2,7,5,4,6,3,8,1]=>0110101=>[2,1,2,2,1]
[2,8,5,4,7,6,3,1]=>0110111=>[2,1,2,1,1,1]
[2,8,7,5,4,6,3,1]=>0111011=>[2,1,1,2,1,1]
[2,8,7,5,6,4,3,1]=>0110111=>[2,1,2,1,1,1]
[3,2,1,4,8,6,7,5]=>1100101=>[1,1,3,2,1]
[3,2,1,5,8,6,7,4]=>1100101=>[1,1,3,2,1]
[3,2,1,7,5,6,8,4]=>1101001=>[1,1,2,3,1]
[3,2,1,8,5,6,7,4]=>1101001=>[1,1,2,3,1]
[3,2,1,8,5,7,6,4]=>1101011=>[1,1,2,2,1,1]
[3,2,1,8,6,5,7,4]=>1101101=>[1,1,2,1,2,1]
[3,2,1,8,6,7,5,4]=>1101011=>[1,1,2,2,1,1]
[3,2,4,1,8,6,7,5]=>1010101=>[1,2,2,2,1]
[3,2,4,8,5,6,7,1]=>1001001=>[1,3,3,1]
[3,2,5,4,8,6,7,1]=>1010101=>[1,2,2,2,1]
[3,2,6,4,5,1,8,7]=>1010101=>[1,2,2,2,1]
[3,2,6,4,5,7,1,8]=>1010010=>[1,2,3,2]
[3,2,7,4,6,5,1,8]=>1010110=>[1,2,2,1,2]
[3,2,7,4,6,5,8,1]=>1010101=>[1,2,2,2,1]
[3,2,8,5,4,6,7,1]=>1011001=>[1,2,1,3,1]
[3,2,7,5,6,4,1,8]=>1010110=>[1,2,2,1,2]
[3,2,7,5,6,4,8,1]=>1010101=>[1,2,2,2,1]
[3,2,8,5,6,4,7,1]=>1010101=>[1,2,2,2,1]
[3,2,8,5,7,6,4,1]=>1010111=>[1,2,2,1,1,1]
[4,2,3,1,6,5,8,7]=>1010101=>[1,2,2,2,1]
[4,2,3,1,6,7,8,5]=>1010001=>[1,2,4,1]
[4,2,3,1,6,8,7,5]=>1010011=>[1,2,3,1,1]
[4,2,3,1,7,6,8,5]=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,6,7,5]=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[4,2,3,5,1,7,8,6]=>1001001=>[1,3,3,1]
[4,2,3,5,1,8,7,6]=>1001011=>[1,3,2,1,1]
[4,2,3,5,6,1,8,7]=>1000101=>[1,4,2,1]
[4,2,3,5,6,8,7,1]=>1000011=>[1,5,1,1]
[4,2,3,6,5,1,7,8]=>1001100=>[1,3,1,3]
[4,2,3,6,5,1,8,7]=>1001101=>[1,3,1,2,1]
[4,2,3,6,5,8,7,1]=>1001011=>[1,3,2,1,1]
[4,2,3,7,5,6,1,8]=>1001010=>[1,3,2,2]
[4,2,3,8,5,6,7,1]=>1001001=>[1,3,3,1]
[4,2,3,7,6,5,8,1]=>1001101=>[1,3,1,2,1]
[4,2,3,8,6,7,5,1]=>1001011=>[1,3,2,1,1]
[4,2,3,8,7,6,5,1]=>1001111=>[1,3,1,1,1,1]
[5,2,3,4,1,8,7,6]=>1001011=>[1,3,2,1,1]
[5,2,3,4,8,7,6,1]=>1000111=>[1,4,1,1,1]
[8,2,3,4,7,6,5,1]=>1000111=>[1,4,1,1,1]
[6,2,3,5,4,1,7,8]=>1001100=>[1,3,1,3]
[6,2,3,5,4,1,8,7]=>1001101=>[1,3,1,2,1]
[6,2,3,5,4,7,1,8]=>1001010=>[1,3,2,2]
[8,2,3,5,4,7,6,1]=>1001011=>[1,3,2,1,1]
[7,2,3,5,6,4,1,8]=>1000110=>[1,4,1,2]
[8,2,3,5,6,7,4,1]=>1000011=>[1,5,1,1]
[7,2,3,6,5,4,1,8]=>1001110=>[1,3,1,1,2]
[8,2,3,7,5,6,4,1]=>1001011=>[1,3,2,1,1]
[8,2,3,7,6,5,4,1]=>1001111=>[1,3,1,1,1,1]
[5,2,4,3,1,6,7,8]=>1011000=>[1,2,1,4]
[5,2,4,3,1,6,8,7]=>1011001=>[1,2,1,3,1]
[5,2,4,3,1,7,6,8]=>1011010=>[1,2,1,2,2]
[5,2,4,3,1,8,7,6]=>1011011=>[1,2,1,2,1,1]
[5,2,4,3,6,1,7,8]=>1010100=>[1,2,2,3]
[5,2,4,3,6,1,8,7]=>1010101=>[1,2,2,2,1]
[5,2,4,3,7,6,1,8]=>1010110=>[1,2,2,1,2]
[5,2,4,3,7,6,8,1]=>1010101=>[1,2,2,2,1]
[6,2,4,3,5,1,8,7]=>1010101=>[1,2,2,2,1]
[7,2,4,3,6,5,1,8]=>1010110=>[1,2,2,1,2]
[7,2,4,3,6,5,8,1]=>1010101=>[1,2,2,2,1]
[8,2,4,3,6,5,7,1]=>1010101=>[1,2,2,2,1]
[8,2,4,3,7,6,5,1]=>1010111=>[1,2,2,1,1,1]
[6,2,4,5,3,1,7,8]=>1001100=>[1,3,1,3]
[6,2,4,5,3,1,8,7]=>1001101=>[1,3,1,2,1]
[6,2,4,5,3,8,7,1]=>1001011=>[1,3,2,1,1]
[7,2,4,5,3,6,1,8]=>1001010=>[1,3,2,2]
[7,2,4,5,3,6,8,1]=>1001001=>[1,3,3,1]
[8,2,4,7,5,6,3,1]=>1001011=>[1,3,2,1,1]
[8,2,4,7,6,5,3,1]=>1001111=>[1,3,1,1,1,1]
[6,2,5,4,3,1,8,7]=>1011101=>[1,2,1,1,2,1]
[7,2,5,4,3,6,1,8]=>1011010=>[1,2,1,2,2]
[8,2,5,4,3,7,6,1]=>1011011=>[1,2,1,2,1,1]
[8,2,5,4,7,6,3,1]=>1010111=>[1,2,2,1,1,1]
[8,2,6,4,5,3,7,1]=>1010101=>[1,2,2,2,1]
[8,2,6,4,5,7,3,1]=>1010011=>[1,2,3,1,1]
[8,2,7,4,5,6,3,1]=>1010011=>[1,2,3,1,1]
[8,2,7,4,6,5,3,1]=>1010111=>[1,2,2,1,1,1]
[7,2,6,5,4,3,1,8]=>1011110=>[1,2,1,1,1,2]
[8,2,6,5,4,3,7,1]=>1011101=>[1,2,1,1,2,1]
[8,2,7,5,4,6,3,1]=>1011011=>[1,2,1,2,1,1]
[8,2,7,5,6,4,3,1]=>1010111=>[1,2,2,1,1,1]
[8,2,7,6,5,4,3,1]=>1011111=>[1,2,1,1,1,1,1]
[4,3,2,1,8,6,7,5]=>1110101=>[1,1,1,2,2,1]
[4,3,2,7,5,6,8,1]=>1101001=>[1,1,2,3,1]
[4,3,2,8,5,6,7,1]=>1101001=>[1,1,2,3,1]
[4,3,2,8,6,7,5,1]=>1101011=>[1,1,2,2,1,1]
[5,3,2,4,1,6,8,7]=>1101001=>[1,1,2,3,1]
[5,3,2,4,1,8,7,6]=>1101011=>[1,1,2,2,1,1]
[5,3,2,4,6,1,8,7]=>1100101=>[1,1,3,2,1]
[6,3,2,5,4,1,7,8]=>1101100=>[1,1,2,1,3]
[6,3,2,5,4,1,8,7]=>1101101=>[1,1,2,1,2,1]
[6,3,2,5,4,7,1,8]=>1101010=>[1,1,2,2,2]
[6,3,2,5,4,7,8,1]=>1101001=>[1,1,2,3,1]
[8,3,2,5,4,7,6,1]=>1101011=>[1,1,2,2,1,1]
[8,3,2,5,6,4,7,1]=>1100101=>[1,1,3,2,1]
[8,3,2,5,7,6,4,1]=>1100111=>[1,1,3,1,1,1]
[8,3,2,7,5,6,4,1]=>1101011=>[1,1,2,2,1,1]
[8,3,2,7,6,5,4,1]=>1101111=>[1,1,2,1,1,1,1]
[5,3,4,2,1,6,8,7]=>1011001=>[1,2,1,3,1]
[5,3,4,2,1,7,8,6]=>1011001=>[1,2,1,3,1]
[5,3,4,2,1,8,7,6]=>1011011=>[1,2,1,2,1,1]
[5,3,4,2,6,1,8,7]=>1010101=>[1,2,2,2,1]
[5,3,4,2,7,6,1,8]=>1010110=>[1,2,2,1,2]
[5,3,4,2,7,6,8,1]=>1010101=>[1,2,2,2,1]
[5,3,4,2,8,6,7,1]=>1010101=>[1,2,2,2,1]
[6,3,4,2,5,1,8,7]=>1010101=>[1,2,2,2,1]
[7,3,4,2,6,5,1,8]=>1010110=>[1,2,2,1,2]
[7,3,4,2,6,5,8,1]=>1010101=>[1,2,2,2,1]
[7,3,4,6,5,2,1,8]=>1001110=>[1,3,1,1,2]
[6,3,5,4,2,1,8,7]=>1011101=>[1,2,1,1,2,1]
[6,3,5,4,2,7,1,8]=>1011010=>[1,2,1,2,2]
[6,3,5,4,2,7,8,1]=>1011001=>[1,2,1,3,1]
[8,3,5,4,2,6,7,1]=>1011001=>[1,2,1,3,1]
[7,3,5,4,6,2,1,8]=>1010110=>[1,2,2,1,2]
[8,3,5,4,7,6,2,1]=>1010111=>[1,2,2,1,1,1]
[7,3,6,4,5,2,1,8]=>1010110=>[1,2,2,1,2]
[7,3,6,4,5,2,8,1]=>1010101=>[1,2,2,2,1]
[8,3,6,4,5,2,7,1]=>1010101=>[1,2,2,2,1]
[8,3,7,4,5,6,2,1]=>1010011=>[1,2,3,1,1]
[7,3,6,5,4,2,1,8]=>1011110=>[1,2,1,1,1,2]
[8,3,7,5,6,4,2,1]=>1010111=>[1,2,2,1,1,1]
[5,4,3,2,8,6,7,1]=>1110101=>[1,1,1,2,2,1]
[7,4,3,2,6,5,1,8]=>1110110=>[1,1,1,2,1,2]
[7,4,3,2,6,5,8,1]=>1110101=>[1,1,1,2,2,1]
[8,4,3,2,6,7,5,1]=>1110011=>[1,1,1,3,1,1]
[8,4,3,2,7,6,5,1]=>1110111=>[1,1,1,2,1,1,1]
[6,4,3,5,2,1,8,7]=>1101101=>[1,1,2,1,2,1]
[8,4,3,5,7,6,2,1]=>1100111=>[1,1,3,1,1,1]
[7,4,3,6,5,2,1,8]=>1101110=>[1,1,2,1,1,2]
[7,4,3,6,5,2,8,1]=>1101101=>[1,1,2,1,2,1]
[8,4,3,7,5,6,2,1]=>1101011=>[1,1,2,2,1,1]
[6,5,3,4,2,1,8,7]=>1101101=>[1,1,2,1,2,1]
[8,5,3,4,2,7,6,1]=>1101011=>[1,1,2,2,1,1]
[8,5,3,4,7,6,2,1]=>1100111=>[1,1,3,1,1,1]
[8,7,3,4,6,5,2,1]=>1100111=>[1,1,3,1,1,1]
[7,6,3,5,4,2,1,8]=>1101110=>[1,1,2,1,1,2]
[8,6,3,5,4,2,7,1]=>1101101=>[1,1,2,1,2,1]
[8,7,3,5,4,6,2,1]=>1101011=>[1,1,2,2,1,1]
[8,7,3,5,6,4,2,1]=>1100111=>[1,1,3,1,1,1]
[8,7,3,6,5,4,2,1]=>1101111=>[1,1,2,1,1,1,1]
[8,5,4,3,2,7,6,1]=>1111011=>[1,1,1,1,2,1,1]
[8,5,4,3,7,6,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,7,4,3,6,5,2,1]=>1110111=>[1,1,1,2,1,1,1]
[2,4,1,3,6,5,8,7]=>0100101=>[2,3,2,1]
[2,1,4,6,3,5,8,7]=>1001001=>[1,3,3,1]
[2,4,1,6,3,5,8,7]=>0101001=>[2,2,3,1]
[2,4,6,1,3,5,8,7]=>0010001=>[3,4,1]
[2,1,4,3,6,8,5,7]=>1010010=>[1,2,3,2]
[2,4,1,3,6,8,5,7]=>0100010=>[2,4,2]
[2,1,4,6,3,8,5,7]=>1001010=>[1,3,2,2]
[2,4,1,6,3,8,5,7]=>0101010=>[2,2,2,2]
[2,4,6,1,3,8,5,7]=>0010010=>[3,3,2]
[2,1,4,6,8,3,5,7]=>1000100=>[1,4,3]
[2,4,1,6,8,3,5,7]=>0100100=>[2,3,3]
[2,4,6,1,8,3,5,7]=>0010100=>[3,2,3]
[2,4,6,8,1,3,5,7]=>0001000=>[4,4]
[2,4,1,3,6,5,7,8]=>0100100=>[2,3,3]
[2,4,1,6,3,7,5,8]=>0101010=>[2,2,2,2]
[2,4,6,1,3,7,5,8]=>0010010=>[3,3,2]
[2,4,6,7,1,3,5,8]=>0001000=>[4,4]
[2,4,1,3,6,7,8,5]=>0100001=>[2,5,1]
[2,1,4,6,3,7,8,5]=>1001001=>[1,3,3,1]
[2,4,1,6,3,7,8,5]=>0101001=>[2,2,3,1]
[2,4,6,1,3,7,8,5]=>0010001=>[3,4,1]
[2,4,1,6,7,3,8,5]=>0100101=>[2,3,2,1]
[2,4,6,1,7,3,8,5]=>0010101=>[3,2,2,1]
[2,4,6,7,1,3,8,5]=>0001001=>[4,3,1]
[2,4,1,6,7,8,3,5]=>0100010=>[2,4,2]
[2,4,6,1,7,8,3,5]=>0010010=>[3,3,2]
[2,4,6,7,1,8,3,5]=>0001010=>[4,2,2]
[2,4,6,7,8,1,3,5]=>0000100=>[5,3]
[2,1,4,3,7,5,8,6]=>1010101=>[1,2,2,2,1]
[2,4,1,3,7,5,8,6]=>0100101=>[2,3,2,1]
[2,4,1,7,3,5,8,6]=>0101001=>[2,2,3,1]
[2,4,7,1,3,5,8,6]=>0010001=>[3,4,1]
[2,1,4,3,7,8,5,6]=>1010010=>[1,2,3,2]
[2,4,1,3,7,8,5,6]=>0100010=>[2,4,2]
[2,4,1,7,3,8,5,6]=>0101010=>[2,2,2,2]
[2,4,1,7,8,3,5,6]=>0100100=>[2,3,3]
[2,4,7,1,8,3,5,6]=>0010100=>[3,2,3]
[2,4,1,5,3,7,6,8]=>0101010=>[2,2,2,2]
[2,4,5,1,7,3,6,8]=>0010100=>[3,2,3]
[2,4,1,3,5,7,8,6]=>0100001=>[2,5,1]
[2,4,1,5,3,7,8,6]=>0101001=>[2,2,3,1]
[2,4,5,1,3,7,8,6]=>0010001=>[3,4,1]
[2,1,4,5,7,3,8,6]=>1000101=>[1,4,2,1]
[2,4,1,5,7,3,8,6]=>0100101=>[2,3,2,1]
[2,4,5,1,7,3,8,6]=>0010101=>[3,2,2,1]
[2,4,5,7,1,3,8,6]=>0001001=>[4,3,1]
[2,4,5,7,8,1,3,6]=>0000100=>[5,3]
[2,1,4,3,8,5,6,7]=>1010100=>[1,2,2,3]
[2,4,1,3,8,5,6,7]=>0100100=>[2,3,3]
[2,1,4,8,3,5,6,7]=>1001000=>[1,3,4]
[2,4,1,8,3,5,6,7]=>0101000=>[2,2,4]
[2,4,1,5,3,8,6,7]=>0101010=>[2,2,2,2]
[2,1,4,5,8,3,6,7]=>1000100=>[1,4,3]
[2,4,1,5,8,3,6,7]=>0100100=>[2,3,3]
[2,4,5,8,1,3,6,7]=>0001000=>[4,4]
[2,4,1,5,6,3,8,7]=>0100101=>[2,3,2,1]
[2,1,4,5,6,8,3,7]=>1000010=>[1,5,2]
[2,4,5,1,6,8,3,7]=>0010010=>[3,3,2]
[2,4,5,6,1,8,3,7]=>0001010=>[4,2,2]
[2,4,5,6,8,1,3,7]=>0000100=>[5,3]
[2,4,1,3,5,6,7,8]=>0100000=>[2,6]
[2,4,1,5,6,3,7,8]=>0100100=>[2,3,3]
[2,4,5,1,6,3,7,8]=>0010100=>[3,2,3]
[2,4,5,6,1,3,7,8]=>0001000=>[4,4]
[2,4,5,6,7,1,3,8]=>0000100=>[5,3]
[2,4,1,5,6,7,8,3]=>0100001=>[2,5,1]
[2,4,5,6,7,1,8,3]=>0000101=>[5,2,1]
[2,1,5,3,6,4,8,7]=>1010101=>[1,2,2,2,1]
[2,1,5,6,3,4,8,7]=>1001001=>[1,3,3,1]
[2,1,5,3,6,8,4,7]=>1010010=>[1,2,3,2]
[2,5,1,3,6,8,4,7]=>0100010=>[2,4,2]
[2,5,1,6,8,3,4,7]=>0100100=>[2,3,3]
[2,1,5,6,3,4,7,8]=>1001000=>[1,3,4]
[2,5,1,6,3,4,7,8]=>0101000=>[2,2,4]
[2,1,5,3,6,7,4,8]=>1010010=>[1,2,3,2]
[2,1,5,6,3,7,4,8]=>1001010=>[1,3,2,2]
[2,5,1,6,3,7,4,8]=>0101010=>[2,2,2,2]
[2,5,6,1,3,7,4,8]=>0010010=>[3,3,2]
[2,1,5,6,7,3,4,8]=>1000100=>[1,4,3]
[2,5,1,6,7,3,4,8]=>0100100=>[2,3,3]
[2,1,5,3,6,7,8,4]=>1010001=>[1,2,4,1]
[2,5,1,3,6,7,8,4]=>0100001=>[2,5,1]
[2,1,5,6,3,7,8,4]=>1001001=>[1,3,3,1]
[2,5,1,6,3,7,8,4]=>0101001=>[2,2,3,1]
[2,5,6,1,3,7,8,4]=>0010001=>[3,4,1]
[2,1,5,6,7,3,8,4]=>1000101=>[1,4,2,1]
[2,5,1,6,7,3,8,4]=>0100101=>[2,3,2,1]
[2,1,5,6,7,8,3,4]=>1000010=>[1,5,2]
[2,5,1,6,7,8,3,4]=>0100010=>[2,4,2]
[2,5,6,1,7,8,3,4]=>0010010=>[3,3,2]
[2,5,6,7,8,1,3,4]=>0000100=>[5,3]
[2,1,5,3,7,4,8,6]=>1010101=>[1,2,2,2,1]
[2,5,1,3,7,4,8,6]=>0100101=>[2,3,2,1]
[2,1,5,7,3,4,8,6]=>1001001=>[1,3,3,1]
[2,5,1,7,3,4,8,6]=>0101001=>[2,2,3,1]
[2,5,7,1,3,4,8,6]=>0010001=>[3,4,1]
[2,1,5,3,7,8,4,6]=>1010010=>[1,2,3,2]
[2,5,1,3,7,8,4,6]=>0100010=>[2,4,2]
[2,1,5,7,3,8,4,6]=>1001010=>[1,3,2,2]
[2,1,5,7,8,3,4,6]=>1000100=>[1,4,3]
[2,5,1,7,8,3,4,6]=>0100100=>[2,3,3]
[2,5,1,3,7,4,6,8]=>0100100=>[2,3,3]
[2,1,5,7,3,4,6,8]=>1001000=>[1,3,4]
[2,3,5,7,1,4,6,8]=>0001000=>[4,4]
[2,3,5,1,7,4,8,6]=>0010101=>[3,2,2,1]
[2,3,5,7,1,4,8,6]=>0001001=>[4,3,1]
[2,3,5,7,1,8,4,6]=>0001010=>[4,2,2]
[2,1,5,3,8,4,6,7]=>1010100=>[1,2,2,3]
[2,1,5,8,3,4,6,7]=>1001000=>[1,3,4]
[2,5,1,8,3,4,6,7]=>0101000=>[2,2,4]
[2,3,5,1,4,8,6,7]=>0010010=>[3,3,2]
[2,3,5,8,1,4,6,7]=>0001000=>[4,4]
[2,1,5,3,4,6,8,7]=>1010001=>[1,2,4,1]
[2,3,5,1,6,4,8,7]=>0010101=>[3,2,2,1]
[2,3,5,6,1,4,8,7]=>0001001=>[4,3,1]
[2,3,5,6,1,8,4,7]=>0001010=>[4,2,2]
[2,3,5,6,8,1,4,7]=>0000100=>[5,3]
[2,3,5,6,1,4,7,8]=>0001000=>[4,4]
[2,3,5,6,1,7,4,8]=>0001010=>[4,2,2]
[2,3,5,1,6,7,8,4]=>0010001=>[3,4,1]
[2,3,5,6,1,7,8,4]=>0001001=>[4,3,1]
[2,3,5,6,7,1,8,4]=>0000101=>[5,2,1]
[2,3,5,6,7,8,1,4]=>0000010=>[6,2]
[2,1,6,3,7,4,8,5]=>1010101=>[1,2,2,2,1]
[2,6,1,3,7,4,8,5]=>0100101=>[2,3,2,1]
[2,6,7,1,3,4,8,5]=>0010001=>[3,4,1]
[2,1,6,3,7,8,4,5]=>1010010=>[1,2,3,2]
[2,1,6,7,3,8,4,5]=>1001010=>[1,3,2,2]
[2,6,1,7,3,8,4,5]=>0101010=>[2,2,2,2]
[2,1,6,7,8,3,4,5]=>1000100=>[1,4,3]
[2,6,1,7,8,3,4,5]=>0100100=>[2,3,3]
[2,6,7,8,1,3,4,5]=>0001000=>[4,4]
[2,6,1,7,3,4,5,8]=>0101000=>[2,2,4]
[2,6,7,1,3,4,5,8]=>0010000=>[3,5]
[2,3,1,6,4,7,5,8]=>0101010=>[2,2,2,2]
[2,3,6,1,4,7,5,8]=>0010010=>[3,3,2]
[2,3,6,7,1,4,5,8]=>0001000=>[4,4]
[2,1,6,3,4,7,8,5]=>1010001=>[1,2,4,1]
[2,3,6,1,4,7,8,5]=>0010001=>[3,4,1]
[2,1,3,6,7,4,8,5]=>1000101=>[1,4,2,1]
[2,3,6,7,1,4,8,5]=>0001001=>[4,3,1]
[2,3,1,6,7,8,4,5]=>0100010=>[2,4,2]
[2,3,6,1,7,8,4,5]=>0010010=>[3,3,2]
[2,3,6,7,1,8,4,5]=>0001010=>[4,2,2]
[2,3,6,7,8,1,4,5]=>0000100=>[5,3]
[2,6,1,8,3,4,5,7]=>0101000=>[2,2,4]
[2,6,8,1,3,4,5,7]=>0010000=>[3,5]
[2,1,6,3,4,8,5,7]=>1010010=>[1,2,3,2]
[2,3,1,6,4,8,5,7]=>0101010=>[2,2,2,2]
[2,3,6,1,4,8,5,7]=>0010010=>[3,3,2]
[2,3,1,6,8,4,5,7]=>0100100=>[2,3,3]
[2,3,6,1,8,4,5,7]=>0010100=>[3,2,3]
[2,3,6,8,1,4,5,7]=>0001000=>[4,4]
[2,1,6,3,4,5,8,7]=>1010001=>[1,2,4,1]
[2,6,1,3,4,5,8,7]=>0100001=>[2,5,1]
[2,3,6,1,4,5,8,7]=>0010001=>[3,4,1]
[2,3,4,1,6,8,5,7]=>0010010=>[3,3,2]
[2,3,4,6,1,8,5,7]=>0001010=>[4,2,2]
[2,3,6,1,4,5,7,8]=>0010000=>[3,5]
[2,3,4,6,7,8,1,5]=>0000010=>[6,2]
[2,7,1,3,8,4,5,6]=>0100100=>[2,3,3]
[2,1,7,8,3,4,5,6]=>1001000=>[1,3,4]
[2,7,1,8,3,4,5,6]=>0101000=>[2,2,4]
[2,7,8,1,3,4,5,6]=>0010000=>[3,5]
[2,1,7,3,4,8,5,6]=>1010010=>[1,2,3,2]
[2,1,3,7,4,8,5,6]=>1001010=>[1,3,2,2]
[2,3,1,7,4,8,5,6]=>0101010=>[2,2,2,2]
[2,3,1,7,8,4,5,6]=>0100100=>[2,3,3]
[2,3,7,8,1,4,5,6]=>0001000=>[4,4]
[2,1,7,3,4,5,8,6]=>1010001=>[1,2,4,1]
[2,3,1,7,4,5,8,6]=>0101001=>[2,2,3,1]
[2,3,7,1,4,5,8,6]=>0010001=>[3,4,1]
[2,3,4,1,7,5,8,6]=>0010101=>[3,2,2,1]
[2,3,4,7,1,5,8,6]=>0001001=>[4,3,1]
[2,1,3,4,7,8,5,6]=>1000010=>[1,5,2]
[2,3,1,4,7,8,5,6]=>0100010=>[2,4,2]
[2,3,4,1,7,8,5,6]=>0010010=>[3,3,2]
[2,3,4,7,8,1,5,6]=>0000100=>[5,3]
[2,3,4,1,7,5,6,8]=>0010100=>[3,2,3]
[2,3,4,7,1,5,6,8]=>0001000=>[4,4]
[2,1,8,3,4,5,6,7]=>1010000=>[1,2,5]
[2,8,1,3,4,5,6,7]=>0100000=>[2,6]
[2,3,8,1,4,5,6,7]=>0010000=>[3,5]
[2,1,3,4,8,5,6,7]=>1000100=>[1,4,3]
[2,3,1,4,8,5,6,7]=>0100100=>[2,3,3]
[2,3,4,1,8,5,6,7]=>0010100=>[3,2,3]
[2,3,4,8,1,5,6,7]=>0001000=>[4,4]
[2,3,4,1,5,8,6,7]=>0010010=>[3,3,2]
[2,3,4,5,8,1,6,7]=>0000100=>[5,3]
[3,1,4,2,6,5,8,7]=>1010101=>[1,2,2,2,1]
[3,4,1,2,6,5,8,7]=>0100101=>[2,3,2,1]
[3,1,4,2,6,8,5,7]=>1010010=>[1,2,3,2]
[3,4,1,2,6,8,5,7]=>0100010=>[2,4,2]
[3,1,4,6,2,8,5,7]=>1001010=>[1,3,2,2]
[3,1,4,6,8,2,5,7]=>1000100=>[1,4,3]
[3,4,1,6,8,2,5,7]=>0100100=>[2,3,3]
[3,1,4,2,6,5,7,8]=>1010100=>[1,2,2,3]
[3,4,1,2,6,5,7,8]=>0100100=>[2,3,3]
[3,1,4,2,6,7,5,8]=>1010010=>[1,2,3,2]
[3,4,1,2,6,7,5,8]=>0100010=>[2,4,2]
[3,4,1,6,2,7,5,8]=>0101010=>[2,2,2,2]
[3,4,6,1,2,7,5,8]=>0010010=>[3,3,2]
[3,1,4,2,6,7,8,5]=>1010001=>[1,2,4,1]
[3,4,1,2,6,7,8,5]=>0100001=>[2,5,1]
[3,4,6,1,2,7,8,5]=>0010001=>[3,4,1]
[3,4,6,1,7,2,8,5]=>0010101=>[3,2,2,1]
[3,1,4,6,7,8,2,5]=>1000010=>[1,5,2]
[3,4,6,1,7,8,2,5]=>0010010=>[3,3,2]
[3,4,6,7,1,8,2,5]=>0001010=>[4,2,2]
[3,4,6,7,8,1,2,5]=>0000100=>[5,3]
[3,1,4,2,7,5,8,6]=>1010101=>[1,2,2,2,1]
[3,4,1,2,7,5,8,6]=>0100101=>[2,3,2,1]
[3,4,7,1,2,5,8,6]=>0010001=>[3,4,1]
[3,1,4,2,7,8,5,6]=>1010010=>[1,2,3,2]
[3,4,1,2,7,8,5,6]=>0100010=>[2,4,2]
[3,4,7,1,8,2,5,6]=>0010100=>[3,2,3]
[3,1,4,2,7,5,6,8]=>1010100=>[1,2,2,3]
[3,4,1,2,7,5,6,8]=>0100100=>[2,3,3]
[3,4,1,2,5,7,6,8]=>0100010=>[2,4,2]
[3,1,4,5,2,7,6,8]=>1001010=>[1,3,2,2]
[3,4,1,5,2,7,6,8]=>0101010=>[2,2,2,2]
[3,4,1,5,7,2,6,8]=>0100100=>[2,3,3]
[3,1,4,2,5,7,8,6]=>1010001=>[1,2,4,1]
[3,4,1,2,5,7,8,6]=>0100001=>[2,5,1]
[3,1,4,5,2,7,8,6]=>1001001=>[1,3,3,1]
[3,4,1,5,7,2,8,6]=>0100101=>[2,3,2,1]
[3,4,5,7,1,2,8,6]=>0001001=>[4,3,1]
[3,1,4,5,7,8,2,6]=>1000010=>[1,5,2]
[3,4,1,5,7,8,2,6]=>0100010=>[2,4,2]
[3,4,5,1,7,8,2,6]=>0010010=>[3,3,2]
[3,1,4,2,8,5,6,7]=>1010100=>[1,2,2,3]
[3,4,1,2,8,5,6,7]=>0100100=>[2,3,3]
[3,1,4,8,2,5,6,7]=>1001000=>[1,3,4]
[3,4,1,8,2,5,6,7]=>0101000=>[2,2,4]
[3,4,8,1,2,5,6,7]=>0010000=>[3,5]
[3,1,4,2,5,8,6,7]=>1010010=>[1,2,3,2]
[3,4,1,2,5,8,6,7]=>0100010=>[2,4,2]
[3,4,1,5,2,8,6,7]=>0101010=>[2,2,2,2]
[3,4,5,1,2,8,6,7]=>0010010=>[3,3,2]
[3,4,1,5,8,2,6,7]=>0100100=>[2,3,3]
[3,4,5,8,1,2,6,7]=>0001000=>[4,4]
[3,4,1,2,5,6,8,7]=>0100001=>[2,5,1]
[3,1,4,5,6,2,8,7]=>1000101=>[1,4,2,1]
[3,4,5,1,6,2,8,7]=>0010101=>[3,2,2,1]
[3,4,5,6,1,2,8,7]=>0001001=>[4,3,1]
[3,4,1,5,6,8,2,7]=>0100010=>[2,4,2]
[3,4,5,6,1,8,2,7]=>0001010=>[4,2,2]
[3,4,5,6,8,1,2,7]=>0000100=>[5,3]
[3,1,4,2,5,6,7,8]=>1010000=>[1,2,5]
[3,4,1,5,6,2,7,8]=>0100100=>[2,3,3]
[3,4,5,1,6,2,7,8]=>0010100=>[3,2,3]
[3,4,1,5,6,7,2,8]=>0100010=>[2,4,2]
[3,4,5,6,1,7,2,8]=>0001010=>[4,2,2]
[3,1,4,5,6,7,8,2]=>1000001=>[1,6,1]
[3,4,5,1,6,7,8,2]=>0010001=>[3,4,1]
[3,4,5,6,1,7,8,2]=>0001001=>[4,3,1]
[3,1,5,2,6,4,8,7]=>1010101=>[1,2,2,2,1]
[3,1,5,6,2,4,8,7]=>1001001=>[1,3,3,1]
[3,5,1,6,2,4,8,7]=>0101001=>[2,2,3,1]
[3,5,6,1,2,4,8,7]=>0010001=>[3,4,1]
[3,5,1,2,6,8,4,7]=>0100010=>[2,4,2]
[3,1,5,6,2,8,4,7]=>1001010=>[1,3,2,2]
[3,5,6,1,2,8,4,7]=>0010010=>[3,3,2]
[3,1,5,6,8,2,4,7]=>1000100=>[1,4,3]
[3,5,6,1,8,2,4,7]=>0010100=>[3,2,3]
[3,1,5,6,2,4,7,8]=>1001000=>[1,3,4]
[3,5,1,6,2,4,7,8]=>0101000=>[2,2,4]
[3,5,6,1,2,4,7,8]=>0010000=>[3,5]
[3,5,1,6,2,7,4,8]=>0101010=>[2,2,2,2]
[3,5,6,1,2,7,4,8]=>0010010=>[3,3,2]
[3,5,6,1,7,2,4,8]=>0010100=>[3,2,3]
[3,1,5,2,6,7,8,4]=>1010001=>[1,2,4,1]
[3,5,1,2,6,7,8,4]=>0100001=>[2,5,1]
[3,1,5,6,2,7,8,4]=>1001001=>[1,3,3,1]
[3,5,1,6,2,7,8,4]=>0101001=>[2,2,3,1]
[3,5,6,1,2,7,8,4]=>0010001=>[3,4,1]
[3,1,5,6,7,2,8,4]=>1000101=>[1,4,2,1]
[3,5,1,6,7,2,8,4]=>0100101=>[2,3,2,1]
[3,5,6,1,7,2,8,4]=>0010101=>[3,2,2,1]
[3,1,5,6,7,8,2,4]=>1000010=>[1,5,2]
[3,5,1,6,7,8,2,4]=>0100010=>[2,4,2]
[3,5,6,1,7,8,2,4]=>0010010=>[3,3,2]
[3,5,6,7,8,1,2,4]=>0000100=>[5,3]
[3,1,5,2,7,4,8,6]=>1010101=>[1,2,2,2,1]
[3,5,1,2,7,4,8,6]=>0100101=>[2,3,2,1]
[3,1,5,7,2,4,8,6]=>1001001=>[1,3,3,1]
[3,5,1,7,2,4,8,6]=>0101001=>[2,2,3,1]
[3,5,7,1,2,4,8,6]=>0010001=>[3,4,1]
[3,1,5,2,7,8,4,6]=>1010010=>[1,2,3,2]
[3,5,1,2,7,8,4,6]=>0100010=>[2,4,2]
[3,1,5,7,2,8,4,6]=>1001010=>[1,3,2,2]
[3,5,1,7,2,8,4,6]=>0101010=>[2,2,2,2]
[3,1,5,7,8,2,4,6]=>1000100=>[1,4,3]
[3,5,1,7,8,2,4,6]=>0100100=>[2,3,3]
[3,5,7,8,1,2,4,6]=>0001000=>[4,4]
[3,1,5,2,7,4,6,8]=>1010100=>[1,2,2,3]
[3,5,1,2,7,4,6,8]=>0100100=>[2,3,3]
[3,1,5,7,2,4,6,8]=>1001000=>[1,3,4]
[3,5,1,7,2,4,6,8]=>0101000=>[2,2,4]
[3,5,7,1,2,4,6,8]=>0010000=>[3,5]
[3,1,5,2,4,7,6,8]=>1010010=>[1,2,3,2]
[3,5,1,2,4,7,6,8]=>0100010=>[2,4,2]
[3,1,2,5,4,7,6,8]=>1001010=>[1,3,2,2]
[1,3,5,2,4,7,6,8]=>0010010=>[3,3,2]
[3,1,2,5,7,4,6,8]=>1000100=>[1,4,3]
[1,3,2,5,7,4,6,8]=>0100100=>[2,3,3]
[1,3,5,2,7,4,6,8]=>0010100=>[3,2,3]
[1,3,5,7,2,4,6,8]=>0001000=>[4,4]
[3,5,1,2,4,7,8,6]=>0100001=>[2,5,1]
[1,3,5,2,4,7,8,6]=>0010001=>[3,4,1]
[3,1,2,5,7,4,8,6]=>1000101=>[1,4,2,1]
[1,3,2,5,7,4,8,6]=>0100101=>[2,3,2,1]
[1,3,5,2,7,4,8,6]=>0010101=>[3,2,2,1]
[1,3,5,7,2,4,8,6]=>0001001=>[4,3,1]
[1,3,2,5,7,8,4,6]=>0100010=>[2,4,2]
[1,3,5,2,7,8,4,6]=>0010010=>[3,3,2]
[1,3,5,7,2,8,4,6]=>0001010=>[4,2,2]
[1,3,5,7,8,2,4,6]=>0000100=>[5,3]
[3,1,5,2,8,4,6,7]=>1010100=>[1,2,2,3]
[3,5,1,2,8,4,6,7]=>0100100=>[2,3,3]
[3,1,5,8,2,4,6,7]=>1001000=>[1,3,4]
[3,5,1,8,2,4,6,7]=>0101000=>[2,2,4]
[3,1,5,2,4,8,6,7]=>1010010=>[1,2,3,2]
[3,5,1,2,4,8,6,7]=>0100010=>[2,4,2]
[1,3,2,5,4,8,6,7]=>0101010=>[2,2,2,2]
[1,3,5,2,4,8,6,7]=>0010010=>[3,3,2]
[3,1,2,5,8,4,6,7]=>1000100=>[1,4,3]
[1,3,2,5,8,4,6,7]=>0100100=>[2,3,3]
[1,3,5,2,8,4,6,7]=>0010100=>[3,2,3]
[1,3,5,8,2,4,6,7]=>0001000=>[4,4]
[3,5,1,2,4,6,8,7]=>0100001=>[2,5,1]
[3,1,2,5,4,6,8,7]=>1001001=>[1,3,3,1]
[1,3,5,2,4,6,8,7]=>0010001=>[3,4,1]
[1,3,5,6,2,4,8,7]=>0001001=>[4,3,1]
[3,1,2,5,6,8,4,7]=>1000010=>[1,5,2]
[1,3,5,2,6,8,4,7]=>0010010=>[3,3,2]
[3,5,1,2,4,6,7,8]=>0100000=>[2,6]
[1,3,5,2,4,6,7,8]=>0010000=>[3,5]
[1,3,5,2,6,4,7,8]=>0010100=>[3,2,3]
[1,3,5,6,2,4,7,8]=>0001000=>[4,4]
[3,1,2,5,6,7,4,8]=>1000010=>[1,5,2]
[1,3,5,2,6,7,4,8]=>0010010=>[3,3,2]
[1,3,5,6,2,7,4,8]=>0001010=>[4,2,2]
[1,3,5,6,7,2,4,8]=>0000100=>[5,3]
[3,1,2,5,6,7,8,4]=>1000001=>[1,6,1]
[1,3,5,6,2,7,8,4]=>0001001=>[4,3,1]
[1,3,5,6,7,8,2,4]=>0000010=>[6,2]
[3,1,6,2,7,4,8,5]=>1010101=>[1,2,2,2,1]
[3,6,1,2,7,4,8,5]=>0100101=>[2,3,2,1]
[3,6,1,7,2,4,8,5]=>0101001=>[2,2,3,1]
[3,6,7,1,2,4,8,5]=>0010001=>[3,4,1]
[3,1,6,7,2,8,4,5]=>1001010=>[1,3,2,2]
[3,6,1,7,2,8,4,5]=>0101010=>[2,2,2,2]
[3,6,7,1,2,8,4,5]=>0010010=>[3,3,2]
[3,6,1,7,8,2,4,5]=>0100100=>[2,3,3]
[3,6,7,8,1,2,4,5]=>0001000=>[4,4]
[3,1,6,7,2,4,5,8]=>1001000=>[1,3,4]
[3,6,7,1,2,4,5,8]=>0010000=>[3,5]
[3,1,6,2,4,7,5,8]=>1010010=>[1,2,3,2]
[3,6,1,2,4,7,5,8]=>0100010=>[2,4,2]
[3,1,2,6,4,7,5,8]=>1001010=>[1,3,2,2]
[1,3,2,6,4,7,5,8]=>0101010=>[2,2,2,2]
[1,3,6,2,4,7,5,8]=>0010010=>[3,3,2]
[1,3,2,6,7,4,5,8]=>0100100=>[2,3,3]
[3,1,6,2,4,7,8,5]=>1010001=>[1,2,4,1]
[3,6,1,2,4,7,8,5]=>0100001=>[2,5,1]
[3,1,2,6,4,7,8,5]=>1001001=>[1,3,3,1]
[1,3,2,6,4,7,8,5]=>0101001=>[2,2,3,1]
[1,3,6,2,4,7,8,5]=>0010001=>[3,4,1]
[3,1,2,6,7,4,8,5]=>1000101=>[1,4,2,1]
[1,3,6,2,7,4,8,5]=>0010101=>[3,2,2,1]
[1,3,6,2,7,8,4,5]=>0010010=>[3,3,2]
[3,1,6,2,8,4,5,7]=>1010100=>[1,2,2,3]
[3,1,6,8,2,4,5,7]=>1001000=>[1,3,4]
[3,6,8,1,2,4,5,7]=>0010000=>[3,5]
[3,1,6,2,4,8,5,7]=>1010010=>[1,2,3,2]
[3,6,1,2,4,8,5,7]=>0100010=>[2,4,2]
[1,3,2,6,4,8,5,7]=>0101010=>[2,2,2,2]
[1,3,6,2,4,8,5,7]=>0010010=>[3,3,2]
[3,1,6,2,4,5,8,7]=>1010001=>[1,2,4,1]
[3,1,2,6,4,5,8,7]=>1001001=>[1,3,3,1]
[1,3,4,6,2,5,8,7]=>0001001=>[4,3,1]
[3,1,2,4,6,8,5,7]=>1000010=>[1,5,2]
[1,3,2,4,6,8,5,7]=>0100010=>[2,4,2]
[1,3,4,6,8,2,5,7]=>0000100=>[5,3]
[3,1,6,2,4,5,7,8]=>1010000=>[1,2,5]
[1,3,2,6,4,5,7,8]=>0101000=>[2,2,4]
[1,3,6,2,4,5,7,8]=>0010000=>[3,5]
[3,1,2,4,6,7,5,8]=>1000010=>[1,5,2]
[3,1,2,4,6,7,8,5]=>1000001=>[1,6,1]
[1,3,4,6,7,2,8,5]=>0000101=>[5,2,1]
[3,7,1,2,8,4,5,6]=>0100100=>[2,3,3]
[3,1,7,8,2,4,5,6]=>1001000=>[1,3,4]
[3,1,2,7,4,8,5,6]=>1001010=>[1,3,2,2]
[1,3,2,7,4,8,5,6]=>0101010=>[2,2,2,2]
[1,3,7,2,4,8,5,6]=>0010010=>[3,3,2]
[3,1,2,7,8,4,5,6]=>1000100=>[1,4,3]
[3,7,1,2,4,5,8,6]=>0100001=>[2,5,1]
[1,3,7,2,4,5,8,6]=>0010001=>[3,4,1]
[3,1,2,4,7,5,8,6]=>1000101=>[1,4,2,1]
[1,3,2,4,7,5,8,6]=>0100101=>[2,3,2,1]
[3,1,2,4,7,8,5,6]=>1000010=>[1,5,2]
[1,3,2,4,7,8,5,6]=>0100010=>[2,4,2]
[1,3,4,2,7,8,5,6]=>0010010=>[3,3,2]
[3,7,1,2,4,5,6,8]=>0100000=>[2,6]
[1,3,2,7,4,5,6,8]=>0101000=>[2,2,4]
[3,1,2,4,7,5,6,8]=>1000100=>[1,4,3]
[1,3,4,5,7,2,6,8]=>0000100=>[5,3]
[1,3,4,5,7,2,8,6]=>0000101=>[5,2,1]
[1,3,4,5,7,8,2,6]=>0000010=>[6,2]
[3,1,8,2,4,5,6,7]=>1010000=>[1,2,5]
[1,3,2,8,4,5,6,7]=>0101000=>[2,2,4]
[1,3,8,2,4,5,6,7]=>0010000=>[3,5]
[3,1,2,4,8,5,6,7]=>1000100=>[1,4,3]
[1,3,2,4,8,5,6,7]=>0100100=>[2,3,3]
[1,3,4,2,8,5,6,7]=>0010100=>[3,2,3]
[1,3,4,8,2,5,6,7]=>0001000=>[4,4]
[3,1,2,4,5,8,6,7]=>1000010=>[1,5,2]
[1,3,2,4,5,8,6,7]=>0100010=>[2,4,2]
[1,3,4,2,5,8,6,7]=>0010010=>[3,3,2]
[1,3,4,5,2,8,6,7]=>0001010=>[4,2,2]
[1,3,4,5,8,2,6,7]=>0000100=>[5,3]
[4,1,5,2,6,3,8,7]=>1010101=>[1,2,2,2,1]
[4,1,5,6,2,3,8,7]=>1001001=>[1,3,3,1]
[4,5,1,6,2,3,8,7]=>0101001=>[2,2,3,1]
[4,5,6,1,2,3,8,7]=>0010001=>[3,4,1]
[4,1,5,2,6,8,3,7]=>1010010=>[1,2,3,2]
[4,5,1,2,6,8,3,7]=>0100010=>[2,4,2]
[4,1,5,6,2,8,3,7]=>1001010=>[1,3,2,2]
[4,5,1,6,2,8,3,7]=>0101010=>[2,2,2,2]
[4,1,5,6,8,2,3,7]=>1000100=>[1,4,3]
[4,5,6,8,1,2,3,7]=>0001000=>[4,4]
[4,1,5,6,2,3,7,8]=>1001000=>[1,3,4]
[4,5,1,6,2,3,7,8]=>0101000=>[2,2,4]
[4,5,1,6,2,7,3,8]=>0101010=>[2,2,2,2]
[4,1,5,6,7,2,3,8]=>1000100=>[1,4,3]
[4,5,1,6,7,2,3,8]=>0100100=>[2,3,3]
[4,1,5,2,6,7,8,3]=>1010001=>[1,2,4,1]
[4,5,1,2,6,7,8,3]=>0100001=>[2,5,1]
[4,5,1,6,2,7,8,3]=>0101001=>[2,2,3,1]
[4,1,5,6,7,2,8,3]=>1000101=>[1,4,2,1]
[4,5,1,6,7,2,8,3]=>0100101=>[2,3,2,1]
[4,5,6,1,7,2,8,3]=>0010101=>[3,2,2,1]
[4,5,6,7,1,2,8,3]=>0001001=>[4,3,1]
[4,1,5,6,7,8,2,3]=>1000010=>[1,5,2]
[4,5,1,6,7,8,2,3]=>0100010=>[2,4,2]
[4,5,6,7,1,8,2,3]=>0001010=>[4,2,2]
[4,1,5,2,7,3,8,6]=>1010101=>[1,2,2,2,1]
[4,5,1,7,2,3,8,6]=>0101001=>[2,2,3,1]
[4,1,5,2,7,8,3,6]=>1010010=>[1,2,3,2]
[4,5,1,2,7,8,3,6]=>0100010=>[2,4,2]
[4,1,5,7,2,8,3,6]=>1001010=>[1,3,2,2]
[4,5,1,7,2,8,3,6]=>0101010=>[2,2,2,2]
[4,5,7,1,2,8,3,6]=>0010010=>[3,3,2]
[4,5,1,7,8,2,3,6]=>0100100=>[2,3,3]
[4,1,5,2,7,3,6,8]=>1010100=>[1,2,2,3]
[4,5,1,2,7,3,6,8]=>0100100=>[2,3,3]
[4,1,5,7,2,3,6,8]=>1001000=>[1,3,4]
[4,5,1,7,2,3,6,8]=>0101000=>[2,2,4]
[4,5,1,2,3,7,6,8]=>0100010=>[2,4,2]
[1,4,2,5,3,7,6,8]=>0101010=>[2,2,2,2]
[1,4,5,2,3,7,6,8]=>0010010=>[3,3,2]
[4,1,2,5,7,3,6,8]=>1000100=>[1,4,3]
[1,4,2,5,7,3,6,8]=>0100100=>[2,3,3]
[1,4,5,2,7,3,6,8]=>0010100=>[3,2,3]
[1,4,5,7,2,3,6,8]=>0001000=>[4,4]
[4,1,5,2,3,7,8,6]=>1010001=>[1,2,4,1]
[4,1,2,5,3,7,8,6]=>1001001=>[1,3,3,1]
[1,4,2,5,3,7,8,6]=>0101001=>[2,2,3,1]
[1,4,5,2,3,7,8,6]=>0010001=>[3,4,1]
[4,1,2,5,7,3,8,6]=>1000101=>[1,4,2,1]
[1,4,2,5,7,3,8,6]=>0100101=>[2,3,2,1]
[1,4,5,2,7,3,8,6]=>0010101=>[3,2,2,1]
[1,4,5,7,2,3,8,6]=>0001001=>[4,3,1]
[4,1,2,5,7,8,3,6]=>1000010=>[1,5,2]
[1,4,2,5,7,8,3,6]=>0100010=>[2,4,2]
[1,4,5,2,7,8,3,6]=>0010010=>[3,3,2]
[1,4,5,7,8,2,3,6]=>0000100=>[5,3]
[4,1,5,2,8,3,6,7]=>1010100=>[1,2,2,3]
[4,5,1,2,8,3,6,7]=>0100100=>[2,3,3]
[4,1,5,8,2,3,6,7]=>1001000=>[1,3,4]
[4,5,1,8,2,3,6,7]=>0101000=>[2,2,4]
[4,5,8,1,2,3,6,7]=>0010000=>[3,5]
[4,1,5,2,3,8,6,7]=>1010010=>[1,2,3,2]
[4,5,1,2,3,8,6,7]=>0100010=>[2,4,2]
[4,1,2,5,3,8,6,7]=>1001010=>[1,3,2,2]
[1,4,2,5,3,8,6,7]=>0101010=>[2,2,2,2]
[1,4,5,2,3,8,6,7]=>0010010=>[3,3,2]
[4,1,2,5,8,3,6,7]=>1000100=>[1,4,3]
[1,4,2,5,8,3,6,7]=>0100100=>[2,3,3]
[1,4,5,2,8,3,6,7]=>0010100=>[3,2,3]
[1,4,5,8,2,3,6,7]=>0001000=>[4,4]
[1,4,2,5,3,6,8,7]=>0101001=>[2,2,3,1]
[4,1,2,5,6,3,8,7]=>1000101=>[1,4,2,1]
[1,4,5,2,6,3,8,7]=>0010101=>[3,2,2,1]
[4,1,2,5,6,8,3,7]=>1000010=>[1,5,2]
[1,4,5,2,6,8,3,7]=>0010010=>[3,3,2]
[1,4,5,6,2,8,3,7]=>0001010=>[4,2,2]
[1,4,5,6,8,2,3,7]=>0000100=>[5,3]
[1,4,2,5,3,6,7,8]=>0101000=>[2,2,4]
[1,4,5,2,3,6,7,8]=>0010000=>[3,5]
[4,1,2,5,6,3,7,8]=>1000100=>[1,4,3]
[1,4,5,2,6,3,7,8]=>0010100=>[3,2,3]
[4,1,2,5,6,7,3,8]=>1000010=>[1,5,2]
[1,4,2,5,6,7,3,8]=>0100010=>[2,4,2]
[1,4,5,6,7,2,3,8]=>0000100=>[5,3]
[4,1,2,5,6,7,8,3]=>1000001=>[1,6,1]
[1,4,5,2,6,7,8,3]=>0010001=>[3,4,1]
[1,4,5,6,7,2,8,3]=>0000101=>[5,2,1]
[4,1,6,2,7,3,8,5]=>1010101=>[1,2,2,2,1]
[4,1,6,7,2,3,8,5]=>1001001=>[1,3,3,1]
[4,6,7,1,2,3,8,5]=>0010001=>[3,4,1]
[4,6,7,1,2,8,3,5]=>0010010=>[3,3,2]
[4,6,7,1,8,2,3,5]=>0010100=>[3,2,3]
[4,6,7,8,1,2,3,5]=>0001000=>[4,4]
[4,1,6,2,7,3,5,8]=>1010100=>[1,2,2,3]
[4,6,1,2,7,3,5,8]=>0100100=>[2,3,3]
[4,1,6,7,2,3,5,8]=>1001000=>[1,3,4]
[4,6,1,7,2,3,5,8]=>0101000=>[2,2,4]
[4,1,6,2,3,7,5,8]=>1010010=>[1,2,3,2]
[4,6,1,2,3,7,5,8]=>0100010=>[2,4,2]
[4,1,2,6,3,7,5,8]=>1001010=>[1,3,2,2]
[1,4,2,6,3,7,5,8]=>0101010=>[2,2,2,2]
[4,1,2,6,7,3,5,8]=>1000100=>[1,4,3]
[1,4,2,6,7,3,5,8]=>0100100=>[2,3,3]
[1,4,6,2,7,3,5,8]=>0010100=>[3,2,3]
[4,1,6,2,3,7,8,5]=>1010001=>[1,2,4,1]
[4,1,2,6,3,7,8,5]=>1001001=>[1,3,3,1]
[1,4,6,2,3,7,8,5]=>0010001=>[3,4,1]
[4,1,2,6,7,3,8,5]=>1000101=>[1,4,2,1]
[1,4,6,2,7,3,8,5]=>0010101=>[3,2,2,1]
[1,4,2,6,7,8,3,5]=>0100010=>[2,4,2]
[1,4,6,2,7,8,3,5]=>0010010=>[3,3,2]
[1,4,6,7,2,8,3,5]=>0001010=>[4,2,2]
[4,1,6,2,8,3,5,7]=>1010100=>[1,2,2,3]
[4,6,1,2,8,3,5,7]=>0100100=>[2,3,3]
[4,1,6,8,2,3,5,7]=>1001000=>[1,3,4]
[4,6,1,8,2,3,5,7]=>0101000=>[2,2,4]
[4,6,8,1,2,3,5,7]=>0010000=>[3,5]
[4,6,1,2,3,8,5,7]=>0100010=>[2,4,2]
[4,1,2,6,3,8,5,7]=>1001010=>[1,3,2,2]
[1,4,2,6,3,8,5,7]=>0101010=>[2,2,2,2]
[1,4,6,2,3,8,5,7]=>0010010=>[3,3,2]
[1,4,2,6,8,3,5,7]=>0100100=>[2,3,3]
[1,4,6,2,8,3,5,7]=>0010100=>[3,2,3]
[4,1,2,6,3,5,8,7]=>1001001=>[1,3,3,1]
[1,4,2,6,3,5,8,7]=>0101001=>[2,2,3,1]
[4,1,2,3,6,5,8,7]=>1000101=>[1,4,2,1]
[1,4,2,3,6,5,8,7]=>0100101=>[2,3,2,1]
[4,1,2,3,6,8,5,7]=>1000010=>[1,5,2]
[1,2,4,3,6,8,5,7]=>0010010=>[3,3,2]
[1,2,4,6,8,3,5,7]=>0000100=>[5,3]
[1,4,2,6,3,5,7,8]=>0101000=>[2,2,4]
[4,1,2,3,6,5,7,8]=>1000100=>[1,4,3]
[1,4,2,3,6,5,7,8]=>0100100=>[2,3,3]
[1,2,4,6,3,5,7,8]=>0001000=>[4,4]
[4,1,2,3,6,7,5,8]=>1000010=>[1,5,2]
[4,1,2,3,6,7,8,5]=>1000001=>[1,6,1]
[1,4,2,3,6,7,8,5]=>0100001=>[2,5,1]
[1,2,4,6,7,3,8,5]=>0000101=>[5,2,1]
[4,1,7,2,8,3,5,6]=>1010100=>[1,2,2,3]
[4,7,1,2,8,3,5,6]=>0100100=>[2,3,3]
[4,7,1,8,2,3,5,6]=>0101000=>[2,2,4]
[1,4,2,7,3,8,5,6]=>0101010=>[2,2,2,2]
[4,1,2,7,8,3,5,6]=>1000100=>[1,4,3]
[1,4,2,7,8,3,5,6]=>0100100=>[2,3,3]
[4,1,7,2,3,5,8,6]=>1010001=>[1,2,4,1]
[4,1,2,7,3,5,8,6]=>1001001=>[1,3,3,1]
[1,4,2,7,3,5,8,6]=>0101001=>[2,2,3,1]
[1,4,7,2,3,5,8,6]=>0010001=>[3,4,1]
[4,1,2,3,7,5,8,6]=>1000101=>[1,4,2,1]
[1,2,4,3,7,5,8,6]=>0010101=>[3,2,2,1]
[4,1,2,3,7,8,5,6]=>1000010=>[1,5,2]
[1,4,2,3,7,8,5,6]=>0100010=>[2,4,2]
[1,2,4,3,7,8,5,6]=>0010010=>[3,3,2]
[1,2,4,7,8,3,5,6]=>0000100=>[5,3]
[1,4,2,7,3,5,6,8]=>0101000=>[2,2,4]
[4,1,2,3,7,5,6,8]=>1000100=>[1,4,3]
[1,4,2,3,7,5,6,8]=>0100100=>[2,3,3]
[4,1,2,3,5,7,6,8]=>1000010=>[1,5,2]
[1,4,2,3,5,7,6,8]=>0100010=>[2,4,2]
[4,1,2,3,5,7,8,6]=>1000001=>[1,6,1]
[1,4,2,3,5,7,8,6]=>0100001=>[2,5,1]
[1,2,4,5,7,3,8,6]=>0000101=>[5,2,1]
[4,8,1,2,3,5,6,7]=>0100000=>[2,6]
[4,1,2,8,3,5,6,7]=>1001000=>[1,3,4]
[1,4,2,8,3,5,6,7]=>0101000=>[2,2,4]
[1,4,8,2,3,5,6,7]=>0010000=>[3,5]
[4,1,2,3,8,5,6,7]=>1000100=>[1,4,3]
[1,4,2,3,8,5,6,7]=>0100100=>[2,3,3]
[1,2,4,3,8,5,6,7]=>0010100=>[3,2,3]
[1,2,4,8,3,5,6,7]=>0001000=>[4,4]
[4,1,2,3,5,8,6,7]=>1000010=>[1,5,2]
[1,4,2,3,5,8,6,7]=>0100010=>[2,4,2]
[1,2,4,3,5,8,6,7]=>0010010=>[3,3,2]
[1,2,4,5,3,8,6,7]=>0001010=>[4,2,2]
[1,2,4,5,8,3,6,7]=>0000100=>[5,3]
[4,1,2,3,5,6,8,7]=>1000001=>[1,6,1]
[1,4,2,3,5,6,8,7]=>0100001=>[2,5,1]
[1,2,4,5,6,8,3,7]=>0000010=>[6,2]
[1,4,2,3,5,6,7,8]=>0100000=>[2,6]
[5,1,6,2,7,3,8,4]=>1010101=>[1,2,2,2,1]
[5,6,1,2,7,3,8,4]=>0100101=>[2,3,2,1]
[5,1,6,7,2,3,8,4]=>1001001=>[1,3,3,1]
[5,6,1,7,2,3,8,4]=>0101001=>[2,2,3,1]
[5,6,7,1,2,3,8,4]=>0010001=>[3,4,1]
[5,1,6,7,2,8,3,4]=>1001010=>[1,3,2,2]
[5,6,7,1,2,8,3,4]=>0010010=>[3,3,2]
[5,1,6,7,8,2,3,4]=>1000100=>[1,4,3]
[5,6,1,7,8,2,3,4]=>0100100=>[2,3,3]
[5,6,7,1,8,2,3,4]=>0010100=>[3,2,3]
[5,1,6,2,7,3,4,8]=>1010100=>[1,2,2,3]
[5,1,6,2,3,7,4,8]=>1010010=>[1,2,3,2]
[5,1,2,6,3,7,4,8]=>1001010=>[1,3,2,2]
[1,5,2,6,3,7,4,8]=>0101010=>[2,2,2,2]
[5,1,2,6,7,3,4,8]=>1000100=>[1,4,3]
[1,5,2,6,7,3,4,8]=>0100100=>[2,3,3]
[1,5,6,7,2,3,4,8]=>0001000=>[4,4]
[5,1,6,2,3,7,8,4]=>1010001=>[1,2,4,1]
[5,6,1,2,3,7,8,4]=>0100001=>[2,5,1]
[5,1,2,6,3,7,8,4]=>1001001=>[1,3,3,1]
[1,5,2,6,3,7,8,4]=>0101001=>[2,2,3,1]
[1,5,6,2,3,7,8,4]=>0010001=>[3,4,1]
[5,1,2,6,7,3,8,4]=>1000101=>[1,4,2,1]
[1,5,6,7,2,3,8,4]=>0001001=>[4,3,1]
[5,1,2,6,7,8,3,4]=>1000010=>[1,5,2]
[1,5,6,7,8,2,3,4]=>0000100=>[5,3]
[5,1,6,2,8,3,4,7]=>1010100=>[1,2,2,3]
[5,6,1,2,8,3,4,7]=>0100100=>[2,3,3]
[5,6,8,1,2,3,4,7]=>0010000=>[3,5]
[5,1,6,2,3,8,4,7]=>1010010=>[1,2,3,2]
[5,6,1,2,3,8,4,7]=>0100010=>[2,4,2]
[5,1,2,6,3,8,4,7]=>1001010=>[1,3,2,2]
[1,5,2,6,3,8,4,7]=>0101010=>[2,2,2,2]
[1,5,6,2,3,8,4,7]=>0010010=>[3,3,2]
[5,1,2,6,8,3,4,7]=>1000100=>[1,4,3]
[1,5,2,6,8,3,4,7]=>0100100=>[2,3,3]
[1,5,6,2,8,3,4,7]=>0010100=>[3,2,3]
[1,5,6,8,2,3,4,7]=>0001000=>[4,4]
[5,1,2,6,3,4,8,7]=>1001001=>[1,3,3,1]
[1,5,2,6,3,4,8,7]=>0101001=>[2,2,3,1]
[1,5,6,2,3,4,8,7]=>0010001=>[3,4,1]
[1,2,5,3,6,4,8,7]=>0010101=>[3,2,2,1]
[1,2,5,6,3,4,8,7]=>0001001=>[4,3,1]
[5,1,2,3,6,8,4,7]=>1000010=>[1,5,2]
[1,5,2,3,6,8,4,7]=>0100010=>[2,4,2]
[1,2,5,6,3,8,4,7]=>0001010=>[4,2,2]
[5,1,6,2,3,4,7,8]=>1010000=>[1,2,5]
[5,1,2,6,3,4,7,8]=>1001000=>[1,3,4]
[1,5,2,6,3,4,7,8]=>0101000=>[2,2,4]
[1,2,5,6,3,4,7,8]=>0001000=>[4,4]
[5,1,2,3,6,7,4,8]=>1000010=>[1,5,2]
[1,2,5,6,3,7,4,8]=>0001010=>[4,2,2]
[5,1,2,3,6,7,8,4]=>1000001=>[1,6,1]
[1,5,2,3,6,7,8,4]=>0100001=>[2,5,1]
[1,2,5,3,6,7,8,4]=>0010001=>[3,4,1]
[1,2,5,6,3,7,8,4]=>0001001=>[4,3,1]
[1,2,5,6,7,8,3,4]=>0000010=>[6,2]
[5,1,7,2,8,3,4,6]=>1010100=>[1,2,2,3]
[5,7,1,2,8,3,4,6]=>0100100=>[2,3,3]
[5,7,8,1,2,3,4,6]=>0010000=>[3,5]
[5,1,2,7,3,8,4,6]=>1001010=>[1,3,2,2]
[1,5,2,7,3,8,4,6]=>0101010=>[2,2,2,2]
[1,5,7,2,3,8,4,6]=>0010010=>[3,3,2]
[5,1,2,7,8,3,4,6]=>1000100=>[1,4,3]
[1,5,2,7,8,3,4,6]=>0100100=>[2,3,3]
[1,5,7,2,8,3,4,6]=>0010100=>[3,2,3]
[1,5,7,8,2,3,4,6]=>0001000=>[4,4]
[5,1,7,2,3,4,8,6]=>1010001=>[1,2,4,1]
[5,1,2,7,3,4,8,6]=>1001001=>[1,3,3,1]
[1,5,2,7,3,4,8,6]=>0101001=>[2,2,3,1]
[1,5,7,2,3,4,8,6]=>0010001=>[3,4,1]
[5,1,2,3,7,4,8,6]=>1000101=>[1,4,2,1]
[1,5,2,3,7,4,8,6]=>0100101=>[2,3,2,1]
[1,2,5,3,7,4,8,6]=>0010101=>[3,2,2,1]
[1,2,5,7,3,4,8,6]=>0001001=>[4,3,1]
[5,1,2,3,7,8,4,6]=>1000010=>[1,5,2]
[1,5,2,3,7,8,4,6]=>0100010=>[2,4,2]
[1,2,5,7,3,8,4,6]=>0001010=>[4,2,2]
[5,7,1,2,3,4,6,8]=>0100000=>[2,6]
[5,1,2,7,3,4,6,8]=>1001000=>[1,3,4]
[1,5,2,7,3,4,6,8]=>0101000=>[2,2,4]
[1,2,5,7,3,4,6,8]=>0001000=>[4,4]
[1,5,2,3,4,7,6,8]=>0100010=>[2,4,2]
[1,2,3,5,7,4,6,8]=>0000100=>[5,3]
[1,5,2,3,4,7,8,6]=>0100001=>[2,5,1]
[1,2,5,3,4,7,8,6]=>0010001=>[3,4,1]
[1,2,3,5,7,4,8,6]=>0000101=>[5,2,1]
[1,2,3,5,7,8,4,6]=>0000010=>[6,2]
[5,1,2,8,3,4,6,7]=>1001000=>[1,3,4]
[1,5,2,8,3,4,6,7]=>0101000=>[2,2,4]
[1,5,2,3,8,4,6,7]=>0100100=>[2,3,3]
[1,2,5,3,8,4,6,7]=>0010100=>[3,2,3]
[1,2,5,8,3,4,6,7]=>0001000=>[4,4]
[1,5,2,3,4,8,6,7]=>0100010=>[2,4,2]
[1,2,5,3,4,8,6,7]=>0010010=>[3,3,2]
[1,2,3,5,4,8,6,7]=>0001010=>[4,2,2]
[1,2,3,5,8,4,6,7]=>0000100=>[5,3]
[1,5,2,3,4,6,8,7]=>0100001=>[2,5,1]
[1,2,3,5,6,8,4,7]=>0000010=>[6,2]
[1,5,2,3,4,6,7,8]=>0100000=>[2,6]
[6,1,7,2,8,3,4,5]=>1010100=>[1,2,2,3]
[6,1,7,8,2,3,4,5]=>1001000=>[1,3,4]
[6,7,1,8,2,3,4,5]=>0101000=>[2,2,4]
[6,1,7,2,3,8,4,5]=>1010010=>[1,2,3,2]
[6,7,1,2,3,8,4,5]=>0100010=>[2,4,2]
[6,1,2,7,3,8,4,5]=>1001010=>[1,3,2,2]
[1,6,2,7,3,8,4,5]=>0101010=>[2,2,2,2]
[1,6,7,2,3,8,4,5]=>0010010=>[3,3,2]
[1,6,7,2,8,3,4,5]=>0010100=>[3,2,3]
[1,6,7,8,2,3,4,5]=>0001000=>[4,4]
[6,1,7,2,3,4,8,5]=>1010001=>[1,2,4,1]
[6,7,1,2,3,4,8,5]=>0100001=>[2,5,1]
[6,1,2,7,3,4,8,5]=>1001001=>[1,3,3,1]
[1,6,2,7,3,4,8,5]=>0101001=>[2,2,3,1]
[1,6,7,2,3,4,8,5]=>0010001=>[3,4,1]
[1,6,2,3,7,4,8,5]=>0100101=>[2,3,2,1]
[1,2,6,3,7,4,8,5]=>0010101=>[3,2,2,1]
[6,1,2,3,7,8,4,5]=>1000010=>[1,5,2]
[1,2,6,3,7,8,4,5]=>0010010=>[3,3,2]
[1,2,6,7,3,8,4,5]=>0001010=>[4,2,2]
[6,1,7,2,3,4,5,8]=>1010000=>[1,2,5]
[1,6,2,7,3,4,5,8]=>0101000=>[2,2,4]
[1,6,7,2,3,4,5,8]=>0010000=>[3,5]
[1,6,2,3,4,7,5,8]=>0100010=>[2,4,2]
[1,2,6,3,4,7,5,8]=>0010010=>[3,3,2]
[1,2,3,6,4,7,5,8]=>0001010=>[4,2,2]
[1,2,3,6,7,4,5,8]=>0000100=>[5,3]
[6,1,2,3,4,7,8,5]=>1000001=>[1,6,1]
[1,6,2,3,4,7,8,5]=>0100001=>[2,5,1]
[1,2,6,3,4,7,8,5]=>0010001=>[3,4,1]
[1,2,3,6,4,7,8,5]=>0001001=>[4,3,1]
[1,2,3,6,7,4,8,5]=>0000101=>[5,2,1]
[1,2,3,6,7,8,4,5]=>0000010=>[6,2]
[6,1,8,2,3,4,5,7]=>1010000=>[1,2,5]
[6,1,2,8,3,4,5,7]=>1001000=>[1,3,4]
[1,6,2,8,3,4,5,7]=>0101000=>[2,2,4]
[1,6,8,2,3,4,5,7]=>0010000=>[3,5]
[1,6,2,3,8,4,5,7]=>0100100=>[2,3,3]
[1,2,6,3,8,4,5,7]=>0010100=>[3,2,3]
[1,2,6,8,3,4,5,7]=>0001000=>[4,4]
[1,6,2,3,4,8,5,7]=>0100010=>[2,4,2]
[1,2,6,3,4,8,5,7]=>0010010=>[3,3,2]
[1,2,3,6,4,8,5,7]=>0001010=>[4,2,2]
[6,1,2,3,4,5,8,7]=>1000001=>[1,6,1]
[1,6,2,3,4,5,8,7]=>0100001=>[2,5,1]
[1,2,6,3,4,5,8,7]=>0010001=>[3,4,1]
[1,2,3,6,4,5,8,7]=>0001001=>[4,3,1]
[1,2,3,4,6,8,5,7]=>0000010=>[6,2]
[1,6,2,3,4,5,7,8]=>0100000=>[2,6]
[1,2,6,3,4,5,7,8]=>0010000=>[3,5]
[1,2,3,6,4,5,7,8]=>0001000=>[4,4]
[7,1,2,8,3,4,5,6]=>1001000=>[1,3,4]
[1,7,2,8,3,4,5,6]=>0101000=>[2,2,4]
[1,7,8,2,3,4,5,6]=>0010000=>[3,5]
[7,1,2,3,8,4,5,6]=>1000100=>[1,4,3]
[1,2,7,8,3,4,5,6]=>0001000=>[4,4]
[1,2,7,3,4,8,5,6]=>0010010=>[3,3,2]
[1,2,3,7,4,8,5,6]=>0001010=>[4,2,2]
[1,2,3,7,8,4,5,6]=>0000100=>[5,3]
[1,2,7,3,4,5,8,6]=>0010001=>[3,4,1]
[1,2,3,7,4,5,8,6]=>0001001=>[4,3,1]
[1,2,3,4,7,5,8,6]=>0000101=>[5,2,1]
[1,2,3,4,7,8,5,6]=>0000010=>[6,2]
[1,7,2,3,4,5,6,8]=>0100000=>[2,6]
[1,2,7,3,4,5,6,8]=>0010000=>[3,5]
[1,2,3,7,4,5,6,8]=>0001000=>[4,4]
[1,2,3,4,7,5,6,8]=>0000100=>[5,3]
[1,8,2,3,4,5,6,7]=>0100000=>[2,6]
[1,2,8,3,4,5,6,7]=>0010000=>[3,5]
[1,2,3,8,4,5,6,7]=>0001000=>[4,4]
[1,2,3,4,8,5,6,7]=>0000100=>[5,3]
[1,2,3,4,5,8,6,7]=>0000010=>[6,2]
[5,3,2,6,1,4,8,7]=>1101001=>[1,1,2,3,1]
[7,3,2,5,4,8,1,6]=>1101010=>[1,1,2,2,2]
[8,4,5,2,3,7,6,1]=>1010011=>[1,2,3,1,1]
[7,4,5,2,3,8,1,6]=>1010010=>[1,2,3,2]
[6,4,5,2,3,1,8,7]=>1010101=>[1,2,2,2,1]
[5,4,6,2,1,3,8,7]=>1011001=>[1,2,1,3,1]
[3,6,1,5,4,2,8,7]=>0101101=>[2,2,1,2,1]
[4,6,5,1,3,2,8,7]=>0110101=>[2,1,2,2,1]
[5,6,4,3,1,2,8,7]=>0111001=>[2,1,1,3,1]
[7,5,4,3,2,8,1,6]=>1111010=>[1,1,1,1,2,2]
[8,6,4,3,7,2,5,1]=>1110101=>[1,1,1,2,2,1]
[7,6,4,3,8,2,1,5]=>1110110=>[1,1,1,2,1,2]
[6,7,4,3,8,1,2,5]=>0110100=>[2,1,2,3]
[5,7,4,3,1,8,2,6]=>0111010=>[2,1,1,2,2]
[4,7,5,1,3,8,2,6]=>0110010=>[2,1,3,2]
[3,7,1,5,4,8,2,6]=>0101010=>[2,2,2,2]
[2,1,7,5,4,8,3,6]=>1011010=>[1,2,1,2,2]
[3,8,1,5,4,7,6,2]=>0101011=>[2,2,2,1,1]
[4,8,5,1,3,7,6,2]=>0110011=>[2,1,3,1,1]
[5,8,4,3,1,7,6,2]=>0111011=>[2,1,1,2,1,1]
[6,8,4,3,7,1,5,2]=>0110101=>[2,1,2,2,1]
[7,8,4,3,6,5,1,2]=>0110110=>[2,1,2,1,2]
[6,8,5,7,3,1,4,2]=>0101101=>[2,2,1,2,1]
[5,8,6,7,1,3,4,2]=>0101001=>[2,2,3,1]
[4,8,6,1,7,3,5,2]=>0110101=>[2,1,2,2,1]
[3,8,1,6,7,4,5,2]=>0100101=>[2,3,2,1]
[2,1,8,6,7,4,5,3]=>1010101=>[1,2,2,2,1]
[2,1,7,6,8,4,3,5]=>1010110=>[1,2,2,1,2]
[3,7,1,6,8,4,2,5]=>0100110=>[2,3,1,2]
[4,7,6,1,8,3,2,5]=>0110110=>[2,1,2,1,2]
[5,7,6,8,1,3,2,4]=>0101010=>[2,2,2,2]
[5,4,7,2,1,8,3,6]=>1011010=>[1,2,1,2,2]
[6,4,7,2,8,1,3,5]=>1010100=>[1,2,2,3]
[7,4,6,2,8,3,1,5]=>1010110=>[1,2,2,1,2]
[8,4,6,2,7,3,5,1]=>1010101=>[1,2,2,2,1]
[8,3,2,6,7,4,5,1]=>1100101=>[1,1,3,2,1]
[7,3,2,6,8,4,1,5]=>1100110=>[1,1,3,1,2]
[6,3,2,7,8,1,4,5]=>1100100=>[1,1,3,3]
[5,3,2,7,1,8,4,6]=>1101010=>[1,1,2,2,2]
[4,3,2,1,7,8,5,6]=>1110010=>[1,1,1,3,2]
[3,4,1,2,8,7,6,5]=>0100111=>[2,3,1,1,1]
[5,3,2,8,1,7,6,4]=>1101011=>[1,1,2,2,1,1]
[6,3,2,8,7,1,5,4]=>1101101=>[1,1,2,1,2,1]
[7,3,2,8,6,5,1,4]=>1101110=>[1,1,2,1,1,2]
[8,4,7,2,6,5,3,1]=>1010111=>[1,2,2,1,1,1]
[7,4,8,2,6,5,1,3]=>1010110=>[1,2,2,1,2]
[6,4,8,2,7,1,5,3]=>1010101=>[1,2,2,2,1]
[5,4,8,2,1,7,6,3]=>1011011=>[1,2,1,2,1,1]
[4,5,8,1,2,7,6,3]=>0010011=>[3,3,1,1]
[3,5,1,8,2,7,6,4]=>0101011=>[2,2,2,1,1]
[2,1,5,8,3,7,6,4]=>1001011=>[1,3,2,1,1]
[2,1,6,8,7,3,5,4]=>1001101=>[1,3,1,2,1]
[3,6,1,8,7,2,5,4]=>0101101=>[2,2,1,2,1]
[4,6,8,1,7,2,5,3]=>0010101=>[3,2,2,1]
[5,6,8,7,1,2,4,3]=>0011001=>[3,1,3,1]
[6,5,8,7,2,1,4,3]=>1011101=>[1,2,1,1,2,1]
[7,5,8,6,2,4,1,3]=>1011010=>[1,2,1,2,2]
[8,5,7,6,2,4,3,1]=>1011011=>[1,2,1,2,1,1]
[5,7,8,6,1,4,2,3]=>0011010=>[3,1,2,2]
[4,7,8,1,6,5,2,3]=>0010110=>[3,2,1,2]
[3,7,1,8,6,5,2,4]=>0101110=>[2,2,1,1,2]
[2,1,7,8,6,5,3,4]=>1001110=>[1,3,1,1,2]
[3,8,1,7,6,5,4,2]=>0101111=>[2,2,1,1,1,1]
[4,8,7,1,6,5,3,2]=>0110111=>[2,1,2,1,1,1]
[5,8,7,6,1,4,3,2]=>0111011=>[2,1,1,2,1,1]
[6,8,7,5,4,1,3,2]=>0111101=>[2,1,1,1,2,1]
[2,1,4,3,6,5,8,7,10,9]=>101010101=>[1,2,2,2,2,1]
[5,2,4,1,3,6,7,8]=>1010000=>[1,2,5]
[3,2,6,1,4,5,7,8]=>1010000=>[1,2,5]
[6,3,5,1,2,4,7,8]=>1010000=>[1,2,5]
[5,2,7,1,3,4,6,8]=>1010000=>[1,2,5]
[5,3,7,1,2,4,6,8]=>1010000=>[1,2,5]
[5,4,7,1,2,3,6,8]=>1010000=>[1,2,5]
[6,2,7,1,3,4,5,8]=>1010000=>[1,2,5]
[6,3,7,1,2,4,5,8]=>1010000=>[1,2,5]
[6,4,7,1,2,3,5,8]=>1010000=>[1,2,5]
[7,3,5,1,2,4,6,8]=>1010000=>[1,2,5]
[7,4,6,1,2,3,5,8]=>1010000=>[1,2,5]
[3,2,8,1,4,5,6,7]=>1010000=>[1,2,5]
[5,2,8,1,3,4,6,7]=>1010000=>[1,2,5]
[5,4,8,1,2,3,6,7]=>1010000=>[1,2,5]
[6,2,8,1,3,4,5,7]=>1010000=>[1,2,5]
[6,5,8,1,2,3,4,7]=>1010000=>[1,2,5]
[7,5,8,1,2,3,4,6]=>1010000=>[1,2,5]
[8,3,5,1,2,4,6,7]=>1010000=>[1,2,5]
[8,3,6,1,2,4,5,7]=>1010000=>[1,2,5]
[8,4,7,1,2,3,5,6]=>1010000=>[1,2,5]
[8,5,7,1,2,3,4,6]=>1010000=>[1,2,5]
[3,2,5,7,1,4,6,8]=>1001000=>[1,3,4]
[4,2,5,7,1,3,6,8]=>1001000=>[1,3,4]
[4,3,5,7,1,2,6,8]=>1001000=>[1,3,4]
[5,3,4,7,1,2,6,8]=>1001000=>[1,3,4]
[4,2,6,7,1,3,5,8]=>1001000=>[1,3,4]
[5,2,6,7,1,3,4,8]=>1001000=>[1,3,4]
[7,3,5,6,1,2,4,8]=>1001000=>[1,3,4]
[3,2,5,8,1,4,6,7]=>1001000=>[1,3,4]
[4,2,5,8,1,3,6,7]=>1001000=>[1,3,4]
[4,3,5,8,1,2,6,7]=>1001000=>[1,3,4]
[5,2,4,8,1,3,6,7]=>1001000=>[1,3,4]
[3,2,6,8,1,4,5,7]=>1001000=>[1,3,4]
[4,2,6,8,1,3,5,7]=>1001000=>[1,3,4]
[4,3,6,8,1,2,5,7]=>1001000=>[1,3,4]
[5,2,6,8,1,3,4,7]=>1001000=>[1,3,4]
[6,2,4,8,1,3,5,7]=>1001000=>[1,3,4]
[6,2,5,8,1,3,4,7]=>1001000=>[1,3,4]
[6,3,5,8,1,2,4,7]=>1001000=>[1,3,4]
[3,2,7,8,1,4,5,6]=>1001000=>[1,3,4]
[4,3,7,8,1,2,5,6]=>1001000=>[1,3,4]
[6,2,7,8,1,3,4,5]=>1001000=>[1,3,4]
[6,3,7,8,1,2,4,5]=>1001000=>[1,3,4]
[6,4,7,8,1,2,3,5]=>1001000=>[1,3,4]
[7,2,4,8,1,3,5,6]=>1001000=>[1,3,4]
[7,3,5,8,1,2,4,6]=>1001000=>[1,3,4]
[7,4,5,8,1,2,3,6]=>1001000=>[1,3,4]
[8,2,5,6,1,3,4,7]=>1001000=>[1,3,4]
[8,2,4,7,1,3,5,6]=>1001000=>[1,3,4]
[8,2,5,7,1,3,4,6]=>1001000=>[1,3,4]
[8,3,5,7,1,2,4,6]=>1001000=>[1,3,4]
[8,2,6,7,1,3,4,5]=>1001000=>[1,3,4]
[8,4,6,7,1,2,3,5]=>1001000=>[1,3,4]
[4,6,2,5,1,3,7,8]=>0101000=>[2,2,4]
[4,6,3,5,1,2,7,8]=>0101000=>[2,2,4]
[4,7,3,5,1,2,6,8]=>0101000=>[2,2,4]
[5,7,2,4,1,3,6,8]=>0101000=>[2,2,4]
[5,7,3,4,1,2,6,8]=>0101000=>[2,2,4]
[3,7,2,6,1,4,5,8]=>0101000=>[2,2,4]
[5,7,2,6,1,3,4,8]=>0101000=>[2,2,4]
[6,7,2,5,1,3,4,8]=>0101000=>[2,2,4]
[4,8,2,5,1,3,6,7]=>0101000=>[2,2,4]
[5,8,3,4,1,2,6,7]=>0101000=>[2,2,4]
[5,8,3,6,1,2,4,7]=>0101000=>[2,2,4]
[6,8,2,4,1,3,5,7]=>0101000=>[2,2,4]
[6,8,3,4,1,2,5,7]=>0101000=>[2,2,4]
[6,8,3,5,1,2,4,7]=>0101000=>[2,2,4]
[6,8,4,5,1,2,3,7]=>0101000=>[2,2,4]
[3,8,2,7,1,4,5,6]=>0101000=>[2,2,4]
[4,8,2,7,1,3,5,6]=>0101000=>[2,2,4]
[5,8,2,7,1,3,4,6]=>0101000=>[2,2,4]
[5,8,3,7,1,2,4,6]=>0101000=>[2,2,4]
[5,8,4,7,1,2,3,6]=>0101000=>[2,2,4]
[6,8,2,7,1,3,4,5]=>0101000=>[2,2,4]
[6,8,3,7,1,2,4,5]=>0101000=>[2,2,4]
[6,8,5,7,1,2,3,4]=>0101000=>[2,2,4]
[7,8,2,4,1,3,5,6]=>0101000=>[2,2,4]
[7,8,2,5,1,3,4,6]=>0101000=>[2,2,4]
[7,8,3,5,1,2,4,6]=>0101000=>[2,2,4]
[7,8,4,6,1,2,3,5]=>0101000=>[2,2,4]
[4,3,2,6,1,5,7,8]=>1101000=>[1,1,2,4]
[5,3,2,6,1,4,7,8]=>1101000=>[1,1,2,4]
[6,4,2,5,1,3,7,8]=>1101000=>[1,1,2,4]
[6,5,2,4,1,3,7,8]=>1101000=>[1,1,2,4]
[4,3,2,7,1,5,6,8]=>1101000=>[1,1,2,4]
[5,3,2,7,1,4,6,8]=>1101000=>[1,1,2,4]
[5,4,3,7,1,2,6,8]=>1101000=>[1,1,2,4]
[6,3,2,7,1,4,5,8]=>1101000=>[1,1,2,4]
[6,4,2,7,1,3,5,8]=>1101000=>[1,1,2,4]
[6,4,3,7,1,2,5,8]=>1101000=>[1,1,2,4]
[6,5,3,7,1,2,4,8]=>1101000=>[1,1,2,4]
[7,3,2,5,1,4,6,8]=>1101000=>[1,1,2,4]
[7,4,2,5,1,3,6,8]=>1101000=>[1,1,2,4]
[7,3,2,6,1,4,5,8]=>1101000=>[1,1,2,4]
[7,4,3,6,1,2,5,8]=>1101000=>[1,1,2,4]
[7,5,2,6,1,3,4,8]=>1101000=>[1,1,2,4]
[7,5,3,6,1,2,4,8]=>1101000=>[1,1,2,4]
[7,6,3,5,1,2,4,8]=>1101000=>[1,1,2,4]
[4,3,2,8,1,5,6,7]=>1101000=>[1,1,2,4]
[5,3,2,8,1,4,6,7]=>1101000=>[1,1,2,4]
[5,4,3,8,1,2,6,7]=>1101000=>[1,1,2,4]
[6,3,2,8,1,4,5,7]=>1101000=>[1,1,2,4]
[6,4,3,8,1,2,5,7]=>1101000=>[1,1,2,4]
[6,5,2,8,1,3,4,7]=>1101000=>[1,1,2,4]
[6,5,3,8,1,2,4,7]=>1101000=>[1,1,2,4]
[6,5,4,8,1,2,3,7]=>1101000=>[1,1,2,4]
[7,3,2,8,1,4,5,6]=>1101000=>[1,1,2,4]
[7,4,2,8,1,3,5,6]=>1101000=>[1,1,2,4]
[7,5,3,8,1,2,4,6]=>1101000=>[1,1,2,4]
[7,6,2,8,1,3,4,5]=>1101000=>[1,1,2,4]
[8,4,2,5,1,3,6,7]=>1101000=>[1,1,2,4]
[8,3,2,6,1,4,5,7]=>1101000=>[1,1,2,4]
[8,4,2,6,1,3,5,7]=>1101000=>[1,1,2,4]
[8,5,3,6,1,2,4,7]=>1101000=>[1,1,2,4]
[8,6,2,4,1,3,5,7]=>1101000=>[1,1,2,4]
[8,6,2,5,1,3,4,7]=>1101000=>[1,1,2,4]
[8,3,2,7,1,4,5,6]=>1101000=>[1,1,2,4]
[8,4,2,7,1,3,5,6]=>1101000=>[1,1,2,4]
[8,4,3,7,1,2,5,6]=>1101000=>[1,1,2,4]
[8,5,2,7,1,3,4,6]=>1101000=>[1,1,2,4]
[8,5,3,7,1,2,4,6]=>1101000=>[1,1,2,4]
[8,5,4,7,1,2,3,6]=>1101000=>[1,1,2,4]
[8,6,3,7,1,2,4,5]=>1101000=>[1,1,2,4]
[8,7,2,4,1,3,5,6]=>1101000=>[1,1,2,4]
[8,7,2,5,1,3,4,6]=>1101000=>[1,1,2,4]
[8,7,3,5,1,2,4,6]=>1101000=>[1,1,2,4]
[8,7,2,6,1,3,4,5]=>1101000=>[1,1,2,4]
[8,7,3,6,1,2,4,5]=>1101000=>[1,1,2,4]
[8,7,4,6,1,2,3,5]=>1101000=>[1,1,2,4]
[4,6,3,5,8,1,2,7]=>0100100=>[2,3,3]
[5,6,2,4,8,1,3,7]=>0100100=>[2,3,3]
[4,7,2,5,8,1,3,6]=>0100100=>[2,3,3]
[4,7,3,5,8,1,2,6]=>0100100=>[2,3,3]
[5,7,3,4,8,1,2,6]=>0100100=>[2,3,3]
[3,7,2,6,8,1,4,5]=>0100100=>[2,3,3]
[4,7,3,6,8,1,2,5]=>0100100=>[2,3,3]
[5,7,4,6,8,1,2,3]=>0100100=>[2,3,3]
[6,7,3,5,8,1,2,4]=>0100100=>[2,3,3]
[3,8,2,5,7,1,4,6]=>0100100=>[2,3,3]
[4,8,2,5,7,1,3,6]=>0100100=>[2,3,3]
[4,8,3,5,7,1,2,6]=>0100100=>[2,3,3]
[3,8,2,6,7,1,4,5]=>0100100=>[2,3,3]
[4,8,3,6,7,1,2,5]=>0100100=>[2,3,3]
[6,8,2,5,7,1,3,4]=>0100100=>[2,3,3]
[6,8,3,5,7,1,2,4]=>0100100=>[2,3,3]
[6,8,4,5,7,1,2,3]=>0100100=>[2,3,3]
[7,8,2,4,6,1,3,5]=>0100100=>[2,3,3]
[7,8,2,5,6,1,3,4]=>0100100=>[2,3,3]
[7,8,3,5,6,1,2,4]=>0100100=>[2,3,3]
[4,3,2,6,8,1,5,7]=>1100100=>[1,1,3,3]
[5,4,2,6,8,1,3,7]=>1100100=>[1,1,3,3]
[5,4,3,6,8,1,2,7]=>1100100=>[1,1,3,3]
[6,3,2,5,8,1,4,7]=>1100100=>[1,1,3,3]
[6,4,3,5,8,1,2,7]=>1100100=>[1,1,3,3]
[6,5,2,4,8,1,3,7]=>1100100=>[1,1,3,3]
[4,3,2,7,8,1,5,6]=>1100100=>[1,1,3,3]
[5,3,2,7,8,1,4,6]=>1100100=>[1,1,3,3]
[5,4,2,7,8,1,3,6]=>1100100=>[1,1,3,3]
[5,4,3,7,8,1,2,6]=>1100100=>[1,1,3,3]
[6,4,2,7,8,1,3,5]=>1100100=>[1,1,3,3]
[6,4,3,7,8,1,2,5]=>1100100=>[1,1,3,3]
[6,5,2,7,8,1,3,4]=>1100100=>[1,1,3,3]
[7,4,2,5,8,1,3,6]=>1100100=>[1,1,3,3]
[7,3,2,6,8,1,4,5]=>1100100=>[1,1,3,3]
[7,5,3,6,8,1,2,4]=>1100100=>[1,1,3,3]
[7,6,3,5,8,1,2,4]=>1100100=>[1,1,3,3]
[8,4,2,5,7,1,3,6]=>1100100=>[1,1,3,3]
[8,5,2,6,7,1,3,4]=>1100100=>[1,1,3,3]
[8,5,3,6,7,1,2,4]=>1100100=>[1,1,3,3]
[8,6,3,5,7,1,2,4]=>1100100=>[1,1,3,3]
[8,7,2,4,6,1,3,5]=>1100100=>[1,1,3,3]
[8,7,3,4,6,1,2,5]=>1100100=>[1,1,3,3]
[8,7,2,5,6,1,3,4]=>1100100=>[1,1,3,3]
[8,7,3,5,6,1,2,4]=>1100100=>[1,1,3,3]
[4,3,7,2,6,1,5,8]=>1010100=>[1,2,2,3]
[5,3,7,2,6,1,4,8]=>1010100=>[1,2,2,3]
[5,4,7,2,6,1,3,8]=>1010100=>[1,2,2,3]
[6,3,7,2,5,1,4,8]=>1010100=>[1,2,2,3]
[6,4,7,2,5,1,3,8]=>1010100=>[1,2,2,3]
[7,3,6,2,5,1,4,8]=>1010100=>[1,2,2,3]
[4,3,8,2,6,1,5,7]=>1010100=>[1,2,2,3]
[5,3,8,2,6,1,4,7]=>1010100=>[1,2,2,3]
[5,4,8,2,6,1,3,7]=>1010100=>[1,2,2,3]
[6,4,8,2,5,1,3,7]=>1010100=>[1,2,2,3]
[6,4,8,3,5,1,2,7]=>1010100=>[1,2,2,3]
[6,5,8,3,4,1,2,7]=>1010100=>[1,2,2,3]
[4,3,8,2,7,1,5,6]=>1010100=>[1,2,2,3]
[5,3,8,2,7,1,4,6]=>1010100=>[1,2,2,3]
[5,4,8,2,7,1,3,6]=>1010100=>[1,2,2,3]
[6,4,8,2,7,1,3,5]=>1010100=>[1,2,2,3]
[7,3,8,2,5,1,4,6]=>1010100=>[1,2,2,3]
[7,4,8,3,5,1,2,6]=>1010100=>[1,2,2,3]
[7,5,8,2,4,1,3,6]=>1010100=>[1,2,2,3]
[7,5,8,3,4,1,2,6]=>1010100=>[1,2,2,3]
[7,3,8,2,6,1,4,5]=>1010100=>[1,2,2,3]
[7,4,8,2,6,1,3,5]=>1010100=>[1,2,2,3]
[7,5,8,2,6,1,3,4]=>1010100=>[1,2,2,3]
[7,5,8,3,6,1,2,4]=>1010100=>[1,2,2,3]
[7,5,8,4,6,1,2,3]=>1010100=>[1,2,2,3]
[8,3,6,2,5,1,4,7]=>1010100=>[1,2,2,3]
[8,3,7,2,5,1,4,6]=>1010100=>[1,2,2,3]
[8,3,7,2,6,1,4,5]=>1010100=>[1,2,2,3]
[8,4,7,2,6,1,3,5]=>1010100=>[1,2,2,3]
[8,4,7,3,6,1,2,5]=>1010100=>[1,2,2,3]
[8,5,7,2,6,1,3,4]=>1010100=>[1,2,2,3]
[8,6,7,2,5,1,3,4]=>1010100=>[1,2,2,3]
[8,6,7,3,5,1,2,4]=>1010100=>[1,2,2,3]
[5,4,3,2,7,1,6,8]=>1110100=>[1,1,1,2,3]
[6,4,3,2,7,1,5,8]=>1110100=>[1,1,1,2,3]
[6,5,3,2,7,1,4,8]=>1110100=>[1,1,1,2,3]
[6,5,4,2,7,1,3,8]=>1110100=>[1,1,1,2,3]
[7,5,3,2,6,1,4,8]=>1110100=>[1,1,1,2,3]
[5,4,3,2,8,1,6,7]=>1110100=>[1,1,1,2,3]
[6,5,3,2,8,1,4,7]=>1110100=>[1,1,1,2,3]
[6,5,4,3,8,1,2,7]=>1110100=>[1,1,1,2,3]
[7,5,3,2,8,1,4,6]=>1110100=>[1,1,1,2,3]
[7,6,4,3,8,1,2,5]=>1110100=>[1,1,1,2,3]
[8,5,3,2,6,1,4,7]=>1110100=>[1,1,1,2,3]
[8,5,4,2,6,1,3,7]=>1110100=>[1,1,1,2,3]
[8,6,5,2,4,1,3,7]=>1110100=>[1,1,1,2,3]
[8,5,3,2,7,1,4,6]=>1110100=>[1,1,1,2,3]
[8,6,3,2,7,1,4,5]=>1110100=>[1,1,1,2,3]
[8,7,3,2,6,1,4,5]=>1110100=>[1,1,1,2,3]
[8,7,4,2,6,1,3,5]=>1110100=>[1,1,1,2,3]
[8,7,4,3,6,1,2,5]=>1110100=>[1,1,1,2,3]
[8,7,5,2,6,1,3,4]=>1110100=>[1,1,1,2,3]
[8,7,6,2,4,1,3,5]=>1110100=>[1,1,1,2,3]
[8,7,6,2,5,1,3,4]=>1110100=>[1,1,1,2,3]
[8,7,6,3,5,1,2,4]=>1110100=>[1,1,1,2,3]
[4,8,3,7,2,6,1,5]=>0101010=>[2,2,2,2]
[5,8,3,7,2,6,1,4]=>0101010=>[2,2,2,2]
[5,8,4,7,2,6,1,3]=>0101010=>[2,2,2,2]
[5,8,4,7,3,6,1,2]=>0101010=>[2,2,2,2]
[6,8,3,7,2,5,1,4]=>0101010=>[2,2,2,2]
[6,8,4,7,2,5,1,3]=>0101010=>[2,2,2,2]
[6,8,4,7,3,5,1,2]=>0101010=>[2,2,2,2]
[6,8,5,7,2,4,1,3]=>0101010=>[2,2,2,2]
[6,8,5,7,3,4,1,2]=>0101010=>[2,2,2,2]
[7,8,3,6,2,5,1,4]=>0101010=>[2,2,2,2]
[7,8,4,6,2,5,1,3]=>0101010=>[2,2,2,2]
[7,8,4,6,3,5,1,2]=>0101010=>[2,2,2,2]
[7,8,5,6,2,4,1,3]=>0101010=>[2,2,2,2]
[6,4,3,8,2,7,1,5]=>1101010=>[1,1,2,2,2]
[6,5,3,8,2,7,1,4]=>1101010=>[1,1,2,2,2]
[6,5,4,8,2,7,1,3]=>1101010=>[1,1,2,2,2]
[7,4,3,8,2,6,1,5]=>1101010=>[1,1,2,2,2]
[7,5,3,8,2,6,1,4]=>1101010=>[1,1,2,2,2]
[7,5,4,8,2,6,1,3]=>1101010=>[1,1,2,2,2]
[7,6,3,8,2,5,1,4]=>1101010=>[1,1,2,2,2]
[7,6,4,8,2,5,1,3]=>1101010=>[1,1,2,2,2]
[7,6,5,8,2,4,1,3]=>1101010=>[1,1,2,2,2]
[8,4,3,7,2,6,1,5]=>1101010=>[1,1,2,2,2]
[8,5,3,7,2,6,1,4]=>1101010=>[1,1,2,2,2]
[8,6,3,7,2,5,1,4]=>1101010=>[1,1,2,2,2]
[8,6,4,7,2,5,1,3]=>1101010=>[1,1,2,2,2]
[8,6,5,7,2,4,1,3]=>1101010=>[1,1,2,2,2]
[8,7,3,6,2,5,1,4]=>1101010=>[1,1,2,2,2]
[8,7,4,6,3,5,1,2]=>1101010=>[1,1,2,2,2]
[8,7,5,6,2,4,1,3]=>1101010=>[1,1,2,2,2]
[6,5,4,3,2,8,1,7]=>1111010=>[1,1,1,1,2,2]
[7,6,4,3,2,8,1,5]=>1111010=>[1,1,1,1,2,2]
[8,5,4,3,2,7,1,6]=>1111010=>[1,1,1,1,2,2]
[8,7,4,3,2,6,1,5]=>1111010=>[1,1,1,1,2,2]
[8,7,5,3,2,6,1,4]=>1111010=>[1,1,1,1,2,2]
[8,7,5,4,2,6,1,3]=>1111010=>[1,1,1,1,2,2]
[8,7,6,3,2,5,1,4]=>1111010=>[1,1,1,1,2,2]
[8,7,6,5,2,4,1,3]=>1111010=>[1,1,1,1,2,2]
[8,1,2,3,7,4,5,6]=>1000100=>[1,4,3]
[8,1,2,5,3,4,6,7]=>1001000=>[1,3,4]
[6,1,2,5,3,8,4,7]=>1001010=>[1,3,2,2]
[8,1,2,6,3,7,4,5]=>1001010=>[1,3,2,2]
[4,1,2,8,7,3,5,6]=>1001100=>[1,3,1,3]
[4,1,2,7,6,3,8,5]=>1001101=>[1,3,1,2,1]
[8,1,2,5,6,3,4,7]=>1000100=>[1,4,3]
[8,1,2,7,6,3,4,5]=>1001100=>[1,3,1,3]
[7,1,2,5,6,3,8,4]=>1000101=>[1,4,2,1]
[4,1,2,5,8,7,3,6]=>1000110=>[1,4,1,2]
[8,1,2,5,6,7,3,4]=>1000010=>[1,5,2]
[3,1,7,2,6,4,8,5]=>1010101=>[1,2,2,2,1]
[3,1,5,2,8,7,4,6]=>1010110=>[1,2,2,1,2]
[3,1,8,2,6,7,4,5]=>1010010=>[1,2,3,2]
[8,1,4,2,3,5,6,7]=>1010000=>[1,2,5]
[7,1,4,2,3,5,8,6]=>1010001=>[1,2,4,1]
[6,1,4,2,3,8,5,7]=>1010010=>[1,2,3,2]
[7,1,5,2,3,4,8,6]=>1010001=>[1,2,4,1]
[6,1,5,2,3,8,4,7]=>1010010=>[1,2,3,2]
[6,1,8,2,3,7,4,5]=>1010010=>[1,2,3,2]
[6,1,5,2,3,7,8,4]=>1010001=>[1,2,4,1]
[5,1,4,2,8,3,6,7]=>1010100=>[1,2,2,3]
[5,1,4,2,7,3,8,6]=>1010101=>[1,2,2,2,1]
[8,1,4,2,6,3,5,7]=>1010100=>[1,2,2,3]
[7,1,4,2,6,3,8,5]=>1010101=>[1,2,2,2,1]
[8,1,5,2,6,3,4,7]=>1010100=>[1,2,2,3]
[8,1,5,2,7,3,4,6]=>1010100=>[1,2,2,3]
[7,1,8,2,6,3,4,5]=>1010100=>[1,2,2,3]
[7,1,5,2,6,3,8,4]=>1010101=>[1,2,2,2,1]
[5,1,4,2,8,7,3,6]=>1010110=>[1,2,2,1,2]
[8,1,4,2,6,7,3,5]=>1010010=>[1,2,3,2]
[8,1,5,2,6,7,3,4]=>1010010=>[1,2,3,2]
[5,1,4,2,6,7,8,3]=>1010001=>[1,2,4,1]
[3,1,8,6,2,4,5,7]=>1011000=>[1,2,1,4]
[3,1,6,5,2,8,4,7]=>1011010=>[1,2,1,2,2]
[3,1,8,5,2,7,4,6]=>1011010=>[1,2,1,2,2]
[3,1,8,6,2,7,4,5]=>1011010=>[1,2,1,2,2]
[8,1,4,5,2,3,6,7]=>1001000=>[1,3,4]
[7,1,8,5,2,3,4,6]=>1011000=>[1,2,1,4]
[7,1,8,6,2,3,4,5]=>1011000=>[1,2,1,4]
[7,1,6,5,2,3,8,4]=>1011001=>[1,2,1,3,1]
[3,1,4,8,6,2,5,7]=>1001100=>[1,3,1,3]
[3,1,8,5,7,2,4,6]=>1010100=>[1,2,2,3]
[3,1,7,5,6,2,8,4]=>1010101=>[1,2,2,2,1]
[8,1,4,5,7,2,3,6]=>1000100=>[1,4,3]
[8,1,4,7,6,2,3,5]=>1001100=>[1,3,1,3]
[3,1,4,5,8,7,2,6]=>1000110=>[1,4,1,2]
[3,1,8,5,6,7,2,4]=>1010010=>[1,2,3,2]
[8,1,4,5,6,7,2,3]=>1000010=>[1,5,2]
[2,8,1,3,7,4,5,6]=>0100100=>[2,3,3]
[2,8,1,3,6,7,4,5]=>0100010=>[2,4,2]
[2,6,1,5,3,8,4,7]=>0101010=>[2,2,2,2]
[2,6,1,5,3,7,8,4]=>0101001=>[2,2,3,1]
[2,4,1,8,6,3,5,7]=>0101100=>[2,2,1,3]
[2,8,1,5,7,3,4,6]=>0100100=>[2,3,3]
[2,8,1,7,6,3,4,5]=>0101100=>[2,2,1,3]
[2,4,1,5,8,7,3,6]=>0100110=>[2,3,1,2]
[7,3,1,2,4,5,8,6]=>1100001=>[1,1,5,1]
[6,3,1,2,4,8,5,7]=>1100010=>[1,1,4,2]
[6,3,1,2,4,7,8,5]=>1100001=>[1,1,5,1]
[5,3,1,2,8,4,6,7]=>1100100=>[1,1,3,3]
[8,3,1,2,6,4,5,7]=>1100100=>[1,1,3,3]
[8,3,1,2,7,4,5,6]=>1100100=>[1,1,3,3]
[7,3,1,2,6,4,8,5]=>1100101=>[1,1,3,2,1]
[5,3,1,2,8,7,4,6]=>1100110=>[1,1,3,1,2]
[5,3,1,2,6,7,8,4]=>1100001=>[1,1,5,1]
[8,4,1,2,3,7,5,6]=>1100010=>[1,1,4,2]
[7,6,1,2,3,4,8,5]=>1100001=>[1,1,5,1]
[8,6,1,2,3,7,4,5]=>1100010=>[1,1,4,2]
[5,4,1,2,8,3,6,7]=>1100100=>[1,1,3,3]
[8,4,1,2,7,3,5,6]=>1100100=>[1,1,3,3]
[7,4,1,2,6,3,8,5]=>1100101=>[1,1,3,2,1]
[5,8,1,2,7,3,4,6]=>0100100=>[2,3,3]
[8,7,1,2,6,3,4,5]=>1100100=>[1,1,3,3]
[5,7,1,2,6,3,8,4]=>0100101=>[2,3,2,1]
[5,8,1,2,6,7,3,4]=>0100010=>[2,4,2]
[5,4,1,2,6,7,8,3]=>1100001=>[1,1,5,1]
[4,3,1,8,2,5,6,7]=>1101000=>[1,1,2,4]
[4,3,1,7,2,5,8,6]=>1101001=>[1,1,2,3,1]
[4,3,1,6,2,8,5,7]=>1101010=>[1,1,2,2,2]
[4,3,1,6,2,7,8,5]=>1101001=>[1,1,2,3,1]
[8,3,1,5,2,4,6,7]=>1101000=>[1,1,2,4]
[8,3,1,6,2,4,5,7]=>1101000=>[1,1,2,4]
[7,3,1,6,2,4,8,5]=>1101001=>[1,1,2,3,1]
[8,3,1,5,2,7,4,6]=>1101010=>[1,1,2,2,2]
[8,3,1,6,2,7,4,5]=>1101010=>[1,1,2,2,2]
[6,3,1,5,2,7,8,4]=>1101001=>[1,1,2,3,1]
[7,4,1,5,2,3,8,6]=>1101001=>[1,1,2,3,1]
[8,4,1,6,2,3,5,7]=>1101000=>[1,1,2,4]
[7,4,1,8,2,3,5,6]=>1101000=>[1,1,2,4]
[7,4,1,6,2,3,8,5]=>1101001=>[1,1,2,3,1]
[8,7,1,6,2,3,4,5]=>1101000=>[1,1,2,4]
[6,7,1,5,2,3,8,4]=>0101001=>[2,2,3,1]
[6,4,1,5,2,8,3,7]=>1101010=>[1,1,2,2,2]
[8,4,1,6,2,7,3,5]=>1101010=>[1,1,2,2,2]
[6,8,1,5,2,7,3,4]=>0101010=>[2,2,2,2]
[6,4,1,5,2,7,8,3]=>1101001=>[1,1,2,3,1]
[4,3,1,8,7,2,5,6]=>1101100=>[1,1,2,1,3]
[4,3,1,7,6,2,8,5]=>1101101=>[1,1,2,1,2,1]
[8,3,1,5,6,2,4,7]=>1100100=>[1,1,3,3]
[8,3,1,5,7,2,4,6]=>1100100=>[1,1,3,3]
[8,3,1,7,6,2,4,5]=>1101100=>[1,1,2,1,3]
[7,3,1,5,6,2,8,4]=>1100101=>[1,1,3,2,1]
[8,4,1,5,6,2,3,7]=>1100100=>[1,1,3,3]
[7,8,1,5,6,2,3,4]=>0100100=>[2,3,3]
[4,3,1,5,6,8,2,7]=>1100010=>[1,1,4,2]
[8,4,1,5,6,7,2,3]=>1100010=>[1,1,4,2]
[4,3,1,5,6,7,8,2]=>1100001=>[1,1,5,1]
[2,3,7,1,6,4,8,5]=>0010101=>[3,2,2,1]
[2,3,5,1,8,7,4,6]=>0010110=>[3,2,1,2]
[2,3,8,1,6,7,4,5]=>0010010=>[3,3,2]
[2,8,4,1,3,5,6,7]=>0110000=>[2,1,5]
[2,6,4,1,3,8,5,7]=>0110010=>[2,1,3,2]
[2,6,4,1,3,7,8,5]=>0110001=>[2,1,4,1]
[2,8,4,1,7,3,5,6]=>0110100=>[2,1,2,3]
[2,7,4,1,6,3,8,5]=>0110101=>[2,1,2,2,1]
[2,8,5,1,7,3,4,6]=>0110100=>[2,1,2,3]
[2,7,5,1,6,3,8,4]=>0110101=>[2,1,2,2,1]
[2,8,4,1,6,7,3,5]=>0110010=>[2,1,3,2]
[2,5,4,1,6,7,8,3]=>0110001=>[2,1,4,1]
[6,3,4,1,2,7,8,5]=>1010001=>[1,2,4,1]
[7,3,5,1,2,4,8,6]=>1010001=>[1,2,4,1]
[6,3,7,1,2,4,8,5]=>1010001=>[1,2,4,1]
[8,3,5,1,2,7,4,6]=>1010010=>[1,2,3,2]
[6,3,8,1,2,7,4,5]=>1010010=>[1,2,3,2]
[6,7,4,1,2,3,8,5]=>0110001=>[2,1,4,1]
[6,8,5,1,2,3,4,7]=>0110000=>[2,1,5]
[8,5,4,1,2,7,3,6]=>1110010=>[1,1,1,3,2]
[6,8,4,1,2,7,3,5]=>0110010=>[2,1,3,2]
[6,8,5,1,2,7,3,4]=>0110010=>[2,1,3,2]
[8,3,4,1,7,2,5,6]=>1010100=>[1,2,2,3]
[7,3,4,1,6,2,8,5]=>1010101=>[1,2,2,2,1]
[8,3,5,1,6,2,4,7]=>1010100=>[1,2,2,3]
[7,3,8,1,6,2,4,5]=>1010100=>[1,2,2,3]
[7,3,5,1,6,2,8,4]=>1010101=>[1,2,2,2,1]
[8,5,4,1,6,2,3,7]=>1110100=>[1,1,1,2,3]
[7,8,4,1,6,2,3,5]=>0110100=>[2,1,2,3]
[7,8,5,1,6,2,3,4]=>0110100=>[2,1,2,3]
[7,5,4,1,6,2,8,3]=>1110101=>[1,1,1,2,2,1]
[5,3,4,1,6,7,8,2]=>1010001=>[1,2,4,1]
[2,3,4,8,1,7,5,6]=>0001010=>[4,2,2]
[2,3,7,6,1,4,8,5]=>0011001=>[3,1,3,1]
[2,3,6,5,1,8,4,7]=>0011010=>[3,1,2,2]
[2,3,6,5,1,7,8,4]=>0011001=>[3,1,3,1]
[2,8,4,5,1,3,6,7]=>0101000=>[2,2,4]
[2,7,4,8,1,3,5,6]=>0101000=>[2,2,4]
[2,7,4,6,1,3,8,5]=>0101001=>[2,2,3,1]
[2,8,6,5,1,3,4,7]=>0111000=>[2,1,1,4]
[2,7,8,5,1,3,4,6]=>0011000=>[3,1,4]
[2,7,6,5,1,3,8,4]=>0111001=>[2,1,1,3,1]
[2,6,4,5,1,8,3,7]=>0101010=>[2,2,2,2]
[2,8,4,6,1,7,3,5]=>0101010=>[2,2,2,2]
[7,3,8,5,1,2,4,6]=>1011000=>[1,2,1,4]
[8,6,4,5,1,7,2,3]=>1101010=>[1,1,2,2,2]
[2,3,4,8,6,1,5,7]=>0001100=>[4,1,3]
[2,3,4,8,7,1,5,6]=>0001100=>[4,1,3]
[2,3,4,7,6,1,8,5]=>0001101=>[4,1,2,1]
[2,3,8,5,7,1,4,6]=>0010100=>[3,2,3]
[2,3,7,5,6,1,8,4]=>0010101=>[3,2,2,1]
[2,8,4,7,6,1,3,5]=>0101100=>[2,2,1,3]
[2,8,7,5,6,1,3,4]=>0110100=>[2,1,2,3]
[8,3,4,7,6,1,2,5]=>1001100=>[1,3,1,3]
[8,3,7,5,6,1,2,4]=>1010100=>[1,2,2,3]
[2,3,4,5,8,7,1,6]=>0000110=>[5,1,2]
[2,3,4,8,6,7,1,5]=>0001010=>[4,2,2]
[2,8,4,5,6,7,1,3]=>0100010=>[2,4,2]
[6,5,8,7,3,4,1,2]=>1011010=>[1,2,1,2,2]
[4,6,7,3,8,5,1,2]=>0010110=>[3,2,1,2]
[3,6,7,4,5,8,1,2]=>0010010=>[3,3,2]
[2,6,7,4,5,1,8,3]=>0010101=>[3,2,2,1]
[1,6,7,4,5,2,3,8]=>0010100=>[3,2,3]
[1,5,4,7,6,2,3,8]=>0101100=>[2,2,1,3]
[2,5,4,7,6,1,8,3]=>0101101=>[2,2,1,2,1]
[3,5,4,7,6,8,1,2]=>0101010=>[2,2,2,2]
[4,5,3,7,8,6,1,2]=>0100110=>[2,3,1,2]
[5,4,3,8,7,6,1,2]=>1101110=>[1,1,2,1,1,2]
[6,4,8,3,7,5,1,2]=>1010110=>[1,2,2,1,2]
[6,3,8,4,5,7,1,2]=>1010010=>[1,2,3,2]
[5,3,4,8,6,7,1,2]=>1001010=>[1,3,2,2]
[4,3,5,6,8,7,1,2]=>1000110=>[1,4,1,2]
[3,2,5,6,1,8,7,4]=>1001011=>[1,3,2,1,1]
[4,2,5,6,8,1,7,3]=>1000101=>[1,4,2,1]
[5,2,4,8,6,1,7,3]=>1001101=>[1,3,1,2,1]
[6,2,8,4,5,1,7,3]=>1010101=>[1,2,2,2,1]
[7,8,2,4,5,1,6,3]=>0100101=>[2,3,2,1]
[7,8,1,4,5,2,3,6]=>0100100=>[2,3,3]
[6,1,8,4,5,2,3,7]=>1010100=>[1,2,2,3]
[5,1,4,8,6,2,3,7]=>1001100=>[1,3,1,3]
[4,1,3,2,8,6,5,7]=>1010110=>[1,2,2,1,2]
[5,1,3,8,2,6,4,7]=>1001010=>[1,3,2,2]
[6,1,8,3,2,5,4,7]=>1011010=>[1,2,1,2,2]
[7,8,1,3,2,5,4,6]=>0101010=>[2,2,2,2]
[7,8,2,3,1,5,6,4]=>0101001=>[2,2,3,1]
[6,2,8,3,1,5,7,4]=>1011001=>[1,2,1,3,1]
[5,2,3,8,1,6,7,4]=>1001001=>[1,3,3,1]
[6,3,8,2,1,7,5,4]=>1011011=>[1,2,1,2,1,1]
[7,8,3,2,1,6,5,4]=>0111011=>[2,1,1,2,1,1]
[7,8,4,2,6,1,5,3]=>0110101=>[2,1,2,2,1]
[5,4,2,8,7,1,6,3]=>1101101=>[1,1,2,1,2,1]
[4,5,2,7,8,1,6,3]=>0100101=>[2,3,2,1]
[3,5,2,7,1,8,6,4]=>0101011=>[2,2,2,1,1]
[2,5,3,7,1,6,8,4]=>0101001=>[2,2,3,1]
[1,5,3,7,2,6,4,8]=>0101010=>[2,2,2,2]
[1,6,7,3,2,5,4,8]=>0011010=>[3,1,2,2]
[2,6,7,3,1,5,8,4]=>0011001=>[3,1,3,1]
[3,6,7,2,1,8,5,4]=>0011011=>[3,1,2,1,1]
[4,6,7,2,8,1,5,3]=>0010101=>[3,2,2,1]
[5,6,7,8,2,1,4,3]=>0001101=>[4,1,2,1]
[7,8,5,6,2,1,4,3]=>0101101=>[2,2,1,2,1]
[6,5,8,7,1,2,3,4]=>1011000=>[1,2,1,4]
[5,4,1,8,7,2,3,6]=>1101100=>[1,1,2,1,3]
[6,4,8,1,7,2,3,5]=>1010100=>[1,2,2,3]
[7,8,3,1,2,6,4,5]=>0110010=>[2,1,3,2]
[5,3,1,8,2,7,4,6]=>1101010=>[1,1,2,2,2]
[4,3,1,2,8,7,5,6]=>1100110=>[1,1,3,1,2]
[4,2,1,3,8,5,7,6]=>1100101=>[1,1,3,2,1]
[5,2,1,8,3,4,7,6]=>1101001=>[1,1,2,3,1]
[6,2,8,1,3,4,7,5]=>1010001=>[1,2,4,1]
[7,8,2,1,3,4,6,5]=>0110001=>[2,1,4,1]
[4,5,2,3,7,6,1,8]=>0100110=>[2,3,1,2]
[6,4,3,7,2,5,1,8]=>1101010=>[1,1,2,2,2]
[8,4,3,6,5,1,2,7]=>1101100=>[1,1,2,1,3]
[1,5,6,3,4,8,7,2]=>0010011=>[3,3,1,1]
[4,6,2,7,3,5,1,8]=>0101010=>[2,2,2,2]
[3,2,6,7,4,5,1,8]=>1001010=>[1,3,2,2]
[8,7,5,4,1,3,2,6]=>1111010=>[1,1,1,1,2,2]
[5,8,6,2,4,1,3,7]=>0110100=>[2,1,2,3]
[4,8,2,6,5,1,3,7]=>0101100=>[2,2,1,3]
[4,1,2,6,5,8,7,3]=>1001011=>[1,3,2,1,1]
[5,1,6,2,4,8,7,3]=>1010011=>[1,2,3,1,1]
[6,1,5,4,2,8,7,3]=>1011011=>[1,2,1,2,1,1]
[7,1,5,4,8,2,6,3]=>1010101=>[1,2,2,2,1]
[8,1,5,4,7,6,2,3]=>1010110=>[1,2,2,1,2]
[1,8,6,7,4,5,3,2]=>0101011=>[2,2,2,1,1]
[8,1,6,7,4,5,2,3]=>1001010=>[1,3,2,2]
[6,1,7,8,2,4,5,3]=>1001001=>[1,3,3,1]
[5,1,7,2,8,4,6,3]=>1010101=>[1,2,2,2,1]
[4,1,2,7,8,5,6,3]=>1000101=>[1,4,2,1]
[3,2,1,7,8,5,6,4]=>1100101=>[1,1,3,2,1]
[3,2,8,7,1,5,4,6]=>1011010=>[1,2,1,2,2]
[4,8,2,7,1,5,3,6]=>0101010=>[2,2,2,2]
[5,8,7,2,1,4,3,6]=>0111010=>[2,1,1,2,2]
[6,8,7,1,2,4,3,5]=>0110010=>[2,1,3,2]
[7,8,6,1,4,2,3,5]=>0110100=>[2,1,2,3]
[8,7,6,1,4,3,2,5]=>1110110=>[1,1,1,2,1,2]
[1,6,7,8,3,4,5,2]=>0001001=>[4,3,1]
[8,6,7,1,3,4,2,5]=>1010010=>[1,2,3,2]
[7,6,8,1,3,2,4,5]=>1010100=>[1,2,2,3]
[5,7,8,2,1,3,4,6]=>0011000=>[3,1,4]
[4,7,2,8,1,3,5,6]=>0101000=>[2,2,4]
[3,2,6,8,4,1,5,7]=>1001100=>[1,3,1,3]
[4,6,2,8,3,1,5,7]=>0101100=>[2,2,1,3]
[5,6,8,2,3,1,4,7]=>0010100=>[3,2,3]
[7,5,8,3,1,2,4,6]=>1011000=>[1,2,1,4]
[8,5,7,3,1,4,2,6]=>1011010=>[1,2,1,2,2]
[1,5,7,3,8,4,6,2]=>0010101=>[3,2,2,1]
[1,4,3,7,8,5,6,2]=>0100101=>[2,3,2,1]
[6,4,3,8,2,1,5,7]=>1101100=>[1,1,2,1,3]
[4,5,2,3,8,1,6,7]=>0100100=>[2,3,3]
[3,2,5,4,8,1,6,7]=>1010100=>[1,2,2,3]
[4,5,2,3,1,8,7,6]=>0101011=>[2,2,2,1,1]
[6,4,3,1,2,8,7,5]=>1110011=>[1,1,1,3,1,1]
[7,4,3,1,8,2,6,5]=>1110101=>[1,1,1,2,2,1]
[1,5,8,3,7,6,4,2]=>0010111=>[3,2,1,1,1]
[7,5,1,3,8,2,6,4]=>1100101=>[1,1,3,2,1]
[5,6,1,2,3,8,7,4]=>0100011=>[2,4,1,1]
[4,6,2,1,3,8,7,5]=>0110011=>[2,1,3,1,1]
[3,2,6,1,4,8,7,5]=>1010011=>[1,2,3,1,1]
[3,2,7,1,8,4,6,5]=>1010101=>[1,2,2,2,1]
[5,7,1,2,8,3,6,4]=>0100101=>[2,3,2,1]
[6,7,1,8,2,3,5,4]=>0101001=>[2,2,3,1]
[7,6,1,8,3,2,5,4]=>1101101=>[1,1,2,1,2,1]
[8,7,1,6,5,3,2,4]=>1101110=>[1,1,2,1,1,2]
[7,8,1,6,5,2,3,4]=>0101100=>[2,2,1,3]
[6,8,1,7,2,5,3,4]=>0101010=>[2,2,2,2]
[5,8,1,2,7,6,3,4]=>0100110=>[2,3,1,2]
[4,8,2,1,7,6,3,5]=>0110110=>[2,1,2,1,2]
[3,2,8,1,7,6,4,5]=>1010110=>[1,2,2,1,2]
[4,1,2,8,7,6,5,3]=>1001111=>[1,3,1,1,1,1]
[5,1,8,2,7,6,4,3]=>1010111=>[1,2,2,1,1,1]
[6,1,8,7,2,5,4,3]=>1011011=>[1,2,1,2,1,1]
[8,1,7,6,5,4,2,3]=>1011110=>[1,2,1,1,1,2]
[3,2,5,1,6,4,8,7]=>1010101=>[1,2,2,2,1]
[3,2,5,4,7,1,8,6]=>1010101=>[1,2,2,2,1]
[4,2,5,3,7,6,8,1]=>1010101=>[1,2,2,2,1]
[4,2,5,3,6,1,8,7]=>1010101=>[1,2,2,2,1]
[4,1,5,3,6,2,8,7]=>1010101=>[1,2,2,2,1]
[4,3,5,2,7,1,8,6]=>1010101=>[1,2,2,2,1]
[4,3,5,1,7,2,8,6]=>1010101=>[1,2,2,2,1]
[4,1,5,3,7,2,8,6]=>1010101=>[1,2,2,2,1]
[2,1,5,4,7,3,8,6]=>1010101=>[1,2,2,2,1]
[4,3,6,5,7,1,8,2]=>1010101=>[1,2,2,2,1]
[5,3,6,4,7,1,8,2]=>1010101=>[1,2,2,2,1]
[4,1,6,3,7,5,8,2]=>1010101=>[1,2,2,2,1]
[2,1,6,4,7,5,8,3]=>1010101=>[1,2,2,2,1]
[2,1,6,4,7,3,8,5]=>1010101=>[1,2,2,2,1]
[3,1,6,4,7,2,8,5]=>1010101=>[1,2,2,2,1]
[4,1,6,3,7,2,8,5]=>1010101=>[1,2,2,2,1]
[5,3,6,2,7,4,8,1]=>1010101=>[1,2,2,2,1]
[5,2,6,3,7,4,8,1]=>1010101=>[1,2,2,2,1]
[5,2,6,3,7,1,8,4]=>1010101=>[1,2,2,2,1]
[5,2,6,1,7,3,8,4]=>1010101=>[1,2,2,2,1]
[4,2,6,1,7,3,8,5]=>1010101=>[1,2,2,2,1]
[4,2,6,3,7,1,8,5]=>1010101=>[1,2,2,2,1]
[4,2,6,3,7,5,8,1]=>1010101=>[1,2,2,2,1]
[3,2,6,4,7,5,8,1]=>1010101=>[1,2,2,2,1]
[3,2,6,4,7,1,8,5]=>1010101=>[1,2,2,2,1]
[3,2,6,1,7,4,8,5]=>1010101=>[1,2,2,2,1]
[3,2,5,1,7,4,8,6]=>1010101=>[1,2,2,2,1]
[3,2,4,1,7,5,8,6]=>1010101=>[1,2,2,2,1]
[3,1,4,2,7,6,8,5]=>1010101=>[1,2,2,2,1]
[3,2,5,1,7,6,8,4]=>1010101=>[1,2,2,2,1]
[3,2,6,1,7,5,8,4]=>1010101=>[1,2,2,2,1]
[4,2,6,1,7,5,8,3]=>1010101=>[1,2,2,2,1]
[3,1,5,2,7,6,8,4]=>1010101=>[1,2,2,2,1]
[2,1,5,3,7,6,8,4]=>1010101=>[1,2,2,2,1]
[2,1,6,3,7,5,8,4]=>1010101=>[1,2,2,2,1]
[3,1,6,2,7,5,8,4]=>1010101=>[1,2,2,2,1]
[4,1,6,2,7,5,8,3]=>1010101=>[1,2,2,2,1]
[5,1,6,2,7,4,8,3]=>1010101=>[1,2,2,2,1]
[5,2,6,1,7,4,8,3]=>1010101=>[1,2,2,2,1]
[5,4,6,2,7,1,8,3]=>1010101=>[1,2,2,2,1]
[5,1,6,4,7,2,8,3]=>1010101=>[1,2,2,2,1]
[3,1,6,5,7,2,8,4]=>1010101=>[1,2,2,2,1]
[3,1,6,5,7,4,8,2]=>1010101=>[1,2,2,2,1]
[4,1,6,5,7,3,8,2]=>1010101=>[1,2,2,2,1]
[5,1,6,4,7,3,8,2]=>1010101=>[1,2,2,2,1]
[8,6,1,3,4,2,5,7]=>1100100=>[1,1,3,3]
[8,3,5,2,1,6,4,7]=>1011010=>[1,2,1,2,2]
[8,6,3,5,2,4,1,7]=>1101010=>[1,1,2,2,2]
[8,3,7,5,2,4,6,1]=>1011001=>[1,2,1,3,1]
[8,2,4,5,7,3,6,1]=>1000101=>[1,4,2,1]
[2,4,5,7,3,1,8,6]=>0001101=>[4,1,2,1]
[8,2,4,6,5,3,1,7]=>1001110=>[1,3,1,1,2]
[8,1,2,4,5,6,3,7]=>1000010=>[1,5,2]
[8,2,5,1,3,6,4,7]=>1010010=>[1,2,3,2]
[8,6,1,4,5,3,2,7]=>1100110=>[1,1,3,1,2]
[8,1,5,6,4,3,2,7]=>1001110=>[1,3,1,1,2]
[8,5,7,4,3,2,6,1]=>1011101=>[1,2,1,1,2,1]
[8,5,7,4,2,1,6,3]=>1011101=>[1,2,1,1,2,1]
[4,6,3,8,7,1,5,2]=>0101101=>[2,2,1,2,1]
[1,7,4,8,6,3,5,2]=>0101101=>[2,2,1,2,1]
[8,4,7,6,3,5,2,1]=>1011011=>[1,2,1,2,1,1]
[3,1,5,8,6,7,4,2]=>1001011=>[1,3,2,1,1]
[4,8,1,6,7,3,5,2]=>0100101=>[2,3,2,1]
[3,6,4,1,8,7,5,2]=>0110111=>[2,1,2,1,1,1]
[8,2,6,1,4,7,5,3]=>1010011=>[1,2,3,1,1]
[2,7,6,8,1,4,3,5]=>0101010=>[2,2,2,2]
[1,7,3,5,6,8,2,4]=>0100010=>[2,4,2]
[3,7,6,5,8,2,1,4]=>0110110=>[2,1,2,1,2]
[3,6,8,5,7,2,4,1]=>0010101=>[3,2,2,1]
[2,3,5,7,6,8,1,4]=>0001010=>[4,2,2]
[2,1,6,5,7,8,3,4]=>1010010=>[1,2,3,2]
[5,2,7,1,3,8,4,6]=>1010010=>[1,2,3,2]
[5,3,1,7,8,2,4,6]=>1100100=>[1,1,3,3]
[3,7,2,6,4,8,1,5]=>0101010=>[2,2,2,2]
[3,2,6,1,4,7,8,5]=>1010001=>[1,2,4,1]
[5,3,7,2,1,8,4,6]=>1011010=>[1,2,1,2,2]
[4,7,3,2,1,5,8,6]=>0111001=>[2,1,1,3,1]
[1,7,3,4,2,5,8,6]=>0101001=>[2,2,3,1]
[4,7,2,1,3,5,8,6]=>0110001=>[2,1,4,1]
[8,7,6,1,3,4,2,5]=>1110010=>[1,1,1,3,2]
[8,5,7,3,2,1,6,4]=>1011101=>[1,2,1,1,2,1]
[3,7,8,6,2,1,5,4]=>0011101=>[3,1,1,2,1]
[8,7,6,3,5,2,4,1]=>1110101=>[1,1,1,2,2,1]
[2,7,4,8,1,6,5,3]=>0101011=>[2,2,2,1,1]
[4,6,8,2,1,7,5,3]=>0011011=>[3,1,2,1,1]
[8,5,3,7,1,6,2,4]=>1101010=>[1,1,2,2,2]
[8,5,7,2,1,3,6,4]=>1011001=>[1,2,1,3,1]
[4,6,1,8,7,2,5,3]=>0101101=>[2,2,1,2,1]
[8,1,2,5,6,7,4,3]=>1000011=>[1,5,1,1]
[8,2,6,5,7,4,1,3]=>1010110=>[1,2,2,1,2]
[2,1,7,8,5,6,4,3]=>1001011=>[1,3,2,1,1]
[2,7,6,8,5,4,1,3]=>0101110=>[2,2,1,1,2]
[3,7,8,1,6,5,2,4]=>0010110=>[3,2,1,2]
[8,7,6,3,5,1,4,2]=>1110101=>[1,1,1,2,2,1]
[8,4,7,6,5,1,3,2]=>1011101=>[1,2,1,1,2,1]
[8,7,1,5,6,4,3,2]=>1100111=>[1,1,3,1,1,1]
[8,1,6,7,5,4,3,2]=>1001111=>[1,3,1,1,1,1]
[3,2,5,1,6,8,4,7]=>1010010=>[1,2,3,2]
[3,6,2,5,4,8,1,7]=>0101010=>[2,2,2,2]
[3,5,2,4,7,1,8,6]=>0100101=>[2,3,2,1]
[3,5,8,2,4,7,6,1]=>0010011=>[3,3,1,1]
[4,2,6,5,3,8,1,7]=>1011010=>[1,2,1,2,2]
[5,3,1,6,8,2,4,7]=>1100100=>[1,1,3,3]
[5,6,2,8,1,3,4,7]=>0101000=>[2,2,4]
[5,4,3,2,7,1,8,6]=>1110101=>[1,1,1,2,2,1]
[5,4,3,8,2,7,6,1]=>1101011=>[1,1,2,2,1,1]
[4,3,7,6,2,1,8,5]=>1011101=>[1,2,1,1,2,1]
[6,4,3,1,7,2,8,5]=>1110101=>[1,1,1,2,2,1]
[1,4,7,5,8,3,2,6]=>0010110=>[3,2,1,2]
[7,2,5,8,4,1,3,6]=>1001100=>[1,3,1,3]
[2,8,5,7,4,6,1,3]=>0101010=>[2,2,2,2]
[3,5,8,7,1,4,6,2]=>0011001=>[3,1,3,1]
[4,3,7,1,8,6,5,2]=>1010111=>[1,2,2,1,1,1]
[4,8,3,7,6,5,2,1]=>0101111=>[2,2,1,1,1,1]
[7,5,3,1,8,6,4,2]=>1110111=>[1,1,1,2,1,1,1]
[1,5,8,6,3,7,4,2]=>0011011=>[3,1,2,1,1]
[6,2,8,7,4,5,1,3]=>1011010=>[1,2,1,2,2]
[6,1,7,5,3,2,8,4]=>1011101=>[1,2,1,1,2,1]
[5,2,6,3,8,7,4,1]=>1010111=>[1,2,2,1,1,1]
[6,5,2,1,7,3,8,4]=>1110101=>[1,1,1,2,2,1]
[6,1,7,4,2,8,3,5]=>1011010=>[1,2,1,2,2]
[6,7,2,1,8,3,4,5]=>0110100=>[2,1,2,3]
[7,5,8,2,1,3,4,6]=>1011000=>[1,2,1,4]
[5,7,3,1,8,2,4,6]=>0110100=>[2,1,2,3]
[4,7,1,5,2,8,3,6]=>0101010=>[2,2,2,2]
[2,4,8,6,3,7,5,1]=>0011011=>[3,1,2,1,1]
[3,8,6,2,4,7,5,1]=>0110011=>[2,1,3,1,1]
[7,3,6,2,4,1,8,5]=>1010101=>[1,2,2,2,1]
[3,5,2,7,1,8,4,6]=>0101010=>[2,2,2,2]
[4,3,7,8,2,1,5,6]=>1001100=>[1,3,1,3]
[8,3,7,1,4,6,2,5]=>1010010=>[1,2,3,2]
[3,8,2,5,7,1,6,4]=>0100101=>[2,3,2,1]
[7,8,3,6,2,1,5,4]=>0101101=>[2,2,1,2,1]
[8,7,3,6,2,5,4,1]=>1101011=>[1,1,2,2,1,1]
[4,2,6,8,1,7,5,3]=>1001011=>[1,3,2,1,1]
[5,4,8,2,7,1,6,3]=>1010101=>[1,2,2,2,1]
[5,8,3,7,1,6,2,4]=>0101010=>[2,2,2,2]
[5,8,7,2,6,1,3,4]=>0110100=>[2,1,2,3]
[6,4,8,1,7,2,5,3]=>1010101=>[1,2,2,2,1]
[5,1,6,8,2,7,4,3]=>1001011=>[1,3,2,1,1]
[6,5,2,8,1,7,4,3]=>1101011=>[1,1,2,2,1,1]
[5,2,7,1,8,6,4,3]=>1010111=>[1,2,2,1,1,1]
[5,8,2,7,6,4,3,1]=>0101111=>[2,2,1,1,1,1]
[6,2,8,7,5,4,3,1]=>1011111=>[1,2,1,1,1,1,1]
[6,1,7,2,8,5,4,3]=>1010111=>[1,2,2,1,1,1]
[4,7,1,8,6,2,5,3]=>0101101=>[2,2,1,2,1]
[7,8,3,1,6,5,2,4]=>0110110=>[2,1,2,1,2]
[8,7,4,6,1,5,3,2]=>1101011=>[1,1,2,2,1,1]
[8,5,7,1,6,4,3,2]=>1010111=>[1,2,2,1,1,1]
[6,8,1,7,5,4,3,2]=>0101111=>[2,2,1,1,1,1]
[7,1,8,6,5,4,3,2]=>1011111=>[1,2,1,1,1,1,1]
[4,1,3,2,6,5,8,7]=>1010101=>[1,2,2,2,1]
[6,3,5,1,2,4,8,7]=>1010001=>[1,2,4,1]
[4,3,5,6,1,2,8,7]=>1001001=>[1,3,3,1]
[8,3,7,5,2,1,4,6]=>1011100=>[1,2,1,1,3]
[6,3,7,5,1,8,4,2]=>1011011=>[1,2,1,2,1,1]
[6,5,2,7,1,8,3,4]=>1101010=>[1,1,2,2,2]
[3,5,2,6,4,1,8,7]=>0101101=>[2,2,1,2,1]
[6,1,2,4,5,3,8,7]=>1000101=>[1,4,2,1]
[5,6,3,2,1,4,8,7]=>0111001=>[2,1,1,3,1]
[2,1,6,3,5,4,8,7]=>1010101=>[1,2,2,2,1]
[6,4,3,5,1,2,8,7]=>1101001=>[1,1,2,3,1]
[5,3,1,4,6,2,8,7]=>1100101=>[1,1,3,2,1]
[5,7,4,6,2,8,3,1]=>0101011=>[2,2,2,1,1]
[3,4,7,8,5,2,1,6]=>0001110=>[4,1,1,2]
[2,1,8,5,7,3,4,6]=>1010100=>[1,2,2,3]
[8,6,3,5,1,7,4,2]=>1101011=>[1,1,2,2,1,1]
[3,4,8,6,5,7,1,2]=>0011010=>[3,1,2,2]
[5,1,4,6,8,2,7,3]=>1000101=>[1,4,2,1]
[2,5,4,6,7,1,8,3]=>0100101=>[2,3,2,1]
[2,4,6,3,7,5,8,1]=>0010101=>[3,2,2,1]
[4,1,6,3,8,5,7,2]=>1010101=>[1,2,2,2,1]
[3,7,4,2,8,6,5,1]=>0110111=>[2,1,2,1,1,1]
[8,5,3,7,4,1,6,2]=>1101101=>[1,1,2,1,2,1]
[2,1,5,7,4,8,6,3]=>1001011=>[1,3,2,1,1]
[3,1,8,2,7,6,5,4]=>1010111=>[1,2,2,1,1,1]
[2,3,8,1,6,7,5,4]=>0010011=>[3,3,1,1]
[4,3,7,2,6,8,5,1]=>1010011=>[1,2,3,1,1]
[2,8,1,3,6,5,7,4]=>0100101=>[2,3,2,1]
[8,1,2,3,5,6,7,4]=>1000001=>[1,6,1]
[7,8,2,4,3,6,1,5]=>0101010=>[2,2,2,2]
[6,8,3,2,4,1,7,5]=>0110101=>[2,1,2,2,1]
[2,1,8,3,4,6,7,5]=>1010001=>[1,2,4,1]
[2,1,7,8,5,4,3,6]=>1001110=>[1,3,1,1,2]
[5,7,3,8,1,4,2,6]=>0101010=>[2,2,2,2]
[7,1,8,4,5,3,2,6]=>1010110=>[1,2,2,1,2]
[8,7,1,6,3,4,2,5]=>1101010=>[1,1,2,2,2]
[5,3,8,7,4,2,6,1]=>1011101=>[1,2,1,1,2,1]
[8,3,6,1,4,2,7,5]=>1010101=>[1,2,2,2,1]
[7,3,5,8,2,4,1,6]=>1001010=>[1,3,2,2]
[2,3,4,1,8,5,7,6]=>0010101=>[3,2,2,1]
[4,1,3,2,8,5,7,6]=>1010101=>[1,2,2,2,1]
[2,1,4,3,8,5,7,6]=>1010101=>[1,2,2,2,1]
[4,1,3,2,6,7,8,5]=>1010001=>[1,2,4,1]
[8,3,5,6,2,7,1,4]=>1001010=>[1,3,2,2]
[5,3,6,1,8,7,2,4]=>1010110=>[1,2,2,1,2]
[5,6,2,8,7,4,1,3]=>0101110=>[2,2,1,1,2]
[7,8,5,6,1,4,2,3]=>0101010=>[2,2,2,2]
[8,1,6,4,5,7,2,3]=>1010010=>[1,2,3,2]
[5,8,3,6,1,7,2,4]=>0101010=>[2,2,2,2]
[2,1,8,6,5,7,3,4]=>1011010=>[1,2,1,2,2]
[2,1,7,5,3,6,8,4]=>1011001=>[1,2,1,3,1]
[7,1,4,2,5,6,8,3]=>1010001=>[1,2,4,1]
[2,7,4,1,6,5,8,3]=>0110101=>[2,1,2,2,1]
[7,3,5,4,6,1,8,2]=>1010101=>[1,2,2,2,1]
[6,3,4,1,5,7,8,2]=>1010001=>[1,2,4,1]
[3,1,4,5,6,8,7,2]=>1000011=>[1,5,1,1]
[4,5,2,6,3,1,8,7]=>0101101=>[2,2,1,2,1]
[6,5,2,1,4,3,8,7]=>1110101=>[1,1,1,2,2,1]
[6,5,2,7,4,8,3,1]=>1101011=>[1,1,2,2,1,1]
[8,5,2,7,4,1,6,3]=>1101101=>[1,1,2,1,2,1]
[8,3,7,5,2,1,6,4]=>1011101=>[1,2,1,1,2,1]
[6,3,7,5,2,8,4,1]=>1011011=>[1,2,1,2,1,1]
[6,3,1,5,2,4,8,7]=>1101001=>[1,1,2,3,1]
[3,1,6,5,4,2,8,7]=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,1,2,8,7]=>1101001=>[1,1,2,3,1]
[5,6,3,2,4,1,8,7]=>0110101=>[2,1,2,2,1]
[6,7,2,3,4,8,5,1]=>0100011=>[2,4,1,1]
[8,7,2,3,4,1,6,5]=>1100101=>[1,1,3,2,1]
[5,1,7,3,8,4,6,2]=>1010101=>[1,2,2,2,1]
[2,5,7,3,8,6,4,1]=>0010111=>[3,2,1,1,1]
[3,6,7,4,1,8,5,2]=>0011011=>[3,1,2,1,1]
[5,6,3,7,4,8,1,2]=>0101010=>[2,2,2,2]
[2,1,6,7,4,8,5,3]=>1001011=>[1,3,2,1,1]
[2,1,8,7,4,3,6,5]=>1011101=>[1,2,1,1,2,1]
[5,8,3,7,4,2,6,1]=>0101101=>[2,2,1,2,1]
[7,8,1,3,5,2,6,4]=>0100101=>[2,3,2,1]
[5,8,7,3,2,6,1,4]=>0111010=>[2,1,1,2,2]
[2,8,6,3,1,5,7,4]=>0111001=>[2,1,1,3,1]
[8,1,6,3,2,5,4,7]=>1011010=>[1,2,1,2,2]
[2,8,4,1,6,3,7,5]=>0110101=>[2,1,2,2,1]
[4,8,1,2,7,6,3,5]=>0100110=>[2,3,1,2]
[6,8,3,5,2,7,4,1]=>0101011=>[2,2,2,1,1]
[2,1,8,5,3,7,4,6]=>1011010=>[1,2,1,2,2]
[6,5,3,2,8,7,1,4]=>1110110=>[1,1,1,2,1,2]
[2,4,1,8,7,6,5,3]=>0101111=>[2,2,1,1,1,1]
[4,1,2,8,7,5,6,3]=>1001101=>[1,3,1,2,1]
[8,4,2,1,7,5,3,6]=>1110110=>[1,1,1,2,1,2]
[4,3,1,8,6,7,5,2]=>1101011=>[1,1,2,2,1,1]
[3,1,4,8,6,5,7,2]=>1001101=>[1,3,1,2,1]
[7,3,5,4,8,6,1,2]=>1010110=>[1,2,2,1,2]
[6,4,3,5,8,1,7,2]=>1100101=>[1,1,3,2,1]
[2,1,7,6,5,8,3,4]=>1011010=>[1,2,1,2,2]
[5,7,3,6,1,8,2,4]=>0101010=>[2,2,2,2]
[2,7,6,4,5,8,1,3]=>0110010=>[2,1,3,2]
[3,7,5,6,8,4,2,1]=>0100111=>[2,3,1,1,1]
[5,7,1,6,8,2,4,3]=>0100101=>[2,3,2,1]
[8,6,2,5,1,7,4,3]=>1101011=>[1,1,2,2,1,1]
[7,5,2,6,3,8,1,4]=>1101010=>[1,1,2,2,2]
[4,1,2,3,6,8,7,5]=>1000011=>[1,5,1,1]
[2,4,3,1,8,5,6,7]=>0110100=>[2,1,2,3]
[7,5,2,8,3,4,6,1]=>1101001=>[1,1,2,3,1]
[4,7,2,8,1,5,3,6]=>0101010=>[2,2,2,2]
[8,7,2,1,4,5,6,3]=>1110001=>[1,1,1,4,1]
[3,6,8,7,1,5,4,2]=>0011011=>[3,1,2,1,1]
[5,7,8,6,3,4,1,2]=>0011010=>[3,1,2,2]
[5,7,3,8,1,4,6,2]=>0101001=>[2,2,3,1]
[2,1,7,8,5,4,6,3]=>1001101=>[1,3,1,2,1]
[7,5,8,4,3,6,2,1]=>1011011=>[1,2,1,2,1,1]
[2,4,8,3,5,6,1,7]=>0010010=>[3,3,2]
[4,1,8,3,6,5,2,7]=>1010110=>[1,2,2,1,2]
[8,4,1,3,7,2,6,5]=>1100101=>[1,1,3,2,1]
[4,3,8,2,5,1,7,6]=>1010101=>[1,2,2,2,1]
[2,1,4,8,3,5,7,6]=>1001001=>[1,3,3,1]
[6,8,2,4,3,5,1,7]=>0101010=>[2,2,2,2]
[4,8,2,3,5,1,6,7]=>0100100=>[2,3,3]
[7,8,5,6,1,4,3,2]=>0101011=>[2,2,2,1,1]
[7,8,4,2,1,5,3,6]=>0111010=>[2,1,1,2,2]
[7,8,2,1,6,5,3,4]=>0110110=>[2,1,2,1,2]
[6,4,1,2,5,7,3,8]=>1100010=>[1,1,4,2]
[4,3,8,1,7,2,5,6]=>1010100=>[1,2,2,3]
[7,8,1,4,6,2,5,3]=>0100101=>[2,3,2,1]
[7,8,3,5,4,2,1,6]=>0101110=>[2,2,1,1,2]
[7,8,4,1,2,3,6,5]=>0110001=>[2,1,4,1]
[7,8,3,6,5,4,1,2]=>0101110=>[2,2,1,1,2]
[7,8,2,6,4,1,3,5]=>0101100=>[2,2,1,3]
[7,8,1,6,5,4,3,2]=>0101111=>[2,2,1,1,1,1]
[2,1,8,7,5,4,3,6]=>1011110=>[1,2,1,1,1,2]
[1,3,8,2,6,4,7,5]=>0010101=>[3,2,2,1]
[5,3,7,1,6,4,8,2]=>1010101=>[1,2,2,2,1]
[6,1,2,5,8,7,4,3]=>1000111=>[1,4,1,1,1]
[6,3,1,8,4,2,7,5]=>1101101=>[1,1,2,1,2,1]
[6,4,2,1,5,3,8,7]=>1110101=>[1,1,1,2,2,1]
[6,4,3,7,5,8,1,2]=>1101010=>[1,1,2,2,2]
[4,3,8,7,5,6,1,2]=>1011010=>[1,2,1,2,2]
[2,4,7,1,5,3,6,8]=>0010100=>[3,2,3]
[3,7,2,8,6,4,1,5]=>0101110=>[2,2,1,1,2]
[3,8,1,7,6,4,5,2]=>0101101=>[2,2,1,2,1]
[1,8,5,7,3,6,4,2]=>0101011=>[2,2,2,1,1]
[2,7,5,8,3,6,1,4]=>0101010=>[2,2,2,2]
[1,5,6,8,2,4,7,3]=>0001001=>[4,3,1]
[2,6,1,4,7,3,5,8]=>0100100=>[2,3,3]
[3,6,8,4,7,5,1,2]=>0010110=>[3,2,1,2]
[5,6,7,3,8,4,1,2]=>0010110=>[3,2,1,2]
[4,5,6,7,2,8,1,3]=>0001010=>[4,2,2]
[4,5,7,6,1,8,3,2]=>0011011=>[3,1,2,1,1]
[1,5,8,6,2,7,3,4]=>0011010=>[3,1,2,2]
[4,7,5,6,3,1,8,2]=>0101101=>[2,2,1,2,1]
[5,1,6,3,4,2,8,7]=>1010101=>[1,2,2,2,1]
[5,7,1,4,2,3,8,6]=>0101001=>[2,2,3,1]
[5,7,6,4,3,8,1,2]=>0111010=>[2,1,1,2,2]
[6,3,4,5,8,7,1,2]=>1000110=>[1,4,1,2]
[6,2,4,1,8,3,7,5]=>1010101=>[1,2,2,2,1]
[6,2,3,5,4,8,1,7]=>1001010=>[1,3,2,2]
[5,1,4,2,7,6,8,3]=>1010101=>[1,2,2,2,1]
[1,6,2,4,7,8,3,5]=>0100010=>[2,4,2]
[5,7,2,4,1,6,3,8]=>0101010=>[2,2,2,2]
[6,1,4,2,8,5,3,7]=>1010110=>[1,2,2,1,2]
[6,7,5,8,1,4,3,2]=>0101011=>[2,2,2,1,1]
[5,8,7,6,3,4,1,2]=>0111010=>[2,1,1,2,2]
[5,8,7,6,2,3,1,4]=>0111010=>[2,1,1,2,2]
[4,1,7,2,6,5,3,8]=>1010110=>[1,2,2,1,2]
[4,8,2,1,5,6,3,7]=>0110010=>[2,1,3,2]
[4,2,7,8,1,6,3,5]=>1001010=>[1,3,2,2]
[2,1,8,7,6,5,3,4]=>1011110=>[1,2,1,1,1,2]
[4,2,7,1,6,3,8,5]=>1010101=>[1,2,2,2,1]
[4,3,7,5,6,8,1,2]=>1010010=>[1,2,3,2]
[3,8,6,5,2,4,1,7]=>0111010=>[2,1,1,2,2]
[3,8,5,6,1,4,7,2]=>0101001=>[2,2,3,1]
[5,3,7,8,2,1,6,4]=>1001101=>[1,3,1,2,1]
[5,2,8,7,1,6,4,3]=>1011011=>[1,2,1,2,1,1]
[3,6,7,8,5,1,4,2]=>0001101=>[4,1,2,1]
[3,7,8,5,1,2,4,6]=>0011000=>[3,1,4]
[4,1,8,6,2,3,5,7]=>1011000=>[1,2,1,4]
[4,7,8,6,3,5,1,2]=>0011010=>[3,1,2,2]
[3,8,7,6,5,4,1,2]=>0111110=>[2,1,1,1,1,2]
[2,8,6,7,5,1,3,4]=>0101100=>[2,2,1,3]
[5,3,7,8,2,1,4,6]=>1001100=>[1,3,1,3]
[7,6,1,2,5,8,3,4]=>1100010=>[1,1,4,2]
[2,1,7,8,4,3,5,6]=>1001100=>[1,3,1,3]
[7,8,1,2,5,4,6,3]=>0100101=>[2,3,2,1]
[2,6,8,3,1,4,7,5]=>0011001=>[3,1,3,1]
[8,4,1,3,7,6,2,5]=>1100110=>[1,1,3,1,2]
[6,5,2,1,8,7,4,3]=>1110111=>[1,1,1,2,1,1,1]
[4,7,2,8,1,3,6,5]=>0101001=>[2,2,3,1]
[7,3,8,6,1,2,5,4]=>1011001=>[1,2,1,3,1]
[3,4,7,1,8,2,6,5]=>0010101=>[3,2,2,1]
[1,8,2,4,3,5,6,7]=>0101000=>[2,2,4]
[1,7,2,4,3,5,6,8]=>0101000=>[2,2,4]
[1,5,2,4,3,6,7,8]=>0101000=>[2,2,4]
[1,7,2,5,3,4,6,8]=>0101000=>[2,2,4]
[1,8,2,5,3,4,6,7]=>0101000=>[2,2,4]
[1,8,2,6,3,4,5,7]=>0101000=>[2,2,4]
[1,8,2,7,3,4,5,6]=>0101000=>[2,2,4]
[1,8,2,7,3,5,4,6]=>0101010=>[2,2,2,2]
[1,7,2,8,3,5,4,6]=>0101010=>[2,2,2,2]
[1,6,2,8,3,5,4,7]=>0101010=>[2,2,2,2]
[1,5,2,8,3,6,4,7]=>0101010=>[2,2,2,2]
[1,4,2,8,3,6,5,7]=>0101010=>[2,2,2,2]
[1,3,2,8,4,6,5,7]=>0101010=>[2,2,2,2]
[1,2,3,8,4,6,5,7]=>0001010=>[4,2,2]
[1,2,3,7,4,6,5,8]=>0001010=>[4,2,2]
[1,3,2,7,4,6,5,8]=>0101010=>[2,2,2,2]
[1,4,2,7,3,6,5,8]=>0101010=>[2,2,2,2]
[1,5,2,7,3,6,4,8]=>0101010=>[2,2,2,2]
[1,6,2,7,3,5,4,8]=>0101010=>[2,2,2,2]
[1,7,2,6,3,5,4,8]=>0101010=>[2,2,2,2]
[1,8,2,6,3,5,4,7]=>0101010=>[2,2,2,2]
[1,8,2,5,3,6,4,7]=>0101010=>[2,2,2,2]
[1,7,2,5,3,6,4,8]=>0101010=>[2,2,2,2]
[1,6,2,5,3,7,4,8]=>0101010=>[2,2,2,2]
[1,5,2,4,3,7,6,8]=>0101010=>[2,2,2,2]
[1,6,2,4,3,7,5,8]=>0101010=>[2,2,2,2]
[1,7,2,4,3,6,5,8]=>0101010=>[2,2,2,2]
[1,8,2,4,3,6,5,7]=>0101010=>[2,2,2,2]
[1,8,2,4,3,7,5,6]=>0101010=>[2,2,2,2]
[1,7,2,4,3,8,5,6]=>0101010=>[2,2,2,2]
[1,6,2,4,3,8,5,7]=>0101010=>[2,2,2,2]
[1,5,2,4,3,8,6,7]=>0101010=>[2,2,2,2]
[1,6,2,5,3,8,4,7]=>0101010=>[2,2,2,2]
[1,7,2,5,3,8,4,6]=>0101010=>[2,2,2,2]
[1,8,2,5,3,7,4,6]=>0101010=>[2,2,2,2]
[1,8,2,6,3,7,4,5]=>0101010=>[2,2,2,2]
[1,7,2,6,3,8,4,5]=>0101010=>[2,2,2,2]
[1,2,3,8,4,7,5,6]=>0001010=>[4,2,2]
[1,3,2,8,4,7,5,6]=>0101010=>[2,2,2,2]
[1,4,2,8,3,7,5,6]=>0101010=>[2,2,2,2]
[1,5,2,8,3,7,4,6]=>0101010=>[2,2,2,2]
[1,6,2,8,3,7,4,5]=>0101010=>[2,2,2,2]
[1,7,2,8,3,6,4,5]=>0101010=>[2,2,2,2]
[1,8,2,7,3,6,4,5]=>0101010=>[2,2,2,2]
[2,8,4,1,6,5,3,7]=>0110110=>[2,1,2,1,2]
[2,8,4,1,5,6,7,3]=>0110001=>[2,1,4,1]
[2,8,7,4,1,6,3,5]=>0111010=>[2,1,1,2,2]
[7,2,8,5,1,6,4,3]=>1011011=>[1,2,1,2,1,1]
[1,3,7,5,2,6,4,8]=>0011010=>[3,1,2,2]
[1,3,7,5,4,2,6,8]=>0011100=>[3,1,1,3]
[7,2,8,5,4,1,6,3]=>1011101=>[1,2,1,1,2,1]
[2,8,5,3,4,1,6,7]=>0110100=>[2,1,2,3]
[2,8,7,6,1,4,5,3]=>0111001=>[2,1,1,3,1]
[2,8,6,5,7,3,1,4]=>0110110=>[2,1,2,1,2]
[7,2,8,4,5,6,1,3]=>1010010=>[1,2,3,2]
[6,2,3,8,5,1,7,4]=>1001101=>[1,3,1,2,1]
[6,3,2,8,5,1,4,7]=>1101100=>[1,1,2,1,3]
[7,4,8,5,2,1,3,6]=>1011100=>[1,2,1,1,3]
[6,4,8,5,1,3,7,2]=>1011001=>[1,2,1,3,1]
[4,3,7,5,1,2,8,6]=>1011001=>[1,2,1,3,1]
[4,3,7,1,5,6,8,2]=>1010001=>[1,2,4,1]
[3,6,1,7,5,2,8,4]=>0101101=>[2,2,1,2,1]
[3,4,1,2,7,6,8,5]=>0100101=>[2,3,2,1]
[6,5,2,7,4,1,8,3]=>1101101=>[1,1,2,1,2,1]
[3,5,2,6,4,8,7,1]=>0101011=>[2,2,2,1,1]
[4,3,2,1,8,6,5,7]=>1110110=>[1,1,1,2,1,2]
[4,2,1,3,8,7,6,5]=>1100111=>[1,1,3,1,1,1]
[7,1,6,8,4,3,5,2]=>1001101=>[1,3,1,2,1]
[6,1,2,8,4,5,7,3]=>1001001=>[1,3,3,1]
[5,6,8,2,3,1,7,4]=>0010101=>[3,2,2,1]
[6,5,8,2,4,3,1,7]=>1010110=>[1,2,2,1,2]
[6,5,8,4,2,3,7,1]=>1011001=>[1,2,1,3,1]
[7,5,3,8,2,4,1,6]=>1101010=>[1,1,2,2,2]
[1,6,5,7,3,4,2,8]=>0101010=>[2,2,2,2]
[5,2,1,8,7,6,3,4]=>1101110=>[1,1,2,1,1,2]
[7,1,3,8,4,6,2,5]=>1001010=>[1,3,2,2]
[5,7,8,4,3,6,2,1]=>0011011=>[3,1,2,1,1]
[4,1,8,3,5,6,7,2]=>1010001=>[1,2,4,1]
[4,1,8,3,6,2,7,5]=>1010101=>[1,2,2,2,1]
[2,3,4,8,6,1,7,5]=>0001101=>[4,1,2,1]
[2,3,4,8,6,5,1,7]=>0001110=>[4,1,1,2]
[2,7,3,5,8,6,1,4]=>0100110=>[2,3,1,2]
[3,2,4,7,8,6,1,5]=>1000110=>[1,4,1,2]
[1,5,4,6,2,7,3,8]=>0101010=>[2,2,2,2]
[5,2,4,7,1,8,3,6]=>1001010=>[1,3,2,2]
[5,3,6,4,1,8,7,2]=>1011011=>[1,2,1,2,1,1]
[5,3,6,1,4,8,2,7]=>1010010=>[1,2,3,2]
[7,3,5,6,8,4,2,1]=>1000111=>[1,4,1,1,1]
[6,3,5,1,8,2,7,4]=>1010101=>[1,2,2,2,1]
[5,7,1,6,3,8,4,2]=>0101011=>[2,2,2,1,1]
[3,2,4,1,7,8,5,6]=>1010010=>[1,2,3,2]
[2,5,4,6,1,7,8,3]=>0101001=>[2,2,3,1]
[7,2,1,4,3,6,5,8]=>1101010=>[1,1,2,2,2]
[7,3,4,1,2,6,5,8]=>1010010=>[1,2,3,2]
[7,4,3,2,1,6,5,8]=>1111010=>[1,1,1,1,2,2]
[6,7,3,2,5,4,8,1]=>0110101=>[2,1,2,2,1]
[1,8,3,2,5,4,7,6]=>0110101=>[2,1,2,2,1]
[1,8,4,5,2,3,7,6]=>0101001=>[2,2,3,1]
[7,3,5,1,6,2,4,8]=>1010100=>[1,2,2,3]
[7,2,1,5,6,3,4,8]=>1100100=>[1,1,3,3]
[1,8,5,4,3,2,7,6]=>0111101=>[2,1,1,1,2,1]
[6,4,7,5,1,3,8,2]=>1011001=>[1,2,1,3,1]
[3,2,1,8,5,4,7,6]=>1101101=>[1,1,2,1,2,1]
[2,3,8,1,5,4,7,6]=>0010101=>[3,2,2,1]
[2,4,8,5,1,3,7,6]=>0011001=>[3,1,3,1]
[2,6,8,4,3,7,1,5]=>0011010=>[3,1,2,2]
[2,7,8,4,3,6,5,1]=>0011011=>[3,1,2,1,1]
[1,8,7,5,6,3,4,2]=>0110101=>[2,1,2,2,1]
[2,7,8,5,6,3,4,1]=>0010101=>[3,2,2,1]
[2,5,8,6,7,1,3,4]=>0010100=>[3,2,3]
[2,4,8,6,1,7,3,5]=>0011010=>[3,1,2,2]
[3,2,1,8,6,7,4,5]=>1101010=>[1,1,2,2,2]
[5,2,1,7,6,8,4,3]=>1101011=>[1,1,2,2,1,1]
[5,3,7,1,6,8,4,2]=>1010011=>[1,2,3,1,1]
[5,4,7,6,1,8,3,2]=>1011011=>[1,2,1,2,1,1]
[4,5,7,6,8,1,3,2]=>0010101=>[3,2,2,1]
[4,6,7,5,8,3,1,2]=>0010110=>[3,2,1,2]
[1,8,5,6,7,2,3,4]=>0100100=>[2,3,3]
[4,6,5,7,8,2,1,3]=>0100110=>[2,3,1,2]
[5,4,6,7,1,8,2,3]=>1001010=>[1,3,2,2]
[5,3,6,1,7,8,2,4]=>1010010=>[1,2,3,2]
[5,2,1,6,7,8,3,4]=>1100010=>[1,1,4,2]
[6,2,1,5,7,3,8,4]=>1100101=>[1,1,3,2,1]
[6,3,5,1,7,2,8,4]=>1010101=>[1,2,2,2,1]
[6,4,5,7,1,2,8,3]=>1001001=>[1,3,3,1]
[5,6,4,7,2,8,1,3]=>0101010=>[2,2,2,2]
[1,8,4,6,2,7,3,5]=>0101010=>[2,2,2,2]
[1,8,3,2,6,7,4,5]=>0110010=>[2,1,3,2]
[5,7,3,2,6,8,4,1]=>0110011=>[2,1,3,1,1]
[6,5,3,2,7,1,8,4]=>1110101=>[1,1,1,2,2,1]
[6,4,3,2,1,7,8,5]=>1111001=>[1,1,1,1,3,1]
[6,2,1,4,3,7,8,5]=>1101001=>[1,1,2,3,1]
[5,2,1,4,3,8,7,6]=>1101011=>[1,1,2,2,1,1]
[5,3,4,1,2,8,7,6]=>1010011=>[1,2,3,1,1]
[4,5,3,2,8,1,7,6]=>0110101=>[2,1,2,2,1]
[4,6,3,2,8,7,1,5]=>0110110=>[2,1,2,1,2]
[1,8,3,2,7,6,5,4]=>0110111=>[2,1,2,1,1,1]
[1,8,4,7,2,6,5,3]=>0101011=>[2,2,2,1,1]
[3,6,4,8,2,7,1,5]=>0101010=>[2,2,2,2]
[3,4,5,8,1,2,7,6]=>0001001=>[4,3,1]
[4,3,5,1,8,2,7,6]=>1010101=>[1,2,2,2,1]
[4,2,1,5,8,3,7,6]=>1100101=>[1,1,3,2,1]
[4,2,1,6,8,7,3,5]=>1100110=>[1,1,3,1,2]
[3,4,6,8,1,7,2,5]=>0001010=>[4,2,2]
[3,5,6,8,7,1,2,4]=>0001100=>[4,1,3]
[3,6,5,8,7,2,1,4]=>0101110=>[2,2,1,1,2]
[3,6,7,8,5,4,1,2]=>0001110=>[4,1,1,2]
[3,5,7,8,6,1,4,2]=>0001101=>[4,1,2,1]
[4,2,1,7,8,6,5,3]=>1100111=>[1,1,3,1,1,1]
[2,3,8,1,7,6,5,4]=>0010111=>[3,2,1,1,1]
[2,4,8,7,1,6,5,3]=>0011011=>[3,1,2,1,1]
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[8,1,6,7,3,2,5,4]=>1001101=>[1,3,1,2,1]
[8,1,6,7,2,3,4,5]=>1001000=>[1,3,4]
[8,1,2,4,3,6,5,7]=>1001010=>[1,3,2,2]
[8,1,4,3,2,7,6,5]=>1011011=>[1,2,1,2,1,1]
[8,1,5,3,7,2,6,4]=>1010101=>[1,2,2,2,1]
[8,1,3,5,6,2,7,4]=>1000101=>[1,4,2,1]
[6,3,2,1,4,5,8,7]=>1110001=>[1,1,1,4,1]
[4,7,8,5,6,1,2,3]=>0010100=>[3,2,3]
[3,7,8,5,6,2,1,4]=>0010110=>[3,2,1,2]
[3,7,8,4,2,6,1,5]=>0011010=>[3,1,2,2]
[3,7,8,2,4,5,1,6]=>0010010=>[3,3,2]
[3,6,2,8,4,5,1,7]=>0101010=>[2,2,2,2]
[2,3,6,7,4,5,8,1]=>0001001=>[4,3,1]
[3,5,2,4,8,6,1,7]=>0100110=>[2,3,1,2]
[3,5,4,2,8,7,1,6]=>0110110=>[2,1,2,1,2]
[4,6,5,8,7,1,2,3]=>0101100=>[2,2,1,3]
[6,4,5,1,7,8,2,3]=>1010010=>[1,2,3,2]
[5,4,2,3,1,8,6,7]=>1101010=>[1,1,2,2,2]
[6,5,3,1,8,2,7,4]=>1110101=>[1,1,1,2,2,1]
[6,5,4,1,8,7,2,3]=>1110110=>[1,1,1,2,1,2]
[7,5,1,4,8,6,2,3]=>1100110=>[1,1,3,1,2]
[7,4,1,3,2,8,6,5]=>1101011=>[1,1,2,2,1,1]
[7,4,1,2,3,8,5,6]=>1100010=>[1,1,4,2]
[6,4,2,1,3,8,5,7]=>1110010=>[1,1,1,3,2]
[2,6,4,8,3,7,5,1]=>0101011=>[2,2,2,1,1]
[2,6,5,8,7,3,4,1]=>0101101=>[2,2,1,2,1]
[6,5,2,1,8,3,4,7]=>1110100=>[1,1,1,2,3]
[7,5,1,2,8,3,4,6]=>1100100=>[1,1,3,3]
[7,6,1,8,2,3,4,5]=>1101000=>[1,1,2,4]
[7,6,1,8,4,5,2,3]=>1101010=>[1,1,2,2,2]
[6,7,8,1,4,5,2,3]=>0010010=>[3,3,2]
[6,7,8,1,3,2,5,4]=>0010101=>[3,2,2,1]
[2,5,6,7,8,3,4,1]=>0000101=>[5,2,1]
[2,4,6,7,3,8,5,1]=>0001011=>[4,2,1,1]
[4,2,6,7,3,1,5,8]=>1001100=>[1,3,1,3]
[4,7,8,2,3,1,5,6]=>0010100=>[3,2,3]
[4,7,8,3,2,1,6,5]=>0011101=>[3,1,1,2,1]
[5,7,8,3,1,2,6,4]=>0011001=>[3,1,3,1]
[5,7,8,4,1,6,2,3]=>0011010=>[3,1,2,2]
[5,6,4,8,1,7,2,3]=>0101010=>[2,2,2,2]
[4,6,3,8,2,1,7,5]=>0101101=>[2,2,1,2,1]
[4,2,5,3,7,1,6,8]=>1010100=>[1,2,2,3]
[5,3,6,7,1,2,8,4]=>1001001=>[1,3,3,1]
[3,5,6,7,8,2,1,4]=>0000110=>[5,1,2]
[3,4,6,7,2,8,1,5]=>0001010=>[4,2,2]
[7,4,6,1,8,3,5,2]=>1010101=>[1,2,2,2,1]
[7,3,5,1,8,4,6,2]=>1010101=>[1,2,2,2,1]
[7,3,4,1,8,5,6,2]=>1010101=>[1,2,2,2,1]
[4,5,7,3,1,8,6,2]=>0011011=>[3,1,2,1,1]
[4,5,6,2,1,8,7,3]=>0011011=>[3,1,2,1,1]
[1,6,5,2,7,4,3,8]=>0110110=>[2,1,2,1,2]
[7,4,3,1,8,6,5,2]=>1110111=>[1,1,1,2,1,1,1]
[3,6,7,5,1,8,4,2]=>0011011=>[3,1,2,1,1]
[7,5,6,1,8,3,4,2]=>1010101=>[1,2,2,2,1]
[7,6,5,1,8,4,3,2]=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,1,8,5,3,2]=>1110111=>[1,1,1,2,1,1,1]
[6,4,2,1,8,7,5,3]=>1110111=>[1,1,1,2,1,1,1]
[1,5,3,2,7,6,4,8]=>0110110=>[2,1,2,1,2]
[2,6,5,1,7,8,4,3]=>0110011=>[2,1,3,1,1]
[4,5,7,1,6,8,2,3]=>0010010=>[3,3,2]
[4,5,7,1,3,8,2,6]=>0010010=>[3,3,2]
[6,4,1,2,8,5,3,7]=>1100110=>[1,1,3,1,2]
[5,3,1,2,8,6,4,7]=>1100110=>[1,1,3,1,2]
[4,3,1,2,8,6,5,7]=>1100110=>[1,1,3,1,2]
[6,1,2,5,8,3,4,7]=>1000100=>[1,4,3]
[7,1,3,4,8,2,5,6]=>1000100=>[1,4,3]
[2,6,1,5,7,8,3,4]=>0100010=>[2,4,2]
[7,6,1,5,8,3,2,4]=>1100110=>[1,1,3,1,2]
[3,6,7,1,5,8,2,4]=>0010010=>[3,3,2]
[7,1,6,5,8,2,4,3]=>1010101=>[1,2,2,2,1]
[7,5,1,6,8,4,2,3]=>1100110=>[1,1,3,1,2]
[7,4,1,6,8,5,2,3]=>1100110=>[1,1,3,1,2]
[5,2,3,1,8,6,7,4]=>1010101=>[1,2,2,2,1]
[7,3,1,5,8,6,2,4]=>1100110=>[1,1,3,1,2]
[6,2,4,1,8,5,7,3]=>1010101=>[1,2,2,2,1]
[6,2,5,1,8,4,7,3]=>1010101=>[1,2,2,2,1]
[7,1,6,4,8,2,5,3]=>1010101=>[1,2,2,2,1]
[7,1,5,3,8,2,6,4]=>1010101=>[1,2,2,2,1]
[6,1,5,2,8,3,7,4]=>1010101=>[1,2,2,2,1]
[7,3,1,4,8,6,2,5]=>1100110=>[1,1,3,1,2]
[6,2,1,4,8,7,3,5]=>1100110=>[1,1,3,1,2]
[5,2,1,3,8,7,4,6]=>1100110=>[1,1,3,1,2]
[7,4,1,3,8,5,2,6]=>1100110=>[1,1,3,1,2]
[6,1,4,2,8,3,7,5]=>1010101=>[1,2,2,2,1]
[7,1,4,3,8,2,6,5]=>1010101=>[1,2,2,2,1]
[3,6,7,1,4,8,2,5]=>0010010=>[3,3,2]
[7,6,1,4,8,3,2,5]=>1100110=>[1,1,3,1,2]
[5,1,3,2,8,4,7,6]=>1010101=>[1,2,2,2,1]
[4,2,1,3,8,7,5,6]=>1100110=>[1,1,3,1,2]
[2,6,1,4,7,8,3,5]=>0100010=>[2,4,2]
[7,1,3,5,8,2,4,6]=>1000100=>[1,4,3]
[7,8,5,6,1,3,4,2]=>0101001=>[2,2,3,1]
[7,8,1,3,6,2,5,4]=>0100101=>[2,3,2,1]
[1,3,8,4,7,2,5,6]=>0010100=>[3,2,3]
[4,6,1,2,5,7,3,8]=>0100010=>[2,4,2]
[1,4,8,2,5,7,3,6]=>0010010=>[3,3,2]
[7,8,4,2,5,1,3,6]=>0110100=>[2,1,2,3]
[7,8,1,5,4,6,3,2]=>0101011=>[2,2,2,1,1]
[7,8,2,1,6,3,4,5]=>0110100=>[2,1,2,3]
[7,8,3,5,6,4,1,2]=>0100110=>[2,3,1,2]
[7,8,4,5,3,1,6,2]=>0101101=>[2,2,1,2,1]
[2,6,4,8,3,7,1,5]=>0101010=>[2,2,2,2]
[1,4,6,8,3,7,5,2]=>0001011=>[4,2,1,1]
[2,4,8,5,3,1,6,7]=>0011100=>[3,1,1,3]
[2,5,8,1,4,7,6,3]=>0010011=>[3,3,1,1]
[2,1,8,4,7,3,6,5]=>1010101=>[1,2,2,2,1]
[3,5,8,4,7,6,1,2]=>0010110=>[3,2,1,2]
[1,6,2,4,7,3,8,5]=>0100101=>[2,3,2,1]
[4,6,2,5,3,1,8,7]=>0101101=>[2,2,1,2,1]
[4,7,5,1,3,6,8,2]=>0110001=>[2,1,4,1]
[7,5,3,6,2,4,1,8]=>1101010=>[1,1,2,2,2]
[5,7,3,6,1,4,8,2]=>0101001=>[2,2,3,1]
[5,3,6,7,2,1,8,4]=>1001101=>[1,3,1,2,1]
[6,3,1,2,4,5,8,7]=>1100001=>[1,1,5,1]
[1,4,7,2,5,3,8,6]=>0010101=>[3,2,2,1]
[6,4,7,3,5,8,1,2]=>1010010=>[1,2,3,2]
[3,5,6,7,8,1,4,2]=>0000101=>[5,2,1]
[3,6,5,7,8,2,1,4]=>0100110=>[2,3,1,2]
[5,2,7,6,1,4,3,8]=>1011010=>[1,2,1,2,2]
[2,7,5,6,8,4,1,3]=>0100110=>[2,3,1,2]
[2,1,6,8,4,5,3,7]=>1001010=>[1,3,2,2]
[2,7,1,8,5,3,4,6]=>0101100=>[2,2,1,3]
[3,7,6,8,5,4,1,2]=>0101110=>[2,2,1,1,2]
[4,3,8,5,6,7,1,2]=>1010010=>[1,2,3,2]
[4,2,8,1,6,3,7,5]=>1010101=>[1,2,2,2,1]
[3,1,8,5,4,6,7,2]=>1011001=>[1,2,1,3,1]
[3,4,2,8,6,1,7,5]=>0101101=>[2,2,1,2,1]
[1,7,3,8,5,2,6,4]=>0101101=>[2,2,1,2,1]
[4,1,8,3,6,2,5,7]=>1010100=>[1,2,2,3]
[5,7,8,6,3,2,1,4]=>0011110=>[3,1,1,1,2]
[5,7,8,6,1,3,4,2]=>0011001=>[3,1,3,1]
[7,6,5,8,1,3,4,2]=>1101001=>[1,1,2,3,1]
[1,6,4,3,8,2,5,7]=>0110100=>[2,1,2,3]
[2,6,3,4,5,8,1,7]=>0100010=>[2,4,2]
[2,6,4,1,8,3,7,5]=>0110101=>[2,1,2,2,1]
[3,6,4,5,8,7,1,2]=>0100110=>[2,3,1,2]
[7,1,6,5,3,8,4,2]=>1011011=>[1,2,1,2,1,1]
[7,2,5,6,3,8,1,4]=>1001010=>[1,3,2,2]
[5,6,2,7,3,1,4,8]=>0101100=>[2,2,1,3]
[5,7,6,4,1,8,3,2]=>0111011=>[2,1,1,2,1,1]
[6,7,1,5,2,8,3,4]=>0101010=>[2,2,2,2]
[6,1,5,2,8,3,4,7]=>1010100=>[1,2,2,3]
[7,5,2,4,3,1,6,8]=>1101100=>[1,1,2,1,3]
[6,8,1,3,7,5,4,2]=>0100111=>[2,3,1,1,1]
[7,4,2,6,5,1,3,8]=>1101100=>[1,1,2,1,3]
[7,4,6,3,1,5,2,8]=>1011010=>[1,2,1,2,2]
[7,2,3,5,4,1,6,8]=>1001100=>[1,3,1,3]
[6,8,1,2,3,4,7,5]=>0100001=>[2,5,1]
[2,5,1,7,8,3,6,4]=>0100101=>[2,3,2,1]
[2,5,3,6,8,4,7,1]=>0100101=>[2,3,2,1]
[2,1,4,7,8,5,6,3]=>1000101=>[1,4,2,1]
[2,5,7,8,1,4,6,3]=>0001001=>[4,3,1]
[3,5,7,4,1,6,2,8]=>0011010=>[3,1,2,2]
[5,2,8,4,6,1,7,3]=>1010101=>[1,2,2,2,1]
[4,2,8,5,7,6,3,1]=>1010111=>[1,2,2,1,1,1]
[4,1,2,8,5,6,7,3]=>1001001=>[1,3,3,1]
[1,4,2,7,5,8,6,3]=>0101011=>[2,2,2,1,1]
[4,1,8,6,7,5,3,2]=>1010111=>[1,2,2,1,1,1]
[5,3,8,7,6,2,4,1]=>1011101=>[1,2,1,1,2,1]
[5,8,4,7,6,2,1,3]=>0101110=>[2,2,1,1,2]
[5,8,7,4,3,6,1,2]=>0111010=>[2,1,1,2,2]
[6,4,8,3,1,7,2,5]=>1011010=>[1,2,1,2,2]
[6,4,2,8,7,1,3,5]=>1101100=>[1,1,2,1,3]
[6,3,8,7,2,5,1,4]=>1011010=>[1,2,1,2,2]
[6,3,1,8,7,2,4,5]=>1101100=>[1,1,2,1,3]
[5,8,3,7,1,6,4,2]=>0101011=>[2,2,2,1,1]
[5,1,8,4,6,2,7,3]=>1010101=>[1,2,2,2,1]
[5,8,7,4,1,6,2,3]=>0111010=>[2,1,1,2,2]
[6,8,5,2,4,3,7,1]=>0110101=>[2,1,2,2,1]
[6,8,5,3,1,2,7,4]=>0111001=>[2,1,1,3,1]
[4,5,1,2,7,6,3,8]=>0100110=>[2,3,1,2]
[4,5,1,2,6,8,7,3]=>0100011=>[2,4,1,1]
[3,5,6,1,8,4,7,2]=>0010101=>[3,2,2,1]
[3,5,7,1,2,8,6,4]=>0010011=>[3,3,1,1]
[4,2,6,1,7,3,5,8]=>1010100=>[1,2,2,3]
[4,6,3,1,2,7,5,8]=>0110010=>[2,1,3,2]
[3,5,2,7,8,1,6,4]=>0100101=>[2,3,2,1]
[3,1,4,7,5,6,2,8]=>1001010=>[1,3,2,2]
[4,2,5,6,1,8,7,3]=>1001011=>[1,3,2,1,1]
[2,1,7,5,8,6,4,3]=>1010111=>[1,2,2,1,1,1]
[1,2,7,5,3,8,6,4]=>0011011=>[3,1,2,1,1]
[4,1,2,7,3,8,6,5]=>1001011=>[1,3,2,1,1]
[7,1,4,2,5,3,8,6]=>1010101=>[1,2,2,2,1]
[6,1,3,7,5,2,4,8]=>1001100=>[1,3,1,3]
[3,1,2,6,8,5,4,7]=>1000110=>[1,4,1,2]
[3,7,1,2,5,4,8,6]=>0100101=>[2,3,2,1]
[1,3,7,2,4,8,6,5]=>0010011=>[3,3,1,1]
[3,2,7,8,1,6,5,4]=>1001011=>[1,3,2,1,1]
[2,4,1,7,8,6,5,3]=>0100111=>[2,3,1,1,1]
[2,6,8,3,1,5,7,4]=>0011001=>[3,1,3,1]
[3,6,4,8,5,1,7,2]=>0101101=>[2,2,1,2,1]
[6,3,7,4,5,1,8,2]=>1010101=>[1,2,2,2,1]
[6,4,7,5,2,8,1,3]=>1011010=>[1,2,1,2,2]
[2,6,3,7,5,8,1,4]=>0101010=>[2,2,2,2]
[5,2,1,7,8,3,4,6]=>1100100=>[1,1,3,3]
[5,7,4,6,2,8,1,3]=>0101010=>[2,2,2,2]
[5,7,3,4,6,1,8,2]=>0100101=>[2,3,2,1]
[4,2,8,3,6,7,1,5]=>1010010=>[1,2,3,2]
[4,8,3,1,7,2,5,6]=>0110100=>[2,1,2,3]
[5,2,8,4,7,1,6,3]=>1010101=>[1,2,2,2,1]
[5,8,4,7,3,1,6,2]=>0101101=>[2,2,1,2,1]
[4,6,8,3,1,7,5,2]=>0011011=>[3,1,2,1,1]
[6,3,8,2,7,1,5,4]=>1010101=>[1,2,2,2,1]
[6,3,1,8,2,4,7,5]=>1101001=>[1,1,2,3,1]
[3,5,1,8,2,7,4,6]=>0101010=>[2,2,2,2]
[7,5,1,3,6,2,4,8]=>1100100=>[1,1,3,3]
[8,5,4,1,2,6,3,7]=>1110010=>[1,1,1,3,2]
[5,1,8,4,2,7,3,6]=>1011010=>[1,2,1,2,2]
[4,1,6,2,8,3,7,5]=>1010101=>[1,2,2,2,1]
[1,6,2,8,5,3,7,4]=>0101101=>[2,2,1,2,1]
[6,8,5,3,1,7,4,2]=>0111011=>[2,1,1,2,1,1]
[5,6,7,3,1,8,4,2]=>0011011=>[3,1,2,1,1]
[5,6,2,1,7,8,4,3]=>0110011=>[2,1,3,1,1]
[8,4,5,1,2,6,3,7]=>1010010=>[1,2,3,2]
[1,6,3,7,2,8,4,5]=>0101010=>[2,2,2,2]
[6,3,2,7,8,5,1,4]=>1100110=>[1,1,3,1,2]
[6,4,7,2,8,1,5,3]=>1010101=>[1,2,2,2,1]
[6,7,4,8,3,1,5,2]=>0101101=>[2,2,1,2,1]
[4,5,7,8,3,1,6,2]=>0001101=>[4,1,2,1]
[4,7,2,5,8,1,6,3]=>0100101=>[2,3,2,1]
[5,7,3,8,2,6,1,4]=>0101010=>[2,2,2,2]
[3,4,7,8,2,6,1,5]=>0001010=>[4,2,2]
[8,1,3,4,6,2,5,7]=>1000100=>[1,4,3]
[3,8,2,4,6,7,1,5]=>0100010=>[2,4,2]
[2,4,5,6,8,1,7,3]=>0000101=>[5,2,1]
[4,8,3,5,6,1,7,2]=>0100101=>[2,3,2,1]
[8,4,3,6,5,1,7,2]=>1101101=>[1,1,2,1,2,1]
[8,6,5,4,3,1,7,2]=>1111101=>[1,1,1,1,1,2,1]
[1,8,6,5,2,7,3,4]=>0111010=>[2,1,1,2,2]
[8,7,5,4,1,6,3,2]=>1111011=>[1,1,1,1,2,1,1]
[7,8,5,4,1,3,6,2]=>0111001=>[2,1,1,3,1]
[6,8,5,4,2,1,7,3]=>0111101=>[2,1,1,1,2,1]
[5,8,6,2,4,1,7,3]=>0110101=>[2,1,2,2,1]
[3,2,8,6,5,1,7,4]=>1011101=>[1,2,1,1,2,1]
[5,1,7,3,6,2,4,8]=>1010100=>[1,2,2,3]
[8,1,6,5,2,3,7,4]=>1011001=>[1,2,1,3,1]
[1,2,8,3,7,4,5,6]=>0010100=>[3,2,3]
[8,1,7,2,6,3,5,4]=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,4,3,5]=>1010110=>[1,2,2,1,2]
[5,1,8,3,2,7,4,6]=>1011010=>[1,2,1,2,2]
[3,2,1,8,4,7,5,6]=>1101010=>[1,1,2,2,2]
[3,2,8,7,1,6,5,4]=>1011011=>[1,2,1,2,1,1]
[4,8,2,7,1,6,5,3]=>0101011=>[2,2,2,1,1]
[5,8,7,2,1,6,4,3]=>0111011=>[2,1,1,2,1,1]
[8,7,6,1,5,4,3,2]=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,1,4,5,3,2]=>1010011=>[1,2,3,1,1]
[7,6,8,1,4,3,5,2]=>1010101=>[1,2,2,2,1]
[6,7,8,1,3,4,5,2]=>0010001=>[3,4,1]
[5,7,8,2,1,4,6,3]=>0011001=>[3,1,3,1]
[4,7,2,8,1,5,6,3]=>0101001=>[2,2,3,1]
[3,2,7,8,1,5,6,4]=>1001001=>[1,3,3,1]
[3,2,6,8,4,1,7,5]=>1001101=>[1,3,1,2,1]
[4,6,2,8,3,1,7,5]=>0101101=>[2,2,1,2,1]
[6,5,8,3,2,1,7,4]=>1011101=>[1,2,1,1,2,1]
[7,5,8,3,1,4,6,2]=>1011001=>[1,2,1,3,1]
[8,4,3,7,1,6,5,2]=>1101011=>[1,1,2,2,1,1]
[6,4,3,8,2,1,7,5]=>1101101=>[1,1,2,1,2,1]
[5,4,3,2,8,1,7,6]=>1110101=>[1,1,1,2,2,1]
[4,5,2,3,8,1,7,6]=>0100101=>[2,3,2,1]
[3,2,5,4,8,1,7,6]=>1010101=>[1,2,2,2,1]
[6,4,3,1,5,2,7,8]=>1110100=>[1,1,1,2,3]
[7,4,3,1,2,6,5,8]=>1110010=>[1,1,1,3,2]
[1,5,4,2,3,6,7,8]=>0110000=>[2,1,5]
[8,5,1,4,2,3,7,6]=>1101001=>[1,1,2,3,1]
[7,5,1,4,2,6,3,8]=>1101010=>[1,1,2,2,2]
[4,6,2,1,5,3,7,8]=>0110100=>[2,1,2,3]
[3,2,6,1,5,4,7,8]=>1010100=>[1,2,2,3]
[5,7,1,3,2,6,4,8]=>0101010=>[2,2,2,2]
[6,7,1,2,4,5,3,8]=>0100010=>[2,4,2]
[7,6,1,2,5,4,3,8]=>1100110=>[1,1,3,1,2]
[7,8,1,2,3,5,6,4]=>0100001=>[2,5,1]
[6,8,1,2,4,3,7,5]=>0100101=>[2,3,2,1]
[4,8,2,1,3,5,7,6]=>0110001=>[2,1,4,1]
[3,2,8,1,4,5,7,6]=>1010001=>[1,2,4,1]
[4,1,3,2,5,6,7,8]=>1010000=>[1,2,5]
[5,1,2,4,3,6,7,8]=>1001000=>[1,3,4]
[5,8,7,3,4,1,2,6]=>0110100=>[2,1,2,3]
[6,7,3,8,5,1,2,4]=>0101100=>[2,2,1,3]
[6,7,4,5,1,8,3,2]=>0101011=>[2,2,2,1,1]
[5,4,7,6,2,3,8,1]=>1011001=>[1,2,1,3,1]
[5,4,7,6,8,1,2,3]=>1010100=>[1,2,2,3]
[5,3,7,8,6,1,2,4]=>1001100=>[1,3,1,3]
[4,3,8,7,6,1,2,5]=>1011100=>[1,2,1,1,3]
[4,8,3,7,5,1,2,6]=>0101100=>[2,2,1,3]
[4,5,6,7,1,8,3,2]=>0001011=>[4,2,1,1]
[3,5,6,2,7,4,8,1]=>0010101=>[3,2,2,1]
[3,5,6,1,7,8,4,2]=>0010011=>[3,3,1,1]
[2,5,6,8,1,7,3,4]=>0001010=>[4,2,2]
[8,2,4,5,1,6,3,7]=>1001010=>[1,3,2,2]
[1,4,8,6,2,3,7,5]=>0011001=>[3,1,3,1]
[1,5,6,8,2,3,7,4]=>0001001=>[4,3,1]
[1,5,6,2,8,4,7,3]=>0010101=>[3,2,2,1]
[1,4,2,6,8,5,7,3]=>0100101=>[2,3,2,1]
[8,1,3,2,5,4,6,7]=>1010100=>[1,2,2,3]
[2,4,1,6,8,7,5,3]=>0100111=>[2,3,1,1,1]
[4,3,1,7,6,8,5,2]=>1101011=>[1,1,2,2,1,1]
[3,8,2,1,7,5,4,6]=>0110110=>[2,1,2,1,2]
[8,3,2,1,6,5,4,7]=>1110110=>[1,1,1,2,1,2]
[8,4,2,6,1,5,3,7]=>1101010=>[1,1,2,2,2]
[4,2,8,7,1,6,3,5]=>1011010=>[1,2,1,2,2]
[5,2,7,8,1,6,3,4]=>1001010=>[1,3,2,2]
[5,3,7,2,6,4,8,1]=>1010101=>[1,2,2,2,1]
[6,7,3,1,5,8,4,2]=>0110011=>[2,1,3,1,1]
[6,7,2,1,8,5,4,3]=>0110111=>[2,1,2,1,1,1]
[6,7,2,8,1,5,3,4]=>0101010=>[2,2,2,2]
[6,7,8,2,1,4,3,5]=>0011010=>[3,1,2,2]
[8,5,6,2,1,4,3,7]=>1011010=>[1,2,1,2,2]
[5,8,7,1,2,3,4,6]=>0110000=>[2,1,5]
[6,7,1,2,8,4,5,3]=>0100101=>[2,3,2,1]
[6,7,1,3,4,8,5,2]=>0100011=>[2,4,1,1]
[5,1,7,3,4,8,6,2]=>1010011=>[1,2,3,1,1]
[5,1,7,8,2,3,6,4]=>1001001=>[1,3,3,1]
[4,8,1,7,2,3,5,6]=>0101000=>[2,2,4]
[3,8,1,2,7,4,5,6]=>0100100=>[2,3,3]
[3,1,8,2,7,4,6,5]=>1010101=>[1,2,2,2,1]
[3,1,2,8,7,5,6,4]=>1001101=>[1,3,1,2,1]
[4,1,3,7,5,8,6,2]=>1001011=>[1,3,2,1,1]
[2,1,8,3,4,7,6,5]=>1010011=>[1,2,3,1,1]
[1,8,2,3,4,5,7,6]=>0100001=>[2,5,1]
[1,2,8,3,4,6,7,5]=>0010001=>[3,4,1]
[6,3,8,5,2,7,4,1]=>1011011=>[1,2,1,2,1,1]
[6,5,2,8,4,7,3,1]=>1101011=>[1,1,2,2,1,1]
[6,3,4,5,8,7,2,1]=>1000111=>[1,4,1,1,1]
[5,8,1,4,7,2,3,6]=>0100100=>[2,3,3]
[3,6,4,8,5,7,1,2]=>0101010=>[2,2,2,2]
[5,1,4,8,6,3,7,2]=>1001101=>[1,3,1,2,1]
[3,4,7,1,8,6,5,2]=>0010111=>[3,2,1,1,1]
[6,3,8,4,2,7,1,5]=>1011010=>[1,2,1,2,2]
[3,6,8,7,1,4,2,5]=>0011010=>[3,1,2,2]
[5,3,7,1,6,8,2,4]=>1010010=>[1,2,3,2]
[4,6,1,2,7,8,5,3]=>0100011=>[2,4,1,1]
[3,6,4,2,8,7,5,1]=>0110111=>[2,1,2,1,1,1]
[6,3,7,5,2,8,1,4]=>1011010=>[1,2,1,2,2]
[6,5,2,7,4,8,1,3]=>1101010=>[1,1,2,2,2]
[5,8,1,4,6,7,2,3]=>0100010=>[2,4,2]
[6,3,7,4,2,8,5,1]=>1011011=>[1,2,1,2,1,1]
[8,7,1,6,2,4,5,3]=>1101001=>[1,1,2,3,1]
[5,6,1,8,7,3,2,4]=>0101110=>[2,2,1,1,2]
[3,6,4,5,7,2,8,1]=>0100101=>[2,3,2,1]
[5,4,2,7,3,6,8,1]=>1101001=>[1,1,2,3,1]
[6,4,1,5,3,8,2,7]=>1101010=>[1,1,2,2,2]
[8,2,6,3,4,7,5,1]=>1010011=>[1,2,3,1,1]
[4,2,5,7,3,6,8,1]=>1001001=>[1,3,3,1]
[1,6,5,3,4,8,2,7]=>0110010=>[2,1,3,2]
[6,8,3,1,7,2,5,4]=>0110101=>[2,1,2,2,1]
[1,8,6,3,7,5,2,4]=>0110110=>[2,1,2,1,2]
[8,7,5,2,6,4,3,1]=>1110111=>[1,1,1,2,1,1,1]
[8,7,1,6,2,5,4,3]=>1101011=>[1,1,2,2,1,1]
[2,8,1,7,3,5,6,4]=>0101001=>[2,2,3,1]
[4,8,1,3,7,2,6,5]=>0100101=>[2,3,2,1]
[4,2,8,5,7,3,6,1]=>1010101=>[1,2,2,2,1]
[6,7,3,1,8,4,2,5]=>0110110=>[2,1,2,1,2]
[1,7,3,8,4,5,2,6]=>0101010=>[2,2,2,2]
[1,7,2,8,5,3,4,6]=>0101100=>[2,2,1,3]
[7,6,1,8,4,3,2,5]=>1101110=>[1,1,2,1,1,2]
[7,1,2,8,3,5,4,6]=>1001010=>[1,3,2,2]
[6,3,7,2,1,8,4,5]=>1011010=>[1,2,1,2,2]
[8,2,6,1,7,3,5,4]=>1010101=>[1,2,2,2,1]
[4,2,1,5,8,3,6,7]=>1100100=>[1,1,3,3]
[5,4,3,1,6,8,2,7]=>1110010=>[1,1,1,3,2]
[1,5,3,4,6,8,2,7]=>0100010=>[2,4,2]
[4,3,5,1,6,8,2,7]=>1010010=>[1,2,3,2]
[4,7,5,6,8,3,2,1]=>0100111=>[2,3,1,1,1]
[6,5,1,8,7,4,2,3]=>1101110=>[1,1,2,1,1,2]
[8,6,4,7,5,3,2,1]=>1101111=>[1,1,2,1,1,1,1]
[5,7,3,8,2,6,4,1]=>0101011=>[2,2,2,1,1]
[2,3,8,7,4,5,6,1]=>0011001=>[3,1,3,1]
[7,2,8,6,4,3,5,1]=>1011101=>[1,2,1,1,2,1]
[2,1,8,7,5,6,3,4]=>1011010=>[1,2,1,2,2]
[7,1,8,6,5,3,2,4]=>1011110=>[1,2,1,1,1,2]
[4,7,1,8,6,5,2,3]=>0101110=>[2,2,1,1,2]
[6,8,7,2,5,4,3,1]=>0110111=>[2,1,2,1,1,1]
[6,7,4,8,3,5,1,2]=>0101010=>[2,2,2,2]
[6,7,4,5,2,8,1,3]=>0101010=>[2,2,2,2]
[5,7,4,6,2,3,1,8]=>0101010=>[2,2,2,2]
[5,7,4,6,3,8,1,2]=>0101010=>[2,2,2,2]
[5,7,4,8,3,6,1,2]=>0101010=>[2,2,2,2]
[6,8,4,5,3,7,1,2]=>0101010=>[2,2,2,2]
[5,8,4,6,3,7,1,2]=>0101010=>[2,2,2,2]
[5,6,4,8,3,7,1,2]=>0101010=>[2,2,2,2]
[5,6,3,7,2,4,1,8]=>0101010=>[2,2,2,2]
[5,6,3,7,2,8,1,4]=>0101010=>[2,2,2,2]
[5,6,3,8,2,7,1,4]=>0101010=>[2,2,2,2]
[5,6,4,8,2,7,1,3]=>0101010=>[2,2,2,2]
[5,8,4,6,2,7,1,3]=>0101010=>[2,2,2,2]
[6,8,4,5,2,7,1,3]=>0101010=>[2,2,2,2]
[7,8,4,5,2,6,1,3]=>0101010=>[2,2,2,2]
[6,8,4,5,2,3,1,7]=>0101010=>[2,2,2,2]
[5,8,4,6,2,3,1,7]=>0101010=>[2,2,2,2]
[5,6,4,8,2,3,1,7]=>0101010=>[2,2,2,2]
[5,6,3,8,2,4,1,7]=>0101010=>[2,2,2,2]
[5,6,3,4,2,8,1,7]=>0101010=>[2,2,2,2]
[4,6,3,5,2,7,1,8]=>0101010=>[2,2,2,2]
[4,6,3,5,2,8,1,7]=>0101010=>[2,2,2,2]
[4,6,3,8,2,5,1,7]=>0101010=>[2,2,2,2]
[4,8,3,6,2,5,1,7]=>0101010=>[2,2,2,2]
[5,8,3,6,2,4,1,7]=>0101010=>[2,2,2,2]
[6,8,3,5,2,4,1,7]=>0101010=>[2,2,2,2]
[7,8,3,5,2,4,1,6]=>0101010=>[2,2,2,2]
[7,8,3,5,2,6,1,4]=>0101010=>[2,2,2,2]
[6,8,3,5,2,7,1,4]=>0101010=>[2,2,2,2]
[5,8,3,6,2,7,1,4]=>0101010=>[2,2,2,2]
[4,8,3,6,2,7,1,5]=>0101010=>[2,2,2,2]
[4,6,3,8,2,7,1,5]=>0101010=>[2,2,2,2]
[4,6,3,7,2,8,1,5]=>0101010=>[2,2,2,2]
[4,6,3,7,2,5,1,8]=>0101010=>[2,2,2,2]
[4,7,3,6,2,5,1,8]=>0101010=>[2,2,2,2]
[4,7,3,6,2,8,1,5]=>0101010=>[2,2,2,2]
[4,7,3,8,2,6,1,5]=>0101010=>[2,2,2,2]
[5,7,4,8,2,6,1,3]=>0101010=>[2,2,2,2]
[5,7,3,6,2,8,1,4]=>0101010=>[2,2,2,2]
[5,7,3,6,2,4,1,8]=>0101010=>[2,2,2,2]
[6,7,3,5,2,4,1,8]=>0101010=>[2,2,2,2]
[6,7,3,5,2,8,1,4]=>0101010=>[2,2,2,2]
[6,7,3,8,2,5,1,4]=>0101010=>[2,2,2,2]
[6,7,4,8,2,5,1,3]=>0101010=>[2,2,2,2]
[6,7,5,8,2,4,1,3]=>0101010=>[2,2,2,2]
[6,8,5,7,2,3,1,4]=>0101010=>[2,2,2,2]
[6,7,4,8,2,3,1,5]=>0101010=>[2,2,2,2]
[6,7,3,8,2,4,1,5]=>0101010=>[2,2,2,2]
[6,7,3,4,2,8,1,5]=>0101010=>[2,2,2,2]
[5,7,3,4,2,6,1,8]=>0101010=>[2,2,2,2]
[5,7,3,4,2,8,1,6]=>0101010=>[2,2,2,2]
[5,7,3,8,2,4,1,6]=>0101010=>[2,2,2,2]
[5,7,4,8,2,3,1,6]=>0101010=>[2,2,2,2]
[5,8,4,7,2,3,1,6]=>0101010=>[2,2,2,2]
[6,8,4,7,2,3,1,5]=>0101010=>[2,2,2,2]
[7,8,4,6,2,3,1,5]=>0101010=>[2,2,2,2]
[7,8,3,6,2,4,1,5]=>0101010=>[2,2,2,2]
[6,8,3,7,2,4,1,5]=>0101010=>[2,2,2,2]
[5,8,3,7,2,4,1,6]=>0101010=>[2,2,2,2]
[4,8,3,7,2,5,1,6]=>0101010=>[2,2,2,2]
[4,7,3,8,2,5,1,6]=>0101010=>[2,2,2,2]
[4,7,3,5,2,8,1,6]=>0101010=>[2,2,2,2]
[4,7,3,5,2,6,1,8]=>0101010=>[2,2,2,2]
[4,5,3,7,2,6,1,8]=>0101010=>[2,2,2,2]
[4,5,3,7,2,8,1,6]=>0101010=>[2,2,2,2]
[4,5,3,8,2,7,1,6]=>0101010=>[2,2,2,2]
[4,8,3,5,2,7,1,6]=>0101010=>[2,2,2,2]
[5,8,3,4,2,7,1,6]=>0101010=>[2,2,2,2]
[6,8,3,4,2,7,1,5]=>0101010=>[2,2,2,2]
[7,8,3,4,2,6,1,5]=>0101010=>[2,2,2,2]
[6,8,3,4,2,5,1,7]=>0101010=>[2,2,2,2]
[5,8,3,4,2,6,1,7]=>0101010=>[2,2,2,2]
[4,8,3,5,2,6,1,7]=>0101010=>[2,2,2,2]
[4,5,3,8,2,6,1,7]=>0101010=>[2,2,2,2]
[4,5,3,6,2,8,1,7]=>0101010=>[2,2,2,2]
[4,7,5,2,1,8,3,6]=>0111010=>[2,1,1,2,2]
[4,6,5,2,1,3,8,7]=>0111001=>[2,1,1,3,1]
[5,6,4,2,3,1,8,7]=>0110101=>[2,1,2,2,1]
[6,4,5,3,1,2,8,7]=>1011001=>[1,2,1,3,1]
[5,4,6,1,3,2,8,7]=>1010101=>[1,2,2,2,1]
[4,6,8,1,7,3,2,5]=>0010110=>[3,2,1,2]
[4,7,8,1,6,3,5,2]=>0010101=>[3,2,2,1]
[7,4,8,1,6,5,3,2]=>1010111=>[1,2,2,1,1,1]
[7,4,5,3,1,8,2,6]=>1011010=>[1,2,1,2,2]
[6,4,8,1,7,5,2,3]=>1010110=>[1,2,2,1,2]
[6,4,7,1,8,2,5,3]=>1010101=>[1,2,2,2,1]
[8,5,7,6,4,2,1,3]=>1011110=>[1,2,1,1,1,2]
[2,1,6,8,7,4,3,5]=>1001110=>[1,3,1,1,2]
[2,1,7,8,6,4,5,3]=>1001101=>[1,3,1,2,1]
[8,4,7,3,6,2,5,1]=>1010101=>[1,2,2,2,1]
[7,6,8,5,2,4,3,1]=>1011011=>[1,2,1,2,1,1]
[5,7,8,6,2,3,1,4]=>0011010=>[3,1,2,2]
[5,8,7,6,3,2,1,4]=>0111110=>[2,1,1,1,1,2]
[6,8,7,5,3,2,4,1]=>0111101=>[2,1,1,1,2,1]
[7,8,4,2,6,5,3,1]=>0110111=>[2,1,2,1,1,1]
[4,8,6,2,7,3,1,5]=>0110110=>[2,1,2,1,2]
[3,6,1,8,7,4,2,5]=>0101110=>[2,2,1,1,2]
[4,7,6,2,8,1,3,5]=>0110100=>[2,1,2,3]
[6,7,4,2,8,1,5,3]=>0110101=>[2,1,2,2,1]
[6,8,4,2,7,5,1,3]=>0110110=>[2,1,2,1,2]
[5,7,4,2,3,8,1,6]=>0110010=>[2,1,3,2]
[2,1,8,6,7,5,3,4]=>1010110=>[1,2,2,1,2]
[8,6,4,3,7,5,1,2]=>1110110=>[1,1,1,2,1,2]
[5,8,6,7,3,1,2,4]=>0101100=>[2,2,1,3]
[6,7,5,8,1,3,4,2]=>0101001=>[2,2,3,1]
[7,6,5,8,1,4,3,2]=>1101011=>[1,1,2,2,1,1]
[8,6,5,7,4,1,3,2]=>1101101=>[1,1,2,1,2,1]
[7,6,4,3,8,1,5,2]=>1110101=>[1,1,1,2,2,1]
[2,1,7,6,8,3,5,4]=>1010101=>[1,2,2,2,1]
[7,5,6,8,1,4,2,3]=>1001010=>[1,3,2,2]
[4,1,7,3,6,5,8,2]=>1010101=>[1,2,2,2,1]
[5,1,8,4,7,6,2,3]=>1010110=>[1,2,2,1,2]
[8,1,3,7,4,6,5,2]=>1001011=>[1,3,2,1,1]
[6,1,5,4,3,8,7,2]=>1011011=>[1,2,1,2,1,1]
[6,1,4,5,3,7,8,2]=>1001001=>[1,3,3,1]
[5,1,7,8,6,2,4,3]=>1001101=>[1,3,1,2,1]
[6,1,8,3,4,5,7,2]=>1010001=>[1,2,4,1]
[8,5,2,1,4,3,7,6]=>1110101=>[1,1,1,2,2,1]
[5,6,2,1,4,8,3,7]=>0110010=>[2,1,3,2]
[3,6,1,8,5,2,4,7]=>0101100=>[2,2,1,3]
[3,4,1,2,8,6,5,7]=>0100110=>[2,3,1,2]
[6,3,8,5,2,1,4,7]=>1011100=>[1,2,1,1,3]
[8,5,2,7,3,1,6,4]=>1101101=>[1,1,2,1,2,1]
[2,3,8,5,6,1,7,4]=>0010101=>[3,2,2,1]
[7,4,5,6,3,1,8,2]=>1001101=>[1,3,1,2,1]
[8,5,6,4,2,1,7,3]=>1011101=>[1,2,1,1,2,1]
[7,5,3,6,2,8,1,4]=>1101010=>[1,1,2,2,2]
[1,7,5,6,3,2,4,8]=>0101100=>[2,2,1,3]
[8,7,5,4,1,6,2,3]=>1111010=>[1,1,1,1,2,2]
[2,6,4,1,8,5,7,3]=>0110101=>[2,1,2,2,1]
[6,1,2,3,8,5,7,4]=>1000101=>[1,4,2,1]
[7,1,2,3,6,5,8,4]=>1000101=>[1,4,2,1]
[7,2,1,3,8,6,4,5]=>1100110=>[1,1,3,1,2]
[1,5,7,3,2,4,6,8]=>0011000=>[3,1,4]
[5,2,7,3,1,8,4,6]=>1011010=>[1,2,1,2,2]
[5,8,2,4,1,3,7,6]=>0101001=>[2,2,3,1]
[8,7,2,6,3,4,1,5]=>1101010=>[1,1,2,2,2]
[4,8,1,6,3,2,7,5]=>0101101=>[2,2,1,2,1]
[3,1,8,6,4,2,7,5]=>1011101=>[1,2,1,1,2,1]
[8,1,6,7,4,3,2,5]=>1001110=>[1,3,1,1,2]
[3,5,8,7,2,4,1,6]=>0011010=>[3,1,2,2]
[4,2,1,3,7,8,5,6]=>1100010=>[1,1,4,2]
[8,6,1,3,7,2,4,5]=>1100100=>[1,1,3,3]
[5,1,8,3,2,4,6,7]=>1011000=>[1,2,1,4]
[5,2,7,8,6,4,1,3]=>1001110=>[1,3,1,1,2]
[1,4,2,7,8,6,3,5]=>0100110=>[2,3,1,2]
[1,6,2,4,8,5,3,7]=>0100110=>[2,3,1,2]
[1,6,2,4,7,5,3,8]=>0100110=>[2,3,1,2]
[1,7,3,8,5,2,4,6]=>0101100=>[2,2,1,3]
[1,7,3,2,8,6,4,5]=>0110110=>[2,1,2,1,2]
[7,8,3,6,5,2,1,4]=>0101110=>[2,2,1,1,2]
[4,7,2,8,6,1,5,3]=>0101101=>[2,2,1,2,1]
[4,2,5,7,8,6,1,3]=>1000110=>[1,4,1,2]
[8,2,5,1,7,3,4,6]=>1010100=>[1,2,2,3]
[1,3,6,4,8,5,7,2]=>0010101=>[3,2,2,1]
[1,3,6,4,7,5,8,2]=>0010101=>[3,2,2,1]
[6,2,4,7,5,8,1,3]=>1001010=>[1,3,2,2]
[6,2,7,3,5,1,8,4]=>1010101=>[1,2,2,2,1]
[6,2,1,3,7,8,4,5]=>1100010=>[1,1,4,2]
[7,2,5,1,8,3,4,6]=>1010100=>[1,2,2,3]
[7,8,2,1,4,3,5,6]=>0110100=>[2,1,2,3]
[7,6,4,2,3,1,8,5]=>1110101=>[1,1,1,2,2,1]
[7,5,4,2,6,8,1,3]=>1110010=>[1,1,1,3,2]
[1,7,5,3,4,6,8,2]=>0110001=>[2,1,4,1]
[8,2,5,4,6,7,1,3]=>1010010=>[1,2,3,2]
[8,2,6,4,3,1,7,5]=>1011101=>[1,2,1,1,2,1]
[8,2,7,4,1,3,5,6]=>1011000=>[1,2,1,4]
[1,2,8,4,3,5,6,7]=>0011000=>[3,1,4]
[1,8,7,4,3,2,5,6]=>0111100=>[2,1,1,1,3]
[5,8,4,7,2,1,6,3]=>0101101=>[2,2,1,2,1]
[1,8,7,5,4,3,6,2]=>0111101=>[2,1,1,1,2,1]
[1,6,8,4,3,7,5,2]=>0011011=>[3,1,2,1,1]
[6,8,7,3,2,5,1,4]=>0111010=>[2,1,1,2,2]
[5,3,8,1,2,7,4,6]=>1010010=>[1,2,3,2]
[5,1,8,3,2,6,4,7]=>1011010=>[1,2,1,2,2]
[5,7,3,1,2,6,4,8]=>0110010=>[2,1,3,2]
[1,4,6,2,8,3,7,5]=>0010101=>[3,2,2,1]
[5,2,6,7,8,4,1,3]=>1000110=>[1,4,1,2]
[5,3,6,1,2,8,4,7]=>1010010=>[1,2,3,2]
[1,6,3,2,7,8,4,5]=>0110010=>[2,1,3,2]
[6,7,3,8,5,2,1,4]=>0101110=>[2,2,1,1,2]
[4,6,2,7,8,1,5,3]=>0100101=>[2,3,2,1]
[1,6,4,7,8,3,5,2]=>0100101=>[2,3,2,1]
[4,5,7,2,1,8,6,3]=>0011011=>[3,1,2,1,1]
[7,8,3,4,2,1,6,5]=>0101101=>[2,2,1,2,1]
[6,3,4,1,2,5,8,7]=>1010001=>[1,2,4,1]
[6,3,1,4,2,7,5,8]=>1101010=>[1,1,2,2,2]
[1,8,3,2,4,5,6,7]=>0110000=>[2,1,5]
[8,6,3,2,4,1,7,5]=>1110101=>[1,1,1,2,2,1]
[8,5,3,2,6,7,1,4]=>1110010=>[1,1,1,3,2]
[4,5,2,6,8,1,7,3]=>0100101=>[2,3,2,1]
[4,2,5,6,7,8,1,3]=>1000010=>[1,5,2]
[7,2,3,1,4,5,8,6]=>1010001=>[1,2,4,1]
[2,4,6,8,10,1,3,5,7,9]=>000010000=>[5,5]
[10,9,8,7,6,1,2,3,4,5]=>111110000=>[1,1,1,1,1,5]
[9,10,7,8,5,6,3,4,1,2]=>010101010=>[2,2,2,2,2]
[5,6,3,4,1,2,8,7]=>0101001=>[2,2,3,1]
[7,8,3,5,4,6,1,2]=>0101010=>[2,2,2,2]
[6,8,3,7,5,1,4,2]=>0101101=>[2,2,1,2,1]
[2,1,7,8,5,6,3,4]=>1001010=>[1,3,2,2]
[5,7,3,8,1,6,2,4]=>0101010=>[2,2,2,2]
[7,5,8,4,2,6,1,3]=>1011010=>[1,2,1,2,2]
[8,6,3,7,5,2,4,1]=>1101101=>[1,1,2,1,2,1]
[8,5,3,7,2,6,4,1]=>1101011=>[1,1,2,2,1,1]
[8,5,7,4,2,6,3,1]=>1011011=>[1,2,1,2,1,1]
[7,8,4,6,1,5,2,3]=>0101010=>[2,2,2,2]
[7,8,1,6,4,5,2,3]=>0101010=>[2,2,2,2]
[6,8,1,7,4,5,2,3]=>0101010=>[2,2,2,2]
[1,8,6,7,4,5,2,3]=>0101010=>[2,2,2,2]
[1,8,6,7,3,5,2,4]=>0101010=>[2,2,2,2]
[6,8,1,7,3,5,2,4]=>0101010=>[2,2,2,2]
[7,8,1,6,3,5,2,4]=>0101010=>[2,2,2,2]
[7,8,3,6,1,5,2,4]=>0101010=>[2,2,2,2]
[7,8,3,6,4,5,1,2]=>0101010=>[2,2,2,2]
[7,8,2,6,4,5,1,3]=>0101010=>[2,2,2,2]
[7,8,2,6,3,5,1,4]=>0101010=>[2,2,2,2]
[7,8,2,6,1,5,3,4]=>0101010=>[2,2,2,2]
[7,8,1,6,2,5,3,4]=>0101010=>[2,2,2,2]
[1,8,6,7,2,5,3,4]=>0101010=>[2,2,2,2]
[1,8,5,7,2,6,3,4]=>0101010=>[2,2,2,2]
[5,8,1,7,2,6,3,4]=>0101010=>[2,2,2,2]
[5,8,2,7,1,6,3,4]=>0101010=>[2,2,2,2]
[6,8,2,7,1,5,3,4]=>0101010=>[2,2,2,2]
[6,8,2,7,3,5,1,4]=>0101010=>[2,2,2,2]
[6,8,2,7,4,5,1,3]=>0101010=>[2,2,2,2]
[6,8,3,7,4,5,1,2]=>0101010=>[2,2,2,2]
[3,8,6,7,4,5,1,2]=>0101010=>[2,2,2,2]
[2,8,6,7,4,5,1,3]=>0101010=>[2,2,2,2]
[2,8,6,7,3,5,1,4]=>0101010=>[2,2,2,2]
[2,8,6,7,1,5,3,4]=>0101010=>[2,2,2,2]
[2,8,5,7,1,6,3,4]=>0101010=>[2,2,2,2]
[2,8,1,7,5,6,3,4]=>0101010=>[2,2,2,2]
[1,8,2,7,5,6,3,4]=>0101010=>[2,2,2,2]
[1,8,2,7,4,6,3,5]=>0101010=>[2,2,2,2]
[2,8,1,7,4,6,3,5]=>0101010=>[2,2,2,2]
[2,8,4,7,1,6,3,5]=>0101010=>[2,2,2,2]
[2,8,4,7,3,6,1,5]=>0101010=>[2,2,2,2]
[2,8,5,7,3,6,1,4]=>0101010=>[2,2,2,2]
[3,8,5,7,4,6,1,2]=>0101010=>[2,2,2,2]
[5,8,3,7,4,6,1,2]=>0101010=>[2,2,2,2]
[5,8,2,7,4,6,1,3]=>0101010=>[2,2,2,2]
[5,8,2,7,3,6,1,4]=>0101010=>[2,2,2,2]
[4,8,2,7,3,6,1,5]=>0101010=>[2,2,2,2]
[4,8,2,7,1,6,3,5]=>0101010=>[2,2,2,2]
[4,8,1,7,2,6,3,5]=>0101010=>[2,2,2,2]
[1,8,4,7,2,6,3,5]=>0101010=>[2,2,2,2]
[1,8,4,7,3,6,2,5]=>0101010=>[2,2,2,2]
[4,8,1,7,3,6,2,5]=>0101010=>[2,2,2,2]
[4,8,3,7,1,6,2,5]=>0101010=>[2,2,2,2]
[6,8,3,7,1,5,2,4]=>0101010=>[2,2,2,2]
[5,8,1,7,3,6,2,4]=>0101010=>[2,2,2,2]
[1,8,5,7,3,6,2,4]=>0101010=>[2,2,2,2]
[1,8,5,7,4,6,2,3]=>0101010=>[2,2,2,2]
[5,8,1,7,4,6,2,3]=>0101010=>[2,2,2,2]
[5,8,4,7,1,6,2,3]=>0101010=>[2,2,2,2]
[6,8,4,7,1,5,2,3]=>0101010=>[2,2,2,2]
[6,8,5,7,1,4,2,3]=>0101010=>[2,2,2,2]
[5,8,6,7,3,4,1,2]=>0101010=>[2,2,2,2]
[5,8,6,7,2,4,1,3]=>0101010=>[2,2,2,2]
[5,8,6,7,1,4,2,3]=>0101010=>[2,2,2,2]
[4,8,6,7,1,5,2,3]=>0101010=>[2,2,2,2]
[4,8,5,7,1,6,2,3]=>0101010=>[2,2,2,2]
[4,8,1,7,5,6,2,3]=>0101010=>[2,2,2,2]
[1,8,4,7,5,6,2,3]=>0101010=>[2,2,2,2]
[1,8,3,7,5,6,2,4]=>0101010=>[2,2,2,2]
[3,8,1,7,5,6,2,4]=>0101010=>[2,2,2,2]
[3,8,5,7,1,6,2,4]=>0101010=>[2,2,2,2]
[3,8,6,7,1,5,2,4]=>0101010=>[2,2,2,2]
[3,8,6,7,2,5,1,4]=>0101010=>[2,2,2,2]
[4,8,6,7,2,5,1,3]=>0101010=>[2,2,2,2]
[4,8,6,7,3,5,1,2]=>0101010=>[2,2,2,2]
[4,8,5,7,3,6,1,2]=>0101010=>[2,2,2,2]
[4,8,5,7,2,6,1,3]=>0101010=>[2,2,2,2]
[3,8,5,7,2,6,1,4]=>0101010=>[2,2,2,2]
[3,8,4,7,2,6,1,5]=>0101010=>[2,2,2,2]
[3,8,4,7,1,6,2,5]=>0101010=>[2,2,2,2]
[3,8,1,7,4,6,2,5]=>0101010=>[2,2,2,2]
[1,8,3,7,4,6,2,5]=>0101010=>[2,2,2,2]
[1,8,3,7,2,6,4,5]=>0101010=>[2,2,2,2]
[3,8,1,7,2,6,4,5]=>0101010=>[2,2,2,2]
[3,8,2,7,1,6,4,5]=>0101010=>[2,2,2,2]
[3,8,2,7,4,6,1,5]=>0101010=>[2,2,2,2]
[3,8,2,7,5,6,1,4]=>0101010=>[2,2,2,2]
[4,8,2,7,5,6,1,3]=>0101010=>[2,2,2,2]
[4,8,3,7,5,6,1,2]=>0101010=>[2,2,2,2]
[3,8,4,7,5,6,1,2]=>0101010=>[2,2,2,2]
[2,8,4,7,5,6,1,3]=>0101010=>[2,2,2,2]
[2,8,3,7,5,6,1,4]=>0101010=>[2,2,2,2]
[2,8,3,7,4,6,1,5]=>0101010=>[2,2,2,2]
[2,8,3,7,1,6,4,5]=>0101010=>[2,2,2,2]
[2,8,1,7,3,6,4,5]=>0101010=>[2,2,2,2]
[7,5,2,8,6,4,1,3]=>1101110=>[1,1,2,1,1,2]
[7,4,8,6,1,5,2,3]=>1011010=>[1,2,1,2,2]
[7,1,8,4,5,2,6,3]=>1010101=>[1,2,2,2,1]
[1,6,7,4,2,8,5,3]=>0011011=>[3,1,2,1,1]
[1,6,7,3,8,5,2,4]=>0010110=>[3,2,1,2]
[7,1,8,3,5,6,2,4]=>1010010=>[1,2,3,2]
[7,3,8,6,2,5,1,4]=>1011010=>[1,2,1,2,2]
[7,4,2,8,6,1,3,5]=>1101100=>[1,1,2,1,3]
[6,8,1,7,2,3,4,5]=>0101000=>[2,2,4]
[2,6,3,7,8,5,4,1]=>0100111=>[2,3,1,1,1]
[2,5,3,7,8,1,6,4]=>0100101=>[2,3,2,1]
[2,5,4,1,3,7,8,6]=>0110001=>[2,1,4,1]
[3,1,5,4,7,8,2,6]=>1010010=>[1,2,3,2]
[5,2,4,8,6,1,3,7]=>1001100=>[1,3,1,3]
[4,8,1,3,6,7,2,5]=>0100010=>[2,4,2]
[5,3,8,2,4,7,1,6]=>1010010=>[1,2,3,2]
[5,4,3,8,1,2,7,6]=>1101001=>[1,1,2,3,1]
[6,4,3,1,2,8,5,7]=>1110010=>[1,1,1,3,2]
[6,4,2,8,1,3,7,5]=>1101001=>[1,1,2,3,1]
[6,3,8,2,5,1,7,4]=>1010101=>[1,2,2,2,1]
[6,3,8,1,4,7,2,5]=>1010010=>[1,2,3,2]
[1,5,7,3,6,8,4,2]=>0010011=>[3,3,1,1]
[1,5,7,4,2,6,8,3]=>0011001=>[3,1,3,1]
[5,8,1,4,2,6,3,7]=>0101010=>[2,2,2,2]
[6,5,1,2,8,7,3,4]=>1100110=>[1,1,3,1,2]
[6,5,3,1,4,2,8,7]=>1110101=>[1,1,1,2,2,1]
[5,3,1,6,4,2,7,8]=>1101100=>[1,1,2,1,3]
[5,2,6,4,1,7,3,8]=>1011010=>[1,2,1,2,2]
[4,6,1,7,5,2,8,3]=>0101101=>[2,2,1,2,1]
[3,5,7,1,8,6,2,4]=>0010110=>[3,2,1,2]
[3,6,2,7,5,1,8,4]=>0101101=>[2,2,1,2,1]
[3,4,7,2,8,6,1,5]=>0010110=>[3,2,1,2]
[3,4,5,8,2,7,1,6]=>0001010=>[4,2,2]
[3,4,6,2,8,1,5,7]=>0010100=>[3,2,3]
[3,5,2,6,8,1,7,4]=>0100101=>[2,3,2,1]
[5,3,6,8,4,7,2,1]=>1001011=>[1,3,2,1,1]
[3,7,2,5,4,8,6,1]=>0101011=>[2,2,2,1,1]
[4,2,6,5,8,3,7,1]=>1010101=>[1,2,2,2,1]
[4,1,6,5,8,3,2,7]=>1010110=>[1,2,2,1,2]
[5,1,6,8,4,3,2,7]=>1001110=>[1,3,1,1,2]
[6,7,8,1,4,3,2,5]=>0010110=>[3,2,1,2]
[4,7,1,5,8,3,2,6]=>0100110=>[2,3,1,2]
[8,3,1,5,4,7,2,6]=>1101010=>[1,1,2,2,2]
[8,4,1,5,7,3,2,6]=>1100110=>[1,1,3,1,2]
[8,4,6,1,7,3,2,5]=>1010110=>[1,2,2,1,2]
[8,3,6,1,4,7,2,5]=>1010010=>[1,2,3,2]
[8,2,6,1,4,3,7,5]=>1010101=>[1,2,2,2,1]
[3,7,6,1,4,8,2,5]=>0110010=>[2,1,3,2]
[6,7,8,5,1,3,2,4]=>0011010=>[3,1,2,2]
[6,7,8,2,4,3,5,1]=>0010101=>[3,2,2,1]
[4,7,6,2,8,3,5,1]=>0110101=>[2,1,2,2,1]
[3,7,6,2,4,8,5,1]=>0110011=>[2,1,3,1,1]
[5,7,3,8,4,6,2,1]=>0101011=>[2,2,2,1,1]
[8,7,3,1,4,6,2,5]=>1110010=>[1,1,1,3,2]
[8,7,6,3,2,5,4,1]=>1111011=>[1,1,1,1,2,1,1]
[8,7,3,5,1,6,2,4]=>1101010=>[1,1,2,2,2]
[8,7,2,5,1,3,6,4]=>1101001=>[1,1,2,3,1]
[8,4,6,5,7,1,2,3]=>1010100=>[1,2,2,3]
[4,7,6,5,8,1,2,3]=>0110100=>[2,1,2,3]
[8,7,6,5,2,1,4,3]=>1111101=>[1,1,1,1,1,2,1]
[3,6,4,8,7,5,1,2]=>0101110=>[2,2,1,1,2]
[5,6,4,3,8,7,1,2]=>0110110=>[2,1,2,1,2]
[1,6,2,4,7,8,5,3]=>0100011=>[2,4,1,1]
[3,6,2,4,8,1,5,7]=>0100100=>[2,3,3]
[3,4,7,2,8,1,6,5]=>0010101=>[3,2,2,1]
[1,4,7,2,5,8,6,3]=>0010011=>[3,3,1,1]
[3,8,7,5,4,6,1,2]=>0111010=>[2,1,1,2,2]
[4,3,6,7,8,5,1,2]=>1000110=>[1,4,1,2]
[3,5,6,4,8,7,1,2]=>0010110=>[3,2,1,2]
[4,6,8,5,3,7,1,2]=>0011010=>[3,1,2,2]
[4,2,7,5,1,8,6,3]=>1011011=>[1,2,1,2,1,1]
[2,1,6,4,8,7,5,3]=>1010111=>[1,2,2,1,1,1]
[7,8,1,4,2,6,5,3]=>0101011=>[2,2,2,1,1]
[6,5,1,3,4,2,8,7]=>1100101=>[1,1,3,2,1]
[4,8,5,3,1,7,2,6]=>0111010=>[2,1,1,2,2]
[7,4,5,3,2,8,1,6]=>1011010=>[1,2,1,2,2]
[5,8,3,6,1,4,2,7]=>0101010=>[2,2,2,2]
[1,4,6,2,5,8,3,7]=>0010010=>[3,3,2]
[1,6,8,7,4,2,3,5]=>0011100=>[3,1,1,3]
[7,6,1,8,3,2,4,5]=>1101100=>[1,1,2,1,3]
[7,1,8,6,3,4,2,5]=>1011010=>[1,2,1,2,2]
[1,8,7,6,4,3,2,5]=>0111110=>[2,1,1,1,1,2]
[2,1,7,5,6,3,8,4]=>1010101=>[1,2,2,2,1]
[3,1,6,7,5,8,2,4]=>1001010=>[1,3,2,2]
[7,8,1,6,5,3,2,4]=>0101110=>[2,2,1,1,2]
[7,8,2,1,4,5,6,3]=>0110001=>[2,1,4,1]
[4,2,6,1,8,5,7,3]=>1010101=>[1,2,2,2,1]
[2,8,1,5,4,6,7,3]=>0101001=>[2,2,3,1]
[1,2,8,3,6,5,7,4]=>0010101=>[3,2,2,1]
[6,1,3,2,7,5,8,4]=>1010101=>[1,2,2,2,1]
[2,6,4,1,7,5,8,3]=>0110101=>[2,1,2,2,1]
[7,6,5,8,1,4,2,3]=>1101010=>[1,1,2,2,2]
[5,8,6,7,3,2,1,4]=>0101110=>[2,2,1,1,2]
[1,6,4,3,7,2,8,5]=>0110101=>[2,1,2,2,1]
[4,6,3,8,1,2,7,5]=>0101001=>[2,2,3,1]
[4,1,6,3,8,2,7,5]=>1010101=>[1,2,2,2,1]
[7,8,1,3,4,2,6,5]=>0100101=>[2,3,2,1]
[2,8,5,7,4,3,1,6]=>0101110=>[2,2,1,1,2]
[7,2,5,8,3,4,1,6]=>1001010=>[1,3,2,2]
[5,3,8,7,1,2,6,4]=>1011001=>[1,2,1,3,1]
[6,5,3,8,2,1,7,4]=>1101101=>[1,1,2,1,2,1]
[3,5,7,8,4,1,2,6]=>0001100=>[4,1,3]
[5,4,7,3,6,8,1,2]=>1010010=>[1,2,3,2]
[3,4,7,2,5,1,6,8]=>0010100=>[3,2,3]
[1,4,7,2,5,8,3,6]=>0010010=>[3,3,2]
[3,6,2,4,7,1,5,8]=>0100100=>[2,3,3]
[7,6,3,5,4,8,1,2]=>1101010=>[1,1,2,2,2]
[4,5,6,3,8,7,1,2]=>0010110=>[3,2,1,2]
[6,3,7,5,8,4,1,2]=>1010110=>[1,2,2,1,2]
[4,8,2,6,1,5,3,7]=>0101010=>[2,2,2,2]
[4,3,6,2,5,1,8,7]=>1010101=>[1,2,2,2,1]
[7,8,1,2,5,6,3,4]=>0100010=>[2,4,2]
[4,1,6,2,5,7,3,8]=>1010010=>[1,2,3,2]
[2,1,8,6,4,7,3,5]=>1011010=>[1,2,1,2,2]
[7,1,3,6,8,4,2,5]=>1000110=>[1,4,1,2]
[1,8,3,6,7,4,5,2]=>0100101=>[2,3,2,1]
[7,1,5,8,3,6,2,4]=>1001010=>[1,3,2,2]
[3,1,6,4,7,2,5,8]=>1010100=>[1,2,2,3]
[5,8,7,1,2,4,3,6]=>0110010=>[2,1,3,2]
[1,5,7,8,2,4,6,3]=>0001001=>[4,3,1]
[6,8,5,1,3,4,2,7]=>0110010=>[2,1,3,2]
[7,6,5,1,4,3,2,8]=>1110110=>[1,1,1,2,1,2]
[2,6,4,5,1,3,8,7]=>0101001=>[2,2,3,1]
[3,5,6,4,1,8,2,7]=>0011010=>[3,1,2,2]
[7,8,5,4,1,3,2,6]=>0111010=>[2,1,1,2,2]
[7,8,2,3,4,1,6,5]=>0100101=>[2,3,2,1]
[4,2,6,3,8,1,7,5]=>1010101=>[1,2,2,2,1]
[7,2,3,5,4,1,8,6]=>1001101=>[1,3,1,2,1]
[6,2,4,3,1,5,7,8]=>1011000=>[1,2,1,4]
[4,2,8,3,1,7,5,6]=>1011010=>[1,2,1,2,2]
[1,3,7,4,8,2,5,6]=>0010100=>[3,2,3]
[5,3,7,4,1,6,2,8]=>1011010=>[1,2,1,2,2]
[2,4,7,3,6,1,8,5]=>0010101=>[3,2,2,1]
[5,8,7,6,3,1,2,4]=>0111100=>[2,1,1,1,3]
[7,5,6,8,1,4,3,2]=>1001011=>[1,3,2,1,1]
[2,4,7,1,6,5,3,8]=>0010110=>[3,2,1,2]
[5,2,7,1,8,4,6,3]=>1010101=>[1,2,2,2,1]
[6,3,1,2,8,4,5,7]=>1100100=>[1,1,3,3]
[4,2,1,3,6,5,8,7]=>1100101=>[1,1,3,2,1]
[4,2,6,1,8,5,3,7]=>1010110=>[1,2,2,1,2]
[7,8,2,1,4,5,3,6]=>0110010=>[2,1,3,2]
[7,8,4,1,5,3,6,2]=>0110101=>[2,1,2,2,1]
[7,5,1,6,4,3,8,2]=>1101101=>[1,1,2,1,2,1]
[5,8,1,6,3,4,7,2]=>0101001=>[2,2,3,1]
[6,8,1,7,5,2,3,4]=>0101100=>[2,2,1,3]
[5,6,1,7,4,8,2,3]=>0101010=>[2,2,2,2]
[7,8,5,1,6,4,2,3]=>0110110=>[2,1,2,1,2]
[2,6,5,7,3,4,8,1]=>0101001=>[2,2,3,1]
[1,6,4,7,5,8,2,3]=>0101010=>[2,2,2,2]
[1,3,7,4,6,8,2,5]=>0010010=>[3,3,2]
[5,2,4,7,3,6,8,1]=>1001001=>[1,3,3,1]
[8,1,6,5,7,2,4,3]=>1010101=>[1,2,2,2,1]
[7,1,6,5,8,3,2,4]=>1010110=>[1,2,2,1,2]
[1,2,7,6,8,3,4,5]=>0010100=>[3,2,3]
[3,8,6,4,2,7,5,1]=>0111011=>[2,1,1,2,1,1]
[7,8,1,6,2,4,5,3]=>0101001=>[2,2,3,1]
[2,8,1,7,4,3,6,5]=>0101101=>[2,2,1,2,1]
[3,7,4,1,8,5,2,6]=>0110110=>[2,1,2,1,2]
[6,7,1,4,8,3,2,5]=>0100110=>[2,3,1,2]
[2,7,1,8,4,5,3,6]=>0101010=>[2,2,2,2]
[6,1,2,8,4,3,5,7]=>1001100=>[1,3,1,3]
[5,1,2,4,8,3,6,7]=>1000100=>[1,4,3]
[4,1,3,2,8,5,6,7]=>1010100=>[1,2,2,3]
[3,2,1,4,8,5,6,7]=>1100100=>[1,1,3,3]
[4,3,6,1,5,8,2,7]=>1010010=>[1,2,3,2]
[2,6,1,4,5,8,3,7]=>0100010=>[2,4,2]
[1,6,2,5,8,3,4,7]=>0100100=>[2,3,3]
[7,4,2,1,8,5,3,6]=>1110110=>[1,1,1,2,1,2]
[1,5,4,2,8,3,6,7]=>0110100=>[2,1,2,3]
[6,4,3,1,5,8,2,7]=>1110010=>[1,1,1,3,2]
[5,4,3,2,1,8,6,7]=>1111010=>[1,1,1,1,2,2]
[2,5,3,4,1,8,6,7]=>0101010=>[2,2,2,2]
[4,3,5,2,1,8,6,7]=>1011010=>[1,2,1,2,2]
[3,7,6,8,4,5,2,1]=>0101011=>[2,2,2,1,1]
[1,7,6,8,5,4,2,3]=>0101110=>[2,2,1,1,2]
[2,4,8,6,7,3,5,1]=>0010101=>[3,2,2,1]
[3,4,8,5,6,7,2,1]=>0010011=>[3,3,1,1]
[6,3,5,8,4,7,2,1]=>1001011=>[1,3,2,1,1]
[5,4,3,8,6,7,2,1]=>1101011=>[1,1,2,2,1,1]
[3,2,8,5,7,4,6,1]=>1010101=>[1,2,2,2,1]
[2,1,8,7,4,6,3,5]=>1011010=>[1,2,1,2,2]
[3,1,8,5,7,6,2,4]=>1010110=>[1,2,2,1,2]
[6,1,5,8,7,4,2,3]=>1001110=>[1,3,1,1,2]
[5,8,6,7,4,3,2,1]=>0101111=>[2,2,1,1,1,1]
[4,8,7,5,6,3,2,1]=>0110111=>[2,1,2,1,1,1]
[4,2,1,6,3,5,8,7]=>1101001=>[1,1,2,3,1]
[6,2,1,4,3,8,5,7]=>1101010=>[1,1,2,2,2]
[8,2,1,4,3,6,5,7]=>1101010=>[1,1,2,2,2]
[6,2,4,1,3,8,5,7]=>1010010=>[1,2,3,2]
[2,1,6,4,3,5,8,7]=>1011001=>[1,2,1,3,1]
[6,4,2,1,3,5,8,7]=>1110001=>[1,1,1,4,1]
[8,4,2,1,3,6,5,7]=>1110010=>[1,1,1,3,2]
[8,4,2,1,6,3,5,7]=>1110100=>[1,1,1,2,3]
[6,4,2,1,8,3,5,7]=>1110100=>[1,1,1,2,3]
[4,6,2,1,3,8,5,7]=>0110010=>[2,1,3,2]
[2,6,1,4,3,8,5,7]=>0101010=>[2,2,2,2]
[2,1,6,4,3,8,5,7]=>1011010=>[1,2,1,2,2]
[4,8,2,1,3,6,5,7]=>0110010=>[2,1,3,2]
[6,8,2,1,4,3,5,7]=>0110100=>[2,1,2,3]
[8,6,2,1,4,3,5,7]=>1110100=>[1,1,1,2,3]
[2,8,1,4,6,3,5,7]=>0100100=>[2,3,3]
[2,6,1,4,8,3,5,7]=>0100100=>[2,3,3]
[2,6,4,1,8,3,5,7]=>0110100=>[2,1,2,3]
[2,6,4,8,1,3,5,7]=>0101000=>[2,2,4]
[4,2,6,1,8,3,5,7]=>1010100=>[1,2,2,3]
[6,2,4,1,8,3,5,7]=>1010100=>[1,2,2,3]
[4,2,1,6,8,3,5,7]=>1100100=>[1,1,3,3]
[4,2,1,6,3,8,5,7]=>1101010=>[1,1,2,2,2]
[4,2,1,3,6,8,5,7]=>1100010=>[1,1,4,2]
[2,1,4,3,8,6,5,7]=>1010110=>[1,2,2,1,2]
[2,4,1,3,8,6,5,7]=>0100110=>[2,3,1,2]
[4,2,1,3,8,6,5,7]=>1100110=>[1,1,3,1,2]
[4,2,1,8,3,6,5,7]=>1101010=>[1,1,2,2,2]
[4,2,1,8,6,3,5,7]=>1101100=>[1,1,2,1,3]
[8,2,1,6,4,3,5,7]=>1101100=>[1,1,2,1,3]
[4,2,8,1,6,3,5,7]=>1010100=>[1,2,2,3]
[2,4,1,8,3,6,5,7]=>0101010=>[2,2,2,2]
[2,1,4,8,3,6,5,7]=>1001010=>[1,3,2,2]
[2,4,8,1,6,3,5,7]=>0010100=>[3,2,3]
[2,4,8,6,1,3,5,7]=>0011000=>[3,1,4]
[4,2,8,6,1,3,5,7]=>1011000=>[1,2,1,4]
[2,1,8,6,4,3,5,7]=>1011100=>[1,2,1,1,3]
[2,8,6,1,4,3,5,7]=>0110100=>[2,1,2,3]
[2,8,6,4,1,3,5,7]=>0111000=>[2,1,1,4]
[4,8,6,2,1,3,5,7]=>0111000=>[2,1,1,4]
[3,2,6,1,5,4,8,7]=>1010101=>[1,2,2,2,1]
[6,1,5,2,4,3,8,7]=>1010101=>[1,2,2,2,1]
[6,1,3,2,5,4,8,7]=>1010101=>[1,2,2,2,1]
[4,3,6,1,5,2,8,7]=>1010101=>[1,2,2,2,1]
[4,3,5,2,8,1,7,6]=>1010101=>[1,2,2,2,1]
[4,3,7,2,6,5,8,1]=>1010101=>[1,2,2,2,1]
[4,3,8,2,6,1,7,5]=>1010101=>[1,2,2,2,1]
[4,3,8,1,5,2,7,6]=>1010101=>[1,2,2,2,1]
[5,4,7,6,8,1,3,2]=>1010101=>[1,2,2,2,1]
[4,3,7,1,8,5,6,2]=>1010101=>[1,2,2,2,1]
[4,3,6,5,8,1,7,2]=>1010101=>[1,2,2,2,1]
[6,3,5,4,7,2,8,1]=>1010101=>[1,2,2,2,1]
[6,3,5,4,8,1,7,2]=>1010101=>[1,2,2,2,1]
[7,1,6,3,8,4,5,2]=>1010101=>[1,2,2,2,1]
[7,1,6,5,8,3,4,2]=>1010101=>[1,2,2,2,1]
[7,4,6,5,8,1,3,2]=>1010101=>[1,2,2,2,1]
[8,4,6,1,3,2,7,5]=>1010101=>[1,2,2,2,1]
[8,1,6,3,4,2,7,5]=>1010101=>[1,2,2,2,1]
[8,3,5,2,6,1,7,4]=>1010101=>[1,2,2,2,1]
[7,3,5,2,6,4,8,1]=>1010101=>[1,2,2,2,1]
[8,2,7,1,5,3,6,4]=>1010101=>[1,2,2,2,1]
[8,1,7,2,4,3,6,5]=>1010101=>[1,2,2,2,1]
[8,1,3,2,7,4,6,5]=>1010101=>[1,2,2,2,1]
[2,1,8,3,7,4,6,5]=>1010101=>[1,2,2,2,1]
[2,1,8,3,5,4,7,6]=>1010101=>[1,2,2,2,1]
[8,1,3,2,5,4,7,6]=>1010101=>[1,2,2,2,1]
[8,1,5,2,4,3,7,6]=>1010101=>[1,2,2,2,1]
[8,2,4,1,5,3,7,6]=>1010101=>[1,2,2,2,1]
[8,2,4,1,7,3,6,5]=>1010101=>[1,2,2,2,1]
[3,2,8,4,6,1,7,5]=>1010101=>[1,2,2,2,1]
[3,2,8,1,7,4,6,5]=>1010101=>[1,2,2,2,1]
[3,2,8,1,5,4,7,6]=>1010101=>[1,2,2,2,1]
[3,2,4,1,8,5,7,6]=>1010101=>[1,2,2,2,1]
[4,1,3,2,7,6,8,5]=>1010101=>[1,2,2,2,1]
[3,2,7,6,8,1,5,4]=>1010101=>[1,2,2,2,1]
[3,2,7,1,8,5,6,4]=>1010101=>[1,2,2,2,1]
[3,2,6,5,8,1,7,4]=>1010101=>[1,2,2,2,1]
[7,2,4,1,8,5,6,3]=>1010101=>[1,2,2,2,1]
[7,6,8,1,5,2,4,3]=>1010101=>[1,2,2,2,1]
[7,6,8,1,3,2,5,4]=>1010101=>[1,2,2,2,1]
[7,1,8,5,6,2,4,3]=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,4,5,3]=>1010101=>[1,2,2,2,1]
[7,2,8,1,5,4,6,3]=>1010101=>[1,2,2,2,1]
[5,4,7,2,6,3,8,1]=>1010101=>[1,2,2,2,1]
[5,4,8,2,6,1,7,3]=>1010101=>[1,2,2,2,1]
[6,1,8,4,7,2,5,3]=>1010101=>[1,2,2,2,1]
[6,5,8,1,3,2,7,4]=>1010101=>[1,2,2,2,1]
[6,5,7,4,8,1,3,2]=>1010101=>[1,2,2,2,1]
[5,4,6,3,8,1,7,2]=>1010101=>[1,2,2,2,1]
[3,2,1,5,8,4,6,7]=>1100100=>[1,1,3,3]
[2,4,8,3,5,7,6,1]=>0010011=>[3,3,1,1]
[4,2,5,3,1,8,6,7]=>1011010=>[1,2,1,2,2]
[1,8,4,2,5,3,6,7]=>0110100=>[2,1,2,3]
[8,1,5,3,2,4,6,7]=>1011000=>[1,2,1,4]
[3,8,1,5,2,4,6,7]=>0101000=>[2,2,4]
[5,4,1,3,8,2,6,7]=>1100100=>[1,1,3,3]
[1,5,7,3,8,4,2,6]=>0010110=>[3,2,1,2]
[5,1,4,7,8,3,2,6]=>1000110=>[1,4,1,2]
[8,1,5,3,7,4,6,2]=>1010101=>[1,2,2,2,1]
[1,4,3,8,7,5,6,2]=>0101101=>[2,2,1,2,1]
[1,6,8,5,3,7,4,2]=>0011011=>[3,1,2,1,1]
[6,4,8,1,7,3,5,2]=>1010101=>[1,2,2,2,1]
[6,4,8,7,1,5,2,3]=>1011010=>[1,2,1,2,2]
[7,1,6,8,4,3,2,5]=>1001110=>[1,3,1,1,2]
[1,6,7,2,8,4,3,5]=>0010110=>[3,2,1,2]
[6,7,1,4,2,8,3,5]=>0101010=>[2,2,2,2]
[6,3,7,1,4,8,2,5]=>1010010=>[1,2,3,2]
[3,7,8,1,5,2,4,6]=>0010100=>[3,2,3]
[7,1,2,8,5,3,4,6]=>1001100=>[1,3,1,3]
[1,7,2,8,4,5,3,6]=>0101010=>[2,2,2,2]
[4,2,1,7,8,5,3,6]=>1100110=>[1,1,3,1,2]
[6,2,4,8,3,7,5,1]=>1001011=>[1,3,2,1,1]
[7,2,6,3,4,1,8,5]=>1010101=>[1,2,2,2,1]
[2,7,1,8,3,5,4,6]=>0101010=>[2,2,2,2]
[2,1,7,3,5,8,4,6]=>1010010=>[1,2,3,2]
[1,2,7,5,8,3,4,6]=>0010100=>[3,2,3]
[8,7,1,3,6,2,4,5]=>1100100=>[1,1,3,3]
[8,2,1,7,3,5,6,4]=>1101001=>[1,1,2,3,1]
[2,7,8,4,1,6,5,3]=>0011011=>[3,1,2,1,1]
[2,8,4,1,6,7,5,3]=>0110011=>[2,1,3,1,1]
[2,1,8,4,7,5,6,3]=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,6,2,4]=>1010010=>[1,2,3,2]
[8,6,1,2,7,5,3,4]=>1100110=>[1,1,3,1,2]
[8,1,6,2,7,4,5,3]=>1010101=>[1,2,2,2,1]
[1,8,5,2,6,7,4,3]=>0110011=>[2,1,3,1,1]
[5,2,1,8,6,7,4,3]=>1101011=>[1,1,2,2,1,1]
[8,7,6,5,1,4,2,3]=>1111010=>[1,1,1,1,2,2]
[8,7,6,1,5,3,4,2]=>1110101=>[1,1,1,2,2,1]
[8,1,7,5,6,4,3,2]=>1010111=>[1,2,2,1,1,1]
[1,8,6,7,5,4,3,2]=>0101111=>[2,2,1,1,1,1]
[6,3,5,2,1,4,8,7]=>1011001=>[1,2,1,3,1]
[8,3,5,7,2,4,1,6]=>1001010=>[1,3,2,2]
[8,5,2,7,4,3,1,6]=>1101110=>[1,1,2,1,1,2]
[6,5,3,1,2,4,8,7]=>1110001=>[1,1,1,4,1]
[4,5,3,6,1,2,8,7]=>0101001=>[2,2,3,1]
[3,5,1,4,6,2,8,7]=>0100101=>[2,3,2,1]
[8,1,4,7,3,6,2,5]=>1001010=>[1,3,2,2]
[8,5,1,4,7,3,2,6]=>1100110=>[1,1,3,1,2]
[8,5,3,7,1,4,2,6]=>1101010=>[1,1,2,2,2]
[6,3,4,7,5,8,1,2]=>1001010=>[1,3,2,2]
[5,1,4,6,8,3,7,2]=>1000101=>[1,4,2,1]
[4,7,1,3,5,8,6,2]=>0100011=>[2,4,1,1]
[4,8,3,7,1,2,6,5]=>0101001=>[2,2,3,1]
[8,7,1,4,2,6,3,5]=>1101010=>[1,1,2,2,2]
[8,6,3,1,2,4,7,5]=>1110001=>[1,1,1,4,1]
[2,1,8,7,5,3,4,6]=>1011100=>[1,2,1,1,3]
[8,1,7,4,5,2,3,6]=>1010100=>[1,2,2,3]
[2,8,7,5,4,1,3,6]=>0111100=>[2,1,1,1,3]
[8,7,2,6,4,1,3,5]=>1101100=>[1,1,2,1,3]
[5,3,7,8,2,4,6,1]=>1001001=>[1,3,3,1]
[5,3,7,6,2,1,8,4]=>1011101=>[1,2,1,1,2,1]
[5,7,8,6,4,2,1,3]=>0011110=>[3,1,1,1,2]
[2,6,7,5,4,8,1,3]=>0011010=>[3,1,2,2]
[6,7,3,5,1,8,2,4]=>0101010=>[2,2,2,2]
[2,1,6,7,5,8,3,4]=>1001010=>[1,3,2,2]
[2,1,5,7,3,6,8,4]=>1001001=>[1,3,3,1]
[4,1,7,2,5,6,8,3]=>1010001=>[1,2,4,1]
[2,4,7,1,6,5,8,3]=>0010101=>[3,2,2,1]
[3,4,6,2,7,8,5,1]=>0010011=>[3,3,1,1]
[4,6,1,2,5,8,7,3]=>0100011=>[2,4,1,1]
[5,6,3,1,8,7,2,4]=>0110110=>[2,1,2,1,2]
[3,5,6,4,7,1,8,2]=>0010101=>[3,2,2,1]
[3,4,6,1,5,7,8,2]=>0010001=>[3,4,1]
[3,4,1,5,7,6,8,2]=>0100101=>[2,3,2,1]
[4,2,1,7,3,5,8,6]=>1101001=>[1,1,2,3,1]
[7,3,1,5,4,2,8,6]=>1101101=>[1,1,2,1,2,1]
[6,3,1,4,2,8,5,7]=>1101010=>[1,1,2,2,2]
[8,4,1,5,2,7,6,3]=>1101011=>[1,1,2,2,1,1]
[7,2,5,1,4,3,8,6]=>1010101=>[1,2,2,2,1]
[3,6,2,7,1,4,8,5]=>0101001=>[2,2,3,1]
[2,7,5,4,1,3,8,6]=>0111001=>[2,1,1,3,1]
[6,4,3,2,1,8,5,7]=>1111010=>[1,1,1,1,2,2]
[1,7,6,2,4,8,3,5]=>0110010=>[2,1,3,2]
[2,7,3,6,4,8,1,5]=>0101010=>[2,2,2,2]
[6,2,7,5,3,8,1,4]=>1011010=>[1,2,1,2,2]
[7,1,8,5,3,6,4,2]=>1011011=>[1,2,1,2,1,1]
[5,8,3,2,7,1,6,4]=>0110101=>[2,1,2,2,1]
[8,7,2,6,1,5,4,3]=>1101011=>[1,1,2,2,1,1]
[1,8,5,7,4,3,6,2]=>0101101=>[2,2,1,2,1]
[1,8,5,7,2,4,6,3]=>0101001=>[2,2,3,1]
[3,8,6,1,7,2,5,4]=>0110101=>[2,1,2,2,1]
[7,2,8,5,6,1,4,3]=>1010101=>[1,2,2,2,1]
[3,6,5,8,1,4,2,7]=>0101010=>[2,2,2,2]
[4,3,6,8,2,1,5,7]=>1001100=>[1,3,1,3]
[4,3,6,7,8,1,2,5]=>1000100=>[1,4,3]
[5,4,6,7,2,8,1,3]=>1001010=>[1,3,2,2]
[3,5,7,1,4,8,2,6]=>0010010=>[3,3,2]
[8,1,5,2,7,4,6,3]=>1010101=>[1,2,2,2,1]
[8,4,1,5,7,3,6,2]=>1100101=>[1,1,3,2,1]
[6,4,2,5,8,3,1,7]=>1100110=>[1,1,3,1,2]
[5,4,1,6,8,2,3,7]=>1100100=>[1,1,3,3]
[5,3,1,7,2,8,4,6]=>1101010=>[1,1,2,2,2]
[5,3,6,4,7,8,1,2]=>1010010=>[1,2,3,2]
[6,3,7,4,8,5,2,1]=>1010111=>[1,2,2,1,1,1]
[4,7,2,5,8,6,3,1]=>0100111=>[2,3,1,1,1]
[6,3,1,8,4,7,5,2]=>1101011=>[1,1,2,2,1,1]
[5,4,8,1,7,6,2,3]=>1010110=>[1,2,2,1,2]
[5,2,8,1,7,3,6,4]=>1010101=>[1,2,2,2,1]
[5,7,3,8,1,6,4,2]=>0101011=>[2,2,2,1,1]
[6,4,7,8,1,5,3,2]=>1001011=>[1,3,2,1,1]
[4,6,8,2,7,1,5,3]=>0010101=>[3,2,2,1]
[2,5,8,7,1,3,6,4]=>0011001=>[3,1,3,1]
[8,3,7,6,1,5,4,2]=>1011011=>[1,2,1,2,1,1]
[8,2,7,6,5,1,4,3]=>1011101=>[1,2,1,1,2,1]
[4,3,8,7,6,2,1,5]=>1011110=>[1,2,1,1,1,2]
[2,4,8,7,6,1,3,5]=>0011100=>[3,1,1,3]
[3,5,8,7,2,6,1,4]=>0011010=>[3,1,2,2]
[4,7,3,8,6,5,1,2]=>0101110=>[2,2,1,1,2]
[7,5,8,6,4,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[5,8,7,3,6,4,2,1]=>0110111=>[2,1,2,1,1,1]
[3,8,7,6,5,1,4,2]=>0111101=>[2,1,1,1,2,1]
[2,8,7,6,5,4,1,3]=>0111110=>[2,1,1,1,1,2]
[5,4,3,2,1,6,7,8,9,10]=>111100000=>[1,1,1,1,6]
[6,4,3,2,7,1,5,8,9,10]=>111010000=>[1,1,1,2,5]
[7,5,3,8,2,6,1,4,9,10]=>110101000=>[1,1,2,2,4]
[8,6,9,4,7,2,5,1,3,10]=>101010100=>[1,2,2,2,3]
[7,8,5,6,3,1,4,2]=>0101101=>[2,2,1,2,1]
[7,8,5,3,6,1,2,4]=>0110100=>[2,1,2,3]
[7,5,6,3,1,4,2,8]=>1011010=>[1,2,1,2,2]
[7,5,8,3,1,4,2,6]=>1011010=>[1,2,1,2,2]
[7,8,5,3,1,4,2,6]=>0111010=>[2,1,1,2,2]
[7,8,5,3,1,6,2,4]=>0111010=>[2,1,1,2,2]
[7,8,5,3,1,6,4,2]=>0111011=>[2,1,1,2,1,1]
[7,8,5,3,6,1,4,2]=>0110101=>[2,1,2,2,1]
[7,8,5,3,6,4,1,2]=>0110110=>[2,1,2,1,2]
[7,8,5,3,4,1,6,2]=>0110101=>[2,1,2,2,1]
[7,8,5,3,1,4,6,2]=>0111001=>[2,1,1,3,1]
[7,5,8,3,1,2,6,4]=>1011001=>[1,2,1,3,1]
[7,5,8,3,4,1,6,2]=>1010101=>[1,2,2,2,1]
[7,5,8,3,4,6,1,2]=>1010010=>[1,2,3,2]
[7,5,6,3,4,1,8,2]=>1010101=>[1,2,2,2,1]
[7,5,6,3,1,4,8,2]=>1011001=>[1,2,1,3,1]
[7,5,3,1,6,4,8,2]=>1110101=>[1,1,1,2,2,1]
[7,5,3,6,1,4,8,2]=>1101001=>[1,1,2,3,1]
[7,5,3,6,4,1,8,2]=>1101101=>[1,1,2,1,2,1]
[7,5,3,6,4,8,1,2]=>1101010=>[1,1,2,2,2]
[7,5,3,8,4,6,1,2]=>1101010=>[1,1,2,2,2]
[7,5,3,8,4,1,6,2]=>1101101=>[1,1,2,1,2,1]
[7,5,3,8,1,4,6,2]=>1101001=>[1,1,2,3,1]
[7,5,3,1,8,4,6,2]=>1110101=>[1,1,1,2,2,1]
[7,5,3,1,8,2,6,4]=>1110101=>[1,1,1,2,2,1]
[7,5,3,1,6,2,4,8]=>1110100=>[1,1,1,2,3]
[7,5,3,1,6,4,2,8]=>1110110=>[1,1,1,2,1,2]
[7,5,3,1,8,4,2,6]=>1110110=>[1,1,1,2,1,2]
[7,5,3,1,8,6,2,4]=>1110110=>[1,1,1,2,1,2]
[7,5,3,8,1,6,4,2]=>1101011=>[1,1,2,2,1,1]
[7,5,3,8,6,1,4,2]=>1101101=>[1,1,2,1,2,1]
[7,5,3,8,6,4,1,2]=>1101110=>[1,1,2,1,1,2]
[7,5,8,3,6,4,1,2]=>1010110=>[1,2,2,1,2]
[7,5,8,3,6,1,4,2]=>1010101=>[1,2,2,2,1]
[7,5,8,3,1,6,4,2]=>1011011=>[1,2,1,2,1,1]
[7,5,8,3,1,6,2,4]=>1011010=>[1,2,1,2,2]
[7,5,3,8,1,6,2,4]=>1101010=>[1,1,2,2,2]
[7,5,3,8,1,4,2,6]=>1101010=>[1,1,2,2,2]
[7,5,3,6,1,4,2,8]=>1101010=>[1,1,2,2,2]
[7,5,3,6,4,1,2,8]=>1101100=>[1,1,2,1,3]
[7,5,3,8,4,1,2,6]=>1101100=>[1,1,2,1,3]
[7,5,3,8,6,1,2,4]=>1101100=>[1,1,2,1,3]
[7,5,8,6,3,1,2,4]=>1011100=>[1,2,1,1,3]
[7,5,8,6,3,1,4,2]=>1011101=>[1,2,1,1,2,1]
[7,5,8,6,3,4,1,2]=>1011010=>[1,2,1,2,2]
[7,5,6,8,3,1,4,2]=>1001101=>[1,3,1,2,1]
[7,5,6,3,8,1,2,4]=>1010100=>[1,2,2,3]
[7,5,3,6,1,8,2,4]=>1101010=>[1,1,2,2,2]
[7,5,6,3,1,8,2,4]=>1011010=>[1,2,1,2,2]
[7,5,6,3,1,8,4,2]=>1011011=>[1,2,1,2,1,1]
[7,5,6,3,8,1,4,2]=>1010101=>[1,2,2,2,1]
[7,5,6,3,8,4,1,2]=>1010110=>[1,2,2,1,2]
[7,5,3,6,8,4,1,2]=>1100110=>[1,1,3,1,2]
[7,5,3,6,8,1,4,2]=>1100101=>[1,1,3,2,1]
[7,5,3,6,1,8,4,2]=>1101011=>[1,1,2,2,1,1]
[7,5,3,1,6,8,4,2]=>1110011=>[1,1,1,3,1,1]
[7,5,3,1,6,8,2,4]=>1110010=>[1,1,1,3,2]
[7,5,3,1,2,8,6,4]=>1110011=>[1,1,1,3,1,1]
[7,5,3,4,1,6,8,2]=>1101001=>[1,1,2,3,1]
[4,6,8,3,5,7,1,2]=>0010010=>[3,3,2]
[6,8,1,2,4,5,7,3]=>0100001=>[2,5,1]
[3,6,8,2,5,7,1,4]=>0010010=>[3,3,2]
[8,3,5,2,4,1,6,7]=>1010100=>[1,2,2,3]
[3,5,7,2,4,6,1,8]=>0010010=>[3,3,2]
[4,2,5,7,3,6,1,8]=>1001010=>[1,3,2,2]
[4,5,2,8,3,1,6,7]=>0101100=>[2,2,1,3]
[2,1,6,8,4,7,3,5]=>1001010=>[1,3,2,2]
[1,2,5,8,3,6,7,4]=>0001001=>[4,3,1]
[5,3,6,8,4,7,1,2]=>1001010=>[1,3,2,2]
[3,1,2,6,8,5,7,4]=>1000101=>[1,4,2,1]
[4,3,6,2,7,5,1,8]=>1010110=>[1,2,2,1,2]
[4,3,1,7,8,2,6,5]=>1100101=>[1,1,3,2,1]
[5,4,7,3,8,6,1,2]=>1010110=>[1,2,2,1,2]
[5,8,4,7,6,3,1,2]=>0101110=>[2,2,1,1,2]
[8,3,5,1,2,7,6,4]=>1010011=>[1,2,3,1,1]
[4,7,3,6,5,2,1,8]=>0101110=>[2,2,1,1,2]
[5,3,7,6,4,2,1,8]=>1011110=>[1,2,1,1,1,2]
[5,3,1,6,4,2,8,7]=>1101101=>[1,1,2,1,2,1]
[1,3,8,5,4,2,7,6]=>0011101=>[3,1,1,2,1]
[1,8,3,6,2,7,5,4]=>0101011=>[2,2,2,1,1]
[1,6,8,7,4,2,5,3]=>0011101=>[3,1,1,2,1]
[6,4,8,7,5,3,1,2]=>1011110=>[1,2,1,1,1,2]
[3,1,2,7,6,4,8,5]=>1001101=>[1,3,1,2,1]
[5,2,6,3,7,4,1,8]=>1010110=>[1,2,2,1,2]
[2,8,5,3,1,6,4,7]=>0111010=>[2,1,1,2,2]
[2,1,7,3,8,5,4,6]=>1010110=>[1,2,2,1,2]
[1,6,2,3,7,8,5,4]=>0100011=>[2,4,1,1]
[1,6,7,2,8,4,5,3]=>0010101=>[3,2,2,1]
[6,3,7,4,8,5,1,2]=>1010110=>[1,2,2,1,2]
[5,7,1,8,2,4,6,3]=>0101001=>[2,2,3,1]
[5,1,2,7,8,3,6,4]=>1000101=>[1,4,2,1]
[4,2,1,7,3,8,5,6]=>1101010=>[1,1,2,2,2]
[6,2,8,4,3,1,5,7]=>1011100=>[1,2,1,1,3]
[6,4,2,7,3,5,1,8]=>1101010=>[1,1,2,2,2]
[7,3,2,1,8,4,5,6]=>1110100=>[1,1,1,2,3]
[3,7,2,8,6,1,4,5]=>0101100=>[2,2,1,3]
[7,8,3,2,5,6,1,4]=>0110010=>[2,1,3,2]
[7,1,8,2,4,5,6,3]=>1010001=>[1,2,4,1]
[8,7,6,1,2,4,5,3]=>1110001=>[1,1,1,4,1]
[8,3,6,5,2,1,4,7]=>1011100=>[1,2,1,1,3]
[8,2,4,1,6,5,3,7]=>1010110=>[1,2,2,1,2]
[8,2,4,1,7,6,3,5]=>1010110=>[1,2,2,1,2]
[8,5,1,2,7,3,6,4]=>1100101=>[1,1,3,2,1]
[6,1,8,2,3,7,5,4]=>1010011=>[1,2,3,1,1]
[2,8,1,7,5,4,3,6]=>0101110=>[2,2,1,1,2]
[1,7,2,8,3,6,5,4]=>0101011=>[2,2,2,1,1]
[7,3,8,6,5,4,1,2]=>1011110=>[1,2,1,1,1,2]
[1,8,7,6,5,2,4,3]=>0111101=>[2,1,1,1,2,1]
[8,1,7,3,2,6,5,4]=>1011011=>[1,2,1,2,1,1]
[4,3,1,2,8,7,6,5]=>1100111=>[1,1,3,1,1,1]
[5,1,4,3,2,8,7,6]=>1011011=>[1,2,1,2,1,1]
[8,6,4,3,1,5,7,2]=>1111001=>[1,1,1,1,3,1]
[8,6,4,1,5,2,7,3]=>1110101=>[1,1,1,2,2,1]
[8,6,5,3,2,1,7,4]=>1111101=>[1,1,1,1,1,2,1]
[8,7,2,4,5,3,1,6]=>1100110=>[1,1,3,1,2]
[8,5,1,2,6,7,3,4]=>1100010=>[1,1,4,2]
[8,5,1,6,4,2,7,3]=>1101101=>[1,1,2,1,2,1]
[8,5,1,3,6,4,7,2]=>1100101=>[1,1,3,2,1]
[8,6,5,1,7,3,2,4]=>1110110=>[1,1,1,2,1,2]
[7,4,8,3,1,6,2,5]=>1011010=>[1,2,1,2,2]
[7,1,5,8,3,2,6,4]=>1001101=>[1,3,1,2,1]
[5,7,4,1,8,2,6,3]=>0110101=>[2,1,2,2,1]
[5,7,4,3,1,8,6,2]=>0111011=>[2,1,1,2,1,1]
[8,5,7,4,6,1,3,2]=>1010101=>[1,2,2,2,1]
[1,8,7,2,5,4,6,3]=>0110101=>[2,1,2,2,1]
[4,3,1,8,7,5,2,6]=>1101110=>[1,1,2,1,1,2]
[1,3,5,6,8,4,2,7]=>0000110=>[5,1,2]
[3,1,4,6,8,7,2,5]=>1000110=>[1,4,1,2]
[1,6,3,8,7,2,5,4]=>0101101=>[2,2,1,2,1]
[1,6,2,4,8,7,5,3]=>0100111=>[2,3,1,1,1]
[8,4,1,6,7,5,3,2]=>1100111=>[1,1,3,1,1,1]
[7,3,6,8,5,1,2,4]=>1001100=>[1,3,1,3]
[1,3,7,2,6,8,4,5]=>0010010=>[3,3,2]
[3,6,5,2,8,1,4,7]=>0110100=>[2,1,2,3]
[6,1,2,7,8,5,3,4]=>1000110=>[1,4,1,2]
[6,1,2,7,4,8,5,3]=>1001011=>[1,3,2,1,1]
[3,1,6,4,7,8,5,2]=>1010011=>[1,2,3,1,1]
[5,7,1,3,8,4,6,2]=>0100101=>[2,3,2,1]
[5,7,1,8,4,2,6,3]=>0101101=>[2,2,1,2,1]
[5,7,1,2,8,6,3,4]=>0100110=>[2,3,1,2]
[4,2,6,3,8,1,5,7]=>1010100=>[1,2,2,3]
[4,2,6,7,3,5,1,8]=>1001010=>[1,3,2,2]
[3,6,2,4,7,5,1,8]=>0100110=>[2,3,1,2]
[3,6,2,4,1,8,5,7]=>0101010=>[2,2,2,2]
[7,1,4,5,2,8,6,3]=>1001011=>[1,3,2,1,1]
[4,7,3,1,5,8,6,2]=>0110011=>[2,1,3,1,1]
[8,7,6,4,1,5,2,3]=>1111010=>[1,1,1,1,2,2]
[3,8,2,7,1,5,4,6]=>0101010=>[2,2,2,2]
[3,6,8,2,1,5,4,7]=>0011010=>[3,1,2,2]
[2,4,8,1,6,5,3,7]=>0010110=>[3,2,1,2]
[4,2,8,1,5,7,3,6]=>1010010=>[1,2,3,2]
[8,5,7,6,1,4,2,3]=>1011010=>[1,2,1,2,2]
[1,8,2,4,6,7,3,5]=>0100010=>[2,4,2]
[2,1,5,8,6,4,3,7]=>1001110=>[1,3,1,1,2]
[1,2,5,7,8,4,3,6]=>0000110=>[5,1,2]
[1,2,7,4,8,6,3,5]=>0010110=>[3,2,1,2]
[1,2,7,8,3,6,5,4]=>0001011=>[4,2,1,1]
[1,8,5,7,4,3,2,6]=>0101110=>[2,2,1,1,2]
[1,6,8,5,4,3,2,7]=>0011110=>[3,1,1,1,2]
[7,1,5,8,3,4,6,2]=>1001001=>[1,3,3,1]
[7,1,5,8,4,3,2,6]=>1001110=>[1,3,1,1,2]
[7,1,2,5,8,3,6,4]=>1000101=>[1,4,2,1]
[7,1,6,4,2,3,5,8]=>1011000=>[1,2,1,4]
[2,7,1,4,8,3,5,6]=>0100100=>[2,3,3]
[7,1,4,6,5,8,3,2]=>1001011=>[1,3,2,1,1]
[7,1,2,3,8,5,4,6]=>1000110=>[1,4,1,2]
[7,1,5,4,3,8,2,6]=>1011010=>[1,2,1,2,2]
[7,1,3,4,2,6,8,5]=>1001001=>[1,3,3,1]
[3,6,7,1,4,8,5,2]=>0010011=>[3,3,1,1]
[3,5,1,4,8,6,2,7]=>0100110=>[2,3,1,2]
[3,6,2,4,7,8,1,5]=>0100010=>[2,4,2]
[5,6,2,4,8,7,1,3]=>0100110=>[2,3,1,2]
[6,5,8,7,2,3,1,4]=>1011010=>[1,2,1,2,2]
[3,4,7,2,5,8,1,6]=>0010010=>[3,3,2]
[4,3,8,1,2,7,5,6]=>1010010=>[1,2,3,2]
[5,6,7,8,1,3,4,2]=>0001001=>[4,3,1]
[5,7,8,6,1,2,3,4]=>0011000=>[3,1,4]
[2,8,3,1,5,6,4,7]=>0110010=>[2,1,3,2]
[3,8,7,1,5,4,2,6]=>0110110=>[2,1,2,1,2]
[4,3,1,7,6,8,2,5]=>1101010=>[1,1,2,2,2]
[3,4,1,7,5,6,8,2]=>0101001=>[2,2,3,1]
[3,4,1,5,7,6,2,8]=>0100110=>[2,3,1,2]
[2,4,6,1,7,5,8,3]=>0010101=>[3,2,2,1]
[4,7,8,1,2,3,6,5]=>0010001=>[3,4,1]
[4,2,1,5,6,3,7,8]=>1100100=>[1,1,3,3]
[5,8,1,6,4,3,2,7]=>0101110=>[2,2,1,1,2]
[5,8,1,6,3,7,2,4]=>0101010=>[2,2,2,2]
[7,6,5,1,3,8,2,4]=>1110010=>[1,1,1,3,2]
[7,6,5,1,3,4,8,2]=>1110001=>[1,1,1,4,1]
[7,2,6,4,1,3,8,5]=>1011001=>[1,2,1,3,1]
[8,4,5,3,7,2,6,1]=>1010101=>[1,2,2,2,1]
[4,7,5,2,8,1,6,3]=>0110101=>[2,1,2,2,1]
[4,6,3,8,5,1,7,2]=>0101101=>[2,2,1,2,1]
[2,6,4,3,1,5,7,8]=>0111000=>[2,1,1,4]
[3,6,4,8,1,7,2,5]=>0101010=>[2,2,2,2]
[7,3,8,4,1,5,2,6]=>1011010=>[1,2,1,2,2]
[4,2,8,3,6,1,5,7]=>1010100=>[1,2,2,3]
[6,7,5,8,2,1,4,3]=>0101101=>[2,2,1,2,1]
[6,8,5,7,2,1,3,4]=>0101100=>[2,2,1,3]
[4,8,5,2,7,1,3,6]=>0110100=>[2,1,2,3]
[6,3,5,2,1,7,4,8]=>1011010=>[1,2,1,2,2]
[3,6,5,4,2,8,1,7]=>0111010=>[2,1,1,2,2]
[7,4,5,3,8,2,1,6]=>1010110=>[1,2,2,1,2]
[1,6,4,7,2,5,3,8]=>0101010=>[2,2,2,2]
[1,4,3,7,2,6,5,8]=>0101010=>[2,2,2,2]
[1,5,7,2,4,8,3,6]=>0010010=>[3,3,2]
[1,6,5,7,2,4,3,8]=>0101010=>[2,2,2,2]
[1,7,6,2,8,3,4,5]=>0110100=>[2,1,2,3]
[1,4,2,3,5,8,7,6]=>0100011=>[2,4,1,1]
[1,5,2,3,4,8,7,6]=>0100011=>[2,4,1,1]
[1,6,5,2,3,8,7,4]=>0110011=>[2,1,3,1,1]
[1,7,6,5,2,8,4,3]=>0111011=>[2,1,1,2,1,1]
[1,6,5,2,3,8,4,7]=>0110010=>[2,1,3,2]
[1,6,7,5,2,3,8,4]=>0011001=>[3,1,3,1]
[1,7,5,2,8,4,3,6]=>0110110=>[2,1,2,1,2]
[1,7,5,6,2,8,3,4]=>0101010=>[2,2,2,2]
[1,5,7,6,2,4,8,3]=>0011001=>[3,1,3,1]
[1,4,7,6,2,5,8,3]=>0011001=>[3,1,3,1]
[1,2,6,5,3,7,4,8]=>0011010=>[3,1,2,2]
[1,3,7,5,2,6,8,4]=>0011001=>[3,1,3,1]
[1,7,4,6,2,8,3,5]=>0101010=>[2,2,2,2]
[1,7,3,5,2,8,4,6]=>0101010=>[2,2,2,2]
[1,3,7,4,2,6,8,5]=>0011001=>[3,1,3,1]
[1,4,7,3,2,5,8,6]=>0011001=>[3,1,3,1]
[1,5,7,3,2,4,8,6]=>0011001=>[3,1,3,1]
[1,7,3,4,2,8,5,6]=>0101010=>[2,2,2,2]
[1,7,4,2,8,5,3,6]=>0110110=>[2,1,2,1,2]
[1,6,7,4,2,3,8,5]=>0011001=>[3,1,3,1]
[1,4,3,2,5,8,6,7]=>0110010=>[2,1,3,2]
[1,5,3,2,4,8,6,7]=>0110010=>[2,1,3,2]
[1,6,4,2,3,8,5,7]=>0110010=>[2,1,3,2]
[1,7,6,4,2,8,5,3]=>0111011=>[2,1,1,2,1,1]
[1,7,5,3,2,8,6,4]=>0111011=>[2,1,1,2,1,1]
[1,6,4,2,3,8,7,5]=>0110011=>[2,1,3,1,1]
[1,5,3,2,4,8,7,6]=>0110011=>[2,1,3,1,1]
[6,8,5,4,3,2,1,7]=>0111110=>[2,1,1,1,1,2]
[2,8,5,4,3,7,1,6]=>0111010=>[2,1,1,2,2]
[7,6,1,4,3,8,5,2]=>1101011=>[1,1,2,2,1,1]
[7,6,5,1,3,8,4,2]=>1110011=>[1,1,1,3,1,1]
[7,3,5,4,8,1,6,2]=>1010101=>[1,2,2,2,1]
[5,6,8,4,3,1,7,2]=>0011101=>[3,1,1,2,1]
[6,8,5,4,1,2,7,3]=>0111001=>[2,1,1,3,1]
[6,8,2,4,3,7,1,5]=>0101010=>[2,2,2,2]
[1,8,3,4,7,2,6,5]=>0100101=>[2,3,2,1]
[7,5,8,4,3,2,1,6]=>1011110=>[1,2,1,1,1,2]
[4,8,5,7,3,2,1,6]=>0101110=>[2,2,1,1,2]
[7,8,1,2,4,3,5,6]=>0100100=>[2,3,3]
[7,8,2,1,4,3,6,5]=>0110101=>[2,1,2,2,1]
[3,4,6,5,7,8,1,2]=>0010010=>[3,3,2]
[4,3,6,5,8,7,1,2]=>1010110=>[1,2,2,1,2]
[4,2,6,1,8,3,7,5]=>1010101=>[1,2,2,2,1]
[6,7,3,8,4,5,1,2]=>0101010=>[2,2,2,2]
[6,7,4,5,1,8,2,3]=>0101010=>[2,2,2,2]
[4,5,3,8,6,7,1,2]=>0101010=>[2,2,2,2]
[5,6,3,8,4,7,1,2]=>0101010=>[2,2,2,2]
[5,6,4,7,1,8,2,3]=>0101010=>[2,2,2,2]
[5,6,2,7,3,4,1,8]=>0101010=>[2,2,2,2]
[4,5,1,8,6,7,2,3]=>0101010=>[2,2,2,2]
[7,8,4,5,1,6,2,3]=>0101010=>[2,2,2,2]
[4,5,2,3,1,8,6,7]=>0101010=>[2,2,2,2]
[5,6,2,3,1,8,4,7]=>0101010=>[2,2,2,2]
[5,6,3,4,1,8,2,7]=>0101010=>[2,2,2,2]
[3,6,4,5,2,7,1,8]=>0101010=>[2,2,2,2]
[3,6,4,5,1,8,2,7]=>0101010=>[2,2,2,2]
[2,6,4,8,1,5,3,7]=>0101010=>[2,2,2,2]
[2,8,3,6,1,5,4,7]=>0101010=>[2,2,2,2]
[2,8,3,4,1,6,5,7]=>0101010=>[2,2,2,2]
[7,8,1,5,3,6,2,4]=>0101010=>[2,2,2,2]
[1,8,3,6,5,7,2,4]=>0101010=>[2,2,2,2]
[1,6,4,7,3,8,2,5]=>0101010=>[2,2,2,2]
[1,7,3,6,4,8,2,5]=>0101010=>[2,2,2,2]
[1,7,2,8,4,6,3,5]=>0101010=>[2,2,2,2]
[1,7,5,8,2,6,3,4]=>0101010=>[2,2,2,2]
[6,7,1,5,3,8,2,4]=>0101010=>[2,2,2,2]
[6,7,1,8,2,5,3,4]=>0101010=>[2,2,2,2]
[6,7,1,8,4,5,2,3]=>0101010=>[2,2,2,2]
[6,7,5,8,1,4,2,3]=>0101010=>[2,2,2,2]
[5,8,6,7,2,3,1,4]=>0101010=>[2,2,2,2]
[6,7,2,3,1,8,4,5]=>0101010=>[2,2,2,2]
[6,7,2,8,1,4,3,5]=>0101010=>[2,2,2,2]
[6,7,3,4,1,8,2,5]=>0101010=>[2,2,2,2]
[3,4,2,7,5,6,1,8]=>0101010=>[2,2,2,2]
[2,7,5,8,1,4,3,6]=>0101010=>[2,2,2,2]
[2,3,1,8,4,7,5,6]=>0101010=>[2,2,2,2]
[2,3,1,8,6,7,4,5]=>0101010=>[2,2,2,2]
[7,8,2,3,1,6,4,5]=>0101010=>[2,2,2,2]
[2,8,1,4,3,7,5,6]=>0101010=>[2,2,2,2]
[2,8,1,7,3,5,4,6]=>0101010=>[2,2,2,2]
[4,5,1,7,3,8,2,6]=>0101010=>[2,2,2,2]
[3,8,1,5,2,7,4,6]=>0101010=>[2,2,2,2]
[3,4,1,8,6,7,2,5]=>0101010=>[2,2,2,2]
[7,8,3,4,1,6,2,5]=>0101010=>[2,2,2,2]
[3,4,2,5,1,8,6,7]=>0101010=>[2,2,2,2]
[3,4,2,8,1,6,5,7]=>0101010=>[2,2,2,2]
[2,5,4,1,6,3,8,7]=>0110101=>[2,1,2,2,1]
[3,6,5,1,2,4,8,7]=>0110001=>[2,1,4,1]
[5,2,3,6,4,1,8,7]=>1001101=>[1,3,1,2,1]
[6,1,4,5,3,2,8,7]=>1001101=>[1,3,1,2,1]
[5,6,7,8,1,4,3,2]=>0001011=>[4,2,1,1]
[4,2,6,8,5,7,3,1]=>1001011=>[1,3,2,1,1]
[2,1,5,8,7,6,3,4]=>1001110=>[1,3,1,1,2]
[2,1,4,7,6,3,8,5]=>1001101=>[1,3,1,2,1]
[6,3,7,1,5,2,8,4]=>1010101=>[1,2,2,2,1]
[4,2,8,6,7,3,1,5]=>1010110=>[1,2,2,1,2]
[7,4,3,8,2,1,5,6]=>1101100=>[1,1,2,1,3]
[2,4,1,5,8,3,7,6]=>0100101=>[2,3,2,1]
[4,7,5,8,1,6,3,2]=>0101011=>[2,2,2,1,1]
[2,1,5,8,7,3,4,6]=>1001100=>[1,3,1,3]
[8,5,7,3,6,1,4,2]=>1010101=>[1,2,2,2,1]
[4,2,5,1,6,7,8,3]=>1010001=>[1,2,4,1]
[7,2,3,4,8,5,6,1]=>1000101=>[1,4,2,1]
[6,1,8,5,2,7,4,3]=>1011011=>[1,2,1,2,1,1]
[2,1,7,4,5,8,6,3]=>1010011=>[1,2,3,1,1]
[2,1,8,3,6,7,5,4]=>1010011=>[1,2,3,1,1]
[6,8,7,2,5,3,1,4]=>0110110=>[2,1,2,1,2]
[8,2,1,6,4,7,5,3]=>1101011=>[1,1,2,2,1,1]
[7,8,4,2,5,1,6,3]=>0110101=>[2,1,2,2,1]
[6,1,2,3,7,5,8,4]=>1000101=>[1,4,2,1]
[7,6,8,4,2,5,3,1]=>1011011=>[1,2,1,2,1,1]
[8,5,7,1,6,3,2,4]=>1010110=>[1,2,2,1,2]
[4,1,2,3,7,6,8,5]=>1000101=>[1,4,2,1]
[3,2,4,1,8,5,6,7]=>1010100=>[1,2,2,3]
[3,4,8,6,5,2,1,7]=>0011110=>[3,1,1,1,2]
[4,1,6,3,5,8,7,2]=>1010011=>[1,2,3,1,1]
[8,6,7,1,5,4,3,2]=>1010111=>[1,2,2,1,1,1]
[2,1,6,5,8,4,7,3]=>1010101=>[1,2,2,2,1]
[4,1,8,5,6,2,3,7]=>1010100=>[1,2,2,3]
[2,6,4,8,7,3,5,1]=>0101101=>[2,2,1,2,1]
[3,1,8,2,7,5,4,6]=>1010110=>[1,2,2,1,2]
[8,2,3,1,7,4,6,5]=>1010101=>[1,2,2,2,1]
[7,4,8,6,3,2,5,1]=>1011101=>[1,2,1,1,2,1]
[5,8,4,7,2,1,3,6]=>0101100=>[2,2,1,3]
[2,1,8,4,3,7,5,6]=>1011010=>[1,2,1,2,2]
[6,3,8,2,4,5,7,1]=>1010001=>[1,2,4,1]
[5,8,2,4,3,1,6,7]=>0101100=>[2,2,1,3]
[7,3,5,8,1,4,2,6]=>1001010=>[1,3,2,2]
[3,8,7,6,1,4,2,5]=>0111010=>[2,1,1,2,2]
[5,1,8,3,6,7,2,4]=>1010010=>[1,2,3,2]
[3,6,1,4,7,8,5,2]=>0100011=>[2,4,1,1]
[1,6,8,4,7,5,2,3]=>0010110=>[3,2,1,2]
[6,8,1,3,5,7,2,4]=>0100010=>[2,4,2]
[7,6,1,4,3,8,2,5]=>1101010=>[1,1,2,2,2]
[8,4,2,6,7,5,3,1]=>1100111=>[1,1,3,1,1,1]
[7,4,1,6,8,2,5,3]=>1100101=>[1,1,3,2,1]
[1,8,6,2,5,3,4,7]=>0110100=>[2,1,2,3]
[4,7,1,2,5,3,8,6]=>0100101=>[2,3,2,1]
[8,7,3,6,4,5,2,1]=>1101011=>[1,1,2,2,1,1]
[5,7,8,6,2,1,4,3]=>0011101=>[3,1,1,2,1]
[1,8,6,4,5,2,3,7]=>0110100=>[2,1,2,3]
[1,4,7,2,6,8,3,5]=>0010010=>[3,3,2]
[2,5,4,3,6,8,1,7]=>0110010=>[2,1,3,2]
[3,8,5,4,6,2,1,7]=>0110110=>[2,1,2,1,2]
[4,8,2,1,3,7,5,6]=>0110010=>[2,1,3,2]
[1,8,3,2,5,6,7,4]=>0110001=>[2,1,4,1]
[6,4,1,2,7,5,8,3]=>1100101=>[1,1,3,2,1]
[4,3,7,8,5,1,6,2]=>1001101=>[1,3,1,2,1]
[1,2,7,3,6,5,8,4]=>0010101=>[3,2,2,1]
[2,8,7,6,3,4,1,5]=>0111010=>[2,1,1,2,2]
[5,8,2,6,3,4,1,7]=>0101010=>[2,2,2,2]
[4,1,7,5,8,6,2,3]=>1010110=>[1,2,2,1,2]
[1,2,4,5,8,3,7,6]=>0000101=>[5,2,1]
[4,8,1,5,2,3,7,6]=>0101001=>[2,2,3,1]
[2,4,6,3,7,1,8,5]=>0010101=>[3,2,2,1]
[6,5,8,7,1,3,4,2]=>1011001=>[1,2,1,3,1]
[3,6,7,2,4,8,1,5]=>0010010=>[3,3,2]
[1,5,2,7,4,3,8,6]=>0101101=>[2,2,1,2,1]
[7,6,1,2,8,3,5,4]=>1100101=>[1,1,3,2,1]
[6,7,8,1,5,2,4,3]=>0010101=>[3,2,2,1]
[5,7,8,4,1,2,6,3]=>0011001=>[3,1,3,1]
[4,7,8,5,6,1,3,2]=>0010101=>[3,2,2,1]
[5,6,4,8,1,2,7,3]=>0101001=>[2,2,3,1]
[6,5,4,1,2,3,8,7]=>1110001=>[1,1,1,4,1]
[7,5,1,6,2,3,8,4]=>1101001=>[1,1,2,3,1]
[4,5,6,7,8,1,3,2]=>0000101=>[5,2,1]
[8,1,3,6,7,4,5,2]=>1000101=>[1,4,2,1]
[4,2,6,7,3,1,8,5]=>1001101=>[1,3,1,2,1]
[7,3,1,5,4,8,2,6]=>1101010=>[1,1,2,2,2]
[4,5,3,2,8,1,6,7]=>0110100=>[2,1,2,3]
[7,4,1,5,3,2,6,8]=>1101100=>[1,1,2,1,3]
[8,1,5,4,3,2,6,7]=>1011100=>[1,2,1,1,3]
[8,1,6,4,2,5,3,7]=>1011010=>[1,2,1,2,2]
[6,5,3,1,2,7,4,8]=>1110010=>[1,1,1,3,2]
[5,6,3,8,1,4,2,7]=>0101010=>[2,2,2,2]
[4,6,3,8,2,1,5,7]=>0101100=>[2,2,1,3]
[4,7,8,3,2,1,5,6]=>0011100=>[3,1,1,3]
[5,7,8,3,1,4,2,6]=>0011010=>[3,1,2,2]
[8,1,7,2,5,4,3,6]=>1010110=>[1,2,2,1,2]
[8,1,7,2,4,5,6,3]=>1010001=>[1,2,4,1]
[7,6,1,2,4,5,8,3]=>1100001=>[1,1,5,1]
[4,7,8,2,3,1,6,5]=>0010101=>[3,2,2,1]
[7,5,1,3,2,6,8,4]=>1101001=>[1,1,2,3,1]
[8,1,6,3,2,5,7,4]=>1011001=>[1,2,1,3,1]
[8,1,5,3,4,2,7,6]=>1010101=>[1,2,2,2,1]
[5,4,2,3,1,6,8,7]=>1101001=>[1,1,2,3,1]
[6,3,2,1,5,7,4,8]=>1110010=>[1,1,1,3,2]
[8,1,4,3,5,6,2,7]=>1010010=>[1,2,3,2]
[3,6,5,8,2,4,1,7]=>0101010=>[2,2,2,2]
[6,2,4,5,8,3,1,7]=>1000110=>[1,4,1,2]
[4,8,1,2,5,6,3,7]=>0100010=>[2,4,2]
[8,1,3,5,2,6,4,7]=>1001010=>[1,3,2,2]
[5,2,1,6,3,8,4,7]=>1101010=>[1,1,2,2,2]
[6,1,4,5,8,3,2,7]=>1000110=>[1,4,1,2]
[6,5,4,3,8,2,1,7]=>1110110=>[1,1,1,2,1,2]
[4,6,8,3,7,2,5,1]=>0010101=>[3,2,2,1]
[1,4,3,6,2,7,8,5]=>0101001=>[2,2,3,1]
[4,7,8,5,3,1,2,6]=>0011100=>[3,1,1,3]
[8,5,7,4,3,6,1,2]=>1011010=>[1,2,1,2,2]
[4,7,8,3,6,1,5,2]=>0010101=>[3,2,2,1]
[8,4,6,1,7,3,5,2]=>1010101=>[1,2,2,2,1]
[1,3,8,6,4,7,5,2]=>0011011=>[3,1,2,1,1]
[7,6,2,1,4,3,8,5]=>1110101=>[1,1,1,2,2,1]
[7,6,8,1,4,3,2,5]=>1010110=>[1,2,2,1,2]
[1,5,7,3,2,6,8,4]=>0011001=>[3,1,3,1]
[3,2,6,8,5,7,4,1]=>1001011=>[1,3,2,1,1]
[7,5,2,3,1,6,8,4]=>1101001=>[1,1,2,3,1]
[1,6,4,7,2,3,8,5]=>0101001=>[2,2,3,1]
[3,1,7,5,2,8,4,6]=>1011010=>[1,2,1,2,2]
[1,7,4,5,2,8,3,6]=>0101010=>[2,2,2,2]
[3,2,6,8,7,4,5,1]=>1001101=>[1,3,1,2,1]
[6,3,2,1,7,8,4,5]=>1110010=>[1,1,1,3,2]
[5,7,3,8,2,1,4,6]=>0101100=>[2,2,1,3]
[3,7,1,8,4,2,5,6]=>0101100=>[2,2,1,3]
[4,2,1,3,7,5,8,6]=>1100101=>[1,1,3,2,1]
[8,4,3,7,6,2,1,5]=>1101110=>[1,1,2,1,1,2]
[3,6,2,8,7,1,5,4]=>0101101=>[2,2,1,2,1]
[7,3,2,8,1,6,5,4]=>1101011=>[1,1,2,2,1,1]
[3,8,7,2,6,5,4,1]=>0110111=>[2,1,2,1,1,1]
[4,2,7,8,6,1,5,3]=>1001101=>[1,3,1,2,1]
[5,8,4,2,7,1,6,3]=>0110101=>[2,1,2,2,1]
[8,5,3,1,7,2,6,4]=>1110101=>[1,1,1,2,2,1]
[8,2,1,6,3,7,5,4]=>1101011=>[1,1,2,2,1,1]
[1,4,6,8,2,7,5,3]=>0001011=>[4,2,1,1]
[2,1,7,3,8,6,5,4]=>1010111=>[1,2,2,1,1,1]
[8,2,1,7,6,5,4,3]=>1101111=>[1,1,2,1,1,1,1]
[8,6,7,5,1,4,3,2]=>1011011=>[1,2,1,2,1,1]
[6,4,7,3,2,1,8,5]=>1011101=>[1,2,1,1,2,1]
[4,8,7,3,2,1,6,5]=>0111101=>[2,1,1,1,2,1]
[6,5,3,7,2,1,4,8]=>1101100=>[1,1,2,1,3]
[5,8,3,6,2,1,4,7]=>0101100=>[2,2,1,3]
[6,4,3,7,2,1,8,5]=>1101101=>[1,1,2,1,2,1]
[4,8,3,6,2,1,7,5]=>0101101=>[2,2,1,2,1]
[6,3,7,8,2,1,4,5]=>1001100=>[1,3,1,3]
[5,3,7,6,2,1,4,8]=>1011100=>[1,2,1,1,3]
[3,8,7,6,2,1,4,5]=>0111100=>[2,1,1,1,3]
[5,8,4,2,6,1,3,7]=>0110100=>[2,1,2,3]
[4,8,7,2,5,1,3,6]=>0110100=>[2,1,2,3]
[5,8,3,2,6,1,4,7]=>0110100=>[2,1,2,3]
[4,8,3,2,5,1,7,6]=>0110101=>[2,1,2,2,1]
[4,3,7,2,5,1,8,6]=>1010101=>[1,2,2,2,1]
[6,4,2,7,5,1,3,8]=>1101100=>[1,1,2,1,3]
[5,4,2,6,7,1,3,8]=>1100100=>[1,1,3,3]
[6,2,7,8,5,1,3,4]=>1001100=>[1,3,1,3]
[2,8,7,6,5,1,3,4]=>0111100=>[2,1,1,1,3]
[6,4,7,3,1,5,8,2]=>1011001=>[1,2,1,3,1]
[4,8,7,3,1,5,6,2]=>0111001=>[2,1,1,3,1]
[6,5,3,7,1,4,8,2]=>1101001=>[1,1,2,3,1]
[5,8,3,6,1,4,7,2]=>0101001=>[2,2,3,1]
[6,4,3,7,1,5,8,2]=>1101001=>[1,1,2,3,1]
[4,8,3,6,1,5,7,2]=>0101001=>[2,2,3,1]
[5,3,7,6,1,4,8,2]=>1011001=>[1,2,1,3,1]
[4,3,7,6,1,5,8,2]=>1011001=>[1,2,1,3,1]
[3,8,7,6,1,4,5,2]=>0111001=>[2,1,1,3,1]
[5,8,4,2,1,7,3,6]=>0111010=>[2,1,1,2,2]
[6,4,7,2,1,5,3,8]=>1011010=>[1,2,1,2,2]
[5,8,3,2,1,4,7,6]=>0111001=>[2,1,1,3,1]
[6,3,7,2,1,4,5,8]=>1011000=>[1,2,1,4]
[6,5,2,7,1,4,3,8]=>1101010=>[1,1,2,2,2]
[5,8,2,6,1,4,3,7]=>0101010=>[2,2,2,2]
[6,4,2,7,1,5,3,8]=>1101010=>[1,1,2,2,2]
[2,8,7,6,1,4,3,5]=>0111010=>[2,1,1,2,2]
[6,5,4,1,8,7,3,2]=>1110111=>[1,1,1,2,1,1,1]
[6,4,7,1,5,8,3,2]=>1010011=>[1,2,3,1,1]
[4,8,7,1,5,6,3,2]=>0110011=>[2,1,3,1,1]
[6,5,3,1,8,4,7,2]=>1110101=>[1,1,1,2,2,1]
[5,8,3,1,6,4,7,2]=>0110101=>[2,1,2,2,1]
[6,4,3,1,5,8,7,2]=>1110011=>[1,1,1,3,1,1]
[5,8,2,1,6,4,3,7]=>0110110=>[2,1,2,1,2]
[6,4,2,1,5,8,3,7]=>1110010=>[1,1,1,3,2]
[3,8,2,1,5,4,6,7]=>0110100=>[2,1,2,3]
[6,2,7,1,5,4,3,8]=>1010110=>[1,2,2,1,2]
[3,2,7,1,5,4,6,8]=>1010100=>[1,2,2,3]
[2,8,7,1,5,4,3,6]=>0110110=>[2,1,2,1,2]
[6,5,1,7,8,4,3,2]=>1100111=>[1,1,3,1,1,1]
[5,4,1,6,7,8,3,2]=>1100011=>[1,1,4,1,1]
[4,3,1,6,5,7,8,2]=>1101001=>[1,1,2,3,1]
[4,2,1,6,5,7,3,8]=>1101010=>[1,1,2,2,2]
[2,8,1,6,5,4,3,7]=>0101110=>[2,2,1,1,2]
[6,1,7,8,5,4,3,2]=>1001111=>[1,3,1,1,1,1]
[5,1,7,6,8,4,3,2]=>1010111=>[1,2,2,1,1,1]
[4,1,7,6,5,8,3,2]=>1011011=>[1,2,1,2,1,1]
[4,5,8,1,7,2,3,6]=>0010100=>[3,2,3]
[4,5,8,1,2,6,3,7]=>0010010=>[3,3,2]
[8,1,3,5,7,2,4,6]=>1000100=>[1,4,3]
[3,6,8,1,7,2,4,5]=>0010100=>[3,2,3]
[3,4,5,6,8,1,7,2]=>0000101=>[5,2,1]
[8,2,3,5,6,7,1,4]=>1000010=>[1,5,2]
[8,1,2,3,5,4,6,7]=>1000100=>[1,4,3]
[4,5,8,1,7,6,3,2]=>0010111=>[3,2,1,1,1]
[8,7,2,1,6,3,4,5]=>1110100=>[1,1,1,2,3]
[8,7,2,1,3,5,4,6]=>1110010=>[1,1,1,3,2]
[8,6,4,1,7,5,3,2]=>1110111=>[1,1,1,2,1,1,1]
[2,3,6,7,8,1,5,4]=>0000101=>[5,2,1]
[7,4,2,6,8,5,1,3]=>1100110=>[1,1,3,1,2]
[7,3,2,5,8,6,1,4]=>1100110=>[1,1,3,1,2]
[7,3,1,8,6,2,4,5]=>1101100=>[1,1,2,1,3]
[3,1,7,2,5,4,8,6]=>1010101=>[1,2,2,2,1]
[7,1,4,2,8,3,6,5]=>1010101=>[1,2,2,2,1]
[7,1,8,2,5,3,6,4]=>1010101=>[1,2,2,2,1]
[7,3,8,4,5,1,6,2]=>1010101=>[1,2,2,2,1]
[8,3,7,4,6,1,5,2]=>1010101=>[1,2,2,2,1]
[8,2,7,1,6,4,5,3]=>1010101=>[1,2,2,2,1]
[8,1,7,5,4,2,3,6]=>1011100=>[1,2,1,1,3]
[8,1,2,6,5,4,3,7]=>1001110=>[1,3,1,1,2]
[8,1,7,6,3,2,4,5]=>1011100=>[1,2,1,1,3]
[8,2,7,5,6,1,4,3]=>1010101=>[1,2,2,2,1]
[3,6,8,1,7,5,4,2]=>0010111=>[3,2,1,1,1]
[8,2,6,7,5,4,1,3]=>1001110=>[1,3,1,1,2]
[8,6,7,2,3,1,5,4]=>1010101=>[1,2,2,2,1]
[2,7,8,6,3,1,5,4]=>0011101=>[3,1,1,2,1]
[7,3,1,8,6,5,4,2]=>1101111=>[1,1,2,1,1,1,1]
[8,1,7,6,5,4,3,2]=>1011111=>[1,2,1,1,1,1,1]
[2,1,8,6,3,7,4,5]=>1011010=>[1,2,1,2,2]
[8,6,1,5,2,7,4,3]=>1101011=>[1,1,2,2,1,1]
[8,5,1,7,4,2,6,3]=>1101101=>[1,1,2,1,2,1]
[2,1,7,8,3,6,5,4]=>1001011=>[1,3,2,1,1]
[2,1,4,8,5,7,3,6]=>1001010=>[1,3,2,2]
[7,8,1,5,2,6,3,4]=>0101010=>[2,2,2,2]
[6,4,1,5,2,3,8,7]=>1101001=>[1,1,2,3,1]
[4,3,7,8,5,2,1,6]=>1001110=>[1,3,1,1,2]
[5,3,7,4,6,8,1,2]=>1010010=>[1,2,3,2]
[5,8,3,7,6,2,1,4]=>0101110=>[2,2,1,1,2]
[4,2,6,3,8,5,1,7]=>1010110=>[1,2,2,1,2]
[5,8,2,1,7,6,4,3]=>0110111=>[2,1,2,1,1,1]
[8,3,2,4,1,7,5,6]=>1101010=>[1,1,2,2,2]
[6,3,4,2,1,7,8,5]=>1011001=>[1,2,1,3,1]
[7,2,8,1,4,6,5,3]=>1010011=>[1,2,3,1,1]
[6,8,1,4,5,3,2,7]=>0100110=>[2,3,1,2]
[8,2,6,1,4,7,3,5]=>1010010=>[1,2,3,2]
[4,2,1,3,6,7,8,5]=>1100001=>[1,1,5,1]
[2,3,4,1,8,6,5,7]=>0010110=>[3,2,1,2]
[6,3,5,4,1,2,8,7]=>1011001=>[1,2,1,3,1]
[8,7,3,6,5,1,4,2]=>1101101=>[1,1,2,1,2,1]
[3,4,7,2,8,1,5,6]=>0010100=>[3,2,3]
[3,8,4,7,1,6,5,2]=>0101011=>[2,2,2,1,1]
[3,2,4,6,1,5,8,7]=>1001001=>[1,3,3,1]
[6,8,5,4,3,7,2,1]=>0111011=>[2,1,1,2,1,1]
[5,8,4,3,2,1,7,6]=>0111101=>[2,1,1,1,2,1]
[6,5,4,3,1,8,7,2]=>1111011=>[1,1,1,1,2,1,1]
[8,7,5,4,3,1,6,2]=>1111101=>[1,1,1,1,1,2,1]
[3,4,6,2,8,5,1,7]=>0010110=>[3,2,1,2]
[3,4,6,7,1,8,5,2]=>0001011=>[4,2,1,1]
[3,4,6,8,1,5,2,7]=>0001010=>[4,2,2]
[3,4,7,2,8,5,6,1]=>0010101=>[3,2,2,1]
[3,4,8,2,1,5,6,7]=>0011000=>[3,1,4]
[3,5,2,6,8,4,1,7]=>0100110=>[2,3,1,2]
[3,5,2,7,4,8,6,1]=>0101011=>[2,2,2,1,1]
[3,5,6,2,7,8,1,4]=>0010010=>[3,3,2]
[3,5,6,2,8,4,1,7]=>0010110=>[3,2,1,2]
[3,5,6,8,4,1,2,7]=>0001100=>[4,1,3]
[3,5,7,2,4,8,6,1]=>0010011=>[3,3,1,1]
[3,5,7,2,8,4,6,1]=>0010101=>[3,2,2,1]
[3,5,7,8,4,1,6,2]=>0001101=>[4,1,2,1]
[3,5,8,2,4,1,6,7]=>0010100=>[3,2,3]
[3,6,2,1,7,8,5,4]=>0110011=>[2,1,3,1,1]
[3,6,2,1,8,5,4,7]=>0110110=>[2,1,2,1,2]
[3,6,2,7,4,8,5,1]=>0101011=>[2,2,2,1,1]
[3,6,2,7,8,5,4,1]=>0100111=>[2,3,1,1,1]
[3,6,8,2,4,5,1,7]=>0010010=>[3,3,2]
[3,7,2,1,4,8,6,5]=>0110011=>[2,1,3,1,1]
[3,7,2,8,4,5,6,1]=>0101001=>[2,2,3,1]
[3,8,2,1,4,5,6,7]=>0110000=>[2,1,5]
[4,1,5,6,7,8,3,2]=>1000011=>[1,5,1,1]
[4,1,5,7,3,8,6,2]=>1001011=>[1,3,2,1,1]
[4,1,5,7,8,2,6,3]=>1000101=>[1,4,2,1]
[4,1,5,8,3,2,6,7]=>1001100=>[1,3,1,3]
[4,1,6,3,7,8,5,2]=>1010011=>[1,2,3,1,1]
[4,1,6,3,8,5,2,7]=>1010110=>[1,2,2,1,2]
[4,1,6,7,3,8,5,2]=>1001011=>[1,3,2,1,1]
[4,1,6,8,3,5,2,7]=>1001010=>[1,3,2,2]
[4,1,7,3,8,5,6,2]=>1010101=>[1,2,2,2,1]
[4,1,8,3,2,5,6,7]=>1011000=>[1,2,1,4]
[4,5,2,7,3,8,6,1]=>0101011=>[2,2,2,1,1]
[4,5,7,3,2,8,6,1]=>0011011=>[3,1,2,1,1]
[4,5,8,3,2,1,6,7]=>0011100=>[3,1,1,3]
[4,6,2,3,8,5,1,7]=>0100110=>[2,3,1,2]
[4,6,2,8,3,5,1,7]=>0101010=>[2,2,2,2]
[4,6,7,3,2,8,5,1]=>0011011=>[3,1,2,1,1]
[4,7,2,8,3,5,6,1]=>0101001=>[2,2,3,1]
[4,7,8,3,2,5,6,1]=>0011001=>[3,1,3,1]
[4,8,2,3,1,5,6,7]=>0101000=>[2,2,4]
[5,1,2,6,8,4,3,7]=>1000110=>[1,4,1,2]
[5,1,2,8,4,3,6,7]=>1001100=>[1,3,1,3]
[5,1,6,3,7,8,2,4]=>1010010=>[1,2,3,2]
[5,1,6,3,8,4,2,7]=>1010110=>[1,2,2,1,2]
[5,1,6,7,4,8,2,3]=>1001010=>[1,3,2,2]
[5,6,2,3,8,4,1,7]=>0100110=>[2,3,1,2]
[5,6,2,7,4,8,1,3]=>0101010=>[2,2,2,2]
[5,6,2,7,8,4,1,3]=>0100110=>[2,3,1,2]
[5,6,8,3,4,2,1,7]=>0010110=>[3,2,1,2]
[5,7,8,3,4,2,6,1]=>0010101=>[3,2,2,1]
[6,1,2,3,7,8,5,4]=>1000011=>[1,5,1,1]
[6,1,2,3,8,5,4,7]=>1000110=>[1,4,1,2]
[6,1,2,7,8,5,4,3]=>1000111=>[1,4,1,1,1]
[6,1,7,8,4,5,3,2]=>1001011=>[1,3,2,1,1]
[6,7,2,8,4,5,3,1]=>0101011=>[2,2,2,1,1]
[7,1,2,3,4,8,6,5]=>1000011=>[1,5,1,1]
[7,1,2,3,8,5,6,4]=>1000101=>[1,4,2,1]
[7,1,2,8,4,5,6,3]=>1001001=>[1,3,3,1]
[7,1,8,3,4,5,6,2]=>1010001=>[1,2,4,1]
[2,4,6,1,8,5,7,3]=>0010101=>[3,2,2,1]
[6,4,1,8,2,3,7,5]=>1101001=>[1,1,2,3,1]
[5,8,1,2,4,3,7,6]=>0100101=>[2,3,2,1]
[5,8,1,6,2,4,3,7]=>0101010=>[2,2,2,2]
[1,3,5,7,2,6,4,8]=>0001010=>[4,2,2]
[3,5,8,6,1,2,4,7]=>0011000=>[3,1,4]
[3,5,1,8,2,4,7,6]=>0101001=>[2,2,3,1]
[3,1,6,8,2,4,7,5]=>1001001=>[1,3,3,1]
[2,3,5,6,8,1,7,4]=>0000101=>[5,2,1]
[5,6,4,8,2,1,7,3]=>0101101=>[2,2,1,2,1]
[7,1,8,6,3,4,5,2]=>1011001=>[1,2,1,3,1]
[7,6,5,2,4,8,1,3]=>1110010=>[1,1,1,3,2]
[6,7,4,5,2,1,8,3]=>0101101=>[2,2,1,2,1]
[5,1,7,8,6,4,3,2]=>1001111=>[1,3,1,1,1,1]
[2,5,7,8,6,3,1,4]=>0001110=>[4,1,1,2]
[7,1,8,6,3,2,4,5]=>1011100=>[1,2,1,1,3]
[7,8,1,6,4,2,3,5]=>0101100=>[2,2,1,3]
[2,4,8,1,5,6,7,3]=>0010001=>[3,4,1]
[8,4,1,2,5,6,3,7]=>1100010=>[1,1,4,2]
[8,3,1,6,5,2,4,7]=>1101100=>[1,1,2,1,3]
[2,5,3,8,7,6,1,4]=>0101110=>[2,2,1,1,2]
[5,8,7,4,2,6,1,3]=>0111010=>[2,1,1,2,2]
[5,1,8,4,7,6,3,2]=>1010111=>[1,2,2,1,1,1]
[7,3,2,6,5,1,8,4]=>1101101=>[1,1,2,1,2,1]
[8,2,3,6,5,1,7,4]=>1001101=>[1,3,1,2,1]
[4,8,6,5,7,3,2,1]=>0110111=>[2,1,2,1,1,1]
[4,8,5,6,7,3,2,1]=>0100111=>[2,3,1,1,1]
[3,8,7,4,5,6,2,1]=>0110011=>[2,1,3,1,1]
[2,8,7,6,3,4,5,1]=>0111001=>[2,1,1,3,1]
[1,8,7,6,5,2,3,4]=>0111100=>[2,1,1,1,3]
[7,2,8,6,5,4,1,3]=>1011110=>[1,2,1,1,1,2]
[6,3,2,8,5,1,7,4]=>1101101=>[1,1,2,1,2,1]
[8,4,7,2,5,6,3,1]=>1010011=>[1,2,3,1,1]
[6,8,5,4,3,1,7,2]=>0111101=>[2,1,1,1,2,1]
[5,8,6,4,1,3,7,2]=>0111001=>[2,1,1,3,1]
[3,6,1,8,5,2,7,4]=>0101101=>[2,2,1,2,1]
[3,4,1,2,8,6,7,5]=>0100101=>[2,3,2,1]
[6,8,3,5,4,1,7,2]=>0101101=>[2,2,1,2,1]
[7,6,3,8,5,2,1,4]=>1101110=>[1,1,2,1,1,2]
[5,8,7,4,1,6,3,2]=>0111011=>[2,1,1,2,1,1]
[4,2,3,1,7,8,5,6]=>1010010=>[1,2,3,2]
[8,6,3,4,7,2,5,1]=>1100101=>[1,1,3,2,1]
[5,2,8,4,1,6,7,3]=>1011001=>[1,2,1,3,1]
[4,1,3,6,8,2,5,7]=>1000100=>[1,4,3]
[1,6,3,2,5,8,4,7]=>0110010=>[2,1,3,2]
[8,3,2,1,5,4,7,6]=>1110101=>[1,1,1,2,2,1]
[5,3,6,2,4,8,1,7]=>1010010=>[1,2,3,2]
[1,6,2,4,5,8,3,7]=>0100010=>[2,4,2]
[5,3,2,1,6,8,4,7]=>1110010=>[1,1,1,3,2]
[2,6,5,8,1,3,4,7]=>0101000=>[2,2,4]
[4,3,1,6,5,8,2,7]=>1101010=>[1,1,2,2,2]
[3,4,6,5,7,1,8,2]=>0010101=>[3,2,2,1]
[8,2,6,4,1,7,3,5]=>1011010=>[1,2,1,2,2]
[5,4,6,8,1,2,7,3]=>1001001=>[1,3,3,1]
[3,4,7,8,6,2,5,1]=>0001101=>[4,1,2,1]
[7,5,8,2,4,6,1,3]=>1010010=>[1,2,3,2]
[8,2,7,4,6,1,3,5]=>1010100=>[1,2,2,3]
[4,7,3,2,8,1,6,5]=>0110101=>[2,1,2,2,1]
[3,8,1,7,2,5,6,4]=>0101001=>[2,2,3,1]
[8,3,2,5,7,6,1,4]=>1100110=>[1,1,3,1,2]
[2,8,6,1,5,7,3,4]=>0110010=>[2,1,3,2]
[1,2,8,3,5,6,7,4]=>0010001=>[3,4,1]
[4,2,3,7,1,8,6,5]=>1001011=>[1,3,2,1,1]
[3,2,6,4,8,1,7,5]=>1010101=>[1,2,2,2,1]
[8,2,1,6,7,3,4,5]=>1100100=>[1,1,3,3]
[2,7,8,5,4,1,3,6]=>0011100=>[3,1,1,3]
[1,7,5,3,8,4,2,6]=>0110110=>[2,1,2,1,2]
[4,7,5,3,1,2,8,6]=>0111001=>[2,1,1,3,1]
[5,6,7,3,8,4,2,1]=>0010111=>[3,2,1,1,1]
[5,7,3,2,4,1,8,6]=>0110101=>[2,1,2,2,1]
[8,4,1,3,7,2,5,6]=>1100100=>[1,1,3,3]
[2,8,4,7,1,3,5,6]=>0101000=>[2,2,4]
[3,5,2,8,6,1,7,4]=>0101101=>[2,2,1,2,1]
[1,7,6,3,2,5,8,4]=>0111001=>[2,1,1,3,1]
[3,8,1,5,6,2,7,4]=>0100101=>[2,3,2,1]
[4,3,5,6,7,1,8,2]=>1000101=>[1,4,2,1]
[7,1,5,2,8,6,4,3]=>1010111=>[1,2,2,1,1,1]
[6,5,4,8,7,2,1,3]=>1101110=>[1,1,2,1,1,2]
[1,8,5,3,6,2,7,4]=>0110101=>[2,1,2,2,1]
[6,5,8,7,2,1,3,4]=>1011100=>[1,2,1,1,3]
[3,6,2,1,7,5,8,4]=>0110101=>[2,1,2,2,1]
[4,7,2,6,5,8,1,3]=>0101010=>[2,2,2,2]
[6,8,1,4,2,7,3,5]=>0101010=>[2,2,2,2]
[6,3,4,7,1,8,2,5]=>1001010=>[1,3,2,2]
[3,4,7,8,2,5,6,1]=>0001001=>[4,3,1]
[1,8,2,4,5,6,7,3]=>0100001=>[2,5,1]
[2,1,4,6,8,5,7,3]=>1000101=>[1,4,2,1]
[3,2,5,7,6,1,8,4]=>1001101=>[1,3,1,2,1]
[3,1,4,6,5,7,8,2]=>1001001=>[1,3,3,1]
[1,2,3,4,8,6,5,7]=>0000110=>[5,1,2]
[1,2,3,8,5,4,6,7]=>0001100=>[4,1,3]
[1,2,3,8,5,6,4,7]=>0001010=>[4,2,2]
[1,2,3,8,6,5,4,7]=>0001110=>[4,1,1,2]
[1,8,3,4,2,5,6,7]=>0101000=>[2,2,4]
[1,2,8,5,4,3,6,7]=>0011100=>[3,1,1,3]
[1,8,4,3,2,5,6,7]=>0111000=>[2,1,1,4]
[8,5,7,6,4,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[8,4,7,6,5,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[8,4,7,5,6,3,2,1]=>1010111=>[1,2,2,1,1,1]
[8,5,7,4,6,3,2,1]=>1010111=>[1,2,2,1,1,1]
[8,7,6,3,5,4,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,6,7,3,5,4,2,1]=>1010111=>[1,2,2,1,1,1]
[8,5,7,3,6,4,2,1]=>1010111=>[1,2,2,1,1,1]
[8,4,7,3,6,5,2,1]=>1010111=>[1,2,2,1,1,1]
[8,1,7,4,6,5,3,2]=>1010111=>[1,2,2,1,1,1]
[8,3,7,2,6,5,4,1]=>1010111=>[1,2,2,1,1,1]
[8,5,7,2,6,4,3,1]=>1010111=>[1,2,2,1,1,1]
[8,6,7,2,5,4,3,1]=>1010111=>[1,2,2,1,1,1]
[8,7,6,2,5,4,3,1]=>1110111=>[1,1,1,2,1,1,1]
[8,4,7,1,6,5,3,2]=>1010111=>[1,2,2,1,1,1]
[8,3,7,1,6,5,4,2]=>1010111=>[1,2,2,1,1,1]
[8,2,7,1,6,5,4,3]=>1010111=>[1,2,2,1,1,1]
[8,1,7,2,6,5,4,3]=>1010111=>[1,2,2,1,1,1]
[8,1,7,2,6,4,5,3]=>1010101=>[1,2,2,2,1]
[8,3,7,1,6,4,5,2]=>1010101=>[1,2,2,2,1]
[8,4,7,1,6,3,5,2]=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,3,4,2]=>1010101=>[1,2,2,2,1]
[8,6,7,1,5,3,4,2]=>1010101=>[1,2,2,2,1]
[8,7,6,2,5,3,4,1]=>1110101=>[1,1,1,2,2,1]
[8,6,7,2,5,3,4,1]=>1010101=>[1,2,2,2,1]
[8,5,7,2,6,3,4,1]=>1010101=>[1,2,2,2,1]
[8,4,7,2,6,3,5,1]=>1010101=>[1,2,2,2,1]
[8,3,7,2,6,4,5,1]=>1010101=>[1,2,2,2,1]
[8,2,7,3,6,4,5,1]=>1010101=>[1,2,2,2,1]
[8,1,7,3,6,4,5,2]=>1010101=>[1,2,2,2,1]
[8,1,7,4,6,3,5,2]=>1010101=>[1,2,2,2,1]
[8,2,7,4,6,3,5,1]=>1010101=>[1,2,2,2,1]
[8,3,7,4,6,2,5,1]=>1010101=>[1,2,2,2,1]
[8,5,7,3,6,2,4,1]=>1010101=>[1,2,2,2,1]
[8,6,7,3,5,2,4,1]=>1010101=>[1,2,2,2,1]
[8,5,7,4,6,2,3,1]=>1010101=>[1,2,2,2,1]
[8,4,7,5,6,2,3,1]=>1010101=>[1,2,2,2,1]
[8,3,7,5,6,2,4,1]=>1010101=>[1,2,2,2,1]
[8,2,7,5,6,3,4,1]=>1010101=>[1,2,2,2,1]
[8,1,7,5,6,3,4,2]=>1010101=>[1,2,2,2,1]
[8,3,7,6,5,2,4,1]=>1011101=>[1,2,1,1,2,1]
[8,4,7,6,5,2,3,1]=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,4,2,3,1]=>1011101=>[1,2,1,1,2,1]
[8,7,6,5,4,1,3,2]=>1111101=>[1,1,1,1,1,2,1]
[8,6,7,5,4,1,3,2]=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,4,1,3,2]=>1011101=>[1,2,1,1,2,1]
[8,3,7,6,5,1,4,2]=>1011101=>[1,2,1,1,2,1]
[8,1,7,5,6,2,4,3]=>1010101=>[1,2,2,2,1]
[8,3,7,5,6,1,4,2]=>1010101=>[1,2,2,2,1]
[8,4,7,5,6,1,3,2]=>1010101=>[1,2,2,2,1]
[8,6,7,4,5,1,3,2]=>1010101=>[1,2,2,2,1]
[8,7,6,4,5,1,3,2]=>1110101=>[1,1,1,2,2,1]
[8,6,7,3,5,1,4,2]=>1010101=>[1,2,2,2,1]
[8,4,7,3,6,1,5,2]=>1010101=>[1,2,2,2,1]
[8,2,7,4,6,1,5,3]=>1010101=>[1,2,2,2,1]
[8,1,7,4,6,2,5,3]=>1010101=>[1,2,2,2,1]
[8,1,7,3,6,2,5,4]=>1010101=>[1,2,2,2,1]
[8,2,7,3,6,1,5,4]=>1010101=>[1,2,2,2,1]
[8,3,7,2,6,1,5,4]=>1010101=>[1,2,2,2,1]
[8,4,7,2,6,1,5,3]=>1010101=>[1,2,2,2,1]
[8,5,7,2,6,1,4,3]=>1010101=>[1,2,2,2,1]
[8,6,7,2,5,1,4,3]=>1010101=>[1,2,2,2,1]
[8,7,6,2,5,1,4,3]=>1110101=>[1,1,1,2,2,1]
[8,7,6,1,5,2,4,3]=>1110101=>[1,1,1,2,2,1]
[8,6,7,1,5,2,4,3]=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,2,4,3]=>1010101=>[1,2,2,2,1]
[8,4,7,1,6,2,5,3]=>1010101=>[1,2,2,2,1]
[8,3,7,1,6,2,5,4]=>1010101=>[1,2,2,2,1]
[8,2,7,1,6,3,5,4]=>1010101=>[1,2,2,2,1]
[4,6,7,3,8,5,2,1]=>0010111=>[3,2,1,1,1]
[6,7,8,9,10,5,4,3,2,1]=>000011111=>[5,1,1,1,1,1]
[5,7,8,9,4,10,6,3,2,1]=>000101111=>[4,2,1,1,1,1]
[4,6,8,3,9,5,10,7,2,1]=>001010111=>[3,2,2,1,1,1]
[3,5,2,7,4,9,6,10,8,1]=>010101011=>[2,2,2,2,1,1]
[1,4,8,2,6,3,5,7]=>0010100=>[3,2,3]
[1,6,2,4,8,3,5,7]=>0100100=>[2,3,3]
[1,5,2,3,8,4,7,6]=>0100101=>[2,3,2,1]
[1,7,2,3,5,4,8,6]=>0100101=>[2,3,2,1]
[1,8,2,3,5,4,6,7]=>0100100=>[2,3,3]
[1,7,8,2,4,5,3,6]=>0010010=>[3,3,2]
[1,2,8,3,6,4,5,7]=>0010100=>[3,2,3]
[1,5,8,2,3,7,4,6]=>0010010=>[3,3,2]
[1,6,8,2,3,5,4,7]=>0010010=>[3,3,2]
[5,7,2,6,3,8,1,4]=>0101010=>[2,2,2,2]
[5,7,1,6,8,4,3,2]=>0100111=>[2,3,1,1,1]
[4,8,1,2,5,7,3,6]=>0100010=>[2,4,2]
[1,7,8,4,6,2,5,3]=>0010101=>[3,2,2,1]
[3,7,4,8,5,1,6,2]=>0101101=>[2,2,1,2,1]
[3,7,5,4,8,2,1,6]=>0110110=>[2,1,2,1,2]
[4,7,1,3,2,8,6,5]=>0101011=>[2,2,2,1,1]
[2,7,3,1,5,8,4,6]=>0110010=>[2,1,3,2]
[2,7,5,8,6,4,1,3]=>0101110=>[2,2,1,1,2]
[3,4,2,7,8,1,6,5]=>0100101=>[2,3,2,1]
[4,3,2,1,5,8,6,7]=>1110010=>[1,1,1,3,2]
[4,1,3,7,5,6,8,2]=>1001001=>[1,3,3,1]
[3,4,6,1,5,8,2,7]=>0010010=>[3,3,2]
[6,5,8,7,1,4,2,3]=>1011010=>[1,2,1,2,2]
[4,1,7,3,8,5,2,6]=>1010110=>[1,2,2,1,2]
[6,1,7,3,5,4,8,2]=>1010101=>[1,2,2,2,1]
[5,6,8,7,2,4,1,3]=>0011010=>[3,1,2,2]
[6,8,5,7,1,2,4,3]=>0101001=>[2,2,3,1]
[7,1,3,4,2,8,5,6]=>1001010=>[1,3,2,2]
[7,6,1,4,3,5,8,2]=>1101001=>[1,1,2,3,1]
[3,5,4,1,6,7,8,2]=>0110001=>[2,1,4,1]
[2,5,3,4,8,6,1,7]=>0100110=>[2,3,1,2]
[2,4,8,3,6,1,7,5]=>0010101=>[3,2,2,1]
[8,2,4,3,7,5,6,1]=>1010101=>[1,2,2,2,1]
[6,8,2,1,5,7,3,4]=>0110010=>[2,1,3,2]
[7,2,8,4,1,6,3,5]=>1011010=>[1,2,1,2,2]
[1,2,4,8,6,5,3,7]=>0001110=>[4,1,1,2]
[7,1,5,6,8,4,3,2]=>1000111=>[1,4,1,1,1]
[7,3,5,6,1,4,8,2]=>1001001=>[1,3,3,1]
[3,7,6,5,1,4,8,2]=>0111001=>[2,1,1,3,1]
[2,7,6,5,3,8,1,4]=>0111010=>[2,1,1,2,2]
[2,7,8,1,4,6,3,5]=>0010010=>[3,3,2]
[4,8,2,5,7,1,6,3]=>0100101=>[2,3,2,1]
[4,1,6,8,5,3,7,2]=>1001101=>[1,3,1,2,1]
[5,2,6,4,8,3,1,7]=>1010110=>[1,2,2,1,2]
[1,2,6,3,4,8,7,5]=>0010011=>[3,3,1,1]
[5,3,6,1,4,7,8,2]=>1010001=>[1,2,4,1]
[6,7,1,3,4,5,8,2]=>0100001=>[2,5,1]
[1,7,3,2,4,8,5,6]=>0110010=>[2,1,3,2]
[6,1,4,2,8,3,5,7]=>1010100=>[1,2,2,3]
[5,8,6,7,2,1,4,3]=>0101101=>[2,2,1,2,1]
[7,4,1,5,8,2,3,6]=>1100100=>[1,1,3,3]
[6,3,4,2,8,7,5,1]=>1010111=>[1,2,2,1,1,1]
[4,3,8,7,5,2,6,1]=>1011101=>[1,2,1,1,2,1]
[6,8,7,4,2,3,5,1]=>0111001=>[2,1,1,3,1]
[8,6,1,3,5,4,2,7]=>1100110=>[1,1,3,1,2]
[2,7,6,3,4,5,8,1]=>0110001=>[2,1,4,1]
[5,3,8,6,1,2,4,7]=>1011000=>[1,2,1,4]
[2,4,8,7,3,5,6,1]=>0011001=>[3,1,3,1]
[2,5,3,6,8,7,4,1]=>0100111=>[2,3,1,1,1]
[3,8,7,2,6,4,5,1]=>0110101=>[2,1,2,2,1]
[4,5,8,7,2,6,3,1]=>0011011=>[3,1,2,1,1]
[8,5,2,7,1,4,3,6]=>1101010=>[1,1,2,2,2]
[5,1,7,2,4,3,8,6]=>1010101=>[1,2,2,2,1]
[4,5,2,8,3,7,6,1]=>0101011=>[2,2,2,1,1]
[8,2,3,7,6,4,5,1]=>1001101=>[1,3,1,2,1]
[3,7,5,8,2,6,1,4]=>0101010=>[2,2,2,2]
[1,6,7,4,8,2,3,5]=>0010100=>[3,2,3]
[8,2,1,3,5,6,7,4]=>1100001=>[1,1,5,1]
[4,1,3,8,2,6,7,5]=>1001001=>[1,3,3,1]
[3,6,1,4,7,2,8,5]=>0100101=>[2,3,2,1]
[6,2,7,4,5,8,1,3]=>1010010=>[1,2,3,2]
[2,1,8,4,5,7,3,6]=>1010010=>[1,2,3,2]
[1,8,5,7,3,2,4,6]=>0101100=>[2,2,1,3]
[3,2,1,6,4,8,5,7]=>1101010=>[1,1,2,2,2]
[2,1,8,5,4,3,6,7]=>1011100=>[1,2,1,1,3]
[2,7,4,1,5,3,8,6]=>0110101=>[2,1,2,2,1]
[7,4,8,6,2,3,1,5]=>1011010=>[1,2,1,2,2]
[7,3,2,4,8,6,1,5]=>1100110=>[1,1,3,1,2]
[7,1,3,2,8,5,4,6]=>1010110=>[1,2,2,1,2]
[5,1,7,4,2,3,8,6]=>1011001=>[1,2,1,3,1]
[1,3,4,8,6,5,2,7]=>0001110=>[4,1,1,2]
[4,1,8,6,5,3,2,7]=>1011110=>[1,2,1,1,1,2]
[4,8,5,3,6,2,7,1]=>0110101=>[2,1,2,2,1]
[5,7,4,3,6,2,8,1]=>0110101=>[2,1,2,2,1]
[6,7,5,1,2,8,3,4]=>0110010=>[2,1,3,2]
[7,5,1,4,2,6,8,3]=>1101001=>[1,1,2,3,1]
[5,2,6,8,3,4,7,1]=>1001001=>[1,3,3,1]
[7,6,2,4,5,8,3,1]=>1100011=>[1,1,4,1,1]
[2,6,3,8,4,7,5,1]=>0101011=>[2,2,2,1,1]
[6,2,7,5,8,3,1,4]=>1010110=>[1,2,2,1,2]
[2,1,5,6,8,3,7,4]=>1000101=>[1,4,2,1]
[1,2,7,4,8,3,6,5]=>0010101=>[3,2,2,1]
[1,6,8,3,2,7,4,5]=>0011010=>[3,1,2,2]
[1,6,7,5,2,8,3,4]=>0011010=>[3,1,2,2]
[7,5,1,2,8,4,6,3]=>1100101=>[1,1,3,2,1]
[5,4,8,3,6,2,7,1]=>1010101=>[1,2,2,2,1]
[5,8,2,7,4,3,6,1]=>0101101=>[2,2,1,2,1]
[5,7,3,8,2,4,6,1]=>0101001=>[2,2,3,1]
[6,4,5,8,2,7,3,1]=>1001011=>[1,3,2,1,1]
[5,7,3,6,4,8,2,1]=>0101011=>[2,2,2,1,1]
[1,5,6,4,8,2,7,3]=>0010101=>[3,2,2,1]
[3,6,2,4,7,1,8,5]=>0100101=>[2,3,2,1]
[4,2,8,5,1,6,7,3]=>1011001=>[1,2,1,3,1]
[2,1,6,4,8,5,3,7]=>1010110=>[1,2,2,1,2]
[1,2,8,3,7,5,4,6]=>0010110=>[3,2,1,2]
[1,6,3,8,7,4,2,5]=>0101110=>[2,2,1,1,2]
[4,3,8,1,2,6,7,5]=>1010001=>[1,2,4,1]
[6,4,5,8,1,2,7,3]=>1001001=>[1,3,3,1]
[7,4,6,5,2,1,8,3]=>1011101=>[1,2,1,1,2,1]
[5,1,8,6,7,4,3,2]=>1010111=>[1,2,2,1,1,1]
[3,8,5,7,1,4,2,6]=>0101010=>[2,2,2,2]
[4,7,2,5,1,3,8,6]=>0101001=>[2,2,3,1]
[5,1,7,4,8,6,3,2]=>1010111=>[1,2,2,1,1,1]
[3,6,5,2,1,8,7,4]=>0111011=>[2,1,1,2,1,1]
[5,2,8,4,7,3,1,6]=>1010110=>[1,2,2,1,2]
[5,2,7,4,1,3,6,8]=>1011000=>[1,2,1,4]
[5,2,6,4,1,8,7,3]=>1011011=>[1,2,1,2,1,1]
[6,3,2,1,4,8,7,5]=>1110011=>[1,1,1,3,1,1]
[3,1,4,6,2,8,7,5]=>1001011=>[1,3,2,1,1]
[6,3,5,1,7,4,2,8]=>1010110=>[1,2,2,1,2]
[4,6,3,7,5,8,1,2]=>0101010=>[2,2,2,2]
[5,7,4,3,8,1,2,6]=>0110100=>[2,1,2,3]
[1,5,7,4,8,6,3,2]=>0010111=>[3,2,1,1,1]
[1,8,2,7,6,5,4,3]=>0101111=>[2,2,1,1,1,1]
[3,8,1,6,7,5,4,2]=>0100111=>[2,3,1,1,1]
[3,7,2,6,8,5,1,4]=>0100110=>[2,3,1,2]
[8,2,4,3,6,1,5,7]=>1010100=>[1,2,2,3]
[1,7,8,5,4,3,6,2]=>0011101=>[3,1,1,2,1]
[7,3,8,1,4,2,6,5]=>1010101=>[1,2,2,2,1]
[1,8,4,5,3,2,6,7]=>0101100=>[2,2,1,3]
[3,8,7,4,2,6,1,5]=>0111010=>[2,1,1,2,2]
[3,7,8,1,2,6,5,4]=>0010011=>[3,3,1,1]
[3,5,6,2,7,1,4,8]=>0010100=>[3,2,3]
[3,7,1,6,8,2,4,5]=>0100100=>[2,3,3]
[8,1,7,6,2,4,3,5]=>1011010=>[1,2,1,2,2]
[1,6,4,5,7,2,3,8]=>0100100=>[2,3,3]
[8,3,6,1,7,2,4,5]=>1010100=>[1,2,2,3]
[1,7,5,3,6,8,4,2]=>0110011=>[2,1,3,1,1]
[7,3,5,2,1,8,4,6]=>1011010=>[1,2,1,2,2]
[7,4,1,6,5,8,3,2]=>1101011=>[1,1,2,2,1,1]
[6,4,2,8,7,5,1,3]=>1101110=>[1,1,2,1,1,2]
[4,2,1,5,8,7,3,6]=>1100110=>[1,1,3,1,2]
[1,5,3,6,8,7,4,2]=>0100111=>[2,3,1,1,1]
[3,5,4,6,1,8,2,7]=>0101010=>[2,2,2,2]
[3,1,5,7,6,8,2,4]=>1001010=>[1,3,2,2]
[6,4,5,7,2,8,1,3]=>1001010=>[1,3,2,2]
[5,3,6,4,2,8,1,7]=>1011010=>[1,2,1,2,2]
[4,1,5,3,8,2,7,6]=>1010101=>[1,2,2,2,1]
[2,6,3,5,4,8,1,7]=>0101010=>[2,2,2,2]
[3,7,4,5,6,8,1,2]=>0100010=>[2,4,2]
[2,5,7,3,6,8,1,4]=>0010010=>[3,3,2]
[7,6,4,5,2,8,1,3]=>1101010=>[1,1,2,2,2]
[5,4,3,1,8,2,7,6]=>1110101=>[1,1,1,2,2,1]
[8,2,6,4,7,3,1,5]=>1010110=>[1,2,2,1,2]
[8,6,1,7,4,5,2,3]=>1101010=>[1,1,2,2,2]
[1,2,8,3,5,4,6,7]=>0010100=>[3,2,3]
[1,7,8,4,3,5,6,2]=>0011001=>[3,1,3,1]
[3,1,6,8,4,5,7,2]=>1001001=>[1,3,3,1]
[1,4,5,8,3,6,7,2]=>0001001=>[4,3,1]
[2,5,7,1,8,3,6,4]=>0010101=>[3,2,2,1]
[6,2,7,1,8,4,5,3]=>1010101=>[1,2,2,2,1]
[4,7,1,3,8,5,6,2]=>0100101=>[2,3,2,1]
[3,7,2,1,8,4,5,6]=>0110100=>[2,1,2,3]
[2,1,5,8,3,6,7,4]=>1001001=>[1,3,3,1]
[4,2,7,1,8,3,6,5]=>1010101=>[1,2,2,2,1]
[4,3,1,6,8,2,7,5]=>1100101=>[1,1,3,2,1]
[5,3,4,6,8,2,7,1]=>1000101=>[1,4,2,1]
[3,5,1,6,8,2,7,4]=>0100101=>[2,3,2,1]
[5,1,8,7,4,2,3,6]=>1011100=>[1,2,1,1,3]
[5,8,3,2,6,4,1,7]=>0110110=>[2,1,2,1,2]
[6,8,2,4,7,5,1,3]=>0100110=>[2,3,1,2]
[7,3,8,2,6,4,1,5]=>1010110=>[1,2,2,1,2]
[3,8,7,4,5,6,1,2]=>0110010=>[2,1,3,2]
[2,7,6,3,5,4,1,8]=>0110110=>[2,1,2,1,2]
[3,8,7,4,6,2,5,1]=>0110101=>[2,1,2,2,1]
[5,8,3,7,6,2,4,1]=>0101101=>[2,2,1,2,1]
[8,7,2,5,4,3,1,6]=>1101110=>[1,1,2,1,1,2]
[6,8,3,2,5,4,7,1]=>0110101=>[2,1,2,2,1]
[5,8,7,4,3,6,2,1]=>0111011=>[2,1,1,2,1,1]
[5,8,6,4,3,7,1,2]=>0111010=>[2,1,1,2,2]
[6,5,8,4,3,1,7,2]=>1011101=>[1,2,1,1,2,1]
[2,6,4,7,1,5,3,8]=>0101010=>[2,2,2,2]
[2,5,6,8,4,3,7,1]=>0001101=>[4,1,2,1]
[5,3,8,1,7,6,4,2]=>1010111=>[1,2,2,1,1,1]
[5,4,8,7,1,6,3,2]=>1011011=>[1,2,1,2,1,1]
[4,8,6,7,5,3,1,2]=>0101110=>[2,2,1,1,2]
[4,8,6,5,7,2,1,3]=>0110110=>[2,1,2,1,2]
[4,8,5,6,7,1,2,3]=>0100100=>[2,3,3]
[5,4,8,6,1,7,2,3]=>1011010=>[1,2,1,2,2]
[5,3,8,1,6,7,2,4]=>1010010=>[1,2,3,2]
[5,2,1,8,6,7,3,4]=>1101010=>[1,1,2,2,2]
[6,2,1,5,8,3,7,4]=>1100101=>[1,1,3,2,1]
[6,5,4,8,2,1,7,3]=>1101101=>[1,1,2,1,2,1]
[5,8,4,7,2,6,3,1]=>0101011=>[2,2,2,1,1]
[5,8,3,2,7,6,4,1]=>0110111=>[2,1,2,1,1,1]
[5,8,3,2,6,7,1,4]=>0110010=>[2,1,3,2]
[6,5,3,2,8,1,7,4]=>1110101=>[1,1,1,2,2,1]
[6,4,3,2,1,8,7,5]=>1111011=>[1,1,1,1,2,1,1]
[6,3,4,1,2,8,7,5]=>1010011=>[1,2,3,1,1]
[6,2,1,4,3,8,7,5]=>1101011=>[1,1,2,2,1,1]
[5,2,1,4,3,6,7,8]=>1101000=>[1,1,2,4]
[4,6,3,2,5,1,7,8]=>0110100=>[2,1,2,3]
[3,5,7,4,2,6,1,8]=>0011010=>[3,1,2,2]
[4,3,6,1,5,2,7,8]=>1010100=>[1,2,2,3]
[4,2,1,6,5,3,7,8]=>1101100=>[1,1,2,1,3]
[4,2,1,5,7,6,3,8]=>1100110=>[1,1,3,1,2]
[3,5,4,7,1,6,2,8]=>0101010=>[2,2,2,2]
[3,4,7,5,6,1,2,8]=>0010100=>[3,2,3]
[3,4,5,8,6,7,1,2]=>0001010=>[4,2,2]
[3,4,6,5,8,1,7,2]=>0010101=>[3,2,2,1]
[4,3,5,1,6,8,7,2]=>1010011=>[1,2,3,1,1]
[2,1,5,3,8,4,7,6]=>1010101=>[1,2,2,2,1]
[3,1,8,2,5,4,7,6]=>1010101=>[1,2,2,2,1]
[8,1,3,2,6,4,7,5]=>1010101=>[1,2,2,2,1]
[3,1,8,2,6,4,7,5]=>1010101=>[1,2,2,2,1]
[2,1,8,3,6,4,7,5]=>1010101=>[1,2,2,2,1]
[2,1,6,3,8,4,7,5]=>1010101=>[1,2,2,2,1]
[2,1,7,3,5,4,8,6]=>1010101=>[1,2,2,2,1]
[2,1,7,3,6,4,8,5]=>1010101=>[1,2,2,2,1]
[2,1,7,3,8,4,6,5]=>1010101=>[1,2,2,2,1]
[8,1,4,2,7,3,6,5]=>1010101=>[1,2,2,2,1]
[4,1,8,2,7,3,6,5]=>1010101=>[1,2,2,2,1]
[4,1,7,2,8,3,6,5]=>1010101=>[1,2,2,2,1]
[3,1,7,2,8,4,6,5]=>1010101=>[1,2,2,2,1]
[3,1,6,2,5,4,8,7]=>1010101=>[1,2,2,2,1]
[7,1,3,2,5,4,8,6]=>1010101=>[1,2,2,2,1]
[7,1,3,2,6,4,8,5]=>1010101=>[1,2,2,2,1]
[7,1,3,2,8,4,6,5]=>1010101=>[1,2,2,2,1]
[7,1,8,2,4,3,6,5]=>1010101=>[1,2,2,2,1]
[8,1,7,2,5,3,6,4]=>1010101=>[1,2,2,2,1]
[7,1,5,2,8,3,6,4]=>1010101=>[1,2,2,2,1]
[6,1,4,2,5,3,8,7]=>1010101=>[1,2,2,2,1]
[4,1,6,2,5,3,8,7]=>1010101=>[1,2,2,2,1]
[4,1,7,2,5,3,8,6]=>1010101=>[1,2,2,2,1]
[4,1,7,2,6,3,8,5]=>1010101=>[1,2,2,2,1]
[5,1,7,2,6,3,8,4]=>1010101=>[1,2,2,2,1]
[5,1,7,2,8,3,6,4]=>1010101=>[1,2,2,2,1]
[5,1,8,2,7,3,6,4]=>1010101=>[1,2,2,2,1]
[8,1,5,2,7,3,6,4]=>1010101=>[1,2,2,2,1]
[8,1,5,2,6,3,7,4]=>1010101=>[1,2,2,2,1]
[5,1,8,2,6,3,7,4]=>1010101=>[1,2,2,2,1]
[5,1,6,2,8,3,7,4]=>1010101=>[1,2,2,2,1]
[3,1,6,2,8,4,7,5]=>1010101=>[1,2,2,2,1]
[4,1,8,2,6,3,7,5]=>1010101=>[1,2,2,2,1]
[8,1,4,2,6,3,7,5]=>1010101=>[1,2,2,2,1]
[8,1,4,2,5,3,7,6]=>1010101=>[1,2,2,2,1]
[4,1,8,2,5,3,7,6]=>1010101=>[1,2,2,2,1]
[4,1,5,2,8,3,7,6]=>1010101=>[1,2,2,2,1]
[3,1,5,2,8,4,7,6]=>1010101=>[1,2,2,2,1]
[3,1,4,2,8,5,7,6]=>1010101=>[1,2,2,2,1]
[4,1,3,2,7,5,8,6]=>1010101=>[1,2,2,2,1]
[5,1,4,2,8,3,7,6]=>1010101=>[1,2,2,2,1]
[5,1,8,2,4,3,7,6]=>1010101=>[1,2,2,2,1]
[8,1,6,2,4,3,7,5]=>1010101=>[1,2,2,2,1]
[6,1,8,2,4,3,7,5]=>1010101=>[1,2,2,2,1]
[6,1,3,2,8,4,7,5]=>1010101=>[1,2,2,2,1]
[6,1,3,2,7,4,8,5]=>1010101=>[1,2,2,2,1]
[5,1,3,2,7,4,8,6]=>1010101=>[1,2,2,2,1]
[5,1,3,2,6,4,8,7]=>1010101=>[1,2,2,2,1]
[5,1,4,2,6,3,8,7]=>1010101=>[1,2,2,2,1]
[6,1,4,2,7,3,8,5]=>1010101=>[1,2,2,2,1]
[6,1,5,2,7,3,8,4]=>1010101=>[1,2,2,2,1]
[6,1,8,2,5,3,7,4]=>1010101=>[1,2,2,2,1]
[8,1,6,2,5,3,7,4]=>1010101=>[1,2,2,2,1]
[8,1,6,2,7,3,5,4]=>1010101=>[1,2,2,2,1]
[6,1,8,2,7,3,5,4]=>1010101=>[1,2,2,2,1]
[6,1,7,2,8,3,5,4]=>1010101=>[1,2,2,2,1]
[6,1,7,2,5,3,8,4]=>1010101=>[1,2,2,2,1]
[6,1,7,2,4,3,8,5]=>1010101=>[1,2,2,2,1]
[5,1,6,2,4,3,8,7]=>1010101=>[1,2,2,2,1]
[7,1,5,2,4,3,8,6]=>1010101=>[1,2,2,2,1]
[7,1,6,2,4,3,8,5]=>1010101=>[1,2,2,2,1]
[7,1,6,2,5,3,8,4]=>1010101=>[1,2,2,2,1]
[7,1,6,2,8,3,5,4]=>1010101=>[1,2,2,2,1]
[7,1,8,2,6,3,5,4]=>1010101=>[1,2,2,2,1]
[7,8,3,1,2,5,6,4]=>0110001=>[2,1,4,1]
[7,8,1,3,2,4,6,5]=>0101001=>[2,2,3,1]
[6,2,8,1,3,5,4,7]=>1010010=>[1,2,3,2]
[6,2,8,3,1,7,4,5]=>1011010=>[1,2,1,2,2]
[3,2,5,7,1,8,4,6]=>1001010=>[1,3,2,2]
[3,5,2,8,1,7,4,6]=>0101010=>[2,2,2,2]
[4,3,1,2,7,8,6,5]=>1100011=>[1,1,4,1,1]
[5,3,4,7,8,6,1,2]=>1000110=>[1,4,1,2]
[4,1,3,2,6,8,7,5]=>1010011=>[1,2,3,1,1]
[5,1,3,7,2,6,8,4]=>1001001=>[1,3,3,1]
[5,2,4,7,8,1,6,3]=>1000101=>[1,4,2,1]
[2,5,4,6,8,1,7,3]=>0100101=>[2,3,2,1]
[4,3,5,7,6,8,1,2]=>1001010=>[1,3,2,2]
[4,2,1,3,7,6,8,5]=>1100101=>[1,1,3,2,1]
[2,4,3,1,8,5,7,6]=>0110101=>[2,1,2,2,1]
[3,2,4,1,8,6,5,7]=>1010110=>[1,2,2,1,2]
[3,4,2,1,8,7,5,6]=>0110110=>[2,1,2,1,2]
[7,6,4,3,2,1,8,5]=>1111101=>[1,1,1,1,1,2,1]
[7,6,5,8,2,1,4,3]=>1101101=>[1,1,2,1,2,1]
[7,6,8,3,2,1,5,4]=>1011101=>[1,2,1,1,2,1]
[7,8,4,3,2,1,6,5]=>0111101=>[2,1,1,1,2,1]
[8,5,4,3,2,1,7,6]=>1111101=>[1,1,1,1,1,2,1]
[7,6,3,8,2,1,5,4]=>1101101=>[1,1,2,1,2,1]
[7,6,5,8,4,1,3,2]=>1101101=>[1,1,2,1,2,1]
[7,4,8,3,2,1,6,5]=>1011101=>[1,2,1,1,2,1]
[7,6,8,5,2,1,4,3]=>1011101=>[1,2,1,1,2,1]
[4,8,6,1,7,5,2,3]=>0110110=>[2,1,2,1,2]
[4,8,7,2,6,5,1,3]=>0110110=>[2,1,2,1,2]
[4,7,8,2,6,1,5,3]=>0010101=>[3,2,2,1]
[4,6,8,2,7,1,3,5]=>0010100=>[3,2,3]
[8,6,4,2,7,5,3,1]=>1110111=>[1,1,1,2,1,1,1]
[8,4,7,3,6,5,1,2]=>1010110=>[1,2,2,1,2]
[6,4,7,1,8,3,2,5]=>1010110=>[1,2,2,1,2]
[7,4,8,3,6,1,5,2]=>1010101=>[1,2,2,2,1]
[7,8,4,3,6,2,5,1]=>0110101=>[2,1,2,2,1]
[6,8,4,3,7,2,1,5]=>0110110=>[2,1,2,1,2]
[6,7,4,2,8,3,1,5]=>0110110=>[2,1,2,1,2]
[2,8,7,6,5,1,4,3]=>0111101=>[2,1,1,1,2,1]
[7,3,2,5,4,1,6,8]=>1101100=>[1,1,2,1,3]
[7,3,5,4,2,1,6,8]=>1011100=>[1,2,1,1,3]
[2,7,6,3,1,5,8,4]=>0111001=>[2,1,1,3,1]
[1,8,4,3,6,5,2,7]=>0110110=>[2,1,2,1,2]
[1,8,4,6,5,3,2,7]=>0101110=>[2,2,1,1,2]
[7,1,4,2,6,3,5,8]=>1010100=>[1,2,2,3]
[7,3,4,1,5,6,2,8]=>1010010=>[1,2,3,2]
[7,3,2,5,1,6,4,8]=>1101010=>[1,1,2,2,2]
[7,4,1,3,5,2,6,8]=>1100100=>[1,1,3,3]
[7,3,1,2,4,6,5,8]=>1100010=>[1,1,4,2]
[3,6,2,1,4,8,5,7]=>0110010=>[2,1,3,2]
[2,3,6,1,4,8,7,5]=>0010011=>[3,3,1,1]
[3,6,7,4,1,5,8,2]=>0011001=>[3,1,3,1]
[3,1,2,8,6,5,4,7]=>1001110=>[1,3,1,1,2]
[5,4,8,6,1,2,3,7]=>1011000=>[1,2,1,4]
[5,6,8,2,4,1,3,7]=>0010100=>[3,2,3]
[5,6,8,7,4,3,1,2]=>0011110=>[3,1,1,1,2]
[6,4,8,5,3,1,7,2]=>1011101=>[1,2,1,1,2,1]
[5,7,8,6,1,3,2,4]=>0011010=>[3,1,2,2]
[2,4,8,1,6,3,7,5]=>0010101=>[3,2,2,1]
[1,8,4,5,2,6,7,3]=>0101001=>[2,2,3,1]
[3,1,4,6,5,8,7,2]=>1001011=>[1,3,2,1,1]
[3,7,5,4,6,8,2,1]=>0110011=>[2,1,3,1,1]
[5,3,2,1,7,6,8,4]=>1110101=>[1,1,1,2,2,1]
[5,6,1,4,7,2,8,3]=>0100101=>[2,3,2,1]
[4,3,1,7,5,6,8,2]=>1101001=>[1,1,2,3,1]
[1,8,4,3,6,2,7,5]=>0110101=>[2,1,2,2,1]
[5,6,7,3,2,8,1,4]=>0011010=>[3,1,2,2]
[5,3,2,1,4,8,6,7]=>1110010=>[1,1,1,3,2]
[3,4,7,8,1,2,6,5]=>0001001=>[4,3,1]
[3,6,7,8,1,4,5,2]=>0001001=>[4,3,1]
[2,3,6,8,5,1,4,7]=>0001100=>[4,1,3]
[3,1,6,4,8,2,5,7]=>1010100=>[1,2,2,3]
[7,3,2,6,8,5,1,4]=>1100110=>[1,1,3,1,2]
[7,3,5,8,4,6,1,2]=>1001010=>[1,3,2,2]
[7,5,2,8,4,1,6,3]=>1101101=>[1,1,2,1,2,1]
[1,8,4,2,3,5,7,6]=>0110001=>[2,1,4,1]
[6,3,4,8,2,5,7,1]=>1001001=>[1,3,3,1]
[7,5,4,8,3,6,2,1]=>1101011=>[1,1,2,2,1,1]
[7,3,2,5,8,4,6,1]=>1100101=>[1,1,3,2,1]
[5,7,8,3,1,4,6,2]=>0011001=>[3,1,3,1]
[7,4,8,3,2,5,1,6]=>1011010=>[1,2,1,2,2]
[7,3,8,2,4,5,6,1]=>1010001=>[1,2,4,1]
[4,2,7,1,5,3,8,6]=>1010101=>[1,2,2,2,1]
[2,7,1,3,5,4,8,6]=>0100101=>[2,3,2,1]
[1,2,7,3,4,8,6,5]=>0010011=>[3,3,1,1]
[4,7,2,1,5,8,6,3]=>0110011=>[2,1,3,1,1]
[2,3,4,8,1,6,5,7]=>0001010=>[4,2,2]
[3,1,4,8,2,6,7,5]=>1001001=>[1,3,3,1]
[4,8,3,6,5,1,7,2]=>0101101=>[2,2,1,2,1]
[6,4,7,3,5,1,8,2]=>1010101=>[1,2,2,2,1]
[3,1,6,4,7,8,2,5]=>1010010=>[1,2,3,2]
[7,3,1,6,8,2,4,5]=>1100100=>[1,1,3,3]
[7,3,5,1,6,8,2,4]=>1010010=>[1,2,3,2]
[4,7,3,5,6,1,8,2]=>0100101=>[2,3,2,1]
[4,6,8,2,1,5,7,3]=>0011001=>[3,1,3,1]
[1,8,2,3,5,7,4,6]=>0100010=>[2,4,2]
[2,7,3,6,1,4,5,8]=>0101000=>[2,2,4]
[1,2,5,8,3,7,4,6]=>0001010=>[4,2,2]
[8,2,4,1,7,5,6,3]=>1010101=>[1,2,2,2,1]
[3,8,4,7,5,1,6,2]=>0101101=>[2,2,1,2,1]
[8,4,3,6,1,7,5,2]=>1101011=>[1,1,2,2,1,1]
[2,1,8,6,7,3,5,4]=>1010101=>[1,2,2,2,1]
[1,2,8,6,3,4,7,5]=>0011001=>[3,1,3,1]
[7,3,2,5,6,1,4,8]=>1100100=>[1,1,3,3]
[8,4,1,2,7,5,3,6]=>1100110=>[1,1,3,1,2]
[1,5,2,8,6,3,7,4]=>0101101=>[2,2,1,2,1]
[5,8,6,3,1,7,4,2]=>0111011=>[2,1,1,2,1,1]
[7,8,1,4,2,5,3,6]=>0101010=>[2,2,2,2]
[1,6,2,7,4,8,3,5]=>0101010=>[2,2,2,2]
[6,2,1,7,8,5,3,4]=>1100110=>[1,1,3,1,2]
[6,7,3,8,4,1,5,2]=>0101101=>[2,2,1,2,1]
[2,7,1,8,5,6,3,4]=>0101010=>[2,2,2,2]
[2,1,7,8,6,3,4,5]=>1001100=>[1,3,1,3]
[7,8,6,2,1,3,5,4]=>0111001=>[2,1,1,3,1]
[5,2,6,3,4,1,8,7]=>1010101=>[1,2,2,2,1]
[4,1,2,6,5,3,8,7]=>1001101=>[1,3,1,2,1]
[2,6,5,3,1,4,8,7]=>0111001=>[2,1,1,3,1]
[6,1,3,4,2,8,7,5]=>1001011=>[1,3,2,1,1]
[8,2,6,4,7,3,5,1]=>1010101=>[1,2,2,2,1]
[3,8,5,1,7,2,4,6]=>0110100=>[2,1,2,3]
[2,1,7,4,8,5,6,3]=>1010101=>[1,2,2,2,1]
[2,5,1,8,7,4,6,3]=>0101101=>[2,2,1,2,1]
[7,1,3,8,6,4,5,2]=>1001101=>[1,3,1,2,1]
[2,3,5,8,6,7,4,1]=>0001011=>[4,2,1,1]
[7,4,2,1,8,6,5,3]=>1110111=>[1,1,1,2,1,1,1]
[2,1,6,3,4,8,7,5]=>1010011=>[1,2,3,1,1]
[4,6,7,2,5,8,3,1]=>0010011=>[3,3,1,1]
[7,6,2,5,3,8,1,4]=>1101010=>[1,1,2,2,2]
[6,2,1,3,4,8,7,5]=>1100011=>[1,1,4,1,1]
[8,1,4,2,5,6,7,3]=>1010001=>[1,2,4,1]
[3,4,2,1,8,6,7,5]=>0110101=>[2,1,2,2,1]
[2,7,6,8,1,5,3,4]=>0101010=>[2,2,2,2]
[8,1,3,2,5,6,7,4]=>1010001=>[1,2,4,1]
[3,2,8,7,4,5,1,6]=>1011010=>[1,2,1,2,2]
[6,3,8,5,7,4,2,1]=>1010111=>[1,2,2,1,1,1]
[7,4,6,8,5,1,2,3]=>1001100=>[1,3,1,3]
[2,1,4,8,7,5,3,6]=>1001110=>[1,3,1,1,2]
[7,1,5,8,2,6,3,4]=>1001010=>[1,3,2,2]
[3,6,8,2,4,1,5,7]=>0010100=>[3,2,3]
[6,2,8,1,7,5,4,3]=>1010111=>[1,2,2,1,1,1]
[2,8,5,3,6,7,1,4]=>0110010=>[2,1,3,2]
[3,8,1,4,5,6,2,7]=>0100010=>[2,4,2]
[5,8,7,3,6,1,4,2]=>0110101=>[2,1,2,2,1]
[5,8,3,7,6,1,4,2]=>0101101=>[2,2,1,2,1]
[7,5,8,4,6,1,3,2]=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,1,3,2]=>1010101=>[1,2,2,2,1]
[2,4,8,1,3,7,6,5]=>0010011=>[3,3,1,1]
[2,5,1,3,8,4,7,6]=>0100101=>[2,3,2,1]
[2,8,1,5,4,7,3,6]=>0101010=>[2,2,2,2]
[3,1,8,2,5,7,4,6]=>1010010=>[1,2,3,2]
[8,3,2,6,1,4,7,5]=>1101001=>[1,1,2,3,1]
[2,6,1,3,8,7,5,4]=>0100111=>[2,3,1,1,1]
[2,5,7,1,3,8,6,4]=>0010011=>[3,3,1,1]
[2,8,1,7,6,5,4,3]=>0101111=>[2,2,1,1,1,1]
[8,3,2,7,1,6,5,4]=>1101011=>[1,1,2,2,1,1]
[7,4,2,8,1,6,5,3]=>1101011=>[1,1,2,2,1,1]
[8,7,5,3,2,1,6,4]=>1111101=>[1,1,1,1,1,2,1]
[7,5,2,6,3,1,4,8]=>1101100=>[1,1,2,1,3]
[7,4,6,2,1,8,3,5]=>1011010=>[1,2,1,2,2]
[7,4,5,8,6,2,1,3]=>1001110=>[1,3,1,1,2]
[6,8,4,5,2,1,7,3]=>0101101=>[2,2,1,2,1]
[4,6,8,5,1,7,3,2]=>0011011=>[3,1,2,1,1]
[4,7,5,1,3,8,6,2]=>0110011=>[2,1,3,1,1]
[5,1,7,6,4,2,8,3]=>1011101=>[1,2,1,1,2,1]
[5,1,8,7,6,4,3,2]=>1011111=>[1,2,1,1,1,1,1]
[8,5,2,1,6,3,7,4]=>1110101=>[1,1,1,2,2,1]
[5,1,6,2,8,7,4,3]=>1010111=>[1,2,2,1,1,1]
[4,5,6,1,8,7,2,3]=>0010110=>[3,2,1,2]
[3,5,6,8,7,1,4,2]=>0001101=>[4,1,2,1]
[3,6,1,7,4,8,2,5]=>0101010=>[2,2,2,2]
[8,4,2,6,3,1,5,7]=>1101100=>[1,1,2,1,3]
[4,1,8,5,7,3,6,2]=>1010101=>[1,2,2,2,1]
[4,1,5,8,7,2,3,6]=>1001100=>[1,3,1,3]
[3,4,8,7,1,2,6,5]=>0011001=>[3,1,3,1]
[3,4,6,8,5,7,1,2]=>0001010=>[4,2,2]
[4,6,8,3,5,7,2,1]=>0010011=>[3,3,1,1]
[4,7,3,5,8,2,6,1]=>0100101=>[2,3,2,1]
[5,4,8,2,7,3,6,1]=>1010101=>[1,2,2,2,1]
[6,3,7,2,4,8,1,5]=>1010010=>[1,2,3,2]
[5,6,8,3,7,2,1,4]=>0010110=>[3,2,1,2]
[6,5,2,7,1,3,8,4]=>1101001=>[1,1,2,3,1]
[6,5,4,1,7,2,8,3]=>1110101=>[1,1,1,2,2,1]
[6,4,7,3,1,8,2,5]=>1011010=>[1,2,1,2,2]
[6,8,5,7,4,3,2,1]=>0101111=>[2,2,1,1,1,1]
[7,5,8,4,6,3,2,1]=>1010111=>[1,2,2,1,1,1]
[5,6,3,7,4,2,1,8]=>0101110=>[2,2,1,1,2]
[6,1,3,8,5,2,4,7]=>1001100=>[1,3,1,3]
[7,4,2,6,3,5,1,8]=>1101010=>[1,1,2,2,2]
[3,4,7,5,6,2,1,8]=>0010110=>[3,2,1,2]
[8,1,3,4,5,2,6,7]=>1000100=>[1,4,3]
[1,6,8,4,2,5,3,7]=>0011010=>[3,1,2,2]
[3,6,8,4,1,7,5,2]=>0011011=>[3,1,2,1,1]
[8,7,2,3,6,1,4,5]=>1100100=>[1,1,3,3]
[6,7,4,8,5,1,2,3]=>0101100=>[2,2,1,3]
[3,2,8,1,5,4,6,7]=>1010100=>[1,2,2,3]
[6,1,4,8,5,3,7,2]=>1001101=>[1,3,1,2,1]
[1,4,8,5,2,6,7,3]=>0011001=>[3,1,3,1]
[8,1,2,3,6,5,7,4]=>1000101=>[1,4,2,1]
[6,1,8,4,3,7,2,5]=>1011010=>[1,2,1,2,2]
[3,2,6,4,1,8,7,5]=>1011011=>[1,2,1,2,1,1]
[7,6,4,3,1,8,2,5]=>1111010=>[1,1,1,1,2,2]
[8,4,6,5,1,7,2,3]=>1011010=>[1,2,1,2,2]
[7,5,4,6,1,2,8,3]=>1101001=>[1,1,2,3,1]
[3,2,5,6,1,7,8,4]=>1001001=>[1,3,3,1]
[3,2,8,7,6,1,4,5]=>1011100=>[1,2,1,1,3]
[6,8,4,7,2,1,3,5]=>0101100=>[2,2,1,3]
[3,8,7,5,6,1,2,4]=>0110100=>[2,1,2,3]
[8,2,7,6,5,1,3,4]=>1011100=>[1,2,1,1,3]
[4,8,6,7,1,5,3,2]=>0101011=>[2,2,2,1,1]
[1,8,6,7,2,3,4,5]=>0101000=>[2,2,4]
[7,6,3,2,1,8,5,4]=>1111011=>[1,1,1,1,2,1,1]
[3,5,4,2,7,1,8,6]=>0110101=>[2,1,2,2,1]
[8,6,3,1,4,5,7,2]=>1110001=>[1,1,1,4,1]
[3,2,6,1,5,7,4,8]=>1010010=>[1,2,3,2]
[5,2,1,4,7,6,3,8]=>1100110=>[1,1,3,1,2]
[4,2,1,3,5,8,7,6]=>1100011=>[1,1,4,1,1]
[7,4,1,5,3,6,8,2]=>1101001=>[1,1,2,3,1]
[3,1,5,2,7,4,9,6,8,10]=>101010100=>[1,2,2,2,3]
[6,8,2,4,5,1,3,7]=>0100100=>[2,3,3]
[6,8,3,4,1,5,2,7]=>0101010=>[2,2,2,2]
[5,8,4,1,7,2,6,3]=>0110101=>[2,1,2,2,1]
[6,8,3,1,4,5,7,2]=>0110001=>[2,1,4,1]
[5,3,8,4,2,6,7,1]=>1011001=>[1,2,1,3,1]
[4,1,8,3,5,7,2,6]=>1010010=>[1,2,3,2]
[2,4,6,3,5,8,1,7]=>0010010=>[3,3,2]
[4,5,7,2,3,6,8,1]=>0010001=>[3,4,1]
[2,6,3,4,7,5,8,1]=>0100101=>[2,3,2,1]
[4,5,2,7,1,6,8,3]=>0101001=>[2,2,3,1]
[2,3,1,7,6,4,8,5]=>0101101=>[2,2,1,2,1]
[3,4,1,6,5,8,2,7]=>0101010=>[2,2,2,2]
[7,3,1,4,8,5,6,2]=>1100101=>[1,1,3,2,1]
[6,4,2,8,7,1,5,3]=>1101101=>[1,1,2,1,2,1]
[3,1,8,2,7,6,4,5]=>1010110=>[1,2,2,1,2]
[6,2,8,4,1,7,5,3]=>1011011=>[1,2,1,2,1,1]
[3,6,4,7,2,5,1,8]=>0101010=>[2,2,2,2]
[7,3,2,8,6,1,4,5]=>1101100=>[1,1,2,1,3]
[4,3,8,7,1,2,5,6]=>1011000=>[1,2,1,4]
[1,2,5,8,4,7,3,6]=>0001010=>[4,2,2]
[1,3,6,8,5,2,7,4]=>0001101=>[4,1,2,1]
[2,5,7,4,1,8,6,3]=>0011011=>[3,1,2,1,1]
[2,4,6,1,8,3,7,5]=>0010101=>[3,2,2,1]
[3,5,1,7,2,8,6,4]=>0101011=>[2,2,2,1,1]
[4,6,3,1,7,8,5,2]=>0110011=>[2,1,3,1,1]
[5,3,1,6,7,8,4,2]=>1100011=>[1,1,4,1,1]
[4,1,6,2,7,8,5,3]=>1010011=>[1,2,3,1,1]
[2,1,3,4,8,7,5,6]=>1000110=>[1,4,1,2]
[4,8,7,3,6,5,1,2]=>0110110=>[2,1,2,1,2]
[6,3,8,7,5,4,1,2]=>1011110=>[1,2,1,1,1,2]
[4,3,8,7,6,5,1,2]=>1011110=>[1,2,1,1,1,2]
[2,8,7,6,1,5,4,3]=>0111011=>[2,1,1,2,1,1]
[5,2,8,7,6,1,4,3]=>1011101=>[1,2,1,1,2,1]
[6,2,8,7,5,1,4,3]=>1011101=>[1,2,1,1,2,1]
[7,8,2,6,5,1,4,3]=>0101101=>[2,2,1,2,1]
[6,1,8,7,5,4,3,2]=>1011111=>[1,2,1,1,1,1,1]
[4,1,8,7,6,5,3,2]=>1011111=>[1,2,1,1,1,1,1]
[3,1,8,7,6,5,4,2]=>1011111=>[1,2,1,1,1,1,1]
[7,8,2,6,1,5,4,3]=>0101011=>[2,2,2,1,1]
[4,2,8,1,7,6,5,3]=>1010111=>[1,2,2,1,1,1]
[3,2,8,1,7,6,5,4]=>1010111=>[1,2,2,1,1,1]
[2,8,7,1,6,5,4,3]=>0110111=>[2,1,2,1,1,1]
[3,8,2,1,7,6,5,4]=>0110111=>[2,1,2,1,1,1]
[4,8,2,7,6,1,5,3]=>0101101=>[2,2,1,2,1]
[3,8,2,7,1,6,5,4]=>0101011=>[2,2,2,1,1]
[3,8,7,2,1,6,5,4]=>0111011=>[2,1,1,2,1,1]
[4,8,7,2,6,1,5,3]=>0110101=>[2,1,2,2,1]
[5,8,7,6,2,1,4,3]=>0111101=>[2,1,1,1,2,1]
[6,5,8,7,1,4,3,2]=>1011011=>[1,2,1,2,1,1]
[3,8,7,1,6,5,4,2]=>0110111=>[2,1,2,1,1,1]
[4,8,1,7,6,5,3,2]=>0101111=>[2,2,1,1,1,1]
[5,4,1,8,7,6,3,2]=>1101111=>[1,1,2,1,1,1,1]
[6,4,8,1,7,5,3,2]=>1010111=>[1,2,2,1,1,1]
[7,8,4,1,6,5,3,2]=>0110111=>[2,1,2,1,1,1]
[7,8,3,1,6,5,4,2]=>0110111=>[2,1,2,1,1,1]
[5,3,1,8,7,6,4,2]=>1101111=>[1,1,2,1,1,1,1]
[4,3,1,8,7,6,5,2]=>1101111=>[1,1,2,1,1,1,1]
[4,2,1,8,7,6,5,3]=>1101111=>[1,1,2,1,1,1,1]
[6,5,3,1,8,7,4,2]=>1110111=>[1,1,1,2,1,1,1]
[7,5,2,1,8,6,4,3]=>1110111=>[1,1,1,2,1,1,1]
[5,4,2,1,8,7,6,3]=>1110111=>[1,1,1,2,1,1,1]
[7,3,2,1,8,6,5,4]=>1110111=>[1,1,1,2,1,1,1]
[6,1,4,2,3,5,8,7]=>1010001=>[1,2,4,1]
[8,6,1,4,2,3,5,7]=>1101000=>[1,1,2,4]
[6,8,1,4,2,3,5,7]=>0101000=>[2,2,4]
[4,6,2,3,8,1,5,7]=>0100100=>[2,3,3]
[8,2,3,6,4,1,5,7]=>1001100=>[1,3,1,3]
[6,2,3,8,4,1,5,7]=>1001100=>[1,3,1,3]
[8,4,2,3,6,1,5,7]=>1100100=>[1,1,3,3]
[6,4,2,3,8,1,5,7]=>1100100=>[1,1,3,3]
[2,8,4,3,6,1,5,7]=>0110100=>[2,1,2,3]
[2,6,3,8,4,1,5,7]=>0101100=>[2,2,1,3]
[6,3,8,4,2,1,5,7]=>1011100=>[1,2,1,1,3]
[2,4,8,3,6,1,5,7]=>0010100=>[3,2,3]
[2,4,6,3,8,1,5,7]=>0010100=>[3,2,3]
[8,3,6,2,4,1,5,7]=>1010100=>[1,2,2,3]
[8,3,6,2,1,4,5,7]=>1011000=>[1,2,1,4]
[2,1,8,3,6,4,5,7]=>1010100=>[1,2,2,3]
[6,3,8,2,1,4,5,7]=>1011000=>[1,2,1,4]
[6,2,4,3,8,1,5,7]=>1010100=>[1,2,2,3]
[3,6,4,7,8,5,1,2]=>0100110=>[2,3,1,2]
[1,6,4,2,7,5,8,3]=>0110101=>[2,1,2,2,1]
[3,4,6,8,7,5,1,2]=>0001110=>[4,1,1,2]
[5,4,6,3,8,7,1,2]=>1010110=>[1,2,2,1,2]
[6,4,8,5,3,7,1,2]=>1011010=>[1,2,1,2,2]
[1,8,5,2,6,3,7,4]=>0110101=>[2,1,2,2,1]
[1,4,6,2,8,5,7,3]=>0010101=>[3,2,2,1]
[7,8,1,4,2,5,6,3]=>0101001=>[2,2,3,1]
[3,6,5,2,4,1,8,7]=>0110101=>[2,1,2,2,1]
[4,8,5,3,1,6,2,7]=>0111010=>[2,1,1,2,2]
[5,1,6,2,8,7,3,4]=>1010110=>[1,2,2,1,2]
[6,1,8,7,4,2,3,5]=>1011100=>[1,2,1,1,3]
[1,2,8,5,7,3,6,4]=>0010101=>[3,2,2,1]
[1,3,6,8,7,5,2,4]=>0001110=>[4,1,1,2]
[7,8,1,2,4,6,5,3]=>0100011=>[2,4,1,1]
[1,2,6,4,8,7,5,3]=>0010111=>[3,2,1,1,1]
[1,8,2,5,4,7,6,3]=>0101011=>[2,2,2,1,1]
[1,2,7,3,5,8,6,4]=>0010011=>[3,3,1,1]
[4,6,2,1,7,5,3,8]=>0110110=>[2,1,2,1,2]
[4,6,2,3,7,8,1,5]=>0100010=>[2,4,2]
[4,2,1,3,5,7,8,6]=>1100001=>[1,1,5,1]
[7,3,2,4,5,1,8,6]=>1100101=>[1,1,3,2,1]
[7,8,3,2,4,1,6,5]=>0110101=>[2,1,2,2,1]
[7,8,4,2,6,3,1,5]=>0110110=>[2,1,2,1,2]
[4,2,6,3,8,7,1,5]=>1010110=>[1,2,2,1,2]
[5,8,2,7,4,3,1,6]=>0101110=>[2,2,1,1,2]
[7,5,2,8,3,4,1,6]=>1101010=>[1,1,2,2,2]
[4,3,6,8,1,2,7,5]=>1001001=>[1,3,3,1]
[6,4,3,5,2,8,1,7]=>1101010=>[1,1,2,2,2]
[6,5,8,4,2,3,1,7]=>1011010=>[1,2,1,2,2]
[4,1,3,6,5,8,7,2]=>1001011=>[1,3,2,1,1]
[2,4,1,3,8,5,7,6]=>0100101=>[2,3,2,1]
[2,4,1,3,5,8,7,6]=>0100011=>[2,4,1,1]
[4,6,1,3,5,8,7,2]=>0100011=>[2,4,1,1]
[1,4,6,3,5,8,7,2]=>0010011=>[3,3,1,1]
[4,2,1,3,6,5,7,8]=>1100100=>[1,1,3,3]
[4,2,1,6,3,5,7,8]=>1101000=>[1,1,2,4]
[4,2,1,8,3,5,7,6]=>1101001=>[1,1,2,3,1]
[6,2,1,8,3,5,7,4]=>1101001=>[1,1,2,3,1]
[6,4,1,3,8,5,7,2]=>1100101=>[1,1,3,2,1]
[6,1,4,3,8,5,7,2]=>1010101=>[1,2,2,2,1]
[1,6,4,3,8,5,7,2]=>0110101=>[2,1,2,2,1]
[8,1,4,3,6,5,7,2]=>1010101=>[1,2,2,2,1]
[8,2,1,3,6,5,7,4]=>1100101=>[1,1,3,2,1]
[8,2,1,4,3,5,7,6]=>1101001=>[1,1,2,3,1]
[8,1,4,6,3,5,7,2]=>1001001=>[1,3,3,1]
[6,1,4,8,3,5,7,2]=>1001001=>[1,3,3,1]
[6,4,8,1,3,5,7,2]=>1010001=>[1,2,4,1]
[2,4,8,1,3,5,7,6]=>0010001=>[3,4,1]
[4,6,8,1,3,5,7,2]=>0010001=>[3,4,1]
[4,6,1,8,3,5,7,2]=>0101001=>[2,2,3,1]
[4,1,6,8,3,5,7,2]=>1001001=>[1,3,3,1]
[1,4,6,8,3,5,7,2]=>0001001=>[4,3,1]
[1,4,6,3,8,5,7,2]=>0010101=>[3,2,2,1]
[4,6,1,3,8,5,7,2]=>0100101=>[2,3,2,1]
[2,6,1,3,8,5,7,4]=>0100101=>[2,3,2,1]
[2,1,6,3,8,5,7,4]=>1010101=>[1,2,2,2,1]
[2,1,3,6,8,5,7,4]=>1000101=>[1,4,2,1]
[4,1,3,6,8,5,7,2]=>1000101=>[1,4,2,1]
[1,4,3,6,8,5,7,2]=>0100101=>[2,3,2,1]
[2,1,8,3,6,5,7,4]=>1010101=>[1,2,2,2,1]
[2,1,8,4,3,5,7,6]=>1011001=>[1,2,1,3,1]
[4,1,8,3,6,5,7,2]=>1010101=>[1,2,2,2,1]
[2,8,4,1,3,5,7,6]=>0110001=>[2,1,4,1]
[6,8,1,4,3,5,7,2]=>0101001=>[2,2,3,1]
[1,8,6,4,3,5,7,2]=>0111001=>[2,1,1,3,1]
[8,6,1,4,3,5,7,2]=>1101001=>[1,1,2,3,1]
[8,6,4,1,3,5,7,2]=>1110001=>[1,1,1,4,1]
[8,4,2,1,3,5,7,6]=>1110001=>[1,1,1,4,1]
[8,5,7,4,3,2,1,6]=>1011110=>[1,2,1,1,1,2]
[8,7,6,5,1,4,3,2]=>1111011=>[1,1,1,1,2,1,1]
[8,7,4,3,6,2,1,5]=>1110110=>[1,1,1,2,1,2]
[8,7,3,6,5,2,1,4]=>1101110=>[1,1,2,1,1,2]
[6,5,8,4,3,2,1,7]=>1011110=>[1,2,1,1,1,2]
[8,4,7,6,3,2,1,5]=>1011110=>[1,2,1,1,1,2]
[5,8,7,4,3,2,1,6]=>0111110=>[2,1,1,1,1,2]
[4,5,2,7,3,1,8,6]=>0101101=>[2,2,1,2,1]
[4,8,2,6,3,5,7,1]=>0101001=>[2,2,3,1]
[8,6,1,2,7,4,3,5]=>1100110=>[1,1,3,1,2]
[4,6,2,1,7,8,5,3]=>0110011=>[2,1,3,1,1]
[2,3,8,7,4,1,6,5]=>0011101=>[3,1,1,2,1]
[1,6,2,5,8,4,3,7]=>0100110=>[2,3,1,2]
[1,5,8,6,2,3,7,4]=>0011001=>[3,1,3,1]
[5,2,7,1,8,6,3,4]=>1010110=>[1,2,2,1,2]
[1,2,8,3,7,6,5,4]=>0010111=>[3,2,1,1,1]
[6,5,2,8,1,7,3,4]=>1101010=>[1,1,2,2,2]
[2,8,3,5,1,7,4,6]=>0101010=>[2,2,2,2]
[2,8,5,6,1,7,3,4]=>0101010=>[2,2,2,2]
[5,4,2,8,6,1,7,3]=>1101101=>[1,1,2,1,2,1]
[8,5,4,3,7,2,6,1]=>1110101=>[1,1,1,2,2,1]
[8,3,7,4,2,6,5,1]=>1011011=>[1,2,1,2,1,1]
[3,8,7,4,1,6,5,2]=>0111011=>[2,1,1,2,1,1]
[6,3,2,8,4,1,7,5]=>1101101=>[1,1,2,1,2,1]
[2,8,3,4,1,7,5,6]=>0101010=>[2,2,2,2]
[5,4,2,8,3,1,7,6]=>1101101=>[1,1,2,1,2,1]
[2,8,6,4,1,7,5,3]=>0111011=>[2,1,1,2,1,1]
[8,4,7,6,2,5,3,1]=>1011011=>[1,2,1,2,1,1]
[4,8,7,6,1,5,3,2]=>0111011=>[2,1,1,2,1,1]
[7,3,8,5,2,1,6,4]=>1011101=>[1,2,1,1,2,1]
[7,3,8,4,2,1,6,5]=>1011101=>[1,2,1,1,2,1]
[7,5,4,3,8,2,1,6]=>1110110=>[1,1,1,2,1,2]
[5,4,2,3,8,1,6,7]=>1100100=>[1,1,3,3]
[3,7,8,4,1,2,6,5]=>0011001=>[3,1,3,1]
[8,7,4,6,3,5,2,1]=>1101011=>[1,1,2,2,1,1]
[7,3,4,8,2,1,5,6]=>1001100=>[1,3,1,3]
[7,5,8,6,2,1,4,3]=>1011101=>[1,2,1,1,2,1]
[6,5,8,7,3,1,4,2]=>1011101=>[1,2,1,1,2,1]
[2,4,8,3,1,5,7,6]=>0011001=>[3,1,3,1]
[6,3,2,4,8,1,5,7]=>1100100=>[1,1,3,3]
[2,4,3,8,1,6,5,7]=>0101010=>[2,2,2,2]
[2,3,8,4,1,6,7,5]=>0011001=>[3,1,3,1]
[8,3,4,7,2,5,6,1]=>1001001=>[1,3,3,1]
[3,4,8,7,1,5,6,2]=>0011001=>[3,1,3,1]
[2,5,3,8,1,6,4,7]=>0101010=>[2,2,2,2]
[3,7,4,8,1,5,2,6]=>0101010=>[2,2,2,2]
[8,4,6,7,2,3,5,1]=>1001001=>[1,3,3,1]
[2,6,8,5,1,3,7,4]=>0011001=>[3,1,3,1]
[2,6,8,4,1,3,7,5]=>0011001=>[3,1,3,1]
[3,7,5,8,1,4,2,6]=>0101010=>[2,2,2,2]
[2,6,5,8,1,4,3,7]=>0101010=>[2,2,2,2]
[2,5,8,3,1,4,7,6]=>0011001=>[3,1,3,1]
[4,7,6,8,1,3,2,5]=>0101010=>[2,2,2,2]
[5,6,8,7,1,3,4,2]=>0011001=>[3,1,3,1]
[8,7,4,1,6,2,5,3]=>1110101=>[1,1,1,2,2,1]
[6,3,7,4,5,8,2,1]=>1010011=>[1,2,3,1,1]
[3,5,7,4,6,8,2,1]=>0010011=>[3,3,1,1]
[6,8,4,1,7,2,5,3]=>0110101=>[2,1,2,2,1]
[3,8,5,4,6,7,2,1]=>0110011=>[2,1,3,1,1]
[6,8,3,4,5,7,2,1]=>0100011=>[2,4,1,1]
[2,5,7,4,6,3,8,1]=>0010101=>[3,2,2,1]
[5,4,2,7,8,3,6,1]=>1100101=>[1,1,3,2,1]
[8,1,6,2,4,3,5,7]=>1010100=>[1,2,2,3]
[8,7,1,2,4,3,5,6]=>1100100=>[1,1,3,3]
[6,8,3,1,4,7,2,5]=>0110010=>[2,1,3,2]
[6,4,7,2,8,5,1,3]=>1010110=>[1,2,2,1,2]
[5,8,1,4,7,3,2,6]=>0100110=>[2,3,1,2]
[8,7,1,4,5,3,2,6]=>1100110=>[1,1,3,1,2]
[1,7,6,2,4,3,5,8]=>0110100=>[2,1,2,3]
[8,7,4,2,6,5,1,3]=>1110110=>[1,1,1,2,1,2]
[8,7,3,2,4,6,5,1]=>1110011=>[1,1,1,3,1,1]
[1,7,2,5,4,3,6,8]=>0101100=>[2,2,1,3]
[6,8,4,3,7,5,2,1]=>0110111=>[2,1,2,1,1,1]
[6,4,7,3,8,5,2,1]=>1010111=>[1,2,2,1,1,1]
[6,3,7,2,4,8,5,1]=>1010011=>[1,2,3,1,1]
[8,1,2,5,4,3,6,7]=>1001100=>[1,3,1,3]
[2,6,3,1,4,5,8,7]=>0110001=>[2,1,4,1]
[4,7,3,2,5,6,1,8]=>0110010=>[2,1,3,2]
[3,6,4,1,2,8,7,5]=>0110011=>[2,1,3,1,1]
[3,6,5,1,8,2,7,4]=>0110101=>[2,1,2,2,1]
[4,6,5,1,8,7,2,3]=>0110110=>[2,1,2,1,2]
[5,7,1,4,8,6,2,3]=>0100110=>[2,3,1,2]
[5,7,1,3,8,2,6,4]=>0100101=>[2,3,2,1]
[6,3,7,2,8,4,5,1]=>1010101=>[1,2,2,2,1]
[6,7,1,8,3,2,5,4]=>0101101=>[2,2,1,2,1]
[8,7,6,1,4,5,2,3]=>1110010=>[1,1,1,3,2]
[8,7,6,1,3,2,5,4]=>1110101=>[1,1,1,2,2,1]
[8,7,3,5,1,2,6,4]=>1101001=>[1,1,2,3,1]
[8,7,4,5,1,6,2,3]=>1101010=>[1,1,2,2,2]
[8,5,6,4,1,7,2,3]=>1011010=>[1,2,1,2,2]
[8,4,6,2,3,1,7,5]=>1010101=>[1,2,2,2,1]
[8,3,5,4,2,1,7,6]=>1011101=>[1,2,1,1,2,1]
[7,1,6,8,4,5,3,2]=>1001011=>[1,3,2,1,1]
[7,5,1,6,4,2,3,8]=>1101100=>[1,1,2,1,3]
[8,1,5,7,4,6,3,2]=>1001011=>[1,3,2,1,1]
[1,8,4,6,7,5,3,2]=>0100111=>[2,3,1,1,1]
[6,1,8,4,7,5,3,2]=>1010111=>[1,2,2,1,1,1]
[8,4,1,5,6,7,3,2]=>1100011=>[1,1,4,1,1]
[8,2,5,6,1,4,7,3]=>1001001=>[1,3,3,1]
[4,8,5,2,1,6,7,3]=>0111001=>[2,1,1,3,1]
[1,8,4,6,2,5,3,7]=>0101010=>[2,2,2,2]
[8,5,6,1,2,4,3,7]=>1010010=>[1,2,3,2]
[2,8,3,1,5,6,7,4]=>0110001=>[2,1,4,1]
[8,2,4,3,6,7,1,5]=>1010010=>[1,2,3,2]
[8,3,2,7,1,5,6,4]=>1101001=>[1,1,2,3,1]
[3,2,8,5,7,1,6,4]=>1010101=>[1,2,2,2,1]
[3,6,2,8,5,1,7,4]=>0101101=>[2,2,1,2,1]
[6,2,1,8,4,7,5,3]=>1101011=>[1,1,2,2,1,1]
[2,8,7,1,4,6,5,3]=>0110011=>[2,1,3,1,1]
[8,2,7,1,5,4,6,3]=>1010101=>[1,2,2,2,1]
[7,3,1,5,6,2,4,8]=>1100100=>[1,1,3,3]
[2,7,3,6,5,8,1,4]=>0101010=>[2,2,2,2]
[7,2,8,1,6,4,5,3]=>1010101=>[1,2,2,2,1]
[7,8,2,6,4,1,5,3]=>0101101=>[2,2,1,2,1]
[8,7,2,4,1,6,5,3]=>1101011=>[1,1,2,2,1,1]
[1,2,8,6,3,7,5,4]=>0011011=>[3,1,2,1,1]
[1,8,7,2,3,6,5,4]=>0110011=>[2,1,3,1,1]
[1,7,8,2,6,4,3,5]=>0010110=>[3,2,1,2]
[7,2,1,5,8,3,4,6]=>1100100=>[1,1,3,3]
[7,1,5,8,3,2,4,6]=>1001100=>[1,3,1,3]
[7,8,1,5,2,4,3,6]=>0101010=>[2,2,2,2]
[8,7,1,2,5,4,3,6]=>1100110=>[1,1,3,1,2]
[1,6,2,8,4,3,7,5]=>0101101=>[2,2,1,2,1]
[1,8,3,7,2,5,4,6]=>0101010=>[2,2,2,2]
[8,1,4,7,3,2,5,6]=>1001100=>[1,3,1,3]
[4,7,8,1,3,2,5,6]=>0010100=>[3,2,3]
[2,1,8,3,5,7,4,6]=>1010010=>[1,2,3,2]
[1,2,3,4,8,5,7,6]=>0000101=>[5,2,1]
[8,3,5,2,4,1,7,6]=>1010101=>[1,2,2,2,1]
[8,6,2,5,3,1,7,4]=>1101101=>[1,1,2,1,2,1]
[3,7,2,5,6,4,1,8]=>0100110=>[2,3,1,2]
[7,6,2,5,4,3,1,8]=>1101110=>[1,1,2,1,1,2]
[4,7,5,2,6,3,1,8]=>0110110=>[2,1,2,1,2]
[5,6,7,2,4,3,1,8]=>0010110=>[3,2,1,2]
[1,8,3,4,2,7,5,6]=>0101010=>[2,2,2,2]
[2,8,3,4,1,6,7,5]=>0101001=>[2,2,3,1]
[7,8,2,4,3,1,6,5]=>0101101=>[2,2,1,2,1]
[6,1,3,5,7,2,4,8]=>1000100=>[1,4,3]
[8,1,3,6,2,4,7,5]=>1001001=>[1,3,3,1]
[2,1,8,3,7,5,4,6]=>1010110=>[1,2,2,1,2]
[7,1,8,2,5,6,3,4]=>1010010=>[1,2,3,2]
[6,1,5,8,2,7,3,4]=>1001010=>[1,3,2,2]
[6,2,5,8,1,4,7,3]=>1001001=>[1,3,3,1]
[2,3,8,1,5,6,7,4]=>0010001=>[3,4,1]
[1,3,8,2,5,7,4,6]=>0010010=>[3,3,2]
[2,8,7,1,6,4,5,3]=>0110101=>[2,1,2,2,1]
[3,8,7,1,5,6,4,2]=>0110011=>[2,1,3,1,1]
[4,8,7,5,1,6,3,2]=>0111011=>[2,1,1,2,1,1]
[5,8,6,7,1,4,3,2]=>0101011=>[2,2,2,1,1]
[6,7,8,5,1,4,3,2]=>0011011=>[3,1,2,1,1]
[5,6,3,8,4,1,7,2]=>0101101=>[2,2,1,2,1]
[7,3,8,5,4,1,6,2]=>1011101=>[1,2,1,1,2,1]
[3,4,8,5,6,1,7,2]=>0010101=>[3,2,2,1]
[8,3,7,4,1,6,5,2]=>1011011=>[1,2,1,2,1,1]
[3,5,6,8,4,1,7,2]=>0001101=>[4,1,2,1]
[5,6,4,7,8,1,3,2]=>0100101=>[2,3,2,1]
[6,2,3,1,5,4,7,8]=>1010100=>[1,2,2,3]
[8,5,1,3,2,4,7,6]=>1101001=>[1,1,2,3,1]
[7,5,1,3,2,6,4,8]=>1101010=>[1,1,2,2,2]
[3,6,4,1,5,2,7,8]=>0110100=>[2,1,2,3]
[4,5,6,1,3,2,7,8]=>0010100=>[3,2,3]
[6,7,1,4,2,5,3,8]=>0101010=>[2,2,2,2]
[2,7,1,3,5,6,4,8]=>0100010=>[2,4,2]
[8,6,1,2,4,3,7,5]=>1100101=>[1,1,3,2,1]
[7,8,1,2,5,3,6,4]=>0100101=>[2,3,2,1]
[6,8,1,4,2,3,7,5]=>0101001=>[2,2,3,1]
[4,5,8,1,2,3,7,6]=>0010001=>[3,4,1]
[1,8,2,7,5,4,6,3]=>0101101=>[2,2,1,2,1]
[1,8,6,3,7,2,4,5]=>0110100=>[2,1,2,3]
[1,8,5,3,4,7,2,6]=>0110010=>[2,1,3,2]
[1,8,2,5,4,6,7,3]=>0101001=>[2,2,3,1]
[7,4,3,8,2,5,6,1]=>1101001=>[1,1,2,3,1]
[7,2,8,4,3,5,6,1]=>1011001=>[1,2,1,3,1]
[7,2,8,1,3,6,4,5]=>1010010=>[1,2,3,2]
[1,4,7,5,2,6,8,3]=>0011001=>[3,1,3,1]
[4,6,5,3,7,1,8,2]=>0110101=>[2,1,2,2,1]
[5,6,2,7,3,1,8,4]=>0101101=>[2,2,1,2,1]
[1,6,3,7,5,8,2,4]=>0101010=>[2,2,2,2]
[5,2,4,8,1,3,7,6]=>1001001=>[1,3,3,1]
[6,2,5,4,8,3,7,1]=>1010101=>[1,2,2,2,1]
[3,5,2,4,7,1,6,8]=>0100100=>[2,3,3]
[6,4,5,3,8,2,1,7]=>1010110=>[1,2,2,1,2]
[6,5,3,4,8,7,1,2]=>1100110=>[1,1,3,1,2]
[7,6,3,8,5,4,1,2]=>1101110=>[1,1,2,1,1,2]
[5,4,8,1,2,7,3,6]=>1010010=>[1,2,3,2]
[6,2,4,8,5,1,3,7]=>1001100=>[1,3,1,3]
[7,6,3,8,5,1,2,4]=>1101100=>[1,1,2,1,3]
[6,3,8,1,7,2,4,5]=>1010100=>[1,2,2,3]
[7,2,8,6,1,3,4,5]=>1011000=>[1,2,1,4]
[7,2,8,6,1,5,3,4]=>1011010=>[1,2,1,2,2]
[3,2,4,7,8,1,5,6]=>1000100=>[1,4,3]
[1,5,7,4,2,8,6,3]=>0011011=>[3,1,2,1,1]
[1,3,7,2,8,6,4,5]=>0010110=>[3,2,1,2]
[1,5,3,6,8,2,7,4]=>0100101=>[2,3,2,1]
[4,3,6,5,7,8,1,2]=>1010010=>[1,2,3,2]
[4,2,3,5,6,8,1,7]=>1000010=>[1,5,2]
[4,2,6,7,3,8,5,1]=>1001011=>[1,3,2,1,1]
[3,2,5,6,8,1,7,4]=>1000101=>[1,4,2,1]
[4,2,3,6,8,1,5,7]=>1000100=>[1,4,3]
[2,6,1,5,4,8,3,7]=>0101010=>[2,2,2,2]
[3,2,1,8,7,5,6,4]=>1101101=>[1,1,2,1,2,1]
[3,1,6,2,5,8,4,7]=>1010010=>[1,2,3,2]
[6,5,1,3,4,8,2,7]=>1100010=>[1,1,4,2]
[6,2,4,5,8,1,3,7]=>1000100=>[1,4,3]
[2,6,1,5,8,3,4,7]=>0100100=>[2,3,3]
[2,3,4,8,1,7,6,5]=>0001011=>[4,2,1,1]
[6,3,1,7,8,4,5,2]=>1100101=>[1,1,3,2,1]
[6,2,7,8,4,5,1,3]=>1001010=>[1,3,2,2]
[3,1,4,8,7,6,2,5]=>1001110=>[1,3,1,1,2]
[2,3,6,5,8,7,1,4]=>0010110=>[3,2,1,2]
[8,4,1,2,7,6,3,5]=>1100110=>[1,1,3,1,2]
[3,4,8,2,7,5,1,6]=>0010110=>[3,2,1,2]
[6,3,2,8,5,7,4,1]=>1101011=>[1,1,2,2,1,1]
[3,2,6,8,5,1,7,4]=>1001101=>[1,3,1,2,1]
[5,2,4,1,7,8,6,3]=>1010011=>[1,2,3,1,1]
[3,8,4,7,2,5,6,1]=>0101001=>[2,2,3,1]
[1,8,7,2,4,5,6,3]=>0110001=>[2,1,4,1]
[5,3,4,7,1,8,6,2]=>1001011=>[1,3,2,1,1]
[5,3,7,1,6,2,8,4]=>1010101=>[1,2,2,2,1]
[4,7,6,5,8,2,1,3]=>0110110=>[2,1,2,1,2]
[7,5,1,2,6,8,4,3]=>1100011=>[1,1,4,1,1]
[1,2,5,3,8,7,6,4]=>0010111=>[3,2,1,1,1]
[2,8,1,5,6,3,7,4]=>0100101=>[2,3,2,1]
[4,8,2,3,6,7,1,5]=>0100010=>[2,4,2]
[8,2,4,6,7,1,3,5]=>1000100=>[1,4,3]
[3,7,5,1,8,4,6,2]=>0110101=>[2,1,2,2,1]
[6,5,3,1,8,4,2,7]=>1110110=>[1,1,1,2,1,2]
[5,7,4,3,8,6,2,1]=>0110111=>[2,1,2,1,1,1]
[4,2,3,8,5,6,1,7]=>1001010=>[1,3,2,2]
[3,6,4,2,8,5,7,1]=>0110101=>[2,1,2,2,1]
[4,7,3,2,5,1,8,6]=>0110101=>[2,1,2,2,1]
[2,4,8,7,1,3,5,6]=>0011000=>[3,1,4]
[2,4,3,5,1,8,6,7]=>0101010=>[2,2,2,2]
[8,6,1,2,4,3,5,7]=>1100100=>[1,1,3,3]
[8,6,2,5,4,1,3,7]=>1101100=>[1,1,2,1,3]
[8,3,5,7,6,2,1,4]=>1001110=>[1,3,1,1,2]
[6,7,5,3,8,2,4,1]=>0110101=>[2,1,2,2,1]
[8,2,6,3,4,5,1,7]=>1010010=>[1,2,3,2]
[8,1,5,4,3,6,2,7]=>1011010=>[1,2,1,2,2]
[8,6,4,2,1,5,3,7]=>1111010=>[1,1,1,1,2,2]
[8,3,2,4,6,1,5,7]=>1100100=>[1,1,3,3]
[8,2,3,4,7,6,1,5]=>1000110=>[1,4,1,2]
[5,7,1,8,3,4,6,2]=>0101001=>[2,2,3,1]
[1,5,6,7,3,4,8,2]=>0001001=>[4,3,1]
[4,8,1,2,7,3,6,5]=>0100101=>[2,3,2,1]
[2,5,7,8,4,1,3,6]=>0001100=>[4,1,3]
[6,3,5,8,7,2,4,1]=>1001101=>[1,3,1,2,1]
[5,2,8,7,1,3,4,6]=>1011000=>[1,2,1,4]
[5,2,7,4,8,1,6,3]=>1010101=>[1,2,2,2,1]
[8,3,7,4,2,5,6,1]=>1011001=>[1,2,1,3,1]
[8,1,7,4,5,2,6,3]=>1010101=>[1,2,2,2,1]
[1,7,8,3,5,4,6,2]=>0010101=>[3,2,2,1]
[4,6,3,5,8,1,7,2]=>0100101=>[2,3,2,1]
[8,2,4,1,5,6,7,3]=>1010001=>[1,2,4,1]
[3,5,1,7,6,8,2,4]=>0101010=>[2,2,2,2]
[2,1,7,6,4,5,8,3]=>1011001=>[1,2,1,3,1]
[1,7,6,5,2,4,8,3]=>0111001=>[2,1,1,3,1]
[5,1,7,6,2,8,4,3]=>1011011=>[1,2,1,2,1,1]
[4,6,2,5,3,8,7,1]=>0101011=>[2,2,2,1,1]
[8,6,4,2,3,1,7,5]=>1110101=>[1,1,1,2,2,1]
[8,6,4,2,1,3,7,5]=>1111001=>[1,1,1,1,3,1]
[4,2,8,3,1,5,6,7]=>1011000=>[1,2,1,4]
[2,5,7,3,8,4,6,1]=>0010101=>[3,2,2,1]
[4,2,7,1,8,5,3,6]=>1010110=>[1,2,2,1,2]
[1,3,7,5,8,6,4,2]=>0010111=>[3,2,1,1,1]
[2,7,4,5,8,3,6,1]=>0100101=>[2,3,2,1]
[3,5,7,1,4,8,6,2]=>0010011=>[3,3,1,1]
[3,4,1,2,8,5,7,6]=>0100101=>[2,3,2,1]
[6,2,3,1,4,8,7,5]=>1010011=>[1,2,3,1,1]
[8,4,3,2,5,7,1,6]=>1110010=>[1,1,1,3,2]
[5,3,6,8,2,1,4,7]=>1001100=>[1,3,1,3]
[3,2,6,8,5,4,1,7]=>1001110=>[1,3,1,1,2]
[7,3,8,2,5,4,1,6]=>1010110=>[1,2,2,1,2]
[7,4,2,5,8,3,1,6]=>1100110=>[1,1,3,1,2]
[3,1,2,8,5,6,4,7]=>1001010=>[1,3,2,2]
[5,2,1,6,8,3,4,7]=>1100100=>[1,1,3,3]
[3,1,8,6,5,4,2,7]=>1011110=>[1,2,1,1,1,2]
[5,6,8,1,4,3,2,7]=>0010110=>[3,2,1,2]
[6,4,8,3,7,2,5,1]=>1010101=>[1,2,2,2,1]
[4,7,3,6,2,1,8,5]=>0101101=>[2,2,1,2,1]
[7,8,4,1,5,3,2,6]=>0110110=>[2,1,2,1,2]
[7,3,8,5,1,4,2,6]=>1011010=>[1,2,1,2,2]
[1,5,4,8,3,7,6,2]=>0101011=>[2,2,2,1,1]
[4,7,8,3,1,6,5,2]=>0011011=>[3,1,2,1,1]
[8,7,5,3,6,4,2,1]=>1110111=>[1,1,1,2,1,1,1]
[4,6,1,3,8,7,5,2]=>0100111=>[2,3,1,1,1]
[3,1,2,7,5,6,8,4]=>1001001=>[1,3,3,1]
[3,6,1,2,7,5,8,4]=>0100101=>[2,3,2,1]
[3,6,2,5,8,7,4,1]=>0100111=>[2,3,1,1,1]
[8,5,2,3,6,7,4,1]=>1100011=>[1,1,4,1,1]
[6,7,1,3,2,8,4,5]=>0101010=>[2,2,2,2]
[6,2,7,1,3,4,8,5]=>1010001=>[1,2,4,1]
[5,2,1,7,3,8,4,6]=>1101010=>[1,1,2,2,2]
[4,7,2,6,3,8,1,5]=>0101010=>[2,2,2,2]
[4,8,2,6,3,7,5,1]=>0101011=>[2,2,2,1,1]
[3,7,2,4,6,1,8,5]=>0100101=>[2,3,2,1]
[5,3,7,2,8,1,4,6]=>1010100=>[1,2,2,3]
[7,1,8,3,4,2,5,6]=>1010100=>[1,2,2,3]
[7,2,4,1,8,3,5,6]=>1010100=>[1,2,2,3]
[4,8,7,6,3,2,1,5]=>0111110=>[2,1,1,1,1,2]
[7,3,8,2,6,5,1,4]=>1010110=>[1,2,2,1,2]
[7,8,2,4,6,1,5,3]=>0100101=>[2,3,2,1]
[3,5,1,8,7,2,6,4]=>0101101=>[2,2,1,2,1]
[5,2,8,1,7,6,3,4]=>1010110=>[1,2,2,1,2]
[6,2,1,3,8,7,5,4]=>1100111=>[1,1,3,1,1,1]
[6,7,8,1,2,5,4,3]=>0010011=>[3,3,1,1]
[5,8,7,1,6,4,3,2]=>0110111=>[2,1,2,1,1,1]
[6,8,7,5,1,4,3,2]=>0111011=>[2,1,1,2,1,1]
[8,6,4,3,2,1,7,5]=>1111101=>[1,1,1,1,1,2,1]
[6,5,4,3,8,2,7,1]=>1110101=>[1,1,1,2,2,1]
[7,5,4,3,2,8,6,1]=>1111011=>[1,1,1,1,2,1,1]
[8,5,4,3,7,2,1,6]=>1110110=>[1,1,1,2,1,2]
[8,4,3,2,1,7,6,5]=>1111011=>[1,1,1,1,2,1,1]
[3,7,5,8,1,4,6,2]=>0101001=>[2,2,3,1]
[4,7,5,8,3,2,1,6]=>0101110=>[2,2,1,1,2]
[5,7,2,3,6,1,8,4]=>0100101=>[2,3,2,1]
[7,3,1,4,8,2,5,6]=>1100100=>[1,1,3,3]
[7,4,1,2,5,8,3,6]=>1100010=>[1,1,4,2]
[4,7,1,6,5,8,3,2]=>0101011=>[2,2,2,1,1]
[2,7,5,4,3,8,1,6]=>0111010=>[2,1,1,2,2]
[8,6,4,2,3,7,5,1]=>1110011=>[1,1,1,3,1,1]
[7,6,4,2,3,8,1,5]=>1110010=>[1,1,1,3,2]
[6,4,7,1,3,8,5,2]=>1010011=>[1,2,3,1,1]
[3,1,2,4,8,7,6,5]=>1000111=>[1,4,1,1,1]
[6,5,8,7,3,1,2,4]=>1011100=>[1,2,1,1,3]
[5,6,7,8,1,4,2,3]=>0001010=>[4,2,2]
[2,6,7,4,5,3,1,8]=>0010110=>[3,2,1,2]
[1,3,7,4,2,8,5,6]=>0011010=>[3,1,2,2]
[4,6,1,3,7,2,5,8]=>0100100=>[2,3,3]
[6,5,7,8,3,1,4,2]=>1001101=>[1,3,1,2,1]
[7,5,8,6,2,1,3,4]=>1011100=>[1,2,1,1,3]
[2,8,1,3,6,5,4,7]=>0100110=>[2,3,1,2]
[2,8,7,3,5,4,1,6]=>0110110=>[2,1,2,1,2]
[3,4,2,6,8,7,1,5]=>0100110=>[2,3,1,2]
[6,1,4,2,7,8,5,3]=>1010011=>[1,2,3,1,1]
[7,3,8,4,1,2,6,5]=>1011001=>[1,2,1,3,1]
[6,8,3,2,7,1,5,4]=>0110101=>[2,1,2,2,1]
[5,1,4,3,6,2,7,8]=>1010100=>[1,2,2,3]
[4,8,5,6,3,2,1,7]=>0101110=>[2,2,1,1,2]
[2,8,5,6,3,7,1,4]=>0101010=>[2,2,2,2]
[6,7,3,1,4,2,8,5]=>0110101=>[2,1,2,2,1]
[3,2,6,7,4,8,1,5]=>1001010=>[1,3,2,2]
[3,7,1,2,4,6,5,8]=>0100010=>[2,4,2]
[4,1,8,2,6,3,5,7]=>1010100=>[1,2,2,3]
[7,5,6,8,2,1,4,3]=>1001101=>[1,3,1,2,1]
[5,8,6,7,1,2,3,4]=>0101000=>[2,2,4]
[4,8,1,5,7,2,3,6]=>0100100=>[2,3,3]
[3,5,1,4,7,6,8,2]=>0100101=>[2,3,2,1]
[5,3,2,7,1,6,8,4]=>1101001=>[1,1,2,3,1]
[8,4,3,7,5,1,6,2]=>1101101=>[1,1,2,1,2,1]
[5,1,7,2,4,6,8,3]=>1010001=>[1,2,4,1]
[4,5,7,1,2,6,8,3]=>0010001=>[3,4,1]
[5,4,1,7,3,6,8,2]=>1101001=>[1,1,2,3,1]
[3,6,4,7,5,2,8,1]=>0101101=>[2,2,1,2,1]
[3,4,7,6,2,5,8,1]=>0011001=>[3,1,3,1]
[4,8,3,6,5,2,1,7]=>0101110=>[2,2,1,1,2]
[1,8,6,5,4,2,3,7]=>0111100=>[2,1,1,1,3]
[8,1,7,4,2,5,6,3]=>1011001=>[1,2,1,3,1]
[1,8,7,2,5,3,4,6]=>0110100=>[2,1,2,3]
[4,8,1,5,2,6,3,7]=>0101010=>[2,2,2,2]
[3,6,8,5,1,2,4,7]=>0011000=>[3,1,4]
[1,5,2,7,8,4,6,3]=>0100101=>[2,3,2,1]
[6,7,2,8,5,3,1,4]=>0101110=>[2,2,1,1,2]
[6,7,2,8,3,1,5,4]=>0101101=>[2,2,1,2,1]
[7,1,2,8,3,5,6,4]=>1001001=>[1,3,3,1]
[6,7,5,2,8,1,4,3]=>0110101=>[2,1,2,2,1]
[7,1,4,5,8,6,2,3]=>1000110=>[1,4,1,2]
[3,1,4,6,7,8,5,2]=>1000011=>[1,5,1,1]
[5,7,6,4,2,8,1,3]=>0111010=>[2,1,1,2,2]
[7,4,6,1,8,2,3,5]=>1010100=>[1,2,2,3]
[3,4,5,1,6,8,7,2]=>0010011=>[3,3,1,1]
[5,1,6,8,4,2,7,3]=>1001101=>[1,3,1,2,1]
[7,4,8,2,3,6,5,1]=>1010011=>[1,2,3,1,1]
[7,5,8,6,3,4,2,1]=>1011011=>[1,2,1,2,1,1]
[5,7,8,3,1,6,4,2]=>0011011=>[3,1,2,1,1]
[7,5,8,3,2,4,1,6]=>1011010=>[1,2,1,2,2]
[6,4,1,8,2,5,7,3]=>1101001=>[1,1,2,3,1]
[5,8,2,6,3,1,4,7]=>0101100=>[2,2,1,3]
[3,6,5,1,8,4,7,2]=>0110101=>[2,1,2,2,1]
[8,2,7,5,4,1,3,6]=>1011100=>[1,2,1,1,3]
[6,8,5,2,3,4,1,7]=>0110010=>[2,1,3,2]
[2,6,8,7,1,5,3,4]=>0011010=>[3,1,2,2]
[7,5,1,6,2,8,4,3]=>1101011=>[1,1,2,2,1,1]
[6,2,7,3,8,4,1,5]=>1010110=>[1,2,2,1,2]
[3,7,2,4,8,5,1,6]=>0100110=>[2,3,1,2]
[1,5,2,6,3,8,7,4]=>0101011=>[2,2,2,1,1]
[1,3,6,2,4,8,7,5]=>0010011=>[3,3,1,1]
[7,3,5,2,4,1,6,8]=>1010100=>[1,2,2,3]
[8,3,6,2,5,4,1,7]=>1010110=>[1,2,2,1,2]
[3,5,8,2,4,6,1,7]=>0010010=>[3,3,2]
[6,4,7,8,2,3,1,5]=>1001010=>[1,3,2,2]
[7,4,8,5,3,2,1,6]=>1011110=>[1,2,1,1,1,2]
[1,5,3,2,8,4,7,6]=>0110101=>[2,1,2,2,1]
[2,8,7,3,5,1,4,6]=>0110100=>[2,1,2,3]
[3,8,4,7,5,1,2,6]=>0101100=>[2,2,1,3]
[6,1,2,7,3,8,5,4]=>1001011=>[1,3,2,1,1]
[2,1,7,3,4,8,6,5]=>1010011=>[1,2,3,1,1]
[8,3,1,6,7,2,5,4]=>1100101=>[1,1,3,2,1]
[4,8,3,7,1,5,2,6]=>0101010=>[2,2,2,2]
[1,3,5,8,2,4,7,6]=>0001001=>[4,3,1]
[5,3,7,2,1,4,6,8]=>1011000=>[1,2,1,4]
[6,4,2,8,3,1,5,7]=>1101100=>[1,1,2,1,3]
[5,7,2,3,8,1,4,6]=>0100100=>[2,3,3]
[6,4,7,5,8,1,2,3]=>1010100=>[1,2,2,3]
[8,6,4,2,1,7,5,3]=>1111011=>[1,1,1,1,2,1,1]
[7,4,2,1,5,8,6,3]=>1110011=>[1,1,1,3,1,1]
[7,6,4,1,8,5,2,3]=>1110110=>[1,1,1,2,1,2]
[1,6,4,8,7,5,3,2]=>0101111=>[2,2,1,1,1,1]
[6,3,1,2,8,4,7,5]=>1100101=>[1,1,3,2,1]
[3,6,1,8,2,4,7,5]=>0101001=>[2,2,3,1]
[6,4,1,8,3,2,7,5]=>1101101=>[1,1,2,1,2,1]
[1,4,8,7,2,6,5,3]=>0011011=>[3,1,2,1,1]
[5,4,1,8,7,3,2,6]=>1101110=>[1,1,2,1,1,2]
[5,8,4,1,7,6,2,3]=>0110110=>[2,1,2,1,2]
[8,6,1,7,5,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[3,1,8,7,6,5,2,4]=>1011110=>[1,2,1,1,1,2]
[8,1,2,4,5,3,6,7]=>1000100=>[1,4,3]
[1,8,7,6,4,5,3,2]=>0111011=>[2,1,1,2,1,1]
[2,6,8,1,3,7,5,4]=>0010011=>[3,3,1,1]
[2,4,8,1,5,7,6,3]=>0010011=>[3,3,1,1]
[3,2,8,6,1,7,5,4]=>1011011=>[1,2,1,2,1,1]
[6,2,8,3,1,7,5,4]=>1011011=>[1,2,1,2,1,1]
[7,4,3,8,5,2,1,6]=>1101110=>[1,1,2,1,1,2]
[6,5,2,8,4,3,1,7]=>1101110=>[1,1,2,1,1,2]
[4,3,8,7,5,1,6,2]=>1011101=>[1,2,1,1,2,1]
[4,2,3,8,5,1,6,7]=>1001100=>[1,3,1,3]
[4,2,8,5,1,7,6,3]=>1011011=>[1,2,1,2,1,1]
[3,4,2,8,5,6,1,7]=>0101010=>[2,2,2,2]
[3,2,4,8,6,1,5,7]=>1001100=>[1,3,1,3]
[3,2,5,8,6,1,4,7]=>1001100=>[1,3,1,3]
[8,4,3,7,5,2,6,1]=>1101101=>[1,1,2,1,2,1]
[4,3,7,8,5,1,2,6]=>1001100=>[1,3,1,3]
[4,2,6,8,5,1,3,7]=>1001100=>[1,3,1,3]
[3,5,2,8,4,6,1,7]=>0101010=>[2,2,2,2]
[5,2,6,8,4,1,3,7]=>1001100=>[1,3,1,3]
[5,3,7,8,4,1,2,6]=>1001100=>[1,3,1,3]
[5,6,2,8,3,4,1,7]=>0101010=>[2,2,2,2]
[5,3,8,7,4,1,6,2]=>1011101=>[1,2,1,1,2,1]
[6,4,2,8,5,3,1,7]=>1101110=>[1,1,2,1,1,2]
[8,7,5,3,6,2,4,1]=>1110101=>[1,1,1,2,2,1]
[8,7,4,3,6,2,5,1]=>1110101=>[1,1,1,2,2,1]
[8,6,5,3,7,2,4,1]=>1110101=>[1,1,1,2,2,1]
[7,6,4,3,8,2,5,1]=>1110101=>[1,1,1,2,2,1]
[6,4,5,3,8,2,7,1]=>1010101=>[1,2,2,2,1]
[7,4,5,3,8,2,6,1]=>1010101=>[1,2,2,2,1]
[7,5,6,3,8,2,4,1]=>1010101=>[1,2,2,2,1]
[8,5,6,3,7,2,4,1]=>1010101=>[1,2,2,2,1]
[8,4,6,3,7,2,5,1]=>1010101=>[1,2,2,2,1]
[8,4,7,3,5,2,6,1]=>1010101=>[1,2,2,2,1]
[8,5,7,3,4,2,6,1]=>1010101=>[1,2,2,2,1]
[7,5,8,4,3,2,6,1]=>1011101=>[1,2,1,1,2,1]
[6,5,8,3,4,2,7,1]=>1010101=>[1,2,2,2,1]
[7,5,8,3,4,2,6,1]=>1010101=>[1,2,2,2,1]
[7,6,8,3,5,2,4,1]=>1010101=>[1,2,2,2,1]
[7,5,8,4,6,2,3,1]=>1010101=>[1,2,2,2,1]
[7,5,8,3,6,2,4,1]=>1010101=>[1,2,2,2,1]
[7,4,8,3,6,2,5,1]=>1010101=>[1,2,2,2,1]
[7,4,8,3,5,2,6,1]=>1010101=>[1,2,2,2,1]
[6,4,8,3,5,2,7,1]=>1010101=>[1,2,2,2,1]
[5,4,7,3,6,2,8,1]=>1010101=>[1,2,2,2,1]
[5,4,8,3,7,2,6,1]=>1010101=>[1,2,2,2,1]
[6,5,8,3,7,2,4,1]=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,2,3,1]=>1010101=>[1,2,2,2,1]
[6,5,8,4,7,3,2,1]=>1010111=>[1,2,2,1,1,1]
[6,5,7,3,8,2,4,1]=>1010101=>[1,2,2,2,1]
[5,4,6,3,8,2,7,1]=>1010101=>[1,2,2,2,1]
[6,5,3,7,8,2,1,4]=>1100110=>[1,1,3,1,2]
[6,5,4,2,8,7,1,3]=>1110110=>[1,1,1,2,1,2]
[6,4,3,7,5,2,1,8]=>1101110=>[1,1,2,1,1,2]
[6,3,7,8,5,2,1,4]=>1001110=>[1,3,1,1,2]
[6,3,7,2,5,4,1,8]=>1010110=>[1,2,2,1,2]
[6,3,2,7,5,4,1,8]=>1101110=>[1,1,2,1,1,2]
[4,8,2,6,3,7,1,5]=>0101010=>[2,2,2,2]
[5,8,4,1,2,7,3,6]=>0110010=>[2,1,3,2]
[5,4,8,1,2,3,7,6]=>1010001=>[1,2,4,1]
[1,4,7,6,3,2,5,8]=>0011100=>[3,1,1,3]
[4,8,3,2,7,6,1,5]=>0110110=>[2,1,2,1,2]
[5,8,1,7,4,2,3,6]=>0101100=>[2,2,1,3]
[4,8,6,7,2,3,1,5]=>0101010=>[2,2,2,2]
[4,8,7,3,6,2,1,5]=>0110110=>[2,1,2,1,2]
[4,3,8,2,7,1,6,5]=>1010101=>[1,2,2,2,1]
[4,1,8,7,3,2,5,6]=>1011100=>[1,2,1,1,3]
[4,7,8,1,2,5,3,6]=>0010010=>[3,3,2]
[4,7,5,1,2,8,3,6]=>0110010=>[2,1,3,2]
[2,3,6,7,4,1,8,5]=>0001101=>[4,1,2,1]
[2,6,3,4,7,8,1,5]=>0100010=>[2,4,2]
[3,1,7,8,4,2,5,6]=>1001100=>[1,3,1,3]
[4,3,1,2,8,5,7,6]=>1100101=>[1,1,3,2,1]
[3,7,6,8,4,2,1,5]=>0101110=>[2,2,1,1,2]
[4,7,1,8,5,2,3,6]=>0101100=>[2,2,1,3]
[2,6,8,7,4,3,1,5]=>0011110=>[3,1,1,1,2]
[3,7,8,6,2,4,1,5]=>0011010=>[3,1,2,2]
[3,7,8,2,6,4,1,5]=>0010110=>[3,2,1,2]
[4,2,3,8,1,6,7,5]=>1001001=>[1,3,3,1]
[3,7,2,8,4,6,1,5]=>0101010=>[2,2,2,2]
[4,2,8,3,6,1,7,5]=>1010101=>[1,2,2,2,1]
[4,2,8,6,3,1,7,5]=>1011101=>[1,2,1,1,2,1]
[2,6,8,4,7,3,1,5]=>0010110=>[3,2,1,2]
[2,4,6,8,3,1,7,5]=>0001101=>[4,1,2,1]
[3,7,2,4,8,6,1,5]=>0100110=>[2,3,1,2]
[1,3,6,4,7,2,5,8]=>0010100=>[3,2,3]
[2,4,6,3,8,1,7,5]=>0010101=>[3,2,2,1]
[2,6,4,3,8,7,1,5]=>0110110=>[2,1,2,1,2]
[2,4,3,6,1,8,7,5]=>0101011=>[2,2,2,1,1]
[3,1,7,4,8,2,5,6]=>1010100=>[1,2,2,3]
[2,6,3,7,4,8,1,5]=>0101010=>[2,2,2,2]
[1,3,5,7,6,8,2,4]=>0001010=>[4,2,2]
[1,3,5,7,6,2,8,4]=>0001101=>[4,1,2,1]
[1,3,5,7,2,6,8,4]=>0001001=>[4,3,1]
[1,3,5,2,7,6,8,4]=>0010101=>[3,2,2,1]
[1,3,5,2,7,6,4,8]=>0010110=>[3,2,1,2]
[1,3,5,7,6,2,4,8]=>0001100=>[4,1,3]
[1,3,5,7,4,6,8,2]=>0001001=>[4,3,1]
[1,3,5,7,4,6,2,8]=>0001010=>[4,2,2]
[1,3,5,7,4,2,6,8]=>0001100=>[4,1,3]
[1,3,5,4,7,2,6,8]=>0010100=>[3,2,3]
[1,3,5,4,7,8,2,6]=>0010010=>[3,3,2]
[1,3,5,4,7,2,8,6]=>0010101=>[3,2,2,1]
[1,3,5,7,4,2,8,6]=>0001101=>[4,1,2,1]
[1,3,5,7,4,8,2,6]=>0001010=>[4,2,2]
[1,3,5,7,4,8,6,2]=>0001011=>[4,2,1,1]
[1,3,5,7,8,4,6,2]=>0000101=>[5,2,1]
[1,3,5,7,8,4,2,6]=>0000110=>[5,1,2]
[1,3,5,2,7,8,6,4]=>0010011=>[3,3,1,1]
[1,3,5,7,2,8,6,4]=>0001011=>[4,2,1,1]
[1,3,5,7,8,2,6,4]=>0000101=>[5,2,1]
[1,3,5,7,8,6,2,4]=>0000110=>[5,1,2]
[2,3,6,1,7,8,5,4]=>0010011=>[3,3,1,1]
[2,3,7,1,4,8,6,5]=>0010011=>[3,3,1,1]
[2,6,1,3,7,8,5,4]=>0100011=>[2,4,1,1]
[2,3,6,8,4,5,1,7]=>0001010=>[4,2,2]
[2,5,7,3,4,8,6,1]=>0010011=>[3,3,1,1]
[2,6,7,3,4,8,5,1]=>0010011=>[3,3,1,1]
[6,5,2,4,3,7,1,8]=>1101010=>[1,1,2,2,2]
[2,5,4,6,7,1,3,8]=>0100100=>[2,3,3]
[1,7,6,3,5,4,8,2]=>0110101=>[2,1,2,2,1]
[2,4,6,3,7,5,1,8]=>0010110=>[3,2,1,2]
[4,7,2,3,5,6,1,8]=>0100010=>[2,4,2]
[5,3,2,7,4,6,1,8]=>1101010=>[1,1,2,2,2]
[1,6,8,5,7,3,4,2]=>0010101=>[3,2,2,1]
[4,1,2,5,8,3,7,6]=>1000101=>[1,4,2,1]
[4,6,1,2,5,8,3,7]=>0100010=>[2,4,2]
[4,1,7,2,6,5,8,3]=>1010101=>[1,2,2,2,1]
[5,6,7,2,1,4,8,3]=>0011001=>[3,1,3,1]
[6,4,5,7,1,3,8,2]=>1001001=>[1,3,3,1]
[6,8,5,2,4,1,7,3]=>0110101=>[2,1,2,2,1]
[5,7,6,8,1,4,2,3]=>0101010=>[2,2,2,2]
[4,1,6,2,8,5,7,3]=>1010101=>[1,2,2,2,1]
[7,1,4,2,3,6,8,5]=>1010001=>[1,2,4,1]
[6,4,2,1,3,8,7,5]=>1110011=>[1,1,1,3,1,1]
[1,5,8,3,4,6,7,2]=>0010001=>[3,4,1]
[8,1,2,3,4,6,7,5]=>1000001=>[1,6,1]
[2,8,1,3,5,4,7,6]=>0100101=>[2,3,2,1]
[8,7,1,4,3,5,2,6]=>1101010=>[1,1,2,2,2]
[8,3,2,1,4,5,7,6]=>1110001=>[1,1,1,4,1]
[4,3,2,8,1,6,5,7]=>1101010=>[1,1,2,2,2]
[3,8,6,4,2,1,5,7]=>0111100=>[2,1,1,1,3]
[3,8,2,1,5,6,4,7]=>0110010=>[2,1,3,2]
[8,5,2,4,3,1,6,7]=>1101100=>[1,1,2,1,3]
[8,3,2,5,4,1,6,7]=>1101100=>[1,1,2,1,3]
[6,1,2,7,5,3,8,4]=>1001101=>[1,3,1,2,1]
[2,6,1,4,7,3,8,5]=>0100101=>[2,3,2,1]
[7,3,2,8,6,4,1,5]=>1101110=>[1,1,2,1,1,2]
[7,8,2,5,3,6,1,4]=>0101010=>[2,2,2,2]
[6,3,7,5,1,8,2,4]=>1011010=>[1,2,1,2,2]
[8,1,6,3,5,7,2,4]=>1010010=>[1,2,3,2]
[8,3,2,6,4,7,1,5]=>1101010=>[1,1,2,2,2]
[5,8,4,6,1,7,2,3]=>0101010=>[2,2,2,2]
[8,4,2,5,6,7,1,3]=>1100010=>[1,1,4,2]
[2,3,8,7,6,5,1,4]=>0011110=>[3,1,1,1,2]
[1,5,8,7,2,6,4,3]=>0011011=>[3,1,2,1,1]
[2,5,8,7,3,6,1,4]=>0011010=>[3,1,2,2]
[4,1,8,7,2,6,5,3]=>1011011=>[1,2,1,2,1,1]
[1,2,8,7,3,6,5,4]=>0011011=>[3,1,2,1,1]
[4,5,8,7,1,2,6,3]=>0011001=>[3,1,3,1]
[1,5,8,7,3,2,6,4]=>0011101=>[3,1,1,2,1]
[4,5,8,7,3,2,1,6]=>0011110=>[3,1,1,1,2]
[2,6,8,1,7,5,4,3]=>0010111=>[3,2,1,1,1]
[2,6,8,3,7,5,1,4]=>0010110=>[3,2,1,2]
[1,6,8,4,7,2,5,3]=>0010101=>[3,2,2,1]
[1,6,8,3,7,2,5,4]=>0010101=>[3,2,2,1]
[2,5,8,1,7,6,4,3]=>0010111=>[3,2,1,1,1]
[2,5,8,3,7,6,1,4]=>0010110=>[3,2,1,2]
[3,2,8,4,7,6,1,5]=>1010110=>[1,2,2,1,2]
[1,5,8,4,7,2,6,3]=>0010101=>[3,2,2,1]
[1,5,8,3,7,2,6,4]=>0010101=>[3,2,2,1]
[3,1,8,4,7,2,6,5]=>1010101=>[1,2,2,2,1]
[5,6,8,1,2,7,4,3]=>0010011=>[3,3,1,1]
[1,6,8,2,3,7,5,4]=>0010011=>[3,3,1,1]
[1,5,8,4,2,7,6,3]=>0011011=>[3,1,2,1,1]
[5,6,8,4,3,2,1,7]=>0011110=>[3,1,1,1,2]
[7,1,4,8,6,2,5,3]=>1001101=>[1,3,1,2,1]
[7,3,4,8,6,2,1,5]=>1001110=>[1,3,1,1,2]
[7,1,5,8,2,6,4,3]=>1001011=>[1,3,2,1,1]
[7,1,4,8,2,6,5,3]=>1001011=>[1,3,2,1,1]
[7,4,5,8,1,2,6,3]=>1001001=>[1,3,3,1]
[3,6,2,8,7,5,1,4]=>0101110=>[2,2,1,1,2]
[1,6,4,8,7,2,5,3]=>0101101=>[2,2,1,2,1]
[3,2,4,8,7,6,1,5]=>1001110=>[1,3,1,1,2]
[1,4,5,8,7,2,6,3]=>0001101=>[4,1,2,1]
[3,1,4,8,7,2,6,5]=>1001101=>[1,3,1,2,1]
[1,6,5,8,2,7,4,3]=>0101011=>[2,2,2,1,1]
[2,6,5,8,3,7,1,4]=>0101010=>[2,2,2,2]
[1,6,4,8,2,7,5,3]=>0101011=>[2,2,2,1,1]
[2,6,1,8,3,7,5,4]=>0101011=>[2,2,2,1,1]
[1,4,5,8,3,2,7,6]=>0001101=>[4,1,2,1]
[4,6,5,8,3,2,1,7]=>0101110=>[2,2,1,1,2]
[7,6,2,3,8,5,1,4]=>1100110=>[1,1,3,1,2]
[7,6,1,4,8,2,5,3]=>1100101=>[1,1,3,2,1]
[7,6,3,4,8,2,1,5]=>1100110=>[1,1,3,1,2]
[7,2,5,3,8,6,1,4]=>1010110=>[1,2,2,1,2]
[7,2,1,4,8,6,5,3]=>1100111=>[1,1,3,1,1,1]
[7,2,1,3,8,6,5,4]=>1100111=>[1,1,3,1,1,1]
[2,6,5,3,8,7,1,4]=>0110110=>[2,1,2,1,2]
[2,6,1,4,8,7,5,3]=>0100111=>[2,3,1,1,1]
[1,3,5,4,8,2,7,6]=>0010101=>[3,2,2,1]
[7,6,5,1,2,8,4,3]=>1110011=>[1,1,1,3,1,1]
[7,1,5,2,3,8,6,4]=>1010011=>[1,2,3,1,1]
[7,1,2,4,3,8,6,5]=>1001011=>[1,3,2,1,1]
[7,2,5,4,3,8,1,6]=>1011010=>[1,2,1,2,2]
[1,6,2,4,3,8,7,5]=>0101011=>[2,2,2,1,1]
[2,6,5,4,3,8,1,7]=>0111010=>[2,1,1,2,2]
[7,6,5,1,3,2,8,4]=>1110101=>[1,1,1,2,2,1]
[8,2,7,6,5,4,1,3]=>1011110=>[1,2,1,1,1,2]
[7,2,8,6,5,4,3,1]=>1011111=>[1,2,1,1,1,1,1]
[3,2,8,7,6,5,1,4]=>1011110=>[1,2,1,1,1,2]
[4,8,7,6,5,3,1,2]=>0111110=>[2,1,1,1,1,2]
[7,8,6,1,5,4,3,2]=>0110111=>[2,1,2,1,1,1]
[4,8,5,7,6,3,2,1]=>0101111=>[2,2,1,1,1,1]
[3,2,4,6,8,1,5,7]=>1000100=>[1,4,3]
[3,5,7,2,4,8,1,6]=>0010010=>[3,3,2]
[3,5,7,2,4,6,8,1]=>0010001=>[3,4,1]
[4,5,1,3,6,8,2,7]=>0100010=>[2,4,2]
[4,3,5,7,2,6,8,1]=>1001001=>[1,3,3,1]
[4,3,5,1,7,8,2,6]=>1010010=>[1,2,3,2]
[4,6,3,5,1,7,8,2]=>0101001=>[2,2,3,1]
[4,6,3,5,7,2,8,1]=>0100101=>[2,3,2,1]
[5,1,6,7,3,4,8,2]=>1001001=>[1,3,3,1]
[1,6,7,3,4,5,8,2]=>0010001=>[3,4,1]
[2,6,7,4,5,8,1,3]=>0010010=>[3,3,2]
[2,6,7,4,8,1,3,5]=>0010100=>[3,2,3]
[1,4,6,7,3,8,2,5]=>0001010=>[4,2,2]
[3,5,2,6,7,4,8,1]=>0100101=>[2,3,2,1]
[6,3,1,7,8,2,4,5]=>1100100=>[1,1,3,3]
[5,7,2,8,1,3,4,6]=>0101000=>[2,2,4]
[6,3,7,2,8,1,4,5]=>1010100=>[1,2,2,3]
[6,3,7,2,5,8,1,4]=>1010010=>[1,2,3,2]
[6,2,4,5,7,3,8,1]=>1000101=>[1,4,2,1]
[2,4,6,7,1,5,8,3]=>0001001=>[4,3,1]
[2,4,7,1,5,6,8,3]=>0010001=>[3,4,1]
[3,7,1,5,6,8,2,4]=>0100010=>[2,4,2]
[4,6,7,1,2,5,8,3]=>0010001=>[3,4,1]
[1,5,6,7,2,4,8,3]=>0001001=>[4,3,1]
[5,6,2,4,1,7,8,3]=>0101001=>[2,2,3,1]
[1,5,4,6,2,7,8,3]=>0101001=>[2,2,3,1]
[5,6,4,7,1,3,8,2]=>0101001=>[2,2,3,1]
[8,4,5,2,6,1,3,7]=>1010100=>[1,2,2,3]
[6,4,3,7,2,5,8,1]=>1101001=>[1,1,2,3,1]
[6,4,3,7,2,8,1,5]=>1101010=>[1,1,2,2,2]
[7,4,5,3,1,6,8,2]=>1011001=>[1,2,1,3,1]
[6,4,3,7,5,1,8,2]=>1101101=>[1,1,2,1,2,1]
[5,6,3,7,4,1,8,2]=>0101101=>[2,2,1,2,1]
[6,7,4,2,1,5,8,3]=>0111001=>[2,1,1,3,1]
[6,7,4,2,1,8,3,5]=>0111010=>[2,1,1,2,2]
[5,6,7,3,1,8,2,4]=>0011010=>[3,1,2,2]
[5,6,3,7,8,1,2,4]=>0100100=>[2,3,3]
[5,6,3,7,2,4,8,1]=>0101001=>[2,2,3,1]
[5,6,7,2,3,8,1,4]=>0010010=>[3,3,2]
[5,6,7,2,8,1,3,4]=>0010100=>[3,2,3]
[6,7,3,8,1,2,4,5]=>0101000=>[2,2,4]
[6,7,3,2,8,1,4,5]=>0110100=>[2,1,2,3]
[7,6,4,2,1,3,8,5]=>1111001=>[1,1,1,1,3,1]
[7,6,3,4,1,2,8,5]=>1101001=>[1,1,2,3,1]
[7,6,3,2,4,1,8,5]=>1110101=>[1,1,1,2,2,1]
[7,5,3,2,6,1,8,4]=>1110101=>[1,1,1,2,2,1]
[6,5,3,2,7,8,1,4]=>1110010=>[1,1,1,3,2]
[6,4,7,2,5,1,8,3]=>1010101=>[1,2,2,2,1]
[6,4,7,5,1,2,8,3]=>1011001=>[1,2,1,3,1]
[5,6,4,2,7,3,8,1]=>0110101=>[2,1,2,2,1]
[6,5,3,7,1,8,2,4]=>1101010=>[1,1,2,2,2]
[6,5,7,2,1,4,8,3]=>1011001=>[1,2,1,3,1]
[5,4,6,7,3,1,8,2]=>1001101=>[1,3,1,2,1]
[5,7,8,3,6,4,1,2]=>0010110=>[3,2,1,2]
[3,7,8,5,6,4,1,2]=>0010110=>[3,2,1,2]
[3,7,8,5,6,1,4,2]=>0010101=>[3,2,2,1]
[1,7,8,5,6,3,4,2]=>0010101=>[3,2,2,1]
[1,7,5,8,6,3,4,2]=>0101101=>[2,2,1,2,1]
[3,7,5,8,6,1,4,2]=>0101101=>[2,2,1,2,1]
[3,7,5,8,6,4,1,2]=>0101110=>[2,2,1,1,2]
[5,7,3,8,6,4,1,2]=>0101110=>[2,2,1,1,2]
[7,3,8,5,6,4,1,2]=>1010110=>[1,2,2,1,2]
[7,3,5,8,6,4,1,2]=>1001110=>[1,3,1,1,2]
[3,5,7,8,6,4,1,2]=>0001110=>[4,1,1,2]
[1,5,7,8,6,3,4,2]=>0001101=>[4,1,2,1]
[1,5,7,8,3,6,4,2]=>0001011=>[4,2,1,1]
[5,3,7,8,1,6,4,2]=>1001011=>[1,3,2,1,1]
[5,3,7,8,6,1,4,2]=>1001101=>[1,3,1,2,1]
[7,3,5,8,6,1,4,2]=>1001101=>[1,3,1,2,1]
[7,3,8,5,6,1,4,2]=>1010101=>[1,2,2,2,1]
[7,8,3,5,6,1,4,2]=>0100101=>[2,3,2,1]
[7,8,1,5,6,3,4,2]=>0100101=>[2,3,2,1]
[7,1,8,5,6,3,4,2]=>1010101=>[1,2,2,2,1]
[7,1,5,8,6,3,4,2]=>1001101=>[1,3,1,2,1]
[5,1,7,8,6,3,4,2]=>1001101=>[1,3,1,2,1]
[5,1,7,8,3,6,4,2]=>1001011=>[1,3,2,1,1]
[3,1,7,8,5,6,4,2]=>1001011=>[1,3,2,1,1]
[1,3,7,8,5,6,4,2]=>0001011=>[4,2,1,1]
[3,1,7,5,8,6,4,2]=>1010111=>[1,2,2,1,1,1]
[5,1,7,3,8,6,4,2]=>1010111=>[1,2,2,1,1,1]
[7,1,5,3,8,6,4,2]=>1010111=>[1,2,2,1,1,1]
[7,1,5,8,3,6,4,2]=>1001011=>[1,3,2,1,1]
[7,8,1,5,3,6,4,2]=>0101011=>[2,2,2,1,1]
[7,8,3,5,1,6,4,2]=>0101011=>[2,2,2,1,1]
[7,3,8,5,1,6,4,2]=>1011011=>[1,2,1,2,1,1]
[7,3,5,8,1,6,4,2]=>1001011=>[1,3,2,1,1]
[7,3,5,1,8,6,4,2]=>1010111=>[1,2,2,1,1,1]
[5,3,7,1,8,6,4,2]=>1010111=>[1,2,2,1,1,1]
[3,5,7,1,8,6,4,2]=>0010111=>[3,2,1,1,1]
[1,5,7,3,8,6,4,2]=>0010111=>[3,2,1,1,1]
[1,7,5,3,8,6,4,2]=>0110111=>[2,1,2,1,1,1]
[3,7,5,1,8,6,4,2]=>0110111=>[2,1,2,1,1,1]
[5,7,3,1,8,6,4,2]=>0110111=>[2,1,2,1,1,1]
[5,7,3,8,6,1,4,2]=>0101101=>[2,2,1,2,1]
[3,7,5,8,1,6,4,2]=>0101011=>[2,2,2,1,1]
[1,7,5,8,3,6,4,2]=>0101011=>[2,2,2,1,1]
[1,7,8,5,3,6,4,2]=>0011011=>[3,1,2,1,1]
[3,7,8,5,1,6,4,2]=>0011011=>[3,1,2,1,1]
[5,7,8,3,6,1,4,2]=>0010101=>[3,2,2,1]
[5,7,8,6,3,1,4,2]=>0011101=>[3,1,1,2,1]
[7,5,8,6,1,3,4,2]=>1011001=>[1,2,1,3,1]
[5,7,8,1,6,3,4,2]=>0010101=>[3,2,2,1]
[5,7,8,1,3,6,4,2]=>0010011=>[3,3,1,1]
[1,7,8,3,5,6,4,2]=>0010011=>[3,3,1,1]
[1,7,3,8,5,6,4,2]=>0101011=>[2,2,2,1,1]
[3,7,1,8,5,6,4,2]=>0101011=>[2,2,2,1,1]
[5,7,1,8,3,6,4,2]=>0101011=>[2,2,2,1,1]
[5,7,1,8,6,3,4,2]=>0101101=>[2,2,1,2,1]
[7,5,1,8,6,3,4,2]=>1101101=>[1,1,2,1,2,1]
[7,5,8,1,6,3,4,2]=>1010101=>[1,2,2,2,1]
[7,8,5,1,6,3,4,2]=>0110101=>[2,1,2,2,1]
[7,8,5,1,3,6,4,2]=>0110011=>[2,1,3,1,1]
[7,5,8,1,3,6,4,2]=>1010011=>[1,2,3,1,1]
[7,5,1,8,3,6,4,2]=>1101011=>[1,1,2,2,1,1]
[7,5,1,3,8,6,4,2]=>1100111=>[1,1,3,1,1,1]
[5,7,1,3,8,6,4,2]=>0100111=>[2,3,1,1,1]
[3,7,1,5,8,6,4,2]=>0100111=>[2,3,1,1,1]
[1,7,3,5,8,6,4,2]=>0100111=>[2,3,1,1,1]
[1,5,3,7,8,6,4,2]=>0100111=>[2,3,1,1,1]
[3,5,1,7,8,6,4,2]=>0100111=>[2,3,1,1,1]
[5,3,1,7,8,6,4,2]=>1100111=>[1,1,3,1,1,1]
[7,3,1,5,8,6,4,2]=>1100111=>[1,1,3,1,1,1]
[7,3,1,8,5,6,4,2]=>1101011=>[1,1,2,2,1,1]
[7,8,1,3,5,6,4,2]=>0100011=>[2,4,1,1]
[7,1,8,3,5,6,4,2]=>1010011=>[1,2,3,1,1]
[7,1,3,8,5,6,4,2]=>1001011=>[1,3,2,1,1]
[7,1,3,5,8,6,4,2]=>1000111=>[1,4,1,1,1]
[5,1,3,7,8,6,4,2]=>1000111=>[1,4,1,1,1]
[3,1,5,7,8,6,4,2]=>1000111=>[1,4,1,1,1]
[4,3,1,2,6,5,8,7]=>1100101=>[1,1,3,2,1]
[6,1,4,3,5,2,8,7]=>1010101=>[1,2,2,2,1]
[4,6,3,5,1,2,8,7]=>0101001=>[2,2,3,1]
[6,2,4,5,1,3,8,7]=>1001001=>[1,3,3,1]
[2,3,6,1,5,4,8,7]=>0010101=>[3,2,2,1]
[2,1,6,5,3,4,8,7]=>1011001=>[1,2,1,3,1]
[3,5,6,2,4,1,8,7]=>0010101=>[3,2,2,1]
[8,7,6,1,3,2,4,5]=>1110100=>[1,1,1,2,3]
[2,5,3,4,8,1,7,6]=>0100101=>[2,3,2,1]
[5,1,8,2,3,4,7,6]=>1010001=>[1,2,4,1]
[5,4,7,6,2,8,1,3]=>1011010=>[1,2,1,2,2]
[2,1,6,8,5,7,3,4]=>1001010=>[1,3,2,2]
[2,1,8,4,6,7,3,5]=>1010010=>[1,2,3,2]
[3,1,8,6,2,7,5,4]=>1011011=>[1,2,1,2,1,1]
[3,8,1,5,6,7,2,4]=>0100010=>[2,4,2]
[8,2,3,5,7,1,6,4]=>1000101=>[1,4,2,1]
[5,8,4,3,7,1,6,2]=>0110101=>[2,1,2,2,1]
[2,8,3,6,7,5,1,4]=>0100110=>[2,3,1,2]
[8,1,2,7,3,5,6,4]=>1001001=>[1,3,3,1]
[6,8,4,2,1,3,7,5]=>0111001=>[2,1,1,3,1]
[4,3,8,2,7,6,1,5]=>1010110=>[1,2,2,1,2]
[2,1,4,5,8,3,7,6]=>1000101=>[1,4,2,1]
[8,4,7,1,5,2,3,6]=>1010100=>[1,2,2,3]
[7,3,5,8,4,2,1,6]=>1001110=>[1,3,1,1,2]
[2,4,8,3,5,6,7,1]=>0010001=>[3,4,1]
[6,4,7,5,2,3,8,1]=>1011001=>[1,2,1,3,1]
[6,4,8,1,7,3,2,5]=>1010110=>[1,2,2,1,2]
[2,1,4,3,8,7,5,6]=>1010110=>[1,2,2,1,2]
[4,3,1,2,8,6,7,5]=>1100101=>[1,1,3,2,1]
[5,1,6,7,8,4,3,2]=>1000111=>[1,4,1,1,1]
[8,7,2,6,4,1,5,3]=>1101101=>[1,1,2,1,2,1]
[2,1,5,7,8,4,6,3]=>1000101=>[1,4,2,1]
[6,4,1,5,7,2,8,3]=>1100101=>[1,1,3,2,1]
[7,4,8,1,2,5,6,3]=>1010001=>[1,2,4,1]
[6,1,7,4,3,2,8,5]=>1011101=>[1,2,1,1,2,1]
[6,8,3,4,2,1,7,5]=>0101101=>[2,2,1,2,1]
[4,2,6,1,5,7,8,3]=>1010001=>[1,2,4,1]
[7,1,4,8,3,5,6,2]=>1001001=>[1,3,3,1]
[3,4,8,2,5,7,6,1]=>0010011=>[3,3,1,1]
[3,7,1,4,5,6,8,2]=>0100001=>[2,5,1]
[6,5,3,8,4,7,1,2]=>1101010=>[1,1,2,2,2]
[8,6,4,7,5,3,1,2]=>1101110=>[1,1,2,1,1,2]
[1,6,3,7,5,8,4,2]=>0101011=>[2,2,2,1,1]
[1,3,7,4,5,8,6,2]=>0010011=>[3,3,1,1]
[7,3,8,5,4,6,1,2]=>1011010=>[1,2,1,2,2]
[3,4,8,5,6,7,1,2]=>0010010=>[3,3,2]
[4,7,3,8,5,6,1,2]=>0101010=>[2,2,2,2]
[6,8,4,7,5,3,1,2]=>0101110=>[2,2,1,1,2]
[1,7,6,5,3,8,4,2]=>0111011=>[2,1,1,2,1,1]
[2,7,6,3,1,4,5,8]=>0111000=>[2,1,1,4]
[2,7,6,4,5,1,3,8]=>0110100=>[2,1,2,3]
[5,7,2,6,4,1,3,8]=>0101100=>[2,2,1,3]
[7,6,1,5,3,8,4,2]=>1101011=>[1,1,2,2,1,1]
[1,8,2,7,3,6,5,4]=>0101011=>[2,2,2,1,1]
[2,1,3,8,4,7,5,6]=>1001010=>[1,3,2,2]
[3,1,2,8,4,6,7,5]=>1001001=>[1,3,3,1]
[4,1,7,2,8,5,6,3]=>1010101=>[1,2,2,2,1]
[5,1,2,4,8,3,7,6]=>1000101=>[1,4,2,1]
[2,8,4,1,5,6,3,7]=>0110010=>[2,1,3,2]
[1,7,2,8,5,3,6,4]=>0101101=>[2,2,1,2,1]
[1,2,3,8,4,5,7,6]=>0001001=>[4,3,1]
[2,4,8,3,1,5,6,7]=>0011000=>[3,1,4]
[3,2,5,6,1,4,7,8]=>1001000=>[1,3,4]
[4,7,3,8,2,1,5,6]=>0101100=>[2,2,1,3]
[7,4,8,3,2,1,5,6]=>1011100=>[1,2,1,1,3]
[7,6,8,5,1,4,3,2]=>1011011=>[1,2,1,2,1,1]
[6,5,1,2,8,3,7,4]=>1100101=>[1,1,3,2,1]
[6,8,4,1,3,7,5,2]=>0110011=>[2,1,3,1,1]
[6,3,7,1,8,4,5,2]=>1010101=>[1,2,2,2,1]
[5,8,3,1,7,4,6,2]=>0110101=>[2,1,2,2,1]
[4,7,1,2,8,3,6,5]=>0100101=>[2,3,2,1]
[3,4,1,8,5,6,7,2]=>0101001=>[2,2,3,1]
[1,2,8,7,6,3,5,4]=>0011101=>[3,1,1,2,1]
[2,3,1,8,7,4,5,6]=>0101100=>[2,2,1,3]
[2,6,1,4,8,7,3,5]=>0100110=>[2,3,1,2]
[5,8,2,1,7,6,3,4]=>0110110=>[2,1,2,1,2]
[8,7,1,6,5,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[3,1,8,7,6,4,5,2]=>1011101=>[1,2,1,1,2,1]
[1,2,3,4,8,7,5,6]=>0000110=>[5,1,2]
[1,2,3,8,6,4,5,7]=>0001100=>[4,1,3]
[1,2,8,5,3,4,6,7]=>0011000=>[3,1,4]
[1,8,4,2,3,5,6,7]=>0110000=>[2,1,5]
[2,4,7,5,6,8,3,1]=>0010011=>[3,3,1,1]
[2,5,3,8,7,4,6,1]=>0101101=>[2,2,1,2,1]
[3,1,8,5,7,4,2,6]=>1010110=>[1,2,2,1,2]
[8,3,5,7,4,2,6,1]=>1001101=>[1,3,1,2,1]
[8,3,6,2,4,5,7,1]=>1010001=>[1,2,4,1]
[2,7,6,4,5,8,3,1]=>0110011=>[2,1,3,1,1]
[4,8,1,7,6,3,2,5]=>0101110=>[2,2,1,1,2]
[3,7,1,8,6,2,5,4]=>0101101=>[2,2,1,2,1]
[7,3,6,4,2,8,5,1]=>1011011=>[1,2,1,2,1,1]
[5,8,7,1,4,3,2,6]=>0110110=>[2,1,2,1,2]
[5,6,1,2,4,3,8,7]=>0100101=>[2,3,2,1]
[3,6,8,1,2,7,5,4]=>0010011=>[3,3,1,1]
[8,4,6,2,1,3,7,5]=>1011001=>[1,2,1,3,1]
[4,8,1,5,3,7,2,6]=>0101010=>[2,2,2,2]
[5,4,8,7,3,1,2,6]=>1011100=>[1,2,1,1,3]
[6,4,3,8,1,5,2,7]=>1101010=>[1,1,2,2,2]
[6,8,3,7,2,5,4,1]=>0101011=>[2,2,2,1,1]
[5,3,6,8,7,2,4,1]=>1001101=>[1,3,1,2,1]
[5,7,4,2,8,3,6,1]=>0110101=>[2,1,2,2,1]
[6,4,7,2,1,8,3,5]=>1011010=>[1,2,1,2,2]
[5,7,8,2,6,4,1,3]=>0010110=>[3,2,1,2]
[2,6,8,4,5,7,1,3]=>0010010=>[3,3,2]
[1,7,4,8,6,2,3,5]=>0101100=>[2,2,1,3]
[2,7,4,8,5,6,1,3]=>0101010=>[2,2,2,2]
[6,3,7,2,8,5,1,4]=>1010110=>[1,2,2,1,2]
[3,6,2,5,7,8,1,4]=>0100010=>[2,4,2]
[5,3,6,7,1,8,4,2]=>1001011=>[1,3,2,1,1]
[8,1,3,6,7,2,4,5]=>1000100=>[1,4,3]
[8,1,4,2,7,5,3,6]=>1010110=>[1,2,2,1,2]
[6,1,3,8,2,7,4,5]=>1001010=>[1,3,2,2]
[4,1,5,3,2,8,6,7]=>1011010=>[1,2,1,2,2]
[2,7,1,4,3,8,5,6]=>0101010=>[2,2,2,2]
[1,7,5,2,8,6,3,4]=>0110110=>[2,1,2,1,2]
[7,4,2,5,1,8,6,3]=>1101011=>[1,1,2,2,1,1]
[5,6,3,2,1,8,7,4]=>0111011=>[2,1,1,2,1,1]
[4,5,3,2,7,1,8,6]=>0110101=>[2,1,2,2,1]
[5,3,6,2,8,1,7,4]=>1010101=>[1,2,2,2,1]
[6,4,2,8,5,1,7,3]=>1101101=>[1,1,2,1,2,1]
[1,8,4,7,2,5,3,6]=>0101010=>[2,2,2,2]
[1,5,8,4,2,6,3,7]=>0011010=>[3,1,2,2]
[3,5,7,4,1,6,8,2]=>0011001=>[3,1,3,1]
[4,5,8,3,1,7,6,2]=>0011011=>[3,1,2,1,1]
[3,4,7,8,2,1,6,5]=>0001101=>[4,1,2,1]
[4,6,3,5,2,1,8,7]=>0101101=>[2,2,1,2,1]
[3,5,7,1,2,6,4,8]=>0010010=>[3,3,2]
[7,4,1,2,8,6,3,5]=>1100110=>[1,1,3,1,2]
[5,2,6,1,3,4,8,7]=>1010001=>[1,2,4,1]
[3,8,2,6,5,4,1,7]=>0101110=>[2,2,1,1,2]
[3,8,7,2,5,4,1,6]=>0110110=>[2,1,2,1,2]
[7,5,1,6,8,4,3,2]=>1100111=>[1,1,3,1,1,1]
[7,4,2,1,5,6,3,8]=>1110010=>[1,1,1,3,2]
[7,3,8,1,5,4,6,2]=>1010101=>[1,2,2,2,1]
[7,2,8,6,5,1,3,4]=>1011100=>[1,2,1,1,3]
[6,2,7,8,5,4,1,3]=>1001110=>[1,3,1,1,2]
[5,3,2,6,7,4,1,8]=>1100110=>[1,1,3,1,2]
[4,8,2,6,5,7,1,3]=>0101010=>[2,2,2,2]
[4,3,7,2,5,6,1,8]=>1010010=>[1,2,3,2]
[3,8,7,6,2,4,1,5]=>0111010=>[2,1,1,2,2]
[6,7,1,4,3,2,5,8]=>0101100=>[2,2,1,3]
[3,5,6,2,4,7,1,8]=>0010010=>[3,3,2]
[3,5,8,7,2,4,6,1]=>0011001=>[3,1,3,1]
[1,7,8,2,5,4,3,6]=>0010110=>[3,2,1,2]
[2,7,1,3,6,5,4,8]=>0100110=>[2,3,1,2]
[5,7,1,4,6,3,2,8]=>0100110=>[2,3,1,2]
[6,3,7,1,5,4,2,8]=>1010110=>[1,2,2,1,2]
[4,7,1,6,3,5,2,8]=>0101010=>[2,2,2,2]
[8,7,3,6,1,5,4,2]=>1101011=>[1,1,2,2,1,1]
[5,7,8,3,2,1,4,6]=>0011100=>[3,1,1,3]
[5,4,2,1,7,8,3,6]=>1110010=>[1,1,1,3,2]
[4,7,8,3,5,2,1,6]=>0010110=>[3,2,1,2]
[8,3,7,6,4,2,1,5]=>1011110=>[1,2,1,1,1,2]
[8,3,2,1,4,7,6,5]=>1110011=>[1,1,1,3,1,1]
[6,4,1,7,3,8,5,2]=>1101011=>[1,1,2,2,1,1]
[1,7,5,3,8,2,6,4]=>0110101=>[2,1,2,2,1]
[5,1,7,4,2,8,6,3]=>1011011=>[1,2,1,2,1,1]
[8,6,3,2,7,5,1,4]=>1110110=>[1,1,1,2,1,2]
[2,7,5,1,3,8,6,4]=>0110011=>[2,1,3,1,1]
[8,7,4,2,6,1,5,3]=>1110101=>[1,1,1,2,2,1]
[5,2,6,1,8,7,4,3]=>1010111=>[1,2,2,1,1,1]
[1,7,6,4,3,8,2,5]=>0111010=>[2,1,1,2,2]
[1,3,8,2,4,7,6,5]=>0010011=>[3,3,1,1]
[3,7,5,1,8,6,2,4]=>0110110=>[2,1,2,1,2]
[5,1,4,3,2,7,8,6]=>1011001=>[1,2,1,3,1]
[3,7,6,2,4,1,8,5]=>0110101=>[2,1,2,2,1]
[5,3,1,7,8,4,2,6]=>1100110=>[1,1,3,1,2]
[4,1,7,8,5,3,2,6]=>1001110=>[1,3,1,1,2]
[2,7,6,4,1,3,8,5]=>0111001=>[2,1,1,3,1]
[8,4,2,7,6,3,1,5]=>1101110=>[1,1,2,1,1,2]
[6,3,1,7,5,2,8,4]=>1101101=>[1,1,2,1,2,1]
[6,2,7,5,3,1,8,4]=>1011101=>[1,2,1,1,2,1]
[1,5,8,2,7,4,6,3]=>0010101=>[3,2,2,1]
[8,4,7,3,1,6,5,2]=>1011011=>[1,2,1,2,1,1]
[4,1,6,8,5,7,3,2]=>1001011=>[1,3,2,1,1]
[1,8,6,7,3,4,2,5]=>0101010=>[2,2,2,2]
[6,7,1,8,3,4,2,5]=>0101010=>[2,2,2,2]
[7,8,1,6,3,4,2,5]=>0101010=>[2,2,2,2]
[7,8,2,5,1,6,3,4]=>0101010=>[2,2,2,2]
[1,8,5,6,2,7,3,4]=>0101010=>[2,2,2,2]
[5,7,1,6,2,8,3,4]=>0101010=>[2,2,2,2]
[5,6,2,7,1,8,3,4]=>0101010=>[2,2,2,2]
[6,7,2,5,1,8,3,4]=>0101010=>[2,2,2,2]
[6,7,2,4,3,8,1,5]=>0101010=>[2,2,2,2]
[2,5,1,8,6,7,3,4]=>0101010=>[2,2,2,2]
[2,6,5,8,1,7,3,4]=>0101010=>[2,2,2,2]
[1,8,2,7,4,5,3,6]=>0101010=>[2,2,2,2]
[2,4,3,8,5,6,1,7]=>0101010=>[2,2,2,2]
[2,3,1,8,5,6,4,7]=>0101010=>[2,2,2,2]
[4,6,2,7,1,5,3,8]=>0101010=>[2,2,2,2]
[4,7,1,6,2,5,3,8]=>0101010=>[2,2,2,2]
[4,6,3,5,1,7,2,8]=>0101010=>[2,2,2,2]
[5,6,3,7,1,4,2,8]=>0101010=>[2,2,2,2]
[1,8,5,6,3,4,2,7]=>0101010=>[2,2,2,2]
[4,7,1,8,5,6,2,3]=>0101010=>[2,2,2,2]
[3,4,2,6,5,8,1,7]=>0101010=>[2,2,2,2]
[3,5,4,6,2,8,1,7]=>0101010=>[2,2,2,2]
[3,7,1,6,2,8,4,5]=>0101010=>[2,2,2,2]
[3,5,2,7,4,8,1,6]=>0101010=>[2,2,2,2]
[4,7,2,3,1,8,5,6]=>0101010=>[2,2,2,2]
[2,4,3,8,1,7,5,6]=>0101010=>[2,2,2,2]
[6,1,2,7,4,5,8,3]=>1001001=>[1,3,3,1]
[2,5,8,3,4,1,6,7]=>0010100=>[3,2,3]
[5,6,2,7,4,3,8,1]=>0101101=>[2,2,1,2,1]
[5,1,7,3,4,2,8,6]=>1010101=>[1,2,2,2,1]
[4,6,7,3,2,5,8,1]=>0011001=>[3,1,3,1]
[3,7,2,1,4,5,8,6]=>0110001=>[2,1,4,1]
[2,7,1,3,4,8,6,5]=>0100011=>[2,4,1,1]
[2,6,7,3,8,5,4,1]=>0010111=>[3,2,1,1,1]
[2,6,1,8,4,5,3,7]=>0101010=>[2,2,2,2]
[4,2,1,6,5,3,8,7]=>1101101=>[1,1,2,1,2,1]
[6,2,4,3,1,5,8,7]=>1011001=>[1,2,1,3,1]
[4,6,2,1,5,3,8,7]=>0110101=>[2,1,2,2,1]
[8,4,2,1,6,5,3,7]=>1110110=>[1,1,1,2,1,2]
[2,6,4,5,1,8,7,3]=>0101011=>[2,2,2,1,1]
[6,8,7,2,1,4,3,5]=>0111010=>[2,1,1,2,2]
[6,8,2,1,7,4,3,5]=>0110110=>[2,1,2,1,2]
[6,8,2,1,4,3,7,5]=>0110101=>[2,1,2,2,1]
[8,6,2,4,3,1,5,7]=>1101100=>[1,1,2,1,3]
[6,8,2,4,3,1,7,5]=>0101101=>[2,2,1,2,1]
[2,8,4,6,7,3,1,5]=>0100110=>[2,3,1,2]
[2,8,6,7,4,3,1,5]=>0101110=>[2,2,1,1,2]
[6,8,7,2,4,3,1,5]=>0110110=>[2,1,2,1,2]
[4,6,5,2,8,3,7,1]=>0110101=>[2,1,2,2,1]
[2,6,4,5,8,3,7,1]=>0100101=>[2,3,2,1]
[6,4,2,8,3,5,7,1]=>1101001=>[1,1,2,3,1]
[8,4,2,6,3,5,1,7]=>1101010=>[1,1,2,2,2]
[4,2,6,3,8,7,5,1]=>1010111=>[1,2,2,1,1,1]
[8,2,4,3,6,5,1,7]=>1010110=>[1,2,2,1,2]
[4,2,1,6,8,7,5,3]=>1100111=>[1,1,3,1,1,1]
[4,2,1,6,5,8,7,3]=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,6,8,7,5]=>1100011=>[1,1,4,1,1]
[2,4,3,1,8,6,5,7]=>0110110=>[2,1,2,1,2]
[6,2,1,8,7,4,3,5]=>1101110=>[1,1,2,1,1,2]
[4,6,8,7,5,2,1,3]=>0011110=>[3,1,1,1,2]
[4,6,5,8,7,2,1,3]=>0101110=>[2,2,1,1,2]
[2,6,8,7,4,5,1,3]=>0011010=>[3,1,2,2]
[2,4,8,6,7,5,1,3]=>0010110=>[3,2,1,2]
[4,2,8,6,5,7,1,3]=>1011010=>[1,2,1,2,2]
[6,4,8,2,1,5,7,3]=>1011001=>[1,2,1,3,1]
[2,6,8,4,7,1,5,3]=>0010101=>[3,2,2,1]
[4,6,5,8,2,1,7,3]=>0101101=>[2,2,1,2,1]
[4,8,6,7,2,1,3,5]=>0101100=>[2,2,1,3]
[6,2,3,5,1,4,8,7]=>1001001=>[1,3,3,1]
[7,4,5,2,3,8,6,1]=>1010011=>[1,2,3,1,1]
[7,3,2,5,4,8,6,1]=>1101011=>[1,1,2,2,1,1]
[3,5,1,6,4,2,8,7]=>0101101=>[2,2,1,2,1]
[3,6,2,4,5,1,8,7]=>0100101=>[2,3,2,1]
[7,2,3,4,5,8,6,1]=>1000011=>[1,5,1,1]
[8,2,3,4,5,7,1,6]=>1000010=>[1,5,2]
[6,7,3,4,8,5,2,1]=>0100111=>[2,3,1,1,1]
[5,7,1,3,8,6,2,4]=>0100110=>[2,3,1,2]
[4,7,3,2,8,6,1,5]=>0110110=>[2,1,2,1,2]
[3,8,2,6,7,4,5,1]=>0100101=>[2,3,2,1]
[4,8,1,5,6,7,3,2]=>0100011=>[2,4,1,1]
[6,8,2,5,1,7,3,4]=>0101010=>[2,2,2,2]
[7,8,3,4,6,2,1,5]=>0100110=>[2,3,1,2]
[4,8,2,5,1,6,7,3]=>0101001=>[2,2,3,1]
[3,8,2,5,4,7,6,1]=>0101011=>[2,2,2,1,1]
[3,7,6,1,8,5,2,4]=>0110110=>[2,1,2,1,2]
[4,7,2,3,8,5,1,6]=>0100110=>[2,3,1,2]
[4,6,7,1,8,5,3,2]=>0010111=>[3,2,1,1,1]
[3,6,1,7,8,5,4,2]=>0100111=>[2,3,1,1,1]
[2,1,5,7,3,8,6,4]=>1001011=>[1,3,2,1,1]
[6,4,7,2,8,5,3,1]=>1010111=>[1,2,2,1,1,1]
[7,6,1,4,8,5,2,3]=>1100110=>[1,1,3,1,2]
[4,1,2,3,7,8,6,5]=>1000011=>[1,5,1,1]
[3,4,2,1,8,5,6,7]=>0110100=>[2,1,2,3]
[8,2,3,5,7,1,4,6]=>1000100=>[1,4,3]
[8,1,3,6,4,7,2,5]=>1001010=>[1,3,2,2]
[5,4,8,3,6,7,1,2]=>1010010=>[1,2,3,2]
[4,5,8,3,6,7,2,1]=>0010011=>[3,3,1,1]
[2,1,5,8,4,6,7,3]=>1001001=>[1,3,3,1]
[4,6,8,3,5,2,7,1]=>0010101=>[3,2,2,1]
[3,8,2,4,5,6,7,1]=>0100001=>[2,5,1]
[6,8,2,3,1,4,5,7]=>0101000=>[2,2,4]
[4,3,1,6,5,8,7,2]=>1101011=>[1,1,2,2,1,1]
[8,2,7,4,1,3,6,5]=>1011001=>[1,2,1,3,1]
[3,7,8,2,1,4,6,5]=>0011001=>[3,1,3,1]
[3,7,5,2,8,4,1,6]=>0110110=>[2,1,2,1,2]
[3,1,5,2,4,8,7,6]=>1010011=>[1,2,3,1,1]
[3,6,4,5,1,8,7,2]=>0101011=>[2,2,2,1,1]
[4,3,6,1,2,8,7,5]=>1010011=>[1,2,3,1,1]
[6,1,3,5,4,8,7,2]=>1001011=>[1,3,2,1,1]
[1,7,3,8,4,6,2,5]=>0101010=>[2,2,2,2]
[1,6,7,4,8,5,3,2]=>0010111=>[3,2,1,1,1]
[8,1,2,5,4,6,3,7]=>1001010=>[1,3,2,2]
[6,8,3,1,4,7,5,2]=>0110011=>[2,1,3,1,1]
[8,4,2,5,7,1,6,3]=>1100101=>[1,1,3,2,1]
[1,8,5,3,7,4,6,2]=>0110101=>[2,1,2,2,1]
[5,3,2,8,7,1,4,6]=>1101100=>[1,1,2,1,3]
[1,2,8,7,5,6,3,4]=>0011010=>[3,1,2,2]
[1,4,8,6,5,7,2,3]=>0011010=>[3,1,2,2]
[3,5,4,8,6,1,2,7]=>0101100=>[2,2,1,3]
[4,3,5,8,1,7,2,6]=>1001010=>[1,3,2,2]
[1,4,5,8,6,7,3,2]=>0001011=>[4,2,1,1]
[1,7,6,5,8,3,4,2]=>0110101=>[2,1,2,2,1]
[7,3,6,1,8,2,4,5]=>1010100=>[1,2,2,3]
[7,6,4,5,8,1,3,2]=>1100101=>[1,1,3,2,1]
[1,6,5,4,8,2,3,7]=>0110100=>[2,1,2,3]
[5,2,6,3,8,1,4,7]=>1010100=>[1,2,2,3]
[4,3,1,6,8,7,5,2]=>1100111=>[1,1,3,1,1,1]
[4,3,1,8,5,6,7,2]=>1101001=>[1,1,2,3,1]
[6,2,8,4,3,1,7,5]=>1011101=>[1,2,1,1,2,1]
[7,1,6,2,3,4,5,8]=>1010000=>[1,2,5]
[3,8,6,1,2,5,4,7]=>0110010=>[2,1,3,2]
[1,8,5,4,3,6,2,7]=>0111010=>[2,1,1,2,2]
[5,3,8,4,1,2,7,6]=>1011001=>[1,2,1,3,1]
[1,8,3,6,5,2,7,4]=>0101101=>[2,2,1,2,1]
[4,7,1,8,2,6,5,3]=>0101011=>[2,2,2,1,1]
[1,8,2,4,7,6,5,3]=>0100111=>[2,3,1,1,1]
[1,4,8,3,5,7,6,2]=>0010011=>[3,3,1,1]
[8,2,1,4,6,5,7,3]=>1100101=>[1,1,3,2,1]
[6,1,5,2,4,7,8,3]=>1010001=>[1,2,4,1]
[4,1,8,5,2,7,6,3]=>1011011=>[1,2,1,2,1,1]
[4,3,8,5,1,2,6,7]=>1011000=>[1,2,1,4]
[6,3,5,1,4,2,8,7]=>1010101=>[1,2,2,2,1]
[4,1,8,2,3,7,5,6]=>1010010=>[1,2,3,2]
[5,3,8,7,2,1,4,6]=>1011100=>[1,2,1,1,3]
[7,6,5,4,1,3,2,8]=>1111010=>[1,1,1,1,2,2]
[1,8,7,6,2,5,4,3]=>0111011=>[2,1,1,2,1,1]
[1,2,3,4,5,10,9,8,7,6]=>000001111=>[6,1,1,1,1]
[4,6,3,1,5,2,7,8]=>0110100=>[2,1,2,3]
[6,2,7,4,5,1,3,8]=>1010100=>[1,2,2,3]
[5,2,7,4,1,6,3,8]=>1011010=>[1,2,1,2,2]
[5,7,3,4,1,6,2,8]=>0101010=>[2,2,2,2]
[4,2,8,1,5,6,7,3]=>1010001=>[1,2,4,1]
[1,7,8,4,5,6,2,3]=>0010010=>[3,3,2]
[1,6,8,4,5,2,7,3]=>0010101=>[3,2,2,1]
[1,5,8,4,2,6,7,3]=>0011001=>[3,1,3,1]
[1,5,3,8,2,6,7,4]=>0101001=>[2,2,3,1]
[1,6,3,8,5,2,7,4]=>0101101=>[2,2,1,2,1]
[1,7,3,8,5,6,2,4]=>0101010=>[2,2,2,2]
[6,2,3,7,5,1,4,8]=>1001100=>[1,3,1,3]
[4,2,6,1,5,3,7,8]=>1010100=>[1,2,2,3]
[5,2,6,4,1,3,7,8]=>1011000=>[1,2,1,4]
[1,2,7,8,5,6,3,4]=>0001010=>[4,2,2]
[1,2,6,4,8,3,7,5]=>0010101=>[3,2,2,1]
[8,7,3,2,1,6,5,4]=>1111011=>[1,1,1,1,2,1,1]
[8,7,4,1,6,2,3,5]=>1110100=>[1,1,1,2,3]
[8,5,1,7,2,3,4,6]=>1101000=>[1,1,2,4]
[10,9,8,5,1,7,2,3,4,6]=>111101000=>[1,1,1,1,2,4]
[10,9,4,1,6,2,8,3,5,7]=>111010100=>[1,1,1,2,2,3]
[10,3,1,5,2,7,4,9,6,8]=>110101010=>[1,1,2,2,2,2]
[1,8,3,2,6,4,5,7]=>0110100=>[2,1,2,3]
[7,3,8,1,5,2,4,6]=>1010100=>[1,2,2,3]
[3,1,7,2,6,4,5,8]=>1010100=>[1,2,2,3]
[1,8,4,2,3,6,7,5]=>0110001=>[2,1,4,1]
[2,5,8,3,4,6,7,1]=>0010001=>[3,4,1]
[4,1,7,2,3,6,8,5]=>1010001=>[1,2,4,1]
[3,1,7,5,4,2,8,6]=>1011101=>[1,2,1,1,2,1]
[4,6,2,1,5,7,8,3]=>0110001=>[2,1,4,1]
[4,5,2,3,1,7,8,6]=>0101001=>[2,2,3,1]
[3,2,6,7,4,1,8,5]=>1001101=>[1,3,1,2,1]
[5,6,2,7,1,4,8,3]=>0101001=>[2,2,3,1]
[6,4,2,8,1,5,7,3]=>1101001=>[1,1,2,3,1]
[7,3,6,8,5,2,4,1]=>1001101=>[1,3,1,2,1]
[2,7,8,3,6,5,1,4]=>0010110=>[3,2,1,2]
[2,7,8,5,4,6,3,1]=>0011011=>[3,1,2,1,1]
[2,6,8,3,4,7,1,5]=>0010010=>[3,3,2]
[2,5,6,8,3,4,1,7]=>0001010=>[4,2,2]
[2,7,8,3,6,1,4,5]=>0010100=>[3,2,3]
[2,1,3,7,8,5,6,4]=>1000101=>[1,4,2,1]
[5,1,2,4,8,7,3,6]=>1000110=>[1,4,1,2]
[2,3,6,1,8,5,7,4]=>0010101=>[3,2,2,1]
[5,2,6,1,7,8,4,3]=>1010011=>[1,2,3,1,1]
[3,6,5,4,1,8,7,2]=>0111011=>[2,1,1,2,1,1]
[5,4,2,3,7,8,6,1]=>1100011=>[1,1,4,1,1]
[4,1,8,2,5,7,3,6]=>1010010=>[1,2,3,2]
[3,1,8,4,7,2,5,6]=>1010100=>[1,2,2,3]
[2,6,4,1,5,3,8,7]=>0110101=>[2,1,2,2,1]
[1,5,8,2,4,7,3,6]=>0010010=>[3,3,2]
[6,2,1,4,7,8,3,5]=>1100010=>[1,1,4,2]
[3,8,1,4,2,6,5,7]=>0101010=>[2,2,2,2]
[8,3,4,2,1,6,5,7]=>1011010=>[1,2,1,2,2]
[5,3,2,8,1,6,4,7]=>1101010=>[1,1,2,2,2]
[2,4,5,8,3,6,1,7]=>0001010=>[4,2,2]
[3,5,8,1,2,6,4,7]=>0010010=>[3,3,2]
[8,6,1,3,5,2,4,7]=>1100100=>[1,1,3,3]
[5,7,4,3,6,1,8,2]=>0110101=>[2,1,2,2,1]
[2,6,4,3,7,8,5,1]=>0110011=>[2,1,3,1,1]
[7,4,1,8,3,2,5,6]=>1101100=>[1,1,2,1,3]
[2,4,6,5,1,7,8,3]=>0011001=>[3,1,3,1]
[5,6,1,7,4,2,8,3]=>0101101=>[2,2,1,2,1]
[1,3,8,6,2,7,4,5]=>0011010=>[3,1,2,2]
[6,4,7,8,2,1,3,5]=>1001100=>[1,3,1,3]
[6,7,3,8,4,1,2,5]=>0101100=>[2,2,1,3]
[2,7,8,3,4,6,1,5]=>0010010=>[3,3,2]
[3,7,8,1,5,4,2,6]=>0010110=>[3,2,1,2]
[7,5,8,4,1,3,2,6]=>1011010=>[1,2,1,2,2]
[4,7,5,8,3,1,2,6]=>0101100=>[2,2,1,3]
[5,7,3,1,6,8,4,2]=>0110011=>[2,1,3,1,1]
[4,6,7,2,8,3,1,5]=>0010110=>[3,2,1,2]
[4,8,1,2,3,5,7,6]=>0100001=>[2,5,1]
[4,5,6,7,3,1,8,2]=>0001101=>[4,1,2,1]
[8,5,3,2,7,6,1,4]=>1110110=>[1,1,1,2,1,2]
[7,5,4,6,2,8,1,3]=>1101010=>[1,1,2,2,2]
[2,5,1,3,6,8,7,4]=>0100011=>[2,4,1,1]
[7,5,2,8,4,1,3,6]=>1101100=>[1,1,2,1,3]
[7,3,8,5,2,1,4,6]=>1011100=>[1,2,1,1,3]
[5,8,3,6,4,7,1,2]=>0101010=>[2,2,2,2]
[3,7,8,4,1,5,6,2]=>0011001=>[3,1,3,1]
[3,5,8,6,7,4,2,1]=>0010111=>[3,2,1,1,1]
[3,7,6,8,1,2,5,4]=>0101001=>[2,2,3,1]
[4,1,6,3,2,5,8,7]=>1011001=>[1,2,1,3,1]
[8,6,1,7,2,5,4,3]=>1101011=>[1,1,2,2,1,1]
[8,7,6,1,2,3,5,4]=>1110001=>[1,1,1,4,1]
[5,4,1,6,2,3,8,7]=>1101001=>[1,1,2,3,1]
[2,6,5,3,4,1,8,7]=>0110101=>[2,1,2,2,1]
[5,8,7,6,1,2,3,4]=>0111000=>[2,1,1,4]
[8,2,7,1,5,4,3,6]=>1010110=>[1,2,2,1,2]
[2,1,6,3,8,5,4,7]=>1010110=>[1,2,2,1,2]
[2,6,3,1,8,5,4,7]=>0110110=>[2,1,2,1,2]
[4,6,2,8,5,1,3,7]=>0101100=>[2,2,1,3]
[6,5,2,7,4,3,8,1]=>1101101=>[1,1,2,1,2,1]
[4,6,5,2,7,3,8,1]=>0110101=>[2,1,2,2,1]
[3,1,6,2,4,8,7,5]=>1010011=>[1,2,3,1,1]
[8,7,5,1,2,6,4,3]=>1110011=>[1,1,1,3,1,1]
[2,1,7,6,3,8,4,5]=>1011010=>[1,2,1,2,2]
[8,2,3,4,6,7,1,5]=>1000010=>[1,5,2]
[2,8,5,7,4,1,3,6]=>0101100=>[2,2,1,3]
[7,8,5,3,6,4,2,1]=>0110111=>[2,1,2,1,1,1]
[2,1,4,8,7,5,6,3]=>1001101=>[1,3,1,2,1]
[7,4,6,8,5,1,3,2]=>1001101=>[1,3,1,2,1]
[6,4,8,3,5,7,1,2]=>1010010=>[1,2,3,2]
[8,5,7,4,6,2,1,3]=>1010110=>[1,2,2,1,2]
[4,1,8,5,6,3,2,7]=>1010110=>[1,2,2,1,2]
[5,8,3,2,4,6,1,7]=>0110010=>[2,1,3,2]
[2,8,4,1,5,3,7,6]=>0110101=>[2,1,2,2,1]
[4,8,7,6,5,2,3,1]=>0111101=>[2,1,1,1,2,1]
[2,1,8,6,4,3,7,5]=>1011101=>[1,2,1,1,2,1]
[3,6,7,1,8,5,2,4]=>0010110=>[3,2,1,2]
[4,2,3,6,8,7,5,1]=>1000111=>[1,4,1,1,1]
[6,5,7,3,1,8,4,2]=>1011011=>[1,2,1,2,1,1]
[8,4,2,5,6,1,7,3]=>1100101=>[1,1,3,2,1]
[6,1,5,7,2,4,8,3]=>1001001=>[1,3,3,1]
[8,4,7,6,2,1,5,3]=>1011101=>[1,2,1,1,2,1]
[3,5,7,6,4,1,8,2]=>0011101=>[3,1,1,2,1]
[2,4,7,5,6,3,8,1]=>0010101=>[3,2,2,1]
[5,4,1,7,6,2,8,3]=>1101101=>[1,1,2,1,2,1]
[3,5,6,7,1,4,8,2]=>0001001=>[4,3,1]
[4,7,5,2,1,3,8,6]=>0111001=>[2,1,1,3,1]
[5,7,2,3,6,4,8,1]=>0100101=>[2,3,2,1]
[7,1,2,3,5,8,4,6]=>1000010=>[1,5,2]
[8,6,2,3,7,1,4,5]=>1100100=>[1,1,3,3]
[6,1,8,2,7,3,4,5]=>1010100=>[1,2,2,3]
[7,8,6,1,3,2,5,4]=>0110101=>[2,1,2,2,1]
[8,1,5,7,2,3,6,4]=>1001001=>[1,3,3,1]
[1,4,5,2,8,6,7,3]=>0010101=>[3,2,2,1]
[2,3,1,7,8,6,4,5]=>0100110=>[2,3,1,2]
[2,1,4,6,8,3,7,5]=>1000101=>[1,4,2,1]
[3,5,7,6,2,8,1,4]=>0011010=>[3,1,2,2]
[5,4,1,6,3,8,7,2]=>1101011=>[1,1,2,2,1,1]
[4,5,6,1,2,8,7,3]=>0010011=>[3,3,1,1]
[3,5,6,2,4,8,7,1]=>0010011=>[3,3,1,1]
[5,4,1,2,8,7,6,3]=>1100111=>[1,1,3,1,1,1]
[5,6,3,7,8,4,2,1]=>0100111=>[2,3,1,1,1]
[4,3,2,6,8,1,7,5]=>1100101=>[1,1,3,2,1]
[7,1,5,6,3,8,2,4]=>1001010=>[1,3,2,2]
[1,5,4,2,7,8,3,6]=>0110010=>[2,1,3,2]
[6,1,2,8,7,4,3,5]=>1001110=>[1,3,1,1,2]
[5,1,6,8,4,7,2,3]=>1001010=>[1,3,2,2]
[5,1,3,8,4,2,7,6]=>1001101=>[1,3,1,2,1]
[3,1,6,8,7,4,2,5]=>1001110=>[1,3,1,1,2]
[3,6,5,8,4,7,1,2]=>0101010=>[2,2,2,2]
[6,5,8,4,3,1,2,7]=>1011100=>[1,2,1,1,3]
[8,5,1,3,7,4,6,2]=>1100101=>[1,1,3,2,1]
[3,2,8,1,4,7,6,5]=>1010011=>[1,2,3,1,1]
[6,4,3,8,2,5,7,1]=>1101001=>[1,1,2,3,1]
[3,2,5,8,4,1,7,6]=>1001101=>[1,3,1,2,1]
[6,8,2,3,4,7,5,1]=>0100011=>[2,4,1,1]
[2,1,7,8,3,4,6,5]=>1001001=>[1,3,3,1]
[7,5,1,8,4,2,6,3]=>1101101=>[1,1,2,1,2,1]
[5,6,1,8,2,7,4,3]=>0101011=>[2,2,2,1,1]
[3,6,8,5,2,7,4,1]=>0011011=>[3,1,2,1,1]
[2,1,6,5,4,8,3,7]=>1011010=>[1,2,1,2,2]
[2,1,7,3,5,8,6,4]=>1010011=>[1,2,3,1,1]
[7,8,1,2,4,5,6,3]=>0100001=>[2,5,1]
[3,6,8,1,5,7,2,4]=>0010010=>[3,3,2]
[3,5,7,8,4,6,1,2]=>0001010=>[4,2,2]
[7,5,2,8,4,6,3,1]=>1101011=>[1,1,2,2,1,1]
[7,8,2,4,3,1,5,6]=>0101100=>[2,2,1,3]
[8,4,3,1,7,5,2,6]=>1110110=>[1,1,1,2,1,2]
[7,6,2,8,5,1,4,3]=>1101101=>[1,1,2,1,2,1]
[4,3,8,7,1,6,5,2]=>1011011=>[1,2,1,2,1,1]
[4,7,1,8,5,2,6,3]=>0101101=>[2,2,1,2,1]
[3,7,5,8,1,6,2,4]=>0101010=>[2,2,2,2]
[3,7,6,4,5,1,8,2]=>0110101=>[2,1,2,2,1]
[4,7,5,6,3,8,2,1]=>0101011=>[2,2,2,1,1]
[4,2,7,5,8,3,6,1]=>1010101=>[1,2,2,2,1]
[5,8,2,7,3,4,6,1]=>0101001=>[2,2,3,1]
[5,7,2,1,8,3,6,4]=>0110101=>[2,1,2,2,1]
[7,8,1,2,3,4,6,5]=>0100001=>[2,5,1]
[5,6,2,4,3,1,8,7]=>0101101=>[2,2,1,2,1]
[4,6,2,1,7,8,3,5]=>0110010=>[2,1,3,2]
[6,3,2,1,4,8,5,7]=>1110010=>[1,1,1,3,2]
[7,1,8,3,5,4,6,2]=>1010101=>[1,2,2,2,1]
[7,1,2,4,8,5,6,3]=>1000101=>[1,4,2,1]
[8,7,6,5,1,3,2,4]=>1111010=>[1,1,1,1,2,2]
[8,7,6,2,4,3,1,5]=>1110110=>[1,1,1,2,1,2]
[7,6,8,1,5,4,3,2]=>1010111=>[1,2,2,1,1,1]
[7,6,1,8,5,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[6,5,8,1,7,4,3,2]=>1010111=>[1,2,2,1,1,1]
[4,3,8,7,6,1,5,2]=>1011101=>[1,2,1,1,2,1]
[6,5,8,7,4,1,3,2]=>1011101=>[1,2,1,1,2,1]
[5,4,8,7,6,3,1,2]=>1011110=>[1,2,1,1,1,2]
[1,4,8,6,3,2,5,7]=>0011100=>[3,1,1,3]
[7,4,1,6,3,8,5,2]=>1101011=>[1,1,2,2,1,1]
[7,6,3,1,5,8,4,2]=>1110011=>[1,1,1,3,1,1]
[1,6,3,8,5,2,4,7]=>0101100=>[2,2,1,3]
[4,6,3,7,5,2,1,8]=>0101110=>[2,2,1,1,2]
[3,7,2,6,5,4,1,8]=>0101110=>[2,2,1,1,2]
[1,7,4,6,2,8,5,3]=>0101011=>[2,2,2,1,1]
[6,2,5,1,7,4,8,3]=>1010101=>[1,2,2,2,1]
[3,5,7,4,8,6,1,2]=>0010110=>[3,2,1,2]
[5,2,7,4,1,6,8,3]=>1011001=>[1,2,1,3,1]
[4,5,8,2,1,7,6,3]=>0011011=>[3,1,2,1,1]
[1,6,4,8,5,2,7,3]=>0101101=>[2,2,1,2,1]
[7,4,1,5,3,8,2,6]=>1101010=>[1,1,2,2,2]
[3,4,1,2,7,8,6,5]=>0100011=>[2,4,1,1]
[4,1,3,2,8,6,7,5]=>1010101=>[1,2,2,2,1]
[3,1,2,4,7,6,8,5]=>1000101=>[1,4,2,1]
[8,1,3,5,4,7,2,6]=>1001010=>[1,3,2,2]
[7,1,4,3,5,2,8,6]=>1010101=>[1,2,2,2,1]
[3,2,8,1,6,5,4,7]=>1010110=>[1,2,2,1,2]
[6,8,4,1,2,5,3,7]=>0110010=>[2,1,3,2]
[8,2,1,5,6,4,3,7]=>1100110=>[1,1,3,1,2]
[4,7,1,8,2,5,3,6]=>0101010=>[2,2,2,2]
[6,7,8,1,4,5,3,2]=>0010011=>[3,3,1,1]
[3,2,5,4,7,8,1,6]=>1010010=>[1,2,3,2]
[8,4,7,6,2,3,1,5]=>1011010=>[1,2,1,2,2]
[6,1,2,8,7,3,5,4]=>1001101=>[1,3,1,2,1]
[1,2,7,5,6,8,3,4]=>0010010=>[3,3,2]
[5,7,2,3,8,1,6,4]=>0100101=>[2,3,2,1]
[3,5,2,6,1,8,7,4]=>0101011=>[2,2,2,1,1]
[3,2,5,6,7,8,1,4]=>1000010=>[1,5,2]
[5,4,2,6,8,7,1,3]=>1100110=>[1,1,3,1,2]
[6,4,1,2,8,7,3,5]=>1100110=>[1,1,3,1,2]
[4,3,8,5,2,1,6,7]=>1011100=>[1,2,1,1,3]
[3,6,4,5,2,1,8,7]=>0101101=>[2,2,1,2,1]
[7,5,4,2,3,8,1,6]=>1110010=>[1,1,1,3,2]
[5,6,3,1,8,2,7,4]=>0110101=>[2,1,2,2,1]
[6,5,4,3,1,2,8,7]=>1111001=>[1,1,1,1,3,1]
[4,5,2,1,6,8,3,7]=>0110010=>[2,1,3,2]
[5,6,2,8,1,7,4,3]=>0101011=>[2,2,2,1,1]
[2,1,4,5,8,6,3,7]=>1000110=>[1,4,1,2]
[6,7,1,3,4,8,2,5]=>0100010=>[2,4,2]
[6,7,8,2,3,5,4,1]=>0010011=>[3,3,1,1]
[5,8,6,2,3,7,4,1]=>0110011=>[2,1,3,1,1]
[1,8,3,4,7,6,2,5]=>0100110=>[2,3,1,2]
[5,8,6,1,7,2,4,3]=>0110101=>[2,1,2,2,1]
[3,1,2,8,6,4,5,7]=>1001100=>[1,3,1,3]
[1,3,2,8,5,4,6,7]=>0101100=>[2,2,1,3]
[3,2,1,8,6,5,4,7]=>1101110=>[1,1,2,1,1,2]
[5,2,7,1,8,4,3,6]=>1010110=>[1,2,2,1,2]
[6,7,2,1,8,4,3,5]=>0110110=>[2,1,2,1,2]
[6,7,3,1,5,8,2,4]=>0110010=>[2,1,3,2]
[2,4,1,6,8,5,3,7]=>0100110=>[2,3,1,2]
[2,5,6,1,8,4,3,7]=>0010110=>[3,2,1,2]
[5,4,7,6,1,8,2,3]=>1011010=>[1,2,1,2,2]
[3,5,6,8,4,7,2,1]=>0001011=>[4,2,1,1]
[2,5,6,8,7,3,4,1]=>0001101=>[4,1,2,1]
[2,4,8,5,7,3,6,1]=>0010101=>[3,2,2,1]
[5,3,7,8,4,6,2,1]=>1001011=>[1,3,2,1,1]
[6,7,3,8,4,5,2,1]=>0101011=>[2,2,2,1,1]
[4,2,8,6,7,3,5,1]=>1010101=>[1,2,2,2,1]
[3,2,8,7,5,4,6,1]=>1011101=>[1,2,1,1,2,1]
[2,1,8,7,6,4,3,5]=>1011110=>[1,2,1,1,1,2]
[6,3,8,7,5,1,2,4]=>1011100=>[1,2,1,1,3]
[2,8,7,4,1,3,5,6]=>0111000=>[2,1,1,4]
[2,5,3,7,6,8,1,4]=>0101010=>[2,2,2,2]
[2,8,7,1,4,5,3,6]=>0110010=>[2,1,3,2]
[4,2,1,8,7,3,5,6]=>1101100=>[1,1,2,1,3]
[8,7,4,6,2,3,1,5]=>1101010=>[1,1,2,2,2]
[5,1,6,3,2,8,7,4]=>1011011=>[1,2,1,2,1,1]
[8,7,2,3,5,4,1,6]=>1100110=>[1,1,3,1,2]
[3,4,2,8,6,1,5,7]=>0101100=>[2,2,1,3]
[8,1,4,2,3,6,7,5]=>1010001=>[1,2,4,1]
[6,8,3,5,4,7,1,2]=>0101010=>[2,2,2,2]
[1,8,2,5,7,6,3,4]=>0100110=>[2,3,1,2]
[4,1,6,8,2,3,7,5]=>1001001=>[1,3,3,1]
[1,4,6,3,7,2,8,5]=>0010101=>[3,2,2,1]
[6,2,1,8,4,5,3,7]=>1101010=>[1,1,2,2,2]
[4,7,3,8,5,2,1,6]=>0101110=>[2,2,1,1,2]
[3,1,7,4,8,5,2,6]=>1010110=>[1,2,2,1,2]
[7,4,1,6,3,2,8,5]=>1101101=>[1,1,2,1,2,1]
[3,8,6,2,7,4,1,5]=>0110110=>[2,1,2,1,2]
[7,3,1,4,5,2,8,6]=>1100101=>[1,1,3,2,1]
[8,1,2,4,6,7,5,3]=>1000011=>[1,5,1,1]
[8,1,3,6,7,5,4,2]=>1000111=>[1,4,1,1,1]
[6,4,2,8,5,1,3,7]=>1101100=>[1,1,2,1,3]
[8,6,2,4,1,3,7,5]=>1101001=>[1,1,2,3,1]
[4,7,5,1,8,6,3,2]=>0110111=>[2,1,2,1,1,1]
[6,7,5,1,4,2,8,3]=>0110101=>[2,1,2,2,1]
[6,2,4,1,7,5,8,3]=>1010101=>[1,2,2,2,1]
[3,6,5,8,4,1,7,2]=>0101101=>[2,2,1,2,1]
[7,3,8,2,5,6,4,1]=>1010011=>[1,2,3,1,1]
[5,7,3,1,6,4,8,2]=>0110101=>[2,1,2,2,1]
[6,1,3,7,4,8,5,2]=>1001011=>[1,3,2,1,1]
[3,2,1,7,4,8,5,6]=>1101010=>[1,1,2,2,2]
[4,1,5,2,7,6,3,8]=>1010110=>[1,2,2,1,2]
[6,2,7,1,4,8,5,3]=>1010011=>[1,2,3,1,1]
[7,5,4,1,3,8,6,2]=>1110011=>[1,1,1,3,1,1]
[4,3,2,1,8,5,7,6]=>1110101=>[1,1,1,2,2,1]
[4,2,1,7,3,6,5,8]=>1101010=>[1,1,2,2,2]
[7,4,3,2,8,1,6,5]=>1110101=>[1,1,1,2,2,1]
[2,7,5,3,8,1,4,6]=>0110100=>[2,1,2,3]
[1,8,5,3,6,4,2,7]=>0110110=>[2,1,2,1,2]
[8,1,6,2,7,4,3,5]=>1010110=>[1,2,2,1,2]
[7,3,1,6,5,4,2,8]=>1101110=>[1,1,2,1,1,2]
[8,5,7,4,3,6,2,1]=>1011011=>[1,2,1,2,1,1]
[2,8,5,6,1,4,3,7]=>0101010=>[2,2,2,2]
[3,7,5,8,2,1,4,6]=>0101100=>[2,2,1,3]
[5,4,8,3,2,1,7,6]=>1011101=>[1,2,1,1,2,1]
[2,4,7,1,3,6,5,8]=>0010010=>[3,3,2]
[5,7,4,8,1,3,6,2]=>0101001=>[2,2,3,1]
[5,1,7,8,2,4,6,3]=>1001001=>[1,3,3,1]
[3,6,7,8,1,2,5,4]=>0001001=>[4,3,1]
[4,6,7,2,8,1,3,5]=>0010100=>[3,2,3]
[6,3,7,1,8,2,5,4]=>1010101=>[1,2,2,2,1]
[5,7,1,4,8,2,6,3]=>0100101=>[2,3,2,1]
[2,7,4,1,8,3,6,5]=>0110101=>[2,1,2,2,1]
[6,1,2,7,8,3,5,4]=>1000101=>[1,4,2,1]
[3,6,4,7,8,1,2,5]=>0100100=>[2,3,3]
[3,7,4,8,5,2,1,6]=>0101110=>[2,2,1,1,2]
[7,2,5,8,6,3,1,4]=>1001110=>[1,3,1,1,2]
[4,8,1,7,6,2,3,5]=>0101100=>[2,2,1,3]
[4,8,2,1,7,5,3,6]=>0110110=>[2,1,2,1,2]
[5,8,7,1,3,6,4,2]=>0110011=>[2,1,3,1,1]
[2,8,7,1,6,3,5,4]=>0110101=>[2,1,2,2,1]
[2,7,6,5,1,4,3,8]=>0111010=>[2,1,1,2,2]
[3,8,7,6,2,1,5,4]=>0111101=>[2,1,1,1,2,1]
[5,8,7,2,6,1,4,3]=>0110101=>[2,1,2,2,1]
[7,3,8,6,5,1,2,4]=>1011100=>[1,2,1,1,3]
[5,8,6,4,3,2,1,7]=>0111110=>[2,1,1,1,1,2]
[8,7,6,2,5,3,1,4]=>1110110=>[1,1,1,2,1,2]
[8,1,2,3,4,7,6,5]=>1000011=>[1,5,1,1]
[3,8,2,7,6,5,4,1]=>0101111=>[2,2,1,1,1,1]
[4,2,8,7,6,5,3,1]=>1011111=>[1,2,1,1,1,1,1]
[8,3,1,7,6,5,4,2]=>1101111=>[1,1,2,1,1,1,1]
[5,2,8,7,6,4,3,1]=>1011111=>[1,2,1,1,1,1,1]
[8,3,2,1,7,6,5,4]=>1110111=>[1,1,1,2,1,1,1]
[8,4,1,7,6,5,3,2]=>1101111=>[1,1,2,1,1,1,1]
[6,4,1,3,2,8,5,7]=>1101010=>[1,1,2,2,2]
[2,5,8,6,3,1,4,7]=>0011100=>[3,1,1,3]
[3,2,7,4,5,8,1,6]=>1010010=>[1,2,3,2]
[8,1,6,2,4,5,3,7]=>1010010=>[1,2,3,2]
[5,8,1,6,2,3,4,7]=>0101000=>[2,2,4]
[5,4,6,1,3,8,2,7]=>1010010=>[1,2,3,2]
[2,4,1,7,5,8,3,6]=>0101010=>[2,2,2,2]
[2,4,7,6,8,3,5,1]=>0010101=>[3,2,2,1]
[4,8,6,5,7,1,2,3]=>0110100=>[2,1,2,3]
[8,5,7,4,3,1,6,2]=>1011101=>[1,2,1,1,2,1]
[8,1,7,4,2,3,6,5]=>1011001=>[1,2,1,3,1]
[8,2,3,1,5,7,6,4]=>1010011=>[1,2,3,1,1]
[1,4,8,2,3,6,7,5]=>0010001=>[3,4,1]
[3,1,2,7,8,6,4,5]=>1000110=>[1,4,1,2]
[7,5,1,8,2,4,3,6]=>1101010=>[1,1,2,2,2]
[3,5,8,1,2,4,7,6]=>0010001=>[3,4,1]
[8,4,1,5,2,3,7,6]=>1101001=>[1,1,2,3,1]
[3,8,4,1,2,7,6,5]=>0110011=>[2,1,3,1,1]
[2,7,5,8,3,4,1,6]=>0101010=>[2,2,2,2]
[1,4,7,3,2,8,5,6]=>0011010=>[3,1,2,2]
[6,4,1,3,2,7,8,5]=>1101001=>[1,1,2,3,1]
[2,3,7,6,8,1,5,4]=>0010101=>[3,2,2,1]
[2,6,3,5,1,8,7,4]=>0101011=>[2,2,2,1,1]
[2,7,1,6,8,3,5,4]=>0100101=>[2,3,2,1]
[6,7,5,4,2,1,8,3]=>0111101=>[2,1,1,1,2,1]
[4,2,1,5,8,7,6,3]=>1100111=>[1,1,3,1,1,1]
[8,5,3,2,6,1,7,4]=>1110101=>[1,1,1,2,2,1]
[6,2,1,5,3,8,7,4]=>1101011=>[1,1,2,2,1,1]
[7,8,4,1,2,5,3,6]=>0110010=>[2,1,3,2]
[7,8,1,2,6,5,3,4]=>0100110=>[2,3,1,2]
[6,1,4,2,7,5,3,8]=>1010110=>[1,2,2,1,2]
[1,2,8,7,5,4,3,6]=>0011110=>[3,1,1,1,2]
[1,2,8,3,6,4,7,5]=>0010101=>[3,2,2,1]
[5,1,7,3,6,4,8,2]=>1010101=>[1,2,2,2,1]
[6,2,3,7,4,1,5,8]=>1001100=>[1,3,1,3]
[6,2,4,1,7,3,5,8]=>1010100=>[1,2,2,3]
[3,4,8,7,5,6,1,2]=>0011010=>[3,1,2,2]
[2,7,3,8,6,4,1,5]=>0101110=>[2,2,1,1,2]
[1,8,3,7,6,4,5,2]=>0101101=>[2,2,1,2,1]
[2,6,8,5,3,1,7,4]=>0011101=>[3,1,1,2,1]
[5,6,2,1,7,3,8,4]=>0110101=>[2,1,2,2,1]
[5,3,6,2,4,1,7,8]=>1010100=>[1,2,2,3]
[5,7,4,2,1,3,6,8]=>0111000=>[2,1,1,4]
[6,4,2,1,5,3,7,8]=>1110100=>[1,1,1,2,3]
[5,3,1,4,6,2,7,8]=>1100100=>[1,1,3,3]
[5,1,2,4,7,6,8,3]=>1000101=>[1,4,2,1]
[1,6,4,2,8,7,3,5]=>0110110=>[2,1,2,1,2]
[4,8,1,2,6,7,3,5]=>0100010=>[2,4,2]
[3,1,2,4,6,8,7,5]=>1000011=>[1,5,1,1]
[4,2,8,1,5,3,7,6]=>1010101=>[1,2,2,2,1]
[4,3,8,5,7,6,1,2]=>1010110=>[1,2,2,1,2]
[4,8,6,3,7,5,1,2]=>0110110=>[2,1,2,1,2]
[3,8,6,5,2,7,1,4]=>0111010=>[2,1,1,2,2]
[3,8,5,6,1,7,4,2]=>0101011=>[2,2,2,1,1]
[3,7,8,5,2,1,6,4]=>0011101=>[3,1,1,2,1]
[4,2,7,8,1,3,6,5]=>1001001=>[1,3,3,1]
[2,1,8,7,6,3,5,4]=>1011101=>[1,2,1,1,2,1]
[5,4,1,6,3,2,8,7]=>1101101=>[1,1,2,1,2,1]
[6,8,1,5,4,7,3,2]=>0101011=>[2,2,2,1,1]
[4,6,2,5,1,3,8,7]=>0101001=>[2,2,3,1]
[2,6,4,3,1,5,8,7]=>0111001=>[2,1,1,3,1]
[5,1,7,2,8,6,4,3]=>1010111=>[1,2,2,1,1,1]
[6,8,2,7,4,3,1,5]=>0101110=>[2,2,1,1,2]
[6,8,2,5,4,7,1,3]=>0101010=>[2,2,2,2]
[2,1,7,6,3,8,5,4]=>1011011=>[1,2,1,2,1,1]
[7,6,2,8,4,3,1,5]=>1101110=>[1,1,2,1,1,2]
[2,6,5,1,8,4,3,7]=>0110110=>[2,1,2,1,2]
[4,2,1,6,3,8,7,5]=>1101011=>[1,1,2,2,1,1]
[5,8,3,2,7,6,1,4]=>0110110=>[2,1,2,1,2]
[2,4,8,3,1,7,5,6]=>0011010=>[3,1,2,2]
[4,8,3,2,1,7,6,5]=>0111011=>[2,1,1,2,1,1]
[3,5,8,2,7,1,4,6]=>0010100=>[3,2,3]
[4,5,8,2,6,1,3,7]=>0010100=>[3,2,3]
[2,6,8,3,7,1,4,5]=>0010100=>[3,2,3]
[6,8,3,7,2,1,5,4]=>0101101=>[2,2,1,2,1]
[5,8,3,1,6,2,7,4]=>0110101=>[2,1,2,2,1]
[5,1,7,3,6,2,8,4]=>1010101=>[1,2,2,2,1]
[4,5,8,1,6,3,2,7]=>0010110=>[3,2,1,2]
[6,8,4,7,1,5,3,2]=>0101011=>[2,2,2,1,1]
[4,3,2,1,6,8,5,7]=>1110010=>[1,1,1,3,2]
[2,4,1,3,8,7,6,5]=>0100111=>[2,3,1,1,1]
[4,8,6,5,1,7,3,2]=>0111011=>[2,1,1,2,1,1]
[6,5,3,1,7,2,8,4]=>1110101=>[1,1,1,2,2,1]
[2,1,5,4,8,7,3,6]=>1010110=>[1,2,2,1,2]
[3,8,5,4,2,1,7,6]=>0111101=>[2,1,1,1,2,1]
[2,3,8,5,4,1,6,7]=>0011100=>[3,1,1,3]
[2,1,4,8,6,5,3,7]=>1001110=>[1,3,1,1,2]
[4,3,2,8,7,6,1,5]=>1101110=>[1,1,2,1,1,2]
[3,2,8,7,5,4,1,6]=>1011110=>[1,2,1,1,1,2]
[2,8,6,5,4,3,1,7]=>0111110=>[2,1,1,1,1,2]
[5,4,2,6,3,1,8,7]=>1101101=>[1,1,2,1,2,1]
[7,5,2,6,3,8,4,1]=>1101011=>[1,1,2,2,1,1]
[7,3,6,5,2,8,4,1]=>1011011=>[1,2,1,2,1,1]
[5,6,3,1,2,4,8,7]=>0110001=>[2,1,4,1]
[7,1,5,3,8,4,6,2]=>1010101=>[1,2,2,2,1]
[2,7,5,3,8,6,4,1]=>0110111=>[2,1,2,1,1,1]
[3,7,6,4,2,8,5,1]=>0111011=>[2,1,1,2,1,1]
[5,7,3,6,2,8,4,1]=>0101011=>[2,2,2,1,1]
[2,1,8,7,4,3,5,6]=>1011100=>[1,2,1,1,3]
[2,8,6,3,1,4,7,5]=>0111001=>[2,1,1,3,1]
[3,5,7,4,8,6,2,1]=>0010111=>[3,2,1,1,1]
[4,5,3,6,8,2,7,1]=>0100101=>[2,3,2,1]
[5,6,3,7,4,8,2,1]=>0101011=>[2,2,2,1,1]
[2,6,7,4,5,8,3,1]=>0010011=>[3,3,1,1]
[6,3,7,5,8,4,2,1]=>1010111=>[1,2,2,1,1,1]
[8,5,2,6,1,7,3,4]=>1101010=>[1,1,2,2,2]
[5,4,2,6,8,3,7,1]=>1100101=>[1,1,3,2,1]
[7,6,8,5,1,4,2,3]=>1011010=>[1,2,1,2,2]
[7,1,8,5,4,2,3,6]=>1011100=>[1,2,1,1,3]
[5,7,3,8,4,1,2,6]=>0101100=>[2,2,1,3]
[2,1,7,8,5,3,4,6]=>1001100=>[1,3,1,3]
[2,4,8,1,5,6,3,7]=>0010010=>[3,3,2]
[4,1,8,2,6,5,3,7]=>1010110=>[1,2,2,1,2]
[4,7,3,8,1,2,6,5]=>0101001=>[2,2,3,1]
[4,8,1,2,5,3,6,7]=>0100100=>[2,3,3]
[3,8,1,2,4,6,5,7]=>0100010=>[2,4,2]
[4,8,7,6,3,5,2,1]=>0111011=>[2,1,1,2,1,1]
[3,8,7,6,5,2,4,1]=>0111101=>[2,1,1,1,2,1]
[4,8,7,3,6,5,2,1]=>0110111=>[2,1,2,1,1,1]
[4,8,7,6,3,2,5,1]=>0111101=>[2,1,1,1,2,1]
[3,8,7,6,5,2,1,4]=>0111110=>[2,1,1,1,1,2]
[7,5,8,3,6,2,1,4]=>1010110=>[1,2,2,1,2]
[7,5,8,3,2,6,1,4]=>1011010=>[1,2,1,2,2]
[7,5,8,3,2,1,6,4]=>1011101=>[1,2,1,1,2,1]
[2,3,7,8,4,1,6,5]=>0001101=>[4,1,2,1]
[2,1,7,5,8,4,6,3]=>1010101=>[1,2,2,2,1]
[2,5,6,8,1,7,4,3]=>0001011=>[4,2,1,1]
[4,2,8,6,1,7,3,5]=>1011010=>[1,2,1,2,2]
[8,6,4,1,3,2,5,7]=>1110100=>[1,1,1,2,3]
[8,1,3,2,6,5,4,7]=>1010110=>[1,2,2,1,2]
[8,5,3,6,2,4,1,7]=>1101010=>[1,1,2,2,2]
[8,4,1,2,6,5,3,7]=>1100110=>[1,1,3,1,2]
[8,3,5,6,2,1,4,7]=>1001100=>[1,3,1,3]
[8,4,2,1,5,6,3,7]=>1110010=>[1,1,1,3,2]
[5,4,7,6,8,2,3,1]=>1010101=>[1,2,2,2,1]
[4,1,8,2,3,7,6,5]=>1010011=>[1,2,3,1,1]
[3,7,4,5,8,2,1,6]=>0100110=>[2,3,1,2]
[6,3,8,5,7,4,1,2]=>1010110=>[1,2,2,1,2]
[7,4,1,8,3,5,6,2]=>1101001=>[1,1,2,3,1]
[5,3,8,7,4,6,1,2]=>1011010=>[1,2,1,2,2]
[7,5,8,2,1,4,6,3]=>1011001=>[1,2,1,3,1]
[8,7,4,2,1,3,6,5]=>1111001=>[1,1,1,1,3,1]
[7,4,8,3,2,6,1,5]=>1011010=>[1,2,1,2,2]
[6,8,2,3,1,7,5,4]=>0101011=>[2,2,2,1,1]
[7,4,3,2,6,8,5,1]=>1110011=>[1,1,1,3,1,1]
[5,1,2,3,6,8,7,4]=>1000011=>[1,5,1,1]
[2,4,7,3,8,1,6,5]=>0010101=>[3,2,2,1]
[6,3,8,2,7,4,1,5]=>1010110=>[1,2,2,1,2]
[8,2,1,3,6,4,7,5]=>1100101=>[1,1,3,2,1]
[5,7,8,2,1,4,3,6]=>0011010=>[3,1,2,2]
[3,5,1,7,8,4,2,6]=>0100110=>[2,3,1,2]
[1,7,8,4,5,3,2,6]=>0010110=>[3,2,1,2]
[3,2,4,8,6,7,1,5]=>1001010=>[1,3,2,2]
[8,3,1,6,7,4,2,5]=>1100110=>[1,1,3,1,2]
[3,2,5,7,4,8,1,6]=>1001010=>[1,3,2,2]
[8,4,7,1,3,2,5,6]=>1010100=>[1,2,2,3]
[8,4,7,2,1,3,5,6]=>1011000=>[1,2,1,4]
[6,4,2,1,3,7,8,5]=>1110001=>[1,1,1,4,1]
[7,1,6,3,5,8,2,4]=>1010010=>[1,2,3,2]
[3,8,5,1,6,7,2,4]=>0110010=>[2,1,3,2]
[5,3,6,7,8,4,2,1]=>1000111=>[1,4,1,1,1]
[1,5,2,7,8,6,4,3]=>0100111=>[2,3,1,1,1]
[1,4,2,8,6,5,7,3]=>0101101=>[2,2,1,2,1]
[4,1,7,5,2,6,8,3]=>1011001=>[1,2,1,3,1]
[7,6,2,4,5,1,8,3]=>1100101=>[1,1,3,2,1]
[8,1,4,5,2,6,7,3]=>1001001=>[1,3,3,1]
[8,4,6,5,2,1,7,3]=>1011101=>[1,2,1,1,2,1]
[3,5,7,2,1,6,8,4]=>0011001=>[3,1,3,1]
[4,2,1,5,6,7,8,3]=>1100001=>[1,1,5,1]
[3,7,5,4,6,8,1,2]=>0110010=>[2,1,3,2]
[8,3,4,1,5,6,7,2]=>1010001=>[1,2,4,1]
[3,5,2,4,7,6,1,8]=>0100110=>[2,3,1,2]
[7,3,5,2,4,6,1,8]=>1010010=>[1,2,3,2]
[5,3,7,2,4,6,1,8]=>1010010=>[1,2,3,2]
[3,5,2,7,4,6,1,8]=>0101010=>[2,2,2,2]
[3,2,5,7,4,6,1,8]=>1001010=>[1,3,2,2]
[3,7,5,2,4,6,1,8]=>0110010=>[2,1,3,2]
[5,7,3,2,4,6,1,8]=>0110010=>[2,1,3,2]
[1,5,3,2,4,7,6,8]=>0110010=>[2,1,3,2]
[1,5,3,2,7,4,6,8]=>0110100=>[2,1,2,3]
[3,7,2,5,4,1,6,8]=>0101100=>[2,2,1,3]
[3,2,7,5,4,1,6,8]=>1011100=>[1,2,1,1,3]
[5,1,3,2,4,7,6,8]=>1010010=>[1,2,3,2]
[5,1,3,2,7,4,6,8]=>1010100=>[1,2,2,3]
[7,1,3,2,5,4,6,8]=>1010100=>[1,2,2,3]
[1,7,3,2,5,4,6,8]=>0110100=>[2,1,2,3]
[1,7,3,5,2,4,6,8]=>0101000=>[2,2,4]
[7,1,3,5,2,4,6,8]=>1001000=>[1,3,4]
[5,1,3,7,2,4,6,8]=>1001000=>[1,3,4]
[3,7,5,1,2,4,6,8]=>0110000=>[2,1,5]
[5,7,3,1,2,4,6,8]=>0110000=>[2,1,5]
[1,5,3,7,2,4,6,8]=>0101000=>[2,2,4]
[3,5,7,2,1,4,6,8]=>0011000=>[3,1,4]
[3,5,2,7,1,4,6,8]=>0101000=>[2,2,4]
[3,2,5,7,4,1,6,8]=>1001100=>[1,3,1,3]
[3,5,2,7,4,1,6,8]=>0101100=>[2,2,1,3]
[3,5,7,2,4,1,6,8]=>0010100=>[3,2,3]
[5,3,7,2,4,1,6,8]=>1010100=>[1,2,2,3]
[7,3,5,2,1,4,6,8]=>1011000=>[1,2,1,4]
[5,3,2,4,7,1,6,8]=>1100100=>[1,1,3,3]
[3,2,5,4,7,1,6,8]=>1010100=>[1,2,2,3]
[1,3,2,7,5,4,6,8]=>0101100=>[2,2,1,3]
[1,3,7,2,5,4,6,8]=>0010100=>[3,2,3]
[7,3,1,2,5,4,6,8]=>1100100=>[1,1,3,3]
[5,3,1,2,7,4,6,8]=>1100100=>[1,1,3,3]
[5,3,1,2,4,7,6,8]=>1100010=>[1,1,4,2]
[3,5,2,1,4,7,6,8]=>0110010=>[2,1,3,2]
[3,2,5,1,7,4,6,8]=>1010100=>[1,2,2,3]
[3,5,2,1,7,4,6,8]=>0110100=>[2,1,2,3]
[5,3,1,7,2,4,6,8]=>1101000=>[1,1,2,4]
[7,3,1,5,2,4,6,8]=>1101000=>[1,1,2,4]
[1,3,7,5,2,4,6,8]=>0011000=>[3,1,4]
[7,5,1,3,2,4,6,8]=>1101000=>[1,1,2,4]
[5,7,1,3,2,4,6,8]=>0101000=>[2,2,4]
[3,7,1,5,2,4,6,8]=>0101000=>[2,2,4]
[3,7,1,2,5,4,6,8]=>0100100=>[2,3,3]
[3,1,2,7,5,4,6,8]=>1001100=>[1,3,1,3]
[3,1,7,2,5,4,6,8]=>1010100=>[1,2,2,3]
[3,1,7,5,2,4,6,8]=>1011000=>[1,2,1,4]
[5,1,7,3,2,4,6,8]=>1011000=>[1,2,1,4]
[7,1,5,3,2,4,6,8]=>1011000=>[1,2,1,4]
[1,7,5,3,2,4,6,8]=>0111000=>[2,1,1,4]
[5,8,7,1,2,6,4,3]=>0110011=>[2,1,3,1,1]
[6,8,2,1,7,5,4,3]=>0110111=>[2,1,2,1,1,1]
[1,8,7,6,3,2,5,4]=>0111101=>[2,1,1,1,2,1]
[5,8,7,4,1,2,6,3]=>0111001=>[2,1,1,3,1]
[2,8,7,4,3,6,1,5]=>0111010=>[2,1,1,2,2]
[1,8,5,4,2,7,6,3]=>0111011=>[2,1,1,2,1,1]
[7,6,4,2,8,5,3,1]=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,8,5,1,2,3]=>1101100=>[1,1,2,1,3]
[1,6,7,5,3,8,4,2]=>0011011=>[3,1,2,1,1]
[7,6,3,5,2,4,8,1]=>1101001=>[1,1,2,3,1]
[7,6,4,2,5,1,8,3]=>1110101=>[1,1,1,2,2,1]
[7,6,2,8,3,1,4,5]=>1101100=>[1,1,2,1,3]
[1,6,7,5,8,2,3,4]=>0010100=>[3,2,3]
[2,6,5,7,8,3,4,1]=>0100101=>[2,3,2,1]
[3,2,5,1,7,8,4,6]=>1010010=>[1,2,3,2]
[5,2,3,4,8,6,1,7]=>1000110=>[1,4,1,2]
[5,3,4,8,2,7,6,1]=>1001011=>[1,3,2,1,1]
[5,3,8,2,4,1,7,6]=>1010101=>[1,2,2,2,1]
[5,2,8,4,1,7,3,6]=>1011010=>[1,2,1,2,2]
[6,4,2,5,1,8,7,3]=>1101011=>[1,1,2,2,1,1]
[6,4,3,5,8,2,1,7]=>1100110=>[1,1,3,1,2]
[6,3,5,4,8,2,7,1]=>1010101=>[1,2,2,2,1]
[6,3,5,8,7,1,2,4]=>1001100=>[1,3,1,3]
[1,5,7,3,4,8,6,2]=>0010011=>[3,3,1,1]
[5,8,4,1,3,7,6,2]=>0110011=>[2,1,3,1,1]
[6,4,3,8,5,7,2,1]=>1101011=>[1,1,2,2,1,1]
[5,4,2,6,3,1,7,8]=>1101100=>[1,1,2,1,3]
[4,6,5,3,7,1,2,8]=>0110100=>[2,1,2,3]
[3,5,6,1,4,8,7,2]=>0010011=>[3,3,1,1]
[3,5,7,6,1,4,8,2]=>0011001=>[3,1,3,1]
[3,6,5,7,4,8,1,2]=>0101010=>[2,2,2,2]
[4,2,6,5,1,7,3,8]=>1011010=>[1,2,1,2,2]
[4,3,5,7,2,1,6,8]=>1001100=>[1,3,1,3]
[3,5,4,7,2,6,1,8]=>0101010=>[2,2,2,2]
[3,4,7,6,8,1,2,5]=>0010100=>[3,2,3]
[1,8,4,3,7,5,6,2]=>0110101=>[2,1,2,2,1]
[5,2,8,6,4,7,3,1]=>1011011=>[1,2,1,2,1,1]
[1,8,6,3,7,4,2,5]=>0110110=>[2,1,2,1,2]
[1,8,6,5,7,2,3,4]=>0110100=>[2,1,2,3]
[4,2,8,3,5,7,1,6]=>1010010=>[1,2,3,2]
[4,3,8,6,5,7,1,2]=>1011010=>[1,2,1,2,2]
[1,3,7,2,6,5,8,4]=>0010101=>[3,2,2,1]
[1,5,7,2,4,6,8,3]=>0010001=>[3,4,1]
[1,3,6,4,2,5,8,7]=>0011001=>[3,1,3,1]
[5,6,3,4,7,1,8,2]=>0100101=>[2,3,2,1]
[3,5,2,7,4,1,8,6]=>0101101=>[2,2,1,2,1]
[5,2,3,8,4,1,7,6]=>1001101=>[1,3,1,2,1]
[7,5,3,4,8,2,1,6]=>1100110=>[1,1,3,1,2]
[7,6,3,8,4,2,1,5]=>1101110=>[1,1,2,1,1,2]
[7,2,8,5,1,6,3,4]=>1011010=>[1,2,1,2,2]
[7,4,3,8,5,2,6,1]=>1101101=>[1,1,2,1,2,1]
[7,2,8,5,1,3,4,6]=>1011000=>[1,2,1,4]
[7,6,8,1,2,5,3,4]=>1010010=>[1,2,3,2]
[1,5,3,7,6,8,4,2]=>0101011=>[2,2,2,1,1]
[1,2,6,4,5,8,3,7]=>0010010=>[3,3,2]
[1,2,7,4,8,5,3,6]=>0010110=>[3,2,1,2]
[1,6,3,7,8,2,4,5]=>0100100=>[2,3,3]
[3,2,6,7,8,1,4,5]=>1000100=>[1,4,3]
[1,4,7,3,5,2,6,8]=>0010100=>[3,2,3]
[3,8,4,7,6,1,5,2]=>0101101=>[2,2,1,2,1]
[5,7,4,2,6,3,1,8]=>0110110=>[2,1,2,1,2]
[2,4,5,8,1,6,7,3]=>0001001=>[4,3,1]
[6,1,3,7,4,2,5,8]=>1001100=>[1,3,1,3]
[2,1,8,3,6,7,4,5]=>1010010=>[1,2,3,2]
[5,1,8,6,2,7,3,4]=>1011010=>[1,2,1,2,2]
[5,7,1,4,2,6,3,8]=>0101010=>[2,2,2,2]
[3,2,6,8,1,5,7,4]=>1001001=>[1,3,3,1]
[8,2,6,1,5,4,7,3]=>1010101=>[1,2,2,2,1]
[7,8,5,4,1,6,3,2]=>0111011=>[2,1,1,2,1,1]
[3,6,2,7,8,1,5,4]=>0100101=>[2,3,2,1]
[2,7,3,8,1,5,6,4]=>0101001=>[2,2,3,1]
[2,6,8,4,1,5,7,3]=>0011001=>[3,1,3,1]
[5,7,8,4,1,6,3,2]=>0011011=>[3,1,2,1,1]
[3,4,8,1,2,5,7,6]=>0010001=>[3,4,1]
[6,3,1,7,5,2,4,8]=>1101100=>[1,1,2,1,3]
[6,3,1,8,2,7,4,5]=>1101010=>[1,1,2,2,2]
[7,8,1,2,4,3,6,5]=>0100101=>[2,3,2,1]
[5,2,8,1,3,4,7,6]=>1010001=>[1,2,4,1]
[3,2,1,6,4,7,8,5]=>1101001=>[1,1,2,3,1]
[4,1,3,6,5,7,8,2]=>1001001=>[1,3,3,1]
[5,1,3,4,2,7,8,6]=>1001001=>[1,3,3,1]
[6,1,3,4,2,8,5,7]=>1001010=>[1,3,2,2]
[8,1,4,3,5,7,6,2]=>1010011=>[1,2,3,1,1]
[5,2,4,1,3,7,8,6]=>1010001=>[1,2,4,1]
[3,2,6,1,5,7,8,4]=>1010001=>[1,2,4,1]
[1,4,6,3,5,7,8,2]=>0010001=>[3,4,1]
[3,5,1,6,4,7,8,2]=>0101001=>[2,2,3,1]
[3,6,4,2,1,7,8,5]=>0111001=>[2,1,1,3,1]
[3,8,6,1,4,7,5,2]=>0110011=>[2,1,3,1,1]
[1,8,3,2,6,7,5,4]=>0110011=>[2,1,3,1,1]
[8,7,1,3,6,5,4,2]=>1100111=>[1,1,3,1,1,1]
[1,8,5,7,4,2,6,3]=>0101101=>[2,2,1,2,1]
[4,7,5,3,8,2,1,6]=>0110110=>[2,1,2,1,2]
[2,7,6,5,8,3,1,4]=>0110110=>[2,1,2,1,2]
[1,4,7,6,8,2,3,5]=>0010100=>[3,2,3]
[3,5,7,4,8,1,2,6]=>0010100=>[3,2,3]
[4,6,1,7,5,8,2,3]=>0101010=>[2,2,2,2]
[2,3,6,7,5,8,1,4]=>0001010=>[4,2,2]
[1,3,7,5,6,8,2,4]=>0010010=>[3,3,2]
[3,2,7,1,6,8,4,5]=>1010010=>[1,2,3,2]
[8,1,5,4,7,2,6,3]=>1010101=>[1,2,2,2,1]
[8,2,5,3,7,1,6,4]=>1010101=>[1,2,2,2,1]
[2,1,4,7,5,8,3,6]=>1001010=>[1,3,2,2]
[1,2,6,7,4,8,3,5]=>0001010=>[4,2,2]
[3,6,4,7,8,5,2,1]=>0100111=>[2,3,1,1,1]
[3,2,5,8,6,7,4,1]=>1001011=>[1,3,2,1,1]
[6,3,5,8,7,4,1,2]=>1001110=>[1,3,1,1,2]
[8,3,5,7,6,4,2,1]=>1001111=>[1,3,1,1,1,1]
[4,1,8,3,7,5,6,2]=>1010101=>[1,2,2,2,1]
[4,7,2,8,5,6,3,1]=>0101011=>[2,2,2,1,1]
[1,4,8,7,3,5,6,2]=>0011001=>[3,1,3,1]
[3,2,8,7,1,5,6,4]=>1011001=>[1,2,1,3,1]
[1,5,8,7,4,6,2,3]=>0011010=>[3,1,2,2]
[4,7,6,8,5,3,1,2]=>0101110=>[2,2,1,1,2]
[4,8,6,7,5,3,2,1]=>0101111=>[2,2,1,1,1,1]
[3,8,7,5,6,4,2,1]=>0110111=>[2,1,2,1,1,1]
[8,1,5,6,3,2,4,7]=>1001100=>[1,3,1,3]
[1,7,8,3,5,2,4,6]=>0010100=>[3,2,3]
[8,2,5,3,1,6,4,7]=>1011010=>[1,2,1,2,2]
[8,3,2,1,5,6,4,7]=>1110010=>[1,1,1,3,2]
[8,6,5,1,3,4,2,7]=>1110010=>[1,1,1,3,2]
[1,7,8,5,4,3,2,6]=>0011110=>[3,1,1,1,2]
[2,6,8,7,4,3,5,1]=>0011101=>[3,1,1,2,1]
[2,7,6,8,4,3,1,5]=>0101110=>[2,2,1,1,2]
[1,2,6,7,8,4,3,5]=>0000110=>[5,1,2]
[8,5,7,1,3,4,6,2]=>1010001=>[1,2,4,1]
[3,5,8,6,7,4,1,2]=>0010110=>[3,2,1,2]
[3,1,6,5,8,7,4,2]=>1010111=>[1,2,2,1,1,1]
[3,7,6,4,8,1,2,5]=>0110100=>[2,1,2,3]
[2,3,6,5,7,1,8,4]=>0010101=>[3,2,2,1]
[2,3,6,4,1,7,8,5]=>0011001=>[3,1,3,1]
[4,7,2,1,5,3,8,6]=>0110101=>[2,1,2,2,1]
[3,1,7,4,5,2,8,6]=>1010101=>[1,2,2,2,1]
[3,7,5,4,2,1,8,6]=>0111101=>[2,1,1,1,2,1]
[1,3,6,7,4,2,8,5]=>0001101=>[4,1,2,1]
[4,3,7,2,6,8,1,5]=>1010010=>[1,2,3,2]
[5,4,2,1,3,7,8,6]=>1110001=>[1,1,1,4,1]
[8,7,1,5,6,3,2,4]=>1100110=>[1,1,3,1,2]
[8,7,2,5,4,6,1,3]=>1101010=>[1,1,2,2,2]
[8,7,1,2,4,5,6,3]=>1100001=>[1,1,5,1]
[8,7,2,5,3,1,6,4]=>1101101=>[1,1,2,1,2,1]
[8,7,3,2,1,5,6,4]=>1111001=>[1,1,1,1,3,1]
[8,7,6,5,1,3,4,2]=>1111001=>[1,1,1,1,3,1]
[8,7,6,1,4,5,3,2]=>1110011=>[1,1,1,3,1,1]
[8,7,5,6,1,4,3,2]=>1101011=>[1,1,2,2,1,1]
[6,8,7,1,5,4,3,2]=>0110111=>[2,1,2,1,1,1]
[8,5,7,6,1,4,3,2]=>1011011=>[1,2,1,2,1,1]
[6,7,8,1,5,4,3,2]=>0010111=>[3,2,1,1,1]
[8,7,4,6,5,1,3,2]=>1101101=>[1,1,2,1,2,1]
[8,5,6,7,1,4,3,2]=>1001011=>[1,3,2,1,1]
[8,7,6,3,5,4,1,2]=>1110110=>[1,1,1,2,1,2]
[8,7,4,5,6,1,3,2]=>1100101=>[1,1,3,2,1]
[8,7,6,5,2,4,3,1]=>1111011=>[1,1,1,1,2,1,1]
[4,2,8,7,6,5,1,3]=>1011110=>[1,2,1,1,1,2]
[7,5,8,1,6,4,3,2]=>1010111=>[1,2,2,1,1,1]
[1,5,8,7,6,2,4,3]=>0011101=>[3,1,1,2,1]
[7,5,8,4,1,6,3,2]=>1011011=>[1,2,1,2,1,1]
[6,8,5,1,7,4,3,2]=>0110111=>[2,1,2,1,1,1]
[1,6,8,7,2,5,4,3]=>0011011=>[3,1,2,1,1]
[7,3,8,4,6,1,5,2]=>1010101=>[1,2,2,2,1]
[4,8,5,7,1,6,3,2]=>0101011=>[2,2,2,1,1]
[4,3,7,6,5,1,8,2]=>1011101=>[1,2,1,1,2,1]
[5,4,3,6,7,1,8,2]=>1100101=>[1,1,3,2,1]
[5,4,7,3,6,1,8,2]=>1010101=>[1,2,2,2,1]
[4,8,7,6,3,1,5,2]=>0111101=>[2,1,1,1,2,1]
[2,4,6,3,1,7,8,5]=>0011001=>[3,1,3,1]
[6,8,5,7,3,2,1,4]=>0101110=>[2,2,1,1,2]
[6,8,5,3,7,2,1,4]=>0110110=>[2,1,2,1,2]
[6,8,5,7,4,2,1,3]=>0101110=>[2,2,1,1,2]
[2,1,8,7,6,3,4,5]=>1011100=>[1,2,1,1,3]
[5,8,7,6,2,4,1,3]=>0111010=>[2,1,1,2,2]
[6,8,2,7,5,1,4,3]=>0101101=>[2,2,1,2,1]
[5,8,7,2,6,4,1,3]=>0110110=>[2,1,2,1,2]
[6,8,7,5,2,4,1,3]=>0111010=>[2,1,1,2,2]
[5,8,7,6,4,2,3,1]=>0111101=>[2,1,1,1,2,1]
[2,3,6,1,7,5,8,4]=>0010101=>[3,2,2,1]
[2,3,6,1,8,5,4,7]=>0010110=>[3,2,1,2]
[2,4,1,6,7,5,8,3]=>0100101=>[2,3,2,1]
[2,4,1,7,3,8,6,5]=>0101011=>[2,2,2,1,1]
[2,4,5,3,7,1,8,6]=>0010101=>[3,2,2,1]
[2,4,5,7,3,8,6,1]=>0001011=>[4,2,1,1]
[2,4,6,3,1,8,5,7]=>0011010=>[3,1,2,2]
[2,4,6,3,8,5,1,7]=>0010110=>[3,2,1,2]
[2,4,6,8,3,5,1,7]=>0001010=>[4,2,2]
[2,4,7,3,1,5,8,6]=>0011001=>[3,1,3,1]
[2,4,7,3,1,8,6,5]=>0011011=>[3,1,2,1,1]
[2,4,7,8,3,5,6,1]=>0001001=>[4,3,1]
[2,5,1,6,4,8,3,7]=>0101010=>[2,2,2,2]
[2,5,1,6,7,4,8,3]=>0100101=>[2,3,2,1]
[2,5,1,7,4,3,8,6]=>0101101=>[2,2,1,2,1]
[2,5,6,3,4,8,1,7]=>0010010=>[3,3,2]
[2,5,6,3,7,4,8,1]=>0010101=>[3,2,2,1]
[2,5,6,3,8,4,1,7]=>0010110=>[3,2,1,2]
[2,5,6,7,8,4,1,3]=>0000110=>[5,1,2]
[2,5,6,8,4,3,1,7]=>0001110=>[4,1,1,2]
[2,6,1,7,4,8,5,3]=>0101011=>[2,2,2,1,1]
[1,4,2,6,3,8,5,10,7,9]=>010101010=>[2,2,2,2,2]
[6,8,4,3,2,1,7,5]=>0111101=>[2,1,1,1,2,1]
[7,6,5,2,8,4,1,3]=>1110110=>[1,1,1,2,1,2]
[7,6,3,8,2,4,1,5]=>1101010=>[1,1,2,2,2]
[5,1,2,3,4,8,7,6]=>1000011=>[1,5,1,1]
[4,1,2,3,7,6,5,8]=>1000110=>[1,4,1,2]
[7,6,5,8,2,4,3,1]=>1101011=>[1,1,2,2,1,1]
[6,8,7,4,5,2,3,1]=>0110101=>[2,1,2,2,1]
[6,8,4,7,5,2,3,1]=>0101101=>[2,2,1,2,1]
[6,8,4,7,2,5,3,1]=>0101011=>[2,2,2,1,1]
[6,4,8,7,5,2,3,1]=>1011101=>[1,2,1,1,2,1]
[6,8,4,2,7,5,3,1]=>0110111=>[2,1,2,1,1,1]
[6,8,4,7,2,1,5,3]=>0101101=>[2,2,1,2,1]
[6,8,4,7,3,5,2,1]=>0101011=>[2,2,2,1,1]
[6,4,8,2,7,5,3,1]=>1010111=>[1,2,2,1,1,1]
[6,8,4,2,7,1,5,3]=>0110101=>[2,1,2,2,1]
[6,4,2,8,7,5,3,1]=>1101111=>[1,1,2,1,1,1,1]
[6,8,4,7,3,2,5,1]=>0101101=>[2,2,1,2,1]
[6,8,4,2,1,7,5,3]=>0111011=>[2,1,1,2,1,1]
[6,8,4,7,3,2,1,5]=>0101110=>[2,2,1,1,2]
[6,8,5,7,1,4,3,2]=>0101011=>[2,2,2,1,1]
[1,8,7,3,6,2,5,4]=>0110101=>[2,1,2,2,1]
[5,8,7,2,3,6,1,4]=>0110010=>[2,1,3,2]
[6,8,2,7,5,4,1,3]=>0101110=>[2,2,1,1,2]
[6,8,3,7,5,2,1,4]=>0101110=>[2,2,1,1,2]
[6,8,1,7,3,5,4,2]=>0101011=>[2,2,2,1,1]
[6,8,4,7,3,1,5,2]=>0101101=>[2,2,1,2,1]
[6,8,1,7,3,2,5,4]=>0101101=>[2,2,1,2,1]
[3,8,2,7,6,5,1,4]=>0101110=>[2,2,1,1,2]
[1,8,4,7,6,2,5,3]=>0101101=>[2,2,1,2,1]
[3,8,1,7,6,2,5,4]=>0101101=>[2,2,1,2,1]
[1,8,4,7,3,6,5,2]=>0101011=>[2,2,2,1,1]
[4,8,5,7,1,2,6,3]=>0101001=>[2,2,3,1]
[1,8,4,7,3,2,6,5]=>0101101=>[2,2,1,2,1]
[6,8,5,2,7,4,1,3]=>0110110=>[2,1,2,1,2]
[6,8,3,4,7,1,5,2]=>0100101=>[2,3,2,1]
[6,8,1,3,7,2,5,4]=>0100101=>[2,3,2,1]
[2,8,1,3,7,6,5,4]=>0100111=>[2,3,1,1,1]
[2,8,3,4,7,6,1,5]=>0100110=>[2,3,1,2]
[6,8,5,4,2,7,1,3]=>0111010=>[2,1,1,2,2]
[6,8,1,4,3,7,5,2]=>0101011=>[2,2,2,1,1]
[6,8,1,4,2,7,5,3]=>0101011=>[2,2,2,1,1]
[6,5,4,3,8,7,1,2]=>1110110=>[1,1,1,2,1,2]
[3,1,7,2,8,5,6,4]=>1010101=>[1,2,2,2,1]
[3,1,6,7,4,8,5,2]=>1001011=>[1,3,2,1,1]
[3,1,5,7,8,4,6,2]=>1000101=>[1,4,2,1]
[8,6,5,7,1,4,3,2]=>1101011=>[1,1,2,2,1,1]
[8,6,4,2,7,5,1,3]=>1110110=>[1,1,1,2,1,2]
[6,4,8,2,7,5,1,3]=>1010110=>[1,2,2,1,2]
[8,4,7,6,2,5,1,3]=>1011010=>[1,2,1,2,2]
[3,4,5,6,8,7,1,2]=>0000110=>[5,1,2]
[3,4,5,7,8,6,1,2]=>0000110=>[5,1,2]
[3,4,5,8,7,6,1,2]=>0001110=>[4,1,1,2]
[3,4,6,7,8,5,1,2]=>0000110=>[5,1,2]
[6,4,7,3,5,2,1,8]=>1010110=>[1,2,2,1,2]
[5,4,7,3,6,2,1,8]=>1010110=>[1,2,2,1,2]
[4,8,7,3,5,2,1,6]=>0110110=>[2,1,2,1,2]
[7,5,3,6,8,2,1,4]=>1100110=>[1,1,3,1,2]
[5,8,3,6,7,2,1,4]=>0100110=>[2,3,1,2]
[5,8,7,3,2,4,1,6]=>0111010=>[2,1,1,2,2]
[6,4,7,3,2,5,1,8]=>1011010=>[1,2,1,2,2]
[6,5,3,7,2,4,1,8]=>1101010=>[1,1,2,2,2]
[7,3,8,6,2,4,1,5]=>1011010=>[1,2,1,2,2]
[6,3,7,8,2,4,1,5]=>1001010=>[1,3,2,2]
[5,3,7,6,2,4,1,8]=>1011010=>[1,2,1,2,2]
[7,5,8,2,6,4,1,3]=>1010110=>[1,2,2,1,2]
[7,4,8,2,5,6,1,3]=>1010010=>[1,2,3,2]
[5,4,7,2,6,8,1,3]=>1010010=>[1,2,3,2]
[4,8,7,2,5,6,1,3]=>0110010=>[2,1,3,2]
[5,4,3,2,6,8,1,7]=>1110010=>[1,1,1,3,2]
[4,8,3,2,5,6,1,7]=>0110010=>[2,1,3,2]
[5,3,7,2,6,4,1,8]=>1010110=>[1,2,2,1,2]
[7,5,2,6,8,4,1,3]=>1100110=>[1,1,3,1,2]
[6,4,2,7,5,8,1,3]=>1101010=>[1,1,2,2,2]
[7,5,8,4,1,2,6,3]=>1011001=>[1,2,1,3,1]
[7,1,8,2,3,6,5,4]=>1010011=>[1,2,3,1,1]
[7,3,8,4,6,2,1,5]=>1010110=>[1,2,2,1,2]
[7,1,8,4,2,6,5,3]=>1011011=>[1,2,1,2,1,1]
[7,1,8,3,6,2,5,4]=>1010101=>[1,2,2,2,1]
[7,2,3,4,5,1,8,6]=>1000101=>[1,4,2,1]
[2,8,3,4,5,1,6,7]=>0100100=>[2,3,3]
[2,7,3,4,1,5,6,8]=>0101000=>[2,2,4]
[5,3,6,1,2,7,4,8]=>1010010=>[1,2,3,2]
[10,8,6,4,2,1,3,5,7,9]=>111110000=>[1,1,1,1,1,5]
[2,8,5,3,4,6,7,1]=>0110001=>[2,1,4,1]
[6,5,4,3,7,8,9,10,1,2]=>111000010=>[1,1,1,5,2]
[3,8,1,4,5,6,7,2]=>0100001=>[2,5,1]
[4,5,3,1,2,8,7,6]=>0110011=>[2,1,3,1,1]
[5,7,3,4,1,6,8,2]=>0101001=>[2,2,3,1]
[4,5,3,1,2,6,8,7]=>0110001=>[2,1,4,1]
[3,4,1,2,5,8,7,6]=>0100011=>[2,4,1,1]
[6,5,3,2,1,8,7,4]=>1111011=>[1,1,1,1,2,1,1]
[4,5,2,1,8,7,6,3]=>0110111=>[2,1,2,1,1,1]
[3,4,1,8,7,6,5,2]=>0101111=>[2,2,1,1,1,1]
[8,1,2,4,5,6,7,3]=>1000001=>[1,6,1]
[7,1,2,3,4,6,8,5]=>1000001=>[1,6,1]
[6,1,2,3,5,8,7,4]=>1000011=>[1,5,1,1]
[5,1,2,4,8,6,7,3]=>1000101=>[1,4,2,1]
[4,1,3,8,5,6,7,2]=>1001001=>[1,3,3,1]
[7,1,2,3,5,8,6,4]=>1000011=>[1,5,1,1]
[6,1,2,3,5,7,8,4]=>1000001=>[1,6,1]
[10,1,2,3,4,6,7,8,9,5]=>100000001=>[1,8,1]
[5,1,3,8,4,6,7,2]=>1001001=>[1,3,3,1]
[4,1,3,5,8,6,7,2]=>1000101=>[1,4,2,1]
[8,6,3,5,2,7,4,1]=>1101011=>[1,1,2,2,1,1]
[7,5,2,8,6,3,4,1]=>1101101=>[1,1,2,1,2,1]
[5,2,8,6,7,3,4,1]=>1010101=>[1,2,2,2,1]
[7,5,2,3,8,6,4,1]=>1100111=>[1,1,3,1,1,1]
[5,2,3,8,6,7,4,1]=>1001011=>[1,3,2,1,1]
[8,4,1,7,3,5,6,2]=>1101001=>[1,1,2,3,1]
[7,4,1,2,6,8,5,3]=>1100011=>[1,1,4,1,1]
[5,3,8,4,1,2,6,7]=>1011000=>[1,2,1,4]
[6,3,5,8,4,1,2,7]=>1001100=>[1,3,1,3]
[7,3,5,6,8,4,1,2]=>1000110=>[1,4,1,2]
[7,4,5,1,2,8,6,3]=>1010011=>[1,2,3,1,1]
[6,3,8,4,5,1,2,7]=>1010100=>[1,2,2,3]
[8,5,1,7,4,6,2,3]=>1101010=>[1,1,2,2,2]
[7,4,5,1,8,6,2,3]=>1010110=>[1,2,2,1,2]
[8,4,5,1,7,3,6,2]=>1010101=>[1,2,2,2,1]
[4,2,7,5,8,6,3,1]=>1010111=>[1,2,2,1,1,1]
[4,2,8,5,6,3,1,7]=>1010110=>[1,2,2,1,2]
[8,6,3,1,5,7,4,2]=>1110011=>[1,1,1,3,1,1]
[7,4,2,8,5,6,3,1]=>1101011=>[1,1,2,2,1,1]
[4,2,8,5,6,7,3,1]=>1010011=>[1,2,3,1,1]
[7,4,8,5,6,1,2,3]=>1010100=>[1,2,2,3]
[7,5,8,6,1,2,3,4]=>1011000=>[1,2,1,4]
[7,3,4,8,5,6,1,2]=>1001010=>[1,3,2,2]
[7,3,4,5,8,6,1,2]=>1000110=>[1,4,1,2]
[6,4,8,5,2,3,1,7]=>1011010=>[1,2,1,2,2]
[8,6,3,1,7,5,2,4]=>1110110=>[1,1,1,2,1,2]
[7,2,8,3,4,5,6,1]=>1010001=>[1,2,4,1]
[7,4,5,2,8,6,3,1]=>1010111=>[1,2,2,1,1,1]
[8,5,2,7,4,6,3,1]=>1101011=>[1,1,2,2,1,1]
[5,2,4,8,6,7,3,1]=>1001011=>[1,3,2,1,1]
[7,5,8,6,2,3,1,4]=>1011010=>[1,2,1,2,2]
[7,4,8,5,6,2,3,1]=>1010101=>[1,2,2,2,1]
[7,3,1,8,4,5,6,2]=>1101001=>[1,1,2,3,1]
[7,2,4,5,6,8,3,1]=>1000011=>[1,5,1,1]
[3,4,5,7,6,8,1,2]=>0001010=>[4,2,2]
[4,8,2,5,1,3,7,6]=>0101001=>[2,2,3,1]
[2,1,8,7,3,4,6,5]=>1011001=>[1,2,1,3,1]
[2,7,4,5,6,8,1,3]=>0100010=>[2,4,2]
[4,1,2,8,7,5,3,6]=>1001110=>[1,3,1,1,2]
[4,1,2,6,8,3,7,5]=>1000101=>[1,4,2,1]
[3,1,7,6,8,2,4,5]=>1010100=>[1,2,2,3]
[8,2,6,3,1,5,4,7]=>1011010=>[1,2,1,2,2]
[2,1,7,8,9,10,6,5,4,3]=>100001111=>[1,5,1,1,1,1]
[7,3,5,1,8,2,4,6]=>1010100=>[1,2,2,3]
[7,8,3,1,5,2,4,6]=>0110100=>[2,1,2,3]
[9,8,7,6,1,2,3,4,5,10]=>111100000=>[1,1,1,1,6]
[1,5,6,7,8,3,4,2]=>0000101=>[5,2,1]
[1,4,6,7,8,3,5,2]=>0000101=>[5,2,1]
[1,5,6,3,7,8,4,2]=>0010011=>[3,3,1,1]
[6,1,2,3,4,8,7,5]=>1000011=>[1,5,1,1]
[5,1,2,3,8,7,6,4]=>1000111=>[1,4,1,1,1]
[5,1,2,3,8,6,7,4]=>1000101=>[1,4,2,1]
[2,8,5,3,1,4,6,7]=>0111000=>[2,1,1,4]
[2,4,3,5,7,8,1,6]=>0100010=>[2,4,2]
[2,6,3,7,8,1,4,5]=>0100100=>[2,3,3]
[3,4,6,1,7,8,5,2]=>0010011=>[3,3,1,1]
[3,4,6,1,8,5,7,2]=>0010101=>[3,2,2,1]
[3,4,8,1,5,6,7,2]=>0010001=>[3,4,1]
[3,5,1,7,4,8,6,2]=>0101011=>[2,2,2,1,1]
[3,5,6,4,8,1,7,2]=>0010101=>[3,2,2,1]
[3,5,8,4,1,6,7,2]=>0011001=>[3,1,3,1]
[3,6,1,8,5,4,7,2]=>0101101=>[2,2,1,2,1]
[3,6,7,4,8,5,1,2]=>0010110=>[3,2,1,2]
[3,6,8,4,5,1,7,2]=>0010101=>[3,2,2,1]
[4,1,5,6,8,3,7,2]=>1000101=>[1,4,2,1]
[4,1,5,7,8,6,3,2]=>1000111=>[1,4,1,1,1]
[4,1,7,3,5,8,6,2]=>1010011=>[1,2,3,1,1]
[4,1,7,8,5,6,3,2]=>1001011=>[1,3,2,1,1]
[4,5,7,3,8,6,1,2]=>0010110=>[3,2,1,2]
[4,5,7,8,1,6,3,2]=>0001011=>[4,2,1,1]
[4,5,8,3,1,6,7,2]=>0011001=>[3,1,3,1]
[4,6,3,1,8,5,7,2]=>0110101=>[2,1,2,2,1]
[4,6,7,3,5,8,1,2]=>0010010=>[3,3,2]
[4,6,7,8,5,1,3,2]=>0001101=>[4,1,2,1]
[4,6,8,3,5,1,7,2]=>0010101=>[3,2,2,1]
[4,7,3,1,8,6,5,2]=>0110111=>[2,1,2,1,1,1]
[4,7,8,3,5,6,1,2]=>0010010=>[3,3,2]
[5,1,6,7,4,8,3,2]=>1001011=>[1,3,2,1,1]
[5,1,6,7,8,3,4,2]=>1000101=>[1,4,2,1]
[5,6,3,4,8,1,7,2]=>0100101=>[2,3,2,1]
[5,6,7,8,4,1,3,2]=>0001101=>[4,1,2,1]
[5,7,3,4,1,8,6,2]=>0101011=>[2,2,2,1,1]
[5,7,3,4,8,6,1,2]=>0100110=>[2,3,1,2]
[5,7,3,8,4,6,1,2]=>0101010=>[2,2,2,2]
[5,7,8,4,3,6,1,2]=>0011010=>[3,1,2,2]
[6,1,3,7,8,5,4,2]=>1000111=>[1,4,1,1,1]
[6,1,7,4,5,8,3,2]=>1010011=>[1,2,3,1,1]
[6,1,8,4,5,3,7,2]=>1010101=>[1,2,2,2,1]
[6,7,3,8,5,4,1,2]=>0101110=>[2,2,1,1,2]
[7,1,3,4,8,6,5,2]=>1000111=>[1,4,1,1,1]
[8,4,1,3,2,5,6,7]=>1101000=>[1,1,2,4]
[8,5,1,2,4,3,6,7]=>1100100=>[1,1,3,3]
[8,6,1,2,3,5,4,7]=>1100010=>[1,1,4,2]
[8,7,1,2,3,4,6,5]=>1100001=>[1,1,5,1]
[8,5,1,4,2,3,6,7]=>1101000=>[1,1,2,4]
[8,6,1,2,5,3,4,7]=>1100100=>[1,1,3,3]
[8,7,1,2,3,6,4,5]=>1100010=>[1,1,4,2]
[8,6,1,2,5,4,3,7]=>1100110=>[1,1,3,1,2]
[2,5,8,6,1,7,3,4]=>0011010=>[3,1,2,2]
[4,5,6,8,7,2,1,3]=>0001110=>[4,1,1,2]
[5,6,8,7,2,3,1,4]=>0011010=>[3,1,2,2]
[4,5,7,6,2,8,1,3]=>0011010=>[3,1,2,2]
[4,8,2,5,6,1,3,7]=>0100100=>[2,3,3]
[5,2,3,6,7,8,1,4]=>1000010=>[1,5,2]
[4,2,8,7,5,3,1,6]=>1011110=>[1,2,1,1,1,2]
[4,2,8,6,7,5,3,1]=>1010111=>[1,2,2,1,1,1]
[1,3,2,4,8,5,7,6]=>0100101=>[2,3,2,1]
[1,6,3,2,5,7,8,4]=>0110001=>[2,1,4,1]
[2,5,6,1,8,7,3,4]=>0010110=>[3,2,1,2]
[7,6,2,1,4,8,3,5]=>1110010=>[1,1,1,3,2]
[2,6,5,1,8,7,3,4]=>0110110=>[2,1,2,1,2]
[2,7,3,1,8,4,5,6]=>0110100=>[2,1,2,3]
[1,4,2,7,3,8,6,5]=>0101011=>[2,2,2,1,1]
[1,2,7,3,8,6,5,4]=>0010111=>[3,2,1,1,1]
[3,1,8,4,6,2,7,5]=>1010101=>[1,2,2,2,1]
[3,4,5,1,8,2,7,6]=>0010101=>[3,2,2,1]
[3,8,1,6,5,2,7,4]=>0101101=>[2,2,1,2,1]
[1,5,2,3,8,7,4,6]=>0100110=>[2,3,1,2]
[2,8,7,6,3,1,4,5]=>0111100=>[2,1,1,1,3]
[8,7,2,5,3,1,4,6]=>1101100=>[1,1,2,1,3]
[7,6,2,3,4,8,1,5]=>1100010=>[1,1,4,2]
[8,7,6,2,1,4,3,5]=>1111010=>[1,1,1,1,2,2]
[8,2,7,4,1,5,3,6]=>1011010=>[1,2,1,2,2]
[1,7,3,2,4,5,8,6]=>0110001=>[2,1,4,1]
[1,3,8,6,2,4,7,5]=>0011001=>[3,1,3,1]
[1,2,3,8,4,7,6,5]=>0001011=>[4,2,1,1]
[1,6,2,3,7,5,8,4]=>0100101=>[2,3,2,1]
[4,5,1,2,8,3,7,6]=>0100101=>[2,3,2,1]
[1,4,8,2,6,3,7,5]=>0010101=>[3,2,2,1]
[8,4,1,7,3,2,5,6]=>1101100=>[1,1,2,1,3]
[1,8,7,3,2,4,6,5]=>0111001=>[2,1,1,3,1]
[8,3,1,5,6,2,7,4]=>1100101=>[1,1,3,2,1]
[3,4,1,6,5,7,2,8]=>0101010=>[2,2,2,2]
[3,5,1,6,2,8,7,4]=>0101011=>[2,2,2,1,1]
[5,4,3,6,1,7,2,8]=>1101010=>[1,1,2,2,2]
[4,8,7,2,1,6,5,3]=>0111011=>[2,1,1,2,1,1]
[6,2,1,8,7,5,4,3]=>1101111=>[1,1,2,1,1,1,1]
[7,5,8,6,3,2,4,1]=>1011101=>[1,2,1,1,2,1]
[5,8,7,6,3,2,4,1]=>0111101=>[2,1,1,1,2,1]
[5,4,7,2,8,1,6,3]=>1010101=>[1,2,2,2,1]
[8,1,5,4,6,3,7,2]=>1010101=>[1,2,2,2,1]
[2,1,5,8,3,7,4,6]=>1001010=>[1,3,2,2]
[2,1,7,4,8,3,6,5]=>1010101=>[1,2,2,2,1]
[1,2,3,5,8,7,4,6]=>0000110=>[5,1,2]
[6,1,2,7,8,4,3,5]=>1000110=>[1,4,1,2]
[5,1,4,8,2,7,3,6]=>1001010=>[1,3,2,2]
[3,4,1,2,8,7,5,6]=>0100110=>[2,3,1,2]
[1,2,5,7,8,6,3,4]=>0000110=>[5,1,2]
[2,1,3,4,8,5,7,6]=>1000101=>[1,4,2,1]
[6,2,5,1,7,3,8,4]=>1010101=>[1,2,2,2,1]
[1,5,4,8,6,2,7,3]=>0101101=>[2,2,1,2,1]
[2,5,1,8,6,3,7,4]=>0101101=>[2,2,1,2,1]
[2,1,3,7,4,8,6,5]=>1001011=>[1,3,2,1,1]
[4,2,5,8,1,7,3,6]=>1001010=>[1,3,2,2]
[2,6,8,5,1,7,3,4]=>0011010=>[3,1,2,2]
[1,3,2,7,8,5,4,6]=>0100110=>[2,3,1,2]
[7,1,2,3,6,8,4,5]=>1000010=>[1,5,2]
[5,1,2,3,8,4,7,6]=>1000101=>[1,4,2,1]
[3,4,5,1,8,7,2,6]=>0010110=>[3,2,1,2]
[4,1,2,3,8,7,5,6]=>1000110=>[1,4,1,2]
[2,3,1,8,5,4,7,6]=>0101101=>[2,2,1,2,1]
[2,3,8,4,1,5,7,6]=>0011001=>[3,1,3,1]
[5,3,1,8,7,2,4,6]=>1101100=>[1,1,2,1,3]
[3,6,1,8,7,2,4,5]=>0101100=>[2,2,1,3]
[1,3,8,4,2,7,6,5]=>0011011=>[3,1,2,1,1]
[1,2,3,8,5,7,4,6]=>0001010=>[4,2,2]
[6,1,7,2,5,8,3,4]=>1010010=>[1,2,3,2]
[4,5,1,8,7,2,3,6]=>0101100=>[2,2,1,3]
[1,4,2,8,5,3,7,6]=>0101101=>[2,2,1,2,1]
[3,1,5,2,8,6,7,4]=>1010101=>[1,2,2,2,1]
[7,8,6,5,2,1,4,3]=>0111101=>[2,1,1,1,2,1]
[8,6,7,5,2,1,4,3]=>1011101=>[1,2,1,1,2,1]
[6,7,8,2,1,5,4,3]=>0011011=>[3,1,2,1,1]
[8,7,5,6,2,1,4,3]=>1101101=>[1,1,2,1,2,1]
[3,2,8,5,6,7,1,4]=>1010010=>[1,2,3,2]
[4,2,5,1,8,7,3,6]=>1010110=>[1,2,2,1,2]
[5,2,7,8,6,3,1,4]=>1001110=>[1,3,1,1,2]
[4,2,6,1,5,8,3,7]=>1010010=>[1,2,3,2]
[7,2,4,5,8,3,6,1]=>1000101=>[1,4,2,1]
[2,4,7,8,6,1,5,3]=>0001101=>[4,1,2,1]
[4,2,7,1,5,6,8,3]=>1010001=>[1,2,4,1]
[3,2,5,8,1,6,7,4]=>1001001=>[1,3,3,1]
[8,1,4,3,2,5,6,7]=>1011000=>[1,2,1,4]
[1,7,3,2,4,5,6,8]=>0110000=>[2,1,5]
[1,6,3,2,4,5,7,8]=>0110000=>[2,1,5]
[1,3,8,4,2,5,6,7]=>0011000=>[3,1,4]
[6,2,5,1,8,3,4,7]=>1010100=>[1,2,2,3]
[5,1,8,2,4,3,6,7]=>1010100=>[1,2,2,3]
[8,2,3,1,5,6,7,4]=>1010001=>[1,2,4,1]
[1,7,2,4,5,8,6,3]=>0100011=>[2,4,1,1]
[1,5,7,8,4,6,2,3]=>0001010=>[4,2,2]
[6,5,8,3,4,2,1,7]=>1010110=>[1,2,2,1,2]
[6,5,8,2,3,4,1,7]=>1010010=>[1,2,3,2]
[3,2,5,4,7,6,9,8,1,10]=>101010110=>[1,2,2,2,1,2]
[1,4,3,6,5,8,7,10,9,2]=>010101011=>[2,2,2,2,1,1]
[4,2,1,3,5,8,6,7]=>1100010=>[1,1,4,2]
[1,3,8,2,6,4,5,7]=>0010100=>[3,2,3]
[6,1,2,7,4,3,8,5]=>1001101=>[1,3,1,2,1]
[5,4,1,2,3,8,6,7]=>1100010=>[1,1,4,2]
[7,6,8,5,2,4,1,3]=>1011010=>[1,2,1,2,2]
[6,7,8,5,2,4,1,3]=>0011010=>[3,1,2,2]
[3,4,5,8,2,1,7,6]=>0001101=>[4,1,2,1]
[3,4,6,2,7,1,5,8]=>0010100=>[3,2,3]
[3,4,6,2,8,1,7,5]=>0010101=>[3,2,2,1]
[3,4,6,8,1,5,7,2]=>0001001=>[4,3,1]
[3,4,6,1,5,2,7,8]=>0010100=>[3,2,3]
[3,4,7,2,1,6,5,8]=>0011010=>[3,1,2,2]
[3,4,7,1,5,6,2,8]=>0010010=>[3,3,2]
[3,5,2,6,1,4,7,8]=>0101000=>[2,2,4]
[3,5,2,7,1,6,4,8]=>0101010=>[2,2,2,2]
[3,5,6,4,8,2,1,7]=>0010110=>[3,2,1,2]
[3,5,6,4,1,2,7,8]=>0011000=>[3,1,4]
[3,5,6,8,4,2,1,7]=>0001110=>[4,1,1,2]
[3,5,6,8,1,2,7,4]=>0001001=>[4,3,1]
[3,5,6,1,4,2,7,8]=>0010100=>[3,2,3]
[3,5,7,4,2,8,1,6]=>0011010=>[3,1,2,2]
[3,5,7,4,2,1,6,8]=>0011100=>[3,1,1,3]
[3,5,7,4,8,1,6,2]=>0010101=>[3,2,2,1]
[3,5,7,8,1,6,2,4]=>0001010=>[4,2,2]
[3,5,7,1,4,6,2,8]=>0010010=>[3,3,2]
[3,5,8,4,2,6,1,7]=>0011010=>[3,1,2,2]
[3,5,8,1,4,6,7,2]=>0010001=>[3,4,1]
[3,6,2,4,8,1,7,5]=>0100101=>[2,3,2,1]
[3,6,2,7,8,5,1,4]=>0100110=>[2,3,1,2]
[3,6,2,7,8,1,4,5]=>0100100=>[2,3,3]
[3,6,2,1,5,4,7,8]=>0110100=>[2,1,2,3]
[3,6,7,8,5,1,2,4]=>0001100=>[4,1,3]
[3,6,7,8,1,5,2,4]=>0001010=>[4,2,2]
[3,7,2,4,5,8,1,6]=>0100010=>[2,4,2]
[3,7,2,4,8,1,6,5]=>0100101=>[2,3,2,1]
[3,7,2,4,1,6,5,8]=>0101010=>[2,2,2,2]
[3,7,2,8,5,6,1,4]=>0101010=>[2,2,2,2]
[3,7,8,4,5,1,6,2]=>0010101=>[3,2,2,1]
[3,7,8,4,1,6,5,2]=>0011011=>[3,1,2,1,1]
[3,8,2,4,1,6,7,5]=>0101001=>[2,2,3,1]
[3,8,2,1,5,6,7,4]=>0110001=>[2,1,4,1]
[8,1,5,4,3,6,7,2]=>1011001=>[1,2,1,3,1]
[8,1,4,5,3,6,7,2]=>1001001=>[1,3,3,1]
[4,1,6,3,5,7,8,2]=>1010001=>[1,2,4,1]
[4,1,7,3,5,6,8,2]=>1010001=>[1,2,4,1]
[4,1,3,6,7,8,5,2]=>1000011=>[1,5,1,1]
[4,6,2,3,5,1,7,8]=>0100100=>[2,3,3]
[3,5,2,4,1,6,7,8]=>0101000=>[2,2,4]
[5,8,2,3,4,6,1,7]=>0100010=>[2,4,2]
[4,7,2,3,5,1,6,8]=>0100100=>[2,3,3]
[5,7,2,3,4,6,8,1]=>0100001=>[2,5,1]
[4,6,2,3,5,7,1,8]=>0100010=>[2,4,2]
[2,3,7,8,1,6,5,4]=>0001011=>[4,2,1,1]
[2,7,6,1,4,8,3,5]=>0110010=>[2,1,3,2]
[2,6,8,1,4,5,7,3]=>0010001=>[3,4,1]
[2,6,5,8,1,3,7,4]=>0101001=>[2,2,3,1]
[6,4,7,5,8,2,3,1]=>1010101=>[1,2,2,2,1]
[6,7,4,1,8,2,3,5]=>0110100=>[2,1,2,3]
[6,7,8,1,4,2,5,3]=>0010101=>[3,2,2,1]
[5,2,6,1,4,8,3,7]=>1010010=>[1,2,3,2]
[7,2,3,5,8,1,4,6]=>1000100=>[1,4,3]
[2,4,7,5,8,1,3,6]=>0010100=>[3,2,3]
[2,3,6,5,1,8,7,4]=>0011011=>[3,1,2,1,1]
[2,3,4,8,1,5,7,6]=>0001001=>[4,3,1]
[2,3,4,7,8,1,6,5]=>0000101=>[5,2,1]
[2,7,8,5,1,4,6,3]=>0011001=>[3,1,3,1]
[2,3,7,5,8,1,4,6]=>0010100=>[3,2,3]
[2,3,6,8,5,1,7,4]=>0001101=>[4,1,2,1]
[7,6,4,5,1,8,2,3]=>1101010=>[1,1,2,2,2]
[7,4,6,8,1,5,2,3]=>1001010=>[1,3,2,2]
[2,7,4,6,5,8,3,1]=>0101011=>[2,2,2,1,1]
[2,6,7,8,5,3,1,4]=>0001110=>[4,1,1,2]
[2,5,6,1,4,8,3,7]=>0010010=>[3,3,2]
[2,6,4,8,5,7,3,1]=>0101011=>[2,2,2,1,1]
[2,5,8,1,4,6,7,3]=>0010001=>[3,4,1]
[7,2,3,4,8,1,6,5]=>1000101=>[1,4,2,1]
[3,2,5,7,8,1,6,4]=>1000101=>[1,4,2,1]
[6,4,1,7,8,2,3,5]=>1100100=>[1,1,3,3]
[5,7,1,6,2,8,4,3]=>0101011=>[2,2,2,1,1]
[5,6,1,8,2,3,7,4]=>0101001=>[2,2,3,1]
[7,3,5,1,6,8,4,2]=>1010011=>[1,2,3,1,1]
[6,3,4,5,8,2,1,7]=>1000110=>[1,4,1,2]
[5,7,6,1,2,8,3,4]=>0110010=>[2,1,3,2]
[5,6,8,1,2,4,7,3]=>0010001=>[3,4,1]
[6,2,3,4,5,8,1,7]=>1000010=>[1,5,2]
[4,7,1,3,8,2,6,5]=>0100101=>[2,3,2,1]
[5,4,1,6,7,8,2,3]=>1100010=>[1,1,4,2]
[7,4,1,5,8,2,6,3]=>1100101=>[1,1,3,2,1]
[5,7,1,8,6,2,3,4]=>0101100=>[2,2,1,3]
[7,3,5,1,8,2,6,4]=>1010101=>[1,2,2,2,1]
[4,8,1,3,5,6,7,2]=>0100001=>[2,5,1]
[8,1,2,3,7,5,6,4]=>1000101=>[1,4,2,1]
[2,1,8,3,7,5,6,4]=>1010101=>[1,2,2,2,1]
[5,6,7,3,8,2,1,4]=>0010110=>[3,2,1,2]
[5,6,8,3,1,2,7,4]=>0011001=>[3,1,3,1]
[5,7,3,2,8,6,1,4]=>0110110=>[2,1,2,1,2]
[5,7,8,3,1,6,2,4]=>0011010=>[3,1,2,2]
[5,8,3,2,1,6,7,4]=>0111001=>[2,1,1,3,1]
[6,2,7,3,8,5,1,4]=>1010110=>[1,2,2,1,2]
[6,2,3,7,8,5,1,4]=>1000110=>[1,4,1,2]
[6,7,3,2,8,5,1,4]=>0110110=>[2,1,2,1,2]
[6,7,8,3,5,1,2,4]=>0010100=>[3,2,3]
[1,5,6,7,8,3,2,4]=>0000110=>[5,1,2]
[1,5,8,3,2,6,7,4]=>0011001=>[3,1,3,1]
[1,6,8,3,5,2,7,4]=>0010101=>[3,2,2,1]
[1,7,3,2,8,6,5,4]=>0110111=>[2,1,2,1,1,1]
[1,7,8,3,5,6,2,4]=>0010010=>[3,3,2]
[1,6,7,8,4,2,3,5]=>0001100=>[4,1,3]
[1,2,6,8,4,3,7,5]=>0001101=>[4,1,2,1]
[1,8,3,4,2,6,7,5]=>0101001=>[2,2,3,1]
[1,2,8,4,3,6,7,5]=>0011001=>[3,1,3,1]
[6,2,7,8,4,1,3,5]=>1001100=>[1,3,1,3]
[6,2,3,7,8,1,4,5]=>1000100=>[1,4,3]
[4,5,7,1,8,6,2,3]=>0010110=>[3,2,1,2]
[4,5,7,8,2,6,1,3]=>0001010=>[4,2,2]
[4,6,2,8,5,1,7,3]=>0101101=>[2,2,1,2,1]
[4,6,7,1,8,5,2,3]=>0010110=>[3,2,1,2]
[4,7,2,8,5,6,1,3]=>0101010=>[2,2,2,2]
[4,8,2,1,5,6,7,3]=>0110001=>[2,1,4,1]
[1,2,8,4,5,3,7,6]=>0010101=>[3,2,2,1]
[1,2,3,8,5,4,7,6]=>0001101=>[4,1,2,1]
[1,7,3,8,5,4,2,6]=>0101110=>[2,2,1,1,2]
[5,2,7,4,8,6,1,3]=>1010110=>[1,2,2,1,2]
[5,2,7,8,4,6,1,3]=>1001010=>[1,3,2,2]
[7,2,3,8,5,4,1,6]=>1001110=>[1,3,1,1,2]
[5,6,2,7,8,1,4,3]=>0100101=>[2,3,2,1]
[5,8,2,4,1,6,7,3]=>0101001=>[2,2,3,1]
[6,2,1,7,8,5,4,3]=>1100111=>[1,1,3,1,1,1]
[6,7,2,4,8,5,1,3]=>0100110=>[2,3,1,2]
[6,7,2,8,5,4,1,3]=>0101110=>[2,2,1,1,2]
[6,8,2,4,5,1,7,3]=>0100101=>[2,3,2,1]
[3,2,5,6,8,1,4,7]=>1000100=>[1,4,3]
[8,1,2,3,7,5,4,6]=>1000110=>[1,4,1,2]
[4,1,8,2,7,5,3,6]=>1010110=>[1,2,2,1,2]
[7,1,8,3,4,5,2,6]=>1010010=>[1,2,3,2]
[7,1,6,3,8,2,4,5]=>1010100=>[1,2,2,3]
[6,1,5,8,2,3,4,7]=>1001000=>[1,3,4]
[8,1,6,7,4,2,3,5]=>1001100=>[1,3,1,3]
[6,1,5,8,2,3,7,4]=>1001001=>[1,3,3,1]
[4,1,7,2,5,8,3,6]=>1010010=>[1,2,3,2]
[8,1,6,3,4,7,2,5]=>1010010=>[1,2,3,2]
[7,1,6,8,2,5,3,4]=>1001010=>[1,3,2,2]
[4,1,8,2,5,6,3,7]=>1010010=>[1,2,3,2]
[4,1,8,2,5,6,7,3]=>1010001=>[1,2,4,1]
[3,8,1,2,7,5,4,6]=>0100110=>[2,3,1,2]
[3,8,1,7,4,5,2,6]=>0101010=>[2,2,2,2]
[5,4,7,1,2,8,3,6]=>1010010=>[1,2,3,2]
[8,4,7,1,3,2,6,5]=>1010101=>[1,2,2,2,1]
[8,5,7,3,1,2,6,4]=>1011001=>[1,2,1,3,1]
[3,8,1,2,4,5,7,6]=>0100001=>[2,5,1]
[7,6,2,1,8,4,3,5]=>1110110=>[1,1,1,2,1,2]
[8,5,2,3,6,1,4,7]=>1100100=>[1,1,3,3]
[8,5,7,1,4,3,2,6]=>1010110=>[1,2,2,1,2]
[3,6,1,4,2,8,5,7]=>0101010=>[2,2,2,2]
[7,6,8,1,4,5,2,3]=>1010010=>[1,2,3,2]
[3,7,1,4,2,8,6,5]=>0101011=>[2,2,2,1,1]
[5,4,3,8,2,1,7,6]=>1101101=>[1,1,2,1,2,1]
[5,8,7,3,2,1,6,4]=>0111101=>[2,1,1,1,2,1]
[2,3,7,1,6,8,5,4]=>0010011=>[3,3,1,1]
[2,6,1,5,7,4,8,3]=>0100101=>[2,3,2,1]
[2,3,6,1,8,4,7,5]=>0010101=>[3,2,2,1]
[3,5,1,4,6,7,8,2]=>0100001=>[2,5,1]
[4,5,6,2,1,7,8,3]=>0011001=>[3,1,3,1]
[5,2,4,7,6,3,8,1]=>1001101=>[1,3,1,2,1]
[8,7,6,1,4,3,5,2]=>1110101=>[1,1,1,2,2,1]
[8,7,6,1,3,4,5,2]=>1110001=>[1,1,1,4,1]
[8,7,1,4,5,6,3,2]=>1100011=>[1,1,4,1,1]
[8,1,5,6,7,4,3,2]=>1000111=>[1,4,1,1,1]
[5,8,3,4,1,6,2,7]=>0101010=>[2,2,2,2]
[4,2,6,1,7,8,5,3]=>1010011=>[1,2,3,1,1]
[1,5,2,6,7,8,4,3]=>0100011=>[2,4,1,1]
[4,5,2,7,8,6,1,3]=>0100110=>[2,3,1,2]
[1,5,6,7,4,8,2,3]=>0001010=>[4,2,2]
[4,2,6,8,5,1,7,3]=>1001101=>[1,3,1,2,1]
[4,2,7,8,5,6,1,3]=>1001010=>[1,3,2,2]
[3,5,2,7,4,6,8,1]=>0101001=>[2,2,3,1]
[5,6,2,7,3,8,4,1]=>0101011=>[2,2,2,1,1]
[3,5,2,8,4,6,7,1]=>0101001=>[2,2,3,1]
[3,7,2,8,4,1,5,6]=>0101100=>[2,2,1,3]
[3,5,2,4,7,8,6,1]=>0100011=>[2,4,1,1]
[3,7,1,5,8,2,4,6]=>0100100=>[2,3,3]
[5,1,3,8,2,4,6,7]=>1001000=>[1,3,4]
[4,2,1,3,8,5,6,7]=>1100100=>[1,1,3,3]
[1,8,7,6,3,4,5,2]=>0111001=>[2,1,1,3,1]
[8,5,7,6,3,1,4,2]=>1011101=>[1,2,1,1,2,1]
[8,5,7,6,3,2,1,4]=>1011110=>[1,2,1,1,1,2]
[8,7,5,3,1,6,4,2]=>1111011=>[1,1,1,1,2,1,1]
[4,2,8,3,1,6,7,5]=>1011001=>[1,2,1,3,1]
[7,8,1,4,5,6,3,2]=>0100011=>[2,4,1,1]
[4,2,8,3,5,1,7,6]=>1010101=>[1,2,2,2,1]
[4,2,7,8,1,6,5,3]=>1001011=>[1,3,2,1,1]
[6,8,1,4,5,3,7,2]=>0100101=>[2,3,2,1]
[5,1,3,4,2,6,7,8]=>1001000=>[1,3,4]
[4,2,7,3,1,6,5,8]=>1011010=>[1,2,1,2,2]
[2,3,4,5,8,1,7,6]=>0000101=>[5,2,1]
[4,1,5,3,6,7,8,2]=>1010001=>[1,2,4,1]
[2,3,4,8,1,6,7,5]=>0001001=>[4,3,1]
[5,1,4,6,3,7,8,2]=>1001001=>[1,3,3,1]
[5,1,6,3,4,7,8,2]=>1010001=>[1,2,4,1]
[2,1,7,5,3,8,6,4]=>1011011=>[1,2,1,2,1,1]
[2,1,8,7,5,3,6,4]=>1011101=>[1,2,1,1,2,1]
[7,5,3,2,1,8,6,4]=>1111011=>[1,1,1,1,2,1,1]
[5,2,3,4,1,8,6,7]=>1001010=>[1,3,2,2]
[3,8,1,2,5,4,7,6]=>0100101=>[2,3,2,1]
[7,4,6,8,5,3,2,1]=>1001111=>[1,3,1,1,1,1]
[7,5,8,6,3,2,1,4]=>1011110=>[1,2,1,1,1,2]
[7,4,8,5,6,3,2,1]=>1010111=>[1,2,2,1,1,1]
[7,5,8,6,4,2,1,3]=>1011110=>[1,2,1,1,1,2]
[6,4,2,1,8,5,3,7]=>1110110=>[1,1,1,2,1,2]
[5,3,8,7,4,2,1,6]=>1011110=>[1,2,1,1,1,2]
[7,4,2,1,6,8,5,3]=>1110011=>[1,1,1,3,1,1]
[5,3,8,4,2,1,6,7]=>1011100=>[1,2,1,1,3]
[8,6,3,5,7,4,2,1]=>1100111=>[1,1,3,1,1,1]
[6,3,5,8,4,2,1,7]=>1001110=>[1,3,1,1,2]
[6,4,8,7,5,2,1,3]=>1011110=>[1,2,1,1,1,2]
[7,5,2,1,3,8,6,4]=>1110011=>[1,1,1,3,1,1]
[6,3,8,7,4,5,2,1]=>1011011=>[1,2,1,2,1,1]
[7,4,5,2,1,8,6,3]=>1011011=>[1,2,1,2,1,1]
[8,5,2,1,7,4,6,3]=>1110101=>[1,1,1,2,2,1]
[6,3,8,4,5,2,1,7]=>1010110=>[1,2,2,1,2]
[7,3,6,8,4,5,2,1]=>1001011=>[1,3,2,1,1]
[7,3,4,5,8,6,2,1]=>1000111=>[1,4,1,1,1]
[7,3,8,4,5,6,2,1]=>1010011=>[1,2,3,1,1]
[1,8,7,2,6,5,4,3]=>0110111=>[2,1,2,1,1,1]
[1,8,7,6,2,3,4,5]=>0111000=>[2,1,1,4]
[1,8,2,5,7,6,4,3]=>0100111=>[2,3,1,1,1]
[1,8,2,5,6,7,4,3]=>0100011=>[2,4,1,1]
[1,2,8,3,4,5,7,6]=>0010001=>[3,4,1]
[7,6,1,2,3,8,4,5]=>1100010=>[1,1,4,2]
[1,6,2,3,4,8,7,5]=>0100011=>[2,4,1,1]
[6,4,1,2,8,3,5,7]=>1100100=>[1,1,3,3]
[4,8,1,2,3,7,5,6]=>0100010=>[2,4,2]
[6,4,1,7,2,3,8,5]=>1101001=>[1,1,2,3,1]
[7,1,6,2,3,8,4,5]=>1010010=>[1,2,3,2]
[6,5,1,2,3,8,4,7]=>1100010=>[1,1,4,2]
[1,8,5,2,3,7,4,6]=>0110010=>[2,1,3,2]
[6,5,1,2,7,3,8,4]=>1100101=>[1,1,3,2,1]
[7,6,4,1,8,2,3,5]=>1110100=>[1,1,1,2,3]
[1,5,2,3,6,8,7,4]=>0100011=>[2,4,1,1]
[7,3,1,2,8,4,5,6]=>1100100=>[1,1,3,3]
[7,6,3,1,8,2,4,5]=>1110100=>[1,1,1,2,3]
[5,3,6,1,2,4,8,7]=>1010001=>[1,2,4,1]
[5,8,3,1,7,2,4,6]=>0110100=>[2,1,2,3]
[7,5,4,1,8,2,3,6]=>1110100=>[1,1,1,2,3]
[7,6,1,4,8,2,3,5]=>1100100=>[1,1,3,3]
[1,2,8,5,3,7,4,6]=>0011010=>[3,1,2,2]
[1,2,7,3,8,6,4,5]=>0010110=>[3,2,1,2]
[7,5,1,6,8,2,3,4]=>1100100=>[1,1,3,3]
[4,1,2,8,6,3,7,5]=>1001101=>[1,3,1,2,1]
[6,3,4,1,7,2,8,5]=>1010101=>[1,2,2,2,1]
[6,5,3,1,8,2,4,7]=>1110100=>[1,1,1,2,3]
[3,8,1,6,7,2,4,5]=>0100100=>[2,3,3]
[6,5,3,7,1,2,8,4]=>1101001=>[1,1,2,3,1]
[7,1,4,2,8,5,3,6]=>1010110=>[1,2,2,1,2]
[1,2,6,8,3,5,4,7]=>0001010=>[4,2,2]
[1,2,3,7,8,6,4,5]=>0000110=>[5,1,2]
[1,6,8,5,2,7,3,4]=>0011010=>[3,1,2,2]
[7,6,3,4,1,8,2,5]=>1101010=>[1,1,2,2,2]
[1,4,8,2,3,7,6,5]=>0010011=>[3,3,1,1]
[1,2,8,3,5,7,6,4]=>0010011=>[3,3,1,1]
[4,5,1,7,6,8,2,3]=>0101010=>[2,2,2,2]
[3,4,8,1,2,6,7,5]=>0010001=>[3,4,1]
[3,1,8,2,5,6,7,4]=>1010001=>[1,2,4,1]
[1,4,2,5,6,8,7,3]=>0100011=>[2,4,1,1]
[4,5,6,3,7,1,8,2]=>0010101=>[3,2,2,1]
[4,2,5,6,7,8,3,1]=>1000011=>[1,5,1,1]
[8,2,7,3,1,5,6,4]=>1011001=>[1,2,1,3,1]
[7,2,1,8,4,5,6,3]=>1101001=>[1,1,2,3,1]
[4,2,7,1,3,8,6,5]=>1010011=>[1,2,3,1,1]
[8,2,6,3,4,7,1,5]=>1010010=>[1,2,3,2]
[7,2,3,4,1,8,6,5]=>1001011=>[1,3,2,1,1]
[6,1,8,2,7,5,3,4]=>1010110=>[1,2,2,1,2]
[4,2,8,1,5,6,3,7]=>1010010=>[1,2,3,2]
[8,2,7,3,1,4,5,6]=>1011000=>[1,2,1,4]
[5,2,1,3,6,7,8,4]=>1100001=>[1,1,5,1]
[6,4,8,7,3,2,1,5]=>1011110=>[1,2,1,1,1,2]
[6,5,3,8,7,2,1,4]=>1101110=>[1,1,2,1,1,2]
[5,4,8,7,3,2,1,6]=>1011110=>[1,2,1,1,1,2]
[6,4,3,8,7,2,1,5]=>1101110=>[1,1,2,1,1,2]
[6,3,8,7,5,2,1,4]=>1011110=>[1,2,1,1,1,2]
[5,6,8,1,4,2,7,3]=>0010101=>[3,2,2,1]
[5,6,3,1,4,2,7,8]=>0110100=>[2,1,2,3]
[5,7,3,8,4,1,6,2]=>0101101=>[2,2,1,2,1]
[5,7,3,1,4,6,2,8]=>0110010=>[2,1,3,2]
[5,7,3,4,8,1,6,2]=>0100101=>[2,3,2,1]
[5,2,6,1,4,3,7,8]=>1010100=>[1,2,2,3]
[5,8,3,1,4,6,7,2]=>0110001=>[2,1,4,1]
[6,2,7,4,1,5,3,8]=>1011010=>[1,2,1,2,2]
[6,7,3,8,1,5,2,4]=>0101010=>[2,2,2,2]
[6,7,3,4,1,5,2,8]=>0101010=>[2,2,2,2]
[6,7,8,1,5,4,2,3]=>0010110=>[3,2,1,2]
[4,5,6,7,1,3,2,8]=>0001010=>[4,2,2]
[6,7,1,4,5,3,2,8]=>0100110=>[2,3,1,2]
[4,5,7,8,2,1,6,3]=>0001101=>[4,1,2,1]
[7,2,3,8,1,6,5,4]=>1001011=>[1,3,2,1,1]
[7,2,3,8,5,1,6,4]=>1001101=>[1,3,1,2,1]
[7,2,3,1,5,6,4,8]=>1010010=>[1,2,3,2]
[7,2,8,4,1,6,5,3]=>1011011=>[1,2,1,2,1,1]
[7,2,8,4,5,1,6,3]=>1010101=>[1,2,2,2,1]
[4,6,3,8,1,5,7,2]=>0101001=>[2,2,3,1]
[7,8,3,4,1,6,5,2]=>0101011=>[2,2,2,1,1]
[4,6,7,3,8,1,2,5]=>0010100=>[3,2,3]
[4,6,7,8,1,5,3,2]=>0001011=>[4,2,1,1]
[4,6,7,1,5,2,3,8]=>0010100=>[3,2,3]
[4,6,8,3,1,5,7,2]=>0011001=>[3,1,3,1]
[4,6,1,3,5,2,7,8]=>0100100=>[2,3,3]
[4,7,3,8,5,1,6,2]=>0101101=>[2,2,1,2,1]
[4,7,3,8,1,6,5,2]=>0101011=>[2,2,2,1,1]
[1,7,2,3,4,6,8,5]=>0100001=>[2,5,1]
[8,1,2,3,5,6,4,7]=>1000010=>[1,5,2]
[4,1,8,2,7,3,5,6]=>1010100=>[1,2,2,3]
[1,8,4,2,7,3,5,6]=>0110100=>[2,1,2,3]
[7,4,1,2,6,8,3,5]=>1100010=>[1,1,4,2]
[8,7,1,2,4,5,3,6]=>1100010=>[1,1,4,2]
[4,1,8,2,3,5,7,6]=>1010001=>[1,2,4,1]
[6,1,2,8,3,4,7,5]=>1001001=>[1,3,3,1]
[5,4,1,2,7,8,3,6]=>1100010=>[1,1,4,2]
[1,5,2,8,3,4,7,6]=>0101001=>[2,2,3,1]
[7,1,2,5,3,6,8,4]=>1001001=>[1,3,3,1]
[1,8,2,5,6,3,7,4]=>0100101=>[2,3,2,1]
[1,5,2,4,6,7,8,3]=>0100001=>[2,5,1]
[6,8,1,3,4,2,5,7]=>0100100=>[2,3,3]
[3,1,8,2,5,4,6,7]=>1010100=>[1,2,2,3]
[3,1,7,5,8,2,4,6]=>1010100=>[1,2,2,3]
[1,7,3,2,8,4,5,6]=>0110100=>[2,1,2,3]
[6,3,5,1,8,2,4,7]=>1010100=>[1,2,2,3]
[1,6,4,2,3,5,8,7]=>0110001=>[2,1,4,1]
[1,7,4,2,3,5,8,6]=>0110001=>[2,1,4,1]
[1,7,4,2,3,6,8,5]=>0110001=>[2,1,4,1]
[1,2,7,3,8,4,6,5]=>0010101=>[3,2,2,1]
[7,1,3,4,5,8,2,6]=>1000010=>[1,5,2]
[7,6,1,3,4,8,2,5]=>1100010=>[1,1,4,2]
[1,8,7,6,3,2,4,5]=>0111100=>[2,1,1,1,3]
[1,8,2,7,5,3,6,4]=>0101101=>[2,2,1,2,1]
[1,7,4,5,2,6,8,3]=>0101001=>[2,2,3,1]
[1,4,8,5,6,2,7,3]=>0010101=>[3,2,2,1]
[3,2,1,8,7,6,4,5]=>1101110=>[1,1,2,1,1,2]
[3,2,1,8,7,5,4,6]=>1101110=>[1,1,2,1,1,2]
[3,2,1,8,7,4,6,5]=>1101101=>[1,1,2,1,2,1]
[3,2,1,8,7,4,5,6]=>1101100=>[1,1,2,1,3]
[3,2,1,8,4,7,6,5]=>1101011=>[1,1,2,2,1,1]
[3,2,8,7,6,1,5,4]=>1011101=>[1,2,1,1,2,1]
[5,3,8,7,6,2,1,4]=>1011110=>[1,2,1,1,1,2]
[6,5,8,7,3,2,1,4]=>1011110=>[1,2,1,1,1,2]
[7,4,8,5,6,3,1,2]=>1010110=>[1,2,2,1,2]
[4,5,3,8,6,2,7,1]=>0101101=>[2,2,1,2,1]
[4,6,2,8,5,3,7,1]=>0101101=>[2,2,1,2,1]
[5,3,8,4,6,2,7,1]=>1010101=>[1,2,2,2,1]
[4,6,2,7,1,8,5,3]=>0101011=>[2,2,2,1,1]
[4,7,1,6,2,8,5,3]=>0101011=>[2,2,2,1,1]
[6,2,5,3,8,4,7,1]=>1010101=>[1,2,2,2,1]
[4,6,5,3,8,2,7,1]=>0110101=>[2,1,2,2,1]
[6,3,7,4,5,2,8,1]=>1010101=>[1,2,2,2,1]
[5,7,8,4,3,2,1,6]=>0011110=>[3,1,1,1,2]
[4,6,8,7,3,2,1,5]=>0011110=>[3,1,1,1,2]
[2,4,8,7,6,5,1,3]=>0011110=>[3,1,1,1,2]
[4,7,6,8,3,2,1,5]=>0101110=>[2,2,1,1,2]
[3,6,8,5,7,2,1,4]=>0010110=>[3,2,1,2]
[4,6,7,8,3,2,1,5]=>0001110=>[4,1,1,2]
[3,5,6,8,7,2,1,4]=>0001110=>[4,1,1,2]
[1,4,8,7,6,3,5,2]=>0011101=>[3,1,1,2,1]
[2,4,5,8,7,6,1,3]=>0001110=>[4,1,1,2]
[2,5,4,7,3,8,1,6]=>0101010=>[2,2,2,2]
[2,6,4,7,8,3,1,5]=>0100110=>[2,3,1,2]
[2,4,7,1,8,3,6,5]=>0010101=>[3,2,2,1]
[2,4,6,1,5,8,3,7]=>0010010=>[3,3,2]
[3,4,1,7,6,8,5,2]=>0101011=>[2,2,2,1,1]
[3,6,1,7,8,4,2,5]=>0100110=>[2,3,1,2]
[3,5,1,7,2,6,8,4]=>0101001=>[2,2,3,1]
[4,3,6,2,8,1,7,5]=>1010101=>[1,2,2,2,1]
[5,3,4,7,2,8,1,6]=>1001010=>[1,3,2,2]
[4,5,7,2,1,8,3,6]=>0011010=>[3,1,2,2]
[4,5,7,2,1,6,8,3]=>0011001=>[3,1,3,1]
[4,6,5,2,8,7,3,1]=>0110111=>[2,1,2,1,1,1]
[4,5,8,2,1,6,7,3]=>0011001=>[3,1,3,1]
[3,4,1,5,6,8,7,2]=>0100011=>[2,4,1,1]
[3,6,1,7,2,5,8,4]=>0101001=>[2,2,3,1]
[7,3,4,5,8,2,1,6]=>1000110=>[1,4,1,2]
[6,3,7,8,2,5,1,4]=>1001010=>[1,3,2,2]
[6,7,4,8,2,5,3,1]=>0101011=>[2,2,2,1,1]
[3,5,1,4,7,2,8,6]=>0100101=>[2,3,2,1]
[4,3,7,5,6,2,8,1]=>1010101=>[1,2,2,2,1]
[7,3,4,8,6,2,5,1]=>1001101=>[1,3,1,2,1]
[4,7,8,5,6,2,1,3]=>0010110=>[3,2,1,2]
[3,5,1,4,8,7,2,6]=>0100110=>[2,3,1,2]
[4,5,6,3,8,2,1,7]=>0010110=>[3,2,1,2]
[4,2,6,3,7,8,1,5]=>1010010=>[1,2,3,2]
[4,2,7,3,5,8,1,6]=>1010010=>[1,2,3,2]
[4,5,3,7,8,1,6,2]=>0100101=>[2,3,2,1]
[4,2,6,8,5,3,1,7]=>1001110=>[1,3,1,1,2]
[5,1,2,7,8,6,4,3]=>1000111=>[1,4,1,1,1]
[4,1,2,7,8,6,3,5]=>1000110=>[1,4,1,2]
[4,1,8,7,2,6,3,5]=>1011010=>[1,2,1,2,2]
[4,1,5,8,7,3,2,6]=>1001110=>[1,3,1,1,2]
[5,1,8,2,7,6,3,4]=>1010110=>[1,2,2,1,2]
[7,1,6,2,8,3,4,5]=>1010100=>[1,2,2,3]
[4,7,8,3,2,5,1,6]=>0011010=>[3,1,2,2]
[4,5,2,8,7,3,1,6]=>0101110=>[2,2,1,1,2]
[4,5,7,6,8,3,1,2]=>0010110=>[3,2,1,2]
[8,2,1,7,4,6,3,5]=>1101010=>[1,1,2,2,2]
[5,2,1,6,8,4,7,3]=>1100101=>[1,1,3,2,1]
[4,5,2,8,7,1,6,3]=>0101101=>[2,2,1,2,1]
[5,2,7,6,8,3,4,1]=>1010101=>[1,2,2,2,1]
[4,2,5,7,3,1,8,6]=>1001101=>[1,3,1,2,1]
[4,2,8,7,1,3,6,5]=>1011001=>[1,2,1,3,1]
[8,2,1,7,3,5,4,6]=>1101010=>[1,1,2,2,2]
[5,2,6,3,8,7,1,4]=>1010110=>[1,2,2,1,2]
[5,2,8,6,4,1,7,3]=>1011101=>[1,2,1,1,2,1]
[5,2,3,8,7,1,4,6]=>1001100=>[1,3,1,3]
[5,1,8,3,7,4,2,6]=>1010110=>[1,2,2,1,2]
[8,1,2,7,5,4,3,6]=>1001110=>[1,3,1,1,2]
[6,1,2,8,3,7,4,5]=>1001010=>[1,3,2,2]
[5,6,7,3,8,1,2,4]=>0010100=>[3,2,3]
[4,1,7,6,8,3,2,5]=>1010110=>[1,2,2,1,2]
[8,1,7,3,5,4,2,6]=>1010110=>[1,2,2,1,2]
[7,1,6,3,4,2,8,5]=>1010101=>[1,2,2,2,1]
[7,1,6,8,5,2,3,4]=>1001100=>[1,3,1,3]
[8,1,7,3,5,2,6,4]=>1010101=>[1,2,2,2,1]
[6,2,3,8,7,5,1,4]=>1001110=>[1,3,1,1,2]
[3,8,5,7,2,4,1,6]=>0101010=>[2,2,2,2]
[3,6,5,8,2,1,7,4]=>0101101=>[2,2,1,2,1]
[4,7,1,8,3,5,2,6]=>0101010=>[2,2,2,2]
[7,6,2,3,4,1,8,5]=>1100101=>[1,1,3,2,1]
[4,8,6,7,1,2,3,5]=>0101000=>[2,2,4]
[8,5,7,3,1,6,2,4]=>1011010=>[1,2,1,2,2]
[3,4,7,2,1,5,8,6]=>0011001=>[3,1,3,1]
[3,8,6,1,4,7,2,5]=>0110010=>[2,1,3,2]
[3,7,6,8,2,5,1,4]=>0101010=>[2,2,2,2]
[8,6,2,3,1,5,7,4]=>1101001=>[1,1,2,3,1]
[3,8,7,1,2,5,6,4]=>0110001=>[2,1,4,1]
[3,4,8,2,5,6,7,1]=>0010001=>[3,4,1]
[4,2,1,3,7,6,5,8]=>1100110=>[1,1,3,1,2]
[6,3,4,8,7,5,1,2]=>1001110=>[1,3,1,1,2]
[8,3,5,7,6,1,4,2]=>1001101=>[1,3,1,2,1]
[2,1,8,5,6,7,3,4]=>1010010=>[1,2,3,2]
[6,8,4,5,7,2,3,1]=>0100101=>[2,3,2,1]
[8,3,2,5,6,7,1,4]=>1100010=>[1,1,4,2]
[7,3,2,6,8,5,4,1]=>1100111=>[1,1,3,1,1,1]
[4,8,5,3,2,7,6,1]=>0111011=>[2,1,1,2,1,1]
[7,3,5,6,8,1,4,2]=>1000101=>[1,4,2,1]
[7,4,8,3,6,5,2,1]=>1010111=>[1,2,2,1,1,1]
[7,5,6,3,8,4,2,1]=>1010111=>[1,2,2,1,1,1]
[7,4,5,2,8,3,6,1]=>1010101=>[1,2,2,2,1]
[4,8,6,7,3,5,2,1]=>0101011=>[2,2,2,1,1]
[4,3,1,2,6,7,8,5]=>1100001=>[1,1,5,1]
[7,4,6,5,8,3,2,1]=>1010111=>[1,2,2,1,1,1]
[4,8,5,2,6,7,3,1]=>0110011=>[2,1,3,1,1]
[2,5,8,6,7,3,1,4]=>0010110=>[3,2,1,2]
[1,4,6,5,2,7,3,8]=>0011010=>[3,1,2,2]
[3,7,4,8,6,2,5,1]=>0101101=>[2,2,1,2,1]
[2,3,4,1,8,7,5,6]=>0010110=>[3,2,1,2]
[4,2,6,5,1,8,7,3]=>1011011=>[1,2,1,2,1,1]
[6,5,4,1,3,2,8,7]=>1110101=>[1,1,1,2,2,1]
[6,5,4,2,1,3,8,7]=>1111001=>[1,1,1,1,3,1]
[8,7,4,3,6,1,5,2]=>1110101=>[1,1,1,2,2,1]
[7,8,4,2,1,5,6,3]=>0111001=>[2,1,1,3,1]
[8,6,7,2,4,5,1,3]=>1010010=>[1,2,3,2]
[7,8,2,3,6,1,5,4]=>0100101=>[2,3,2,1]
[6,8,2,7,3,5,4,1]=>0101011=>[2,2,2,1,1]
[2,1,7,8,4,5,6,3]=>1001001=>[1,3,3,1]
[7,5,8,3,2,4,6,1]=>1011001=>[1,2,1,3,1]
[8,6,7,3,4,1,5,2]=>1010101=>[1,2,2,2,1]
[8,6,2,7,1,3,5,4]=>1101001=>[1,1,2,3,1]
[8,3,2,7,6,4,1,5]=>1101110=>[1,1,2,1,1,2]
[8,5,4,1,3,7,6,2]=>1110011=>[1,1,1,3,1,1]
[5,8,2,3,4,7,6,1]=>0100011=>[2,4,1,1]
[6,8,2,7,3,4,1,5]=>0101010=>[2,2,2,2]
[5,6,1,4,7,2,3,8]=>0100100=>[2,3,3]
[4,5,1,6,3,2,8,7]=>0101101=>[2,2,1,2,1]
[3,6,7,4,1,2,5,8]=>0011000=>[3,1,4]
[2,5,1,4,3,7,6,8]=>0101010=>[2,2,2,2]
[1,4,5,3,7,2,8,6]=>0010101=>[3,2,2,1]
[5,1,4,3,7,2,8,6]=>1010101=>[1,2,2,2,1]
[1,6,7,4,3,2,8,5]=>0011101=>[3,1,1,2,1]
[2,6,7,3,1,4,5,8]=>0011000=>[3,1,4]
[5,1,4,6,7,2,3,8]=>1000100=>[1,4,3]
[2,6,4,3,1,8,5,7]=>0111010=>[2,1,1,2,2]
[1,6,5,2,3,4,8,7]=>0110001=>[2,1,4,1]
[7,8,2,1,5,4,3,6]=>0110110=>[2,1,2,1,2]
[7,8,1,2,3,6,4,5]=>0100010=>[2,4,2]
[1,4,7,8,5,2,3,6]=>0001100=>[4,1,3]
[1,3,2,6,5,8,4,7]=>0101010=>[2,2,2,2]
[2,1,5,7,8,4,3,6]=>1000110=>[1,4,1,2]
[3,1,7,2,6,5,8,4]=>1010101=>[1,2,2,2,1]
[1,3,2,7,5,4,8,6]=>0101101=>[2,2,1,2,1]
[1,4,5,8,6,2,3,7]=>0001100=>[4,1,3]
[1,6,7,2,3,5,8,4]=>0010001=>[3,4,1]
[2,4,1,8,6,5,3,7]=>0101110=>[2,2,1,1,2]
[7,1,4,5,8,3,6,2]=>1000101=>[1,4,2,1]
[3,7,8,5,4,6,1,2]=>0011010=>[3,1,2,2]
[5,1,7,2,6,4,8,3]=>1010101=>[1,2,2,2,1]
[2,3,4,6,8,5,7,1]=>0000101=>[5,2,1]
[3,6,2,4,7,5,8,1]=>0100101=>[2,3,2,1]
[3,7,2,8,4,6,5,1]=>0101011=>[2,2,2,1,1]
[4,7,5,2,3,6,8,1]=>0110001=>[2,1,4,1]
[4,3,5,8,7,2,6,1]=>1001101=>[1,3,1,2,1]
[2,3,4,8,7,5,6,1]=>0001101=>[4,1,2,1]
[5,1,6,3,7,8,4,2]=>1010011=>[1,2,3,1,1]
[4,2,6,7,5,1,8,3]=>1001101=>[1,3,1,2,1]
[5,7,6,3,4,8,1,2]=>0110010=>[2,1,3,2]
[6,4,7,5,8,3,2,1]=>1010111=>[1,2,2,1,1,1]
[3,6,7,5,8,1,4,2]=>0010101=>[3,2,2,1]
[1,8,5,6,7,3,4,2]=>0100101=>[2,3,2,1]
[3,2,7,4,6,1,8,5]=>1010101=>[1,2,2,2,1]
[3,8,4,5,6,7,2,1]=>0100011=>[2,4,1,1]
[8,2,4,1,6,7,5,3]=>1010011=>[1,2,3,1,1]
[3,4,8,7,6,1,5,2]=>0011101=>[3,1,1,2,1]
[4,3,8,7,6,2,5,1]=>1011101=>[1,2,1,1,2,1]
[3,7,8,5,6,4,2,1]=>0010111=>[3,2,1,1,1]
[3,4,7,5,8,6,1,2]=>0010110=>[3,2,1,2]
[5,4,6,2,3,1,8,7]=>1010101=>[1,2,2,2,1]
[6,3,1,5,4,2,8,7]=>1101101=>[1,1,2,1,2,1]
[6,4,5,3,2,1,8,7]=>1011101=>[1,2,1,1,2,1]
[7,8,3,4,6,5,1,2]=>0100110=>[2,3,1,2]
[2,1,7,6,8,4,5,3]=>1010101=>[1,2,2,2,1]
[2,5,4,8,6,3,7,1]=>0101101=>[2,2,1,2,1]
[3,5,4,7,6,1,8,2]=>0101101=>[2,2,1,2,1]
[2,6,5,3,7,4,8,1]=>0110101=>[2,1,2,2,1]
[2,1,8,5,3,7,6,4]=>1011011=>[1,2,1,2,1,1]
[6,5,4,2,7,8,3,1]=>1110011=>[1,1,1,3,1,1]
[2,6,8,5,7,4,3,1]=>0010111=>[3,2,1,1,1]
[2,1,8,6,7,5,4,3]=>1010111=>[1,2,2,1,1,1]
[2,5,3,1,6,4,7,8]=>0110100=>[2,1,2,3]
[7,5,4,2,3,1,8,6]=>1110101=>[1,1,1,2,2,1]
[6,3,2,4,5,8,1,7]=>1100010=>[1,1,4,2]
[3,5,4,2,8,6,1,7]=>0110110=>[2,1,2,1,2]
[5,6,8,7,3,2,1,4]=>0011110=>[3,1,1,1,2]
[6,4,5,3,2,8,1,7]=>1011010=>[1,2,1,2,2]
[4,2,5,7,3,1,6,8]=>1001100=>[1,3,1,3]
[7,4,1,3,2,6,8,5]=>1101001=>[1,1,2,3,1]
[6,1,4,3,2,7,8,5]=>1011001=>[1,2,1,3,1]
[1,6,4,2,3,7,8,5]=>0110001=>[2,1,4,1]
[1,4,5,3,8,2,6,7]=>0010100=>[3,2,3]
[2,5,4,3,8,1,6,7]=>0110100=>[2,1,2,3]
[6,2,5,1,3,7,4,8]=>1010010=>[1,2,3,2]
[7,6,5,8,1,2,4,3]=>1101001=>[1,1,2,3,1]
[5,7,4,1,3,6,2,8]=>0110010=>[2,1,3,2]
[4,3,8,1,6,7,2,5]=>1010010=>[1,2,3,2]
[4,3,8,1,6,5,7,2]=>1010101=>[1,2,2,2,1]
[4,3,8,2,5,6,7,1]=>1010001=>[1,2,4,1]
[5,4,8,2,3,6,7,1]=>1010001=>[1,2,4,1]
[3,2,8,1,6,7,4,5]=>1010010=>[1,2,3,2]
[5,2,8,1,6,7,3,4]=>1010010=>[1,2,3,2]
[7,2,6,3,8,1,5,4]=>1010101=>[1,2,2,2,1]
[6,3,4,5,8,2,7,1]=>1000101=>[1,4,2,1]
[7,3,8,1,4,5,6,2]=>1010001=>[1,2,4,1]
[7,3,4,5,8,1,6,2]=>1000101=>[1,4,2,1]
[7,4,8,1,5,6,2,3]=>1010010=>[1,2,3,2]
[7,2,8,1,6,5,4,3]=>1010111=>[1,2,2,1,1,1]
[8,1,3,4,6,5,2,7]=>1000110=>[1,4,1,2]
[8,6,5,7,2,1,4,3]=>1101101=>[1,1,2,1,2,1]
[1,8,6,3,7,4,5,2]=>0110101=>[2,1,2,2,1]
[3,8,5,1,7,6,4,2]=>0110111=>[2,1,2,1,1,1]
[2,8,1,3,5,6,7,4]=>0100001=>[2,5,1]
[2,4,8,7,5,6,3,1]=>0011011=>[3,1,2,1,1]
[3,8,7,5,2,6,4,1]=>0111011=>[2,1,1,2,1,1]
[1,8,7,3,4,6,5,2]=>0110011=>[2,1,3,1,1]
[2,8,1,4,5,7,6,3]=>0100011=>[2,4,1,1]
[1,2,7,6,8,4,5,3]=>0010101=>[3,2,2,1]
[1,2,5,3,7,6,8,4]=>0010101=>[3,2,2,1]
[3,7,8,1,5,6,2,4]=>0010010=>[3,3,2]
[1,2,4,8,3,6,5,7]=>0001010=>[4,2,2]
[4,1,3,7,6,8,5,2]=>1001011=>[1,3,2,1,1]
[6,5,7,8,1,4,3,2]=>1001011=>[1,3,2,1,1]
[3,1,8,6,7,5,4,2]=>1010111=>[1,2,2,1,1,1]
[2,8,3,1,7,5,4,6]=>0110110=>[2,1,2,1,2]
[2,8,3,7,1,4,5,6]=>0101000=>[2,2,4]
[4,8,2,7,5,1,3,6]=>0101100=>[2,2,1,3]
[4,1,2,6,7,5,3,8]=>1000110=>[1,4,1,2]
[1,2,5,3,8,6,4,7]=>0010110=>[3,2,1,2]
[5,8,7,6,2,1,3,4]=>0111100=>[2,1,1,1,3]
[6,4,8,3,7,5,2,1]=>1010111=>[1,2,2,1,1,1]
[3,6,8,2,5,7,4,1]=>0010011=>[3,3,1,1]
[4,8,7,5,2,6,3,1]=>0111011=>[2,1,1,2,1,1]
[3,2,8,5,6,1,7,4]=>1010101=>[1,2,2,2,1]
[3,4,8,1,5,7,6,2]=>0010011=>[3,3,1,1]
[4,5,6,2,7,3,8,1]=>0010101=>[3,2,2,1]
[4,7,5,6,2,3,8,1]=>0101001=>[2,2,3,1]
[3,5,7,6,2,4,8,1]=>0011001=>[3,1,3,1]
[1,6,8,7,4,5,3,2]=>0011011=>[3,1,2,1,1]
[8,3,5,7,6,2,4,1]=>1001101=>[1,3,1,2,1]
[6,4,5,2,8,7,3,1]=>1010111=>[1,2,2,1,1,1]
[6,4,2,7,8,5,3,1]=>1100111=>[1,1,3,1,1,1]
[2,4,5,8,6,7,1,3]=>0001010=>[4,2,2]
[1,3,5,6,8,7,2,4]=>0000110=>[5,1,2]
[5,7,4,1,6,2,8,3]=>0110101=>[2,1,2,2,1]
[3,5,6,7,8,2,4,1]=>0000101=>[5,2,1]
[5,2,4,1,6,7,8,3]=>1010001=>[1,2,4,1]
[8,5,6,7,2,4,3,1]=>1001011=>[1,3,2,1,1]
[7,8,4,5,1,6,3,2]=>0101011=>[2,2,2,1,1]
[3,5,8,6,4,7,2,1]=>0011011=>[3,1,2,1,1]
[4,5,6,8,3,7,2,1]=>0001011=>[4,2,1,1]
[8,4,5,7,6,2,3,1]=>1001101=>[1,3,1,2,1]
[4,8,6,7,5,2,3,1]=>0101101=>[2,2,1,2,1]
[8,7,4,3,6,5,1,2]=>1110110=>[1,1,1,2,1,2]
[8,1,4,3,6,5,2,7]=>1010110=>[1,2,2,1,2]
[6,1,2,5,4,3,8,7]=>1001101=>[1,3,1,2,1]
[2,8,6,3,4,7,1,5]=>0110010=>[2,1,3,2]
[8,1,2,3,5,7,4,6]=>1000010=>[1,5,2]
[8,1,2,3,6,5,4,7]=>1000110=>[1,4,1,2]
[8,1,2,3,7,6,5,4]=>1000111=>[1,4,1,1,1]
[2,8,1,6,7,5,3,4]=>0100110=>[2,3,1,2]
[8,1,2,3,5,4,7,6]=>1000101=>[1,4,2,1]
[4,8,5,2,7,1,6,3]=>0110101=>[2,1,2,2,1]
[3,7,8,6,4,2,1,5]=>0011110=>[3,1,1,1,2]
[3,7,8,4,6,2,1,5]=>0010110=>[3,2,1,2]
[8,3,1,5,7,6,2,4]=>1100110=>[1,1,3,1,2]
[4,5,2,8,6,7,1,3]=>0101010=>[2,2,2,2]
[8,4,5,1,3,2,6,7]=>1010100=>[1,2,2,3]
[8,1,2,3,6,7,5,4]=>1000011=>[1,5,1,1]
[8,1,6,7,2,5,4,3]=>1001011=>[1,3,2,1,1]
[5,4,1,3,2,8,7,6]=>1101011=>[1,1,2,2,1,1]
[5,4,2,1,3,8,7,6]=>1110011=>[1,1,1,3,1,1]
[3,2,7,4,1,6,5,8]=>1011010=>[1,2,1,2,2]
[5,7,3,2,1,6,4,8]=>0111010=>[2,1,1,2,2]
[7,6,5,1,3,4,2,8]=>1110010=>[1,1,1,3,2]
[7,6,5,2,1,4,3,8]=>1111010=>[1,1,1,1,2,2]
[8,6,2,4,3,5,1,7]=>1101010=>[1,1,2,2,2]
[7,6,5,1,4,2,3,8]=>1110100=>[1,1,1,2,3]
[1,7,6,3,2,4,5,8]=>0111000=>[2,1,1,4]
[8,7,3,2,1,6,4,5]=>1111010=>[1,1,1,1,2,2]
[1,5,7,2,4,3,6,8]=>0010100=>[3,2,3]
[5,2,8,1,4,3,7,6]=>1010101=>[1,2,2,2,1]
[7,1,6,8,2,4,5,3]=>1001001=>[1,3,3,1]
[8,4,6,2,3,7,1,5]=>1010010=>[1,2,3,2]
[8,6,1,3,7,5,2,4]=>1100110=>[1,1,3,1,2]
[5,8,1,3,4,7,2,6]=>0100010=>[2,4,2]
[5,8,6,2,3,1,4,7]=>0110100=>[2,1,2,3]
[5,8,7,3,2,4,6,1]=>0111001=>[2,1,1,3,1]
[7,6,2,8,3,5,4,1]=>1101011=>[1,1,2,2,1,1]
[8,7,5,2,6,3,1,4]=>1110110=>[1,1,1,2,1,2]
[8,4,7,3,1,5,2,6]=>1011010=>[1,2,1,2,2]
[8,2,6,3,1,4,7,5]=>1011001=>[1,2,1,3,1]
[8,3,2,7,6,1,4,5]=>1101100=>[1,1,2,1,3]
[3,8,2,7,6,4,1,5]=>0101110=>[2,2,1,1,2]
[3,6,7,5,8,2,1,4]=>0010110=>[3,2,1,2]
[6,3,5,2,8,7,4,1]=>1010111=>[1,2,2,1,1,1]
[5,8,4,3,2,7,6,1]=>0111011=>[2,1,1,2,1,1]
[2,4,6,8,7,3,5,1]=>0001101=>[4,1,2,1]
[6,3,5,7,8,2,4,1]=>1000101=>[1,4,2,1]
[4,6,8,7,5,2,3,1]=>0011101=>[3,1,1,2,1]
[3,5,6,8,7,2,4,1]=>0001101=>[4,1,2,1]
[1,6,8,4,7,5,3,2]=>0010111=>[3,2,1,1,1]
[3,8,6,5,1,7,2,4]=>0111010=>[2,1,1,2,2]
[8,4,6,7,5,2,3,1]=>1001101=>[1,3,1,2,1]
[8,4,5,7,2,6,3,1]=>1001011=>[1,3,2,1,1]
[6,7,4,3,8,5,2,1]=>0110111=>[2,1,2,1,1,1]
[2,6,8,5,4,7,3,1]=>0011011=>[3,1,2,1,1]
[2,7,4,6,8,5,3,1]=>0100111=>[2,3,1,1,1]
[6,4,7,8,3,5,2,1]=>1001011=>[1,3,2,1,1]
[5,2,4,1,6,3,8,7]=>1010101=>[1,2,2,2,1]
[6,3,5,2,7,4,8,1]=>1010101=>[1,2,2,2,1]
[7,3,4,2,6,1,8,5]=>1010101=>[1,2,2,2,1]
[2,3,7,4,6,1,8,5]=>0010101=>[3,2,2,1]
[2,1,7,4,6,3,8,5]=>1010101=>[1,2,2,2,1]
[7,5,4,2,6,3,8,1]=>1110101=>[1,1,1,2,2,1]
[5,4,7,2,6,1,8,3]=>1010101=>[1,2,2,2,1]
[5,2,7,4,6,1,8,3]=>1010101=>[1,2,2,2,1]
[5,2,4,1,7,6,8,3]=>1010101=>[1,2,2,2,1]
[4,2,7,5,6,1,8,3]=>1010101=>[1,2,2,2,1]
[4,2,7,5,6,3,8,1]=>1010101=>[1,2,2,2,1]
[6,2,4,3,7,5,8,1]=>1010101=>[1,2,2,2,1]
[2,6,4,3,7,5,8,1]=>0110101=>[2,1,2,2,1]
[2,7,5,4,8,6,3,1]=>0110111=>[2,1,2,1,1,1]
[4,3,7,5,8,6,1,2]=>1010110=>[1,2,2,1,2]
[6,7,4,8,3,5,2,1]=>0101011=>[2,2,2,1,1]
[2,1,5,8,7,4,6,3]=>1001101=>[1,3,1,2,1]
[5,8,3,4,6,7,2,1]=>0100011=>[2,4,1,1]
[6,4,3,8,7,2,5,1]=>1101101=>[1,1,2,1,2,1]
[3,6,8,5,4,7,1,2]=>0011010=>[3,1,2,2]
[7,5,3,6,8,4,2,1]=>1100111=>[1,1,3,1,1,1]
[8,4,3,5,7,2,6,1]=>1100101=>[1,1,3,2,1]
[4,7,8,6,3,5,2,1]=>0011011=>[3,1,2,1,1]
[6,7,5,8,2,4,3,1]=>0101011=>[2,2,2,1,1]
[2,5,4,1,7,8,6,3]=>0110011=>[2,1,3,1,1]
[4,3,1,5,6,8,7,2]=>1100011=>[1,1,4,1,1]
[1,6,3,2,5,8,7,4]=>0110011=>[2,1,3,1,1]
[8,1,5,3,2,6,7,4]=>1011001=>[1,2,1,3,1]
[1,6,8,3,2,4,7,5]=>0011001=>[3,1,3,1]
[1,8,7,6,4,2,3,5]=>0111100=>[2,1,1,1,3]
[8,1,7,3,5,4,6,2]=>1010101=>[1,2,2,2,1]
[7,1,3,8,4,6,5,2]=>1001011=>[1,3,2,1,1]
[3,2,8,1,5,6,7,4]=>1010001=>[1,2,4,1]
[8,6,1,2,4,5,7,3]=>1100001=>[1,1,5,1]
[1,8,6,7,3,4,5,2]=>0101001=>[2,2,3,1]
[1,7,3,8,2,4,6,5]=>0101001=>[2,2,3,1]
[8,4,3,1,5,6,7,2]=>1110001=>[1,1,1,4,1]
[1,8,7,6,3,4,2,5]=>0111010=>[2,1,1,2,2]
[1,8,5,3,7,6,2,4]=>0110110=>[2,1,2,1,2]
[3,5,2,6,1,4,8,7]=>0101001=>[2,2,3,1]
[4,5,7,2,3,8,6,1]=>0010011=>[3,3,1,1]
[4,5,7,2,3,8,1,6]=>0010010=>[3,3,2]
[4,5,6,2,3,1,8,7]=>0010101=>[3,2,2,1]
[4,5,6,2,1,3,8,7]=>0011001=>[3,1,3,1]
[4,5,6,1,3,2,8,7]=>0010101=>[3,2,2,1]
[4,5,6,3,1,2,8,7]=>0011001=>[3,1,3,1]
[4,5,7,3,2,8,1,6]=>0011010=>[3,1,2,2]
[4,6,7,3,8,2,5,1]=>0010101=>[3,2,2,1]
[4,6,7,3,8,2,1,5]=>0010110=>[3,2,1,2]
[4,5,7,3,1,8,2,6]=>0011010=>[3,1,2,2]
[3,5,1,7,4,8,2,6]=>0101010=>[2,2,2,2]
[2,1,5,7,4,8,3,6]=>1001010=>[1,3,2,2]
[4,5,7,1,3,8,6,2]=>0010011=>[3,3,1,1]
[4,6,7,3,8,1,5,2]=>0010101=>[3,2,2,1]
[5,6,7,8,3,1,4,2]=>0001101=>[4,1,2,1]
[4,6,7,1,8,3,5,2]=>0010101=>[3,2,2,1]
[3,6,1,7,8,4,5,2]=>0100101=>[2,3,2,1]
[2,1,6,7,8,4,5,3]=>1000101=>[1,4,2,1]
[2,1,6,7,8,4,3,5]=>1000110=>[1,4,1,2]
[4,6,7,1,8,3,2,5]=>0010110=>[3,2,1,2]
[5,6,7,8,1,3,2,4]=>0001010=>[4,2,2]
[4,6,7,2,8,3,5,1]=>0010101=>[3,2,2,1]
[3,6,2,7,8,4,5,1]=>0100101=>[2,3,2,1]
[3,6,2,7,8,4,1,5]=>0100110=>[2,3,1,2]
[3,4,2,1,7,8,5,6]=>0110010=>[2,1,3,2]
[4,6,7,2,8,5,3,1]=>0010111=>[3,2,1,1,1]
[4,6,7,2,8,5,1,3]=>0010110=>[3,2,1,2]
[4,5,7,1,2,8,6,3]=>0010011=>[3,3,1,1]
[2,1,6,7,8,3,5,4]=>1000101=>[1,4,2,1]
[3,6,1,7,8,2,5,4]=>0100101=>[2,3,2,1]
[4,6,7,1,8,2,5,3]=>0010101=>[3,2,2,1]
[5,6,7,8,1,2,4,3]=>0001001=>[4,3,1]
[5,6,7,8,2,4,1,3]=>0001010=>[4,2,2]
[5,6,7,8,2,4,3,1]=>0001011=>[4,2,1,1]
[3,6,1,7,8,5,2,4]=>0100110=>[2,3,1,2]
[2,1,6,7,8,5,3,4]=>1000110=>[1,4,1,2]
[3,4,2,1,6,5,8,7,10,9]=>011010101=>[2,1,2,2,2,1]
[3,5,2,6,4,1,8,7,10,9]=>010110101=>[2,2,1,2,2,1]
[3,5,2,7,4,8,6,1,10,9]=>010101101=>[2,2,2,1,2,1]
[2,1,5,6,4,3,8,7,10,9]=>100110101=>[1,3,1,2,2,1]
[4,5,6,3,2,1,8,7,10,9]=>001110101=>[3,1,1,2,2,1]
[4,5,7,3,2,8,6,1,10,9]=>001101101=>[3,1,2,1,2,1]
[4,5,7,3,2,9,6,10,8,1]=>001101011=>[3,1,2,2,1,1]
[2,1,5,7,4,8,6,3,10,9]=>100101101=>[1,3,2,1,2,1]
[4,6,7,3,8,5,2,1,10,9]=>001011101=>[3,2,1,1,2,1]
[4,6,7,3,9,5,2,10,8,1]=>001011011=>[3,2,1,2,1,1]
[2,1,5,7,4,9,6,10,8,3]=>100101011=>[1,3,2,2,1,1]
[2,1,4,3,7,8,6,5,10,9]=>101001101=>[1,2,3,1,2,1]
[3,4,2,1,7,8,6,5,10,9]=>011001101=>[2,1,3,1,2,1]
[3,6,2,7,8,5,4,1,10,9]=>010011101=>[2,3,1,1,2,1]
[3,6,2,7,9,5,4,10,8,1]=>010011011=>[2,3,1,2,1,1]
[2,1,6,7,8,5,4,3,10,9]=>100011101=>[1,4,1,1,2,1]
[5,6,7,8,4,3,2,1,10,9]=>000111101=>[4,1,1,1,2,1]
[5,6,7,9,4,3,2,10,8,1]=>000111011=>[4,1,1,2,1,1]
[2,1,6,7,9,5,4,10,8,3]=>100011011=>[1,4,1,2,1,1]
[5,6,8,9,4,3,10,7,2,1]=>000110111=>[4,1,2,1,1,1]
[2,1,4,3,7,9,6,10,8,5]=>101001011=>[1,2,3,2,1,1]
[3,4,2,1,7,9,6,10,8,5]=>011001011=>[2,1,3,2,1,1]
[3,6,2,8,9,5,10,7,4,1]=>010010111=>[2,3,2,1,1,1]
[2,1,6,8,9,5,10,7,4,3]=>100010111=>[1,4,2,1,1,1]
[2,1,4,3,6,5,9,10,8,7]=>101010011=>[1,2,2,3,1,1]
[3,4,2,1,6,5,9,10,8,7]=>011010011=>[2,1,2,3,1,1]
[3,5,2,6,4,1,9,10,8,7]=>010110011=>[2,2,1,3,1,1]
[3,5,2,8,4,9,10,7,6,1]=>010100111=>[2,2,3,1,1,1]
[2,1,5,6,4,3,9,10,8,7]=>100110011=>[1,3,1,3,1,1]
[4,5,6,3,2,1,9,10,8,7]=>001110011=>[3,1,1,3,1,1]
[4,5,8,3,2,9,10,7,6,1]=>001100111=>[3,1,3,1,1,1]
[2,1,5,8,4,9,10,7,6,3]=>100100111=>[1,3,3,1,1,1]
[4,7,8,3,9,10,6,5,2,1]=>001001111=>[3,3,1,1,1,1]
[2,1,4,3,8,9,10,7,6,5]=>101000111=>[1,2,4,1,1,1]
[3,4,2,1,8,9,10,7,6,5]=>011000111=>[2,1,4,1,1,1]
[3,7,2,8,9,10,6,5,4,1]=>010001111=>[2,4,1,1,1,1]
[5,3,1,6,2,4,8,7]=>1101001=>[1,1,2,3,1]
[7,3,1,5,2,8,4,6]=>1101010=>[1,1,2,2,2]
[8,4,5,1,2,7,3,6]=>1010010=>[1,2,3,2]
[7,4,5,1,2,8,3,6]=>1010010=>[1,2,3,2]
[6,4,5,1,2,3,8,7]=>1010001=>[1,2,4,1]
[5,4,6,1,2,3,8,7]=>1010001=>[1,2,4,1]
[3,6,1,5,2,4,8,7]=>0101001=>[2,2,3,1]
[4,6,5,1,2,3,8,7]=>0110001=>[2,1,4,1]
[5,6,4,1,2,3,8,7]=>0110001=>[2,1,4,1]
[7,5,4,1,2,8,3,6]=>1110010=>[1,1,1,3,2]
[8,6,4,1,7,2,3,5]=>1110100=>[1,1,1,2,3]
[5,7,4,1,2,8,3,6]=>0110010=>[2,1,3,2]
[3,7,1,5,2,8,4,6]=>0101010=>[2,2,2,2]
[2,1,7,5,3,8,4,6]=>1011010=>[1,2,1,2,2]
[4,8,5,1,2,7,3,6]=>0110010=>[2,1,3,2]
[6,8,4,1,7,2,3,5]=>0110100=>[2,1,2,3]
[4,8,6,1,7,2,3,5]=>0110100=>[2,1,2,3]
[2,1,8,6,7,3,4,5]=>1010100=>[1,2,2,3]
[2,1,7,6,8,3,4,5]=>1010100=>[1,2,2,3]
[4,7,6,1,8,2,3,5]=>0110100=>[2,1,2,3]
[5,7,6,8,1,2,3,4]=>0101000=>[2,2,4]
[6,4,7,1,8,2,3,5]=>1010100=>[1,2,2,3]
[8,4,6,1,7,2,3,5]=>1010100=>[1,2,2,3]
[8,3,1,6,7,2,4,5]=>1100100=>[1,1,3,3]
[4,3,1,2,7,8,5,6]=>1100010=>[1,1,4,2]
[8,4,7,1,6,2,3,5]=>1010100=>[1,2,2,3]
[7,4,8,1,6,2,3,5]=>1010100=>[1,2,2,3]
[4,5,8,1,2,7,3,6]=>0010010=>[3,3,2]
[2,1,6,8,7,3,4,5]=>1001100=>[1,3,1,3]
[4,6,8,1,7,2,3,5]=>0010100=>[3,2,3]
[5,6,8,7,1,2,3,4]=>0011000=>[3,1,4]
[8,5,7,6,1,2,3,4]=>1011000=>[1,2,1,4]
[4,7,8,1,6,2,3,5]=>0010100=>[3,2,3]
[3,7,1,8,6,2,4,5]=>0101100=>[2,2,1,3]
[3,8,1,7,6,2,4,5]=>0101100=>[2,2,1,3]
[4,8,7,1,6,2,3,5]=>0110100=>[2,1,2,3]
[6,8,7,5,1,2,3,4]=>0111000=>[2,1,1,4]
[6,4,7,3,8,5,1,2]=>1010110=>[1,2,2,1,2]
[5,4,2,7,6,1,3,8]=>1101100=>[1,1,2,1,3]
[5,4,2,7,6,1,8,3]=>1101101=>[1,1,2,1,2,1]
[5,4,3,7,6,8,1,2]=>1101010=>[1,1,2,2,2]
[5,4,3,7,8,6,1,2]=>1100110=>[1,1,3,1,2]
[5,4,3,8,6,7,1,2]=>1101010=>[1,1,2,2,2]
[5,4,3,6,8,7,1,2]=>1100110=>[1,1,3,1,2]
[5,4,2,6,7,1,8,3]=>1100101=>[1,1,3,2,1]
[5,3,2,6,1,7,4,8]=>1101010=>[1,1,2,2,2]
[5,3,2,6,1,7,8,4]=>1101001=>[1,1,2,3,1]
[5,3,2,6,1,8,7,4]=>1101011=>[1,1,2,2,1,1]
[5,4,2,6,8,1,7,3]=>1100101=>[1,1,3,2,1]
[6,4,8,2,5,1,7,3]=>1010101=>[1,2,2,2,1]
[5,4,2,8,6,1,3,7]=>1101100=>[1,1,2,1,3]
[5,3,2,6,1,8,4,7]=>1101010=>[1,1,2,2,2]
[6,3,8,2,1,5,4,7]=>1011010=>[1,2,1,2,2]
[7,8,3,2,1,5,4,6]=>0111010=>[2,1,1,2,2]
[7,8,3,2,1,5,6,4]=>0111001=>[2,1,1,3,1]
[6,3,8,2,1,5,7,4]=>1011001=>[1,2,1,3,1]
[5,3,2,8,1,6,7,4]=>1101001=>[1,1,2,3,1]
[5,4,2,7,8,1,6,3]=>1100101=>[1,1,3,2,1]
[5,3,2,7,1,8,6,4]=>1101011=>[1,1,2,2,1,1]
[5,3,2,7,1,6,4,8]=>1101010=>[1,1,2,2,2]
[6,3,7,2,1,5,4,8]=>1011010=>[1,2,1,2,2]
[6,3,7,2,1,5,8,4]=>1011001=>[1,2,1,3,1]
[6,3,7,2,1,8,5,4]=>1011011=>[1,2,1,2,1,1]
[6,5,7,8,2,1,4,3]=>1001101=>[1,3,1,2,1]
[6,3,7,2,1,4,8,5]=>1011001=>[1,2,1,3,1]
[5,3,2,7,1,4,8,6]=>1101001=>[1,1,2,3,1]
[5,4,2,8,7,1,3,6]=>1101100=>[1,1,2,1,3]
[7,8,4,2,6,1,3,5]=>0110100=>[2,1,2,3]
[7,8,3,2,1,6,4,5]=>0111010=>[2,1,1,2,2]
[6,3,8,2,1,7,4,5]=>1011010=>[1,2,1,2,2]
[5,3,2,8,1,7,4,6]=>1101010=>[1,1,2,2,2]
[4,3,2,1,8,7,5,6]=>1110110=>[1,1,1,2,1,2]
[4,3,2,1,7,5,8,6]=>1110101=>[1,1,1,2,2,1]
[4,3,2,1,7,5,6,8]=>1110100=>[1,1,1,2,3]
[5,3,2,8,1,4,7,6]=>1101001=>[1,1,2,3,1]
[6,3,8,2,1,4,7,5]=>1011001=>[1,2,1,3,1]
[7,8,3,2,1,4,6,5]=>0111001=>[2,1,1,3,1]
[4,3,2,1,8,5,6,7]=>1110100=>[1,1,1,2,3]
[7,8,5,6,1,2,4,3]=>0101001=>[2,2,3,1]
[7,8,4,1,6,2,5,3]=>0110101=>[2,1,2,2,1]
[1,6,8,3,2,7,5,4]=>0011011=>[3,1,2,1,1]
[6,1,8,3,2,7,5,4]=>1011011=>[1,2,1,2,1,1]
[7,8,1,3,2,6,5,4]=>0101011=>[2,2,2,1,1]
[7,8,3,1,2,6,5,4]=>0110011=>[2,1,3,1,1]
[7,8,2,3,1,6,5,4]=>0101011=>[2,2,2,1,1]
[7,8,2,1,3,6,5,4]=>0110011=>[2,1,3,1,1]
[7,8,1,2,3,6,5,4]=>0100011=>[2,4,1,1]
[1,5,2,8,3,7,6,4]=>0101011=>[2,2,2,1,1]
[5,1,2,8,3,7,6,4]=>1001011=>[1,3,2,1,1]
[5,2,1,8,3,7,6,4]=>1101011=>[1,1,2,2,1,1]
[6,2,8,1,3,7,5,4]=>1010011=>[1,2,3,1,1]
[6,2,8,4,7,1,5,3]=>1010101=>[1,2,2,2,1]
[6,3,8,4,7,5,1,2]=>1010110=>[1,2,2,1,2]
[2,6,8,3,1,7,5,4]=>0011011=>[3,1,2,1,1]
[2,5,1,8,3,7,6,4]=>0101011=>[2,2,2,1,1]
[1,2,5,8,3,7,6,4]=>0001011=>[4,2,1,1]
[2,5,3,8,1,7,6,4]=>0101011=>[2,2,2,1,1]
[2,5,4,8,7,1,6,3]=>0101101=>[2,2,1,2,1]
[3,5,4,8,7,6,1,2]=>0101110=>[2,2,1,1,2]
[5,3,4,8,7,6,1,2]=>1001110=>[1,3,1,1,2]
[5,2,4,8,7,1,6,3]=>1001101=>[1,3,1,2,1]
[5,2,3,8,1,7,6,4]=>1001011=>[1,3,2,1,1]
[4,1,2,3,8,7,6,5]=>1000111=>[1,4,1,1,1]
[1,4,2,3,8,7,6,5]=>0100111=>[2,3,1,1,1]
[4,1,3,2,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[6,3,8,1,2,7,5,4]=>1010011=>[1,2,3,1,1]
[5,3,1,8,2,7,6,4]=>1101011=>[1,1,2,2,1,1]
[5,1,3,8,2,7,6,4]=>1001011=>[1,3,2,1,1]
[1,5,3,8,2,7,6,4]=>0101011=>[2,2,2,1,1]
[1,5,4,8,7,2,6,3]=>0101101=>[2,2,1,2,1]
[5,1,4,8,7,2,6,3]=>1001101=>[1,3,1,2,1]
[5,4,1,8,7,2,6,3]=>1101101=>[1,1,2,1,2,1]
[6,5,8,7,1,2,4,3]=>1011001=>[1,2,1,3,1]
[5,6,8,7,3,4,1,2]=>0011010=>[3,1,2,2]
[5,6,8,7,2,1,4,3]=>0011101=>[3,1,1,2,1]
[4,5,1,8,7,2,6,3]=>0101101=>[2,2,1,2,1]
[4,1,5,8,7,2,6,3]=>1001101=>[1,3,1,2,1]
[1,3,5,8,2,7,6,4]=>0001011=>[4,2,1,1]
[3,1,5,8,2,7,6,4]=>1001011=>[1,3,2,1,1]
[3,6,8,2,1,7,5,4]=>0011011=>[3,1,2,1,1]
[4,6,8,3,7,5,1,2]=>0010110=>[3,2,1,2]
[4,5,3,8,7,6,1,2]=>0101110=>[2,2,1,1,2]
[3,5,2,8,1,7,6,4]=>0101011=>[2,2,2,1,1]
[3,1,4,2,8,7,6,5]=>1010111=>[1,2,2,1,1,1]
[3,2,5,8,1,7,6,4]=>1001011=>[1,3,2,1,1]
[4,2,5,8,7,1,6,3]=>1001101=>[1,3,1,2,1]
[4,3,5,8,7,6,1,2]=>1001110=>[1,3,1,1,2]
[2,4,5,8,7,1,6,3]=>0001101=>[4,1,2,1]
[2,3,5,8,1,7,6,4]=>0001011=>[4,2,1,1]
[6,2,5,1,4,3,8,7]=>1010101=>[1,2,2,2,1]
[5,2,6,1,4,3,8,7]=>1010101=>[1,2,2,2,1]
[5,2,7,1,4,3,8,6]=>1010101=>[1,2,2,2,1]
[6,2,8,1,4,3,7,5]=>1010101=>[1,2,2,2,1]
[6,2,7,1,4,3,8,5]=>1010101=>[1,2,2,2,1]
[7,2,6,1,4,3,8,5]=>1010101=>[1,2,2,2,1]
[8,2,5,1,4,3,7,6]=>1010101=>[1,2,2,2,1]
[8,1,4,3,7,2,6,5]=>1010101=>[1,2,2,2,1]
[8,2,6,1,5,3,7,4]=>1010101=>[1,2,2,2,1]
[7,2,6,1,5,3,8,4]=>1010101=>[1,2,2,2,1]
[6,2,7,1,5,3,8,4]=>1010101=>[1,2,2,2,1]
[6,2,8,1,5,3,7,4]=>1010101=>[1,2,2,2,1]
[7,4,8,1,3,2,6,5]=>1010101=>[1,2,2,2,1]
[8,3,7,1,4,2,6,5]=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,2,6,4]=>1010101=>[1,2,2,2,1]
[7,3,8,1,5,2,6,4]=>1010101=>[1,2,2,2,1]
[6,2,7,3,8,1,5,4]=>1010101=>[1,2,2,2,1]
[6,2,8,3,7,1,5,4]=>1010101=>[1,2,2,2,1]
[5,1,8,3,7,2,6,4]=>1010101=>[1,2,2,2,1]
[4,1,8,3,7,2,6,5]=>1010101=>[1,2,2,2,1]
[3,1,7,4,8,2,6,5]=>1010101=>[1,2,2,2,1]
[4,1,7,3,8,2,6,5]=>1010101=>[1,2,2,2,1]
[5,1,7,3,8,2,6,4]=>1010101=>[1,2,2,2,1]
[7,3,8,2,6,1,5,4]=>1010101=>[1,2,2,2,1]
[8,2,6,3,7,1,5,4]=>1010101=>[1,2,2,2,1]
[3,4,2,6,8,1,5,7]=>0100100=>[2,3,3]
[5,3,6,2,8,1,4,7]=>1010100=>[1,2,2,3]
[7,4,2,5,8,3,6,1]=>1100101=>[1,1,3,2,1]
[4,5,2,6,3,8,1,7]=>0101010=>[2,2,2,2]
[3,5,6,1,4,8,2,7]=>0010010=>[3,3,2]
[4,1,5,6,3,8,2,7]=>1001010=>[1,3,2,2]
[4,5,1,6,3,8,2,7]=>0101010=>[2,2,2,2]
[4,5,6,3,2,8,1,7]=>0011010=>[3,1,2,2]
[6,7,4,8,3,2,5,1]=>0101101=>[2,2,1,2,1]
[6,7,4,8,3,2,1,5]=>0101110=>[2,2,1,1,2]
[6,7,4,1,8,3,2,5]=>0110110=>[2,1,2,1,2]
[5,3,7,8,1,4,2,6]=>1001010=>[1,3,2,2]
[7,3,5,8,1,4,6,2]=>1001001=>[1,3,3,1]
[4,5,1,7,8,3,6,2]=>0100101=>[2,3,2,1]
[7,4,1,5,8,3,6,2]=>1100101=>[1,1,3,2,1]
[6,7,4,3,8,1,5,2]=>0110101=>[2,1,2,2,1]
[5,6,1,7,3,8,4,2]=>0101011=>[2,2,2,1,1]
[5,1,6,7,3,8,4,2]=>1001011=>[1,3,2,1,1]
[6,4,7,1,8,3,5,2]=>1010101=>[1,2,2,2,1]
[6,7,8,3,1,4,5,2]=>0011001=>[3,1,3,1]
[6,7,2,8,4,5,1,3]=>0101010=>[2,2,2,2]
[6,7,2,8,4,1,3,5]=>0101100=>[2,2,1,3]
[6,1,7,4,8,3,2,5]=>1010110=>[1,2,2,1,2]
[5,1,6,7,3,2,8,4]=>1001101=>[1,3,1,2,1]
[5,6,1,7,3,2,8,4]=>0101101=>[2,2,1,2,1]
[5,6,7,3,2,1,8,4]=>0011101=>[3,1,1,2,1]
[5,6,7,3,2,8,4,1]=>0011011=>[3,1,2,1,1]
[7,4,2,5,1,8,3,6]=>1101010=>[1,1,2,2,2]
[6,7,4,2,8,3,5,1]=>0110101=>[2,1,2,2,1]
[3,6,7,2,8,4,5,1]=>0010101=>[3,2,2,1]
[3,6,7,2,8,4,1,5]=>0010110=>[3,2,1,2]
[3,6,7,2,1,8,4,5]=>0011010=>[3,1,2,2]
[3,4,7,8,2,1,5,6]=>0001100=>[4,1,3]
[3,7,8,1,4,6,2,5]=>0010010=>[3,3,2]
[3,6,7,2,8,5,1,4]=>0010110=>[3,2,1,2]
[3,6,7,8,5,2,1,4]=>0001110=>[4,1,1,2]
[3,6,7,8,5,2,4,1]=>0001101=>[4,1,2,1]
[6,4,7,8,2,5,3,1]=>1001011=>[1,3,2,1,1]
[6,4,7,8,2,1,5,3]=>1001101=>[1,3,1,2,1]
[5,3,7,8,1,6,2,4]=>1001010=>[1,3,2,2]
[6,7,2,8,5,1,3,4]=>0101100=>[2,2,1,3]
[6,4,1,7,8,2,5,3]=>1100101=>[1,1,3,2,1]
[5,1,6,2,7,8,4,3]=>1010011=>[1,2,3,1,1]
[5,6,2,7,1,8,4,3]=>0101011=>[2,2,2,1,1]
[5,6,2,7,8,4,3,1]=>0100111=>[2,3,1,1,1]
[5,6,7,2,8,4,3,1]=>0010111=>[3,2,1,1,1]
[5,6,7,2,1,8,4,3]=>0011011=>[3,1,2,1,1]
[5,6,1,7,2,8,4,3]=>0101011=>[2,2,2,1,1]
[5,1,6,7,2,8,4,3]=>1001011=>[1,3,2,1,1]
[6,7,8,3,5,1,4,2]=>0010101=>[3,2,2,1]
[5,6,1,7,8,4,3,2]=>0100111=>[2,3,1,1,1]
[5,6,7,1,8,4,3,2]=>0010111=>[3,2,1,1,1]
[8,3,2,5,1,6,4,7]=>1101010=>[1,1,2,2,2]
[5,3,2,7,4,1,8,6]=>1101101=>[1,1,2,1,2,1]
[7,5,3,8,2,4,6,1]=>1101001=>[1,1,2,3,1]
[8,2,4,5,6,3,1,7]=>1000110=>[1,4,1,2]
[8,2,4,5,6,1,3,7]=>1000100=>[1,4,3]
[8,5,3,6,4,1,2,7]=>1101100=>[1,1,2,1,3]
[8,4,1,5,6,3,2,7]=>1100110=>[1,1,3,1,2]
[8,1,4,5,6,3,2,7]=>1000110=>[1,4,1,2]
[4,5,3,7,2,1,8,6]=>0101101=>[2,2,1,2,1]
[7,4,5,8,3,2,6,1]=>1001101=>[1,3,1,2,1]
[4,3,6,7,2,8,5,1]=>1001011=>[1,3,2,1,1]
[4,3,6,7,2,8,1,5]=>1001010=>[1,3,2,2]
[1,4,3,6,7,2,8,5]=>0100101=>[2,3,2,1]
[4,5,3,7,1,8,2,6]=>0101010=>[2,2,2,2]
[5,3,4,7,1,2,8,6]=>1001001=>[1,3,3,1]
[7,4,5,8,3,6,1,2]=>1001010=>[1,3,2,2]
[4,3,6,7,8,1,5,2]=>1000101=>[1,4,2,1]
[3,5,6,7,8,4,1,2]=>0000110=>[5,1,2]
[3,1,5,6,7,8,4,2]=>1000011=>[1,5,1,1]
[4,6,1,7,8,3,5,2]=>0100101=>[2,3,2,1]
[6,2,4,1,7,8,5,3]=>1010011=>[1,2,3,1,1]
[2,6,7,1,4,8,3,5]=>0010010=>[3,3,2]
[1,5,3,6,7,8,2,4]=>0100010=>[2,4,2]
[4,5,2,7,8,1,3,6]=>0100100=>[2,3,3]
[4,2,6,7,8,3,1,5]=>1000110=>[1,4,1,2]
[4,2,6,7,8,3,5,1]=>1000101=>[1,4,2,1]
[3,6,2,7,4,8,1,5]=>0101010=>[2,2,2,2]
[3,7,4,2,1,5,8,6]=>0111001=>[2,1,1,3,1]
[7,8,4,2,1,3,6,5]=>0111001=>[2,1,1,3,1]
[6,3,2,7,1,8,5,4]=>1101011=>[1,1,2,2,1,1]
[3,6,2,7,1,8,5,4]=>0101011=>[2,2,2,1,1]
[6,7,3,8,2,5,4,1]=>0101011=>[2,2,2,1,1]
[6,4,7,8,5,2,3,1]=>1001101=>[1,3,1,2,1]
[2,6,4,7,8,1,5,3]=>0100101=>[2,3,2,1]
[7,4,1,5,8,6,2,3]=>1100110=>[1,1,3,1,2]
[7,5,8,2,1,6,3,4]=>1011010=>[1,2,1,2,2]
[6,2,7,1,3,8,5,4]=>1010011=>[1,2,3,1,1]
[6,3,1,7,8,2,5,4]=>1100101=>[1,1,3,2,1]
[4,6,1,7,8,5,2,3]=>0100110=>[2,3,1,2]
[5,1,2,6,7,8,4,3]=>1000011=>[1,5,1,1]
[5,2,6,7,8,4,3,1]=>1000111=>[1,4,1,1,1]
[1,6,4,7,8,5,2,3]=>0100110=>[2,3,1,2]
[2,6,7,1,3,8,5,4]=>0010011=>[3,3,1,1]
[6,7,3,8,5,1,4,2]=>0101101=>[2,2,1,2,1]
[6,4,7,8,5,3,1,2]=>1001110=>[1,3,1,1,2]
[3,1,2,6,5,8,7,4]=>1001011=>[1,3,2,1,1]
[4,5,1,2,3,8,7,6]=>0100011=>[2,4,1,1]
[4,6,1,2,3,8,7,5]=>0100011=>[2,4,1,1]
[1,6,5,3,4,8,7,2]=>0110011=>[2,1,3,1,1]
[6,1,5,2,4,8,7,3]=>1010011=>[1,2,3,1,1]
[6,5,1,2,3,8,7,4]=>1100011=>[1,1,4,1,1]
[6,4,1,2,3,8,7,5]=>1100011=>[1,1,4,1,1]
[5,4,1,2,3,8,7,6]=>1100011=>[1,1,4,1,1]
[5,4,1,2,7,3,6,8]=>1100100=>[1,1,3,3]
[6,4,1,7,2,3,5,8]=>1101000=>[1,1,2,4]
[6,4,1,8,2,3,5,7]=>1101000=>[1,1,2,4]
[7,4,1,2,8,3,6,5]=>1100101=>[1,1,3,2,1]
[7,5,1,2,8,3,6,4]=>1100101=>[1,1,3,2,1]
[7,1,5,2,8,4,6,3]=>1010101=>[1,2,2,2,1]
[1,7,5,3,8,4,6,2]=>0110101=>[2,1,2,2,1]
[8,4,1,2,7,3,6,5]=>1100101=>[1,1,3,2,1]
[8,4,1,7,2,3,5,6]=>1101000=>[1,1,2,4]
[7,4,1,6,2,3,5,8]=>1101000=>[1,1,2,4]
[8,6,1,7,2,3,5,4]=>1101001=>[1,1,2,3,1]
[8,1,6,7,2,4,5,3]=>1001001=>[1,3,3,1]
[1,7,6,8,3,4,5,2]=>0101001=>[2,2,3,1]
[7,6,1,8,2,3,5,4]=>1101001=>[1,1,2,3,1]
[3,1,2,7,8,5,6,4]=>1000101=>[1,4,2,1]
[3,1,8,7,2,4,5,6]=>1011000=>[1,2,1,4]
[3,1,7,6,2,4,5,8]=>1011000=>[1,2,1,4]
[4,7,1,6,2,3,5,8]=>0101000=>[2,2,4]
[4,8,1,6,2,3,5,7]=>0101000=>[2,2,4]
[5,8,1,2,7,3,6,4]=>0100101=>[2,3,2,1]
[5,1,8,2,7,4,6,3]=>1010101=>[1,2,2,2,1]
[1,5,8,3,7,4,6,2]=>0010101=>[3,2,2,1]
[1,6,8,7,3,4,5,2]=>0011001=>[3,1,3,1]
[6,1,8,7,2,4,5,3]=>1011001=>[1,2,1,3,1]
[6,8,1,7,2,3,5,4]=>0101001=>[2,2,3,1]
[6,8,7,1,2,3,4,5]=>0110000=>[2,1,5]
[5,8,6,1,2,3,4,7]=>0110000=>[2,1,5]
[5,7,6,1,2,3,4,8]=>0110000=>[2,1,5]
[7,8,1,6,2,3,5,4]=>0101001=>[2,2,3,1]
[7,1,8,6,2,4,5,3]=>1011001=>[1,2,1,3,1]
[1,7,8,6,3,4,5,2]=>0011001=>[3,1,3,1]
[8,1,7,6,2,4,5,3]=>1011001=>[1,2,1,3,1]
[8,7,1,6,2,3,5,4]=>1101001=>[1,1,2,3,1]
[8,5,3,7,2,1,4,6]=>1101100=>[1,1,2,1,3]
[6,8,1,4,5,7,3,2]=>0100011=>[2,4,1,1]
[8,7,2,4,5,1,3,6]=>1100100=>[1,1,3,3]
[2,6,1,4,5,3,8,7]=>0100101=>[2,3,2,1]
[6,3,1,4,5,2,8,7]=>1100101=>[1,1,3,2,1]
[3,1,6,4,5,2,8,7]=>1010101=>[1,2,2,2,1]
[8,3,7,4,5,1,2,6]=>1010100=>[1,2,2,3]
[5,8,7,4,2,6,3,1]=>0111011=>[2,1,1,2,1,1]
[8,1,7,4,2,6,3,5]=>1011010=>[1,2,1,2,2]
[3,7,8,4,5,1,2,6]=>0010100=>[3,2,3]
[5,6,3,8,1,7,2,4]=>0101010=>[2,2,2,2]
[7,6,1,4,5,8,3,2]=>1100011=>[1,1,4,1,1]
[3,7,6,4,5,8,2,1]=>0110011=>[2,1,3,1,1]
[8,5,7,4,1,6,3,2]=>1011011=>[1,2,1,2,1,1]
[2,5,8,4,7,6,1,3]=>0010110=>[3,2,1,2]
[3,8,4,2,5,6,7,1]=>0110001=>[2,1,4,1]
[8,4,1,3,5,6,7,2]=>1100001=>[1,1,5,1]
[7,5,8,4,3,6,1,2]=>1011010=>[1,2,1,2,2]
[6,5,3,8,4,1,7,2]=>1101101=>[1,1,2,1,2,1]
[2,1,4,8,3,6,7,5]=>1001001=>[1,3,3,1]
[7,3,8,4,2,6,1,5]=>1011010=>[1,2,1,2,2]
[8,3,1,2,5,6,7,4]=>1100001=>[1,1,5,1]
[4,8,2,3,5,6,7,1]=>0100001=>[2,5,1]
[2,7,8,4,5,3,1,6]=>0010110=>[3,2,1,2]
[8,7,1,4,3,6,2,5]=>1101010=>[1,1,2,2,2]
[5,6,3,8,4,2,7,1]=>0101101=>[2,2,1,2,1]
[8,6,3,1,4,2,7,5]=>1110101=>[1,1,1,2,2,1]
[8,6,3,5,1,2,7,4]=>1101001=>[1,1,2,3,1]
[5,8,3,2,6,1,7,4]=>0110101=>[2,1,2,2,1]
[3,5,8,4,7,6,2,1]=>0010111=>[3,2,1,1,1]
[5,8,2,4,7,6,1,3]=>0100110=>[2,3,1,2]
[7,1,6,4,5,8,2,3]=>1010010=>[1,2,3,2]
[2,1,8,5,3,6,7,4]=>1011001=>[1,2,1,3,1]
[6,8,3,5,2,1,7,4]=>0101101=>[2,2,1,2,1]
[7,8,5,4,2,6,1,3]=>0111010=>[2,1,1,2,2]
[4,8,1,2,5,6,7,3]=>0100001=>[2,5,1]
[3,4,2,8,5,6,7,1]=>0101001=>[2,2,3,1]
[2,4,1,8,5,6,7,3]=>0101001=>[2,2,3,1]
[8,4,2,1,5,6,7,3]=>1110001=>[1,1,1,4,1]
[7,5,2,4,8,6,1,3]=>1100110=>[1,1,3,1,2]
[2,1,5,3,8,6,7,4]=>1010101=>[1,2,2,2,1]
[3,1,4,8,5,6,7,2]=>1001001=>[1,3,3,1]
[6,5,3,7,2,8,4,1]=>1101011=>[1,1,2,2,1,1]
[6,7,2,4,5,8,3,1]=>0100011=>[2,4,1,1]
[2,5,7,4,8,6,3,1]=>0010111=>[3,2,1,1,1]
[5,6,3,7,1,8,4,2]=>0101011=>[2,2,2,1,1]
[3,8,7,4,5,2,1,6]=>0110110=>[2,1,2,1,2]
[3,7,5,4,8,6,2,1]=>0110111=>[2,1,2,1,1,1]
[4,6,3,5,8,2,7,1]=>0100101=>[2,3,2,1]
[3,7,8,4,1,6,2,5]=>0011010=>[3,1,2,2]
[5,4,2,3,7,6,1,8]=>1100110=>[1,1,3,1,2]
[3,2,7,6,4,5,1,8]=>1011010=>[1,2,1,2,2]
[4,7,2,6,3,5,1,8]=>0101010=>[2,2,2,2]
[5,7,6,2,3,4,1,8]=>0110010=>[2,1,3,2]
[1,7,5,2,8,3,4,6]=>0110100=>[2,1,2,3]
[6,8,5,2,3,1,4,7]=>0110100=>[2,1,2,3]
[4,8,2,6,3,1,5,7]=>0101100=>[2,2,1,3]
[3,2,8,6,4,1,5,7]=>1011100=>[1,2,1,1,3]
[7,1,5,2,8,3,4,6]=>1010100=>[1,2,2,3]
[1,8,5,2,7,3,4,6]=>0110100=>[2,1,2,3]
[7,1,6,8,2,3,4,5]=>1001000=>[1,3,4]
[3,2,1,7,8,4,5,6]=>1100100=>[1,1,3,3]
[3,2,8,7,1,4,5,6]=>1011000=>[1,2,1,4]
[5,8,7,2,1,3,4,6]=>0111000=>[2,1,1,4]
[1,7,6,8,2,3,4,5]=>0101000=>[2,2,4]
[6,5,8,2,3,1,4,7]=>1010100=>[1,2,2,3]
[8,5,7,2,1,3,4,6]=>1011000=>[1,2,1,4]
[3,2,5,4,1,8,6,7]=>1011010=>[1,2,1,2,2]
[7,4,2,1,8,3,5,6]=>1110100=>[1,1,1,2,3]
[8,4,2,1,7,3,5,6]=>1110100=>[1,1,1,2,3]
[1,4,2,8,7,3,5,6]=>0101100=>[2,2,1,3]
[1,5,8,2,7,3,4,6]=>0010100=>[3,2,3]
[8,5,1,2,7,3,4,6]=>1100100=>[1,1,3,3]
[3,2,6,1,4,8,5,7]=>1010010=>[1,2,3,2]
[3,2,7,1,8,4,5,6]=>1010100=>[1,2,2,3]
[4,7,2,1,8,3,5,6]=>0110100=>[2,1,2,3]
[8,6,1,7,2,3,4,5]=>1101000=>[1,1,2,4]
[1,6,8,7,2,3,4,5]=>0011000=>[3,1,4]
[1,7,8,6,2,3,4,5]=>0011000=>[3,1,4]
[7,8,1,6,2,3,4,5]=>0101000=>[2,2,4]
[4,8,2,1,7,3,5,6]=>0110100=>[2,1,2,3]
[3,2,8,1,7,4,5,6]=>1010100=>[1,2,2,3]
[5,1,8,2,7,3,4,6]=>1010100=>[1,2,2,3]
[6,1,8,7,2,3,4,5]=>1011000=>[1,2,1,4]
[8,1,7,6,2,3,4,5]=>1011000=>[1,2,1,4]
[2,8,4,1,6,5,7,3]=>0110101=>[2,1,2,2,1]
[2,8,5,6,7,4,3,1]=>0100111=>[2,3,1,1,1]
[7,5,8,6,1,4,2,3]=>1011010=>[1,2,1,2,2]
[3,5,7,6,1,4,2,8]=>0011010=>[3,1,2,2]
[7,5,8,2,4,1,6,3]=>1010101=>[1,2,2,2,1]
[2,8,5,3,4,7,6,1]=>0110011=>[2,1,3,1,1]
[2,8,5,3,4,1,7,6]=>0110101=>[2,1,2,2,1]
[2,8,5,3,6,1,7,4]=>0110101=>[2,1,2,2,1]
[2,8,5,6,7,4,1,3]=>0100110=>[2,3,1,2]
[2,8,5,3,4,7,1,6]=>0110010=>[2,1,3,2]
[2,8,5,3,4,6,1,7]=>0110010=>[2,1,3,2]
[6,5,2,7,3,1,4,8]=>1101100=>[1,1,2,1,3]
[6,5,2,8,3,1,7,4]=>1101101=>[1,1,2,1,2,1]
[6,5,2,8,3,1,4,7]=>1101100=>[1,1,2,1,3]
[7,5,8,2,4,6,3,1]=>1010011=>[1,2,3,1,1]
[7,5,8,6,1,4,3,2]=>1011011=>[1,2,1,2,1,1]
[6,5,8,2,1,3,7,4]=>1011001=>[1,2,1,3,1]
[3,5,6,2,1,8,7,4]=>0011011=>[3,1,2,1,1]
[3,5,7,2,4,1,8,6]=>0010101=>[3,2,2,1]
[6,5,2,7,3,1,8,4]=>1101101=>[1,1,2,1,2,1]
[4,5,2,6,3,1,7,8]=>0101100=>[2,2,1,3]
[6,5,2,7,3,4,8,1]=>1101001=>[1,1,2,3,1]
[5,1,6,7,4,3,8,2]=>1001101=>[1,3,1,2,1]
[5,1,2,6,4,8,7,3]=>1001011=>[1,3,2,1,1]
[5,1,2,8,6,4,7,3]=>1001101=>[1,3,1,2,1]
[5,1,6,8,7,3,4,2]=>1001101=>[1,3,1,2,1]
[6,5,2,8,3,7,4,1]=>1101011=>[1,1,2,2,1,1]
[4,1,2,3,8,6,5,7]=>1000110=>[1,4,1,2]
[4,1,2,3,8,6,7,5]=>1000101=>[1,4,2,1]
[4,1,2,3,8,5,7,6]=>1000101=>[1,4,2,1]
[6,5,8,2,4,3,7,1]=>1010101=>[1,2,2,2,1]
[6,5,2,8,3,7,1,4]=>1101010=>[1,1,2,2,2]
[6,5,2,7,3,4,1,8]=>1101010=>[1,1,2,2,2]
[5,1,6,7,4,3,2,8]=>1001110=>[1,3,1,1,2]
[5,1,6,8,7,3,2,4]=>1001110=>[1,3,1,1,2]
[5,7,8,6,3,4,2,1]=>0011011=>[3,1,2,1,1]
[3,1,4,8,6,2,7,5]=>1001101=>[1,3,1,2,1]
[3,1,4,8,6,5,2,7]=>1001110=>[1,3,1,1,2]
[4,1,6,7,8,3,2,5]=>1000110=>[1,4,1,2]
[4,1,6,5,7,3,2,8]=>1010110=>[1,2,2,1,2]
[4,5,2,6,3,7,1,8]=>0101010=>[2,2,2,2]
[4,5,2,7,3,8,1,6]=>0101010=>[2,2,2,2]
[3,5,6,2,4,8,1,7]=>0010010=>[3,3,2]
[3,7,5,6,8,4,1,2]=>0100110=>[2,3,1,2]
[3,6,5,2,8,1,7,4]=>0110101=>[2,1,2,2,1]
[6,1,2,5,8,4,7,3]=>1000101=>[1,4,2,1]
[4,1,2,3,5,8,7,6]=>1000011=>[1,5,1,1]
[4,1,6,7,8,3,5,2]=>1000101=>[1,4,2,1]
[4,1,2,6,8,5,7,3]=>1000101=>[1,4,2,1]
[4,1,2,5,6,8,7,3]=>1000011=>[1,5,1,1]
[4,5,2,6,3,7,8,1]=>0101001=>[2,2,3,1]
[6,4,2,7,1,3,8,5]=>1101001=>[1,1,2,3,1]
[7,4,2,5,1,3,8,6]=>1101001=>[1,1,2,3,1]
[8,5,3,6,1,7,2,4]=>1101010=>[1,1,2,2,2]
[7,3,6,2,4,8,1,5]=>1010010=>[1,2,3,2]
[6,3,7,4,1,2,8,5]=>1011001=>[1,2,1,3,1]
[3,7,5,1,2,4,8,6]=>0110001=>[2,1,4,1]
[7,4,8,5,2,6,1,3]=>1011010=>[1,2,1,2,2]
[5,8,2,6,3,7,1,4]=>0101010=>[2,2,2,2]
[3,8,6,2,4,7,1,5]=>0110010=>[2,1,3,2]
[3,8,5,7,1,2,4,6]=>0101000=>[2,2,4]
[2,8,5,7,1,3,4,6]=>0101000=>[2,2,4]
[4,8,6,2,7,1,3,5]=>0110100=>[2,1,2,3]
[3,6,5,8,1,2,4,7]=>0101000=>[2,2,4]
[5,4,7,3,8,1,2,6]=>1010100=>[1,2,2,3]
[8,4,1,6,7,2,3,5]=>1100100=>[1,1,3,3]
[6,5,1,2,7,8,3,4]=>1100010=>[1,1,4,2]
[4,7,1,5,8,6,2,3]=>0100110=>[2,3,1,2]
[7,6,1,8,5,2,3,4]=>1101100=>[1,1,2,1,3]
[5,7,2,8,1,6,3,4]=>0101010=>[2,2,2,2]
[6,3,7,8,5,1,2,4]=>1001100=>[1,3,1,3]
[3,6,8,2,7,1,4,5]=>0010100=>[3,2,3]
[5,3,8,7,1,2,4,6]=>1011000=>[1,2,1,4]
[8,3,7,6,1,2,4,5]=>1011000=>[1,2,1,4]
[8,4,7,6,1,2,3,5]=>1011000=>[1,2,1,4]
[5,4,8,7,1,2,3,6]=>1011000=>[1,2,1,4]
[3,5,8,7,1,2,4,6]=>0011000=>[3,1,4]
[2,5,8,7,1,3,4,6]=>0011000=>[3,1,4]
[6,8,4,7,5,1,2,3]=>0101100=>[2,2,1,3]
[5,8,7,1,6,2,3,4]=>0110100=>[2,1,2,3]
[2,8,7,6,1,3,4,5]=>0111000=>[2,1,1,4]
[3,8,7,6,1,2,4,5]=>0111000=>[2,1,1,4]
[4,8,7,6,1,2,3,5]=>0111000=>[2,1,1,4]
[5,6,3,1,4,2,8,7]=>0110101=>[2,1,2,2,1]
[7,5,3,8,2,1,6,4]=>1101101=>[1,1,2,1,2,1]
[3,8,7,4,5,1,6,2]=>0110101=>[2,1,2,2,1]
[6,7,1,4,5,8,2,3]=>0100010=>[2,4,2]
[2,1,7,8,5,3,6,4]=>1001101=>[1,3,1,2,1]
[5,7,3,8,1,2,6,4]=>0101001=>[2,2,3,1]
[7,5,1,4,8,6,3,2]=>1100111=>[1,1,3,1,1,1]
[6,4,3,8,1,5,7,2]=>1101001=>[1,1,2,3,1]
[8,6,3,1,2,5,7,4]=>1110001=>[1,1,1,4,1]
[8,7,1,4,2,6,5,3]=>1101011=>[1,1,2,2,1,1]
[7,3,8,4,1,6,5,2]=>1011011=>[1,2,1,2,1,1]
[5,3,2,7,4,6,8,1]=>1101001=>[1,1,2,3,1]
[7,5,3,6,2,4,8,1]=>1101001=>[1,1,2,3,1]
[6,3,2,5,1,8,4,7]=>1101010=>[1,1,2,2,2]
[8,5,3,6,2,7,1,4]=>1101010=>[1,1,2,2,2]
[7,2,6,3,4,5,8,1]=>1010001=>[1,2,4,1]
[6,2,7,3,4,5,8,1]=>1010001=>[1,2,4,1]
[6,7,3,5,2,4,8,1]=>0101001=>[2,2,3,1]
[3,7,6,2,4,5,8,1]=>0110001=>[2,1,4,1]
[6,5,3,1,2,8,4,7]=>1110010=>[1,1,1,3,2]
[8,6,5,2,3,7,1,4]=>1110010=>[1,1,1,3,2]
[8,5,2,1,7,3,4,6]=>1110100=>[1,1,1,2,3]
[7,5,2,1,8,3,4,6]=>1110100=>[1,1,1,2,3]
[1,6,3,2,8,4,5,7]=>0110100=>[2,1,2,3]
[4,2,6,5,1,8,3,7]=>1011010=>[1,2,1,2,2]
[5,4,8,6,2,7,1,3]=>1011010=>[1,2,1,2,2]
[7,8,5,2,3,6,1,4]=>0110010=>[2,1,3,2]
[6,8,2,1,7,3,4,5]=>0110100=>[2,1,2,3]
[2,8,1,7,3,4,5,6]=>0101000=>[2,2,4]
[3,8,6,1,7,2,4,5]=>0110100=>[2,1,2,3]
[4,2,8,3,7,1,5,6]=>1010100=>[1,2,2,3]
[8,1,2,7,3,4,5,6]=>1001000=>[1,3,4]
[6,3,7,1,2,8,4,5]=>1010010=>[1,2,3,2]
[7,2,6,1,8,3,4,5]=>1010100=>[1,2,2,3]
[7,3,1,5,8,2,4,6]=>1100100=>[1,1,3,3]
[5,4,1,3,6,8,2,7]=>1100010=>[1,1,4,2]
[8,5,3,7,6,1,2,4]=>1101100=>[1,1,2,1,3]
[6,1,8,3,7,2,4,5]=>1010100=>[1,2,2,3]
[7,6,8,2,3,5,1,4]=>1010010=>[1,2,3,2]
[3,7,8,2,4,6,1,5]=>0010010=>[3,3,2]
[5,4,7,8,2,6,1,3]=>1001010=>[1,3,2,2]
[4,2,5,8,7,1,3,6]=>1001100=>[1,3,1,3]
[2,3,8,7,1,4,5,6]=>0011000=>[3,1,4]
[2,1,8,7,3,4,5,6]=>1011000=>[1,2,1,4]
[8,2,7,6,1,3,4,5]=>1011000=>[1,2,1,4]
[1,2,8,7,3,4,5,6]=>0011000=>[3,1,4]
[1,3,8,7,2,4,5,6]=>0011000=>[3,1,4]
[1,7,8,3,6,2,4,5]=>0010100=>[3,2,3]
[5,4,8,7,6,1,2,3]=>1011100=>[1,2,1,1,3]
[6,8,3,7,5,1,2,4]=>0101100=>[2,2,1,3]
[7,8,6,2,5,1,3,4]=>0110100=>[2,1,2,3]
[8,1,6,7,3,2,4,5]=>1001100=>[1,3,1,3]
[8,1,5,3,7,2,4,6]=>1010100=>[1,2,2,3]
[8,1,5,3,6,2,4,7]=>1010100=>[1,2,2,3]
[7,4,8,3,2,6,5,1]=>1011011=>[1,2,1,2,1,1]
[7,4,1,3,2,6,5,8]=>1101010=>[1,1,2,2,2]
[8,1,4,3,2,6,5,7]=>1011010=>[1,2,1,2,2]
[8,1,4,3,2,7,5,6]=>1011010=>[1,2,1,2,2]
[8,1,5,4,6,7,2,3]=>1010010=>[1,2,3,2]
[8,1,5,3,6,2,7,4]=>1010101=>[1,2,2,2,1]
[8,1,4,3,2,6,7,5]=>1011001=>[1,2,1,3,1]
[8,1,4,3,2,5,7,6]=>1011001=>[1,2,1,3,1]
[7,4,1,3,2,5,6,8]=>1101000=>[1,1,2,4]
[7,4,8,3,2,5,6,1]=>1011001=>[1,2,1,3,1]
[6,4,3,1,2,5,8,7]=>1110001=>[1,1,1,4,1]
[7,4,1,3,2,5,8,6]=>1101001=>[1,1,2,3,1]
[7,5,1,3,6,2,8,4]=>1100101=>[1,1,3,2,1]
[7,5,1,4,6,8,2,3]=>1100010=>[1,1,4,2]
[6,4,3,8,2,5,1,7]=>1101010=>[1,1,2,2,2]
[5,4,3,2,8,6,1,7]=>1110110=>[1,1,1,2,1,2]
[5,4,3,2,8,7,1,6]=>1110110=>[1,1,1,2,1,2]
[6,5,4,8,7,1,2,3]=>1101100=>[1,1,2,1,3]
[6,5,4,1,7,8,2,3]=>1110010=>[1,1,1,3,2]
[6,4,3,1,2,7,8,5]=>1110001=>[1,1,1,4,1]
[7,4,1,3,2,8,5,6]=>1101010=>[1,1,2,2,2]
[6,4,3,1,2,7,5,8]=>1110010=>[1,1,1,3,2]
[6,4,3,8,2,7,5,1]=>1101011=>[1,1,2,2,1,1]
[6,5,3,8,7,2,4,1]=>1101101=>[1,1,2,1,2,1]
[6,5,3,1,7,2,4,8]=>1110100=>[1,1,1,2,3]
[7,5,1,3,8,2,4,6]=>1100100=>[1,1,3,3]
[6,5,3,7,8,2,4,1]=>1100101=>[1,1,3,2,1]
[6,4,3,7,2,8,5,1]=>1101011=>[1,1,2,2,1,1]
[6,4,3,7,2,1,5,8]=>1101100=>[1,1,2,1,3]
[7,5,8,4,1,6,2,3]=>1011010=>[1,2,1,2,2]
[6,5,4,8,1,7,2,3]=>1101010=>[1,1,2,2,2]
[6,5,3,8,1,2,7,4]=>1101001=>[1,1,2,3,1]
[6,5,4,7,1,8,2,3]=>1101010=>[1,1,2,2,2]
[5,4,3,2,7,8,1,6]=>1110010=>[1,1,1,3,2]
[4,6,3,8,5,1,2,7]=>0101100=>[2,2,1,3]
[5,6,8,3,4,1,2,7]=>0010100=>[3,2,3]
[5,6,8,3,4,1,7,2]=>0010101=>[3,2,2,1]
[4,6,2,7,5,3,1,8]=>0101110=>[2,2,1,1,2]
[5,6,8,4,3,1,2,7]=>0011100=>[3,1,1,3]
[5,7,8,4,1,3,6,2]=>0011001=>[3,1,3,1]
[5,6,8,4,2,1,7,3]=>0011101=>[3,1,1,2,1]
[5,6,8,2,4,1,7,3]=>0010101=>[3,2,2,1]
[3,2,6,8,5,1,4,7]=>1001100=>[1,3,1,3]
[5,6,8,4,2,1,3,7]=>0011100=>[3,1,1,3]
[5,7,8,4,1,3,2,6]=>0011010=>[3,1,2,2]
[5,7,8,4,1,2,3,6]=>0011000=>[3,1,4]
[6,7,8,1,5,2,3,4]=>0010100=>[3,2,3]
[6,7,8,1,5,3,2,4]=>0010110=>[3,2,1,2]
[6,7,8,1,3,5,2,4]=>0010010=>[3,3,2]
[5,7,8,2,1,6,3,4]=>0011010=>[3,1,2,2]
[4,7,2,8,1,6,3,5]=>0101010=>[2,2,2,2]
[3,2,7,8,1,6,4,5]=>1001010=>[1,3,2,2]
[4,7,2,8,1,6,5,3]=>0101011=>[2,2,2,1,1]
[5,7,8,2,1,6,4,3]=>0011011=>[3,1,2,1,1]
[6,7,8,1,3,5,4,2]=>0010011=>[3,3,1,1]
[6,7,8,1,5,3,4,2]=>0010101=>[3,2,2,1]
[6,7,8,1,4,3,5,2]=>0010101=>[3,2,2,1]
[5,6,8,3,2,1,7,4]=>0011101=>[3,1,1,2,1]
[4,7,3,8,1,6,2,5]=>0101010=>[2,2,2,2]
[4,7,3,8,1,5,6,2]=>0101001=>[2,2,3,1]
[4,7,3,8,1,5,2,6]=>0101010=>[2,2,2,2]
[4,7,3,8,1,2,5,6]=>0101000=>[2,2,4]
[5,7,8,3,1,2,4,6]=>0011000=>[3,1,4]
[5,6,8,3,2,1,4,7]=>0011100=>[3,1,1,3]
[3,2,7,8,1,5,4,6]=>1001010=>[1,3,2,2]
[6,7,8,1,3,4,2,5]=>0010010=>[3,3,2]
[6,7,8,1,4,2,3,5]=>0010100=>[3,2,3]
[6,7,8,1,2,5,3,4]=>0010010=>[3,3,2]
[6,7,8,1,2,4,5,3]=>0010001=>[3,4,1]
[5,7,8,2,1,3,6,4]=>0011001=>[3,1,3,1]
[3,2,7,8,1,4,6,5]=>1001001=>[1,3,3,1]
[6,7,8,1,3,2,4,5]=>0010100=>[3,2,3]
[6,7,8,1,2,4,3,5]=>0010010=>[3,3,2]
[6,7,8,1,2,3,5,4]=>0010001=>[3,4,1]
[8,3,5,1,7,4,6,2]=>1010101=>[1,2,2,2,1]
[8,3,4,1,7,5,6,2]=>1010101=>[1,2,2,2,1]
[4,8,3,1,7,5,6,2]=>0110101=>[2,1,2,2,1]
[4,6,2,1,7,5,8,3]=>0110101=>[2,1,2,2,1]
[1,4,6,2,7,5,8,3]=>0010101=>[3,2,2,1]
[1,7,5,2,6,8,4,3]=>0110011=>[2,1,3,1,1]
[7,5,2,1,6,8,4,3]=>1110011=>[1,1,1,3,1,1]
[6,8,4,3,1,7,5,2]=>0111011=>[2,1,1,2,1,1]
[4,7,5,6,1,8,3,2]=>0101011=>[2,2,2,1,1]
[6,7,5,1,8,4,3,2]=>0110111=>[2,1,2,1,1,1]
[6,8,4,1,7,5,3,2]=>0110111=>[2,1,2,1,1,1]
[6,7,5,3,1,8,4,2]=>0111011=>[2,1,1,2,1,1]
[8,4,2,1,6,7,5,3]=>1110011=>[1,1,1,3,1,1]
[1,8,4,2,6,7,5,3]=>0110011=>[2,1,3,1,1]
[1,5,3,2,7,6,8,4]=>0110101=>[2,1,2,2,1]
[2,5,3,1,7,6,8,4]=>0110101=>[2,1,2,2,1]
[2,7,5,1,6,8,4,3]=>0110011=>[2,1,3,1,1]
[4,7,1,6,5,8,2,3]=>0101010=>[2,2,2,2]
[4,6,1,2,7,5,8,3]=>0100101=>[2,3,2,1]
[8,4,1,2,6,7,5,3]=>1100011=>[1,1,4,1,1]
[5,3,1,2,7,6,8,4]=>1100101=>[1,1,3,2,1]
[4,3,1,2,7,6,8,5]=>1100101=>[1,1,3,2,1]
[3,5,1,2,7,6,8,4]=>0100101=>[2,3,2,1]
[6,7,1,5,8,2,3,4]=>0100100=>[2,3,3]
[2,7,6,1,5,8,3,4]=>0110010=>[2,1,3,2]
[2,3,5,1,7,6,8,4]=>0010101=>[3,2,2,1]
[8,4,1,6,7,5,2,3]=>1100110=>[1,1,3,1,2]
[5,2,3,1,7,6,8,4]=>1010101=>[1,2,2,2,1]
[3,5,2,1,7,6,8,4]=>0110101=>[2,1,2,2,1]
[1,7,6,2,5,8,3,4]=>0110010=>[2,1,3,2]
[7,6,2,1,5,8,3,4]=>1110010=>[1,1,1,3,2]
[8,2,6,4,7,1,5,3]=>1010101=>[1,2,2,2,1]
[6,1,5,2,7,4,8,3]=>1010101=>[1,2,2,2,1]
[7,6,2,5,8,3,1,4]=>1100110=>[1,1,3,1,2]
[1,8,3,5,7,6,2,4]=>0100110=>[2,3,1,2]
[1,5,2,3,7,6,8,4]=>0100101=>[2,3,2,1]
[5,2,1,3,7,6,8,4]=>1100101=>[1,1,3,2,1]
[8,4,2,6,7,5,1,3]=>1100110=>[1,1,3,1,2]
[6,1,4,2,7,5,8,3]=>1010101=>[1,2,2,2,1]
[8,2,6,5,7,1,4,3]=>1010101=>[1,2,2,2,1]
[5,1,3,2,7,6,8,4]=>1010101=>[1,2,2,2,1]
[1,4,2,3,7,6,8,5]=>0100101=>[2,3,2,1]
[2,4,1,3,7,6,8,5]=>0100101=>[2,3,2,1]
[2,5,1,3,7,6,8,4]=>0100101=>[2,3,2,1]
[2,8,3,5,7,6,1,4]=>0100110=>[2,3,1,2]
[6,8,2,3,5,7,1,4]=>0100010=>[2,4,2]
[6,7,1,3,5,8,2,4]=>0100010=>[2,4,2]
[8,3,5,7,6,1,2,4]=>1001100=>[1,3,1,3]
[5,1,2,3,7,6,8,4]=>1000101=>[1,4,2,1]
[4,7,1,2,8,6,5,3]=>0100111=>[2,3,1,1,1]
[4,6,8,1,2,7,5,3]=>0010011=>[3,3,1,1]
[6,8,7,1,5,3,2,4]=>0110110=>[2,1,2,1,2]
[6,8,7,3,5,1,2,4]=>0110100=>[2,1,2,3]
[7,8,1,3,6,5,2,4]=>0100110=>[2,3,1,2]
[1,7,3,4,8,6,5,2]=>0100111=>[2,3,1,1,1]
[4,2,7,1,8,6,5,3]=>1010111=>[1,2,2,1,1,1]
[7,8,2,3,6,5,1,4]=>0100110=>[2,3,1,2]
[8,5,7,1,6,2,3,4]=>1010100=>[1,2,2,3]
[8,5,7,1,2,6,3,4]=>1010010=>[1,2,3,2]
[6,8,2,7,1,3,5,4]=>0101001=>[2,2,3,1]
[6,2,4,8,7,1,5,3]=>1001101=>[1,3,1,2,1]
[1,6,8,3,7,4,5,2]=>0010101=>[3,2,2,1]
[1,6,8,3,4,7,5,2]=>0010011=>[3,3,1,1]
[6,2,4,8,1,7,5,3]=>1001011=>[1,3,2,1,1]
[6,8,7,2,3,5,1,4]=>0110010=>[2,1,3,2]
[6,8,2,1,7,3,5,4]=>0110101=>[2,1,2,2,1]
[8,5,7,2,1,6,3,4]=>1011010=>[1,2,1,2,2]
[8,5,7,1,2,3,6,4]=>1010001=>[1,2,4,1]
[8,5,7,2,3,1,6,4]=>1010101=>[1,2,2,2,1]
[1,8,7,5,3,4,6,2]=>0111001=>[2,1,1,3,1]
[1,8,7,3,5,4,6,2]=>0110101=>[2,1,2,2,1]
[8,2,5,4,7,1,6,3]=>1010101=>[1,2,2,2,1]
[8,7,6,1,2,4,3,5]=>1110010=>[1,1,1,3,2]
[8,7,6,1,4,2,3,5]=>1110100=>[1,1,1,2,3]
[8,7,6,4,1,3,2,5]=>1111010=>[1,1,1,1,2,2]
[8,5,7,1,3,2,6,4]=>1010101=>[1,2,2,2,1]
[5,8,4,7,1,2,6,3]=>0101001=>[2,2,3,1]
[8,1,2,6,5,7,4,3]=>1001011=>[1,3,2,1,1]
[8,2,5,6,7,4,1,3]=>1000110=>[1,4,1,2]
[4,8,5,1,7,2,6,3]=>0110101=>[2,1,2,2,1]
[8,5,3,7,1,2,6,4]=>1101001=>[1,1,2,3,1]
[4,6,2,8,1,7,5,3]=>0101011=>[2,2,2,1,1]
[1,6,4,8,3,7,5,2]=>0101011=>[2,2,2,1,1]
[1,8,7,4,5,3,6,2]=>0110101=>[2,1,2,2,1]
[4,8,5,7,2,1,6,3]=>0101101=>[2,2,1,2,1]
[8,5,3,7,2,1,6,4]=>1101101=>[1,1,2,1,2,1]
[8,7,6,3,1,4,2,5]=>1111010=>[1,1,1,1,2,2]
[8,5,3,2,7,1,6,4]=>1110101=>[1,1,1,2,2,1]
[1,8,7,4,3,5,6,2]=>0111001=>[2,1,1,3,1]
[1,8,7,3,4,5,6,2]=>0110001=>[2,1,4,1]
[8,2,4,5,7,1,6,3]=>1000101=>[1,4,2,1]
[8,5,2,3,7,1,6,4]=>1100101=>[1,1,3,2,1]
[8,3,1,5,2,7,6,4]=>1101011=>[1,1,2,2,1,1]
[8,5,4,2,1,7,3,6]=>1111010=>[1,1,1,1,2,2]
[8,5,4,2,1,7,6,3]=>1111011=>[1,1,1,1,2,1,1]
[6,5,4,2,3,1,8,7]=>1110101=>[1,1,1,2,2,1]
[6,3,2,5,1,4,8,7]=>1101001=>[1,1,2,3,1]
[8,5,4,1,2,7,6,3]=>1110011=>[1,1,1,3,1,1]
[8,7,4,1,6,3,2,5]=>1110110=>[1,1,1,2,1,2]
[8,7,4,1,6,3,5,2]=>1110101=>[1,1,1,2,2,1]
[8,7,4,1,6,5,3,2]=>1110111=>[1,1,1,2,1,1,1]
[8,5,4,3,1,7,6,2]=>1111011=>[1,1,1,1,2,1,1]
[8,3,2,5,1,7,6,4]=>1101011=>[1,1,2,2,1,1]
[8,3,2,5,1,7,4,6]=>1101010=>[1,1,2,2,2]
[8,5,4,3,1,7,2,6]=>1111010=>[1,1,1,1,2,2]
[8,5,4,1,3,7,2,6]=>1110010=>[1,1,1,3,2]
[8,7,4,1,6,5,2,3]=>1110110=>[1,1,1,2,1,2]
[2,1,8,7,6,4,5,3]=>1011101=>[1,2,1,1,2,1]
[8,3,2,7,6,4,5,1]=>1101101=>[1,1,2,1,2,1]
[8,5,4,2,3,7,6,1]=>1110011=>[1,1,1,3,1,1]
[8,7,4,2,6,5,3,1]=>1110111=>[1,1,1,2,1,1,1]
[8,7,4,2,6,3,5,1]=>1110101=>[1,1,1,2,2,1]
[8,7,4,2,6,3,1,5]=>1110110=>[1,1,1,2,1,2]
[8,3,1,7,6,4,2,5]=>1101110=>[1,1,2,1,1,2]
[8,3,1,7,6,4,5,2]=>1101101=>[1,1,2,1,2,1]
[8,3,1,5,4,7,6,2]=>1101011=>[1,1,2,2,1,1]
[8,3,1,7,6,5,2,4]=>1101110=>[1,1,2,1,1,2]
[8,3,1,7,6,2,5,4]=>1101101=>[1,1,2,1,2,1]
[8,5,4,2,3,7,1,6]=>1110010=>[1,1,1,3,2]
[8,3,2,5,4,7,1,6]=>1101010=>[1,1,2,2,2]
[2,1,8,5,4,7,3,6]=>1011010=>[1,2,1,2,2]
[8,3,2,7,6,5,1,4]=>1101110=>[1,1,2,1,1,2]
[8,7,6,5,3,1,4,2]=>1111101=>[1,1,1,1,1,2,1]
[8,3,2,7,6,1,5,4]=>1101101=>[1,1,2,1,2,1]
[8,7,6,5,1,2,4,3]=>1111001=>[1,1,1,1,3,1]
[5,2,3,1,6,4,8,7]=>1010101=>[1,2,2,2,1]
[7,4,5,2,3,1,8,6]=>1010101=>[1,2,2,2,1]
[7,3,5,2,4,1,8,6]=>1010101=>[1,2,2,2,1]
[6,3,5,2,4,1,8,7]=>1010101=>[1,2,2,2,1]
[4,1,6,3,5,2,8,7]=>1010101=>[1,2,2,2,1]
[6,3,4,1,5,2,8,7]=>1010101=>[1,2,2,2,1]
[5,2,7,3,4,1,8,6]=>1010101=>[1,2,2,2,1]
[6,2,8,5,7,3,4,1]=>1010101=>[1,2,2,2,1]
[6,2,7,3,4,1,8,5]=>1010101=>[1,2,2,2,1]
[7,3,4,1,5,2,8,6]=>1010101=>[1,2,2,2,1]
[4,1,7,3,5,2,8,6]=>1010101=>[1,2,2,2,1]
[2,1,7,4,5,3,8,6]=>1010101=>[1,2,2,2,1]
[3,1,8,6,7,4,5,2]=>1010101=>[1,2,2,2,1]
[4,1,8,6,7,3,5,2]=>1010101=>[1,2,2,2,1]
[8,5,7,3,4,1,6,2]=>1010101=>[1,2,2,2,1]
[8,5,6,2,7,3,4,1]=>1010101=>[1,2,2,2,1]
[8,4,7,3,5,1,6,2]=>1010101=>[1,2,2,2,1]
[5,1,8,4,7,3,6,2]=>1010101=>[1,2,2,2,1]
[3,1,8,5,7,4,6,2]=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,4,6,3]=>1010101=>[1,2,2,2,1]
[3,1,7,4,6,2,8,5]=>1010101=>[1,2,2,2,1]
[4,1,7,3,6,2,8,5]=>1010101=>[1,2,2,2,1]
[6,2,8,4,7,3,5,1]=>1010101=>[1,2,2,2,1]
[7,3,6,2,5,1,8,4]=>1010101=>[1,2,2,2,1]
[5,2,4,1,7,3,8,6]=>1010101=>[1,2,2,2,1]
[6,2,4,1,7,3,8,5]=>1010101=>[1,2,2,2,1]
[7,4,6,2,3,1,8,5]=>1010101=>[1,2,2,2,1]
[6,2,3,1,7,4,8,5]=>1010101=>[1,2,2,2,1]
[5,2,3,1,7,4,8,6]=>1010101=>[1,2,2,2,1]
[4,2,3,1,7,5,8,6]=>1010101=>[1,2,2,2,1]
[3,1,4,2,8,6,7,5]=>1010101=>[1,2,2,2,1]
[6,2,3,1,8,5,7,4]=>1010101=>[1,2,2,2,1]
[8,5,6,2,3,1,7,4]=>1010101=>[1,2,2,2,1]
[7,3,8,5,6,2,4,1]=>1010101=>[1,2,2,2,1]
[8,5,6,2,4,1,7,3]=>1010101=>[1,2,2,2,1]
[5,2,4,1,8,6,7,3]=>1010101=>[1,2,2,2,1]
[4,1,5,2,8,6,7,3]=>1010101=>[1,2,2,2,1]
[3,1,6,2,8,5,7,4]=>1010101=>[1,2,2,2,1]
[5,1,6,2,8,4,7,3]=>1010101=>[1,2,2,2,1]
[8,4,6,2,5,1,7,3]=>1010101=>[1,2,2,2,1]
[7,3,8,4,6,2,5,1]=>1010101=>[1,2,2,2,1]
[6,2,7,3,8,4,5,1]=>1010101=>[1,2,2,2,1]
[8,4,5,1,6,2,7,3]=>1010101=>[1,2,2,2,1]
[4,1,8,5,6,2,7,3]=>1010101=>[1,2,2,2,1]
[3,1,8,5,6,2,7,4]=>1010101=>[1,2,2,2,1]
[2,1,8,5,6,3,7,4]=>1010101=>[1,2,2,2,1]
[3,1,7,4,8,5,6,2]=>1010101=>[1,2,2,2,1]
[7,3,6,2,8,4,5,1]=>1010101=>[1,2,2,2,1]
[6,8,7,3,4,1,2,5]=>0110100=>[2,1,2,3]
[5,4,8,7,2,6,3,1]=>1011011=>[1,2,1,2,1,1]
[5,3,8,7,6,1,2,4]=>1011100=>[1,2,1,1,3]
[8,3,4,6,5,1,2,7]=>1001100=>[1,3,1,3]
[3,4,8,7,6,1,2,5]=>0011100=>[3,1,1,3]
[3,5,8,7,6,1,2,4]=>0011100=>[3,1,1,3]
[4,5,8,7,6,1,2,3]=>0011100=>[3,1,1,3]
[4,5,8,7,1,6,3,2]=>0011011=>[3,1,2,1,1]
[3,5,8,2,7,6,4,1]=>0010111=>[3,2,1,1,1]
[3,5,8,1,7,6,4,2]=>0010111=>[3,2,1,1,1]
[2,5,8,7,1,6,3,4]=>0011010=>[3,1,2,2]
[2,4,8,7,1,6,3,5]=>0011010=>[3,1,2,2]
[2,8,4,7,1,5,3,6]=>0101010=>[2,2,2,2]
[8,2,4,6,1,5,3,7]=>1001010=>[1,3,2,2]
[8,1,4,6,2,5,3,7]=>1001010=>[1,3,2,2]
[1,4,8,7,2,6,3,5]=>0011010=>[3,1,2,2]
[1,5,8,7,2,6,3,4]=>0011010=>[3,1,2,2]
[1,5,8,2,7,6,4,3]=>0010111=>[3,2,1,1,1]
[2,5,8,3,7,6,4,1]=>0010111=>[3,2,1,1,1]
[1,4,2,8,7,6,5,3]=>0101111=>[2,2,1,1,1,1]
[1,3,8,2,7,6,4,5]=>0010110=>[3,2,1,2]
[1,8,3,2,7,5,4,6]=>0110110=>[2,1,2,1,2]
[8,2,3,1,6,5,4,7]=>1010110=>[1,2,2,1,2]
[2,3,8,1,7,6,4,5]=>0010110=>[3,2,1,2]
[5,2,8,7,1,6,3,4]=>1011010=>[1,2,1,2,2]
[5,2,8,1,7,6,4,3]=>1010111=>[1,2,2,1,1,1]
[5,3,8,2,7,6,4,1]=>1010111=>[1,2,2,1,1,1]
[6,8,3,2,7,5,4,1]=>0110111=>[2,1,2,1,1,1]
[6,8,3,1,7,5,4,2]=>0110111=>[2,1,2,1,1,1]
[6,8,1,2,7,5,4,3]=>0100111=>[2,3,1,1,1]
[6,8,2,3,7,5,4,1]=>0100111=>[2,3,1,1,1]
[5,2,8,3,7,6,4,1]=>1010111=>[1,2,2,1,1,1]
[5,1,8,3,7,6,4,2]=>1010111=>[1,2,2,1,1,1]
[5,1,8,7,2,6,3,4]=>1011010=>[1,2,1,2,2]
[4,8,1,7,2,5,3,6]=>0101010=>[2,2,2,2]
[8,4,1,6,2,5,3,7]=>1101010=>[1,1,2,2,2]
[8,3,1,2,6,5,4,7]=>1100110=>[1,1,3,1,2]
[3,1,2,8,7,6,5,4]=>1001111=>[1,3,1,1,1,1]
[4,1,3,8,7,6,5,2]=>1001111=>[1,3,1,1,1,1]
[3,1,4,8,7,6,5,2]=>1001111=>[1,3,1,1,1,1]
[2,1,8,3,7,6,4,5]=>1010110=>[1,2,2,1,2]
[2,8,1,3,7,5,4,6]=>0100110=>[2,3,1,2]
[8,2,1,3,6,5,4,7]=>1100110=>[1,1,3,1,2]
[1,8,2,3,7,5,4,6]=>0100110=>[2,3,1,2]
[1,2,8,3,7,6,4,5]=>0010110=>[3,2,1,2]
[1,4,3,6,8,2,5,7]=>0100100=>[2,3,3]
[1,4,5,2,8,3,7,6]=>0010101=>[3,2,2,1]
[1,4,2,6,5,8,3,7]=>0101010=>[2,2,2,2]
[1,5,4,2,6,8,3,7]=>0110010=>[2,1,3,2]
[3,1,6,5,8,2,4,7]=>1010100=>[1,2,2,3]
[1,6,4,2,5,8,3,7]=>0110010=>[2,1,3,2]
[1,5,2,6,4,8,3,7]=>0101010=>[2,2,2,2]
[1,2,6,5,4,8,3,7]=>0011010=>[3,1,2,2]
[1,2,5,4,7,3,8,6]=>0010101=>[3,2,2,1]
[4,1,2,6,3,8,7,5]=>1001011=>[1,3,2,1,1]
[7,1,5,4,2,8,3,6]=>1011010=>[1,2,1,2,2]
[1,4,7,5,2,8,3,6]=>0011010=>[3,1,2,2]
[7,1,3,5,2,8,4,6]=>1001010=>[1,3,2,2]
[1,4,5,2,8,7,3,6]=>0010110=>[3,2,1,2]
[1,6,4,2,8,3,7,5]=>0110101=>[2,1,2,2,1]
[1,4,2,8,3,7,6,5]=>0101011=>[2,2,2,1,1]
[1,2,8,6,5,3,7,4]=>0011101=>[3,1,1,2,1]
[6,2,1,8,7,3,4,5]=>1101100=>[1,1,2,1,3]
[7,6,2,1,8,3,4,5]=>1110100=>[1,1,1,2,3]
[7,3,1,6,2,8,4,5]=>1101010=>[1,1,2,2,2]
[1,7,6,4,2,8,3,5]=>0111010=>[2,1,1,2,2]
[1,7,5,2,6,3,8,4]=>0110101=>[2,1,2,2,1]
[1,6,2,7,5,3,8,4]=>0101101=>[2,2,1,2,1]
[1,2,7,6,5,3,8,4]=>0011101=>[3,1,1,2,1]
[1,2,6,5,3,8,7,4]=>0011011=>[3,1,2,1,1]
[1,5,2,7,6,3,8,4]=>0101101=>[2,2,1,2,1]
[1,6,5,2,7,3,8,4]=>0110101=>[2,1,2,2,1]
[1,5,7,4,2,8,3,6]=>0011010=>[3,1,2,2]
[3,1,8,6,2,4,7,5]=>1011001=>[1,2,1,3,1]
[4,3,7,1,8,2,5,6]=>1010100=>[1,2,2,3]
[8,3,1,6,2,4,7,5]=>1101001=>[1,1,2,3,1]
[7,1,8,3,2,4,6,5]=>1011001=>[1,2,1,3,1]
[1,4,2,8,7,3,6,5]=>0101101=>[2,2,1,2,1]
[1,7,4,2,8,3,6,5]=>0110101=>[2,1,2,2,1]
[8,1,5,4,2,7,3,6]=>1011010=>[1,2,1,2,2]
[1,4,8,5,2,7,3,6]=>0011010=>[3,1,2,2]
[8,5,3,1,7,2,4,6]=>1110100=>[1,1,1,2,3]
[8,6,2,1,7,3,4,5]=>1110100=>[1,1,1,2,3]
[1,8,6,4,2,7,3,5]=>0111010=>[2,1,1,2,2]
[1,5,2,7,3,8,6,4]=>0101011=>[2,2,2,1,1]
[1,2,8,5,3,7,6,4]=>0011011=>[3,1,2,1,1]
[1,2,6,3,8,7,5,4]=>0010111=>[3,2,1,1,1]
[1,2,7,6,3,8,5,4]=>0011011=>[3,1,2,1,1]
[1,6,2,7,3,8,5,4]=>0101011=>[2,2,2,1,1]
[1,7,4,2,8,6,3,5]=>0110110=>[2,1,2,1,2]
[7,1,8,3,2,6,4,5]=>1011010=>[1,2,1,2,2]
[7,2,1,8,6,3,4,5]=>1101100=>[1,1,2,1,3]
[1,8,7,3,2,6,4,5]=>0111010=>[2,1,1,2,2]
[1,4,2,8,7,6,3,5]=>0101110=>[2,2,1,1,2]
[1,2,8,7,5,3,6,4]=>0011101=>[3,1,1,2,1]
[5,1,8,7,6,2,4,3]=>1011101=>[1,2,1,1,2,1]
[8,1,7,6,3,4,5,2]=>1011001=>[1,2,1,3,1]
[5,7,8,6,2,4,1,3]=>0011010=>[3,1,2,2]
[5,7,1,6,2,4,3,8]=>0101010=>[2,2,2,2]
[6,4,1,5,2,7,3,8]=>1101010=>[1,1,2,2,2]
[8,1,4,5,3,7,6,2]=>1001011=>[1,3,2,1,1]
[6,1,4,5,3,8,7,2]=>1001011=>[1,3,2,1,1]
[7,1,4,5,3,8,6,2]=>1001011=>[1,3,2,1,1]
[7,1,4,5,3,6,8,2]=>1001001=>[1,3,3,1]
[7,4,1,5,2,6,3,8]=>1101010=>[1,1,2,2,2]
[6,3,5,7,2,1,4,8]=>1001100=>[1,3,1,3]
[6,3,5,8,2,1,7,4]=>1001101=>[1,3,1,2,1]
[6,3,5,7,2,1,8,4]=>1001101=>[1,3,1,2,1]
[8,4,5,7,3,6,1,2]=>1001010=>[1,3,2,2]
[6,4,5,8,3,7,2,1]=>1001011=>[1,3,2,1,1]
[5,4,8,6,3,1,7,2]=>1011101=>[1,2,1,1,2,1]
[5,4,1,8,2,3,7,6]=>1101001=>[1,1,2,3,1]
[8,4,1,5,2,6,3,7]=>1101010=>[1,1,2,2,2]
[6,3,5,8,2,1,4,7]=>1001100=>[1,3,1,3]
[2,3,8,5,1,4,7,6]=>0011001=>[3,1,3,1]
[2,3,8,6,1,5,7,4]=>0011001=>[3,1,3,1]
[2,8,6,7,1,3,5,4]=>0101001=>[2,2,3,1]
[8,3,5,7,2,1,6,4]=>1001101=>[1,3,1,2,1]
[8,4,5,6,3,1,7,2]=>1001101=>[1,3,1,2,1]
[7,3,5,6,2,8,1,4]=>1001010=>[1,3,2,2]
[7,3,5,8,2,1,6,4]=>1001101=>[1,3,1,2,1]
[7,3,5,6,2,1,4,8]=>1001100=>[1,3,1,3]
[2,7,6,5,1,3,4,8]=>0111000=>[2,1,1,4]
[2,7,6,8,1,3,5,4]=>0101001=>[2,2,3,1]
[8,7,5,6,1,4,2,3]=>1101010=>[1,1,2,2,2]
[2,7,1,3,6,5,8,4]=>0100101=>[2,3,2,1]
[2,7,6,1,8,3,4,5]=>0110100=>[2,1,2,3]
[2,7,6,1,4,3,5,8]=>0110100=>[2,1,2,3]
[7,3,5,1,2,8,4,6]=>1010010=>[1,2,3,2]
[2,3,8,6,4,1,7,5]=>0011101=>[3,1,1,2,1]
[2,8,6,1,7,3,4,5]=>0110100=>[2,1,2,3]
[2,3,8,1,6,4,7,5]=>0010101=>[3,2,2,1]
[2,3,8,1,4,5,7,6]=>0010001=>[3,4,1]
[5,2,6,1,4,8,7,3]=>1010011=>[1,2,3,1,1]
[5,7,2,3,8,6,1,4]=>0100110=>[2,3,1,2]
[5,6,2,3,1,8,7,4]=>0101011=>[2,2,2,1,1]
[5,6,2,1,3,8,7,4]=>0110011=>[2,1,3,1,1]
[5,1,6,4,2,8,7,3]=>1011011=>[1,2,1,2,1,1]
[5,6,1,3,2,8,7,4]=>0101011=>[2,2,2,1,1]
[5,6,3,1,2,8,7,4]=>0110011=>[2,1,3,1,1]
[5,7,3,2,8,1,6,4]=>0110101=>[2,1,2,2,1]
[6,7,3,8,2,1,5,4]=>0101101=>[2,2,1,2,1]
[6,7,3,8,1,2,5,4]=>0101001=>[2,2,3,1]
[5,7,3,1,8,2,6,4]=>0110101=>[2,1,2,2,1]
[5,1,7,4,8,2,6,3]=>1010101=>[1,2,2,2,1]
[1,5,7,4,8,3,6,2]=>0010101=>[3,2,2,1]
[5,1,7,4,8,6,2,3]=>1010110=>[1,2,2,1,2]
[5,7,3,1,8,6,2,4]=>0110110=>[2,1,2,1,2]
[6,7,8,3,1,4,2,5]=>0011010=>[3,1,2,2]
[6,7,1,8,3,5,2,4]=>0101010=>[2,2,2,2]
[6,1,7,8,4,5,2,3]=>1001010=>[1,3,2,2]
[1,6,7,8,4,5,3,2]=>0001011=>[4,2,1,1]
[1,6,7,8,4,3,5,2]=>0001101=>[4,1,2,1]
[6,1,7,8,4,2,5,3]=>1001101=>[1,3,1,2,1]
[6,7,2,8,1,3,5,4]=>0101001=>[2,2,3,1]
[6,7,2,8,3,5,1,4]=>0101010=>[2,2,2,2]
[6,2,7,8,4,1,5,3]=>1001101=>[1,3,1,2,1]
[6,2,7,8,1,4,5,3]=>1001001=>[1,3,3,1]
[4,2,1,7,8,5,6,3]=>1100101=>[1,1,3,2,1]
[4,1,2,7,8,6,5,3]=>1000111=>[1,4,1,1,1]
[6,2,7,8,1,5,4,3]=>1001011=>[1,3,2,1,1]
[6,2,7,8,5,1,4,3]=>1001101=>[1,3,1,2,1]
[5,7,2,1,8,6,3,4]=>0110110=>[2,1,2,1,2]
[1,6,7,8,3,5,4,2]=>0001011=>[4,2,1,1]
[6,1,7,8,2,5,4,3]=>1001011=>[1,3,2,1,1]
[6,7,8,2,4,1,3,5]=>0010100=>[3,2,3]
[6,7,8,2,4,3,1,5]=>0010110=>[3,2,1,2]
[6,7,1,8,5,2,3,4]=>0101100=>[2,2,1,3]
[6,1,7,8,5,2,4,3]=>1001101=>[1,3,1,2,1]
[1,6,7,8,5,3,4,2]=>0001101=>[4,1,2,1]
[6,1,7,8,5,4,2,3]=>1001110=>[1,3,1,1,2]
[6,7,1,8,5,3,2,4]=>0101110=>[2,2,1,1,2]
[6,7,8,4,1,3,2,5]=>0011010=>[3,1,2,2]
[3,7,4,8,5,6,1,2]=>0101010=>[2,2,2,2]
[3,7,1,8,5,6,2,4]=>0101010=>[2,2,2,2]
[2,7,3,8,5,6,1,4]=>0101010=>[2,2,2,2]
[1,7,4,8,5,6,2,3]=>0101010=>[2,2,2,2]
[2,7,3,8,4,6,1,5]=>0101010=>[2,2,2,2]
[3,7,1,8,4,6,2,5]=>0101010=>[2,2,2,2]
[1,5,2,8,6,7,3,4]=>0101010=>[2,2,2,2]
[2,6,1,8,5,7,3,4]=>0101010=>[2,2,2,2]
[1,6,2,8,5,7,3,4]=>0101010=>[2,2,2,2]
[1,6,2,8,4,7,3,5]=>0101010=>[2,2,2,2]
[2,6,1,8,4,7,3,5]=>0101010=>[2,2,2,2]
[3,7,2,6,1,8,4,5]=>0101010=>[2,2,2,2]
[4,8,1,6,2,7,3,5]=>0101010=>[2,2,2,2]
[5,8,1,6,2,7,3,4]=>0101010=>[2,2,2,2]
[5,8,2,6,1,7,3,4]=>0101010=>[2,2,2,2]
[4,8,2,6,1,7,3,5]=>0101010=>[2,2,2,2]
[1,7,3,6,2,8,4,5]=>0101010=>[2,2,2,2]
[2,7,3,6,1,8,4,5]=>0101010=>[2,2,2,2]
[8,6,1,4,3,2,5,7]=>1101100=>[1,1,2,1,3]
[3,7,5,1,8,2,4,6]=>0110100=>[2,1,2,3]
[4,1,5,2,8,7,3,6]=>1010110=>[1,2,2,1,2]
[8,1,2,4,6,5,3,7]=>1000110=>[1,4,1,2]
[8,2,6,5,1,3,4,7]=>1011000=>[1,2,1,4]
[8,3,1,6,2,5,4,7]=>1101010=>[1,1,2,2,2]
[8,1,2,6,4,5,3,7]=>1001010=>[1,3,2,2]
[8,1,2,5,6,4,3,7]=>1000110=>[1,4,1,2]
[1,7,5,4,2,8,3,6]=>0111010=>[2,1,1,2,2]
[1,4,6,8,2,7,3,5]=>0001010=>[4,2,2]
[1,4,7,6,2,8,3,5]=>0011010=>[3,1,2,2]
[5,1,4,7,2,8,3,6]=>1001010=>[1,3,2,2]
[3,7,5,1,2,8,4,6]=>0110010=>[2,1,3,2]
[4,1,5,8,2,7,3,6]=>1001010=>[1,3,2,2]
[1,4,6,2,8,7,3,5]=>0010110=>[3,2,1,2]
[1,4,2,8,6,7,3,5]=>0101010=>[2,2,2,2]
[3,1,2,6,4,8,7,5]=>1001011=>[1,3,2,1,1]
[2,1,7,6,3,4,8,5]=>1011001=>[1,2,1,3,1]
[3,1,2,7,4,6,8,5]=>1001001=>[1,3,3,1]
[1,2,3,6,8,5,7,4]=>0000101=>[5,2,1]
[5,1,4,2,7,8,3,6]=>1010010=>[1,2,3,2]
[1,4,2,7,6,8,3,5]=>0101010=>[2,2,2,2]
[1,4,2,6,8,7,3,5]=>0100110=>[2,3,1,2]
[5,3,7,1,8,2,4,6]=>1010100=>[1,2,2,3]
[1,7,4,3,2,5,8,6]=>0111001=>[2,1,1,3,1]
[4,8,7,2,1,3,5,6]=>0111000=>[2,1,1,4]
[1,8,7,3,4,2,5,6]=>0110100=>[2,1,2,3]
[3,1,7,8,2,6,4,5]=>1001010=>[1,3,2,2]
[1,4,2,7,8,3,6,5]=>0100101=>[2,3,2,1]
[2,1,8,6,3,4,7,5]=>1011001=>[1,2,1,3,1]
[1,4,2,6,8,3,7,5]=>0100101=>[2,3,2,1]
[1,2,3,7,8,5,6,4]=>0000101=>[5,2,1]
[1,2,3,7,5,8,6,4]=>0001011=>[4,2,1,1]
[3,1,7,2,8,6,4,5]=>1010110=>[1,2,2,1,2]
[1,2,3,8,7,5,6,4]=>0001101=>[4,1,2,1]
[5,7,8,4,2,6,1,3]=>0011010=>[3,1,2,2]
[6,7,8,4,2,5,1,3]=>0011010=>[3,1,2,2]
[8,6,3,7,2,1,5,4]=>1101101=>[1,1,2,1,2,1]
[6,7,8,3,2,1,5,4]=>0011101=>[3,1,1,2,1]
[5,7,8,3,2,1,6,4]=>0011101=>[3,1,1,2,1]
[2,7,8,4,3,5,6,1]=>0011001=>[3,1,3,1]
[3,7,8,4,2,5,1,6]=>0011010=>[3,1,2,2]
[7,6,3,8,2,1,4,5]=>1101100=>[1,1,2,1,3]
[8,6,3,7,2,1,4,5]=>1101100=>[1,1,2,1,3]
[5,6,3,8,2,1,4,7]=>0101100=>[2,2,1,3]
[3,6,4,8,2,5,1,7]=>0101010=>[2,2,2,2]
[2,6,4,8,3,5,7,1]=>0101001=>[2,2,3,1]
[2,6,4,7,3,5,8,1]=>0101001=>[2,2,3,1]
[4,6,3,7,2,1,5,8]=>0101100=>[2,2,1,3]
[5,6,3,7,2,1,4,8]=>0101100=>[2,2,1,3]
[8,4,3,2,1,6,5,7]=>1111010=>[1,1,1,1,2,2]
[6,4,3,2,1,7,5,8]=>1111010=>[1,1,1,1,2,2]
[4,5,3,2,7,1,6,8]=>0110100=>[2,1,2,3]
[7,4,3,2,1,8,5,6]=>1111010=>[1,1,1,1,2,2]
[8,4,3,2,1,7,5,6]=>1111010=>[1,1,1,1,2,2]
[7,4,3,2,1,8,6,5]=>1111011=>[1,1,1,1,2,1,1]
[5,6,3,8,2,1,7,4]=>0101101=>[2,2,1,2,1]
[7,5,3,2,8,1,6,4]=>1110101=>[1,1,1,2,2,1]
[8,5,4,2,7,6,1,3]=>1110110=>[1,1,1,2,1,2]
[7,5,4,2,8,6,1,3]=>1110110=>[1,1,1,2,1,2]
[6,5,4,2,7,8,1,3]=>1110010=>[1,1,1,3,2]
[8,5,4,2,6,7,1,3]=>1110010=>[1,1,1,3,2]
[5,6,3,7,2,1,8,4]=>0101101=>[2,2,1,2,1]
[4,6,3,7,2,1,8,5]=>0101101=>[2,2,1,2,1]
[3,6,4,7,2,8,1,5]=>0101010=>[2,2,2,2]
[2,6,4,7,3,8,5,1]=>0101011=>[2,2,2,1,1]
[3,5,4,2,7,8,1,6]=>0110010=>[2,1,3,2]
[7,4,3,2,1,6,8,5]=>1111001=>[1,1,1,1,3,1]
[8,4,3,2,1,6,7,5]=>1111001=>[1,1,1,1,3,1]
[8,4,3,2,1,5,7,6]=>1111001=>[1,1,1,1,3,1]
[7,4,3,2,1,5,8,6]=>1111001=>[1,1,1,1,3,1]
[6,4,3,2,1,5,8,7]=>1111001=>[1,1,1,1,3,1]
[3,5,4,2,6,8,1,7]=>0110010=>[2,1,3,2]
[3,2,6,4,8,5,1,7]=>1010110=>[1,2,2,1,2]
[4,2,5,8,3,1,6,7]=>1001100=>[1,3,1,3]
[4,3,2,7,5,1,6,8]=>1101100=>[1,1,2,1,3]
[4,3,6,2,5,1,7,8]=>1010100=>[1,2,2,3]
[4,5,1,7,3,2,6,8]=>0101100=>[2,2,1,3]
[5,2,1,4,3,7,8,6]=>1101001=>[1,1,2,3,1]
[5,3,6,4,1,2,7,8]=>1011000=>[1,2,1,4]
[4,3,6,1,7,2,5,8]=>1010100=>[1,2,2,3]
[6,2,4,1,3,7,8,5]=>1010001=>[1,2,4,1]
[3,6,4,1,2,7,5,8]=>0110010=>[2,1,3,2]
[4,6,3,1,7,2,5,8]=>0110100=>[2,1,2,3]
[4,5,2,7,3,1,6,8]=>0101100=>[2,2,1,3]
[4,6,2,1,7,3,5,8]=>0110100=>[2,1,2,3]
[3,2,6,1,4,7,5,8]=>1010010=>[1,2,3,2]
[7,3,1,4,6,8,2,5]=>1100010=>[1,1,4,2]
[7,4,1,5,6,2,3,8]=>1100100=>[1,1,3,3]
[7,3,1,5,2,6,4,8]=>1101010=>[1,1,2,2,2]
[6,3,5,1,2,7,4,8]=>1010010=>[1,2,3,2]
[3,6,5,1,2,7,4,8]=>0110010=>[2,1,3,2]
[2,4,1,5,3,8,7,6]=>0101011=>[2,2,2,1,1]
[3,4,5,1,2,8,7,6]=>0010011=>[3,3,1,1]
[1,8,4,5,3,2,7,6]=>0101101=>[2,2,1,2,1]
[2,4,8,5,3,1,7,6]=>0011101=>[3,1,1,2,1]
[3,4,5,2,8,1,7,6]=>0010101=>[3,2,2,1]
[3,4,6,2,1,7,8,5]=>0011001=>[3,1,3,1]
[3,4,6,2,1,7,5,8]=>0011010=>[3,1,2,2]
[3,5,6,2,7,1,8,4]=>0010101=>[3,2,2,1]
[3,4,6,2,8,7,1,5]=>0010110=>[3,2,1,2]
[3,4,6,8,2,7,1,5]=>0001010=>[4,2,2]
[2,4,8,6,3,7,1,5]=>0011010=>[3,1,2,2]
[1,8,4,6,3,7,2,5]=>0101010=>[2,2,2,2]
[1,8,4,6,3,7,5,2]=>0101011=>[2,2,2,1,1]
[3,4,6,8,2,7,5,1]=>0001011=>[4,2,1,1]
[3,4,6,2,8,7,5,1]=>0010111=>[3,2,1,1,1]
[3,5,6,2,7,8,4,1]=>0010011=>[3,3,1,1]
[3,5,6,2,7,4,1,8]=>0010110=>[3,2,1,2]
[4,5,6,7,2,8,3,1]=>0001011=>[4,2,1,1]
[2,5,8,6,7,3,4,1]=>0010101=>[3,2,2,1]
[1,8,5,6,7,3,2,4]=>0100110=>[2,3,1,2]
[4,5,6,7,2,1,8,3]=>0001101=>[4,1,2,1]
[3,4,6,1,8,7,2,5]=>0010110=>[3,2,1,2]
[2,4,1,6,8,7,3,5]=>0100110=>[2,3,1,2]
[2,5,1,6,7,8,4,3]=>0100011=>[2,4,1,1]
[2,5,1,6,7,4,3,8]=>0100110=>[2,3,1,2]
[3,5,6,1,7,4,2,8]=>0010110=>[3,2,1,2]
[3,5,6,1,7,4,8,2]=>0010101=>[3,2,2,1]
[3,4,6,1,8,7,5,2]=>0010111=>[3,2,1,1,1]
[3,4,6,8,1,7,5,2]=>0001011=>[4,2,1,1]
[2,4,8,6,1,7,5,3]=>0011011=>[3,1,2,1,1]
[1,8,4,6,2,7,5,3]=>0101011=>[2,2,2,1,1]
[1,8,5,6,7,2,4,3]=>0100101=>[2,3,2,1]
[2,5,8,6,7,1,4,3]=>0010101=>[3,2,2,1]
[4,5,6,7,1,3,8,2]=>0001001=>[4,3,1]
[3,5,6,8,7,4,1,2]=>0001110=>[4,1,1,2]
[2,5,8,6,7,4,1,3]=>0010110=>[3,2,1,2]
[1,8,5,6,7,4,2,3]=>0100110=>[2,3,1,2]
[1,8,5,6,7,4,3,2]=>0100111=>[2,3,1,1,1]
[2,5,8,6,7,4,3,1]=>0010111=>[3,2,1,1,1]
[8,2,4,3,7,1,6,5]=>1010101=>[1,2,2,2,1]
[5,8,2,4,3,7,1,6]=>0101010=>[2,2,2,2]
[4,2,5,6,1,8,3,7]=>1001010=>[1,3,2,2]
[4,2,5,6,1,7,3,8]=>1001010=>[1,3,2,2]
[6,1,5,7,3,2,4,8]=>1001100=>[1,3,1,3]
[6,1,5,8,3,2,4,7]=>1001100=>[1,3,1,3]
[3,8,2,4,7,1,5,6]=>0100100=>[2,3,3]
[3,6,8,2,4,7,1,5]=>0010010=>[3,3,2]
[7,3,2,4,6,1,5,8]=>1100100=>[1,1,3,3]
[3,2,5,1,8,4,6,7]=>1010100=>[1,2,2,3]
[7,8,3,2,4,6,1,5]=>0110010=>[2,1,3,2]
[6,1,5,7,8,3,2,4]=>1000110=>[1,4,1,2]
[4,2,5,6,1,7,8,3]=>1001001=>[1,3,3,1]
[5,7,6,1,8,3,4,2]=>0110101=>[2,1,2,2,1]
[5,8,6,1,7,3,4,2]=>0110101=>[2,1,2,2,1]
[6,1,5,8,7,3,2,4]=>1001110=>[1,3,1,1,2]
[8,7,3,2,4,6,1,5]=>1110010=>[1,1,1,3,2]
[3,2,5,1,8,7,4,6]=>1010110=>[1,2,2,1,2]
[3,2,5,1,6,4,7,8]=>1010100=>[1,2,2,3]
[3,2,4,1,8,7,5,6]=>1010110=>[1,2,2,1,2]
[3,2,5,1,6,8,7,4]=>1010011=>[1,2,3,1,1]
[3,8,6,5,1,7,4,2]=>0111011=>[2,1,1,2,1,1]
[3,7,6,5,1,8,4,2]=>0111011=>[2,1,1,2,1,1]
[6,5,1,7,8,4,2,3]=>1100110=>[1,1,3,1,2]
[3,2,5,1,6,7,8,4]=>1010001=>[1,2,4,1]
[3,2,4,1,7,5,6,8]=>1010100=>[1,2,2,3]
[3,2,4,1,6,8,5,7]=>1010010=>[1,2,3,2]
[8,3,2,4,7,6,1,5]=>1100110=>[1,1,3,1,2]
[3,2,5,1,8,4,7,6]=>1010101=>[1,2,2,2,1]
[3,2,5,1,6,7,4,8]=>1010010=>[1,2,3,2]
[6,5,1,7,4,2,3,8]=>1101100=>[1,1,2,1,3]
[6,5,1,8,4,2,3,7]=>1101100=>[1,1,2,1,3]
[8,4,2,3,7,5,1,6]=>1100110=>[1,1,3,1,2]
[5,2,6,1,8,3,7,4]=>1010101=>[1,2,2,2,1]
[5,2,6,1,8,4,7,3]=>1010101=>[1,2,2,2,1]
[7,4,2,3,8,5,1,6]=>1100110=>[1,1,3,1,2]
[8,5,1,6,4,2,3,7]=>1101100=>[1,1,2,1,3]
[3,2,5,1,7,6,4,8]=>1010110=>[1,2,2,1,2]
[3,2,5,1,8,6,4,7]=>1010110=>[1,2,2,1,2]
[8,6,1,5,7,3,2,4]=>1100110=>[1,1,3,1,2]
[8,5,6,1,7,3,4,2]=>1010101=>[1,2,2,2,1]
[3,6,8,5,1,7,4,2]=>0011011=>[3,1,2,1,1]
[8,5,1,6,7,4,2,3]=>1100110=>[1,1,3,1,2]
[3,2,5,1,8,6,7,4]=>1010101=>[1,2,2,2,1]
[3,2,4,1,5,8,6,7]=>1010010=>[1,2,3,2]
[3,2,5,1,7,8,6,4]=>1010011=>[1,2,3,1,1]
[8,7,5,1,6,4,2,3]=>1110110=>[1,1,1,2,1,2]
[3,2,5,1,8,7,6,4]=>1010111=>[1,2,2,1,1,1]
[4,6,3,7,1,8,5,2]=>0101011=>[2,2,2,1,1]
[4,6,3,7,5,1,8,2]=>0101101=>[2,2,1,2,1]
[4,2,6,1,7,5,3,8]=>1010110=>[1,2,2,1,2]
[2,5,7,4,1,6,3,8]=>0011010=>[3,1,2,2]
[2,5,7,4,1,6,8,3]=>0011001=>[3,1,3,1]
[5,4,7,8,3,1,6,2]=>1001101=>[1,3,1,2,1]
[4,3,7,5,1,8,6,2]=>1011011=>[1,2,1,2,1,1]
[6,4,3,8,5,1,7,2]=>1101101=>[1,1,2,1,2,1]
[5,8,4,3,6,1,7,2]=>0110101=>[2,1,2,2,1]
[5,4,8,3,6,1,7,2]=>1010101=>[1,2,2,2,1]
[2,5,4,6,1,7,3,8]=>0101010=>[2,2,2,2]
[4,6,2,1,8,5,7,3]=>0110101=>[2,1,2,2,1]
[2,4,1,7,5,8,6,3]=>0101011=>[2,2,2,1,1]
[2,4,1,7,5,3,8,6]=>0101101=>[2,2,1,2,1]
[2,6,4,1,8,5,3,7]=>0110110=>[2,1,2,1,2]
[5,4,8,2,1,6,3,7]=>1011010=>[1,2,1,2,2]
[2,5,8,4,1,6,3,7]=>0011010=>[3,1,2,2]
[3,2,5,6,1,8,4,7]=>1001010=>[1,3,2,2]
[4,8,3,2,6,1,5,7]=>0110100=>[2,1,2,3]
[3,5,2,8,1,6,4,7]=>0101010=>[2,2,2,2]
[3,2,1,6,8,5,4,7]=>1100110=>[1,1,3,1,2]
[3,2,7,1,5,4,8,6]=>1010101=>[1,2,2,2,1]
[3,2,7,1,5,8,6,4]=>1010011=>[1,2,3,1,1]
[3,8,2,5,1,6,7,4]=>0101001=>[2,2,3,1]
[4,8,3,2,6,7,1,5]=>0110010=>[2,1,3,2]
[4,3,8,2,6,7,1,5]=>1010010=>[1,2,3,2]
[4,3,2,6,7,8,1,5]=>1100010=>[1,1,4,2]
[4,3,2,6,7,1,5,8]=>1100100=>[1,1,3,3]
[4,3,7,8,2,6,1,5]=>1001010=>[1,3,2,2]
[2,5,7,4,8,1,6,3]=>0010101=>[3,2,2,1]
[3,2,5,7,1,6,8,4]=>1001001=>[1,3,3,1]
[3,2,5,7,1,6,4,8]=>1001010=>[1,3,2,2]
[6,3,2,7,1,5,4,8]=>1101010=>[1,1,2,2,2]
[6,3,2,7,1,5,8,4]=>1101001=>[1,1,2,3,1]
[6,3,2,7,8,1,5,4]=>1100101=>[1,1,3,2,1]
[6,5,2,1,7,8,4,3]=>1110011=>[1,1,1,3,1,1]
[6,2,1,8,5,3,7,4]=>1101101=>[1,1,2,1,2,1]
[6,3,2,7,1,4,8,5]=>1101001=>[1,1,2,3,1]
[6,3,2,1,4,7,8,5]=>1110001=>[1,1,1,4,1]
[6,3,2,1,4,7,5,8]=>1110010=>[1,1,1,3,2]
[3,5,2,1,7,8,4,6]=>0110010=>[2,1,3,2]
[4,6,2,1,8,3,7,5]=>0110101=>[2,1,2,2,1]
[3,2,7,1,4,8,6,5]=>1010011=>[1,2,3,1,1]
[3,5,8,2,1,7,4,6]=>0011010=>[3,1,2,2]
[4,8,3,7,2,1,5,6]=>0101100=>[2,2,1,3]
[4,3,7,2,8,1,5,6]=>1010100=>[1,2,2,3]
[4,3,7,2,1,5,6,8]=>1011000=>[1,2,1,4]
[4,8,3,2,7,1,5,6]=>0110100=>[2,1,2,3]
[6,3,2,8,1,4,7,5]=>1101001=>[1,1,2,3,1]
[3,2,1,4,7,5,8,6]=>1100101=>[1,1,3,2,1]
[5,3,2,1,8,4,6,7]=>1110100=>[1,1,1,2,3]
[4,8,3,2,1,5,6,7]=>0111000=>[2,1,1,4]
[4,3,8,2,1,5,6,7]=>1011000=>[1,2,1,4]
[6,2,3,1,5,4,8,7]=>1010101=>[1,2,2,2,1]
[8,4,5,2,3,1,7,6]=>1010101=>[1,2,2,2,1]
[8,2,5,3,4,1,7,6]=>1010101=>[1,2,2,2,1]
[6,2,5,3,4,1,8,7]=>1010101=>[1,2,2,2,1]
[6,4,5,1,3,2,8,7]=>1010101=>[1,2,2,2,1]
[6,1,5,3,4,2,8,7]=>1010101=>[1,2,2,2,1]
[8,3,7,2,4,1,6,5]=>1010101=>[1,2,2,2,1]
[8,3,5,1,4,2,7,6]=>1010101=>[1,2,2,2,1]
[8,4,5,1,3,2,7,6]=>1010101=>[1,2,2,2,1]
[2,1,8,4,5,3,7,6]=>1010101=>[1,2,2,2,1]
[8,1,7,3,4,2,6,5]=>1010101=>[1,2,2,2,1]
[8,2,7,1,4,3,6,5]=>1010101=>[1,2,2,2,1]
[8,2,7,3,4,1,6,5]=>1010101=>[1,2,2,2,1]
[8,4,7,2,3,1,6,5]=>1010101=>[1,2,2,2,1]
[8,2,3,1,5,4,7,6]=>1010101=>[1,2,2,2,1]
[4,2,3,1,8,5,7,6]=>1010101=>[1,2,2,2,1]
[8,2,3,1,7,5,6,4]=>1010101=>[1,2,2,2,1]
[8,6,7,1,3,2,5,4]=>1010101=>[1,2,2,2,1]
[8,1,3,2,7,5,6,4]=>1010101=>[1,2,2,2,1]
[2,1,8,5,7,3,6,4]=>1010101=>[1,2,2,2,1]
[4,5,8,6,3,2,7,1]=>0011101=>[3,1,1,2,1]
[1,5,8,7,3,6,2,4]=>0011010=>[3,1,2,2]
[1,7,2,8,4,6,5,3]=>0101011=>[2,2,2,1,1]
[6,7,2,8,4,1,5,3]=>0101101=>[2,2,1,2,1]
[3,6,2,8,4,5,7,1]=>0101001=>[2,2,3,1]
[2,6,1,8,4,5,7,3]=>0101001=>[2,2,3,1]
[2,8,4,6,1,5,7,3]=>0101001=>[2,2,3,1]
[6,3,1,8,4,5,7,2]=>1101001=>[1,1,2,3,1]
[2,3,6,8,4,5,7,1]=>0001001=>[4,3,1]
[6,3,7,8,4,1,5,2]=>1001101=>[1,3,1,2,1]
[1,3,7,8,4,6,5,2]=>0001011=>[4,2,1,1]
[3,6,7,8,4,2,5,1]=>0001101=>[4,1,2,1]
[7,6,1,8,4,2,5,3]=>1101101=>[1,1,2,1,2,1]
[2,8,3,7,1,6,5,4]=>0101011=>[2,2,2,1,1]
[5,2,8,7,3,6,1,4]=>1011010=>[1,2,1,2,2]
[7,2,1,8,4,6,5,3]=>1101011=>[1,1,2,2,1,1]
[3,2,7,8,4,6,5,1]=>1001011=>[1,3,2,1,1]
[5,2,7,8,1,4,6,3]=>1001001=>[1,3,3,1]
[1,2,7,8,5,4,6,3]=>0001101=>[4,1,2,1]
[7,2,5,8,3,4,6,1]=>1001001=>[1,3,3,1]
[6,2,8,5,4,3,1,7]=>1011110=>[1,2,1,1,1,2]
[2,8,3,5,4,1,6,7]=>0101100=>[2,2,1,3]
[2,8,4,5,3,1,6,7]=>0101100=>[2,2,1,3]
[7,3,5,8,2,4,6,1]=>1001001=>[1,3,3,1]
[4,3,1,2,8,5,6,7]=>1100100=>[1,1,3,3]
[2,7,6,8,4,3,5,1]=>0101101=>[2,2,1,2,1]
[1,7,5,8,3,4,6,2]=>0101001=>[2,2,3,1]
[4,6,8,5,1,3,2,7]=>0011010=>[3,1,2,2]
[2,4,8,3,6,5,1,7]=>0010110=>[3,2,1,2]
[4,1,8,3,5,6,2,7]=>1010010=>[1,2,3,2]
[5,6,8,4,1,3,2,7]=>0011010=>[3,1,2,2]
[4,6,8,1,5,3,2,7]=>0010110=>[3,2,1,2]
[1,6,8,4,5,3,2,7]=>0010110=>[3,2,1,2]
[1,7,3,8,5,4,6,2]=>0101101=>[2,2,1,2,1]
[3,7,1,8,5,4,6,2]=>0101101=>[2,2,1,2,1]
[2,7,3,8,4,6,5,1]=>0101011=>[2,2,2,1,1]
[2,8,7,4,1,6,5,3]=>0111011=>[2,1,1,2,1,1]
[2,8,5,4,3,1,6,7]=>0111100=>[2,1,1,1,3]
[1,4,3,2,8,5,6,7]=>0110100=>[2,1,2,3]
[7,3,2,8,5,4,6,1]=>1101101=>[1,1,2,1,2,1]
[6,4,8,2,5,3,1,7]=>1010110=>[1,2,2,1,2]
[2,8,4,3,5,1,6,7]=>0110100=>[2,1,2,3]
[6,2,8,4,5,3,1,7]=>1010110=>[1,2,2,1,2]
[7,2,3,8,5,4,6,1]=>1001101=>[1,3,1,2,1]
[4,2,3,1,8,5,6,7]=>1010100=>[1,2,2,3]
[5,1,3,2,4,8,6,7]=>1010010=>[1,2,3,2]
[2,8,1,5,3,4,7,6]=>0101001=>[2,2,3,1]
[1,4,2,8,5,3,6,7]=>0101100=>[2,2,1,3]
[3,5,1,4,8,2,6,7]=>0100100=>[2,3,3]
[1,5,2,8,4,3,6,7]=>0101100=>[2,2,1,3]
[1,2,5,4,3,8,6,7]=>0011010=>[3,1,2,2]
[1,2,4,8,5,3,7,6]=>0001101=>[4,1,2,1]
[1,5,2,7,8,4,3,6]=>0100110=>[2,3,1,2]
[5,1,2,7,4,8,3,6]=>1001010=>[1,3,2,2]
[8,3,5,1,4,7,2,6]=>1010010=>[1,2,3,2]
[1,2,8,5,7,4,3,6]=>0010110=>[3,2,1,2]
[1,2,4,8,7,5,3,6]=>0001110=>[4,1,1,2]
[2,8,1,4,3,7,6,5]=>0101011=>[2,2,2,1,1]
[7,6,1,4,2,8,3,5]=>1101010=>[1,1,2,2,2]
[7,1,6,2,8,4,3,5]=>1010110=>[1,2,2,1,2]
[1,4,2,7,8,5,3,6]=>0100110=>[2,3,1,2]
[6,1,2,8,4,3,7,5]=>1001101=>[1,3,1,2,1]
[6,4,1,2,8,3,7,5]=>1100101=>[1,1,3,2,1]
[7,6,1,3,2,4,8,5]=>1101001=>[1,1,2,3,1]
[6,7,1,3,2,4,8,5]=>0101001=>[2,2,3,1]
[1,2,7,3,5,8,4,6]=>0010010=>[3,3,2]
[5,8,1,3,7,2,4,6]=>0100100=>[2,3,3]
[1,2,5,8,7,3,4,6]=>0001100=>[4,1,3]
[8,6,1,3,2,4,7,5]=>1101001=>[1,1,2,3,1]
[4,2,8,1,7,3,6,5]=>1010101=>[1,2,2,2,1]
[7,1,2,8,4,3,6,5]=>1001101=>[1,3,1,2,1]
[1,2,8,4,7,5,3,6]=>0010110=>[3,2,1,2]
[1,2,8,7,4,5,3,6]=>0011010=>[3,1,2,2]
[2,8,1,7,5,3,4,6]=>0101100=>[2,2,1,3]
[8,3,7,1,5,2,4,6]=>1010100=>[1,2,2,3]
[8,6,1,4,2,7,3,5]=>1101010=>[1,1,2,2,2]
[7,1,2,8,6,4,3,5]=>1001110=>[1,3,1,1,2]
[3,7,4,8,1,6,2,5]=>0101010=>[2,2,2,2]
[3,4,8,7,1,6,2,5]=>0011010=>[3,1,2,2]
[4,2,8,1,7,6,3,5]=>1010110=>[1,2,2,1,2]
[2,8,1,7,6,4,3,5]=>0101110=>[2,2,1,1,2]
[7,8,3,4,1,5,2,6]=>0101010=>[2,2,2,2]
[6,8,3,4,1,7,2,5]=>0101010=>[2,2,2,2]
[5,7,3,4,1,8,2,6]=>0101010=>[2,2,2,2]
[5,8,3,4,1,7,2,6]=>0101010=>[2,2,2,2]
[4,7,3,5,1,6,2,8]=>0101010=>[2,2,2,2]
[4,8,3,5,1,6,2,7]=>0101010=>[2,2,2,2]
[4,8,3,5,1,7,2,6]=>0101010=>[2,2,2,2]
[4,7,3,5,1,8,2,6]=>0101010=>[2,2,2,2]
[5,6,2,3,1,7,4,8]=>0101010=>[2,2,2,2]
[5,6,2,4,1,8,3,7]=>0101010=>[2,2,2,2]
[5,6,2,4,1,7,3,8]=>0101010=>[2,2,2,2]
[4,6,2,5,1,7,3,8]=>0101010=>[2,2,2,2]
[4,6,2,5,1,8,3,7]=>0101010=>[2,2,2,2]
[4,5,1,8,3,7,2,6]=>0101010=>[2,2,2,2]
[4,6,2,7,3,8,1,5]=>0101010=>[2,2,2,2]
[5,6,2,7,3,8,1,4]=>0101010=>[2,2,2,2]
[5,6,2,8,4,7,1,3]=>0101010=>[2,2,2,2]
[5,6,2,8,3,7,1,4]=>0101010=>[2,2,2,2]
[4,6,2,8,3,7,1,5]=>0101010=>[2,2,2,2]
[4,5,1,7,3,6,2,8]=>0101010=>[2,2,2,2]
[4,5,1,8,3,6,2,7]=>0101010=>[2,2,2,2]
[6,5,3,2,1,4,8,7]=>1111001=>[1,1,1,1,3,1]
[8,7,3,5,2,4,1,6]=>1101010=>[1,1,2,2,2]
[6,8,2,4,5,7,3,1]=>0100011=>[2,4,1,1]
[3,6,1,4,5,2,8,7]=>0100101=>[2,3,2,1]
[8,3,7,4,5,2,1,6]=>1010110=>[1,2,2,1,2]
[6,3,8,4,5,7,2,1]=>1010011=>[1,2,3,1,1]
[8,1,7,4,3,6,2,5]=>1011010=>[1,2,1,2,2]
[8,7,3,5,1,4,2,6]=>1101010=>[1,1,2,2,2]
[2,1,6,8,5,7,4,3]=>1001011=>[1,3,2,1,1]
[6,8,3,5,1,7,4,2]=>0101011=>[2,2,2,1,1]
[2,5,8,4,7,6,3,1]=>0010111=>[3,2,1,1,1]
[4,3,8,1,5,6,7,2]=>1010001=>[1,2,4,1]
[4,8,3,6,1,2,7,5]=>0101001=>[2,2,3,1]
[3,8,7,4,1,6,2,5]=>0111010=>[2,1,1,2,2]
[3,8,1,2,5,6,7,4]=>0100001=>[2,5,1]
[2,8,7,4,5,1,3,6]=>0110100=>[2,1,2,3]
[8,7,2,4,1,6,3,5]=>1101010=>[1,1,2,2,2]
[5,8,3,6,2,4,7,1]=>0101001=>[2,2,3,1]
[8,6,3,2,1,4,7,5]=>1111001=>[1,1,1,1,3,1]
[8,7,3,5,2,1,4,6]=>1101100=>[1,1,2,1,3]
[5,8,3,6,2,1,7,4]=>0101101=>[2,2,1,2,1]
[6,1,8,4,5,7,2,3]=>1010010=>[1,2,3,2]
[6,8,3,5,1,7,2,4]=>0101010=>[2,2,2,2]
[5,8,3,6,1,2,7,4]=>0101001=>[2,2,3,1]
[5,8,1,4,7,6,2,3]=>0100110=>[2,3,1,2]
[4,5,3,8,6,1,7,2]=>0101101=>[2,2,1,2,1]
[4,5,7,6,2,3,8,1]=>0011001=>[3,1,3,1]
[3,5,7,2,6,4,8,1]=>0010101=>[3,2,2,1]
[2,5,7,3,6,4,8,1]=>0010101=>[3,2,2,1]
[8,4,3,7,6,1,5,2]=>1101101=>[1,1,2,1,2,1]
[6,7,2,3,5,4,8,1]=>0100101=>[2,3,2,1]
[5,2,7,3,6,4,8,1]=>1010101=>[1,2,2,2,1]
[8,3,4,7,6,1,5,2]=>1001101=>[1,3,1,2,1]
[8,2,4,7,1,6,5,3]=>1001011=>[1,3,2,1,1]
[3,1,4,7,6,8,5,2]=>1001011=>[1,3,2,1,1]
[5,1,7,3,6,8,4,2]=>1010011=>[1,2,3,1,1]
[6,7,1,3,5,8,4,2]=>0100011=>[2,4,1,1]
[4,8,3,7,6,1,5,2]=>0101101=>[2,2,1,2,1]
[2,8,4,7,1,6,5,3]=>0101011=>[2,2,2,1,1]
[8,1,4,7,2,6,5,3]=>1001011=>[1,3,2,1,1]
[8,1,3,2,7,6,5,4]=>1010111=>[1,2,2,1,1,1]
[2,8,3,1,7,6,5,4]=>0110111=>[2,1,2,1,1,1]
[6,7,1,2,8,5,4,3]=>0100111=>[2,3,1,1,1]
[8,2,3,1,7,6,5,4]=>1010111=>[1,2,2,1,1,1]
[1,4,2,7,8,6,5,3]=>0100111=>[2,3,1,1,1]
[8,4,2,7,1,6,5,3]=>1101011=>[1,1,2,2,1,1]
[8,5,7,2,1,6,4,3]=>1011011=>[1,2,1,2,1,1]
[1,5,7,2,8,6,4,3]=>0010111=>[3,2,1,1,1]
[2,5,7,1,8,6,4,3]=>0010111=>[3,2,1,1,1]
[3,5,7,1,6,8,4,2]=>0010011=>[3,3,1,1]
[6,7,4,5,8,1,3,2]=>0100101=>[2,3,2,1]
[2,5,7,8,1,6,4,3]=>0001011=>[4,2,1,1]
[1,5,7,8,2,6,4,3]=>0001011=>[4,2,1,1]
[8,5,7,1,2,6,4,3]=>1010011=>[1,2,3,1,1]
[8,4,1,7,2,6,5,3]=>1101011=>[1,1,2,2,1,1]
[6,7,2,8,1,5,4,3]=>0101011=>[2,2,2,1,1]
[5,2,7,8,1,6,4,3]=>1001011=>[1,3,2,1,1]
[4,2,8,7,1,6,5,3]=>1011011=>[1,2,1,2,1,1]
[1,3,8,2,7,6,5,4]=>0010111=>[3,2,1,1,1]
[8,3,1,2,7,6,5,4]=>1100111=>[1,1,3,1,1,1]
[8,2,1,3,7,6,5,4]=>1100111=>[1,1,3,1,1,1]
[2,1,8,3,7,6,5,4]=>1010111=>[1,2,2,1,1,1]
[5,1,7,8,2,6,4,3]=>1001011=>[1,3,2,1,1]
[6,7,1,8,2,5,4,3]=>0101011=>[2,2,2,1,1]
[4,8,1,7,2,6,5,3]=>0101011=>[2,2,2,1,1]
[3,8,1,2,7,6,5,4]=>0100111=>[2,3,1,1,1]
[1,8,2,3,7,6,5,4]=>0100111=>[2,3,1,1,1]
[3,7,1,5,8,2,6,4]=>0100101=>[2,3,2,1]
[2,7,1,5,8,3,6,4]=>0100101=>[2,3,2,1]
[2,6,5,1,8,3,7,4]=>0110101=>[2,1,2,2,1]
[5,6,4,1,8,7,2,3]=>0110110=>[2,1,2,1,2]
[8,1,4,5,7,6,2,3]=>1000110=>[1,4,1,2]
[6,4,5,1,8,7,2,3]=>1010110=>[1,2,2,1,2]
[5,4,6,1,8,7,2,3]=>1010110=>[1,2,2,1,2]
[3,5,6,1,8,2,7,4]=>0010101=>[3,2,2,1]
[2,5,6,1,8,3,7,4]=>0010101=>[3,2,2,1]
[2,4,6,1,3,8,7,5]=>0010011=>[3,3,1,1]
[3,4,6,1,2,8,7,5]=>0010011=>[3,3,1,1]
[5,3,6,1,8,2,7,4]=>1010101=>[1,2,2,2,1]
[7,3,1,5,8,2,6,4]=>1100101=>[1,1,3,2,1]
[8,1,3,5,7,2,6,4]=>1000101=>[1,4,2,1]
[8,1,2,5,7,3,6,4]=>1000101=>[1,4,2,1]
[7,2,1,5,8,3,6,4]=>1100101=>[1,1,3,2,1]
[6,2,5,1,8,3,7,4]=>1010101=>[1,2,2,2,1]
[4,2,6,1,3,8,7,5]=>1010011=>[1,2,3,1,1]
[4,2,5,3,1,8,7,6]=>1011011=>[1,2,1,2,1,1]
[6,2,4,1,3,8,7,5]=>1010011=>[1,2,3,1,1]
[7,2,1,4,3,8,6,5]=>1101011=>[1,1,2,2,1,1]
[8,1,2,4,3,7,6,5]=>1001011=>[1,3,2,1,1]
[8,1,3,4,2,7,6,5]=>1001011=>[1,3,2,1,1]
[7,3,1,4,2,8,6,5]=>1101011=>[1,1,2,2,1,1]
[4,6,3,1,2,8,7,5]=>0110011=>[2,1,3,1,1]
[2,6,4,1,3,8,7,5]=>0110011=>[2,1,3,1,1]
[2,7,1,4,3,8,6,5]=>0101011=>[2,2,2,1,1]
[8,1,6,7,2,3,5,4]=>1001001=>[1,3,3,1]
[4,7,1,2,3,8,6,5]=>0100011=>[2,4,1,1]
[3,7,1,2,4,8,6,5]=>0100011=>[2,4,1,1]
[2,6,3,1,4,8,7,5]=>0110011=>[2,1,3,1,1]
[3,6,2,1,4,8,7,5]=>0110011=>[2,1,3,1,1]
[5,6,2,1,8,3,7,4]=>0110101=>[2,1,2,2,1]
[6,5,2,1,8,3,7,4]=>1110101=>[1,1,1,2,2,1]
[8,1,4,2,3,7,6,5]=>1010011=>[1,2,3,1,1]
[7,4,1,2,3,8,6,5]=>1100011=>[1,1,4,1,1]
[5,4,2,3,1,8,7,6]=>1101011=>[1,1,2,2,1,1]
[3,5,2,4,1,8,7,6]=>0101011=>[2,2,2,1,1]
[7,3,1,2,4,8,6,5]=>1100011=>[1,1,4,1,1]
[8,1,3,2,4,7,6,5]=>1010011=>[1,2,3,1,1]
[7,2,1,3,4,8,6,5]=>1100011=>[1,1,4,1,1]
[2,4,3,6,1,5,8,7]=>0101001=>[2,2,3,1]
[2,4,3,6,5,8,1,7]=>0101010=>[2,2,2,2]
[2,4,6,3,5,8,7,1]=>0010011=>[3,3,1,1]
[2,4,6,3,5,1,8,7]=>0010101=>[3,2,2,1]
[2,4,6,3,1,5,8,7]=>0011001=>[3,1,3,1]
[2,4,1,6,5,3,8,7]=>0101101=>[2,2,1,2,1]
[2,4,6,1,5,3,8,7]=>0010101=>[3,2,2,1]
[4,2,6,5,3,1,8,7]=>1011101=>[1,2,1,1,2,1]
[4,2,6,5,1,3,8,7]=>1011001=>[1,2,1,3,1]
[4,2,6,5,8,1,7,3]=>1010101=>[1,2,2,2,1]
[4,2,6,5,8,1,3,7]=>1010100=>[1,2,2,3]
[4,2,6,5,8,3,1,7]=>1010110=>[1,2,2,1,2]
[2,4,1,6,5,8,3,7]=>0101010=>[2,2,2,2]
[2,1,4,6,5,8,3,7]=>1001010=>[1,3,2,2]
[2,4,1,6,5,8,7,3]=>0101011=>[2,2,2,1,1]
[2,4,6,1,5,8,7,3]=>0010011=>[3,3,1,1]
[4,2,6,5,3,8,7,1]=>1011011=>[1,2,1,2,1,1]
[2,6,4,3,8,7,5,1]=>0110111=>[2,1,2,1,1,1]
[4,2,6,8,5,3,7,1]=>1001101=>[1,3,1,2,1]
[2,4,6,8,1,5,7,3]=>0001001=>[4,3,1]
[2,4,1,6,8,5,7,3]=>0100101=>[2,3,2,1]
[2,1,4,6,8,5,3,7]=>1000110=>[1,4,1,2]
[2,4,6,1,8,5,3,7]=>0010110=>[3,2,1,2]
[2,4,6,8,1,5,3,7]=>0001010=>[4,2,2]
[2,4,6,8,3,5,7,1]=>0001001=>[4,3,1]
[2,4,6,8,3,1,5,7]=>0001100=>[4,1,3]
[2,4,6,3,8,5,7,1]=>0010101=>[3,2,2,1]
[2,4,3,6,8,5,7,1]=>0100101=>[2,3,2,1]
[2,4,3,6,8,5,1,7]=>0100110=>[2,3,1,2]
[2,4,3,6,8,1,5,7]=>0100100=>[2,3,3]
[2,4,3,6,1,8,5,7]=>0101010=>[2,2,2,2]
[2,4,3,1,6,8,5,7]=>0110010=>[2,1,3,2]
[2,4,1,3,6,8,7,5]=>0100011=>[2,4,1,1]
[2,4,3,6,8,1,7,5]=>0100101=>[2,3,2,1]
[4,6,5,2,8,7,1,3]=>0110110=>[2,1,2,1,2]
[4,6,2,5,8,7,1,3]=>0100110=>[2,3,1,2]
[4,6,2,5,8,7,3,1]=>0100111=>[2,3,1,1,1]
[2,4,6,3,1,8,7,5]=>0011011=>[3,1,2,1,1]
[2,4,1,6,3,8,7,5]=>0101011=>[2,2,2,1,1]
[2,1,4,6,3,8,7,5]=>1001011=>[1,3,2,1,1]
[2,4,1,6,8,3,7,5]=>0100101=>[2,3,2,1]
[2,4,6,8,1,3,7,5]=>0001001=>[4,3,1]
[4,6,2,8,5,7,3,1]=>0101011=>[2,2,2,1,1]
[4,6,2,8,5,7,1,3]=>0101010=>[2,2,2,2]
[6,2,4,8,7,1,3,5]=>1001100=>[1,3,1,3]
[2,6,4,8,1,7,5,3]=>0101011=>[2,2,2,1,1]
[2,6,4,1,8,7,5,3]=>0110111=>[2,1,2,1,1,1]
[2,1,6,4,8,7,3,5]=>1010110=>[1,2,2,1,2]
[2,6,4,1,8,7,3,5]=>0110110=>[2,1,2,1,2]
[2,6,4,8,1,7,3,5]=>0101010=>[2,2,2,2]
[6,2,4,8,7,3,5,1]=>1001101=>[1,3,1,2,1]
[6,2,4,8,7,3,1,5]=>1001110=>[1,3,1,1,2]
[1,3,7,4,5,8,2,6]=>0010010=>[3,3,2]
[1,7,6,3,4,8,2,5]=>0110010=>[2,1,3,2]
[8,1,6,3,7,2,4,5]=>1010100=>[1,2,2,3]
[1,2,7,4,8,3,5,6]=>0010100=>[3,2,3]
[6,1,7,3,4,8,2,5]=>1010010=>[1,2,3,2]
[2,1,7,4,5,8,3,6]=>1010010=>[1,2,3,2]
[5,1,4,7,3,8,2,6]=>1001010=>[1,3,2,2]
[4,3,1,7,5,8,2,6]=>1101010=>[1,1,2,2,2]
[2,8,6,3,7,1,4,5]=>0110100=>[2,1,2,3]
[6,8,1,3,7,2,4,5]=>0100100=>[2,3,3]
[5,8,2,1,7,3,4,6]=>0110100=>[2,1,2,3]
[5,7,2,1,8,3,4,6]=>0110100=>[2,1,2,3]
[6,7,1,3,8,2,4,5]=>0100100=>[2,3,3]
[8,5,1,3,7,2,4,6]=>1100100=>[1,1,3,3]
[1,5,3,2,8,4,6,7]=>0110100=>[2,1,2,3]
[2,6,4,8,7,1,3,5]=>0101100=>[2,2,1,3]
[1,6,4,8,7,2,3,5]=>0101100=>[2,2,1,3]
[4,3,2,8,7,1,5,6]=>1101100=>[1,1,2,1,3]
[5,2,4,8,7,1,3,6]=>1001100=>[1,3,1,3]
[6,2,8,3,7,1,4,5]=>1010100=>[1,2,2,3]
[5,1,4,8,7,2,3,6]=>1001100=>[1,3,1,3]
[3,7,2,1,5,4,8,6]=>0110101=>[2,1,2,2,1]
[3,8,2,1,5,4,7,6]=>0110101=>[2,1,2,2,1]
[8,3,2,1,5,4,6,7]=>1110100=>[1,1,1,2,3]
[8,3,2,1,6,4,5,7]=>1110100=>[1,1,1,2,3]
[8,4,2,5,1,6,3,7]=>1101010=>[1,1,2,2,2]
[8,3,2,1,4,6,5,7]=>1110010=>[1,1,1,3,2]
[3,8,2,1,4,5,7,6]=>0110001=>[2,1,4,1]
[3,2,7,1,4,6,8,5]=>1010001=>[1,2,4,1]
[3,2,8,1,4,6,7,5]=>1010001=>[1,2,4,1]
[3,8,2,1,4,7,5,6]=>0110010=>[2,1,3,2]
[3,8,2,1,5,7,4,6]=>0110010=>[2,1,3,2]
[4,8,2,5,1,7,3,6]=>0101010=>[2,2,2,2]
[4,7,2,5,1,8,3,6]=>0101010=>[2,2,2,2]
[3,7,2,1,5,8,4,6]=>0110010=>[2,1,3,2]
[3,7,2,1,4,8,5,6]=>0110010=>[2,1,3,2]
[3,2,1,7,5,8,6,4]=>1101011=>[1,1,2,2,1,1]
[4,2,7,6,1,8,3,5]=>1011010=>[1,2,1,2,2]
[4,3,7,6,8,1,2,5]=>1010100=>[1,2,2,3]
[4,3,8,6,7,1,2,5]=>1010100=>[1,2,2,3]
[3,8,2,1,7,4,5,6]=>0110100=>[2,1,2,3]
[3,2,8,1,6,4,7,5]=>1010101=>[1,2,2,2,1]
[3,2,7,1,6,4,8,5]=>1010101=>[1,2,2,2,1]
[4,2,7,6,1,3,8,5]=>1011001=>[1,2,1,3,1]
[4,2,8,6,1,3,7,5]=>1011001=>[1,2,1,3,1]
[5,7,8,3,4,1,2,6]=>0010100=>[3,2,3]
[4,2,6,8,1,3,7,5]=>1001001=>[1,3,3,1]
[4,2,6,7,1,3,8,5]=>1001001=>[1,3,3,1]
[3,2,6,1,8,4,7,5]=>1010101=>[1,2,2,2,1]
[3,7,2,1,8,5,4,6]=>0110110=>[2,1,2,1,2]
[4,7,3,8,5,1,2,6]=>0101100=>[2,2,1,3]
[4,3,7,8,6,1,2,5]=>1001100=>[1,3,1,3]
[3,2,7,1,8,6,4,5]=>1010110=>[1,2,2,1,2]
[3,2,1,6,8,5,7,4]=>1100101=>[1,1,3,2,1]
[3,2,6,1,8,7,4,5]=>1010110=>[1,2,2,1,2]
[4,2,6,8,1,7,3,5]=>1001010=>[1,3,2,2]
[4,3,6,8,7,1,2,5]=>1001100=>[1,3,1,3]
[4,2,6,7,1,8,3,5]=>1001010=>[1,3,2,2]
[3,2,6,1,7,8,4,5]=>1010010=>[1,2,3,2]
[5,3,6,4,8,7,1,2]=>1010110=>[1,2,2,1,2]
[1,4,6,2,7,8,5,3]=>0010011=>[3,3,1,1]
[3,1,8,5,4,2,6,7]=>1011100=>[1,2,1,1,3]
[1,2,7,5,4,8,6,3]=>0011011=>[3,1,2,1,1]
[6,3,7,5,4,8,1,2]=>1011010=>[1,2,1,2,2]
[1,6,2,5,4,8,7,3]=>0101011=>[2,2,2,1,1]
[1,8,2,5,7,3,6,4]=>0100101=>[2,3,2,1]
[6,2,1,5,4,8,7,3]=>1101011=>[1,1,2,2,1,1]
[4,1,6,2,8,7,5,3]=>1010111=>[1,2,2,1,1,1]
[7,8,3,1,4,2,6,5]=>0110101=>[2,1,2,2,1]
[4,3,6,1,8,2,7,5]=>1010101=>[1,2,2,2,1]
[7,5,1,6,4,3,2,8]=>1101110=>[1,1,2,1,1,2]
[6,1,5,7,4,3,2,8]=>1001110=>[1,3,1,1,2]
[1,5,8,6,4,3,2,7]=>0011110=>[3,1,1,1,2]
[7,8,5,1,6,3,2,4]=>0110110=>[2,1,2,1,2]
[2,6,1,5,7,3,8,4]=>0100101=>[2,3,2,1]
[1,6,8,7,4,3,2,5]=>0011110=>[3,1,1,1,2]
[6,8,1,7,4,3,2,5]=>0101110=>[2,2,1,1,2]
[5,6,1,7,4,3,2,8]=>0101110=>[2,2,1,1,2]
[5,1,7,6,4,3,2,8]=>1011110=>[1,2,1,1,1,2]
[6,1,7,8,4,3,2,5]=>1001110=>[1,3,1,1,2]
[7,1,8,6,4,3,2,5]=>1011110=>[1,2,1,1,1,2]
[7,2,1,5,4,6,8,3]=>1101001=>[1,1,2,3,1]
[1,2,8,5,6,3,7,4]=>0010101=>[3,2,2,1]
[6,1,2,5,7,3,8,4]=>1000101=>[1,4,2,1]
[4,3,6,1,5,7,2,8]=>1010010=>[1,2,3,2]
[1,3,6,8,5,7,2,4]=>0001010=>[4,2,2]
[1,3,6,4,8,7,2,5]=>0010110=>[3,2,1,2]
[4,1,6,7,3,8,2,5]=>1001010=>[1,3,2,2]
[5,4,6,1,3,7,2,8]=>1010010=>[1,2,3,2]
[6,4,1,5,2,3,7,8]=>1101000=>[1,1,2,4]
[4,1,7,5,2,3,8,6]=>1011001=>[1,2,1,3,1]
[2,8,3,5,4,1,7,6]=>0101101=>[2,2,1,2,1]
[7,8,1,4,6,3,2,5]=>0100110=>[2,3,1,2]
[5,1,8,7,4,3,2,6]=>1011110=>[1,2,1,1,1,2]
[6,5,1,8,4,3,2,7]=>1101110=>[1,1,2,1,1,2]
[6,5,7,1,4,3,2,8]=>1010110=>[1,2,2,1,2]
[7,5,8,1,4,3,2,6]=>1010110=>[1,2,2,1,2]
[1,5,7,8,4,3,2,6]=>0001110=>[4,1,1,2]
[2,4,7,5,1,3,8,6]=>0011001=>[3,1,3,1]
[7,8,4,6,1,3,2,5]=>0101010=>[2,2,2,2]
[1,6,5,8,4,3,2,7]=>0101110=>[2,2,1,1,2]
[6,8,5,1,4,3,2,7]=>0110110=>[2,1,2,1,2]
[3,6,2,5,4,1,7,8]=>0101100=>[2,2,1,3]
[4,3,6,2,8,1,5,7]=>1010100=>[1,2,2,3]
[6,1,2,5,4,7,8,3]=>1001001=>[1,3,3,1]
[6,2,4,5,1,3,7,8]=>1001000=>[1,3,4]
[4,2,8,5,1,3,7,6]=>1011001=>[1,2,1,3,1]
[4,3,6,8,1,7,2,5]=>1001010=>[1,3,2,2]
[5,3,6,4,1,7,2,8]=>1011010=>[1,2,1,2,2]
[1,6,7,4,8,3,5,2]=>0010101=>[3,2,2,1]
[1,4,6,3,7,5,8,2]=>0010101=>[3,2,2,1]
[4,6,7,2,5,8,1,3]=>0010010=>[3,3,2]
[2,4,6,1,7,5,3,8]=>0010110=>[3,2,1,2]
[2,7,5,4,1,6,3,8]=>0111010=>[2,1,1,2,2]
[1,7,5,4,3,8,6,2]=>0111011=>[2,1,1,2,1,1]
[1,5,8,4,3,6,7,2]=>0011001=>[3,1,3,1]
[5,4,6,2,7,8,1,3]=>1010010=>[1,2,3,2]
[2,5,4,1,6,7,3,8]=>0110010=>[2,1,3,2]
[5,6,3,2,7,1,4,8]=>0110100=>[2,1,2,3]
[5,6,3,2,7,1,8,4]=>0110101=>[2,1,2,2,1]
[8,5,6,3,2,7,1,4]=>1011010=>[1,2,1,2,2]
[5,4,6,2,8,1,7,3]=>1010101=>[1,2,2,2,1]
[2,4,1,7,8,5,3,6]=>0100110=>[2,3,1,2]
[5,6,3,2,1,8,4,7]=>0111010=>[2,1,1,2,2]
[3,5,2,1,6,4,7,8]=>0110100=>[2,1,2,3]
[6,8,4,3,2,1,5,7]=>0111100=>[2,1,1,1,3]
[5,3,8,2,1,6,4,7]=>1011010=>[1,2,1,2,2]
[7,3,2,8,5,1,6,4]=>1101101=>[1,1,2,1,2,1]
[8,4,6,3,2,1,7,5]=>1011101=>[1,2,1,1,2,1]
[5,4,7,2,1,8,6,3]=>1011011=>[1,2,1,2,1,1]
[5,7,3,2,1,6,8,4]=>0111001=>[2,1,1,3,1]
[6,3,7,2,5,1,8,4]=>1010101=>[1,2,2,2,1]
[6,7,8,3,5,2,1,4]=>0010110=>[3,2,1,2]
[6,2,5,7,8,4,1,3]=>1000110=>[1,4,1,2]
[2,1,5,7,8,6,3,4]=>1000110=>[1,4,1,2]
[3,6,7,2,8,1,4,5]=>0010100=>[3,2,3]
[3,2,6,1,7,4,5,8]=>1010100=>[1,2,2,3]
[2,5,8,4,1,3,7,6]=>0011001=>[3,1,3,1]
[2,4,1,7,8,3,6,5]=>0100101=>[2,3,2,1]
[3,6,8,2,1,7,4,5]=>0011010=>[3,1,2,2]
[5,3,8,2,1,4,7,6]=>1011001=>[1,2,1,3,1]
[4,8,7,3,2,1,5,6]=>0111100=>[2,1,1,1,3]
[4,7,3,2,1,5,6,8]=>0111000=>[2,1,1,4]
[8,4,7,3,2,1,5,6]=>1011100=>[1,2,1,1,3]
[8,3,5,2,1,4,7,6]=>1011001=>[1,2,1,3,1]
[3,5,2,1,4,6,8,7]=>0110001=>[2,1,4,1]
[2,7,6,5,1,8,3,4]=>0111010=>[2,1,1,2,2]
[2,7,6,5,1,8,4,3]=>0111011=>[2,1,1,2,1,1]
[2,3,6,5,1,4,8,7]=>0011001=>[3,1,3,1]
[2,3,6,4,1,5,8,7]=>0011001=>[3,1,3,1]
[2,7,6,1,4,8,5,3]=>0110011=>[2,1,3,1,1]
[7,3,5,1,8,4,2,6]=>1010110=>[1,2,2,1,2]
[2,7,6,1,5,8,4,3]=>0110011=>[2,1,3,1,1]
[2,7,6,4,1,8,5,3]=>0111011=>[2,1,1,2,1,1]
[2,7,6,4,1,8,3,5]=>0111010=>[2,1,1,2,2]
[7,3,5,1,8,6,2,4]=>1010110=>[1,2,2,1,2]
[2,3,4,8,7,6,1,5]=>0001110=>[4,1,1,2]
[2,3,4,8,5,7,1,6]=>0001010=>[4,2,2]
[7,3,5,4,8,1,2,6]=>1010100=>[1,2,2,3]
[6,4,3,5,8,7,2,1]=>1100111=>[1,1,3,1,1,1]
[2,1,4,5,8,7,3,6]=>1000110=>[1,4,1,2]
[6,4,3,5,8,7,1,2]=>1100110=>[1,1,3,1,2]
[2,3,4,8,7,5,1,6]=>0001110=>[4,1,1,2]
[2,7,6,5,4,8,1,3]=>0111010=>[2,1,1,2,2]
[7,3,5,6,8,1,2,4]=>1000100=>[1,4,3]
[6,4,1,5,8,7,2,3]=>1100110=>[1,1,3,1,2]
[6,4,1,5,8,7,3,2]=>1100111=>[1,1,3,1,1,1]
[6,4,1,5,8,3,7,2]=>1100101=>[1,1,3,2,1]
[5,7,1,6,3,8,2,4]=>0101010=>[2,2,2,2]
[6,4,1,5,8,3,2,7]=>1100110=>[1,1,3,1,2]
[6,3,5,7,8,2,1,4]=>1000110=>[1,4,1,2]
[5,7,3,6,1,8,4,2]=>0101011=>[2,2,2,1,1]
[7,3,5,4,8,6,2,1]=>1010111=>[1,2,2,1,1,1]
[2,3,4,8,5,6,1,7]=>0001010=>[4,2,2]
[2,3,4,8,7,1,6,5]=>0001101=>[4,1,2,1]
[2,3,4,8,5,1,7,6]=>0001101=>[4,1,2,1]
[7,4,3,5,8,2,1,6]=>1100110=>[1,1,3,1,2]
[7,4,3,5,8,2,6,1]=>1100101=>[1,1,3,2,1]
[6,3,5,4,8,2,1,7]=>1010110=>[1,2,2,1,2]
[2,3,4,8,5,1,6,7]=>0001100=>[4,1,3]
[6,1,4,2,8,5,7,3]=>1010101=>[1,2,2,2,1]
[4,8,6,5,3,2,7,1]=>0111101=>[2,1,1,1,2,1]
[8,6,5,1,2,4,7,3]=>1110001=>[1,1,1,4,1]
[1,7,5,8,2,6,4,3]=>0101011=>[2,2,2,1,1]
[1,3,8,5,7,6,2,4]=>0010110=>[3,2,1,2]
[6,3,8,5,7,1,2,4]=>1010100=>[1,2,2,3]
[6,8,5,2,1,4,7,3]=>0111001=>[2,1,1,3,1]
[3,8,2,5,6,1,7,4]=>0100101=>[2,3,2,1]
[8,1,2,5,6,3,7,4]=>1000101=>[1,4,2,1]
[8,6,1,5,7,2,3,4]=>1100100=>[1,1,3,3]
[3,8,6,5,7,1,2,4]=>0110100=>[2,1,2,3]
[5,1,7,6,8,4,2,3]=>1010110=>[1,2,2,1,2]
[5,1,3,7,8,6,2,4]=>1000110=>[1,4,1,2]
[7,2,5,8,1,6,4,3]=>1001011=>[1,3,2,1,1]
[3,2,8,5,7,6,1,4]=>1010110=>[1,2,2,1,2]
[8,2,1,5,7,6,3,4]=>1100110=>[1,1,3,1,2]
[5,2,8,6,1,7,3,4]=>1011010=>[1,2,1,2,2]
[1,2,8,6,5,7,3,4]=>0011010=>[3,1,2,2]
[8,2,5,6,3,7,1,4]=>1001010=>[1,3,2,2]
[7,2,6,5,4,1,8,3]=>1011101=>[1,2,1,1,2,1]
[6,1,3,5,4,7,8,2]=>1001001=>[1,3,3,1]
[6,1,5,3,4,7,8,2]=>1010001=>[1,2,4,1]
[7,5,6,2,4,1,8,3]=>1010101=>[1,2,2,2,1]
[8,5,2,6,3,7,1,4]=>1101010=>[1,1,2,2,2]
[8,1,6,5,7,3,2,4]=>1010110=>[1,2,2,1,2]
[3,5,8,6,2,7,1,4]=>0011010=>[3,1,2,2]
[1,8,5,6,3,7,2,4]=>0101010=>[2,2,2,2]
[1,7,6,5,4,2,8,3]=>0111101=>[2,1,1,1,2,1]
[5,7,6,1,4,2,8,3]=>0110101=>[2,1,2,2,1]
[7,1,4,2,6,5,8,3]=>1010101=>[1,2,2,2,1]
[2,7,4,1,5,6,8,3]=>0110001=>[2,1,4,1]
[5,7,6,4,1,2,8,3]=>0111001=>[2,1,1,3,1]
[4,7,6,1,5,2,8,3]=>0110101=>[2,1,2,2,1]
[1,7,6,4,5,2,8,3]=>0110101=>[2,1,2,2,1]
[3,8,1,6,5,7,2,4]=>0101010=>[2,2,2,2]
[8,1,3,5,7,6,2,4]=>1000110=>[1,4,1,2]
[7,8,5,4,1,6,2,3]=>0111010=>[2,1,1,2,2]
[6,1,5,4,3,7,8,2]=>1011001=>[1,2,1,3,1]
[7,5,6,4,2,1,8,3]=>1011101=>[1,2,1,1,2,1]
[8,3,2,6,5,7,1,4]=>1101010=>[1,1,2,2,2]
[7,4,6,2,5,1,8,3]=>1010101=>[1,2,2,2,1]
[6,1,4,3,5,7,8,2]=>1010001=>[1,2,4,1]
[6,1,3,4,5,7,8,2]=>1000001=>[1,6,1]
[7,2,6,4,5,1,8,3]=>1010101=>[1,2,2,2,1]
[8,2,3,6,5,7,1,4]=>1001010=>[1,3,2,2]
[3,4,2,1,6,5,8,7,10,9,12,11]=>01101010101=>[2,1,2,2,2,2,1]
[5,6,9,10,4,3,11,12,8,7,2,1]=>00011001111=>[4,1,3,1,1,1,1]
[6,7,9,10,11,5,4,12,8,3,2,1]=>00001101111=>[5,1,2,1,1,1,1]
[3,8,2,7,6,1,5,4]=>0101101=>[2,2,1,2,1]
[4,8,7,2,6,5,3,1]=>0110111=>[2,1,2,1,1,1]
[4,8,7,3,1,6,5,2]=>0111011=>[2,1,1,2,1,1]
[4,8,7,3,2,6,1,5]=>0111010=>[2,1,1,2,2]
[4,8,7,3,2,6,5,1]=>0111011=>[2,1,1,2,1,1]
[4,8,7,3,6,2,5,1]=>0110101=>[2,1,2,2,1]
[4,8,7,3,6,1,5,2]=>0110101=>[2,1,2,2,1]
[5,8,7,6,3,4,2,1]=>0111011=>[2,1,1,2,1,1]
[5,8,7,6,3,1,4,2]=>0111101=>[2,1,1,1,2,1]
[5,8,7,6,2,4,3,1]=>0111011=>[2,1,1,2,1,1]
[5,8,7,6,4,2,1,3]=>0111110=>[2,1,1,1,1,2]
[5,8,7,6,4,1,3,2]=>0111101=>[2,1,1,1,2,1]
[5,8,7,6,4,3,1,2]=>0111110=>[2,1,1,1,1,2]
[7,3,4,2,1,6,5,8]=>1011010=>[1,2,1,2,2]
[7,3,5,2,6,1,4,8]=>1010100=>[1,2,2,3]
[7,3,5,2,6,4,1,8]=>1010110=>[1,2,2,1,2]
[7,2,1,5,6,4,3,8]=>1100110=>[1,1,3,1,2]
[7,3,5,1,6,4,2,8]=>1010110=>[1,2,2,1,2]
[7,4,5,6,1,3,2,8]=>1001010=>[1,3,2,2]
[1,4,5,7,3,2,8,6]=>0001101=>[4,1,2,1]
[6,4,5,7,3,1,8,2]=>1001101=>[1,3,1,2,1]
[6,3,5,1,7,4,8,2]=>1010101=>[1,2,2,2,1]
[6,2,1,5,7,4,8,3]=>1100101=>[1,1,3,2,1]
[3,2,1,5,7,4,8,6]=>1100101=>[1,1,3,2,1]
[2,4,6,7,3,8,1,5]=>0001010=>[4,2,2]
[1,4,6,7,3,8,5,2]=>0001011=>[4,2,1,1]
[2,5,6,7,8,3,1,4]=>0000110=>[5,1,2]
[3,2,1,6,7,8,4,5]=>1100010=>[1,1,4,2]
[5,2,1,6,7,8,4,3]=>1100011=>[1,1,4,1,1]
[5,3,6,1,7,8,4,2]=>1010011=>[1,2,3,1,1]
[5,4,6,7,1,8,3,2]=>1001011=>[1,3,2,1,1]
[6,4,5,7,2,1,8,3]=>1001101=>[1,3,1,2,1]
[5,4,6,7,2,8,3,1]=>1001011=>[1,3,2,1,1]
[5,3,6,2,7,8,4,1]=>1010011=>[1,2,3,1,1]
[5,3,6,2,7,8,1,4]=>1010010=>[1,2,3,2]
[6,3,5,2,7,1,8,4]=>1010101=>[1,2,2,2,1]
[5,3,4,1,2,7,8,6]=>1010001=>[1,2,4,1]
[4,3,6,2,7,8,1,5]=>1010010=>[1,2,3,2]
[4,3,6,2,7,8,5,1]=>1010011=>[1,2,3,1,1]
[1,3,6,2,7,8,5,4]=>0010011=>[3,3,1,1]
[1,4,6,7,2,8,5,3]=>0001011=>[4,2,1,1]
[3,4,6,7,2,8,5,1]=>0001011=>[4,2,1,1]
[3,4,5,7,2,1,8,6]=>0001101=>[4,1,2,1]
[4,2,1,5,7,3,8,6]=>1100101=>[1,1,3,2,1]
[4,2,1,6,7,8,3,5]=>1100010=>[1,1,4,2]
[4,3,6,1,7,8,2,5]=>1010010=>[1,2,3,2]
[1,5,6,7,8,2,4,3]=>0000101=>[5,2,1]
[1,5,6,7,8,4,2,3]=>0000110=>[5,1,2]
[4,3,6,1,7,8,5,2]=>1010011=>[1,2,3,1,1]
[4,2,1,6,7,8,5,3]=>1100011=>[1,1,4,1,1]
[2,4,6,7,1,8,5,3]=>0001011=>[4,2,1,1]
[2,5,6,7,8,1,4,3]=>0000101=>[5,2,1]
[1,4,3,6,2,5,7,8]=>0101000=>[2,2,4]
[1,4,3,7,2,5,6,8]=>0101000=>[2,2,4]
[1,4,3,7,6,8,2,5]=>0101010=>[2,2,2,2]
[1,4,3,7,5,8,2,6]=>0101010=>[2,2,2,2]
[1,5,3,7,4,8,2,6]=>0101010=>[2,2,2,2]
[1,5,4,8,2,6,3,7]=>0101010=>[2,2,2,2]
[1,5,4,8,3,7,2,6]=>0101010=>[2,2,2,2]
[1,2,3,6,5,8,4,7]=>0001010=>[4,2,2]
[6,8,2,4,5,7,1,3]=>0100010=>[2,4,2]
[3,7,8,4,5,2,6,1]=>0010101=>[3,2,2,1]
[7,8,1,4,5,3,6,2]=>0100101=>[2,3,2,1]
[5,8,1,4,7,6,3,2]=>0100111=>[2,3,1,1,1]
[7,5,1,8,6,2,4,3]=>1101101=>[1,1,2,1,2,1]
[7,4,1,8,2,6,3,5]=>1101010=>[1,1,2,2,2]
[7,1,8,4,2,6,3,5]=>1011010=>[1,2,1,2,2]
[7,3,1,8,4,2,6,5]=>1101101=>[1,1,2,1,2,1]
[7,2,8,3,6,5,1,4]=>1010110=>[1,2,2,1,2]
[7,2,8,3,6,1,5,4]=>1010101=>[1,2,2,2,1]
[6,1,2,8,3,5,4,7]=>1001010=>[1,3,2,2]
[5,2,3,8,1,4,7,6]=>1001001=>[1,3,3,1]
[6,2,4,1,8,7,3,5]=>1010110=>[1,2,2,1,2]
[3,1,6,4,2,8,5,7]=>1011010=>[1,2,1,2,2]
[2,6,3,8,7,1,5,4]=>0101101=>[2,2,1,2,1]
[2,6,3,8,5,1,4,7]=>0101100=>[2,2,1,3]
[2,5,1,8,3,4,7,6]=>0101001=>[2,2,3,1]
[1,2,5,3,8,4,7,6]=>0010101=>[3,2,2,1]
[1,2,4,8,3,7,6,5]=>0001011=>[4,2,1,1]
[2,4,8,3,7,1,6,5]=>0010101=>[3,2,2,1]
[2,4,8,3,7,6,1,5]=>0010110=>[3,2,1,2]
[2,5,3,8,1,7,4,6]=>0101010=>[2,2,2,2]
[2,5,4,1,3,8,7,6]=>0110011=>[2,1,3,1,1]
[3,1,5,4,8,2,7,6]=>1010101=>[1,2,2,2,1]
[5,3,1,4,8,2,7,6]=>1100101=>[1,1,3,2,1]
[5,2,3,8,4,7,1,6]=>1001010=>[1,3,2,2]
[4,8,2,3,7,6,1,5]=>0100110=>[2,3,1,2]
[4,8,2,3,7,1,6,5]=>0100101=>[2,3,2,1]
[4,8,1,2,3,7,6,5]=>0100011=>[2,4,1,1]
[1,4,8,3,7,2,6,5]=>0010101=>[3,2,2,1]
[6,3,8,1,5,2,4,7]=>1010100=>[1,2,2,3]
[5,3,8,1,2,4,7,6]=>1010001=>[1,2,4,1]
[5,1,3,8,2,4,7,6]=>1001001=>[1,3,3,1]
[1,5,3,8,2,4,7,6]=>0101001=>[2,2,3,1]
[1,5,4,8,2,7,6,3]=>0101011=>[2,2,2,1,1]
[5,1,4,8,2,7,6,3]=>1001011=>[1,3,2,1,1]
[5,4,8,1,2,7,6,3]=>1010011=>[1,2,3,1,1]
[6,5,1,2,8,7,4,3]=>1100111=>[1,1,3,1,1,1]
[4,1,5,8,2,7,6,3]=>1001011=>[1,3,2,1,1]
[4,1,2,5,8,7,6,3]=>1000111=>[1,4,1,1,1]
[1,4,2,5,8,7,6,3]=>0100111=>[2,3,1,1,1]
[1,3,5,2,8,7,4,6]=>0010110=>[3,2,1,2]
[3,5,1,2,8,7,4,6]=>0100110=>[2,3,1,2]
[4,2,6,1,8,7,3,5]=>1010110=>[1,2,2,1,2]
[4,3,1,5,8,2,7,6]=>1100101=>[1,1,3,2,1]
[3,5,2,8,7,1,4,6]=>0101100=>[2,2,1,3]
[3,4,8,7,2,6,1,5]=>0011010=>[3,1,2,2]
[3,4,8,1,7,2,6,5]=>0010101=>[3,2,2,1]
[1,3,4,8,7,2,6,5]=>0001101=>[4,1,2,1]
[1,3,4,8,2,7,6,5]=>0001011=>[4,2,1,1]
[3,4,8,1,2,7,6,5]=>0010011=>[3,3,1,1]
[3,4,8,2,7,1,6,5]=>0010101=>[3,2,2,1]
[3,4,8,2,7,6,1,5]=>0010110=>[3,2,1,2]
[4,2,5,8,1,7,6,3]=>1001011=>[1,3,2,1,1]
[4,3,1,2,5,8,7,6]=>1100011=>[1,1,4,1,1]
[3,1,4,2,5,8,7,6]=>1010011=>[1,2,3,1,1]
[2,3,5,1,8,7,6,4]=>0010111=>[3,2,1,1,1]
[7,8,2,1,5,3,6,4]=>0110101=>[2,1,2,2,1]
[6,4,1,2,7,3,5,8]=>1100100=>[1,1,3,3]
[2,3,7,5,4,1,8,6]=>0011101=>[3,1,1,2,1]
[6,3,1,5,4,2,7,8]=>1101100=>[1,1,2,1,3]
[7,8,1,5,4,2,6,3]=>0101101=>[2,2,1,2,1]
[7,8,3,5,4,1,6,2]=>0101101=>[2,2,1,2,1]
[7,8,2,5,4,1,3,6]=>0101100=>[2,2,1,3]
[7,8,2,5,4,6,1,3]=>0101010=>[2,2,2,2]
[6,2,1,5,4,7,3,8]=>1101010=>[1,1,2,2,2]
[5,3,6,2,4,7,1,8]=>1010010=>[1,2,3,2]
[6,4,2,1,7,3,8,5]=>1110101=>[1,1,1,2,2,1]
[2,7,6,5,3,1,4,8]=>0111100=>[2,1,1,1,3]
[3,7,6,4,8,5,1,2]=>0110110=>[2,1,2,1,2]
[5,7,6,3,8,4,1,2]=>0110110=>[2,1,2,1,2]
[5,1,6,2,4,8,3,7]=>1010010=>[1,2,3,2]
[4,7,6,5,2,1,3,8]=>0111100=>[2,1,1,1,3]
[4,7,6,5,2,8,1,3]=>0111010=>[2,1,1,2,2]
[4,7,6,5,1,8,3,2]=>0111011=>[2,1,1,2,1,1]
[1,7,6,5,2,8,3,4]=>0111010=>[2,1,1,2,2]
[1,7,6,5,3,2,8,4]=>0111101=>[2,1,1,1,2,1]
[4,7,6,5,1,2,8,3]=>0111001=>[2,1,1,3,1]
[4,7,6,5,3,1,8,2]=>0111101=>[2,1,1,1,2,1]
[5,2,6,3,4,1,7,8]=>1010100=>[1,2,2,3]
[5,1,6,2,4,7,8,3]=>1010001=>[1,2,4,1]
[1,7,2,4,8,3,6,5]=>0100101=>[2,3,2,1]
[4,7,2,1,5,3,6,8]=>0110100=>[2,1,2,3]
[4,7,1,6,2,3,8,5]=>0101001=>[2,2,3,1]
[1,7,2,6,8,3,5,4]=>0100101=>[2,3,2,1]
[1,2,6,7,4,8,5,3]=>0001011=>[4,2,1,1]
[3,1,6,7,4,2,8,5]=>1001101=>[1,3,1,2,1]
[3,2,8,5,4,6,1,7]=>1011010=>[1,2,1,2,2]
[4,7,6,3,5,8,1,2]=>0110010=>[2,1,3,2]
[3,7,6,5,2,4,1,8]=>0111010=>[2,1,1,2,2]
[3,7,6,5,2,1,8,4]=>0111101=>[2,1,1,1,2,1]
[1,7,6,5,8,2,4,3]=>0110101=>[2,1,2,2,1]
[3,7,6,5,8,1,4,2]=>0110101=>[2,1,2,2,1]
[3,7,6,5,1,2,4,8]=>0111000=>[2,1,1,4]
[3,1,6,8,4,2,5,7]=>1001100=>[1,3,1,3]
[4,7,6,8,3,5,1,2]=>0101010=>[2,2,2,2]
[2,7,6,5,8,1,3,4]=>0110100=>[2,1,2,3]
[2,7,6,5,8,4,1,3]=>0110110=>[2,1,2,1,2]
[3,7,5,8,2,4,1,6]=>0101010=>[2,2,2,2]
[5,1,7,8,4,3,2,6]=>1001110=>[1,3,1,1,2]
[5,1,2,6,4,3,8,7]=>1001101=>[1,3,1,2,1]
[5,1,2,4,6,3,8,7]=>1000101=>[1,4,2,1]
[4,1,5,7,8,3,2,6]=>1000110=>[1,4,1,2]
[4,7,1,8,3,6,2,5]=>0101010=>[2,2,2,2]
[4,1,7,8,5,2,3,6]=>1001100=>[1,3,1,3]
[5,1,7,4,8,2,3,6]=>1010100=>[1,2,2,3]
[5,1,8,4,7,2,3,6]=>1010100=>[1,2,2,3]
[4,1,8,7,5,2,3,6]=>1011100=>[1,2,1,1,3]
[4,7,1,6,3,2,8,5]=>0101101=>[2,2,1,2,1]
[7,1,2,3,8,6,5,4]=>1000111=>[1,4,1,1,1]
[6,8,1,4,3,7,2,5]=>0101010=>[2,2,2,2]
[8,7,3,2,4,1,6,5]=>1110101=>[1,1,1,2,2,1]
[6,7,1,4,3,8,2,5]=>0101010=>[2,2,2,2]
[8,1,2,3,5,7,6,4]=>1000011=>[1,5,1,1]
[7,1,2,3,6,8,5,4]=>1000011=>[1,5,1,1]
[7,1,8,5,4,3,2,6]=>1011110=>[1,2,1,1,1,2]
[7,8,2,6,3,4,1,5]=>0101010=>[2,2,2,2]
[6,7,2,8,3,4,1,5]=>0101010=>[2,2,2,2]
[3,8,7,1,4,2,6,5]=>0110101=>[2,1,2,2,1]
[3,7,8,1,4,2,6,5]=>0010101=>[3,2,2,1]
[3,6,8,1,4,2,7,5]=>0010101=>[3,2,2,1]
[3,5,7,8,2,4,1,6]=>0001010=>[4,2,2]
[3,6,7,1,4,2,8,5]=>0010101=>[3,2,2,1]
[8,6,2,7,3,1,4,5]=>1101100=>[1,1,2,1,3]
[8,1,7,5,4,3,2,6]=>1011110=>[1,2,1,1,1,2]
[8,1,7,4,5,3,2,6]=>1010110=>[1,2,2,1,2]
[5,8,3,7,1,4,2,6]=>0101010=>[2,2,2,2]
[2,1,7,3,4,6,8,5]=>1010001=>[1,2,4,1]
[6,7,3,2,4,1,8,5]=>0110101=>[2,1,2,2,1]
[8,7,2,4,3,6,1,5]=>1101010=>[1,1,2,2,2]
[7,1,2,3,5,6,8,4]=>1000001=>[1,6,1]
[6,1,2,3,8,7,4,5]=>1000110=>[1,4,1,2]
[5,1,2,3,7,8,6,4]=>1000011=>[1,5,1,1]
[8,6,2,4,3,1,7,5]=>1101101=>[1,1,2,1,2,1]
[7,6,3,2,4,8,1,5]=>1110010=>[1,1,1,3,2]
[8,6,3,2,4,7,1,5]=>1110010=>[1,1,1,3,2]
[7,6,2,4,3,1,8,5]=>1101101=>[1,1,2,1,2,1]
[7,8,1,2,6,3,5,4]=>0100101=>[2,3,2,1]
[1,4,8,2,7,3,5,6]=>0010100=>[3,2,3]
[1,2,8,5,4,7,3,6]=>0011010=>[3,1,2,2]
[2,3,6,8,4,7,1,5]=>0001010=>[4,2,2]
[1,3,6,8,4,7,5,2]=>0001011=>[4,2,1,1]
[2,4,8,1,7,3,6,5]=>0010101=>[3,2,2,1]
[3,4,8,5,7,6,1,2]=>0010110=>[3,2,1,2]
[1,2,6,8,4,5,7,3]=>0001001=>[4,3,1]
[7,5,1,2,4,3,6,8]=>1100100=>[1,1,3,3]
[7,4,6,1,5,2,3,8]=>1010100=>[1,2,2,3]
[6,8,1,4,7,2,3,5]=>0100100=>[2,3,3]
[1,6,4,2,8,3,5,7]=>0110100=>[2,1,2,3]
[1,6,3,8,5,4,2,7]=>0101110=>[2,2,1,1,2]
[7,1,3,6,5,4,2,8]=>1001110=>[1,3,1,1,2]
[7,2,1,4,6,3,5,8]=>1100100=>[1,1,3,3]
[7,2,3,6,5,1,4,8]=>1001100=>[1,3,1,3]
[7,1,2,3,6,5,4,8]=>1000110=>[1,4,1,2]
[6,8,1,2,7,3,5,4]=>0100101=>[2,3,2,1]
[1,6,2,3,8,5,4,7]=>0100110=>[2,3,1,2]
[1,5,8,2,7,6,3,4]=>0010110=>[3,2,1,2]
[5,8,2,7,6,3,4,1]=>0101101=>[2,2,1,2,1]
[6,2,8,1,7,3,5,4]=>1010101=>[1,2,2,2,1]
[3,6,4,1,2,8,5,7]=>0110010=>[2,1,3,2]
[2,5,1,8,7,6,3,4]=>0101110=>[2,2,1,1,2]
[1,2,5,3,8,7,4,6]=>0010110=>[3,2,1,2]
[2,5,3,8,7,1,6,4]=>0101101=>[2,2,1,2,1]
[2,5,8,4,1,7,6,3]=>0011011=>[3,1,2,1,1]
[3,5,8,7,1,4,2,6]=>0011010=>[3,1,2,2]
[5,3,8,4,1,7,6,2]=>1011011=>[1,2,1,2,1,1]
[4,2,8,7,6,3,5,1]=>1011101=>[1,2,1,1,2,1]
[6,3,1,8,7,2,5,4]=>1101101=>[1,1,2,1,2,1]
[5,1,3,8,7,6,2,4]=>1001110=>[1,3,1,1,2]
[1,5,3,8,7,6,2,4]=>0101110=>[2,2,1,1,2]
[5,1,8,4,7,2,6,3]=>1010101=>[1,2,2,2,1]
[5,8,7,4,6,1,2,3]=>0110100=>[2,1,2,3]
[6,8,5,1,2,4,7,3]=>0110001=>[2,1,4,1]
[4,5,8,1,7,2,6,3]=>0010101=>[3,2,2,1]
[1,3,2,5,8,7,4,6]=>0100110=>[2,3,1,2]
[3,5,1,8,7,4,6,2]=>0101101=>[2,2,1,2,1]
[4,3,6,1,2,8,5,7]=>1010010=>[1,2,3,2]
[4,5,8,3,1,7,2,6]=>0011010=>[3,1,2,2]
[4,5,2,8,7,1,3,6]=>0101100=>[2,2,1,3]
[3,2,5,8,7,1,6,4]=>1001101=>[1,3,1,2,1]
[3,4,8,7,6,2,1,5]=>0011110=>[3,1,1,1,2]
[3,4,8,7,6,5,1,2]=>0011110=>[3,1,1,1,2]
[1,3,4,8,7,6,2,5]=>0001110=>[4,1,1,2]
[3,4,8,7,6,2,5,1]=>0011101=>[3,1,1,2,1]
[3,2,5,8,7,4,6,1]=>1001101=>[1,3,1,2,1]
[2,1,3,5,8,7,4,6]=>1000110=>[1,4,1,2]
[1,2,7,5,8,6,4,3]=>0010111=>[3,2,1,1,1]
[6,8,1,3,7,5,2,4]=>0100110=>[2,3,1,2]
[1,3,7,8,2,6,5,4]=>0001011=>[4,2,1,1]
[2,7,8,1,3,6,5,4]=>0010011=>[3,3,1,1]
[8,1,2,6,7,3,5,4]=>1000101=>[1,4,2,1]
[8,1,2,6,7,5,3,4]=>1000110=>[1,4,1,2]
[8,2,5,7,1,3,6,4]=>1001001=>[1,3,3,1]
[2,8,1,6,7,3,5,4]=>0100101=>[2,3,2,1]
[2,6,8,3,7,1,5,4]=>0010101=>[3,2,2,1]
[2,8,6,4,7,1,5,3]=>0110101=>[2,1,2,2,1]
[6,8,3,4,1,7,5,2]=>0101011=>[2,2,2,1,1]
[6,8,3,7,4,1,5,2]=>0101101=>[2,2,1,2,1]
[8,2,5,7,1,6,3,4]=>1001010=>[1,3,2,2]
[8,4,7,2,3,6,1,5]=>1010010=>[1,2,3,2]
[8,5,7,4,2,6,1,3]=>1011010=>[1,2,1,2,2]
[8,3,5,7,4,1,6,2]=>1001101=>[1,3,1,2,1]
[8,5,2,4,7,1,6,3]=>1100101=>[1,1,3,2,1]
[8,2,4,7,3,6,1,5]=>1001010=>[1,3,2,2]
[8,2,7,1,4,6,3,5]=>1010010=>[1,2,3,2]
[8,7,1,2,4,6,3,5]=>1100010=>[1,1,4,2]
[8,7,1,4,6,2,3,5]=>1100100=>[1,1,3,3]
[8,4,7,1,3,6,2,5]=>1010010=>[1,2,3,2]
[8,3,5,7,1,2,6,4]=>1001001=>[1,3,3,1]
[5,8,7,1,3,6,2,4]=>0110010=>[2,1,3,2]
[8,5,4,7,1,6,2,3]=>1101010=>[1,1,2,2,2]
[8,5,4,7,1,2,6,3]=>1101001=>[1,1,2,3,1]
[8,5,1,4,7,2,6,3]=>1100101=>[1,1,3,2,1]
[8,5,6,3,1,7,4,2]=>1011011=>[1,2,1,2,1,1]
[1,8,4,5,7,2,6,3]=>0100101=>[2,3,2,1]
[5,8,7,3,6,1,2,4]=>0110100=>[2,1,2,3]
[8,3,5,7,1,6,2,4]=>1001010=>[1,3,2,2]
[1,6,8,3,7,5,2,4]=>0010110=>[3,2,1,2]
[6,3,8,2,7,5,1,4]=>1010110=>[1,2,2,1,2]
[8,6,4,7,3,1,5,2]=>1101101=>[1,1,2,1,2,1]
[8,4,5,7,3,1,6,2]=>1001101=>[1,3,1,2,1]
[8,3,4,7,2,6,1,5]=>1001010=>[1,3,2,2]
[8,7,1,3,4,6,2,5]=>1100010=>[1,1,4,2]
[8,3,7,2,4,6,1,5]=>1010010=>[1,2,3,2]
[2,8,4,5,7,1,6,3]=>0100101=>[2,3,2,1]
[8,7,3,4,5,1,6,2]=>1100101=>[1,1,3,2,1]
[8,7,4,5,2,6,1,3]=>1101010=>[1,1,2,2,2]
[8,7,2,3,4,6,1,5]=>1100010=>[1,1,4,2]
[8,6,5,1,3,2,7,4]=>1110101=>[1,1,1,2,2,1]
[8,6,3,1,7,2,4,5]=>1110100=>[1,1,1,2,3]
[8,7,3,1,5,2,4,6]=>1110100=>[1,1,1,2,3]
[8,6,1,2,4,7,3,5]=>1100010=>[1,1,4,2]
[8,6,1,5,3,4,7,2]=>1101001=>[1,1,2,3,1]
[8,6,1,5,2,4,7,3]=>1101001=>[1,1,2,3,1]
[8,6,1,2,5,7,3,4]=>1100010=>[1,1,4,2]
[5,1,4,2,3,8,6,7]=>1010010=>[1,2,3,2]
[5,1,4,2,7,3,6,8]=>1010100=>[1,2,2,3]
[5,7,8,1,2,4,6,3]=>0010001=>[3,4,1]
[5,7,8,1,3,4,6,2]=>0010001=>[3,4,1]
[5,8,1,7,3,4,6,2]=>0101001=>[2,2,3,1]
[8,1,5,7,2,4,6,3]=>1001001=>[1,3,3,1]
[1,4,2,3,8,7,5,6]=>0100110=>[2,3,1,2]
[1,4,2,7,6,3,5,8]=>0101100=>[2,2,1,3]
[6,1,2,8,7,5,3,4]=>1001110=>[1,3,1,1,2]
[6,1,2,4,8,7,5,3]=>1000111=>[1,4,1,1,1]
[3,1,8,4,6,7,5,2]=>1010011=>[1,2,3,1,1]
[3,1,7,6,4,8,5,2]=>1011011=>[1,2,1,2,1,1]
[7,1,2,4,6,8,5,3]=>1000011=>[1,5,1,1]
[7,1,2,6,8,5,3,4]=>1000110=>[1,4,1,2]
[7,1,5,3,2,8,6,4]=>1011011=>[1,2,1,2,1,1]
[8,1,7,5,3,2,6,4]=>1011101=>[1,2,1,1,2,1]
[8,3,7,1,2,6,4,5]=>1010010=>[1,2,3,2]
[3,1,2,8,4,7,5,6]=>1001010=>[1,3,2,2]
[1,4,2,3,8,6,5,7]=>0100110=>[2,3,1,2]
[1,4,2,3,8,5,7,6]=>0100101=>[2,3,2,1]
[5,8,1,7,2,4,6,3]=>0101001=>[2,2,3,1]
[5,8,1,3,4,7,6,2]=>0100011=>[2,4,1,1]
[3,1,8,6,4,7,5,2]=>1011011=>[1,2,1,2,1,1]
[8,1,2,6,7,4,5,3]=>1000101=>[1,4,2,1]
[1,2,3,5,8,4,7,6]=>0000101=>[5,2,1]
[1,2,3,5,8,6,4,7]=>0000110=>[5,1,2]
[7,1,2,8,3,6,5,4]=>1001011=>[1,3,2,1,1]
[7,1,2,8,6,4,5,3]=>1001101=>[1,3,1,2,1]
[3,1,7,8,4,6,5,2]=>1001011=>[1,3,2,1,1]
[8,1,2,7,4,6,5,3]=>1001011=>[1,3,2,1,1]
[8,1,2,7,3,6,5,4]=>1001011=>[1,3,2,1,1]
[1,2,3,6,8,5,4,7]=>0000110=>[5,1,2]
[3,6,2,5,4,1,8,7]=>0101101=>[2,2,1,2,1]
[3,5,2,8,4,7,6,1]=>0101011=>[2,2,2,1,1]
[5,4,7,3,2,8,6,1]=>1011011=>[1,2,1,2,1,1]
[5,4,8,3,2,7,6,1]=>1011011=>[1,2,1,2,1,1]
[5,3,2,6,4,1,8,7]=>1101101=>[1,1,2,1,2,1]
[4,5,8,3,2,7,6,1]=>0011011=>[3,1,2,1,1]
[4,7,6,3,8,5,2,1]=>0110111=>[2,1,2,1,1,1]
[4,8,6,3,7,5,2,1]=>0110111=>[2,1,2,1,1,1]
[5,3,2,8,4,7,6,1]=>1101011=>[1,1,2,2,1,1]
[2,1,5,8,4,7,6,3]=>1001011=>[1,3,2,1,1]
[5,3,2,7,4,8,6,1]=>1101011=>[1,1,2,2,1,1]
[5,7,4,3,2,8,6,1]=>0111011=>[2,1,1,2,1,1]
[4,7,5,3,2,8,6,1]=>0111011=>[2,1,1,2,1,1]
[4,7,8,3,6,5,2,1]=>0010111=>[3,2,1,1,1]
[4,6,8,3,7,5,2,1]=>0010111=>[3,2,1,1,1]
[7,6,4,3,8,5,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,3,2,6,7,5,4,1]=>1100111=>[1,1,3,1,1,1]
[8,6,4,3,7,5,2,1]=>1110111=>[1,1,1,2,1,1,1]
[8,4,5,3,2,7,6,1]=>1011011=>[1,2,1,2,1,1]
[8,4,6,3,7,5,2,1]=>1010111=>[1,2,2,1,1,1]
[7,4,6,3,8,5,2,1]=>1010111=>[1,2,2,1,1,1]
[3,7,2,6,8,5,4,1]=>0100111=>[2,3,1,1,1]
[3,8,2,6,7,5,4,1]=>0100111=>[2,3,1,1,1]
[3,7,2,8,6,5,4,1]=>0101111=>[2,2,1,1,1,1]
[3,6,2,8,7,5,4,1]=>0101111=>[2,2,1,1,1,1]
[7,4,5,3,2,8,6,1]=>1011011=>[1,2,1,2,1,1]
[2,1,7,5,4,8,6,3]=>1011011=>[1,2,1,2,1,1]
[7,3,2,8,6,5,4,1]=>1101111=>[1,1,2,1,1,1,1]
[7,8,4,3,6,5,2,1]=>0110111=>[2,1,2,1,1,1]
[6,3,2,8,7,5,4,1]=>1101111=>[1,1,2,1,1,1,1]
[6,3,2,7,8,5,4,1]=>1100111=>[1,1,3,1,1,1]
[1,6,4,8,2,5,3,7]=>0101010=>[2,2,2,2]
[1,6,5,8,2,4,3,7]=>0101010=>[2,2,2,2]
[1,6,8,2,4,3,7,5]=>0010101=>[3,2,2,1]
[1,6,2,4,3,7,8,5]=>0101001=>[2,2,3,1]
[1,5,6,2,4,7,3,8]=>0010010=>[3,3,2]
[1,5,6,2,4,7,8,3]=>0010001=>[3,4,1]
[1,6,7,2,4,3,8,5]=>0010101=>[3,2,2,1]
[1,5,8,2,4,6,7,3]=>0010001=>[3,4,1]
[1,5,7,8,3,2,4,6]=>0001100=>[4,1,3]
[1,5,8,3,2,4,6,7]=>0011000=>[3,1,4]
[1,5,6,2,4,8,3,7]=>0010010=>[3,3,2]
[1,7,3,4,2,8,6,5]=>0101011=>[2,2,2,1,1]
[1,5,6,2,4,8,7,3]=>0010011=>[3,3,1,1]
[1,5,8,7,3,2,4,6]=>0011100=>[3,1,1,3]
[1,7,4,2,8,6,5,3]=>0110111=>[2,1,2,1,1,1]
[1,5,8,3,2,4,7,6]=>0011001=>[3,1,3,1]
[1,6,5,2,3,7,4,8]=>0110010=>[2,1,3,2]
[1,6,5,2,3,7,8,4]=>0110001=>[2,1,4,1]
[1,6,8,4,2,3,7,5]=>0011001=>[3,1,3,1]
[1,6,8,5,2,3,7,4]=>0011001=>[3,1,3,1]
[1,6,4,2,3,7,5,8]=>0110010=>[2,1,3,2]
[1,5,8,6,2,4,7,3]=>0011001=>[3,1,3,1]
[1,7,5,2,8,6,4,3]=>0110111=>[2,1,2,1,1,1]
[3,7,5,6,1,4,8,2]=>0101001=>[2,2,3,1]
[8,6,1,4,2,7,5,3]=>1101011=>[1,1,2,2,1,1]
[1,6,7,4,3,5,8,2]=>0011001=>[3,1,3,1]
[6,7,1,4,3,5,8,2]=>0101001=>[2,2,3,1]
[4,7,1,6,3,5,8,2]=>0101001=>[2,2,3,1]
[3,1,4,7,6,5,8,2]=>1001101=>[1,3,1,2,1]
[6,1,7,4,3,5,8,2]=>1011001=>[1,2,1,3,1]
[7,1,6,4,3,5,8,2]=>1011001=>[1,2,1,3,1]
[1,7,6,4,3,5,8,2]=>0111001=>[2,1,1,3,1]
[8,1,6,4,2,7,5,3]=>1011011=>[1,2,1,2,1,1]
[4,7,1,3,8,2,5,6]=>0100100=>[2,3,3]
[7,4,1,3,8,2,5,6]=>1100100=>[1,1,3,3]
[1,3,6,4,2,8,5,7]=>0011010=>[3,1,2,2]
[4,7,3,1,2,8,5,6]=>0110010=>[2,1,3,2]
[4,7,8,1,2,6,5,3]=>0010011=>[3,3,1,1]
[1,8,6,4,2,7,5,3]=>0111011=>[2,1,1,2,1,1]
[4,8,1,3,7,2,5,6]=>0100100=>[2,3,3]
[8,7,1,3,6,2,5,4]=>1100101=>[1,1,3,2,1]
[1,8,4,3,7,2,5,6]=>0110100=>[2,1,2,3]
[3,7,4,6,8,2,1,5]=>0100110=>[2,3,1,2]
[2,4,3,7,8,6,1,5]=>0100110=>[2,3,1,2]
[1,4,7,3,8,2,5,6]=>0010100=>[3,2,3]
[5,7,6,8,3,2,1,4]=>0101110=>[2,2,1,1,2]
[6,1,4,3,8,2,5,7]=>1010100=>[1,2,2,3]
[4,1,7,3,8,2,5,6]=>1010100=>[1,2,2,3]
[8,1,4,3,7,2,5,6]=>1010100=>[1,2,2,3]
[4,2,3,7,8,6,1,5]=>1000110=>[1,4,1,2]
[2,7,5,6,3,8,1,4]=>0101010=>[2,2,2,2]
[5,7,2,6,8,4,1,3]=>0100110=>[2,3,1,2]
[7,2,5,6,8,4,1,3]=>1000110=>[1,4,1,2]
[5,2,3,8,7,6,1,4]=>1001110=>[1,3,1,1,2]
[8,2,3,7,5,6,1,4]=>1001010=>[1,3,2,2]
[6,1,8,3,7,2,5,4]=>1010101=>[1,2,2,2,1]
[1,7,8,4,2,6,5,3]=>0011011=>[3,1,2,1,1]
[4,7,1,8,2,5,6,3]=>0101001=>[2,2,3,1]
[1,4,8,3,6,2,5,7]=>0010100=>[3,2,3]
[3,7,5,8,6,2,1,4]=>0101110=>[2,2,1,1,2]
[3,7,8,6,5,2,1,4]=>0011110=>[3,1,1,1,2]
[6,8,7,5,3,2,1,4]=>0111110=>[2,1,1,1,1,2]
[5,7,6,8,3,4,1,2]=>0101010=>[2,2,2,2]
[3,7,6,8,4,5,1,2]=>0101010=>[2,2,2,2]
[1,5,4,7,6,8,2,3]=>0101010=>[2,2,2,2]
[1,7,4,6,5,8,2,3]=>0101010=>[2,2,2,2]
[3,7,4,6,5,8,1,2]=>0101010=>[2,2,2,2]
[3,5,4,8,6,7,1,2]=>0101010=>[2,2,2,2]
[3,8,4,6,5,7,1,2]=>0101010=>[2,2,2,2]
[3,6,4,7,5,8,1,2]=>0101010=>[2,2,2,2]
[1,6,2,7,5,8,3,4]=>0101010=>[2,2,2,2]
[1,6,4,8,5,7,2,3]=>0101010=>[2,2,2,2]
[1,8,4,6,5,7,2,3]=>0101010=>[2,2,2,2]
[1,5,4,8,6,7,2,3]=>0101010=>[2,2,2,2]
[7,8,1,5,4,6,2,3]=>0101010=>[2,2,2,2]
[1,8,2,6,5,7,3,4]=>0101010=>[2,2,2,2]
[1,7,2,8,5,6,3,4]=>0101010=>[2,2,2,2]
[1,7,2,6,5,8,3,4]=>0101010=>[2,2,2,2]
[1,5,2,7,6,8,3,4]=>0101010=>[2,2,2,2]
[1,7,6,8,2,5,3,4]=>0101010=>[2,2,2,2]
[1,7,6,8,4,5,2,3]=>0101010=>[2,2,2,2]
[7,8,5,6,1,3,2,4]=>0101010=>[2,2,2,2]
[5,8,6,7,1,3,2,4]=>0101010=>[2,2,2,2]
[1,3,2,7,6,8,4,5]=>0101010=>[2,2,2,2]
[1,7,6,8,2,4,3,5]=>0101010=>[2,2,2,2]
[1,3,2,8,6,7,4,5]=>0101010=>[2,2,2,2]
[7,8,1,3,2,6,4,5]=>0101010=>[2,2,2,2]
[7,8,1,6,2,4,3,5]=>0101010=>[2,2,2,2]
[1,8,6,7,2,4,3,5]=>0101010=>[2,2,2,2]
[7,8,1,4,2,6,3,5]=>0101010=>[2,2,2,2]
[6,4,8,5,2,7,1,3]=>1011010=>[1,2,1,2,2]
[8,4,7,5,2,6,1,3]=>1011010=>[1,2,1,2,2]
[5,4,6,8,2,1,7,3]=>1001101=>[1,3,1,2,1]
[4,8,7,5,6,1,3,2]=>0110101=>[2,1,2,2,1]
[2,7,5,1,8,4,3,6]=>0110110=>[2,1,2,1,2]
[2,8,6,7,4,3,5,1]=>0101101=>[2,2,1,2,1]
[3,8,7,1,4,6,5,2]=>0110011=>[2,1,3,1,1]
[5,7,1,2,4,3,8,6]=>0100101=>[2,3,2,1]
[4,3,7,6,8,2,5,1]=>1010101=>[1,2,2,2,1]
[5,3,6,8,1,7,2,4]=>1001010=>[1,3,2,2]
[3,2,6,8,5,7,1,4]=>1001010=>[1,3,2,2]
[7,4,8,6,5,2,1,3]=>1011110=>[1,2,1,1,1,2]
[7,1,8,2,5,4,3,6]=>1010110=>[1,2,2,1,2]
[2,5,3,7,4,1,8,6]=>0101101=>[2,2,1,2,1]
[3,6,4,7,5,1,8,2]=>0101101=>[2,2,1,2,1]
[8,4,7,1,2,5,6,3]=>1010001=>[1,2,4,1]
[4,2,8,7,3,5,6,1]=>1011001=>[1,2,1,3,1]
[6,4,1,5,8,2,7,3]=>1100101=>[1,1,3,2,1]
[8,3,5,6,7,4,1,2]=>1000110=>[1,4,1,2]
[7,4,3,2,8,5,6,1]=>1110101=>[1,1,1,2,2,1]
[4,2,7,1,8,5,6,3]=>1010101=>[1,2,2,2,1]
[4,7,8,3,1,5,6,2]=>0011001=>[3,1,3,1]
[3,7,1,4,8,5,6,2]=>0100101=>[2,3,2,1]
[2,6,3,5,8,7,1,4]=>0100110=>[2,3,1,2]
[7,6,2,1,5,8,4,3]=>1110011=>[1,1,1,3,1,1]
[4,5,2,7,6,1,8,3]=>0101101=>[2,2,1,2,1]
[3,6,8,7,5,2,1,4]=>0011110=>[3,1,1,1,2]
[7,4,8,6,5,2,3,1]=>1011101=>[1,2,1,1,2,1]
[8,1,6,4,7,3,2,5]=>1010110=>[1,2,2,1,2]
[7,6,4,1,2,3,8,5]=>1110001=>[1,1,1,4,1]
[2,6,4,8,5,3,7,1]=>0101101=>[2,2,1,2,1]
[4,8,7,5,6,1,2,3]=>0110100=>[2,1,2,3]
[6,1,4,8,7,3,5,2]=>1001101=>[1,3,1,2,1]
[4,7,8,1,3,5,6,2]=>0010001=>[3,4,1]
[8,7,3,4,1,5,6,2]=>1101001=>[1,1,2,3,1]
[4,8,2,7,3,5,6,1]=>0101001=>[2,2,3,1]
[3,1,8,7,2,5,6,4]=>1011001=>[1,2,1,3,1]
[8,2,3,7,1,5,6,4]=>1001001=>[1,3,3,1]
[6,4,8,7,1,3,2,5]=>1011010=>[1,2,1,2,2]
[7,8,2,4,3,5,6,1]=>0101001=>[2,2,3,1]
[2,8,3,7,1,5,6,4]=>0101001=>[2,2,3,1]
[5,3,8,6,2,1,4,7]=>1011100=>[1,2,1,1,3]
[4,6,5,2,8,3,1,7]=>0110110=>[2,1,2,1,2]
[4,3,7,5,1,8,2,6]=>1011010=>[1,2,1,2,2]
[6,8,5,2,7,4,3,1]=>0110111=>[2,1,2,1,1,1]
[3,6,8,1,4,5,2,7]=>0010010=>[3,3,2]
[6,8,1,2,4,5,3,7]=>0100010=>[2,4,2]
[4,1,6,5,8,2,3,7]=>1010100=>[1,2,2,3]
[4,3,8,6,2,5,1,7]=>1011010=>[1,2,1,2,2]
[8,3,6,1,4,5,2,7]=>1010010=>[1,2,3,2]
[6,3,8,7,4,2,5,1]=>1011101=>[1,2,1,1,2,1]
[5,8,4,3,7,6,1,2]=>0110110=>[2,1,2,1,2]
[8,7,4,3,1,6,2,5]=>1111010=>[1,1,1,1,2,2]
[1,7,4,3,8,6,2,5]=>0110110=>[2,1,2,1,2]
[7,1,5,3,4,8,2,6]=>1010010=>[1,2,3,2]
[2,8,6,1,7,4,5,3]=>0110101=>[2,1,2,2,1]
[4,7,6,8,2,1,5,3]=>0101101=>[2,2,1,2,1]
[6,1,8,7,4,3,5,2]=>1011101=>[1,2,1,1,2,1]
[8,5,4,3,1,6,7,2]=>1111001=>[1,1,1,1,3,1]
[1,5,8,6,3,4,7,2]=>0011001=>[3,1,3,1]
[2,5,8,6,3,4,7,1]=>0011001=>[3,1,3,1]
[4,6,5,2,8,1,7,3]=>0110101=>[2,1,2,2,1]
[1,8,5,2,3,6,7,4]=>0110001=>[2,1,4,1]
[4,8,3,2,5,6,7,1]=>0110001=>[2,1,4,1]
[2,1,8,3,5,6,7,4]=>1010001=>[1,2,4,1]
[4,2,7,1,8,6,3,5]=>1010110=>[1,2,2,1,2]
[3,8,4,1,2,6,7,5]=>0110001=>[2,1,4,1]
[5,8,3,6,7,4,1,2]=>0100110=>[2,3,1,2]
[2,3,1,6,8,4,7,5]=>0100101=>[2,3,2,1]
[2,4,3,7,1,8,5,6]=>0101010=>[2,2,2,2]
[2,4,1,8,6,3,7,5]=>0101101=>[2,2,1,2,1]
[8,4,1,3,6,2,7,5]=>1100101=>[1,1,3,2,1]
[6,8,5,1,7,2,3,4]=>0110100=>[2,1,2,3]
[7,3,6,5,8,2,1,4]=>1010110=>[1,2,2,1,2]
[7,6,3,5,8,2,1,4]=>1100110=>[1,1,3,1,2]
[4,5,8,7,3,6,1,2]=>0011010=>[3,1,2,2]
[8,6,5,4,1,2,7,3]=>1111001=>[1,1,1,1,3,1]
[6,1,5,3,8,7,2,4]=>1010110=>[1,2,2,1,2]
[2,8,6,3,7,1,5,4]=>0110101=>[2,1,2,2,1]
[7,6,1,5,8,2,3,4]=>1100100=>[1,1,3,3]
[3,6,8,5,1,2,7,4]=>0011001=>[3,1,3,1]
[6,5,2,4,8,1,7,3]=>1100101=>[1,1,3,2,1]
[5,1,4,8,2,6,7,3]=>1001001=>[1,3,3,1]
[3,4,8,5,2,6,7,1]=>0011001=>[3,1,3,1]
[4,2,1,8,5,6,7,3]=>1101001=>[1,1,2,3,1]
[1,5,4,8,2,6,7,3]=>0101001=>[2,2,3,1]
[7,2,1,5,8,6,3,4]=>1100110=>[1,1,3,1,2]
[2,8,4,5,1,6,7,3]=>0101001=>[2,2,3,1]
[5,4,8,3,7,6,1,2]=>1010110=>[1,2,2,1,2]
[3,1,5,8,6,2,7,4]=>1001101=>[1,3,1,2,1]
[6,3,4,8,5,1,7,2]=>1001101=>[1,3,1,2,1]
[5,3,4,8,1,6,7,2]=>1001001=>[1,3,3,1]
[6,5,4,8,7,1,3,2]=>1101101=>[1,1,2,1,2,1]
[6,5,4,8,1,2,7,3]=>1101001=>[1,1,2,3,1]
[7,5,1,6,8,2,4,3]=>1100101=>[1,1,3,2,1]
[6,5,4,1,8,2,7,3]=>1110101=>[1,1,1,2,2,1]
[6,5,4,7,1,2,8,3]=>1101001=>[1,1,2,3,1]
[6,5,4,7,8,1,3,2]=>1100101=>[1,1,3,2,1]
[6,5,3,7,1,4,2,8]=>1101010=>[1,1,2,2,2]
[7,5,1,4,8,3,2,6]=>1100110=>[1,1,3,1,2]
[8,1,6,4,7,3,5,2]=>1010101=>[1,2,2,2,1]
[7,5,1,4,8,3,6,2]=>1100101=>[1,1,3,2,1]
[7,4,1,5,3,8,6,2]=>1101011=>[1,1,2,2,1,1]
[8,1,5,4,3,7,6,2]=>1011011=>[1,2,1,2,1,1]
[8,1,5,4,3,7,2,6]=>1011010=>[1,2,1,2,2]
[6,5,3,8,1,4,2,7]=>1101010=>[1,1,2,2,2]
[8,1,7,2,5,4,6,3]=>1010101=>[1,2,2,2,1]
[7,6,1,2,5,4,8,3]=>1100101=>[1,1,3,2,1]
[6,5,3,8,1,4,7,2]=>1101001=>[1,1,2,3,1]
[6,5,3,1,2,7,8,4]=>1110001=>[1,1,1,4,1]
[8,1,6,4,2,5,7,3]=>1011001=>[1,2,1,3,1]
[8,1,5,4,3,2,7,6]=>1011101=>[1,2,1,1,2,1]
[7,4,1,5,3,2,8,6]=>1101101=>[1,1,2,1,2,1]
[6,4,3,1,5,2,8,7]=>1110101=>[1,1,1,2,2,1]
[6,4,3,1,5,7,2,8]=>1110010=>[1,1,1,3,2]
[7,4,1,5,3,6,2,8]=>1101010=>[1,1,2,2,2]
[6,4,3,1,5,7,8,2]=>1110001=>[1,1,1,4,1]
[8,6,7,1,4,2,5,3]=>1010101=>[1,2,2,2,1]
[8,6,3,7,5,1,2,4]=>1101100=>[1,1,2,1,3]
[7,6,1,8,3,5,2,4]=>1101010=>[1,1,2,2,2]
[7,6,2,8,3,5,1,4]=>1101010=>[1,1,2,2,2]
[8,7,1,5,2,6,3,4]=>1101010=>[1,1,2,2,2]
[8,7,1,5,2,3,6,4]=>1101001=>[1,1,2,3,1]
[8,5,2,3,1,7,6,4]=>1101011=>[1,1,2,2,1,1]
[8,6,2,3,7,1,5,4]=>1100101=>[1,1,3,2,1]
[8,6,2,7,3,1,5,4]=>1101101=>[1,1,2,1,2,1]
[8,7,2,5,1,6,3,4]=>1101010=>[1,1,2,2,2]
[8,5,7,2,1,4,3,6]=>1011010=>[1,2,1,2,2]
[5,8,7,3,1,4,2,6]=>0111010=>[2,1,1,2,2]
[8,5,7,2,1,4,6,3]=>1011001=>[1,2,1,3,1]
[8,6,1,3,7,2,5,4]=>1100101=>[1,1,3,2,1]
[8,4,7,5,1,6,2,3]=>1011010=>[1,2,1,2,2]
[8,4,7,5,1,2,3,6]=>1011000=>[1,2,1,4]
[8,3,2,6,5,1,4,7]=>1101100=>[1,1,2,1,3]
[4,8,7,3,1,5,2,6]=>0111010=>[2,1,1,2,2]
[8,4,7,2,1,5,3,6]=>1011010=>[1,2,1,2,2]
[8,7,3,1,2,4,6,5]=>1110001=>[1,1,1,4,1]
[8,4,7,2,1,5,6,3]=>1011001=>[1,2,1,3,1]
[1,2,7,3,5,4,8,6]=>0010101=>[3,2,2,1]
[1,5,7,2,3,6,4,8]=>0010010=>[3,3,2]
[1,3,8,2,4,5,7,6]=>0010001=>[3,4,1]
[1,2,3,8,4,6,7,5]=>0001001=>[4,3,1]
[1,7,8,2,3,6,4,5]=>0010010=>[3,3,2]
[1,6,7,8,2,3,5,4]=>0001001=>[4,3,1]
[1,7,8,2,5,3,6,4]=>0010101=>[3,2,2,1]
[1,8,2,3,6,4,5,7]=>0100100=>[2,3,3]
[1,2,7,8,3,6,4,5]=>0001010=>[4,2,2]
[1,5,2,7,8,3,6,4]=>0100101=>[2,3,2,1]
[1,3,2,8,4,6,7,5]=>0101001=>[2,2,3,1]
[1,8,2,3,4,6,7,5]=>0100001=>[2,5,1]
[1,7,8,2,4,3,6,5]=>0010101=>[3,2,2,1]
[7,6,3,1,5,2,4,8]=>1110100=>[1,1,1,2,3]
[6,7,3,1,5,2,8,4]=>0110101=>[2,1,2,2,1]
[6,8,3,1,5,2,7,4]=>0110101=>[2,1,2,2,1]
[6,8,4,5,1,2,7,3]=>0101001=>[2,2,3,1]
[6,7,4,5,1,2,8,3]=>0101001=>[2,2,3,1]
[7,2,1,6,5,3,4,8]=>1101100=>[1,1,2,1,3]
[7,3,6,1,5,2,4,8]=>1010100=>[1,2,2,3]
[7,4,6,5,1,2,3,8]=>1011000=>[1,2,1,4]
[6,7,5,4,1,2,8,3]=>0111001=>[2,1,1,3,1]
[5,8,6,4,1,7,2,3]=>0111010=>[2,1,1,2,2]
[5,7,6,4,1,8,2,3]=>0111010=>[2,1,1,2,2]
[5,6,7,4,1,8,2,3]=>0011010=>[3,1,2,2]
[6,5,7,4,1,2,8,3]=>1011001=>[1,2,1,3,1]
[6,2,1,7,5,3,8,4]=>1101101=>[1,1,2,1,2,1]
[6,3,8,1,5,2,7,4]=>1010101=>[1,2,2,2,1]
[6,4,8,5,1,2,7,3]=>1011001=>[1,2,1,3,1]
[6,5,8,4,1,2,7,3]=>1011001=>[1,2,1,3,1]
[5,6,8,4,1,7,2,3]=>0011010=>[3,1,2,2]
[4,6,8,5,7,1,2,3]=>0010100=>[3,2,3]
[4,5,8,6,7,1,2,3]=>0010100=>[3,2,3]
[5,2,1,7,6,8,3,4]=>1101010=>[1,1,2,2,2]
[4,5,7,6,8,1,2,3]=>0010100=>[3,2,3]
[4,6,7,5,8,1,2,3]=>0010100=>[3,2,3]
[4,7,5,6,8,1,2,3]=>0100100=>[2,3,3]
[4,6,5,7,8,1,2,3]=>0100100=>[2,3,3]
[5,7,4,6,1,8,2,3]=>0101010=>[2,2,2,2]
[5,8,3,1,6,7,2,4]=>0110010=>[2,1,3,2]
[5,7,3,1,6,8,2,4]=>0110010=>[2,1,3,2]
[5,6,3,1,7,8,2,4]=>0110010=>[2,1,3,2]
[5,8,3,1,7,6,2,4]=>0110110=>[2,1,2,1,2]
[5,7,4,8,1,6,2,3]=>0101010=>[2,2,2,2]
[5,2,1,6,8,7,3,4]=>1100110=>[1,1,3,1,2]
[5,4,6,8,1,7,2,3]=>1001010=>[1,3,2,2]
[4,5,6,8,7,1,2,3]=>0001100=>[4,1,3]
[4,7,5,8,6,1,2,3]=>0101100=>[2,2,1,3]
[4,8,5,7,6,1,2,3]=>0101100=>[2,2,1,3]
[4,8,6,7,5,1,2,3]=>0101100=>[2,2,1,3]
[4,7,6,8,5,1,2,3]=>0101100=>[2,2,1,3]
[4,6,7,8,5,1,2,3]=>0001100=>[4,1,3]
[4,5,7,8,6,1,2,3]=>0001100=>[4,1,3]
[5,4,7,8,1,6,2,3]=>1001010=>[1,3,2,2]
[5,3,7,1,8,6,2,4]=>1010110=>[1,2,2,1,2]
[5,2,1,7,8,6,3,4]=>1100110=>[1,1,3,1,2]
[5,3,8,1,7,6,2,4]=>1010110=>[1,2,2,1,2]
[5,4,8,7,1,6,2,3]=>1011010=>[1,2,1,2,2]
[4,6,8,7,5,1,2,3]=>0011100=>[3,1,1,3]
[4,7,8,6,5,1,2,3]=>0011100=>[3,1,1,3]
[4,8,7,6,5,1,2,3]=>0111100=>[2,1,1,1,3]
[2,5,4,7,3,6,1,8]=>0101010=>[2,2,2,2]
[4,2,7,3,6,5,1,8]=>1010110=>[1,2,2,1,2]
[4,2,6,3,1,5,8,7]=>1011001=>[1,2,1,3,1]
[2,5,3,1,6,4,8,7]=>0110101=>[2,1,2,2,1]
[2,5,3,7,6,4,1,8]=>0101110=>[2,2,1,1,2]
[2,6,5,3,7,4,1,8]=>0110110=>[2,1,2,1,2]
[4,2,7,6,3,5,1,8]=>1011010=>[1,2,1,2,2]
[2,7,5,3,6,4,1,8]=>0110110=>[2,1,2,1,2]
[2,6,3,7,5,4,1,8]=>0101110=>[2,2,1,1,2]
[1,7,5,2,3,8,4,6]=>0110010=>[2,1,3,2]
[2,1,3,7,5,4,8,6]=>1001101=>[1,3,1,2,1]
[2,3,1,8,6,5,4,7]=>0101110=>[2,2,1,1,2]
[2,5,3,1,8,6,4,7]=>0110110=>[2,1,2,1,2]
[4,2,8,3,1,6,5,7]=>1011010=>[1,2,1,2,2]
[8,3,2,6,4,1,5,7]=>1101100=>[1,1,2,1,3]
[3,6,8,2,1,4,5,7]=>0011000=>[3,1,4]
[1,2,6,3,8,7,4,5]=>0010110=>[3,2,1,2]
[1,2,7,6,3,4,8,5]=>0011001=>[3,1,3,1]
[2,1,3,8,7,5,4,6]=>1001110=>[1,3,1,1,2]
[1,2,3,8,6,4,7,5]=>0001101=>[4,1,2,1]
[1,2,3,7,4,8,6,5]=>0001011=>[4,2,1,1]
[1,2,7,6,3,8,4,5]=>0011010=>[3,1,2,2]
[1,2,3,6,4,8,7,5]=>0001011=>[4,2,1,1]
[1,2,3,7,6,4,8,5]=>0001101=>[4,1,2,1]
[2,1,3,8,5,4,7,6]=>1001101=>[1,3,1,2,1]
[7,1,8,4,2,3,5,6]=>1011000=>[1,2,1,4]
[4,2,6,3,1,8,5,7]=>1011010=>[1,2,1,2,2]
[5,4,2,8,3,1,6,7]=>1101100=>[1,1,2,1,3]
[2,5,4,8,3,1,6,7]=>0101100=>[2,2,1,3]
[1,8,7,4,2,3,5,6]=>0111000=>[2,1,1,4]
[1,5,2,8,7,3,4,6]=>0101100=>[2,2,1,3]
[1,2,7,3,6,4,8,5]=>0010101=>[3,2,2,1]
[1,2,8,6,3,7,4,5]=>0011010=>[3,1,2,2]
[1,2,6,3,8,4,7,5]=>0010101=>[3,2,2,1]
[4,2,1,8,3,7,5,6]=>1101010=>[1,1,2,2,2]
[8,3,2,1,7,4,5,6]=>1110100=>[1,1,1,2,3]
[1,2,3,8,7,4,6,5]=>0001101=>[4,1,2,1]
[1,2,3,8,7,6,4,5]=>0001110=>[4,1,1,2]
[2,6,5,7,1,4,3,8]=>0101010=>[2,2,2,2]
[2,6,5,7,1,3,8,4]=>0101001=>[2,2,3,1]
[3,8,5,7,1,2,6,4]=>0101001=>[2,2,3,1]
[3,8,5,7,2,6,4,1]=>0101011=>[2,2,2,1,1]
[3,4,8,6,2,5,7,1]=>0011001=>[3,1,3,1]
[3,4,8,6,1,2,5,7]=>0011000=>[3,1,4]
[2,5,7,1,4,8,6,3]=>0010011=>[3,3,1,1]
[2,8,1,7,5,6,4,3]=>0101011=>[2,2,2,1,1]
[2,3,8,1,6,5,7,4]=>0010101=>[3,2,2,1]
[3,5,7,6,1,2,4,8]=>0011000=>[3,1,4]
[4,8,6,7,2,3,5,1]=>0101001=>[2,2,3,1]
[4,8,6,7,1,3,5,2]=>0101001=>[2,2,3,1]
[3,4,8,6,1,5,7,2]=>0011001=>[3,1,3,1]
[3,8,5,7,1,6,4,2]=>0101011=>[2,2,2,1,1]
[3,8,5,7,2,1,6,4]=>0101101=>[2,2,1,2,1]
[3,4,8,6,2,1,5,7]=>0011100=>[3,1,1,3]
[3,5,7,6,2,1,4,8]=>0011100=>[3,1,1,3]
[5,8,6,7,3,4,2,1]=>0101011=>[2,2,2,1,1]
[5,8,6,7,2,1,3,4]=>0101100=>[2,2,1,3]
[4,8,6,7,2,1,5,3]=>0101101=>[2,2,1,2,1]
[4,3,1,7,5,2,8,6]=>1101101=>[1,1,2,1,2,1]
[4,3,2,8,5,1,7,6]=>1101101=>[1,1,2,1,2,1]
[4,3,8,5,1,6,7,2]=>1011001=>[1,2,1,3,1]
[5,8,6,7,2,3,4,1]=>0101001=>[2,2,3,1]
[5,8,6,7,2,4,3,1]=>0101011=>[2,2,2,1,1]
[5,8,6,7,1,2,4,3]=>0101001=>[2,2,3,1]
[3,2,5,7,6,1,4,8]=>1001100=>[1,3,1,3]
[4,8,6,7,1,3,2,5]=>0101010=>[2,2,2,2]
[4,8,6,7,1,2,5,3]=>0101001=>[2,2,3,1]
[4,8,6,7,2,5,3,1]=>0101011=>[2,2,2,1,1]
[4,3,8,5,2,6,7,1]=>1011001=>[1,2,1,3,1]
[4,2,6,7,5,1,3,8]=>1001100=>[1,3,1,3]
[3,8,4,7,1,5,2,6]=>0101010=>[2,2,2,2]
[3,5,1,7,4,6,2,8]=>0101010=>[2,2,2,2]
[3,8,4,7,2,5,1,6]=>0101010=>[2,2,2,2]
[4,1,3,8,5,2,6,7]=>1001100=>[1,3,1,3]
[4,2,6,7,5,3,8,1]=>1001101=>[1,3,1,2,1]
[4,8,6,7,3,2,5,1]=>0101101=>[2,2,1,2,1]
[4,8,6,7,3,1,2,5]=>0101100=>[2,2,1,3]
[3,1,5,7,6,2,4,8]=>1001100=>[1,3,1,3]
[3,4,1,7,5,6,2,8]=>0101010=>[2,2,2,2]
[4,1,7,5,2,8,6,3]=>1011011=>[1,2,1,2,1,1]
[4,1,6,7,5,2,3,8]=>1001100=>[1,3,1,3]
[5,8,6,7,3,2,4,1]=>0101101=>[2,2,1,2,1]
[5,8,6,7,4,2,3,1]=>0101101=>[2,2,1,2,1]
[5,8,6,7,4,1,2,3]=>0101100=>[2,2,1,3]
[5,8,6,7,4,1,3,2]=>0101101=>[2,2,1,2,1]
[5,8,6,7,3,1,4,2]=>0101101=>[2,2,1,2,1]
[4,8,6,7,3,1,5,2]=>0101101=>[2,2,1,2,1]
[4,1,6,7,5,3,8,2]=>1001101=>[1,3,1,2,1]
[4,1,7,5,3,2,8,6]=>1011101=>[1,2,1,1,2,1]
[4,2,8,5,3,1,7,6]=>1011101=>[1,2,1,1,2,1]
[4,2,1,6,7,5,3,8]=>1100110=>[1,1,3,1,2]
[4,8,6,7,3,2,1,5]=>0101110=>[2,2,1,1,2]
[5,8,6,7,4,2,1,3]=>0101110=>[2,2,1,1,2]
[5,8,6,7,4,3,1,2]=>0101110=>[2,2,1,1,2]
[6,1,5,2,8,4,7,3]=>1010101=>[1,2,2,2,1]
[4,6,1,8,5,7,2,3]=>0101010=>[2,2,2,2]
[4,7,1,2,8,5,6,3]=>0100101=>[2,3,2,1]
[1,4,7,2,8,5,6,3]=>0010101=>[3,2,2,1]
[1,7,3,5,8,6,2,4]=>0100110=>[2,3,1,2]
[7,3,5,8,6,1,2,4]=>1001100=>[1,3,1,3]
[6,8,1,5,7,2,3,4]=>0100100=>[2,3,3]
[7,1,2,5,8,6,3,4]=>1000110=>[1,4,1,2]
[1,7,2,5,8,6,3,4]=>0100110=>[2,3,1,2]
[1,7,6,8,2,3,5,4]=>0101001=>[2,2,3,1]
[7,6,8,1,2,3,5,4]=>1010001=>[1,2,4,1]
[2,7,1,5,8,6,3,4]=>0100110=>[2,3,1,2]
[2,4,7,1,8,5,6,3]=>0010101=>[3,2,2,1]
[4,7,5,8,3,1,6,2]=>0101101=>[2,2,1,2,1]
[4,7,2,1,8,5,6,3]=>0110101=>[2,1,2,2,1]
[7,3,5,8,6,2,1,4]=>1001110=>[1,3,1,1,2]
[7,6,8,2,1,3,5,4]=>1011001=>[1,2,1,3,1]
[1,2,7,6,8,3,5,4]=>0010101=>[3,2,2,1]
[3,7,6,8,2,1,5,4]=>0101101=>[2,2,1,2,1]
[6,7,4,1,8,5,3,2]=>0110111=>[2,1,2,1,1,1]
[6,7,4,3,1,8,5,2]=>0111011=>[2,1,1,2,1,1]
[2,7,4,1,6,8,5,3]=>0110011=>[2,1,3,1,1]
[3,1,7,6,8,2,5,4]=>1010101=>[1,2,2,2,1]
[1,3,7,6,8,2,5,4]=>0010101=>[3,2,2,1]
[1,7,4,2,6,8,5,3]=>0110011=>[2,1,3,1,1]
[7,1,4,2,8,5,6,3]=>1010101=>[1,2,2,2,1]
[7,1,8,2,5,4,6,3]=>1010101=>[1,2,2,2,1]
[7,1,6,8,5,4,2,3]=>1001110=>[1,3,1,1,2]
[7,1,2,6,8,5,4,3]=>1000111=>[1,4,1,1,1]
[1,7,2,6,8,5,4,3]=>0100111=>[2,3,1,1,1]
[1,7,6,8,3,2,5,4]=>0101101=>[2,2,1,2,1]
[7,6,8,3,1,2,5,4]=>1011001=>[1,2,1,3,1]
[7,1,5,8,6,3,2,4]=>1001110=>[1,3,1,1,2]
[3,6,7,1,8,5,4,2]=>0010111=>[3,2,1,1,1]
[7,2,6,8,5,4,1,3]=>1001110=>[1,3,1,1,2]
[7,6,8,2,3,1,5,4]=>1010101=>[1,2,2,2,1]
[2,7,6,8,3,1,5,4]=>0101101=>[2,2,1,2,1]
[2,7,1,6,8,5,4,3]=>0100111=>[2,3,1,1,1]
[6,7,3,1,8,5,4,2]=>0110111=>[2,1,2,1,1,1]
[6,7,1,8,5,4,3,2]=>0101111=>[2,2,1,1,1,1]
[7,2,1,6,8,5,4,3]=>1100111=>[1,1,3,1,1,1]
[7,8,4,2,1,6,5,3]=>0111011=>[2,1,1,2,1,1]
[6,2,3,4,8,7,1,5]=>1000110=>[1,4,1,2]
[6,2,3,4,7,8,1,5]=>1000010=>[1,5,2]
[7,8,3,6,4,2,1,5]=>0101110=>[2,2,1,1,2]
[7,8,3,5,6,2,1,4]=>0100110=>[2,3,1,2]
[5,2,6,3,8,1,7,4]=>1010101=>[1,2,2,2,1]
[6,3,2,5,8,7,1,4]=>1100110=>[1,1,3,1,2]
[6,3,2,8,4,7,1,5]=>1101010=>[1,1,2,2,2]
[6,4,3,8,7,5,1,2]=>1101110=>[1,1,2,1,1,2]
[6,4,3,7,8,5,1,2]=>1100110=>[1,1,3,1,2]
[6,3,2,7,4,8,1,5]=>1101010=>[1,1,2,2,2]
[6,3,2,5,7,8,1,4]=>1100010=>[1,1,4,2]
[5,8,2,3,6,1,7,4]=>0100101=>[2,3,2,1]
[4,5,6,8,3,2,1,7]=>0001110=>[4,1,1,2]
[4,6,8,5,3,2,1,7]=>0011110=>[3,1,1,1,2]
[5,6,1,4,2,3,7,8]=>0101000=>[2,2,4]
[5,6,8,4,3,7,1,2]=>0011010=>[3,1,2,2]
[5,6,1,4,2,3,8,7]=>0101001=>[2,2,3,1]
[5,2,8,3,4,1,7,6]=>1010101=>[1,2,2,2,1]
[4,5,8,6,3,2,1,7]=>0011110=>[3,1,1,1,2]
[4,7,5,6,3,2,1,8]=>0101110=>[2,2,1,1,2]
[5,1,4,3,6,2,8,7]=>1010101=>[1,2,2,2,1]
[5,1,4,3,8,2,7,6]=>1010101=>[1,2,2,2,1]
[5,6,2,4,1,8,7,3]=>0101011=>[2,2,2,1,1]
[5,7,2,4,1,8,6,3]=>0101011=>[2,2,2,1,1]
[6,1,4,2,8,7,5,3]=>1010111=>[1,2,2,1,1,1]
[5,8,2,4,1,7,6,3]=>0101011=>[2,2,2,1,1]
[5,4,1,3,7,2,6,8]=>1100100=>[1,1,3,3]
[5,8,1,4,2,3,7,6]=>0101001=>[2,2,3,1]
[5,1,6,3,4,2,7,8]=>1010100=>[1,2,2,3]
[4,8,6,5,3,2,1,7]=>0111110=>[2,1,1,1,1,2]
[5,4,7,8,3,2,1,6]=>1001110=>[1,3,1,1,2]
[4,7,8,5,3,2,1,6]=>0011110=>[3,1,1,1,2]
[5,7,1,3,4,2,6,8]=>0100100=>[2,3,3]
[5,1,8,4,2,3,6,7]=>1011000=>[1,2,1,4]
[5,1,7,4,2,3,6,8]=>1011000=>[1,2,1,4]
[5,8,1,3,4,2,6,7]=>0100100=>[2,3,3]
[4,8,7,5,3,2,1,6]=>0111110=>[2,1,1,1,1,2]
[4,7,8,6,3,2,1,5]=>0011110=>[3,1,1,1,2]
[4,8,2,3,6,7,5,1]=>0100011=>[2,4,1,1]
[4,8,3,1,6,7,5,2]=>0110011=>[2,1,3,1,1]
[4,3,8,1,6,2,5,7]=>1010100=>[1,2,2,3]
[1,4,8,7,3,5,2,6]=>0011010=>[3,1,2,2]
[4,3,8,7,2,5,1,6]=>1011010=>[1,2,1,2,2]
[5,8,1,4,7,2,6,3]=>0100101=>[2,3,2,1]
[6,8,1,2,4,3,5,7]=>0100100=>[2,3,3]
[5,8,7,1,3,4,2,6]=>0110010=>[2,1,3,2]
[4,8,7,6,3,1,2,5]=>0111100=>[2,1,1,1,3]
[5,8,4,7,3,1,2,6]=>0101100=>[2,2,1,3]
[4,3,8,2,7,5,6,1]=>1010101=>[1,2,2,2,1]
[1,4,8,3,7,5,6,2]=>0010101=>[3,2,2,1]
[1,4,3,8,2,6,5,7]=>0101010=>[2,2,2,2]
[4,1,3,8,2,6,5,7]=>1001010=>[1,3,2,2]
[4,1,8,7,3,5,2,6]=>1011010=>[1,2,1,2,2]
[3,4,8,1,6,2,5,7]=>0010100=>[3,2,3]
[3,4,8,7,2,5,1,6]=>0011010=>[3,1,2,2]
[3,4,8,2,7,5,6,1]=>0010101=>[3,2,2,1]
[1,2,4,3,8,6,5,7]=>0010110=>[3,2,1,2]
[3,4,2,1,8,6,5,7]=>0110110=>[2,1,2,1,2]
[3,4,1,8,2,6,5,7]=>0101010=>[2,2,2,2]
[3,6,7,8,4,1,2,5]=>0001100=>[4,1,3]
[4,1,2,8,3,6,5,7]=>1001010=>[1,3,2,2]
[1,4,3,2,8,6,5,7]=>0110110=>[2,1,2,1,2]
[4,2,3,1,8,6,5,7]=>1010110=>[1,2,2,1,2]
[3,7,8,2,6,4,5,1]=>0010101=>[3,2,2,1]
[4,2,3,8,1,6,5,7]=>1001010=>[1,3,2,2]
[4,3,1,8,2,6,5,7]=>1101010=>[1,1,2,2,2]
[1,4,7,8,5,3,2,6]=>0001110=>[4,1,1,2]
[4,2,8,6,3,1,5,7]=>1011100=>[1,2,1,1,3]
[2,4,8,6,3,1,5,7]=>0011100=>[3,1,1,3]
[7,3,6,8,4,2,1,5]=>1001110=>[1,3,1,1,2]
[1,7,3,8,4,6,5,2]=>0101011=>[2,2,2,1,1]
[1,3,4,8,2,6,5,7]=>0001010=>[4,2,2]
[3,2,4,8,1,6,5,7]=>1001010=>[1,3,2,2]
[7,3,8,2,6,4,5,1]=>1010101=>[1,2,2,2,1]
[6,2,8,7,4,3,5,1]=>1011101=>[1,2,1,1,2,1]
[7,4,1,8,5,2,6,3]=>1101101=>[1,1,2,1,2,1]
[7,3,2,8,4,6,5,1]=>1101011=>[1,1,2,2,1,1]
[1,3,4,2,8,6,5,7]=>0010110=>[3,2,1,2]
[1,3,2,4,8,6,5,7]=>0100110=>[2,3,1,2]
[3,2,1,4,8,6,5,7]=>1100110=>[1,1,3,1,2]
[3,1,2,4,8,6,5,7]=>1000110=>[1,4,1,2]
[3,1,4,2,8,6,5,7]=>1010110=>[1,2,2,1,2]
[3,1,4,8,2,6,5,7]=>1001010=>[1,3,2,2]
[7,3,4,8,5,1,6,2]=>1001101=>[1,3,1,2,1]
[3,7,4,8,5,1,2,6]=>0101100=>[2,2,1,3]
[6,7,2,8,3,5,4,1]=>0101011=>[2,2,2,1,1]
[2,3,1,4,8,6,5,7]=>0100110=>[2,3,1,2]
[2,1,3,4,8,6,5,7]=>1000110=>[1,4,1,2]
[3,5,7,8,6,1,2,4]=>0001100=>[4,1,3]
[3,1,5,6,8,2,7,4]=>1000101=>[1,4,2,1]
[5,1,6,3,8,4,7,2]=>1010101=>[1,2,2,2,1]
[2,5,1,6,8,3,7,4]=>0100101=>[2,3,2,1]
[5,1,2,6,8,3,7,4]=>1000101=>[1,4,2,1]
[1,5,2,7,8,6,3,4]=>0100110=>[2,3,1,2]
[6,1,7,5,2,8,3,4]=>1011010=>[1,2,1,2,2]
[2,6,7,5,1,8,3,4]=>0011010=>[3,1,2,2]
[5,7,2,8,6,1,3,4]=>0101100=>[2,2,1,3]
[3,5,7,8,6,2,1,4]=>0001110=>[4,1,1,2]
[3,2,5,7,8,6,1,4]=>1000110=>[1,4,1,2]
[6,2,7,5,1,8,3,4]=>1011010=>[1,2,1,2,2]
[1,2,6,7,5,8,3,4]=>0001010=>[4,2,2]
[6,2,7,5,4,1,8,3]=>1011101=>[1,2,1,1,2,1]
[6,7,5,2,4,1,8,3]=>0110101=>[2,1,2,2,1]
[6,7,2,5,3,8,1,4]=>0101010=>[2,2,2,2]
[5,1,7,8,6,3,2,4]=>1001110=>[1,3,1,1,2]
[1,6,7,5,3,8,2,4]=>0011010=>[3,1,2,2]
[1,6,7,5,4,2,8,3]=>0011101=>[3,1,1,2,1]
[5,7,8,6,4,1,2,3]=>0011100=>[3,1,1,3]
[6,7,4,1,5,2,8,3]=>0110101=>[2,1,2,2,1]
[1,6,7,4,5,2,8,3]=>0010101=>[3,2,2,1]
[6,3,1,7,5,8,2,4]=>1101010=>[1,1,2,2,2]
[2,5,3,7,8,6,1,4]=>0100110=>[2,3,1,2]
[6,3,2,7,5,8,1,4]=>1101010=>[1,1,2,2,2]
[6,7,4,2,5,1,8,3]=>0110101=>[2,1,2,2,1]
[6,2,7,4,5,1,8,3]=>1010101=>[1,2,2,2,1]
[6,2,3,7,5,8,1,4]=>1001010=>[1,3,2,2]
[7,5,1,6,3,8,2,4]=>1101010=>[1,1,2,2,2]
[7,5,1,6,3,8,4,2]=>1101011=>[1,1,2,2,1,1]
[2,7,6,1,3,8,4,5]=>0110010=>[2,1,3,2]
[2,7,6,1,3,8,5,4]=>0110011=>[2,1,3,1,1]
[2,6,7,1,5,8,3,4]=>0010010=>[3,3,2]
[2,6,7,4,1,8,3,5]=>0011010=>[3,1,2,2]
[2,1,6,7,3,8,5,4]=>1001011=>[1,3,2,1,1]
[2,6,7,4,1,8,5,3]=>0011011=>[3,1,2,1,1]
[2,6,7,1,5,8,4,3]=>0010011=>[3,3,1,1]
[3,6,5,1,8,4,2,7]=>0110110=>[2,1,2,1,2]
[3,7,5,4,8,1,6,2]=>0110101=>[2,1,2,2,1]
[3,7,5,4,8,1,2,6]=>0110100=>[2,1,2,3]
[4,6,1,5,8,7,3,2]=>0100111=>[2,3,1,1,1]
[4,6,1,5,8,7,2,3]=>0100110=>[2,3,1,2]
[4,6,1,5,8,2,7,3]=>0100101=>[2,3,2,1]
[7,5,1,6,2,8,3,4]=>1101010=>[1,1,2,2,2]
[4,6,1,5,8,2,3,7]=>0100100=>[2,3,3]
[4,7,1,5,8,3,6,2]=>0100101=>[2,3,2,1]
[8,3,4,6,2,1,5,7]=>1001100=>[1,3,1,3]
[3,5,6,2,1,8,4,7]=>0011010=>[3,1,2,2]
[7,5,3,2,8,4,1,6]=>1110110=>[1,1,1,2,1,2]
[7,5,3,2,8,4,6,1]=>1110101=>[1,1,1,2,2,1]
[4,2,5,6,8,3,1,7]=>1000110=>[1,4,1,2]
[5,3,6,8,1,4,2,7]=>1001010=>[1,3,2,2]
[4,5,6,8,1,3,2,7]=>0001010=>[4,2,2]
[1,4,5,6,8,3,2,7]=>0000110=>[5,1,2]
[4,5,3,7,2,8,6,1]=>0101011=>[2,2,2,1,1]
[6,4,7,3,2,8,5,1]=>1011011=>[1,2,1,2,1,1]
[6,1,4,7,3,2,8,5]=>1001101=>[1,3,1,2,1]
[5,1,7,3,8,4,2,6]=>1010110=>[1,2,2,1,2]
[5,3,7,1,4,8,6,2]=>1010011=>[1,2,3,1,1]
[6,4,3,1,7,8,5,2]=>1110011=>[1,1,1,3,1,1]
[5,6,1,3,7,8,4,2]=>0100011=>[2,4,1,1]
[5,6,1,7,8,3,4,2]=>0100101=>[2,3,2,1]
[1,6,3,7,4,8,5,2]=>0101011=>[2,2,2,1,1]
[6,7,2,4,1,8,5,3]=>0101011=>[2,2,2,1,1]
[6,7,2,1,4,3,8,5]=>0110101=>[2,1,2,2,1]
[6,4,7,3,1,2,8,5]=>1011001=>[1,2,1,3,1]
[5,6,3,1,2,7,8,4]=>0110001=>[2,1,4,1]
[5,6,1,3,2,7,8,4]=>0101001=>[2,2,3,1]
[5,6,3,2,1,7,8,4]=>0111001=>[2,1,1,3,1]
[5,6,3,2,7,8,4,1]=>0110011=>[2,1,3,1,1]
[2,5,6,3,7,8,4,1]=>0010011=>[3,3,1,1]
[2,5,6,3,1,7,8,4]=>0011001=>[3,1,3,1]
[2,6,4,7,3,1,8,5]=>0101101=>[2,2,1,2,1]
[6,3,7,2,8,4,1,5]=>1010110=>[1,2,2,1,2]
[6,3,2,7,1,8,4,5]=>1101010=>[1,1,2,2,2]
[7,5,3,2,1,8,4,6]=>1111010=>[1,1,1,1,2,2]
[7,3,8,4,2,1,5,6]=>1011100=>[1,2,1,1,3]
[4,7,2,1,3,8,6,5]=>0110011=>[2,1,3,1,1]
[1,3,7,8,6,4,2,5]=>0001110=>[4,1,1,2]
[5,7,3,8,2,1,6,4]=>0101101=>[2,2,1,2,1]
[4,6,2,7,8,5,3,1]=>0100111=>[2,3,1,1,1]
[2,5,1,7,3,8,6,4]=>0101011=>[2,2,2,1,1]
[6,7,2,1,3,8,5,4]=>0110011=>[2,1,3,1,1]
[5,1,6,7,8,2,4,3]=>1000101=>[1,4,2,1]
[6,3,7,1,8,5,2,4]=>1010110=>[1,2,2,1,2]
[6,2,1,7,3,8,5,4]=>1101011=>[1,1,2,2,1,1]
[6,2,7,1,8,5,4,3]=>1010111=>[1,2,2,1,1,1]
[6,3,1,7,8,5,4,2]=>1100111=>[1,1,3,1,1,1]
[5,3,2,1,8,4,7,6]=>1110101=>[1,1,1,2,2,1]
[4,5,2,1,3,8,7,6]=>0110011=>[2,1,3,1,1]
[3,2,6,4,5,8,1,7]=>1010010=>[1,2,3,2]
[2,4,6,5,8,1,3,7]=>0010100=>[3,2,3]
[1,3,4,6,5,8,2,7]=>0001010=>[4,2,2]
[1,6,3,4,5,8,2,7]=>0100010=>[2,4,2]
[3,4,1,8,5,2,7,6]=>0101101=>[2,2,1,2,1]
[2,8,4,1,7,6,3,5]=>0110110=>[2,1,2,1,2]
[1,5,3,2,8,7,4,6]=>0110110=>[2,1,2,1,2]
[8,2,1,7,5,3,4,6]=>1101100=>[1,1,2,1,3]
[1,7,6,4,5,8,3,2]=>0110011=>[2,1,3,1,1]
[5,8,7,4,6,2,1,3]=>0110110=>[2,1,2,1,2]
[3,4,2,5,8,6,7,1]=>0100101=>[2,3,2,1]
[4,1,3,5,6,8,7,2]=>1000011=>[1,5,1,1]
[2,4,8,6,7,1,3,5]=>0010100=>[3,2,3]
[3,7,4,8,2,1,6,5]=>0101101=>[2,2,1,2,1]
[2,3,5,8,6,7,1,4]=>0001010=>[4,2,2]
[3,2,5,6,8,7,1,4]=>1000110=>[1,4,1,2]
[7,2,4,8,5,3,1,6]=>1001110=>[1,3,1,1,2]
[4,8,3,1,2,7,6,5]=>0110011=>[2,1,3,1,1]
[8,4,2,3,7,1,5,6]=>1100100=>[1,1,3,3]
[3,5,2,7,6,1,8,4]=>0101101=>[2,2,1,2,1]
[5,8,7,3,4,6,2,1]=>0110011=>[2,1,3,1,1]
[5,8,2,7,4,1,6,3]=>0101101=>[2,2,1,2,1]
[5,1,4,2,8,7,6,3]=>1010111=>[1,2,2,1,1,1]
[5,2,6,8,7,1,3,4]=>1001100=>[1,3,1,3]
[6,3,2,1,8,5,7,4]=>1110101=>[1,1,1,2,2,1]
[2,7,5,4,1,8,6,3]=>0111011=>[2,1,1,2,1,1]
[4,2,5,6,8,7,1,3]=>1000110=>[1,4,1,2]
[1,8,4,2,5,6,7,3]=>0110001=>[2,1,4,1]
[3,8,4,1,5,6,7,2]=>0110001=>[2,1,4,1]
[4,2,8,5,6,7,1,3]=>1010010=>[1,2,3,2]
[5,2,4,7,1,8,6,3]=>1001011=>[1,3,2,1,1]
[8,1,3,6,5,2,4,7]=>1001100=>[1,3,1,3]
[8,3,2,4,6,5,1,7]=>1100110=>[1,1,3,1,2]
[8,3,6,4,1,5,2,7]=>1011010=>[1,2,1,2,2]
[1,3,4,8,5,7,2,6]=>0001010=>[4,2,2]
[5,8,4,7,6,2,3,1]=>0101101=>[2,2,1,2,1]
[1,3,4,7,5,8,2,6]=>0001010=>[4,2,2]
[1,3,5,2,4,8,7,6]=>0010011=>[3,3,1,1]
[2,6,5,1,3,8,7,4]=>0110011=>[2,1,3,1,1]
[2,8,5,1,4,7,6,3]=>0110011=>[2,1,3,1,1]
[4,3,1,5,8,6,7,2]=>1100101=>[1,1,3,2,1]
[5,4,2,1,6,8,7,3]=>1110011=>[1,1,1,3,1,1]
[6,8,4,3,2,7,1,5]=>0111010=>[2,1,1,2,2]
[5,1,3,2,8,6,7,4]=>1010101=>[1,2,2,2,1]
[5,3,1,2,8,6,7,4]=>1100101=>[1,1,3,2,1]
[5,2,3,1,6,8,7,4]=>1010011=>[1,2,3,1,1]
[5,3,2,1,8,6,7,4]=>1110101=>[1,1,1,2,2,1]
[5,2,1,3,6,8,7,4]=>1100011=>[1,1,4,1,1]
[2,7,4,5,8,3,1,6]=>0100110=>[2,3,1,2]
[1,8,4,3,7,2,6,5]=>0110101=>[2,1,2,2,1]
[3,4,8,7,2,1,6,5]=>0011101=>[3,1,1,2,1]
[5,4,7,8,3,6,2,1]=>1001011=>[1,3,2,1,1]
[6,3,8,7,4,1,2,5]=>1011100=>[1,2,1,1,3]
[8,4,7,2,3,1,5,6]=>1010100=>[1,2,2,3]
[8,6,4,1,3,2,7,5]=>1110101=>[1,1,1,2,2,1]
[3,5,7,2,6,1,8,4]=>0010101=>[3,2,2,1]
[6,1,3,8,5,7,2,4]=>1001010=>[1,3,2,2]
[2,8,1,5,4,7,6,3]=>0101011=>[2,2,2,1,1]
[1,7,2,4,6,5,8,3]=>0100101=>[2,3,2,1]
[5,8,2,6,1,3,7,4]=>0101001=>[2,2,3,1]
[6,3,5,8,7,2,1,4]=>1001110=>[1,3,1,1,2]
[2,5,7,8,4,1,6,3]=>0001101=>[4,1,2,1]
[4,1,5,2,6,8,7,3]=>1010011=>[1,2,3,1,1]
[4,1,8,5,2,6,7,3]=>1011001=>[1,2,1,3,1]
[2,7,1,8,5,4,6,3]=>0101101=>[2,2,1,2,1]
[5,8,6,2,1,3,7,4]=>0111001=>[2,1,1,3,1]
[3,4,5,1,8,6,7,2]=>0010101=>[3,2,2,1]
[1,3,2,7,5,8,6,4]=>0101011=>[2,2,2,1,1]
[1,4,2,5,8,3,7,6]=>0100101=>[2,3,2,1]
[4,1,2,6,8,5,3,7]=>1000110=>[1,4,1,2]
[1,5,2,4,8,7,6,3]=>0100111=>[2,3,1,1,1]
[1,2,7,4,8,6,5,3]=>0010111=>[3,2,1,1,1]
[1,3,2,8,5,7,4,6]=>0101010=>[2,2,2,2]
[1,2,6,4,8,7,3,5]=>0010110=>[3,2,1,2]
[1,3,8,2,6,7,4,5]=>0010010=>[3,3,2]
[1,6,7,8,2,5,3,4]=>0001010=>[4,2,2]
[1,5,7,8,2,3,6,4]=>0001001=>[4,3,1]
[1,2,8,4,7,3,6,5]=>0010101=>[3,2,2,1]
[1,5,2,4,8,3,7,6]=>0100101=>[2,3,2,1]
[1,8,3,5,2,7,4,6]=>0101010=>[2,2,2,2]
[1,4,8,6,7,2,3,5]=>0010100=>[3,2,3]
[1,5,7,8,6,2,3,4]=>0001100=>[4,1,3]
[1,3,7,6,2,8,4,5]=>0011010=>[3,1,2,2]
[1,2,5,8,7,6,3,4]=>0001110=>[4,1,1,2]
[1,2,6,8,7,5,3,4]=>0001110=>[4,1,1,2]
[1,2,7,8,6,5,3,4]=>0001110=>[4,1,1,2]
[5,2,6,7,3,4,8,1]=>1001001=>[1,3,3,1]
[5,6,2,1,7,8,3,4]=>0110010=>[2,1,3,2]
[5,6,2,1,4,8,7,3]=>0110011=>[2,1,3,1,1]
[2,6,1,4,5,8,7,3]=>0100011=>[2,4,1,1]
[5,4,2,7,6,3,8,1]=>1101101=>[1,1,2,1,2,1]
[2,3,7,6,4,5,8,1]=>0011001=>[3,1,3,1]
[2,6,1,7,5,8,3,4]=>0101010=>[2,2,2,2]
[5,1,2,7,8,4,3,6]=>1000110=>[1,4,1,2]
[2,6,1,7,4,8,3,5]=>0101010=>[2,2,2,2]
[3,6,4,1,7,8,2,5]=>0110010=>[2,1,3,2]
[5,4,6,1,7,8,2,3]=>1010010=>[1,2,3,2]
[5,4,6,1,3,8,7,2]=>1010011=>[1,2,3,1,1]
[3,6,4,1,5,8,7,2]=>0110011=>[2,1,3,1,1]
[2,6,1,5,4,8,7,3]=>0101011=>[2,2,2,1,1]
[2,6,1,4,7,8,5,3]=>0100011=>[2,4,1,1]
[5,1,2,4,8,7,6,3]=>1000111=>[1,4,1,1,1]
[2,1,5,3,8,6,4,7]=>1010110=>[1,2,2,1,2]
[5,1,2,4,8,6,3,7]=>1000110=>[1,4,1,2]
[5,6,3,1,4,8,2,7]=>0110010=>[2,1,3,2]
[2,5,4,3,1,8,6,7]=>0111010=>[2,1,1,2,2]
[5,4,6,3,1,8,7,2]=>1011011=>[1,2,1,2,1,1]
[2,1,3,7,8,6,4,5]=>1000110=>[1,4,1,2]
[5,1,4,2,8,6,7,3]=>1010101=>[1,2,2,2,1]
[1,2,3,8,6,7,4,5]=>0001010=>[4,2,2]
[1,2,3,8,7,5,4,6]=>0001110=>[4,1,1,2]
[1,2,3,8,7,4,5,6]=>0001100=>[4,1,3]
[2,1,3,6,8,7,4,5]=>1000110=>[1,4,1,2]
[3,1,6,2,8,7,5,4]=>1010111=>[1,2,2,1,1,1]
[6,8,1,3,2,5,4,7]=>0101010=>[2,2,2,2]
[6,8,1,4,2,5,3,7]=>0101010=>[2,2,2,2]
[7,8,3,6,1,4,2,5]=>0101010=>[2,2,2,2]
[7,8,2,5,1,4,3,6]=>0101010=>[2,2,2,2]
[7,8,1,4,3,6,2,5]=>0101010=>[2,2,2,2]
[5,8,1,4,3,7,2,6]=>0101010=>[2,2,2,2]
[6,8,2,5,1,4,3,7]=>0101010=>[2,2,2,2]
[6,8,2,5,3,7,1,4]=>0101010=>[2,2,2,2]
[2,5,4,7,6,8,1,3]=>0101010=>[2,2,2,2]
[2,6,1,4,3,7,5,8]=>0101010=>[2,2,2,2]
[2,6,1,5,3,7,4,8]=>0101010=>[2,2,2,2]
[2,6,4,7,5,8,1,3]=>0101010=>[2,2,2,2]
[5,8,2,6,4,7,1,3]=>0101010=>[2,2,2,2]
[6,8,3,7,1,4,2,5]=>0101010=>[2,2,2,2]
[5,8,1,3,2,6,4,7]=>0101010=>[2,2,2,2]
[5,8,4,7,1,3,2,6]=>0101010=>[2,2,2,2]
[6,8,4,7,1,3,2,5]=>0101010=>[2,2,2,2]
[6,8,5,7,1,3,2,4]=>0101010=>[2,2,2,2]
[5,7,6,8,2,4,1,3]=>0101010=>[2,2,2,2]
[4,7,5,8,1,3,2,6]=>0101010=>[2,2,2,2]
[4,7,1,3,2,6,5,8]=>0101010=>[2,2,2,2]
[3,7,1,4,2,6,5,8]=>0101010=>[2,2,2,2]
[3,7,6,8,1,4,2,5]=>0101010=>[2,2,2,2]
[4,7,6,8,2,5,1,3]=>0101010=>[2,2,2,2]
[4,7,5,8,3,6,1,2]=>0101010=>[2,2,2,2]
[4,7,5,8,2,6,1,3]=>0101010=>[2,2,2,2]
[3,7,4,8,2,6,1,5]=>0101010=>[2,2,2,2]
[3,7,1,5,2,6,4,8]=>0101010=>[2,2,2,2]
[3,7,2,6,1,5,4,8]=>0101010=>[2,2,2,2]
[3,7,2,6,5,8,1,4]=>0101010=>[2,2,2,2]
[4,7,3,6,5,8,1,2]=>0101010=>[2,2,2,2]
[2,6,5,8,4,7,1,3]=>0101010=>[2,2,2,2]
[2,6,3,7,1,5,4,8]=>0101010=>[2,2,2,2]
[7,6,4,8,5,2,3,1]=>1101101=>[1,1,2,1,2,1]
[6,7,4,3,5,1,8,2]=>0110101=>[2,1,2,2,1]
[6,7,3,5,4,8,2,1]=>0101011=>[2,2,2,1,1]
[6,8,3,7,5,2,4,1]=>0101101=>[2,2,1,2,1]
[7,6,3,5,8,2,4,1]=>1100101=>[1,1,3,2,1]
[7,6,2,8,4,1,5,3]=>1101101=>[1,1,2,1,2,1]
[7,6,3,4,8,2,5,1]=>1100101=>[1,1,3,2,1]
[6,8,3,7,4,5,2,1]=>0101011=>[2,2,2,1,1]
[6,7,3,5,8,4,2,1]=>0100111=>[2,3,1,1,1]
[5,7,8,3,6,2,1,4]=>0010110=>[3,2,1,2]
[6,3,4,8,7,2,5,1]=>1001101=>[1,3,1,2,1]
[6,3,8,4,7,2,1,5]=>1010110=>[1,2,2,1,2]
[6,3,4,7,5,8,2,1]=>1001011=>[1,3,2,1,1]
[6,3,5,7,8,4,2,1]=>1000111=>[1,4,1,1,1]
[5,7,3,6,8,2,1,4]=>0100110=>[2,3,1,2]
[5,6,7,3,4,1,8,2]=>0010101=>[3,2,2,1]
[4,6,7,8,3,5,2,1]=>0001011=>[4,2,1,1]
[4,7,3,5,6,8,2,1]=>0100011=>[2,4,1,1]
[5,3,4,7,8,2,1,6]=>1000110=>[1,4,1,2]
[5,3,8,2,4,1,6,7]=>1010100=>[1,2,2,3]
[5,3,4,8,2,6,1,7]=>1001010=>[1,3,2,2]
[4,8,3,6,2,5,7,1]=>0101001=>[2,2,3,1]
[4,8,3,5,7,2,6,1]=>0100101=>[2,3,2,1]
[4,8,3,5,6,7,2,1]=>0100011=>[2,4,1,1]
[4,7,8,3,5,6,2,1]=>0010011=>[3,3,1,1]
[4,7,8,3,6,2,5,1]=>0010101=>[3,2,2,1]
[4,8,3,6,7,2,5,1]=>0100101=>[2,3,2,1]
[4,8,3,7,2,5,6,1]=>0101001=>[2,2,3,1]
[5,8,3,7,2,6,4,1]=>0101011=>[2,2,2,1,1]
[5,7,3,4,8,2,1,6]=>0100110=>[2,3,1,2]
[5,8,4,2,3,1,6,7]=>0110100=>[2,1,2,3]
[5,8,4,2,3,1,7,6]=>0110101=>[2,1,2,2,1]
[6,4,8,5,3,7,2,1]=>1011011=>[1,2,1,2,1,1]
[6,4,2,7,3,1,8,5]=>1101101=>[1,1,2,1,2,1]
[6,4,3,7,8,5,2,1]=>1100111=>[1,1,3,1,1,1]
[6,4,5,3,7,1,8,2]=>1010101=>[1,2,2,2,1]
[5,7,4,2,3,1,6,8]=>0110100=>[2,1,2,3]
[5,6,3,7,1,8,2,4]=>0101010=>[2,2,2,2]
[5,6,3,4,8,2,1,7]=>0100110=>[2,3,1,2]
[6,3,5,7,4,8,2,1]=>1001011=>[1,3,2,1,1]
[6,3,5,4,7,8,2,1]=>1010011=>[1,2,3,1,1]
[6,4,3,5,7,1,8,2]=>1100101=>[1,1,3,2,1]
[6,4,2,5,1,7,3,8]=>1101010=>[1,1,2,2,2]
[5,3,4,7,2,6,1,8]=>1001010=>[1,3,2,2]
[4,7,3,6,2,5,8,1]=>0101001=>[2,2,3,1]
[4,7,3,6,8,2,5,1]=>0100101=>[2,3,2,1]
[4,6,7,3,5,8,2,1]=>0010011=>[3,3,1,1]
[4,5,7,8,3,6,2,1]=>0001011=>[4,2,1,1]
[4,5,8,3,7,2,6,1]=>0010101=>[3,2,2,1]
[5,3,4,6,8,2,1,7]=>1000110=>[1,4,1,2]
[5,3,6,7,1,8,2,4]=>1001010=>[1,3,2,2]
[5,3,4,6,7,1,8,2]=>1000101=>[1,4,2,1]
[4,6,3,5,7,8,2,1]=>0100011=>[2,4,1,1]
[4,5,7,3,6,8,2,1]=>0010011=>[3,3,1,1]
[7,1,5,8,4,2,3,6]=>1001100=>[1,3,1,3]
[8,1,5,7,4,2,3,6]=>1001100=>[1,3,1,3]
[7,1,4,5,8,2,3,6]=>1000100=>[1,4,3]
[7,4,1,6,2,8,3,5]=>1101010=>[1,1,2,2,2]
[8,4,1,7,2,6,3,5]=>1101010=>[1,1,2,2,2]
[8,1,4,7,5,2,3,6]=>1001100=>[1,3,1,3]
[8,1,5,4,7,2,3,6]=>1010100=>[1,2,2,3]
[2,1,7,5,8,3,4,6]=>1010100=>[1,2,2,3]
[7,1,5,4,8,2,3,6]=>1010100=>[1,2,2,3]
[7,1,4,8,5,2,3,6]=>1001100=>[1,3,1,3]
[7,8,3,1,2,4,6,5]=>0110001=>[2,1,4,1]
[8,7,1,6,4,2,3,5]=>1101100=>[1,1,2,1,3]
[8,6,1,7,4,2,3,5]=>1101100=>[1,1,2,1,3]
[7,6,1,8,4,2,3,5]=>1101100=>[1,1,2,1,3]
[7,3,8,1,2,4,6,5]=>1010001=>[1,2,4,1]
[8,3,7,1,2,4,6,5]=>1010001=>[1,2,4,1]
[8,3,6,1,2,4,7,5]=>1010001=>[1,2,4,1]
[8,3,7,5,1,2,4,6]=>1011000=>[1,2,1,4]
[7,3,6,1,2,4,8,5]=>1010001=>[1,2,4,1]
[6,7,1,8,4,2,3,5]=>0101100=>[2,2,1,3]
[6,8,1,7,4,2,3,5]=>0101100=>[2,2,1,3]
[7,1,8,4,5,2,3,6]=>1010100=>[1,2,2,3]
[7,6,3,1,2,4,8,5]=>1110001=>[1,1,1,4,1]
[6,1,2,3,8,7,5,4]=>1000111=>[1,4,1,1,1]
[6,8,3,1,2,7,4,5]=>0110010=>[2,1,3,2]
[6,7,3,1,2,8,4,5]=>0110010=>[2,1,3,2]
[6,7,1,4,2,3,8,5]=>0101001=>[2,2,3,1]
[4,3,6,8,5,7,1,2]=>1001010=>[1,3,2,2]
[6,1,2,5,4,8,3,7]=>1001010=>[1,3,2,2]
[3,2,8,5,4,1,7,6]=>1011101=>[1,2,1,1,2,1]
[7,8,2,1,4,6,3,5]=>0110010=>[2,1,3,2]
[2,4,8,5,1,3,6,7]=>0011000=>[3,1,4]
[3,5,6,1,8,4,2,7]=>0010110=>[3,2,1,2]
[1,3,6,8,7,4,2,5]=>0001110=>[4,1,1,2]
[1,2,8,5,7,3,4,6]=>0010100=>[3,2,3]
[3,1,5,6,4,8,7,2]=>1001011=>[1,3,2,1,1]
[1,3,6,2,5,7,8,4]=>0010001=>[3,4,1]
[3,6,1,4,2,7,8,5]=>0101001=>[2,2,3,1]
[1,3,6,5,2,7,8,4]=>0011001=>[3,1,3,1]
[1,2,6,4,3,8,5,7]=>0011010=>[3,1,2,2]
[1,2,6,3,5,8,7,4]=>0010011=>[3,3,1,1]
[2,3,5,1,8,4,7,6]=>0010101=>[3,2,2,1]
[1,2,7,4,6,8,3,5]=>0010010=>[3,3,2]
[2,3,7,5,1,8,4,6]=>0011010=>[3,1,2,2]
[4,7,2,5,3,8,6,1]=>0101011=>[2,2,2,1,1]
[3,1,7,5,4,8,6,2]=>1011011=>[1,2,1,2,1,1]
[1,2,7,6,4,8,5,3]=>0011011=>[3,1,2,1,1]
[1,2,7,3,6,8,5,4]=>0010011=>[3,3,1,1]
[3,1,5,4,8,7,6,2]=>1010111=>[1,2,2,1,1,1]
[1,2,6,8,5,4,7,3]=>0001101=>[4,1,2,1]
[3,5,7,4,8,2,1,6]=>0010110=>[3,2,1,2]
[2,4,7,6,8,3,1,5]=>0010110=>[3,2,1,2]
[1,4,6,8,3,5,2,7]=>0001010=>[4,2,2]
[1,3,6,8,5,2,4,7]=>0001100=>[4,1,3]
[1,2,6,8,5,4,3,7]=>0001110=>[4,1,1,2]
[1,2,5,8,4,3,7,6]=>0001101=>[4,1,2,1]
[1,3,6,8,2,5,4,7]=>0001010=>[4,2,2]
[1,4,6,8,3,2,5,7]=>0001100=>[4,1,3]
[2,3,6,5,8,1,7,4]=>0010101=>[3,2,2,1]
[3,5,4,6,8,2,1,7]=>0100110=>[2,3,1,2]
[3,5,4,6,8,1,2,7]=>0100100=>[2,3,3]
[1,2,4,7,5,8,3,6]=>0001010=>[4,2,2]
[3,6,4,7,1,8,5,2]=>0101011=>[2,2,2,1,1]
[1,2,6,7,3,8,5,4]=>0001011=>[4,2,1,1]
[1,2,5,7,3,8,6,4]=>0001011=>[4,2,1,1]
[3,1,5,7,6,8,4,2]=>1001011=>[1,3,2,1,1]
[3,5,4,6,8,2,7,1]=>0100101=>[2,3,2,1]
[4,2,6,1,8,7,5,3]=>1010111=>[1,2,2,1,1,1]
[1,2,7,4,6,8,5,3]=>0010011=>[3,3,1,1]
[1,2,7,5,6,8,4,3]=>0010011=>[3,3,1,1]
[3,1,6,7,5,8,4,2]=>1001011=>[1,3,2,1,1]
[4,6,2,7,5,8,3,1]=>0101011=>[2,2,2,1,1]
[3,5,7,4,8,2,6,1]=>0010101=>[3,2,2,1]
[1,3,6,8,2,5,7,4]=>0001001=>[4,3,1]
[1,3,5,8,2,7,4,6]=>0001010=>[4,2,2]
[1,2,5,8,4,7,6,3]=>0001011=>[4,2,1,1]
[1,2,4,8,7,3,6,5]=>0001101=>[4,1,2,1]
[1,2,5,8,7,4,3,6]=>0001110=>[4,1,1,2]
[1,3,5,8,7,2,4,6]=>0001100=>[4,1,3]
[2,3,7,6,8,5,1,4]=>0010110=>[3,2,1,2]
[5,7,1,2,8,6,4,3]=>0100111=>[2,3,1,1,1]
[3,1,7,6,8,5,4,2]=>1010111=>[1,2,2,1,1,1]
[1,2,6,8,5,7,4,3]=>0001011=>[4,2,1,1]
[1,2,5,8,7,4,6,3]=>0001101=>[4,1,2,1]
[1,2,4,8,7,6,3,5]=>0001110=>[4,1,1,2]
[3,2,7,4,6,8,1,5]=>1010010=>[1,2,3,2]
[5,3,6,2,7,1,4,8]=>1010100=>[1,2,2,3]
[2,6,3,4,7,1,5,8]=>0100100=>[2,3,3]
[2,7,3,4,5,8,1,6]=>0100010=>[2,4,2]
[4,7,6,2,3,8,1,5]=>0110010=>[2,1,3,2]
[7,3,5,2,4,8,1,6]=>1010010=>[1,2,3,2]
[7,6,2,4,5,8,1,3]=>1100010=>[1,1,4,2]
[6,5,2,3,4,8,1,7]=>1100010=>[1,1,4,2]
[5,3,1,2,8,4,7,6]=>1100101=>[1,1,3,2,1]
[6,5,2,3,7,1,4,8]=>1100100=>[1,1,3,3]
[5,2,1,7,3,4,6,8]=>1101000=>[1,1,2,4]
[5,2,1,8,3,4,6,7]=>1101000=>[1,1,2,4]
[6,3,2,8,4,5,7,1]=>1101001=>[1,1,2,3,1]
[7,3,1,2,8,4,6,5]=>1100101=>[1,1,3,2,1]
[6,2,3,1,8,4,7,5]=>1010101=>[1,2,2,2,1]
[8,3,5,2,7,1,4,6]=>1010100=>[1,2,2,3]
[8,6,2,4,7,1,5,3]=>1100101=>[1,1,3,2,1]
[8,2,1,7,3,4,5,6]=>1101000=>[1,1,2,4]
[8,6,3,7,2,4,5,1]=>1101001=>[1,1,2,3,1]
[8,2,7,3,4,5,6,1]=>1010001=>[1,2,4,1]
[8,1,6,2,3,4,5,7]=>1010000=>[1,2,5]
[8,1,7,3,4,5,6,2]=>1010001=>[1,2,4,1]
[8,6,1,7,2,4,5,3]=>1101001=>[1,1,2,3,1]
[1,7,5,8,2,3,6,4]=>0101001=>[2,2,3,1]
[7,2,1,8,3,4,5,6]=>1101000=>[1,1,2,4]
[1,7,8,3,4,5,6,2]=>0010001=>[3,4,1]
[1,6,2,8,4,5,7,3]=>0101001=>[2,2,3,1]
[4,1,3,6,8,2,7,5]=>1000101=>[1,4,2,1]
[4,6,3,8,7,1,2,5]=>0101100=>[2,2,1,3]
[6,4,5,8,7,1,2,3]=>1001100=>[1,3,1,3]
[5,3,4,8,7,1,2,6]=>1001100=>[1,3,1,3]
[3,2,8,7,1,4,6,5]=>1011001=>[1,2,1,3,1]
[3,1,8,7,2,4,6,5]=>1011001=>[1,2,1,3,1]
[5,3,7,6,1,2,4,8]=>1011000=>[1,2,1,4]
[1,8,3,7,2,4,5,6]=>0101000=>[2,2,4]
[3,8,1,7,2,4,5,6]=>0101000=>[2,2,4]
[6,8,2,3,5,1,4,7]=>0100100=>[2,3,3]
[4,7,8,2,6,1,3,5]=>0010100=>[3,2,3]
[6,2,8,7,1,4,5,3]=>1011001=>[1,2,1,3,1]
[3,8,7,1,4,5,6,2]=>0110001=>[2,1,4,1]
[2,8,6,1,3,4,5,7]=>0110000=>[2,1,5]
[2,7,6,1,3,4,5,8]=>0110000=>[2,1,5]
[1,7,6,2,3,4,5,8]=>0110000=>[2,1,5]
[1,8,6,2,3,4,5,7]=>0110000=>[2,1,5]
[2,8,7,3,4,5,6,1]=>0110001=>[2,1,4,1]
[3,8,7,2,4,5,6,1]=>0110001=>[2,1,4,1]
[7,8,3,6,2,4,5,1]=>0101001=>[2,2,3,1]
[1,5,8,7,2,3,6,4]=>0011001=>[3,1,3,1]
[7,8,10,9,5,6,3,4,1,2]=>001101010=>[3,1,2,2,2]
[9,10,5,6,8,7,3,4,1,2]=>010011010=>[2,3,1,2,2]
[5,8,10,6,9,7,3,4,1,2]=>001011010=>[3,2,1,2,2]
[5,6,7,10,9,8,3,4,1,2]=>000111010=>[4,1,1,2,2]
[9,10,7,8,3,4,6,5,1,2]=>010100110=>[2,2,3,1,2]
[7,8,10,9,3,4,6,5,1,2]=>001100110=>[3,1,3,1,2]
[9,10,3,6,8,4,7,5,1,2]=>010010110=>[2,3,2,1,2]
[3,8,10,6,9,4,7,5,1,2]=>001010110=>[3,2,2,1,2]
[3,6,7,10,9,4,8,5,1,2]=>000110110=>[4,1,2,1,2]
[9,10,3,4,5,8,7,6,1,2]=>010001110=>[2,4,1,1,2]
[3,8,10,4,5,9,7,6,1,2]=>001001110=>[3,3,1,1,2]
[3,4,7,10,5,9,8,6,1,2]=>000101110=>[4,2,1,1,2]
[3,4,5,6,10,9,8,7,1,2]=>000011110=>[5,1,1,1,2]
[9,10,7,8,5,6,1,2,4,3]=>010101001=>[2,2,2,3,1]
[7,8,10,9,5,6,1,2,4,3]=>001101001=>[3,1,2,3,1]
[9,10,5,6,8,7,1,2,4,3]=>010011001=>[2,3,1,3,1]
[5,8,10,6,9,7,1,2,4,3]=>001011001=>[3,2,1,3,1]
[5,6,7,10,9,8,1,2,4,3]=>000111001=>[4,1,1,3,1]
[9,10,7,8,1,4,6,2,5,3]=>010100101=>[2,2,3,2,1]
[7,8,10,9,1,4,6,2,5,3]=>001100101=>[3,1,3,2,1]
[9,10,1,6,8,4,7,2,5,3]=>010010101=>[2,3,2,2,1]
[1,8,10,6,9,4,7,2,5,3]=>001010101=>[3,2,2,2,1]
[1,6,7,10,9,4,8,2,5,3]=>000110101=>[4,1,2,2,1]
[9,10,1,4,5,8,7,2,6,3]=>010001101=>[2,4,1,2,1]
[1,8,10,4,5,9,7,2,6,3]=>001001101=>[3,3,1,2,1]
[1,4,7,10,5,9,8,2,6,3]=>000101101=>[4,2,1,2,1]
[1,4,5,6,10,9,8,2,7,3]=>000011101=>[5,1,1,2,1]
[9,10,7,8,1,2,3,6,5,4]=>010100011=>[2,2,4,1,1]
[7,8,10,9,1,2,3,6,5,4]=>001100011=>[3,1,4,1,1]
[9,10,1,6,8,2,3,7,5,4]=>010010011=>[2,3,3,1,1]
[1,8,10,6,9,2,3,7,5,4]=>001010011=>[3,2,3,1,1]
[1,6,7,10,9,2,3,8,5,4]=>000110011=>[4,1,3,1,1]
[9,10,1,2,5,8,3,7,6,4]=>010001011=>[2,4,2,1,1]
[1,8,10,2,5,9,3,7,6,4]=>001001011=>[3,3,2,1,1]
[1,2,7,10,5,9,3,8,6,4]=>000101011=>[4,2,2,1,1]
[1,2,5,6,10,9,3,8,7,4]=>000011011=>[5,1,2,1,1]
[9,10,1,2,3,4,8,7,6,5]=>010000111=>[2,5,1,1,1]
[1,8,10,2,3,4,9,7,6,5]=>001000111=>[3,4,1,1,1]
[1,2,7,10,3,4,9,8,6,5]=>000100111=>[4,3,1,1,1]
[1,2,3,6,10,4,9,8,7,5]=>000010111=>[5,2,1,1,1]
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000111110=>[6,1,1,1,1,2]
[1,2,7,8,12,11,3,4,10,9,6,5]=>00001100111=>[5,1,3,1,1,1]
[1,2,3,6,7,12,11,4,10,9,8,5]=>00000110111=>[6,1,2,1,1,1]
[1,7,3,6,5,2,8,4]=>0101101=>[2,2,1,2,1]
[8,6,2,5,4,1,7,3]=>1101101=>[1,1,2,1,2,1]
[3,2,6,4,7,5,1,8]=>1010110=>[1,2,2,1,2]
[6,2,3,7,5,4,1,8]=>1001110=>[1,3,1,1,2]
[1,3,4,7,6,2,8,5]=>0001101=>[4,1,2,1]
[2,8,3,6,1,7,5,4]=>0101011=>[2,2,2,1,1]
[8,7,2,5,1,6,4,3]=>1101011=>[1,1,2,2,1,1]
[3,8,2,6,5,1,7,4]=>0101101=>[2,2,1,2,1]
[7,8,2,5,4,1,6,3]=>0101101=>[2,2,1,2,1]
[4,8,5,2,6,1,7,3]=>0110101=>[2,1,2,2,1]
[4,5,1,3,7,2,8,6]=>0100101=>[2,3,2,1]
[6,1,3,7,5,2,8,4]=>1001101=>[1,3,1,2,1]
[7,1,3,6,2,8,5,4]=>1001011=>[1,3,2,1,1]
[8,1,3,6,2,7,5,4]=>1001011=>[1,3,2,1,1]
[1,2,4,7,3,8,6,5]=>0001011=>[4,2,1,1]
[7,1,8,2,6,5,4,3]=>1010111=>[1,2,2,1,1,1]
[4,1,7,8,2,6,5,3]=>1001011=>[1,3,2,1,1]
[3,4,8,6,5,1,7,2]=>0011101=>[3,1,1,2,1]
[8,3,7,5,1,6,4,2]=>1011011=>[1,2,1,2,1,1]
[1,4,8,6,2,7,5,3]=>0011011=>[3,1,2,1,1]
[8,4,6,7,1,5,3,2]=>1001011=>[1,3,2,1,1]
[3,4,6,5,1,2,8,7]=>0011001=>[3,1,3,1]
[7,3,5,1,2,8,6,4]=>1010011=>[1,2,3,1,1]
[1,4,6,2,3,8,7,5]=>0010011=>[3,3,1,1]
[1,3,2,7,4,8,6,5]=>0101011=>[2,2,2,1,1]
[7,2,1,6,3,8,5,4]=>1101011=>[1,1,2,2,1,1]
[4,5,2,1,7,3,8,6]=>0110101=>[2,1,2,2,1]
[5,6,7,1,2,8,4,3]=>0010011=>[3,3,1,1]
[4,7,5,1,2,8,6,3]=>0110011=>[2,1,3,1,1]
[3,7,1,6,2,8,5,4]=>0101011=>[2,2,2,1,1]
[7,6,1,2,8,5,4,3]=>1100111=>[1,1,3,1,1,1]
[2,7,1,3,8,6,5,4]=>0100111=>[2,3,1,1,1]
[8,6,1,2,7,5,4,3]=>1100111=>[1,1,3,1,1,1]
[1,7,2,3,8,6,5,4]=>0100111=>[2,3,1,1,1]
[8,7,1,2,6,5,4,3]=>1100111=>[1,1,3,1,1,1]
[7,8,1,2,6,5,4,3]=>0100111=>[2,3,1,1,1]
[3,8,1,6,2,7,5,4]=>0101011=>[2,2,2,1,1]
[4,8,5,1,2,7,6,3]=>0110011=>[2,1,3,1,1]
[2,1,4,3,6,5,10,9,7,8]=>101010110=>[1,2,2,2,1,2]
[2,1,4,3,8,7,5,6,10,9]=>101011001=>[1,2,2,1,3,1]
[2,1,4,3,10,7,5,9,6,8]=>101011010=>[1,2,2,1,2,2]
[2,1,4,3,10,9,8,5,6,7]=>101011100=>[1,2,2,1,1,3]
[2,1,6,5,3,4,8,7,10,9]=>101100101=>[1,2,1,3,2,1]
[2,1,6,5,3,4,10,9,7,8]=>101100110=>[1,2,1,3,1,2]
[2,1,8,5,3,7,4,6,10,9]=>101101001=>[1,2,1,2,3,1]
[2,1,10,5,3,7,4,9,6,8]=>101101010=>[1,2,1,2,2,2]
[2,1,10,5,3,9,8,4,6,7]=>101101100=>[1,2,1,2,1,3]
[2,1,8,7,6,3,4,5,10,9]=>101110001=>[1,2,1,1,4,1]
[2,1,10,7,6,3,4,9,5,8]=>101110010=>[1,2,1,1,3,2]
[2,1,10,9,6,3,8,4,5,7]=>101110100=>[1,2,1,1,2,3]
[2,1,10,9,8,7,3,4,5,6]=>101111000=>[1,2,1,1,1,4]
[4,3,1,2,6,5,8,7,10,9]=>110010101=>[1,1,3,2,2,1]
[4,3,1,2,6,5,10,9,7,8]=>110010110=>[1,1,3,2,1,2]
[4,3,1,2,8,7,5,6,10,9]=>110011001=>[1,1,3,1,3,1]
[4,3,1,2,10,7,5,9,6,8]=>110011010=>[1,1,3,1,2,2]
[4,3,1,2,10,9,8,5,6,7]=>110011100=>[1,1,3,1,1,3]
[6,3,1,5,2,4,8,7,10,9]=>110100101=>[1,1,2,3,2,1]
[6,3,1,5,2,4,10,9,7,8]=>110100110=>[1,1,2,3,1,2]
[8,3,1,5,2,7,4,6,10,9]=>110101001=>[1,1,2,2,3,1]
[10,3,1,5,2,9,8,4,6,7]=>110101100=>[1,1,2,2,1,3]
[8,3,1,7,6,2,4,5,10,9]=>110110001=>[1,1,2,1,4,1]
[10,3,1,7,6,2,4,9,5,8]=>110110010=>[1,1,2,1,3,2]
[10,3,1,9,6,2,8,4,5,7]=>110110100=>[1,1,2,1,2,3]
[10,3,1,9,8,7,2,4,5,6]=>110111000=>[1,1,2,1,1,4]
[6,5,4,1,2,3,8,7,10,9]=>111000101=>[1,1,1,4,2,1]
[6,5,4,1,2,3,10,9,7,8]=>111000110=>[1,1,1,4,1,2]
[8,5,4,1,2,7,3,6,10,9]=>111001001=>[1,1,1,3,3,1]
[10,5,4,1,2,7,3,9,6,8]=>111001010=>[1,1,1,3,2,2]
[10,5,4,1,2,9,8,3,6,7]=>111001100=>[1,1,1,3,1,3]
[8,7,4,1,6,2,3,5,10,9]=>111010001=>[1,1,1,2,4,1]
[10,7,4,1,6,2,3,9,5,8]=>111010010=>[1,1,1,2,3,2]
[10,9,4,1,8,7,2,3,5,6]=>111011000=>[1,1,1,2,1,4]
[8,7,6,5,1,2,3,4,10,9]=>111100001=>[1,1,1,1,5,1]
[10,7,6,5,1,2,3,9,4,8]=>111100010=>[1,1,1,1,4,2]
[10,9,6,5,1,2,8,3,4,7]=>111100100=>[1,1,1,1,3,3]
[1,8,2,7,4,3,5,6]=>0101100=>[2,2,1,3]
[1,8,6,4,7,2,3,5]=>0110100=>[2,1,2,3]
[1,8,4,2,6,3,5,7]=>0110100=>[2,1,2,3]
[7,4,8,1,5,2,3,6]=>1010100=>[1,2,2,3]
[4,1,7,2,6,3,5,8]=>1010100=>[1,2,2,3]
[5,1,7,4,3,6,2,8]=>1011010=>[1,2,1,2,2]
[1,8,5,4,3,7,2,6]=>0111010=>[2,1,1,2,2]
[1,8,4,2,5,3,7,6]=>0110101=>[2,1,2,2,1]
[1,8,5,4,2,6,7,3]=>0111001=>[2,1,1,3,1]
[7,4,8,2,1,3,5,6]=>1011000=>[1,2,1,4]
[4,1,7,3,2,5,6,8]=>1011000=>[1,2,1,4]
[7,5,4,8,2,3,6,1]=>1101001=>[1,1,2,3,1]
[7,3,8,1,5,6,2,4]=>1010010=>[1,2,3,2]
[3,1,7,2,6,8,4,5]=>1010010=>[1,2,3,2]
[5,1,7,4,2,6,8,3]=>1011001=>[1,2,1,3,1]
[4,3,1,6,2,5,7,8]=>1101000=>[1,1,2,4]
[6,5,4,3,7,1,8,2]=>1110101=>[1,1,1,2,2,1]
[6,3,2,8,5,7,1,4]=>1101010=>[1,1,2,2,2]
[5,4,8,2,1,7,3,6]=>1011010=>[1,2,1,2,2]
[7,2,8,6,3,1,4,5]=>1011100=>[1,2,1,1,3]
[2,1,7,8,3,6,4,5]=>1001010=>[1,3,2,2]
[4,2,1,6,7,3,5,8]=>1100100=>[1,1,3,3]
[4,3,1,5,2,7,6,8]=>1101010=>[1,1,2,2,2]
[5,4,2,7,3,8,1,6]=>1101010=>[1,1,2,2,2]
[3,1,6,2,8,7,4,5]=>1010110=>[1,2,2,1,2]
[6,3,1,7,8,5,2,4]=>1100110=>[1,1,3,1,2]
[6,5,4,1,7,8,3,2]=>1110011=>[1,1,1,3,1,1]
[5,4,3,1,6,7,2,8]=>1110010=>[1,1,1,3,2]
[5,4,2,6,3,8,7,1]=>1101011=>[1,1,2,2,1,1]
[4,3,1,5,2,6,8,7]=>1101001=>[1,1,2,3,1]
[5,4,2,1,6,7,8,3]=>1110001=>[1,1,1,4,1]
[5,4,3,1,6,7,8,2]=>1110001=>[1,1,1,4,1]
[7,8,2,4,5,1,3,6]=>0100100=>[2,3,3]
[4,6,7,2,5,1,3,8]=>0010100=>[3,2,3]
[7,8,1,3,2,4,5,6]=>0101000=>[2,2,4]
[7,8,4,1,5,2,3,6]=>0110100=>[2,1,2,3]
[3,6,7,2,1,4,5,8]=>0011000=>[3,1,4]
[5,2,3,6,1,4,7,8]=>1001000=>[1,3,4]
[2,5,3,6,1,4,7,8]=>0101000=>[2,2,4]
[6,4,7,1,5,2,3,8]=>1010100=>[1,2,2,3]
[6,2,7,3,1,4,5,8]=>1011000=>[1,2,1,4]
[3,5,4,6,7,8,1,2]=>0100010=>[2,4,2]
[1,5,4,6,7,2,3,8]=>0100100=>[2,3,3]
[1,6,7,3,2,4,5,8]=>0011000=>[3,1,4]
[1,5,3,6,2,4,7,8]=>0101000=>[2,2,4]
[5,1,3,6,2,4,7,8]=>1001000=>[1,3,4]
[5,2,4,6,7,1,3,8]=>1000100=>[1,4,3]
[2,6,7,4,5,1,3,8]=>0010100=>[3,2,3]
[4,2,5,6,7,1,3,8]=>1000100=>[1,4,3]
[4,5,2,6,7,1,3,8]=>0100100=>[2,3,3]
[5,3,1,6,2,4,7,8]=>1101000=>[1,1,2,4]
[6,1,7,3,2,4,5,8]=>1011000=>[1,2,1,4]
[6,1,7,4,5,2,3,8]=>1010100=>[1,2,2,3]
[6,3,7,4,5,8,1,2]=>1010010=>[1,2,3,2]
[5,4,1,6,7,2,3,8]=>1100100=>[1,1,3,3]
[5,2,1,6,3,4,7,8]=>1101000=>[1,1,2,4]
[1,3,6,7,5,2,8,4]=>0001101=>[4,1,2,1]
[7,3,4,1,6,2,5,8]=>1010100=>[1,2,2,3]
[7,3,4,1,6,5,2,8]=>1010110=>[1,2,2,1,2]
[7,3,4,1,5,2,6,8]=>1010100=>[1,2,2,3]
[1,3,6,7,2,5,8,4]=>0001001=>[4,3,1]
[4,3,1,7,2,6,8,5]=>1101001=>[1,1,2,3,1]
[5,6,1,4,7,3,8,2]=>0100101=>[2,3,2,1]
[5,3,2,1,7,4,8,6]=>1110101=>[1,1,1,2,2,1]
[1,3,4,5,8,7,2,6]=>0000110=>[5,1,2]
[6,3,4,5,8,1,7,2]=>1000101=>[1,4,2,1]
[2,4,5,1,6,8,7,3]=>0010011=>[3,3,1,1]
[3,1,2,5,6,8,7,4]=>1000011=>[1,5,1,1]
[4,3,2,5,6,8,1,7]=>1100010=>[1,1,4,2]
[3,1,4,6,5,8,2,7]=>1001010=>[1,3,2,2]
[2,3,4,5,8,6,1,7]=>0000110=>[5,1,2]
[4,3,1,7,6,5,8,2]=>1101101=>[1,1,2,1,2,1]
[1,4,5,2,6,8,7,3]=>0010011=>[3,3,1,1]
[3,7,5,2,6,8,1,4]=>0110010=>[2,1,3,2]
[3,7,5,2,6,8,4,1]=>0110011=>[2,1,3,1,1]
[5,6,1,2,7,4,8,3]=>0100101=>[2,3,2,1]
[6,3,5,2,4,7,8,1]=>1010001=>[1,2,4,1]
[5,3,2,1,4,7,8,6]=>1110001=>[1,1,1,4,1]
[5,3,1,4,2,7,8,6]=>1101001=>[1,1,2,3,1]
[5,3,1,2,4,7,8,6]=>1100001=>[1,1,5,1]
[7,1,5,2,6,8,4,3]=>1010011=>[1,2,3,1,1]
[7,1,5,2,6,8,3,4]=>1010010=>[1,2,3,2]
[1,7,4,6,5,8,3,2]=>0101011=>[2,2,2,1,1]
[2,7,4,6,1,8,3,5]=>0101010=>[2,2,2,2]
[2,7,4,6,1,8,5,3]=>0101011=>[2,2,2,1,1]
[2,3,6,7,1,5,8,4]=>0001001=>[4,3,1]
[2,3,6,7,5,1,8,4]=>0001101=>[4,1,2,1]
[4,3,2,6,7,1,8,5]=>1100101=>[1,1,3,2,1]
[7,3,2,5,6,8,1,4]=>1100010=>[1,1,4,2]
[7,1,5,4,6,8,2,3]=>1010010=>[1,2,3,2]
[2,7,4,6,5,8,1,3]=>0101010=>[2,2,2,2]
[7,3,4,5,8,1,2,6]=>1000100=>[1,4,3]
[1,3,4,5,8,6,2,7]=>0000110=>[5,1,2]
[1,3,4,5,8,2,7,6]=>0000101=>[5,2,1]
[7,1,5,4,6,8,3,2]=>1010011=>[1,2,3,1,1]
[7,3,2,5,6,8,4,1]=>1100011=>[1,1,4,1,1]
[5,7,4,6,1,8,3,2]=>0101011=>[2,2,2,1,1]
[6,3,4,5,8,1,2,7]=>1000100=>[1,4,3]
[7,3,4,5,8,2,6,1]=>1000101=>[1,4,2,1]
[4,2,1,8,3,6,7,5]=>1101001=>[1,1,2,3,1]
[6,2,1,7,3,5,8,4]=>1101001=>[1,1,2,3,1]
[2,7,3,1,4,8,5,6]=>0110010=>[2,1,3,2]
[3,2,1,5,7,8,4,6]=>1100010=>[1,1,4,2]
[4,3,6,8,5,1,7,2]=>1001101=>[1,3,1,2,1]
[2,1,6,8,3,7,4,5]=>1001010=>[1,3,2,2]
[3,2,1,5,6,8,4,7]=>1100010=>[1,1,4,2]
[2,4,7,1,8,5,3,6]=>0010110=>[3,2,1,2]
[2,4,8,5,1,6,3,7]=>0011010=>[3,1,2,2]
[6,2,1,7,3,4,8,5]=>1101001=>[1,1,2,3,1]
[6,2,1,7,8,3,5,4]=>1100101=>[1,1,3,2,1]
[3,2,1,6,7,4,5,8]=>1100100=>[1,1,3,3]
[2,4,8,5,1,6,7,3]=>0011001=>[3,1,3,1]
[3,2,1,8,4,5,6,7]=>1101000=>[1,1,2,4]
[1,6,8,3,7,2,4,5]=>0010100=>[3,2,3]
[3,8,1,5,7,2,4,6]=>0100100=>[2,3,3]
[1,2,6,8,4,7,3,5]=>0001010=>[4,2,2]
[6,1,5,8,2,4,7,3]=>1001001=>[1,3,3,1]
[1,2,4,8,3,6,7,5]=>0001001=>[4,3,1]
[4,1,2,7,8,3,6,5]=>1000101=>[1,4,2,1]
[5,3,8,4,7,6,1,2]=>1010110=>[1,2,2,1,2]
[8,7,1,2,5,4,6,3]=>1100101=>[1,1,3,2,1]
[5,8,1,2,3,7,6,4]=>0100011=>[2,4,1,1]
[1,2,8,4,3,5,7,6]=>0011001=>[3,1,3,1]
[1,2,5,3,7,6,4,8]=>0010110=>[3,2,1,2]
[6,1,2,8,7,4,5,3]=>1001101=>[1,3,1,2,1]
[7,1,6,2,8,4,5,3]=>1010101=>[1,2,2,2,1]
[1,2,6,3,8,5,4,7]=>0010110=>[3,2,1,2]
[1,2,8,5,3,6,4,7]=>0011010=>[3,1,2,2]
[1,2,7,3,8,5,4,6]=>0010110=>[3,2,1,2]
[1,6,2,8,4,3,5,7]=>0101100=>[2,2,1,3]
[1,6,4,2,7,3,5,8]=>0110100=>[2,1,2,3]
[1,8,6,3,2,4,5,7]=>0111000=>[2,1,1,4]
[3,1,7,8,6,2,4,5]=>1001100=>[1,3,1,3]
[1,8,7,3,5,6,2,4]=>0110010=>[2,1,3,2]
[1,3,2,8,7,4,5,6]=>0101100=>[2,2,1,3]
[1,2,8,4,3,7,5,6]=>0011010=>[3,1,2,2]
[8,5,1,7,2,4,6,3]=>1101001=>[1,1,2,3,1]
[3,8,6,4,7,5,1,2]=>0110110=>[2,1,2,1,2]
[6,1,8,2,7,4,5,3]=>1010101=>[1,2,2,2,1]
[1,2,7,5,3,6,4,8]=>0011010=>[3,1,2,2]
[1,2,6,3,7,5,4,8]=>0010110=>[3,2,1,2]
[1,2,3,7,5,4,8,6]=>0001101=>[4,1,2,1]
[3,7,4,8,6,5,1,2]=>0101110=>[2,2,1,1,2]
[1,8,2,7,6,4,5,3]=>0101101=>[2,2,1,2,1]
[7,4,6,3,8,5,1,2]=>1010110=>[1,2,2,1,2]
[8,4,6,2,7,5,3,1]=>1010111=>[1,2,2,1,1,1]
[6,5,7,8,4,1,3,2]=>1001101=>[1,3,1,2,1]
[7,5,6,8,2,4,1,3]=>1001010=>[1,3,2,2]
[7,4,6,2,8,5,1,3]=>1010110=>[1,2,2,1,2]
[4,3,2,6,8,5,1,7]=>1100110=>[1,1,3,1,2]
[3,5,6,8,2,4,1,7]=>0001010=>[4,2,2]
[2,6,7,8,1,4,5,3]=>0001001=>[4,3,1]
[3,6,7,8,1,4,2,5]=>0001010=>[4,2,2]
[3,5,7,8,2,1,4,6]=>0001100=>[4,1,3]
[2,6,7,8,1,4,3,5]=>0001010=>[4,2,2]
[2,5,7,8,3,1,4,6]=>0001100=>[4,1,3]
[2,4,7,3,8,1,5,6]=>0010100=>[3,2,3]
[6,4,7,3,8,1,5,2]=>1010101=>[1,2,2,2,1]
[6,4,7,3,8,1,2,5]=>1010100=>[1,2,2,3]
[7,4,6,3,8,2,1,5]=>1010110=>[1,2,2,1,2]
[6,3,2,5,4,8,1,7]=>1101010=>[1,1,2,2,2]
[6,4,5,2,3,8,1,7]=>1010010=>[1,2,3,2]
[5,4,6,3,8,2,1,7]=>1010110=>[1,2,2,1,2]
[5,4,7,3,8,1,6,2]=>1010101=>[1,2,2,2,1]
[2,5,7,8,3,1,6,4]=>0001101=>[4,1,2,1]
[4,5,7,8,3,1,2,6]=>0001100=>[4,1,3]
[4,5,6,8,2,3,1,7]=>0001010=>[4,2,2]
[5,4,6,2,8,3,1,7]=>1010110=>[1,2,2,1,2]
[5,3,2,6,8,4,1,7]=>1100110=>[1,1,3,1,2]
[5,4,7,2,8,1,3,6]=>1010100=>[1,2,2,3]
[4,5,7,8,2,1,3,6]=>0001100=>[4,1,3]
[4,6,7,8,1,3,2,5]=>0001010=>[4,2,2]
[4,6,7,8,1,3,5,2]=>0001001=>[4,3,1]
[2,6,7,8,1,3,5,4]=>0001001=>[4,3,1]
[2,6,7,8,1,5,3,4]=>0001010=>[4,2,2]
[4,6,7,8,1,5,2,3]=>0001010=>[4,2,2]
[4,6,7,8,1,2,5,3]=>0001001=>[4,3,1]
[5,3,2,7,8,1,6,4]=>1100101=>[1,1,3,2,1]
[4,3,2,7,8,1,6,5]=>1100101=>[1,1,3,2,1]
[3,5,7,8,2,1,6,4]=>0001101=>[4,1,2,1]
[3,6,7,8,1,5,4,2]=>0001011=>[4,2,1,1]
[2,6,7,8,1,5,4,3]=>0001011=>[4,2,1,1]
[4,5,8,3,6,7,1,2]=>0010010=>[3,3,2]
[4,5,8,3,7,6,1,2]=>0010110=>[3,2,1,2]
[4,2,8,3,7,1,6,5]=>1010101=>[1,2,2,2,1]
[7,2,3,4,8,1,5,6]=>1000100=>[1,4,3]
[7,6,3,4,8,5,1,2]=>1100110=>[1,1,3,1,2]
[7,6,3,5,8,4,1,2]=>1100110=>[1,1,3,1,2]
[7,6,3,8,4,5,1,2]=>1101010=>[1,1,2,2,2]
[7,2,3,8,5,1,4,6]=>1001100=>[1,3,1,3]
[2,6,4,8,1,5,7,3]=>0101001=>[2,2,3,1]
[7,2,3,8,4,1,5,6]=>1001100=>[1,3,1,3]
[7,8,2,3,6,1,4,5]=>0100100=>[2,3,3]
[4,2,6,3,7,1,5,8]=>1010100=>[1,2,2,3]
[7,2,3,5,8,1,6,4]=>1000101=>[1,4,2,1]
[7,2,3,8,4,1,6,5]=>1001101=>[1,3,1,2,1]
[2,6,4,8,1,3,7,5]=>0101001=>[2,2,3,1]
[3,6,4,8,1,7,5,2]=>0101011=>[2,2,2,1,1]
[7,6,5,1,2,3,8,4]=>1110001=>[1,1,1,4,1]
[7,6,5,1,4,2,8,3]=>1110101=>[1,1,1,2,2,1]
[7,8,5,4,1,2,6,3]=>0111001=>[2,1,1,3,1]
[3,5,6,4,1,2,8,7]=>0011001=>[3,1,3,1]
[7,6,5,1,2,4,3,8]=>1110010=>[1,1,1,3,2]
[7,6,5,1,2,4,8,3]=>1110001=>[1,1,1,4,1]
[7,6,5,1,3,2,4,8]=>1110100=>[1,1,1,2,3]
[2,6,4,3,1,8,7,5]=>0111011=>[2,1,1,2,1,1]
[3,5,8,4,1,2,7,6]=>0011001=>[3,1,3,1]
[3,5,8,4,1,2,6,7]=>0011000=>[3,1,4]
[3,5,8,4,1,6,2,7]=>0011010=>[3,1,2,2]
[2,5,8,4,1,7,3,6]=>0011010=>[3,1,2,2]
[3,6,4,2,1,7,5,8]=>0111010=>[2,1,1,2,2]
[3,5,6,4,1,8,7,2]=>0011011=>[3,1,2,1,1]
[2,6,4,5,1,3,7,8]=>0101000=>[2,2,4]
[7,6,5,1,4,3,8,2]=>1110101=>[1,1,1,2,2,1]
[7,6,5,1,2,8,3,4]=>1110010=>[1,1,1,3,2]
[7,6,5,1,8,2,4,3]=>1110101=>[1,1,1,2,2,1]
[7,6,5,1,8,2,3,4]=>1110100=>[1,1,1,2,3]
[7,6,5,1,8,3,2,4]=>1110110=>[1,1,1,2,1,2]
[7,6,5,1,4,8,2,3]=>1110010=>[1,1,1,3,2]
[3,6,4,5,1,7,2,8]=>0101010=>[2,2,2,2]
[2,5,6,4,1,7,8,3]=>0011001=>[3,1,3,1]
[2,5,6,4,1,7,3,8]=>0011010=>[3,1,2,2]
[3,6,4,5,1,7,8,2]=>0101001=>[2,2,3,1]
[7,6,5,1,4,8,3,2]=>1110011=>[1,1,1,3,1,1]
[7,6,5,1,8,3,4,2]=>1110101=>[1,1,1,2,2,1]
[7,6,5,1,8,4,2,3]=>1110110=>[1,1,1,2,1,2]
[6,7,4,2,5,3,1,8]=>0110110=>[2,1,2,1,2]
[7,6,4,8,3,1,5,2]=>1101101=>[1,1,2,1,2,1]
[7,4,8,5,6,1,3,2]=>1010101=>[1,2,2,2,1]
[7,4,2,5,6,3,1,8]=>1100110=>[1,1,3,1,2]
[4,2,7,5,6,3,1,8]=>1010110=>[1,2,2,1,2]
[4,7,3,5,6,2,1,8]=>0100110=>[2,3,1,2]
[1,6,8,5,2,7,4,3]=>0011011=>[3,1,2,1,1]
[6,2,8,5,1,7,4,3]=>1011011=>[1,2,1,2,1,1]
[6,7,4,8,2,1,5,3]=>0101101=>[2,2,1,2,1]
[3,2,7,8,6,1,5,4]=>1001101=>[1,3,1,2,1]
[6,8,4,1,2,3,7,5]=>0110001=>[2,1,4,1]
[1,8,2,5,6,4,3,7]=>0100110=>[2,3,1,2]
[6,1,8,5,3,7,4,2]=>1011011=>[1,2,1,2,1,1]
[3,8,1,5,2,7,6,4]=>0101011=>[2,2,2,1,1]
[8,2,1,5,3,7,6,4]=>1101011=>[1,1,2,2,1,1]
[8,1,6,5,3,7,2,4]=>1011010=>[1,2,1,2,2]
[7,1,4,6,3,2,8,5]=>1001101=>[1,3,1,2,1]
[3,2,6,4,1,7,8,5]=>1011001=>[1,2,1,3,1]
[7,6,4,3,1,2,8,5]=>1111001=>[1,1,1,1,3,1]
[8,6,3,5,1,7,2,4]=>1101010=>[1,1,2,2,2]
[4,5,3,1,6,7,8,2]=>0110001=>[2,1,4,1]
[3,5,2,1,6,7,8,4]=>0110001=>[2,1,4,1]
[5,2,3,1,6,7,8,4]=>1010001=>[1,2,4,1]
[1,5,3,2,6,7,8,4]=>0110001=>[2,1,4,1]
[8,2,7,5,6,1,3,4]=>1010100=>[1,2,2,3]
[1,7,4,6,2,3,8,5]=>0101001=>[2,2,3,1]
[7,6,4,2,1,5,8,3]=>1111001=>[1,1,1,1,3,1]
[5,7,4,6,1,3,8,2]=>0101001=>[2,2,3,1]
[8,6,4,7,3,1,2,5]=>1101100=>[1,1,2,1,3]
[5,2,4,3,7,1,8,6]=>1010101=>[1,2,2,2,1]
[8,6,4,1,3,5,2,7]=>1110010=>[1,1,1,3,2]
[6,7,4,1,5,3,8,2]=>0110101=>[2,1,2,2,1]
[7,5,4,1,2,6,8,3]=>1110001=>[1,1,1,4,1]
[1,8,2,5,3,7,6,4]=>0101011=>[2,2,2,1,1]
[3,8,1,5,6,4,2,7]=>0100110=>[2,3,1,2]
[7,6,4,1,5,2,8,3]=>1110101=>[1,1,1,2,2,1]
[8,6,1,5,4,7,2,3]=>1101010=>[1,1,2,2,2]
[5,2,1,4,6,7,8,3]=>1100001=>[1,1,5,1]
[5,4,1,3,6,7,8,2]=>1100001=>[1,1,5,1]
[8,4,1,5,3,7,2,6]=>1101010=>[1,1,2,2,2]
[7,5,4,1,3,2,8,6]=>1110101=>[1,1,1,2,2,1]
[3,2,5,1,4,7,8,6]=>1010001=>[1,2,4,1]
[5,1,3,4,6,7,8,2]=>1000001=>[1,6,1]
[3,8,1,7,5,6,4,2]=>0101011=>[2,2,2,1,1]
[8,2,5,7,3,6,4,1]=>1001011=>[1,3,2,1,1]
[1,8,6,7,5,3,4,2]=>0101101=>[2,2,1,2,1]
[8,2,6,7,5,3,4,1]=>1001101=>[1,3,1,2,1]
[5,4,8,6,2,3,7,1]=>1011001=>[1,2,1,3,1]
[2,7,6,1,3,5,4,8]=>0110010=>[2,1,3,2]
[2,8,6,1,3,5,4,7]=>0110010=>[2,1,3,2]
[5,7,4,1,8,6,3,2]=>0110111=>[2,1,2,1,1,1]
[5,6,4,2,8,3,7,1]=>0110101=>[2,1,2,2,1]
[5,6,4,2,7,3,1,8]=>0110110=>[2,1,2,1,2]
[5,8,1,4,6,3,7,2]=>0100101=>[2,3,2,1]
[3,6,7,4,5,8,2,1]=>0010011=>[3,3,1,1]
[5,4,6,1,7,8,3,2]=>1010011=>[1,2,3,1,1]
[5,6,4,1,8,7,3,2]=>0110111=>[2,1,2,1,1,1]
[3,5,8,4,6,7,2,1]=>0010011=>[3,3,1,1]
[3,6,8,4,5,7,2,1]=>0010011=>[3,3,1,1]
[3,7,8,4,5,6,2,1]=>0010011=>[3,3,1,1]
[3,7,1,5,4,6,2,8]=>0101010=>[2,2,2,2]
[3,8,1,5,4,6,7,2]=>0101001=>[2,2,3,1]
[3,7,1,5,4,6,8,2]=>0101001=>[2,2,3,1]
[6,7,1,4,5,3,8,2]=>0100101=>[2,3,2,1]
[5,7,1,4,6,3,8,2]=>0100101=>[2,3,2,1]
[5,4,7,2,8,3,1,6]=>1010110=>[1,2,2,1,2]
[5,4,7,2,8,3,6,1]=>1010101=>[1,2,2,2,1]
[5,6,4,2,8,3,1,7]=>0110110=>[2,1,2,1,2]
[5,8,1,4,6,3,2,7]=>0100110=>[2,3,1,2]
[3,8,1,5,4,6,2,7]=>0101010=>[2,2,2,2]
[3,6,1,5,4,2,7,8]=>0101100=>[2,2,1,3]
[3,6,1,5,4,8,2,7]=>0101010=>[2,2,2,2]
[6,8,3,1,4,2,5,7]=>0110100=>[2,1,2,3]
[7,3,8,1,4,2,5,6]=>1010100=>[1,2,2,3]
[3,6,1,5,4,7,8,2]=>0101001=>[2,2,3,1]
[3,4,1,2,7,6,5,8]=>0100110=>[2,3,1,2]
[3,4,1,2,6,8,7,5]=>0100011=>[2,4,1,1]
[7,8,1,4,5,3,2,6]=>0100110=>[2,3,1,2]
[3,8,1,5,4,7,2,6]=>0101010=>[2,2,2,2]
[3,6,1,5,4,8,7,2]=>0101011=>[2,2,2,1,1]
[3,6,1,5,4,7,2,8]=>0101010=>[2,2,2,2]
[6,7,3,1,4,2,5,8]=>0110100=>[2,1,2,3]
[6,8,3,1,4,2,7,5]=>0110101=>[2,1,2,2,1]
[7,8,3,1,4,6,2,5]=>0110010=>[2,1,3,2]
[7,8,4,2,6,5,1,3]=>0110110=>[2,1,2,1,2]
[6,5,8,7,3,4,2,1]=>1011011=>[1,2,1,2,1,1]
[7,8,3,1,4,6,5,2]=>0110011=>[2,1,3,1,1]
[6,7,3,1,4,5,2,8]=>0110010=>[2,1,3,2]
[3,7,1,5,4,2,6,8]=>0101100=>[2,2,1,3]
[3,8,1,5,4,2,7,6]=>0101101=>[2,2,1,2,1]
[5,8,1,4,7,3,6,2]=>0100101=>[2,3,2,1]
[6,3,7,1,4,8,5,2]=>1010011=>[1,2,3,1,1]
[3,7,1,5,4,8,6,2]=>0101011=>[2,2,2,1,1]
[3,7,1,5,4,2,8,6]=>0101101=>[2,2,1,2,1]
[6,7,3,1,4,5,8,2]=>0110001=>[2,1,4,1]
[7,3,8,1,4,5,2,6]=>1010010=>[1,2,3,2]
[6,8,3,1,4,5,2,7]=>0110010=>[2,1,3,2]
[3,8,1,5,4,2,6,7]=>0101100=>[2,2,1,3]
[2,3,5,4,1,8,6,7]=>0011010=>[3,1,2,2]
[2,3,6,4,8,1,5,7]=>0010100=>[3,2,3]
[1,8,4,6,3,5,2,7]=>0101010=>[2,2,2,2]
[5,4,8,6,2,1,3,7]=>1011100=>[1,2,1,1,3]
[2,3,6,8,1,5,4,7]=>0001010=>[4,2,2]
[2,5,6,1,4,7,8,3]=>0010001=>[3,4,1]
[2,5,6,1,4,7,3,8]=>0010010=>[3,3,2]
[2,7,6,1,8,5,4,3]=>0110111=>[2,1,2,1,1,1]
[2,7,6,8,1,4,5,3]=>0101001=>[2,2,3,1]
[5,7,8,6,2,3,4,1]=>0011001=>[3,1,3,1]
[2,7,6,1,8,5,3,4]=>0110110=>[2,1,2,1,2]
[6,3,5,1,7,2,4,8]=>1010100=>[1,2,2,3]
[2,3,4,7,6,1,5,8]=>0001100=>[4,1,3]
[7,3,5,8,4,1,2,6]=>1001100=>[1,3,1,3]
[1,8,4,5,2,7,3,6]=>0101010=>[2,2,2,2]
[1,8,4,5,2,7,6,3]=>0101011=>[2,2,2,1,1]
[7,3,5,8,4,1,6,2]=>1001101=>[1,3,1,2,1]
[2,7,6,4,8,5,1,3]=>0110110=>[2,1,2,1,2]
[7,3,5,4,6,8,1,2]=>1010010=>[1,2,3,2]
[6,3,5,4,7,1,8,2]=>1010101=>[1,2,2,2,1]
[6,3,5,4,7,1,2,8]=>1010100=>[1,2,2,3]
[3,7,1,6,8,5,2,4]=>0100110=>[2,3,1,2]
[2,3,1,8,6,4,7,5]=>0101101=>[2,2,1,2,1]
[1,8,4,3,6,2,5,7]=>0110100=>[2,1,2,3]
[2,3,1,8,6,4,5,7]=>0101100=>[2,2,1,3]
[3,7,1,6,8,5,4,2]=>0100111=>[2,3,1,1,1]
[6,3,5,4,7,2,1,8]=>1010110=>[1,2,2,1,2]
[7,3,5,4,6,8,2,1]=>1010011=>[1,2,3,1,1]
[2,7,6,4,8,5,3,1]=>0110111=>[2,1,2,1,1,1]
[1,8,4,5,2,6,3,7]=>0101010=>[2,2,2,2]
[6,4,8,5,3,1,2,7]=>1011100=>[1,2,1,1,3]
[7,3,5,8,4,6,2,1]=>1001011=>[1,3,2,1,1]
[2,3,4,6,5,8,1,7]=>0001010=>[4,2,2]
[2,3,4,7,5,1,8,6]=>0001101=>[4,1,2,1]
[2,3,4,7,5,1,6,8]=>0001100=>[4,1,3]
[2,3,4,7,1,6,5,8]=>0001010=>[4,2,2]
[2,3,4,7,1,6,8,5]=>0001001=>[4,3,1]
[2,3,4,6,1,8,7,5]=>0001011=>[4,2,1,1]
[6,3,5,8,4,2,7,1]=>1001101=>[1,3,1,2,1]
[1,8,4,5,2,3,6,7]=>0101000=>[2,2,4]
[7,4,8,5,3,2,6,1]=>1011101=>[1,2,1,1,2,1]
[3,4,8,7,5,2,6,1]=>0011101=>[3,1,1,2,1]
[3,2,8,6,1,5,4,7]=>1011010=>[1,2,1,2,2]
[8,7,3,6,4,2,5,1]=>1101101=>[1,1,2,1,2,1]
[3,8,7,2,5,4,6,1]=>0110101=>[2,1,2,2,1]
[8,7,2,4,5,6,3,1]=>1100011=>[1,1,4,1,1]
[5,3,6,2,4,8,7,1]=>1010011=>[1,2,3,1,1]
[3,5,2,8,6,1,4,7]=>0101100=>[2,2,1,3]
[3,7,2,5,1,4,8,6]=>0101001=>[2,2,3,1]
[5,1,8,6,2,3,4,7]=>1011000=>[1,2,1,4]
[2,5,4,1,8,6,3,7]=>0110110=>[2,1,2,1,2]
[3,7,6,1,8,2,5,4]=>0110101=>[2,1,2,2,1]
[8,2,3,6,1,4,7,5]=>1001001=>[1,3,3,1]
[1,8,2,6,3,4,7,5]=>0101001=>[2,2,3,1]
[7,1,3,6,4,8,2,5]=>1001010=>[1,3,2,2]
[8,2,1,3,5,7,4,6]=>1100010=>[1,1,4,2]
[7,5,4,1,3,8,2,6]=>1110010=>[1,1,1,3,2]
[7,3,8,5,4,1,2,6]=>1011100=>[1,2,1,1,3]
[7,2,3,6,1,4,8,5]=>1001001=>[1,3,3,1]
[1,3,7,2,5,8,4,6]=>0010010=>[3,3,2]
[1,7,2,3,5,8,4,6]=>0100010=>[2,4,2]
[7,4,8,1,3,6,2,5]=>1010010=>[1,2,3,2]
[8,6,1,4,7,3,2,5]=>1100110=>[1,1,3,1,2]
[2,6,3,7,1,4,8,5]=>0101001=>[2,2,3,1]
[2,6,3,8,1,4,7,5]=>0101001=>[2,2,3,1]
[7,5,4,8,1,3,2,6]=>1101010=>[1,1,2,2,2]
[8,5,4,7,1,3,2,6]=>1101010=>[1,1,2,2,2]
[2,3,1,8,5,4,6,7]=>0101100=>[2,2,1,3]
[8,5,1,7,6,3,4,2]=>1101101=>[1,1,2,1,2,1]
[3,4,7,6,1,8,5,2]=>0011011=>[3,1,2,1,1]
[3,5,2,6,7,1,8,4]=>0100101=>[2,3,2,1]
[3,2,8,4,7,5,1,6]=>1010110=>[1,2,2,1,2]
[8,4,7,5,1,3,2,6]=>1011010=>[1,2,1,2,2]
[6,8,3,1,7,2,4,5]=>0110100=>[2,1,2,3]
[3,7,2,5,6,1,8,4]=>0100101=>[2,3,2,1]
[6,8,4,2,5,1,7,3]=>0110101=>[2,1,2,2,1]
[2,7,5,3,8,4,1,6]=>0110110=>[2,1,2,1,2]
[8,3,1,4,7,2,6,5]=>1100101=>[1,1,3,2,1]
[8,3,2,1,5,7,4,6]=>1110010=>[1,1,1,3,2]
[2,8,3,6,4,7,1,5]=>0101010=>[2,2,2,2]
[7,3,6,4,8,1,2,5]=>1010100=>[1,2,2,3]
[8,3,6,4,7,1,2,5]=>1010100=>[1,2,2,3]
[1,2,8,3,5,7,4,6]=>0010010=>[3,3,2]
[1,8,3,2,5,7,4,6]=>0110010=>[2,1,3,2]
[6,5,1,7,4,2,8,3]=>1101101=>[1,1,2,1,2,1]
[7,3,6,4,8,2,1,5]=>1010110=>[1,2,2,1,2]
[4,6,1,7,3,5,2,8]=>0101010=>[2,2,2,2]
[5,6,1,7,3,4,2,8]=>0101010=>[2,2,2,2]
[6,1,7,3,4,2,8,5]=>1010101=>[1,2,2,2,1]
[7,3,8,1,6,5,2,4]=>1010110=>[1,2,2,1,2]
[8,3,7,1,6,5,2,4]=>1010110=>[1,2,2,1,2]
[2,8,1,7,6,5,3,4]=>0101110=>[2,2,1,1,2]
[4,2,8,6,5,1,7,3]=>1011101=>[1,2,1,1,2,1]
[8,6,4,7,1,5,2,3]=>1101010=>[1,1,2,2,2]
[7,6,4,8,1,5,2,3]=>1101010=>[1,1,2,2,2]
[5,1,6,4,2,3,8,7]=>1011001=>[1,2,1,3,1]
[4,2,3,8,7,5,1,6]=>1001110=>[1,3,1,1,2]
[3,8,7,1,6,5,2,4]=>0110110=>[2,1,2,1,2]
[2,4,3,8,1,6,7,5]=>0101001=>[2,2,3,1]
[2,4,3,7,1,6,8,5]=>0101001=>[2,2,3,1]
[4,2,3,7,8,5,1,6]=>1000110=>[1,4,1,2]
[5,1,6,4,2,3,7,8]=>1011000=>[1,2,1,4]
[6,4,7,8,1,5,2,3]=>1001010=>[1,3,2,2]
[8,7,4,6,1,5,2,3]=>1101010=>[1,1,2,2,2]
[6,5,7,8,1,4,2,3]=>1001010=>[1,3,2,2]
[4,7,8,6,1,5,2,3]=>0011010=>[3,1,2,2]
[3,2,4,8,7,1,5,6]=>1001100=>[1,3,1,3]
[4,8,7,6,1,5,2,3]=>0111010=>[2,1,1,2,2]
[5,8,7,6,1,4,2,3]=>0111010=>[2,1,1,2,2]
[8,6,5,7,1,4,2,3]=>1101010=>[1,1,2,2,2]
[5,1,6,7,4,2,3,8]=>1001100=>[1,3,1,3]
[6,7,4,8,1,5,2,3]=>0101010=>[2,2,2,2]
[8,4,7,6,1,5,2,3]=>1011010=>[1,2,1,2,2]
[8,3,2,4,7,1,5,6]=>1100100=>[1,1,3,3]
[7,3,2,4,8,1,5,6]=>1100100=>[1,1,3,3]
[2,5,3,7,1,6,4,8]=>0101010=>[2,2,2,2]
[8,4,6,7,1,5,2,3]=>1001010=>[1,3,2,2]
[5,1,6,8,4,2,3,7]=>1001100=>[1,3,1,3]
[4,2,3,7,5,1,6,8]=>1001100=>[1,3,1,3]
[2,4,3,7,1,6,5,8]=>0101010=>[2,2,2,2]
[2,4,7,1,5,8,6,3]=>0010011=>[3,3,1,1]
[3,2,4,7,6,1,5,8]=>1001100=>[1,3,1,3]
[4,7,6,8,1,5,2,3]=>0101010=>[2,2,2,2]
[8,5,6,7,1,4,2,3]=>1001010=>[1,3,2,2]
[8,6,7,5,1,4,2,3]=>1011010=>[1,2,1,2,2]
[6,8,7,5,1,4,2,3]=>0111010=>[2,1,1,2,2]
[5,6,8,7,1,4,2,3]=>0011010=>[3,1,2,2]
[4,6,8,7,1,5,2,3]=>0011010=>[3,1,2,2]
[3,2,4,6,1,5,7,8]=>1001000=>[1,3,4]
[6,7,8,5,1,4,2,3]=>0011010=>[3,1,2,2]
[7,8,6,5,1,4,2,3]=>0111010=>[2,1,1,2,2]
[2,1,8,5,4,6,3,7]=>1011010=>[1,2,1,2,2]
[4,1,8,5,2,3,6,7]=>1011000=>[1,2,1,4]
[5,4,1,3,6,7,2,8]=>1100010=>[1,1,4,2]
[8,4,1,2,6,3,7,5]=>1100101=>[1,1,3,2,1]
[8,2,7,1,5,3,4,6]=>1010100=>[1,2,2,3]
[3,2,7,1,5,8,4,6]=>1010010=>[1,2,3,2]
[7,3,8,1,5,4,2,6]=>1010110=>[1,2,2,1,2]
[7,1,5,3,8,4,2,6]=>1010110=>[1,2,2,1,2]
[3,6,8,1,5,4,2,7]=>0010110=>[3,2,1,2]
[6,8,3,1,5,4,2,7]=>0110110=>[2,1,2,1,2]
[7,6,3,1,5,4,2,8]=>1110110=>[1,1,1,2,1,2]
[3,6,2,1,5,8,4,7]=>0110010=>[2,1,3,2]
[8,6,2,1,5,3,4,7]=>1110100=>[1,1,1,2,3]
[2,3,8,1,5,7,4,6]=>0010010=>[3,3,2]
[7,1,3,2,8,6,4,5]=>1010110=>[1,2,2,1,2]
[4,7,1,2,6,3,8,5]=>0100101=>[2,3,2,1]
[2,7,8,1,5,3,4,6]=>0010100=>[3,2,3]
[6,7,2,1,5,3,4,8]=>0110100=>[2,1,2,3]
[4,7,2,1,8,5,3,6]=>0110110=>[2,1,2,1,2]
[8,7,2,1,4,5,3,6]=>1110010=>[1,1,1,3,2]
[5,7,8,6,1,4,3,2]=>0011011=>[3,1,2,1,1]
[2,7,4,1,6,5,3,8]=>0110110=>[2,1,2,1,2]
[7,1,6,4,5,8,3,2]=>1010011=>[1,2,3,1,1]
[2,6,4,1,7,5,3,8]=>0110110=>[2,1,2,1,2]
[5,6,8,7,1,4,3,2]=>0011011=>[3,1,2,1,1]
[4,2,8,1,6,5,3,7]=>1010110=>[1,2,2,1,2]
[6,2,4,1,8,5,3,7]=>1010110=>[1,2,2,1,2]
[8,3,1,4,5,6,7,2]=>1100001=>[1,1,5,1]
[5,3,1,4,8,6,7,2]=>1100101=>[1,1,3,2,1]
[7,5,1,6,3,4,8,2]=>1101001=>[1,1,2,3,1]
[7,1,5,8,4,3,6,2]=>1001101=>[1,3,1,2,1]
[5,8,1,6,4,3,7,2]=>0101101=>[2,2,1,2,1]
[5,3,1,8,4,6,7,2]=>1101001=>[1,1,2,3,1]
[8,3,1,5,4,6,7,2]=>1101001=>[1,1,2,3,1]
[8,2,6,1,4,5,3,7]=>1010010=>[1,2,3,2]
[6,2,8,1,4,5,3,7]=>1010010=>[1,2,3,2]
[7,2,6,1,5,3,4,8]=>1010100=>[1,2,2,3]
[2,8,6,1,5,3,4,7]=>0110100=>[2,1,2,3]
[4,2,1,5,6,3,8,7]=>1100101=>[1,1,3,2,1]
[7,1,2,5,8,3,4,6]=>1000100=>[1,4,3]
[7,1,4,5,6,8,3,2]=>1000011=>[1,5,1,1]
[2,6,7,1,4,5,3,8]=>0010010=>[3,3,2]
[3,5,1,7,4,6,8,2]=>0101001=>[2,2,3,1]
[7,1,5,6,4,8,3,2]=>1001011=>[1,3,2,1,1]
[7,1,6,5,4,8,3,2]=>1011011=>[1,2,1,2,1,1]
[2,7,6,1,4,5,3,8]=>0110010=>[2,1,3,2]
[5,7,6,8,1,4,3,2]=>0101011=>[2,2,2,1,1]
[7,8,6,5,1,4,3,2]=>0111011=>[2,1,1,2,1,1]
[5,3,1,2,4,8,7,6]=>1100011=>[1,1,4,1,1]
[5,3,6,2,1,8,7,4]=>1011011=>[1,2,1,2,1,1]
[5,3,7,2,8,4,1,6]=>1010110=>[1,2,2,1,2]
[7,2,4,5,8,3,1,6]=>1000110=>[1,4,1,2]
[7,2,4,5,1,3,6,8]=>1001000=>[1,3,4]
[6,2,4,5,1,8,7,3]=>1001011=>[1,3,2,1,1]
[3,1,4,5,2,8,7,6]=>1001011=>[1,3,2,1,1]
[1,6,4,5,2,8,7,3]=>0101011=>[2,2,2,1,1]
[3,7,4,5,1,2,6,8]=>0101000=>[2,2,4]
[1,7,4,2,6,3,5,8]=>0110100=>[2,1,2,3]
[8,7,4,5,2,1,6,3]=>1101101=>[1,1,2,1,2,1]
[6,3,7,1,8,4,2,5]=>1010110=>[1,2,2,1,2]
[5,7,4,1,6,3,2,8]=>0110110=>[2,1,2,1,2]
[1,7,4,8,6,3,2,5]=>0101110=>[2,2,1,1,2]
[5,7,4,8,6,3,1,2]=>0101110=>[2,2,1,1,2]
[4,8,3,5,6,7,1,2]=>0100010=>[2,4,2]
[1,8,3,5,6,7,2,4]=>0100010=>[2,4,2]
[4,8,1,5,6,7,2,3]=>0100010=>[2,4,2]
[4,1,3,5,6,7,2,8]=>1000010=>[1,5,2]
[5,8,4,3,6,1,2,7]=>0110100=>[2,1,2,3]
[5,3,8,4,1,7,2,6]=>1011010=>[1,2,1,2,2]
[1,5,8,4,6,7,3,2]=>0010011=>[3,3,1,1]
[1,4,8,3,6,7,5,2]=>0010011=>[3,3,1,1]
[4,3,8,2,1,7,5,6]=>1011010=>[1,2,1,2,2]
[3,8,4,2,6,1,5,7]=>0110100=>[2,1,2,3]
[3,8,1,5,6,7,4,2]=>0100011=>[2,4,1,1]
[3,8,2,5,6,7,1,4]=>0100010=>[2,4,2]
[8,2,1,5,6,7,4,3]=>1100011=>[1,1,4,1,1]
[8,1,3,5,6,7,4,2]=>1000011=>[1,5,1,1]
[7,1,4,3,6,2,5,8]=>1010100=>[1,2,2,3]
[7,8,4,3,6,2,1,5]=>0110110=>[2,1,2,1,2]
[4,3,1,8,5,7,6,2]=>1101011=>[1,1,2,2,1,1]
[6,3,5,8,2,7,1,4]=>1001010=>[1,3,2,2]
[7,5,4,8,6,2,1,3]=>1101110=>[1,1,2,1,1,2]
[7,1,4,8,6,2,3,5]=>1001100=>[1,3,1,3]
[7,5,4,1,6,2,3,8]=>1110100=>[1,1,1,2,3]
[1,6,4,5,8,2,3,7]=>0100100=>[2,3,3]
[1,8,5,3,6,7,4,2]=>0110011=>[2,1,3,1,1]
[8,3,5,2,1,7,4,6]=>1011010=>[1,2,1,2,2]
[4,1,8,5,6,7,3,2]=>1010011=>[1,2,3,1,1]
[1,2,8,5,6,7,3,4]=>0010010=>[3,3,2]
[4,2,1,5,6,7,3,8]=>1100010=>[1,1,4,2]
[1,5,3,8,6,7,4,2]=>0101011=>[2,2,2,1,1]
[1,4,8,5,6,7,2,3]=>0010010=>[3,3,2]
[6,2,4,3,8,7,5,1]=>1010111=>[1,2,2,1,1,1]
[7,3,5,4,1,8,6,2]=>1011011=>[1,2,1,2,1,1]
[5,2,7,1,3,4,8,6]=>1010001=>[1,2,4,1]
[2,6,5,7,3,1,4,8]=>0101100=>[2,2,1,3]
[2,6,5,7,3,1,8,4]=>0101101=>[2,2,1,2,1]
[6,3,1,4,7,8,5,2]=>1100011=>[1,1,4,1,1]
[6,8,2,1,3,4,5,7]=>0110000=>[2,1,5]
[3,7,1,8,4,5,2,6]=>0101010=>[2,2,2,2]
[6,3,2,4,7,5,8,1]=>1100101=>[1,1,3,2,1]
[6,3,2,4,7,5,1,8]=>1100110=>[1,1,3,1,2]
[4,2,1,6,3,7,5,8]=>1101010=>[1,1,2,2,2]
[4,2,1,6,3,7,8,5]=>1101001=>[1,1,2,3,1]
[7,4,3,5,8,6,1,2]=>1100110=>[1,1,3,1,2]
[2,7,6,8,3,1,4,5]=>0101100=>[2,2,1,3]
[7,4,3,5,8,6,2,1]=>1100111=>[1,1,3,1,1,1]
[4,2,1,7,3,8,6,5]=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,7,8,6,5]=>1100011=>[1,1,4,1,1]
[5,8,1,7,4,3,6,2]=>0101101=>[2,2,1,2,1]
[5,8,1,7,4,3,2,6]=>0101110=>[2,2,1,1,2]
[3,7,8,6,2,1,4,5]=>0011100=>[3,1,1,3]
[4,2,1,8,3,5,6,7]=>1101000=>[1,1,2,4]
[4,2,1,3,6,7,5,8]=>1100010=>[1,1,4,2]
[4,2,1,3,7,5,6,8]=>1100100=>[1,1,3,3]
[7,3,2,4,8,6,5,1]=>1100111=>[1,1,3,1,1,1]
[4,2,1,7,3,5,6,8]=>1101000=>[1,1,2,4]
[3,6,7,5,2,1,4,8]=>0011100=>[3,1,1,3]
[3,6,7,5,2,1,8,4]=>0011101=>[3,1,1,2,1]
[7,3,4,2,6,8,5,1]=>1010011=>[1,2,3,1,1]
[4,8,6,2,7,3,5,1]=>0110101=>[2,1,2,2,1]
[7,3,4,2,6,8,1,5]=>1010010=>[1,2,3,2]
[3,6,7,5,2,4,8,1]=>0011001=>[3,1,3,1]
[3,6,7,5,2,4,1,8]=>0011010=>[3,1,2,2]
[4,2,1,7,3,6,8,5]=>1101001=>[1,1,2,3,1]
[3,7,6,8,4,2,5,1]=>0101101=>[2,2,1,2,1]
[5,8,1,7,4,2,6,3]=>0101101=>[2,2,1,2,1]
[3,7,8,6,2,4,5,1]=>0011001=>[3,1,3,1]
[4,2,1,3,8,6,7,5]=>1100101=>[1,1,3,2,1]
[4,2,1,3,5,7,6,8]=>1100010=>[1,1,4,2]
[4,8,1,7,3,6,5,2]=>0101011=>[2,2,2,1,1]
[4,2,1,8,3,7,6,5]=>1101011=>[1,1,2,2,1,1]
[4,2,1,3,5,6,8,7]=>1100001=>[1,1,5,1]
[7,8,2,4,1,3,6,5]=>0101001=>[2,2,3,1]
[2,6,1,5,4,7,8,3]=>0101001=>[2,2,3,1]
[4,6,3,5,8,7,1,2]=>0100110=>[2,3,1,2]
[2,3,6,8,4,1,5,7]=>0001100=>[4,1,3]
[2,7,5,1,8,3,4,6]=>0110100=>[2,1,2,3]
[4,7,5,2,1,3,6,8]=>0111000=>[2,1,1,4]
[3,5,6,2,4,1,7,8]=>0010100=>[3,2,3]
[3,1,8,5,2,7,6,4]=>1011011=>[1,2,1,2,1,1]
[8,3,7,6,1,4,5,2]=>1011001=>[1,2,1,3,1]
[3,1,7,8,2,5,6,4]=>1001001=>[1,3,3,1]
[4,8,1,5,2,7,3,6]=>0101010=>[2,2,2,2]
[4,1,2,5,3,8,7,6]=>1001011=>[1,3,2,1,1]
[4,3,6,8,7,5,1,2]=>1001110=>[1,3,1,1,2]
[6,4,8,1,2,5,3,7]=>1010010=>[1,2,3,2]
[6,7,3,1,4,8,5,2]=>0110011=>[2,1,3,1,1]
[6,5,1,2,3,4,8,7]=>1100001=>[1,1,5,1]
[1,2,6,7,5,3,8,4]=>0001101=>[4,1,2,1]
[1,7,5,3,2,8,4,6]=>0111010=>[2,1,1,2,2]
[1,6,5,7,2,3,8,4]=>0101001=>[2,2,3,1]
[1,3,8,2,6,5,7,4]=>0010101=>[3,2,2,1]
[1,2,5,7,6,3,4,8]=>0001100=>[4,1,3]
[1,3,4,8,2,5,7,6]=>0001001=>[4,3,1]
[1,5,7,6,2,3,4,8]=>0011000=>[3,1,4]
[1,5,3,8,2,6,4,7]=>0101010=>[2,2,2,2]
[1,4,8,3,2,5,7,6]=>0011001=>[3,1,3,1]
[1,2,4,8,3,5,7,6]=>0001001=>[4,3,1]
[1,3,8,4,2,6,7,5]=>0011001=>[3,1,3,1]
[1,4,8,2,3,5,7,6]=>0010001=>[3,4,1]
[4,2,6,7,5,8,3,1]=>1001011=>[1,3,2,1,1]
[6,7,5,2,1,8,4,3]=>0111011=>[2,1,1,2,1,1]
[3,4,8,7,5,2,1,6]=>0011110=>[3,1,1,1,2]
[1,7,5,2,8,4,6,3]=>0110101=>[2,1,2,2,1]
[5,6,8,3,1,7,2,4]=>0011010=>[3,1,2,2]
[6,1,4,8,3,2,7,5]=>1001101=>[1,3,1,2,1]
[3,4,7,1,8,6,2,5]=>0010110=>[3,2,1,2]
[3,4,6,8,2,1,5,7]=>0001100=>[4,1,3]
[3,8,2,5,6,1,4,7]=>0100100=>[2,3,3]
[3,5,2,8,6,4,1,7]=>0101110=>[2,2,1,1,2]
[4,2,5,7,3,8,6,1]=>1001011=>[1,3,2,1,1]
[7,4,2,5,3,8,1,6]=>1101010=>[1,1,2,2,2]
[1,5,6,8,3,4,2,7]=>0001010=>[4,2,2]
[4,5,1,6,8,3,2,7]=>0100110=>[2,3,1,2]
[4,5,7,3,8,2,6,1]=>0010101=>[3,2,2,1]
[6,4,3,7,8,2,5,1]=>1100101=>[1,1,3,2,1]
[6,4,3,1,7,8,2,5]=>1110010=>[1,1,1,3,2]
[4,5,3,1,7,8,2,6]=>0110010=>[2,1,3,2]
[7,1,3,5,4,8,2,6]=>1001010=>[1,3,2,2]
[7,5,2,8,1,4,3,6]=>1101010=>[1,1,2,2,2]
[1,4,5,7,3,8,6,2]=>0001011=>[4,2,1,1]
[4,6,3,7,8,5,2,1]=>0100111=>[2,3,1,1,1]
[1,5,3,6,7,8,4,2]=>0100011=>[2,4,1,1]
[4,6,1,7,3,8,5,2]=>0101011=>[2,2,2,1,1]
[6,7,2,4,8,1,5,3]=>0100101=>[2,3,2,1]
[5,2,3,6,7,8,4,1]=>1000011=>[1,5,1,1]
[6,4,2,7,1,8,3,5]=>1101010=>[1,1,2,2,2]
[4,2,6,3,7,8,5,1]=>1010011=>[1,2,3,1,1]
[6,7,3,8,2,4,5,1]=>0101001=>[2,2,3,1]
[3,6,2,7,4,1,8,5]=>0101101=>[2,2,1,2,1]
[6,7,3,2,1,4,8,5]=>0111001=>[2,1,1,3,1]
[7,2,4,8,6,1,3,5]=>1001100=>[1,3,1,3]
[3,5,7,2,1,8,6,4]=>0011011=>[3,1,2,1,1]
[6,7,8,3,2,5,1,4]=>0011010=>[3,1,2,2]
[6,3,7,8,2,5,4,1]=>1001011=>[1,3,2,1,1]
[2,6,7,4,8,5,3,1]=>0010111=>[3,2,1,1,1]
[6,2,4,7,1,8,5,3]=>1001011=>[1,3,2,1,1]
[1,7,4,8,5,2,6,3]=>0101101=>[2,2,1,2,1]
[1,3,7,8,5,2,6,4]=>0001101=>[4,1,2,1]
[2,5,7,8,1,6,3,4]=>0001010=>[4,2,2]
[1,6,4,7,8,2,5,3]=>0100101=>[2,3,2,1]
[2,5,6,1,7,8,4,3]=>0010011=>[3,3,1,1]
[5,6,1,2,7,8,4,3]=>0100011=>[2,4,1,1]
[6,7,2,1,8,5,3,4]=>0110110=>[2,1,2,1,2]
[6,4,5,2,3,8,7,1]=>1010011=>[1,2,3,1,1]
[4,6,5,2,3,1,8,7]=>0110101=>[2,1,2,2,1]
[6,4,2,5,3,1,8,7]=>1101101=>[1,1,2,1,2,1]
[6,4,2,5,3,8,7,1]=>1101011=>[1,1,2,2,1,1]
[8,6,4,7,5,2,3,1]=>1101101=>[1,1,2,1,2,1]
[8,6,2,7,4,5,3,1]=>1101011=>[1,1,2,2,1,1]
[6,4,2,5,8,7,3,1]=>1100111=>[1,1,3,1,1,1]
[4,6,5,2,3,8,7,1]=>0110011=>[2,1,3,1,1]
[6,8,2,7,4,5,3,1]=>0101011=>[2,2,2,1,1]
[8,6,4,7,2,5,3,1]=>1101011=>[1,1,2,2,1,1]
[8,6,2,4,7,5,3,1]=>1100111=>[1,1,3,1,1,1]
[6,8,2,4,7,5,3,1]=>0100111=>[2,3,1,1,1]
[4,8,2,6,7,5,3,1]=>0100111=>[2,3,1,1,1]
[2,8,4,6,7,5,3,1]=>0100111=>[2,3,1,1,1]
[2,8,6,7,4,5,3,1]=>0101011=>[2,2,2,1,1]
[6,8,7,2,4,5,3,1]=>0110011=>[2,1,3,1,1]
[2,6,4,5,8,7,3,1]=>0100111=>[2,3,1,1,1]
[2,6,4,8,7,5,3,1]=>0101111=>[2,2,1,1,1,1]
[4,6,2,8,7,5,3,1]=>0101111=>[2,2,1,1,1,1]
[8,2,4,6,7,5,3,1]=>1000111=>[1,4,1,1,1]
[6,2,4,8,7,5,3,1]=>1001111=>[1,3,1,1,1,1]
[4,2,6,8,7,5,3,1]=>1001111=>[1,3,1,1,1,1]
[4,2,6,5,8,7,3,1]=>1010111=>[1,2,2,1,1,1]
[6,2,4,5,8,7,3,1]=>1000111=>[1,4,1,1,1]
[8,2,6,7,4,5,3,1]=>1001011=>[1,3,2,1,1]
[8,6,7,2,4,5,3,1]=>1010011=>[1,2,3,1,1]
[6,4,5,8,7,2,3,1]=>1001101=>[1,3,1,2,1]
[8,6,7,4,2,5,3,1]=>1011011=>[1,2,1,2,1,1]
[8,4,6,7,2,5,3,1]=>1001011=>[1,3,2,1,1]
[6,4,8,7,2,5,3,1]=>1011011=>[1,2,1,2,1,1]
[6,2,8,7,4,5,3,1]=>1011011=>[1,2,1,2,1,1]
[4,6,5,8,7,2,3,1]=>0101101=>[2,2,1,2,1]
[2,1,6,8,7,4,5,3]=>1001101=>[1,3,1,2,1]
[2,6,8,7,4,5,3,1]=>0011011=>[3,1,2,1,1]
[2,4,8,6,7,5,3,1]=>0010111=>[3,2,1,1,1]
[6,2,8,4,7,5,3,1]=>1010111=>[1,2,2,1,1,1]
[8,2,6,4,7,5,3,1]=>1010111=>[1,2,2,1,1,1]
[4,6,8,2,7,5,3,1]=>0010111=>[3,2,1,1,1]
[2,6,8,4,7,5,3,1]=>0010111=>[3,2,1,1,1]
[4,6,8,7,2,5,3,1]=>0011011=>[3,1,2,1,1]
[4,6,5,8,2,7,3,1]=>0101011=>[2,2,2,1,1]
[2,1,6,8,4,7,5,3]=>1001011=>[1,3,2,1,1]
[2,1,8,6,4,7,5,3]=>1011011=>[1,2,1,2,1,1]
[6,8,7,4,2,5,3,1]=>0111011=>[2,1,1,2,1,1]
[2,8,6,4,7,5,3,1]=>0110111=>[2,1,2,1,1,1]
[4,8,6,2,7,5,3,1]=>0110111=>[2,1,2,1,1,1]
[3,7,8,5,6,1,2,4]=>0010100=>[3,2,3]
[3,6,1,8,4,7,2,5]=>0101010=>[2,2,2,2]
[3,1,6,8,4,7,2,5]=>1001010=>[1,3,2,2]
[4,1,6,8,3,2,7,5]=>1001101=>[1,3,1,2,1]
[4,6,1,8,3,2,7,5]=>0101101=>[2,2,1,2,1]
[4,7,8,1,3,2,6,5]=>0010101=>[3,2,2,1]
[4,7,8,3,1,2,6,5]=>0011001=>[3,1,3,1]
[2,7,8,3,4,6,5,1]=>0010011=>[3,3,1,1]
[4,7,8,2,1,3,6,5]=>0011001=>[3,1,3,1]
[4,6,1,8,2,3,7,5]=>0101001=>[2,2,3,1]
[4,5,2,1,8,3,7,6]=>0110101=>[2,1,2,2,1]
[4,6,2,8,1,3,7,5]=>0101001=>[2,2,3,1]
[3,6,2,8,4,7,1,5]=>0101010=>[2,2,2,2]
[2,3,6,8,4,7,5,1]=>0001011=>[4,2,1,1]
[3,2,6,8,4,7,1,5]=>1001010=>[1,3,2,2]
[4,2,6,8,3,1,7,5]=>1001101=>[1,3,1,2,1]
[4,2,5,1,8,3,7,6]=>1010101=>[1,2,2,2,1]
[5,1,2,4,3,8,7,6]=>1001011=>[1,3,2,1,1]
[5,2,4,1,3,8,7,6]=>1010011=>[1,2,3,1,1]
[4,2,5,3,8,1,7,6]=>1010101=>[1,2,2,2,1]
[3,2,5,4,8,7,1,6]=>1010110=>[1,2,2,1,2]
[3,5,2,4,8,7,1,6]=>0100110=>[2,3,1,2]
[5,1,4,2,3,8,7,6]=>1010011=>[1,2,3,1,1]
[5,4,3,1,2,8,7,6]=>1110011=>[1,1,1,3,1,1]
[4,5,3,1,8,2,7,6]=>0110101=>[2,1,2,2,1]
[4,5,1,3,8,2,7,6]=>0100101=>[2,3,2,1]
[3,1,5,4,8,7,2,6]=>1010110=>[1,2,2,1,2]
[3,5,4,1,8,7,2,6]=>0110110=>[2,1,2,1,2]
[3,6,5,8,7,1,2,4]=>0101100=>[2,2,1,3]
[3,4,1,5,8,7,2,6]=>0100110=>[2,3,1,2]
[4,1,3,5,8,2,7,6]=>1000101=>[1,4,2,1]
[4,3,6,8,2,1,7,5]=>1001101=>[1,3,1,2,1]
[2,4,6,8,3,7,5,1]=>0001011=>[4,2,1,1]
[3,4,5,2,8,7,1,6]=>0010110=>[3,2,1,2]
[5,3,1,4,2,8,7,6]=>1101011=>[1,1,2,2,1,1]
[5,1,3,4,2,8,7,6]=>1001011=>[1,3,2,1,1]
[5,1,3,2,4,8,7,6]=>1010011=>[1,2,3,1,1]
[5,3,2,1,4,8,7,6]=>1110011=>[1,1,1,3,1,1]
[4,3,2,5,8,1,7,6]=>1100101=>[1,1,3,2,1]
[3,4,2,5,8,7,1,6]=>0100110=>[2,3,1,2]
[3,2,4,5,8,7,1,6]=>1000110=>[1,4,1,2]
[4,2,3,5,8,1,7,6]=>1000101=>[1,4,2,1]
[5,2,3,1,4,8,7,6]=>1010011=>[1,2,3,1,1]
[5,2,1,3,4,8,7,6]=>1100011=>[1,1,4,1,1]
[1,7,2,3,5,6,8,4]=>0100001=>[2,5,1]
[3,7,4,2,1,5,6,8]=>0111000=>[2,1,1,4]
[3,4,6,2,8,5,7,1]=>0010101=>[3,2,2,1]
[4,2,1,7,5,8,3,6]=>1101010=>[1,1,2,2,2]
[4,7,2,6,5,1,3,8]=>0101100=>[2,2,1,3]
[3,7,4,1,2,5,8,6]=>0110001=>[2,1,4,1]
[4,7,1,6,5,2,8,3]=>0101101=>[2,2,1,2,1]
[4,7,3,6,5,1,8,2]=>0101101=>[2,2,1,2,1]
[4,3,7,1,6,8,5,2]=>1010011=>[1,2,3,1,1]
[4,2,1,7,5,6,8,3]=>1101001=>[1,1,2,3,1]
[4,2,6,8,7,3,1,5]=>1001110=>[1,3,1,1,2]
[3,4,6,1,8,5,2,7]=>0010110=>[3,2,1,2]
[4,1,6,7,5,8,2,3]=>1001010=>[1,3,2,2]
[4,3,6,7,5,1,2,8]=>1001100=>[1,3,1,3]
[4,3,7,1,6,8,2,5]=>1010010=>[1,2,3,2]
[4,3,7,5,6,8,2,1]=>1010011=>[1,2,3,1,1]
[4,1,7,3,6,5,2,8]=>1010110=>[1,2,2,1,2]
[2,8,7,4,5,3,1,6]=>0110110=>[2,1,2,1,2]
[2,8,7,4,3,5,1,6]=>0111010=>[2,1,1,2,2]
[4,1,7,3,6,2,5,8]=>1010100=>[1,2,2,3]
[5,8,7,6,1,2,4,3]=>0111001=>[2,1,1,3,1]
[4,1,7,2,6,8,5,3]=>1010011=>[1,2,3,1,1]
[4,2,7,3,6,1,8,5]=>1010101=>[1,2,2,2,1]
[4,2,7,3,6,5,8,1]=>1010101=>[1,2,2,2,1]
[3,8,5,6,2,4,1,7]=>0101010=>[2,2,2,2]
[2,8,6,5,3,7,1,4]=>0111010=>[2,1,1,2,2]
[3,8,6,5,1,4,7,2]=>0111001=>[2,1,1,3,1]
[3,8,2,1,4,6,7,5]=>0110001=>[2,1,4,1]
[3,8,2,5,4,6,7,1]=>0101001=>[2,2,3,1]
[4,2,6,7,5,3,1,8]=>1001110=>[1,3,1,1,2]
[3,2,6,1,4,5,8,7]=>1010001=>[1,2,4,1]
[2,8,7,3,4,5,1,6]=>0110010=>[2,1,3,2]
[5,8,7,6,1,3,4,2]=>0111001=>[2,1,1,3,1]
[5,8,7,6,2,3,4,1]=>0111001=>[2,1,1,3,1]
[4,1,7,5,6,2,3,8]=>1010100=>[1,2,2,3]
[3,8,1,5,2,6,4,7]=>0101010=>[2,2,2,2]
[2,8,7,5,3,4,1,6]=>0111010=>[2,1,1,2,2]
[2,8,7,5,4,3,1,6]=>0111110=>[2,1,1,1,1,2]
[4,1,7,5,6,3,2,8]=>1010110=>[1,2,2,1,2]
[5,8,7,6,1,3,2,4]=>0111010=>[2,1,1,2,2]
[5,8,7,6,4,1,2,3]=>0111100=>[2,1,1,1,3]
[8,1,7,2,4,5,3,6]=>1010010=>[1,2,3,2]
[8,1,3,6,2,5,4,7]=>1001010=>[1,3,2,2]
[7,2,1,6,3,5,4,8]=>1101010=>[1,1,2,2,2]
[2,7,1,6,3,5,4,8]=>0101010=>[2,2,2,2]
[2,7,1,5,4,3,6,8]=>0101100=>[2,2,1,3]
[7,2,1,5,4,3,6,8]=>1101100=>[1,1,2,1,3]
[8,1,3,5,4,2,6,7]=>1001100=>[1,3,1,3]
[8,1,5,3,4,2,6,7]=>1010100=>[1,2,2,3]
[8,1,5,6,2,3,7,4]=>1001001=>[1,3,3,1]
[8,1,4,5,3,2,6,7]=>1001100=>[1,3,1,3]
[8,1,4,3,5,2,6,7]=>1010100=>[1,2,2,3]
[7,2,1,4,5,3,6,8]=>1100100=>[1,1,3,3]
[2,7,1,4,5,3,6,8]=>0100100=>[2,3,3]
[2,6,3,1,5,4,7,8]=>0110100=>[2,1,2,3]
[6,3,2,1,5,4,7,8]=>1110100=>[1,1,1,2,3]
[7,3,1,4,5,2,6,8]=>1100100=>[1,1,3,3]
[7,3,1,5,4,2,6,8]=>1101100=>[1,1,2,1,3]
[7,3,1,6,2,5,4,8]=>1101010=>[1,1,2,2,2]
[3,7,1,6,2,5,4,8]=>0101010=>[2,2,2,2]
[3,7,1,4,5,2,6,8]=>0100100=>[2,3,3]
[2,3,6,1,5,4,7,8]=>0010100=>[3,2,3]
[6,3,4,1,5,2,7,8]=>1010100=>[1,2,2,3]
[6,2,4,1,5,3,7,8]=>1010100=>[1,2,2,3]
[2,6,4,1,5,3,7,8]=>0110100=>[2,1,2,3]
[2,6,5,1,3,7,4,8]=>0110010=>[2,1,3,2]
[6,5,2,1,3,7,4,8]=>1110010=>[1,1,1,3,2]
[7,6,1,2,4,5,3,8]=>1100010=>[1,1,4,2]
[6,7,1,2,8,3,5,4]=>0100101=>[2,3,2,1]
[6,7,1,2,5,4,3,8]=>0100110=>[2,3,1,2]
[5,6,2,1,3,7,4,8]=>0110010=>[2,1,3,2]
[5,2,6,1,3,7,4,8]=>1010010=>[1,2,3,2]
[2,4,6,1,5,3,7,8]=>0010100=>[3,2,3]
[4,7,1,3,5,2,6,8]=>0100100=>[2,3,3]
[4,7,1,5,3,2,6,8]=>0101100=>[2,2,1,3]
[5,7,1,6,2,3,8,4]=>0101001=>[2,2,3,1]
[5,6,3,1,2,7,4,8]=>0110010=>[2,1,3,2]
[4,2,5,3,1,6,7,8]=>1011000=>[1,2,1,4]
[8,5,6,2,7,1,4,3]=>1010101=>[1,2,2,2,1]
[6,5,1,2,7,8,4,3]=>1100011=>[1,1,4,1,1]
[4,7,6,1,5,3,8,2]=>0110101=>[2,1,2,2,1]
[5,7,6,4,1,3,8,2]=>0111001=>[2,1,1,3,1]
[7,6,2,4,5,3,8,1]=>1100101=>[1,1,3,2,1]
[6,1,7,5,3,8,4,2]=>1011011=>[1,2,1,2,1,1]
[8,6,7,5,3,1,4,2]=>1011101=>[1,2,1,1,2,1]
[8,5,2,7,1,6,4,3]=>1101011=>[1,1,2,2,1,1]
[5,6,2,4,7,8,1,3]=>0100010=>[2,4,2]
[3,4,8,6,7,1,5,2]=>0010101=>[3,2,2,1]
[4,8,5,6,7,2,3,1]=>0100101=>[2,3,2,1]
[5,8,6,4,1,2,7,3]=>0111001=>[2,1,1,3,1]
[5,8,7,3,2,6,4,1]=>0111011=>[2,1,1,2,1,1]
[5,8,1,7,2,6,4,3]=>0101011=>[2,2,2,1,1]
[8,1,5,7,2,6,4,3]=>1001011=>[1,3,2,1,1]
[8,1,7,2,5,6,3,4]=>1010010=>[1,2,3,2]
[6,8,7,2,5,1,3,4]=>0110100=>[2,1,2,3]
[5,8,7,2,1,6,3,4]=>0111010=>[2,1,1,2,2]
[4,8,1,5,2,6,7,3]=>0101001=>[2,2,3,1]
[3,7,8,5,1,6,2,4]=>0011010=>[3,1,2,2]
[6,5,2,7,8,1,4,3]=>1100101=>[1,1,3,2,1]
[7,1,2,8,5,6,3,4]=>1001010=>[1,3,2,2]
[8,7,2,1,5,6,3,4]=>1110010=>[1,1,1,3,2]
[8,6,7,1,5,2,3,4]=>1010100=>[1,2,2,3]
[6,1,7,8,5,2,3,4]=>1001100=>[1,3,1,3]
[7,5,6,2,1,8,4,3]=>1011011=>[1,2,1,2,1,1]
[8,7,5,2,1,6,4,3]=>1111011=>[1,1,1,1,2,1,1]
[7,1,3,5,8,6,2,4]=>1000110=>[1,4,1,2]
[5,1,3,4,6,8,7,2]=>1000011=>[1,5,1,1]
[8,4,3,1,2,6,7,5]=>1110001=>[1,1,1,4,1]
[8,5,1,6,3,4,7,2]=>1101001=>[1,1,2,3,1]
[5,1,8,6,3,4,7,2]=>1011001=>[1,2,1,3,1]
[4,6,8,1,5,3,7,2]=>0010101=>[3,2,2,1]
[6,4,5,8,3,2,7,1]=>1001101=>[1,3,1,2,1]
[3,6,4,8,7,1,5,2]=>0101101=>[2,2,1,2,1]
[6,5,8,1,3,4,7,2]=>1010001=>[1,2,4,1]
[6,1,8,3,5,2,7,4]=>1010101=>[1,2,2,2,1]
[7,6,8,3,5,2,1,4]=>1010110=>[1,2,2,1,2]
[8,6,1,3,5,2,7,4]=>1100101=>[1,1,3,2,1]
[8,7,1,3,5,6,2,4]=>1100010=>[1,1,4,2]
[5,8,2,4,3,6,7,1]=>0101001=>[2,2,3,1]
[5,8,2,3,1,6,7,4]=>0101001=>[2,2,3,1]
[6,8,2,3,5,1,7,4]=>0100101=>[2,3,2,1]
[7,8,2,3,5,6,1,4]=>0100010=>[2,4,2]
[8,6,5,1,4,3,7,2]=>1110101=>[1,1,1,2,2,1]
[2,4,8,6,1,3,7,5]=>0011001=>[3,1,3,1]
[6,7,1,8,4,3,5,2]=>0101101=>[2,2,1,2,1]
[2,7,8,6,1,4,3,5]=>0011010=>[3,1,2,2]
[2,7,3,8,1,6,4,5]=>0101010=>[2,2,2,2]
[7,5,1,8,2,4,6,3]=>1101001=>[1,1,2,3,1]
[2,7,8,4,1,6,3,5]=>0011010=>[3,1,2,2]
[2,6,5,4,1,3,8,7]=>0111001=>[2,1,1,3,1]
[4,1,7,6,3,8,2,5]=>1011010=>[1,2,1,2,2]
[4,8,2,5,7,6,3,1]=>0100111=>[2,3,1,1,1]
[3,4,6,5,1,8,2,7]=>0011010=>[3,1,2,2]
[4,6,1,5,2,3,8,7]=>0101001=>[2,2,3,1]
[2,6,7,5,1,8,4,3]=>0011011=>[3,1,2,1,1]
[7,6,5,2,8,3,4,1]=>1110101=>[1,1,1,2,2,1]
[2,4,7,6,5,8,1,3]=>0011010=>[3,1,2,2]
[2,1,4,8,7,6,3,5]=>1001110=>[1,3,1,1,2]
[8,1,3,5,7,4,6,2]=>1000101=>[1,4,2,1]
[3,2,8,7,5,1,6,4]=>1011101=>[1,2,1,1,2,1]
[4,8,5,1,6,7,2,3]=>0110010=>[2,1,3,2]
[7,8,6,1,3,5,2,4]=>0110010=>[2,1,3,2]
[2,5,1,8,6,7,4,3]=>0101011=>[2,2,2,1,1]
[3,5,1,8,6,7,4,2]=>0101011=>[2,2,2,1,1]
[8,3,5,4,6,7,1,2]=>1010010=>[1,2,3,2]
[5,1,3,8,6,7,4,2]=>1001011=>[1,3,2,1,1]
[5,6,3,2,8,1,4,7]=>0110100=>[2,1,2,3]
[8,1,6,3,5,2,7,4]=>1010101=>[1,2,2,2,1]
[4,7,6,8,3,2,5,1]=>0101101=>[2,2,1,2,1]
[2,7,5,8,1,3,4,6]=>0101000=>[2,2,4]
[8,1,3,7,5,2,6,4]=>1001101=>[1,3,1,2,1]
[3,4,8,7,5,1,6,2]=>0011101=>[3,1,1,2,1]
[6,3,8,1,4,2,5,7]=>1010100=>[1,2,2,3]
[3,6,8,2,4,1,7,5]=>0010101=>[3,2,2,1]
[4,5,8,2,6,7,3,1]=>0010011=>[3,3,1,1]
[2,5,8,4,6,7,3,1]=>0010011=>[3,3,1,1]
[8,4,3,2,6,7,1,5]=>1110010=>[1,1,1,3,2]
[4,2,8,1,6,7,3,5]=>1010010=>[1,2,3,2]
[2,4,8,1,6,7,3,5]=>0010010=>[3,3,2]
[5,1,8,2,6,7,3,4]=>1010010=>[1,2,3,2]
[3,4,8,7,2,1,5,6]=>0011100=>[3,1,1,3]
[5,8,4,1,6,7,2,3]=>0110010=>[2,1,3,2]
[3,8,1,4,6,7,2,5]=>0100010=>[2,4,2]
[1,6,4,5,2,3,7,8]=>0101000=>[2,2,4]
[1,7,4,5,2,3,6,8]=>0101000=>[2,2,4]
[1,6,3,5,2,4,7,8]=>0101000=>[2,2,4]
[1,6,3,4,2,5,7,8]=>0101000=>[2,2,4]
[1,7,3,4,2,5,6,8]=>0101000=>[2,2,4]
[1,8,5,7,3,4,2,6]=>0101010=>[2,2,2,2]
[1,7,3,4,2,6,5,8]=>0101010=>[2,2,2,2]
[1,5,2,8,4,7,3,6]=>0101010=>[2,2,2,2]
[1,4,2,8,5,7,3,6]=>0101010=>[2,2,2,2]
[1,7,3,5,2,6,4,8]=>0101010=>[2,2,2,2]
[1,8,4,7,3,5,2,6]=>0101010=>[2,2,2,2]
[1,7,3,6,2,5,4,8]=>0101010=>[2,2,2,2]
[1,7,3,6,2,4,5,8]=>0101000=>[2,2,4]
[1,7,4,6,2,3,5,8]=>0101000=>[2,2,4]
[1,8,5,6,2,3,4,7]=>0101000=>[2,2,4]
[1,8,5,6,2,4,3,7]=>0101010=>[2,2,2,2]
[1,3,2,8,5,6,4,7]=>0101010=>[2,2,2,2]
[1,4,2,8,5,6,3,7]=>0101010=>[2,2,2,2]
[1,5,2,8,4,6,3,7]=>0101010=>[2,2,2,2]
[1,6,2,8,4,5,3,7]=>0101010=>[2,2,2,2]
[8,6,4,7,2,1,3,5]=>1101100=>[1,1,2,1,3]
[3,8,6,2,4,5,1,7]=>0110010=>[2,1,3,2]
[1,7,6,4,8,2,3,5]=>0110100=>[2,1,2,3]
[5,8,7,4,1,2,3,6]=>0111000=>[2,1,1,4]
[6,8,3,7,2,1,4,5]=>0101100=>[2,2,1,3]
[6,1,3,7,4,8,2,5]=>1001010=>[1,3,2,2]
[7,1,6,4,8,2,3,5]=>1010100=>[1,2,2,3]
[3,8,7,5,1,2,4,6]=>0111000=>[2,1,1,4]
[3,7,6,1,2,4,5,8]=>0110000=>[2,1,5]
[4,7,6,1,2,3,5,8]=>0110000=>[2,1,5]
[8,5,7,4,1,2,3,6]=>1011000=>[1,2,1,4]
[8,6,2,3,1,7,4,5]=>1101010=>[1,1,2,2,2]
[1,7,2,8,6,3,4,5]=>0101100=>[2,2,1,3]
[7,5,8,1,3,6,2,4]=>1010010=>[1,2,3,2]
[5,4,1,8,2,3,6,7]=>1101000=>[1,1,2,4]
[1,4,8,7,2,3,5,6]=>0011000=>[3,1,4]
[1,5,8,7,2,3,4,6]=>0011000=>[3,1,4]
[5,7,1,3,8,2,4,6]=>0100100=>[2,3,3]
[7,1,5,8,6,2,3,4]=>1001100=>[1,3,1,3]
[5,1,8,7,2,3,4,6]=>1011000=>[1,2,1,4]
[7,1,5,8,3,4,2,6]=>1001010=>[1,3,2,2]
[7,1,4,3,2,5,6,8]=>1011000=>[1,2,1,4]
[6,4,2,3,8,5,7,1]=>1100101=>[1,1,3,2,1]
[6,4,2,7,5,8,3,1]=>1101011=>[1,1,2,2,1,1]
[7,1,4,6,5,2,3,8]=>1001100=>[1,3,1,3]
[7,1,4,6,5,8,2,3]=>1001010=>[1,3,2,2]
[7,1,4,6,3,8,2,5]=>1001010=>[1,3,2,2]
[7,1,4,3,2,5,8,6]=>1011001=>[1,2,1,3,1]
[7,1,4,6,5,2,8,3]=>1001101=>[1,3,1,2,1]
[7,1,4,6,5,3,8,2]=>1001101=>[1,3,1,2,1]
[7,1,4,6,5,3,2,8]=>1001110=>[1,3,1,1,2]
[6,4,2,7,5,3,8,1]=>1101101=>[1,1,2,1,2,1]
[3,4,7,2,6,8,5,1]=>0010011=>[3,3,1,1]
[3,4,7,1,6,8,2,5]=>0010010=>[3,3,2]
[3,4,7,1,6,8,5,2]=>0010011=>[3,3,1,1]
[2,4,1,7,5,3,6,8]=>0101100=>[2,2,1,3]
[3,4,1,7,8,6,2,5]=>0100110=>[2,3,1,2]
[6,4,2,3,8,5,1,7]=>1100110=>[1,1,3,1,2]
[6,4,2,7,5,3,1,8]=>1101110=>[1,1,2,1,1,2]
[3,4,7,2,6,8,1,5]=>0010010=>[3,3,2]
[5,4,7,3,6,8,2,1]=>1010011=>[1,2,3,1,1]
[3,4,7,2,6,5,1,8]=>0010110=>[3,2,1,2]
[4,8,7,3,5,1,2,6]=>0110100=>[2,1,2,3]
[4,8,7,1,3,5,2,6]=>0110010=>[2,1,3,2]
[4,8,3,1,2,6,5,7]=>0110010=>[2,1,3,2]
[3,4,7,1,6,2,5,8]=>0010100=>[3,2,3]
[3,4,7,1,6,2,8,5]=>0010101=>[3,2,2,1]
[3,4,7,2,6,5,8,1]=>0010101=>[3,2,2,1]
[4,8,3,1,2,6,7,5]=>0110001=>[2,1,4,1]
[5,8,1,6,3,4,2,7]=>0101010=>[2,2,2,2]
[6,8,5,1,3,7,2,4]=>0110010=>[2,1,3,2]
[6,8,5,1,3,4,7,2]=>0110001=>[2,1,4,1]
[5,8,3,4,2,6,7,1]=>0101001=>[2,2,3,1]
[6,4,3,7,5,1,2,8]=>1101100=>[1,1,2,1,3]
[3,8,7,4,1,5,2,6]=>0111010=>[2,1,1,2,2]
[2,4,7,3,6,1,5,8]=>0010100=>[3,2,3]
[5,8,3,2,1,6,4,7]=>0111010=>[2,1,1,2,2]
[5,8,7,4,3,1,2,6]=>0111100=>[2,1,1,1,3]
[5,3,6,2,4,7,8,1]=>1010001=>[1,2,4,1]
[5,3,6,1,4,8,7,2]=>1010011=>[1,2,3,1,1]
[5,3,7,2,4,6,8,1]=>1010001=>[1,2,4,1]
[4,2,1,5,8,6,3,7]=>1100110=>[1,1,3,1,2]
[4,2,1,5,8,6,7,3]=>1100101=>[1,1,3,2,1]
[4,3,1,5,7,8,6,2]=>1100011=>[1,1,4,1,1]
[4,3,1,7,5,8,6,2]=>1101011=>[1,1,2,2,1,1]
[6,7,3,1,4,8,2,5]=>0110010=>[2,1,3,2]
[5,3,7,1,4,8,2,6]=>1010010=>[1,2,3,2]
[4,3,1,5,7,8,2,6]=>1100010=>[1,1,4,2]
[3,2,1,8,5,4,6,7]=>1101100=>[1,1,2,1,3]
[3,2,1,8,5,7,4,6]=>1101010=>[1,1,2,2,2]
[6,7,2,1,8,4,5,3]=>0110101=>[2,1,2,2,1]
[3,2,1,8,5,6,4,7]=>1101010=>[1,1,2,2,2]
[4,3,1,6,7,8,5,2]=>1100011=>[1,1,4,1,1]
[4,2,1,6,8,5,7,3]=>1100101=>[1,1,3,2,1]
[4,2,1,6,8,5,3,7]=>1100110=>[1,1,3,1,2]
[5,2,6,1,8,4,3,7]=>1010110=>[1,2,2,1,2]
[5,2,6,1,8,7,3,4]=>1010110=>[1,2,2,1,2]
[5,2,6,1,8,3,4,7]=>1010100=>[1,2,2,3]
[4,2,1,6,8,3,7,5]=>1100101=>[1,1,3,2,1]
[4,3,1,6,7,8,2,5]=>1100010=>[1,1,4,2]
[4,2,1,7,8,6,3,5]=>1100110=>[1,1,3,1,2]
[3,2,1,8,6,4,7,5]=>1101101=>[1,1,2,1,2,1]
[3,2,1,8,6,4,5,7]=>1101100=>[1,1,2,1,3]
[3,2,1,8,4,6,5,7]=>1101010=>[1,1,2,2,2]
[3,2,1,8,4,6,7,5]=>1101001=>[1,1,2,3,1]
[4,2,1,7,8,3,6,5]=>1100101=>[1,1,3,2,1]
[5,2,7,1,8,3,6,4]=>1010101=>[1,2,2,2,1]
[6,7,2,1,8,3,5,4]=>0110101=>[2,1,2,2,1]
[5,2,7,1,8,3,4,6]=>1010100=>[1,2,2,3]
[4,2,1,7,8,3,5,6]=>1100100=>[1,1,3,3]
[3,2,1,8,4,5,7,6]=>1101001=>[1,1,2,3,1]
[7,4,8,6,2,5,3,1]=>1011011=>[1,2,1,2,1,1]
[7,3,8,6,2,4,5,1]=>1011001=>[1,2,1,3,1]
[7,4,3,1,8,2,5,6]=>1110100=>[1,1,1,2,3]
[7,4,2,8,5,6,1,3]=>1101010=>[1,1,2,2,2]
[7,3,8,5,2,4,6,1]=>1011001=>[1,2,1,3,1]
[6,3,8,2,4,5,1,7]=>1010010=>[1,2,3,2]
[6,3,8,2,5,7,4,1]=>1010011=>[1,2,3,1,1]
[5,6,7,3,8,2,4,1]=>0010101=>[3,2,2,1]
[5,3,8,2,4,6,7,1]=>1010001=>[1,2,4,1]
[6,3,8,2,4,7,5,1]=>1010011=>[1,2,3,1,1]
[5,7,4,2,6,8,1,3]=>0110010=>[2,1,3,2]
[6,5,3,1,4,2,7,8]=>1110100=>[1,1,1,2,3]
[5,7,4,2,6,1,3,8]=>0110100=>[2,1,2,3]
[5,6,4,2,3,8,1,7]=>0110010=>[2,1,3,2]
[5,6,3,7,8,2,4,1]=>0100101=>[2,3,2,1]
[5,6,3,8,2,4,7,1]=>0101001=>[2,2,3,1]
[6,3,7,2,4,5,1,8]=>1010010=>[1,2,3,2]
[6,3,7,2,5,8,4,1]=>1010011=>[1,2,3,1,1]
[5,3,6,8,2,4,7,1]=>1001001=>[1,3,3,1]
[5,4,6,2,3,8,1,7]=>1010010=>[1,2,3,2]
[5,3,6,7,8,2,4,1]=>1000101=>[1,4,2,1]
[3,6,4,2,1,5,8,7]=>0111001=>[2,1,1,3,1]
[3,5,8,6,4,2,1,7]=>0011110=>[3,1,1,1,2]
[5,8,6,3,4,2,1,7]=>0110110=>[2,1,2,1,2]
[5,6,3,4,2,1,8,7]=>0101101=>[2,2,1,2,1]
[6,3,4,2,1,5,8,7]=>1011001=>[1,2,1,3,1]
[5,6,4,2,1,3,8,7]=>0111001=>[2,1,1,3,1]
[2,7,8,5,4,1,6,3]=>0011101=>[3,1,1,2,1]
[2,8,5,4,1,6,3,7]=>0111010=>[2,1,1,2,2]
[2,6,3,8,5,4,1,7]=>0101110=>[2,2,1,1,2]
[2,8,6,3,5,4,1,7]=>0110110=>[2,1,2,1,2]
[5,8,6,4,2,1,3,7]=>0111100=>[2,1,1,1,3]
[4,2,1,5,7,8,6,3]=>1100011=>[1,1,4,1,1]
[2,7,8,6,3,5,4,1]=>0011011=>[3,1,2,1,1]
[4,3,8,5,7,6,2,1]=>1010111=>[1,2,2,1,1,1]
[2,1,8,5,6,4,3,7]=>1010110=>[1,2,2,1,2]
[4,2,1,8,5,6,3,7]=>1101010=>[1,1,2,2,2]
[6,3,4,2,1,8,5,7]=>1011010=>[1,2,1,2,2]
[3,8,5,6,4,2,1,7]=>0101110=>[2,2,1,1,2]
[3,6,4,2,1,8,5,7]=>0111010=>[2,1,1,2,2]
[8,5,3,7,6,2,4,1]=>1101101=>[1,1,2,1,2,1]
[7,6,2,4,1,8,5,3]=>1101011=>[1,1,2,2,1,1]
[8,5,4,1,7,6,2,3]=>1110110=>[1,1,1,2,1,2]
[7,6,2,3,8,5,4,1]=>1100111=>[1,1,3,1,1,1]
[2,1,7,8,6,4,3,5]=>1001110=>[1,3,1,1,2]
[2,1,6,4,3,7,8,5]=>1011001=>[1,2,1,3,1]
[6,3,7,8,4,2,1,5]=>1001110=>[1,3,1,1,2]
[7,8,4,2,1,6,3,5]=>0111010=>[2,1,1,2,2]
[5,7,6,2,3,8,4,1]=>0110011=>[2,1,3,1,1]
[2,6,1,8,4,3,7,5]=>0101101=>[2,2,1,2,1]
[2,6,1,7,5,8,4,3]=>0101011=>[2,2,2,1,1]
[8,4,2,3,7,5,6,1]=>1100101=>[1,1,3,2,1]
[8,5,7,6,2,1,4,3]=>1011101=>[1,2,1,1,2,1]
[4,8,5,7,6,2,1,3]=>0101110=>[2,2,1,1,2]
[4,7,6,2,1,3,8,5]=>0111001=>[2,1,1,3,1]
[7,5,6,1,8,4,2,3]=>1010110=>[1,2,2,1,2]
[2,7,5,8,4,3,6,1]=>0101101=>[2,2,1,2,1]
[2,8,4,3,6,1,7,5]=>0110101=>[2,1,2,2,1]
[8,4,2,6,3,1,7,5]=>1101101=>[1,1,2,1,2,1]
[1,5,3,7,4,2,8,6]=>0101101=>[2,2,1,2,1]
[1,6,7,3,4,2,8,5]=>0010101=>[3,2,2,1]
[8,6,5,2,3,1,7,4]=>1110101=>[1,1,1,2,2,1]
[1,7,6,3,4,2,8,5]=>0110101=>[2,1,2,2,1]
[1,8,6,3,2,5,7,4]=>0111001=>[2,1,1,3,1]
[8,7,5,2,1,4,6,3]=>1111001=>[1,1,1,1,3,1]
[7,8,5,2,1,4,6,3]=>0111001=>[2,1,1,3,1]
[6,8,5,2,3,1,7,4]=>0110101=>[2,1,2,2,1]
[5,8,6,2,3,1,7,4]=>0110101=>[2,1,2,2,1]
[4,8,2,6,3,1,7,5]=>0101101=>[2,2,1,2,1]
[3,2,8,6,4,1,7,5]=>1011101=>[1,2,1,1,2,1]
[3,2,1,7,5,4,8,6]=>1101101=>[1,1,2,1,2,1]
[4,1,3,7,5,2,8,6]=>1001101=>[1,3,1,2,1]
[7,1,6,3,2,5,8,4]=>1011001=>[1,2,1,3,1]
[1,2,7,4,3,6,8,5]=>0011001=>[3,1,3,1]
[6,1,8,2,4,5,7,3]=>1010001=>[1,2,4,1]
[5,1,8,3,2,6,7,4]=>1011001=>[1,2,1,3,1]
[4,8,2,7,1,5,6,3]=>0101001=>[2,2,3,1]
[5,8,7,2,1,4,6,3]=>0111001=>[2,1,1,3,1]
[6,8,7,1,3,4,5,2]=>0110001=>[2,1,4,1]
[7,8,6,1,3,4,5,2]=>0110001=>[2,1,4,1]
[1,7,8,2,4,5,6,3]=>0010001=>[3,4,1]
[8,6,7,1,3,4,5,2]=>1010001=>[1,2,4,1]
[7,6,8,1,3,4,5,2]=>1010001=>[1,2,4,1]
[6,5,8,2,3,1,7,4]=>1010101=>[1,2,2,2,1]
[1,6,8,3,2,5,7,4]=>0011001=>[3,1,3,1]
[8,4,2,7,1,5,6,3]=>1101001=>[1,1,2,3,1]
[7,4,2,8,1,5,6,3]=>1101001=>[1,1,2,3,1]
[6,4,2,8,3,1,7,5]=>1101101=>[1,1,2,1,2,1]
[5,4,2,3,8,1,7,6]=>1100101=>[1,1,3,2,1]
[4,5,2,3,1,6,8,7]=>0101001=>[2,2,3,1]
[7,4,2,1,3,6,8,5]=>1110001=>[1,1,1,4,1]
[8,4,2,1,3,6,7,5]=>1110001=>[1,1,1,4,1]
[1,5,3,2,4,7,8,6]=>0110001=>[2,1,4,1]
[8,5,1,3,2,6,7,4]=>1101001=>[1,1,2,3,1]
[5,6,1,3,4,2,8,7]=>0100101=>[2,3,2,1]
[4,7,2,1,3,6,8,5]=>0110001=>[2,1,4,1]
[5,7,1,3,2,6,8,4]=>0101001=>[2,2,3,1]
[6,7,1,2,4,5,8,3]=>0100001=>[2,5,1]
[1,8,2,3,5,6,7,4]=>0100001=>[2,5,1]
[5,8,1,3,2,6,7,4]=>0101001=>[2,2,3,1]
[4,8,2,1,3,6,7,5]=>0110001=>[2,1,4,1]
[4,1,3,2,5,7,8,6]=>1010001=>[1,2,4,1]
[5,1,2,4,3,7,8,6]=>1001001=>[1,3,3,1]
[8,7,5,2,6,3,4,1]=>1110101=>[1,1,1,2,2,1]
[8,6,5,2,7,3,4,1]=>1110101=>[1,1,1,2,2,1]
[1,2,6,4,7,5,8,3]=>0010101=>[3,2,2,1]
[3,1,7,5,4,2,6,8]=>1011100=>[1,2,1,1,3]
[6,3,8,5,4,7,1,2]=>1011010=>[1,2,1,2,2]
[1,6,2,5,4,7,8,3]=>0101001=>[2,2,3,1]
[1,2,6,4,8,5,7,3]=>0010101=>[3,2,2,1]
[7,8,3,1,4,2,5,6]=>0110100=>[2,1,2,3]
[4,8,1,5,2,3,6,7]=>0101000=>[2,2,4]
[7,4,1,5,2,3,6,8]=>1101000=>[1,1,2,4]
[5,6,1,8,4,3,2,7]=>0101110=>[2,2,1,1,2]
[5,1,8,6,4,3,2,7]=>1011110=>[1,2,1,1,1,2]
[5,1,6,3,8,7,2,4]=>1010110=>[1,2,2,1,2]
[6,1,2,5,8,3,7,4]=>1000101=>[1,4,2,1]
[6,1,8,7,4,3,2,5]=>1011110=>[1,2,1,1,1,2]
[7,1,2,5,4,8,6,3]=>1001011=>[1,3,2,1,1]
[1,2,7,5,8,3,6,4]=>0010101=>[3,2,2,1]
[4,1,6,3,7,5,2,8]=>1010110=>[1,2,2,1,2]
[1,3,6,7,8,5,2,4]=>0000110=>[5,1,2]
[1,2,6,4,7,8,5,3]=>0010011=>[3,3,1,1]
[4,1,6,3,7,8,2,5]=>1010010=>[1,2,3,2]
[3,1,6,4,8,2,7,5]=>1010101=>[1,2,2,2,1]
[7,8,4,1,6,3,2,5]=>0110110=>[2,1,2,1,2]
[4,1,6,3,8,7,2,5]=>1010110=>[1,2,2,1,2]
[7,5,1,8,4,3,2,6]=>1101110=>[1,1,2,1,1,2]
[6,5,1,7,4,3,2,8]=>1101110=>[1,1,2,1,1,2]
[4,1,8,5,2,3,7,6]=>1011001=>[1,2,1,3,1]
[4,1,6,8,3,7,2,5]=>1001010=>[1,3,2,2]
[6,5,8,1,4,3,2,7]=>1010110=>[1,2,2,1,2]
[1,6,3,2,7,4,8,5]=>0110101=>[2,1,2,2,1]
[1,3,7,2,5,4,8,6]=>0010101=>[3,2,2,1]
[1,3,7,5,2,4,8,6]=>0011001=>[3,1,3,1]
[2,5,3,7,4,8,1,6]=>0101010=>[2,2,2,2]
[3,2,6,7,8,1,5,4]=>1000101=>[1,4,2,1]
[3,5,2,7,8,4,1,6]=>0100110=>[2,3,1,2]
[3,5,2,6,8,4,7,1]=>0100101=>[2,3,2,1]
[2,5,7,4,3,8,6,1]=>0011011=>[3,1,2,1,1]
[1,5,7,2,4,8,6,3]=>0010011=>[3,3,1,1]
[4,6,3,7,2,8,5,1]=>0101011=>[2,2,2,1,1]
[1,4,7,3,8,6,2,5]=>0010110=>[3,2,1,2]
[5,1,6,8,2,4,3,7]=>1001010=>[1,3,2,2]
[5,3,7,8,2,4,1,6]=>1001010=>[1,3,2,2]
[8,5,3,7,2,4,1,6]=>1101010=>[1,1,2,2,2]
[8,2,4,7,3,1,5,6]=>1001100=>[1,3,1,3]
[2,4,7,8,3,1,5,6]=>0001100=>[4,1,3]
[6,3,1,5,8,2,4,7]=>1100100=>[1,1,3,3]
[6,5,3,4,2,8,1,7]=>1101010=>[1,1,2,2,2]
[5,2,4,3,8,1,6,7]=>1010100=>[1,2,2,3]
[3,2,4,8,1,5,6,7]=>1001000=>[1,3,4]
[8,1,5,7,3,2,4,6]=>1001100=>[1,3,1,3]
[8,4,6,7,2,3,1,5]=>1001010=>[1,3,2,2]
[4,6,7,8,2,3,1,5]=>0001010=>[4,2,2]
[7,4,6,8,2,3,1,5]=>1001010=>[1,3,2,2]
[7,2,4,8,3,1,5,6]=>1001100=>[1,3,1,3]
[5,3,8,7,2,4,1,6]=>1011010=>[1,2,1,2,2]
[2,4,8,7,3,1,5,6]=>0011100=>[3,1,1,3]
[4,6,8,7,2,3,1,5]=>0011010=>[3,1,2,2]
[6,4,8,7,2,3,1,5]=>1011010=>[1,2,1,2,2]
[3,1,7,4,2,8,6,5]=>1011011=>[1,2,1,2,1,1]
[3,2,8,4,1,7,6,5]=>1011011=>[1,2,1,2,1,1]
[7,6,4,8,2,3,1,5]=>1101010=>[1,1,2,2,2]
[5,7,6,8,2,3,1,4]=>0101010=>[2,2,2,2]
[4,7,6,8,2,3,1,5]=>0101010=>[2,2,2,2]
[8,6,4,7,2,3,1,5]=>1101010=>[1,1,2,2,2]
[8,2,3,7,4,1,6,5]=>1001101=>[1,3,1,2,1]
[3,7,4,8,2,5,1,6]=>0101010=>[2,2,2,2]
[2,3,7,4,1,6,8,5]=>0011001=>[3,1,3,1]
[8,1,6,4,2,3,7,5]=>1011001=>[1,2,1,3,1]
[4,7,8,6,2,3,1,5]=>0011010=>[3,1,2,2]
[6,3,1,7,4,2,8,5]=>1101101=>[1,1,2,1,2,1]
[8,5,7,6,2,3,1,4]=>1011010=>[1,2,1,2,2]
[7,1,6,4,2,3,8,5]=>1011001=>[1,2,1,3,1]
[3,1,7,6,4,2,8,5]=>1011101=>[1,2,1,1,2,1]
[4,8,7,6,2,3,1,5]=>0111010=>[2,1,1,2,2]
[6,8,7,5,2,3,1,4]=>0111010=>[2,1,1,2,2]
[4,3,6,1,5,8,7,2]=>1010011=>[1,2,3,1,1]
[4,3,6,5,1,8,7,2]=>1011011=>[1,2,1,2,1,1]
[4,6,3,5,1,8,7,2]=>0101011=>[2,2,2,1,1]
[4,6,3,1,5,8,7,2]=>0110011=>[2,1,3,1,1]
[4,1,6,5,3,8,7,2]=>1011011=>[1,2,1,2,1,1]
[4,6,1,5,3,8,7,2]=>0101011=>[2,2,2,1,1]
[2,6,5,3,1,8,7,4]=>0111011=>[2,1,1,2,1,1]
[2,6,5,8,3,1,7,4]=>0101101=>[2,2,1,2,1]
[2,6,5,3,8,1,7,4]=>0110101=>[2,1,2,2,1]
[4,6,1,5,8,3,7,2]=>0100101=>[2,3,2,1]
[4,1,6,5,8,3,7,2]=>1010101=>[1,2,2,2,1]
[1,4,6,5,8,3,7,2]=>0010101=>[3,2,2,1]
[4,1,6,5,8,7,3,2]=>1010111=>[1,2,2,1,1,1]
[6,4,3,8,7,1,5,2]=>1101101=>[1,1,2,1,2,1]
[6,4,8,3,7,1,5,2]=>1010101=>[1,2,2,2,1]
[2,6,8,5,3,7,1,4]=>0011010=>[3,1,2,2]
[4,6,8,1,5,7,3,2]=>0010011=>[3,3,1,1]
[4,6,1,8,5,7,3,2]=>0101011=>[2,2,2,1,1]
[1,4,6,8,5,7,3,2]=>0001011=>[4,2,1,1]
[1,4,6,8,5,3,7,2]=>0001101=>[4,1,2,1]
[4,6,1,8,5,3,7,2]=>0101101=>[2,2,1,2,1]
[4,6,3,8,5,7,1,2]=>0101010=>[2,2,2,2]
[4,3,6,8,1,5,7,2]=>1001001=>[1,3,3,1]
[4,3,6,1,8,5,7,2]=>1010101=>[1,2,2,2,1]
[4,3,1,6,8,5,7,2]=>1100101=>[1,1,3,2,1]
[4,1,3,6,8,7,5,2]=>1000111=>[1,4,1,1,1]
[4,3,6,1,8,7,5,2]=>1010111=>[1,2,2,1,1,1]
[4,3,6,8,1,7,5,2]=>1001011=>[1,3,2,1,1]
[6,5,2,8,7,3,1,4]=>1101110=>[1,1,2,1,1,2]
[6,5,2,8,7,1,3,4]=>1101100=>[1,1,2,1,3]
[6,2,5,8,7,1,3,4]=>1001100=>[1,3,1,3]
[6,2,5,8,7,3,1,4]=>1001110=>[1,3,1,1,2]
[4,6,3,8,1,7,5,2]=>0101011=>[2,2,2,1,1]
[4,6,3,1,8,7,5,2]=>0110111=>[2,1,2,1,1,1]
[4,1,6,3,8,7,5,2]=>1010111=>[1,2,2,1,1,1]
[1,4,6,3,8,7,5,2]=>0010111=>[3,2,1,1,1]
[4,1,6,8,3,7,5,2]=>1001011=>[1,3,2,1,1]
[4,6,1,8,3,7,5,2]=>0101011=>[2,2,2,1,1]
[4,6,8,1,3,7,5,2]=>0010011=>[3,3,1,1]
[6,2,8,5,7,3,1,4]=>1010110=>[1,2,2,1,2]
[6,2,8,5,7,1,3,4]=>1010100=>[1,2,2,3]
[2,4,8,7,1,5,3,6]=>0011010=>[3,1,2,2]
[6,4,1,8,7,5,3,2]=>1101111=>[1,1,2,1,1,1,1]
[6,1,4,8,7,5,3,2]=>1001111=>[1,3,1,1,1,1]
[1,6,4,8,7,3,5,2]=>0101101=>[2,2,1,2,1]
[6,4,1,8,7,3,5,2]=>1101101=>[1,1,2,1,2,1]
[4,2,8,7,5,1,3,6]=>1011100=>[1,2,1,1,3]
[2,4,8,7,3,5,1,6]=>0011010=>[3,1,2,2]
[1,5,3,2,6,4,7,8]=>0110100=>[2,1,2,3]
[1,5,3,2,6,7,4,8]=>0110010=>[2,1,3,2]
[1,7,3,2,8,5,4,6]=>0110110=>[2,1,2,1,2]
[1,7,3,2,5,8,4,6]=>0110010=>[2,1,3,2]
[6,4,2,5,3,7,1,8]=>1101010=>[1,1,2,2,2]
[5,4,7,6,2,3,1,8]=>1011010=>[1,2,1,2,2]
[3,6,4,8,2,1,5,7]=>0101100=>[2,2,1,3]
[1,6,2,8,5,3,4,7]=>0101100=>[2,2,1,3]
[4,6,2,3,7,5,1,8]=>0100110=>[2,3,1,2]
[4,7,2,3,6,5,1,8]=>0100110=>[2,3,1,2]
[5,3,2,6,4,7,1,8]=>1101010=>[1,1,2,2,2]
[3,5,2,1,6,8,4,7]=>0110010=>[2,1,3,2]
[1,5,2,6,8,4,3,7]=>0100110=>[2,3,1,2]
[1,5,7,2,8,4,3,6]=>0010110=>[3,2,1,2]
[3,5,2,1,8,6,4,7]=>0110110=>[2,1,2,1,2]
[3,6,8,4,2,1,5,7]=>0011100=>[3,1,1,3]
[4,3,2,6,1,8,5,7]=>1101010=>[1,1,2,2,2]
[1,5,8,2,7,4,3,6]=>0010110=>[3,2,1,2]
[1,7,2,3,4,8,6,5]=>0100011=>[2,4,1,1]
[6,8,2,3,4,1,7,5]=>0100101=>[2,3,2,1]
[2,3,1,8,4,5,7,6]=>0101001=>[2,2,3,1]
[7,3,2,1,4,5,8,6]=>1110001=>[1,1,1,4,1]
[7,8,1,4,3,5,2,6]=>0101010=>[2,2,2,2]
[1,8,2,3,4,7,6,5]=>0100011=>[2,4,1,1]
[3,8,2,1,6,5,4,7]=>0110110=>[2,1,2,1,2]
[1,7,8,3,5,4,2,6]=>0010110=>[3,2,1,2]
[7,4,1,8,3,5,2,6]=>1101010=>[1,1,2,2,2]
[8,4,1,7,3,5,2,6]=>1101010=>[1,1,2,2,2]
[3,8,4,6,2,1,5,7]=>0101100=>[2,2,1,3]
[8,4,2,5,3,1,6,7]=>1101100=>[1,1,2,1,3]
[4,3,2,5,1,8,6,7]=>1101010=>[1,1,2,2,2]
[3,5,2,4,1,8,6,7]=>0101010=>[2,2,2,2]
[2,4,7,8,1,5,3,6]=>0001010=>[4,2,2]
[1,8,7,3,5,4,2,6]=>0110110=>[2,1,2,1,2]
[5,1,8,2,7,4,3,6]=>1010110=>[1,2,2,1,2]
[5,1,7,2,8,4,3,6]=>1010110=>[1,2,2,1,2]
[6,1,2,8,5,3,4,7]=>1001100=>[1,3,1,3]
[6,3,2,1,8,4,5,7]=>1110100=>[1,1,1,2,3]
[7,3,2,8,4,5,1,6]=>1101010=>[1,1,2,2,2]
[2,7,8,4,3,5,1,6]=>0011010=>[3,1,2,2]
[7,1,8,3,5,4,2,6]=>1010110=>[1,2,2,1,2]
[7,8,2,3,4,6,1,5]=>0100010=>[2,4,2]
[6,8,1,3,4,7,2,5]=>0100010=>[2,4,2]
[8,6,2,3,4,1,7,5]=>1100101=>[1,1,3,2,1]
[8,3,2,7,4,5,1,6]=>1101010=>[1,1,2,2,2]
[6,7,2,3,4,1,8,5]=>0100101=>[2,3,2,1]
[8,6,2,3,4,7,1,5]=>1100010=>[1,1,4,2]
[4,8,7,3,5,6,1,2]=>0110010=>[2,1,3,2]
[4,8,7,5,3,6,1,2]=>0111010=>[2,1,1,2,2]
[5,8,7,3,4,6,1,2]=>0110010=>[2,1,3,2]
[5,8,4,2,1,6,7,3]=>0111001=>[2,1,1,3,1]
[5,8,4,1,2,6,7,3]=>0110001=>[2,1,4,1]
[5,3,7,2,6,1,8,4]=>1010101=>[1,2,2,2,1]
[5,2,8,1,6,3,7,4]=>1010101=>[1,2,2,2,1]
[5,8,2,1,4,7,6,3]=>0110011=>[2,1,3,1,1]
[4,8,2,5,1,7,6,3]=>0101011=>[2,2,2,1,1]
[7,8,4,1,2,6,5,3]=>0110011=>[2,1,3,1,1]
[4,8,1,5,2,7,6,3]=>0101011=>[2,2,2,1,1]
[5,8,1,2,4,7,6,3]=>0100011=>[2,4,1,1]
[5,2,8,3,6,7,1,4]=>1010010=>[1,2,3,2]
[2,8,7,6,4,1,3,5]=>0111100=>[2,1,1,1,3]
[7,8,2,6,5,1,3,4]=>0101100=>[2,2,1,3]
[1,8,7,6,2,4,3,5]=>0111010=>[2,1,1,2,2]
[2,8,1,4,5,6,7,3]=>0100001=>[2,5,1]
[2,1,7,3,6,5,8,4]=>1010101=>[1,2,2,2,1]
[3,2,7,1,6,5,8,4]=>1010101=>[1,2,2,2,1]
[6,1,2,8,5,7,3,4]=>1001010=>[1,3,2,2]
[6,2,1,8,5,7,3,4]=>1101010=>[1,1,2,2,2]
[6,3,1,8,5,7,2,4]=>1101010=>[1,1,2,2,2]
[6,4,2,1,7,5,8,3]=>1110101=>[1,1,1,2,2,1]
[6,1,3,8,5,2,7,4]=>1001101=>[1,3,1,2,1]
[1,3,7,2,6,8,5,4]=>0010011=>[3,3,1,1]
[7,8,2,6,5,3,1,4]=>0101110=>[2,2,1,1,2]
[3,2,6,7,5,8,1,4]=>1001010=>[1,3,2,2]
[1,2,7,5,6,3,8,4]=>0010101=>[3,2,2,1]
[2,8,7,6,4,3,1,5]=>0111110=>[2,1,1,1,1,2]
[3,8,7,6,1,2,5,4]=>0111001=>[2,1,1,3,1]
[4,8,7,6,2,1,3,5]=>0111100=>[2,1,1,1,3]
[4,8,7,6,1,3,2,5]=>0111010=>[2,1,1,2,2]
[3,8,7,6,4,1,2,5]=>0111100=>[2,1,1,1,3]
[7,8,3,6,5,1,2,4]=>0101100=>[2,2,1,3]
[2,3,7,5,6,8,1,4]=>0010010=>[3,3,2]
[3,8,7,6,4,2,1,5]=>0111110=>[2,1,1,1,1,2]
[3,4,2,6,7,8,1,5]=>0100010=>[2,4,2]
[3,1,4,2,6,8,7,5]=>1010011=>[1,2,3,1,1]
[8,3,4,2,6,1,7,5]=>1010101=>[1,2,2,2,1]
[2,6,7,3,5,4,1,8]=>0010110=>[3,2,1,2]
[2,7,8,3,5,4,1,6]=>0010110=>[3,2,1,2]
[2,6,8,3,5,4,1,7]=>0010110=>[3,2,1,2]
[4,7,1,2,8,5,3,6]=>0100110=>[2,3,1,2]
[4,8,1,2,7,5,3,6]=>0100110=>[2,3,1,2]
[2,1,6,3,7,5,4,8]=>1010110=>[1,2,2,1,2]
[2,7,1,3,6,8,4,5]=>0100010=>[2,4,2]
[7,4,1,2,8,5,3,6]=>1100110=>[1,1,3,1,2]
[8,7,4,2,1,5,3,6]=>1111010=>[1,1,1,1,2,2]
[7,4,1,2,6,5,3,8]=>1100110=>[1,1,3,1,2]
[7,4,3,1,5,6,8,2]=>1110001=>[1,1,1,4,1]
[6,7,4,1,5,8,3,2]=>0110011=>[2,1,3,1,1]
[4,7,5,1,6,8,3,2]=>0110011=>[2,1,3,1,1]
[4,5,3,1,7,6,8,2]=>0110101=>[2,1,2,2,1]
[4,6,1,2,7,5,3,8]=>0100110=>[2,3,1,2]
[4,6,1,2,8,5,3,7]=>0100110=>[2,3,1,2]
[4,5,3,1,8,6,7,2]=>0110101=>[2,1,2,2,1]
[4,8,5,6,3,1,7,2]=>0101101=>[2,2,1,2,1]
[5,1,3,4,8,6,7,2]=>1000101=>[1,4,2,1]
[5,4,3,8,1,6,7,2]=>1101001=>[1,1,2,3,1]
[8,5,3,4,1,6,7,2]=>1101001=>[1,1,2,3,1]
[6,4,8,2,1,5,3,7]=>1011010=>[1,2,1,2,2]
[6,7,3,2,5,1,4,8]=>0110100=>[2,1,2,3]
[6,8,3,2,5,1,4,7]=>0110100=>[2,1,2,3]
[5,7,1,4,6,8,3,2]=>0100011=>[2,4,1,1]
[5,1,3,4,7,6,8,2]=>1000101=>[1,4,2,1]
[5,4,3,7,1,6,8,2]=>1101001=>[1,1,2,3,1]
[6,7,5,4,1,8,3,2]=>0111011=>[2,1,1,2,1,1]
[7,6,4,2,1,5,3,8]=>1111010=>[1,1,1,1,2,2]
[8,5,6,1,3,2,4,7]=>1010100=>[1,2,2,3]
[8,6,1,5,3,2,4,7]=>1101100=>[1,1,2,1,3]
[7,8,1,5,3,2,4,6]=>0101100=>[2,2,1,3]
[8,1,7,5,3,2,4,6]=>1011100=>[1,2,1,1,3]
[8,6,1,4,5,2,3,7]=>1100100=>[1,1,3,3]
[8,6,3,1,5,2,4,7]=>1110100=>[1,1,1,2,3]
[8,4,6,1,5,2,3,7]=>1010100=>[1,2,2,3]
[8,6,2,1,5,4,3,7]=>1110110=>[1,1,1,2,1,2]
[8,5,2,6,1,4,3,7]=>1101010=>[1,1,2,2,2]
[8,5,2,1,7,4,3,6]=>1110110=>[1,1,1,2,1,2]
[8,2,7,5,1,3,4,6]=>1011000=>[1,2,1,4]
[8,4,1,7,5,2,3,6]=>1101100=>[1,1,2,1,3]
[8,2,6,1,7,4,3,5]=>1010110=>[1,2,2,1,2]
[8,1,7,4,3,2,6,5]=>1011101=>[1,2,1,1,2,1]
[8,1,5,7,3,2,6,4]=>1001101=>[1,3,1,2,1]
[5,7,8,1,3,2,6,4]=>0010101=>[3,2,2,1]
[8,2,6,1,5,7,3,4]=>1010010=>[1,2,3,2]
[5,8,1,6,7,2,3,4]=>0100100=>[2,3,3]
[5,7,6,1,8,2,3,4]=>0110100=>[2,1,2,3]
[8,1,5,6,7,2,3,4]=>1000100=>[1,4,3]
[6,5,7,1,8,2,3,4]=>1010100=>[1,2,2,3]
[8,1,6,4,7,2,3,5]=>1010100=>[1,2,2,3]
[7,5,8,1,3,2,4,6]=>1010100=>[1,2,2,3]
[7,8,4,1,3,2,5,6]=>0110100=>[2,1,2,3]
[8,3,7,4,1,2,5,6]=>1011000=>[1,2,1,4]
[8,5,1,7,3,2,4,6]=>1101100=>[1,1,2,1,3]
[6,8,1,7,3,2,4,5]=>0101100=>[2,2,1,3]
[7,1,8,4,3,6,2,5]=>1011010=>[1,2,1,2,2]
[7,3,1,8,6,4,2,5]=>1101110=>[1,1,2,1,1,2]
[8,3,1,7,4,6,2,5]=>1101010=>[1,1,2,2,2]
[8,4,5,1,7,2,3,6]=>1010100=>[1,2,2,3]
[5,6,8,1,7,2,3,4]=>0010100=>[3,2,3]
[6,5,8,1,2,7,3,4]=>1010010=>[1,2,3,2]
[7,3,1,8,5,6,2,4]=>1101010=>[1,1,2,2,2]
[6,2,7,8,3,1,5,4]=>1001101=>[1,3,1,2,1]
[5,8,1,7,3,2,6,4]=>0101101=>[2,2,1,2,1]
[8,4,1,7,3,2,6,5]=>1101101=>[1,1,2,1,2,1]
[8,3,4,7,1,2,6,5]=>1001001=>[1,3,3,1]
[7,4,8,2,1,3,6,5]=>1011001=>[1,2,1,3,1]
[7,4,3,8,1,2,6,5]=>1101001=>[1,1,2,3,1]
[8,2,3,6,7,1,5,4]=>1000101=>[1,4,2,1]
[2,6,8,7,1,5,4,3]=>0011011=>[3,1,2,1,1]
[7,8,5,2,3,6,4,1]=>0110011=>[2,1,3,1,1]
[8,7,5,2,3,1,6,4]=>1110101=>[1,1,1,2,2,1]
[6,8,5,2,3,4,7,1]=>0110001=>[2,1,4,1]
[5,7,3,4,6,8,1,2]=>0100010=>[2,4,2]
[5,7,3,4,6,1,2,8]=>0100100=>[2,3,3]
[7,3,5,6,1,2,8,4]=>1001001=>[1,3,3,1]
[5,7,3,1,4,6,8,2]=>0110001=>[2,1,4,1]
[5,7,3,1,4,8,6,2]=>0110011=>[2,1,3,1,1]
[5,7,3,1,4,8,2,6]=>0110010=>[2,1,3,2]
[5,3,7,4,1,2,8,6]=>1011001=>[1,2,1,3,1]
[5,3,7,4,1,2,6,8]=>1011000=>[1,2,1,4]
[5,3,7,1,4,2,6,8]=>1010100=>[1,2,2,3]
[5,3,7,1,4,2,8,6]=>1010101=>[1,2,2,2,1]
[3,7,5,1,2,8,6,4]=>0110011=>[2,1,3,1,1]
[7,8,3,5,1,2,6,4]=>0101001=>[2,2,3,1]
[7,3,8,5,1,2,6,4]=>1011001=>[1,2,1,3,1]
[7,3,5,8,1,2,6,4]=>1001001=>[1,3,3,1]
[3,7,5,1,2,6,4,8]=>0110010=>[2,1,3,2]
[3,7,5,1,2,6,8,4]=>0110001=>[2,1,4,1]
[3,5,7,2,8,6,1,4]=>0010110=>[3,2,1,2]
[2,5,7,4,8,6,1,3]=>0010110=>[3,2,1,2]
[2,6,4,8,7,5,1,3]=>0101110=>[2,2,1,1,2]
[3,6,2,5,8,7,1,4]=>0100110=>[2,3,1,2]
[5,2,8,4,7,6,1,3]=>1010110=>[1,2,2,1,2]
[6,2,4,8,7,5,1,3]=>1001110=>[1,3,1,1,2]
[2,5,1,4,7,3,8,6]=>0100101=>[2,3,2,1]
[3,1,5,6,2,8,7,4]=>1001011=>[1,3,2,1,1]
[7,1,4,2,8,6,5,3]=>1010111=>[1,2,2,1,1,1]
[4,1,5,3,2,8,7,6]=>1011011=>[1,2,1,2,1,1]
[7,2,3,5,1,8,6,4]=>1001011=>[1,3,2,1,1]
[1,6,4,2,8,7,5,3]=>0110111=>[2,1,2,1,1,1]
[4,6,2,7,5,1,8,3]=>0101101=>[2,2,1,2,1]
[1,5,3,6,2,8,7,4]=>0101011=>[2,2,2,1,1]
[3,6,2,5,1,4,8,7]=>0101001=>[2,2,3,1]
[5,2,8,4,1,3,7,6]=>1011001=>[1,2,1,3,1]
[2,4,8,7,1,3,6,5]=>0011001=>[3,1,3,1]
[6,3,1,7,2,8,5,4]=>1101011=>[1,1,2,2,1,1]
[7,5,1,2,8,6,4,3]=>1100111=>[1,1,3,1,1,1]
[1,5,2,3,8,7,6,4]=>0100111=>[2,3,1,1,1]
[4,5,1,2,8,7,6,3]=>0100111=>[2,3,1,1,1]
[3,5,8,7,2,6,4,1]=>0011011=>[3,1,2,1,1]
[5,8,2,7,1,6,4,3]=>0101011=>[2,2,2,1,1]
[2,1,6,4,5,8,3,7]=>1010010=>[1,2,3,2]
[8,6,3,7,5,2,1,4]=>1101110=>[1,1,2,1,1,2]
[4,6,3,8,5,2,1,7]=>0101110=>[2,2,1,1,2]
[4,6,3,7,5,2,8,1]=>0101101=>[2,2,1,2,1]
[3,5,7,8,2,6,1,4]=>0001010=>[4,2,2]
[4,2,3,6,1,5,8,7]=>1001001=>[1,3,3,1]
[3,8,6,4,5,1,2,7]=>0110100=>[2,1,2,3]
[4,8,3,7,5,2,1,6]=>0101110=>[2,2,1,1,2]
[8,7,3,6,5,1,2,4]=>1101100=>[1,1,2,1,3]
[5,2,8,3,7,6,1,4]=>1010110=>[1,2,2,1,2]
[8,2,7,3,1,6,4,5]=>1011010=>[1,2,1,2,2]
[8,6,7,4,1,5,3,2]=>1011011=>[1,2,1,2,1,1]
[4,8,6,7,5,1,3,2]=>0101101=>[2,2,1,2,1]
[7,1,8,4,6,5,2,3]=>1010110=>[1,2,2,1,2]
[8,7,1,5,4,6,2,3]=>1101010=>[1,1,2,2,2]
[8,5,7,1,4,6,3,2]=>1010011=>[1,2,3,1,1]
[6,4,8,5,1,7,3,2]=>1011011=>[1,2,1,2,1,1]
[8,4,7,1,5,6,3,2]=>1010011=>[1,2,3,1,1]
[8,7,5,1,4,6,2,3]=>1110010=>[1,1,1,3,2]
[8,7,2,5,1,4,6,3]=>1101001=>[1,1,2,3,1]
[4,8,7,2,5,1,6,3]=>0110101=>[2,1,2,2,1]
[8,7,1,4,2,5,6,3]=>1101001=>[1,1,2,3,1]
[8,7,5,1,2,4,6,3]=>1110001=>[1,1,1,4,1]
[7,1,8,5,6,2,3,4]=>1010100=>[1,2,2,3]
[3,5,8,7,1,2,6,4]=>0011001=>[3,1,3,1]
[2,3,8,5,7,1,6,4]=>0010101=>[3,2,2,1]
[3,8,7,1,5,6,2,4]=>0110010=>[2,1,3,2]
[3,5,8,7,1,6,2,4]=>0011010=>[3,1,2,2]
[2,3,8,6,7,5,1,4]=>0010110=>[3,2,1,2]
[3,2,8,6,7,5,1,4]=>1010110=>[1,2,2,1,2]
[4,1,8,6,2,7,5,3]=>1011011=>[1,2,1,2,1,1]
[8,7,4,1,2,6,5,3]=>1110011=>[1,1,1,3,1,1]
[1,3,8,6,7,5,2,4]=>0010110=>[3,2,1,2]
[5,7,1,8,2,6,3,4]=>0101010=>[2,2,2,2]
[2,8,7,1,5,6,3,4]=>0110010=>[2,1,3,2]
[8,7,1,5,2,4,6,3]=>1101001=>[1,1,2,3,1]
[7,1,8,2,4,6,5,3]=>1010011=>[1,2,3,1,1]
[1,6,2,8,4,7,5,3]=>0101011=>[2,2,2,1,1]
[1,3,8,5,7,2,6,4]=>0010101=>[3,2,2,1]
[1,8,3,7,2,5,6,4]=>0101001=>[2,2,3,1]
[2,8,7,1,3,5,6,4]=>0110001=>[2,1,4,1]
[5,7,1,8,2,3,6,4]=>0101001=>[2,2,3,1]
[7,1,8,2,3,5,6,4]=>1010001=>[1,2,4,1]
[8,6,3,7,4,1,5,2]=>1101101=>[1,1,2,1,2,1]
[4,2,8,6,7,5,1,3]=>1010110=>[1,2,2,1,2]
[8,4,2,7,5,6,1,3]=>1101010=>[1,1,2,2,2]
[4,8,3,6,1,7,5,2]=>0101011=>[2,2,2,1,1]
[8,3,4,7,5,1,6,2]=>1001101=>[1,3,1,2,1]
[8,3,7,4,5,1,6,2]=>1010101=>[1,2,2,2,1]
[8,7,4,2,5,6,1,3]=>1110010=>[1,1,1,3,2]
[8,7,5,1,6,2,3,4]=>1110100=>[1,1,1,2,3]
[8,7,2,4,1,5,6,3]=>1101001=>[1,1,2,3,1]
[4,8,6,1,7,2,5,3]=>0110101=>[2,1,2,2,1]
[4,2,8,6,7,1,5,3]=>1010101=>[1,2,2,2,1]
[8,7,4,1,2,5,6,3]=>1110001=>[1,1,1,4,1]
[8,2,7,1,6,3,4,5]=>1010100=>[1,2,2,3]
[8,2,7,1,3,6,4,5]=>1010010=>[1,2,3,2]
[2,8,3,6,7,1,5,4]=>0100101=>[2,3,2,1]
[8,7,2,1,3,5,6,4]=>1110001=>[1,1,1,4,1]
[1,8,7,2,3,6,4,5]=>0110010=>[2,1,3,2]
[1,8,7,2,6,3,4,5]=>0110100=>[2,1,2,3]
[8,2,7,3,6,1,4,5]=>1010100=>[1,2,2,3]
[1,8,7,3,6,2,4,5]=>0110100=>[2,1,2,3]
[1,8,2,7,6,3,4,5]=>0101100=>[2,2,1,3]
[8,2,7,4,1,5,6,3]=>1011001=>[1,2,1,3,1]
[8,2,1,7,5,6,3,4]=>1101010=>[1,1,2,2,2]
[8,7,3,1,5,6,2,4]=>1110010=>[1,1,1,3,2]
[2,8,7,3,5,6,1,4]=>0110010=>[2,1,3,2]
[8,3,1,6,7,5,2,4]=>1100110=>[1,1,3,1,2]
[8,5,2,1,6,7,4,3]=>1110011=>[1,1,1,3,1,1]
[1,5,2,8,6,7,4,3]=>0101011=>[2,2,2,1,1]
[1,2,8,6,7,5,3,4]=>0010110=>[3,2,1,2]
[1,8,3,6,7,5,2,4]=>0100110=>[2,3,1,2]
[8,2,3,6,7,5,1,4]=>1000110=>[1,4,1,2]
[8,3,7,2,5,6,1,4]=>1010010=>[1,2,3,2]
[8,1,3,7,5,6,2,4]=>1001010=>[1,3,2,2]
[8,4,1,2,7,5,6,3]=>1100101=>[1,1,3,2,1]
[8,1,4,2,6,7,5,3]=>1010011=>[1,2,3,1,1]
[1,2,8,6,7,3,5,4]=>0010101=>[3,2,2,1]
[8,1,2,7,3,6,4,5]=>1001010=>[1,3,2,2]
[8,1,7,3,6,2,4,5]=>1010100=>[1,2,2,3]
[8,1,7,2,6,3,4,5]=>1010100=>[1,2,2,3]
[8,1,7,2,3,6,4,5]=>1010010=>[1,2,3,2]
[8,1,3,7,2,5,6,4]=>1001001=>[1,3,3,1]
[1,8,3,6,7,2,5,4]=>0100101=>[2,3,2,1]
[1,7,8,2,3,6,5,4]=>0010011=>[3,3,1,1]
[8,3,7,1,2,5,6,4]=>1010001=>[1,2,4,1]
[7,4,2,6,1,5,3,8]=>1101010=>[1,1,2,2,2]
[7,4,2,5,6,1,3,8]=>1100100=>[1,1,3,3]
[7,3,5,6,4,2,1,8]=>1001110=>[1,3,1,1,2]
[7,4,3,1,5,6,2,8]=>1110010=>[1,1,1,3,2]
[7,4,5,2,6,1,3,8]=>1010100=>[1,2,2,3]
[5,3,7,2,8,6,4,1]=>1010111=>[1,2,2,1,1,1]
[5,3,8,2,6,7,4,1]=>1010011=>[1,2,3,1,1]
[6,3,8,2,5,4,7,1]=>1010101=>[1,2,2,2,1]
[6,4,3,1,8,2,7,5]=>1110101=>[1,1,1,2,2,1]
[5,3,7,8,2,6,4,1]=>1001011=>[1,3,2,1,1]
[4,7,8,5,6,3,2,1]=>0010111=>[3,2,1,1,1]
[5,3,7,6,8,2,4,1]=>1010101=>[1,2,2,2,1]
[5,7,8,4,6,2,1,3]=>0010110=>[3,2,1,2]
[5,8,4,3,6,7,1,2]=>0110010=>[2,1,3,2]
[5,8,6,4,7,2,1,3]=>0110110=>[2,1,2,1,2]
[5,3,8,6,2,7,4,1]=>1011011=>[1,2,1,2,1,1]
[4,7,5,8,6,3,2,1]=>0101111=>[2,2,1,1,1,1]
[6,3,8,7,2,4,1,5]=>1011010=>[1,2,1,2,2]
[5,3,8,7,2,6,4,1]=>1011011=>[1,2,1,2,1,1]
[5,3,8,6,7,2,4,1]=>1010101=>[1,2,2,2,1]
[5,3,7,8,6,2,4,1]=>1001101=>[1,3,1,2,1]
[5,7,6,4,8,2,1,3]=>0110110=>[2,1,2,1,2]
[5,8,4,6,7,2,1,3]=>0100110=>[2,3,1,2]
[6,4,2,8,1,7,3,5]=>1101010=>[1,1,2,2,2]
[6,5,2,4,3,7,8,1]=>1101001=>[1,1,2,3,1]
[5,4,6,2,8,7,1,3]=>1010110=>[1,2,2,1,2]
[5,6,3,8,7,2,4,1]=>0101101=>[2,2,1,2,1]
[6,7,4,3,1,8,2,5]=>0111010=>[2,1,1,2,2]
[5,7,4,3,6,8,1,2]=>0110010=>[2,1,3,2]
[5,7,3,8,6,2,4,1]=>0101101=>[2,2,1,2,1]
[4,5,8,6,7,3,2,1]=>0010111=>[3,2,1,1,1]
[4,6,8,5,7,3,2,1]=>0010111=>[3,2,1,1,1]
[5,6,8,3,7,2,4,1]=>0010101=>[3,2,2,1]
[5,4,6,8,2,7,1,3]=>1001010=>[1,3,2,2]
[7,8,4,5,1,3,2,6]=>0101010=>[2,2,2,2]
[6,7,1,3,2,5,4,8]=>0101010=>[2,2,2,2]
[6,7,1,4,3,5,2,8]=>0101010=>[2,2,2,2]
[7,8,2,3,1,5,4,6]=>0101010=>[2,2,2,2]
[7,8,2,4,3,5,1,6]=>0101010=>[2,2,2,2]
[7,8,2,4,1,5,3,6]=>0101010=>[2,2,2,2]
[1,4,2,6,5,7,3,8]=>0101010=>[2,2,2,2]
[5,6,1,4,2,7,3,8]=>0101010=>[2,2,2,2]
[6,7,2,4,1,5,3,8]=>0101010=>[2,2,2,2]
[6,7,2,4,3,5,1,8]=>0101010=>[2,2,2,2]
[6,7,2,3,1,5,4,8]=>0101010=>[2,2,2,2]
[6,7,3,5,4,8,1,2]=>0101010=>[2,2,2,2]
[2,4,1,6,5,7,3,8]=>0101010=>[2,2,2,2]
[1,5,2,6,4,7,3,8]=>0101010=>[2,2,2,2]
[2,5,1,6,4,7,3,8]=>0101010=>[2,2,2,2]
[5,6,2,4,3,7,1,8]=>0101010=>[2,2,2,2]
[4,5,2,6,1,7,3,8]=>0101010=>[2,2,2,2]
[4,5,1,6,3,7,2,8]=>0101010=>[2,2,2,2]
[4,5,3,6,1,7,2,8]=>0101010=>[2,2,2,2]
[5,6,3,4,1,7,2,8]=>0101010=>[2,2,2,2]
[5,6,1,4,3,7,2,8]=>0101010=>[2,2,2,2]
[5,6,1,3,2,7,4,8]=>0101010=>[2,2,2,2]
[5,6,4,7,1,3,2,8]=>0101010=>[2,2,2,2]
[6,7,4,5,1,3,2,8]=>0101010=>[2,2,2,2]
[6,7,5,8,1,3,2,4]=>0101010=>[2,2,2,2]
[4,5,1,3,2,7,6,8]=>0101010=>[2,2,2,2]
[4,6,5,7,1,3,2,8]=>0101010=>[2,2,2,2]
[4,6,1,3,2,7,5,8]=>0101010=>[2,2,2,2]
[1,4,3,6,2,7,5,8]=>0101010=>[2,2,2,2]
[4,5,2,3,1,7,6,8]=>0101010=>[2,2,2,2]
[4,5,3,7,6,8,1,2]=>0101010=>[2,2,2,2]
[4,6,5,7,3,8,1,2]=>0101010=>[2,2,2,2]
[4,6,5,7,2,3,1,8]=>0101010=>[2,2,2,2]
[3,5,4,6,1,7,2,8]=>0101010=>[2,2,2,2]
[3,5,1,6,4,7,2,8]=>0101010=>[2,2,2,2]
[1,5,3,6,4,7,2,8]=>0101010=>[2,2,2,2]
[1,5,3,6,2,7,4,8]=>0101010=>[2,2,2,2]
[3,5,2,6,1,7,4,8]=>0101010=>[2,2,2,2]
[3,5,2,6,4,7,1,8]=>0101010=>[2,2,2,2]
[3,4,2,6,1,7,5,8]=>0101010=>[2,2,2,2]
[4,6,2,3,1,7,5,8]=>0101010=>[2,2,2,2]
[2,4,3,6,1,7,5,8]=>0101010=>[2,2,2,2]
[2,5,3,6,4,7,1,8]=>0101010=>[2,2,2,2]
[2,5,3,6,1,7,4,8]=>0101010=>[2,2,2,2]
[3,6,2,7,5,4,8,1]=>0101101=>[2,2,1,2,1]
[5,2,6,7,4,3,8,1]=>1001101=>[1,3,1,2,1]
[3,5,2,7,6,4,8,1]=>0101101=>[2,2,1,2,1]
[1,3,7,2,8,5,6,4]=>0010101=>[3,2,2,1]
[2,1,5,6,8,4,3,7]=>1000110=>[1,4,1,2]
[1,3,7,2,8,5,4,6]=>0010110=>[3,2,1,2]
[1,5,4,3,6,8,2,7]=>0110010=>[2,1,3,2]
[1,6,4,5,7,8,3,2]=>0100011=>[2,4,1,1]
[2,1,5,6,8,4,7,3]=>1000101=>[1,4,2,1]
[2,1,5,6,8,7,3,4]=>1000110=>[1,4,1,2]
[3,6,5,2,7,8,4,1]=>0110011=>[2,1,3,1,1]
[6,2,4,7,5,8,3,1]=>1001011=>[1,3,2,1,1]
[1,5,7,8,4,2,6,3]=>0001101=>[4,1,2,1]
[3,7,4,1,8,6,2,5]=>0110110=>[2,1,2,1,2]
[3,4,6,8,5,7,2,1]=>0001011=>[4,2,1,1]
[4,5,6,2,8,7,3,1]=>0010111=>[3,2,1,1,1]
[4,5,6,1,8,7,3,2]=>0010111=>[3,2,1,1,1]
[4,5,6,3,1,8,7,2]=>0011011=>[3,1,2,1,1]
[4,3,6,2,1,7,5,8]=>1011010=>[1,2,1,2,2]
[4,6,3,2,1,7,5,8]=>0111010=>[2,1,1,2,2]
[4,6,3,1,7,5,2,8]=>0110110=>[2,1,2,1,2]
[4,5,3,7,6,1,8,2]=>0101101=>[2,2,1,2,1]
[4,5,1,7,3,8,6,2]=>0101011=>[2,2,2,1,1]
[2,5,7,1,4,3,8,6]=>0010101=>[3,2,2,1]
[4,3,5,7,6,1,8,2]=>1001101=>[1,3,1,2,1]
[4,3,6,1,7,5,2,8]=>1010110=>[1,2,2,1,2]
[4,3,2,6,1,7,5,8]=>1101010=>[1,1,2,2,2]
[5,3,2,1,6,4,7,8]=>1110100=>[1,1,1,2,3]
[5,3,1,6,2,7,4,8]=>1101010=>[1,1,2,2,2]
[5,1,6,3,2,7,4,8]=>1011010=>[1,2,1,2,2]
[2,6,1,4,7,5,3,8]=>0100110=>[2,3,1,2]
[3,6,1,7,4,2,5,8]=>0101100=>[2,2,1,3]
[4,6,1,7,5,3,2,8]=>0101110=>[2,2,1,1,2]
[5,1,6,3,7,4,2,8]=>1010110=>[1,2,2,1,2]
[5,3,6,4,2,1,7,8]=>1011100=>[1,2,1,1,3]
[5,3,2,6,4,1,7,8]=>1101100=>[1,1,2,1,3]
[5,2,1,6,3,7,4,8]=>1101010=>[1,1,2,2,2]
[5,2,6,3,1,7,4,8]=>1011010=>[1,2,1,2,2]
[4,2,6,3,1,7,8,5]=>1011001=>[1,2,1,3,1]
[3,6,2,1,7,4,5,8]=>0110100=>[2,1,2,3]
[3,6,2,7,4,1,5,8]=>0101100=>[2,2,1,3]
[3,5,7,2,8,6,4,1]=>0010111=>[3,2,1,1,1]
[2,6,1,3,7,5,4,8]=>0100110=>[2,3,1,2]
[3,6,1,7,5,2,4,8]=>0101100=>[2,2,1,3]
[5,1,6,2,7,4,3,8]=>1010110=>[1,2,2,1,2]
[5,2,6,4,3,1,7,8]=>1011100=>[1,2,1,1,3]
[5,2,1,6,4,3,7,8]=>1101100=>[1,1,2,1,3]
[5,4,2,1,6,3,7,8]=>1110100=>[1,1,1,2,3]
[5,4,1,6,2,7,3,8]=>1101010=>[1,1,2,2,2]
[5,1,6,4,2,7,3,8]=>1011010=>[1,2,1,2,2]
[3,6,1,7,5,4,8,2]=>0101101=>[2,2,1,2,1]
[2,6,1,5,4,3,7,8]=>0101100=>[2,2,1,3]
[3,1,6,2,5,4,7,8]=>1010100=>[1,2,2,3]
[4,1,6,3,2,7,8,5]=>1011001=>[1,2,1,3,1]
[5,1,6,4,3,2,7,8]=>1011100=>[1,2,1,1,3]
[5,4,1,6,3,2,7,8]=>1101100=>[1,1,2,1,3]
[5,4,3,1,6,2,7,8]=>1110100=>[1,1,1,2,3]
[1,2,8,7,4,6,3,5]=>0011010=>[3,1,2,2]
[4,5,1,8,7,6,2,3]=>0101110=>[2,2,1,1,2]
[4,1,5,8,7,6,2,3]=>1001110=>[1,3,1,1,2]
[7,5,8,4,2,6,3,1]=>1011011=>[1,2,1,2,1,1]
[6,8,4,5,2,7,3,1]=>0101011=>[2,2,2,1,1]
[6,8,2,5,3,7,4,1]=>0101011=>[2,2,2,1,1]
[6,3,8,4,2,7,5,1]=>1011011=>[1,2,1,2,1,1]
[7,2,5,3,8,6,4,1]=>1010111=>[1,2,2,1,1,1]
[3,4,7,5,8,6,2,1]=>0010111=>[3,2,1,1,1]
[3,6,7,4,8,5,2,1]=>0010111=>[3,2,1,1,1]
[6,7,4,2,8,5,3,1]=>0110111=>[2,1,2,1,1,1]
[4,7,5,2,8,6,3,1]=>0110111=>[2,1,2,1,1,1]
[5,6,2,8,3,7,4,1]=>0101011=>[2,2,2,1,1]
[1,5,8,2,7,3,6,4]=>0010101=>[3,2,2,1]
[5,8,4,7,2,3,6,1]=>0101001=>[2,2,3,1]
[6,7,4,8,1,5,3,2]=>0101011=>[2,2,2,1,1]
[6,8,5,3,7,2,4,1]=>0110101=>[2,1,2,2,1]
[7,5,3,8,2,6,4,1]=>1101011=>[1,1,2,2,1,1]
[3,7,4,5,8,6,2,1]=>0100111=>[2,3,1,1,1]
[7,4,2,5,8,6,3,1]=>1100111=>[1,1,3,1,1,1]
[6,8,4,2,5,7,3,1]=>0110011=>[2,1,3,1,1]
[7,5,8,3,4,6,2,1]=>1010011=>[1,2,3,1,1]
[7,4,5,8,1,6,3,2]=>1001011=>[1,3,2,1,1]
[6,3,4,7,8,5,2,1]=>1000111=>[1,4,1,1,1]
[3,6,8,4,5,7,1,2]=>0010010=>[3,3,2]
[1,6,8,4,7,2,3,5]=>0010100=>[3,2,3]
[1,4,5,7,8,2,6,3]=>0000101=>[5,2,1]
[1,4,5,8,7,2,3,6]=>0001100=>[4,1,3]
[1,2,5,8,3,6,4,7]=>0001010=>[4,2,2]
[7,8,1,4,6,2,3,5]=>0100100=>[2,3,3]
[1,6,7,4,8,2,5,3]=>0010101=>[3,2,2,1]
[1,4,5,6,8,2,7,3]=>0000101=>[5,2,1]
[1,4,5,8,6,2,7,3]=>0001101=>[4,1,2,1]
[1,2,5,8,3,4,7,6]=>0001001=>[4,3,1]
[7,8,1,2,3,5,4,6]=>0100010=>[2,4,2]
[1,6,7,2,3,5,4,8]=>0010010=>[3,3,2]
[1,4,5,7,6,2,3,8]=>0001100=>[4,1,3]
[1,2,5,7,3,6,4,8]=>0001010=>[4,2,2]
[1,2,5,7,3,6,8,4]=>0001001=>[4,3,1]
[1,6,8,2,3,5,7,4]=>0010001=>[3,4,1]
[1,6,8,4,5,2,3,7]=>0010100=>[3,2,3]
[1,6,8,2,3,4,7,5]=>0010001=>[3,4,1]
[1,6,8,2,3,7,4,5]=>0010010=>[3,3,2]
[1,4,5,7,6,2,8,3]=>0001101=>[4,1,2,1]
[7,8,1,4,5,2,6,3]=>0100101=>[2,3,2,1]
[1,6,7,2,3,8,5,4]=>0010011=>[3,3,1,1]
[1,2,5,6,3,8,7,4]=>0001011=>[4,2,1,1]
[2,7,4,8,3,5,1,6]=>0101010=>[2,2,2,2]
[2,7,4,8,3,5,6,1]=>0101001=>[2,2,3,1]
[7,2,8,4,3,5,1,6]=>1011010=>[1,2,1,2,2]
[8,4,2,1,5,3,6,7]=>1110100=>[1,1,1,2,3]
[8,4,1,5,3,2,6,7]=>1101100=>[1,1,2,1,3]
[6,7,3,8,4,2,5,1]=>0101101=>[2,2,1,2,1]
[6,7,3,8,4,2,1,5]=>0101110=>[2,2,1,1,2]
[7,1,8,4,3,5,2,6]=>1011010=>[1,2,1,2,2]
[1,7,8,4,3,5,2,6]=>0011010=>[3,1,2,2]
[7,1,4,8,3,5,2,6]=>1001010=>[1,3,2,2]
[7,1,8,4,3,5,6,2]=>1011001=>[1,2,1,3,1]
[6,7,3,1,8,4,5,2]=>0110101=>[2,1,2,2,1]
[6,7,1,4,8,3,5,2]=>0100101=>[2,3,2,1]
[6,7,4,1,3,8,2,5]=>0110010=>[2,1,3,2]
[1,6,7,8,4,3,2,5]=>0001110=>[4,1,1,2]
[7,2,1,8,4,5,3,6]=>1101010=>[1,1,2,2,2]
[6,2,7,1,8,4,3,5]=>1010110=>[1,2,2,1,2]
[6,2,7,8,4,3,1,5]=>1001110=>[1,3,1,1,2]
[6,2,7,8,4,3,5,1]=>1001101=>[1,3,1,2,1]
[2,6,7,4,8,3,5,1]=>0010101=>[3,2,2,1]
[2,6,7,4,8,3,1,5]=>0010110=>[3,2,1,2]
[7,8,1,3,6,2,4,5]=>0100100=>[2,3,3]
[1,2,7,8,6,3,4,5]=>0001100=>[4,1,3]
[2,6,7,1,8,5,3,4]=>0010110=>[3,2,1,2]
[2,6,7,8,5,3,4,1]=>0001101=>[4,1,2,1]
[6,2,7,8,4,5,3,1]=>1001011=>[1,3,2,1,1]
[1,7,2,8,4,5,6,3]=>0101001=>[2,2,3,1]
[6,3,7,8,1,5,2,4]=>1001010=>[1,3,2,2]
[6,7,1,2,8,5,3,4]=>0100110=>[2,3,1,2]
[1,6,7,8,4,2,5,3]=>0001101=>[4,1,2,1]
[3,1,2,7,6,5,8,4]=>1001101=>[1,3,1,2,1]
[6,1,2,4,7,3,8,5]=>1000101=>[1,4,2,1]
[1,7,5,3,6,4,8,2]=>0110101=>[2,1,2,2,1]
[5,1,2,6,7,4,8,3]=>1000101=>[1,4,2,1]
[4,1,5,7,3,2,6,8]=>1001100=>[1,3,1,3]
[4,6,1,7,3,2,5,8]=>0101100=>[2,2,1,3]
[4,6,1,8,3,2,5,7]=>0101100=>[2,2,1,3]
[4,1,7,8,6,2,3,5]=>1001100=>[1,3,1,3]
[1,6,5,7,8,3,4,2]=>0100101=>[2,3,2,1]
[1,6,5,8,7,3,4,2]=>0101101=>[2,2,1,2,1]
[4,1,8,7,6,2,3,5]=>1011100=>[1,2,1,1,3]
[4,8,1,7,3,5,2,6]=>0101010=>[2,2,2,2]
[4,8,1,6,3,2,5,7]=>0101100=>[2,2,1,3]
[4,7,1,6,3,2,5,8]=>0101100=>[2,2,1,3]
[6,1,2,3,7,5,4,8]=>1000110=>[1,4,1,2]
[6,8,1,5,3,7,2,4]=>0101010=>[2,2,2,2]
[8,7,5,2,4,1,6,3]=>1110101=>[1,1,1,2,2,1]
[1,5,8,3,4,7,6,2]=>0010011=>[3,3,1,1]
[7,8,5,2,4,1,6,3]=>0110101=>[2,1,2,2,1]
[7,1,2,3,5,6,4,8]=>1000010=>[1,5,2]
[7,1,8,4,6,3,2,5]=>1010110=>[1,2,2,1,2]
[6,8,2,4,3,1,5,7]=>0101100=>[2,2,1,3]
[6,7,2,4,3,1,5,8]=>0101100=>[2,2,1,3]
[3,7,1,8,6,4,2,5]=>0101110=>[2,2,1,1,2]
[1,6,4,3,7,5,8,2]=>0110101=>[2,1,2,2,1]
[3,1,2,6,7,5,8,4]=>1000101=>[1,4,2,1]
[3,8,1,7,6,4,2,5]=>0101110=>[2,2,1,1,2]
[7,6,2,4,3,1,5,8]=>1101100=>[1,1,2,1,3]
[8,7,2,4,3,5,1,6]=>1101010=>[1,1,2,2,2]
[8,1,7,4,6,3,2,5]=>1010110=>[1,2,2,1,2]
[8,1,7,6,5,3,2,4]=>1011110=>[1,2,1,1,1,2]
[1,5,7,3,4,6,8,2]=>0010001=>[3,4,1]
[8,7,2,5,3,6,1,4]=>1101010=>[1,1,2,2,2]
[7,1,2,3,5,4,8,6]=>1000101=>[1,4,2,1]
[6,1,2,3,5,8,4,7]=>1000010=>[1,5,2]
[6,1,2,3,5,7,4,8]=>1000010=>[1,5,2]
[5,1,2,3,7,6,4,8]=>1000110=>[1,4,1,2]
[5,1,2,3,8,6,4,7]=>1000110=>[1,4,1,2]
[1,5,6,3,4,7,8,2]=>0010001=>[3,4,1]
[8,6,5,2,4,7,1,3]=>1110010=>[1,1,1,3,2]
[7,6,2,5,3,1,8,4]=>1101101=>[1,1,2,1,2,1]
[6,7,3,5,1,4,8,2]=>0101001=>[2,2,3,1]
[5,3,6,7,4,8,2,1]=>1001011=>[1,3,2,1,1]
[5,3,2,8,6,7,4,1]=>1101011=>[1,1,2,2,1,1]
[5,4,8,2,6,7,3,1]=>1010011=>[1,2,3,1,1]
[5,4,8,6,2,7,3,1]=>1011011=>[1,2,1,2,1,1]
[5,6,3,8,4,7,2,1]=>0101011=>[2,2,2,1,1]
[6,7,3,8,5,2,4,1]=>0101101=>[2,2,1,2,1]
[3,5,7,8,4,6,2,1]=>0001011=>[4,2,1,1]
[5,7,8,2,4,6,3,1]=>0010011=>[3,3,1,1]
[2,5,8,4,3,7,6,1]=>0011011=>[3,1,2,1,1]
[3,7,4,8,6,2,1,5]=>0101110=>[2,2,1,1,2]
[3,6,4,8,7,2,5,1]=>0101101=>[2,2,1,2,1]
[3,5,4,8,2,7,6,1]=>0101011=>[2,2,2,1,1]
[4,5,7,3,8,6,2,1]=>0010111=>[3,2,1,1,1]
[6,3,1,8,7,5,4,2]=>1101111=>[1,1,2,1,1,1,1]
[5,4,8,1,7,6,3,2]=>1010111=>[1,2,2,1,1,1]
[5,8,4,1,7,6,3,2]=>0110111=>[2,1,2,1,1,1]
[7,5,4,1,8,6,3,2]=>1110111=>[1,1,1,2,1,1,1]
[8,5,4,1,7,6,3,2]=>1110111=>[1,1,1,2,1,1,1]
[1,8,2,5,6,3,4,7]=>0100100=>[2,3,3]
[7,2,8,4,5,1,3,6]=>1010100=>[1,2,2,3]
[1,3,7,5,6,2,4,8]=>0010100=>[3,2,3]
[1,6,7,4,3,5,2,8]=>0011010=>[3,1,2,2]
[1,8,2,5,3,6,7,4]=>0101001=>[2,2,3,1]
[2,6,8,4,3,5,7,1]=>0011001=>[3,1,3,1]
[7,2,8,4,1,5,6,3]=>1011001=>[1,2,1,3,1]
[7,5,8,1,2,6,3,4]=>1010010=>[1,2,3,2]
[1,5,2,6,4,7,8,3]=>0101001=>[2,2,3,1]
[1,5,4,6,2,3,7,8]=>0101000=>[2,2,4]
[6,2,5,7,1,4,8,3]=>1001001=>[1,3,3,1]
[6,5,4,3,8,1,7,2]=>1110101=>[1,1,1,2,2,1]
[2,6,5,8,3,4,1,7]=>0101010=>[2,2,2,2]
[2,6,5,7,3,4,1,8]=>0101010=>[2,2,2,2]
[6,2,5,7,4,1,3,8]=>1001100=>[1,3,1,3]
[6,2,5,8,4,1,3,7]=>1001100=>[1,3,1,3]
[2,7,8,4,6,1,3,5]=>0010100=>[3,2,3]
[6,1,2,8,5,4,7,3]=>1001101=>[1,3,1,2,1]
[6,2,5,7,8,1,3,4]=>1000100=>[1,4,3]
[1,5,4,2,6,7,3,8]=>0110010=>[2,1,3,2]
[2,6,5,7,3,8,1,4]=>0101010=>[2,2,2,2]
[1,6,2,7,5,8,4,3]=>0101011=>[2,2,2,1,1]
[1,3,2,7,8,5,6,4]=>0100101=>[2,3,2,1]
[1,6,2,4,8,7,3,5]=>0100110=>[2,3,1,2]
[6,5,2,1,8,7,3,4]=>1110110=>[1,1,1,2,1,2]
[2,6,5,3,7,8,4,1]=>0110011=>[2,1,3,1,1]
[6,5,2,3,8,7,1,4]=>1100110=>[1,1,3,1,2]
[5,1,4,2,3,7,8,6]=>1010001=>[1,2,4,1]
[1,5,4,2,6,3,8,7]=>0110101=>[2,1,2,2,1]
[5,1,6,3,8,2,7,4]=>1010101=>[1,2,2,2,1]
[6,5,8,7,4,3,1,2]=>1011110=>[1,2,1,1,1,2]
[6,4,2,7,8,5,1,3]=>1100110=>[1,1,3,1,2]
[6,1,4,8,7,5,2,3]=>1001110=>[1,3,1,1,2]
[1,6,4,8,7,5,2,3]=>0101110=>[2,2,1,1,2]
[1,8,6,2,4,7,3,5]=>0110010=>[2,1,3,2]
[8,1,6,2,4,7,3,5]=>1010010=>[1,2,3,2]
[6,4,1,7,8,5,2,3]=>1100110=>[1,1,3,1,2]
[7,6,1,2,4,8,3,5]=>1100010=>[1,1,4,2]
[1,8,6,3,4,7,2,5]=>0110010=>[2,1,3,2]
[1,7,2,5,4,8,3,6]=>0101010=>[2,2,2,2]
[7,1,2,5,4,8,3,6]=>1001010=>[1,3,2,2]
[2,7,1,5,4,8,3,6]=>0101010=>[2,2,2,2]
[2,8,6,1,4,7,3,5]=>0110010=>[2,1,3,2]
[7,2,1,5,4,8,3,6]=>1101010=>[1,1,2,2,2]
[1,2,7,5,4,8,3,6]=>0011010=>[3,1,2,2]
[3,2,7,5,4,8,1,6]=>1011010=>[1,2,1,2,2]
[2,5,8,4,7,3,1,6]=>0010110=>[3,2,1,2]
[2,3,7,5,4,8,1,6]=>0011010=>[3,1,2,2]
[6,8,3,2,4,7,1,5]=>0110010=>[2,1,3,2]
[3,7,2,5,4,8,1,6]=>0101010=>[2,2,2,2]
[3,1,7,5,4,8,2,6]=>1011010=>[1,2,1,2,2]
[1,3,7,5,4,8,2,6]=>0011010=>[3,1,2,2]
[1,5,8,4,7,3,2,6]=>0010110=>[3,2,1,2]
[5,1,8,4,7,3,2,6]=>1010110=>[1,2,2,1,2]
[5,8,2,4,7,3,1,6]=>0100110=>[2,3,1,2]
[6,8,4,3,7,5,1,2]=>0110110=>[2,1,2,1,2]
[8,5,2,4,7,3,1,6]=>1100110=>[1,1,3,1,2]
[8,1,5,4,7,3,2,6]=>1010110=>[1,2,2,1,2]
[1,8,5,4,7,3,2,6]=>0110110=>[2,1,2,1,2]
[1,7,3,5,4,8,2,6]=>0101010=>[2,2,2,2]
[8,6,3,1,4,7,2,5]=>1110010=>[1,1,1,3,2]
[8,6,4,1,7,2,5,3]=>1110101=>[1,1,1,2,2,1]
[5,3,7,4,6,8,2,1]=>1010011=>[1,2,3,1,1]
[4,1,3,2,7,8,5,6]=>1010010=>[1,2,3,2]
[1,4,3,2,7,8,5,6]=>0110010=>[2,1,3,2]
[2,4,3,1,7,8,5,6]=>0110010=>[2,1,3,2]
[2,7,3,5,4,8,1,6]=>0101010=>[2,2,2,2]
[2,8,5,4,7,3,1,6]=>0110110=>[2,1,2,1,2]
[5,7,3,4,6,8,2,1]=>0100011=>[2,4,1,1]
[8,2,5,4,7,3,1,6]=>1010110=>[1,2,2,1,2]
[7,2,3,5,4,8,1,6]=>1001010=>[1,3,2,2]
[3,2,1,4,7,8,5,6]=>1100010=>[1,1,4,2]
[8,1,7,6,4,3,5,2]=>1011101=>[1,2,1,1,2,1]
[8,6,4,5,2,7,1,3]=>1101010=>[1,1,2,2,2]
[7,1,8,6,4,3,5,2]=>1011101=>[1,2,1,1,2,1]
[7,4,2,5,1,6,3,8]=>1101010=>[1,1,2,2,2]
[7,3,6,5,2,1,4,8]=>1011100=>[1,2,1,1,3]
[8,3,6,5,2,1,7,4]=>1011101=>[1,2,1,1,2,1]
[7,3,6,5,2,1,8,4]=>1011101=>[1,2,1,1,2,1]
[5,4,2,8,1,3,7,6]=>1101001=>[1,1,2,3,1]
[5,8,2,6,4,1,3,7]=>0101100=>[2,2,1,3]
[6,4,2,5,1,8,3,7]=>1101010=>[1,1,2,2,2]
[6,3,5,2,1,4,7,8]=>1011000=>[1,2,1,4]
[2,3,5,8,1,4,7,6]=>0001001=>[4,3,1]
[2,3,6,8,1,5,7,4]=>0001001=>[4,3,1]
[6,3,8,5,2,7,1,4]=>1011010=>[1,2,1,2,2]
[6,3,7,5,2,1,4,8]=>1011100=>[1,2,1,1,3]
[2,5,7,6,3,1,4,8]=>0011100=>[3,1,1,3]
[2,8,7,6,3,1,5,4]=>0111101=>[2,1,1,1,2,1]
[2,5,8,7,6,3,1,4]=>0011110=>[3,1,1,1,2]
[2,4,8,1,6,5,7,3]=>0010101=>[3,2,2,1]
[2,8,7,3,6,1,4,5]=>0110100=>[2,1,2,3]
[8,4,2,5,1,3,7,6]=>1101001=>[1,1,2,3,1]
[2,3,6,8,1,4,7,5]=>0001001=>[4,3,1]
[2,7,8,6,3,1,4,5]=>0011100=>[3,1,1,3]
[2,8,6,3,1,4,5,7]=>0111000=>[2,1,1,4]
[8,3,5,2,1,4,6,7]=>1011000=>[1,2,1,4]
[2,5,8,1,7,3,6,4]=>0010101=>[3,2,2,1]
[2,7,1,5,8,3,4,6]=>0100100=>[2,3,3]
[3,7,5,8,1,2,6,4]=>0101001=>[2,2,3,1]
[7,3,6,1,2,8,4,5]=>1010010=>[1,2,3,2]
[7,4,8,1,6,5,2,3]=>1010110=>[1,2,2,1,2]
[6,8,4,5,1,7,2,3]=>0101010=>[2,2,2,2]
[5,1,8,7,6,2,3,4]=>1011100=>[1,2,1,1,3]
[4,6,1,8,7,5,2,3]=>0101110=>[2,2,1,1,2]
[3,4,8,7,1,2,5,6]=>0011000=>[3,1,4]
[6,4,8,7,1,2,5,3]=>1011001=>[1,2,1,3,1]
[6,5,1,8,2,7,3,4]=>1101010=>[1,1,2,2,2]
[6,5,1,7,2,8,3,4]=>1101010=>[1,1,2,2,2]
[6,5,1,7,2,3,8,4]=>1101001=>[1,1,2,3,1]
[5,6,8,7,4,1,2,3]=>0011100=>[3,1,1,3]
[6,8,3,1,5,2,4,7]=>0110100=>[2,1,2,3]
[4,2,7,1,6,3,5,8]=>1010100=>[1,2,2,3]
[5,1,7,4,2,6,3,8]=>1011010=>[1,2,1,2,2]
[5,8,2,1,4,7,3,6]=>0110010=>[2,1,3,2]
[6,8,4,3,1,5,7,2]=>0111001=>[2,1,1,3,1]
[6,8,4,2,1,5,7,3]=>0111001=>[2,1,1,3,1]
[6,8,3,2,1,4,5,7]=>0111000=>[2,1,1,4]
[4,2,1,6,5,8,3,7]=>1101010=>[1,1,2,2,2]
[6,3,2,1,7,4,5,8]=>1110100=>[1,1,1,2,3]
[6,4,2,1,7,5,3,8]=>1110110=>[1,1,1,2,1,2]
[5,3,2,7,6,1,4,8]=>1101100=>[1,1,2,1,3]
[5,3,2,8,6,1,4,7]=>1101100=>[1,1,2,1,3]
[6,3,2,8,7,1,4,5]=>1101100=>[1,1,2,1,3]
[4,2,8,1,7,3,5,6]=>1010100=>[1,2,2,3]
[4,3,8,7,2,1,5,6]=>1011100=>[1,2,1,1,3]
[2,1,5,8,4,7,3,6]=>1001010=>[1,3,2,2]
[4,3,2,5,8,1,6,7]=>1100100=>[1,1,3,3]
[4,3,2,5,7,1,6,8]=>1100100=>[1,1,3,3]
[4,3,1,6,2,7,5,8]=>1101010=>[1,1,2,2,2]
[5,4,1,7,2,8,6,3]=>1101011=>[1,1,2,2,1,1]
[3,2,1,4,8,7,5,6]=>1100110=>[1,1,3,1,2]
[3,2,1,4,6,8,5,7]=>1100010=>[1,1,4,2]
[8,6,1,4,5,7,2,3]=>1100010=>[1,1,4,2]
[3,8,6,4,5,7,1,2]=>0110010=>[2,1,3,2]
[5,2,8,3,7,4,6,1]=>1010101=>[1,2,2,2,1]
[6,2,8,5,4,7,3,1]=>1011011=>[1,2,1,2,1,1]
[5,2,8,4,3,6,7,1]=>1011001=>[1,2,1,3,1]
[5,4,2,7,3,6,1,8]=>1101010=>[1,1,2,2,2]
[5,4,2,8,3,6,1,7]=>1101010=>[1,1,2,2,2]
[6,5,3,8,4,7,2,1]=>1101011=>[1,1,2,2,1,1]
[5,2,8,4,3,7,1,6]=>1011010=>[1,2,1,2,2]
[6,2,8,3,7,4,1,5]=>1010110=>[1,2,2,1,2]
[5,4,2,7,3,1,8,6]=>1101101=>[1,1,2,1,2,1]
[6,4,3,7,1,2,8,5]=>1101001=>[1,1,2,3,1]
[6,4,3,8,1,2,7,5]=>1101001=>[1,1,2,3,1]
[7,2,8,4,3,1,5,6]=>1011100=>[1,2,1,1,3]
[7,5,3,8,4,2,6,1]=>1101101=>[1,1,2,1,2,1]
[6,4,2,7,3,1,5,8]=>1101100=>[1,1,2,1,3]
[7,6,4,8,2,3,5,1]=>1101001=>[1,1,2,3,1]
[5,3,1,7,8,4,6,2]=>1100101=>[1,1,3,2,1]
[5,3,2,7,8,4,6,1]=>1100101=>[1,1,3,2,1]
[6,5,1,7,8,2,3,4]=>1100100=>[1,1,3,3]
[6,3,1,7,8,4,2,5]=>1100110=>[1,1,3,1,2]
[5,4,1,7,3,8,2,6]=>1101010=>[1,1,2,2,2]
[6,3,2,7,8,4,1,5]=>1100110=>[1,1,3,1,2]
[6,1,5,4,3,2,8,7]=>1011101=>[1,2,1,1,2,1]
[8,7,6,1,3,5,2,4]=>1110010=>[1,1,1,3,2]
[8,1,6,5,7,3,4,2]=>1010101=>[1,2,2,2,1]
[8,4,1,5,7,6,2,3]=>1100110=>[1,1,3,1,2]
[7,8,6,2,5,3,1,4]=>0110110=>[2,1,2,1,2]
[6,1,3,5,2,8,4,7]=>1001010=>[1,3,2,2]
[8,1,3,7,4,2,5,6]=>1001100=>[1,3,1,3]
[4,3,8,7,5,2,1,6]=>1011110=>[1,2,1,1,1,2]
[6,7,1,8,5,3,4,2]=>0101101=>[2,2,1,2,1]
[2,7,6,4,8,3,5,1]=>0110101=>[2,1,2,2,1]
[6,5,2,7,1,4,8,3]=>1101001=>[1,1,2,3,1]
[7,4,6,1,3,2,8,5]=>1010101=>[1,2,2,2,1]
[7,5,2,1,3,8,4,6]=>1110010=>[1,1,1,3,2]
[8,4,7,6,3,1,5,2]=>1011101=>[1,2,1,1,2,1]
[7,4,1,5,6,3,8,2]=>1100101=>[1,1,3,2,1]
[3,4,7,5,6,1,8,2]=>0010101=>[3,2,2,1]
[2,7,6,1,3,4,8,5]=>0110001=>[2,1,4,1]
[5,7,2,1,6,3,8,4]=>0110101=>[2,1,2,2,1]
[4,7,2,5,6,3,8,1]=>0100101=>[2,3,2,1]
[8,6,2,5,7,1,4,3]=>1100101=>[1,1,3,2,1]
[2,7,4,5,3,8,1,6]=>0101010=>[2,2,2,2]
[6,8,7,1,3,2,5,4]=>0110101=>[2,1,2,2,1]
[2,8,6,5,7,1,4,3]=>0110101=>[2,1,2,2,1]
[5,8,4,3,2,6,7,1]=>0111001=>[2,1,1,3,1]
[1,8,5,6,2,4,7,3]=>0101001=>[2,2,3,1]
[8,1,5,6,2,4,7,3]=>1001001=>[1,3,3,1]
[6,4,8,1,3,2,7,5]=>1010101=>[1,2,2,2,1]
[5,4,1,2,8,6,7,3]=>1100101=>[1,1,3,2,1]
[8,4,5,2,1,6,7,3]=>1011001=>[1,2,1,3,1]
[3,1,2,6,8,4,7,5]=>1000101=>[1,4,2,1]
[5,1,3,2,7,8,4,6]=>1010010=>[1,2,3,2]
[4,6,7,8,3,1,5,2]=>0001101=>[4,1,2,1]
[5,2,8,6,3,4,7,1]=>1011001=>[1,2,1,3,1]
[5,6,8,4,3,2,7,1]=>0011101=>[3,1,1,2,1]
[5,3,8,1,7,2,4,6]=>1010100=>[1,2,2,3]
[3,6,7,8,4,2,1,5]=>0001110=>[4,1,1,2]
[6,5,1,8,4,3,7,2]=>1101101=>[1,1,2,1,2,1]
[6,3,8,4,2,1,7,5]=>1011101=>[1,2,1,1,2,1]
[2,5,8,3,1,6,7,4]=>0011001=>[3,1,3,1]
[3,5,8,1,2,6,7,4]=>0010001=>[3,4,1]
[3,2,7,8,4,6,1,5]=>1001010=>[1,3,2,2]
[5,1,8,3,4,6,7,2]=>1010001=>[1,2,4,1]
[4,8,7,2,1,6,3,5]=>0111010=>[2,1,1,2,2]
[2,8,1,6,3,4,7,5]=>0101001=>[2,2,3,1]
[3,6,1,2,5,8,4,7]=>0100010=>[2,4,2]
[1,4,5,8,2,3,7,6]=>0001001=>[4,3,1]
[1,5,2,4,6,8,3,7]=>0100010=>[2,4,2]
[3,6,1,5,8,2,4,7]=>0100100=>[2,3,3]
[2,6,5,1,4,8,3,7]=>0110010=>[2,1,3,2]
[2,5,1,8,4,7,3,6]=>0101010=>[2,2,2,2]
[2,7,1,4,3,6,8,5]=>0101001=>[2,2,3,1]
[1,3,7,5,8,2,4,6]=>0010100=>[3,2,3]
[8,2,1,5,7,3,4,6]=>1100100=>[1,1,3,3]
[2,5,4,8,1,3,7,6]=>0101001=>[2,2,3,1]
[2,4,1,3,8,6,7,5]=>0100101=>[2,3,2,1]
[8,4,3,7,1,2,6,5]=>1101001=>[1,1,2,3,1]
[1,7,3,5,8,2,6,4]=>0100101=>[2,3,2,1]
[1,8,4,2,6,7,3,5]=>0110010=>[2,1,3,2]
[3,1,6,8,7,2,4,5]=>1001100=>[1,3,1,3]
[7,2,1,6,8,3,4,5]=>1100100=>[1,1,3,3]
[4,1,7,2,6,8,3,5]=>1010010=>[1,2,3,2]
[5,1,7,2,3,6,8,4]=>1010001=>[1,2,4,1]
[7,2,1,6,3,5,8,4]=>1101001=>[1,1,2,3,1]
[2,6,1,7,3,5,8,4]=>0101001=>[2,2,3,1]
[8,1,3,2,4,6,7,5]=>1010001=>[1,2,4,1]
[7,3,1,2,4,6,8,5]=>1100001=>[1,1,5,1]
[1,8,3,4,7,2,5,6]=>0100100=>[2,3,3]
[3,5,8,1,2,7,4,6]=>0010010=>[3,3,2]
[3,6,8,1,2,4,7,5]=>0010001=>[3,4,1]
[4,1,3,8,7,2,6,5]=>1001101=>[1,3,1,2,1]
[1,3,7,4,8,2,6,5]=>0010101=>[3,2,2,1]
[1,4,6,8,2,3,7,5]=>0001001=>[4,3,1]
[3,5,8,1,7,2,4,6]=>0010100=>[3,2,3]
[2,6,8,1,7,3,4,5]=>0010100=>[3,2,3]
[1,8,3,2,7,5,6,4]=>0110101=>[2,1,2,2,1]
[2,6,7,3,8,1,5,4]=>0010101=>[3,2,2,1]
[8,4,1,7,3,6,2,5]=>1101010=>[1,1,2,2,2]
[3,7,2,8,6,1,5,4]=>0101101=>[2,2,1,2,1]
[6,2,3,8,7,1,5,4]=>1001101=>[1,3,1,2,1]
[5,1,7,8,4,2,6,3]=>1001101=>[1,3,1,2,1]
[5,1,8,7,4,2,6,3]=>1011101=>[1,2,1,1,2,1]
[4,7,2,8,3,6,5,1]=>0101011=>[2,2,2,1,1]
[4,1,7,8,5,3,6,2]=>1001101=>[1,3,1,2,1]
[5,1,7,4,8,3,6,2]=>1010101=>[1,2,2,2,1]
[4,1,8,7,5,3,6,2]=>1011101=>[1,2,1,1,2,1]
[4,8,2,7,3,6,5,1]=>0101011=>[2,2,2,1,1]
[4,7,2,6,3,5,8,1]=>0101001=>[2,2,3,1]
[6,8,2,4,3,7,5,1]=>0101011=>[2,2,2,1,1]
[6,7,2,4,3,8,5,1]=>0101011=>[2,2,2,1,1]
[3,8,7,2,4,1,5,6]=>0110100=>[2,1,2,3]
[3,7,8,2,4,1,5,6]=>0010100=>[3,2,3]
[3,6,8,2,4,5,7,1]=>0010001=>[3,4,1]
[3,6,7,2,4,5,8,1]=>0010001=>[3,4,1]
[1,7,5,3,8,2,4,6]=>0110100=>[2,1,2,3]
[1,7,2,4,5,8,3,6]=>0100010=>[2,4,2]
[1,7,4,5,8,3,2,6]=>0100110=>[2,3,1,2]
[2,6,4,7,8,3,5,1]=>0100101=>[2,3,2,1]
[1,2,6,4,7,8,3,5]=>0010010=>[3,3,2]
[2,7,4,5,8,1,3,6]=>0100100=>[2,3,3]
[2,7,5,3,1,8,4,6]=>0111010=>[2,1,1,2,2]
[6,1,4,7,8,3,5,2]=>1000101=>[1,4,2,1]
[3,6,4,7,8,1,5,2]=>0100101=>[2,3,2,1]
[4,3,6,7,1,8,5,2]=>1001011=>[1,3,2,1,1]
[4,3,6,7,1,8,2,5]=>1001010=>[1,3,2,2]
[3,7,4,5,2,1,8,6]=>0101101=>[2,2,1,2,1]
[1,3,6,4,7,2,8,5]=>0010101=>[3,2,2,1]
[3,6,4,7,2,8,5,1]=>0101011=>[2,2,2,1,1]
[6,1,7,3,8,2,5,4]=>1010101=>[1,2,2,2,1]
[1,6,7,3,8,2,5,4]=>0010101=>[3,2,2,1]
[6,1,4,7,8,5,2,3]=>1000110=>[1,4,1,2]
[6,3,2,1,7,8,5,4]=>1110011=>[1,1,1,3,1,1]
[6,2,7,3,1,8,5,4]=>1011011=>[1,2,1,2,1,1]
[6,2,4,7,8,1,5,3]=>1000101=>[1,4,2,1]
[2,6,7,3,1,8,5,4]=>0011011=>[3,1,2,1,1]
[8,6,5,1,3,2,4,7]=>1110100=>[1,1,1,2,3]
[6,4,7,8,3,2,5,1]=>1001101=>[1,3,1,2,1]
[3,8,4,7,1,2,5,6]=>0101000=>[2,2,4]
[4,8,6,1,5,3,2,7]=>0110110=>[2,1,2,1,2]
[5,8,6,4,1,3,2,7]=>0111010=>[2,1,1,2,2]
[8,3,6,4,5,2,1,7]=>1010110=>[1,2,2,1,2]
[6,8,5,7,4,2,3,1]=>0101101=>[2,2,1,2,1]
[2,3,8,7,1,6,4,5]=>0011010=>[3,1,2,2]
[4,3,7,8,1,6,2,5]=>1001010=>[1,3,2,2]
[3,5,8,7,4,1,2,6]=>0011100=>[3,1,1,3]
[7,3,8,4,1,2,5,6]=>1011000=>[1,2,1,4]
[4,8,1,2,7,3,5,6]=>0100100=>[2,3,3]
[6,8,1,2,7,4,5,3]=>0100101=>[2,3,2,1]
[5,6,8,4,1,3,7,2]=>0011001=>[3,1,3,1]
[8,5,4,7,1,6,3,2]=>1101011=>[1,1,2,2,1,1]
[2,5,8,7,3,6,4,1]=>0011011=>[3,1,2,1,1]
[2,4,8,7,5,6,1,3]=>0011010=>[3,1,2,2]
[3,7,4,8,5,6,2,1]=>0101011=>[2,2,2,1,1]
[6,4,8,7,5,1,2,3]=>1011100=>[1,2,1,1,3]
[3,8,5,2,4,6,7,1]=>0110001=>[2,1,4,1]
[5,7,1,8,4,6,2,3]=>0101010=>[2,2,2,2]
[6,3,8,7,2,1,4,5]=>1011100=>[1,2,1,1,3]
[2,3,7,8,5,6,1,4]=>0001010=>[4,2,2]
[3,7,6,8,5,1,2,4]=>0101100=>[2,2,1,3]
[2,6,7,8,5,1,3,4]=>0001100=>[4,1,3]
[2,4,7,8,1,6,3,5]=>0001010=>[4,2,2]
[5,4,7,8,2,6,3,1]=>1001011=>[1,3,2,1,1]
[2,8,3,4,1,5,7,6]=>0101001=>[2,2,3,1]
[6,8,3,4,1,2,7,5]=>0101001=>[2,2,3,1]
[6,8,7,1,5,2,3,4]=>0110100=>[2,1,2,3]
[2,5,3,1,8,6,7,4]=>0110101=>[2,1,2,2,1]
[4,5,3,2,8,6,7,1]=>0110101=>[2,1,2,2,1]
[3,5,8,6,1,4,7,2]=>0011001=>[3,1,3,1]
[2,8,5,6,1,4,7,3]=>0101001=>[2,2,3,1]
[4,8,6,1,5,2,7,3]=>0110101=>[2,1,2,2,1]
[5,8,2,3,7,6,1,4]=>0100110=>[2,3,1,2]
[4,6,8,5,3,2,7,1]=>0011101=>[3,1,1,2,1]
[2,6,4,8,5,1,7,3]=>0101101=>[2,2,1,2,1]
[7,6,4,8,5,2,1,3]=>1101110=>[1,1,2,1,1,2]
[3,4,8,6,5,2,7,1]=>0011101=>[3,1,1,2,1]
[3,4,8,7,5,6,2,1]=>0011011=>[3,1,2,1,1]
[7,5,3,2,8,6,1,4]=>1110110=>[1,1,1,2,1,2]
[2,5,1,3,8,6,7,4]=>0100101=>[2,3,2,1]
[4,5,1,2,8,6,7,3]=>0100101=>[2,3,2,1]
[5,4,8,1,3,6,7,2]=>1010001=>[1,2,4,1]
[8,3,5,4,1,6,7,2]=>1011001=>[1,2,1,3,1]
[5,1,6,4,3,2,8,7]=>1011101=>[1,2,1,1,2,1]
[8,3,7,1,4,6,5,2]=>1010011=>[1,2,3,1,1]
[2,8,3,6,4,7,5,1]=>0101011=>[2,2,2,1,1]
[6,2,1,7,5,8,3,4]=>1101010=>[1,1,2,2,2]
[6,7,2,1,5,8,4,3]=>0110011=>[2,1,3,1,1]
[1,6,4,8,3,2,5,7]=>0101100=>[2,2,1,3]
[1,8,3,5,6,2,4,7]=>0100100=>[2,3,3]
[1,4,8,5,6,2,3,7]=>0010100=>[3,2,3]
[6,1,4,8,2,3,5,7]=>1001000=>[1,3,4]
[8,7,2,5,6,1,4,3]=>1100101=>[1,1,3,2,1]
[1,8,2,5,4,7,3,6]=>0101010=>[2,2,2,2]
[5,7,4,1,2,3,8,6]=>0110001=>[2,1,4,1]
[1,7,4,2,5,3,8,6]=>0110101=>[2,1,2,2,1]
[6,7,4,2,1,3,8,5]=>0111001=>[2,1,1,3,1]
[6,4,3,8,5,7,1,2]=>1101010=>[1,1,2,2,2]
[6,8,4,2,3,1,5,7]=>0110100=>[2,1,2,3]
[8,6,4,1,3,7,2,5]=>1110010=>[1,1,1,3,2]
[5,3,6,1,8,2,4,7]=>1010100=>[1,2,2,3]
[3,1,8,5,4,7,6,2]=>1011011=>[1,2,1,2,1,1]
[4,1,5,8,3,7,6,2]=>1001011=>[1,3,2,1,1]
[4,1,5,3,8,7,6,2]=>1010111=>[1,2,2,1,1,1]
[4,5,1,8,2,7,6,3]=>0101011=>[2,2,2,1,1]
[4,8,5,3,1,7,6,2]=>0111011=>[2,1,1,2,1,1]
[4,5,2,8,1,7,6,3]=>0101011=>[2,2,2,1,1]
[4,6,2,8,7,1,5,3]=>0101101=>[2,2,1,2,1]
[4,8,6,3,7,1,5,2]=>0110101=>[2,1,2,2,1]
[4,6,8,2,7,5,1,3]=>0010110=>[3,2,1,2]
[4,6,2,8,7,5,1,3]=>0101110=>[2,2,1,1,2]
[5,6,2,7,4,1,8,3]=>0101101=>[2,2,1,2,1]
[5,6,7,2,3,1,8,4]=>0010101=>[3,2,2,1]
[5,6,7,2,8,3,1,4]=>0010110=>[3,2,1,2]
[5,6,7,2,1,8,3,4]=>0011010=>[3,1,2,2]
[5,6,7,2,1,3,8,4]=>0011001=>[3,1,3,1]
[5,6,1,7,8,2,4,3]=>0100101=>[2,3,2,1]
[5,6,1,7,2,4,8,3]=>0101001=>[2,2,3,1]
[4,1,6,8,7,3,5,2]=>1001101=>[1,3,1,2,1]
[4,1,6,8,7,5,3,2]=>1001111=>[1,3,1,1,1,1]
[5,6,1,7,8,4,2,3]=>0100110=>[2,3,1,2]
[4,6,8,1,7,5,2,3]=>0010110=>[3,2,1,2]
[4,8,6,1,7,5,3,2]=>0110111=>[2,1,2,1,1,1]
[5,6,7,1,8,3,2,4]=>0010110=>[3,2,1,2]
[5,6,7,1,3,8,2,4]=>0010010=>[3,3,2]
[5,6,7,1,3,2,8,4]=>0010101=>[3,2,2,1]
[5,6,7,3,1,2,8,4]=>0011001=>[3,1,3,1]
[5,6,8,7,4,2,1,3]=>0011110=>[3,1,1,1,2]
[7,8,1,3,5,6,2,4]=>0100010=>[2,4,2]
[7,8,3,1,5,6,2,4]=>0110010=>[2,1,3,2]
[7,1,3,8,5,6,2,4]=>1001010=>[1,3,2,2]
[5,1,7,8,3,4,6,2]=>1001001=>[1,3,3,1]
[1,5,7,8,3,4,6,2]=>0001001=>[4,3,1]
[3,7,1,5,8,6,2,4]=>0100110=>[2,3,1,2]
[1,3,7,8,2,5,6,4]=>0001001=>[4,3,1]
[3,1,7,8,5,2,6,4]=>1001101=>[1,3,1,2,1]
[1,3,7,5,8,2,6,4]=>0010101=>[3,2,2,1]
[3,1,7,5,8,2,6,4]=>1010101=>[1,2,2,2,1]
[3,5,7,1,8,4,6,2]=>0010101=>[3,2,2,1]
[3,5,7,8,1,4,6,2]=>0001001=>[4,3,1]
[5,3,7,8,4,6,1,2]=>1001010=>[1,3,2,2]
[5,3,7,8,4,1,6,2]=>1001101=>[1,3,1,2,1]
[5,3,7,8,1,4,6,2]=>1001001=>[1,3,3,1]
[5,3,7,1,8,4,6,2]=>1010101=>[1,2,2,2,1]
[1,5,3,7,8,4,2,6]=>0100110=>[2,3,1,2]
[5,1,3,7,8,4,2,6]=>1000110=>[1,4,1,2]
[3,6,2,1,4,5,8,7]=>0110001=>[2,1,4,1]
[6,4,2,5,1,3,8,7]=>1101001=>[1,1,2,3,1]
[8,6,1,7,3,2,4,5]=>1101100=>[1,1,2,1,3]
[2,5,8,1,7,3,4,6]=>0010100=>[3,2,3]
[6,8,2,7,3,1,4,5]=>0101100=>[2,2,1,3]
[6,8,2,3,7,1,4,5]=>0100100=>[2,3,3]
[8,6,2,7,4,5,1,3]=>1101010=>[1,1,2,2,2]
[5,2,8,1,7,3,4,6]=>1010100=>[1,2,2,3]
[4,2,3,8,1,5,6,7]=>1001000=>[1,3,4]
[5,2,8,3,7,1,4,6]=>1010100=>[1,2,2,3]
[5,2,8,4,6,1,3,7]=>1010100=>[1,2,2,3]
[2,1,5,8,4,3,6,7]=>1001100=>[1,3,1,3]
[5,8,3,2,7,1,4,6]=>0110100=>[2,1,2,3]
[4,1,3,8,2,5,6,7]=>1001000=>[1,3,4]
[5,1,8,3,7,2,4,6]=>1010100=>[1,2,2,3]
[5,1,8,4,6,2,3,7]=>1010100=>[1,2,2,3]
[5,8,4,1,6,2,3,7]=>0110100=>[2,1,2,3]
[4,5,8,1,6,2,3,7]=>0010100=>[3,2,3]
[5,4,8,1,6,2,3,7]=>1010100=>[1,2,2,3]
[4,8,5,1,6,2,3,7]=>0110100=>[2,1,2,3]
[2,1,5,4,8,3,6,7]=>1010100=>[1,2,2,3]
[2,4,3,8,1,5,6,7]=>0101000=>[2,2,4]
[3,1,8,4,2,5,6,7]=>1011000=>[1,2,1,4]
[3,8,4,2,1,5,6,7]=>0111000=>[2,1,1,4]
[2,3,8,4,1,5,6,7]=>0011000=>[3,1,4]
[3,4,2,8,1,5,6,7]=>0101000=>[2,2,4]
[3,8,5,2,7,1,4,6]=>0110100=>[2,1,2,3]
[4,8,5,2,6,1,3,7]=>0110100=>[2,1,2,3]
[2,1,4,8,5,3,6,7]=>1001100=>[1,3,1,3]
[3,2,8,4,1,5,6,7]=>1011000=>[1,2,1,4]
[2,8,4,3,1,5,6,7]=>0111000=>[2,1,1,4]
[4,1,7,5,6,2,8,3]=>1010101=>[1,2,2,2,1]
[5,7,4,3,8,1,6,2]=>0110101=>[2,1,2,2,1]
[5,7,4,3,8,2,6,1]=>0110101=>[2,1,2,2,1]
[3,8,4,2,6,7,5,1]=>0110011=>[2,1,3,1,1]
[3,8,4,1,6,7,5,2]=>0110011=>[2,1,3,1,1]
[6,1,7,5,2,8,4,3]=>1011011=>[1,2,1,2,1,1]
[5,6,4,3,2,8,1,7]=>0111010=>[2,1,1,2,2]
[2,6,7,5,3,8,4,1]=>0011011=>[3,1,2,1,1]
[2,1,6,7,5,3,8,4]=>1001101=>[1,3,1,2,1]
[3,8,4,2,1,6,7,5]=>0111001=>[2,1,1,3,1]
[5,7,4,3,8,2,1,6]=>0110110=>[2,1,2,1,2]
[6,7,4,8,1,2,5,3]=>0101001=>[2,2,3,1]
[6,7,5,8,1,2,4,3]=>0101001=>[2,2,3,1]
[6,7,4,8,3,1,2,5]=>0101100=>[2,2,1,3]
[6,1,3,4,8,2,5,7]=>1000100=>[1,4,3]
[6,2,3,4,8,1,5,7]=>1000100=>[1,4,3]
[3,4,8,2,1,5,7,6]=>0011001=>[3,1,3,1]
[6,7,5,8,3,1,4,2]=>0101101=>[2,2,1,2,1]
[2,5,7,6,1,4,8,3]=>0011001=>[3,1,3,1]
[6,7,4,8,2,3,5,1]=>0101001=>[2,2,3,1]
[6,7,4,8,1,3,5,2]=>0101001=>[2,2,3,1]
[2,6,7,5,1,3,8,4]=>0011001=>[3,1,3,1]
[6,3,1,4,8,2,5,7]=>1100100=>[1,1,3,3]
[6,7,4,8,1,3,2,5]=>0101010=>[2,2,2,2]
[6,7,5,8,4,1,3,2]=>0101101=>[2,2,1,2,1]
[6,7,4,8,2,1,3,5]=>0101100=>[2,2,1,3]
[6,7,4,8,1,2,3,5]=>0101000=>[2,2,4]
[7,8,3,2,6,1,4,5]=>0110100=>[2,1,2,3]
[3,4,8,2,6,1,7,5]=>0010101=>[3,2,2,1]
[7,8,4,1,5,6,3,2]=>0110011=>[2,1,3,1,1]
[7,8,1,2,6,3,4,5]=>0100100=>[2,3,3]
[7,8,5,1,4,6,3,2]=>0110011=>[2,1,3,1,1]
[5,3,8,4,1,6,7,2]=>1011001=>[1,2,1,3,1]
[6,2,4,8,1,5,3,7]=>1001010=>[1,3,2,2]
[3,4,8,5,1,6,7,2]=>0011001=>[3,1,3,1]
[5,3,8,1,4,6,7,2]=>1010001=>[1,2,4,1]
[4,2,6,8,1,5,3,7]=>1001010=>[1,3,2,2]
[7,4,2,8,1,5,3,6]=>1101010=>[1,1,2,2,2]
[6,1,7,5,8,4,3,2]=>1010111=>[1,2,2,1,1,1]
[1,2,7,8,5,3,4,6]=>0001100=>[4,1,3]
[6,3,7,8,5,4,1,2]=>1001110=>[1,3,1,1,2]
[6,1,5,7,8,4,3,2]=>1000111=>[1,4,1,1,1]
[1,7,5,6,8,4,3,2]=>0100111=>[2,3,1,1,1]
[3,1,8,4,5,6,7,2]=>1010001=>[1,2,4,1]
[4,2,1,8,6,5,3,7]=>1101110=>[1,1,2,1,1,2]
[3,2,7,8,5,1,4,6]=>1001100=>[1,3,1,3]
[2,3,7,8,5,1,4,6]=>0001100=>[4,1,3]
[2,7,3,8,5,1,4,6]=>0101100=>[2,2,1,3]
[3,6,2,8,5,1,4,7]=>0101100=>[2,2,1,3]
[1,4,2,8,7,5,3,6]=>0101110=>[2,2,1,1,2]
[7,3,6,8,5,4,1,2]=>1001110=>[1,3,1,1,2]
[7,2,1,8,5,3,4,6]=>1101100=>[1,1,2,1,3]
[1,2,6,8,4,5,3,7]=>0001010=>[4,2,2]
[7,1,6,5,8,4,3,2]=>1010111=>[1,2,2,1,1,1]
[6,5,7,1,8,4,3,2]=>1010111=>[1,2,2,1,1,1]
[5,7,6,1,8,4,3,2]=>0110111=>[2,1,2,1,1,1]
[6,7,1,5,8,4,3,2]=>0100111=>[2,3,1,1,1]
[7,1,2,8,4,5,3,6]=>1001010=>[1,3,2,2]
[7,6,1,5,8,4,3,2]=>1100111=>[1,1,3,1,1,1]
[7,5,6,1,8,4,3,2]=>1010111=>[1,2,2,1,1,1]
[9,10,7,8,5,6,2,1,3,4]=>010101100=>[2,2,2,1,3]
[9,10,7,8,4,3,5,6,1,2]=>010110010=>[2,2,1,3,2]
[9,10,7,8,4,2,5,1,3,6]=>010110100=>[2,2,1,2,3]
[9,10,7,8,3,2,1,4,5,6]=>010111000=>[2,2,1,1,4]
[9,10,6,5,7,8,3,4,1,2]=>011001010=>[2,1,3,2,2]
[9,10,6,5,7,8,2,1,3,4]=>011001100=>[2,1,3,1,3]
[9,10,6,4,7,3,5,8,1,2]=>011010010=>[2,1,2,3,2]
[9,10,6,4,7,2,5,1,3,8]=>011010100=>[2,1,2,2,3]
[9,10,6,3,7,2,1,4,5,8]=>011011000=>[2,1,2,1,4]
[9,10,5,4,3,6,7,8,1,2]=>011100010=>[2,1,1,4,2]
[9,10,5,4,2,6,7,1,3,8]=>011100100=>[2,1,1,3,3]
[9,10,5,3,2,6,1,4,7,8]=>011101000=>[2,1,1,2,4]
[9,10,4,3,2,1,5,6,7,8]=>011110000=>[2,1,1,1,5]
[8,7,9,10,5,6,3,4,1,2]=>100101010=>[1,3,2,2,2]
[8,7,9,10,5,6,2,1,3,4]=>100101100=>[1,3,2,1,3]
[8,7,9,10,4,3,5,6,1,2]=>100110010=>[1,3,1,3,2]
[8,7,9,10,4,2,5,1,3,6]=>100110100=>[1,3,1,2,3]
[8,7,9,10,3,2,1,4,5,6]=>100111000=>[1,3,1,1,4]
[8,6,9,5,7,10,3,4,1,2]=>101001010=>[1,2,3,2,2]
[8,6,9,5,7,10,2,1,3,4]=>101001100=>[1,2,3,1,3]
[8,6,9,4,7,3,5,10,1,2]=>101010010=>[1,2,2,3,2]
[8,6,9,3,7,2,1,4,5,10]=>101011000=>[1,2,2,1,4]
[8,5,9,4,3,6,7,10,1,2]=>101100010=>[1,2,1,4,2]
[8,5,9,4,2,6,7,1,3,10]=>101100100=>[1,2,1,3,3]
[8,5,9,3,2,6,1,4,7,10]=>101101000=>[1,2,1,2,4]
[8,4,9,3,2,1,5,6,7,10]=>101110000=>[1,2,1,1,5]
[7,6,5,8,9,10,3,4,1,2]=>110001010=>[1,1,4,2,2]
[7,6,5,8,9,10,2,1,3,4]=>110001100=>[1,1,4,1,3]
[7,6,4,8,9,3,5,10,1,2]=>110010010=>[1,1,3,3,2]
[7,6,4,8,9,2,5,1,3,10]=>110010100=>[1,1,3,2,3]
[7,6,3,8,9,2,1,4,5,10]=>110011000=>[1,1,3,1,4]
[7,5,4,8,3,6,9,10,1,2]=>110100010=>[1,1,2,4,2]
[7,5,4,8,2,6,9,1,3,10]=>110100100=>[1,1,2,3,3]
[7,4,3,8,2,1,5,6,9,10]=>110110000=>[1,1,2,1,5]
[6,5,4,2,7,8,9,1,3,10]=>111000100=>[1,1,1,4,3]
[6,5,3,2,7,8,1,4,9,10]=>111001000=>[1,1,1,3,4]
[7,1,6,5,3,2,4,8]=>1011100=>[1,2,1,1,3]
[1,8,7,5,3,2,4,6]=>0111100=>[2,1,1,1,3]
[1,8,7,4,2,5,3,6]=>0111010=>[2,1,1,2,2]
[8,7,4,2,5,3,6,1]=>1110101=>[1,1,1,2,2,1]
[7,1,6,4,2,5,3,8]=>1011010=>[1,2,1,2,2]
[2,6,5,4,7,1,3,8]=>0110100=>[2,1,2,3]
[7,1,5,3,6,4,2,8]=>1010110=>[1,2,2,1,2]
[5,3,7,1,6,4,2,8]=>1010110=>[1,2,2,1,2]
[5,3,6,4,2,7,1,8]=>1011010=>[1,2,1,2,2]
[1,5,3,8,7,4,2,6]=>0101110=>[2,2,1,1,2]
[7,4,2,8,6,3,5,1]=>1101101=>[1,1,2,1,2,1]
[5,3,6,1,8,7,4,2]=>1010111=>[1,2,2,1,1,1]
[6,1,5,3,8,7,4,2]=>1010111=>[1,2,2,1,1,1]
[2,8,7,5,4,6,1,3]=>0111010=>[2,1,1,2,2]
[2,3,1,8,7,5,4,6]=>0101110=>[2,2,1,1,2]
[7,4,2,1,8,6,3,5]=>1110110=>[1,1,1,2,1,2]
[1,8,6,3,5,7,4,2]=>0110011=>[2,1,3,1,1]
[6,3,8,5,2,1,7,4]=>1011101=>[1,2,1,1,2,1]
[8,6,3,7,4,2,1,5]=>1101110=>[1,1,2,1,1,2]
[2,8,6,4,7,5,1,3]=>0110110=>[2,1,2,1,2]
[5,1,8,6,3,7,4,2]=>1011011=>[1,2,1,2,1,1]
[6,3,7,4,1,8,5,2]=>1011011=>[1,2,1,2,1,1]
[8,5,2,6,3,7,4,1]=>1101011=>[1,1,2,2,1,1]
[6,1,8,7,4,2,5,3]=>1011101=>[1,2,1,1,2,1]
[8,6,3,7,4,2,5,1]=>1101101=>[1,1,2,1,2,1]
[1,8,6,3,2,4,7,5]=>0111001=>[2,1,1,3,1]
[8,6,3,2,4,7,5,1]=>1110011=>[1,1,1,3,1,1]
[7,5,1,8,6,3,2,4]=>1101110=>[1,1,2,1,1,2]
[6,1,8,7,5,3,2,4]=>1011110=>[1,2,1,1,1,2]
[2,4,5,1,3,8,7,6]=>0010011=>[3,3,1,1]
[1,7,5,8,6,3,2,4]=>0101110=>[2,2,1,1,2]
[1,7,4,2,5,8,6,3]=>0110011=>[2,1,3,1,1]
[8,6,3,1,7,4,2,5]=>1110110=>[1,1,1,2,1,2]
[8,7,4,2,5,3,1,6]=>1110110=>[1,1,1,2,1,2]
[5,3,1,8,7,4,2,6]=>1101110=>[1,1,2,1,1,2]
[4,1,8,7,5,3,2,6]=>1011110=>[1,2,1,1,1,2]
[2,8,6,4,1,3,7,5]=>0111001=>[2,1,1,3,1]
[4,1,8,6,3,2,7,5]=>1011101=>[1,2,1,1,2,1]
[7,4,2,8,6,3,1,5]=>1101110=>[1,1,2,1,1,2]
[6,3,1,8,5,2,7,4]=>1101101=>[1,1,2,1,2,1]
[8,5,2,6,3,1,7,4]=>1101101=>[1,1,2,1,2,1]
[7,4,8,5,2,6,3,1]=>1011011=>[1,2,1,2,1,1]
[1,8,5,2,7,4,6,3]=>0110101=>[2,1,2,2,1]
[7,4,6,3,1,8,5,2]=>1011011=>[1,2,1,2,1,1]
[6,3,1,7,4,8,5,2]=>1101011=>[1,1,2,2,1,1]
[4,1,7,5,8,6,3,2]=>1010111=>[1,2,2,1,1,1]
[2,3,1,7,5,8,6,4]=>0101011=>[2,2,2,1,1]
[7,4,8,5,2,1,6,3]=>1011101=>[1,2,1,1,2,1]
[1,7,4,6,3,8,5,2]=>0101011=>[2,2,2,1,1]
[3,6,5,2,1,4,8,7]=>0111001=>[2,1,1,3,1]
[3,5,6,2,1,4,8,7]=>0011001=>[3,1,3,1]
[3,5,7,8,1,4,2,6]=>0001010=>[4,2,2]
[4,1,8,5,7,3,2,6]=>1010110=>[1,2,2,1,2]
[4,1,7,5,8,3,2,6]=>1010110=>[1,2,2,1,2]
[2,1,5,8,7,4,3,6]=>1001110=>[1,3,1,1,2]
[5,1,7,4,8,3,2,6]=>1010110=>[1,2,2,1,2]
[4,7,2,8,3,6,1,5]=>0101010=>[2,2,2,2]
[4,6,2,7,3,1,8,5]=>0101101=>[2,2,1,2,1]
[3,7,8,2,4,1,6,5]=>0010101=>[3,2,2,1]
[3,8,7,2,4,1,6,5]=>0110101=>[2,1,2,2,1]
[3,8,6,2,4,1,7,5]=>0110101=>[2,1,2,2,1]
[6,2,8,4,1,7,3,5]=>1011010=>[1,2,1,2,2]
[7,3,4,8,1,6,2,5]=>1001010=>[1,3,2,2]
[6,3,4,8,1,7,2,5]=>1001010=>[1,3,2,2]
[5,3,4,8,1,2,7,6]=>1001001=>[1,3,3,1]
[4,3,5,8,1,2,7,6]=>1001001=>[1,3,3,1]
[1,8,5,4,2,3,7,6]=>0111001=>[2,1,1,3,1]
[3,5,4,8,1,2,7,6]=>0101001=>[2,2,3,1]
[4,5,3,8,1,2,7,6]=>0101001=>[2,2,3,1]
[6,4,3,8,1,7,2,5]=>1101010=>[1,1,2,2,2]
[7,4,3,8,1,6,2,5]=>1101010=>[1,1,2,2,2]
[6,5,3,8,7,1,2,4]=>1101100=>[1,1,2,1,3]
[5,6,3,8,7,1,2,4]=>0101100=>[2,2,1,3]
[4,6,3,8,1,7,2,5]=>0101010=>[2,2,2,2]
[2,6,8,4,1,7,3,5]=>0011010=>[3,1,2,2]
[1,8,7,4,2,6,3,5]=>0111010=>[2,1,1,2,2]
[5,7,3,8,6,1,2,4]=>0101100=>[2,2,1,3]
[3,7,5,8,6,1,2,4]=>0101100=>[2,2,1,3]
[2,7,8,5,6,1,3,4]=>0010100=>[3,2,3]
[1,8,7,5,6,2,3,4]=>0110100=>[2,1,2,3]
[2,6,8,5,7,1,3,4]=>0010100=>[3,2,3]
[5,3,6,8,7,1,2,4]=>1001100=>[1,3,1,3]
[7,2,8,5,6,1,3,4]=>1010100=>[1,2,2,3]
[5,2,8,6,7,1,3,4]=>1010100=>[1,2,2,3]
[1,8,3,2,7,6,4,5]=>0110110=>[2,1,2,1,2]
[5,2,8,7,6,1,3,4]=>1011100=>[1,2,1,1,3]
[6,2,8,7,5,1,3,4]=>1011100=>[1,2,1,1,3]
[3,4,7,8,1,6,2,5]=>0001010=>[4,2,2]
[1,8,5,7,6,2,3,4]=>0101100=>[2,2,1,3]
[2,5,8,7,6,1,3,4]=>0011100=>[3,1,1,3]
[7,4,6,5,8,1,2,3]=>1010100=>[1,2,2,3]
[2,6,8,7,5,1,3,4]=>0011100=>[3,1,1,3]
[1,8,6,7,5,2,3,4]=>0101100=>[2,2,1,3]
[2,7,8,6,5,1,3,4]=>0011100=>[3,1,1,3]
[5,7,6,4,8,1,2,3]=>0110100=>[2,1,2,3]
[6,1,3,2,4,8,7,5]=>1010011=>[1,2,3,1,1]
[8,7,4,2,3,6,1,5]=>1110010=>[1,1,1,3,2]
[8,7,1,5,4,2,3,6]=>1101100=>[1,1,2,1,3]
[3,7,1,5,2,8,6,4]=>0101011=>[2,2,2,1,1]
[8,7,2,5,4,1,3,6]=>1101100=>[1,1,2,1,3]
[5,2,8,7,1,4,3,6]=>1011010=>[1,2,1,2,2]
[7,1,8,6,2,4,3,5]=>1011010=>[1,2,1,2,2]
[8,1,6,2,7,5,3,4]=>1010110=>[1,2,2,1,2]
[7,1,6,2,8,5,3,4]=>1010110=>[1,2,2,1,2]
[7,2,4,3,5,1,8,6]=>1010101=>[1,2,2,2,1]
[5,1,7,2,3,8,6,4]=>1010011=>[1,2,3,1,1]
[8,2,3,5,1,7,6,4]=>1001011=>[1,3,2,1,1]
[7,6,3,1,4,8,2,5]=>1110010=>[1,1,1,3,2]
[7,2,8,1,6,5,3,4]=>1010110=>[1,2,2,1,2]
[7,2,6,4,3,8,1,5]=>1011010=>[1,2,1,2,2]
[5,1,7,4,3,8,2,6]=>1011010=>[1,2,1,2,2]
[5,3,1,7,4,8,2,6]=>1101010=>[1,1,2,2,2]
[7,4,8,2,1,5,3,6]=>1011010=>[1,2,1,2,2]
[8,2,4,1,6,3,7,5]=>1010101=>[1,2,2,2,1]
[8,2,7,5,1,6,4,3]=>1011011=>[1,2,1,2,1,1]
[6,1,7,3,2,8,5,4]=>1011011=>[1,2,1,2,1,1]
[4,7,2,1,6,3,8,5]=>0110101=>[2,1,2,2,1]
[6,2,1,5,3,8,4,7]=>1101010=>[1,1,2,2,2]
[5,3,1,6,2,8,4,7]=>1101010=>[1,1,2,2,2]
[6,1,5,2,8,4,3,7]=>1010110=>[1,2,2,1,2]
[7,4,3,8,1,5,2,6]=>1101010=>[1,1,2,2,2]
[7,4,8,1,5,3,2,6]=>1010110=>[1,2,2,1,2]
[6,1,5,3,2,8,4,7]=>1011010=>[1,2,1,2,2]
[6,3,2,8,4,1,5,7]=>1101100=>[1,1,2,1,3]
[7,3,4,2,8,5,1,6]=>1010110=>[1,2,2,1,2]
[8,5,1,3,7,4,2,6]=>1100110=>[1,1,3,1,2]
[3,8,6,1,5,2,7,4]=>0110101=>[2,1,2,2,1]
[4,8,5,6,1,7,3,2]=>0101011=>[2,2,2,1,1]
[6,7,1,3,8,5,2,4]=>0100110=>[2,3,1,2]
[3,6,7,1,5,2,8,4]=>0010101=>[3,2,2,1]
[7,1,3,8,4,2,6,5]=>1001101=>[1,3,1,2,1]
[5,6,2,7,1,3,8,4]=>0101001=>[2,2,3,1]
[5,6,2,8,1,3,7,4]=>0101001=>[2,2,3,1]
[6,1,8,3,7,5,2,4]=>1010110=>[1,2,2,1,2]
[7,4,2,1,5,8,3,6]=>1110010=>[1,1,1,3,2]
[7,4,1,5,8,3,2,6]=>1100110=>[1,1,3,1,2]
[7,3,2,6,4,8,1,5]=>1101010=>[1,1,2,2,2]
[6,4,2,7,3,8,1,5]=>1101010=>[1,1,2,2,2]
[7,4,8,3,1,5,2,6]=>1011010=>[1,2,1,2,2]
[5,2,1,7,4,8,3,6]=>1101010=>[1,1,2,2,2]
[6,1,8,4,5,2,7,3]=>1010101=>[1,2,2,2,1]
[7,1,6,4,5,2,8,3]=>1010101=>[1,2,2,2,1]
[3,5,2,7,1,6,8,4]=>0101001=>[2,2,3,1]
[4,5,7,3,1,6,8,2]=>0011001=>[3,1,3,1]
[4,5,7,2,8,6,1,3]=>0010110=>[3,2,1,2]
[4,5,7,2,8,1,3,6]=>0010100=>[3,2,3]
[4,6,7,2,1,5,8,3]=>0011001=>[3,1,3,1]
[4,6,7,1,3,8,5,2]=>0010011=>[3,3,1,1]
[3,6,1,5,7,8,4,2]=>0100011=>[2,4,1,1]
[4,6,7,1,5,8,3,2]=>0010011=>[3,3,1,1]
[6,1,4,2,5,3,7,8]=>1010100=>[1,2,2,3]
[1,3,7,5,4,2,8,6]=>0011101=>[3,1,1,2,1]
[6,1,3,5,4,2,7,8]=>1001100=>[1,3,1,3]
[6,1,2,5,4,7,3,8]=>1001010=>[1,3,2,2]
[5,2,6,3,4,7,1,8]=>1010010=>[1,2,3,2]
[2,4,7,1,5,3,8,6]=>0010101=>[3,2,2,1]
[2,3,6,7,4,8,1,5]=>0001010=>[4,2,2]
[1,3,6,7,4,8,5,2]=>0001011=>[4,2,1,1]
[2,7,6,5,3,1,8,4]=>0111101=>[2,1,1,1,2,1]
[5,2,6,1,4,7,8,3]=>1010001=>[1,2,4,1]
[4,7,6,5,2,1,8,3]=>0111101=>[2,1,1,1,2,1]
[6,3,1,5,4,7,8,2]=>1101001=>[1,1,2,3,1]
[5,3,6,1,4,2,7,8]=>1010100=>[1,2,2,3]
[1,7,4,2,6,3,8,5]=>0110101=>[2,1,2,2,1]
[5,7,4,1,2,3,6,8]=>0110000=>[2,1,5]
[6,4,1,2,5,3,7,8]=>1100100=>[1,1,3,3]
[4,7,6,3,8,5,1,2]=>0110110=>[2,1,2,1,2]
[3,7,6,5,2,8,1,4]=>0111010=>[2,1,1,2,2]
[3,7,6,5,1,2,8,4]=>0111001=>[2,1,1,3,1]
[4,7,2,6,1,3,8,5]=>0101001=>[2,2,3,1]
[2,7,6,5,8,1,4,3]=>0110101=>[2,1,2,2,1]
[4,2,6,8,3,1,5,7]=>1001100=>[1,3,1,3]
[3,7,6,2,4,5,1,8]=>0110010=>[2,1,3,2]
[2,3,6,5,8,1,4,7]=>0010100=>[3,2,3]
[2,3,5,8,6,1,4,7]=>0001100=>[4,1,3]
[4,2,3,8,6,1,5,7]=>1001100=>[1,3,1,3]
[1,2,3,7,4,6,8,5]=>0001001=>[4,3,1]
[3,2,7,1,4,5,8,6]=>1010001=>[1,2,4,1]
[2,1,5,3,8,7,4,6]=>1010110=>[1,2,2,1,2]
[5,8,3,2,4,1,6,7]=>0110100=>[2,1,2,3]
[4,2,7,1,8,3,5,6]=>1010100=>[1,2,2,3]
[1,2,7,5,3,8,4,6]=>0011010=>[3,1,2,2]
[3,2,7,1,4,8,5,6]=>1010010=>[1,2,3,2]
[1,2,3,7,6,8,4,5]=>0001010=>[4,2,2]
[1,2,3,6,8,7,4,5]=>0000110=>[5,1,2]
[1,2,3,7,8,4,6,5]=>0000101=>[5,2,1]
[1,2,3,6,8,4,7,5]=>0000101=>[5,2,1]
[6,2,8,3,7,5,1,4]=>1010110=>[1,2,2,1,2]
[4,2,8,3,7,5,6,1]=>1010101=>[1,2,2,2,1]
[7,3,4,8,6,5,1,2]=>1001110=>[1,3,1,1,2]
[5,3,4,8,7,2,6,1]=>1001101=>[1,3,1,2,1]
[4,6,3,8,5,7,2,1]=>0101011=>[2,2,2,1,1]
[7,5,3,8,6,2,4,1]=>1101101=>[1,1,2,1,2,1]
[2,6,8,3,7,4,5,1]=>0010101=>[3,2,2,1]
[2,5,8,3,7,4,6,1]=>0010101=>[3,2,2,1]
[7,4,3,8,6,2,5,1]=>1101101=>[1,1,2,1,2,1]
[3,5,4,8,7,2,6,1]=>0101101=>[2,2,1,2,1]
[4,5,3,8,6,7,2,1]=>0101011=>[2,2,2,1,1]
[3,6,7,8,4,5,2,1]=>0001011=>[4,2,1,1]
[1,8,5,6,4,7,3,2]=>0101011=>[2,2,2,1,1]
[2,5,8,6,4,7,3,1]=>0011011=>[3,1,2,1,1]
[6,3,7,8,4,5,2,1]=>1001011=>[1,3,2,1,1]
[4,3,7,8,5,6,2,1]=>1001011=>[1,3,2,1,1]
[4,2,8,6,5,7,3,1]=>1011011=>[1,2,1,2,1,1]
[3,2,8,6,7,4,5,1]=>1010101=>[1,2,2,2,1]
[2,3,8,7,5,4,6,1]=>0011101=>[3,1,1,2,1]
[1,8,2,7,4,5,6,3]=>0101001=>[2,2,3,1]
[7,2,8,6,3,4,5,1]=>1011001=>[1,2,1,3,1]
[6,2,8,4,5,7,3,1]=>1010011=>[1,2,3,1,1]
[5,2,8,4,6,7,3,1]=>1010011=>[1,2,3,1,1]
[4,3,6,8,5,7,2,1]=>1001011=>[1,3,2,1,1]
[3,4,6,8,7,2,5,1]=>0001101=>[4,1,2,1]
[7,3,5,8,6,2,4,1]=>1001101=>[1,3,1,2,1]
[1,8,3,5,7,4,6,2]=>0100101=>[2,3,2,1]
[2,7,8,4,5,6,3,1]=>0010011=>[3,3,1,1]
[3,7,5,8,4,6,2,1]=>0101011=>[2,2,2,1,1]
[5,7,4,6,8,3,2,1]=>0100111=>[2,3,1,1,1]
[3,6,5,8,4,7,2,1]=>0101011=>[2,2,2,1,1]
[2,6,8,4,5,7,3,1]=>0010011=>[3,3,1,1]
[4,2,7,1,3,8,5,6]=>1010010=>[1,2,3,2]
[4,2,5,1,3,8,6,7]=>1010010=>[1,2,3,2]
[5,3,6,1,7,2,4,8]=>1010100=>[1,2,2,3]
[3,7,1,2,5,8,6,4]=>0100011=>[2,4,1,1]
[3,7,4,1,2,8,5,6]=>0110010=>[2,1,3,2]
[7,5,1,3,4,8,6,2]=>1100011=>[1,1,4,1,1]
[7,5,1,2,4,8,6,3]=>1100011=>[1,1,4,1,1]
[6,4,2,3,7,1,5,8]=>1100100=>[1,1,3,3]
[7,6,3,8,1,2,5,4]=>1101001=>[1,1,2,3,1]
[7,4,2,3,8,1,6,5]=>1100101=>[1,1,3,2,1]
[4,7,5,2,8,1,3,6]=>0110100=>[2,1,2,3]
[8,2,6,3,7,1,4,5]=>1010100=>[1,2,2,3]
[8,6,1,2,7,4,5,3]=>1100101=>[1,1,3,2,1]
[8,4,7,1,2,3,6,5]=>1010001=>[1,2,4,1]
[8,5,7,1,2,4,6,3]=>1010001=>[1,2,4,1]
[3,8,5,6,1,2,4,7]=>0101000=>[2,2,4]
[3,7,5,8,1,2,4,6]=>0101000=>[2,2,4]
[7,6,4,8,1,3,5,2]=>1101001=>[1,1,2,3,1]
[6,5,8,1,2,4,7,3]=>1010001=>[1,2,4,1]
[3,6,8,1,2,5,7,4]=>0010001=>[3,4,1]
[4,6,3,8,1,2,5,7]=>0101000=>[2,2,4]
[4,6,3,7,1,2,5,8]=>0101000=>[2,2,4]
[4,1,7,8,2,3,6,5]=>1001001=>[1,3,3,1]
[5,1,2,8,6,3,4,7]=>1001100=>[1,3,1,3]
[5,3,8,1,6,2,4,7]=>1010100=>[1,2,2,3]
[6,1,8,5,2,3,4,7]=>1011000=>[1,2,1,4]
[6,1,7,5,2,3,4,8]=>1011000=>[1,2,1,4]
[6,8,1,3,7,4,5,2]=>0100101=>[2,3,2,1]
[7,2,8,1,6,3,4,5]=>1010100=>[1,2,2,3]
[4,7,8,2,5,1,3,6]=>0010100=>[3,2,3]
[6,8,2,7,1,4,5,3]=>0101001=>[2,2,3,1]
[4,8,7,1,3,5,6,2]=>0110001=>[2,1,4,1]
[3,8,7,1,2,4,6,5]=>0110001=>[2,1,4,1]
[4,8,7,1,2,3,6,5]=>0110001=>[2,1,4,1]
[5,8,7,1,2,4,6,3]=>0110001=>[2,1,4,1]
[5,8,7,1,3,4,6,2]=>0110001=>[2,1,4,1]
[7,1,8,6,2,3,5,4]=>1011001=>[1,2,1,3,1]
[5,8,6,4,1,2,3,7]=>0111000=>[2,1,1,4]
[5,1,3,4,6,7,2,8]=>1000010=>[1,5,2]
[1,3,4,8,7,5,2,6]=>0001110=>[4,1,1,2]
[8,2,4,1,7,3,5,6]=>1010100=>[1,2,2,3]
[8,6,1,4,2,3,7,5]=>1101001=>[1,1,2,3,1]
[3,6,1,4,2,8,7,5]=>0101011=>[2,2,2,1,1]
[1,6,8,4,3,7,2,5]=>0011010=>[3,1,2,2]
[3,1,4,7,8,5,2,6]=>1000110=>[1,4,1,2]
[6,1,7,4,3,8,2,5]=>1011010=>[1,2,1,2,2]
[1,8,7,4,3,6,2,5]=>0111010=>[2,1,1,2,2]
[7,4,1,3,8,2,6,5]=>1100101=>[1,1,3,2,1]
[4,8,2,3,1,5,7,6]=>0101001=>[2,2,3,1]
[4,8,6,2,1,3,7,5]=>0111001=>[2,1,1,3,1]
[2,7,4,1,8,3,5,6]=>0110100=>[2,1,2,3]
[1,7,8,4,2,3,6,5]=>0011001=>[3,1,3,1]
[8,7,1,3,4,2,6,5]=>1100101=>[1,1,3,2,1]
[1,7,4,3,6,2,8,5]=>0110101=>[2,1,2,2,1]
[3,8,6,4,5,2,1,7]=>0110110=>[2,1,2,1,2]
[3,8,4,6,5,2,1,7]=>0101110=>[2,2,1,1,2]
[2,4,3,7,5,8,1,6]=>0101010=>[2,2,2,2]
[1,4,7,3,6,2,8,5]=>0010101=>[3,2,2,1]
[6,4,1,3,7,2,8,5]=>1100101=>[1,1,3,2,1]
[8,1,4,3,6,2,7,5]=>1010101=>[1,2,2,2,1]
[4,2,3,8,5,7,1,6]=>1001010=>[1,3,2,2]
[2,8,5,7,3,4,1,6]=>0101010=>[2,2,2,2]
[5,8,2,6,4,3,1,7]=>0101110=>[2,2,1,1,2]
[7,2,5,8,4,3,1,6]=>1001110=>[1,3,1,1,2]
[4,2,3,5,8,7,1,6]=>1000110=>[1,4,1,2]
[8,2,3,5,4,7,1,6]=>1001010=>[1,3,2,2]
[6,1,8,3,4,2,7,5]=>1010101=>[1,2,2,2,1]
[1,8,6,4,2,3,7,5]=>0111001=>[2,1,1,3,1]
[3,8,4,5,6,2,1,7]=>0100110=>[2,3,1,2]
[3,8,6,5,4,2,1,7]=>0111110=>[2,1,1,1,1,2]
[6,3,1,4,2,8,7,5]=>1101011=>[1,1,2,2,1,1]
[7,3,8,1,2,6,4,5]=>1010010=>[1,2,3,2]
[7,1,4,5,3,2,6,8]=>1001100=>[1,3,1,3]
[1,8,4,2,6,5,3,7]=>0110110=>[2,1,2,1,2]
[5,1,4,8,6,3,2,7]=>1001110=>[1,3,1,1,2]
[5,3,1,8,4,7,2,6]=>1101010=>[1,1,2,2,2]
[4,3,8,1,5,7,2,6]=>1010010=>[1,2,3,2]
[6,3,1,2,5,7,4,8]=>1100010=>[1,1,4,2]
[7,1,4,2,6,5,3,8]=>1010110=>[1,2,2,1,2]
[3,8,4,1,6,5,2,7]=>0110110=>[2,1,2,1,2]
[7,5,3,6,4,8,2,1]=>1101011=>[1,1,2,2,1,1]
[7,3,6,4,5,8,2,1]=>1010011=>[1,2,3,1,1]
[8,7,2,4,5,1,6,3]=>1100101=>[1,1,3,2,1]
[7,1,5,4,8,6,3,2]=>1010111=>[1,2,2,1,1,1]
[5,8,3,7,4,1,6,2]=>0101101=>[2,2,1,2,1]
[8,1,7,4,2,6,5,3]=>1011011=>[1,2,1,2,1,1]
[5,6,3,1,8,4,7,2]=>0110101=>[2,1,2,2,1]
[5,7,1,4,8,6,3,2]=>0100111=>[2,3,1,1,1]
[5,3,7,4,8,6,2,1]=>1010111=>[1,2,2,1,1,1]
[8,5,3,6,1,4,7,2]=>1101001=>[1,1,2,3,1]
[5,4,3,6,8,2,7,1]=>1100101=>[1,1,3,2,1]
[6,5,3,7,4,8,2,1]=>1101011=>[1,1,2,2,1,1]
[2,7,8,4,5,1,6,3]=>0010101=>[3,2,2,1]
[5,6,3,8,1,4,7,2]=>0101001=>[2,2,3,1]
[8,4,1,2,5,6,7,3]=>1100001=>[1,1,5,1]
[6,8,3,1,2,5,7,4]=>0110001=>[2,1,4,1]
[8,7,1,4,5,2,6,3]=>1100101=>[1,1,3,2,1]
[8,7,3,1,5,4,2,6]=>1110110=>[1,1,1,2,1,2]
[3,5,4,7,6,1,2,8]=>0101100=>[2,2,1,3]
[3,5,7,4,6,1,8,2]=>0010101=>[3,2,2,1]
[3,5,7,4,6,1,2,8]=>0010100=>[3,2,3]
[3,5,7,4,6,2,1,8]=>0010110=>[3,2,1,2]
[3,5,2,7,6,4,1,8]=>0101110=>[2,2,1,1,2]
[3,5,7,2,6,4,1,8]=>0010110=>[3,2,1,2]
[5,3,7,6,1,2,8,4]=>1011001=>[1,2,1,3,1]
[5,3,7,6,1,4,2,8]=>1011010=>[1,2,1,2,2]
[5,3,7,6,4,1,2,8]=>1011100=>[1,2,1,1,3]
[3,5,7,2,6,1,4,8]=>0010100=>[3,2,3]
[3,5,2,7,6,1,4,8]=>0101100=>[2,2,1,3]
[5,3,7,6,4,1,8,2]=>1011101=>[1,2,1,1,2,1]
[3,7,5,4,1,8,2,6]=>0111010=>[2,1,1,2,2]
[3,7,5,4,1,8,6,2]=>0111011=>[2,1,1,2,1,1]
[3,7,5,1,4,8,6,2]=>0110011=>[2,1,3,1,1]
[3,7,5,1,4,8,2,6]=>0110010=>[2,1,3,2]
[3,5,7,1,2,6,8,4]=>0010001=>[3,4,1]
[3,5,7,2,1,6,4,8]=>0011010=>[3,1,2,2]
[5,3,7,1,6,2,4,8]=>1010100=>[1,2,2,3]
[3,5,7,1,4,6,8,2]=>0010001=>[3,4,1]
[3,5,7,1,4,2,6,8]=>0010100=>[3,2,3]
[3,5,7,4,1,2,6,8]=>0011000=>[3,1,4]
[3,5,4,7,1,6,8,2]=>0101001=>[2,2,3,1]
[3,5,4,7,1,2,6,8]=>0101000=>[2,2,4]
[3,5,4,7,2,1,6,8]=>0101100=>[2,2,1,3]
[3,5,4,2,7,1,6,8]=>0110100=>[2,1,2,3]
[3,5,4,7,2,1,8,6]=>0101101=>[2,2,1,2,1]
[3,5,4,7,1,2,8,6]=>0101001=>[2,2,3,1]
[5,7,6,3,1,8,4,2]=>0111011=>[2,1,1,2,1,1]
[5,7,6,3,1,8,2,4]=>0111010=>[2,1,1,2,2]
[3,5,7,4,1,2,8,6]=>0011001=>[3,1,3,1]
[3,5,7,4,2,1,8,6]=>0011101=>[3,1,1,2,1]
[3,2,5,7,4,1,8,6]=>1001101=>[1,3,1,2,1]
[3,2,5,7,1,4,8,6]=>1001001=>[1,3,3,1]
[3,5,2,7,1,4,8,6]=>0101001=>[2,2,3,1]
[3,5,7,2,1,4,8,6]=>0011001=>[3,1,3,1]
[3,5,7,1,4,2,8,6]=>0010101=>[3,2,2,1]
[3,7,5,2,1,8,6,4]=>0111011=>[2,1,1,2,1,1]
[3,7,2,5,1,8,6,4]=>0101011=>[2,2,2,1,1]
[3,2,7,5,1,8,6,4]=>1011011=>[1,2,1,2,1,1]
[3,2,7,5,1,8,4,6]=>1011010=>[1,2,1,2,2]
[3,7,2,5,1,8,4,6]=>0101010=>[2,2,2,2]
[3,7,5,2,1,8,4,6]=>0111010=>[2,1,1,2,2]
[5,8,3,4,1,7,6,2]=>0101011=>[2,2,2,1,1]
[5,8,7,2,4,1,6,3]=>0110101=>[2,1,2,2,1]
[3,8,6,4,1,7,5,2]=>0111011=>[2,1,1,2,1,1]
[4,3,5,6,8,1,7,2]=>1000101=>[1,4,2,1]
[3,7,6,4,1,8,5,2]=>0111011=>[2,1,1,2,1,1]
[3,7,4,1,8,6,5,2]=>0110111=>[2,1,2,1,1,1]
[3,8,4,1,7,6,5,2]=>0110111=>[2,1,2,1,1,1]
[3,2,7,6,1,5,4,8]=>1011010=>[1,2,1,2,2]
[5,7,8,2,4,1,6,3]=>0010101=>[3,2,2,1]
[4,2,5,8,1,6,7,3]=>1001001=>[1,3,3,1]
[5,8,2,4,1,6,3,7]=>0101010=>[2,2,2,2]
[8,4,2,6,5,1,3,7]=>1101100=>[1,1,2,1,3]
[3,2,6,8,1,5,4,7]=>1001010=>[1,3,2,2]
[8,3,2,5,6,1,4,7]=>1100100=>[1,1,3,3]
[3,2,8,6,7,1,5,4]=>1010101=>[1,2,2,2,1]
[3,2,6,8,7,1,5,4]=>1001101=>[1,3,1,2,1]
[3,2,6,7,1,5,4,8]=>1001010=>[1,3,2,2]
[8,7,3,2,5,6,1,4]=>1110010=>[1,1,1,3,2]
[7,2,8,1,5,3,6,4]=>1010101=>[1,2,2,2,1]
[8,4,2,7,5,1,3,6]=>1101100=>[1,1,2,1,3]
[7,4,2,8,5,1,3,6]=>1101100=>[1,1,2,1,3]
[7,2,4,1,8,3,6,5]=>1010101=>[1,2,2,2,1]
[7,5,3,4,2,8,1,6]=>1101010=>[1,1,2,2,2]
[8,5,3,6,2,4,7,1]=>1101001=>[1,1,2,3,1]
[8,5,6,3,7,4,2,1]=>1010111=>[1,2,2,1,1,1]
[8,5,6,2,7,4,3,1]=>1010111=>[1,2,2,1,1,1]
[8,7,6,3,4,1,5,2]=>1110101=>[1,1,1,2,2,1]
[1,7,2,3,6,8,5,4]=>0100011=>[2,4,1,1]
[3,5,6,4,8,2,7,1]=>0010101=>[3,2,2,1]
[3,5,1,4,8,2,7,6]=>0100101=>[2,3,2,1]
[1,7,5,4,8,2,6,3]=>0110101=>[2,1,2,2,1]
[3,7,5,1,6,4,8,2]=>0110101=>[2,1,2,2,1]
[2,7,5,4,8,1,3,6]=>0110100=>[2,1,2,3]
[2,7,5,4,8,6,1,3]=>0110110=>[2,1,2,1,2]
[1,7,5,4,8,6,3,2]=>0110111=>[2,1,2,1,1,1]
[2,5,1,4,8,7,3,6]=>0100110=>[2,3,1,2]
[3,6,4,2,8,7,1,5]=>0110110=>[2,1,2,1,2]
[3,5,2,4,8,1,6,7]=>0100100=>[2,3,3]
[4,5,6,1,7,3,8,2]=>0010101=>[3,2,2,1]
[3,5,6,4,8,1,2,7]=>0010100=>[3,2,3]
[1,5,6,4,8,7,2,3]=>0010110=>[3,2,1,2]
[3,6,4,1,8,7,2,5]=>0110110=>[2,1,2,1,2]
[3,6,4,5,8,7,2,1]=>0100111=>[2,3,1,1,1]
[1,6,4,3,8,5,2,7]=>0110110=>[2,1,2,1,2]
[7,6,1,4,5,3,8,2]=>1100101=>[1,1,3,2,1]
[7,6,1,3,5,4,8,2]=>1100101=>[1,1,3,2,1]
[7,1,3,2,5,8,4,6]=>1010010=>[1,2,3,2]
[1,6,4,2,8,5,3,7]=>0110110=>[2,1,2,1,2]
[7,6,5,8,3,1,4,2]=>1101101=>[1,1,2,1,2,1]
[2,6,4,3,8,1,7,5]=>0110101=>[2,1,2,2,1]
[2,6,4,3,8,5,7,1]=>0110101=>[2,1,2,2,1]
[7,2,3,1,5,8,6,4]=>1010011=>[1,2,3,1,1]
[7,1,5,6,3,8,4,2]=>1001011=>[1,3,2,1,1]
[7,3,6,5,1,4,8,2]=>1011001=>[1,2,1,3,1]
[7,2,6,5,3,8,1,4]=>1011010=>[1,2,1,2,2]
[7,2,3,1,4,8,6,5]=>1010011=>[1,2,3,1,1]
[7,2,3,5,4,8,6,1]=>1001011=>[1,3,2,1,1]
[2,6,4,5,8,1,7,3]=>0100101=>[2,3,2,1]
[1,5,6,4,8,3,7,2]=>0010101=>[3,2,2,1]
[2,5,6,4,8,3,1,7]=>0010110=>[3,2,1,2]
[3,5,6,1,4,7,8,2]=>0010001=>[3,4,1]
[7,6,1,3,4,5,8,2]=>1100001=>[1,1,5,1]
[7,1,3,2,4,8,5,6]=>1010010=>[1,2,3,2]
[7,6,1,5,3,4,8,2]=>1101001=>[1,1,2,3,1]
[7,6,1,5,4,3,8,2]=>1101101=>[1,1,2,1,2,1]
[1,6,4,5,8,3,2,7]=>0100110=>[2,3,1,2]
[7,6,5,8,1,3,2,4]=>1101010=>[1,1,2,2,2]
[3,4,6,8,7,2,1,5]=>0001110=>[4,1,1,2]
[3,5,6,8,2,1,7,4]=>0001101=>[4,1,2,1]
[4,2,1,5,3,7,8,6]=>1101001=>[1,1,2,3,1]
[4,2,5,6,3,1,8,7]=>1001101=>[1,3,1,2,1]
[3,5,6,8,1,7,2,4]=>0001010=>[4,2,2]
[4,1,5,6,3,2,8,7]=>1001101=>[1,3,1,2,1]
[4,5,3,1,7,2,8,6]=>0110101=>[2,1,2,2,1]
[4,1,3,5,2,7,8,6]=>1001001=>[1,3,3,1]
[2,5,4,7,3,8,6,1]=>0101011=>[2,2,2,1,1]
[3,5,7,1,8,4,2,6]=>0010110=>[3,2,1,2]
[4,1,5,3,2,7,8,6]=>1011001=>[1,2,1,3,1]
[4,5,3,7,1,2,8,6]=>0101001=>[2,2,3,1]
[4,3,6,1,2,7,5,8]=>1010010=>[1,2,3,2]
[5,1,3,2,4,6,7,8]=>1010000=>[1,2,5]
[3,6,1,7,4,5,2,8]=>0101010=>[2,2,2,2]
[5,3,1,4,2,6,7,8]=>1101000=>[1,1,2,4]
[4,5,2,3,7,1,8,6]=>0100101=>[2,3,2,1]
[4,2,6,1,3,7,5,8]=>1010010=>[1,2,3,2]
[4,6,2,1,3,7,5,8]=>0110010=>[2,1,3,2]
[3,6,2,1,7,4,8,5]=>0110101=>[2,1,2,2,1]
[3,1,4,7,6,5,2,8]=>1001110=>[1,3,1,1,2]
[3,6,2,7,1,5,8,4]=>0101001=>[2,2,3,1]
[4,6,2,7,1,3,5,8]=>0101000=>[2,2,4]
[3,5,7,1,8,2,6,4]=>0010101=>[3,2,2,1]
[5,1,4,2,3,6,7,8]=>1010000=>[1,2,5]
[2,6,5,3,4,7,8,1]=>0110001=>[2,1,4,1]
[3,6,1,7,5,4,2,8]=>0101110=>[2,2,1,1,2]
[5,1,4,3,2,6,7,8]=>1011000=>[1,2,1,4]
[5,4,1,3,2,6,7,8]=>1101000=>[1,1,2,4]
[6,4,2,5,3,8,1,7]=>1101010=>[1,1,2,2,2]
[4,6,2,3,5,1,8,7]=>0100101=>[2,3,2,1]
[6,2,4,5,1,8,3,7]=>1001010=>[1,3,2,2]
[8,2,6,7,1,4,5,3]=>1001001=>[1,3,3,1]
[8,2,6,7,4,1,5,3]=>1001101=>[1,3,1,2,1]
[4,6,2,3,5,8,1,7]=>0100010=>[2,4,2]
[2,6,4,1,5,8,3,7]=>0110010=>[2,1,3,2]
[2,8,1,6,7,4,5,3]=>0100101=>[2,3,2,1]
[2,8,6,1,4,7,5,3]=>0110011=>[2,1,3,1,1]
[2,8,1,6,4,7,5,3]=>0101011=>[2,2,2,1,1]
[2,6,1,4,8,5,3,7]=>0100110=>[2,3,1,2]
[6,4,5,2,8,3,1,7]=>1010110=>[1,2,2,1,2]
[4,2,3,6,1,8,5,7]=>1001010=>[1,3,2,2]
[4,2,3,1,6,8,5,7]=>1010010=>[1,2,3,2]
[4,2,3,8,6,1,7,5]=>1001101=>[1,3,1,2,1]
[6,4,5,8,2,3,7,1]=>1001001=>[1,3,3,1]
[6,4,8,5,2,3,7,1]=>1011001=>[1,2,1,3,1]
[2,4,8,1,3,6,7,5]=>0010001=>[3,4,1]
[2,4,1,8,3,6,7,5]=>0101001=>[2,2,3,1]
[2,1,4,8,6,3,7,5]=>1001101=>[1,3,1,2,1]
[6,4,8,2,5,3,7,1]=>1010101=>[1,2,2,2,1]
[8,6,2,4,7,5,1,3]=>1100110=>[1,1,3,1,2]
[4,6,8,2,3,5,7,1]=>0010001=>[3,4,1]
[2,1,6,8,4,5,7,3]=>1001001=>[1,3,3,1]
[2,8,1,4,6,7,3,5]=>0100010=>[2,4,2]
[4,8,6,2,3,7,5,1]=>0110011=>[2,1,3,1,1]
[8,4,2,6,7,3,1,5]=>1100110=>[1,1,3,1,2]
[5,1,8,3,6,4,7,2]=>1010101=>[1,2,2,2,1]
[5,1,3,8,7,6,4,2]=>1001111=>[1,3,1,1,1,1]
[3,8,5,6,1,7,2,4]=>0101010=>[2,2,2,2]
[6,7,4,8,5,1,3,2]=>0101101=>[2,2,1,2,1]
[3,6,5,8,7,1,4,2]=>0101101=>[2,2,1,2,1]
[6,5,3,8,2,7,4,1]=>1101011=>[1,1,2,2,1,1]
[6,4,8,1,3,7,5,2]=>1010011=>[1,2,3,1,1]
[7,6,3,1,4,2,5,8]=>1110100=>[1,1,1,2,3]
[1,5,4,3,7,8,2,6]=>0110010=>[2,1,3,2]
[7,8,4,2,5,3,1,6]=>0110110=>[2,1,2,1,2]
[4,2,7,8,5,3,1,6]=>1001110=>[1,3,1,1,2]
[4,2,5,3,1,7,8,6]=>1011001=>[1,2,1,3,1]
[4,2,8,7,6,3,1,5]=>1011110=>[1,2,1,1,1,2]
[4,2,7,6,3,1,5,8]=>1011100=>[1,2,1,1,3]
[6,3,1,8,7,5,2,4]=>1101110=>[1,1,2,1,1,2]
[4,2,7,6,3,1,8,5]=>1011101=>[1,2,1,1,2,1]
[7,6,3,1,8,4,2,5]=>1110110=>[1,1,1,2,1,2]
[7,6,4,2,1,8,3,5]=>1111010=>[1,1,1,1,2,2]
[1,8,2,7,6,4,3,5]=>0101110=>[2,2,1,1,2]
[8,4,2,5,7,6,3,1]=>1100111=>[1,1,3,1,1,1]
[7,5,2,4,8,6,3,1]=>1100111=>[1,1,3,1,1,1]
[8,7,5,2,4,6,3,1]=>1110011=>[1,1,1,3,1,1]
[7,5,2,4,6,3,1,8]=>1100110=>[1,1,3,1,2]
[5,2,8,6,3,7,4,1]=>1011011=>[1,2,1,2,1,1]
[8,4,7,5,2,6,3,1]=>1011011=>[1,2,1,2,1,1]
[8,3,6,4,7,5,2,1]=>1010111=>[1,2,2,1,1,1]
[7,5,2,1,8,3,6,4]=>1110101=>[1,1,1,2,2,1]
[7,5,2,6,3,1,8,4]=>1101101=>[1,1,2,1,2,1]
[5,2,7,4,1,8,6,3]=>1011011=>[1,2,1,2,1,1]
[5,2,8,7,4,1,6,3]=>1011101=>[1,2,1,1,2,1]
[8,7,4,1,5,2,6,3]=>1110101=>[1,1,1,2,2,1]
[7,4,1,5,2,8,6,3]=>1101011=>[1,1,2,2,1,1]
[7,6,3,1,4,2,8,5]=>1110101=>[1,1,1,2,2,1]
[7,5,2,8,6,3,1,4]=>1101110=>[1,1,2,1,1,2]
[7,5,2,1,3,6,4,8]=>1110010=>[1,1,1,3,2]
[8,7,5,2,1,3,6,4]=>1111001=>[1,1,1,1,3,1]
[1,3,7,6,5,8,2,4]=>0011010=>[3,1,2,2]
[8,6,4,7,5,2,1,3]=>1101110=>[1,1,2,1,1,2]
[6,4,7,5,2,1,3,8]=>1011100=>[1,2,1,1,3]
[6,3,1,4,7,5,2,8]=>1100110=>[1,1,3,1,2]
[6,3,1,4,8,7,5,2]=>1100111=>[1,1,3,1,1,1]
[8,6,3,1,4,7,5,2]=>1110011=>[1,1,1,3,1,1]
[1,8,2,6,4,7,5,3]=>0101011=>[2,2,2,1,1]
[7,5,2,1,6,4,8,3]=>1110101=>[1,1,1,2,2,1]
[6,3,8,7,4,1,5,2]=>1011101=>[1,2,1,1,2,1]
[6,3,7,4,1,5,2,8]=>1011010=>[1,2,1,2,2]
[7,4,1,6,3,5,2,8]=>1101010=>[1,1,2,2,2]
[7,4,1,8,6,3,5,2]=>1101101=>[1,1,2,1,2,1]
[8,4,6,3,1,7,5,2]=>1011011=>[1,2,1,2,1,1]
[6,4,7,5,2,1,8,3]=>1011101=>[1,2,1,1,2,1]
[1,6,4,7,5,3,8,2]=>0101101=>[2,2,1,2,1]
[6,3,5,2,7,4,1,8]=>1010110=>[1,2,2,1,2]
[4,6,7,2,5,3,1,8]=>0010110=>[3,2,1,2]
[2,4,7,8,1,6,5,3]=>0001011=>[4,2,1,1]
[4,2,6,8,7,1,5,3]=>1001101=>[1,3,1,2,1]
[5,1,8,4,2,7,6,3]=>1011011=>[1,2,1,2,1,1]
[4,6,7,1,2,8,5,3]=>0010011=>[3,3,1,1]
[5,7,4,1,2,8,6,3]=>0110011=>[2,1,3,1,1]
[6,3,7,1,2,8,5,4]=>1010011=>[1,2,3,1,1]
[1,8,2,3,6,5,4,7]=>0100110=>[2,3,1,2]
[3,5,8,4,7,2,6,1]=>0010101=>[3,2,2,1]
[1,8,5,4,6,2,3,7]=>0110100=>[2,1,2,3]
[3,8,5,4,6,1,2,7]=>0110100=>[2,1,2,3]
[3,8,5,1,6,4,2,7]=>0110110=>[2,1,2,1,2]
[2,8,5,4,6,1,3,7]=>0110100=>[2,1,2,3]
[2,8,5,4,6,3,1,7]=>0110110=>[2,1,2,1,2]
[1,8,5,4,6,3,2,7]=>0110110=>[2,1,2,1,2]
[2,5,8,4,7,3,6,1]=>0010101=>[3,2,2,1]
[3,6,4,2,7,8,5,1]=>0110011=>[2,1,3,1,1]
[3,6,4,2,7,8,1,5]=>0110010=>[2,1,3,2]
[3,5,4,1,6,2,7,8]=>0110100=>[2,1,2,3]
[4,5,8,1,7,6,2,3]=>0010110=>[3,2,1,2]
[3,5,8,4,7,1,6,2]=>0010101=>[3,2,2,1]
[1,5,8,4,7,3,6,2]=>0010101=>[3,2,2,1]
[3,6,4,1,7,8,5,2]=>0110011=>[2,1,3,1,1]
[3,6,4,8,7,5,2,1]=>0101111=>[2,2,1,1,1,1]
[1,6,4,3,7,8,5,2]=>0110011=>[2,1,3,1,1]
[7,6,1,3,8,4,2,5]=>1100110=>[1,1,3,1,2]
[1,6,4,2,7,8,3,5]=>0110010=>[2,1,3,2]
[2,6,4,3,7,1,8,5]=>0110101=>[2,1,2,2,1]
[2,6,4,1,7,8,3,5]=>0110010=>[2,1,3,2]
[7,2,3,4,8,6,5,1]=>1000111=>[1,4,1,1,1]
[7,2,3,1,8,6,4,5]=>1010110=>[1,2,2,1,2]
[7,2,3,4,1,6,8,5]=>1001001=>[1,3,3,1]
[1,2,4,3,8,5,7,6]=>0010101=>[3,2,2,1]
[7,3,8,6,1,4,2,5]=>1011010=>[1,2,1,2,2]
[7,2,8,6,3,4,1,5]=>1011010=>[1,2,1,2,2]
[7,2,3,1,5,6,8,4]=>1010001=>[1,2,4,1]
[7,2,3,8,5,6,4,1]=>1001011=>[1,3,2,1,1]
[2,6,4,8,7,1,5,3]=>0101101=>[2,2,1,2,1]
[1,5,8,4,7,6,2,3]=>0010110=>[3,2,1,2]
[3,5,8,1,6,7,2,4]=>0010010=>[3,3,2]
[7,6,1,3,5,8,2,4]=>1100010=>[1,1,4,2]
[7,1,3,2,5,6,8,4]=>1010001=>[1,2,4,1]
[7,1,3,8,2,6,5,4]=>1001011=>[1,3,2,1,1]
[7,6,1,8,5,4,2,3]=>1101110=>[1,1,2,1,1,2]
[3,2,6,5,8,4,7,1]=>1010101=>[1,2,2,2,1]
[4,3,7,1,6,5,8,2]=>1010101=>[1,2,2,2,1]
[5,2,6,4,8,3,7,1]=>1010101=>[1,2,2,2,1]
[4,3,7,5,8,2,6,1]=>1010101=>[1,2,2,2,1]
[5,3,7,4,8,2,6,1]=>1010101=>[1,2,2,2,1]
[5,3,7,4,8,1,6,2]=>1010101=>[1,2,2,2,1]
[5,4,8,2,6,3,7,1]=>1010101=>[1,2,2,2,1]
[4,1,7,5,2,3,6,8]=>1011000=>[1,2,1,4]
[4,1,7,8,6,3,2,5]=>1001110=>[1,3,1,1,2]
[6,8,3,2,1,4,7,5]=>0111001=>[2,1,1,3,1]
[6,8,2,4,1,3,7,5]=>0101001=>[2,2,3,1]
[6,1,2,7,5,8,4,3]=>1001011=>[1,3,2,1,1]
[4,2,7,3,8,5,6,1]=>1010101=>[1,2,2,2,1]
[4,5,2,6,8,3,7,1]=>0100101=>[2,3,2,1]
[4,8,3,2,5,7,6,1]=>0110011=>[2,1,3,1,1]
[8,4,7,6,2,3,5,1]=>1011001=>[1,2,1,3,1]
[6,8,4,1,5,3,7,2]=>0110101=>[2,1,2,2,1]
[8,3,4,7,6,2,5,1]=>1001101=>[1,3,1,2,1]
[1,8,3,5,2,6,7,4]=>0101001=>[2,2,3,1]
[5,8,2,4,3,7,6,1]=>0101011=>[2,2,2,1,1]
[6,5,3,8,4,2,7,1]=>1101101=>[1,1,2,1,2,1]
[7,4,5,1,6,2,8,3]=>1010101=>[1,2,2,2,1]
[4,7,3,5,6,2,8,1]=>0100101=>[2,3,2,1]
[6,7,8,4,1,3,5,2]=>0011001=>[3,1,3,1]
[3,1,6,8,4,7,5,2]=>1001011=>[1,3,2,1,1]
[8,3,6,1,5,7,4,2]=>1010011=>[1,2,3,1,1]
[3,2,7,5,8,6,1,4]=>1010110=>[1,2,2,1,2]
[2,4,6,7,8,1,5,3]=>0000101=>[5,2,1]
[2,4,6,8,1,7,5,3]=>0001011=>[4,2,1,1]
[7,4,3,8,6,2,1,5]=>1101110=>[1,1,2,1,1,2]
[4,3,6,2,1,8,5,7]=>1011010=>[1,2,1,2,2]
[4,6,2,3,7,5,8,1]=>0100101=>[2,3,2,1]
[5,8,4,2,3,6,7,1]=>0110001=>[2,1,4,1]
[8,4,5,3,2,1,7,6]=>1011101=>[1,2,1,1,2,1]
[6,8,4,2,3,7,5,1]=>0110011=>[2,1,3,1,1]
[6,4,8,3,2,7,1,5]=>1011010=>[1,2,1,2,2]
[5,8,3,7,2,1,6,4]=>0101101=>[2,2,1,2,1]
[2,5,6,4,7,1,8,3]=>0010101=>[3,2,2,1]
[2,5,4,8,1,6,7,3]=>0101001=>[2,2,3,1]
[1,2,6,5,8,7,3,4]=>0010110=>[3,2,1,2]
[5,6,3,4,8,7,2,1]=>0100111=>[2,3,1,1,1]
[6,5,3,4,8,7,2,1]=>1100111=>[1,1,3,1,1,1]
[7,5,3,8,4,6,2,1]=>1101011=>[1,1,2,2,1,1]
[8,5,3,7,4,6,2,1]=>1101011=>[1,1,2,2,1,1]
[5,8,1,2,3,4,7,6]=>0100001=>[2,5,1]
[7,1,2,8,3,6,4,5]=>1001010=>[1,3,2,2]
[6,1,8,2,3,5,7,4]=>1010001=>[1,2,4,1]
[6,1,7,2,3,5,8,4]=>1010001=>[1,2,4,1]
[4,3,8,7,5,6,2,1]=>1011011=>[1,2,1,2,1,1]
[7,1,6,2,3,5,8,4]=>1010001=>[1,2,4,1]
[8,1,6,2,3,5,7,4]=>1010001=>[1,2,4,1]
[8,1,7,2,3,5,6,4]=>1010001=>[1,2,4,1]
[5,8,3,7,4,6,2,1]=>0101011=>[2,2,2,1,1]
[6,8,7,3,4,5,2,1]=>0110011=>[2,1,3,1,1]
[8,6,1,2,3,4,7,5]=>1100001=>[1,1,5,1]
[8,6,2,3,5,1,4,7]=>1100100=>[1,1,3,3]
[8,2,4,5,7,3,1,6]=>1000110=>[1,4,1,2]
[2,6,3,8,7,5,4,1]=>0101111=>[2,2,1,1,1,1]
[8,2,3,7,5,4,1,6]=>1001110=>[1,3,1,1,2]
[8,2,6,3,5,4,1,7]=>1010110=>[1,2,2,1,2]
[8,6,1,5,2,4,3,7]=>1101010=>[1,1,2,2,2]
[8,6,2,4,1,5,3,7]=>1101010=>[1,1,2,2,2]
[8,4,1,6,5,3,2,7]=>1101110=>[1,1,2,1,1,2]
[8,3,6,1,5,4,2,7]=>1010110=>[1,2,2,1,2]
[8,3,2,6,5,4,1,7]=>1101110=>[1,1,2,1,1,2]
[8,3,2,5,7,4,1,6]=>1100110=>[1,1,3,1,2]
[8,3,1,7,5,4,2,6]=>1101110=>[1,1,2,1,1,2]
[6,1,3,8,7,5,4,2]=>1001111=>[1,3,1,1,1,1]
[3,6,1,8,7,5,4,2]=>0101111=>[2,2,1,1,1,1]
[3,8,1,5,7,6,4,2]=>0100111=>[2,3,1,1,1]
[3,5,2,8,7,6,4,1]=>0101111=>[2,2,1,1,1,1]
[3,4,8,2,7,6,5,1]=>0010111=>[3,2,1,1,1]
[3,4,8,7,1,6,5,2]=>0011011=>[3,1,2,1,1]
[8,1,3,5,7,6,4,2]=>1000111=>[1,4,1,1,1]
[4,1,8,5,7,6,3,2]=>1010111=>[1,2,2,1,1,1]
[8,2,7,1,4,5,6,3]=>1010001=>[1,2,4,1]
[8,1,7,3,4,6,2,5]=>1010010=>[1,2,3,2]
[8,3,1,7,2,6,5,4]=>1101011=>[1,1,2,2,1,1]
[3,8,2,4,7,6,5,1]=>0100111=>[2,3,1,1,1]
[2,8,3,7,4,6,5,1]=>0101011=>[2,2,2,1,1]
[8,2,3,7,1,6,5,4]=>1001011=>[1,3,2,1,1]
[8,2,7,1,3,6,5,4]=>1010011=>[1,2,3,1,1]
[8,1,7,2,6,4,3,5]=>1010110=>[1,2,2,1,2]
[8,1,7,5,2,4,3,6]=>1011010=>[1,2,1,2,2]
[8,2,3,7,4,6,1,5]=>1001010=>[1,3,2,2]
[2,4,8,5,7,6,3,1]=>0010111=>[3,2,1,1,1]
[8,2,4,3,7,6,1,5]=>1010110=>[1,2,2,1,2]
[8,2,7,3,5,1,4,6]=>1010100=>[1,2,2,3]
[8,2,7,4,3,1,5,6]=>1011100=>[1,2,1,1,3]
[8,2,1,5,7,6,4,3]=>1100111=>[1,1,3,1,1,1]
[6,1,8,2,7,5,4,3]=>1010111=>[1,2,2,1,1,1]
[8,1,5,2,7,6,4,3]=>1010111=>[1,2,2,1,1,1]
[8,1,7,2,4,6,5,3]=>1010011=>[1,2,3,1,1]
[8,2,4,1,7,6,5,3]=>1010111=>[1,2,2,1,1,1]
[4,2,8,3,7,6,5,1]=>1010111=>[1,2,2,1,1,1]
[4,8,2,1,7,6,5,3]=>0110111=>[2,1,2,1,1,1]
[5,1,8,7,2,6,4,3]=>1011011=>[1,2,1,2,1,1]
[5,8,1,3,7,6,2,4]=>0100110=>[2,3,1,2]
[8,2,5,4,1,7,6,3]=>1011011=>[1,2,1,2,1,1]
[5,1,4,8,7,6,3,2]=>1001111=>[1,3,1,1,1,1]
[8,1,4,3,7,6,5,2]=>1010111=>[1,2,2,1,1,1]
[4,8,1,3,7,6,5,2]=>0100111=>[2,3,1,1,1]
[4,3,8,1,7,6,5,2]=>1010111=>[1,2,2,1,1,1]
[6,2,8,1,5,7,3,4]=>1010010=>[1,2,3,2]
[7,2,5,4,1,8,6,3]=>1011011=>[1,2,1,2,1,1]
[7,3,2,8,5,6,1,4]=>1101010=>[1,1,2,2,2]
[5,4,6,8,7,2,1,3]=>1001110=>[1,3,1,1,2]
[1,7,6,3,2,8,4,5]=>0111010=>[2,1,1,2,2]
[6,5,8,3,4,1,7,2]=>1010101=>[1,2,2,2,1]
[4,1,2,8,5,3,6,7]=>1001100=>[1,3,1,3]
[3,5,8,2,6,1,7,4]=>0010101=>[3,2,2,1]
[3,7,6,2,8,4,5,1]=>0110101=>[2,1,2,2,1]
[4,3,6,8,5,1,2,7]=>1001100=>[1,3,1,3]
[2,7,1,5,8,4,3,6]=>0100110=>[2,3,1,2]
[2,7,6,1,8,4,3,5]=>0110110=>[2,1,2,1,2]
[7,1,2,6,3,5,4,8]=>1001010=>[1,3,2,2]
[7,2,6,3,4,5,1,8]=>1010010=>[1,2,3,2]
[4,1,2,7,8,5,3,6]=>1000110=>[1,4,1,2]
[4,7,3,1,2,6,8,5]=>0110001=>[2,1,4,1]
[3,8,5,6,4,2,7,1]=>0101101=>[2,2,1,2,1]
[3,2,6,4,7,8,5,1]=>1010011=>[1,2,3,1,1]
[4,2,7,5,8,3,1,6]=>1010110=>[1,2,2,1,2]
[5,2,1,4,7,8,3,6]=>1100010=>[1,1,4,2]
[5,6,2,7,3,4,8,1]=>0101001=>[2,2,3,1]
[1,5,8,6,4,2,3,7]=>0011100=>[3,1,1,3]
[2,5,8,6,4,1,7,3]=>0011101=>[3,1,1,2,1]
[4,7,2,3,1,6,8,5]=>0101001=>[2,2,3,1]
[7,4,6,2,8,3,5,1]=>1010101=>[1,2,2,2,1]
[3,4,6,5,1,2,7,8]=>0011000=>[3,1,4]
[4,3,8,2,5,7,1,6]=>1010010=>[1,2,3,2]
[4,1,6,2,5,3,7,8]=>1010100=>[1,2,2,3]
[4,2,6,1,5,3,8,7]=>1010101=>[1,2,2,2,1]
[6,7,2,3,1,5,8,4]=>0101001=>[2,2,3,1]
[2,1,5,7,8,3,6,4]=>1000101=>[1,4,2,1]
[4,7,5,8,6,3,1,2]=>0101110=>[2,2,1,1,2]
[2,4,8,3,7,1,5,6]=>0010100=>[3,2,3]
[5,2,8,4,1,6,3,7]=>1011010=>[1,2,1,2,2]
[7,6,5,2,1,8,4,3]=>1111011=>[1,1,1,1,2,1,1]
[2,7,5,1,8,3,6,4]=>0110101=>[2,1,2,2,1]
[5,1,8,7,4,3,6,2]=>1011101=>[1,2,1,1,2,1]
[3,8,7,2,4,6,1,5]=>0110010=>[2,1,3,2]
[5,7,1,3,2,4,8,6]=>0101001=>[2,2,3,1]
[4,2,7,6,3,5,8,1]=>1011001=>[1,2,1,3,1]
[8,4,7,6,3,5,1,2]=>1011010=>[1,2,1,2,2]
[8,1,7,4,2,3,5,6]=>1011000=>[1,2,1,4]
[6,5,1,3,8,7,4,2]=>1100111=>[1,1,3,1,1,1]
[6,1,8,5,3,7,2,4]=>1011010=>[1,2,1,2,2]
[5,1,6,8,3,7,4,2]=>1001011=>[1,3,2,1,1]
[8,6,5,1,7,4,3,2]=>1110111=>[1,1,1,2,1,1,1]
[7,6,4,1,3,5,8,2]=>1110001=>[1,1,1,4,1]
[8,2,3,7,1,4,5,6]=>1001000=>[1,3,4]
[5,6,2,7,4,3,1,8]=>0101110=>[2,2,1,1,2]
[3,7,8,2,6,1,4,5]=>0010100=>[3,2,3]
[3,7,8,5,2,1,4,6]=>0011100=>[3,1,1,3]
[4,8,6,5,1,2,7,3]=>0111001=>[2,1,1,3,1]
[4,8,6,5,1,2,3,7]=>0111000=>[2,1,1,4]
[3,8,7,6,5,1,2,4]=>0111100=>[2,1,1,1,3]
[5,8,2,6,1,4,7,3]=>0101001=>[2,2,3,1]
[3,8,7,5,6,1,4,2]=>0110101=>[2,1,2,2,1]
[4,6,3,8,7,5,1,2]=>0101110=>[2,2,1,1,2]
[2,8,4,1,5,7,6,3]=>0110011=>[2,1,3,1,1]
[1,8,4,2,5,7,6,3]=>0110011=>[2,1,3,1,1]
[2,8,5,4,1,7,6,3]=>0111011=>[2,1,1,2,1,1]
[2,5,8,3,7,1,6,4]=>0010101=>[3,2,2,1]
[1,8,5,2,4,7,6,3]=>0110011=>[2,1,3,1,1]
[1,4,6,2,8,7,5,3]=>0010111=>[3,2,1,1,1]
[7,8,2,4,1,6,5,3]=>0101011=>[2,2,2,1,1]
[2,4,6,1,8,7,5,3]=>0010111=>[3,2,1,1,1]
[2,8,4,5,1,7,6,3]=>0101011=>[2,2,2,1,1]
[3,5,8,1,7,6,2,4]=>0010110=>[3,2,1,2]
[3,5,8,2,7,6,1,4]=>0010110=>[3,2,1,2]
[2,1,6,8,7,5,3,4]=>1001110=>[1,3,1,1,2]
[1,8,2,4,5,7,6,3]=>0100011=>[2,4,1,1]
[1,3,8,2,5,7,6,4]=>0010011=>[3,3,1,1]
[2,3,8,1,5,7,6,4]=>0010011=>[3,3,1,1]
[2,6,1,8,7,5,3,4]=>0101110=>[2,2,1,1,2]
[1,6,2,8,7,5,3,4]=>0101110=>[2,2,1,1,2]
[1,6,3,8,7,5,2,4]=>0101110=>[2,2,1,1,2]
[2,6,3,8,7,5,1,4]=>0101110=>[2,2,1,1,2]
[3,2,8,1,5,7,6,4]=>1010011=>[1,2,3,1,1]
[3,1,8,2,5,7,6,4]=>1010011=>[1,2,3,1,1]
[2,1,8,3,5,7,6,4]=>1010011=>[1,2,3,1,1]
[7,8,2,1,4,6,5,3]=>0110011=>[2,1,3,1,1]
[2,3,6,8,7,5,1,4]=>0001110=>[4,1,1,2]
[3,1,6,8,7,2,5,4]=>1001101=>[1,3,1,2,1]
[3,8,4,5,1,6,2,7]=>0101010=>[2,2,2,2]
[6,1,4,5,7,2,3,8]=>1000100=>[1,4,3]
[8,1,4,7,6,3,2,5]=>1001110=>[1,3,1,1,2]
[8,3,1,6,4,7,2,5]=>1101010=>[1,1,2,2,2]
[5,3,8,6,2,7,1,4]=>1011010=>[1,2,1,2,2]
[8,3,6,1,5,7,2,4]=>1010010=>[1,2,3,2]
[8,4,6,3,1,2,5,7]=>1011000=>[1,2,1,4]
[6,8,1,4,5,2,3,7]=>0100100=>[2,3,3]
[1,5,8,4,6,2,3,7]=>0010100=>[3,2,3]
[5,6,8,1,4,2,3,7]=>0010100=>[3,2,3]
[5,7,4,8,1,2,3,6]=>0101000=>[2,2,4]
[4,7,8,1,2,6,3,5]=>0010010=>[3,3,2]
[8,7,1,5,6,2,3,4]=>1100100=>[1,1,3,3]
[1,6,5,8,7,2,3,4]=>0101100=>[2,2,1,3]
[3,7,1,6,2,4,8,5]=>0101001=>[2,2,3,1]
[5,1,2,7,6,8,3,4]=>1001010=>[1,3,2,2]
[1,7,6,5,8,2,3,4]=>0110100=>[2,1,2,3]
[1,6,8,5,7,2,3,4]=>0010100=>[3,2,3]
[7,5,1,2,6,8,3,4]=>1100010=>[1,1,4,2]
[6,1,5,2,7,8,3,4]=>1010010=>[1,2,3,2]
[5,1,2,6,8,7,3,4]=>1000110=>[1,4,1,2]
[1,8,6,2,5,7,3,4]=>0110010=>[2,1,3,2]
[5,7,8,1,2,6,3,4]=>0010010=>[3,3,2]
[8,1,5,7,6,2,3,4]=>1001100=>[1,3,1,3]
[3,7,1,2,8,4,6,5]=>0100101=>[2,3,2,1]
[1,5,8,7,6,2,3,4]=>0011100=>[3,1,1,3]
[7,8,6,1,5,2,3,4]=>0110100=>[2,1,2,3]
[4,5,7,2,3,1,8,6]=>0010101=>[3,2,2,1]
[3,7,8,1,4,6,5,2]=>0010011=>[3,3,1,1]
[2,5,8,7,4,1,3,6]=>0011100=>[3,1,1,3]
[2,6,4,7,5,3,8,1]=>0101101=>[2,2,1,2,1]
[6,2,4,7,1,3,8,5]=>1001001=>[1,3,3,1]
[7,3,5,1,4,2,8,6]=>1010101=>[1,2,2,2,1]
[5,4,7,1,3,2,8,6]=>1010101=>[1,2,2,2,1]
[6,1,4,7,5,3,8,2]=>1001101=>[1,3,1,2,1]
[8,7,4,3,1,5,6,2]=>1111001=>[1,1,1,1,3,1]
[8,7,1,4,3,5,6,2]=>1101001=>[1,1,2,3,1]
[6,1,8,4,7,3,2,5]=>1010110=>[1,2,2,1,2]
[4,7,3,6,1,2,8,5]=>0101001=>[2,2,3,1]
[5,2,1,7,4,3,8,6]=>1101101=>[1,1,2,1,2,1]
[4,7,6,2,3,1,8,5]=>0110101=>[2,1,2,2,1]
[7,6,8,2,5,3,4,1]=>1010101=>[1,2,2,2,1]
[2,3,6,1,8,7,5,4]=>0010111=>[3,2,1,1,1]
[2,6,8,7,5,3,1,4]=>0011110=>[3,1,1,1,2]
[6,4,1,7,5,2,8,3]=>1101101=>[1,1,2,1,2,1]
[5,7,8,2,3,6,1,4]=>0010010=>[3,3,2]
[4,8,7,1,2,5,6,3]=>0110001=>[2,1,4,1]
[2,8,7,4,1,5,6,3]=>0111001=>[2,1,1,3,1]
[8,6,2,1,5,7,4,3]=>1110011=>[1,1,1,3,1,1]
[3,8,6,7,5,2,1,4]=>0101110=>[2,2,1,1,2]
[6,1,3,7,5,8,2,4]=>1001010=>[1,3,2,2]
[4,7,3,1,8,5,6,2]=>0110101=>[2,1,2,2,1]
[1,3,8,5,2,7,4,6]=>0011010=>[3,1,2,2]
[1,3,8,6,7,2,4,5]=>0010100=>[3,2,3]
[2,8,3,7,6,1,4,5]=>0101100=>[2,2,1,3]
[1,3,8,7,6,2,4,5]=>0011100=>[3,1,1,3]
[1,4,6,8,7,2,3,5]=>0001100=>[4,1,3]
[7,6,4,8,5,1,3,2]=>1101101=>[1,1,2,1,2,1]
[7,2,6,5,8,1,3,4]=>1010100=>[1,2,2,3]
[3,6,7,5,2,8,4,1]=>0011011=>[3,1,2,1,1]
[4,6,5,7,2,8,1,3]=>0101010=>[2,2,2,2]
[5,3,6,7,8,1,4,2]=>1000101=>[1,4,2,1]
[6,3,2,8,5,4,1,7]=>1101110=>[1,1,2,1,1,2]
[3,8,4,1,5,2,6,7]=>0110100=>[2,1,2,3]
[2,5,7,4,3,1,6,8]=>0011100=>[3,1,1,3]
[5,3,4,2,7,1,6,8]=>1010100=>[1,2,2,3]
[3,7,5,4,1,2,6,8]=>0111000=>[2,1,1,4]
[4,2,5,1,3,8,7,6]=>1010011=>[1,2,3,1,1]
[4,3,5,1,2,7,6,8]=>1010010=>[1,2,3,2]
[5,3,4,1,7,2,6,8]=>1010100=>[1,2,2,3]
[4,1,6,3,5,2,7,8]=>1010100=>[1,2,2,3]
[3,1,7,2,5,6,4,8]=>1010010=>[1,2,3,2]
[3,7,5,4,2,1,6,8]=>0111100=>[2,1,1,1,3]
[7,3,2,1,6,4,5,8]=>1110100=>[1,1,1,2,3]
[2,8,6,1,7,4,3,5]=>0110110=>[2,1,2,1,2]
[2,5,4,6,1,3,7,8]=>0101000=>[2,2,4]
[2,5,6,4,1,3,7,8]=>0011000=>[3,1,4]
[8,5,2,6,1,3,7,4]=>1101001=>[1,1,2,3,1]
[7,1,5,6,3,2,4,8]=>1001100=>[1,3,1,3]
[7,1,2,5,4,6,3,8]=>1001010=>[1,3,2,2]
[2,4,1,6,5,3,7,8]=>0101100=>[2,2,1,3]
[4,1,2,7,5,6,3,8]=>1001010=>[1,3,2,2]
[7,1,2,6,5,4,3,8]=>1001110=>[1,3,1,1,2]
[8,2,1,5,6,3,7,4]=>1100101=>[1,1,3,2,1]
[6,1,4,5,3,2,7,8]=>1001100=>[1,3,1,3]
[3,1,6,5,4,2,7,8]=>1011100=>[1,2,1,1,3]
[3,1,4,6,5,2,7,8]=>1001100=>[1,3,1,3]
[5,6,3,8,7,4,1,2]=>0101110=>[2,2,1,1,2]
[5,2,6,8,7,4,1,3]=>1001110=>[1,3,1,1,2]
[5,2,3,1,4,8,6,7]=>1010010=>[1,2,3,2]
[5,4,1,3,2,8,6,7]=>1101010=>[1,1,2,2,2]
[5,1,3,4,2,8,6,7]=>1001010=>[1,3,2,2]
[4,2,7,3,8,5,1,6]=>1010110=>[1,2,2,1,2]
[4,3,7,2,8,5,6,1]=>1010101=>[1,2,2,2,1]
[5,3,1,2,4,8,6,7]=>1100010=>[1,1,4,2]
[1,3,2,6,4,8,7,5]=>0101011=>[2,2,2,1,1]
[1,6,2,5,3,8,7,4]=>0101011=>[2,2,2,1,1]
[1,8,2,6,3,7,5,4]=>0101011=>[2,2,2,1,1]
[1,8,3,6,4,7,5,2]=>0101011=>[2,2,2,1,1]
[1,7,2,6,3,8,5,4]=>0101011=>[2,2,2,1,1]
[1,5,2,7,4,8,6,3]=>0101011=>[2,2,2,1,1]
[1,4,2,8,5,7,6,3]=>0101011=>[2,2,2,1,1]
[4,8,1,3,2,6,5,7]=>0101010=>[2,2,2,2]
[1,5,3,8,4,7,6,2]=>0101011=>[2,2,2,1,1]
[2,6,3,8,1,5,4,7]=>0101010=>[2,2,2,2]
[8,3,1,4,2,6,5,7]=>1101010=>[1,1,2,2,2]
[6,8,7,3,5,2,4,1]=>0110101=>[2,1,2,2,1]
[8,3,5,1,2,6,4,7]=>1010010=>[1,2,3,2]
[8,6,3,1,5,4,2,7]=>1110110=>[1,1,1,2,1,2]
[8,6,4,1,5,3,2,7]=>1110110=>[1,1,1,2,1,2]
[8,6,5,4,1,3,2,7]=>1111010=>[1,1,1,1,2,2]
[5,3,8,7,4,6,2,1]=>1011011=>[1,2,1,2,1,1]
[2,3,8,7,4,6,1,5]=>0011010=>[3,1,2,2]
[8,3,5,7,4,1,2,6]=>1001100=>[1,3,1,3]
[4,8,5,3,1,2,7,6]=>0111001=>[2,1,1,3,1]
[6,8,7,3,1,5,4,2]=>0111011=>[2,1,1,2,1,1]
[6,8,5,4,1,3,7,2]=>0111001=>[2,1,1,3,1]
[2,5,8,7,4,6,3,1]=>0011011=>[3,1,2,1,1]
[4,8,7,6,5,1,3,2]=>0111101=>[2,1,1,1,2,1]
[3,8,7,5,1,6,2,4]=>0111010=>[2,1,1,2,2]
[2,3,8,7,5,6,1,4]=>0011010=>[3,1,2,2]
[2,8,7,1,3,6,4,5]=>0110010=>[2,1,3,2]
[8,5,4,7,2,1,3,6]=>1101100=>[1,1,2,1,3]
[6,8,7,3,5,2,1,4]=>0110110=>[2,1,2,1,2]
[3,5,8,6,4,2,7,1]=>0011101=>[3,1,1,2,1]
[6,8,4,1,5,2,7,3]=>0110101=>[2,1,2,2,1]
[6,8,2,1,7,5,3,4]=>0110110=>[2,1,2,1,2]
[5,8,4,6,1,2,7,3]=>0101001=>[2,2,3,1]
[2,4,8,6,5,1,7,3]=>0011101=>[3,1,1,2,1]
[4,8,7,6,5,2,1,3]=>0111110=>[2,1,1,1,1,2]
[4,8,7,5,1,6,2,3]=>0111010=>[2,1,1,2,2]
[4,5,2,1,8,6,7,3]=>0110101=>[2,1,2,2,1]
[2,8,3,5,6,7,1,4]=>0100010=>[2,4,2]
[5,6,2,4,7,1,8,3]=>0100101=>[2,3,2,1]
[2,7,5,4,6,1,8,3]=>0110101=>[2,1,2,2,1]
[3,7,5,4,6,2,8,1]=>0110101=>[2,1,2,2,1]
[2,6,7,4,1,3,8,5]=>0011001=>[3,1,3,1]
[6,5,7,4,1,3,8,2]=>1011001=>[1,2,1,3,1]
[2,4,6,3,5,7,8,1]=>0010001=>[3,4,1]
[3,6,4,2,5,7,8,1]=>0110001=>[2,1,4,1]
[2,3,6,1,5,7,8,4]=>0010001=>[3,4,1]
[4,3,6,2,5,7,8,1]=>1010001=>[1,2,4,1]
[4,6,1,2,5,7,8,3]=>0100001=>[2,5,1]
[2,6,4,1,5,7,8,3]=>0110001=>[2,1,4,1]
[2,4,1,6,5,7,8,3]=>0101001=>[2,2,3,1]
[7,8,4,1,6,3,5,2]=>0110101=>[2,1,2,2,1]
[8,7,5,6,1,3,4,2]=>1101001=>[1,1,2,3,1]
[1,4,5,8,6,3,2,7]=>0001110=>[4,1,1,2]
[8,4,5,7,2,6,1,3]=>1001010=>[1,3,2,2]
[8,1,7,5,3,6,2,4]=>1011010=>[1,2,1,2,2]
[5,2,8,3,6,1,4,7]=>1010100=>[1,2,2,3]
[5,2,6,3,1,7,8,4]=>1011001=>[1,2,1,3,1]
[5,7,6,1,2,3,8,4]=>0110001=>[2,1,4,1]
[5,3,2,1,8,6,4,7]=>1110110=>[1,1,1,2,1,2]
[4,3,6,2,1,8,7,5]=>1011011=>[1,2,1,2,1,1]
[5,3,6,4,8,2,1,7]=>1010110=>[1,2,2,1,2]
[3,7,4,5,1,6,2,8]=>0101010=>[2,2,2,2]
[3,6,4,5,8,2,1,7]=>0100110=>[2,3,1,2]
[6,1,4,5,2,8,7,3]=>1001011=>[1,3,2,1,1]
[7,2,4,5,1,6,3,8]=>1001010=>[1,3,2,2]
[7,5,4,1,6,3,2,8]=>1110110=>[1,1,1,2,1,2]
[1,5,4,8,6,3,2,7]=>0101110=>[2,2,1,1,2]
[7,5,4,8,6,3,1,2]=>1101110=>[1,1,2,1,1,2]
[1,8,7,5,3,6,4,2]=>0111011=>[2,1,1,2,1,1]
[8,3,7,4,1,6,2,5]=>1011010=>[1,2,1,2,2]
[8,5,4,1,6,3,2,7]=>1110110=>[1,1,1,2,1,2]
[1,7,4,2,6,5,3,8]=>0110110=>[2,1,2,1,2]
[8,2,1,5,6,7,3,4]=>1100010=>[1,1,4,2]
[6,3,1,8,4,7,2,5]=>1101010=>[1,1,2,2,2]
[7,1,4,8,6,3,2,5]=>1001110=>[1,3,1,1,2]
[4,1,8,5,6,7,2,3]=>1010010=>[1,2,3,2]
[5,7,4,8,6,2,1,3]=>0101110=>[2,2,1,1,2]
[5,3,6,8,2,7,1,4]=>1001010=>[1,3,2,2]
[6,3,7,4,8,2,1,5]=>1010110=>[1,2,2,1,2]
[5,3,6,1,4,7,2,8]=>1010010=>[1,2,3,2]
[4,3,6,8,2,7,1,5]=>1001010=>[1,3,2,2]
[5,3,7,4,8,2,1,6]=>1010110=>[1,2,2,1,2]
[5,3,8,4,1,6,2,7]=>1011010=>[1,2,1,2,2]
[5,3,8,1,4,7,2,6]=>1010010=>[1,2,3,2]
[5,8,4,1,6,3,2,7]=>0110110=>[2,1,2,1,2]
[7,3,8,4,1,6,2,5]=>1011010=>[1,2,1,2,2]
[1,5,8,3,6,7,4,2]=>0010011=>[3,3,1,1]
[1,8,2,5,6,7,3,4]=>0100010=>[2,4,2]
[7,8,4,1,6,5,2,3]=>0110110=>[2,1,2,1,2]
[6,3,8,1,5,7,2,4]=>1010010=>[1,2,3,2]
[8,3,1,2,5,7,4,6]=>1100010=>[1,1,4,2]
[8,1,4,2,6,5,3,7]=>1010110=>[1,2,2,1,2]
[3,8,5,6,2,7,1,4]=>0101010=>[2,2,2,2]
[2,4,5,8,7,3,1,6]=>0001110=>[4,1,1,2]
[4,3,1,5,6,2,8,7]=>1100101=>[1,1,3,2,1]
[4,1,5,8,6,7,2,3]=>1001010=>[1,3,2,2]
[4,3,7,6,1,2,8,5]=>1011001=>[1,2,1,3,1]
[4,7,5,6,1,2,8,3]=>0101001=>[2,2,3,1]
[4,5,1,8,6,7,3,2]=>0101011=>[2,2,2,1,1]
[3,4,5,8,6,7,2,1]=>0001011=>[4,2,1,1]
[2,1,5,8,6,7,4,3]=>1001011=>[1,3,2,1,1]
[3,4,5,8,7,1,2,6]=>0001100=>[4,1,3]
[4,7,1,5,6,2,8,3]=>0100101=>[2,3,2,1]
[2,6,4,7,1,3,8,5]=>0101001=>[2,2,3,1]
[5,3,8,6,4,7,2,1]=>1011011=>[1,2,1,2,1,1]
[6,4,1,5,7,8,3,2]=>1100011=>[1,1,4,1,1]
[3,6,4,7,2,1,8,5]=>0101101=>[2,2,1,2,1]
[3,8,4,6,1,7,2,5]=>0101010=>[2,2,2,2]
[3,8,5,6,4,7,2,1]=>0101011=>[2,2,2,1,1]
[3,8,6,5,2,7,4,1]=>0111011=>[2,1,1,2,1,1]
[3,8,7,5,2,1,4,6]=>0111100=>[2,1,1,1,3]
[6,4,1,7,3,2,8,5]=>1101101=>[1,1,2,1,2,1]
[5,1,4,6,7,2,8,3]=>1000101=>[1,4,2,1]
[6,5,4,7,1,3,8,2]=>1101001=>[1,1,2,3,1]
[2,1,6,5,3,7,8,4]=>1011001=>[1,2,1,3,1]
[6,1,4,7,2,3,8,5]=>1001001=>[1,3,3,1]
[1,6,2,5,4,8,3,7]=>0101010=>[2,2,2,2]
[4,1,2,7,5,8,3,6]=>1001010=>[1,3,2,2]
[6,1,3,5,8,2,4,7]=>1000100=>[1,4,3]
[5,6,4,3,1,8,2,7]=>0111010=>[2,1,1,2,2]
[6,2,3,5,8,1,4,7]=>1000100=>[1,4,3]
[6,7,2,3,8,4,5,1]=>0100101=>[2,3,2,1]
[6,7,2,1,3,8,4,5]=>0110010=>[2,1,3,2]
[5,7,4,1,8,3,2,6]=>0110110=>[2,1,2,1,2]
[4,1,7,5,8,3,6,2]=>1010101=>[1,2,2,2,1]
[6,7,1,3,8,4,5,2]=>0100101=>[2,3,2,1]
[1,6,7,4,3,8,5,2]=>0011011=>[3,1,2,1,1]
[6,1,7,4,2,8,5,3]=>1011011=>[1,2,1,2,1,1]
[2,1,6,7,4,3,8,5]=>1001101=>[1,3,1,2,1]
[6,7,3,2,1,8,4,5]=>0111010=>[2,1,1,2,2]
[2,5,7,3,1,4,8,6]=>0011001=>[3,1,3,1]
[6,7,3,2,8,4,5,1]=>0110101=>[2,1,2,2,1]
[2,6,7,4,3,8,5,1]=>0011011=>[3,1,2,1,1]
[1,2,6,7,4,3,8,5]=>0001101=>[4,1,2,1]
[1,7,5,8,2,4,3,6]=>0101010=>[2,2,2,2]
[2,7,1,8,4,6,3,5]=>0101010=>[2,2,2,2]
[2,7,5,8,1,6,3,4]=>0101010=>[2,2,2,2]
[1,6,7,3,8,5,4,2]=>0010111=>[3,2,1,1,1]
[6,7,1,8,4,5,3,2]=>0101011=>[2,2,2,1,1]
[8,6,1,5,4,3,2,7]=>1101110=>[1,1,2,1,1,2]
[2,4,3,8,5,1,6,7]=>0101100=>[2,2,1,3]
[1,5,6,7,3,8,2,4]=>0001010=>[4,2,2]
[1,6,5,4,8,3,2,7]=>0110110=>[2,1,2,1,2]
[3,8,7,2,4,6,5,1]=>0110011=>[2,1,3,1,1]
[1,3,7,6,4,8,5,2]=>0011011=>[3,1,2,1,1]
[3,1,8,7,6,4,2,5]=>1011110=>[1,2,1,1,1,2]
[3,1,8,7,5,4,2,6]=>1011110=>[1,2,1,1,1,2]
[3,1,7,6,5,4,2,8]=>1011110=>[1,2,1,1,1,2]
[4,7,1,6,5,3,2,8]=>0101110=>[2,2,1,1,2]
[4,8,1,6,5,3,2,7]=>0101110=>[2,2,1,1,2]
[4,8,1,7,5,3,2,6]=>0101110=>[2,2,1,1,2]
[8,4,1,7,6,3,2,5]=>1101110=>[1,1,2,1,1,2]
[5,4,1,8,6,3,2,7]=>1101110=>[1,1,2,1,1,2]
[5,4,1,7,6,3,2,8]=>1101110=>[1,1,2,1,1,2]
[6,4,1,7,5,3,2,8]=>1101110=>[1,1,2,1,1,2]
[6,4,1,8,5,3,2,7]=>1101110=>[1,1,2,1,1,2]
[8,4,1,7,5,3,2,6]=>1101110=>[1,1,2,1,1,2]
[7,4,1,6,5,3,2,8]=>1101110=>[1,1,2,1,1,2]
[7,5,6,1,4,3,2,8]=>1010110=>[1,2,2,1,2]
[8,5,6,1,4,3,2,7]=>1010110=>[1,2,2,1,2]
[5,7,6,1,4,3,2,8]=>0110110=>[2,1,2,1,2]
[5,8,6,1,4,3,2,7]=>0110110=>[2,1,2,1,2]
[6,7,5,1,4,3,2,8]=>0110110=>[2,1,2,1,2]
[8,7,5,1,4,3,2,6]=>1110110=>[1,1,1,2,1,2]
[8,6,5,1,4,3,2,7]=>1110110=>[1,1,1,2,1,2]
[1,8,6,3,4,2,5,7]=>0110100=>[2,1,2,3]
[3,1,6,4,5,7,2,8]=>1010010=>[1,2,3,2]
[7,6,3,8,4,5,2,1]=>1101011=>[1,1,2,2,1,1]
[8,2,7,6,1,4,3,5]=>1011010=>[1,2,1,2,2]
[5,2,7,8,1,4,3,6]=>1001010=>[1,3,2,2]
[8,2,7,6,1,4,5,3]=>1011001=>[1,2,1,3,1]
[5,2,3,7,1,6,8,4]=>1001001=>[1,3,3,1]
[1,7,5,2,6,4,8,3]=>0110101=>[2,1,2,2,1]
[7,1,3,6,8,2,4,5]=>1000100=>[1,4,3]
[1,2,5,7,8,4,6,3]=>0000101=>[5,2,1]
[3,1,2,7,5,4,8,6]=>1001101=>[1,3,1,2,1]
[6,7,4,1,3,2,8,5]=>0110101=>[2,1,2,2,1]
[1,7,2,8,4,3,5,6]=>0101100=>[2,2,1,3]
[4,1,6,5,7,8,2,3]=>1010010=>[1,2,3,2]
[1,6,3,5,7,8,2,4]=>0100010=>[2,4,2]
[8,6,1,7,5,2,4,3]=>1101101=>[1,1,2,1,2,1]
[7,6,4,1,8,3,2,5]=>1110110=>[1,1,1,2,1,2]
[8,4,1,6,5,2,7,3]=>1101101=>[1,1,2,1,2,1]
[1,5,3,4,7,8,2,6]=>0100010=>[2,4,2]
[4,2,1,5,7,8,3,6]=>1100010=>[1,1,4,2]
[5,1,4,6,7,8,2,3]=>1000010=>[1,5,2]
[4,1,5,3,7,8,2,6]=>1010010=>[1,2,3,2]
[8,1,4,6,5,2,7,3]=>1001101=>[1,3,1,2,1]
[7,1,5,4,6,3,2,8]=>1010110=>[1,2,2,1,2]
[8,2,1,6,7,5,4,3]=>1100111=>[1,1,3,1,1,1]
[1,2,4,7,6,3,8,5]=>0001101=>[4,1,2,1]
[6,7,4,1,8,5,2,3]=>0110110=>[2,1,2,1,2]
[8,6,4,1,5,7,3,2]=>1110011=>[1,1,1,3,1,1]
[5,2,4,3,7,1,6,8]=>1010100=>[1,2,2,3]
[6,1,5,4,8,3,2,7]=>1010110=>[1,2,2,1,2]
[1,2,8,7,4,3,6,5]=>0011101=>[3,1,1,2,1]
[3,2,1,7,5,8,4,6]=>1101010=>[1,1,2,2,2]
[8,1,7,6,4,2,5,3]=>1011101=>[1,2,1,1,2,1]
[1,3,6,4,7,8,2,5]=>0010010=>[3,3,2]
[5,1,3,4,7,8,2,6]=>1000010=>[1,5,2]
[4,5,1,3,7,8,2,6]=>0100010=>[2,4,2]
[5,2,3,1,7,8,4,6]=>1010010=>[1,2,3,2]
[1,6,4,3,7,8,2,5]=>0110010=>[2,1,3,2]
[7,6,4,3,1,5,2,8]=>1111010=>[1,1,1,1,2,2]
[3,2,6,4,1,8,5,7]=>1011010=>[1,2,1,2,2]
[7,5,4,6,1,3,2,8]=>1101010=>[1,1,2,2,2]
[8,4,6,5,1,2,7,3]=>1011001=>[1,2,1,3,1]
[1,5,6,3,7,8,2,4]=>0010010=>[3,3,2]
[4,2,5,1,7,8,3,6]=>1010010=>[1,2,3,2]
[3,5,8,6,1,4,2,7]=>0011010=>[3,1,2,2]
[1,8,4,2,7,6,3,5]=>0110110=>[2,1,2,1,2]
[7,3,8,1,6,5,4,2]=>1010111=>[1,2,2,1,1,1]
[2,4,1,8,7,3,6,5]=>0101101=>[2,2,1,2,1]
[7,3,8,6,1,5,4,2]=>1011011=>[1,2,1,2,1,1]
[3,5,1,7,8,2,6,4]=>0100101=>[2,3,2,1]
[5,4,7,8,2,1,6,3]=>1001101=>[1,3,1,2,1]
[5,3,6,1,8,4,2,7]=>1010110=>[1,2,2,1,2]
[3,4,6,2,1,8,5,7]=>0011010=>[3,1,2,2]
[5,6,4,8,3,2,1,7]=>0101110=>[2,2,1,1,2]
[5,7,4,8,2,1,6,3]=>0101101=>[2,2,1,2,1]
[4,7,5,8,2,1,6,3]=>0101101=>[2,2,1,2,1]
[4,7,3,2,8,1,5,6]=>0110100=>[2,1,2,3]
[7,1,2,6,3,8,5,4]=>1001011=>[1,3,2,1,1]
[8,1,2,6,3,7,5,4]=>1001011=>[1,3,2,1,1]
[8,1,2,7,6,3,5,4]=>1001101=>[1,3,1,2,1]
[4,8,7,3,1,6,2,5]=>0111010=>[2,1,1,2,2]
[4,7,8,3,1,6,2,5]=>0011010=>[3,1,2,2]
[7,4,3,1,6,2,8,5]=>1110101=>[1,1,1,2,2,1]
[7,4,3,1,8,6,2,5]=>1110110=>[1,1,1,2,1,2]
[6,8,3,2,1,7,4,5]=>0111010=>[2,1,1,2,2]
[3,7,6,2,4,8,1,5]=>0110010=>[2,1,3,2]
[4,3,7,2,8,6,1,5]=>1010110=>[1,2,2,1,2]
[5,1,2,6,3,8,7,4]=>1001011=>[1,3,2,1,1]
[5,1,2,7,3,8,6,4]=>1001011=>[1,3,2,1,1]
[6,1,2,7,3,5,8,4]=>1001001=>[1,3,3,1]
[6,2,5,4,1,8,7,3]=>1011011=>[1,2,1,2,1,1]
[4,6,3,2,1,8,7,5]=>0111011=>[2,1,1,2,1,1]
[8,4,3,2,7,6,1,5]=>1110110=>[1,1,1,2,1,2]
[1,5,8,4,7,6,3,2]=>0010111=>[3,2,1,1,1]
[3,2,7,4,8,6,1,5]=>1010110=>[1,2,2,1,2]
[7,4,3,2,8,6,1,5]=>1110110=>[1,1,1,2,1,2]
[6,4,3,8,5,2,1,7]=>1101110=>[1,1,2,1,1,2]
[8,2,5,4,7,6,1,3]=>1010110=>[1,2,2,1,2]
[7,2,5,4,8,6,1,3]=>1010110=>[1,2,2,1,2]
[6,2,8,7,5,4,1,3]=>1011110=>[1,2,1,1,1,2]
[4,5,3,2,8,6,1,7]=>0110110=>[2,1,2,1,2]
[3,2,5,4,8,6,1,7]=>1010110=>[1,2,2,1,2]
[3,2,8,6,5,4,1,7]=>1011110=>[1,2,1,1,1,2]
[8,4,3,6,5,2,1,7]=>1101110=>[1,1,2,1,1,2]
[8,4,3,7,5,2,1,6]=>1101110=>[1,1,2,1,1,2]
[3,2,7,8,5,4,1,6]=>1001110=>[1,3,1,1,2]
[6,8,7,4,3,2,1,5]=>0111110=>[2,1,1,1,1,2]
[6,3,2,1,8,7,4,5]=>1110110=>[1,1,1,2,1,2]
[6,2,3,1,8,7,4,5]=>1010110=>[1,2,2,1,2]
[7,2,1,5,8,4,6,3]=>1100101=>[1,1,3,2,1]
[7,3,1,5,2,8,6,4]=>1101011=>[1,1,2,2,1,1]
[7,1,6,4,2,8,5,3]=>1011011=>[1,2,1,2,1,1]
[3,7,4,1,5,8,6,2]=>0110011=>[2,1,3,1,1]
[6,7,1,4,3,8,5,2]=>0101011=>[2,2,2,1,1]
[7,1,6,4,8,3,5,2]=>1010101=>[1,2,2,2,1]
[8,5,3,6,1,7,4,2]=>1101011=>[1,1,2,2,1,1]
[8,5,6,1,2,7,4,3]=>1010011=>[1,2,3,1,1]
[3,6,4,1,5,2,8,7]=>0110101=>[2,1,2,2,1]
[4,6,7,2,1,8,3,5]=>0011010=>[3,1,2,2]
[3,7,1,8,2,5,4,6]=>0101010=>[2,2,2,2]
[4,5,8,6,1,3,7,2]=>0011001=>[3,1,3,1]
[4,5,8,6,2,7,3,1]=>0011011=>[3,1,2,1,1]
[4,6,7,1,5,3,8,2]=>0010101=>[3,2,2,1]
[4,6,7,2,1,8,5,3]=>0011011=>[3,1,2,1,1]
[4,1,3,5,6,7,8,2]=>1000001=>[1,6,1]
[4,6,8,3,2,7,1,5]=>0011010=>[3,1,2,2]
[4,6,8,2,3,7,1,5]=>0010010=>[3,3,2]
[4,5,8,3,7,1,2,6]=>0010100=>[3,2,3]
[4,5,8,3,7,2,1,6]=>0010110=>[3,2,1,2]
[3,7,8,4,6,2,5,1]=>0010101=>[3,2,2,1]
[3,6,1,5,7,8,2,4]=>0100010=>[2,4,2]
[3,8,2,5,4,7,1,6]=>0101010=>[2,2,2,2]
[3,8,6,2,5,1,7,4]=>0110101=>[2,1,2,2,1]
[4,5,8,6,2,1,7,3]=>0011101=>[3,1,1,2,1]
[4,5,8,6,1,2,7,3]=>0011001=>[3,1,3,1]
[2,1,5,8,6,3,7,4]=>1001101=>[1,3,1,2,1]
[4,6,8,5,2,7,1,3]=>0011010=>[3,1,2,2]
[3,7,8,5,2,6,1,4]=>0011010=>[3,1,2,2]
[3,7,8,5,4,1,6,2]=>0011101=>[3,1,1,2,1]
[4,6,8,5,3,1,7,2]=>0011101=>[3,1,1,2,1]
[7,8,2,3,5,4,1,6]=>0100110=>[2,3,1,2]
[4,6,5,1,7,3,8,2]=>0110101=>[2,1,2,2,1]
[5,7,3,1,2,4,8,6]=>0110001=>[2,1,4,1]
[6,3,2,5,1,7,4,8]=>1101010=>[1,1,2,2,2]
[6,1,2,4,8,5,3,7]=>1000110=>[1,4,1,2]
[6,3,1,7,2,5,8,4]=>1101001=>[1,1,2,3,1]
[3,7,2,8,5,1,4,6]=>0101100=>[2,2,1,3]
[3,6,5,2,4,7,1,8]=>0110010=>[2,1,3,2]
[1,5,7,8,3,4,2,6]=>0001010=>[4,2,2]
[6,8,4,3,1,7,2,5]=>0111010=>[2,1,1,2,2]
[8,4,1,3,7,5,6,2]=>1100101=>[1,1,3,2,1]
[4,8,1,3,7,5,6,2]=>0100101=>[2,3,2,1]
[1,8,5,7,4,2,3,6]=>0101100=>[2,2,1,3]
[2,1,6,8,5,3,4,7]=>1001100=>[1,3,1,3]
[4,5,1,3,8,6,7,2]=>0100101=>[2,3,2,1]
[1,2,6,8,5,3,4,7]=>0001100=>[4,1,3]
[5,6,8,7,3,1,2,4]=>0011100=>[3,1,1,3]
[1,5,6,8,4,2,3,7]=>0001100=>[4,1,3]
[5,7,8,3,6,1,2,4]=>0010100=>[3,2,3]
[1,5,8,6,2,4,3,7]=>0011010=>[3,1,2,2]
[1,5,3,7,2,6,8,4]=>0101001=>[2,2,3,1]
[1,5,2,4,8,6,7,3]=>0100101=>[2,3,2,1]
[1,5,4,2,6,8,7,3]=>0110011=>[2,1,3,1,1]
[5,7,6,8,3,1,2,4]=>0101100=>[2,2,1,3]
[1,2,5,3,6,8,7,4]=>0010011=>[3,3,1,1]
[7,1,5,6,2,3,8,4]=>1001001=>[1,3,3,1]
[8,2,1,4,6,7,3,5]=>1100010=>[1,1,4,2]
[7,2,6,1,3,4,8,5]=>1010001=>[1,2,4,1]
[4,1,3,7,2,5,8,6]=>1001001=>[1,3,3,1]
[6,2,7,5,1,3,8,4]=>1011001=>[1,2,1,3,1]
[1,7,5,6,2,3,8,4]=>0101001=>[2,2,3,1]
[3,7,6,1,2,4,8,5]=>0110001=>[2,1,4,1]
[8,6,1,3,5,7,2,4]=>1100010=>[1,1,4,2]
[1,7,4,3,8,2,5,6]=>0110100=>[2,1,2,3]
[6,1,5,3,4,8,2,7]=>1010010=>[1,2,3,2]
[3,6,7,5,2,8,1,4]=>0011010=>[3,1,2,2]
[7,8,4,1,5,6,2,3]=>0110010=>[2,1,3,2]
[5,8,1,3,6,7,2,4]=>0100010=>[2,4,2]
[2,8,4,3,7,1,5,6]=>0110100=>[2,1,2,3]
[3,8,4,6,7,1,2,5]=>0100100=>[2,3,3]
[6,3,8,4,7,1,2,5]=>1010100=>[1,2,2,3]
[1,2,5,4,8,3,6,7]=>0010100=>[3,2,3]
[7,1,3,8,2,4,5,6]=>1001000=>[1,3,4]
[8,1,3,7,2,4,5,6]=>1001000=>[1,3,4]
[3,5,4,7,8,1,2,6]=>0100100=>[2,3,3]
[8,3,1,4,7,2,5,6]=>1100100=>[1,1,3,3]
[1,6,4,7,8,2,3,5]=>0100100=>[2,3,3]
[1,3,7,8,5,6,2,4]=>0001010=>[4,2,2]
[7,5,4,8,6,1,2,3]=>1101100=>[1,1,2,1,3]
[8,2,6,7,5,1,3,4]=>1001100=>[1,3,1,3]
[8,1,7,4,6,2,3,5]=>1010100=>[1,2,2,3]
[2,5,8,4,7,1,3,6]=>0010100=>[3,2,3]
[4,5,8,7,1,2,3,6]=>0011000=>[3,1,4]
[4,1,8,5,7,2,3,6]=>1010100=>[1,2,2,3]
[1,8,7,4,6,2,3,5]=>0110100=>[2,1,2,3]
[2,6,5,4,1,8,3,7]=>0111010=>[2,1,1,2,2]
[6,2,5,1,4,8,3,7]=>1010010=>[1,2,3,2]
[6,5,4,1,3,8,2,7]=>1110010=>[1,1,1,3,2]
[6,3,5,4,2,8,1,7]=>1011010=>[1,2,1,2,2]
[1,3,8,7,4,2,6,5]=>0011101=>[3,1,1,2,1]
[8,7,4,3,1,5,2,6]=>1111010=>[1,1,1,1,2,2]
[8,2,5,1,4,6,7,3]=>1010001=>[1,2,4,1]
[3,8,4,5,1,6,7,2]=>0101001=>[2,2,3,1]
[8,5,4,1,3,6,7,2]=>1110001=>[1,1,1,4,1]
[8,3,1,7,5,6,4,2]=>1101011=>[1,1,2,2,1,1]
[8,4,7,6,5,3,1,2]=>1011110=>[1,2,1,1,1,2]
[8,1,3,7,5,6,4,2]=>1001011=>[1,3,2,1,1]
[8,1,4,5,7,6,3,2]=>1000111=>[1,4,1,1,1]
[2,4,1,8,5,7,6,3]=>0101011=>[2,2,2,1,1]
[8,2,1,4,7,6,3,5]=>1100110=>[1,1,3,1,2]
[8,3,1,7,4,2,6,5]=>1101101=>[1,1,2,1,2,1]
[8,2,7,3,1,6,5,4]=>1011011=>[1,2,1,2,1,1]
[1,8,4,2,3,7,6,5]=>0110011=>[2,1,3,1,1]
[3,1,2,8,7,4,6,5]=>1001101=>[1,3,1,2,1]
[8,5,1,2,4,3,7,6]=>1100101=>[1,1,3,2,1]
[2,8,3,7,4,1,6,5]=>0101101=>[2,2,1,2,1]
[2,3,1,8,7,6,4,5]=>0101110=>[2,2,1,1,2]
[4,2,8,7,3,1,5,6]=>1011100=>[1,2,1,1,3]
[1,3,4,8,7,2,5,6]=>0001100=>[4,1,3]
[8,1,3,4,6,7,2,5]=>1000010=>[1,5,2]
[3,4,8,2,6,7,1,5]=>0010010=>[3,3,2]
[3,6,8,2,5,1,7,4]=>0010101=>[3,2,2,1]
[3,8,2,5,7,4,6,1]=>0100101=>[2,3,2,1]
[8,4,2,1,7,5,6,3]=>1110101=>[1,1,1,2,2,1]
[8,2,7,5,6,4,1,3]=>1010110=>[1,2,2,1,2]
[6,2,8,5,4,1,7,3]=>1011101=>[1,2,1,1,2,1]
[6,8,5,4,1,7,2,3]=>0111010=>[2,1,1,2,2]
[2,8,1,5,7,6,3,4]=>0100110=>[2,3,1,2]
[3,1,8,2,7,5,6,4]=>1010101=>[1,2,2,2,1]
[8,5,7,1,6,4,2,3]=>1010110=>[1,2,2,1,2]
[8,4,7,6,5,1,2,3]=>1011100=>[1,2,1,1,3]
[2,8,4,7,3,6,5,1]=>0101011=>[2,2,2,1,1]
[8,4,7,2,1,6,5,3]=>1011011=>[1,2,1,2,1,1]
[1,8,4,7,6,5,2,3]=>0101110=>[2,2,1,1,2]
[8,2,5,7,1,4,6,3]=>1001001=>[1,3,3,1]
[3,5,8,1,7,4,6,2]=>0010101=>[3,2,2,1]
[8,4,7,1,3,6,5,2]=>1010011=>[1,2,3,1,1]
[5,1,7,8,3,4,2,6]=>1001010=>[1,3,2,2]
[5,3,6,1,4,2,8,7]=>1010101=>[1,2,2,2,1]
[5,7,2,1,4,3,8,6]=>0110101=>[2,1,2,2,1]
[7,1,8,3,5,2,4,6]=>1010100=>[1,2,2,3]
[7,2,4,8,1,5,6,3]=>1001001=>[1,3,3,1]
[7,1,8,4,2,5,6,3]=>1011001=>[1,2,1,3,1]
[6,4,2,5,8,1,7,3]=>1100101=>[1,1,3,2,1]
[2,1,7,5,8,3,6,4]=>1010101=>[1,2,2,2,1]
[7,3,8,5,6,2,1,4]=>1010110=>[1,2,2,1,2]
[2,7,4,8,1,5,6,3]=>0101001=>[2,2,3,1]
[7,4,8,3,1,5,6,2]=>1011001=>[1,2,1,3,1]
[6,1,5,8,3,7,4,2]=>1001011=>[1,3,2,1,1]
[2,6,3,5,8,7,4,1]=>0100111=>[2,3,1,1,1]
[6,8,1,2,5,7,4,3]=>0100011=>[2,4,1,1]
[8,6,5,3,7,2,1,4]=>1110110=>[1,1,1,2,1,2]
[4,8,5,3,7,2,1,6]=>0110110=>[2,1,2,1,2]
[7,4,8,6,5,3,2,1]=>1011111=>[1,2,1,1,1,1,1]
[6,4,7,1,3,2,8,5]=>1010101=>[1,2,2,2,1]
[7,8,4,1,3,5,6,2]=>0110001=>[2,1,4,1]
[7,8,3,4,1,5,6,2]=>0101001=>[2,2,3,1]
[7,3,1,8,2,5,6,4]=>1101001=>[1,1,2,3,1]
[7,2,3,8,1,5,6,4]=>1001001=>[1,3,3,1]
[2,7,4,8,6,3,1,5]=>0101110=>[2,2,1,1,2]
[6,4,8,2,3,1,7,5]=>1010101=>[1,2,2,2,1]
[7,2,1,8,3,5,6,4]=>1101001=>[1,1,2,3,1]
[5,1,6,3,8,2,4,7]=>1010100=>[1,2,2,3]
[3,5,6,8,1,4,2,7]=>0001010=>[4,2,2]
[4,3,5,8,2,1,6,7]=>1001100=>[1,3,1,3]
[6,4,7,2,3,1,5,8]=>1010100=>[1,2,2,3]
[6,8,1,5,4,2,7,3]=>0101101=>[2,2,1,2,1]
[7,8,6,3,1,4,2,5]=>0111010=>[2,1,1,2,2]
[7,8,6,3,5,1,2,4]=>0110100=>[2,1,2,3]
[7,2,8,5,4,6,3,1]=>1011011=>[1,2,1,2,1,1]
[6,1,8,4,7,2,3,5]=>1010100=>[1,2,2,3]
[6,5,3,7,2,4,8,1]=>1101001=>[1,1,2,3,1]
[5,6,2,8,4,3,7,1]=>0101101=>[2,2,1,2,1]
[4,6,2,7,8,3,5,1]=>0100101=>[2,3,2,1]
[3,1,2,4,8,5,7,6]=>1000101=>[1,4,2,1]
[5,1,2,4,6,7,8,3]=>1000001=>[1,6,1]
[4,6,3,5,2,8,7,1]=>0101011=>[2,2,2,1,1]
[5,3,2,6,8,4,7,1]=>1100101=>[1,1,3,2,1]
[5,6,3,4,8,2,7,1]=>0100101=>[2,3,2,1]
[5,2,6,4,1,7,8,3]=>1011001=>[1,2,1,3,1]
[5,8,4,6,3,2,7,1]=>0101101=>[2,2,1,2,1]
[5,4,3,8,6,2,7,1]=>1101101=>[1,1,2,1,2,1]
[5,7,8,2,4,3,6,1]=>0010101=>[3,2,2,1]
[5,6,2,4,8,3,7,1]=>0100101=>[2,3,2,1]
[5,4,2,8,6,3,7,1]=>1101101=>[1,1,2,1,2,1]
[5,7,4,2,6,3,8,1]=>0110101=>[2,1,2,2,1]
[6,4,7,8,2,3,5,1]=>1001001=>[1,3,3,1]
[3,7,5,2,4,8,1,6]=>0110010=>[2,1,3,2]
[4,7,5,2,3,8,6,1]=>0110011=>[2,1,3,1,1]
[6,4,7,3,2,5,8,1]=>1011001=>[1,2,1,3,1]
[6,3,7,8,2,4,5,1]=>1001001=>[1,3,3,1]
[5,7,3,2,8,4,6,1]=>0110101=>[2,1,2,2,1]
[5,3,7,2,8,4,6,1]=>1010101=>[1,2,2,2,1]
[4,3,7,2,5,8,6,1]=>1010011=>[1,2,3,1,1]
[4,7,3,2,5,8,6,1]=>0110011=>[2,1,3,1,1]
[4,7,3,2,6,8,5,1]=>0110011=>[2,1,3,1,1]
[7,5,3,2,6,4,8,1]=>1110101=>[1,1,1,2,2,1]
[5,7,3,2,6,4,8,1]=>0110101=>[2,1,2,2,1]
[5,3,2,8,6,4,7,1]=>1101101=>[1,1,2,1,2,1]
[8,5,2,6,7,3,4,1]=>1100101=>[1,1,3,2,1]
[8,4,2,6,3,7,5,1]=>1101011=>[1,1,2,2,1,1]
[7,4,6,2,3,8,5,1]=>1010011=>[1,2,3,1,1]
[7,5,6,2,8,3,4,1]=>1010101=>[1,2,2,2,1]
[6,3,7,5,2,4,8,1]=>1011001=>[1,2,1,3,1]
[5,7,6,2,8,3,4,1]=>0110101=>[2,1,2,2,1]
[4,7,6,2,3,8,5,1]=>0110011=>[2,1,3,1,1]
[7,6,3,2,5,8,1,4]=>1110010=>[1,1,1,3,2]
[7,6,4,2,5,8,3,1]=>1110011=>[1,1,1,3,1,1]
[6,3,8,5,4,7,2,1]=>1011011=>[1,2,1,2,1,1]
[4,8,3,7,1,6,5,2]=>0101011=>[2,2,2,1,1]
[8,7,2,6,5,1,4,3]=>1101101=>[1,1,2,1,2,1]
[5,8,3,2,1,7,6,4]=>0111011=>[2,1,1,2,1,1]
[5,4,3,8,1,7,6,2]=>1101011=>[1,1,2,2,1,1]
[6,5,3,8,7,1,4,2]=>1101101=>[1,1,2,1,2,1]
[4,3,8,2,7,6,5,1]=>1010111=>[1,2,2,1,1,1]
[4,8,2,7,6,5,3,1]=>0101111=>[2,2,1,1,1,1]
[7,8,2,6,5,4,1,3]=>0101110=>[2,2,1,1,2]
[3,8,7,6,2,5,1,4]=>0111010=>[2,1,1,2,2]
[4,8,3,7,2,1,6,5]=>0101101=>[2,2,1,2,1]
[8,6,3,1,7,5,4,2]=>1110111=>[1,1,1,2,1,1,1]
[8,6,3,7,1,5,4,2]=>1101011=>[1,1,2,2,1,1]
[4,8,3,7,6,2,5,1]=>0101101=>[2,2,1,2,1]
[5,8,2,7,6,4,1,3]=>0101110=>[2,2,1,1,2]
[8,4,2,1,7,6,5,3]=>1110111=>[1,1,1,2,1,1,1]
[1,6,4,2,5,3,7,8]=>0110100=>[2,1,2,3]
[1,6,7,2,5,3,4,8]=>0010100=>[3,2,3]
[1,8,6,2,7,3,4,5]=>0110100=>[2,1,2,3]
[1,5,2,6,4,3,7,8]=>0101100=>[2,2,1,3]
[1,5,2,4,6,3,7,8]=>0100100=>[2,3,3]
[1,8,6,2,3,7,4,5]=>0110010=>[2,1,3,2]
[1,5,2,8,6,3,4,7]=>0101100=>[2,2,1,3]
[1,7,3,2,6,8,4,5]=>0110010=>[2,1,3,2]
[1,3,6,8,2,7,4,5]=>0001010=>[4,2,2]
[1,4,3,8,2,5,6,7]=>0101000=>[2,2,4]
[1,7,2,3,8,5,4,6]=>0100110=>[2,3,1,2]
[1,6,2,8,5,4,3,7]=>0101110=>[2,2,1,1,2]
[1,7,2,3,8,6,4,5]=>0100110=>[2,3,1,2]
[1,5,3,8,2,7,4,6]=>0101010=>[2,2,2,2]
[1,7,2,5,3,4,8,6]=>0101001=>[2,2,3,1]
[1,4,8,2,5,6,3,7]=>0010010=>[3,3,2]
[1,2,7,3,6,8,4,5]=>0010010=>[3,3,2]
[1,7,2,3,6,8,4,5]=>0100010=>[2,4,2]
[1,4,8,3,2,5,6,7]=>0011000=>[3,1,4]
[1,7,2,5,8,3,4,6]=>0100100=>[2,3,3]
[1,5,6,3,4,2,7,8]=>0010100=>[3,2,3]
[1,5,6,3,4,7,2,8]=>0010010=>[3,3,2]
[1,5,3,6,4,2,7,8]=>0101100=>[2,2,1,3]
[1,7,5,6,8,3,4,2]=>0100101=>[2,3,2,1]
[1,7,5,6,3,8,4,2]=>0101011=>[2,2,2,1,1]
[1,3,7,5,2,8,6,4]=>0011011=>[3,1,2,1,1]
[1,3,7,2,5,8,6,4]=>0010011=>[3,3,1,1]
[1,5,3,7,4,6,2,8]=>0101010=>[2,2,2,2]
[1,5,3,7,6,4,2,8]=>0101110=>[2,2,1,1,2]
[1,5,3,6,7,4,2,8]=>0100110=>[2,3,1,2]
[1,5,6,3,7,4,2,8]=>0010110=>[3,2,1,2]
[1,5,7,6,3,4,8,2]=>0011001=>[3,1,3,1]
[1,5,7,3,6,4,8,2]=>0010101=>[3,2,2,1]
[1,3,7,2,5,6,8,4]=>0010001=>[3,4,1]
[1,3,7,5,6,2,8,4]=>0010101=>[3,2,2,1]
[2,5,7,4,1,3,8,6]=>0011001=>[3,1,3,1]
[6,7,3,1,8,5,2,4]=>0110110=>[2,1,2,1,2]
[8,3,5,1,7,6,2,4]=>1010110=>[1,2,2,1,2]
[3,5,6,1,8,7,2,4]=>0010110=>[3,2,1,2]
[2,4,6,8,7,3,1,5]=>0001110=>[4,1,1,2]
[2,3,6,4,1,8,7,5]=>0011011=>[3,1,2,1,1]
[4,7,5,2,1,8,6,3]=>0111011=>[2,1,1,2,1,1]
[8,5,3,6,2,1,7,4]=>1101101=>[1,1,2,1,2,1]
[4,5,7,3,1,2,8,6]=>0011001=>[3,1,3,1]
[4,5,1,8,3,2,7,6]=>0101101=>[2,2,1,2,1]
[3,6,1,2,4,8,7,5]=>0100011=>[2,4,1,1]
[2,5,3,8,4,1,7,6]=>0101101=>[2,2,1,2,1]
[8,6,2,3,1,7,5,4]=>1101011=>[1,1,2,2,1,1]
[6,3,1,2,4,8,7,5]=>1100011=>[1,1,4,1,1]
[2,6,4,5,8,1,3,7]=>0100100=>[2,3,3]
[4,2,6,1,3,7,8,5]=>1010001=>[1,2,4,1]
[8,5,4,2,7,6,3,1]=>1110111=>[1,1,1,2,1,1,1]
[2,8,4,6,7,1,3,5]=>0100100=>[2,3,3]
[5,8,2,1,4,6,7,3]=>0110001=>[2,1,4,1]
[3,7,8,4,2,6,5,1]=>0011011=>[3,1,2,1,1]
[7,1,3,8,4,5,6,2]=>1001001=>[1,3,3,1]
[7,8,1,4,3,5,6,2]=>0101001=>[2,2,3,1]
[3,6,7,1,8,2,5,4]=>0010101=>[3,2,2,1]
[3,1,5,7,2,8,6,4]=>1001011=>[1,3,2,1,1]
[4,1,8,3,2,7,6,5]=>1011011=>[1,2,1,2,1,1]
[3,8,2,4,7,1,6,5]=>0100101=>[2,3,2,1]
[3,2,4,8,7,1,6,5]=>1001101=>[1,3,1,2,1]
[3,2,5,7,1,8,6,4]=>1001011=>[1,3,2,1,1]
[4,2,8,3,1,7,6,5]=>1011011=>[1,2,1,2,1,1]
[4,8,2,1,3,7,6,5]=>0110011=>[2,1,3,1,1]
[4,2,8,1,3,7,6,5]=>1010011=>[1,2,3,1,1]
[2,4,6,5,1,3,8,7]=>0011001=>[3,1,3,1]
[2,3,4,6,8,7,1,5]=>0000110=>[5,1,2]
[2,1,4,6,8,7,3,5]=>1000110=>[1,4,1,2]
[4,5,7,1,6,8,3,2]=>0010011=>[3,3,1,1]
[6,7,2,8,3,1,4,5]=>0101100=>[2,2,1,3]
[7,8,5,2,4,1,3,6]=>0110100=>[2,1,2,3]
[7,6,2,3,1,8,4,5]=>1101010=>[1,1,2,2,2]
[4,1,3,7,8,5,2,6]=>1000110=>[1,4,1,2]
[4,3,1,8,5,2,7,6]=>1101101=>[1,1,2,1,2,1]
[3,1,8,5,4,2,7,6]=>1011101=>[1,2,1,1,2,1]
[5,1,3,2,4,7,8,6]=>1010001=>[1,2,4,1]
[2,4,8,5,6,1,7,3]=>0010101=>[3,2,2,1]
[2,8,7,4,5,1,6,3]=>0110101=>[2,1,2,2,1]
[1,3,8,5,2,6,7,4]=>0011001=>[3,1,3,1]
[8,6,2,4,1,5,7,3]=>1101001=>[1,1,2,3,1]
[1,6,4,3,2,7,8,5]=>0111001=>[2,1,1,3,1]
[8,5,3,2,1,6,7,4]=>1111001=>[1,1,1,1,3,1]
[1,7,5,2,3,6,8,4]=>0110001=>[2,1,4,1]
[8,1,2,5,3,6,7,4]=>1001001=>[1,3,3,1]
[8,2,6,4,3,5,1,7]=>1011010=>[1,2,1,2,2]
[8,3,1,4,6,5,2,7]=>1100110=>[1,1,3,1,2]
[5,8,3,1,2,6,4,7]=>0110010=>[2,1,3,2]
[4,8,1,7,5,2,3,6]=>0101100=>[2,2,1,3]
[4,8,1,7,5,2,6,3]=>0101101=>[2,2,1,2,1]
[8,5,1,4,2,6,3,7]=>1101010=>[1,1,2,2,2]
[8,4,1,3,5,6,2,7]=>1100010=>[1,1,4,2]
[8,5,3,2,1,6,4,7]=>1111010=>[1,1,1,1,2,2]
[8,1,5,4,2,6,3,7]=>1011010=>[1,2,1,2,2]
[8,5,2,4,1,6,3,7]=>1101010=>[1,1,2,2,2]
[4,8,7,1,5,2,6,3]=>0110101=>[2,1,2,2,1]
[4,8,7,1,5,2,3,6]=>0110100=>[2,1,2,3]
[7,6,8,4,1,3,2,5]=>1011010=>[1,2,1,2,2]
[7,6,8,4,1,3,5,2]=>1011001=>[1,2,1,3,1]
[8,4,2,7,5,1,6,3]=>1101101=>[1,1,2,1,2,1]
[3,8,7,5,4,1,2,6]=>0111100=>[2,1,1,1,3]
[7,6,8,4,1,5,2,3]=>1011010=>[1,2,1,2,2]
[8,7,6,1,5,2,3,4]=>1110100=>[1,1,1,2,3]
[7,1,4,8,6,3,5,2]=>1001101=>[1,3,1,2,1]
[8,1,6,5,3,4,7,2]=>1011001=>[1,2,1,3,1]
[8,6,2,5,3,4,7,1]=>1101001=>[1,1,2,3,1]
[8,6,5,1,3,4,7,2]=>1110001=>[1,1,1,4,1]
[8,7,5,1,3,6,2,4]=>1110010=>[1,1,1,3,2]
[8,7,1,5,3,6,2,4]=>1101010=>[1,1,2,2,2]
[8,6,1,3,5,4,7,2]=>1100101=>[1,1,3,2,1]
[8,1,6,3,5,4,7,2]=>1010101=>[1,2,2,2,1]
[7,1,4,8,3,6,5,2]=>1001011=>[1,3,2,1,1]
[8,3,2,7,4,6,5,1]=>1101011=>[1,1,2,2,1,1]
[7,8,5,2,4,3,6,1]=>0110101=>[2,1,2,2,1]
[7,3,8,2,5,4,6,1]=>1010101=>[1,2,2,2,1]
[8,4,2,5,3,7,6,1]=>1101011=>[1,1,2,2,1,1]
[4,8,1,5,3,7,6,2]=>0101011=>[2,2,2,1,1]
[7,4,8,2,6,3,5,1]=>1010101=>[1,2,2,2,1]
[7,4,8,2,6,3,1,5]=>1010110=>[1,2,2,1,2]
[8,7,3,1,6,4,2,5]=>1110110=>[1,1,1,2,1,2]
[8,7,3,1,6,4,5,2]=>1110101=>[1,1,1,2,2,1]
[8,7,3,1,4,6,5,2]=>1110011=>[1,1,1,3,1,1]
[8,4,3,2,7,5,6,1]=>1110101=>[1,1,1,2,2,1]
[6,4,1,7,8,5,3,2]=>1100111=>[1,1,3,1,1,1]
[7,6,3,4,1,8,5,2]=>1101011=>[1,1,2,2,1,1]
[8,7,3,1,6,2,5,4]=>1110101=>[1,1,1,2,2,1]
[7,8,6,4,2,5,1,3]=>0111010=>[2,1,1,2,2]
[7,8,2,4,6,5,1,3]=>0100110=>[2,3,1,2]
[8,1,7,3,5,6,2,4]=>1010010=>[1,2,3,2]
[8,7,1,6,5,2,3,4]=>1101100=>[1,1,2,1,3]
[8,7,5,2,4,6,1,3]=>1110010=>[1,1,1,3,2]
[8,1,7,5,4,6,2,3]=>1011010=>[1,2,1,2,2]
[8,7,3,2,6,1,5,4]=>1110101=>[1,1,1,2,2,1]
[8,1,7,6,5,2,3,4]=>1011100=>[1,2,1,1,3]
[8,7,2,6,5,1,3,4]=>1101100=>[1,1,2,1,3]
[1,4,8,6,7,5,3,2]=>0010111=>[3,2,1,1,1]
[8,6,2,5,7,4,3,1]=>1100111=>[1,1,3,1,1,1]
[7,1,3,6,8,5,4,2]=>1000111=>[1,4,1,1,1]
[8,1,7,6,4,5,3,2]=>1011011=>[1,2,1,2,1,1]
[7,1,8,6,4,5,3,2]=>1011011=>[1,2,1,2,1,1]
[6,5,7,2,8,3,4,1]=>1010101=>[1,2,2,2,1]
[6,7,2,5,8,1,4,3]=>0100101=>[2,3,2,1]
[6,3,7,5,8,2,4,1]=>1010101=>[1,2,2,2,1]
[6,5,7,3,8,1,4,2]=>1010101=>[1,2,2,2,1]
[6,3,7,4,8,2,5,1]=>1010101=>[1,2,2,2,1]
[6,3,7,4,8,1,5,2]=>1010101=>[1,2,2,2,1]
[8,7,6,4,2,5,3,1]=>1111011=>[1,1,1,1,2,1,1]
[8,7,4,6,2,3,5,1]=>1101001=>[1,1,2,3,1]
[6,8,4,5,7,3,2,1]=>0100111=>[2,3,1,1,1]
[6,7,5,1,4,3,8,2]=>0110101=>[2,1,2,2,1]
[2,7,6,8,3,5,1,4]=>0101010=>[2,2,2,2]
[7,2,1,5,3,8,6,4]=>1101011=>[1,1,2,2,1,1]
[5,8,2,7,6,1,3,4]=>0101100=>[2,2,1,3]
[4,2,3,1,5,8,6,7]=>1010010=>[1,2,3,2]
[1,5,7,3,6,8,2,4]=>0010010=>[3,3,2]
[8,4,6,2,5,7,1,3]=>1010010=>[1,2,3,2]
[1,3,4,7,6,8,2,5]=>0001010=>[4,2,2]
[8,1,3,6,7,4,2,5]=>1000110=>[1,4,1,2]
[1,2,4,7,8,5,3,6]=>0000110=>[5,1,2]
[2,1,4,7,8,5,3,6]=>1000110=>[1,4,1,2]
[3,1,4,7,6,8,2,5]=>1001010=>[1,3,2,2]
[4,1,3,7,6,8,2,5]=>1001010=>[1,3,2,2]
[5,1,7,3,6,8,2,4]=>1010010=>[1,2,3,2]
[6,7,8,2,4,5,1,3]=>0010010=>[3,3,2]
[5,8,6,2,4,7,1,3]=>0110010=>[2,1,3,2]
[3,8,2,6,5,7,1,4]=>0101010=>[2,2,2,2]
[2,8,3,6,7,4,1,5]=>0100110=>[2,3,1,2]
[1,8,3,6,7,4,2,5]=>0100110=>[2,3,1,2]
[8,7,2,5,6,3,1,4]=>1100110=>[1,1,3,1,2]
[8,7,1,6,4,3,2,5]=>1101110=>[1,1,2,1,1,2]
[1,8,2,7,5,4,3,6]=>0101110=>[2,2,1,1,2]
[3,8,1,7,5,4,2,6]=>0101110=>[2,2,1,1,2]
[4,8,1,6,7,3,2,5]=>0100110=>[2,3,1,2]
[5,8,6,1,7,3,2,4]=>0110110=>[2,1,2,1,2]
[6,7,1,2,8,4,3,5]=>0100110=>[2,3,1,2]
[2,1,3,8,6,5,4,7]=>1001110=>[1,3,1,1,2]
[8,2,1,7,5,4,3,6]=>1101110=>[1,1,2,1,1,2]
[1,3,2,8,6,5,4,7]=>0101110=>[2,2,1,1,2]
[3,4,1,7,6,8,2,5]=>0101010=>[2,2,2,2]
[2,5,7,1,8,4,3,6]=>0010110=>[3,2,1,2]
[3,5,7,1,6,8,2,4]=>0010010=>[3,3,2]
[4,5,7,6,1,8,2,3]=>0011010=>[3,1,2,2]
[5,4,7,6,8,3,1,2]=>1010110=>[1,2,2,1,2]
[1,5,7,8,6,3,2,4]=>0001110=>[4,1,1,2]
[8,4,6,7,5,2,1,3]=>1001110=>[1,3,1,1,2]
[8,3,7,5,6,2,1,4]=>1010110=>[1,2,2,1,2]
[1,4,8,6,7,3,2,5]=>0010110=>[3,2,1,2]
[2,4,8,6,7,3,1,5]=>0010110=>[3,2,1,2]
[2,3,8,7,5,4,1,6]=>0011110=>[3,1,1,1,2]
[1,3,8,7,5,4,2,6]=>0011110=>[3,1,1,1,2]
[8,2,7,6,4,3,1,5]=>1011110=>[1,2,1,1,1,2]
[8,1,7,6,4,3,2,5]=>1011110=>[1,2,1,1,1,2]
[4,1,8,6,7,3,2,5]=>1010110=>[1,2,2,1,2]
[4,8,7,5,6,2,1,3]=>0110110=>[2,1,2,1,2]
[8,1,7,2,5,6,4,3]=>1010011=>[1,2,3,1,1]
[8,1,3,5,2,7,6,4]=>1001011=>[1,3,2,1,1]
[8,1,7,4,3,6,5,2]=>1011011=>[1,2,1,2,1,1]
[2,7,1,5,4,8,6,3]=>0101011=>[2,2,2,1,1]
[8,6,2,4,3,7,5,1]=>1101011=>[1,1,2,2,1,1]
[8,1,4,5,6,3,7,2]=>1000101=>[1,4,2,1]
[8,1,4,5,6,2,7,3]=>1000101=>[1,4,2,1]
[8,1,4,7,6,2,5,3]=>1001101=>[1,3,1,2,1]
[2,5,1,7,8,6,4,3]=>0100111=>[2,3,1,1,1]
[3,5,6,2,8,7,4,1]=>0010111=>[3,2,1,1,1]
[3,5,6,1,8,7,4,2]=>0010111=>[3,2,1,1,1]
[2,4,5,1,7,6,3,8]=>0010110=>[3,2,1,2]
[7,3,1,5,6,4,2,8]=>1100110=>[1,1,3,1,2]
[8,6,2,4,7,3,1,5]=>1100110=>[1,1,3,1,2]
[8,4,7,3,5,2,1,6]=>1010110=>[1,2,2,1,2]
[8,4,5,3,7,6,2,1]=>1010111=>[1,2,2,1,1,1]
[3,4,5,6,2,8,1,7]=>0001010=>[4,2,2]
[3,7,4,2,8,5,1,6]=>0110110=>[2,1,2,1,2]
[7,3,4,1,6,8,2,5]=>1010010=>[1,2,3,2]
[2,6,3,1,4,7,5,8]=>0110010=>[2,1,3,2]
[7,2,1,6,3,4,8,5]=>1101001=>[1,1,2,3,1]
[7,3,4,1,6,5,8,2]=>1010101=>[1,2,2,2,1]
[3,7,4,2,5,8,6,1]=>0110011=>[2,1,3,1,1]
[2,3,5,1,4,8,7,6]=>0010011=>[3,3,1,1]
[2,7,1,3,6,8,5,4]=>0100011=>[2,4,1,1]
[2,7,1,3,8,4,6,5]=>0100101=>[2,3,2,1]
[3,8,7,1,6,2,5,4]=>0110101=>[2,1,2,2,1]
[3,8,7,1,4,5,2,6]=>0110010=>[2,1,3,2]
[3,7,4,2,1,8,6,5]=>0111011=>[2,1,1,2,1,1]
[4,8,5,7,2,6,3,1]=>0101011=>[2,2,2,1,1]
[8,4,5,7,3,2,6,1]=>1001101=>[1,3,1,2,1]
[8,3,7,2,4,1,5,6]=>1010100=>[1,2,2,3]
[8,6,7,2,1,4,3,5]=>1011010=>[1,2,1,2,2]
[8,3,7,5,1,2,6,4]=>1011001=>[1,2,1,3,1]
[7,3,4,6,2,1,5,8]=>1001100=>[1,3,1,3]
[3,7,4,6,1,5,2,8]=>0101010=>[2,2,2,2]
[3,4,7,6,1,2,8,5]=>0011001=>[3,1,3,1]
[4,5,8,7,6,1,3,2]=>0011101=>[3,1,1,2,1]
[8,6,3,7,5,1,4,2]=>1101101=>[1,1,2,1,2,1]
[8,7,3,5,6,1,4,2]=>1100101=>[1,1,3,2,1]
[7,6,3,8,1,4,5,2]=>1101001=>[1,1,2,3,1]
[8,5,2,7,6,1,3,4]=>1101100=>[1,1,2,1,3]
[7,6,4,8,1,2,5,3]=>1101001=>[1,1,2,3,1]
[8,7,3,1,4,5,2,6]=>1110010=>[1,1,1,3,2]
[8,4,2,5,1,6,7,3]=>1101001=>[1,1,2,3,1]
[8,5,3,1,6,4,7,2]=>1110101=>[1,1,1,2,2,1]
[8,7,3,1,4,5,6,2]=>1110001=>[1,1,1,4,1]
[8,7,4,1,5,6,2,3]=>1110010=>[1,1,1,3,2]
[8,6,4,1,7,5,2,3]=>1110110=>[1,1,1,2,1,2]
[8,6,3,1,7,4,5,2]=>1110101=>[1,1,1,2,2,1]
[8,5,3,1,6,7,4,2]=>1110011=>[1,1,1,3,1,1]
[8,5,3,7,1,6,4,2]=>1101011=>[1,1,2,2,1,1]
[7,6,3,8,1,4,2,5]=>1101010=>[1,1,2,2,2]
[7,4,8,2,6,1,5,3]=>1010101=>[1,2,2,2,1]
[8,5,3,1,6,4,2,7]=>1110110=>[1,1,1,2,1,2]
[8,7,4,1,5,2,3,6]=>1110100=>[1,1,1,2,3]
[8,7,5,1,2,6,3,4]=>1110010=>[1,1,1,3,2]
[8,6,4,1,2,7,5,3]=>1110011=>[1,1,1,3,1,1]
[8,7,3,1,4,2,5,6]=>1110100=>[1,1,1,2,3]
[8,7,4,1,2,5,3,6]=>1110010=>[1,1,1,3,2]
[8,7,5,1,2,3,6,4]=>1110001=>[1,1,1,4,1]
[1,6,7,3,2,8,4,5]=>0011010=>[3,1,2,2]
[1,8,6,3,2,7,4,5]=>0111010=>[2,1,1,2,2]
[1,5,3,7,2,8,4,6]=>0101010=>[2,2,2,2]
[1,4,6,2,8,5,3,7]=>0010110=>[3,2,1,2]
[1,5,6,2,8,4,3,7]=>0010110=>[3,2,1,2]
[3,5,2,6,4,7,8,1]=>0101001=>[2,2,3,1]
[1,2,5,3,8,6,7,4]=>0010101=>[3,2,2,1]
[2,4,6,3,1,7,5,8]=>0011010=>[3,1,2,2]
[3,4,8,6,5,7,2,1]=>0011011=>[3,1,2,1,1]
[2,3,8,6,7,1,5,4]=>0010101=>[3,2,2,1]
[1,2,5,7,4,6,8,3]=>0001001=>[4,3,1]
[2,3,6,8,1,7,4,5]=>0001010=>[4,2,2]
[2,4,8,5,6,7,1,3]=>0010010=>[3,3,2]
[1,4,8,5,6,7,3,2]=>0010011=>[3,3,1,1]
[6,1,3,5,4,2,8,7]=>1001101=>[1,3,1,2,1]
[3,6,4,2,5,1,8,7]=>0110101=>[2,1,2,2,1]
[2,1,5,8,6,4,7,3]=>1001101=>[1,3,1,2,1]
[1,8,3,5,6,2,7,4]=>0100101=>[2,3,2,1]
[8,3,2,5,6,1,7,4]=>1100101=>[1,1,3,2,1]
[4,2,5,1,6,8,7,3]=>1010011=>[1,2,3,1,1]
[5,4,2,7,8,6,1,3]=>1100110=>[1,1,3,1,2]
[6,7,1,8,3,2,4,5]=>0101100=>[2,2,1,3]
[6,7,2,8,1,3,4,5]=>0101000=>[2,2,4]
[1,7,8,5,2,6,3,4]=>0011010=>[3,1,2,2]
[5,8,7,2,6,3,4,1]=>0110101=>[2,1,2,2,1]
[7,6,2,4,8,1,5,3]=>1100101=>[1,1,3,2,1]
[4,8,3,1,7,6,5,2]=>0110111=>[2,1,2,1,1,1]
[5,3,8,7,1,6,4,2]=>1011011=>[1,2,1,2,1,1]
[5,8,7,3,1,6,4,2]=>0111011=>[2,1,1,2,1,1]
[5,3,8,2,1,7,6,4]=>1011011=>[1,2,1,2,1,1]
[3,8,7,2,6,5,1,4]=>0110110=>[2,1,2,1,2]
[7,4,1,8,6,5,3,2]=>1101111=>[1,1,2,1,1,1,1]
[5,4,2,8,1,7,6,3]=>1101011=>[1,1,2,2,1,1]
[5,8,4,7,1,6,3,2]=>0101011=>[2,2,2,1,1]
[8,5,6,1,4,7,2,3]=>1010010=>[1,2,3,2]
[6,7,4,1,2,5,8,3]=>0110001=>[2,1,4,1]
[3,6,7,5,8,1,2,4]=>0010100=>[3,2,3]
[6,5,8,7,4,2,3,1]=>1011101=>[1,2,1,1,2,1]
[5,7,6,2,8,3,1,4]=>0110110=>[2,1,2,1,2]
[2,5,6,3,1,4,8,7]=>0011001=>[3,1,3,1]
[3,8,7,2,1,5,4,6]=>0111010=>[2,1,1,2,2]
[4,8,5,6,7,3,1,2]=>0100110=>[2,3,1,2]
[3,7,6,2,8,5,1,4]=>0110110=>[2,1,2,1,2]
[6,1,7,3,8,5,2,4]=>1010110=>[1,2,2,1,2]
[4,8,5,6,7,2,1,3]=>0100110=>[2,3,1,2]
[5,8,6,2,7,4,1,3]=>0110110=>[2,1,2,1,2]
[4,6,5,8,7,3,1,2]=>0101110=>[2,2,1,1,2]
[8,3,1,7,2,6,4,5]=>1101010=>[1,1,2,2,2]
[8,4,5,1,7,6,2,3]=>1010110=>[1,2,2,1,2]
[8,5,6,1,7,2,4,3]=>1010101=>[1,2,2,2,1]
[7,5,6,1,3,8,4,2]=>1010011=>[1,2,3,1,1]
[5,7,6,1,3,8,4,2]=>0110011=>[2,1,3,1,1]
[6,7,1,4,2,8,5,3]=>0101011=>[2,2,2,1,1]
[2,1,6,4,8,3,7,5]=>1010101=>[1,2,2,2,1]
[5,8,7,4,6,2,3,1]=>0110101=>[2,1,2,2,1]
[6,8,7,1,5,3,4,2]=>0110101=>[2,1,2,2,1]
[2,7,8,4,6,5,1,3]=>0010110=>[3,2,1,2]
[3,7,8,5,4,6,2,1]=>0011011=>[3,1,2,1,1]
[2,8,7,5,3,6,4,1]=>0111011=>[2,1,1,2,1,1]
[1,8,7,3,6,4,5,2]=>0110101=>[2,1,2,2,1]
[2,8,7,4,6,1,5,3]=>0110101=>[2,1,2,2,1]
[4,8,7,2,5,6,3,1]=>0110011=>[2,1,3,1,1]
[4,7,8,5,3,6,2,1]=>0011011=>[3,1,2,1,1]
[6,4,8,1,5,7,3,2]=>1010011=>[1,2,3,1,1]
[4,5,8,6,3,7,2,1]=>0011011=>[3,1,2,1,1]
[2,6,7,8,4,5,1,3]=>0001010=>[4,2,2]
[6,1,2,8,4,7,5,3]=>1001011=>[1,3,2,1,1]
[4,7,1,8,5,6,3,2]=>0101011=>[2,2,2,1,1]
[5,7,1,8,2,6,4,3]=>0101011=>[2,2,2,1,1]
[7,2,1,8,6,4,5,3]=>1101101=>[1,1,2,1,2,1]
[5,3,8,4,7,6,2,1]=>1010111=>[1,2,2,1,1,1]
[2,5,8,1,7,4,6,3]=>0010101=>[3,2,2,1]
[4,5,8,3,7,6,2,1]=>0010111=>[3,2,1,1,1]
[1,7,2,8,6,4,5,3]=>0101101=>[2,2,1,2,1]
[2,4,7,8,5,6,1,3]=>0001010=>[4,2,2]
[2,4,8,5,7,6,1,3]=>0010110=>[3,2,1,2]
[2,6,3,8,5,1,7,4]=>0101101=>[2,2,1,2,1]
[4,1,5,8,6,7,3,2]=>1001011=>[1,3,2,1,1]
[3,4,6,8,2,1,7,5]=>0001101=>[4,1,2,1]
[5,3,4,7,6,1,2,8]=>1001100=>[1,3,1,3]
[1,2,7,8,4,3,6,5]=>0001101=>[4,1,2,1]
[2,8,5,4,1,3,7,6]=>0111001=>[2,1,1,3,1]
[4,2,8,7,1,3,5,6]=>1011000=>[1,2,1,4]
[5,4,6,3,1,7,2,8]=>1011010=>[1,2,1,2,2]
[4,3,6,5,1,8,2,7]=>1011010=>[1,2,1,2,2]
[1,5,6,8,7,3,2,4]=>0001110=>[4,1,1,2]
[1,4,8,3,6,5,2,7]=>0010110=>[3,2,1,2]
[1,2,8,6,4,3,7,5]=>0011101=>[3,1,1,2,1]
[6,5,1,8,7,3,2,4]=>1101110=>[1,1,2,1,1,2]
[8,3,2,6,1,7,4,5]=>1101010=>[1,1,2,2,2]
[6,5,1,8,7,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[7,5,1,8,6,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[8,5,1,7,6,4,3,2]=>1101111=>[1,1,2,1,1,1,1]
[8,5,3,7,6,1,4,2]=>1101101=>[1,1,2,1,2,1]
[3,8,7,6,1,5,4,2]=>0111011=>[2,1,1,2,1,1]
[8,5,2,6,1,4,7,3]=>1101001=>[1,1,2,3,1]
[2,7,5,8,1,4,6,3]=>0101001=>[2,2,3,1]
[8,5,6,1,7,3,2,4]=>1010110=>[1,2,2,1,2]
[3,2,6,7,1,8,5,4]=>1001011=>[1,3,2,1,1]
[3,4,6,7,8,2,1,5]=>0000110=>[5,1,2]
[6,7,1,3,8,5,4,2]=>0100111=>[2,3,1,1,1]
[6,7,1,8,5,2,4,3]=>0101101=>[2,2,1,2,1]
[1,6,2,7,8,5,3,4]=>0100110=>[2,3,1,2]
[1,2,6,7,8,5,3,4]=>0000110=>[5,1,2]
[1,6,7,4,8,3,2,5]=>0010110=>[3,2,1,2]
[1,4,6,7,8,3,2,5]=>0000110=>[5,1,2]
[8,6,1,2,7,3,4,5]=>1100100=>[1,1,3,3]
[3,6,8,2,7,1,5,4]=>0010101=>[3,2,2,1]
[2,8,6,1,4,5,7,3]=>0110001=>[2,1,4,1]
[6,8,7,2,5,4,1,3]=>0110110=>[2,1,2,1,2]
[3,7,2,1,8,4,6,5]=>0110101=>[2,1,2,2,1]
[3,7,2,4,1,8,6,5]=>0101011=>[2,2,2,1,1]
[3,2,6,4,8,7,5,1]=>1010111=>[1,2,2,1,1,1]
[4,7,2,8,6,5,1,3]=>0101110=>[2,2,1,1,2]
[4,7,1,8,6,5,3,2]=>0101111=>[2,2,1,1,1,1]
[2,7,4,8,3,6,1,5]=>0101010=>[2,2,2,2]
[4,7,3,8,6,1,5,2]=>0101101=>[2,2,1,2,1]
[4,7,3,8,6,2,1,5]=>0101110=>[2,2,1,1,2]
[4,3,6,8,7,2,5,1]=>1001101=>[1,3,1,2,1]
[4,3,8,2,5,7,6,1]=>1010011=>[1,2,3,1,1]
[4,3,8,1,5,7,6,2]=>1010011=>[1,2,3,1,1]
[4,1,2,6,8,7,5,3]=>1000111=>[1,4,1,1,1]
[2,4,3,6,8,7,1,5]=>0100110=>[2,3,1,2]
[3,1,6,4,8,7,2,5]=>1010110=>[1,2,2,1,2]
[4,1,6,8,7,5,2,3]=>1001110=>[1,3,1,1,2]
[3,8,1,4,5,7,2,6]=>0100010=>[2,4,2]
[3,8,1,4,2,5,7,6]=>0101001=>[2,2,3,1]
[4,1,8,3,5,2,7,6]=>1010101=>[1,2,2,2,1]
[4,2,3,6,8,7,1,5]=>1000110=>[1,4,1,2]
[4,2,8,3,5,7,6,1]=>1010011=>[1,2,3,1,1]
[3,8,2,4,5,7,6,1]=>0100011=>[2,4,1,1]
[3,8,2,4,1,5,7,6]=>0101001=>[2,2,3,1]
[3,8,2,5,1,4,7,6]=>0101001=>[2,2,3,1]
[4,2,8,5,7,1,3,6]=>1010100=>[1,2,2,3]
[3,8,1,5,2,4,7,6]=>0101001=>[2,2,3,1]
[7,5,6,4,1,3,2,8]=>1011010=>[1,2,1,2,2]
[7,8,6,4,1,3,2,5]=>0111010=>[2,1,1,2,2]
[7,1,4,2,5,6,3,8]=>1010010=>[1,2,3,2]
[7,3,2,1,4,6,5,8]=>1110010=>[1,1,1,3,2]
[7,6,1,4,3,2,5,8]=>1101100=>[1,1,2,1,3]
[7,4,1,3,5,6,2,8]=>1100010=>[1,1,4,2]
[7,3,1,2,5,6,4,8]=>1100010=>[1,1,4,2]
[2,7,1,3,5,6,8,4]=>0100001=>[2,5,1]
[3,6,2,1,5,8,7,4]=>0110011=>[2,1,3,1,1]
[2,3,6,1,5,8,7,4]=>0010011=>[3,3,1,1]
[3,1,7,2,5,6,8,4]=>1010001=>[1,2,4,1]
[3,4,7,1,5,6,8,2]=>0010001=>[3,4,1]
[3,6,7,4,1,2,8,5]=>0011001=>[3,1,3,1]
[4,3,2,7,1,6,8,5]=>1101001=>[1,1,2,3,1]
[7,3,2,8,1,6,4,5]=>1101010=>[1,1,2,2,2]
[7,4,8,1,5,6,3,2]=>1010011=>[1,2,3,1,1]
[2,6,8,1,5,3,7,4]=>0010101=>[3,2,2,1]
[6,8,2,1,5,3,7,4]=>0110101=>[2,1,2,2,1]
[4,8,2,5,3,6,7,1]=>0101001=>[2,2,3,1]
[4,5,8,2,3,6,7,1]=>0010001=>[3,4,1]
[2,4,8,5,3,6,7,1]=>0011001=>[3,1,3,1]
[4,1,8,6,5,3,7,2]=>1011101=>[1,2,1,1,2,1]
[5,7,8,4,6,3,2,1]=>0010111=>[3,2,1,1,1]
[5,3,2,6,4,8,7,1]=>1101011=>[1,1,2,2,1,1]
[2,4,5,3,8,6,7,1]=>0010101=>[3,2,2,1]
[4,3,5,2,8,6,7,1]=>1010101=>[1,2,2,2,1]
[4,5,2,3,8,6,7,1]=>0100101=>[2,3,2,1]
[4,8,5,3,2,6,7,1]=>0111001=>[2,1,1,3,1]
[3,8,4,5,2,6,7,1]=>0101001=>[2,2,3,1]
[3,5,4,2,8,6,7,1]=>0110101=>[2,1,2,2,1]
[4,1,2,7,5,6,8,3]=>1001001=>[1,3,3,1]
[4,8,1,6,5,2,7,3]=>0101101=>[2,2,1,2,1]
[5,6,7,4,2,8,3,1]=>0011011=>[3,1,2,1,1]
[2,5,7,4,6,8,3,1]=>0010011=>[3,3,1,1]
[7,3,5,4,2,8,6,1]=>1011011=>[1,2,1,2,1,1]
[7,5,2,4,3,8,6,1]=>1101011=>[1,1,2,2,1,1]
[6,8,1,2,5,4,7,3]=>0100101=>[2,3,2,1]
[6,4,1,8,5,2,7,3]=>1101101=>[1,1,2,1,2,1]
[2,6,1,8,5,4,7,3]=>0101101=>[2,2,1,2,1]
[7,1,2,8,5,6,4,3]=>1001011=>[1,3,2,1,1]
[4,3,2,6,8,5,7,1]=>1100101=>[1,1,3,2,1]
[3,7,6,4,8,5,2,1]=>0110111=>[2,1,2,1,1,1]
[3,1,6,8,5,4,7,2]=>1001101=>[1,3,1,2,1]
[2,3,5,8,4,6,7,1]=>0001001=>[4,3,1]
[3,4,5,8,2,6,7,1]=>0001001=>[4,3,1]
[5,4,2,8,3,6,7,1]=>1101001=>[1,1,2,3,1]
[5,3,4,8,2,6,7,1]=>1001001=>[1,3,3,1]
[2,5,4,8,3,6,7,1]=>0101001=>[2,2,3,1]
[6,3,2,5,8,4,7,1]=>1100101=>[1,1,3,2,1]
[6,1,8,3,5,4,7,2]=>1010101=>[1,2,2,2,1]
[5,4,8,3,2,6,7,1]=>1011001=>[1,2,1,3,1]
[5,8,2,3,4,6,7,1]=>0100001=>[2,5,1]
[3,4,5,2,7,1,6,8]=>0010100=>[3,2,3]
[7,5,6,1,2,3,8,4]=>1010001=>[1,2,4,1]
[1,5,7,6,3,2,8,4]=>0011101=>[3,1,1,2,1]
[8,4,6,7,3,2,5,1]=>1001101=>[1,3,1,2,1]
[8,4,6,2,3,1,5,7]=>1010100=>[1,2,2,3]
[7,5,2,1,4,3,8,6]=>1110101=>[1,1,1,2,2,1]
[3,1,7,8,5,4,2,6]=>1001110=>[1,3,1,1,2]
[3,4,5,2,1,8,6,7]=>0011010=>[3,1,2,2]
[7,6,4,8,3,1,2,5]=>1101100=>[1,1,2,1,3]
[6,2,8,5,1,3,4,7]=>1011000=>[1,2,1,4]
[3,2,7,8,6,1,4,5]=>1001100=>[1,3,1,3]
[6,8,2,5,1,3,7,4]=>0101001=>[2,2,3,1]
[6,7,4,2,1,5,3,8]=>0111010=>[2,1,1,2,2]
[5,6,8,1,3,7,2,4]=>0010010=>[3,3,2]
[1,6,8,5,3,2,4,7]=>0011100=>[3,1,1,3]
[7,2,8,4,6,1,3,5]=>1010100=>[1,2,2,3]
[4,1,6,8,7,3,2,5]=>1001110=>[1,3,1,1,2]
[5,1,4,6,7,3,8,2]=>1000101=>[1,4,2,1]
[7,1,3,4,6,2,8,5]=>1000101=>[1,4,2,1]
[5,8,7,4,2,1,3,6]=>0111100=>[2,1,1,1,3]
[3,1,5,2,7,8,6,4]=>1010011=>[1,2,3,1,1]
[1,8,7,3,2,5,4,6]=>0111010=>[2,1,1,2,2]
[1,2,5,4,8,7,3,6]=>0010110=>[3,2,1,2]
[1,2,4,8,6,3,5,7]=>0001100=>[4,1,3]
[8,5,3,2,1,4,7,6]=>1111001=>[1,1,1,1,3,1]
[1,2,7,6,8,4,3,5]=>0010110=>[3,2,1,2]
[1,7,3,4,2,6,8,5]=>0101001=>[2,2,3,1]
[1,6,3,5,8,4,2,7]=>0100110=>[2,3,1,2]
[1,5,6,3,2,8,4,7]=>0011010=>[3,1,2,2]
[1,2,5,8,4,6,3,7]=>0001010=>[4,2,2]
[1,2,7,8,4,5,3,6]=>0001010=>[4,2,2]
[1,5,3,2,7,8,4,6]=>0110010=>[2,1,3,2]
[4,1,8,6,2,3,7,5]=>1011001=>[1,2,1,3,1]
[1,7,6,4,3,8,5,2]=>0111011=>[2,1,1,2,1,1]
[1,8,5,7,6,3,2,4]=>0101110=>[2,2,1,1,2]
[1,6,3,5,7,8,4,2]=>0100011=>[2,4,1,1]
[1,5,6,3,2,7,8,4]=>0011001=>[3,1,3,1]
[1,8,4,7,5,3,2,6]=>0101110=>[2,2,1,1,2]
[7,6,2,5,3,4,1,8]=>1101010=>[1,1,2,2,2]
[7,6,2,4,5,3,1,8]=>1100110=>[1,1,3,1,2]
[7,6,2,4,3,5,1,8]=>1101010=>[1,1,2,2,2]
[7,6,2,3,5,4,1,8]=>1100110=>[1,1,3,1,2]
[8,4,2,7,1,6,3,5]=>1101010=>[1,1,2,2,2]
[8,7,6,1,5,3,2,4]=>1110110=>[1,1,1,2,1,2]
[8,7,6,1,3,5,4,2]=>1110011=>[1,1,1,3,1,1]
[8,7,6,1,5,4,2,3]=>1110110=>[1,1,1,2,1,2]
[4,5,3,8,2,1,6,7]=>0101100=>[2,2,1,3]
[8,3,5,4,2,1,6,7]=>1011100=>[1,2,1,1,3]
[7,8,4,3,1,5,2,6]=>0111010=>[2,1,1,2,2]
[7,5,8,2,1,4,3,6]=>1011010=>[1,2,1,2,2]
[8,6,3,7,1,5,2,4]=>1101010=>[1,1,2,2,2]
[8,7,6,1,2,5,3,4]=>1110010=>[1,1,1,3,2]
[8,7,6,1,2,5,4,3]=>1110011=>[1,1,1,3,1,1]
[8,7,6,1,4,2,5,3]=>1110101=>[1,1,1,2,2,1]
[2,4,7,3,5,6,1,8]=>0010010=>[3,3,2]
[5,7,6,4,2,3,1,8]=>0111010=>[2,1,1,2,2]
[3,1,4,8,5,6,2,7]=>1001010=>[1,3,2,2]
[5,8,2,4,6,1,3,7]=>0100100=>[2,3,3]
[2,4,1,8,5,6,3,7]=>0101010=>[2,2,2,2]
[6,1,4,8,5,2,7,3]=>1001101=>[1,3,1,2,1]
[4,1,2,8,5,3,7,6]=>1001101=>[1,3,1,2,1]
[2,4,6,8,5,1,7,3]=>0001101=>[4,1,2,1]
[3,1,6,8,5,2,7,4]=>1001101=>[1,3,1,2,1]
[2,3,8,1,5,6,4,7]=>0010010=>[3,3,2]
[5,1,8,2,4,6,7,3]=>1010001=>[1,2,4,1]
[4,1,8,2,3,6,7,5]=>1010001=>[1,2,4,1]
[5,8,2,7,3,4,1,6]=>0101010=>[2,2,2,2]
[3,8,7,5,2,6,1,4]=>0111010=>[2,1,1,2,2]
[5,3,8,1,6,7,4,2]=>1010011=>[1,2,3,1,1]
[5,8,2,1,3,7,6,4]=>0110011=>[2,1,3,1,1]
[4,8,2,1,3,5,6,7]=>0110000=>[2,1,5]
[5,1,8,3,6,7,4,2]=>1010011=>[1,2,3,1,1]
[8,4,1,6,5,2,3,7]=>1101100=>[1,1,2,1,3]
[6,8,7,3,2,4,1,5]=>0111010=>[2,1,1,2,2]
[1,3,7,5,6,8,4,2]=>0010011=>[3,3,1,1]
[3,2,4,7,5,8,1,6]=>1001010=>[1,3,2,2]
[1,2,7,4,6,3,8,5]=>0010101=>[3,2,2,1]
[2,8,7,6,4,5,1,3]=>0111010=>[2,1,1,2,2]
[3,5,2,4,7,6,8,1]=>0100101=>[2,3,2,1]
[3,5,2,4,6,7,8,1]=>0100001=>[2,5,1]
[5,3,2,6,4,7,8,1]=>1101001=>[1,1,2,3,1]
[5,3,2,6,7,4,8,1]=>1100101=>[1,1,3,2,1]
[5,3,2,7,6,4,8,1]=>1101101=>[1,1,2,1,2,1]
[7,3,5,2,8,4,6,1]=>1010101=>[1,2,2,2,1]
[3,2,5,7,4,6,8,1]=>1001001=>[1,3,3,1]
[2,3,5,7,4,6,8,1]=>0001001=>[4,3,1]
[3,2,7,5,4,8,6,1]=>1011011=>[1,2,1,2,1,1]
[3,7,5,2,4,8,6,1]=>0110011=>[2,1,3,1,1]
[7,5,3,2,8,6,4,1]=>1110111=>[1,1,1,2,1,1,1]
[2,3,7,5,4,8,6,1]=>0011011=>[3,1,2,1,1]
[2,4,8,7,5,1,3,6]=>0011100=>[3,1,1,3]
[3,5,7,6,1,8,4,2]=>0011011=>[3,1,2,1,1]
[3,5,7,6,2,8,4,1]=>0011011=>[3,1,2,1,1]
[2,4,6,3,8,7,5,1]=>0010111=>[3,2,1,1,1]
[1,5,3,2,8,7,6,4]=>0110111=>[2,1,2,1,1,1]
[6,3,1,8,7,4,2,5]=>1101110=>[1,1,2,1,1,2]
[5,3,6,2,8,7,4,1]=>1010111=>[1,2,2,1,1,1]
[5,8,3,1,7,6,4,2]=>0110111=>[2,1,2,1,1,1]
[6,3,5,2,1,8,7,4]=>1011011=>[1,2,1,2,1,1]
[3,8,1,4,7,6,5,2]=>0100111=>[2,3,1,1,1]
[6,2,3,8,7,5,4,1]=>1001111=>[1,3,1,1,1,1]
[4,1,3,5,8,7,6,2]=>1000111=>[1,4,1,1,1]
[4,2,5,3,7,6,1,8]=>1010110=>[1,2,2,1,2]
[6,2,4,3,7,5,1,8]=>1010110=>[1,2,2,1,2]
[1,3,6,4,7,5,2,8]=>0010110=>[3,2,1,2]
[8,2,5,3,6,4,1,7]=>1010110=>[1,2,2,1,2]
[7,2,5,3,6,4,1,8]=>1010110=>[1,2,2,1,2]
[6,2,5,3,7,4,1,8]=>1010110=>[1,2,2,1,2]
[4,2,6,3,7,5,1,8]=>1010110=>[1,2,2,1,2]
[5,2,7,3,6,4,1,8]=>1010110=>[1,2,2,1,2]
[7,3,6,2,5,4,1,8]=>1010110=>[1,2,2,1,2]
[6,3,8,2,5,4,1,7]=>1010110=>[1,2,2,1,2]
[7,3,1,4,6,5,2,8]=>1100110=>[1,1,3,1,2]
[8,3,7,2,5,4,1,6]=>1010110=>[1,2,2,1,2]
[5,2,8,3,6,4,1,7]=>1010110=>[1,2,2,1,2]
[4,2,8,3,6,5,1,7]=>1010110=>[1,2,2,1,2]
[3,2,8,4,6,5,1,7]=>1010110=>[1,2,2,1,2]
[1,4,7,3,6,5,2,8]=>0010110=>[3,2,1,2]
[8,2,5,4,1,6,3,7]=>1011010=>[1,2,1,2,2]
[1,3,6,5,2,7,4,8]=>0011010=>[3,1,2,2]
[8,2,6,4,1,5,3,7]=>1011010=>[1,2,1,2,2]
[1,4,8,3,7,5,2,6]=>0010110=>[3,2,1,2]
[6,2,1,4,8,5,3,7]=>1100110=>[1,1,3,1,2]
[5,2,1,4,8,6,3,7]=>1100110=>[1,1,3,1,2]
[3,2,1,5,8,6,4,7]=>1100110=>[1,1,3,1,2]
[4,2,8,3,7,5,1,6]=>1010110=>[1,2,2,1,2]
[5,2,8,3,7,4,1,6]=>1010110=>[1,2,2,1,2]
[8,3,7,2,6,4,1,5]=>1010110=>[1,2,2,1,2]
[7,3,1,4,8,5,2,6]=>1100110=>[1,1,3,1,2]
[1,3,7,4,8,5,2,6]=>0010110=>[3,2,1,2]
[8,2,6,3,7,4,1,5]=>1010110=>[1,2,2,1,2]
[7,2,6,3,8,4,1,5]=>1010110=>[1,2,2,1,2]
[5,2,7,3,8,4,1,6]=>1010110=>[1,2,2,1,2]
[3,2,7,4,8,5,1,6]=>1010110=>[1,2,2,1,2]
[5,2,6,3,8,4,1,7]=>1010110=>[1,2,2,1,2]
[6,2,5,3,8,4,1,7]=>1010110=>[1,2,2,1,2]
[7,2,5,3,8,4,1,6]=>1010110=>[1,2,2,1,2]
[8,2,5,3,7,4,1,6]=>1010110=>[1,2,2,1,2]
[1,3,6,4,8,5,2,7]=>0010110=>[3,2,1,2]
[1,3,5,4,8,6,2,7]=>0010110=>[3,2,1,2]
[8,2,4,3,7,5,1,6]=>1010110=>[1,2,2,1,2]
[7,2,4,3,8,5,1,6]=>1010110=>[1,2,2,1,2]
[6,2,4,3,8,5,1,7]=>1010110=>[1,2,2,1,2]
[5,2,4,3,8,6,1,7]=>1010110=>[1,2,2,1,2]
[4,2,5,3,8,6,1,7]=>1010110=>[1,2,2,1,2]
[4,2,5,3,1,7,6,8]=>1011010=>[1,2,1,2,2]
[6,2,4,3,1,7,5,8]=>1011010=>[1,2,1,2,2]
[7,2,4,3,1,6,5,8]=>1011010=>[1,2,1,2,2]
[8,5,1,3,6,4,2,7]=>1100110=>[1,1,3,1,2]
[8,4,1,3,6,5,2,7]=>1100110=>[1,1,3,1,2]
[1,5,2,4,7,6,3,8]=>0100110=>[2,3,1,2]
[7,2,5,3,1,6,4,8]=>1011010=>[1,2,1,2,2]
[6,2,5,3,1,7,4,8]=>1011010=>[1,2,1,2,2]
[4,2,6,3,1,7,5,8]=>1011010=>[1,2,1,2,2]
[3,2,6,4,1,7,5,8]=>1011010=>[1,2,1,2,2]
[5,2,7,3,1,6,4,8]=>1011010=>[1,2,1,2,2]
[6,2,7,3,1,5,4,8]=>1011010=>[1,2,1,2,2]
[7,2,6,3,1,5,4,8]=>1011010=>[1,2,1,2,2]
[1,5,2,4,8,6,3,7]=>0100110=>[2,3,1,2]
[8,4,1,3,7,5,2,6]=>1100110=>[1,1,3,1,2]
[6,2,1,5,3,7,4,8]=>1101010=>[1,1,2,2,2]
[3,2,1,6,4,7,5,8]=>1101010=>[1,1,2,2,2]
[3,2,8,5,1,6,4,7]=>1011010=>[1,2,1,2,2]
[4,2,8,5,1,6,3,7]=>1011010=>[1,2,1,2,2]
[6,2,8,4,1,5,3,7]=>1011010=>[1,2,1,2,2]
[1,4,8,5,2,6,3,7]=>0011010=>[3,1,2,2]
[8,3,7,4,1,5,2,6]=>1011010=>[1,2,1,2,2]
[7,1,3,2,5,6,4,8]=>1010010=>[1,2,3,2]
[1,5,2,8,7,4,3,6]=>0101110=>[2,2,1,1,2]
[5,7,2,8,1,4,3,6]=>0101010=>[2,2,2,2]
[7,1,5,3,2,6,8,4]=>1011001=>[1,2,1,3,1]
[1,7,3,4,5,2,8,6]=>0100101=>[2,3,2,1]
[8,6,7,3,5,2,1,4]=>1010110=>[1,2,2,1,2]
[3,2,1,7,8,5,4,6]=>1100110=>[1,1,3,1,2]
[7,3,4,2,1,5,8,6]=>1011001=>[1,2,1,3,1]
[1,7,6,3,2,4,8,5]=>0111001=>[2,1,1,3,1]
[1,8,5,3,2,4,7,6]=>0111001=>[2,1,1,3,1]
[1,2,8,4,6,3,5,7]=>0010100=>[3,2,3]
[2,6,1,5,4,7,3,8]=>0101010=>[2,2,2,2]
[1,2,8,5,4,6,3,7]=>0011010=>[3,1,2,2]
[1,3,8,5,4,2,6,7]=>0011100=>[3,1,1,3]
[1,3,6,8,4,5,7,2]=>0001001=>[4,3,1]
[1,2,8,4,6,3,7,5]=>0010101=>[3,2,2,1]
[4,6,3,5,7,8,1,2]=>0100010=>[2,4,2]
[2,7,6,5,1,4,8,3]=>0111001=>[2,1,1,3,1]
[2,7,4,8,1,3,6,5]=>0101001=>[2,2,3,1]
[2,3,6,8,4,1,7,5]=>0001101=>[4,1,2,1]
[1,2,6,8,4,7,5,3]=>0001011=>[4,2,1,1]
[1,7,2,8,6,3,5,4]=>0101101=>[2,2,1,2,1]
[2,3,8,5,4,7,1,6]=>0011010=>[3,1,2,2]
[2,7,4,1,6,3,5,8]=>0110100=>[2,1,2,3]
[1,2,8,4,7,3,5,6]=>0010100=>[3,2,3]
[2,6,1,4,8,3,7,5]=>0100101=>[2,3,2,1]
[3,7,6,5,2,1,4,8]=>0111100=>[2,1,1,1,3]
[2,5,6,1,4,8,7,3]=>0010011=>[3,3,1,1]
[7,1,5,2,6,4,3,8]=>1010110=>[1,2,2,1,2]
[1,8,5,6,2,7,4,3]=>0101011=>[2,2,2,1,1]
[4,2,7,6,1,8,5,3]=>1011011=>[1,2,1,2,1,1]
[7,3,2,1,6,4,8,5]=>1110101=>[1,1,1,2,2,1]
[6,7,2,4,3,5,8,1]=>0101001=>[2,2,3,1]
[4,5,3,7,2,1,6,8]=>0101100=>[2,2,1,3]
[4,3,8,2,1,5,7,6]=>1011001=>[1,2,1,3,1]
[4,3,2,8,1,6,7,5]=>1101001=>[1,1,2,3,1]
[4,5,8,3,2,7,1,6]=>0011010=>[3,1,2,2]
[5,4,7,8,2,3,6,1]=>1001001=>[1,3,3,1]
[4,3,8,2,1,6,7,5]=>1011001=>[1,2,1,3,1]
[4,6,7,2,5,3,8,1]=>0010101=>[3,2,2,1]
[6,4,7,8,3,1,5,2]=>1001101=>[1,3,1,2,1]
[8,4,7,3,1,5,6,2]=>1011001=>[1,2,1,3,1]
[5,6,7,1,8,3,4,2]=>0010101=>[3,2,2,1]
[7,1,8,6,2,5,4,3]=>1011011=>[1,2,1,2,1,1]
[8,5,1,7,6,4,2,3]=>1101110=>[1,1,2,1,1,2]
[1,5,8,2,6,4,7,3]=>0010101=>[3,2,2,1]
[1,5,7,4,6,8,3,2]=>0010011=>[3,3,1,1]
[8,1,2,6,4,5,7,3]=>1001001=>[1,3,3,1]
[3,1,8,6,5,2,7,4]=>1011101=>[1,2,1,1,2,1]
[2,3,7,6,5,8,1,4]=>0011010=>[3,1,2,2]
[2,3,7,6,5,1,8,4]=>0011101=>[3,1,1,2,1]
[7,3,5,2,1,6,8,4]=>1011001=>[1,2,1,3,1]
[3,7,2,6,8,1,5,4]=>0100101=>[2,3,2,1]
[2,7,6,8,5,1,4,3]=>0101101=>[2,2,1,2,1]
[1,5,4,7,8,6,2,3]=>0100110=>[2,3,1,2]
[7,3,1,6,8,2,5,4]=>1100101=>[1,1,3,2,1]
[7,1,6,8,5,2,4,3]=>1001101=>[1,3,1,2,1]
[2,7,6,4,8,1,5,3]=>0110101=>[2,1,2,2,1]
[3,6,2,1,4,7,8,5]=>0110001=>[2,1,4,1]
[6,3,8,7,5,4,2,1]=>1011111=>[1,2,1,1,1,1,1]
[6,8,2,7,5,4,3,1]=>0101111=>[2,2,1,1,1,1]
[5,8,1,7,6,4,3,2]=>0101111=>[2,2,1,1,1,1]
[4,2,6,3,8,5,7,1]=>1010101=>[1,2,2,2,1]
[8,2,6,5,7,3,4,1]=>1010101=>[1,2,2,2,1]
[5,1,8,3,7,4,6,2]=>1010101=>[1,2,2,2,1]
[8,3,7,1,5,4,6,2]=>1010101=>[1,2,2,2,1]
[8,4,7,1,5,3,6,2]=>1010101=>[1,2,2,2,1]
[8,2,7,4,5,1,6,3]=>1010101=>[1,2,2,2,1]
[5,8,7,1,4,2,3,6]=>0110100=>[2,1,2,3]
[1,7,5,2,4,8,6,3]=>0110011=>[2,1,3,1,1]
[2,6,3,7,1,4,5,8]=>0101000=>[2,2,4]
[7,2,8,5,3,1,6,4]=>1011101=>[1,2,1,1,2,1]
[7,2,4,1,3,8,5,6]=>1010010=>[1,2,3,2]
[4,7,6,1,5,8,3,2]=>0110011=>[2,1,3,1,1]
[4,7,3,8,6,2,5,1]=>0101101=>[2,2,1,2,1]
[5,4,7,3,8,2,1,6]=>1010110=>[1,2,2,1,2]
[4,3,5,7,2,6,1,8]=>1001010=>[1,3,2,2]
[1,7,2,8,5,4,3,6]=>0101110=>[2,2,1,1,2]
[5,4,8,3,6,2,1,7]=>1010110=>[1,2,2,1,2]
[6,8,3,5,7,2,4,1]=>0100101=>[2,3,2,1]
[3,8,6,2,7,5,1,4]=>0110110=>[2,1,2,1,2]
[4,7,3,2,5,1,6,8]=>0110100=>[2,1,2,3]
[4,2,5,3,8,7,1,6]=>1010110=>[1,2,2,1,2]
[7,2,5,3,8,4,6,1]=>1010101=>[1,2,2,2,1]
[6,7,3,2,5,4,1,8]=>0110110=>[2,1,2,1,2]
[8,7,3,2,5,4,6,1]=>1110101=>[1,1,1,2,2,1]
[4,5,6,2,7,3,1,8]=>0010110=>[3,2,1,2]
[7,3,4,8,2,1,6,5]=>1001101=>[1,3,1,2,1]
[3,8,1,7,5,2,4,6]=>0101100=>[2,2,1,3]
[4,5,8,2,7,3,1,6]=>0010110=>[3,2,1,2]
[6,5,8,2,7,3,1,4]=>1010110=>[1,2,2,1,2]
[6,4,8,2,7,3,1,5]=>1010110=>[1,2,2,1,2]
[4,3,8,2,7,5,1,6]=>1010110=>[1,2,2,1,2]
[4,5,7,8,3,2,1,6]=>0001110=>[4,1,1,2]
[8,1,5,4,6,2,7,3]=>1010101=>[1,2,2,2,1]
[5,3,7,2,1,8,6,4]=>1011011=>[1,2,1,2,1,1]
[5,4,8,3,2,7,1,6]=>1011010=>[1,2,1,2,2]
[5,4,3,7,8,2,6,1]=>1100101=>[1,1,3,2,1]
[5,4,3,8,2,6,7,1]=>1101001=>[1,1,2,3,1]
[5,4,3,7,8,2,1,6]=>1100110=>[1,1,3,1,2]
[2,3,8,7,5,1,6,4]=>0011101=>[3,1,1,2,1]
[4,1,3,5,6,2,8,7]=>1000101=>[1,4,2,1]
[6,4,8,7,3,5,2,1]=>1011011=>[1,2,1,2,1,1]
[8,3,4,5,1,6,7,2]=>1001001=>[1,3,3,1]
[7,8,1,5,6,3,2,4]=>0100110=>[2,3,1,2]
[1,7,8,3,2,5,4,6]=>0011010=>[3,1,2,2]
[7,8,1,3,5,4,2,6]=>0100110=>[2,3,1,2]
[7,8,1,3,2,5,6,4]=>0101001=>[2,2,3,1]
[7,8,1,3,5,4,6,2]=>0100101=>[2,3,2,1]
[7,8,1,3,5,2,4,6]=>0100100=>[2,3,3]
[1,3,7,8,5,2,4,6]=>0001100=>[4,1,3]
[1,7,8,3,5,2,6,4]=>0010101=>[3,2,2,1]
[1,7,8,3,2,5,6,4]=>0011001=>[3,1,3,1]
[3,5,7,6,4,8,1,2]=>0011010=>[3,1,2,2]
[1,3,7,8,5,4,6,2]=>0001101=>[4,1,2,1]
[1,3,7,8,5,4,2,6]=>0001110=>[4,1,1,2]
[1,3,7,8,2,5,4,6]=>0001010=>[4,2,2]
[1,7,8,5,6,3,2,4]=>0010110=>[3,2,1,2]
[5,7,6,8,1,3,4,2]=>0101001=>[2,2,3,1]
[1,5,7,6,8,3,2,4]=>0010110=>[3,2,1,2]
[3,5,4,7,8,6,1,2]=>0100110=>[2,3,1,2]
[3,5,7,6,8,4,1,2]=>0010110=>[3,2,1,2]
[1,5,7,6,8,3,4,2]=>0010101=>[3,2,2,1]
[3,5,7,4,6,8,1,2]=>0010010=>[3,3,2]
[7,2,8,6,5,1,4,3]=>1011101=>[1,2,1,1,2,1]
[3,2,5,4,7,6,1,10,8,9]=>101011010=>[1,2,2,1,2,2]
[3,2,5,4,9,8,6,7,1,10]=>101011010=>[1,2,2,1,2,2]
[3,2,5,4,1,8,6,10,7,9]=>101101010=>[1,2,1,2,2,2]
[3,2,5,4,1,10,9,6,7,8]=>101101100=>[1,2,1,2,1,3]
[3,2,7,6,4,5,9,8,1,10]=>101100110=>[1,2,1,3,1,2]
[3,2,7,6,4,5,1,10,8,9]=>101101010=>[1,2,1,2,2,2]
[3,2,9,6,4,8,5,7,1,10]=>101101010=>[1,2,1,2,2,2]
[3,2,1,6,4,8,5,10,7,9]=>110101010=>[1,1,2,2,2,2]
[3,2,1,6,4,10,9,5,7,8]=>110101100=>[1,1,2,2,1,3]
[3,2,9,8,7,4,5,6,1,10]=>101110010=>[1,2,1,1,3,2]
[3,2,1,8,7,4,5,10,6,9]=>110110010=>[1,1,2,1,3,2]
[3,2,1,10,7,4,9,5,6,8]=>110110100=>[1,1,2,1,2,3]
[3,2,1,10,9,8,4,5,6,7]=>110111000=>[1,1,2,1,1,4]
[5,4,2,3,7,6,9,8,1,10]=>110010110=>[1,1,3,2,1,2]
[5,4,2,3,7,6,1,10,8,9]=>110011010=>[1,1,3,1,2,2]
[5,4,2,3,9,8,6,7,1,10]=>110011010=>[1,1,3,1,2,2]
[5,4,2,3,1,8,6,10,7,9]=>110101010=>[1,1,2,2,2,2]
[5,4,2,3,1,10,9,6,7,8]=>110101100=>[1,1,2,2,1,3]
[7,4,2,6,3,5,9,8,1,10]=>110100110=>[1,1,2,3,1,2]
[7,4,2,6,3,5,1,10,8,9]=>110101010=>[1,1,2,2,2,2]
[9,4,2,6,3,8,5,7,1,10]=>110101010=>[1,1,2,2,2,2]
[1,4,2,6,3,10,9,5,7,8]=>010101100=>[2,2,2,1,3]
[9,4,2,8,7,3,5,6,1,10]=>110110010=>[1,1,2,1,3,2]
[1,4,2,8,7,3,5,10,6,9]=>010110010=>[2,2,1,3,2]
[1,4,2,10,7,3,9,5,6,8]=>010110100=>[2,2,1,2,3]
[1,4,2,10,9,8,3,5,6,7]=>010111000=>[2,2,1,1,4]
[7,6,5,2,3,4,9,8,1,10]=>111000110=>[1,1,1,4,1,2]
[7,6,5,2,3,4,1,10,8,9]=>111001010=>[1,1,1,3,2,2]
[9,6,5,2,3,8,4,7,1,10]=>111001010=>[1,1,1,3,2,2]
[1,6,5,2,3,8,4,10,7,9]=>011001010=>[2,1,3,2,2]
[1,6,5,2,3,10,9,4,7,8]=>011001100=>[2,1,3,1,3]
[9,8,5,2,7,3,4,6,1,10]=>111010010=>[1,1,1,2,3,2]
[1,8,5,2,7,3,4,10,6,9]=>011010010=>[2,1,2,3,2]
[1,10,5,2,7,3,9,4,6,8]=>011010100=>[2,1,2,2,3]
[1,10,5,2,9,8,3,4,6,7]=>011011000=>[2,1,2,1,4]
[9,8,7,6,2,3,4,5,1,10]=>111100010=>[1,1,1,1,4,2]
[1,8,7,6,2,3,4,10,5,9]=>011100010=>[2,1,1,4,2]
[1,10,7,6,2,3,9,4,5,8]=>011100100=>[2,1,1,3,3]
[1,10,9,6,2,8,3,4,5,7]=>011101000=>[2,1,1,2,4]
[1,10,9,8,7,2,3,4,5,6]=>011110000=>[2,1,1,1,5]
[4,2,7,5,3,1,8,6]=>1011101=>[1,2,1,1,2,1]
[7,3,2,5,4,1,8,6]=>1101101=>[1,1,2,1,2,1]
[3,6,4,1,8,2,7,5]=>0110101=>[2,1,2,2,1]
[4,6,3,8,7,2,1,5]=>0101110=>[2,2,1,1,2]
[4,3,5,1,8,7,2,6]=>1010110=>[1,2,2,1,2]
[8,4,3,2,7,5,1,6]=>1110110=>[1,1,1,2,1,2]
[7,5,2,8,4,3,1,6]=>1101110=>[1,1,2,1,1,2]
[1,7,2,4,5,3,6,8]=>0100100=>[2,3,3]
[1,7,4,5,3,2,6,8]=>0101100=>[2,2,1,3]
[1,6,4,7,3,5,2,8]=>0101010=>[2,2,2,2]
[8,3,5,6,1,4,7,2]=>1001001=>[1,3,3,1]
[1,6,4,7,5,2,3,8]=>0101100=>[2,2,1,3]
[1,5,2,6,7,4,3,8]=>0100110=>[2,3,1,2]
[8,5,6,1,4,3,7,2]=>1010101=>[1,2,2,2,1]
[5,4,7,8,3,1,2,6]=>1001100=>[1,3,1,3]
[2,5,4,7,8,3,1,6]=>0100110=>[2,3,1,2]
[6,4,5,8,2,3,1,7]=>1001010=>[1,3,2,2]
[8,6,1,3,2,5,7,4]=>1101001=>[1,1,2,3,1]
[7,5,8,1,4,6,3,2]=>1010011=>[1,2,3,1,1]
[4,2,6,7,8,1,5,3]=>1000101=>[1,4,2,1]
[3,4,6,7,8,1,5,2]=>0000101=>[5,2,1]
[4,3,2,7,5,8,1,6]=>1101010=>[1,1,2,2,2]
[4,8,5,3,2,6,1,7]=>0111010=>[2,1,1,2,2]
[2,8,4,5,3,6,1,7]=>0101010=>[2,2,2,2]
[8,1,5,3,2,4,7,6]=>1011001=>[1,2,1,3,1]
[8,1,2,4,5,3,7,6]=>1000101=>[1,4,2,1]
[8,1,4,5,3,2,7,6]=>1001101=>[1,3,1,2,1]
[7,8,4,1,3,6,5,2]=>0110011=>[2,1,3,1,1]
[8,6,1,3,2,7,4,5]=>1101010=>[1,1,2,2,2]
[7,3,8,2,4,1,6,5]=>1010101=>[1,2,2,2,1]
[6,2,3,7,8,1,5,4]=>1000101=>[1,4,2,1]
[6,3,7,8,1,5,4,2]=>1001011=>[1,3,2,1,1]
[2,6,3,7,8,1,5,4]=>0100101=>[2,3,2,1]
[7,5,8,1,6,4,2,3]=>1010110=>[1,2,2,1,2]
[7,4,3,2,5,8,1,6]=>1110010=>[1,1,1,3,2]
[7,2,4,3,5,8,1,6]=>1010010=>[1,2,3,2]
[1,3,6,4,2,5,7,8]=>0011000=>[3,1,4]
[1,7,6,4,2,3,5,8]=>0111000=>[2,1,1,4]
[1,2,3,7,6,4,5,8]=>0001100=>[4,1,3]
[1,3,2,5,8,6,4,7]=>0100110=>[2,3,1,2]
[4,8,2,7,1,3,6,5]=>0101001=>[2,2,3,1]
[1,7,4,6,8,3,5,2]=>0100101=>[2,3,2,1]
[4,1,5,2,3,8,7,6]=>1010011=>[1,2,3,1,1]
[6,3,5,8,2,4,7,1]=>1001001=>[1,3,3,1]
[2,8,7,1,4,6,3,5]=>0110010=>[2,1,3,2]
[3,1,2,8,5,7,4,6]=>1001010=>[1,3,2,2]
[6,4,1,5,3,2,8,7]=>1101101=>[1,1,2,1,2,1]
[6,3,8,1,2,5,4,7]=>1010010=>[1,2,3,2]
[2,1,8,6,3,7,5,4]=>1011011=>[1,2,1,2,1,1]
[1,6,5,3,2,4,7,8]=>0111000=>[2,1,1,4]
[1,7,2,4,6,5,3,8]=>0100110=>[2,3,1,2]
[1,4,7,2,6,5,3,8]=>0010110=>[3,2,1,2]
[1,3,7,2,4,6,5,8]=>0010010=>[3,3,2]
[1,7,2,6,4,3,5,8]=>0101100=>[2,2,1,3]
[1,2,6,8,7,4,3,5]=>0001110=>[4,1,1,2]
[1,2,7,4,3,5,8,6]=>0011001=>[3,1,3,1]
[1,8,6,3,5,2,7,4]=>0110101=>[2,1,2,2,1]
[1,6,2,8,7,4,3,5]=>0101110=>[2,2,1,1,2]
[1,3,8,7,5,4,6,2]=>0011101=>[3,1,1,2,1]
[1,2,8,6,3,5,7,4]=>0011001=>[3,1,3,1]
[1,8,5,2,3,6,4,7]=>0110010=>[2,1,3,2]
[1,7,4,8,5,2,3,6]=>0101100=>[2,2,1,3]
[1,4,7,5,8,6,3,2]=>0010111=>[3,2,1,1,1]
[1,4,7,5,2,8,6,3]=>0011011=>[3,1,2,1,1]
[1,6,3,7,4,2,8,5]=>0101101=>[2,2,1,2,1]
[1,8,5,2,7,4,3,6]=>0110110=>[2,1,2,1,2]
[1,4,8,6,3,2,7,5]=>0011101=>[3,1,1,2,1]
[1,4,8,7,5,3,2,6]=>0011110=>[3,1,1,1,2]
[1,2,5,8,6,3,7,4]=>0001101=>[4,1,2,1]
[1,2,4,7,5,8,6,3]=>0001011=>[4,2,1,1]
[1,3,5,8,7,6,2,4]=>0001110=>[4,1,1,2]
[1,5,2,4,3,6,8,7]=>0101001=>[2,2,3,1]
[1,6,8,7,5,3,2,4]=>0011110=>[3,1,1,1,2]
[1,2,5,7,4,3,8,6]=>0001101=>[4,1,2,1]
[1,5,3,2,6,8,7,4]=>0110011=>[2,1,3,1,1]
[1,4,2,6,8,7,5,3]=>0100111=>[2,3,1,1,1]
[1,5,8,6,3,2,7,4]=>0011101=>[3,1,1,2,1]
[1,8,5,2,6,3,4,7]=>0110100=>[2,1,2,3]
[1,7,4,6,3,2,8,5]=>0101101=>[2,2,1,2,1]
[1,6,3,2,8,5,4,7]=>0110110=>[2,1,2,1,2]
[1,4,2,8,6,3,5,7]=>0101100=>[2,2,1,3]
[1,3,8,6,4,2,5,7]=>0011100=>[3,1,1,3]
[1,5,7,4,2,3,8,6]=>0011001=>[3,1,3,1]
[8,2,7,3,1,5,4,6]=>1011010=>[1,2,1,2,2]
[8,4,7,2,5,3,1,6]=>1010110=>[1,2,2,1,2]
[8,3,4,5,2,1,7,6]=>1001101=>[1,3,1,2,1]
[8,6,1,4,7,3,5,2]=>1100101=>[1,1,3,2,1]
[5,3,6,7,2,8,4,1]=>1001011=>[1,3,2,1,1]
[5,3,6,7,2,4,8,1]=>1001001=>[1,3,3,1]
[1,3,8,2,5,6,7,4]=>0010001=>[3,4,1]
[5,4,2,3,6,1,8,7]=>1100101=>[1,1,3,2,1]
[5,1,7,4,3,6,8,2]=>1011001=>[1,2,1,3,1]
[7,1,3,6,5,2,8,4]=>1001101=>[1,3,1,2,1]
[6,1,8,5,2,7,3,4]=>1011010=>[1,2,1,2,2]
[8,7,2,6,3,1,4,5]=>1101100=>[1,1,2,1,3]
[5,4,1,3,7,2,8,6]=>1100101=>[1,1,3,2,1]
[8,3,4,7,6,2,1,5]=>1001110=>[1,3,1,1,2]
[3,1,8,7,5,2,4,6]=>1011100=>[1,2,1,1,3]
[6,5,8,7,2,4,3,1]=>1011011=>[1,2,1,2,1,1]
[4,3,6,5,8,2,1,7]=>1010110=>[1,2,2,1,2]
[3,2,6,8,7,1,4,5]=>1001100=>[1,3,1,3]
[4,7,3,1,8,5,2,6]=>0110110=>[2,1,2,1,2]
[3,7,8,2,5,6,1,4]=>0010010=>[3,3,2]
[3,1,2,5,7,8,6,4]=>1000011=>[1,5,1,1]
[7,5,1,4,2,3,6,8]=>1101000=>[1,1,2,4]
[7,8,6,1,2,4,5,3]=>0110001=>[2,1,4,1]
[1,5,3,4,7,8,6,2]=>0100011=>[2,4,1,1]
[5,1,2,4,7,8,6,3]=>1000011=>[1,5,1,1]
[5,1,7,8,6,2,3,4]=>1001100=>[1,3,1,3]
[8,5,1,6,7,2,3,4]=>1100100=>[1,1,3,3]
[8,5,1,2,4,6,7,3]=>1100001=>[1,1,5,1]
[1,8,5,3,4,6,7,2]=>0110001=>[2,1,4,1]
[7,5,1,2,4,6,8,3]=>1100001=>[1,1,5,1]
[6,1,5,2,7,3,4,8]=>1010100=>[1,2,2,3]
[7,1,2,6,4,5,8,3]=>1001001=>[1,3,3,1]
[1,7,3,6,4,5,8,2]=>0101001=>[2,2,3,1]
[1,8,3,6,4,5,7,2]=>0101001=>[2,2,3,1]
[8,1,6,2,7,3,4,5]=>1010100=>[1,2,2,3]
[7,1,5,2,6,3,4,8]=>1010100=>[1,2,2,3]
[7,1,6,2,5,3,4,8]=>1010100=>[1,2,2,3]
[8,1,6,2,5,3,4,7]=>1010100=>[1,2,2,3]
[8,1,7,2,5,3,4,6]=>1010100=>[1,2,2,3]
[8,1,2,7,4,5,6,3]=>1001001=>[1,3,3,1]
[1,8,3,7,4,5,6,2]=>0101001=>[2,2,3,1]
[8,1,6,7,5,2,3,4]=>1001100=>[1,3,1,3]
[8,1,6,4,2,3,5,7]=>1011000=>[1,2,1,4]
[7,3,1,2,6,4,5,8]=>1100100=>[1,1,3,3]
[8,3,1,2,4,6,7,5]=>1100001=>[1,1,5,1]
[3,1,2,8,5,6,7,4]=>1001001=>[1,3,3,1]
[6,3,1,2,7,4,5,8]=>1100100=>[1,1,3,3]
[6,1,7,4,2,3,5,8]=>1011000=>[1,2,1,4]
[6,1,8,4,2,3,5,7]=>1011000=>[1,2,1,4]
[1,7,3,4,6,8,5,2]=>0100011=>[2,4,1,1]
[1,7,3,8,4,5,6,2]=>0101001=>[2,2,3,1]
[7,1,8,2,5,3,4,6]=>1010100=>[1,2,2,3]
[6,1,8,2,5,3,4,7]=>1010100=>[1,2,2,3]
[6,1,7,2,5,3,4,8]=>1010100=>[1,2,2,3]
[5,1,7,2,6,3,4,8]=>1010100=>[1,2,2,3]
[5,1,8,2,6,3,4,7]=>1010100=>[1,2,2,3]
[1,6,3,8,4,5,7,2]=>0101001=>[2,2,3,1]
[1,6,3,7,4,5,8,2]=>0101001=>[2,2,3,1]
[2,7,4,3,8,5,1,6]=>0110110=>[2,1,2,1,2]
[2,4,7,3,5,1,6,8]=>0010100=>[3,2,3]
[2,5,8,4,6,3,1,7]=>0010110=>[3,2,1,2]
[2,4,8,6,3,5,1,7]=>0011010=>[3,1,2,2]
[2,3,7,5,4,1,6,8]=>0011100=>[3,1,1,3]
[3,4,6,2,1,5,8,7]=>0011001=>[3,1,3,1]
[2,6,8,3,5,1,4,7]=>0010100=>[3,2,3]
[2,3,6,1,5,8,4,7]=>0010010=>[3,3,2]
[2,3,7,1,6,5,8,4]=>0010101=>[3,2,2,1]
[2,4,7,1,3,6,8,5]=>0010001=>[3,4,1]
[5,4,7,8,1,3,2,6]=>1001010=>[1,3,2,2]
[2,5,7,1,4,6,3,8]=>0010010=>[3,3,2]
[2,4,7,1,6,3,5,8]=>0010100=>[3,2,3]
[2,3,7,1,6,5,4,8]=>0010110=>[3,2,1,2]
[2,5,7,1,4,3,6,8]=>0010100=>[3,2,3]
[2,5,7,3,1,4,6,8]=>0011000=>[3,1,4]
[3,4,7,2,1,6,8,5]=>0011001=>[3,1,3,1]
[5,7,3,2,8,1,4,6]=>0110100=>[2,1,2,3]
[3,6,8,5,4,1,7,2]=>0011101=>[3,1,1,2,1]
[5,4,7,8,1,3,6,2]=>1001001=>[1,3,3,1]
[2,5,7,1,4,6,8,3]=>0010001=>[3,4,1]
[2,4,7,1,6,3,8,5]=>0010101=>[3,2,2,1]
[2,4,7,1,6,8,3,5]=>0010010=>[3,3,2]
[2,4,8,3,1,7,6,5]=>0011011=>[3,1,2,1,1]
[8,6,5,1,2,4,3,7]=>1110010=>[1,1,1,3,2]
[7,6,1,4,2,3,5,8]=>1101000=>[1,1,2,4]
[7,5,4,8,3,2,6,1]=>1101101=>[1,1,2,1,2,1]
[8,7,5,1,4,2,3,6]=>1110100=>[1,1,1,2,3]
[8,4,1,2,5,3,6,7]=>1100100=>[1,1,3,3]
[4,3,8,1,5,2,6,7]=>1010100=>[1,2,2,3]
[8,6,1,4,2,5,3,7]=>1101010=>[1,1,2,2,2]
[2,8,3,7,4,5,6,1]=>0101001=>[2,2,3,1]
[8,7,5,2,4,3,6,1]=>1110101=>[1,1,1,2,2,1]
[6,8,3,2,4,5,1,7]=>0110010=>[2,1,3,2]
[3,8,5,2,4,6,1,7]=>0110010=>[2,1,3,2]
[8,2,4,5,3,1,6,7]=>1001100=>[1,3,1,3]
[4,8,2,5,3,1,6,7]=>0101100=>[2,2,1,3]
[4,3,7,5,2,1,6,8]=>1011100=>[1,2,1,1,3]
[1,6,7,4,3,2,5,8]=>0011100=>[3,1,1,3]
[1,4,5,7,3,2,6,8]=>0001100=>[4,1,3]
[3,5,1,4,7,2,6,8]=>0100100=>[2,3,3]
[2,5,4,7,8,1,3,6]=>0100100=>[2,3,3]
[2,5,1,4,7,8,3,6]=>0100010=>[2,4,2]
[4,3,7,1,5,2,6,8]=>1010100=>[1,2,2,3]
[3,5,1,6,4,2,7,8]=>0101100=>[2,2,1,3]
[6,4,3,1,7,2,5,8]=>1110100=>[1,1,1,2,3]
[6,2,7,4,3,1,5,8]=>1011100=>[1,2,1,1,3]
[2,6,4,1,7,3,5,8]=>0110100=>[2,1,2,3]
[6,3,2,7,4,5,1,8]=>1101010=>[1,1,2,2,2]
[7,2,4,1,3,6,8,5]=>1010001=>[1,2,4,1]
[6,3,2,5,7,1,4,8]=>1100100=>[1,1,3,3]
[3,2,6,5,7,1,4,8]=>1010100=>[1,2,2,3]
[1,7,3,2,5,6,4,8]=>0110010=>[2,1,3,2]
[2,1,7,3,5,6,8,4]=>1010001=>[1,2,4,1]
[2,1,6,3,5,7,8,4]=>1010001=>[1,2,4,1]
[1,6,3,2,5,7,4,8]=>0110010=>[2,1,3,2]
[5,6,2,1,4,3,7,8]=>0110100=>[2,1,2,3]
[2,5,1,6,4,3,7,8]=>0101100=>[2,2,1,3]
[2,5,4,1,6,3,7,8]=>0110100=>[2,1,2,3]
[4,6,1,5,2,7,3,8]=>0101010=>[2,2,2,2]
[1,6,5,3,7,2,4,8]=>0110100=>[2,1,2,3]
[2,6,1,8,5,4,3,7]=>0101110=>[2,2,1,1,2]
[5,8,6,2,3,4,1,7]=>0110010=>[2,1,3,2]
[4,5,8,6,2,1,3,7]=>0011100=>[3,1,1,3]
[6,3,7,4,2,5,8,1]=>1011001=>[1,2,1,3,1]
[7,5,6,2,4,3,8,1]=>1010101=>[1,2,2,2,1]
[6,2,5,7,4,3,8,1]=>1001101=>[1,3,1,2,1]
[4,6,2,5,7,3,8,1]=>0100101=>[2,3,2,1]
[4,2,8,5,3,6,1,7]=>1011010=>[1,2,1,2,2]
[8,1,7,4,5,6,2,3]=>1010010=>[1,2,3,2]
[8,4,6,2,5,3,7,1]=>1010101=>[1,2,2,2,1]
[5,6,3,2,8,1,7,4]=>0110101=>[2,1,2,2,1]
[8,2,6,3,1,5,7,4]=>1011001=>[1,2,1,3,1]
[8,2,5,6,7,4,3,1]=>1000111=>[1,4,1,1,1]
[8,2,5,3,4,7,6,1]=>1010011=>[1,2,3,1,1]
[7,5,3,2,4,1,8,6]=>1110101=>[1,1,1,2,2,1]
[6,5,3,2,4,8,1,7]=>1110010=>[1,1,1,3,2]
[3,1,8,4,6,5,7,2]=>1010101=>[1,2,2,2,1]
[3,4,7,5,8,2,6,1]=>0010101=>[3,2,2,1]
[8,7,1,4,6,5,2,3]=>1100110=>[1,1,3,1,2]
[8,3,7,6,4,5,1,2]=>1011010=>[1,2,1,2,2]
[5,3,8,6,4,1,7,2]=>1011101=>[1,2,1,1,2,1]
[6,4,7,1,8,5,2,3]=>1010110=>[1,2,2,1,2]
[5,7,4,2,3,8,6,1]=>0110011=>[2,1,3,1,1]
[3,8,2,5,1,7,4,6]=>0101010=>[2,2,2,2]
[5,8,4,2,3,7,1,6]=>0110010=>[2,1,3,2]
[4,8,5,2,1,7,3,6]=>0111010=>[2,1,1,2,2]
[8,5,7,6,1,2,4,3]=>1011001=>[1,2,1,3,1]
[7,8,6,5,2,4,3,1]=>0111011=>[2,1,1,2,1,1]
[7,8,4,2,6,3,5,1]=>0110101=>[2,1,2,2,1]
[5,7,6,8,4,1,3,2]=>0101101=>[2,2,1,2,1]
[7,3,1,6,8,5,4,2]=>1100111=>[1,1,3,1,1,1]
[5,3,1,7,4,8,6,2]=>1101011=>[1,1,2,2,1,1]
[7,3,1,8,6,4,5,2]=>1101101=>[1,1,2,1,2,1]
[8,6,4,1,7,3,2,5]=>1110110=>[1,1,1,2,1,2]
[4,6,8,3,7,1,2,5]=>0010100=>[3,2,3]
[3,5,2,8,4,7,1,6]=>0101010=>[2,2,2,2]
[3,7,2,8,6,4,5,1]=>0101101=>[2,2,1,2,1]
[8,6,5,7,1,3,2,4]=>1101010=>[1,1,2,2,2]
[6,4,8,3,7,2,1,5]=>1010110=>[1,2,2,1,2]
[3,6,2,8,7,4,1,5]=>0101110=>[2,2,1,1,2]
[6,8,4,2,7,3,1,5]=>0110110=>[2,1,2,1,2]
[3,4,7,8,5,1,2,6]=>0001100=>[4,1,3]
[5,7,2,4,3,6,8,1]=>0101001=>[2,2,3,1]
[4,7,3,2,5,6,8,1]=>0110001=>[2,1,4,1]
[3,2,7,6,4,5,8,1]=>1011001=>[1,2,1,3,1]
[1,7,3,6,8,4,2,5]=>0100110=>[2,3,1,2]
[8,3,1,2,6,4,7,5]=>1100101=>[1,1,3,2,1]
[1,7,8,2,4,3,5,6]=>0010100=>[3,2,3]
[3,6,4,7,1,2,8,5]=>0101001=>[2,2,3,1]
[2,4,7,8,5,1,3,6]=>0001100=>[4,1,3]
[5,7,4,8,1,3,2,6]=>0101010=>[2,2,2,2]
[4,3,7,8,1,5,2,6]=>1001010=>[1,3,2,2]
[8,5,4,2,6,1,7,3]=>1110101=>[1,1,1,2,2,1]
[3,2,6,8,7,4,1,5]=>1001110=>[1,3,1,1,2]
[2,3,7,5,1,8,6,4]=>0011011=>[3,1,2,1,1]
[6,3,1,2,8,7,4,5]=>1100110=>[1,1,3,1,2]
[5,2,1,3,8,7,6,4]=>1100111=>[1,1,3,1,1,1]
[7,2,1,5,3,8,4,6]=>1101010=>[1,1,2,2,2]
[1,5,8,2,4,3,6,7]=>0010100=>[3,2,3]
[4,3,6,8,1,5,2,7]=>1001010=>[1,3,2,2]
[2,4,6,8,5,1,3,7]=>0001100=>[4,1,3]
[1,6,8,2,4,3,5,7]=>0010100=>[3,2,3]
[5,4,6,8,3,1,7,2]=>1001101=>[1,3,1,2,1]
[8,6,1,7,2,4,3,5]=>1101010=>[1,1,2,2,2]
[7,3,1,2,8,6,4,5]=>1100110=>[1,1,3,1,2]
[2,3,7,6,1,8,5,4]=>0011011=>[3,1,2,1,1]
[3,2,7,8,6,4,1,5]=>1001110=>[1,3,1,1,2]
[6,2,8,3,1,4,7,5]=>1011001=>[1,2,1,3,1]
[3,1,2,8,7,4,5,6]=>1001100=>[1,3,1,3]
[2,1,3,8,7,4,6,5]=>1001101=>[1,3,1,2,1]
[2,1,3,8,7,4,5,6]=>1001100=>[1,3,1,3]
[8,5,1,7,2,4,3,6]=>1101010=>[1,1,2,2,2]
[8,3,1,6,2,7,5,4]=>1101011=>[1,1,2,2,1,1]
[1,3,2,8,7,6,4,5]=>0101110=>[2,2,1,1,2]
[2,1,3,8,7,6,4,5]=>1001110=>[1,3,1,1,2]
[5,7,2,8,4,1,3,6]=>0101100=>[2,2,1,3]
[3,5,8,2,4,1,7,6]=>0010101=>[3,2,2,1]
[2,4,8,3,1,6,7,5]=>0011001=>[3,1,3,1]
[1,3,6,8,5,4,2,7]=>0001110=>[4,1,1,2]
[1,4,2,5,7,6,3,8]=>0100110=>[2,3,1,2]
[1,4,2,6,8,5,3,7]=>0100110=>[2,3,1,2]
[1,5,3,2,6,8,4,7]=>0110010=>[2,1,3,2]
[1,5,4,2,3,6,8,7]=>0110001=>[2,1,4,1]
[1,6,8,3,5,4,2,7]=>0010110=>[3,2,1,2]
[1,5,3,2,4,6,8,7]=>0110001=>[2,1,4,1]
[1,5,8,7,6,3,2,4]=>0011110=>[3,1,1,1,2]
[1,5,7,6,3,2,4,8]=>0011100=>[3,1,1,3]
[1,6,3,2,4,7,5,8]=>0110010=>[2,1,3,2]
[1,6,3,2,4,8,7,5]=>0110011=>[2,1,3,1,1]
[1,2,7,6,4,3,5,8]=>0011100=>[3,1,1,3]
[1,8,7,5,2,4,6,3]=>0111001=>[2,1,1,3,1]
[1,7,5,2,4,6,3,8]=>0110010=>[2,1,3,2]
[1,7,4,2,5,3,6,8]=>0110100=>[2,1,2,3]
[1,8,4,7,5,2,6,3]=>0101101=>[2,2,1,2,1]
[1,7,5,2,3,6,4,8]=>0110010=>[2,1,3,2]
[1,7,5,2,6,3,4,8]=>0110100=>[2,1,2,3]
[1,6,3,7,4,2,5,8]=>0101100=>[2,2,1,3]
[1,6,3,2,7,5,4,8]=>0110110=>[2,1,2,1,2]
[1,4,8,7,5,2,6,3]=>0011101=>[3,1,1,2,1]
[1,4,7,5,2,6,3,8]=>0011010=>[3,1,2,2]
[1,3,6,4,8,7,5,2]=>0010111=>[3,2,1,1,1]
[1,3,7,6,4,2,5,8]=>0011100=>[3,1,1,3]
[1,3,8,7,5,2,4,6]=>0011100=>[3,1,1,3]
[1,4,6,3,2,7,5,8]=>0011010=>[3,1,2,2]
[1,4,6,3,2,8,7,5]=>0011011=>[3,1,2,1,1]
[1,5,7,6,4,2,3,8]=>0011100=>[3,1,1,3]
[1,2,6,4,7,5,3,8]=>0010110=>[3,2,1,2]
[1,6,3,2,8,4,7,5]=>0110101=>[2,1,2,2,1]
[1,5,2,7,4,3,6,8]=>0101100=>[2,2,1,3]
[1,6,3,5,2,7,4,8]=>0101010=>[2,2,2,2]
[1,6,3,5,2,8,7,4]=>0101011=>[2,2,2,1,1]
[1,8,3,7,5,2,4,6]=>0101100=>[2,2,1,3]
[1,8,4,6,3,2,7,5]=>0101101=>[2,2,1,2,1]
[6,4,7,1,5,3,8,2]=>1010101=>[1,2,2,2,1]
[5,3,8,2,6,4,7,1]=>1010101=>[1,2,2,2,1]
[4,3,8,2,6,5,7,1]=>1010101=>[1,2,2,2,1]
[2,6,1,8,3,4,7,5]=>0101001=>[2,2,3,1]
[6,5,7,1,4,3,8,2]=>1010101=>[1,2,2,2,1]
[4,8,3,5,7,6,1,2]=>0100110=>[2,3,1,2]
[5,7,6,1,2,4,8,3]=>0110001=>[2,1,4,1]
[4,8,3,5,7,6,2,1]=>0100111=>[2,3,1,1,1]
[5,7,6,2,4,8,3,1]=>0110011=>[2,1,3,1,1]
[6,7,5,2,3,8,4,1]=>0110011=>[2,1,3,1,1]
[6,7,5,3,8,4,2,1]=>0110111=>[2,1,2,1,1,1]
[7,3,1,4,2,6,5,8]=>1101010=>[1,1,2,2,2]
[7,4,1,6,2,5,3,8]=>1101010=>[1,1,2,2,2]
[5,4,1,8,2,6,3,7]=>1101010=>[1,1,2,2,2]
[4,7,1,5,2,6,3,8]=>0101010=>[2,2,2,2]
[6,5,1,4,2,7,3,8]=>1101010=>[1,1,2,2,2]
[5,4,1,6,2,8,3,7]=>1101010=>[1,1,2,2,2]
[8,4,2,3,1,6,5,7]=>1101010=>[1,1,2,2,2]
[4,8,6,2,3,1,7,5]=>0110101=>[2,1,2,2,1]
[2,8,6,4,5,1,7,3]=>0110101=>[2,1,2,2,1]
[8,2,4,6,7,1,5,3]=>1000101=>[1,4,2,1]
[2,8,3,1,4,5,7,6]=>0110001=>[2,1,4,1]
[8,7,4,5,1,6,3,2]=>1101011=>[1,1,2,2,1,1]
[7,2,8,1,4,5,6,3]=>1010001=>[1,2,4,1]
[2,1,4,3,6,5,8,10,9,7]=>101010011=>[1,2,2,3,1,1]
[2,1,4,3,6,8,7,5,10,9]=>101001101=>[1,2,3,1,2,1]
[2,1,4,3,8,10,7,9,5,6]=>101001010=>[1,2,3,2,2]
[2,1,4,3,6,7,10,8,9,5]=>101000101=>[1,2,4,2,1]
[2,1,4,6,5,3,8,7,10,9]=>100110101=>[1,3,1,2,2,1]
[2,1,4,6,5,3,8,10,9,7]=>100110011=>[1,3,1,3,1,1]
[2,1,6,8,5,7,3,4,10,9]=>100101001=>[1,3,2,3,1]
[2,1,8,7,5,10,4,9,3,6]=>101101010=>[1,2,1,2,2,2]
[2,1,6,7,5,10,8,4,9,3]=>100101101=>[1,3,2,1,2,1]
[2,1,4,5,8,6,7,3,10,9]=>100010101=>[1,4,2,2,1]
[2,1,8,5,10,6,7,9,3,4]=>101010010=>[1,2,2,3,2]
[2,1,4,7,10,6,9,8,3,5]=>100010110=>[1,4,2,1,2]
[2,1,4,5,6,10,7,8,9,3]=>100001001=>[1,5,3,1]
[2,4,3,1,6,5,8,7,10,9]=>011010101=>[2,1,2,2,2,1]
[2,4,3,1,6,5,8,10,9,7]=>011010011=>[2,1,2,3,1,1]
[2,4,3,1,6,8,7,5,10,9]=>011001101=>[2,1,3,1,2,1]
[2,4,3,1,8,10,7,9,5,6]=>011001010=>[2,1,3,2,2]
[2,4,3,1,6,7,10,8,9,5]=>011000101=>[2,1,4,2,1]
[4,6,3,5,1,2,8,7,10,9]=>010100101=>[2,2,3,2,1]
[4,6,3,5,1,2,8,10,9,7]=>010100011=>[2,2,4,1,1]
[6,5,3,8,2,7,1,4,10,9]=>110101001=>[1,1,2,2,3,1]
[8,5,3,7,2,10,4,9,1,6]=>110101010=>[1,1,2,2,2,2]
[6,5,3,7,2,10,8,4,9,1]=>110101101=>[1,1,2,2,1,2,1]
[4,5,3,8,6,2,7,1,10,9]=>010110101=>[2,2,1,2,2,1]
[8,6,3,5,10,2,7,9,1,4]=>110010010=>[1,1,3,3,2]
[4,7,3,6,10,1,9,8,2,5]=>010010110=>[2,3,2,1,2]
[4,5,3,6,10,7,1,8,9,2]=>010011001=>[2,3,1,3,1]
[2,3,6,4,5,1,8,7,10,9]=>001010101=>[3,2,2,2,1]
[2,3,6,4,5,1,8,10,9,7]=>001010011=>[3,2,3,1,1]
[6,3,8,4,5,7,1,2,10,9]=>101001001=>[1,2,3,3,1]
[8,3,7,4,5,10,2,9,1,6]=>101001010=>[1,2,3,2,2]
[6,3,7,4,5,10,8,2,9,1]=>101001101=>[1,2,3,1,2,1]
[2,5,8,4,7,6,1,3,10,9]=>001011001=>[3,2,1,3,1]
[8,5,10,4,7,6,2,9,1,3]=>101011010=>[1,2,2,1,2,2]
[2,7,10,4,8,6,9,5,1,3]=>001010110=>[3,2,2,1,2]
[2,5,6,4,10,8,7,3,9,1]=>001011101=>[3,2,1,1,2,1]
[2,3,4,8,5,6,7,1,10,9]=>000100101=>[4,3,2,1]
[8,3,4,10,5,6,7,9,1,2]=>100100010=>[1,3,4,2]
[2,7,4,10,5,6,9,8,1,3]=>010100110=>[2,2,3,1,2]
[2,3,6,10,5,9,7,8,1,4]=>000101010=>[4,2,2,2]
[2,3,4,5,10,6,7,8,9,1]=>000010001=>[5,4,1]
[2,1,4,5,8,6,7,3,10,9,12,11]=>10001010101=>[1,4,2,2,2,1]
[2,4,3,1,6,5,8,7,10,9,12,11]=>01101010101=>[2,1,2,2,2,2,1]
[8,2,3,7,4,5,6,1]=>1001001=>[1,3,3,1]
[8,6,2,5,4,7,3,1]=>1101011=>[1,1,2,2,1,1]
[8,5,7,2,3,6,4,1]=>1010011=>[1,2,3,1,1]
[7,5,2,1,6,8,3,4]=>1110010=>[1,1,1,3,2]
[7,6,1,5,4,8,2,3]=>1101010=>[1,1,2,2,2]
[7,6,3,2,1,8,4,5]=>1111010=>[1,1,1,1,2,2]
[2,8,7,3,4,6,1,5]=>0110010=>[2,1,3,2]
[6,5,1,3,7,2,8,4]=>1100101=>[1,1,3,2,1]
[1,8,7,3,4,5,2,6]=>0110010=>[2,1,3,2]
[8,2,7,3,4,5,1,6]=>1010010=>[1,2,3,2]
[1,7,8,3,4,5,2,6]=>0010010=>[3,3,2]
[8,1,7,3,4,5,2,6]=>1010010=>[1,2,3,2]
[6,8,7,3,4,2,1,5]=>0110110=>[2,1,2,1,2]
[1,8,5,3,4,6,2,7]=>0110010=>[2,1,3,2]
[7,1,6,5,4,3,8,2]=>1011101=>[1,2,1,1,2,1]
[7,1,3,6,4,5,8,2]=>1001001=>[1,3,3,1]
[7,1,5,3,6,4,8,2]=>1010101=>[1,2,2,2,1]
[6,1,5,3,7,8,2,4]=>1010010=>[1,2,3,2]
[5,7,1,3,2,8,6,4]=>0101011=>[2,2,2,1,1]
[5,8,7,1,2,6,3,4]=>0110010=>[2,1,3,2]
[6,8,2,3,4,7,1,5]=>0100010=>[2,4,2]
[6,7,2,3,4,8,1,5]=>0100010=>[2,4,2]
[5,1,7,3,8,6,2,4]=>1010110=>[1,2,2,1,2]
[6,1,3,2,4,7,8,5]=>1010001=>[1,2,4,1]
[6,2,1,3,4,7,8,5]=>1100001=>[1,1,5,1]
[3,2,5,8,7,4,1,6]=>1001110=>[1,3,1,1,2]
[4,2,5,8,7,3,1,6]=>1001110=>[1,3,1,1,2]
[8,3,4,1,6,5,2,7]=>1010110=>[1,2,2,1,2]
[3,4,8,5,7,2,1,6]=>0010110=>[3,2,1,2]
[3,6,4,8,5,7,2,1]=>0101011=>[2,2,2,1,1]
[5,8,4,7,3,6,2,1]=>0101011=>[2,2,2,1,1]
[4,2,8,7,3,1,6,5]=>1011101=>[1,2,1,1,2,1]
[6,5,8,2,1,7,4,3]=>1011011=>[1,2,1,2,1,1]
[6,1,4,3,8,7,2,5]=>1010110=>[1,2,2,1,2]
[5,1,3,2,6,8,7,4]=>1010011=>[1,2,3,1,1]
[6,1,3,8,7,2,4,5]=>1001100=>[1,3,1,3]
[1,2,8,4,5,7,3,6]=>0010010=>[3,3,2]
[4,2,1,8,7,6,3,5]=>1101110=>[1,1,2,1,1,2]
[3,2,5,8,7,1,4,6]=>1001100=>[1,3,1,3]
[5,6,3,8,7,2,1,4]=>0101110=>[2,2,1,1,2]
[2,5,8,4,7,1,6,3]=>0010101=>[3,2,2,1]
[1,6,2,4,8,5,7,3]=>0100101=>[2,3,2,1]
[3,1,6,5,8,7,2,4]=>1010110=>[1,2,2,1,2]
[4,8,5,3,6,7,1,2]=>0110010=>[2,1,3,2]
[1,8,5,3,4,7,6,2]=>0110011=>[2,1,3,1,1]
[1,4,6,2,5,3,7,8]=>0010100=>[3,2,3]
[4,3,6,5,1,2,7,8]=>1011000=>[1,2,1,4]
[1,3,8,7,6,5,2,4]=>0011110=>[3,1,1,1,2]
[1,8,7,2,6,3,5,4]=>0110101=>[2,1,2,2,1]
[8,7,1,2,4,3,6,5]=>1100101=>[1,1,3,2,1]
[2,8,7,1,6,3,4,5]=>0110100=>[2,1,2,3]
[6,2,1,8,7,5,3,4]=>1101110=>[1,1,2,1,1,2]
[3,2,1,4,5,8,6,7]=>1100010=>[1,1,4,2]
[1,3,7,5,4,8,6,2]=>0011011=>[3,1,2,1,1]
[5,2,1,4,3,6,8,7]=>1101001=>[1,1,2,3,1]
[1,5,6,3,8,4,2,7]=>0010110=>[3,2,1,2]
[2,6,5,3,8,4,1,7]=>0110110=>[2,1,2,1,2]
[5,7,3,8,4,2,6,1]=>0101101=>[2,2,1,2,1]
[2,3,6,5,4,8,1,7]=>0011010=>[3,1,2,2]
[2,7,5,1,8,4,6,3]=>0110101=>[2,1,2,2,1]
[1,7,6,4,8,2,5,3]=>0110101=>[2,1,2,2,1]
[6,3,8,7,2,4,5,1]=>1011001=>[1,2,1,3,1]
[2,4,3,8,7,1,6,5]=>0101101=>[2,2,1,2,1]
[2,8,7,6,1,5,3,4]=>0111010=>[2,1,1,2,2]
[5,4,7,6,3,1,2,8]=>1011100=>[1,2,1,1,3]
[3,6,4,8,1,5,2,7]=>0101010=>[2,2,2,2]
[3,6,8,4,1,5,2,7]=>0011010=>[3,1,2,2]
[7,8,1,4,2,3,5,6]=>0101000=>[2,2,4]
[8,7,1,4,2,3,5,6]=>1101000=>[1,1,2,4]
[3,8,6,4,1,5,2,7]=>0111010=>[2,1,1,2,2]
[3,8,4,6,1,5,2,7]=>0101010=>[2,2,2,2]
[8,3,7,2,1,6,5,4]=>1011011=>[1,2,1,2,1,1]
[8,4,7,3,6,2,1,5]=>1010110=>[1,2,2,1,2]
[3,8,7,5,6,4,1,2]=>0110110=>[2,1,2,1,2]
[3,8,7,5,6,2,1,4]=>0110110=>[2,1,2,1,2]
[3,8,7,5,6,2,4,1]=>0110101=>[2,1,2,2,1]
[2,8,7,5,6,4,1,3]=>0110110=>[2,1,2,1,2]
[3,6,2,4,8,7,1,5]=>0100110=>[2,3,1,2]
[1,5,6,3,8,2,7,4]=>0010101=>[3,2,2,1]
[2,6,3,8,4,7,1,5]=>0101010=>[2,2,2,2]
[2,6,3,5,7,8,1,4]=>0100010=>[2,4,2]
[1,5,6,3,7,2,8,4]=>0010101=>[3,2,2,1]
[1,7,5,3,6,2,8,4]=>0110101=>[2,1,2,2,1]
[1,5,7,3,4,2,8,6]=>0010101=>[3,2,2,1]
[1,5,8,3,4,2,7,6]=>0010101=>[3,2,2,1]
[1,4,5,3,8,2,7,6]=>0010101=>[3,2,2,1]
[6,5,1,4,2,7,8,3]=>1101001=>[1,1,2,3,1]
[6,5,1,4,2,8,7,3]=>1101011=>[1,1,2,2,1,1]
[1,7,5,4,2,8,6,3]=>0111011=>[2,1,1,2,1,1]
[5,1,6,8,3,7,2,4]=>1001010=>[1,3,2,2]
[1,4,3,6,5,10,9,7,8,2]=>010101101=>[2,2,2,1,2,1]
[1,4,3,8,7,5,6,10,9,2]=>010110011=>[2,2,1,3,1,1]
[1,4,3,10,7,5,9,6,8,2]=>010110101=>[2,2,1,2,2,1]
[1,4,3,10,9,8,5,6,7,2]=>010111001=>[2,2,1,1,3,1]
[1,6,5,3,4,8,7,10,9,2]=>011001011=>[2,1,3,2,1,1]
[1,6,5,3,4,10,9,7,8,2]=>011001101=>[2,1,3,1,2,1]
[1,8,5,3,7,4,6,10,9,2]=>011010011=>[2,1,2,3,1,1]
[1,10,5,3,7,4,9,6,8,2]=>011010101=>[2,1,2,2,2,1]
[1,10,5,3,9,8,4,6,7,2]=>011011001=>[2,1,2,1,3,1]
[1,8,7,6,3,4,5,10,9,2]=>011100011=>[2,1,1,4,1,1]
[1,10,7,6,3,4,9,5,8,2]=>011100101=>[2,1,1,3,2,1]
[1,10,9,6,3,8,4,5,7,2]=>011101001=>[2,1,1,2,3,1]
[1,10,9,8,7,3,4,5,6,2]=>011110001=>[2,1,1,1,4,1]
[3,1,2,6,5,8,7,10,9,4]=>100101011=>[1,3,2,2,1,1]
[3,1,2,6,5,10,9,7,8,4]=>100101101=>[1,3,2,1,2,1]
[3,1,2,8,7,5,6,10,9,4]=>100110011=>[1,3,1,3,1,1]
[3,1,2,10,7,5,9,6,8,4]=>100110101=>[1,3,1,2,2,1]
[3,1,2,10,9,8,5,6,7,4]=>100111001=>[1,3,1,1,3,1]
[3,1,5,2,4,8,7,10,9,6]=>101001011=>[1,2,3,2,1,1]
[3,1,5,2,4,10,9,7,8,6]=>101001101=>[1,2,3,1,2,1]
[3,1,5,2,7,4,6,10,9,8]=>101010011=>[1,2,2,3,1,1]
[3,1,5,2,9,8,4,6,7,10]=>101011000=>[1,2,2,1,4]
[3,1,7,6,2,4,5,10,9,8]=>101100011=>[1,2,1,4,1,1]
[3,1,7,6,2,4,9,5,8,10]=>101100100=>[1,2,1,3,3]
[3,1,9,6,2,8,4,5,7,10]=>101101000=>[1,2,1,2,4]
[3,1,9,8,7,2,4,5,6,10]=>101110000=>[1,2,1,1,5]
[5,4,1,2,3,8,7,10,9,6]=>110001011=>[1,1,4,2,1,1]
[5,4,1,2,3,10,9,7,8,6]=>110001101=>[1,1,4,1,2,1]
[5,4,1,2,7,3,6,10,9,8]=>110010011=>[1,1,3,3,1,1]
[5,4,1,2,7,3,9,6,8,10]=>110010100=>[1,1,3,2,3]
[5,4,1,2,9,8,3,6,7,10]=>110011000=>[1,1,3,1,4]
[7,4,1,6,2,3,5,10,9,8]=>110100011=>[1,1,2,4,1,1]
[7,4,1,6,2,3,9,5,8,10]=>110100100=>[1,1,2,3,3]
[9,4,1,6,2,8,3,5,7,10]=>110101000=>[1,1,2,2,4]
[9,4,1,8,7,2,3,5,6,10]=>110110000=>[1,1,2,1,5]
[7,6,5,1,2,3,4,10,9,8]=>111000011=>[1,1,1,5,1,1]
[7,6,5,1,2,3,9,4,8,10]=>111000100=>[1,1,1,4,3]
[9,6,5,1,2,8,3,4,7,10]=>111001000=>[1,1,1,3,4]
[9,8,5,1,7,2,3,4,6,10]=>111010000=>[1,1,1,2,5]
[1,12,5,3,7,4,9,6,11,8,10,2]=>01101010101=>[2,1,2,2,2,2,1]
[1,12,11,10,9,8,3,4,5,6,7,2]=>01111100001=>[2,1,1,1,1,5,1]
[3,8,5,2,1,4,7,6]=>0111001=>[2,1,1,3,1]
[3,5,4,8,2,6,7,1]=>0101001=>[2,2,3,1]
[1,4,8,2,6,5,3,7]=>0010110=>[3,2,1,2]
[7,5,1,8,3,4,2,6]=>1101010=>[1,1,2,2,2]
[1,4,8,2,6,7,3,5]=>0010010=>[3,3,2]
[1,2,5,6,8,7,3,4]=>0000110=>[5,1,2]
[1,5,6,8,2,7,4,3]=>0001011=>[4,2,1,1]
[2,6,7,3,4,1,8,5]=>0010101=>[3,2,2,1]
[1,6,5,7,8,2,4,3]=>0100101=>[2,3,2,1]
[1,5,6,7,2,8,4,3]=>0001011=>[4,2,1,1]
[1,3,7,2,6,4,8,5]=>0010101=>[3,2,2,1]
[1,5,8,6,7,3,4,2]=>0010101=>[3,2,2,1]
[1,6,5,8,7,2,4,3]=>0101101=>[2,2,1,2,1]
[1,5,7,6,2,8,3,4]=>0011010=>[3,1,2,2]
[1,2,5,8,6,7,4,3]=>0001011=>[4,2,1,1]
[1,2,6,5,7,3,8,4]=>0010101=>[3,2,2,1]
[1,7,5,8,6,4,2,3]=>0101110=>[2,2,1,1,2]
[7,6,1,2,3,5,4,8]=>1100010=>[1,1,4,2]
[8,5,2,6,4,3,1,7]=>1101110=>[1,1,2,1,1,2]
[5,8,3,7,1,4,6,2]=>0101001=>[2,2,3,1]
[3,8,7,4,2,6,5,1]=>0111011=>[2,1,1,2,1,1]
[5,8,3,2,4,7,6,1]=>0110011=>[2,1,3,1,1]
[6,1,3,4,2,5,7,8]=>1001000=>[1,3,4]
[5,3,8,2,4,6,1,7]=>1010010=>[1,2,3,2]
[4,1,5,6,3,2,7,8]=>1001100=>[1,3,1,3]
[4,5,8,3,2,6,1,7]=>0011010=>[3,1,2,2]
[5,8,2,1,4,6,3,7]=>0110010=>[2,1,3,2]
[4,1,5,8,3,6,2,7]=>1001010=>[1,3,2,2]
[4,5,8,3,6,1,2,7]=>0010100=>[3,2,3]
[1,6,3,4,7,8,5,2]=>0100011=>[2,4,1,1]
[8,1,3,4,2,6,5,7]=>1001010=>[1,3,2,2]
[4,7,8,5,2,3,1,6]=>0011010=>[3,1,2,2]
[4,1,5,8,6,2,3,7]=>1001100=>[1,3,1,3]
[5,8,2,1,6,3,4,7]=>0110100=>[2,1,2,3]
[2,7,1,3,8,5,4,6]=>0100110=>[2,3,1,2]
[2,6,7,8,4,1,3,5]=>0001100=>[4,1,3]
[2,6,7,8,4,3,1,5]=>0001110=>[4,1,1,2]
[1,6,4,3,2,5,7,8]=>0111000=>[2,1,1,4]
[1,7,4,3,2,5,6,8]=>0111000=>[2,1,1,4]
[1,8,4,3,2,7,6,5]=>0111011=>[2,1,1,2,1,1]
[1,7,4,3,6,2,5,8]=>0110100=>[2,1,2,3]
[1,7,8,5,4,2,3,6]=>0011100=>[3,1,1,3]
[8,1,5,3,6,4,7,2]=>1010101=>[1,2,2,2,1]
[2,6,4,8,3,1,5,7]=>0101100=>[2,2,1,3]
[3,6,4,5,2,8,1,7]=>0101010=>[2,2,2,2]
[8,1,5,4,7,3,6,2]=>1010101=>[1,2,2,2,1]
[3,6,4,1,5,7,2,8]=>0110010=>[2,1,3,2]
[8,1,5,4,7,6,3,2]=>1010111=>[1,2,2,1,1,1]
[2,5,1,4,6,7,3,8]=>0100010=>[2,4,2]
[3,6,4,1,5,7,8,2]=>0110001=>[2,1,4,1]
[8,6,3,5,4,1,2,7]=>1101100=>[1,1,2,1,3]
[8,2,6,5,4,1,3,7]=>1011100=>[1,2,1,1,3]
[8,2,6,5,4,3,1,7]=>1011110=>[1,2,1,1,1,2]
[8,3,2,6,1,5,4,7]=>1101010=>[1,1,2,2,2]
[8,1,6,5,4,3,2,7]=>1011110=>[1,2,1,1,1,2]
[4,8,1,7,6,3,5,2]=>0101101=>[2,2,1,2,1]
[8,5,1,7,4,3,6,2]=>1101101=>[1,1,2,1,2,1]
[8,5,7,6,2,1,3,4]=>1011100=>[1,2,1,1,3]
[5,4,8,3,1,7,2,6]=>1011010=>[1,2,1,2,2]
[5,1,4,8,3,2,7,6]=>1001101=>[1,3,1,2,1]
[4,8,1,7,6,5,2,3]=>0101110=>[2,2,1,1,2]
[4,3,8,7,2,6,1,5]=>1011010=>[1,2,1,2,2]
[3,8,7,2,6,4,1,5]=>0110110=>[2,1,2,1,2]
[8,2,7,6,4,1,5,3]=>1011101=>[1,2,1,1,2,1]
[4,3,8,7,2,6,5,1]=>1011011=>[1,2,1,2,1,1]
[8,2,5,7,4,3,6,1]=>1001101=>[1,3,1,2,1]
[3,8,7,4,6,1,2,5]=>0110100=>[2,1,2,3]
[8,3,7,5,4,1,6,2]=>1011101=>[1,2,1,1,2,1]
[2,8,4,7,6,1,5,3]=>0101101=>[2,2,1,2,1]
[2,5,4,8,3,1,7,6]=>0101101=>[2,2,1,2,1]
[5,4,8,2,1,3,7,6]=>1011001=>[1,2,1,3,1]
[3,8,7,2,6,1,5,4]=>0110101=>[2,1,2,2,1]
[1,8,4,7,6,3,5,2]=>0101101=>[2,2,1,2,1]
[1,8,3,7,6,5,2,4]=>0101110=>[2,2,1,1,2]
[1,4,3,8,7,2,6,5]=>0101101=>[2,2,1,2,1]
[8,1,2,7,6,5,4,3]=>1001111=>[1,3,1,1,1,1]
[7,8,3,1,6,2,5,4]=>0110101=>[2,1,2,2,1]
[6,1,5,2,4,8,3,7]=>1010010=>[1,2,3,2]
[1,5,6,3,8,2,4,7]=>0010100=>[3,2,3]
[7,5,2,8,1,4,6,3]=>1101001=>[1,1,2,3,1]
[7,2,8,1,6,4,3,5]=>1010110=>[1,2,2,1,2]
[1,6,4,5,2,7,3,8]=>0101010=>[2,2,2,2]
[1,4,7,3,2,5,6,8]=>0011000=>[3,1,4]
[1,6,7,4,2,8,3,5]=>0011010=>[3,1,2,2]
[1,5,8,7,4,3,2,6]=>0011110=>[3,1,1,1,2]
[1,4,7,2,3,6,8,5]=>0010001=>[3,4,1]
[3,1,2,6,7,8,5,4]=>1000011=>[1,5,1,1]
[1,6,3,4,7,8,2,5]=>0100010=>[2,4,2]
[3,1,5,7,6,2,8,4]=>1001101=>[1,3,1,2,1]
[6,3,1,4,2,7,8,5]=>1101001=>[1,1,2,3,1]
[2,4,3,7,6,1,8,5]=>0101101=>[2,2,1,2,1]
[3,1,6,5,2,8,7,4]=>1011011=>[1,2,1,2,1,1]
[3,1,7,6,5,2,8,4]=>1011101=>[1,2,1,1,2,1]
[1,4,7,6,8,3,2,5]=>0010110=>[3,2,1,2]
[7,2,1,5,6,3,8,4]=>1100101=>[1,1,3,2,1]
[4,3,1,8,6,2,7,5]=>1101101=>[1,1,2,1,2,1]
[3,1,5,2,8,7,6,4]=>1010111=>[1,2,2,1,1,1]
[1,2,8,4,3,7,6,5]=>0011011=>[3,1,2,1,1]
[1,8,5,4,2,7,3,6]=>0111010=>[2,1,1,2,2]
[3,1,8,5,4,7,2,6]=>1011010=>[1,2,1,2,2]
[2,6,1,8,7,4,3,5]=>0101110=>[2,2,1,1,2]
[7,5,1,8,3,2,6,4]=>1101101=>[1,1,2,1,2,1]
[4,7,6,3,1,8,2,5]=>0111010=>[2,1,1,2,2]
[5,3,1,8,6,2,4,7]=>1101100=>[1,1,2,1,3]
[5,1,8,6,3,2,4,7]=>1011100=>[1,2,1,1,3]
[1,5,4,2,8,6,3,7]=>0110110=>[2,1,2,1,2]
[8,3,1,6,4,2,5,7]=>1101100=>[1,1,2,1,3]
[3,6,7,1,8,4,2,5]=>0010110=>[3,2,1,2]
[1,7,4,8,3,5,2,6]=>0101010=>[2,2,2,2]
[7,3,2,4,8,5,1,6]=>1100110=>[1,1,3,1,2]
[6,3,4,7,1,8,5,2]=>1001011=>[1,3,2,1,1]
[5,7,8,1,4,2,6,3]=>0010101=>[3,2,2,1]
[5,7,1,2,3,8,6,4]=>0100011=>[2,4,1,1]
[7,2,8,1,4,3,6,5]=>1010101=>[1,2,2,2,1]
[2,6,3,8,1,7,5,4]=>0101011=>[2,2,2,1,1]
[1,8,3,6,4,7,2,5]=>0101010=>[2,2,2,2]
[2,8,6,4,1,7,3,5]=>0111010=>[2,1,1,2,2]
[1,8,4,2,7,5,3,6]=>0110110=>[2,1,2,1,2]
[6,5,1,7,2,8,4,3]=>1101011=>[1,1,2,2,1,1]
[2,8,1,7,5,3,6,4]=>0101101=>[2,2,1,2,1]
[1,2,8,7,6,4,3,5]=>0011110=>[3,1,1,1,2]
[4,1,7,8,6,3,5,2]=>1001101=>[1,3,1,2,1]
[1,6,5,7,8,4,2,3]=>0100110=>[2,3,1,2]
[1,6,5,8,7,4,2,3]=>0101110=>[2,2,1,1,2]
[4,1,8,7,6,3,5,2]=>1011101=>[1,2,1,1,2,1]
[4,8,2,6,3,5,1,7]=>0101010=>[2,2,2,2]
[6,7,2,5,3,8,4,1]=>0101011=>[2,2,2,1,1]
[4,3,5,7,1,6,2,8]=>1001010=>[1,3,2,2]
[4,2,8,5,3,6,7,1]=>1011001=>[1,2,1,3,1]
[4,1,8,5,3,6,2,7]=>1011010=>[1,2,1,2,2]
[6,4,2,5,3,1,7,8]=>1101100=>[1,1,2,1,3]
[3,1,5,8,2,7,4,6]=>1001010=>[1,3,2,2]
[6,4,1,5,3,2,7,8]=>1101100=>[1,1,2,1,3]
[6,2,1,5,4,3,7,8]=>1101100=>[1,1,2,1,3]
[3,1,8,5,4,6,2,7]=>1011010=>[1,2,1,2,2]
[6,2,8,4,5,3,7,1]=>1010101=>[1,2,2,2,1]
[6,1,8,4,5,3,2,7]=>1010110=>[1,2,2,1,2]
[4,5,2,7,1,6,3,8]=>0101010=>[2,2,2,2]
[4,3,5,7,1,6,8,2]=>1001001=>[1,3,3,1]
[4,1,8,5,3,6,7,2]=>1011001=>[1,2,1,3,1]
[6,3,8,4,5,1,7,2]=>1010101=>[1,2,2,2,1]
[3,1,6,8,5,7,4,2]=>1001011=>[1,3,2,1,1]
[2,6,1,8,5,7,4,3]=>0101011=>[2,2,2,1,1]
[6,5,8,7,1,3,2,4]=>1011010=>[1,2,1,2,2]
[6,5,8,7,2,3,4,1]=>1011001=>[1,2,1,3,1]
[6,5,8,7,3,2,4,1]=>1011101=>[1,2,1,1,2,1]
[6,3,8,4,5,2,7,1]=>1010101=>[1,2,2,2,1]
[3,1,6,8,5,7,2,4]=>1001010=>[1,3,2,2]
[2,1,6,8,5,3,7,4]=>1001101=>[1,3,1,2,1]
[3,1,6,8,5,4,2,7]=>1001110=>[1,3,1,1,2]
[3,2,6,8,5,4,7,1]=>1001101=>[1,3,1,2,1]
[4,1,8,5,2,6,3,7]=>1011010=>[1,2,1,2,2]
[3,1,6,8,5,2,4,7]=>1001100=>[1,3,1,3]
[6,2,8,4,5,1,3,7]=>1010100=>[1,2,2,3]
[6,5,8,7,4,1,2,3]=>1011100=>[1,2,1,1,3]
[6,5,8,7,4,2,1,3]=>1011110=>[1,2,1,1,1,2]
[6,5,8,7,2,4,1,3]=>1011010=>[1,2,1,2,2]
[6,2,8,4,5,7,1,3]=>1010010=>[1,2,3,2]
[6,1,8,4,5,7,3,2]=>1010011=>[1,2,3,1,1]
[4,2,7,3,5,8,6,1]=>1010011=>[1,2,3,1,1]
[3,6,2,4,8,5,7,1]=>0100101=>[2,3,2,1]
[2,7,5,4,3,8,6,1]=>0111011=>[2,1,1,2,1,1]
[3,5,1,8,4,7,6,2]=>0101011=>[2,2,2,1,1]
[2,4,8,3,7,6,5,1]=>0010111=>[3,2,1,1,1]
[3,6,8,5,2,4,7,1]=>0011001=>[3,1,3,1]
[2,6,8,5,4,3,7,1]=>0011101=>[3,1,1,2,1]
[3,6,8,2,5,4,7,1]=>0010101=>[3,2,2,1]
[4,6,8,3,2,5,7,1]=>0011001=>[3,1,3,1]
[4,6,2,8,3,5,7,1]=>0101001=>[2,2,3,1]
[3,6,1,8,5,7,4,2]=>0101011=>[2,2,2,1,1]
[4,6,3,8,7,2,5,1]=>0101101=>[2,2,1,2,1]
[3,5,8,2,7,4,6,1]=>0010101=>[3,2,2,1]
[2,4,8,7,3,6,5,1]=>0011011=>[3,1,2,1,1]
[2,5,8,7,4,3,6,1]=>0011101=>[3,1,1,2,1]
[2,4,8,7,6,3,5,1]=>0011101=>[3,1,1,2,1]
[4,7,2,5,6,3,1,8]=>0100110=>[2,3,1,2]
[6,1,2,8,7,3,4,5]=>1001100=>[1,3,1,3]
[4,1,3,5,7,8,2,6]=>1000010=>[1,5,2]
[6,1,5,8,4,3,2,7]=>1001110=>[1,3,1,1,2]
[2,3,7,8,5,1,6,4]=>0001101=>[4,1,2,1]
[8,1,3,2,5,6,4,7]=>1010010=>[1,2,3,2]
[3,2,5,8,4,7,1,6]=>1001010=>[1,3,2,2]
[8,6,4,1,5,2,3,7]=>1110100=>[1,1,1,2,3]
[2,5,8,1,3,4,7,6]=>0010001=>[3,4,1]
[3,5,1,8,7,4,2,6]=>0101110=>[2,2,1,1,2]
[4,6,1,3,8,2,7,5]=>0100101=>[2,3,2,1]
[6,2,1,8,5,7,4,3]=>1101011=>[1,1,2,2,1,1]
[5,4,7,1,3,8,6,2]=>1010011=>[1,2,3,1,1]
[6,5,7,8,1,3,4,2]=>1001001=>[1,3,3,1]
[4,8,1,2,7,6,5,3]=>0100111=>[2,3,1,1,1]
[3,7,4,8,5,2,6,1]=>0101101=>[2,2,1,2,1]
[8,1,2,6,5,3,4,7]=>1001100=>[1,3,1,3]
[3,4,2,8,6,7,5,1]=>0101011=>[2,2,2,1,1]
[3,7,8,6,1,4,2,5]=>0011010=>[3,1,2,2]
[3,6,1,5,2,7,8,4]=>0101001=>[2,2,3,1]
[6,2,8,4,7,1,3,5]=>1010100=>[1,2,2,3]
[1,8,4,3,7,6,2,5]=>0110110=>[2,1,2,1,2]
[4,3,8,7,1,2,6,5]=>1011001=>[1,2,1,3,1]
[1,8,3,6,7,2,4,5]=>0100100=>[2,3,3]
[1,8,4,5,7,6,2,3]=>0100110=>[2,3,1,2]
[4,3,8,5,7,1,6,2]=>1010101=>[1,2,2,2,1]
[6,3,4,8,7,2,1,5]=>1001110=>[1,3,1,1,2]
[5,3,8,4,7,1,6,2]=>1010101=>[1,2,2,2,1]
[5,2,8,7,1,4,6,3]=>1011001=>[1,2,1,3,1]
[3,2,8,7,1,6,4,5]=>1011010=>[1,2,1,2,2]
[2,7,8,3,1,6,4,5]=>0011010=>[3,1,2,2]
[3,5,8,7,4,1,6,2]=>0011101=>[3,1,1,2,1]
[7,4,6,8,3,5,1,2]=>1001010=>[1,3,2,2]
[7,2,8,4,1,3,6,5]=>1011001=>[1,2,1,3,1]
[2,7,8,1,3,6,4,5]=>0010010=>[3,3,2]
[2,7,8,1,5,4,6,3]=>0010101=>[3,2,2,1]
[2,7,8,1,4,5,6,3]=>0010001=>[3,4,1]
[3,6,7,8,2,4,1,5]=>0001010=>[4,2,2]
[4,5,7,8,6,3,1,2]=>0001110=>[4,1,1,2]
[5,4,6,8,7,3,1,2]=>1001110=>[1,3,1,1,2]
[4,5,8,6,7,1,3,2]=>0010101=>[3,2,2,1]
[5,7,6,8,2,1,3,4]=>0101100=>[2,2,1,3]
[3,7,6,8,2,4,1,5]=>0101010=>[2,2,2,2]
[5,4,7,8,6,3,1,2]=>1001110=>[1,3,1,1,2]
[3,6,7,8,2,1,4,5]=>0001100=>[4,1,3]
[4,5,6,8,7,3,1,2]=>0001110=>[4,1,1,2]
[4,2,5,3,7,8,6,1]=>1010011=>[1,2,3,1,1]
[5,3,6,2,4,1,8,7]=>1010101=>[1,2,2,2,1]
[7,8,6,2,3,5,4,1]=>0110011=>[2,1,3,1,1]
[5,8,2,6,3,7,4,1]=>0101011=>[2,2,2,1,1]
[4,8,2,3,7,5,6,1]=>0100101=>[2,3,2,1]
[7,5,6,2,3,8,4,1]=>1010011=>[1,2,3,1,1]
[2,7,5,6,4,3,8,1]=>0101101=>[2,2,1,2,1]
[2,8,4,3,7,5,6,1]=>0110101=>[2,1,2,2,1]
[2,7,5,6,3,8,4,1]=>0101011=>[2,2,2,1,1]
[7,6,3,8,5,4,2,1]=>1101111=>[1,1,2,1,1,1,1]
[3,8,5,7,6,4,2,1]=>0101111=>[2,2,1,1,1,1]
[7,8,6,3,5,4,2,1]=>0110111=>[2,1,2,1,1,1]
[2,7,6,3,8,5,4,1]=>0110111=>[2,1,2,1,1,1]
[4,2,8,5,3,7,6,1]=>1011011=>[1,2,1,2,1,1]
[7,4,2,5,6,3,8,1]=>1100101=>[1,1,3,2,1]
[6,2,7,5,3,8,4,1]=>1011011=>[1,2,1,2,1,1]
[2,4,8,3,7,5,6,1]=>0010101=>[3,2,2,1]
[4,8,3,7,5,6,2,1]=>0101011=>[2,2,2,1,1]
[6,2,5,8,3,7,4,1]=>1001011=>[1,3,2,1,1]
[7,6,2,5,3,8,4,1]=>1101011=>[1,1,2,2,1,1]
[4,7,3,8,2,5,6,1]=>0101001=>[2,2,3,1]
[8,2,5,6,3,7,4,1]=>1001011=>[1,3,2,1,1]
[4,5,3,7,1,2,6,8]=>0101000=>[2,2,4]
[6,7,2,8,4,3,1,5]=>0101110=>[2,2,1,1,2]
[6,7,3,2,8,4,1,5]=>0110110=>[2,1,2,1,2]
[4,5,8,1,3,2,6,7]=>0010100=>[3,2,3]
[4,5,8,1,3,7,2,6]=>0010010=>[3,3,2]
[2,6,7,4,3,8,1,5]=>0011010=>[3,1,2,2]
[3,7,6,4,5,8,1,2]=>0110010=>[2,1,3,2]
[5,7,2,8,3,4,6,1]=>0101001=>[2,2,3,1]
[3,1,5,8,6,4,7,2]=>1001101=>[1,3,1,2,1]
[3,6,2,8,7,4,5,1]=>0101101=>[2,2,1,2,1]
[3,6,2,8,4,7,5,1]=>0101011=>[2,2,2,1,1]
[8,3,5,1,6,4,2,7]=>1010110=>[1,2,2,1,2]
[5,7,8,3,4,6,2,1]=>0010011=>[3,3,1,1]
[3,1,5,8,6,2,4,7]=>1001100=>[1,3,1,3]
[1,5,8,6,3,4,2,7]=>0011010=>[3,1,2,2]
[3,7,8,5,2,6,4,1]=>0011011=>[3,1,2,1,1]
[5,3,7,8,4,2,6,1]=>1001101=>[1,3,1,2,1]
[5,1,6,4,3,8,7,2]=>1011011=>[1,2,1,2,1,1]
[4,7,1,3,2,5,6,8]=>0101000=>[2,2,4]
[4,7,6,8,3,1,5,2]=>0101101=>[2,2,1,2,1]
[5,4,8,6,1,7,3,2]=>1011011=>[1,2,1,2,1,1]
[3,5,4,7,1,8,6,2]=>0101011=>[2,2,2,1,1]
[1,8,5,4,2,3,6,7]=>0111000=>[2,1,1,4]
[7,1,5,4,2,3,6,8]=>1011000=>[1,2,1,4]
[7,1,3,6,4,5,2,8]=>1001010=>[1,3,2,2]
[6,1,3,8,4,5,2,7]=>1001010=>[1,3,2,2]
[5,8,6,3,1,2,7,4]=>0111001=>[2,1,1,3,1]
[5,8,2,7,1,3,6,4]=>0101001=>[2,2,3,1]
[2,6,5,4,1,3,7,8]=>0111000=>[2,1,1,4]
[4,1,5,7,6,3,2,8]=>1001110=>[1,3,1,1,2]
[7,6,3,2,8,5,1,4]=>1110110=>[1,1,1,2,1,2]
[5,3,8,2,7,1,6,4]=>1010101=>[1,2,2,2,1]
[6,3,4,2,1,8,7,5]=>1011011=>[1,2,1,2,1,1]
[4,5,1,7,6,3,2,8]=>0101110=>[2,2,1,1,2]
[1,5,3,7,4,2,6,8]=>0101100=>[2,2,1,3]
[1,2,7,4,3,8,6,5]=>0011011=>[3,1,2,1,1]
[1,5,4,2,3,8,7,6]=>0110011=>[2,1,3,1,1]
[1,5,4,2,3,8,6,7]=>0110010=>[2,1,3,2]
[1,5,3,2,4,6,7,8]=>0110000=>[2,1,5]
[1,5,4,2,3,7,8,6]=>0110001=>[2,1,4,1]
[3,6,5,2,4,1,7,8]=>0110100=>[2,1,2,3]
[4,6,7,2,5,1,8,3]=>0010101=>[3,2,2,1]
[3,6,2,5,1,7,8,4]=>0101001=>[2,2,3,1]
[3,4,2,7,8,6,1,5]=>0100110=>[2,3,1,2]
[3,4,2,7,8,1,5,6]=>0100100=>[2,3,3]
[3,8,5,2,4,7,1,6]=>0110010=>[2,1,3,2]
[6,4,3,2,8,1,7,5]=>1110101=>[1,1,1,2,2,1]
[6,2,4,3,8,1,7,5]=>1010101=>[1,2,2,2,1]
[8,7,3,6,2,1,5,4]=>1101101=>[1,1,2,1,2,1]
[3,7,5,4,6,1,2,8]=>0110100=>[2,1,2,3]
[5,3,4,7,6,8,1,2]=>1001010=>[1,3,2,2]
[5,3,7,4,6,1,2,8]=>1010100=>[1,2,2,3]
[7,3,5,4,6,1,2,8]=>1010100=>[1,2,2,3]
[7,8,3,5,4,1,2,6]=>0101100=>[2,2,1,3]
[7,3,5,4,1,2,6,8]=>1011000=>[1,2,1,4]
[5,7,6,3,1,2,4,8]=>0111000=>[2,1,1,4]
[5,7,6,3,4,1,2,8]=>0110100=>[2,1,2,3]
[7,5,6,8,1,3,2,4]=>1001010=>[1,3,2,2]
[3,5,4,1,2,7,6,8]=>0110010=>[2,1,3,2]
[5,7,6,1,3,2,4,8]=>0110100=>[2,1,2,3]
[3,5,4,1,7,2,6,8]=>0110100=>[2,1,2,3]
[5,3,4,1,2,7,6,8]=>1010010=>[1,2,3,2]
[7,8,3,1,2,5,4,6]=>0110010=>[2,1,3,2]
[7,8,5,1,3,2,4,6]=>0110100=>[2,1,2,3]
[7,5,6,1,3,2,4,8]=>1010100=>[1,2,2,3]
[7,1,3,8,2,5,4,6]=>1001010=>[1,3,2,2]
[5,1,3,7,6,2,4,8]=>1001100=>[1,3,1,3]
[6,7,1,8,3,4,5,2]=>0101001=>[2,2,3,1]
[3,7,1,6,8,4,5,2]=>0100101=>[2,3,2,1]
[8,7,1,5,3,2,6,4]=>1101101=>[1,1,2,1,2,1]
[3,7,1,6,5,2,8,4]=>0101101=>[2,2,1,2,1]
[8,6,7,2,5,3,1,4]=>1010110=>[1,2,2,1,2]
[1,8,2,6,5,3,4,7]=>0101100=>[2,2,1,3]
[8,6,1,5,2,3,4,7]=>1101000=>[1,1,2,4]
[8,5,1,6,2,3,4,7]=>1101000=>[1,1,2,4]
[8,1,4,2,3,5,7,6]=>1010001=>[1,2,4,1]
[1,7,8,2,5,3,4,6]=>0010100=>[3,2,3]
[2,7,8,4,1,3,5,6]=>0011000=>[3,1,4]
[6,8,1,2,3,7,4,5]=>0100010=>[2,4,2]
[1,2,8,6,4,5,3,7]=>0011010=>[3,1,2,2]
[1,5,8,7,6,3,4,2]=>0011101=>[3,1,1,2,1]
[1,2,7,8,4,3,5,6]=>0001100=>[4,1,3]
[1,5,7,8,4,2,3,6]=>0001100=>[4,1,3]
[1,6,8,5,4,2,3,7]=>0011100=>[3,1,1,3]
[1,2,3,7,5,4,6,8]=>0001100=>[4,1,3]
[4,6,5,2,1,7,8,3]=>0111001=>[2,1,1,3,1]
[4,6,1,7,5,8,3,2]=>0101011=>[2,2,2,1,1]
[3,5,6,2,1,4,7,8]=>0011000=>[3,1,4]
[4,3,6,5,1,7,8,2]=>1011001=>[1,2,1,3,1]
[4,6,5,3,1,7,8,2]=>0111001=>[2,1,1,3,1]
[5,1,3,4,8,2,6,7]=>1000100=>[1,4,3]
[5,8,1,4,2,3,6,7]=>0101000=>[2,2,4]
[4,3,1,8,5,2,6,7]=>1101100=>[1,1,2,1,3]
[4,5,8,2,3,1,6,7]=>0010100=>[3,2,3]
[3,5,4,8,1,7,2,6]=>0101010=>[2,2,2,2]
[5,3,6,8,1,4,7,2]=>1001001=>[1,3,3,1]
[5,1,6,8,3,4,7,2]=>1001001=>[1,3,3,1]
[3,5,1,8,6,4,7,2]=>0101101=>[2,2,1,2,1]
[6,4,8,1,5,7,2,3]=>1010010=>[1,2,3,2]
[4,7,2,8,3,1,6,5]=>0101101=>[2,2,1,2,1]
[1,2,5,6,8,3,7,4]=>0000101=>[5,2,1]
[5,1,6,8,7,2,3,4]=>1001100=>[1,3,1,3]
[1,5,6,8,3,7,2,4]=>0001010=>[4,2,2]
[5,6,8,1,2,3,7,4]=>0010001=>[3,4,1]
[2,8,1,3,5,7,4,6]=>0100010=>[2,4,2]
[7,4,8,1,5,2,6,3]=>1010101=>[1,2,2,2,1]
[8,3,2,1,6,5,7,4]=>1110101=>[1,1,1,2,2,1]
[4,1,5,6,8,7,2,3]=>1000110=>[1,4,1,2]
[1,2,5,6,8,4,7,3]=>0000101=>[5,2,1]
[1,5,6,8,4,7,2,3]=>0001010=>[4,2,2]
[6,8,1,4,5,7,2,3]=>0100010=>[2,4,2]
[4,3,5,1,8,6,7,2]=>1010101=>[1,2,2,2,1]
[1,3,5,6,8,4,7,2]=>0000101=>[5,2,1]
[5,6,8,1,3,4,7,2]=>0010001=>[3,4,1]
[5,6,8,2,3,4,7,1]=>0010001=>[3,4,1]
[5,7,8,3,2,6,1,4]=>0011010=>[3,1,2,2]
[7,5,8,6,4,1,3,2]=>1011101=>[1,2,1,1,2,1]
[5,1,8,6,4,2,7,3]=>1011101=>[1,2,1,1,2,1]
[2,7,6,3,8,5,1,4]=>0110110=>[2,1,2,1,2]
[2,3,1,8,4,6,5,7]=>0101010=>[2,2,2,2]
[2,3,1,7,6,8,4,5]=>0101010=>[2,2,2,2]
[2,3,1,8,4,6,7,5]=>0101001=>[2,2,3,1]
[2,7,4,1,3,6,8,5]=>0110001=>[2,1,4,1]
[6,3,2,8,1,7,5,4]=>1101011=>[1,1,2,2,1,1]
[2,6,8,7,1,3,5,4]=>0011001=>[3,1,3,1]
[3,7,6,1,4,5,2,8]=>0110010=>[2,1,3,2]
[4,1,6,2,7,5,3,8]=>1010110=>[1,2,2,1,2]
[7,6,2,5,3,1,4,8]=>1101100=>[1,1,2,1,3]
[4,3,1,7,6,2,5,8]=>1101100=>[1,1,2,1,3]
[4,5,3,1,2,8,6,7]=>0110010=>[2,1,3,2]
[2,4,5,3,1,8,6,7]=>0011010=>[3,1,2,2]
[5,7,6,2,3,1,4,8]=>0110100=>[2,1,2,3]
[4,1,3,7,5,2,6,8]=>1001100=>[1,3,1,3]
[4,1,6,3,2,7,5,8]=>1011010=>[1,2,1,2,2]
[2,7,5,4,1,3,6,8]=>0111000=>[2,1,1,4]
[7,5,4,1,3,2,6,8]=>1110100=>[1,1,1,2,3]
[2,4,8,5,6,3,1,7]=>0010110=>[3,2,1,2]
[2,5,7,4,1,3,6,8]=>0011000=>[3,1,4]
[5,7,4,1,3,2,6,8]=>0110100=>[2,1,2,3]
[6,2,4,5,7,3,1,8]=>1000110=>[1,4,1,2]
[2,6,8,4,5,3,1,7]=>0010110=>[3,2,1,2]
[2,5,3,8,4,1,6,7]=>0101100=>[2,2,1,3]
[5,2,3,7,4,1,6,8]=>1001100=>[1,3,1,3]
[4,5,1,6,3,2,7,8]=>0101100=>[2,2,1,3]
[5,1,6,3,2,4,7,8]=>1011000=>[1,2,1,4]
[4,2,5,1,6,3,7,8]=>1010100=>[1,2,2,3]
[5,1,6,2,4,3,7,8]=>1010100=>[1,2,2,3]
[4,3,5,1,6,2,7,8]=>1010100=>[1,2,2,3]
[6,2,1,7,5,8,4,3]=>1101011=>[1,1,2,2,1,1]
[1,5,7,8,6,4,2,3]=>0001110=>[4,1,1,2]
[1,6,4,8,5,3,7,2]=>0101101=>[2,2,1,2,1]
[1,6,5,3,4,7,8,2]=>0110001=>[2,1,4,1]
[4,2,6,7,8,1,3,5]=>1000100=>[1,4,3]
[4,5,1,7,6,3,8,2]=>0101101=>[2,2,1,2,1]
[4,6,5,1,3,7,8,2]=>0110001=>[2,1,4,1]
[5,2,1,7,6,4,8,3]=>1101101=>[1,1,2,1,2,1]
[6,8,5,2,7,3,1,4]=>0110110=>[2,1,2,1,2]
[6,1,2,4,3,7,8,5]=>1001001=>[1,3,3,1]
[8,1,5,4,2,3,6,7]=>1011000=>[1,2,1,4]
[7,1,2,4,6,3,8,5]=>1000101=>[1,4,2,1]
[7,1,2,6,5,3,8,4]=>1001101=>[1,3,1,2,1]
[7,5,6,1,2,4,8,3]=>1010001=>[1,2,4,1]
[7,1,4,5,2,3,6,8]=>1001000=>[1,3,4]
[6,1,4,8,7,2,3,5]=>1001100=>[1,3,1,3]
[6,1,8,5,7,2,3,4]=>1010100=>[1,2,2,3]
[1,6,7,5,8,3,4,2]=>0010101=>[3,2,2,1]
[6,1,7,5,8,2,3,4]=>1010100=>[1,2,2,3]
[6,1,4,7,8,2,3,5]=>1000100=>[1,4,3]
[5,8,6,1,2,4,7,3]=>0110001=>[2,1,4,1]
[1,6,8,7,5,3,4,2]=>0011101=>[3,1,1,2,1]
[6,8,7,5,1,2,4,3]=>0111001=>[2,1,1,3,1]
[6,1,8,7,5,2,3,4]=>1011100=>[1,2,1,1,3]
[8,3,1,2,4,6,5,7]=>1100010=>[1,1,4,2]
[8,3,1,2,4,5,7,6]=>1100001=>[1,1,5,1]
[6,3,1,2,4,7,5,8]=>1100010=>[1,1,4,2]
[6,7,1,4,2,3,5,8]=>0101000=>[2,2,4]
[6,1,7,4,8,2,3,5]=>1010100=>[1,2,2,3]
[6,7,8,5,1,2,4,3]=>0011001=>[3,1,3,1]
[4,6,8,2,3,5,1,7]=>0010010=>[3,3,2]
[6,8,2,1,3,5,4,7]=>0110010=>[2,1,3,2]
[3,5,1,6,4,8,2,7]=>0101010=>[2,2,2,2]
[3,5,8,6,2,1,4,7]=>0011100=>[3,1,1,3]
[2,4,8,5,6,1,3,7]=>0010100=>[3,2,3]
[5,3,8,4,2,7,6,1]=>1011011=>[1,2,1,2,1,1]
[2,8,5,3,1,4,7,6]=>0111001=>[2,1,1,3,1]
[3,7,8,5,1,4,2,6]=>0011010=>[3,1,2,2]
[1,7,8,4,6,3,2,5]=>0010110=>[3,2,1,2]
[8,7,2,4,6,3,1,5]=>1100110=>[1,1,3,1,2]
[7,8,3,4,6,5,2,1]=>0100111=>[2,3,1,1,1]
[8,7,3,6,5,2,4,1]=>1101101=>[1,1,2,1,2,1]
[3,1,2,8,6,5,7,4]=>1001101=>[1,3,1,2,1]
[3,8,2,7,5,4,6,1]=>0101101=>[2,2,1,2,1]
[8,7,1,4,5,3,6,2]=>1100101=>[1,1,3,2,1]
[2,8,7,4,6,3,5,1]=>0110101=>[2,1,2,2,1]
[2,8,7,4,6,3,1,5]=>0110110=>[2,1,2,1,2]
[8,3,4,1,2,5,7,6]=>1010001=>[1,2,4,1]
[8,4,1,3,2,5,7,6]=>1101001=>[1,1,2,3,1]
[7,4,8,2,3,5,1,6]=>1010010=>[1,2,3,2]
[7,3,8,6,2,1,4,5]=>1011100=>[1,2,1,1,3]
[7,2,8,4,6,5,1,3]=>1010110=>[1,2,2,1,2]
[5,8,6,4,7,2,3,1]=>0110101=>[2,1,2,2,1]
[4,7,2,6,5,8,3,1]=>0101011=>[2,2,2,1,1]
[3,6,8,5,7,4,2,1]=>0010111=>[3,2,1,1,1]
[6,7,5,2,4,8,3,1]=>0110011=>[2,1,3,1,1]
[8,7,2,4,6,1,5,3]=>1100101=>[1,1,3,2,1]
[8,1,2,7,5,6,3,4]=>1001010=>[1,3,2,2]
[8,2,7,3,4,6,1,5]=>1010010=>[1,2,3,2]
[6,7,5,4,8,1,3,2]=>0110101=>[2,1,2,2,1]
[2,5,1,4,7,3,6,8]=>0100100=>[2,3,3]
[3,1,6,5,7,2,4,8]=>1010100=>[1,2,2,3]
[2,5,7,1,6,3,4,8]=>0010100=>[3,2,3]
[2,5,7,1,6,3,8,4]=>0010101=>[3,2,2,1]
[2,6,1,5,7,4,3,8]=>0100110=>[2,3,1,2]
[3,1,6,5,2,4,7,8]=>1011000=>[1,2,1,4]
[3,6,5,1,4,2,7,8]=>0110100=>[2,1,2,3]
[3,5,6,2,8,1,7,4]=>0010101=>[3,2,2,1]
[3,6,5,1,7,2,4,8]=>0110100=>[2,1,2,3]
[3,6,5,2,1,4,7,8]=>0111000=>[2,1,1,4]
[4,5,2,7,6,1,3,8]=>0101100=>[2,2,1,3]
[4,6,5,3,1,2,7,8]=>0111000=>[2,1,1,4]
[5,4,1,6,3,7,2,8]=>1101010=>[1,1,2,2,2]
[5,4,2,6,3,7,8,1]=>1101001=>[1,1,2,3,1]
[3,6,5,7,1,4,2,8]=>0101010=>[2,2,2,2]
[3,6,5,1,4,7,2,8]=>0110010=>[2,1,3,2]
[4,3,6,5,7,1,2,8]=>1010100=>[1,2,2,3]
[4,2,6,5,1,3,7,8]=>1011000=>[1,2,1,4]
[4,1,6,5,3,7,8,2]=>1011001=>[1,2,1,3,1]
[4,1,5,7,6,3,8,2]=>1001101=>[1,3,1,2,1]
[4,2,5,7,6,1,3,8]=>1001100=>[1,3,1,3]
[3,4,7,6,1,2,5,8]=>0011000=>[3,1,4]
[3,4,7,6,8,2,5,1]=>0010101=>[3,2,2,1]
[4,2,5,7,6,3,8,1]=>1001101=>[1,3,1,2,1]
[4,1,6,5,2,7,3,8]=>1011010=>[1,2,1,2,2]
[4,2,6,5,7,3,1,8]=>1010110=>[1,2,2,1,2]
[3,6,5,7,2,1,4,8]=>0101100=>[2,2,1,3]
[3,5,7,6,2,4,1,8]=>0011010=>[3,1,2,2]
[5,4,2,6,3,7,1,8]=>1101010=>[1,1,2,2,2]
[4,6,5,2,7,3,1,8]=>0110110=>[2,1,2,1,2]
[4,5,2,7,6,3,8,1]=>0101101=>[2,2,1,2,1]
[4,6,5,2,1,7,3,8]=>0111010=>[2,1,1,2,2]
[3,5,8,2,1,4,6,7]=>0011000=>[3,1,4]
[3,5,8,2,4,6,7,1]=>0010001=>[3,4,1]
[5,3,8,2,1,4,6,7]=>1011000=>[1,2,1,4]
[5,3,1,8,2,4,6,7]=>1101000=>[1,1,2,4]
[1,5,3,8,2,4,6,7]=>0101000=>[2,2,4]
[1,5,8,4,2,3,6,7]=>0011000=>[3,1,4]
[5,8,2,1,4,3,6,7]=>0110100=>[2,1,2,3]
[5,8,2,4,6,3,1,7]=>0100110=>[2,3,1,2]
[5,8,2,4,3,6,1,7]=>0101010=>[2,2,2,2]
[5,8,1,4,6,2,3,7]=>0100100=>[2,3,3]
[1,5,8,4,6,7,2,3]=>0010010=>[3,3,2]
[5,1,8,4,6,7,2,3]=>1010010=>[1,2,3,2]
[5,8,2,4,6,3,7,1]=>0100101=>[2,3,2,1]
[3,8,4,6,7,2,1,5]=>0100110=>[2,3,1,2]
[3,8,4,6,7,2,5,1]=>0100101=>[2,3,2,1]
[8,4,3,6,7,2,5,1]=>1100101=>[1,1,3,2,1]
[8,4,3,6,7,2,1,5]=>1100110=>[1,1,3,1,2]
[8,6,2,4,5,3,7,1]=>1100101=>[1,1,3,2,1]
[8,6,4,1,5,7,2,3]=>1110010=>[1,1,1,3,2]
[1,8,6,4,5,7,2,3]=>0110010=>[2,1,3,2]
[8,1,6,4,5,2,3,7]=>1010100=>[1,2,2,3]
[8,6,2,4,5,3,1,7]=>1100110=>[1,1,3,1,2]
[1,8,6,4,2,3,5,7]=>0111000=>[2,1,1,4]
[3,8,1,6,2,4,5,7]=>0101000=>[2,2,4]
[1,3,8,6,2,4,5,7]=>0011000=>[3,1,4]
[3,8,6,2,1,4,5,7]=>0111000=>[2,1,1,4]
[3,8,6,2,4,1,5,7]=>0110100=>[2,1,2,3]
[3,8,6,2,4,5,7,1]=>0110001=>[2,1,4,1]
[8,3,6,2,4,5,1,7]=>1010010=>[1,2,3,2]
[1,8,3,6,2,4,5,7]=>0101000=>[2,2,4]
[8,1,3,6,2,4,5,7]=>1001000=>[1,3,4]
[8,3,6,7,2,1,4,5]=>1001100=>[1,3,1,3]
[2,5,8,4,6,1,7,3]=>0010101=>[3,2,2,1]
[3,8,6,7,2,1,4,5]=>0101100=>[2,2,1,3]
[3,1,8,6,7,2,4,5]=>1010100=>[1,2,2,3]
[8,2,6,4,5,1,7,3]=>1010101=>[1,2,2,2,1]
[8,4,6,1,7,2,5,3]=>1010101=>[1,2,2,2,1]
[1,8,4,6,7,5,2,3]=>0100110=>[2,3,1,2]
[8,1,4,6,7,5,2,3]=>1000110=>[1,4,1,2]
[8,4,6,1,3,7,2,5]=>1010010=>[1,2,3,2]
[8,1,4,6,3,7,2,5]=>1001010=>[1,3,2,2]
[8,4,1,6,3,7,2,5]=>1101010=>[1,1,2,2,2]
[8,2,4,6,1,7,5,3]=>1001011=>[1,3,2,1,1]
[8,4,6,2,3,7,5,1]=>1010011=>[1,2,3,1,1]
[8,4,7,3,1,6,2,5]=>1011010=>[1,2,1,2,2]
[8,4,7,2,1,3,6,5]=>1011001=>[1,2,1,3,1]
[8,4,2,1,5,3,7,6]=>1110101=>[1,1,1,2,2,1]
[8,2,1,4,7,3,6,5]=>1100101=>[1,1,3,2,1]
[3,2,1,7,4,5,8,6]=>1101001=>[1,1,2,3,1]
[2,8,4,1,7,5,3,6]=>0110110=>[2,1,2,1,2]
[2,6,8,5,1,7,4,3]=>0011011=>[3,1,2,1,1]
[4,7,3,1,8,6,2,5]=>0110110=>[2,1,2,1,2]
[2,1,5,8,7,3,6,4]=>1001101=>[1,3,1,2,1]
[3,2,1,6,7,4,8,5]=>1100101=>[1,1,3,2,1]
[4,3,1,7,8,5,2,6]=>1100110=>[1,1,3,1,2]
[5,6,8,2,4,3,7,1]=>0010101=>[3,2,2,1]
[5,8,2,6,4,3,7,1]=>0101101=>[2,2,1,2,1]
[2,8,5,3,6,4,7,1]=>0110101=>[2,1,2,2,1]
[1,2,8,6,4,7,3,5]=>0011010=>[3,1,2,2]
[4,2,7,8,3,5,6,1]=>1001001=>[1,3,3,1]
[2,8,3,7,1,4,6,5]=>0101001=>[2,2,3,1]
[2,8,7,1,5,3,6,4]=>0110101=>[2,1,2,2,1]
[3,8,4,2,7,6,5,1]=>0110111=>[2,1,2,1,1,1]
[3,8,4,2,5,1,7,6]=>0110101=>[2,1,2,2,1]
[4,8,3,2,7,5,6,1]=>0110101=>[2,1,2,2,1]
[3,2,4,8,7,5,6,1]=>1001101=>[1,3,1,2,1]
[3,5,2,6,4,8,1,7]=>0101010=>[2,2,2,2]
[2,6,8,1,5,3,4,7]=>0010100=>[3,2,3]
[8,1,5,2,4,6,3,7]=>1010010=>[1,2,3,2]
[3,8,1,6,4,5,2,7]=>0101010=>[2,2,2,2]
[8,1,3,6,5,4,2,7]=>1001110=>[1,3,1,1,2]
[7,4,3,6,2,1,8,5]=>1101101=>[1,1,2,1,2,1]
[1,2,4,8,6,3,7,5]=>0001101=>[4,1,2,1]
[7,2,1,5,3,4,8,6]=>1101001=>[1,1,2,3,1]
[5,7,2,3,1,4,8,6]=>0101001=>[2,2,3,1]
[7,1,5,2,4,6,8,3]=>1010001=>[1,2,4,1]
[8,4,2,7,3,5,6,1]=>1101001=>[1,1,2,3,1]
[1,8,6,4,7,5,3,2]=>0110111=>[2,1,2,1,1,1]
[7,4,1,5,8,6,3,2]=>1100111=>[1,1,3,1,1,1]
[8,6,3,2,7,4,1,5]=>1110110=>[1,1,1,2,1,2]
[4,5,8,7,3,1,2,6]=>0011100=>[3,1,1,3]
[1,3,8,7,6,4,2,5]=>0011110=>[3,1,1,1,2]
[8,6,4,7,5,1,2,3]=>1101100=>[1,1,2,1,3]
[2,8,5,1,7,4,6,3]=>0110101=>[2,1,2,2,1]
[1,8,6,4,7,5,2,3]=>0110110=>[2,1,2,1,2]
[2,7,4,6,3,8,5,1]=>0101011=>[2,2,2,1,1]
[1,2,8,6,4,7,5,3]=>0011011=>[3,1,2,1,1]
[8,6,2,1,5,7,3,4]=>1110010=>[1,1,1,3,2]
[1,6,5,4,3,8,2,7]=>0111010=>[2,1,1,2,2]
[6,4,2,1,5,7,3,8]=>1110010=>[1,1,1,3,2]
[3,1,5,8,7,2,4,6]=>1001100=>[1,3,1,3]
[3,2,5,7,8,4,1,6]=>1000110=>[1,4,1,2]
[3,2,5,7,8,4,6,1]=>1000101=>[1,4,2,1]
[5,3,7,4,2,6,8,1]=>1011001=>[1,2,1,3,1]
[5,3,7,4,2,6,1,8]=>1011010=>[1,2,1,2,2]
[5,2,8,4,3,1,6,7]=>1011100=>[1,2,1,1,3]
[5,1,8,4,3,2,6,7]=>1011100=>[1,2,1,1,3]
[5,2,7,4,3,6,1,8]=>1011010=>[1,2,1,2,2]
[5,2,7,4,3,6,8,1]=>1011001=>[1,2,1,3,1]
[5,3,7,4,1,6,8,2]=>1011001=>[1,2,1,3,1]
[3,1,5,7,8,4,2,6]=>1000110=>[1,4,1,2]
[1,2,8,6,4,5,7,3]=>0011001=>[3,1,3,1]
[6,2,3,7,4,1,8,5]=>1001101=>[1,3,1,2,1]
[5,2,7,4,1,3,8,6]=>1011001=>[1,2,1,3,1]
[6,2,3,7,4,8,5,1]=>1001011=>[1,3,2,1,1]
[6,2,3,7,4,8,1,5]=>1001010=>[1,3,2,2]
[6,1,3,7,4,2,8,5]=>1001101=>[1,3,1,2,1]
[6,2,3,7,4,5,1,8]=>1001010=>[1,3,2,2]
[6,2,3,7,4,5,8,1]=>1001001=>[1,3,3,1]
[6,1,3,7,4,5,8,2]=>1001001=>[1,3,3,1]
[1,2,8,6,4,3,5,7]=>0011100=>[3,1,1,3]
[6,1,3,7,4,5,2,8]=>1001010=>[1,3,2,2]
[1,8,6,3,5,4,2,7]=>0110110=>[2,1,2,1,2]
[1,8,2,7,5,3,4,6]=>0101100=>[2,2,1,3]
[2,5,4,1,8,6,7,3]=>0110101=>[2,1,2,2,1]
[1,8,5,3,2,6,7,4]=>0111001=>[2,1,1,3,1]
[6,3,8,2,4,1,7,5]=>1010101=>[1,2,2,2,1]
[5,1,7,8,2,4,3,6]=>1001010=>[1,3,2,2]
[5,3,2,4,8,1,7,6]=>1100101=>[1,1,3,2,1]
[5,3,2,4,8,1,6,7]=>1100100=>[1,1,3,3]
[5,3,2,4,7,1,8,6]=>1100101=>[1,1,3,2,1]
[4,8,1,7,3,5,6,2]=>0101001=>[2,2,3,1]
[5,3,2,4,6,8,1,7]=>1100010=>[1,1,4,2]
[7,6,4,2,8,3,1,5]=>1110110=>[1,1,1,2,1,2]
[1,2,6,4,7,3,5,8]=>0010100=>[3,2,3]
[8,5,2,4,3,7,1,6]=>1101010=>[1,1,2,2,2]
[7,5,4,1,3,6,8,2]=>1110001=>[1,1,1,4,1]
[4,2,5,7,8,6,3,1]=>1000111=>[1,4,1,1,1]
[6,7,2,4,5,1,8,3]=>0100101=>[2,3,2,1]
[5,2,7,8,3,6,1,4]=>1001010=>[1,3,2,2]
[8,2,3,4,7,1,5,6]=>1000100=>[1,4,3]
[2,4,7,8,1,3,6,5]=>0001001=>[4,3,1]
[5,2,8,3,1,4,7,6]=>1011001=>[1,2,1,3,1]
[8,7,2,5,1,4,3,6]=>1101010=>[1,1,2,2,2]
[8,3,5,1,2,4,7,6]=>1010001=>[1,2,4,1]
[8,6,5,1,7,4,2,3]=>1110110=>[1,1,1,2,1,2]
[8,3,6,5,4,1,2,7]=>1011100=>[1,2,1,1,3]
[8,7,4,5,1,2,6,3]=>1101001=>[1,1,2,3,1]
[3,4,8,2,1,7,6,5]=>0011011=>[3,1,2,1,1]
[8,3,5,2,7,4,6,1]=>1010101=>[1,2,2,2,1]
[8,3,1,7,5,6,2,4]=>1101010=>[1,1,2,2,2]
[8,4,1,7,5,2,6,3]=>1101101=>[1,1,2,1,2,1]
[8,3,4,2,7,5,6,1]=>1010101=>[1,2,2,2,1]
[8,3,2,7,5,6,1,4]=>1101010=>[1,1,2,2,2]
[8,4,2,7,5,3,1,6]=>1101110=>[1,1,2,1,1,2]
[8,2,6,5,7,1,3,4]=>1010100=>[1,2,2,3]
[8,4,3,7,5,1,2,6]=>1101100=>[1,1,2,1,3]
[8,5,7,6,4,3,1,2]=>1011110=>[1,2,1,1,1,2]
[8,5,7,6,4,1,2,3]=>1011100=>[1,2,1,1,3]
[8,2,4,7,1,5,6,3]=>1001001=>[1,3,3,1]
[8,4,7,6,5,2,1,3]=>1011110=>[1,2,1,1,1,2]
[8,3,1,4,7,6,2,5]=>1100110=>[1,1,3,1,2]
[1,5,2,6,8,3,7,4]=>0100101=>[2,3,2,1]
[7,2,8,4,1,3,5,6]=>1011000=>[1,2,1,4]
[6,7,8,5,2,1,4,3]=>0011101=>[3,1,1,2,1]
[1,6,2,7,8,4,3,5]=>0100110=>[2,3,1,2]
[4,3,8,6,5,2,7,1]=>1011101=>[1,2,1,1,2,1]
[2,3,8,6,5,1,7,4]=>0011101=>[3,1,1,2,1]
[7,3,2,6,1,4,8,5]=>1101001=>[1,1,2,3,1]
[3,2,5,6,8,4,1,7]=>1000110=>[1,4,1,2]
[2,6,8,1,5,4,3,7]=>0010110=>[3,2,1,2]
[8,4,7,1,2,5,3,6]=>1010010=>[1,2,3,2]
[8,5,6,7,2,1,4,3]=>1001101=>[1,3,1,2,1]
[8,5,6,7,3,1,4,2]=>1001101=>[1,3,1,2,1]
[1,8,3,2,5,4,6,7]=>0110100=>[2,1,2,3]
[5,1,7,3,2,8,4,6]=>1011010=>[1,2,1,2,2]
[8,2,5,3,1,7,4,6]=>1011010=>[1,2,1,2,2]
[1,4,8,5,3,2,6,7]=>0011100=>[3,1,1,3]
[5,8,3,1,4,2,6,7]=>0110100=>[2,1,2,3]
[1,5,4,8,2,3,6,7]=>0101000=>[2,2,4]
[1,5,4,8,2,3,7,6]=>0101001=>[2,2,3,1]
[5,7,8,1,3,2,4,6]=>0010100=>[3,2,3]
[8,2,7,5,1,4,6,3]=>1011001=>[1,2,1,3,1]
[8,2,4,1,6,7,3,5]=>1010010=>[1,2,3,2]
[8,7,3,6,2,4,1,5]=>1101010=>[1,1,2,2,2]
[1,7,4,8,3,6,2,5]=>0101010=>[2,2,2,2]
[7,8,6,1,3,5,4,2]=>0110011=>[2,1,3,1,1]
[1,7,5,8,4,3,2,6]=>0101110=>[2,2,1,1,2]
[6,3,1,2,7,8,5,4]=>1100011=>[1,1,4,1,1]
[7,1,8,5,3,4,2,6]=>1011010=>[1,2,1,2,2]
[1,2,7,8,3,5,6,4]=>0001001=>[4,3,1]
[8,2,7,5,3,4,1,6]=>1011010=>[1,2,1,2,2]
[6,3,1,2,8,7,5,4]=>1100111=>[1,1,3,1,1,1]
[8,4,7,2,6,3,1,5]=>1010110=>[1,2,2,1,2]
[8,2,4,7,6,3,1,5]=>1001110=>[1,3,1,1,2]
[7,6,3,4,2,1,8,5]=>1101101=>[1,1,2,1,2,1]
[8,2,4,6,3,7,1,5]=>1001010=>[1,3,2,2]
[3,4,5,8,1,7,2,6]=>0001010=>[4,2,2]
[8,6,3,4,7,2,1,5]=>1100110=>[1,1,3,1,2]
[4,3,8,6,7,5,1,2]=>1010110=>[1,2,2,1,2]
[4,5,6,2,7,8,3,1]=>0010011=>[3,3,1,1]
[4,5,6,2,7,1,8,3]=>0010101=>[3,2,2,1]
[4,5,6,2,1,7,3,8]=>0011010=>[3,1,2,2]
[4,5,6,1,7,8,3,2]=>0010011=>[3,3,1,1]
[4,5,1,6,7,8,3,2]=>0100011=>[2,4,1,1]
[4,5,1,6,7,3,8,2]=>0100101=>[2,3,2,1]
[4,5,1,6,7,3,2,8]=>0100110=>[2,3,1,2]
[4,5,6,1,7,3,2,8]=>0010110=>[3,2,1,2]
[8,6,4,3,7,2,1,5]=>1110110=>[1,1,1,2,1,2]
[5,8,1,4,3,2,7,6]=>0101101=>[2,2,1,2,1]
[1,6,4,3,8,2,7,5]=>0110101=>[2,1,2,2,1]
[7,8,1,4,3,2,5,6]=>0101100=>[2,2,1,3]
[1,7,8,4,5,3,6,2]=>0010101=>[3,2,2,1]
[2,7,6,3,4,1,8,5]=>0110101=>[2,1,2,2,1]
[8,1,7,4,3,5,6,2]=>1011001=>[1,2,1,3,1]
[7,1,8,4,5,3,6,2]=>1010101=>[1,2,2,2,1]
[4,3,1,8,6,5,7,2]=>1101101=>[1,1,2,1,2,1]
[4,3,2,7,5,1,8,6]=>1101101=>[1,1,2,1,2,1]
[5,2,3,7,4,1,8,6]=>1001101=>[1,3,1,2,1]
[2,1,7,4,3,6,8,5]=>1011001=>[1,2,1,3,1]
[7,1,2,4,5,6,8,3]=>1000001=>[1,6,1]
[2,8,7,1,4,5,6,3]=>0110001=>[2,1,4,1]
[8,7,1,3,4,5,6,2]=>1100001=>[1,1,5,1]
[7,8,1,3,4,5,6,2]=>0100001=>[2,5,1]
[1,7,2,5,4,6,8,3]=>0101001=>[2,2,3,1]
[2,5,3,8,1,6,7,4]=>0101001=>[2,2,3,1]
[1,6,4,2,5,7,8,3]=>0110001=>[2,1,4,1]
[8,5,3,1,4,6,7,2]=>1110001=>[1,1,1,4,1]
[6,5,3,4,1,7,8,2]=>1101001=>[1,1,2,3,1]
[5,6,3,4,1,7,8,2]=>0101001=>[2,2,3,1]
[2,5,3,1,4,7,8,6]=>0110001=>[2,1,4,1]
[2,6,1,4,3,7,8,5]=>0101001=>[2,2,3,1]
[6,8,2,3,1,5,7,4]=>0101001=>[2,2,3,1]
[6,1,3,4,2,7,8,5]=>1001001=>[1,3,3,1]
[4,3,1,5,2,7,8,6]=>1101001=>[1,1,2,3,1]
[5,2,3,1,4,7,8,6]=>1010001=>[1,2,4,1]
[7,2,1,3,5,6,8,4]=>1100001=>[1,1,5,1]
[5,2,4,7,8,6,3,1]=>1000111=>[1,4,1,1,1]
[8,4,2,7,6,1,5,3]=>1101101=>[1,1,2,1,2,1]
[5,3,7,6,1,8,4,2]=>1011011=>[1,2,1,2,1,1]
[8,6,4,1,2,5,3,7]=>1110010=>[1,1,1,3,2]
[8,6,1,4,2,5,7,3]=>1101001=>[1,1,2,3,1]
[8,6,4,1,2,5,7,3]=>1110001=>[1,1,1,4,1]
[8,6,1,4,7,2,5,3]=>1100101=>[1,1,3,2,1]
[4,8,6,2,3,1,5,7]=>0110100=>[2,1,2,3]
[2,5,3,7,6,4,8,1]=>0101101=>[2,2,1,2,1]
[3,1,5,7,6,4,2,8]=>1001110=>[1,3,1,1,2]
[3,1,6,5,4,7,2,8]=>1011010=>[1,2,1,2,2]
[2,5,6,8,3,4,7,1]=>0001001=>[4,3,1]
[4,1,3,6,5,2,7,8]=>1001100=>[1,3,1,3]
[3,6,2,4,5,7,1,8]=>0100010=>[2,4,2]
[3,6,2,5,4,7,1,8]=>0101010=>[2,2,2,2]
[3,5,1,7,6,4,2,8]=>0101110=>[2,2,1,1,2]
[3,6,1,4,5,7,2,8]=>0100010=>[2,4,2]
[4,3,1,6,5,2,7,8]=>1101100=>[1,1,2,1,3]
[4,1,2,6,5,3,7,8]=>1001100=>[1,3,1,3]
[3,6,4,2,5,7,1,8]=>0110010=>[2,1,3,2]
[4,2,6,3,5,1,7,8]=>1010100=>[1,2,2,3]
[3,4,6,8,7,1,2,5]=>0001100=>[4,1,3]
[3,4,7,6,5,1,2,8]=>0011100=>[3,1,1,3]
[4,5,2,7,1,3,6,8]=>0101000=>[2,2,4]
[4,6,1,2,5,3,7,8]=>0100100=>[2,3,3]
[2,5,4,8,3,7,6,1]=>0101011=>[2,2,2,1,1]
[1,3,6,2,5,8,7,4]=>0010011=>[3,3,1,1]
[1,3,5,8,6,4,7,2]=>0001101=>[4,1,2,1]
[5,8,7,1,4,6,3,2]=>0110011=>[2,1,3,1,1]
[6,2,5,1,3,4,8,7]=>1010001=>[1,2,4,1]
[2,6,5,1,3,4,8,7]=>0110001=>[2,1,4,1]
[4,6,5,1,2,7,3,8]=>0110010=>[2,1,3,2]
[5,6,4,1,2,7,3,8]=>0110010=>[2,1,3,2]
[8,1,5,6,2,4,3,7]=>1001010=>[1,3,2,2]
[6,4,5,1,2,7,3,8]=>1010010=>[1,2,3,2]
[5,4,6,1,3,2,7,8]=>1010100=>[1,2,2,3]
[5,7,1,4,3,2,6,8]=>0101100=>[2,2,1,3]
[2,6,4,1,3,7,5,8]=>0110010=>[2,1,3,2]
[6,3,2,5,7,4,8,1]=>1100101=>[1,1,3,2,1]
[5,7,3,8,1,2,4,6]=>0101000=>[2,2,4]
[4,5,2,7,6,3,1,8]=>0101110=>[2,2,1,1,2]
[4,5,2,1,7,6,3,8]=>0110110=>[2,1,2,1,2]
[5,4,1,6,7,2,8,3]=>1100101=>[1,1,3,2,1]
[4,1,6,5,2,7,8,3]=>1011001=>[1,2,1,3,1]
[5,4,6,2,7,8,3,1]=>1010011=>[1,2,3,1,1]
[3,5,2,6,7,8,4,1]=>0100011=>[2,4,1,1]
[6,3,2,5,1,7,8,4]=>1101001=>[1,1,2,3,1]
[4,6,3,7,8,2,1,5]=>0100110=>[2,3,1,2]
[5,6,7,1,8,4,2,3]=>0010110=>[3,2,1,2]
[5,6,7,2,8,4,1,3]=>0010110=>[3,2,1,2]
[1,7,8,4,6,5,2,3]=>0010110=>[3,2,1,2]
[6,4,1,8,7,2,5,3]=>1101101=>[1,1,2,1,2,1]
[3,7,2,8,6,5,1,4]=>0101110=>[2,2,1,1,2]
[2,7,8,1,6,5,3,4]=>0010110=>[3,2,1,2]
[2,5,8,1,7,6,3,4]=>0010110=>[3,2,1,2]
[2,8,4,7,6,3,1,5]=>0101110=>[2,2,1,1,2]
[4,5,8,7,1,6,2,3]=>0011010=>[3,1,2,2]
[6,4,8,7,2,1,5,3]=>1011101=>[1,2,1,1,2,1]
[3,2,8,7,6,4,1,5]=>1011110=>[1,2,1,1,1,2]
[2,4,5,8,1,7,6,3]=>0001011=>[4,2,1,1]
[2,6,8,1,4,3,7,5]=>0010101=>[3,2,2,1]
[4,1,8,2,6,7,3,5]=>1010010=>[1,2,3,2]
[8,1,7,3,5,2,4,6]=>1010100=>[1,2,2,3]
[8,1,3,2,7,6,4,5]=>1010110=>[1,2,2,1,2]
[7,5,8,1,6,2,3,4]=>1010100=>[1,2,2,3]
[6,7,5,3,2,8,4,1]=>0111011=>[2,1,1,2,1,1]
[6,2,5,3,8,1,4,7]=>1010100=>[1,2,2,3]
[7,6,1,3,5,2,4,8]=>1100100=>[1,1,3,3]
[6,2,4,5,3,8,1,7]=>1001010=>[1,3,2,2]
[6,1,5,4,7,2,3,8]=>1010100=>[1,2,2,3]
[1,2,5,4,7,8,3,6]=>0010010=>[3,3,2]
[3,6,2,4,7,8,5,1]=>0100011=>[2,4,1,1]
[1,8,5,4,6,7,2,3]=>0110010=>[2,1,3,2]
[1,3,5,4,8,7,2,6]=>0010110=>[3,2,1,2]
[1,6,2,4,8,3,7,5]=>0100101=>[2,3,2,1]
[1,7,3,2,4,6,5,8]=>0110010=>[2,1,3,2]
[8,1,3,2,6,5,7,4]=>1010101=>[1,2,2,2,1]
[1,5,7,3,2,6,4,8]=>0011010=>[3,1,2,2]
[5,1,3,7,2,6,4,8]=>1001010=>[1,3,2,2]
[1,7,8,5,4,2,6,3]=>0011101=>[3,1,1,2,1]
[8,1,7,5,4,2,6,3]=>1011101=>[1,2,1,1,2,1]
[1,5,2,8,6,4,7,3]=>0101101=>[2,2,1,2,1]
[1,6,5,2,7,4,8,3]=>0110101=>[2,1,2,2,1]
[5,1,6,7,4,2,8,3]=>1001101=>[1,3,1,2,1]
[1,5,4,2,8,6,7,3]=>0110101=>[2,1,2,2,1]
[1,6,3,5,2,7,8,4]=>0101001=>[2,2,3,1]
[5,8,4,1,6,2,7,3]=>0110101=>[2,1,2,2,1]
[3,1,2,6,8,7,5,4]=>1000111=>[1,4,1,1,1]
[6,4,8,2,3,5,7,1]=>1010001=>[1,2,4,1]
[4,6,8,2,5,7,1,3]=>0010010=>[3,3,2]
[6,4,8,2,5,7,1,3]=>1010010=>[1,2,3,2]
[6,8,2,4,7,3,5,1]=>0100101=>[2,3,2,1]
[8,6,2,4,5,1,3,7]=>1100100=>[1,1,3,3]
[6,8,4,2,7,1,3,5]=>0110100=>[2,1,2,3]
[6,8,2,4,1,7,3,5]=>0101010=>[2,2,2,2]
[2,5,4,7,6,1,3,8]=>0101100=>[2,2,1,3]
[5,2,3,7,6,1,4,8]=>1001100=>[1,3,1,3]
[4,2,3,7,6,1,5,8]=>1001100=>[1,3,1,3]
[4,2,7,3,5,1,6,8]=>1010100=>[1,2,2,3]
[5,6,2,3,8,4,7,1]=>0100101=>[2,3,2,1]
[5,6,2,3,1,7,8,4]=>0101001=>[2,2,3,1]
[5,7,2,3,4,1,6,8]=>0100100=>[2,3,3]
[6,2,7,3,5,1,4,8]=>1010100=>[1,2,2,3]
[7,2,6,3,5,1,4,8]=>1010100=>[1,2,2,3]
[6,5,2,3,1,7,8,4]=>1101001=>[1,1,2,3,1]
[6,5,2,3,8,4,7,1]=>1100101=>[1,1,3,2,1]
[7,5,2,1,4,6,8,3]=>1110001=>[1,1,1,4,1]
[8,5,2,1,4,6,7,3]=>1110001=>[1,1,1,4,1]
[8,5,2,3,1,6,4,7]=>1101010=>[1,1,2,2,2]
[8,6,2,3,1,5,4,7]=>1101010=>[1,1,2,2,2]
[8,2,6,3,1,7,4,5]=>1011010=>[1,2,1,2,2]
[1,6,3,4,2,7,5,8]=>0101010=>[2,2,2,2]
[8,5,2,7,3,4,6,1]=>1101001=>[1,1,2,3,1]
[1,7,2,4,5,6,8,3]=>0100001=>[2,5,1]
[1,8,3,2,5,6,4,7]=>0110010=>[2,1,3,2]
[8,6,1,3,4,5,7,2]=>1100001=>[1,1,5,1]
[6,8,1,3,4,5,7,2]=>0100001=>[2,5,1]
[7,2,8,1,4,6,3,5]=>1010010=>[1,2,3,2]
[2,7,8,1,5,6,3,4]=>0010010=>[3,3,2]
[6,8,2,3,1,5,4,7]=>0101010=>[2,2,2,2]
[5,8,2,3,1,6,4,7]=>0101010=>[2,2,2,2]
[5,7,2,1,4,6,8,3]=>0110001=>[2,1,4,1]
[4,2,3,8,1,7,5,6]=>1001010=>[1,3,2,2]
[5,2,3,8,1,7,4,6]=>1001010=>[1,3,2,2]
[2,5,4,8,1,7,3,6]=>0101010=>[2,2,2,2]
[2,5,4,1,3,8,6,7]=>0110010=>[2,1,3,2]
[4,2,1,5,3,7,6,8]=>1101010=>[1,1,2,2,2]
[5,1,3,2,6,7,8,4]=>1010001=>[1,2,4,1]
[5,1,3,4,2,7,6,8]=>1001010=>[1,3,2,2]
[6,1,3,4,2,7,5,8]=>1001010=>[1,3,2,2]
[7,2,1,3,5,8,4,6]=>1100010=>[1,1,4,2]
[6,1,2,4,5,7,8,3]=>1000001=>[1,6,1]
[6,8,7,2,3,4,5,1]=>0110001=>[2,1,4,1]
[3,7,2,8,1,4,5,6]=>0101000=>[2,2,4]
[5,2,3,7,4,6,1,8]=>1001010=>[1,3,2,2]
[2,5,3,7,4,6,1,8]=>0101010=>[2,2,2,2]
[2,6,7,3,4,5,1,8]=>0010010=>[3,3,2]
[6,2,7,3,4,5,1,8]=>1010010=>[1,2,3,2]
[6,2,8,3,5,1,4,7]=>1010100=>[1,2,2,3]
[3,8,4,5,2,1,6,7]=>0101100=>[2,2,1,3]
[8,2,6,3,5,1,4,7]=>1010100=>[1,2,2,3]
[2,7,6,3,4,5,1,8]=>0110010=>[2,1,3,2]
[2,8,6,3,5,1,4,7]=>0110100=>[2,1,2,3]
[2,8,7,5,1,3,4,6]=>0111000=>[2,1,1,4]
[1,5,7,3,6,2,8,4]=>0010101=>[3,2,2,1]
[1,6,5,7,2,8,3,4]=>0101010=>[2,2,2,2]
[7,5,2,6,1,8,4,3]=>1101011=>[1,1,2,2,1,1]
[6,1,5,2,7,8,4,3]=>1010011=>[1,2,3,1,1]
[1,6,5,7,2,8,4,3]=>0101011=>[2,2,2,1,1]
[1,5,4,6,2,8,7,3]=>0101011=>[2,2,2,1,1]
[1,5,4,6,2,8,3,7]=>0101010=>[2,2,2,2]
[1,5,6,4,8,2,3,7]=>0010100=>[3,2,3]
[6,2,1,5,8,4,7,3]=>1100101=>[1,1,3,2,1]
[8,3,7,5,1,4,2,6]=>1011010=>[1,2,1,2,2]
[8,3,7,1,6,4,2,5]=>1010110=>[1,2,2,1,2]
[4,2,6,5,3,1,7,8]=>1011100=>[1,2,1,1,3]
[4,3,7,5,1,6,2,8]=>1011010=>[1,2,1,2,2]
[5,3,7,4,2,8,6,1]=>1011011=>[1,2,1,2,1,1]
[5,3,1,4,6,7,8,2]=>1100001=>[1,1,5,1]
[6,2,1,4,7,5,8,3]=>1100101=>[1,1,3,2,1]
[4,5,7,2,3,6,1,8]=>0010010=>[3,3,2]
[4,6,2,1,3,7,8,5]=>0110001=>[2,1,4,1]
[6,5,2,7,4,1,3,8]=>1101100=>[1,1,2,1,3]
[5,4,2,3,6,8,1,7]=>1100010=>[1,1,4,2]
[6,4,1,2,7,8,3,5]=>1100010=>[1,1,4,2]
[5,1,8,3,4,6,2,7]=>1010010=>[1,2,3,2]
[4,5,8,2,3,7,1,6]=>0010010=>[3,3,2]
[5,1,4,7,2,6,8,3]=>1001001=>[1,3,3,1]
[2,6,5,3,8,1,4,7]=>0110100=>[2,1,2,3]
[6,5,8,2,7,3,4,1]=>1010101=>[1,2,2,2,1]
[5,2,6,8,3,7,1,4]=>1001010=>[1,3,2,2]
[1,7,6,5,3,8,2,4]=>0111010=>[2,1,1,2,2]
[1,7,2,4,3,5,8,6]=>0101001=>[2,2,3,1]
[4,6,1,3,7,8,5,2]=>0100011=>[2,4,1,1]
[8,4,1,5,2,6,7,3]=>1101001=>[1,1,2,3,1]
[6,3,1,8,5,4,7,2]=>1101101=>[1,1,2,1,2,1]
[6,1,3,8,7,4,5,2]=>1001101=>[1,3,1,2,1]
[2,8,4,6,5,1,7,3]=>0101101=>[2,2,1,2,1]
[7,4,1,3,6,5,2,8]=>1100110=>[1,1,3,1,2]
[5,7,2,8,1,3,6,4]=>0101001=>[2,2,3,1]
[2,3,8,4,1,7,6,5]=>0011011=>[3,1,2,1,1]
[6,5,1,4,7,3,2,8]=>1100110=>[1,1,3,1,2]
[2,7,8,4,1,3,6,5]=>0011001=>[3,1,3,1]
[3,6,5,1,4,8,2,7]=>0110010=>[2,1,3,2]
[3,6,4,1,2,7,8,5]=>0110001=>[2,1,4,1]
[4,1,7,3,8,6,2,5]=>1010110=>[1,2,2,1,2]
[4,8,2,7,6,5,1,3]=>0101110=>[2,2,1,1,2]
[5,4,2,8,7,6,1,3]=>1101110=>[1,1,2,1,1,2]
[7,4,2,8,6,5,1,3]=>1101110=>[1,1,2,1,1,2]
[6,5,8,2,7,4,1,3]=>1010110=>[1,2,2,1,2]
[8,6,5,2,7,1,4,3]=>1110101=>[1,1,1,2,2,1]
[7,8,5,2,1,6,4,3]=>0111011=>[2,1,1,2,1,1]
[6,8,5,2,7,1,4,3]=>0110101=>[2,1,2,2,1]
[6,5,8,2,7,1,4,3]=>1010101=>[1,2,2,2,1]
[7,5,8,2,1,6,4,3]=>1011011=>[1,2,1,2,1,1]
[3,2,1,6,5,8,4,7]=>1101010=>[1,1,2,2,2]
[6,3,1,4,5,8,2,7]=>1100010=>[1,1,4,2]
[3,4,8,5,2,1,7,6]=>0011101=>[3,1,1,2,1]
[4,8,7,1,3,2,6,5]=>0110101=>[2,1,2,2,1]
[3,5,1,4,2,8,7,6]=>0101011=>[2,2,2,1,1]
[5,8,7,4,6,1,3,2]=>0110101=>[2,1,2,2,1]
[5,1,8,7,4,6,3,2]=>1011011=>[1,2,1,2,1,1]
[3,4,1,8,7,6,2,5]=>0101110=>[2,2,1,1,2]
[3,5,2,8,6,4,7,1]=>0101101=>[2,2,1,2,1]
[2,8,7,5,4,1,6,3]=>0111101=>[2,1,1,1,2,1]
[4,2,5,8,6,7,1,3]=>1001010=>[1,3,2,2]
[8,1,5,7,4,2,6,3]=>1001101=>[1,3,1,2,1]
[8,4,5,3,1,6,7,2]=>1011001=>[1,2,1,3,1]
[5,8,7,3,4,1,6,2]=>0110101=>[2,1,2,2,1]
[2,4,5,8,1,3,7,6]=>0001001=>[4,3,1]
[7,1,4,3,8,5,6,2]=>1010101=>[1,2,2,2,1]
[6,3,2,5,8,4,1,7]=>1100110=>[1,1,3,1,2]
[8,7,1,4,6,3,2,5]=>1100110=>[1,1,3,1,2]
[8,4,1,3,7,6,5,2]=>1100111=>[1,1,3,1,1,1]
[2,7,8,6,5,3,1,4]=>0011110=>[3,1,1,1,2]
[5,1,6,4,7,8,2,3]=>1010010=>[1,2,3,2]
[2,8,3,5,6,1,4,7]=>0100100=>[2,3,3]
[1,3,6,4,2,7,5,8]=>0011010=>[3,1,2,2]
[3,2,8,5,6,1,4,7]=>1010100=>[1,2,2,3]
[7,2,5,8,1,4,6,3]=>1001001=>[1,3,3,1]
[4,7,5,8,1,2,6,3]=>0101001=>[2,2,3,1]
[5,4,7,8,2,1,3,6]=>1001100=>[1,3,1,3]
[4,7,5,8,1,2,3,6]=>0101000=>[2,2,4]
[3,4,7,5,2,8,1,6]=>0011010=>[3,1,2,2]
[4,3,2,5,7,8,1,6]=>1100010=>[1,1,4,2]
[5,4,8,6,2,3,1,7]=>1011010=>[1,2,1,2,2]
[2,4,7,5,8,3,1,6]=>0010110=>[3,2,1,2]
[7,2,5,8,1,6,3,4]=>1001010=>[1,3,2,2]
[3,7,8,4,2,1,6,5]=>0011101=>[3,1,1,2,1]
[8,5,4,7,6,3,1,2]=>1101110=>[1,1,2,1,1,2]
[1,5,4,8,7,6,2,3]=>0101110=>[2,2,1,1,2]
[3,2,4,5,8,1,6,7]=>1000100=>[1,4,3]
[2,4,6,8,3,7,1,5]=>0001010=>[4,2,2]
[1,4,7,6,3,8,2,5]=>0011010=>[3,1,2,2]
[3,6,5,1,7,2,8,4]=>0110101=>[2,1,2,2,1]
[6,4,1,7,2,8,5,3]=>1101011=>[1,1,2,2,1,1]
[7,4,1,6,2,8,5,3]=>1101011=>[1,1,2,2,1,1]
[2,8,3,7,5,1,6,4]=>0101101=>[2,2,1,2,1]
[1,3,6,8,2,4,7,5]=>0001001=>[4,3,1]
[8,5,4,1,6,2,7,3]=>1110101=>[1,1,1,2,2,1]
[4,7,2,8,5,1,6,3]=>0101101=>[2,2,1,2,1]
[8,6,2,7,3,5,1,4]=>1101010=>[1,1,2,2,2]
[5,7,3,2,4,8,6,1]=>0110011=>[2,1,3,1,1]
[2,8,4,6,3,5,1,7]=>0101010=>[2,2,2,2]
[2,7,8,3,6,4,5,1]=>0010101=>[3,2,2,1]
[4,2,3,5,1,8,6,7]=>1001010=>[1,3,2,2]
[4,5,2,6,7,1,8,3]=>0100101=>[2,3,2,1]
[4,7,5,2,6,3,8,1]=>0110101=>[2,1,2,2,1]
[3,5,6,2,8,1,4,7]=>0010100=>[3,2,3]
[5,7,2,1,8,4,3,6]=>0110110=>[2,1,2,1,2]
[6,1,8,2,4,3,5,7]=>1010100=>[1,2,2,3]
[1,6,8,2,5,3,4,7]=>0010100=>[3,2,3]
[8,7,6,2,4,5,1,3]=>1110010=>[1,1,1,3,2]
[8,7,3,5,1,4,6,2]=>1101001=>[1,1,2,3,1]
[8,6,3,5,2,1,4,7]=>1101100=>[1,1,2,1,3]
[8,7,3,2,6,5,1,4]=>1110110=>[1,1,1,2,1,2]
[8,4,2,7,6,5,1,3]=>1101110=>[1,1,2,1,1,2]
[5,2,8,7,6,4,1,3]=>1011110=>[1,2,1,1,1,2]
[8,7,1,4,5,6,2,3]=>1100010=>[1,1,4,2]
[4,1,3,8,5,6,2,7]=>1001010=>[1,3,2,2]
[3,2,4,8,5,7,1,6]=>1001010=>[1,3,2,2]
[6,3,8,5,4,2,7,1]=>1011101=>[1,2,1,1,2,1]
[7,4,6,1,3,5,2,8]=>1010010=>[1,2,3,2]
[6,2,3,8,5,4,7,1]=>1001101=>[1,3,1,2,1]
[1,5,3,8,7,4,6,2]=>0101101=>[2,2,1,2,1]
[5,1,3,8,7,4,6,2]=>1001101=>[1,3,1,2,1]
[2,5,3,8,7,4,1,6]=>0101110=>[2,2,1,1,2]
[5,2,1,8,7,4,6,3]=>1101101=>[1,1,2,1,2,1]
[6,8,3,5,1,2,7,4]=>0101001=>[2,2,3,1]
[5,8,2,7,4,6,3,1]=>0101011=>[2,2,2,1,1]
[6,8,7,3,1,2,4,5]=>0111000=>[2,1,1,4]
[4,5,2,8,3,7,1,6]=>0101010=>[2,2,2,2]
[4,5,8,1,3,7,6,2]=>0010011=>[3,3,1,1]
[7,8,5,1,6,4,3,2]=>0110111=>[2,1,2,1,1,1]
[8,7,5,1,6,4,3,2]=>1110111=>[1,1,1,2,1,1,1]
[4,5,8,3,1,2,7,6]=>0011001=>[3,1,3,1]
[4,6,8,3,2,1,7,5]=>0011101=>[3,1,1,2,1]
[4,6,8,3,5,1,2,7]=>0010100=>[3,2,3]
[7,1,6,8,5,4,3,2]=>1001111=>[1,3,1,1,1,1]
[5,8,1,3,4,2,7,6]=>0100101=>[2,3,2,1]
[1,4,6,3,7,5,2,8]=>0010110=>[3,2,1,2]
[4,5,2,6,8,7,3,1]=>0100111=>[2,3,1,1,1]
[3,2,8,7,4,5,6,1]=>1011001=>[1,2,1,3,1]
[6,4,2,5,1,7,8,3]=>1101001=>[1,1,2,3,1]
[1,3,2,8,7,4,6,5]=>0101101=>[2,2,1,2,1]
[7,5,2,8,3,1,6,4]=>1101101=>[1,1,2,1,2,1]
[5,4,2,7,3,8,6,1]=>1101011=>[1,1,2,2,1,1]
[6,7,1,3,2,5,8,4]=>0101001=>[2,2,3,1]
[8,3,5,4,7,1,2,6]=>1010100=>[1,2,2,3]
[6,3,5,4,8,1,2,7]=>1010100=>[1,2,2,3]
[6,2,5,4,1,7,8,3]=>1011001=>[1,2,1,3,1]
[4,1,5,6,3,8,7,2]=>1001011=>[1,3,2,1,1]
[6,8,7,4,3,2,5,1]=>0111101=>[2,1,1,1,2,1]
[2,8,5,1,3,7,6,4]=>0110011=>[2,1,3,1,1]
[5,6,4,1,8,2,7,3]=>0110101=>[2,1,2,2,1]
[6,1,3,5,4,8,2,7]=>1001010=>[1,3,2,2]
[1,3,8,7,2,5,6,4]=>0011001=>[3,1,3,1]
[2,5,4,1,8,3,7,6]=>0110101=>[2,1,2,2,1]
[6,1,5,4,3,8,2,7]=>1011010=>[1,2,1,2,2]
[1,4,8,3,2,7,6,5]=>0011011=>[3,1,2,1,1]
[5,1,4,8,3,7,6,2]=>1001011=>[1,3,2,1,1]
[3,5,8,2,1,4,7,6]=>0011001=>[3,1,3,1]
[8,4,1,2,7,6,5,3]=>1100111=>[1,1,3,1,1,1]
[4,8,3,2,7,6,5,1]=>0110111=>[2,1,2,1,1,1]
[2,4,8,1,7,6,5,3]=>0010111=>[3,2,1,1,1]
[8,7,3,2,1,4,6,5]=>1111001=>[1,1,1,1,3,1]
[1,4,8,5,2,3,6,7]=>0011000=>[3,1,4]
[1,4,8,5,2,3,7,6]=>0011001=>[3,1,3,1]
[6,1,4,2,8,7,3,5]=>1010110=>[1,2,2,1,2]
[1,5,8,7,2,4,3,6]=>0011010=>[3,1,2,2]
[1,2,8,7,3,5,4,6]=>0011010=>[3,1,2,2]
[8,7,1,3,2,5,4,6]=>1101010=>[1,1,2,2,2]
[6,7,4,2,8,1,3,5]=>0110100=>[2,1,2,3]
[4,7,5,6,2,8,3,1]=>0101011=>[2,2,2,1,1]
[8,4,3,6,7,5,2,1]=>1100111=>[1,1,3,1,1,1]
[6,7,5,2,8,4,3,1]=>0110111=>[2,1,2,1,1,1]
[6,8,4,3,2,7,5,1]=>0111011=>[2,1,1,2,1,1]
[6,1,5,8,7,4,3,2]=>1001111=>[1,3,1,1,1,1]
[8,5,1,4,7,6,3,2]=>1100111=>[1,1,3,1,1,1]
[8,2,1,7,5,3,6,4]=>1101101=>[1,1,2,1,2,1]
[8,1,3,7,2,4,6,5]=>1001001=>[1,3,3,1]
[2,6,7,3,5,8,4,1]=>0010011=>[3,3,1,1]
[2,6,7,3,5,8,1,4]=>0010010=>[3,3,2]
[5,3,1,6,4,8,2,7]=>1101010=>[1,1,2,2,2]
[2,5,6,7,1,4,8,3]=>0001001=>[4,3,1]
[6,4,8,3,5,2,1,7]=>1010110=>[1,2,2,1,2]
[4,7,5,2,8,6,1,3]=>0110110=>[2,1,2,1,2]
[1,6,5,7,3,8,4,2]=>0101011=>[2,2,2,1,1]
[5,8,1,2,7,4,3,6]=>0100110=>[2,3,1,2]
[4,6,3,7,8,1,5,2]=>0100101=>[2,3,2,1]
[2,1,4,7,5,8,6,3]=>1001011=>[1,3,2,1,1]
[8,6,3,5,2,1,7,4]=>1101101=>[1,1,2,1,2,1]
[6,8,3,1,2,5,4,7]=>0110010=>[2,1,3,2]
[5,8,6,4,7,1,2,3]=>0110100=>[2,1,2,3]
[2,5,1,8,7,3,4,6]=>0101100=>[2,2,1,3]
[6,8,1,7,5,4,2,3]=>0101110=>[2,2,1,1,2]
[4,8,2,7,5,3,6,1]=>0101101=>[2,2,1,2,1]
[7,2,4,3,8,6,1,5]=>1010110=>[1,2,2,1,2]
[5,8,4,3,1,6,7,2]=>0111001=>[2,1,1,3,1]
[6,8,7,4,5,1,3,2]=>0110101=>[2,1,2,2,1]
[1,4,7,3,6,8,2,5]=>0010010=>[3,3,2]
[2,4,7,3,6,8,1,5]=>0010010=>[3,3,2]
[2,8,3,1,4,7,5,6]=>0110010=>[2,1,3,2]
[2,7,3,1,8,5,4,6]=>0110110=>[2,1,2,1,2]
[2,3,1,6,8,7,4,5]=>0100110=>[2,3,1,2]
[6,4,8,2,1,7,3,5]=>1011010=>[1,2,1,2,2]
[2,3,1,7,8,5,6,4]=>0100101=>[2,3,2,1]
[2,3,1,8,7,5,6,4]=>0101101=>[2,2,1,2,1]
[8,7,4,5,1,3,2,6]=>1101010=>[1,1,2,2,2]
[8,5,1,2,7,4,3,6]=>1100110=>[1,1,3,1,2]
[1,3,7,6,8,4,2,5]=>0010110=>[3,2,1,2]
[4,5,7,8,6,2,1,3]=>0001110=>[4,1,1,2]
[2,1,5,7,4,6,8,3]=>1001001=>[1,3,3,1]
[2,3,5,7,8,1,6,4]=>0000101=>[5,2,1]
[1,6,4,2,3,5,7,8]=>0110000=>[2,1,5]
[1,5,7,4,2,3,6,8]=>0011000=>[3,1,4]
[1,5,7,2,3,6,8,4]=>0010001=>[3,4,1]
[2,4,7,8,6,1,3,5]=>0001100=>[4,1,3]
[1,3,6,2,5,8,4,7]=>0010010=>[3,3,2]
[1,5,3,6,8,2,4,7]=>0100100=>[2,3,3]
[2,8,5,1,4,3,7,6]=>0110101=>[2,1,2,2,1]
[6,1,5,8,3,2,7,4]=>1001101=>[1,3,1,2,1]
[1,8,6,2,4,3,7,5]=>0110101=>[2,1,2,2,1]
[4,8,5,1,3,2,6,7]=>0110100=>[2,1,2,3]
[5,4,3,1,2,7,6,8]=>1110010=>[1,1,1,3,2]
[4,1,6,5,2,3,7,8]=>1011000=>[1,2,1,4]
[7,1,5,2,3,6,4,8]=>1010010=>[1,2,3,2]
[4,1,6,3,7,2,5,8]=>1010100=>[1,2,2,3]
[4,6,1,2,8,3,7,5]=>0100101=>[2,3,2,1]
[4,1,3,6,7,2,5,8]=>1000100=>[1,4,3]
[2,6,5,1,3,4,7,8]=>0110000=>[2,1,5]
[2,6,7,4,3,1,5,8]=>0011100=>[3,1,1,3]
[2,6,3,1,7,4,5,8]=>0110100=>[2,1,2,3]
[2,3,6,7,1,5,4,8]=>0001010=>[4,2,2]
[3,7,5,6,2,1,4,8]=>0101100=>[2,2,1,3]
[2,7,5,8,1,3,6,4]=>0101001=>[2,2,3,1]
[5,1,6,7,3,2,4,8]=>1001100=>[1,3,1,3]
[5,1,3,6,7,4,2,8]=>1000110=>[1,4,1,2]
[2,5,6,3,8,4,7,1]=>0010101=>[3,2,2,1]
[7,4,1,2,3,6,8,5]=>1100001=>[1,1,5,1]
[8,5,6,2,1,4,7,3]=>1011001=>[1,2,1,3,1]
[9,10,6,4,2,1,3,5,8,7]=>011110001=>[2,1,1,1,4,1]
[10,7,8,4,2,1,3,6,5,9]=>101110010=>[1,2,1,1,3,2]
[9,7,10,4,2,1,3,6,8,5]=>101110001=>[1,2,1,1,4,1]
[8,9,10,4,2,1,3,7,6,5]=>001110011=>[3,1,1,3,1,1]
[10,8,5,6,2,1,4,3,7,9]=>110110100=>[1,1,2,1,2,3]
[9,10,5,6,2,1,4,3,8,7]=>010110101=>[2,2,1,2,2,1]
[10,7,5,8,2,1,4,6,3,9]=>110110010=>[1,1,2,1,3,2]
[9,7,5,10,2,1,4,6,8,3]=>110110001=>[1,1,2,1,4,1]
[8,9,5,10,2,1,4,7,6,3]=>010110011=>[2,2,1,3,1,1]
[10,6,7,8,2,1,5,4,3,9]=>100110110=>[1,3,1,2,1,2]
[9,6,7,10,2,1,5,4,8,3]=>100110101=>[1,3,1,2,2,1]
[8,6,9,10,2,1,5,7,4,3]=>100110011=>[1,3,1,3,1,1]
[7,8,9,10,2,1,6,5,4,3]=>000110111=>[4,1,2,1,1,1]
[10,8,6,3,4,2,1,5,7,9]=>111011000=>[1,1,1,2,1,4]
[9,10,6,3,4,2,1,5,8,7]=>011011001=>[2,1,2,1,3,1]
[10,7,8,3,4,2,1,6,5,9]=>101011010=>[1,2,2,1,2,2]
[9,7,10,3,4,2,1,6,8,5]=>101011001=>[1,2,2,1,3,1]
[8,9,10,3,4,2,1,7,6,5]=>001011011=>[3,2,1,2,1,1]
[10,8,5,3,6,2,4,1,7,9]=>111010100=>[1,1,1,2,2,3]
[9,10,5,3,6,2,4,1,8,7]=>011010101=>[2,1,2,2,2,1]
[10,7,5,3,8,2,4,6,1,9]=>111010010=>[1,1,1,2,3,2]
[9,7,5,3,10,2,4,6,8,1]=>111010001=>[1,1,1,2,4,1]
[8,9,5,3,10,2,4,7,6,1]=>011010011=>[2,1,2,3,1,1]
[10,6,7,3,8,2,5,4,1,9]=>101010110=>[1,2,2,2,1,2]
[9,6,7,3,10,2,5,4,8,1]=>101010101=>[1,2,2,2,2,1]
[8,6,9,3,10,2,5,7,4,1]=>101010011=>[1,2,2,3,1,1]
[7,8,9,3,10,2,6,5,4,1]=>001010111=>[3,2,2,1,1,1]
[10,8,4,5,6,3,2,1,7,9]=>110011100=>[1,1,3,1,1,3]
[9,10,4,5,6,3,2,1,8,7]=>010011101=>[2,3,1,1,2,1]
[10,7,4,5,8,3,2,6,1,9]=>110011010=>[1,1,3,1,2,2]
[9,7,4,5,10,3,2,6,8,1]=>110011001=>[1,1,3,1,3,1]
[8,9,4,5,10,3,2,7,6,1]=>010011011=>[2,3,1,2,1,1]
[10,6,4,7,8,3,5,2,1,9]=>110010110=>[1,1,3,2,1,2]
[9,6,4,7,10,3,5,2,8,1]=>110010101=>[1,1,3,2,2,1]
[8,6,4,9,10,3,5,7,2,1]=>110010011=>[1,1,3,3,1,1]
[7,8,4,9,10,3,6,5,2,1]=>010010111=>[2,3,2,1,1,1]
[10,5,6,7,8,4,3,2,1,9]=>100011110=>[1,4,1,1,1,2]
[9,5,6,7,10,4,3,2,8,1]=>100011101=>[1,4,1,1,2,1]
[8,5,6,9,10,4,3,7,2,1]=>100011011=>[1,4,1,2,1,1]
[7,5,8,9,10,4,6,3,2,1]=>100010111=>[1,4,2,1,1,1]
[11,12,8,6,4,2,1,3,5,7,10,9]=>01111100001=>[2,1,1,1,1,5,1]
[8,9,10,11,12,2,1,7,6,5,4,3]=>00001101111=>[5,1,2,1,1,1,1]
[12,6,7,8,9,10,5,4,3,2,1,11]=>10000111110=>[1,5,1,1,1,1,2]
[2,7,4,1,5,8,3,6]=>0110010=>[2,1,3,2]
[6,1,7,3,4,2,5,8]=>1010100=>[1,2,2,3]
[2,6,4,7,8,5,3,1]=>0100111=>[2,3,1,1,1]
[5,2,8,4,6,7,1,3]=>1010010=>[1,2,3,2]
[1,3,5,8,4,6,7,2]=>0001001=>[4,3,1]
[8,2,7,6,3,4,5,1]=>1011001=>[1,2,1,3,1]
[1,8,3,7,4,2,5,6]=>0101100=>[2,2,1,3]
[8,5,7,2,4,3,6,1]=>1010101=>[1,2,2,2,1]
[7,8,6,2,4,1,3,5]=>0110100=>[2,1,2,3]
[6,8,7,3,2,1,4,5]=>0111100=>[2,1,1,1,3]
[3,4,8,2,7,1,5,6]=>0010100=>[3,2,3]
[7,2,6,1,4,8,3,5]=>1010010=>[1,2,3,2]
[7,8,1,2,4,6,3,5]=>0100010=>[2,4,2]
[7,2,8,3,4,5,1,6]=>1010010=>[1,2,3,2]
[6,1,8,3,4,2,5,7]=>1010100=>[1,2,2,3]
[6,8,4,3,1,5,2,7]=>0111010=>[2,1,1,2,2]
[5,8,2,1,7,4,3,6]=>0110110=>[2,1,2,1,2]
[1,7,2,6,3,4,8,5]=>0101001=>[2,2,3,1]
[7,5,1,2,4,3,8,6]=>1100101=>[1,1,3,2,1]
[7,6,8,1,4,2,3,5]=>1010100=>[1,2,2,3]
[6,3,5,2,1,8,4,7]=>1011010=>[1,2,1,2,2]
[3,2,4,8,6,1,7,5]=>1001101=>[1,3,1,2,1]
[2,1,3,8,4,5,7,6]=>1001001=>[1,3,3,1]
[1,4,7,5,2,3,8,6]=>0011001=>[3,1,3,1]
[2,1,3,7,8,4,6,5]=>1000101=>[1,4,2,1]
[2,1,3,8,4,7,6,5]=>1001011=>[1,3,2,1,1]
[3,1,2,8,4,5,7,6]=>1001001=>[1,3,3,1]
[1,2,8,7,5,4,6,3]=>0011101=>[3,1,1,2,1]
[1,3,6,8,2,7,5,4]=>0001011=>[4,2,1,1]
[3,2,7,5,6,8,1,4]=>1010010=>[1,2,3,2]
[6,1,5,4,2,3,8,7]=>1011001=>[1,2,1,3,1]
[6,4,5,1,2,8,3,7]=>1010010=>[1,2,3,2]
[8,4,1,5,7,6,3,2]=>1100111=>[1,1,3,1,1,1]
[8,1,6,3,5,2,4,7]=>1010100=>[1,2,2,3]
[4,6,2,5,3,8,1,7]=>0101010=>[2,2,2,2]
[4,6,5,2,1,8,3,7]=>0111010=>[2,1,1,2,2]
[5,8,4,3,6,7,2,1]=>0110011=>[2,1,3,1,1]
[6,8,2,1,5,3,4,7]=>0110100=>[2,1,2,3]
[2,5,3,8,6,7,4,1]=>0101011=>[2,2,2,1,1]
[3,2,6,5,1,8,4,7]=>1011010=>[1,2,1,2,2]
[6,4,5,1,8,3,2,7]=>1010110=>[1,2,2,1,2]
[3,6,8,2,5,1,4,7]=>0010100=>[3,2,3]
[7,4,5,8,1,6,2,3]=>1001010=>[1,3,2,2]
[4,5,8,1,6,7,3,2]=>0010011=>[3,3,1,1]
[5,1,8,4,6,7,3,2]=>1010011=>[1,2,3,1,1]
[4,8,3,1,6,7,2,5]=>0110010=>[2,1,3,2]
[7,2,4,6,3,8,5,1]=>1001011=>[1,3,2,1,1]
[2,8,3,7,6,1,5,4]=>0101101=>[2,2,1,2,1]
[5,4,2,6,8,7,3,1]=>1100111=>[1,1,3,1,1,1]
[3,7,2,5,8,6,4,1]=>0100111=>[2,3,1,1,1]
[5,4,3,7,2,8,6,1]=>1101011=>[1,1,2,2,1,1]
[2,4,8,7,6,1,5,3]=>0011101=>[3,1,1,2,1]
[4,8,5,2,7,6,3,1]=>0110111=>[2,1,2,1,1,1]
[2,8,6,5,7,1,3,4]=>0110100=>[2,1,2,3]
[4,1,8,6,2,5,7,3]=>1011001=>[1,2,1,3,1]
[3,8,4,7,2,1,6,5]=>0101101=>[2,2,1,2,1]
[1,8,7,4,5,2,3,6]=>0110100=>[2,1,2,3]
[5,8,1,7,6,2,3,4]=>0101100=>[2,2,1,3]
[6,8,2,1,3,4,7,5]=>0110001=>[2,1,4,1]
[4,8,1,3,7,6,2,5]=>0100110=>[2,3,1,2]
[5,2,1,7,6,4,3,8]=>1101110=>[1,1,2,1,1,2]
[7,4,8,3,6,5,1,2]=>1010110=>[1,2,2,1,2]
[6,4,8,5,1,7,2,3]=>1011010=>[1,2,1,2,2]
[5,2,8,1,3,6,7,4]=>1010001=>[1,2,4,1]
[5,2,7,1,3,8,6,4]=>1010011=>[1,2,3,1,1]
[6,3,7,2,5,4,8,1]=>1010101=>[1,2,2,2,1]
[5,2,1,7,6,3,8,4]=>1101101=>[1,1,2,1,2,1]
[6,3,2,7,4,5,8,1]=>1101001=>[1,1,2,3,1]
[7,4,3,8,5,6,1,2]=>1101010=>[1,1,2,2,2]
[7,3,2,8,4,6,1,5]=>1101010=>[1,1,2,2,2]
[6,2,1,8,7,4,5,3]=>1101101=>[1,1,2,1,2,1]
[6,2,1,8,7,3,5,4]=>1101101=>[1,1,2,1,2,1]
[5,2,1,7,6,3,4,8]=>1101100=>[1,1,2,1,3]
[7,4,3,8,5,6,2,1]=>1101011=>[1,1,2,2,1,1]
[4,2,8,3,6,7,5,1]=>1010011=>[1,2,3,1,1]
[4,2,6,8,5,7,1,3]=>1001010=>[1,3,2,2]
[4,2,1,6,5,7,8,3]=>1101001=>[1,1,2,3,1]
[8,6,1,4,3,5,2,7]=>1101010=>[1,1,2,2,2]
[6,1,8,4,3,5,2,7]=>1011010=>[1,2,1,2,2]
[5,1,6,4,8,2,3,7]=>1010100=>[1,2,2,3]
[2,8,6,4,1,5,3,7]=>0111010=>[2,1,1,2,2]
[8,1,4,2,5,3,6,7]=>1010100=>[1,2,2,3]
[2,8,4,1,5,3,6,7]=>0110100=>[2,1,2,3]
[8,4,1,3,5,2,6,7]=>1100100=>[1,1,3,3]
[3,4,8,1,5,2,6,7]=>0010100=>[3,2,3]
[4,1,8,3,5,2,6,7]=>1010100=>[1,2,2,3]
[8,3,1,2,5,4,6,7]=>1100100=>[1,1,3,3]
[2,8,1,3,5,4,6,7]=>0100100=>[2,3,3]
[1,7,6,2,4,3,8,5]=>0110101=>[2,1,2,2,1]
[1,4,5,8,3,2,6,7]=>0001100=>[4,1,3]
[5,6,8,7,1,3,2,4]=>0011010=>[3,1,2,2]
[2,8,6,5,7,4,3,1]=>0110111=>[2,1,2,1,1,1]
[6,3,7,5,1,4,2,8]=>1011010=>[1,2,1,2,2]
[2,8,6,5,7,4,1,3]=>0110110=>[2,1,2,1,2]
[6,5,2,7,4,3,1,8]=>1101110=>[1,1,2,1,1,2]
[6,5,2,8,4,3,7,1]=>1101101=>[1,1,2,1,2,1]
[7,5,8,3,4,2,1,6]=>1010110=>[1,2,2,1,2]
[6,3,7,5,1,4,8,2]=>1011001=>[1,2,1,3,1]
[5,3,7,2,4,1,8,6]=>1010101=>[1,2,2,2,1]
[5,1,2,8,6,3,7,4]=>1001101=>[1,3,1,2,1]
[6,5,2,8,4,7,1,3]=>1101010=>[1,1,2,2,2]
[6,5,8,3,1,2,7,4]=>1011001=>[1,2,1,3,1]
[6,1,5,7,2,4,3,8]=>1001010=>[1,3,2,2]
[7,1,6,8,2,5,4,3]=>1001011=>[1,3,2,1,1]
[4,1,8,2,6,5,7,3]=>1010101=>[1,2,2,2,1]
[6,1,4,7,8,5,3,2]=>1000111=>[1,4,1,1,1]
[5,1,4,6,7,3,2,8]=>1000110=>[1,4,1,2]
[6,1,5,7,8,4,2,3]=>1000110=>[1,4,1,2]
[1,8,4,5,6,7,2,3]=>0100010=>[2,4,2]
[4,2,8,6,7,1,3,5]=>1010100=>[1,2,2,3]
[6,4,2,7,1,5,8,3]=>1101001=>[1,1,2,3,1]
[5,6,2,7,4,8,3,1]=>0101011=>[2,2,2,1,1]
[5,3,6,7,4,2,8,1]=>1001101=>[1,3,1,2,1]
[2,6,3,7,5,4,8,1]=>0101101=>[2,2,1,2,1]
[1,7,3,2,4,8,6,5]=>0110011=>[2,1,3,1,1]
[6,4,1,3,8,7,5,2]=>1100111=>[1,1,3,1,1,1]
[4,3,1,8,2,6,7,5]=>1101001=>[1,1,2,3,1]
[4,8,1,3,2,5,7,6]=>0101001=>[2,2,3,1]
[7,2,6,5,8,3,4,1]=>1010101=>[1,2,2,2,1]
[1,7,5,3,8,6,2,4]=>0110110=>[2,1,2,1,2]
[2,5,3,8,1,4,7,6]=>0101001=>[2,2,3,1]
[4,2,5,8,1,3,7,6]=>1001001=>[1,3,3,1]
[8,1,2,4,3,5,7,6]=>1001001=>[1,3,3,1]
[2,4,3,8,1,5,7,6]=>0101001=>[2,2,3,1]
[7,5,2,3,8,4,6,1]=>1100101=>[1,1,3,2,1]
[2,7,5,1,4,8,3,6]=>0110010=>[2,1,3,2]
[3,1,7,4,8,6,5,2]=>1010111=>[1,2,2,1,1,1]
[6,4,5,3,2,8,7,1]=>1011011=>[1,2,1,2,1,1]
[2,7,3,8,5,1,6,4]=>0101101=>[2,2,1,2,1]
[8,7,3,2,5,6,4,1]=>1110011=>[1,1,1,3,1,1]
[1,5,8,2,6,4,3,7]=>0010110=>[3,2,1,2]
[3,1,8,2,6,5,4,7]=>1010110=>[1,2,2,1,2]
[7,6,2,8,1,4,5,3]=>1101001=>[1,1,2,3,1]
[8,4,2,3,1,5,7,6]=>1101001=>[1,1,2,3,1]
[8,2,3,4,1,5,7,6]=>1001001=>[1,3,3,1]
[7,1,6,2,4,8,3,5]=>1010010=>[1,2,3,2]
[4,5,2,6,1,3,8,7]=>0101001=>[2,2,3,1]
[2,7,8,1,4,3,6,5]=>0010101=>[3,2,2,1]
[6,5,8,1,3,2,4,7]=>1010100=>[1,2,2,3]
[5,7,2,1,8,4,6,3]=>0110101=>[2,1,2,2,1]
[2,1,8,5,3,4,6,7]=>1011000=>[1,2,1,4]
[7,8,1,5,2,4,6,3]=>0101001=>[2,2,3,1]
[7,4,1,8,2,5,6,3]=>1101001=>[1,1,2,3,1]
[2,1,6,7,4,8,3,5]=>1001010=>[1,3,2,2]
[2,8,6,3,1,5,4,7]=>0111010=>[2,1,1,2,2]
[5,8,6,3,2,1,4,7]=>0111100=>[2,1,1,1,3]
[5,7,2,8,4,1,6,3]=>0101101=>[2,2,1,2,1]
[2,5,6,3,8,1,4,7]=>0010100=>[3,2,3]
[7,3,5,6,1,8,4,2]=>1001011=>[1,3,2,1,1]
[7,4,5,6,8,1,3,2]=>1000101=>[1,4,2,1]
[7,5,1,8,4,6,3,2]=>1101011=>[1,1,2,2,1,1]
[2,8,1,7,4,5,3,6]=>0101010=>[2,2,2,2]
[7,3,6,2,5,4,8,1]=>1010101=>[1,2,2,2,1]
[6,1,5,3,8,4,7,2]=>1010101=>[1,2,2,2,1]
[1,6,5,3,8,4,7,2]=>0110101=>[2,1,2,2,1]
[7,6,2,3,5,4,8,1]=>1100101=>[1,1,3,2,1]
[7,6,2,3,5,1,4,8]=>1100100=>[1,1,3,3]
[6,1,5,2,3,4,8,7]=>1010001=>[1,2,4,1]
[6,2,5,3,4,8,1,7]=>1010010=>[1,2,3,2]
[6,2,5,3,4,8,7,1]=>1010011=>[1,2,3,1,1]
[2,6,5,3,4,8,7,1]=>0110011=>[2,1,3,1,1]
[2,6,5,3,4,8,1,7]=>0110010=>[2,1,3,2]
[2,5,1,4,8,3,7,6]=>0100101=>[2,3,2,1]
[1,2,5,4,8,3,7,6]=>0010101=>[3,2,2,1]
[5,3,4,8,1,7,2,6]=>1001010=>[1,3,2,2]
[5,1,3,4,8,7,2,6]=>1000110=>[1,4,1,2]
[1,5,3,4,8,7,2,6]=>0100110=>[2,3,1,2]
[5,1,3,8,4,7,6,2]=>1001011=>[1,3,2,1,1]
[5,3,8,1,4,7,6,2]=>1010011=>[1,2,3,1,1]
[4,3,5,8,1,7,6,2]=>1001011=>[1,3,2,1,1]
[3,6,5,4,8,1,2,7]=>0110100=>[2,1,2,3]
[3,6,5,4,8,2,7,1]=>0110101=>[2,1,2,2,1]
[4,3,5,8,2,1,7,6]=>1001101=>[1,3,1,2,1]
[3,5,2,4,8,7,6,1]=>0100111=>[2,3,1,1,1]
[5,2,3,8,7,4,1,6]=>1001110=>[1,3,1,1,2]
[2,3,1,7,4,8,6,5]=>0101011=>[2,2,2,1,1]
[2,3,8,7,6,4,1,5]=>0011110=>[3,1,1,1,2]
[7,5,2,3,1,6,4,8]=>1101010=>[1,1,2,2,2]
[4,2,8,5,1,3,6,7]=>1011000=>[1,2,1,4]
[7,4,1,3,6,2,5,8]=>1100100=>[1,1,3,3]
[7,4,6,3,1,2,5,8]=>1011000=>[1,2,1,4]
[8,2,5,3,6,1,4,7]=>1010100=>[1,2,2,3]
[7,2,5,8,1,3,6,4]=>1001001=>[1,3,3,1]
[1,2,6,5,3,4,7,8]=>0011000=>[3,1,4]
[1,4,6,5,7,2,3,8]=>0010100=>[3,2,3]
[2,4,6,5,7,1,8,3]=>0010101=>[3,2,2,1]
[3,5,2,1,7,8,6,4]=>0110011=>[2,1,3,1,1]
[1,2,7,8,6,4,5,3]=>0001101=>[4,1,2,1]
[7,1,6,3,2,4,8,5]=>1011001=>[1,2,1,3,1]
[8,5,1,2,3,6,7,4]=>1100001=>[1,1,5,1]
[6,4,8,1,2,3,7,5]=>1010001=>[1,2,4,1]
[4,3,5,1,7,8,6,2]=>1010011=>[1,2,3,1,1]
[4,6,7,2,3,8,5,1]=>0010011=>[3,3,1,1]
[4,5,3,7,8,1,2,6]=>0100100=>[2,3,3]
[1,7,4,5,8,3,6,2]=>0100101=>[2,3,2,1]
[7,3,6,8,5,2,1,4]=>1001110=>[1,3,1,1,2]
[2,8,3,1,7,4,5,6]=>0110100=>[2,1,2,3]
[4,5,7,6,3,1,8,2]=>0011101=>[3,1,1,2,1]
[4,6,7,5,2,8,3,1]=>0011011=>[3,1,2,1,1]
[4,6,7,5,1,3,8,2]=>0011001=>[3,1,3,1]
[3,6,5,1,4,7,8,2]=>0110001=>[2,1,4,1]
[4,6,7,3,1,5,8,2]=>0011001=>[3,1,3,1]
[4,2,3,6,7,5,1,8]=>1000110=>[1,4,1,2]
[6,2,3,5,7,4,1,8]=>1000110=>[1,4,1,2]
[2,6,4,5,7,3,1,8]=>0100110=>[2,3,1,2]
[7,1,5,2,4,8,3,6]=>1010010=>[1,2,3,2]
[8,1,5,2,4,7,3,6]=>1010010=>[1,2,3,2]
[7,5,8,1,4,2,3,6]=>1010100=>[1,2,2,3]
[1,7,5,8,4,2,3,6]=>0101100=>[2,2,1,3]
[1,3,4,8,5,6,2,7]=>0001010=>[4,2,2]
[4,8,3,6,1,7,2,5]=>0101010=>[2,2,2,2]
[4,6,3,1,2,5,7,8]=>0110000=>[2,1,5]
[7,4,6,8,3,1,2,5]=>1001100=>[1,3,1,3]
[8,5,4,7,3,1,2,6]=>1101100=>[1,1,2,1,3]
[7,3,2,1,5,4,8,6]=>1110101=>[1,1,1,2,2,1]
[2,5,6,4,8,1,3,7]=>0010100=>[3,2,3]
[5,4,1,6,2,3,7,8]=>1101000=>[1,1,2,4]
[1,5,6,4,2,3,7,8]=>0011000=>[3,1,4]
[1,3,6,5,2,4,7,8]=>0011000=>[3,1,4]
[1,5,6,3,2,4,7,8]=>0011000=>[3,1,4]
[5,7,8,1,2,4,3,6]=>0010010=>[3,3,2]
[6,5,1,2,4,3,8,7]=>1100101=>[1,1,3,2,1]
[2,5,1,4,6,3,8,7]=>0100101=>[2,3,2,1]
[5,8,7,3,1,2,4,6]=>0111000=>[2,1,1,4]
[2,7,8,1,4,5,3,6]=>0010010=>[3,3,2]
[4,3,7,1,2,6,8,5]=>1010001=>[1,2,4,1]
[4,1,2,8,7,3,6,5]=>1001101=>[1,3,1,2,1]
[8,7,5,1,2,4,3,6]=>1110010=>[1,1,1,3,2]
[6,1,2,4,3,8,7,5]=>1001011=>[1,3,2,1,1]
[3,7,8,1,2,4,6,5]=>0010001=>[3,4,1]
[7,8,5,1,2,4,3,6]=>0110010=>[2,1,3,2]
[8,3,4,1,2,6,7,5]=>1010001=>[1,2,4,1]
[2,1,4,7,3,6,8,5]=>1001001=>[1,3,3,1]
[7,3,4,1,2,6,8,5]=>1010001=>[1,2,4,1]
[8,4,3,1,2,6,5,7]=>1110010=>[1,1,1,3,2]
[3,8,2,7,4,5,1,6]=>0101010=>[2,2,2,2]
[8,6,2,3,5,4,1,7]=>1100110=>[1,1,3,1,2]
[8,2,6,1,3,5,4,7]=>1010010=>[1,2,3,2]
[8,5,3,4,2,7,1,6]=>1101010=>[1,1,2,2,2]
[8,4,3,7,2,5,6,1]=>1101001=>[1,1,2,3,1]
[5,3,4,1,8,2,7,6]=>1010101=>[1,2,2,2,1]
[8,3,1,7,4,5,2,6]=>1101010=>[1,1,2,2,2]
[8,2,4,5,1,7,3,6]=>1001010=>[1,3,2,2]
[4,3,8,1,7,5,6,2]=>1010101=>[1,2,2,2,1]
[8,4,3,7,1,5,6,2]=>1101001=>[1,1,2,3,1]
[8,3,4,7,2,6,5,1]=>1001011=>[1,3,2,1,1]
[8,1,3,7,6,4,5,2]=>1001101=>[1,3,1,2,1]
[8,1,4,3,7,5,6,2]=>1010101=>[1,2,2,2,1]
[8,3,7,1,4,5,6,2]=>1010001=>[1,2,4,1]
[8,7,3,6,1,2,5,4]=>1101001=>[1,1,2,3,1]
[8,3,7,6,2,4,5,1]=>1011001=>[1,2,1,3,1]
[8,7,2,3,6,1,5,4]=>1100101=>[1,1,3,2,1]
[8,7,1,2,6,5,3,4]=>1100110=>[1,1,3,1,2]
[8,2,7,1,3,4,6,5]=>1010001=>[1,2,4,1]
[5,1,8,4,2,3,7,6]=>1011001=>[1,2,1,3,1]
[8,2,4,7,3,1,6,5]=>1001101=>[1,3,1,2,1]
[8,2,7,6,3,1,4,5]=>1011100=>[1,2,1,1,3]
[6,8,1,4,7,3,2,5]=>0100110=>[2,3,1,2]
[8,5,7,2,6,3,1,4]=>1010110=>[1,2,2,1,2]
[5,8,2,7,3,1,6,4]=>0101101=>[2,2,1,2,1]
[8,1,2,6,7,5,4,3]=>1000111=>[1,4,1,1,1]
[6,2,8,5,1,7,3,4]=>1011010=>[1,2,1,2,2]
[8,4,1,7,5,6,2,3]=>1101010=>[1,1,2,2,2]
[8,1,2,4,7,6,5,3]=>1000111=>[1,4,1,1,1]
[8,2,4,7,6,5,1,3]=>1001110=>[1,3,1,1,2]
[8,2,7,6,4,5,1,3]=>1011010=>[1,2,1,2,2]
[8,4,7,2,3,6,5,1]=>1010011=>[1,2,3,1,1]
[8,2,4,7,3,6,5,1]=>1001011=>[1,3,2,1,1]
[8,1,7,6,4,5,2,3]=>1011010=>[1,2,1,2,2]
[8,1,2,7,6,4,5,3]=>1001101=>[1,3,1,2,1]
[8,1,4,2,7,5,6,3]=>1010101=>[1,2,2,2,1]
[8,1,5,7,3,6,4,2]=>1001011=>[1,3,2,1,1]
[8,1,4,7,3,6,5,2]=>1001011=>[1,3,2,1,1]
[1,7,3,8,6,2,5,4]=>0101101=>[2,2,1,2,1]
[5,8,2,3,7,4,1,6]=>0100110=>[2,3,1,2]
[4,2,8,3,7,6,1,5]=>1010110=>[1,2,2,1,2]
[1,2,4,6,8,3,7,5]=>0000101=>[5,2,1]
[1,3,5,6,4,8,2,7]=>0001010=>[4,2,2]
[3,1,7,8,5,2,4,6]=>1001100=>[1,3,1,3]
[6,3,5,2,8,4,7,1]=>1010101=>[1,2,2,2,1]
[1,6,3,5,2,8,4,7]=>0101010=>[2,2,2,2]
[1,5,4,8,6,3,7,2]=>0101101=>[2,2,1,2,1]
[5,4,8,6,3,7,2,1]=>1011011=>[1,2,1,2,1,1]
[5,4,8,6,3,7,1,2]=>1011010=>[1,2,1,2,2]
[6,4,5,8,3,1,7,2]=>1001101=>[1,3,1,2,1]
[6,4,5,8,1,3,7,2]=>1001001=>[1,3,3,1]
[6,3,5,1,8,4,7,2]=>1010101=>[1,2,2,2,1]
[2,6,3,1,5,8,4,7]=>0110010=>[2,1,3,2]
[2,5,4,8,6,3,1,7]=>0101110=>[2,2,1,1,2]
[1,2,5,4,8,6,3,7]=>0010110=>[3,2,1,2]
[2,4,8,5,6,7,3,1]=>0010011=>[3,3,1,1]
[4,8,5,6,7,1,3,2]=>0100101=>[2,3,2,1]
[6,4,5,8,2,1,7,3]=>1001101=>[1,3,1,2,1]
[5,3,8,2,6,7,1,4]=>1010010=>[1,2,3,2]
[6,3,5,2,8,1,7,4]=>1010101=>[1,2,2,2,1]
[5,3,4,1,2,6,8,7]=>1010001=>[1,2,4,1]
[4,3,5,2,8,6,1,7]=>1010110=>[1,2,2,1,2]
[1,4,3,5,2,8,6,7]=>0101010=>[2,2,2,2]
[1,3,5,4,8,2,6,7]=>0010100=>[3,2,3]
[3,5,4,8,2,6,1,7]=>0101010=>[2,2,2,2]
[3,6,4,5,1,2,8,7]=>0101001=>[2,2,3,1]
[4,3,5,1,8,6,2,7]=>1010110=>[1,2,2,1,2]
[3,5,4,8,1,6,2,7]=>0101010=>[2,2,2,2]
[3,4,8,5,6,1,2,7]=>0010100=>[3,2,3]
[3,4,8,5,6,2,1,7]=>0010110=>[3,2,1,2]
[3,4,8,5,6,2,7,1]=>0010101=>[3,2,2,1]
[3,5,4,8,1,6,7,2]=>0101001=>[2,2,3,1]
[2,4,3,1,5,8,6,7]=>0110010=>[2,1,3,2]
[1,7,6,2,5,4,8,3]=>0110101=>[2,1,2,2,1]
[8,1,6,4,3,5,2,7]=>1011010=>[1,2,1,2,2]
[1,3,7,8,2,6,4,5]=>0001010=>[4,2,2]
[3,8,6,4,5,2,7,1]=>0110101=>[2,1,2,2,1]
[4,5,8,6,2,3,7,1]=>0011001=>[3,1,3,1]
[4,5,8,1,6,7,2,3]=>0010010=>[3,3,2]
[4,6,8,5,3,7,2,1]=>0011011=>[3,1,2,1,1]
[4,5,7,2,8,6,3,1]=>0010111=>[3,2,1,1,1]
[3,7,4,5,1,6,8,2]=>0101001=>[2,2,3,1]
[4,6,8,1,2,5,7,3]=>0010001=>[3,4,1]
[3,7,8,5,1,4,6,2]=>0011001=>[3,1,3,1]
[4,6,8,5,1,3,7,2]=>0011001=>[3,1,3,1]
[4,6,8,5,2,7,3,1]=>0011011=>[3,1,2,1,1]
[3,8,6,2,7,4,5,1]=>0110101=>[2,1,2,2,1]
[3,7,4,5,2,8,6,1]=>0101011=>[2,2,2,1,1]
[3,7,8,4,6,1,5,2]=>0010101=>[3,2,2,1]
[4,6,8,3,7,1,5,2]=>0010101=>[3,2,2,1]
[3,5,1,7,8,4,6,2]=>0100101=>[2,3,2,1]
[4,5,1,6,8,3,7,2]=>0100101=>[2,3,2,1]
[4,3,1,8,5,7,2,6]=>1101010=>[1,1,2,2,2]
[4,8,3,6,1,5,2,7]=>0101010=>[2,2,2,2]
[8,3,2,4,7,1,6,5]=>1100101=>[1,1,3,2,1]
[7,3,2,4,8,1,6,5]=>1100101=>[1,1,3,2,1]
[8,3,2,4,6,1,7,5]=>1100101=>[1,1,3,2,1]
[8,3,2,4,5,7,1,6]=>1100010=>[1,1,4,2]
[8,3,6,2,4,1,7,5]=>1010101=>[1,2,2,2,1]
[7,4,6,2,1,3,8,5]=>1011001=>[1,2,1,3,1]
[3,2,4,5,7,8,1,6]=>1000010=>[1,5,2]
[3,6,7,2,4,1,8,5]=>0010101=>[3,2,2,1]
[5,3,2,8,7,6,4,1]=>1101111=>[1,1,2,1,1,1,1]
[4,3,6,1,8,5,2,7]=>1010110=>[1,2,2,1,2]
[4,3,7,5,8,2,1,6]=>1010110=>[1,2,2,1,2]
[7,3,5,2,8,1,4,6]=>1010100=>[1,2,2,3]
[2,6,8,4,5,1,7,3]=>0010101=>[3,2,2,1]
[1,5,8,7,4,2,3,6]=>0011100=>[3,1,1,3]
[1,5,2,7,6,4,8,3]=>0101101=>[2,2,1,2,1]
[1,4,6,8,7,2,5,3]=>0001101=>[4,1,2,1]
[1,3,6,8,7,2,5,4]=>0001101=>[4,1,2,1]
[1,4,3,6,8,7,2,5]=>0100110=>[2,3,1,2]
[1,6,2,7,5,3,4,8]=>0101100=>[2,2,1,3]
[1,7,2,5,4,3,8,6]=>0101101=>[2,2,1,2,1]
[1,6,3,7,2,4,5,8]=>0101000=>[2,2,4]
[1,3,2,6,8,5,4,7]=>0100110=>[2,3,1,2]
[1,6,3,2,7,4,5,8]=>0110100=>[2,1,2,3]
[1,5,8,6,2,7,4,3]=>0011011=>[3,1,2,1,1]
[1,3,7,2,6,4,5,8]=>0010100=>[3,2,3]
[1,3,7,5,8,6,2,4]=>0010110=>[3,2,1,2]
[1,7,3,2,8,5,6,4]=>0110101=>[2,1,2,2,1]
[1,6,5,2,4,8,3,7]=>0110010=>[2,1,3,2]
[1,4,7,6,2,3,5,8]=>0011000=>[3,1,4]
[1,7,3,8,4,2,5,6]=>0101100=>[2,2,1,3]
[1,6,2,4,7,5,8,3]=>0100101=>[2,3,2,1]
[1,6,2,7,4,3,8,5]=>0101101=>[2,2,1,2,1]
[1,5,8,2,3,6,4,7]=>0010010=>[3,3,2]
[2,6,7,3,4,8,1,5]=>0010010=>[3,3,2]
[4,1,3,8,7,5,2,6]=>1001110=>[1,3,1,1,2]
[3,6,7,2,1,5,8,4]=>0011001=>[3,1,3,1]
[2,5,6,1,3,8,7,4]=>0010011=>[3,3,1,1]
[2,1,3,8,6,7,4,5]=>1001010=>[1,3,2,2]
[3,8,5,2,1,6,4,7]=>0111010=>[2,1,1,2,2]
[5,4,7,8,1,6,3,2]=>1001011=>[1,3,2,1,1]
[7,2,8,5,6,3,4,1]=>1010101=>[1,2,2,2,1]
[3,2,7,6,8,4,5,1]=>1010101=>[1,2,2,2,1]
[4,3,8,6,7,2,5,1]=>1010101=>[1,2,2,2,1]
[8,4,5,2,7,3,6,1]=>1010101=>[1,2,2,2,1]
[4,3,8,5,6,2,7,1]=>1010101=>[1,2,2,2,1]
[5,4,8,6,7,2,3,1]=>1010101=>[1,2,2,2,1]
[7,3,4,2,8,5,6,1]=>1010101=>[1,2,2,2,1]
[4,3,6,5,8,2,7,1]=>1010101=>[1,2,2,2,1]
[8,2,7,4,5,3,6,1]=>1010101=>[1,2,2,2,1]
[7,2,8,4,5,3,6,1]=>1010101=>[1,2,2,2,1]
[6,3,8,2,7,4,5,1]=>1010101=>[1,2,2,2,1]
[3,2,8,4,7,5,6,1]=>1010101=>[1,2,2,2,1]
[3,2,7,4,8,5,6,1]=>1010101=>[1,2,2,2,1]
[7,2,8,3,6,4,5,1]=>1010101=>[1,2,2,2,1]
[8,3,6,2,7,4,5,1]=>1010101=>[1,2,2,2,1]
[1,7,8,4,3,6,5,2]=>0011011=>[3,1,2,1,1]
[1,7,8,3,6,5,4,2]=>0010111=>[3,2,1,1,1]
[6,4,5,8,7,2,1,3]=>1001110=>[1,3,1,1,2]
[1,8,4,2,3,7,5,6]=>0110010=>[2,1,3,2]
[6,4,2,3,8,7,5,1]=>1100111=>[1,1,3,1,1,1]
[6,1,4,2,7,8,3,5]=>1010010=>[1,2,3,2]
[6,5,1,3,7,8,4,2]=>1100011=>[1,1,4,1,1]
[6,4,2,3,7,8,5,1]=>1100011=>[1,1,4,1,1]
[6,7,4,2,3,8,5,1]=>0110011=>[2,1,3,1,1]
[5,1,3,2,6,8,4,7]=>1010010=>[1,2,3,2]
[5,7,1,4,6,8,2,3]=>0100010=>[2,4,2]
[5,7,8,3,2,4,6,1]=>0011001=>[3,1,3,1]
[1,5,7,3,6,4,2,8]=>0010110=>[3,2,1,2]
[1,6,3,5,7,4,8,2]=>0100101=>[2,3,2,1]
[1,7,2,4,8,3,5,6]=>0100100=>[2,3,3]
[1,6,7,2,4,8,3,5]=>0010010=>[3,3,2]
[1,6,7,8,2,4,3,5]=>0001010=>[4,2,2]
[3,1,6,7,8,4,2,5]=>1000110=>[1,4,1,2]
[3,1,6,7,8,4,5,2]=>1000101=>[1,4,2,1]
[1,6,7,8,2,4,5,3]=>0001001=>[4,3,1]
[4,2,7,6,8,5,1,3]=>1010110=>[1,2,2,1,2]
[5,3,4,1,7,8,6,2]=>1010011=>[1,2,3,1,1]
[3,7,5,6,1,8,4,2]=>0101011=>[2,2,2,1,1]
[1,2,6,8,4,3,5,7]=>0001100=>[4,1,3]
[2,4,7,5,8,3,6,1]=>0010101=>[3,2,2,1]
[6,8,7,4,2,5,1,3]=>0111010=>[2,1,1,2,2]
[7,6,3,1,2,8,5,4]=>1110011=>[1,1,1,3,1,1]
[3,1,8,6,4,7,2,5]=>1011010=>[1,2,1,2,2]
[6,2,7,8,3,4,5,1]=>1001001=>[1,3,3,1]
[8,1,3,5,6,4,7,2]=>1000101=>[1,4,2,1]
[2,3,7,5,8,4,6,1]=>0010101=>[3,2,2,1]
[2,5,7,4,6,1,3,8]=>0010100=>[3,2,3]
[4,8,2,6,5,3,7,1]=>0101101=>[2,2,1,2,1]
[5,8,6,4,7,3,2,1]=>0110111=>[2,1,2,1,1,1]
[8,5,2,3,1,6,7,4]=>1101001=>[1,1,2,3,1]
[8,5,4,2,1,6,7,3]=>1111001=>[1,1,1,1,3,1]
[8,3,5,2,1,6,7,4]=>1011001=>[1,2,1,3,1]
[2,8,6,3,5,1,7,4]=>0110101=>[2,1,2,2,1]
[8,3,2,6,4,1,7,5]=>1101101=>[1,1,2,1,2,1]
[8,4,1,5,3,6,7,2]=>1101001=>[1,1,2,3,1]
[8,3,5,1,4,6,7,2]=>1010001=>[1,2,4,1]
[8,5,1,3,4,6,7,2]=>1100001=>[1,1,5,1]
[2,8,6,1,5,4,7,3]=>0110101=>[2,1,2,2,1]
[8,3,2,6,1,5,7,4]=>1101001=>[1,1,2,3,1]
[3,8,6,4,7,1,2,5]=>0110100=>[2,1,2,3]
[3,8,6,2,5,4,7,1]=>0110101=>[2,1,2,2,1]
[3,8,4,6,5,2,7,1]=>0101101=>[2,2,1,2,1]
[2,8,6,4,7,3,1,5]=>0110110=>[2,1,2,1,2]
[8,3,5,4,2,7,1,6]=>1011010=>[1,2,1,2,2]
[8,1,7,4,2,5,3,6]=>1011010=>[1,2,1,2,2]
[8,3,2,5,1,4,7,6]=>1101001=>[1,1,2,3,1]
[8,4,1,3,2,6,7,5]=>1101001=>[1,1,2,3,1]
[8,4,5,1,2,6,7,3]=>1010001=>[1,2,4,1]
[8,1,5,2,4,6,7,3]=>1010001=>[1,2,4,1]
[8,3,1,5,2,6,7,4]=>1101001=>[1,1,2,3,1]
[2,8,1,6,5,3,7,4]=>0101101=>[2,2,1,2,1]
[8,3,2,1,6,4,7,5]=>1110101=>[1,1,1,2,2,1]
[5,2,6,4,1,3,8,7]=>1011001=>[1,2,1,3,1]
[2,1,8,5,4,3,7,6]=>1011101=>[1,2,1,1,2,1]
[6,2,8,5,4,1,3,7]=>1011100=>[1,2,1,1,3]
[7,2,8,5,4,1,3,6]=>1011100=>[1,2,1,1,3]
[3,7,5,8,4,1,2,6]=>0101100=>[2,2,1,3]
[5,2,4,7,8,1,3,6]=>1000100=>[1,4,3]
[1,7,6,2,8,5,3,4]=>0110110=>[2,1,2,1,2]
[5,6,2,8,1,7,3,4]=>0101010=>[2,2,2,2]
[3,1,2,4,8,6,7,5]=>1000101=>[1,4,2,1]
[1,8,7,2,3,4,5,6]=>0110000=>[2,1,5]
[8,6,3,2,5,4,7,1]=>1110101=>[1,1,1,2,2,1]
[8,6,4,2,5,3,7,1]=>1110101=>[1,1,1,2,2,1]
[8,6,5,2,4,3,7,1]=>1110101=>[1,1,1,2,2,1]
[8,5,6,2,4,3,7,1]=>1010101=>[1,2,2,2,1]
[6,2,5,3,7,4,8,1]=>1010101=>[1,2,2,2,1]
[8,4,5,2,6,3,7,1]=>1010101=>[1,2,2,2,1]
[8,5,4,2,6,3,7,1]=>1110101=>[1,1,1,2,2,1]
[8,5,3,2,6,4,7,1]=>1110101=>[1,1,1,2,2,1]
[7,4,6,5,8,2,3,1]=>1010101=>[1,2,2,2,1]
[7,3,6,5,8,2,4,1]=>1010101=>[1,2,2,2,1]
[7,3,6,4,8,2,5,1]=>1010101=>[1,2,2,2,1]
[7,3,5,4,8,2,6,1]=>1010101=>[1,2,2,2,1]
[3,7,5,2,8,1,4,6]=>0110100=>[2,1,2,3]
[1,2,7,4,8,5,6,3]=>0010101=>[3,2,2,1]
[2,6,7,1,8,4,5,3]=>0010101=>[3,2,2,1]
[5,6,3,4,2,8,7,1]=>0101011=>[2,2,2,1,1]
[3,2,7,5,8,1,6,4]=>1010101=>[1,2,2,2,1]
[3,6,5,8,2,7,4,1]=>0101011=>[2,2,2,1,1]
[2,7,1,8,5,6,4,3]=>0101011=>[2,2,2,1,1]
[4,3,6,8,5,2,1,7]=>1001110=>[1,3,1,1,2]
[4,3,6,8,5,2,7,1]=>1001101=>[1,3,1,2,1]
[4,5,3,2,1,8,6,7]=>0111010=>[2,1,1,2,2]
[3,6,5,8,1,7,4,2]=>0101011=>[2,2,2,1,1]
[3,6,5,8,1,2,7,4]=>0101001=>[2,2,3,1]
[4,1,6,8,5,2,3,7]=>1001100=>[1,3,1,3]
[4,5,2,8,6,7,3,1]=>0101011=>[2,2,2,1,1]
[3,5,8,6,2,4,7,1]=>0011001=>[3,1,3,1]
[3,2,4,5,8,6,1,7]=>1000110=>[1,4,1,2]
[3,4,5,8,6,2,1,7]=>0001110=>[4,1,1,2]
[3,4,5,8,6,2,7,1]=>0001101=>[4,1,2,1]
[4,5,2,1,3,8,6,7]=>0110010=>[2,1,3,2]
[4,2,3,6,8,5,1,7]=>1000110=>[1,4,1,2]
[4,1,3,6,8,5,2,7]=>1000110=>[1,4,1,2]
[3,1,4,5,8,6,2,7]=>1000110=>[1,4,1,2]
[4,5,1,3,2,8,6,7]=>0101010=>[2,2,2,2]
[3,4,5,8,6,1,7,2]=>0001101=>[4,1,2,1]
[3,4,5,8,6,1,2,7]=>0001100=>[4,1,3]
[8,2,5,4,1,3,7,6]=>1011001=>[1,2,1,3,1]
[8,2,6,4,1,3,7,5]=>1011001=>[1,2,1,3,1]
[1,5,8,2,4,3,7,6]=>0010101=>[3,2,2,1]
[4,3,7,8,2,6,5,1]=>1001011=>[1,3,2,1,1]
[7,3,8,4,1,5,6,2]=>1011001=>[1,2,1,3,1]
[8,6,7,1,4,3,2,5]=>1010110=>[1,2,2,1,2]
[3,8,5,1,2,6,7,4]=>0110001=>[2,1,4,1]
[3,7,8,2,5,4,6,1]=>0010101=>[3,2,2,1]
[2,4,7,8,3,6,5,1]=>0001011=>[4,2,1,1]
[5,4,7,8,3,6,1,2]=>1001010=>[1,3,2,2]
[6,8,1,3,2,5,7,4]=>0101001=>[2,2,3,1]
[2,4,8,3,5,7,1,6]=>0010010=>[3,3,2]
[1,4,8,5,7,2,3,6]=>0010100=>[3,2,3]
[1,8,7,3,2,4,5,6]=>0111000=>[2,1,1,4]
[2,8,4,3,5,7,1,6]=>0110010=>[2,1,3,2]
[5,6,2,7,8,3,1,4]=>0100110=>[2,3,1,2]
[8,6,2,7,3,4,1,5]=>1101010=>[1,1,2,2,2]
[8,6,2,7,3,4,5,1]=>1101001=>[1,1,2,3,1]
[5,6,2,7,8,3,4,1]=>0100101=>[2,3,2,1]
[5,6,3,2,8,7,1,4]=>0110110=>[2,1,2,1,2]
[6,8,5,3,1,7,2,4]=>0111010=>[2,1,1,2,2]
[8,6,1,7,3,4,2,5]=>1101010=>[1,1,2,2,2]
[5,1,6,7,8,3,2,4]=>1000110=>[1,4,1,2]
[1,5,6,3,7,2,4,8]=>0010100=>[3,2,3]
[6,2,4,8,3,7,1,5]=>1001010=>[1,3,2,2]
[1,6,8,7,5,2,3,4]=>0011100=>[3,1,1,3]
[1,5,6,7,4,2,3,8]=>0001100=>[4,1,3]
[5,1,6,7,3,4,2,8]=>1001010=>[1,3,2,2]
[8,6,1,7,3,4,5,2]=>1101001=>[1,1,2,3,1]
[6,1,8,7,4,5,2,3]=>1011010=>[1,2,1,2,2]
[2,6,8,4,7,5,1,3]=>0010110=>[3,2,1,2]
[6,8,5,1,7,4,2,3]=>0110110=>[2,1,2,1,2]
[4,6,5,7,2,3,8,1]=>0101001=>[2,2,3,1]
[5,3,7,4,6,2,8,1]=>1010101=>[1,2,2,2,1]
[3,6,7,2,5,8,4,1]=>0010011=>[3,3,1,1]
[3,5,7,6,8,2,1,4]=>0010110=>[3,2,1,2]
[5,3,6,7,4,8,1,2]=>1001010=>[1,3,2,2]
[3,5,7,6,8,1,4,2]=>0010101=>[3,2,2,1]
[4,2,7,8,3,6,5,1]=>1001011=>[1,3,2,1,1]
[5,4,3,7,8,1,6,2]=>1100101=>[1,1,3,2,1]
[5,3,6,7,8,2,1,4]=>1000110=>[1,4,1,2]
[3,5,7,8,4,2,1,6]=>0001110=>[4,1,1,2]
[4,6,7,8,2,1,3,5]=>0001100=>[4,1,3]
[4,6,7,3,2,8,1,5]=>0011010=>[3,1,2,2]
[4,6,5,3,7,8,1,2]=>0110010=>[2,1,3,2]
[4,6,5,2,7,8,3,1]=>0110011=>[2,1,3,1,1]
[3,7,5,2,8,6,1,4]=>0110110=>[2,1,2,1,2]
[5,6,2,4,7,8,3,1]=>0100011=>[2,4,1,1]
[5,4,6,2,8,3,7,1]=>1010101=>[1,2,2,2,1]
[5,6,3,2,8,4,7,1]=>0110101=>[2,1,2,2,1]
[5,6,2,8,3,4,7,1]=>0101001=>[2,2,3,1]
[3,7,4,8,1,6,5,2]=>0101011=>[2,2,2,1,1]
[5,2,6,4,8,7,3,1]=>1010111=>[1,2,2,1,1,1]
[2,4,7,8,6,5,1,3]=>0001110=>[4,1,1,2]
[2,5,7,8,6,1,4,3]=>0001101=>[4,1,2,1]
[1,3,6,4,8,2,7,5]=>0010101=>[3,2,2,1]
[2,4,5,3,8,7,1,6]=>0010110=>[3,2,1,2]
[8,6,3,7,2,4,1,5]=>1101010=>[1,1,2,2,2]
[8,4,6,7,3,5,2,1]=>1001011=>[1,3,2,1,1]
[4,8,5,3,2,7,1,6]=>0111010=>[2,1,1,2,2]
[5,4,8,1,3,7,2,6]=>1010010=>[1,2,3,2]
[8,4,5,3,1,7,2,6]=>1011010=>[1,2,1,2,2]
[7,4,5,3,1,8,6,2]=>1011011=>[1,2,1,2,1,1]
[5,6,8,7,2,4,3,1]=>0011011=>[3,1,2,1,1]
[8,4,6,3,7,5,1,2]=>1010110=>[1,2,2,1,2]
[5,7,8,6,4,2,3,1]=>0011101=>[3,1,1,2,1]
[6,8,7,5,1,3,2,4]=>0111010=>[2,1,1,2,2]
[3,8,2,6,7,5,1,4]=>0100110=>[2,3,1,2]
[4,7,6,3,8,2,5,1]=>0110101=>[2,1,2,2,1]
[6,7,4,1,8,2,5,3]=>0110101=>[2,1,2,2,1]
[6,8,4,1,7,5,2,3]=>0110110=>[2,1,2,1,2]
[7,5,4,2,1,8,6,3]=>1111011=>[1,1,1,1,2,1,1]
[5,7,6,8,3,2,4,1]=>0101101=>[2,2,1,2,1]
[7,6,4,2,8,1,5,3]=>1110101=>[1,1,1,2,2,1]
[7,4,6,3,8,1,5,2]=>1010101=>[1,2,2,2,1]
[3,4,6,8,2,5,7,1]=>0001001=>[4,3,1]
[1,8,5,6,4,2,3,7]=>0101100=>[2,2,1,3]
[1,8,4,5,6,2,3,7]=>0100100=>[2,3,3]
[6,4,8,5,7,3,1,2]=>1010110=>[1,2,2,1,2]
[1,7,6,2,3,5,8,4]=>0110001=>[2,1,4,1]
[7,2,5,4,6,8,1,3]=>1010010=>[1,2,3,2]
[7,2,4,5,6,8,1,3]=>1000010=>[1,5,2]
[8,1,6,5,2,7,4,3]=>1011011=>[1,2,1,2,1,1]
[2,7,1,5,3,8,6,4]=>0101011=>[2,2,2,1,1]
[3,5,7,2,8,4,1,6]=>0010110=>[3,2,1,2]
[7,3,2,1,4,8,6,5]=>1110011=>[1,1,1,3,1,1]
[8,3,7,2,6,5,1,4]=>1010110=>[1,2,2,1,2]
[7,8,6,1,4,5,2,3]=>0110010=>[2,1,3,2]
[7,5,8,2,6,1,4,3]=>1010101=>[1,2,2,2,1]
[4,5,7,2,8,3,1,6]=>0010110=>[3,2,1,2]
[8,5,1,3,2,4,6,7]=>1101000=>[1,1,2,4]
[3,8,5,1,2,4,6,7]=>0110000=>[2,1,5]
[5,1,3,2,4,6,8,7]=>1010001=>[1,2,4,1]
[5,3,8,1,4,2,6,7]=>1010100=>[1,2,2,3]
[5,8,4,1,2,3,6,7]=>0110000=>[2,1,5]
[5,1,7,8,4,2,3,6]=>1001100=>[1,3,1,3]
[1,5,7,8,2,4,3,6]=>0001010=>[4,2,2]
[3,5,8,1,4,2,7,6]=>0010101=>[3,2,2,1]
[2,8,5,7,1,4,3,6]=>0101010=>[2,2,2,2]
[4,8,7,5,1,2,3,6]=>0111000=>[2,1,1,4]
[8,6,4,1,2,3,7,5]=>1110001=>[1,1,1,4,1]
[8,1,2,4,6,3,7,5]=>1000101=>[1,4,2,1]
[6,3,8,4,1,7,2,5]=>1011010=>[1,2,1,2,2]
[7,6,1,4,2,3,8,5]=>1101001=>[1,1,2,3,1]
[1,7,5,2,3,4,8,6]=>0110001=>[2,1,4,1]
[7,8,1,2,5,3,4,6]=>0100100=>[2,3,3]
[1,8,7,5,2,3,4,6]=>0111000=>[2,1,1,4]
[7,1,4,8,2,3,6,5]=>1001001=>[1,3,3,1]
[1,8,4,7,5,2,3,6]=>0101100=>[2,2,1,3]
[7,3,4,1,8,6,2,5]=>1010110=>[1,2,2,1,2]
[8,4,7,2,1,6,3,5]=>1011010=>[1,2,1,2,2]
[7,1,5,3,6,8,2,4]=>1010010=>[1,2,3,2]
[8,1,5,3,6,7,2,4]=>1010010=>[1,2,3,2]
[3,6,5,2,4,7,8,1]=>0110001=>[2,1,4,1]
[2,7,5,4,6,8,1,3]=>0110010=>[2,1,3,2]
[1,7,5,4,6,8,2,3]=>0110010=>[2,1,3,2]
[2,7,5,3,6,8,1,4]=>0110010=>[2,1,3,2]
[4,7,8,2,5,6,1,3]=>0010010=>[3,3,2]
[2,8,5,4,6,7,1,3]=>0110010=>[2,1,3,2]
[4,7,5,3,8,1,2,6]=>0110100=>[2,1,2,3]
[4,2,7,6,8,1,3,5]=>1010100=>[1,2,2,3]
[3,1,7,8,5,6,2,4]=>1001010=>[1,3,2,2]
[1,3,8,5,6,7,2,4]=>0010010=>[3,3,2]
[3,4,7,8,6,1,2,5]=>0001100=>[4,1,3]
[6,8,3,2,4,1,5,7]=>0110100=>[2,1,2,3]
[9,10,2,4,6,8,1,3,5,7]=>010001000=>[2,4,4]
[7,8,2,4,6,10,1,3,5,9]=>010001000=>[2,4,4]
[9,7,10,2,4,6,8,1,3,5]=>101000100=>[1,2,4,3]
[8,9,10,7,2,4,6,1,3,5]=>001100100=>[3,1,3,3]
[5,6,2,4,8,10,1,3,7,9]=>010001000=>[2,4,4]
[5,6,9,10,2,4,8,1,3,7]=>000100100=>[4,3,3]
[7,5,8,2,4,6,10,1,3,9]=>101000100=>[1,2,4,3]
[7,9,5,10,2,4,6,8,1,3]=>010100010=>[2,2,4,2]
[5,8,9,10,7,2,4,6,1,3]=>000110010=>[4,1,3,2]
[6,7,8,5,2,4,10,1,3,9]=>001100100=>[3,1,3,3]
[9,6,7,5,10,2,4,8,1,3]=>101010010=>[1,2,2,3,2]
[8,9,6,10,5,7,2,4,1,3]=>010101010=>[2,2,2,2,2]
[7,8,9,10,6,5,2,4,1,3]=>000111010=>[4,1,1,2,2]
[3,4,2,6,8,10,1,5,7,9]=>010001000=>[2,4,4]
[3,4,9,10,2,6,8,1,5,7]=>000100100=>[4,3,3]
[3,4,7,8,2,6,10,1,5,9]=>000100100=>[4,3,3]
[9,3,4,7,10,2,6,8,1,5]=>100010010=>[1,4,3,2]
[8,9,10,3,4,7,2,6,1,5]=>001001010=>[3,3,2,2]
[5,3,6,2,4,8,10,1,7,9]=>101000100=>[1,2,4,3]
[5,3,6,9,10,2,4,8,1,7]=>100010010=>[1,4,3,2]
[5,7,3,8,2,4,6,10,1,9]=>010100010=>[2,2,4,2]
[5,7,9,3,10,2,4,6,8,1]=>001010001=>[3,2,4,1]
[8,5,9,10,3,7,2,4,6,1]=>100101001=>[1,3,2,3,1]
[3,6,7,8,5,2,4,10,1,9]=>000110010=>[4,1,3,2]
[9,3,6,7,5,10,2,4,8,1]=>100101001=>[1,3,2,3,1]
[6,8,3,9,10,5,7,2,4,1]=>010010101=>[2,3,2,2,1]
[7,8,9,10,3,6,5,2,4,1]=>000101101=>[4,2,1,2,1]
[4,5,6,3,2,8,10,1,7,9]=>001100100=>[3,1,3,3]
[4,5,6,3,9,10,2,8,1,7]=>001001010=>[3,3,2,2]
[7,4,5,3,8,2,6,10,1,9]=>101010010=>[1,2,2,3,2]
[7,4,5,9,3,10,2,6,8,1]=>100101001=>[1,3,2,3,1]
[4,8,5,9,10,3,7,2,6,1]=>010010101=>[2,3,2,2,1]
[6,7,4,8,3,5,2,10,1,9]=>010101010=>[2,2,2,2,2]
[6,7,9,4,3,5,10,2,8,1]=>001100101=>[3,1,3,2,1]
[8,6,9,4,10,3,5,7,2,1]=>101010011=>[1,2,2,3,1,1]
[7,4,8,9,10,6,3,5,2,1]=>100011011=>[1,4,1,2,1,1]
[5,6,7,8,4,3,2,10,1,9]=>000111010=>[4,1,1,2,2]
[9,5,6,7,4,3,10,2,8,1]=>100110101=>[1,3,1,2,2,1]
[8,9,5,6,4,10,3,7,2,1]=>010101011=>[2,2,2,2,1,1]
[7,8,9,5,10,4,6,3,2,1]=>001010111=>[3,2,2,1,1,1]
[9,6,10,11,12,3,8,5,7,2,4,1]=>10001010101=>[1,4,2,2,2,1]
[7,6,1,8,2,5,4,3]=>1101011=>[1,1,2,2,1,1]
[7,6,1,8,2,5,3,4]=>1101010=>[1,1,2,2,2]
[5,8,4,2,1,6,3,7]=>0111010=>[2,1,1,2,2]
[7,6,4,1,2,5,3,8]=>1110010=>[1,1,1,3,2]
[8,7,2,6,4,5,3,1]=>1101011=>[1,1,2,2,1,1]
[5,2,3,7,1,8,4,6]=>1001010=>[1,3,2,2]
[1,7,5,4,8,6,2,3]=>0110110=>[2,1,2,1,2]
[4,5,1,6,8,2,7,3]=>0100101=>[2,3,2,1]
[1,6,3,7,2,4,8,5]=>0101001=>[2,2,3,1]
[8,7,2,4,1,5,3,6]=>1101010=>[1,1,2,2,2]
[5,2,4,1,8,3,6,7]=>1010100=>[1,2,2,3]
[4,3,1,6,7,2,5,8]=>1100100=>[1,1,3,3]
[6,3,1,5,7,2,4,8]=>1100100=>[1,1,3,3]
[6,1,8,2,4,5,3,7]=>1010010=>[1,2,3,2]
[4,5,2,1,3,7,6,8]=>0110010=>[2,1,3,2]
[8,2,7,4,1,6,5,3]=>1011011=>[1,2,1,2,1,1]
[3,7,6,4,1,5,8,2]=>0111001=>[2,1,1,3,1]
[2,7,6,4,5,1,8,3]=>0110101=>[2,1,2,2,1]
[4,6,8,1,7,3,5,2]=>0010101=>[3,2,2,1]
[2,8,4,6,3,1,5,7]=>0101100=>[2,2,1,3]
[2,8,3,1,6,7,4,5]=>0110010=>[2,1,3,2]
[1,3,7,6,5,2,4,8]=>0011100=>[3,1,1,3]
[1,3,6,7,5,2,4,8]=>0001100=>[4,1,3]
[1,5,2,6,8,7,3,4]=>0100110=>[2,3,1,2]
[4,8,5,7,1,2,3,6]=>0101000=>[2,2,4]
[7,8,6,1,4,3,2,5]=>0110110=>[2,1,2,1,2]
[7,4,8,3,6,2,1,5]=>1010110=>[1,2,2,1,2]
[1,5,7,4,8,6,2,3]=>0010110=>[3,2,1,2]
[4,8,7,5,2,3,1,6]=>0111010=>[2,1,1,2,2]
[1,2,7,8,6,4,3,5]=>0001110=>[4,1,1,2]
[3,5,1,7,8,6,2,4]=>0100110=>[2,3,1,2]
[1,8,6,7,4,2,3,5]=>0101100=>[2,2,1,3]
[7,1,3,2,6,5,8,4]=>1010101=>[1,2,2,2,1]
[2,4,6,5,8,3,1,7]=>0010110=>[3,2,1,2]
[2,4,6,5,8,1,7,3]=>0010101=>[3,2,2,1]
[2,4,6,3,8,7,1,5]=>0010110=>[3,2,1,2]
[1,5,4,7,3,8,6,2]=>0101011=>[2,2,2,1,1]
[2,5,6,4,1,3,8,7]=>0011001=>[3,1,3,1]
[7,2,3,1,6,8,4,5]=>1010010=>[1,2,3,2]
[5,7,8,1,6,2,3,4]=>0010100=>[3,2,3]
[1,4,8,3,2,7,5,6]=>0011010=>[3,1,2,2]
[1,6,3,8,2,7,4,5]=>0101010=>[2,2,2,2]
[1,6,4,2,7,3,8,5]=>0110101=>[2,1,2,2,1]
[1,4,2,5,8,6,3,7]=>0100110=>[2,3,1,2]
[4,8,2,1,5,7,3,6]=>0110010=>[2,1,3,2]
[5,2,7,1,6,3,4,8]=>1010100=>[1,2,2,3]
[4,8,2,5,1,6,3,7]=>0101010=>[2,2,2,2]
[5,8,1,2,4,6,3,7]=>0100010=>[2,4,2]
[5,1,7,3,6,4,2,8]=>1010110=>[1,2,2,1,2]
[3,1,7,5,6,2,4,8]=>1010100=>[1,2,2,3]
[3,2,7,5,6,1,4,8]=>1010100=>[1,2,2,3]
[3,2,7,1,6,4,5,8]=>1010100=>[1,2,2,3]
[6,3,1,7,5,4,2,8]=>1101110=>[1,1,2,1,1,2]
[5,8,3,2,4,1,7,6]=>0110101=>[2,1,2,2,1]
[6,1,4,3,7,5,8,2]=>1010101=>[1,2,2,2,1]
[1,7,8,6,3,4,2,5]=>0011010=>[3,1,2,2]
[3,7,8,1,6,4,2,5]=>0010110=>[3,2,1,2]
[6,4,1,8,2,7,5,3]=>1101011=>[1,1,2,2,1,1]
[1,5,6,8,4,2,7,3]=>0001101=>[4,1,2,1]
[7,8,5,3,2,1,6,4]=>0111101=>[2,1,1,1,2,1]
[4,7,2,6,1,8,3,5]=>0101010=>[2,2,2,2]
[8,7,3,5,2,1,6,4]=>1101101=>[1,1,2,1,2,1]
[3,8,6,2,1,7,4,5]=>0111010=>[2,1,1,2,2]
[3,6,1,4,7,8,2,5]=>0100010=>[2,4,2]
[2,5,7,1,3,6,4,8]=>0010010=>[3,3,2]
[1,4,7,2,5,3,6,8]=>0010100=>[3,2,3]
[4,5,1,3,8,2,6,7]=>0100100=>[2,3,3]
[4,1,5,3,2,7,6,8]=>1011010=>[1,2,1,2,2]
[7,3,5,1,4,2,6,8]=>1010100=>[1,2,2,3]
[7,5,2,4,1,3,8,6]=>1101001=>[1,1,2,3,1]
[6,2,1,7,4,3,8,5]=>1101101=>[1,1,2,1,2,1]
[2,4,3,6,7,1,5,8]=>0100100=>[2,3,3]
[3,1,7,4,2,6,8,5]=>1011001=>[1,2,1,3,1]
[7,3,5,2,1,6,4,8]=>1011010=>[1,2,1,2,2]
[4,6,5,2,1,3,7,8]=>0111000=>[2,1,1,4]
[1,4,7,2,5,6,3,8]=>0010010=>[3,3,2]
[7,2,5,6,1,3,8,4]=>1001001=>[1,3,3,1]
[2,5,6,1,4,3,7,8]=>0010100=>[3,2,3]
[6,1,5,3,7,2,4,8]=>1010100=>[1,2,2,3]
[3,6,5,4,1,7,2,8]=>0111010=>[2,1,1,2,2]
[1,7,4,5,6,8,2,3]=>0100010=>[2,4,2]
[6,8,5,7,2,1,4,3]=>0101101=>[2,2,1,2,1]
[1,6,8,7,3,4,2,5]=>0011010=>[3,1,2,2]
[1,4,2,6,7,8,5,3]=>0100011=>[2,4,1,1]
[5,6,4,2,1,8,3,7]=>0111010=>[2,1,1,2,2]
[4,1,2,6,7,8,5,3]=>1000011=>[1,5,1,1]
[3,7,8,1,5,2,6,4]=>0010101=>[3,2,2,1]
[2,1,4,3,6,5,10,7,9,8]=>101010101=>[1,2,2,2,2,1]
[2,1,4,3,8,5,7,6,10,9]=>101010101=>[1,2,2,2,2,1]
[2,1,4,3,10,9,7,5,6,8]=>101011100=>[1,2,2,1,1,3]
[2,1,4,3,10,5,6,8,9,7]=>101010001=>[1,2,2,4,1]
[2,1,6,3,5,4,8,7,10,9]=>101010101=>[1,2,2,2,2,1]
[2,1,6,3,5,4,10,7,9,8]=>101010101=>[1,2,2,2,2,1]
[2,1,8,7,5,3,4,6,10,9]=>101110001=>[1,2,1,1,4,1]
[2,1,10,7,5,9,4,3,6,8]=>101101100=>[1,2,1,2,1,3]
[2,1,10,8,5,3,6,4,9,7]=>101110101=>[1,2,1,1,2,2,1]
[2,1,8,3,4,6,7,5,10,9]=>101000101=>[1,2,4,2,1]
[2,1,10,9,4,6,7,3,5,8]=>101100100=>[1,2,1,3,3]
[2,1,10,3,9,6,4,8,5,7]=>101011010=>[1,2,2,1,2,2]
[2,1,10,3,4,5,7,8,9,6]=>101000001=>[1,2,6,1]
[4,1,3,2,6,5,8,7,10,9]=>101010101=>[1,2,2,2,2,1]
[4,1,3,2,6,5,10,7,9,8]=>101010101=>[1,2,2,2,2,1]
[4,1,3,2,8,5,7,6,10,9]=>101010101=>[1,2,2,2,2,1]
[4,1,3,2,10,9,7,5,6,8]=>101011100=>[1,2,2,1,1,3]
[4,1,3,2,10,5,6,8,9,7]=>101010001=>[1,2,2,4,1]
[6,5,3,1,2,4,8,7,10,9]=>111000101=>[1,1,1,4,2,1]
[6,5,3,1,2,4,10,7,9,8]=>111000101=>[1,1,1,4,2,1]
[8,5,3,7,2,1,4,6,10,9]=>110110001=>[1,1,2,1,4,1]
[10,5,3,7,2,9,4,1,6,8]=>110101100=>[1,1,2,2,1,3]
[10,5,3,8,2,1,6,4,9,7]=>110110101=>[1,1,2,1,2,2,1]
[8,6,3,1,4,2,7,5,10,9]=>111010101=>[1,1,1,2,2,2,1]
[10,6,3,9,4,2,7,1,5,8]=>110110100=>[1,1,2,1,2,3]
[10,6,3,1,9,2,4,8,5,7]=>111010010=>[1,1,1,2,3,2]
[10,7,3,1,4,5,2,8,9,6]=>111001001=>[1,1,1,3,3,1]
[6,1,2,4,5,3,8,7,10,9]=>100010101=>[1,4,2,2,1]
[6,1,2,4,5,3,10,7,9,8]=>100010101=>[1,4,2,2,1]
[8,7,2,4,5,1,3,6,10,9]=>110010001=>[1,1,3,4,1]
[10,7,2,4,5,9,3,1,6,8]=>110001100=>[1,1,4,1,3]
[10,8,2,4,5,1,6,3,9,7]=>110010101=>[1,1,3,2,2,1]
[8,1,7,4,2,6,3,5,10,9]=>101101001=>[1,2,1,2,3,1]
[10,9,7,4,2,6,3,1,5,8]=>111101100=>[1,1,1,1,2,1,3]
[10,1,8,4,9,6,2,3,5,7]=>101011000=>[1,2,2,1,4]
[10,1,8,4,2,5,7,3,9,6]=>101100101=>[1,2,1,3,2,1]
[8,1,2,3,5,6,7,4,10,9]=>100000101=>[1,6,2,1]
[10,9,2,3,5,6,7,1,4,8]=>110000100=>[1,1,5,3]
[10,1,9,3,5,6,2,8,4,7]=>101001010=>[1,2,3,2,2]
[10,1,2,9,5,3,7,8,4,6]=>100110010=>[1,3,1,3,2]
[2,1,4,3,6,5,8,7,12,9,11,10]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,4,3,6,5,10,7,9,8,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,4,3,8,5,7,6,10,9,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,4,3,8,5,7,6,12,9,11,10]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,6,3,5,4,8,7,10,9,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,6,3,5,4,8,7,12,9,11,10]=>10101010101=>[1,2,2,2,2,2,1]
[2,1,6,3,5,4,10,7,9,8,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[4,1,3,2,6,5,8,7,10,9,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[4,1,3,2,6,5,8,7,12,9,11,10]=>10101010101=>[1,2,2,2,2,2,1]
[4,1,3,2,6,5,10,7,9,8,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[4,1,3,2,8,5,7,6,10,9,12,11]=>10101010101=>[1,2,2,2,2,2,1]
[4,1,3,2,8,5,7,6,12,9,11,10]=>10101010101=>[1,2,2,2,2,2,1]
[6,1,2,4,5,3,8,7,10,9,12,11]=>10001010101=>[1,4,2,2,2,1]
[6,1,2,4,5,3,8,7,12,9,11,10]=>10001010101=>[1,4,2,2,2,1]
[6,1,2,4,5,3,10,7,9,8,12,11]=>10001010101=>[1,4,2,2,2,1]
[8,1,2,3,5,6,7,4,10,9,12,11]=>10000010101=>[1,6,2,2,1]
[8,1,2,3,5,6,7,4,12,9,11,10]=>10000010101=>[1,6,2,2,1]
[10,1,2,3,4,6,7,8,9,5,12,11]=>10000000101=>[1,8,2,1]
[12,1,2,3,4,5,7,8,9,10,11,6]=>10000000001=>[1,10,1]
[1,5,4,7,8,3,6,2]=>0100101=>[2,3,2,1]
[5,1,4,7,8,3,6,2]=>1000101=>[1,4,2,1]
[5,6,4,1,7,3,8,2]=>0110101=>[2,1,2,2,1]
[8,3,7,5,4,2,6,1]=>1011101=>[1,2,1,1,2,1]
[4,3,7,8,2,5,1,6]=>1001010=>[1,3,2,2]
[3,7,8,5,4,2,1,6]=>0011110=>[3,1,1,1,2]
[1,7,4,5,6,8,3,2]=>0100011=>[2,4,1,1]
[2,7,4,5,6,8,3,1]=>0100011=>[2,4,1,1]
[2,8,3,5,6,4,1,7]=>0100110=>[2,3,1,2]
[2,4,7,8,3,1,6,5]=>0001101=>[4,1,2,1]
[5,4,3,6,8,1,7,2]=>1100101=>[1,1,3,2,1]
[3,7,4,5,8,1,2,6]=>0100100=>[2,3,3]
[3,7,4,5,8,1,6,2]=>0100101=>[2,3,2,1]
[1,4,3,5,6,8,2,7]=>0100010=>[2,4,2]
[1,4,6,5,8,2,7,3]=>0010101=>[3,2,2,1]
[2,4,3,5,8,1,6,7]=>0100100=>[2,3,3]
[4,6,1,7,3,2,8,5]=>0101101=>[2,2,1,2,1]
[1,7,3,6,4,2,8,5]=>0101101=>[2,2,1,2,1]
[1,3,7,6,2,4,8,5]=>0011001=>[3,1,3,1]
[4,7,3,5,1,2,8,6]=>0101001=>[2,2,3,1]
[2,5,1,8,3,7,4,6]=>0101010=>[2,2,2,2]
[5,1,2,4,3,6,8,7]=>1001001=>[1,3,3,1]
[4,8,3,5,2,1,6,7]=>0101100=>[2,2,1,3]
[8,7,3,1,5,2,6,4]=>1110101=>[1,1,1,2,2,1]
[3,8,4,1,7,5,2,6]=>0110110=>[2,1,2,1,2]
[7,8,5,3,6,2,1,4]=>0110110=>[2,1,2,1,2]
[6,7,1,5,2,8,4,3]=>0101011=>[2,2,2,1,1]
[2,7,6,4,8,3,1,5]=>0110110=>[2,1,2,1,2]
[2,6,3,7,5,8,4,1]=>0101011=>[2,2,2,1,1]
[4,7,3,2,6,5,1,8]=>0110110=>[2,1,2,1,2]
[4,7,5,2,3,6,1,8]=>0110010=>[2,1,3,2]
[4,3,7,8,2,1,6,5]=>1001101=>[1,3,1,2,1]
[4,8,7,2,1,5,6,3]=>0111001=>[2,1,1,3,1]
[7,3,8,2,5,1,6,4]=>1010101=>[1,2,2,2,1]
[4,5,3,8,2,1,7,6]=>0101101=>[2,2,1,2,1]
[4,5,3,8,6,1,2,7]=>0101100=>[2,2,1,3]
[7,3,8,4,5,1,2,6]=>1010100=>[1,2,2,3]
[4,8,7,5,1,3,2,6]=>0111010=>[2,1,1,2,2]
[4,8,7,5,1,2,6,3]=>0111001=>[2,1,1,3,1]
[7,8,4,6,1,3,5,2]=>0101001=>[2,2,3,1]
[4,8,7,5,1,3,6,2]=>0111001=>[2,1,1,3,1]
[4,5,3,6,8,1,2,7]=>0100100=>[2,3,3]
[7,8,6,2,1,4,3,5]=>0111010=>[2,1,1,2,2]
[4,7,5,8,2,1,3,6]=>0101100=>[2,2,1,3]
[4,8,5,7,1,3,2,6]=>0101010=>[2,2,2,2]
[7,8,6,3,1,2,5,4]=>0111001=>[2,1,1,3,1]
[4,1,3,6,5,7,2,8]=>1001010=>[1,3,2,2]
[4,1,3,5,7,2,8,6]=>1000101=>[1,4,2,1]
[5,1,8,2,4,6,3,7]=>1010010=>[1,2,3,2]
[6,8,2,1,4,5,3,7]=>0110010=>[2,1,3,2]
[2,1,4,7,5,3,8,6]=>1001101=>[1,3,1,2,1]
[6,8,1,3,5,7,4,2]=>0100011=>[2,4,1,1]
[5,8,3,2,7,4,6,1]=>0110101=>[2,1,2,2,1]
[4,1,3,7,5,6,2,8]=>1001010=>[1,3,2,2]
[5,1,7,2,4,6,3,8]=>1010010=>[1,2,3,2]
[4,2,7,3,6,8,5,1]=>1010011=>[1,2,3,1,1]
[5,8,4,7,1,3,6,2]=>0101001=>[2,2,3,1]
[3,1,5,8,6,7,2,4]=>1001010=>[1,3,2,2]
[6,8,2,1,4,5,7,3]=>0110001=>[2,1,4,1]
[5,3,1,2,4,6,8,7]=>1100001=>[1,1,5,1]
[3,6,7,5,8,4,1,2]=>0010110=>[3,2,1,2]
[6,1,5,2,8,7,4,3]=>1010111=>[1,2,2,1,1,1]
[3,2,6,1,5,8,7,4]=>1010011=>[1,2,3,1,1]
[4,5,2,1,6,7,8,3]=>0110001=>[2,1,4,1]
[8,4,6,3,1,2,7,5]=>1011001=>[1,2,1,3,1]
[3,7,6,4,1,5,2,8]=>0111010=>[2,1,1,2,2]
[3,8,6,4,1,5,7,2]=>0111001=>[2,1,1,3,1]
[8,7,1,4,5,2,3,6]=>1100100=>[1,1,3,3]
[8,7,1,4,2,5,3,6]=>1101010=>[1,1,2,2,2]
[4,8,7,3,1,2,6,5]=>0111001=>[2,1,1,3,1]
[3,8,6,4,5,1,7,2]=>0110101=>[2,1,2,2,1]
[3,7,6,4,5,1,2,8]=>0110100=>[2,1,2,3]
[8,4,6,2,1,7,3,5]=>1011010=>[1,2,1,2,2]
[7,4,6,3,1,2,8,5]=>1011001=>[1,2,1,3,1]
[4,6,3,5,7,1,8,2]=>0100101=>[2,3,2,1]
[4,6,2,5,7,8,1,3]=>0100010=>[2,4,2]
[4,7,3,5,8,1,6,2]=>0100101=>[2,3,2,1]
[4,6,3,5,7,1,2,8]=>0100100=>[2,3,3]
[4,7,3,5,8,6,1,2]=>0100110=>[2,3,1,2]
[4,7,3,5,6,1,2,8]=>0100100=>[2,3,3]
[4,8,3,5,7,1,6,2]=>0100101=>[2,3,2,1]
[4,8,3,5,6,1,2,7]=>0100100=>[2,3,3]
[4,7,2,5,6,8,1,3]=>0100010=>[2,4,2]
[4,8,2,5,6,7,1,3]=>0100010=>[2,4,2]
[1,4,7,2,6,5,8,3]=>0010101=>[3,2,2,1]
[1,2,7,8,3,5,4,6]=>0001010=>[4,2,2]
[1,6,7,8,3,2,5,4]=>0001101=>[4,1,2,1]
[1,7,6,2,8,5,4,3]=>0110111=>[2,1,2,1,1,1]
[1,6,7,8,3,2,4,5]=>0001100=>[4,1,3]
[1,2,7,8,3,4,6,5]=>0001001=>[4,3,1]
[1,7,6,8,3,4,2,5]=>0101010=>[2,2,2,2]
[8,4,7,3,1,2,6,5]=>1011001=>[1,2,1,3,1]
[4,2,8,1,6,5,7,3]=>1010101=>[1,2,2,2,1]
[3,1,8,2,6,5,7,4]=>1010101=>[1,2,2,2,1]
[2,8,4,3,1,6,5,7]=>0111010=>[2,1,1,2,2]
[2,4,3,8,6,5,1,7]=>0101110=>[2,2,1,1,2]
[2,8,6,4,3,1,7,5]=>0111101=>[2,1,1,1,2,1]
[7,4,5,8,1,3,6,2]=>1001001=>[1,3,3,1]
[1,4,6,3,2,5,8,7]=>0011001=>[3,1,3,1]
[4,2,5,7,1,6,8,3]=>1001001=>[1,3,3,1]
[4,5,3,7,1,6,8,2]=>0101001=>[2,2,3,1]
[6,8,4,1,5,7,3,2]=>0110011=>[2,1,3,1,1]
[6,8,4,1,5,7,2,3]=>0110010=>[2,1,3,2]
[5,2,6,7,4,1,8,3]=>1001101=>[1,3,1,2,1]
[5,6,7,4,3,1,8,2]=>0011101=>[3,1,1,2,1]
[8,5,6,4,1,7,3,2]=>1011011=>[1,2,1,2,1,1]
[5,8,2,6,1,7,4,3]=>0101011=>[2,2,2,1,1]
[7,8,3,1,6,4,5,2]=>0110101=>[2,1,2,2,1]
[5,8,2,6,3,1,7,4]=>0101101=>[2,2,1,2,1]
[4,5,8,1,6,3,7,2]=>0010101=>[3,2,2,1]
[8,1,4,6,2,5,7,3]=>1001001=>[1,3,3,1]
[4,8,1,3,6,2,7,5]=>0100101=>[2,3,2,1]
[4,5,8,1,6,2,7,3]=>0010101=>[3,2,2,1]
[5,2,6,8,1,4,3,7]=>1001010=>[1,3,2,2]
[6,2,7,3,8,1,4,5]=>1010100=>[1,2,2,3]
[6,7,3,8,2,1,4,5]=>0101100=>[2,2,1,3]
[6,2,7,8,3,1,4,5]=>1001100=>[1,3,1,3]
[8,7,3,1,2,5,6,4]=>1110001=>[1,1,1,4,1]
[2,8,3,6,4,1,7,5]=>0101101=>[2,2,1,2,1]
[6,1,3,7,2,8,5,4]=>1001011=>[1,3,2,1,1]
[5,4,3,6,1,7,8,2]=>1101001=>[1,1,2,3,1]
[4,8,3,2,1,7,5,6]=>0111010=>[2,1,1,2,2]
[1,2,4,6,5,8,3,7]=>0001010=>[4,2,2]
[2,4,8,6,3,1,7,5]=>0011101=>[3,1,1,2,1]
[3,4,8,1,6,7,2,5]=>0010010=>[3,3,2]
[3,6,7,8,4,1,5,2]=>0001101=>[4,1,2,1]
[2,3,7,8,4,6,1,5]=>0001010=>[4,2,2]
[1,3,7,8,4,6,2,5]=>0001010=>[4,2,2]
[3,1,7,8,4,6,2,5]=>1001010=>[1,3,2,2]
[4,8,7,3,6,1,2,5]=>0110100=>[2,1,2,3]
[5,8,4,3,7,1,2,6]=>0110100=>[2,1,2,3]
[4,1,8,3,7,5,2,6]=>1010110=>[1,2,2,1,2]
[2,4,8,3,6,7,1,5]=>0010010=>[3,3,2]
[2,4,8,6,5,7,1,3]=>0011010=>[3,1,2,2]
[1,6,5,8,7,3,2,4]=>0101110=>[2,2,1,1,2]
[5,6,4,8,7,2,1,3]=>0101110=>[2,2,1,1,2]
[7,2,6,8,3,5,1,4]=>1001010=>[1,3,2,2]
[7,2,8,6,5,3,1,4]=>1011110=>[1,2,1,1,1,2]
[4,8,3,7,6,1,2,5]=>0101100=>[2,2,1,3]
[4,1,7,8,6,5,2,3]=>1001110=>[1,3,1,1,2]
[2,1,8,7,3,5,4,6]=>1011010=>[1,2,1,2,2]
[1,7,6,2,3,8,5,4]=>0110011=>[2,1,3,1,1]
[1,8,5,3,2,7,4,6]=>0111010=>[2,1,1,2,2]
[4,5,1,3,7,6,2,8]=>0100110=>[2,3,1,2]
[7,2,3,8,6,4,5,1]=>1001101=>[1,3,1,2,1]
[3,5,8,1,7,4,2,6]=>0010110=>[3,2,1,2]
[5,8,1,2,7,6,4,3]=>0100111=>[2,3,1,1,1]
[8,7,1,3,2,6,4,5]=>1101010=>[1,1,2,2,2]
[1,3,8,5,2,4,6,7]=>0011000=>[3,1,4]
[7,8,6,1,3,2,4,5]=>0110100=>[2,1,2,3]
[8,1,6,3,7,5,4,2]=>1010111=>[1,2,2,1,1,1]
[8,5,1,3,7,6,4,2]=>1100111=>[1,1,3,1,1,1]
[1,6,4,7,3,8,5,2]=>0101011=>[2,2,2,1,1]
[1,6,7,5,8,4,2,3]=>0010110=>[3,2,1,2]
[7,4,1,6,5,2,8,3]=>1101101=>[1,1,2,1,2,1]
[5,3,8,2,7,6,1,4]=>1010110=>[1,2,2,1,2]
[7,4,2,8,6,5,3,1]=>1101111=>[1,1,2,1,1,1,1]
[5,8,2,7,6,1,4,3]=>0101101=>[2,2,1,2,1]
[7,4,8,3,1,6,5,2]=>1011011=>[1,2,1,2,1,1]
[5,8,7,2,6,4,3,1]=>0110111=>[2,1,2,1,1,1]
[6,8,7,5,2,1,4,3]=>0111101=>[2,1,1,1,2,1]
[6,8,7,3,5,1,4,2]=>0110101=>[2,1,2,2,1]
[1,8,6,4,7,3,2,5]=>0110110=>[2,1,2,1,2]
[7,2,5,4,1,3,8,6]=>1011001=>[1,2,1,3,1]
[8,6,7,2,3,5,4,1]=>1010011=>[1,2,3,1,1]
[5,4,8,6,7,3,1,2]=>1010110=>[1,2,2,1,2]
[4,2,7,3,1,6,8,5]=>1011001=>[1,2,1,3,1]
[7,2,6,8,5,1,3,4]=>1001100=>[1,3,1,3]
[7,3,6,4,2,1,8,5]=>1011101=>[1,2,1,1,2,1]
[4,8,5,2,7,3,1,6]=>0110110=>[2,1,2,1,2]
[5,8,6,3,2,1,7,4]=>0111101=>[2,1,1,1,2,1]
[6,4,3,1,8,5,2,7]=>1110110=>[1,1,1,2,1,2]
[7,4,3,1,5,8,6,2]=>1110011=>[1,1,1,3,1,1]
[7,4,8,6,5,3,1,2]=>1011110=>[1,2,1,1,1,2]
[7,8,5,2,6,4,3,1]=>0110111=>[2,1,2,1,1,1]
[7,3,2,1,8,5,6,4]=>1110101=>[1,1,1,2,2,1]
[1,5,7,2,4,3,8,6]=>0010101=>[3,2,2,1]
[1,2,7,5,8,4,3,6]=>0010110=>[3,2,1,2]
[5,1,3,8,2,7,4,6]=>1001010=>[1,3,2,2]
[5,7,1,3,2,8,4,6]=>0101010=>[2,2,2,2]
[7,1,6,3,2,8,4,5]=>1011010=>[1,2,1,2,2]
[8,1,7,2,3,6,5,4]=>1010011=>[1,2,3,1,1]
[1,7,2,5,8,4,3,6]=>0100110=>[2,3,1,2]
[7,1,2,6,4,3,8,5]=>1001101=>[1,3,1,2,1]
[1,4,7,8,3,2,5,6]=>0001100=>[4,1,3]
[8,7,1,3,2,4,6,5]=>1101001=>[1,1,2,3,1]
[8,1,6,3,2,4,7,5]=>1011001=>[1,2,1,3,1]
[1,8,2,7,6,3,5,4]=>0101101=>[2,2,1,2,1]
[1,8,6,2,7,4,3,5]=>0110110=>[2,1,2,1,2]
[8,1,6,3,2,7,4,5]=>1011010=>[1,2,1,2,2]
[8,2,1,7,6,3,4,5]=>1101100=>[1,1,2,1,3]
[6,8,4,3,5,1,2,7]=>0110100=>[2,1,2,3]
[8,7,3,5,4,1,2,6]=>1101100=>[1,1,2,1,3]
[8,5,3,6,4,2,1,7]=>1101110=>[1,1,2,1,1,2]
[6,3,8,5,7,2,1,4]=>1010110=>[1,2,2,1,2]
[8,7,3,6,4,1,2,5]=>1101100=>[1,1,2,1,3]
[5,2,7,4,6,1,3,8]=>1010100=>[1,2,2,3]
[8,7,2,3,5,1,4,6]=>1100100=>[1,1,3,3]
[6,4,5,3,1,7,8,2]=>1011001=>[1,2,1,3,1]
[6,4,5,3,1,8,7,2]=>1011011=>[1,2,1,2,1,1]
[8,7,3,2,5,1,6,4]=>1110101=>[1,1,1,2,2,1]
[6,3,5,2,8,1,4,7]=>1010100=>[1,2,2,3]
[6,4,5,3,1,7,2,8]=>1011010=>[1,2,1,2,2]
[8,7,2,4,3,1,5,6]=>1101100=>[1,1,2,1,3]
[7,6,2,3,1,4,8,5]=>1101001=>[1,1,2,3,1]
[4,7,6,2,3,1,5,8]=>0110100=>[2,1,2,3]
[1,8,2,3,5,6,4,7]=>0100010=>[2,4,2]
[2,8,1,3,5,6,4,7]=>0100010=>[2,4,2]
[2,5,7,4,8,3,6,1]=>0010101=>[3,2,2,1]
[2,6,3,4,7,8,5,1]=>0100011=>[2,4,1,1]
[2,3,5,4,7,1,8,6]=>0010101=>[3,2,2,1]
[7,4,1,3,6,8,5,2]=>1100011=>[1,1,4,1,1]
[7,2,1,3,6,8,4,5]=>1100010=>[1,1,4,2]
[7,4,2,3,6,8,5,1]=>1100011=>[1,1,4,1,1]
[7,2,3,6,8,5,4,1]=>1000111=>[1,4,1,1,1]
[7,6,3,1,8,5,2,4]=>1110110=>[1,1,1,2,1,2]
[7,2,1,3,6,8,5,4]=>1100011=>[1,1,4,1,1]
[7,6,3,8,1,5,2,4]=>1101010=>[1,1,2,2,2]
[1,6,4,7,8,5,3,2]=>0100111=>[2,3,1,1,1]
[1,2,4,6,8,5,7,3]=>0000101=>[5,2,1]
[8,5,2,3,7,4,1,6]=>1100110=>[1,1,3,1,2]
[2,6,3,7,4,1,8,5]=>0101101=>[2,2,1,2,1]
[6,1,3,2,8,5,7,4]=>1010101=>[1,2,2,2,1]
[3,8,5,1,2,4,7,6]=>0110001=>[2,1,4,1]
[1,8,3,7,5,2,6,4]=>0101101=>[2,2,1,2,1]
[8,1,3,6,5,2,7,4]=>1001101=>[1,3,1,2,1]
[7,1,3,8,5,2,6,4]=>1001101=>[1,3,1,2,1]
[4,7,1,5,2,6,8,3]=>0101001=>[2,2,3,1]
[7,4,1,5,2,6,8,3]=>1101001=>[1,1,2,3,1]
[3,1,6,7,5,2,8,4]=>1001101=>[1,3,1,2,1]
[8,6,2,4,5,1,7,3]=>1100101=>[1,1,3,2,1]
[4,6,2,5,3,1,7,8]=>0101100=>[2,2,1,3]
[7,1,4,5,2,6,8,3]=>1001001=>[1,3,3,1]
[5,7,6,8,2,1,4,3]=>0101101=>[2,2,1,2,1]
[3,5,4,7,8,2,6,1]=>0100101=>[2,3,2,1]
[5,1,4,7,6,8,3,2]=>1001011=>[1,3,2,1,1]
[5,2,4,7,6,8,3,1]=>1001011=>[1,3,2,1,1]
[5,6,4,7,1,8,3,2]=>0101011=>[2,2,2,1,1]
[3,6,7,5,1,4,8,2]=>0011001=>[3,1,3,1]
[6,3,7,1,2,5,8,4]=>1010001=>[1,2,4,1]
[5,1,4,7,8,2,6,3]=>1000101=>[1,4,2,1]
[6,3,7,5,1,2,8,4]=>1011001=>[1,2,1,3,1]
[5,3,7,4,6,1,8,2]=>1010101=>[1,2,2,2,1]
[5,4,1,7,6,8,3,2]=>1101011=>[1,1,2,2,1,1]
[4,2,5,3,6,7,8,1]=>1010001=>[1,2,4,1]
[4,5,1,3,6,7,8,2]=>0100001=>[2,5,1]
[3,6,7,1,5,4,8,2]=>0010101=>[3,2,2,1]
[3,6,4,7,5,8,2,1]=>0101011=>[2,2,2,1,1]
[6,4,7,1,5,2,8,3]=>1010101=>[1,2,2,2,1]
[3,5,6,2,1,7,8,4]=>0011001=>[3,1,3,1]
[2,5,6,7,1,8,4,3]=>0001011=>[4,2,1,1]
[8,1,4,3,5,2,7,6]=>1010101=>[1,2,2,2,1]
[4,8,1,3,5,2,7,6]=>0100101=>[2,3,2,1]
[4,5,1,6,2,8,7,3]=>0101011=>[2,2,2,1,1]
[4,5,1,7,2,8,6,3]=>0101011=>[2,2,2,1,1]
[7,1,4,3,6,8,2,5]=>1010010=>[1,2,3,2]
[5,6,3,2,7,4,1,8]=>0110110=>[2,1,2,1,2]
[5,2,6,7,4,3,1,8]=>1001110=>[1,3,1,1,2]
[8,5,1,6,4,3,2,7]=>1101110=>[1,1,2,1,1,2]
[8,5,1,6,4,3,7,2]=>1101101=>[1,1,2,1,2,1]
[8,5,2,1,6,4,3,7]=>1110110=>[1,1,1,2,1,2]
[8,6,3,5,2,7,1,4]=>1101010=>[1,1,2,2,2]
[8,4,6,2,1,5,7,3]=>1011001=>[1,2,1,3,1]
[5,6,2,1,8,4,7,3]=>0110101=>[2,1,2,2,1]
[8,5,2,1,6,4,7,3]=>1110101=>[1,1,1,2,2,1]
[1,7,2,8,5,4,6,3]=>0101101=>[2,2,1,2,1]
[6,7,1,4,8,5,3,2]=>0100111=>[2,3,1,1,1]
[7,4,8,2,1,5,6,3]=>1011001=>[1,2,1,3,1]
[7,3,2,8,5,1,4,6]=>1101100=>[1,1,2,1,3]
[6,7,1,4,3,2,8,5]=>0101101=>[2,2,1,2,1]
[4,1,7,3,2,8,5,6]=>1011010=>[1,2,1,2,2]
[8,3,5,2,4,7,1,6]=>1010010=>[1,2,3,2]
[4,3,7,8,6,1,5,2]=>1001101=>[1,3,1,2,1]
[6,2,8,4,3,7,1,5]=>1011010=>[1,2,1,2,2]
[1,2,6,3,7,8,5,4]=>0010011=>[3,3,1,1]
[6,1,3,2,7,8,5,4]=>1010011=>[1,2,3,1,1]
[6,7,1,3,2,8,5,4]=>0101011=>[2,2,2,1,1]
[2,6,4,7,5,3,1,8]=>0101110=>[2,2,1,1,2]
[5,6,3,7,2,8,4,1]=>0101011=>[2,2,2,1,1]
[4,5,1,8,6,2,7,3]=>0101101=>[2,2,1,2,1]
[5,6,1,8,7,2,3,4]=>0101100=>[2,2,1,3]
[4,5,1,6,8,7,3,2]=>0100111=>[2,3,1,1,1]
[2,4,6,3,5,1,7,8]=>0010100=>[3,2,3]
[4,1,6,2,5,8,3,7]=>1010010=>[1,2,3,2]
[1,8,2,5,7,3,4,6]=>0100100=>[2,3,3]
[3,8,2,5,4,1,6,7]=>0101100=>[2,2,1,3]
[1,4,6,3,8,5,2,7]=>0010110=>[3,2,1,2]
[4,5,6,3,1,7,2,8]=>0011010=>[3,1,2,2]
[3,4,6,2,5,1,7,8]=>0010100=>[3,2,3]
[6,2,1,5,8,3,4,7]=>1100100=>[1,1,3,3]
[1,5,7,3,6,2,4,8]=>0010100=>[3,2,3]
[1,4,7,5,2,3,6,8]=>0011000=>[3,1,4]
[1,4,6,5,8,2,3,7]=>0010100=>[3,2,3]
[1,5,8,6,2,3,4,7]=>0011000=>[3,1,4]
[1,4,8,3,7,6,2,5]=>0010110=>[3,2,1,2]
[1,4,5,3,7,2,6,8]=>0010100=>[3,2,3]
[1,4,8,7,3,6,2,5]=>0011010=>[3,1,2,2]
[8,3,5,1,6,4,7,2]=>1010101=>[1,2,2,2,1]
[5,8,4,3,6,2,7,1]=>0110101=>[2,1,2,2,1]
[4,6,5,8,3,2,7,1]=>0101101=>[2,2,1,2,1]
[3,4,7,5,6,8,2,1]=>0010011=>[3,3,1,1]
[3,4,7,8,5,2,6,1]=>0001101=>[4,1,2,1]
[2,3,8,4,7,1,6,5]=>0010101=>[3,2,2,1]
[1,8,7,5,2,6,3,4]=>0111010=>[2,1,1,2,2]
[1,8,7,5,4,3,2,6]=>0111110=>[2,1,1,1,1,2]
[1,7,6,3,4,5,8,2]=>0110001=>[2,1,4,1]
[1,8,7,4,5,6,2,3]=>0110010=>[2,1,3,2]
[1,8,7,3,6,4,2,5]=>0110110=>[2,1,2,1,2]
[1,8,7,2,4,6,3,5]=>0110010=>[2,1,3,2]
[1,4,7,8,6,2,5,3]=>0001101=>[4,1,2,1]
[1,7,6,4,2,5,3,8]=>0111010=>[2,1,1,2,2]
[1,4,7,5,8,2,3,6]=>0010100=>[3,2,3]
[1,4,7,5,8,2,6,3]=>0010101=>[3,2,2,1]
[1,6,8,3,4,2,5,7]=>0010100=>[3,2,3]
[1,4,7,2,3,6,5,8]=>0010010=>[3,3,2]
[1,3,2,6,8,4,7,5]=>0100101=>[2,3,2,1]
[1,7,2,5,6,3,4,8]=>0100100=>[2,3,3]
[1,5,8,3,6,4,7,2]=>0010101=>[3,2,2,1]
[1,2,6,5,8,3,4,7]=>0010100=>[3,2,3]
[1,6,8,2,7,3,4,5]=>0010100=>[3,2,3]
[1,4,5,8,2,6,3,7]=>0001010=>[4,2,2]
[3,5,6,7,2,4,1,8]=>0001010=>[4,2,2]
[6,4,7,5,2,3,1,8]=>1011010=>[1,2,1,2,2]
[1,5,6,4,8,3,2,7]=>0010110=>[3,2,1,2]
[5,2,6,4,8,7,1,3]=>1010110=>[1,2,2,1,2]
[2,1,5,6,4,8,3,7]=>1001010=>[1,3,2,2]
[5,1,4,7,8,6,2,3]=>1000110=>[1,4,1,2]
[2,5,7,1,8,6,3,4]=>0010110=>[3,2,1,2]
[1,6,7,2,8,5,4,3]=>0010111=>[3,2,1,1,1]
[4,6,1,7,8,5,3,2]=>0100111=>[2,3,1,1,1]
[5,3,2,1,7,8,6,4]=>1110011=>[1,1,1,3,1,1]
[7,4,3,8,6,1,5,2]=>1101101=>[1,1,2,1,2,1]
[4,3,7,1,5,8,6,2]=>1010011=>[1,2,3,1,1]
[8,2,4,5,3,1,7,6]=>1001101=>[1,3,1,2,1]
[8,5,3,2,4,1,7,6]=>1110101=>[1,1,1,2,2,1]
[1,4,3,2,7,5,8,6]=>0110101=>[2,1,2,2,1]
[4,8,7,2,6,1,3,5]=>0110100=>[2,1,2,3]
[4,5,8,2,1,7,3,6]=>0011010=>[3,1,2,2]
[6,8,4,1,7,3,2,5]=>0110110=>[2,1,2,1,2]
[7,6,2,8,4,5,3,1]=>1101011=>[1,1,2,2,1,1]
[7,8,2,6,4,5,3,1]=>0101011=>[2,2,2,1,1]
[2,8,3,1,7,5,6,4]=>0110101=>[2,1,2,2,1]
[1,8,3,5,2,6,4,7]=>0101010=>[2,2,2,2]
[2,5,8,4,6,1,3,7]=>0010100=>[3,2,3]
[1,8,4,5,6,2,7,3]=>0100101=>[2,3,2,1]
[2,3,8,7,4,5,1,6]=>0011010=>[3,1,2,2]
[2,4,8,5,7,3,1,6]=>0010110=>[3,2,1,2]
[1,8,3,5,7,4,2,6]=>0100110=>[2,3,1,2]
[2,5,8,4,6,7,1,3]=>0010010=>[3,3,2]
[3,5,6,8,4,7,1,2]=>0001010=>[4,2,2]
[3,5,6,8,4,2,7,1]=>0001101=>[4,1,2,1]
[2,5,8,4,6,3,7,1]=>0010101=>[3,2,2,1]
[1,8,4,5,6,3,2,7]=>0100110=>[2,3,1,2]
[7,2,5,3,4,6,1,8]=>1010010=>[1,2,3,2]
[7,1,2,6,4,3,5,8]=>1001100=>[1,3,1,3]
[7,1,2,6,3,4,5,8]=>1001000=>[1,3,4]
[7,1,2,6,4,5,3,8]=>1001010=>[1,3,2,2]
[7,1,2,6,5,3,4,8]=>1001100=>[1,3,1,3]
[5,3,1,4,7,2,8,6]=>1100101=>[1,1,3,2,1]
[7,1,3,8,2,6,4,5]=>1001010=>[1,3,2,2]
[1,8,3,7,2,4,6,5]=>0101001=>[2,2,3,1]
[2,7,5,6,4,8,1,3]=>0101010=>[2,2,2,2]
[2,8,3,6,5,7,1,4]=>0101010=>[2,2,2,2]
[7,4,3,1,6,5,2,8]=>1110110=>[1,1,1,2,1,2]
[3,5,1,2,6,8,7,4]=>0100011=>[2,4,1,1]
[1,5,2,4,3,8,7,6]=>0101011=>[2,2,2,1,1]
[3,1,2,4,8,7,5,6]=>1000110=>[1,4,1,2]
[5,2,1,6,3,8,7,4]=>1101011=>[1,1,2,2,1,1]
[6,2,5,3,4,7,1,8]=>1010010=>[1,2,3,2]
[5,2,7,3,4,6,1,8]=>1010010=>[1,2,3,2]
[7,1,2,6,3,8,4,5]=>1001010=>[1,3,2,2]
[8,1,2,7,5,3,4,6]=>1001100=>[1,3,1,3]
[7,2,8,1,5,3,4,6]=>1010100=>[1,2,2,3]
[4,2,8,1,3,7,5,6]=>1010010=>[1,2,3,2]
[1,7,4,2,3,8,5,6]=>0110010=>[2,1,3,2]
[7,5,1,8,2,3,4,6]=>1101000=>[1,1,2,4]
[8,2,4,1,3,7,5,6]=>1010010=>[1,2,3,2]
[8,1,7,5,2,3,4,6]=>1011000=>[1,2,1,4]
[8,1,6,2,3,7,4,5]=>1010010=>[1,2,3,2]
[7,1,8,2,3,6,4,5]=>1010010=>[1,2,3,2]
[3,4,6,7,2,1,5,8]=>0001100=>[4,1,3]
[2,5,7,4,6,8,1,3]=>0010010=>[3,3,2]
[4,6,2,7,5,8,1,3]=>0101010=>[2,2,2,2]
[4,7,2,5,3,8,1,6]=>0101010=>[2,2,2,2]
[2,4,7,6,3,8,1,5]=>0011010=>[3,1,2,2]
[5,8,3,6,4,1,7,2]=>0101101=>[2,2,1,2,1]
[4,6,8,5,1,2,3,7]=>0011000=>[3,1,4]
[4,6,5,7,1,2,3,8]=>0101000=>[2,2,4]
[4,6,5,7,1,3,8,2]=>0101001=>[2,2,3,1]
[3,4,7,6,1,8,2,5]=>0011010=>[3,1,2,2]
[8,5,6,7,4,1,3,2]=>1001101=>[1,3,1,2,1]
[1,6,5,7,3,8,2,4]=>0101010=>[2,2,2,2]
[7,2,4,8,6,1,5,3]=>1001101=>[1,3,1,2,1]
[7,1,4,8,6,5,2,3]=>1001110=>[1,3,1,1,2]
[8,6,2,1,3,7,5,4]=>1110011=>[1,1,1,3,1,1]
[8,1,4,6,7,2,5,3]=>1000101=>[1,4,2,1]
[8,1,4,6,2,7,5,3]=>1001011=>[1,3,2,1,1]
[8,6,1,3,2,7,5,4]=>1101011=>[1,1,2,2,1,1]
[8,1,7,5,2,4,6,3]=>1011001=>[1,2,1,3,1]
[8,6,2,7,5,3,1,4]=>1101110=>[1,1,2,1,1,2]
[8,2,7,5,4,1,6,3]=>1011101=>[1,2,1,1,2,1]
[8,2,1,6,7,4,5,3]=>1100101=>[1,1,3,2,1]
[8,7,2,1,5,3,6,4]=>1110101=>[1,1,1,2,2,1]
[8,6,1,2,7,3,5,4]=>1100101=>[1,1,3,2,1]
[8,1,6,2,4,7,5,3]=>1010011=>[1,2,3,1,1]
[5,2,6,7,4,8,3,1]=>1001011=>[1,3,2,1,1]
[6,2,3,8,7,4,5,1]=>1001101=>[1,3,1,2,1]
[8,5,7,1,4,2,6,3]=>1010101=>[1,2,2,2,1]
[2,6,7,1,4,3,8,5]=>0010101=>[3,2,2,1]
[4,5,2,1,6,3,8,7]=>0110101=>[2,1,2,2,1]
[4,5,2,1,6,7,3,8]=>0110010=>[2,1,3,2]
[5,3,8,6,2,4,7,1]=>1011001=>[1,2,1,3,1]
[2,5,1,6,4,3,8,7]=>0101101=>[2,2,1,2,1]
[3,6,2,8,5,7,1,4]=>0101010=>[2,2,2,2]
[4,6,8,1,5,7,2,3]=>0010010=>[3,3,2]
[4,1,2,5,7,6,3,8]=>1000110=>[1,4,1,2]
[5,2,3,8,7,1,6,4]=>1001101=>[1,3,1,2,1]
[3,2,8,1,7,5,4,6]=>1010110=>[1,2,2,1,2]
[4,8,5,1,3,7,2,6]=>0110010=>[2,1,3,2]
[4,6,5,8,1,7,3,2]=>0101011=>[2,2,2,1,1]
[2,1,3,6,4,8,7,5]=>1001011=>[1,3,2,1,1]
[4,8,2,1,6,7,5,3]=>0110011=>[2,1,3,1,1]
[4,8,1,2,7,5,6,3]=>0100101=>[2,3,2,1]
[5,2,8,1,7,4,6,3]=>1010101=>[1,2,2,2,1]
[5,7,4,8,1,2,6,3]=>0101001=>[2,2,3,1]
[4,5,1,6,8,7,2,3]=>0100110=>[2,3,1,2]
[3,4,7,1,5,8,2,6]=>0010010=>[3,3,2]
[6,2,7,4,5,3,1,8]=>1010110=>[1,2,2,1,2]
[6,8,7,5,4,1,2,3]=>0111100=>[2,1,1,1,3]
[4,3,8,6,1,2,5,7]=>1011000=>[1,2,1,4]
[4,8,6,5,7,1,3,2]=>0110101=>[2,1,2,2,1]
[4,8,1,5,3,6,7,2]=>0101001=>[2,2,3,1]
[8,4,6,7,5,1,3,2]=>1001101=>[1,3,1,2,1]
[8,3,4,2,7,6,1,5]=>1010110=>[1,2,2,1,2]
[8,7,5,6,4,1,3,2]=>1101101=>[1,1,2,1,2,1]
[8,7,4,2,3,6,5,1]=>1110011=>[1,1,1,3,1,1]
[8,4,2,3,7,6,5,1]=>1100111=>[1,1,3,1,1,1]
[8,6,4,7,5,1,3,2]=>1101101=>[1,1,2,1,2,1]
[5,3,6,4,1,2,8,7]=>1011001=>[1,2,1,3,1]
[5,4,1,7,8,6,2,3]=>1100110=>[1,1,3,1,2]
[6,1,4,7,5,8,2,3]=>1001010=>[1,3,2,2]
[2,1,7,5,8,6,3,4]=>1010110=>[1,2,2,1,2]
[5,3,4,7,8,1,6,2]=>1000101=>[1,4,2,1]
[5,1,4,8,2,3,7,6]=>1001001=>[1,3,3,1]
[5,8,6,3,1,2,4,7]=>0111000=>[2,1,1,4]
[7,4,8,6,3,5,1,2]=>1011010=>[1,2,1,2,2]
[8,4,1,6,2,7,5,3]=>1101011=>[1,1,2,2,1,1]
[4,2,7,1,5,8,3,6]=>1010010=>[1,2,3,2]
[4,6,3,5,1,8,2,7]=>0101010=>[2,2,2,2]
[8,5,7,6,2,3,4,1]=>1011001=>[1,2,1,3,1]
[8,4,2,3,6,7,5,1]=>1100011=>[1,1,4,1,1]
[4,1,7,6,2,8,3,5]=>1011010=>[1,2,1,2,2]
[2,7,5,3,1,4,8,6]=>0111001=>[2,1,1,3,1]
[4,1,7,2,8,5,3,6]=>1010110=>[1,2,2,1,2]
[2,6,5,3,8,4,7,1]=>0110101=>[2,1,2,2,1]
[7,1,4,3,6,5,8,2]=>1010101=>[1,2,2,2,1]
[7,1,6,3,5,4,8,2]=>1010101=>[1,2,2,2,1]
[5,7,3,2,8,4,1,6]=>0110110=>[2,1,2,1,2]
[2,8,7,1,6,5,3,4]=>0110110=>[2,1,2,1,2]
[2,8,6,1,7,5,3,4]=>0110110=>[2,1,2,1,2]
[8,1,5,2,7,4,3,6]=>1010110=>[1,2,2,1,2]
[2,6,8,1,7,5,3,4]=>0010110=>[3,2,1,2]
[1,4,6,5,3,8,2,7]=>0011010=>[3,1,2,2]
[2,4,5,8,7,1,3,6]=>0001100=>[4,1,3]
[3,1,6,8,7,5,4,2]=>1001111=>[1,3,1,1,1,1]
[3,1,8,7,5,6,4,2]=>1011011=>[1,2,1,2,1,1]
[5,1,8,7,6,3,4,2]=>1011101=>[1,2,1,1,2,1]
[1,3,8,4,7,2,6,5]=>0010101=>[3,2,2,1]
[1,8,2,4,7,3,6,5]=>0100101=>[2,3,2,1]
[8,2,7,5,3,6,4,1]=>1011011=>[1,2,1,2,1,1]
[8,4,1,3,6,7,2,5]=>1100010=>[1,1,4,2]
[8,7,2,3,1,5,6,4]=>1101001=>[1,1,2,3,1]
[1,2,8,6,7,5,4,3]=>0010111=>[3,2,1,1,1]
[2,8,5,7,6,1,3,4]=>0101100=>[2,2,1,3]
[1,8,7,2,6,4,5,3]=>0110101=>[2,1,2,2,1]
[8,7,2,1,6,4,5,3]=>1110101=>[1,1,1,2,2,1]
[8,7,2,4,3,6,5,1]=>1101011=>[1,1,2,2,1,1]
[4,2,8,7,3,6,5,1]=>1011011=>[1,2,1,2,1,1]
[8,7,1,6,4,3,5,2]=>1101101=>[1,1,2,1,2,1]
[8,4,1,7,3,6,5,2]=>1101011=>[1,1,2,2,1,1]
[4,5,1,8,7,3,6,2]=>0101101=>[2,2,1,2,1]
[4,3,8,5,2,7,1,6]=>1011010=>[1,2,1,2,2]
[5,6,8,2,3,4,1,7]=>0010010=>[3,3,2]
[3,6,4,7,5,2,1,8]=>0101110=>[2,2,1,1,2]
[5,7,4,1,2,6,8,3]=>0110001=>[2,1,4,1]
[2,8,6,7,5,3,1,4]=>0101110=>[2,2,1,1,2]
[7,4,5,2,6,3,1,8]=>1010110=>[1,2,2,1,2]
[8,4,5,3,6,1,7,2]=>1010101=>[1,2,2,2,1]
[8,6,3,4,5,1,7,2]=>1100101=>[1,1,3,2,1]
[8,6,3,5,4,1,7,2]=>1101101=>[1,1,2,1,2,1]
[8,7,4,5,1,3,6,2]=>1101001=>[1,1,2,3,1]
[8,4,5,2,6,1,7,3]=>1010101=>[1,2,2,2,1]
[8,6,2,5,3,1,4,7]=>1101100=>[1,1,2,1,3]
[8,4,7,3,1,2,5,6]=>1011000=>[1,2,1,4]
[8,7,3,5,1,6,4,2]=>1101011=>[1,1,2,2,1,1]
[8,6,2,3,5,1,7,4]=>1100101=>[1,1,3,2,1]
[4,8,3,2,6,1,7,5]=>0110101=>[2,1,2,2,1]
[5,2,6,3,7,8,4,1]=>1010011=>[1,2,3,1,1]
[3,6,2,5,7,8,4,1]=>0100011=>[2,4,1,1]
[2,7,4,6,8,3,5,1]=>0100101=>[2,3,2,1]
[2,7,3,6,8,5,4,1]=>0100111=>[2,3,1,1,1]
[3,7,6,8,1,5,4,2]=>0101011=>[2,2,2,1,1]
[4,7,6,8,2,3,5,1]=>0101001=>[2,2,3,1]
[3,7,5,6,8,2,4,1]=>0100101=>[2,3,2,1]
[3,7,2,6,8,4,5,1]=>0100101=>[2,3,2,1]
[1,5,7,6,8,4,2,3]=>0010110=>[3,2,1,2]
[2,7,5,6,8,4,3,1]=>0100111=>[2,3,1,1,1]
[3,7,6,8,5,1,4,2]=>0101101=>[2,2,1,2,1]
[7,1,3,8,6,2,4,5]=>1001100=>[1,3,1,3]
[2,7,1,8,6,5,3,4]=>0101110=>[2,2,1,1,2]
[8,1,5,2,6,4,7,3]=>1010101=>[1,2,2,2,1]
[5,3,4,7,6,2,1,8]=>1001110=>[1,3,1,1,2]
[8,7,2,6,4,5,1,3]=>1101010=>[1,1,2,2,2]
[3,1,2,8,7,5,4,6]=>1001110=>[1,3,1,1,2]
[3,1,2,8,7,6,4,5]=>1001110=>[1,3,1,1,2]
[4,5,2,6,7,3,8,1]=>0100101=>[2,3,2,1]
[3,5,1,6,7,4,8,2]=>0100101=>[2,3,2,1]
[6,5,8,1,4,3,7,2]=>1010101=>[1,2,2,2,1]
[6,4,1,2,5,7,8,3]=>1100001=>[1,1,5,1]
[6,1,5,4,2,7,3,8]=>1011010=>[1,2,1,2,2]
[6,4,2,3,1,7,5,8]=>1101010=>[1,1,2,2,2]
[4,6,1,3,5,7,2,8]=>0100010=>[2,4,2]
[2,4,5,7,3,6,1,8]=>0001010=>[4,2,2]
[3,4,6,1,8,2,7,5]=>0010101=>[3,2,2,1]
[2,4,1,7,5,6,3,8]=>0101010=>[2,2,2,2]
[5,3,1,4,7,6,2,8]=>1100110=>[1,1,3,1,2]
[6,4,5,2,7,1,3,8]=>1010100=>[1,2,2,3]
[7,4,3,5,1,6,2,8]=>1101010=>[1,1,2,2,2]
[7,5,3,6,2,1,4,8]=>1101100=>[1,1,2,1,3]
[6,4,3,7,1,8,2,5]=>1101010=>[1,1,2,2,2]
[3,1,2,7,6,4,5,8]=>1001100=>[1,3,1,3]
[5,1,2,7,6,3,4,8]=>1001100=>[1,3,1,3]
[5,6,1,7,2,4,3,8]=>0101010=>[2,2,2,2]
[2,6,5,7,1,3,4,8]=>0101000=>[2,2,4]
[2,3,7,1,5,6,4,8]=>0010010=>[3,3,2]
[5,6,1,3,2,4,7,8]=>0101000=>[2,2,4]
[2,6,5,3,4,1,7,8]=>0110100=>[2,1,2,3]
[2,6,1,3,5,4,7,8]=>0100100=>[2,3,3]
[3,6,7,1,4,2,5,8]=>0010100=>[3,2,3]
[3,6,5,2,7,1,4,8]=>0110100=>[2,1,2,3]
[7,1,5,4,2,6,3,8]=>1011010=>[1,2,1,2,2]
[4,6,1,5,2,8,7,3]=>0101011=>[2,2,2,1,1]
[6,1,5,4,2,7,8,3]=>1011001=>[1,2,1,3,1]
[4,6,1,5,2,7,8,3]=>0101001=>[2,2,3,1]
[4,5,1,7,6,2,8,3]=>0101101=>[2,2,1,2,1]
[2,8,6,5,1,3,7,4]=>0111001=>[2,1,1,3,1]
[5,1,8,6,2,7,4,3]=>1011011=>[1,2,1,2,1,1]
[3,6,8,2,7,5,1,4]=>0010110=>[3,2,1,2]
[7,8,5,3,2,6,1,4]=>0111010=>[2,1,1,2,2]
[6,8,3,2,7,5,1,4]=>0110110=>[2,1,2,1,2]
[5,6,4,1,7,2,8,3]=>0110101=>[2,1,2,2,1]
[1,6,7,2,4,3,5,8]=>0010100=>[3,2,3]
[8,1,3,2,4,6,5,7]=>1010010=>[1,2,3,2]
[1,6,2,7,8,4,5,3]=>0100101=>[2,3,2,1]
[1,6,7,8,3,4,2,5]=>0001010=>[4,2,2]
[7,2,1,8,3,6,4,5]=>1101010=>[1,1,2,2,2]
[5,4,2,3,1,7,8,6]=>1101001=>[1,1,2,3,1]
[2,1,3,8,6,4,7,5]=>1001101=>[1,3,1,2,1]
[4,6,1,3,2,8,5,7]=>0101010=>[2,2,2,2]
[4,6,5,3,8,2,1,7]=>0110110=>[2,1,2,1,2]
[8,2,5,4,3,7,1,6]=>1011010=>[1,2,1,2,2]
[5,8,4,3,7,6,2,1]=>0110111=>[2,1,2,1,1,1]
[8,1,5,3,4,7,2,6]=>1010010=>[1,2,3,2]
[6,1,8,7,4,5,3,2]=>1011011=>[1,2,1,2,1,1]
[1,5,8,6,4,3,7,2]=>0011101=>[3,1,1,2,1]
[2,5,8,6,4,3,7,1]=>0011101=>[3,1,1,2,1]
[8,5,4,1,2,3,7,6]=>1110001=>[1,1,1,4,1]
[8,5,2,4,1,3,7,6]=>1101001=>[1,1,2,3,1]
[4,5,8,7,3,6,2,1]=>0011011=>[3,1,2,1,1]
[5,8,6,4,2,1,7,3]=>0111101=>[2,1,1,1,2,1]
[2,6,1,8,4,7,5,3]=>0101011=>[2,2,2,1,1]
[5,3,8,6,1,2,7,4]=>1011001=>[1,2,1,3,1]
[5,8,1,4,6,2,7,3]=>0100101=>[2,3,2,1]
[6,3,2,8,4,5,1,7]=>1101010=>[1,1,2,2,2]
[5,4,7,2,1,3,8,6]=>1011001=>[1,2,1,3,1]
[8,4,6,5,2,7,3,1]=>1011011=>[1,2,1,2,1,1]
[6,4,7,5,8,3,1,2]=>1010110=>[1,2,2,1,2]
[4,6,7,5,1,8,3,2]=>0011011=>[3,1,2,1,1]
[2,6,4,5,7,1,8,3]=>0100101=>[2,3,2,1]
[4,1,7,6,5,2,8,3]=>1011101=>[1,2,1,1,2,1]
[3,7,4,6,1,5,8,2]=>0101001=>[2,2,3,1]
[3,4,6,5,2,8,1,7]=>0011010=>[3,1,2,2]
[4,6,7,5,8,2,1,3]=>0010110=>[3,2,1,2]
[6,4,7,1,2,3,8,5]=>1010001=>[1,2,4,1]
[5,6,4,2,1,7,3,8]=>0111010=>[2,1,1,2,2]
[6,5,7,1,2,8,3,4]=>1010010=>[1,2,3,2]
[6,4,7,1,2,5,3,8]=>1010010=>[1,2,3,2]
[5,7,6,3,1,2,8,4]=>0111001=>[2,1,1,3,1]
[1,2,7,5,8,6,3,4]=>0010110=>[3,2,1,2]
[7,4,5,1,6,8,2,3]=>1010010=>[1,2,3,2]
[1,7,8,4,2,6,3,5]=>0011010=>[3,1,2,2]
[6,3,2,5,7,4,1,8]=>1100110=>[1,1,3,1,2]
[6,2,1,5,3,7,8,4]=>1101001=>[1,1,2,3,1]
[7,5,6,1,4,3,8,2]=>1010101=>[1,2,2,2,1]
[4,1,7,8,3,6,5,2]=>1001011=>[1,3,2,1,1]
[6,3,2,4,8,5,1,7]=>1100110=>[1,1,3,1,2]
[6,4,2,1,7,3,5,8]=>1110100=>[1,1,1,2,3]
[5,7,4,2,1,6,3,8]=>0111010=>[2,1,1,2,2]
[5,8,4,2,1,3,6,7]=>0111000=>[2,1,1,4]
[2,7,3,8,5,6,4,1]=>0101011=>[2,2,2,1,1]
[8,3,2,6,5,1,7,4]=>1101101=>[1,1,2,1,2,1]
[1,8,5,6,4,3,7,2]=>0101101=>[2,2,1,2,1]
[1,7,5,8,4,6,3,2]=>0101011=>[2,2,2,1,1]
[8,3,5,6,1,7,2,4]=>1001010=>[1,3,2,2]
[1,5,3,7,8,4,6,2]=>0100101=>[2,3,2,1]
[1,4,7,3,5,8,6,2]=>0010011=>[3,3,1,1]
[1,6,3,7,8,5,4,2]=>0100111=>[2,3,1,1,1]
[8,5,6,1,7,4,2,3]=>1010110=>[1,2,2,1,2]
[8,6,1,4,3,7,2,5]=>1101010=>[1,1,2,2,2]
[3,7,8,2,5,1,6,4]=>0010101=>[3,2,2,1]
[8,1,3,5,6,4,2,7]=>1000110=>[1,4,1,2]
[8,6,1,4,3,2,7,5]=>1101101=>[1,1,2,1,2,1]
[7,3,8,2,4,1,5,6]=>1010100=>[1,2,2,3]
[6,3,7,8,1,2,5,4]=>1001001=>[1,3,3,1]
[7,5,8,1,2,3,6,4]=>1010001=>[1,2,4,1]
[8,6,1,5,3,7,2,4]=>1101010=>[1,1,2,2,2]
[8,1,7,5,6,4,2,3]=>1010110=>[1,2,2,1,2]
[8,1,4,7,6,5,2,3]=>1001110=>[1,3,1,1,2]
[6,1,4,8,2,7,5,3]=>1001011=>[1,3,2,1,1]
[4,6,8,5,1,2,7,3]=>0011001=>[3,1,3,1]
[2,8,4,6,1,3,7,5]=>0101001=>[2,2,3,1]
[5,2,7,8,4,1,3,6]=>1001100=>[1,3,1,3]
[4,6,8,5,3,1,2,7]=>0011100=>[3,1,1,3]
[8,6,4,2,7,3,5,1]=>1110101=>[1,1,1,2,2,1]
[6,8,7,5,2,1,3,4]=>0111100=>[2,1,1,1,3]
[7,6,1,5,2,3,8,4]=>1101001=>[1,1,2,3,1]
[5,1,8,6,7,2,3,4]=>1010100=>[1,2,2,3]
[5,7,1,6,8,2,3,4]=>0100100=>[2,3,3]
[5,1,7,6,8,2,3,4]=>1010100=>[1,2,2,3]
[6,1,5,7,2,8,3,4]=>1001010=>[1,3,2,2]
[6,8,4,2,1,7,3,5]=>0111010=>[2,1,1,2,2]
[5,8,6,1,7,2,3,4]=>0110100=>[2,1,2,3]
[6,3,2,8,1,7,4,5]=>1101010=>[1,1,2,2,2]
[1,4,7,8,3,5,2,6]=>0001010=>[4,2,2]
[2,5,6,8,1,4,7,3]=>0001001=>[4,3,1]
[8,4,5,1,6,7,2,3]=>1010010=>[1,2,3,2]
[7,3,6,1,4,2,8,5]=>1010101=>[1,2,2,2,1]
[7,4,1,6,5,2,3,8]=>1101100=>[1,1,2,1,3]
[4,1,6,5,2,3,8,7]=>1011001=>[1,2,1,3,1]
[4,5,1,7,8,6,2,3]=>0100110=>[2,3,1,2]
[8,3,1,4,6,2,7,5]=>1100101=>[1,1,3,2,1]
[2,5,3,4,6,8,1,7]=>0100010=>[2,4,2]
[8,3,6,1,5,2,4,7]=>1010100=>[1,2,2,3]
[4,7,1,2,5,6,3,8]=>0100010=>[2,4,2]
[6,7,3,1,8,2,4,5]=>0110100=>[2,1,2,3]
[7,3,1,4,6,2,8,5]=>1100101=>[1,1,3,2,1]
[7,4,1,2,5,6,3,8]=>1100010=>[1,1,4,2]
[4,5,1,3,6,8,7,2]=>0100011=>[2,4,1,1]
[8,4,1,2,5,7,3,6]=>1100010=>[1,1,4,2]
[8,4,1,3,6,7,5,2]=>1100011=>[1,1,4,1,1]
[5,4,1,6,3,7,8,2]=>1101001=>[1,1,2,3,1]
[6,7,3,1,5,2,4,8]=>0110100=>[2,1,2,3]
[5,4,1,3,6,8,7,2]=>1100011=>[1,1,4,1,1]
[6,4,1,2,5,8,3,7]=>1100010=>[1,1,4,2]
[5,7,4,8,1,6,3,2]=>0101011=>[2,2,2,1,1]
[7,5,3,6,4,2,1,8]=>1101110=>[1,1,2,1,1,2]
[4,3,1,2,6,5,7,8]=>1100100=>[1,1,3,3]
[4,3,1,2,5,7,6,8]=>1100010=>[1,1,4,2]
[4,7,3,1,5,2,8,6]=>0110101=>[2,1,2,2,1]
[8,3,6,5,7,4,2,1]=>1010111=>[1,2,2,1,1,1]
[8,2,6,5,7,4,3,1]=>1010111=>[1,2,2,1,1,1]
[8,1,4,2,6,5,7,3]=>1010101=>[1,2,2,2,1]
[8,4,7,1,5,2,6,3]=>1010101=>[1,2,2,2,1]
[8,2,6,3,7,4,5,1]=>1010101=>[1,2,2,2,1]
[8,2,6,3,7,5,4,1]=>1010111=>[1,2,2,1,1,1]
[8,2,5,3,7,6,4,1]=>1010111=>[1,2,2,1,1,1]
[8,6,7,1,4,3,5,2]=>1010101=>[1,2,2,2,1]
[8,5,7,1,4,3,6,2]=>1010101=>[1,2,2,2,1]
[4,5,3,6,8,7,1,2]=>0100110=>[2,3,1,2]
[6,5,1,2,7,4,8,3]=>1100101=>[1,1,3,2,1]
[6,8,5,1,7,3,4,2]=>0110101=>[2,1,2,2,1]
[5,3,8,1,4,2,7,6]=>1010101=>[1,2,2,2,1]
[6,5,3,4,1,8,2,7]=>1101010=>[1,1,2,2,2]
[3,1,8,4,2,7,6,5]=>1011011=>[1,2,1,2,1,1]
[2,8,7,4,1,3,6,5]=>0111001=>[2,1,1,3,1]
[8,2,3,1,7,6,4,5]=>1010110=>[1,2,2,1,2]
[5,2,4,1,6,8,3,7]=>1010010=>[1,2,3,2]
[8,7,2,3,1,6,4,5]=>1101010=>[1,1,2,2,2]
[6,2,3,1,7,8,4,5]=>1010010=>[1,2,3,2]
[7,2,5,8,3,1,4,6]=>1001100=>[1,3,1,3]
[6,8,2,3,1,7,4,5]=>0101010=>[2,2,2,2]
[8,2,5,7,3,1,4,6]=>1001100=>[1,3,1,3]
[2,5,8,7,3,1,4,6]=>0011100=>[3,1,1,3]
[2,8,7,3,1,4,5,6]=>0111000=>[2,1,1,4]
[8,2,3,1,6,7,4,5]=>1010010=>[1,2,3,2]
[2,8,4,1,3,6,7,5]=>0110001=>[2,1,4,1]
[2,7,3,1,4,5,8,6]=>0110001=>[2,1,4,1]
[7,2,8,3,1,4,5,6]=>1011000=>[1,2,1,4]
[2,7,8,3,1,4,5,6]=>0011000=>[3,1,4]
[5,3,2,8,7,1,6,4]=>1101101=>[1,1,2,1,2,1]
[6,8,7,2,1,5,4,3]=>0111011=>[2,1,1,2,1,1]
[8,2,5,4,1,6,7,3]=>1011001=>[1,2,1,3,1]
[7,2,4,6,8,1,5,3]=>1000101=>[1,4,2,1]
[6,2,5,4,7,8,1,3]=>1010010=>[1,2,3,2]
[6,3,5,2,7,1,4,8]=>1010100=>[1,2,2,3]
[8,5,6,3,7,2,1,4]=>1010110=>[1,2,2,1,2]
[3,8,2,6,1,7,4,5]=>0101010=>[2,2,2,2]
[5,7,1,3,6,2,4,8]=>0100100=>[2,3,3]
[3,6,4,1,2,5,7,8]=>0110000=>[2,1,5]
[3,6,4,1,2,5,8,7]=>0110001=>[2,1,4,1]
[4,7,1,3,2,5,8,6]=>0101001=>[2,2,3,1]
[4,7,1,3,2,6,8,5]=>0101001=>[2,2,3,1]
[5,7,1,3,6,2,8,4]=>0100101=>[2,3,2,1]
[6,8,2,5,7,3,1,4]=>0100110=>[2,3,1,2]
[4,8,5,2,3,6,1,7]=>0110010=>[2,1,3,2]
[5,8,6,3,4,7,2,1]=>0110011=>[2,1,3,1,1]
[3,7,5,4,2,8,1,6]=>0111010=>[2,1,1,2,2]
[4,6,5,1,7,8,2,3]=>0110010=>[2,1,3,2]
[4,7,1,3,2,8,5,6]=>0101010=>[2,2,2,2]
[3,6,5,1,8,2,4,7]=>0110100=>[2,1,2,3]
[5,8,7,3,4,2,6,1]=>0110101=>[2,1,2,2,1]
[3,8,5,4,2,1,6,7]=>0111100=>[2,1,1,1,3]
[4,8,5,3,6,1,7,2]=>0110101=>[2,1,2,2,1]
[6,3,1,5,4,8,2,7]=>1101010=>[1,1,2,2,2]
[8,4,2,6,5,7,3,1]=>1101011=>[1,1,2,2,1,1]
[4,7,6,3,5,2,8,1]=>0110101=>[2,1,2,2,1]
[1,7,5,3,4,8,6,2]=>0110011=>[2,1,3,1,1]
[4,8,6,2,5,7,3,1]=>0110011=>[2,1,3,1,1]
[8,7,3,2,6,4,5,1]=>1110101=>[1,1,1,2,2,1]
[8,3,1,4,7,5,2,6]=>1100110=>[1,1,3,1,2]
[5,3,1,6,4,8,7,2]=>1101011=>[1,1,2,2,1,1]
[3,4,8,5,7,2,6,1]=>0010101=>[3,2,2,1]
[4,1,7,8,3,2,5,6]=>1001100=>[1,3,1,3]
[8,5,1,2,7,6,4,3]=>1100111=>[1,1,3,1,1,1]
[4,6,5,3,1,8,7,2]=>0111011=>[2,1,1,2,1,1]
[8,1,6,7,4,5,3,2]=>1001011=>[1,3,2,1,1]
[6,4,8,1,5,3,7,2]=>1010101=>[1,2,2,2,1]
[6,4,7,2,5,3,1,8]=>1010110=>[1,2,2,1,2]
[4,3,6,1,2,7,8,5]=>1010001=>[1,2,4,1]
[2,7,4,6,3,8,1,5]=>0101010=>[2,2,2,2]
[7,3,5,6,4,1,8,2]=>1001101=>[1,3,1,2,1]
[5,7,6,3,4,2,1,8]=>0110110=>[2,1,2,1,2]
[3,7,5,6,4,2,1,8]=>0101110=>[2,2,1,1,2]
[5,7,3,6,4,2,1,8]=>0101110=>[2,2,1,1,2]
[5,7,3,6,4,1,8,2]=>0101101=>[2,2,1,2,1]
[3,7,5,6,4,1,8,2]=>0101101=>[2,2,1,2,1]
[5,7,6,3,4,1,8,2]=>0110101=>[2,1,2,2,1]
[3,2,7,5,6,1,8,4]=>1010101=>[1,2,2,2,1]
[5,3,4,7,6,1,8,2]=>1001101=>[1,3,1,2,1]
[5,3,4,2,7,1,8,6]=>1010101=>[1,2,2,2,1]
[3,5,4,1,7,8,6,2]=>0110011=>[2,1,3,1,1]
[2,4,6,5,1,8,7,3]=>0011011=>[3,1,2,1,1]
[2,4,6,5,1,8,3,7]=>0011010=>[3,1,2,2]
[2,4,6,1,8,7,3,5]=>0010110=>[3,2,1,2]
[2,4,6,5,8,3,7,1]=>0010101=>[3,2,2,1]
[2,4,6,8,5,3,1,7]=>0001110=>[4,1,1,2]
[2,4,6,8,5,3,7,1]=>0001101=>[4,1,2,1]
[2,4,6,8,5,7,3,1]=>0001011=>[4,2,1,1]
[2,4,6,5,3,8,1,7]=>0011010=>[3,1,2,2]
[2,4,6,5,8,7,1,3]=>0010110=>[3,2,1,2]
[2,4,6,8,7,5,1,3]=>0001110=>[4,1,1,2]
[2,4,6,8,5,7,1,3]=>0001010=>[4,2,2]
[2,4,6,8,7,1,5,3]=>0001101=>[4,1,2,1]
[2,4,6,8,7,1,3,5]=>0001100=>[4,1,3]
[2,4,6,8,1,7,3,5]=>0001010=>[4,2,2]
[2,7,6,4,3,8,5,1]=>0111011=>[2,1,1,2,1,1]
[2,6,7,5,3,8,1,4]=>0011010=>[3,1,2,2]
[3,6,7,5,8,2,4,1]=>0010101=>[3,2,2,1]
[4,5,2,6,8,7,1,3]=>0100110=>[2,3,1,2]
[4,5,2,6,8,3,1,7]=>0100110=>[2,3,1,2]
[4,5,3,6,8,2,1,7]=>0100110=>[2,3,1,2]
[3,1,2,7,5,8,4,6]=>1001010=>[1,3,2,2]
[4,8,1,6,2,5,3,7]=>0101010=>[2,2,2,2]
[1,5,8,3,4,6,2,7]=>0010010=>[3,3,2]
[7,5,8,2,4,3,6,1]=>1010101=>[1,2,2,2,1]
[8,1,5,3,4,6,2,7]=>1010010=>[1,2,3,2]
[8,1,2,4,7,5,6,3]=>1000101=>[1,4,2,1]
[2,7,3,8,4,5,6,1]=>0101001=>[2,2,3,1]
[1,7,8,6,4,5,3,2]=>0011011=>[3,1,2,1,1]
[5,8,7,2,4,3,6,1]=>0110101=>[2,1,2,2,1]
[1,8,2,4,7,5,6,3]=>0100101=>[2,3,2,1]
[1,7,2,4,8,5,6,3]=>0100101=>[2,3,2,1]
[5,8,2,3,7,4,6,1]=>0100101=>[2,3,2,1]
[7,8,2,3,5,4,6,1]=>0100101=>[2,3,2,1]
[8,4,1,3,2,6,5,7]=>1101010=>[1,1,2,2,2]
[2,8,3,1,4,6,5,7]=>0110010=>[2,1,3,2]
[8,7,2,3,5,4,6,1]=>1100101=>[1,1,3,2,1]
[1,7,6,8,4,5,3,2]=>0101011=>[2,2,2,1,1]
[8,5,2,3,7,4,6,1]=>1100101=>[1,1,3,2,1]
[7,4,1,3,8,5,6,2]=>1100101=>[1,1,3,2,1]
[2,7,3,1,8,5,6,4]=>0110101=>[2,1,2,2,1]
[2,8,6,1,5,7,4,3]=>0110011=>[2,1,3,1,1]
[8,3,5,1,7,6,4,2]=>1010111=>[1,2,2,1,1,1]
[8,3,5,4,7,1,6,2]=>1010101=>[1,2,2,2,1]
[6,4,1,5,7,8,2,3]=>1100010=>[1,1,4,2]
[8,4,1,5,6,2,7,3]=>1100101=>[1,1,3,2,1]
[1,8,5,3,2,4,6,7]=>0111000=>[2,1,1,4]
[4,8,5,1,2,3,6,7]=>0110000=>[2,1,5]
[3,5,1,4,2,6,8,7]=>0101001=>[2,2,3,1]
[4,8,7,1,2,5,3,6]=>0110010=>[2,1,3,2]
[8,7,2,6,1,4,3,5]=>1101010=>[1,1,2,2,2]
[1,7,6,8,4,2,3,5]=>0101100=>[2,2,1,3]
[1,7,4,8,2,5,3,6]=>0101010=>[2,2,2,2]
[6,1,7,3,8,2,4,5]=>1010100=>[1,2,2,3]
[1,5,8,2,3,4,7,6]=>0010001=>[3,4,1]
[8,4,2,7,1,3,6,5]=>1101001=>[1,1,2,3,1]
[7,1,8,6,4,2,3,5]=>1011100=>[1,2,1,1,3]
[1,7,8,6,4,2,3,5]=>0011100=>[3,1,1,3]
[3,1,2,5,7,6,8,4]=>1000101=>[1,4,2,1]
[7,1,3,2,4,6,8,5]=>1010001=>[1,2,4,1]
[7,4,2,3,1,6,8,5]=>1101001=>[1,1,2,3,1]
[5,1,7,3,2,6,8,4]=>1011001=>[1,2,1,3,1]
[4,8,2,3,7,5,1,6]=>0100110=>[2,3,1,2]
[6,8,5,3,4,2,1,7]=>0110110=>[2,1,2,1,2]
[8,7,2,4,3,5,6,1]=>1101001=>[1,1,2,3,1]
[8,1,3,6,4,5,2,7]=>1001010=>[1,3,2,2]
[8,1,3,7,4,5,6,2]=>1001001=>[1,3,3,1]
[8,1,3,2,7,5,4,6]=>1010110=>[1,2,2,1,2]
[8,1,2,4,7,3,5,6]=>1000100=>[1,4,3]
[7,1,2,4,8,3,5,6]=>1000100=>[1,4,3]
[7,6,2,8,4,5,1,3]=>1101010=>[1,1,2,2,2]
[8,7,5,3,2,6,4,1]=>1111011=>[1,1,1,1,2,1,1]
[4,8,3,2,5,1,6,7]=>0110100=>[2,1,2,3]
[4,3,8,5,1,2,7,6]=>1011001=>[1,2,1,3,1]
[3,1,8,4,5,2,7,6]=>1010101=>[1,2,2,2,1]
[8,3,6,2,1,5,4,7]=>1011010=>[1,2,1,2,2]
[8,2,1,6,5,3,4,7]=>1101100=>[1,1,2,1,3]
[2,3,7,6,1,8,4,5]=>0011010=>[3,1,2,2]
[4,7,8,2,1,3,5,6]=>0011000=>[3,1,4]
[4,8,5,2,1,3,7,6]=>0111001=>[2,1,1,3,1]
[2,3,7,4,1,8,6,5]=>0011011=>[3,1,2,1,1]
[5,8,4,2,1,3,7,6]=>0111001=>[2,1,1,3,1]
[4,5,2,3,8,7,1,6]=>0100110=>[2,3,1,2]
[4,6,7,5,2,3,1,8]=>0011010=>[3,1,2,2]
[6,5,2,3,1,8,7,4]=>1101011=>[1,1,2,2,1,1]
[6,2,5,3,1,8,7,4]=>1011011=>[1,2,1,2,1,1]
[6,2,5,3,8,7,1,4]=>1010110=>[1,2,2,1,2]
[6,4,5,3,8,7,1,2]=>1010110=>[1,2,2,1,2]
[1,6,4,5,8,7,3,2]=>0100111=>[2,3,1,1,1]
[8,4,7,5,2,3,1,6]=>1011010=>[1,2,1,2,2]
[8,2,7,4,5,3,1,6]=>1010110=>[1,2,2,1,2]
[6,2,4,7,5,3,1,8]=>1001110=>[1,3,1,1,2]
[8,2,4,7,5,3,1,6]=>1001110=>[1,3,1,1,2]
[8,2,6,7,5,3,1,4]=>1001110=>[1,3,1,1,2]
[8,4,6,7,5,3,1,2]=>1001110=>[1,3,1,1,2]
[6,4,5,8,7,3,1,2]=>1001110=>[1,3,1,1,2]
[6,2,8,7,5,3,1,4]=>1011110=>[1,2,1,1,1,2]
[2,4,8,7,5,3,1,6]=>0011110=>[3,1,1,1,2]
[4,6,8,7,5,3,1,2]=>0011110=>[3,1,1,1,2]
[4,6,5,3,8,7,1,2]=>0110110=>[2,1,2,1,2]
[2,6,5,8,7,3,1,4]=>0101110=>[2,2,1,1,2]
[6,7,2,4,5,3,1,8]=>0100110=>[2,3,1,2]
[4,5,8,7,2,3,1,6]=>0011010=>[3,1,2,2]
[4,8,7,2,5,3,1,6]=>0110110=>[2,1,2,1,2]
[6,8,7,4,5,3,1,2]=>0110110=>[2,1,2,1,2]
[2,8,4,7,5,3,1,6]=>0101110=>[2,2,1,1,2]
[4,8,2,7,5,3,1,6]=>0101110=>[2,2,1,1,2]
[6,8,2,7,5,3,1,4]=>0101110=>[2,2,1,1,2]
[7,4,3,8,1,6,5,2]=>1101011=>[1,1,2,2,1,1]
[1,3,6,7,4,5,8,2]=>0001001=>[4,3,1]
[7,4,1,3,6,8,2,5]=>1100010=>[1,1,4,2]
[5,1,7,3,4,6,8,2]=>1010001=>[1,2,4,1]
[6,1,7,3,5,8,2,4]=>1010010=>[1,2,3,2]
[6,8,1,2,7,3,4,5]=>0100100=>[2,3,3]
[5,6,2,1,8,3,4,7]=>0110100=>[2,1,2,3]
[6,4,1,3,7,8,2,5]=>1100010=>[1,1,4,2]
[1,6,2,8,7,3,4,5]=>0101100=>[2,2,1,3]
[5,2,8,4,7,1,3,6]=>1010100=>[1,2,2,3]
[3,8,7,2,6,1,4,5]=>0110100=>[2,1,2,3]
[2,5,1,8,3,6,4,7]=>0101010=>[2,2,2,2]
[2,3,8,1,4,6,5,7]=>0010010=>[3,3,2]
[1,3,8,2,5,4,7,6]=>0010101=>[3,2,2,1]
[3,1,8,4,6,2,5,7]=>1010100=>[1,2,2,3]
[6,3,2,4,8,7,1,5]=>1100110=>[1,1,3,1,2]
[1,4,8,6,2,3,5,7]=>0011000=>[3,1,4]
[3,1,8,4,5,6,2,7]=>1010010=>[1,2,3,2]
[4,5,8,3,6,1,7,2]=>0010101=>[3,2,2,1]
[3,5,4,8,6,1,7,2]=>0101101=>[2,2,1,2,1]
[4,2,7,8,6,3,1,5]=>1001110=>[1,3,1,1,2]
[7,1,4,2,8,6,3,5]=>1010110=>[1,2,2,1,2]
[2,3,7,4,8,1,6,5]=>0010101=>[3,2,2,1]
[1,6,2,7,4,5,3,8]=>0101010=>[2,2,2,2]
[1,7,5,4,6,2,3,8]=>0110100=>[2,1,2,3]
[5,2,8,6,3,1,4,7]=>1011100=>[1,2,1,1,3]
[5,2,8,6,3,1,7,4]=>1011101=>[1,2,1,1,2,1]
[7,1,5,6,3,2,8,4]=>1001101=>[1,3,1,2,1]
[6,2,7,5,3,1,4,8]=>1011100=>[1,2,1,1,3]
[6,1,7,4,8,5,2,3]=>1010110=>[1,2,2,1,2]
[8,2,4,6,3,1,7,5]=>1001101=>[1,3,1,2,1]
[7,4,8,3,5,6,2,1]=>1010011=>[1,2,3,1,1]
[2,6,1,4,7,5,8,3]=>0100101=>[2,3,2,1]
[5,1,4,3,7,8,6,2]=>1010011=>[1,2,3,1,1]
[6,4,1,3,7,8,5,2]=>1100011=>[1,1,4,1,1]
[3,1,5,7,2,6,8,4]=>1001001=>[1,3,3,1]
[7,2,4,8,5,1,6,3]=>1001101=>[1,3,1,2,1]
[3,1,7,5,2,6,8,4]=>1011001=>[1,2,1,3,1]
[3,2,7,5,1,6,8,4]=>1011001=>[1,2,1,3,1]
[5,2,7,3,1,6,8,4]=>1011001=>[1,2,1,3,1]
[6,7,2,1,3,4,8,5]=>0110001=>[2,1,4,1]
[4,6,3,1,2,7,8,5]=>0110001=>[2,1,4,1]
[6,7,3,1,2,4,8,5]=>0110001=>[2,1,4,1]
[3,8,5,2,1,6,7,4]=>0111001=>[2,1,1,3,1]
[6,8,2,3,5,7,4,1]=>0100011=>[2,4,1,1]
[5,3,8,4,6,7,2,1]=>1010011=>[1,2,3,1,1]
[6,2,8,1,7,4,5,3]=>1010101=>[1,2,2,2,1]
[4,2,6,7,8,5,3,1]=>1000111=>[1,4,1,1,1]
[4,3,5,8,6,7,2,1]=>1001011=>[1,3,2,1,1]
[6,2,4,7,8,5,3,1]=>1000111=>[1,4,1,1,1]
[3,2,7,8,5,6,4,1]=>1001011=>[1,3,2,1,1]
[4,7,3,8,5,6,2,1]=>0101011=>[2,2,2,1,1]
[7,1,4,8,5,6,3,2]=>1001011=>[1,3,2,1,1]
[4,3,8,7,2,5,6,1]=>1011001=>[1,2,1,3,1]
[1,7,3,8,6,4,5,2]=>0101101=>[2,2,1,2,1]
[3,4,8,2,6,7,5,1]=>0010011=>[3,3,1,1]
[1,2,6,8,7,4,5,3]=>0001101=>[4,1,2,1]
[1,6,3,8,7,4,5,2]=>0101101=>[2,2,1,2,1]
[1,4,5,8,7,6,2,3]=>0001110=>[4,1,1,2]
[6,4,7,8,3,5,1,2]=>1001010=>[1,3,2,2]
[6,4,7,8,1,2,5,3]=>1001001=>[1,3,3,1]
[3,5,6,7,1,8,4,2]=>0001011=>[4,2,1,1]
[1,7,4,5,2,8,6,3]=>0101011=>[2,2,2,1,1]
[1,7,3,8,2,5,4,6]=>0101010=>[2,2,2,2]
[2,7,8,3,6,1,5,4]=>0010101=>[3,2,2,1]
[1,7,8,3,6,2,5,4]=>0010101=>[3,2,2,1]
[1,4,7,5,8,3,6,2]=>0010101=>[3,2,2,1]
[3,4,7,5,8,2,1,6]=>0010110=>[3,2,1,2]
[7,2,6,4,1,8,5,3]=>1011011=>[1,2,1,2,1,1]
[7,4,3,5,8,1,6,2]=>1100101=>[1,1,3,2,1]
[7,3,6,4,1,8,5,2]=>1011011=>[1,2,1,2,1,1]
[7,8,4,3,6,1,5,2]=>0110101=>[2,1,2,2,1]
[7,1,6,4,3,8,5,2]=>1011011=>[1,2,1,2,1,1]
[8,7,3,4,1,5,2,6]=>1101010=>[1,1,2,2,2]
[7,2,6,4,3,8,5,1]=>1011011=>[1,2,1,2,1,1]
[1,7,5,4,3,8,2,6]=>0111010=>[2,1,1,2,2]
[4,5,8,1,7,3,2,6]=>0010110=>[3,2,1,2]
[4,6,7,1,3,8,2,5]=>0010010=>[3,3,2]
[8,2,3,6,4,1,7,5]=>1001101=>[1,3,1,2,1]
[2,7,3,6,4,1,8,5]=>0101101=>[2,2,1,2,1]
[2,3,7,8,1,4,6,5]=>0001001=>[4,3,1]
[2,7,3,5,4,1,8,6]=>0101101=>[2,2,1,2,1]
[8,2,3,5,4,1,7,6]=>1001101=>[1,3,1,2,1]
[7,1,3,8,2,4,6,5]=>1001001=>[1,3,3,1]
[7,2,3,6,4,1,8,5]=>1001101=>[1,3,1,2,1]
[6,5,2,4,1,8,3,7]=>1101010=>[1,1,2,2,2]
[5,7,2,4,1,3,8,6]=>0101001=>[2,2,3,1]
[6,2,5,4,1,8,3,7]=>1011010=>[1,2,1,2,2]
[8,1,2,5,3,7,6,4]=>1001011=>[1,3,2,1,1]
[1,6,4,3,7,5,2,8]=>0110110=>[2,1,2,1,2]
[1,6,7,5,4,8,2,3]=>0011010=>[3,1,2,2]
[1,8,5,4,2,6,3,7]=>0111010=>[2,1,1,2,2]
[4,2,8,1,5,7,6,3]=>1010011=>[1,2,3,1,1]
[6,7,3,5,4,1,2,8]=>0101100=>[2,2,1,3]
[5,7,3,6,2,1,4,8]=>0101100=>[2,2,1,3]
[5,6,8,4,2,7,1,3]=>0011010=>[3,1,2,2]
[6,8,7,3,2,1,5,4]=>0111101=>[2,1,1,1,2,1]
[3,6,8,7,2,4,1,5]=>0011010=>[3,1,2,2]
[3,7,6,4,2,8,1,5]=>0111010=>[2,1,1,2,2]
[2,8,6,4,7,3,5,1]=>0110101=>[2,1,2,2,1]
[3,8,6,4,2,7,1,5]=>0111010=>[2,1,1,2,2]
[5,7,3,6,2,1,8,4]=>0101101=>[2,2,1,2,1]
[2,4,8,6,5,7,3,1]=>0011011=>[3,1,2,1,1]
[3,6,5,2,4,8,1,7]=>0110010=>[2,1,3,2]
[4,6,3,2,5,1,8,7]=>0110101=>[2,1,2,2,1]
[8,3,6,5,4,2,1,7]=>1011110=>[1,2,1,1,1,2]
[5,4,8,7,6,2,3,1]=>1011101=>[1,2,1,1,2,1]
[6,8,4,7,5,1,3,2]=>0101101=>[2,2,1,2,1]
[6,5,8,3,7,1,4,2]=>1010101=>[1,2,2,2,1]
[7,4,6,1,5,3,8,2]=>1010101=>[1,2,2,2,1]
[6,1,5,4,7,3,8,2]=>1010101=>[1,2,2,2,1]
[7,1,5,4,6,3,8,2]=>1010101=>[1,2,2,2,1]
[2,5,4,7,1,8,3,6]=>0101010=>[2,2,2,2]
[1,5,4,7,3,8,2,6]=>0101010=>[2,2,2,2]
[1,5,6,8,3,2,4,7]=>0001100=>[4,1,3]
[1,2,6,7,3,5,4,8]=>0001010=>[4,2,2]
[1,5,6,7,2,4,3,8]=>0001010=>[4,2,2]
[4,5,8,2,3,7,6,1]=>0010011=>[3,3,1,1]
[1,7,2,5,6,8,3,4]=>0100010=>[2,4,2]
[4,1,7,5,6,8,2,3]=>1010010=>[1,2,3,2]
[5,7,3,4,2,8,6,1]=>0101011=>[2,2,2,1,1]
[5,8,3,4,2,7,6,1]=>0101011=>[2,2,2,1,1]
[7,6,4,2,3,8,5,1]=>1110011=>[1,1,1,3,1,1]
[7,3,8,4,2,6,5,1]=>1011011=>[1,2,1,2,1,1]
[3,5,6,8,2,4,7,1]=>0001001=>[4,3,1]
[8,4,7,3,2,5,6,1]=>1011001=>[1,2,1,3,1]
[4,8,7,3,2,5,6,1]=>0111001=>[2,1,1,3,1]
[8,5,7,3,2,4,6,1]=>1011001=>[1,2,1,3,1]
[3,7,4,2,6,8,5,1]=>0110011=>[2,1,3,1,1]
[7,2,8,4,5,6,3,1]=>1010011=>[1,2,3,1,1]
[6,2,8,3,7,4,5,1]=>1010101=>[1,2,2,2,1]
[4,3,7,8,6,2,5,1]=>1001101=>[1,3,1,2,1]
[1,5,8,3,2,7,4,6]=>0011010=>[3,1,2,2]
[8,1,4,3,6,7,2,5]=>1010010=>[1,2,3,2]
[8,3,1,4,6,7,2,5]=>1100010=>[1,1,4,2]
[7,8,5,1,2,6,3,4]=>0110010=>[2,1,3,2]
[8,3,6,7,5,1,2,4]=>1001100=>[1,3,1,3]
[7,6,4,2,5,3,1,8]=>1110110=>[1,1,1,2,1,2]
[1,8,6,5,2,7,4,3]=>0111011=>[2,1,1,2,1,1]
[8,2,6,5,1,7,4,3]=>1011011=>[1,2,1,2,1,1]
[6,1,4,7,2,5,8,3]=>1001001=>[1,3,3,1]
[6,8,2,5,1,7,4,3]=>0101011=>[2,2,2,1,1]
[1,6,4,7,2,5,8,3]=>0101001=>[2,2,3,1]
[7,6,4,1,2,5,8,3]=>1110001=>[1,1,1,4,1]
[6,8,1,5,2,7,4,3]=>0101011=>[2,2,2,1,1]
[8,6,5,2,1,7,4,3]=>1111011=>[1,1,1,1,2,1,1]
[1,6,5,2,8,7,4,3]=>0110111=>[2,1,2,1,1,1]
[1,8,5,2,7,6,4,3]=>0110111=>[2,1,2,1,1,1]
[1,8,6,7,2,5,4,3]=>0101011=>[2,2,2,1,1]
[1,7,6,8,2,5,4,3]=>0101011=>[2,2,2,1,1]
[1,7,8,6,2,5,4,3]=>0011011=>[3,1,2,1,1]
[8,1,7,6,2,5,4,3]=>1011011=>[1,2,1,2,1,1]
[5,2,4,7,3,8,6,1]=>1001011=>[1,3,2,1,1]
[1,5,6,3,2,8,7,4]=>0011011=>[3,1,2,1,1]
[4,6,5,7,1,8,2,3]=>0101010=>[2,2,2,2]
[6,7,5,3,8,2,1,4]=>0110110=>[2,1,2,1,2]
[7,2,5,6,4,8,3,1]=>1001011=>[1,3,2,1,1]
[7,4,6,2,8,5,3,1]=>1010111=>[1,2,2,1,1,1]
[7,2,6,3,8,5,4,1]=>1010111=>[1,2,2,1,1,1]
[1,2,6,5,3,8,4,7]=>0011010=>[3,1,2,2]
[6,5,3,4,8,2,1,7]=>1100110=>[1,1,3,1,2]
[1,7,8,6,3,5,4,2]=>0011011=>[3,1,2,1,1]
[1,4,2,3,7,8,6,5]=>0100011=>[2,4,1,1]
[1,8,4,2,3,6,5,7]=>0110010=>[2,1,3,2]
[1,3,8,5,6,4,2,7]=>0010110=>[3,2,1,2]
[1,6,3,7,8,4,2,5]=>0100110=>[2,3,1,2]
[1,6,3,8,4,2,5,7]=>0101100=>[2,2,1,3]
[1,7,8,4,2,3,5,6]=>0011000=>[3,1,4]
[1,7,8,5,6,4,2,3]=>0010110=>[3,2,1,2]
[1,6,3,4,2,5,8,7]=>0101001=>[2,2,3,1]
[1,3,5,8,6,4,2,7]=>0001110=>[4,1,1,2]
[1,7,6,2,3,8,4,5]=>0110010=>[2,1,3,2]
[1,5,7,6,2,3,8,4]=>0011001=>[3,1,3,1]
[1,3,7,6,2,4,5,8]=>0011000=>[3,1,4]
[1,4,3,7,6,2,5,8]=>0101100=>[2,2,1,3]
[1,5,8,4,3,7,6,2]=>0011011=>[3,1,2,1,1]
[1,7,5,8,4,3,6,2]=>0101101=>[2,2,1,2,1]
[4,1,5,7,3,8,2,6]=>1001010=>[1,3,2,2]
[1,3,7,4,6,8,5,2]=>0010011=>[3,3,1,1]
[1,5,2,6,8,7,4,3]=>0100111=>[2,3,1,1,1]
[1,3,7,6,4,8,2,5]=>0011010=>[3,1,2,2]
[6,5,1,4,3,8,7,2]=>1101011=>[1,1,2,2,1,1]
[5,6,1,4,3,8,7,2]=>0101011=>[2,2,2,1,1]
[5,8,6,4,3,1,7,2]=>0111101=>[2,1,1,1,2,1]
[4,1,3,7,8,6,5,2]=>1000111=>[1,4,1,1,1]
[8,5,6,4,3,1,7,2]=>1011101=>[1,2,1,1,2,1]
[8,4,3,1,7,6,5,2]=>1110111=>[1,1,1,2,1,1,1]
[3,2,7,1,8,6,5,4]=>1010111=>[1,2,2,1,1,1]
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
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.
searching the database
Sorry, this map was not found in the database.