Identifier
Mp00069:
Permutations
—complement⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00109: Permutations —descent word⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Images
=>
[1]=>[1]=>=>[]
[1,2]=>[2,1]=>1=>[1]
[2,1]=>[1,2]=>0=>[1]
[1,2,3]=>[3,2,1]=>11=>[2]
[1,3,2]=>[3,1,2]=>10=>[1,1]
[2,1,3]=>[2,3,1]=>01=>[1,1]
[2,3,1]=>[2,1,3]=>10=>[1,1]
[3,1,2]=>[1,3,2]=>01=>[1,1]
[3,2,1]=>[1,2,3]=>00=>[2]
[1,2,3,4]=>[4,3,2,1]=>111=>[3]
[1,2,4,3]=>[4,3,1,2]=>110=>[2,1]
[1,3,2,4]=>[4,2,3,1]=>101=>[1,1,1]
[1,3,4,2]=>[4,2,1,3]=>110=>[2,1]
[1,4,2,3]=>[4,1,3,2]=>101=>[1,1,1]
[1,4,3,2]=>[4,1,2,3]=>100=>[1,2]
[2,1,3,4]=>[3,4,2,1]=>011=>[1,2]
[2,1,4,3]=>[3,4,1,2]=>010=>[1,1,1]
[2,3,1,4]=>[3,2,4,1]=>101=>[1,1,1]
[2,3,4,1]=>[3,2,1,4]=>110=>[2,1]
[2,4,1,3]=>[3,1,4,2]=>101=>[1,1,1]
[2,4,3,1]=>[3,1,2,4]=>100=>[1,2]
[3,1,2,4]=>[2,4,3,1]=>011=>[1,2]
[3,1,4,2]=>[2,4,1,3]=>010=>[1,1,1]
[3,2,1,4]=>[2,3,4,1]=>001=>[2,1]
[3,2,4,1]=>[2,3,1,4]=>010=>[1,1,1]
[3,4,1,2]=>[2,1,4,3]=>101=>[1,1,1]
[3,4,2,1]=>[2,1,3,4]=>100=>[1,2]
[4,1,2,3]=>[1,4,3,2]=>011=>[1,2]
[4,1,3,2]=>[1,4,2,3]=>010=>[1,1,1]
[4,2,1,3]=>[1,3,4,2]=>001=>[2,1]
[4,2,3,1]=>[1,3,2,4]=>010=>[1,1,1]
[4,3,1,2]=>[1,2,4,3]=>001=>[2,1]
[4,3,2,1]=>[1,2,3,4]=>000=>[3]
[1,2,3,4,5]=>[5,4,3,2,1]=>1111=>[4]
[1,2,3,5,4]=>[5,4,3,1,2]=>1110=>[3,1]
[1,2,4,3,5]=>[5,4,2,3,1]=>1101=>[2,1,1]
[1,2,4,5,3]=>[5,4,2,1,3]=>1110=>[3,1]
[1,2,5,3,4]=>[5,4,1,3,2]=>1101=>[2,1,1]
[1,2,5,4,3]=>[5,4,1,2,3]=>1100=>[2,2]
[1,3,2,4,5]=>[5,3,4,2,1]=>1011=>[1,1,2]
[1,3,2,5,4]=>[5,3,4,1,2]=>1010=>[1,1,1,1]
[1,3,4,2,5]=>[5,3,2,4,1]=>1101=>[2,1,1]
[1,3,4,5,2]=>[5,3,2,1,4]=>1110=>[3,1]
[1,3,5,2,4]=>[5,3,1,4,2]=>1101=>[2,1,1]
[1,3,5,4,2]=>[5,3,1,2,4]=>1100=>[2,2]
[1,4,2,3,5]=>[5,2,4,3,1]=>1011=>[1,1,2]
[1,4,2,5,3]=>[5,2,4,1,3]=>1010=>[1,1,1,1]
[1,4,3,2,5]=>[5,2,3,4,1]=>1001=>[1,2,1]
[1,4,3,5,2]=>[5,2,3,1,4]=>1010=>[1,1,1,1]
[1,4,5,2,3]=>[5,2,1,4,3]=>1101=>[2,1,1]
[1,4,5,3,2]=>[5,2,1,3,4]=>1100=>[2,2]
[1,5,2,3,4]=>[5,1,4,3,2]=>1011=>[1,1,2]
[1,5,2,4,3]=>[5,1,4,2,3]=>1010=>[1,1,1,1]
[1,5,3,2,4]=>[5,1,3,4,2]=>1001=>[1,2,1]
[1,5,3,4,2]=>[5,1,3,2,4]=>1010=>[1,1,1,1]
[1,5,4,2,3]=>[5,1,2,4,3]=>1001=>[1,2,1]
[1,5,4,3,2]=>[5,1,2,3,4]=>1000=>[1,3]
[2,1,3,4,5]=>[4,5,3,2,1]=>0111=>[1,3]
[2,1,3,5,4]=>[4,5,3,1,2]=>0110=>[1,2,1]
[2,1,4,3,5]=>[4,5,2,3,1]=>0101=>[1,1,1,1]
[2,1,4,5,3]=>[4,5,2,1,3]=>0110=>[1,2,1]
[2,1,5,3,4]=>[4,5,1,3,2]=>0101=>[1,1,1,1]
[2,1,5,4,3]=>[4,5,1,2,3]=>0100=>[1,1,2]
[2,3,1,4,5]=>[4,3,5,2,1]=>1011=>[1,1,2]
[2,3,1,5,4]=>[4,3,5,1,2]=>1010=>[1,1,1,1]
[2,3,4,1,5]=>[4,3,2,5,1]=>1101=>[2,1,1]
[2,3,4,5,1]=>[4,3,2,1,5]=>1110=>[3,1]
[2,3,5,1,4]=>[4,3,1,5,2]=>1101=>[2,1,1]
[2,3,5,4,1]=>[4,3,1,2,5]=>1100=>[2,2]
[2,4,1,3,5]=>[4,2,5,3,1]=>1011=>[1,1,2]
[2,4,1,5,3]=>[4,2,5,1,3]=>1010=>[1,1,1,1]
[2,4,3,1,5]=>[4,2,3,5,1]=>1001=>[1,2,1]
[2,4,3,5,1]=>[4,2,3,1,5]=>1010=>[1,1,1,1]
[2,4,5,1,3]=>[4,2,1,5,3]=>1101=>[2,1,1]
[2,4,5,3,1]=>[4,2,1,3,5]=>1100=>[2,2]
[2,5,1,3,4]=>[4,1,5,3,2]=>1011=>[1,1,2]
[2,5,1,4,3]=>[4,1,5,2,3]=>1010=>[1,1,1,1]
[2,5,3,1,4]=>[4,1,3,5,2]=>1001=>[1,2,1]
[2,5,3,4,1]=>[4,1,3,2,5]=>1010=>[1,1,1,1]
[2,5,4,1,3]=>[4,1,2,5,3]=>1001=>[1,2,1]
[2,5,4,3,1]=>[4,1,2,3,5]=>1000=>[1,3]
[3,1,2,4,5]=>[3,5,4,2,1]=>0111=>[1,3]
[3,1,2,5,4]=>[3,5,4,1,2]=>0110=>[1,2,1]
[3,1,4,2,5]=>[3,5,2,4,1]=>0101=>[1,1,1,1]
[3,1,4,5,2]=>[3,5,2,1,4]=>0110=>[1,2,1]
[3,1,5,2,4]=>[3,5,1,4,2]=>0101=>[1,1,1,1]
[3,1,5,4,2]=>[3,5,1,2,4]=>0100=>[1,1,2]
[3,2,1,4,5]=>[3,4,5,2,1]=>0011=>[2,2]
[3,2,1,5,4]=>[3,4,5,1,2]=>0010=>[2,1,1]
[3,2,4,1,5]=>[3,4,2,5,1]=>0101=>[1,1,1,1]
[3,2,4,5,1]=>[3,4,2,1,5]=>0110=>[1,2,1]
[3,2,5,1,4]=>[3,4,1,5,2]=>0101=>[1,1,1,1]
[3,2,5,4,1]=>[3,4,1,2,5]=>0100=>[1,1,2]
[3,4,1,2,5]=>[3,2,5,4,1]=>1011=>[1,1,2]
[3,4,1,5,2]=>[3,2,5,1,4]=>1010=>[1,1,1,1]
[3,4,2,1,5]=>[3,2,4,5,1]=>1001=>[1,2,1]
[3,4,2,5,1]=>[3,2,4,1,5]=>1010=>[1,1,1,1]
[3,4,5,1,2]=>[3,2,1,5,4]=>1101=>[2,1,1]
[3,4,5,2,1]=>[3,2,1,4,5]=>1100=>[2,2]
[3,5,1,2,4]=>[3,1,5,4,2]=>1011=>[1,1,2]
[3,5,1,4,2]=>[3,1,5,2,4]=>1010=>[1,1,1,1]
[3,5,2,1,4]=>[3,1,4,5,2]=>1001=>[1,2,1]
[3,5,2,4,1]=>[3,1,4,2,5]=>1010=>[1,1,1,1]
[3,5,4,1,2]=>[3,1,2,5,4]=>1001=>[1,2,1]
[3,5,4,2,1]=>[3,1,2,4,5]=>1000=>[1,3]
[4,1,2,3,5]=>[2,5,4,3,1]=>0111=>[1,3]
[4,1,2,5,3]=>[2,5,4,1,3]=>0110=>[1,2,1]
[4,1,3,2,5]=>[2,5,3,4,1]=>0101=>[1,1,1,1]
[4,1,3,5,2]=>[2,5,3,1,4]=>0110=>[1,2,1]
[4,1,5,2,3]=>[2,5,1,4,3]=>0101=>[1,1,1,1]
[4,1,5,3,2]=>[2,5,1,3,4]=>0100=>[1,1,2]
[4,2,1,3,5]=>[2,4,5,3,1]=>0011=>[2,2]
[4,2,1,5,3]=>[2,4,5,1,3]=>0010=>[2,1,1]
[4,2,3,1,5]=>[2,4,3,5,1]=>0101=>[1,1,1,1]
[4,2,3,5,1]=>[2,4,3,1,5]=>0110=>[1,2,1]
[4,2,5,1,3]=>[2,4,1,5,3]=>0101=>[1,1,1,1]
[4,2,5,3,1]=>[2,4,1,3,5]=>0100=>[1,1,2]
[4,3,1,2,5]=>[2,3,5,4,1]=>0011=>[2,2]
[4,3,1,5,2]=>[2,3,5,1,4]=>0010=>[2,1,1]
[4,3,2,1,5]=>[2,3,4,5,1]=>0001=>[3,1]
[4,3,2,5,1]=>[2,3,4,1,5]=>0010=>[2,1,1]
[4,3,5,1,2]=>[2,3,1,5,4]=>0101=>[1,1,1,1]
[4,3,5,2,1]=>[2,3,1,4,5]=>0100=>[1,1,2]
[4,5,1,2,3]=>[2,1,5,4,3]=>1011=>[1,1,2]
[4,5,1,3,2]=>[2,1,5,3,4]=>1010=>[1,1,1,1]
[4,5,2,1,3]=>[2,1,4,5,3]=>1001=>[1,2,1]
[4,5,2,3,1]=>[2,1,4,3,5]=>1010=>[1,1,1,1]
[4,5,3,1,2]=>[2,1,3,5,4]=>1001=>[1,2,1]
[4,5,3,2,1]=>[2,1,3,4,5]=>1000=>[1,3]
[5,1,2,3,4]=>[1,5,4,3,2]=>0111=>[1,3]
[5,1,2,4,3]=>[1,5,4,2,3]=>0110=>[1,2,1]
[5,1,3,2,4]=>[1,5,3,4,2]=>0101=>[1,1,1,1]
[5,1,3,4,2]=>[1,5,3,2,4]=>0110=>[1,2,1]
[5,1,4,2,3]=>[1,5,2,4,3]=>0101=>[1,1,1,1]
[5,1,4,3,2]=>[1,5,2,3,4]=>0100=>[1,1,2]
[5,2,1,3,4]=>[1,4,5,3,2]=>0011=>[2,2]
[5,2,1,4,3]=>[1,4,5,2,3]=>0010=>[2,1,1]
[5,2,3,1,4]=>[1,4,3,5,2]=>0101=>[1,1,1,1]
[5,2,3,4,1]=>[1,4,3,2,5]=>0110=>[1,2,1]
[5,2,4,1,3]=>[1,4,2,5,3]=>0101=>[1,1,1,1]
[5,2,4,3,1]=>[1,4,2,3,5]=>0100=>[1,1,2]
[5,3,1,2,4]=>[1,3,5,4,2]=>0011=>[2,2]
[5,3,1,4,2]=>[1,3,5,2,4]=>0010=>[2,1,1]
[5,3,2,1,4]=>[1,3,4,5,2]=>0001=>[3,1]
[5,3,2,4,1]=>[1,3,4,2,5]=>0010=>[2,1,1]
[5,3,4,1,2]=>[1,3,2,5,4]=>0101=>[1,1,1,1]
[5,3,4,2,1]=>[1,3,2,4,5]=>0100=>[1,1,2]
[5,4,1,2,3]=>[1,2,5,4,3]=>0011=>[2,2]
[5,4,1,3,2]=>[1,2,5,3,4]=>0010=>[2,1,1]
[5,4,2,1,3]=>[1,2,4,5,3]=>0001=>[3,1]
[5,4,2,3,1]=>[1,2,4,3,5]=>0010=>[2,1,1]
[5,4,3,1,2]=>[1,2,3,5,4]=>0001=>[3,1]
[5,4,3,2,1]=>[1,2,3,4,5]=>0000=>[4]
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111=>[5]
[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>11110=>[4,1]
[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>11101=>[3,1,1]
[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>11110=>[4,1]
[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>11101=>[3,1,1]
[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>11100=>[3,2]
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>11011=>[2,1,2]
[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>11010=>[2,1,1,1]
[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>11101=>[3,1,1]
[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>11110=>[4,1]
[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>11101=>[3,1,1]
[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>11100=>[3,2]
[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>11011=>[2,1,2]
[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>11010=>[2,1,1,1]
[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>11001=>[2,2,1]
[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>11010=>[2,1,1,1]
[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>11101=>[3,1,1]
[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>11100=>[3,2]
[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>11011=>[2,1,2]
[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>11010=>[2,1,1,1]
[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>11001=>[2,2,1]
[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>11010=>[2,1,1,1]
[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>11001=>[2,2,1]
[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>11000=>[2,3]
[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>10111=>[1,1,3]
[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>10110=>[1,1,2,1]
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>10101=>[1,1,1,1,1]
[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>10110=>[1,1,2,1]
[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>10101=>[1,1,1,1,1]
[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>10100=>[1,1,1,2]
[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>11011=>[2,1,2]
[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>11010=>[2,1,1,1]
[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>11101=>[3,1,1]
[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>11110=>[4,1]
[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>11101=>[3,1,1]
[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>11100=>[3,2]
[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>11011=>[2,1,2]
[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>11010=>[2,1,1,1]
[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>11001=>[2,2,1]
[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>11010=>[2,1,1,1]
[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>11101=>[3,1,1]
[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>11100=>[3,2]
[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>11011=>[2,1,2]
[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>11010=>[2,1,1,1]
[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>11001=>[2,2,1]
[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>11010=>[2,1,1,1]
[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>11001=>[2,2,1]
[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>11000=>[2,3]
[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>10111=>[1,1,3]
[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>10110=>[1,1,2,1]
[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>10101=>[1,1,1,1,1]
[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>10110=>[1,1,2,1]
[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>10101=>[1,1,1,1,1]
[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>10100=>[1,1,1,2]
[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>10011=>[1,2,2]
[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>10010=>[1,2,1,1]
[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>10101=>[1,1,1,1,1]
[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>10110=>[1,1,2,1]
[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>10101=>[1,1,1,1,1]
[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>10100=>[1,1,1,2]
[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>11011=>[2,1,2]
[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>11010=>[2,1,1,1]
[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>11001=>[2,2,1]
[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>11010=>[2,1,1,1]
[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>11101=>[3,1,1]
[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>11100=>[3,2]
[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>11011=>[2,1,2]
[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>11010=>[2,1,1,1]
[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>11001=>[2,2,1]
[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>11010=>[2,1,1,1]
[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>11001=>[2,2,1]
[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>11000=>[2,3]
[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>10111=>[1,1,3]
[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>10110=>[1,1,2,1]
[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>10101=>[1,1,1,1,1]
[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>10110=>[1,1,2,1]
[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>10101=>[1,1,1,1,1]
[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>10100=>[1,1,1,2]
[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>10011=>[1,2,2]
[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>10010=>[1,2,1,1]
[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>10101=>[1,1,1,1,1]
[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>10110=>[1,1,2,1]
[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>10101=>[1,1,1,1,1]
[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>10100=>[1,1,1,2]
[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>10011=>[1,2,2]
[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>10010=>[1,2,1,1]
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>10001=>[1,3,1]
[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>10010=>[1,2,1,1]
[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>10101=>[1,1,1,1,1]
[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>10100=>[1,1,1,2]
[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>11011=>[2,1,2]
[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>11010=>[2,1,1,1]
[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>11001=>[2,2,1]
[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>11010=>[2,1,1,1]
[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>11001=>[2,2,1]
[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>11000=>[2,3]
[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>10111=>[1,1,3]
[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>10110=>[1,1,2,1]
[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>10101=>[1,1,1,1,1]
[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>10110=>[1,1,2,1]
[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>10101=>[1,1,1,1,1]
[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>10100=>[1,1,1,2]
[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>10011=>[1,2,2]
[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>10010=>[1,2,1,1]
[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>10101=>[1,1,1,1,1]
[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>10110=>[1,1,2,1]
[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>10101=>[1,1,1,1,1]
[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>10100=>[1,1,1,2]
[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>10011=>[1,2,2]
[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>10010=>[1,2,1,1]
[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>10001=>[1,3,1]
[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>10010=>[1,2,1,1]
[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>10101=>[1,1,1,1,1]
[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>10100=>[1,1,1,2]
[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>10011=>[1,2,2]
[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>10010=>[1,2,1,1]
[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>10001=>[1,3,1]
[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>10010=>[1,2,1,1]
[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>10001=>[1,3,1]
[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>10000=>[1,4]
[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>01111=>[1,4]
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>01110=>[1,3,1]
[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>01101=>[1,2,1,1]
[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>01110=>[1,3,1]
[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>01101=>[1,2,1,1]
[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>01100=>[1,2,2]
[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>01011=>[1,1,1,2]
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>01010=>[1,1,1,1,1]
[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>01101=>[1,2,1,1]
[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>01110=>[1,3,1]
[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>01101=>[1,2,1,1]
[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>01100=>[1,2,2]
[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>01011=>[1,1,1,2]
[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>01010=>[1,1,1,1,1]
[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>01001=>[1,1,2,1]
[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>01010=>[1,1,1,1,1]
[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>01101=>[1,2,1,1]
[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>01100=>[1,2,2]
[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>01011=>[1,1,1,2]
[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>01010=>[1,1,1,1,1]
[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>01001=>[1,1,2,1]
[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>01010=>[1,1,1,1,1]
[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>01001=>[1,1,2,1]
[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>01000=>[1,1,3]
[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>10111=>[1,1,3]
[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>10110=>[1,1,2,1]
[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>10101=>[1,1,1,1,1]
[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>10110=>[1,1,2,1]
[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>10101=>[1,1,1,1,1]
[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>10100=>[1,1,1,2]
[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>11011=>[2,1,2]
[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>11010=>[2,1,1,1]
[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>11101=>[3,1,1]
[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>11110=>[4,1]
[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>11101=>[3,1,1]
[2,3,4,6,5,1]=>[5,4,3,1,2,6]=>11100=>[3,2]
[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>11011=>[2,1,2]
[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>11010=>[2,1,1,1]
[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>11001=>[2,2,1]
[2,3,5,4,6,1]=>[5,4,2,3,1,6]=>11010=>[2,1,1,1]
[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>11101=>[3,1,1]
[2,3,5,6,4,1]=>[5,4,2,1,3,6]=>11100=>[3,2]
[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>11011=>[2,1,2]
[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>11010=>[2,1,1,1]
[2,3,6,4,1,5]=>[5,4,1,3,6,2]=>11001=>[2,2,1]
[2,3,6,4,5,1]=>[5,4,1,3,2,6]=>11010=>[2,1,1,1]
[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>11001=>[2,2,1]
[2,3,6,5,4,1]=>[5,4,1,2,3,6]=>11000=>[2,3]
[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>10111=>[1,1,3]
[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>10110=>[1,1,2,1]
[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>10101=>[1,1,1,1,1]
[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>10110=>[1,1,2,1]
[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>10101=>[1,1,1,1,1]
[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>10100=>[1,1,1,2]
[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>10011=>[1,2,2]
[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>10010=>[1,2,1,1]
[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>10101=>[1,1,1,1,1]
[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>10110=>[1,1,2,1]
[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>10101=>[1,1,1,1,1]
[2,4,3,6,5,1]=>[5,3,4,1,2,6]=>10100=>[1,1,1,2]
[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>11011=>[2,1,2]
[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>11010=>[2,1,1,1]
[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>11001=>[2,2,1]
[2,4,5,3,6,1]=>[5,3,2,4,1,6]=>11010=>[2,1,1,1]
[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>11101=>[3,1,1]
[2,4,5,6,3,1]=>[5,3,2,1,4,6]=>11100=>[3,2]
[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>11011=>[2,1,2]
[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>11010=>[2,1,1,1]
[2,4,6,3,1,5]=>[5,3,1,4,6,2]=>11001=>[2,2,1]
[2,4,6,3,5,1]=>[5,3,1,4,2,6]=>11010=>[2,1,1,1]
[2,4,6,5,1,3]=>[5,3,1,2,6,4]=>11001=>[2,2,1]
[2,4,6,5,3,1]=>[5,3,1,2,4,6]=>11000=>[2,3]
[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>10111=>[1,1,3]
[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>10110=>[1,1,2,1]
[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>10101=>[1,1,1,1,1]
[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>10110=>[1,1,2,1]
[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>10101=>[1,1,1,1,1]
[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>10100=>[1,1,1,2]
[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>10011=>[1,2,2]
[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>10010=>[1,2,1,1]
[2,5,3,4,1,6]=>[5,2,4,3,6,1]=>10101=>[1,1,1,1,1]
[2,5,3,4,6,1]=>[5,2,4,3,1,6]=>10110=>[1,1,2,1]
[2,5,3,6,1,4]=>[5,2,4,1,6,3]=>10101=>[1,1,1,1,1]
[2,5,3,6,4,1]=>[5,2,4,1,3,6]=>10100=>[1,1,1,2]
[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>10011=>[1,2,2]
[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>10010=>[1,2,1,1]
[2,5,4,3,1,6]=>[5,2,3,4,6,1]=>10001=>[1,3,1]
[2,5,4,3,6,1]=>[5,2,3,4,1,6]=>10010=>[1,2,1,1]
[2,5,4,6,1,3]=>[5,2,3,1,6,4]=>10101=>[1,1,1,1,1]
[2,5,4,6,3,1]=>[5,2,3,1,4,6]=>10100=>[1,1,1,2]
[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>11011=>[2,1,2]
[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>11010=>[2,1,1,1]
[2,5,6,3,1,4]=>[5,2,1,4,6,3]=>11001=>[2,2,1]
[2,5,6,3,4,1]=>[5,2,1,4,3,6]=>11010=>[2,1,1,1]
[2,5,6,4,1,3]=>[5,2,1,3,6,4]=>11001=>[2,2,1]
[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>11000=>[2,3]
[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>10111=>[1,1,3]
[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>10110=>[1,1,2,1]
[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>10101=>[1,1,1,1,1]
[2,6,1,4,5,3]=>[5,1,6,3,2,4]=>10110=>[1,1,2,1]
[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>10101=>[1,1,1,1,1]
[2,6,1,5,4,3]=>[5,1,6,2,3,4]=>10100=>[1,1,1,2]
[2,6,3,1,4,5]=>[5,1,4,6,3,2]=>10011=>[1,2,2]
[2,6,3,1,5,4]=>[5,1,4,6,2,3]=>10010=>[1,2,1,1]
[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>10101=>[1,1,1,1,1]
[2,6,3,4,5,1]=>[5,1,4,3,2,6]=>10110=>[1,1,2,1]
[2,6,3,5,1,4]=>[5,1,4,2,6,3]=>10101=>[1,1,1,1,1]
[2,6,3,5,4,1]=>[5,1,4,2,3,6]=>10100=>[1,1,1,2]
[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>10011=>[1,2,2]
[2,6,4,1,5,3]=>[5,1,3,6,2,4]=>10010=>[1,2,1,1]
[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>10001=>[1,3,1]
[2,6,4,3,5,1]=>[5,1,3,4,2,6]=>10010=>[1,2,1,1]
[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>10101=>[1,1,1,1,1]
[2,6,4,5,3,1]=>[5,1,3,2,4,6]=>10100=>[1,1,1,2]
[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>10011=>[1,2,2]
[2,6,5,1,4,3]=>[5,1,2,6,3,4]=>10010=>[1,2,1,1]
[2,6,5,3,1,4]=>[5,1,2,4,6,3]=>10001=>[1,3,1]
[2,6,5,3,4,1]=>[5,1,2,4,3,6]=>10010=>[1,2,1,1]
[2,6,5,4,1,3]=>[5,1,2,3,6,4]=>10001=>[1,3,1]
[2,6,5,4,3,1]=>[5,1,2,3,4,6]=>10000=>[1,4]
[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>01111=>[1,4]
[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>01110=>[1,3,1]
[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>01101=>[1,2,1,1]
[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>01110=>[1,3,1]
[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>01101=>[1,2,1,1]
[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>01100=>[1,2,2]
[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>01011=>[1,1,1,2]
[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>01010=>[1,1,1,1,1]
[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>01101=>[1,2,1,1]
[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>01110=>[1,3,1]
[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>01101=>[1,2,1,1]
[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>01100=>[1,2,2]
[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>01011=>[1,1,1,2]
[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>01010=>[1,1,1,1,1]
[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>01001=>[1,1,2,1]
[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>01010=>[1,1,1,1,1]
[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>01101=>[1,2,1,1]
[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>01100=>[1,2,2]
[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>01011=>[1,1,1,2]
[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>01010=>[1,1,1,1,1]
[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>01001=>[1,1,2,1]
[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>01010=>[1,1,1,1,1]
[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>01001=>[1,1,2,1]
[3,1,6,5,4,2]=>[4,6,1,2,3,5]=>01000=>[1,1,3]
[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>00111=>[2,3]
[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>00110=>[2,2,1]
[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>00101=>[2,1,1,1]
[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>00110=>[2,2,1]
[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>00101=>[2,1,1,1]
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>00100=>[2,1,2]
[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>01011=>[1,1,1,2]
[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>01010=>[1,1,1,1,1]
[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>01101=>[1,2,1,1]
[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>01110=>[1,3,1]
[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>01101=>[1,2,1,1]
[3,2,4,6,5,1]=>[4,5,3,1,2,6]=>01100=>[1,2,2]
[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>01011=>[1,1,1,2]
[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>01010=>[1,1,1,1,1]
[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>01001=>[1,1,2,1]
[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>01010=>[1,1,1,1,1]
[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>01101=>[1,2,1,1]
[3,2,5,6,4,1]=>[4,5,2,1,3,6]=>01100=>[1,2,2]
[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>01011=>[1,1,1,2]
[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>01010=>[1,1,1,1,1]
[3,2,6,4,1,5]=>[4,5,1,3,6,2]=>01001=>[1,1,2,1]
[3,2,6,4,5,1]=>[4,5,1,3,2,6]=>01010=>[1,1,1,1,1]
[3,2,6,5,1,4]=>[4,5,1,2,6,3]=>01001=>[1,1,2,1]
[3,2,6,5,4,1]=>[4,5,1,2,3,6]=>01000=>[1,1,3]
[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>10111=>[1,1,3]
[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>10110=>[1,1,2,1]
[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>10101=>[1,1,1,1,1]
[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>10110=>[1,1,2,1]
[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>10101=>[1,1,1,1,1]
[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>10100=>[1,1,1,2]
[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>10011=>[1,2,2]
[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>10010=>[1,2,1,1]
[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>10101=>[1,1,1,1,1]
[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>10110=>[1,1,2,1]
[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>10101=>[1,1,1,1,1]
[3,4,2,6,5,1]=>[4,3,5,1,2,6]=>10100=>[1,1,1,2]
[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>11011=>[2,1,2]
[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>11010=>[2,1,1,1]
[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>11001=>[2,2,1]
[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>11010=>[2,1,1,1]
[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>11101=>[3,1,1]
[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>11100=>[3,2]
[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>11011=>[2,1,2]
[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>11010=>[2,1,1,1]
[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>11001=>[2,2,1]
[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>11010=>[2,1,1,1]
[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>11001=>[2,2,1]
[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>11000=>[2,3]
[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>10111=>[1,1,3]
[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>10110=>[1,1,2,1]
[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>10101=>[1,1,1,1,1]
[3,5,1,4,6,2]=>[4,2,6,3,1,5]=>10110=>[1,1,2,1]
[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>10101=>[1,1,1,1,1]
[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>10100=>[1,1,1,2]
[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>10011=>[1,2,2]
[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>10010=>[1,2,1,1]
[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>10101=>[1,1,1,1,1]
[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>10110=>[1,1,2,1]
[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>10101=>[1,1,1,1,1]
[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>10100=>[1,1,1,2]
[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>10011=>[1,2,2]
[3,5,4,1,6,2]=>[4,2,3,6,1,5]=>10010=>[1,2,1,1]
[3,5,4,2,1,6]=>[4,2,3,5,6,1]=>10001=>[1,3,1]
[3,5,4,2,6,1]=>[4,2,3,5,1,6]=>10010=>[1,2,1,1]
[3,5,4,6,1,2]=>[4,2,3,1,6,5]=>10101=>[1,1,1,1,1]
[3,5,4,6,2,1]=>[4,2,3,1,5,6]=>10100=>[1,1,1,2]
[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>11011=>[2,1,2]
[3,5,6,1,4,2]=>[4,2,1,6,3,5]=>11010=>[2,1,1,1]
[3,5,6,2,1,4]=>[4,2,1,5,6,3]=>11001=>[2,2,1]
[3,5,6,2,4,1]=>[4,2,1,5,3,6]=>11010=>[2,1,1,1]
[3,5,6,4,1,2]=>[4,2,1,3,6,5]=>11001=>[2,2,1]
[3,5,6,4,2,1]=>[4,2,1,3,5,6]=>11000=>[2,3]
[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>10111=>[1,1,3]
[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>10110=>[1,1,2,1]
[3,6,1,4,2,5]=>[4,1,6,3,5,2]=>10101=>[1,1,1,1,1]
[3,6,1,4,5,2]=>[4,1,6,3,2,5]=>10110=>[1,1,2,1]
[3,6,1,5,2,4]=>[4,1,6,2,5,3]=>10101=>[1,1,1,1,1]
[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>10100=>[1,1,1,2]
[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>10011=>[1,2,2]
[3,6,2,1,5,4]=>[4,1,5,6,2,3]=>10010=>[1,2,1,1]
[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>10101=>[1,1,1,1,1]
[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>10110=>[1,1,2,1]
[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>10101=>[1,1,1,1,1]
[3,6,2,5,4,1]=>[4,1,5,2,3,6]=>10100=>[1,1,1,2]
[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>10011=>[1,2,2]
[3,6,4,1,5,2]=>[4,1,3,6,2,5]=>10010=>[1,2,1,1]
[3,6,4,2,1,5]=>[4,1,3,5,6,2]=>10001=>[1,3,1]
[3,6,4,2,5,1]=>[4,1,3,5,2,6]=>10010=>[1,2,1,1]
[3,6,4,5,1,2]=>[4,1,3,2,6,5]=>10101=>[1,1,1,1,1]
[3,6,4,5,2,1]=>[4,1,3,2,5,6]=>10100=>[1,1,1,2]
[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>10011=>[1,2,2]
[3,6,5,1,4,2]=>[4,1,2,6,3,5]=>10010=>[1,2,1,1]
[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>10001=>[1,3,1]
[3,6,5,2,4,1]=>[4,1,2,5,3,6]=>10010=>[1,2,1,1]
[3,6,5,4,1,2]=>[4,1,2,3,6,5]=>10001=>[1,3,1]
[3,6,5,4,2,1]=>[4,1,2,3,5,6]=>10000=>[1,4]
[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>01111=>[1,4]
[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>01110=>[1,3,1]
[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>01101=>[1,2,1,1]
[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>01110=>[1,3,1]
[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>01101=>[1,2,1,1]
[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>01100=>[1,2,2]
[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>01011=>[1,1,1,2]
[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>01010=>[1,1,1,1,1]
[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>01101=>[1,2,1,1]
[4,1,3,5,6,2]=>[3,6,4,2,1,5]=>01110=>[1,3,1]
[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>01101=>[1,2,1,1]
[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>01100=>[1,2,2]
[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>01011=>[1,1,1,2]
[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>01010=>[1,1,1,1,1]
[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>01001=>[1,1,2,1]
[4,1,5,3,6,2]=>[3,6,2,4,1,5]=>01010=>[1,1,1,1,1]
[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>01101=>[1,2,1,1]
[4,1,5,6,3,2]=>[3,6,2,1,4,5]=>01100=>[1,2,2]
[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>01011=>[1,1,1,2]
[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>01010=>[1,1,1,1,1]
[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>01001=>[1,1,2,1]
[4,1,6,3,5,2]=>[3,6,1,4,2,5]=>01010=>[1,1,1,1,1]
[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>01001=>[1,1,2,1]
[4,1,6,5,3,2]=>[3,6,1,2,4,5]=>01000=>[1,1,3]
[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>00111=>[2,3]
[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>00110=>[2,2,1]
[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>00101=>[2,1,1,1]
[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>00110=>[2,2,1]
[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>00101=>[2,1,1,1]
[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>00100=>[2,1,2]
[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>01011=>[1,1,1,2]
[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>01010=>[1,1,1,1,1]
[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>01101=>[1,2,1,1]
[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>01110=>[1,3,1]
[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>01101=>[1,2,1,1]
[4,2,3,6,5,1]=>[3,5,4,1,2,6]=>01100=>[1,2,2]
[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>01011=>[1,1,1,2]
[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>01010=>[1,1,1,1,1]
[4,2,5,3,1,6]=>[3,5,2,4,6,1]=>01001=>[1,1,2,1]
[4,2,5,3,6,1]=>[3,5,2,4,1,6]=>01010=>[1,1,1,1,1]
[4,2,5,6,1,3]=>[3,5,2,1,6,4]=>01101=>[1,2,1,1]
[4,2,5,6,3,1]=>[3,5,2,1,4,6]=>01100=>[1,2,2]
[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>01011=>[1,1,1,2]
[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>01010=>[1,1,1,1,1]
[4,2,6,3,1,5]=>[3,5,1,4,6,2]=>01001=>[1,1,2,1]
[4,2,6,3,5,1]=>[3,5,1,4,2,6]=>01010=>[1,1,1,1,1]
[4,2,6,5,1,3]=>[3,5,1,2,6,4]=>01001=>[1,1,2,1]
[4,2,6,5,3,1]=>[3,5,1,2,4,6]=>01000=>[1,1,3]
[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>00111=>[2,3]
[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>00110=>[2,2,1]
[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>00101=>[2,1,1,1]
[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>00110=>[2,2,1]
[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>00101=>[2,1,1,1]
[4,3,1,6,5,2]=>[3,4,6,1,2,5]=>00100=>[2,1,2]
[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>00011=>[3,2]
[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>00010=>[3,1,1]
[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>00101=>[2,1,1,1]
[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>00110=>[2,2,1]
[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>00101=>[2,1,1,1]
[4,3,2,6,5,1]=>[3,4,5,1,2,6]=>00100=>[2,1,2]
[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>01011=>[1,1,1,2]
[4,3,5,1,6,2]=>[3,4,2,6,1,5]=>01010=>[1,1,1,1,1]
[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>01001=>[1,1,2,1]
[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>01010=>[1,1,1,1,1]
[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>01101=>[1,2,1,1]
[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>01100=>[1,2,2]
[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>01011=>[1,1,1,2]
[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>01010=>[1,1,1,1,1]
[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>01001=>[1,1,2,1]
[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>01010=>[1,1,1,1,1]
[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>01001=>[1,1,2,1]
[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>01000=>[1,1,3]
[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>10111=>[1,1,3]
[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>10110=>[1,1,2,1]
[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>10101=>[1,1,1,1,1]
[4,5,1,3,6,2]=>[3,2,6,4,1,5]=>10110=>[1,1,2,1]
[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>10101=>[1,1,1,1,1]
[4,5,1,6,3,2]=>[3,2,6,1,4,5]=>10100=>[1,1,1,2]
[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>10011=>[1,2,2]
[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>10010=>[1,2,1,1]
[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>10101=>[1,1,1,1,1]
[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>10110=>[1,1,2,1]
[4,5,2,6,1,3]=>[3,2,5,1,6,4]=>10101=>[1,1,1,1,1]
[4,5,2,6,3,1]=>[3,2,5,1,4,6]=>10100=>[1,1,1,2]
[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>10011=>[1,2,2]
[4,5,3,1,6,2]=>[3,2,4,6,1,5]=>10010=>[1,2,1,1]
[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>10001=>[1,3,1]
[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>10010=>[1,2,1,1]
[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>10101=>[1,1,1,1,1]
[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>10100=>[1,1,1,2]
[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011=>[2,1,2]
[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>11010=>[2,1,1,1]
[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>11001=>[2,2,1]
[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>11010=>[2,1,1,1]
[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>11001=>[2,2,1]
[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>11000=>[2,3]
[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>10111=>[1,1,3]
[4,6,1,2,5,3]=>[3,1,6,5,2,4]=>10110=>[1,1,2,1]
[4,6,1,3,2,5]=>[3,1,6,4,5,2]=>10101=>[1,1,1,1,1]
[4,6,1,3,5,2]=>[3,1,6,4,2,5]=>10110=>[1,1,2,1]
[4,6,1,5,2,3]=>[3,1,6,2,5,4]=>10101=>[1,1,1,1,1]
[4,6,1,5,3,2]=>[3,1,6,2,4,5]=>10100=>[1,1,1,2]
[4,6,2,1,3,5]=>[3,1,5,6,4,2]=>10011=>[1,2,2]
[4,6,2,1,5,3]=>[3,1,5,6,2,4]=>10010=>[1,2,1,1]
[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>10101=>[1,1,1,1,1]
[4,6,2,3,5,1]=>[3,1,5,4,2,6]=>10110=>[1,1,2,1]
[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>10101=>[1,1,1,1,1]
[4,6,2,5,3,1]=>[3,1,5,2,4,6]=>10100=>[1,1,1,2]
[4,6,3,1,2,5]=>[3,1,4,6,5,2]=>10011=>[1,2,2]
[4,6,3,1,5,2]=>[3,1,4,6,2,5]=>10010=>[1,2,1,1]
[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>10001=>[1,3,1]
[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>10010=>[1,2,1,1]
[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>10101=>[1,1,1,1,1]
[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>10100=>[1,1,1,2]
[4,6,5,1,2,3]=>[3,1,2,6,5,4]=>10011=>[1,2,2]
[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>10010=>[1,2,1,1]
[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>10001=>[1,3,1]
[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>10010=>[1,2,1,1]
[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>10001=>[1,3,1]
[4,6,5,3,2,1]=>[3,1,2,4,5,6]=>10000=>[1,4]
[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>01111=>[1,4]
[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>01110=>[1,3,1]
[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>01101=>[1,2,1,1]
[5,1,2,4,6,3]=>[2,6,5,3,1,4]=>01110=>[1,3,1]
[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>01101=>[1,2,1,1]
[5,1,2,6,4,3]=>[2,6,5,1,3,4]=>01100=>[1,2,2]
[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>01011=>[1,1,1,2]
[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>01010=>[1,1,1,1,1]
[5,1,3,4,2,6]=>[2,6,4,3,5,1]=>01101=>[1,2,1,1]
[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>01110=>[1,3,1]
[5,1,3,6,2,4]=>[2,6,4,1,5,3]=>01101=>[1,2,1,1]
[5,1,3,6,4,2]=>[2,6,4,1,3,5]=>01100=>[1,2,2]
[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>01011=>[1,1,1,2]
[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>01010=>[1,1,1,1,1]
[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>01001=>[1,1,2,1]
[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>01010=>[1,1,1,1,1]
[5,1,4,6,2,3]=>[2,6,3,1,5,4]=>01101=>[1,2,1,1]
[5,1,4,6,3,2]=>[2,6,3,1,4,5]=>01100=>[1,2,2]
[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>01011=>[1,1,1,2]
[5,1,6,2,4,3]=>[2,6,1,5,3,4]=>01010=>[1,1,1,1,1]
[5,1,6,3,2,4]=>[2,6,1,4,5,3]=>01001=>[1,1,2,1]
[5,1,6,3,4,2]=>[2,6,1,4,3,5]=>01010=>[1,1,1,1,1]
[5,1,6,4,2,3]=>[2,6,1,3,5,4]=>01001=>[1,1,2,1]
[5,1,6,4,3,2]=>[2,6,1,3,4,5]=>01000=>[1,1,3]
[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>00111=>[2,3]
[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>00110=>[2,2,1]
[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>00101=>[2,1,1,1]
[5,2,1,4,6,3]=>[2,5,6,3,1,4]=>00110=>[2,2,1]
[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>00101=>[2,1,1,1]
[5,2,1,6,4,3]=>[2,5,6,1,3,4]=>00100=>[2,1,2]
[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>01011=>[1,1,1,2]
[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>01010=>[1,1,1,1,1]
[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>01101=>[1,2,1,1]
[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>01110=>[1,3,1]
[5,2,3,6,1,4]=>[2,5,4,1,6,3]=>01101=>[1,2,1,1]
[5,2,3,6,4,1]=>[2,5,4,1,3,6]=>01100=>[1,2,2]
[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>01011=>[1,1,1,2]
[5,2,4,1,6,3]=>[2,5,3,6,1,4]=>01010=>[1,1,1,1,1]
[5,2,4,3,1,6]=>[2,5,3,4,6,1]=>01001=>[1,1,2,1]
[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>01010=>[1,1,1,1,1]
[5,2,4,6,1,3]=>[2,5,3,1,6,4]=>01101=>[1,2,1,1]
[5,2,4,6,3,1]=>[2,5,3,1,4,6]=>01100=>[1,2,2]
[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>01011=>[1,1,1,2]
[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>01010=>[1,1,1,1,1]
[5,2,6,3,1,4]=>[2,5,1,4,6,3]=>01001=>[1,1,2,1]
[5,2,6,3,4,1]=>[2,5,1,4,3,6]=>01010=>[1,1,1,1,1]
[5,2,6,4,1,3]=>[2,5,1,3,6,4]=>01001=>[1,1,2,1]
[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>01000=>[1,1,3]
[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>00111=>[2,3]
[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>00110=>[2,2,1]
[5,3,1,4,2,6]=>[2,4,6,3,5,1]=>00101=>[2,1,1,1]
[5,3,1,4,6,2]=>[2,4,6,3,1,5]=>00110=>[2,2,1]
[5,3,1,6,2,4]=>[2,4,6,1,5,3]=>00101=>[2,1,1,1]
[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>00100=>[2,1,2]
[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>00011=>[3,2]
[5,3,2,1,6,4]=>[2,4,5,6,1,3]=>00010=>[3,1,1]
[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>00101=>[2,1,1,1]
[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>00110=>[2,2,1]
[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>00101=>[2,1,1,1]
[5,3,2,6,4,1]=>[2,4,5,1,3,6]=>00100=>[2,1,2]
[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>01011=>[1,1,1,2]
[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>01010=>[1,1,1,1,1]
[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>01001=>[1,1,2,1]
[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>01010=>[1,1,1,1,1]
[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>01101=>[1,2,1,1]
[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>01100=>[1,2,2]
[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>01011=>[1,1,1,2]
[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>01010=>[1,1,1,1,1]
[5,3,6,2,1,4]=>[2,4,1,5,6,3]=>01001=>[1,1,2,1]
[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>01010=>[1,1,1,1,1]
[5,3,6,4,1,2]=>[2,4,1,3,6,5]=>01001=>[1,1,2,1]
[5,3,6,4,2,1]=>[2,4,1,3,5,6]=>01000=>[1,1,3]
[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>00111=>[2,3]
[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>00110=>[2,2,1]
[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>00101=>[2,1,1,1]
[5,4,1,3,6,2]=>[2,3,6,4,1,5]=>00110=>[2,2,1]
[5,4,1,6,2,3]=>[2,3,6,1,5,4]=>00101=>[2,1,1,1]
[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>00100=>[2,1,2]
[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>00011=>[3,2]
[5,4,2,1,6,3]=>[2,3,5,6,1,4]=>00010=>[3,1,1]
[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>00101=>[2,1,1,1]
[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>00110=>[2,2,1]
[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>00101=>[2,1,1,1]
[5,4,2,6,3,1]=>[2,3,5,1,4,6]=>00100=>[2,1,2]
[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>00011=>[3,2]
[5,4,3,1,6,2]=>[2,3,4,6,1,5]=>00010=>[3,1,1]
[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>00001=>[4,1]
[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>00010=>[3,1,1]
[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>00101=>[2,1,1,1]
[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>00100=>[2,1,2]
[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>01011=>[1,1,1,2]
[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>01010=>[1,1,1,1,1]
[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>01001=>[1,1,2,1]
[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>01010=>[1,1,1,1,1]
[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>01001=>[1,1,2,1]
[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>01000=>[1,1,3]
[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>10111=>[1,1,3]
[5,6,1,2,4,3]=>[2,1,6,5,3,4]=>10110=>[1,1,2,1]
[5,6,1,3,2,4]=>[2,1,6,4,5,3]=>10101=>[1,1,1,1,1]
[5,6,1,3,4,2]=>[2,1,6,4,3,5]=>10110=>[1,1,2,1]
[5,6,1,4,2,3]=>[2,1,6,3,5,4]=>10101=>[1,1,1,1,1]
[5,6,1,4,3,2]=>[2,1,6,3,4,5]=>10100=>[1,1,1,2]
[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>10011=>[1,2,2]
[5,6,2,1,4,3]=>[2,1,5,6,3,4]=>10010=>[1,2,1,1]
[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>10101=>[1,1,1,1,1]
[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>10110=>[1,1,2,1]
[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>10101=>[1,1,1,1,1]
[5,6,2,4,3,1]=>[2,1,5,3,4,6]=>10100=>[1,1,1,2]
[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>10011=>[1,2,2]
[5,6,3,1,4,2]=>[2,1,4,6,3,5]=>10010=>[1,2,1,1]
[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>10001=>[1,3,1]
[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>10010=>[1,2,1,1]
[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101=>[1,1,1,1,1]
[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>10100=>[1,1,1,2]
[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>10011=>[1,2,2]
[5,6,4,1,3,2]=>[2,1,3,6,4,5]=>10010=>[1,2,1,1]
[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>10001=>[1,3,1]
[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>10010=>[1,2,1,1]
[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001=>[1,3,1]
[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>10000=>[1,4]
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>01111=>[1,4]
[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>01110=>[1,3,1]
[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>01101=>[1,2,1,1]
[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>01110=>[1,3,1]
[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>01101=>[1,2,1,1]
[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>01100=>[1,2,2]
[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>01011=>[1,1,1,2]
[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>01010=>[1,1,1,1,1]
[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>01101=>[1,2,1,1]
[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>01110=>[1,3,1]
[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>01101=>[1,2,1,1]
[6,1,3,5,4,2]=>[1,6,4,2,3,5]=>01100=>[1,2,2]
[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>01011=>[1,1,1,2]
[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>01010=>[1,1,1,1,1]
[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>01001=>[1,1,2,1]
[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>01010=>[1,1,1,1,1]
[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>01101=>[1,2,1,1]
[6,1,4,5,3,2]=>[1,6,3,2,4,5]=>01100=>[1,2,2]
[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>01011=>[1,1,1,2]
[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>01010=>[1,1,1,1,1]
[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>01001=>[1,1,2,1]
[6,1,5,3,4,2]=>[1,6,2,4,3,5]=>01010=>[1,1,1,1,1]
[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>01001=>[1,1,2,1]
[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>01000=>[1,1,3]
[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>00111=>[2,3]
[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>00110=>[2,2,1]
[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>00101=>[2,1,1,1]
[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>00110=>[2,2,1]
[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>00101=>[2,1,1,1]
[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>00100=>[2,1,2]
[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>01011=>[1,1,1,2]
[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>01010=>[1,1,1,1,1]
[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>01101=>[1,2,1,1]
[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110=>[1,3,1]
[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>01101=>[1,2,1,1]
[6,2,3,5,4,1]=>[1,5,4,2,3,6]=>01100=>[1,2,2]
[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>01011=>[1,1,1,2]
[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>01010=>[1,1,1,1,1]
[6,2,4,3,1,5]=>[1,5,3,4,6,2]=>01001=>[1,1,2,1]
[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>01010=>[1,1,1,1,1]
[6,2,4,5,1,3]=>[1,5,3,2,6,4]=>01101=>[1,2,1,1]
[6,2,4,5,3,1]=>[1,5,3,2,4,6]=>01100=>[1,2,2]
[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>01011=>[1,1,1,2]
[6,2,5,1,4,3]=>[1,5,2,6,3,4]=>01010=>[1,1,1,1,1]
[6,2,5,3,1,4]=>[1,5,2,4,6,3]=>01001=>[1,1,2,1]
[6,2,5,3,4,1]=>[1,5,2,4,3,6]=>01010=>[1,1,1,1,1]
[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>01001=>[1,1,2,1]
[6,2,5,4,3,1]=>[1,5,2,3,4,6]=>01000=>[1,1,3]
[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>00111=>[2,3]
[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>00110=>[2,2,1]
[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>00101=>[2,1,1,1]
[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>00110=>[2,2,1]
[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>00101=>[2,1,1,1]
[6,3,1,5,4,2]=>[1,4,6,2,3,5]=>00100=>[2,1,2]
[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>00011=>[3,2]
[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>00010=>[3,1,1]
[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>00101=>[2,1,1,1]
[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>00110=>[2,2,1]
[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>00101=>[2,1,1,1]
[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>00100=>[2,1,2]
[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>01011=>[1,1,1,2]
[6,3,4,1,5,2]=>[1,4,3,6,2,5]=>01010=>[1,1,1,1,1]
[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>01001=>[1,1,2,1]
[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>01010=>[1,1,1,1,1]
[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>01101=>[1,2,1,1]
[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>01100=>[1,2,2]
[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>01011=>[1,1,1,2]
[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>01010=>[1,1,1,1,1]
[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>01001=>[1,1,2,1]
[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>01010=>[1,1,1,1,1]
[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>01001=>[1,1,2,1]
[6,3,5,4,2,1]=>[1,4,2,3,5,6]=>01000=>[1,1,3]
[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>00111=>[2,3]
[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>00110=>[2,2,1]
[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>00101=>[2,1,1,1]
[6,4,1,3,5,2]=>[1,3,6,4,2,5]=>00110=>[2,2,1]
[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>00101=>[2,1,1,1]
[6,4,1,5,3,2]=>[1,3,6,2,4,5]=>00100=>[2,1,2]
[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>00011=>[3,2]
[6,4,2,1,5,3]=>[1,3,5,6,2,4]=>00010=>[3,1,1]
[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>00101=>[2,1,1,1]
[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>00110=>[2,2,1]
[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>00101=>[2,1,1,1]
[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>00100=>[2,1,2]
[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>00011=>[3,2]
[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>00010=>[3,1,1]
[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>00001=>[4,1]
[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>00010=>[3,1,1]
[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>00101=>[2,1,1,1]
[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>00100=>[2,1,2]
[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>01011=>[1,1,1,2]
[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>01010=>[1,1,1,1,1]
[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>01001=>[1,1,2,1]
[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010=>[1,1,1,1,1]
[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>01001=>[1,1,2,1]
[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>01000=>[1,1,3]
[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>00111=>[2,3]
[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>00110=>[2,2,1]
[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>00101=>[2,1,1,1]
[6,5,1,3,4,2]=>[1,2,6,4,3,5]=>00110=>[2,2,1]
[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>00101=>[2,1,1,1]
[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>00100=>[2,1,2]
[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>00011=>[3,2]
[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>00010=>[3,1,1]
[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>00101=>[2,1,1,1]
[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>00110=>[2,2,1]
[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>00101=>[2,1,1,1]
[6,5,2,4,3,1]=>[1,2,5,3,4,6]=>00100=>[2,1,2]
[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>00011=>[3,2]
[6,5,3,1,4,2]=>[1,2,4,6,3,5]=>00010=>[3,1,1]
[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>00001=>[4,1]
[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>00010=>[3,1,1]
[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>00101=>[2,1,1,1]
[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100=>[2,1,2]
[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>00011=>[3,2]
[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>00010=>[3,1,1]
[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>00001=>[4,1]
[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>00010=>[3,1,1]
[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>00001=>[4,1]
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000=>[5]
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111=>[6]
[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>111110=>[5,1]
[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>111101=>[4,1,1]
[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>111110=>[5,1]
[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>111101=>[4,1,1]
[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>111100=>[4,2]
[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>111011=>[3,1,2]
[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>111010=>[3,1,1,1]
[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>111101=>[4,1,1]
[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>111110=>[5,1]
[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>111101=>[4,1,1]
[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>111100=>[4,2]
[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>111011=>[3,1,2]
[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>111010=>[3,1,1,1]
[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>111001=>[3,2,1]
[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>111010=>[3,1,1,1]
[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>111101=>[4,1,1]
[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>111100=>[4,2]
[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>111011=>[3,1,2]
[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>111010=>[3,1,1,1]
[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>111001=>[3,2,1]
[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>111010=>[3,1,1,1]
[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>111001=>[3,2,1]
[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>111000=>[3,3]
[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>110111=>[2,1,3]
[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>110110=>[2,1,2,1]
[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>110101=>[2,1,1,1,1]
[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>110110=>[2,1,2,1]
[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>110101=>[2,1,1,1,1]
[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>110100=>[2,1,1,2]
[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>111011=>[3,1,2]
[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>111010=>[3,1,1,1]
[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>111101=>[4,1,1]
[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>111110=>[5,1]
[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>111101=>[4,1,1]
[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>111100=>[4,2]
[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>111011=>[3,1,2]
[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>111010=>[3,1,1,1]
[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>111001=>[3,2,1]
[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>111010=>[3,1,1,1]
[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>111101=>[4,1,1]
[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>111100=>[4,2]
[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>111011=>[3,1,2]
[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>111010=>[3,1,1,1]
[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>111001=>[3,2,1]
[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>111010=>[3,1,1,1]
[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>111001=>[3,2,1]
[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>111000=>[3,3]
[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>110111=>[2,1,3]
[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>110110=>[2,1,2,1]
[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>110101=>[2,1,1,1,1]
[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>110110=>[2,1,2,1]
[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>110101=>[2,1,1,1,1]
[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>110100=>[2,1,1,2]
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>110011=>[2,2,2]
[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>110010=>[2,2,1,1]
[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>110101=>[2,1,1,1,1]
[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>110110=>[2,1,2,1]
[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>110101=>[2,1,1,1,1]
[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>110100=>[2,1,1,2]
[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>111011=>[3,1,2]
[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>111010=>[3,1,1,1]
[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>111001=>[3,2,1]
[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>111010=>[3,1,1,1]
[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>111101=>[4,1,1]
[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>111100=>[4,2]
[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>111011=>[3,1,2]
[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>111010=>[3,1,1,1]
[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>111001=>[3,2,1]
[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>111010=>[3,1,1,1]
[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>111001=>[3,2,1]
[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>111000=>[3,3]
[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>110111=>[2,1,3]
[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>110110=>[2,1,2,1]
[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>110101=>[2,1,1,1,1]
[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>110110=>[2,1,2,1]
[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>110101=>[2,1,1,1,1]
[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>110100=>[2,1,1,2]
[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>110011=>[2,2,2]
[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>110010=>[2,2,1,1]
[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>110101=>[2,1,1,1,1]
[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>110110=>[2,1,2,1]
[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>110101=>[2,1,1,1,1]
[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>110100=>[2,1,1,2]
[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>110011=>[2,2,2]
[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>110010=>[2,2,1,1]
[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>110001=>[2,3,1]
[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>110010=>[2,2,1,1]
[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>110101=>[2,1,1,1,1]
[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>110100=>[2,1,1,2]
[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>111011=>[3,1,2]
[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>111010=>[3,1,1,1]
[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>111001=>[3,2,1]
[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>111010=>[3,1,1,1]
[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>111001=>[3,2,1]
[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>111000=>[3,3]
[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>110111=>[2,1,3]
[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>110110=>[2,1,2,1]
[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>110101=>[2,1,1,1,1]
[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>110110=>[2,1,2,1]
[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>110101=>[2,1,1,1,1]
[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>110100=>[2,1,1,2]
[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>110011=>[2,2,2]
[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>110010=>[2,2,1,1]
[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>110101=>[2,1,1,1,1]
[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>110110=>[2,1,2,1]
[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>110101=>[2,1,1,1,1]
[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>110100=>[2,1,1,2]
[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>110011=>[2,2,2]
[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>110010=>[2,2,1,1]
[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>110001=>[2,3,1]
[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>110010=>[2,2,1,1]
[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>110101=>[2,1,1,1,1]
[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>110100=>[2,1,1,2]
[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>110011=>[2,2,2]
[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>110010=>[2,2,1,1]
[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>110001=>[2,3,1]
[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>110010=>[2,2,1,1]
[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>110001=>[2,3,1]
[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>110000=>[2,4]
[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>101111=>[1,1,4]
[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>101110=>[1,1,3,1]
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>101101=>[1,1,2,1,1]
[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>101110=>[1,1,3,1]
[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>101101=>[1,1,2,1,1]
[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>101100=>[1,1,2,2]
[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>101011=>[1,1,1,1,2]
[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>101010=>[1,1,1,1,1,1]
[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>101101=>[1,1,2,1,1]
[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>101110=>[1,1,3,1]
[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>101101=>[1,1,2,1,1]
[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>101100=>[1,1,2,2]
[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>101011=>[1,1,1,1,2]
[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>101010=>[1,1,1,1,1,1]
[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>101001=>[1,1,1,2,1]
[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>101010=>[1,1,1,1,1,1]
[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>101101=>[1,1,2,1,1]
[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>101100=>[1,1,2,2]
[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>101011=>[1,1,1,1,2]
[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>101010=>[1,1,1,1,1,1]
[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>101001=>[1,1,1,2,1]
[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>101010=>[1,1,1,1,1,1]
[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>101001=>[1,1,1,2,1]
[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>101000=>[1,1,1,3]
[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>110111=>[2,1,3]
[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>110110=>[2,1,2,1]
[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>110101=>[2,1,1,1,1]
[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>110110=>[2,1,2,1]
[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>110101=>[2,1,1,1,1]
[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>110100=>[2,1,1,2]
[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>111011=>[3,1,2]
[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>111010=>[3,1,1,1]
[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>111101=>[4,1,1]
[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>111110=>[5,1]
[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>111101=>[4,1,1]
[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>111100=>[4,2]
[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>111011=>[3,1,2]
[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>111010=>[3,1,1,1]
[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>111001=>[3,2,1]
[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>111010=>[3,1,1,1]
[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>111101=>[4,1,1]
[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>111100=>[4,2]
[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>111011=>[3,1,2]
[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>111010=>[3,1,1,1]
[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>111001=>[3,2,1]
[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>111010=>[3,1,1,1]
[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>111001=>[3,2,1]
[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>111000=>[3,3]
[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>110111=>[2,1,3]
[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>110110=>[2,1,2,1]
[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>110101=>[2,1,1,1,1]
[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>110110=>[2,1,2,1]
[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>110101=>[2,1,1,1,1]
[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>110100=>[2,1,1,2]
[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>110011=>[2,2,2]
[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>110010=>[2,2,1,1]
[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>110101=>[2,1,1,1,1]
[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>110110=>[2,1,2,1]
[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>110101=>[2,1,1,1,1]
[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>110100=>[2,1,1,2]
[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>111011=>[3,1,2]
[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>111010=>[3,1,1,1]
[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>111001=>[3,2,1]
[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>111010=>[3,1,1,1]
[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>111101=>[4,1,1]
[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>111100=>[4,2]
[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>111011=>[3,1,2]
[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>111010=>[3,1,1,1]
[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>111001=>[3,2,1]
[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>111010=>[3,1,1,1]
[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>111001=>[3,2,1]
[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>111000=>[3,3]
[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>110111=>[2,1,3]
[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>110110=>[2,1,2,1]
[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>110101=>[2,1,1,1,1]
[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>110110=>[2,1,2,1]
[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>110101=>[2,1,1,1,1]
[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>110100=>[2,1,1,2]
[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>110011=>[2,2,2]
[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>110010=>[2,2,1,1]
[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>110101=>[2,1,1,1,1]
[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>110110=>[2,1,2,1]
[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>110101=>[2,1,1,1,1]
[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>110100=>[2,1,1,2]
[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>110011=>[2,2,2]
[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>110010=>[2,2,1,1]
[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>110001=>[2,3,1]
[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>110010=>[2,2,1,1]
[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>110101=>[2,1,1,1,1]
[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>110100=>[2,1,1,2]
[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>111011=>[3,1,2]
[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>111010=>[3,1,1,1]
[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>111001=>[3,2,1]
[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>111010=>[3,1,1,1]
[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>111001=>[3,2,1]
[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>111000=>[3,3]
[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>110111=>[2,1,3]
[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>110110=>[2,1,2,1]
[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>110101=>[2,1,1,1,1]
[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>110110=>[2,1,2,1]
[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>110101=>[2,1,1,1,1]
[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>110100=>[2,1,1,2]
[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>110011=>[2,2,2]
[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>110010=>[2,2,1,1]
[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>110101=>[2,1,1,1,1]
[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>110110=>[2,1,2,1]
[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>110101=>[2,1,1,1,1]
[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>110100=>[2,1,1,2]
[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>110011=>[2,2,2]
[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>110010=>[2,2,1,1]
[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>110001=>[2,3,1]
[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>110010=>[2,2,1,1]
[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>110101=>[2,1,1,1,1]
[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>110100=>[2,1,1,2]
[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>110011=>[2,2,2]
[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>110010=>[2,2,1,1]
[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>110001=>[2,3,1]
[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>110010=>[2,2,1,1]
[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>110001=>[2,3,1]
[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>110000=>[2,4]
[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>101111=>[1,1,4]
[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>101110=>[1,1,3,1]
[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>101101=>[1,1,2,1,1]
[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>101110=>[1,1,3,1]
[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>101101=>[1,1,2,1,1]
[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>101100=>[1,1,2,2]
[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>101011=>[1,1,1,1,2]
[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>101010=>[1,1,1,1,1,1]
[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>101101=>[1,1,2,1,1]
[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>101110=>[1,1,3,1]
[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>101101=>[1,1,2,1,1]
[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>101100=>[1,1,2,2]
[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>101011=>[1,1,1,1,2]
[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>101010=>[1,1,1,1,1,1]
[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>101001=>[1,1,1,2,1]
[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>101010=>[1,1,1,1,1,1]
[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>101101=>[1,1,2,1,1]
[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>101100=>[1,1,2,2]
[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>101011=>[1,1,1,1,2]
[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>101010=>[1,1,1,1,1,1]
[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>101001=>[1,1,1,2,1]
[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>101010=>[1,1,1,1,1,1]
[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>101001=>[1,1,1,2,1]
[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>101000=>[1,1,1,3]
[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>100111=>[1,2,3]
[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>100110=>[1,2,2,1]
[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>100101=>[1,2,1,1,1]
[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>100110=>[1,2,2,1]
[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>100101=>[1,2,1,1,1]
[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>100100=>[1,2,1,2]
[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>101011=>[1,1,1,1,2]
[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>101010=>[1,1,1,1,1,1]
[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>101101=>[1,1,2,1,1]
[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>101110=>[1,1,3,1]
[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>101101=>[1,1,2,1,1]
[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>101100=>[1,1,2,2]
[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>101011=>[1,1,1,1,2]
[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>101010=>[1,1,1,1,1,1]
[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>101001=>[1,1,1,2,1]
[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>101010=>[1,1,1,1,1,1]
[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>101101=>[1,1,2,1,1]
[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>101100=>[1,1,2,2]
[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>101011=>[1,1,1,1,2]
[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>101010=>[1,1,1,1,1,1]
[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>101001=>[1,1,1,2,1]
[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>101010=>[1,1,1,1,1,1]
[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>101001=>[1,1,1,2,1]
[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>101000=>[1,1,1,3]
[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>110111=>[2,1,3]
[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>110110=>[2,1,2,1]
[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>110101=>[2,1,1,1,1]
[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>110110=>[2,1,2,1]
[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>110101=>[2,1,1,1,1]
[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>110100=>[2,1,1,2]
[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>110011=>[2,2,2]
[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>110010=>[2,2,1,1]
[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>110101=>[2,1,1,1,1]
[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>110110=>[2,1,2,1]
[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>110101=>[2,1,1,1,1]
[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>110100=>[2,1,1,2]
[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>111011=>[3,1,2]
[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>111010=>[3,1,1,1]
[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>111001=>[3,2,1]
[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>111010=>[3,1,1,1]
[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>111101=>[4,1,1]
[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>111100=>[4,2]
[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>111011=>[3,1,2]
[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>111010=>[3,1,1,1]
[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>111001=>[3,2,1]
[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>111010=>[3,1,1,1]
[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>111001=>[3,2,1]
[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>111000=>[3,3]
[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>110111=>[2,1,3]
[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>110110=>[2,1,2,1]
[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>110101=>[2,1,1,1,1]
[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>110110=>[2,1,2,1]
[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>110101=>[2,1,1,1,1]
[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>110100=>[2,1,1,2]
[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>110011=>[2,2,2]
[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>110010=>[2,2,1,1]
[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>110101=>[2,1,1,1,1]
[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>110110=>[2,1,2,1]
[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>110101=>[2,1,1,1,1]
[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>110100=>[2,1,1,2]
[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>110011=>[2,2,2]
[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>110010=>[2,2,1,1]
[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>110001=>[2,3,1]
[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>110010=>[2,2,1,1]
[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>110101=>[2,1,1,1,1]
[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>110100=>[2,1,1,2]
[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>111011=>[3,1,2]
[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>111010=>[3,1,1,1]
[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>111001=>[3,2,1]
[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>111010=>[3,1,1,1]
[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>111001=>[3,2,1]
[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>111000=>[3,3]
[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>110111=>[2,1,3]
[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>110110=>[2,1,2,1]
[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>110101=>[2,1,1,1,1]
[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>110110=>[2,1,2,1]
[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>110101=>[2,1,1,1,1]
[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>110100=>[2,1,1,2]
[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>110011=>[2,2,2]
[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>110010=>[2,2,1,1]
[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>110101=>[2,1,1,1,1]
[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>110110=>[2,1,2,1]
[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>110101=>[2,1,1,1,1]
[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>110100=>[2,1,1,2]
[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>110011=>[2,2,2]
[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>110010=>[2,2,1,1]
[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>110001=>[2,3,1]
[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>110010=>[2,2,1,1]
[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>110101=>[2,1,1,1,1]
[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>110100=>[2,1,1,2]
[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>110011=>[2,2,2]
[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>110010=>[2,2,1,1]
[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>110001=>[2,3,1]
[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>110010=>[2,2,1,1]
[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>110001=>[2,3,1]
[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>110000=>[2,4]
[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>101111=>[1,1,4]
[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>101110=>[1,1,3,1]
[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>101101=>[1,1,2,1,1]
[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>101110=>[1,1,3,1]
[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>101101=>[1,1,2,1,1]
[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>101100=>[1,1,2,2]
[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>101011=>[1,1,1,1,2]
[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>101010=>[1,1,1,1,1,1]
[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>101101=>[1,1,2,1,1]
[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>101110=>[1,1,3,1]
[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>101101=>[1,1,2,1,1]
[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>101100=>[1,1,2,2]
[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>101011=>[1,1,1,1,2]
[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>101010=>[1,1,1,1,1,1]
[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>101001=>[1,1,1,2,1]
[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>101010=>[1,1,1,1,1,1]
[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>101101=>[1,1,2,1,1]
[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>101100=>[1,1,2,2]
[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>101011=>[1,1,1,1,2]
[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>101010=>[1,1,1,1,1,1]
[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>101001=>[1,1,1,2,1]
[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>101010=>[1,1,1,1,1,1]
[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>101001=>[1,1,1,2,1]
[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>101000=>[1,1,1,3]
[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>100111=>[1,2,3]
[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>100110=>[1,2,2,1]
[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>100101=>[1,2,1,1,1]
[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>100110=>[1,2,2,1]
[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>100101=>[1,2,1,1,1]
[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>100100=>[1,2,1,2]
[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>101011=>[1,1,1,1,2]
[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>101010=>[1,1,1,1,1,1]
[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>101101=>[1,1,2,1,1]
[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>101110=>[1,1,3,1]
[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>101101=>[1,1,2,1,1]
[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>101100=>[1,1,2,2]
[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>101011=>[1,1,1,1,2]
[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>101010=>[1,1,1,1,1,1]
[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>101001=>[1,1,1,2,1]
[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>101010=>[1,1,1,1,1,1]
[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>101101=>[1,1,2,1,1]
[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>101100=>[1,1,2,2]
[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>101011=>[1,1,1,1,2]
[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>101010=>[1,1,1,1,1,1]
[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>101001=>[1,1,1,2,1]
[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>101010=>[1,1,1,1,1,1]
[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>101001=>[1,1,1,2,1]
[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>101000=>[1,1,1,3]
[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>100111=>[1,2,3]
[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>100110=>[1,2,2,1]
[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>100101=>[1,2,1,1,1]
[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>100110=>[1,2,2,1]
[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>100101=>[1,2,1,1,1]
[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>100100=>[1,2,1,2]
[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>100011=>[1,3,2]
[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>100010=>[1,3,1,1]
[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>100101=>[1,2,1,1,1]
[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>100110=>[1,2,2,1]
[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>100101=>[1,2,1,1,1]
[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>100100=>[1,2,1,2]
[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>101011=>[1,1,1,1,2]
[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>101010=>[1,1,1,1,1,1]
[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>101001=>[1,1,1,2,1]
[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>101010=>[1,1,1,1,1,1]
[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>101101=>[1,1,2,1,1]
[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>101100=>[1,1,2,2]
[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>101011=>[1,1,1,1,2]
[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>101010=>[1,1,1,1,1,1]
[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>101001=>[1,1,1,2,1]
[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>101010=>[1,1,1,1,1,1]
[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>101001=>[1,1,1,2,1]
[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>101000=>[1,1,1,3]
[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>110111=>[2,1,3]
[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>110110=>[2,1,2,1]
[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>110101=>[2,1,1,1,1]
[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>110110=>[2,1,2,1]
[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>110101=>[2,1,1,1,1]
[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>110100=>[2,1,1,2]
[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>110011=>[2,2,2]
[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>110010=>[2,2,1,1]
[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>110101=>[2,1,1,1,1]
[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>110110=>[2,1,2,1]
[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>110101=>[2,1,1,1,1]
[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>110100=>[2,1,1,2]
[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>110011=>[2,2,2]
[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>110010=>[2,2,1,1]
[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>110001=>[2,3,1]
[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>110010=>[2,2,1,1]
[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>110101=>[2,1,1,1,1]
[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>110100=>[2,1,1,2]
[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>111011=>[3,1,2]
[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>111010=>[3,1,1,1]
[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>111001=>[3,2,1]
[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>111010=>[3,1,1,1]
[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>111001=>[3,2,1]
[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>111000=>[3,3]
[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>110111=>[2,1,3]
[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>110110=>[2,1,2,1]
[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>110101=>[2,1,1,1,1]
[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>110110=>[2,1,2,1]
[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>110101=>[2,1,1,1,1]
[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>110100=>[2,1,1,2]
[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>110011=>[2,2,2]
[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>110010=>[2,2,1,1]
[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>110101=>[2,1,1,1,1]
[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>110110=>[2,1,2,1]
[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>110101=>[2,1,1,1,1]
[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>110100=>[2,1,1,2]
[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>110011=>[2,2,2]
[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>110010=>[2,2,1,1]
[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>110001=>[2,3,1]
[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>110010=>[2,2,1,1]
[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>110101=>[2,1,1,1,1]
[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>110100=>[2,1,1,2]
[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>110011=>[2,2,2]
[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>110010=>[2,2,1,1]
[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>110001=>[2,3,1]
[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>110010=>[2,2,1,1]
[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>110001=>[2,3,1]
[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>110000=>[2,4]
[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>101111=>[1,1,4]
[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>101110=>[1,1,3,1]
[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>101101=>[1,1,2,1,1]
[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>101110=>[1,1,3,1]
[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>101101=>[1,1,2,1,1]
[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>101100=>[1,1,2,2]
[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>101011=>[1,1,1,1,2]
[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>101010=>[1,1,1,1,1,1]
[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>101101=>[1,1,2,1,1]
[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>101110=>[1,1,3,1]
[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>101101=>[1,1,2,1,1]
[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>101100=>[1,1,2,2]
[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>101011=>[1,1,1,1,2]
[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>101010=>[1,1,1,1,1,1]
[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>101001=>[1,1,1,2,1]
[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>101010=>[1,1,1,1,1,1]
[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>101101=>[1,1,2,1,1]
[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>101100=>[1,1,2,2]
[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>101011=>[1,1,1,1,2]
[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>101010=>[1,1,1,1,1,1]
[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>101001=>[1,1,1,2,1]
[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>101010=>[1,1,1,1,1,1]
[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>101001=>[1,1,1,2,1]
[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>101000=>[1,1,1,3]
[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>100111=>[1,2,3]
[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>100110=>[1,2,2,1]
[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>100101=>[1,2,1,1,1]
[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>100110=>[1,2,2,1]
[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>100101=>[1,2,1,1,1]
[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>100100=>[1,2,1,2]
[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>101011=>[1,1,1,1,2]
[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>101010=>[1,1,1,1,1,1]
[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>101101=>[1,1,2,1,1]
[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>101110=>[1,1,3,1]
[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>101101=>[1,1,2,1,1]
[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>101100=>[1,1,2,2]
[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>101011=>[1,1,1,1,2]
[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>101010=>[1,1,1,1,1,1]
[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>101001=>[1,1,1,2,1]
[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>101010=>[1,1,1,1,1,1]
[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>101101=>[1,1,2,1,1]
[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>101100=>[1,1,2,2]
[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>101011=>[1,1,1,1,2]
[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>101010=>[1,1,1,1,1,1]
[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>101001=>[1,1,1,2,1]
[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>101010=>[1,1,1,1,1,1]
[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>101001=>[1,1,1,2,1]
[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>101000=>[1,1,1,3]
[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>100111=>[1,2,3]
[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>100110=>[1,2,2,1]
[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>100101=>[1,2,1,1,1]
[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>100110=>[1,2,2,1]
[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>100101=>[1,2,1,1,1]
[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>100100=>[1,2,1,2]
[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>100011=>[1,3,2]
[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>100010=>[1,3,1,1]
[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>100101=>[1,2,1,1,1]
[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>100110=>[1,2,2,1]
[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>100101=>[1,2,1,1,1]
[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>100100=>[1,2,1,2]
[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>101011=>[1,1,1,1,2]
[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>101010=>[1,1,1,1,1,1]
[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>101001=>[1,1,1,2,1]
[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>101010=>[1,1,1,1,1,1]
[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>101101=>[1,1,2,1,1]
[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>101100=>[1,1,2,2]
[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>101011=>[1,1,1,1,2]
[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>101010=>[1,1,1,1,1,1]
[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>101001=>[1,1,1,2,1]
[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>101010=>[1,1,1,1,1,1]
[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>101001=>[1,1,1,2,1]
[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>101000=>[1,1,1,3]
[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>100111=>[1,2,3]
[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>100110=>[1,2,2,1]
[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>100101=>[1,2,1,1,1]
[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>100110=>[1,2,2,1]
[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>100101=>[1,2,1,1,1]
[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>100100=>[1,2,1,2]
[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>100011=>[1,3,2]
[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>100010=>[1,3,1,1]
[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>100101=>[1,2,1,1,1]
[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>100110=>[1,2,2,1]
[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>100101=>[1,2,1,1,1]
[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>100100=>[1,2,1,2]
[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>100011=>[1,3,2]
[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>100010=>[1,3,1,1]
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>100001=>[1,4,1]
[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>100010=>[1,3,1,1]
[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>100101=>[1,2,1,1,1]
[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>100100=>[1,2,1,2]
[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>101011=>[1,1,1,1,2]
[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>101010=>[1,1,1,1,1,1]
[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>101001=>[1,1,1,2,1]
[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>101010=>[1,1,1,1,1,1]
[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>101001=>[1,1,1,2,1]
[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>101000=>[1,1,1,3]
[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>110111=>[2,1,3]
[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>110110=>[2,1,2,1]
[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>110101=>[2,1,1,1,1]
[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>110110=>[2,1,2,1]
[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>110101=>[2,1,1,1,1]
[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>110100=>[2,1,1,2]
[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>110011=>[2,2,2]
[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>110010=>[2,2,1,1]
[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>110101=>[2,1,1,1,1]
[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>110110=>[2,1,2,1]
[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>110101=>[2,1,1,1,1]
[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>110100=>[2,1,1,2]
[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>110011=>[2,2,2]
[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>110010=>[2,2,1,1]
[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>110001=>[2,3,1]
[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>110010=>[2,2,1,1]
[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>110101=>[2,1,1,1,1]
[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>110100=>[2,1,1,2]
[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>110011=>[2,2,2]
[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>110010=>[2,2,1,1]
[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>110001=>[2,3,1]
[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>110010=>[2,2,1,1]
[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>110001=>[2,3,1]
[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>110000=>[2,4]
[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>101111=>[1,1,4]
[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>101110=>[1,1,3,1]
[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>101101=>[1,1,2,1,1]
[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>101110=>[1,1,3,1]
[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>101101=>[1,1,2,1,1]
[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>101100=>[1,1,2,2]
[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>101011=>[1,1,1,1,2]
[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>101010=>[1,1,1,1,1,1]
[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>101101=>[1,1,2,1,1]
[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>101110=>[1,1,3,1]
[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>101101=>[1,1,2,1,1]
[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>101100=>[1,1,2,2]
[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>101011=>[1,1,1,1,2]
[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>101010=>[1,1,1,1,1,1]
[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>101001=>[1,1,1,2,1]
[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>101010=>[1,1,1,1,1,1]
[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>101101=>[1,1,2,1,1]
[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>101100=>[1,1,2,2]
[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>101011=>[1,1,1,1,2]
[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>101010=>[1,1,1,1,1,1]
[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>101001=>[1,1,1,2,1]
[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>101010=>[1,1,1,1,1,1]
[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>101001=>[1,1,1,2,1]
[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>101000=>[1,1,1,3]
[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>100111=>[1,2,3]
[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>100110=>[1,2,2,1]
[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>100101=>[1,2,1,1,1]
[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>100110=>[1,2,2,1]
[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>100101=>[1,2,1,1,1]
[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>100100=>[1,2,1,2]
[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>101011=>[1,1,1,1,2]
[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>101010=>[1,1,1,1,1,1]
[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>101101=>[1,1,2,1,1]
[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>101110=>[1,1,3,1]
[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>101101=>[1,1,2,1,1]
[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>101100=>[1,1,2,2]
[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>101011=>[1,1,1,1,2]
[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>101010=>[1,1,1,1,1,1]
[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>101001=>[1,1,1,2,1]
[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>101010=>[1,1,1,1,1,1]
[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>101101=>[1,1,2,1,1]
[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>101100=>[1,1,2,2]
[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>101011=>[1,1,1,1,2]
[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>101010=>[1,1,1,1,1,1]
[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>101001=>[1,1,1,2,1]
[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>101010=>[1,1,1,1,1,1]
[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>101001=>[1,1,1,2,1]
[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>101000=>[1,1,1,3]
[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>100111=>[1,2,3]
[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>100110=>[1,2,2,1]
[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>100101=>[1,2,1,1,1]
[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>100110=>[1,2,2,1]
[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>100101=>[1,2,1,1,1]
[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>100100=>[1,2,1,2]
[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>100011=>[1,3,2]
[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>100010=>[1,3,1,1]
[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>100101=>[1,2,1,1,1]
[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>100110=>[1,2,2,1]
[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>100101=>[1,2,1,1,1]
[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>100100=>[1,2,1,2]
[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>101011=>[1,1,1,1,2]
[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>101010=>[1,1,1,1,1,1]
[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>101001=>[1,1,1,2,1]
[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>101010=>[1,1,1,1,1,1]
[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>101101=>[1,1,2,1,1]
[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>101100=>[1,1,2,2]
[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>101011=>[1,1,1,1,2]
[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>101010=>[1,1,1,1,1,1]
[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>101001=>[1,1,1,2,1]
[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>101010=>[1,1,1,1,1,1]
[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>101001=>[1,1,1,2,1]
[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>101000=>[1,1,1,3]
[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>100111=>[1,2,3]
[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>100110=>[1,2,2,1]
[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>100101=>[1,2,1,1,1]
[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>100110=>[1,2,2,1]
[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>100101=>[1,2,1,1,1]
[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>100100=>[1,2,1,2]
[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>100011=>[1,3,2]
[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>100010=>[1,3,1,1]
[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>100101=>[1,2,1,1,1]
[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>100110=>[1,2,2,1]
[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>100101=>[1,2,1,1,1]
[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>100100=>[1,2,1,2]
[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>100011=>[1,3,2]
[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>100010=>[1,3,1,1]
[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>100001=>[1,4,1]
[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>100010=>[1,3,1,1]
[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>100101=>[1,2,1,1,1]
[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>100100=>[1,2,1,2]
[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>101011=>[1,1,1,1,2]
[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>101010=>[1,1,1,1,1,1]
[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>101001=>[1,1,1,2,1]
[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>101010=>[1,1,1,1,1,1]
[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>101001=>[1,1,1,2,1]
[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>101000=>[1,1,1,3]
[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>100111=>[1,2,3]
[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>100110=>[1,2,2,1]
[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>100101=>[1,2,1,1,1]
[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>100110=>[1,2,2,1]
[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>100101=>[1,2,1,1,1]
[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>100100=>[1,2,1,2]
[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>100011=>[1,3,2]
[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>100010=>[1,3,1,1]
[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>100101=>[1,2,1,1,1]
[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>100110=>[1,2,2,1]
[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>100101=>[1,2,1,1,1]
[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>100100=>[1,2,1,2]
[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>100011=>[1,3,2]
[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>100010=>[1,3,1,1]
[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>100001=>[1,4,1]
[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>100010=>[1,3,1,1]
[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>100101=>[1,2,1,1,1]
[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>100100=>[1,2,1,2]
[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>100011=>[1,3,2]
[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>100010=>[1,3,1,1]
[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>100001=>[1,4,1]
[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>100010=>[1,3,1,1]
[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>100001=>[1,4,1]
[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>100000=>[1,5]
[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>011111=>[1,5]
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>011110=>[1,4,1]
[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>011101=>[1,3,1,1]
[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]=>011110=>[1,4,1]
[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>011101=>[1,3,1,1]
[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>011100=>[1,3,2]
[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>011011=>[1,2,1,2]
[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>011010=>[1,2,1,1,1]
[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]=>011101=>[1,3,1,1]
[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]=>011110=>[1,4,1]
[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]=>011101=>[1,3,1,1]
[2,1,3,5,7,6,4]=>[6,7,5,3,1,2,4]=>011100=>[1,3,2]
[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>011011=>[1,2,1,2]
[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]=>011010=>[1,2,1,1,1]
[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>011001=>[1,2,2,1]
[2,1,3,6,5,7,4]=>[6,7,5,2,3,1,4]=>011010=>[1,2,1,1,1]
[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]=>011101=>[1,3,1,1]
[2,1,3,6,7,5,4]=>[6,7,5,2,1,3,4]=>011100=>[1,3,2]
[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>011011=>[1,2,1,2]
[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>011010=>[1,2,1,1,1]
[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>011001=>[1,2,2,1]
[2,1,3,7,5,6,4]=>[6,7,5,1,3,2,4]=>011010=>[1,2,1,1,1]
[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>011001=>[1,2,2,1]
[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>011000=>[1,2,3]
[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>010111=>[1,1,1,3]
[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>010110=>[1,1,1,2,1]
[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>010101=>[1,1,1,1,1,1]
[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]=>010110=>[1,1,1,2,1]
[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>010101=>[1,1,1,1,1,1]
[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>010100=>[1,1,1,1,2]
[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]=>011011=>[1,2,1,2]
[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>011010=>[1,2,1,1,1]
[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]=>011101=>[1,3,1,1]
[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]=>011110=>[1,4,1]
[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]=>011101=>[1,3,1,1]
[2,1,4,5,7,6,3]=>[6,7,4,3,1,2,5]=>011100=>[1,3,2]
[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]=>011011=>[1,2,1,2]
[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]=>011010=>[1,2,1,1,1]
[2,1,4,6,5,3,7]=>[6,7,4,2,3,5,1]=>011001=>[1,2,2,1]
[2,1,4,6,5,7,3]=>[6,7,4,2,3,1,5]=>011010=>[1,2,1,1,1]
[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]=>011101=>[1,3,1,1]
[2,1,4,6,7,5,3]=>[6,7,4,2,1,3,5]=>011100=>[1,3,2]
[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]=>011011=>[1,2,1,2]
[2,1,4,7,3,6,5]=>[6,7,4,1,5,2,3]=>011010=>[1,2,1,1,1]
[2,1,4,7,5,3,6]=>[6,7,4,1,3,5,2]=>011001=>[1,2,2,1]
[2,1,4,7,5,6,3]=>[6,7,4,1,3,2,5]=>011010=>[1,2,1,1,1]
[2,1,4,7,6,3,5]=>[6,7,4,1,2,5,3]=>011001=>[1,2,2,1]
[2,1,4,7,6,5,3]=>[6,7,4,1,2,3,5]=>011000=>[1,2,3]
[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>010111=>[1,1,1,3]
[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>010110=>[1,1,1,2,1]
[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]=>010101=>[1,1,1,1,1,1]
[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]=>010110=>[1,1,1,2,1]
[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]=>010101=>[1,1,1,1,1,1]
[2,1,5,3,7,6,4]=>[6,7,3,5,1,2,4]=>010100=>[1,1,1,1,2]
[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>010011=>[1,1,2,2]
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>010010=>[1,1,2,1,1]
[2,1,5,4,6,3,7]=>[6,7,3,4,2,5,1]=>010101=>[1,1,1,1,1,1]
[2,1,5,4,6,7,3]=>[6,7,3,4,2,1,5]=>010110=>[1,1,1,2,1]
[2,1,5,4,7,3,6]=>[6,7,3,4,1,5,2]=>010101=>[1,1,1,1,1,1]
[2,1,5,4,7,6,3]=>[6,7,3,4,1,2,5]=>010100=>[1,1,1,1,2]
[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]=>011011=>[1,2,1,2]
[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]=>011010=>[1,2,1,1,1]
[2,1,5,6,4,3,7]=>[6,7,3,2,4,5,1]=>011001=>[1,2,2,1]
[2,1,5,6,4,7,3]=>[6,7,3,2,4,1,5]=>011010=>[1,2,1,1,1]
[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]=>011101=>[1,3,1,1]
[2,1,5,6,7,4,3]=>[6,7,3,2,1,4,5]=>011100=>[1,3,2]
[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]=>011011=>[1,2,1,2]
[2,1,5,7,3,6,4]=>[6,7,3,1,5,2,4]=>011010=>[1,2,1,1,1]
[2,1,5,7,4,3,6]=>[6,7,3,1,4,5,2]=>011001=>[1,2,2,1]
[2,1,5,7,4,6,3]=>[6,7,3,1,4,2,5]=>011010=>[1,2,1,1,1]
[2,1,5,7,6,3,4]=>[6,7,3,1,2,5,4]=>011001=>[1,2,2,1]
[2,1,5,7,6,4,3]=>[6,7,3,1,2,4,5]=>011000=>[1,2,3]
[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>010111=>[1,1,1,3]
[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]=>010110=>[1,1,1,2,1]
[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>010101=>[1,1,1,1,1,1]
[2,1,6,3,5,7,4]=>[6,7,2,5,3,1,4]=>010110=>[1,1,1,2,1]
[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]=>010101=>[1,1,1,1,1,1]
[2,1,6,3,7,5,4]=>[6,7,2,5,1,3,4]=>010100=>[1,1,1,1,2]
[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>010011=>[1,1,2,2]
[2,1,6,4,3,7,5]=>[6,7,2,4,5,1,3]=>010010=>[1,1,2,1,1]
[2,1,6,4,5,3,7]=>[6,7,2,4,3,5,1]=>010101=>[1,1,1,1,1,1]
[2,1,6,4,5,7,3]=>[6,7,2,4,3,1,5]=>010110=>[1,1,1,2,1]
[2,1,6,4,7,3,5]=>[6,7,2,4,1,5,3]=>010101=>[1,1,1,1,1,1]
[2,1,6,4,7,5,3]=>[6,7,2,4,1,3,5]=>010100=>[1,1,1,1,2]
[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>010011=>[1,1,2,2]
[2,1,6,5,3,7,4]=>[6,7,2,3,5,1,4]=>010010=>[1,1,2,1,1]
[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>010001=>[1,1,3,1]
[2,1,6,5,4,7,3]=>[6,7,2,3,4,1,5]=>010010=>[1,1,2,1,1]
[2,1,6,5,7,3,4]=>[6,7,2,3,1,5,4]=>010101=>[1,1,1,1,1,1]
[2,1,6,5,7,4,3]=>[6,7,2,3,1,4,5]=>010100=>[1,1,1,1,2]
[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]=>011011=>[1,2,1,2]
[2,1,6,7,3,5,4]=>[6,7,2,1,5,3,4]=>011010=>[1,2,1,1,1]
[2,1,6,7,4,3,5]=>[6,7,2,1,4,5,3]=>011001=>[1,2,2,1]
[2,1,6,7,4,5,3]=>[6,7,2,1,4,3,5]=>011010=>[1,2,1,1,1]
[2,1,6,7,5,3,4]=>[6,7,2,1,3,5,4]=>011001=>[1,2,2,1]
[2,1,6,7,5,4,3]=>[6,7,2,1,3,4,5]=>011000=>[1,2,3]
[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>010111=>[1,1,1,3]
[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>010110=>[1,1,1,2,1]
[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>010101=>[1,1,1,1,1,1]
[2,1,7,3,5,6,4]=>[6,7,1,5,3,2,4]=>010110=>[1,1,1,2,1]
[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>010101=>[1,1,1,1,1,1]
[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>010100=>[1,1,1,1,2]
[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>010011=>[1,1,2,2]
[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>010010=>[1,1,2,1,1]
[2,1,7,4,5,3,6]=>[6,7,1,4,3,5,2]=>010101=>[1,1,1,1,1,1]
[2,1,7,4,5,6,3]=>[6,7,1,4,3,2,5]=>010110=>[1,1,1,2,1]
[2,1,7,4,6,3,5]=>[6,7,1,4,2,5,3]=>010101=>[1,1,1,1,1,1]
[2,1,7,4,6,5,3]=>[6,7,1,4,2,3,5]=>010100=>[1,1,1,1,2]
[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>010011=>[1,1,2,2]
[2,1,7,5,3,6,4]=>[6,7,1,3,5,2,4]=>010010=>[1,1,2,1,1]
[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>010001=>[1,1,3,1]
[2,1,7,5,4,6,3]=>[6,7,1,3,4,2,5]=>010010=>[1,1,2,1,1]
[2,1,7,5,6,3,4]=>[6,7,1,3,2,5,4]=>010101=>[1,1,1,1,1,1]
[2,1,7,5,6,4,3]=>[6,7,1,3,2,4,5]=>010100=>[1,1,1,1,2]
[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>010011=>[1,1,2,2]
[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>010010=>[1,1,2,1,1]
[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>010001=>[1,1,3,1]
[2,1,7,6,4,5,3]=>[6,7,1,2,4,3,5]=>010010=>[1,1,2,1,1]
[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>010001=>[1,1,3,1]
[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>010000=>[1,1,4]
[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>101111=>[1,1,4]
[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]=>101110=>[1,1,3,1]
[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]=>101101=>[1,1,2,1,1]
[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>101110=>[1,1,3,1]
[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>101101=>[1,1,2,1,1]
[2,3,1,4,7,6,5]=>[6,5,7,4,1,2,3]=>101100=>[1,1,2,2]
[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]=>101011=>[1,1,1,1,2]
[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]=>101010=>[1,1,1,1,1,1]
[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]=>101101=>[1,1,2,1,1]
[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]=>101110=>[1,1,3,1]
[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]=>101101=>[1,1,2,1,1]
[2,3,1,5,7,6,4]=>[6,5,7,3,1,2,4]=>101100=>[1,1,2,2]
[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]=>101011=>[1,1,1,1,2]
[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]=>101010=>[1,1,1,1,1,1]
[2,3,1,6,5,4,7]=>[6,5,7,2,3,4,1]=>101001=>[1,1,1,2,1]
[2,3,1,6,5,7,4]=>[6,5,7,2,3,1,4]=>101010=>[1,1,1,1,1,1]
[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]=>101101=>[1,1,2,1,1]
[2,3,1,6,7,5,4]=>[6,5,7,2,1,3,4]=>101100=>[1,1,2,2]
[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]=>101011=>[1,1,1,1,2]
[2,3,1,7,4,6,5]=>[6,5,7,1,4,2,3]=>101010=>[1,1,1,1,1,1]
[2,3,1,7,5,4,6]=>[6,5,7,1,3,4,2]=>101001=>[1,1,1,2,1]
[2,3,1,7,5,6,4]=>[6,5,7,1,3,2,4]=>101010=>[1,1,1,1,1,1]
[2,3,1,7,6,4,5]=>[6,5,7,1,2,4,3]=>101001=>[1,1,1,2,1]
[2,3,1,7,6,5,4]=>[6,5,7,1,2,3,4]=>101000=>[1,1,1,3]
[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>110111=>[2,1,3]
[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]=>110110=>[2,1,2,1]
[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]=>110101=>[2,1,1,1,1]
[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]=>110110=>[2,1,2,1]
[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]=>110101=>[2,1,1,1,1]
[2,3,4,1,7,6,5]=>[6,5,4,7,1,2,3]=>110100=>[2,1,1,2]
[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>111011=>[3,1,2]
[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]=>111010=>[3,1,1,1]
[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>111101=>[4,1,1]
[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>111110=>[5,1]
[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>111101=>[4,1,1]
[2,3,4,5,7,6,1]=>[6,5,4,3,1,2,7]=>111100=>[4,2]
[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>111011=>[3,1,2]
[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>111010=>[3,1,1,1]
[2,3,4,6,5,1,7]=>[6,5,4,2,3,7,1]=>111001=>[3,2,1]
[2,3,4,6,5,7,1]=>[6,5,4,2,3,1,7]=>111010=>[3,1,1,1]
[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]=>111101=>[4,1,1]
[2,3,4,6,7,5,1]=>[6,5,4,2,1,3,7]=>111100=>[4,2]
[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>111011=>[3,1,2]
[2,3,4,7,1,6,5]=>[6,5,4,1,7,2,3]=>111010=>[3,1,1,1]
[2,3,4,7,5,1,6]=>[6,5,4,1,3,7,2]=>111001=>[3,2,1]
[2,3,4,7,5,6,1]=>[6,5,4,1,3,2,7]=>111010=>[3,1,1,1]
[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>111001=>[3,2,1]
[2,3,4,7,6,5,1]=>[6,5,4,1,2,3,7]=>111000=>[3,3]
[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>110111=>[2,1,3]
[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]=>110110=>[2,1,2,1]
[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]=>110101=>[2,1,1,1,1]
[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>110110=>[2,1,2,1]
[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>110101=>[2,1,1,1,1]
[2,3,5,1,7,6,4]=>[6,5,3,7,1,2,4]=>110100=>[2,1,1,2]
[2,3,5,4,1,6,7]=>[6,5,3,4,7,2,1]=>110011=>[2,2,2]
[2,3,5,4,1,7,6]=>[6,5,3,4,7,1,2]=>110010=>[2,2,1,1]
[2,3,5,4,6,1,7]=>[6,5,3,4,2,7,1]=>110101=>[2,1,1,1,1]
[2,3,5,4,6,7,1]=>[6,5,3,4,2,1,7]=>110110=>[2,1,2,1]
[2,3,5,4,7,1,6]=>[6,5,3,4,1,7,2]=>110101=>[2,1,1,1,1]
[2,3,5,4,7,6,1]=>[6,5,3,4,1,2,7]=>110100=>[2,1,1,2]
[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]=>111011=>[3,1,2]
[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]=>111010=>[3,1,1,1]
[2,3,5,6,4,1,7]=>[6,5,3,2,4,7,1]=>111001=>[3,2,1]
[2,3,5,6,4,7,1]=>[6,5,3,2,4,1,7]=>111010=>[3,1,1,1]
[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>111101=>[4,1,1]
[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>111100=>[4,2]
[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]=>111011=>[3,1,2]
[2,3,5,7,1,6,4]=>[6,5,3,1,7,2,4]=>111010=>[3,1,1,1]
[2,3,5,7,4,1,6]=>[6,5,3,1,4,7,2]=>111001=>[3,2,1]
[2,3,5,7,4,6,1]=>[6,5,3,1,4,2,7]=>111010=>[3,1,1,1]
[2,3,5,7,6,1,4]=>[6,5,3,1,2,7,4]=>111001=>[3,2,1]
[2,3,5,7,6,4,1]=>[6,5,3,1,2,4,7]=>111000=>[3,3]
[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>110111=>[2,1,3]
[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>110110=>[2,1,2,1]
[2,3,6,1,5,4,7]=>[6,5,2,7,3,4,1]=>110101=>[2,1,1,1,1]
[2,3,6,1,5,7,4]=>[6,5,2,7,3,1,4]=>110110=>[2,1,2,1]
[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]=>110101=>[2,1,1,1,1]
[2,3,6,1,7,5,4]=>[6,5,2,7,1,3,4]=>110100=>[2,1,1,2]
[2,3,6,4,1,5,7]=>[6,5,2,4,7,3,1]=>110011=>[2,2,2]
[2,3,6,4,1,7,5]=>[6,5,2,4,7,1,3]=>110010=>[2,2,1,1]
[2,3,6,4,5,1,7]=>[6,5,2,4,3,7,1]=>110101=>[2,1,1,1,1]
[2,3,6,4,5,7,1]=>[6,5,2,4,3,1,7]=>110110=>[2,1,2,1]
[2,3,6,4,7,1,5]=>[6,5,2,4,1,7,3]=>110101=>[2,1,1,1,1]
[2,3,6,4,7,5,1]=>[6,5,2,4,1,3,7]=>110100=>[2,1,1,2]
[2,3,6,5,1,4,7]=>[6,5,2,3,7,4,1]=>110011=>[2,2,2]
[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>110010=>[2,2,1,1]
[2,3,6,5,4,1,7]=>[6,5,2,3,4,7,1]=>110001=>[2,3,1]
[2,3,6,5,4,7,1]=>[6,5,2,3,4,1,7]=>110010=>[2,2,1,1]
[2,3,6,5,7,1,4]=>[6,5,2,3,1,7,4]=>110101=>[2,1,1,1,1]
[2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>110100=>[2,1,1,2]
[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]=>111011=>[3,1,2]
[2,3,6,7,1,5,4]=>[6,5,2,1,7,3,4]=>111010=>[3,1,1,1]
[2,3,6,7,4,1,5]=>[6,5,2,1,4,7,3]=>111001=>[3,2,1]
[2,3,6,7,4,5,1]=>[6,5,2,1,4,3,7]=>111010=>[3,1,1,1]
[2,3,6,7,5,1,4]=>[6,5,2,1,3,7,4]=>111001=>[3,2,1]
[2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>111000=>[3,3]
[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>110111=>[2,1,3]
[2,3,7,1,4,6,5]=>[6,5,1,7,4,2,3]=>110110=>[2,1,2,1]
[2,3,7,1,5,4,6]=>[6,5,1,7,3,4,2]=>110101=>[2,1,1,1,1]
[2,3,7,1,5,6,4]=>[6,5,1,7,3,2,4]=>110110=>[2,1,2,1]
[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>110101=>[2,1,1,1,1]
[2,3,7,1,6,5,4]=>[6,5,1,7,2,3,4]=>110100=>[2,1,1,2]
[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>110011=>[2,2,2]
[2,3,7,4,1,6,5]=>[6,5,1,4,7,2,3]=>110010=>[2,2,1,1]
[2,3,7,4,5,1,6]=>[6,5,1,4,3,7,2]=>110101=>[2,1,1,1,1]
[2,3,7,4,5,6,1]=>[6,5,1,4,3,2,7]=>110110=>[2,1,2,1]
[2,3,7,4,6,1,5]=>[6,5,1,4,2,7,3]=>110101=>[2,1,1,1,1]
[2,3,7,4,6,5,1]=>[6,5,1,4,2,3,7]=>110100=>[2,1,1,2]
[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>110011=>[2,2,2]
[2,3,7,5,1,6,4]=>[6,5,1,3,7,2,4]=>110010=>[2,2,1,1]
[2,3,7,5,4,1,6]=>[6,5,1,3,4,7,2]=>110001=>[2,3,1]
[2,3,7,5,4,6,1]=>[6,5,1,3,4,2,7]=>110010=>[2,2,1,1]
[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>110101=>[2,1,1,1,1]
[2,3,7,5,6,4,1]=>[6,5,1,3,2,4,7]=>110100=>[2,1,1,2]
[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>110011=>[2,2,2]
[2,3,7,6,1,5,4]=>[6,5,1,2,7,3,4]=>110010=>[2,2,1,1]
[2,3,7,6,4,1,5]=>[6,5,1,2,4,7,3]=>110001=>[2,3,1]
[2,3,7,6,4,5,1]=>[6,5,1,2,4,3,7]=>110010=>[2,2,1,1]
[2,3,7,6,5,1,4]=>[6,5,1,2,3,7,4]=>110001=>[2,3,1]
[2,3,7,6,5,4,1]=>[6,5,1,2,3,4,7]=>110000=>[2,4]
[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>101111=>[1,1,4]
[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]=>101110=>[1,1,3,1]
[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]=>101101=>[1,1,2,1,1]
[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]=>101110=>[1,1,3,1]
[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]=>101101=>[1,1,2,1,1]
[2,4,1,3,7,6,5]=>[6,4,7,5,1,2,3]=>101100=>[1,1,2,2]
[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]=>101011=>[1,1,1,1,2]
[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]=>101010=>[1,1,1,1,1,1]
[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]=>101101=>[1,1,2,1,1]
[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>101110=>[1,1,3,1]
[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>101101=>[1,1,2,1,1]
[2,4,1,5,7,6,3]=>[6,4,7,3,1,2,5]=>101100=>[1,1,2,2]
[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]=>101011=>[1,1,1,1,2]
[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>101010=>[1,1,1,1,1,1]
[2,4,1,6,5,3,7]=>[6,4,7,2,3,5,1]=>101001=>[1,1,1,2,1]
[2,4,1,6,5,7,3]=>[6,4,7,2,3,1,5]=>101010=>[1,1,1,1,1,1]
[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]=>101101=>[1,1,2,1,1]
[2,4,1,6,7,5,3]=>[6,4,7,2,1,3,5]=>101100=>[1,1,2,2]
[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>101011=>[1,1,1,1,2]
[2,4,1,7,3,6,5]=>[6,4,7,1,5,2,3]=>101010=>[1,1,1,1,1,1]
[2,4,1,7,5,3,6]=>[6,4,7,1,3,5,2]=>101001=>[1,1,1,2,1]
[2,4,1,7,5,6,3]=>[6,4,7,1,3,2,5]=>101010=>[1,1,1,1,1,1]
[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>101001=>[1,1,1,2,1]
[2,4,1,7,6,5,3]=>[6,4,7,1,2,3,5]=>101000=>[1,1,1,3]
[2,4,3,1,5,6,7]=>[6,4,5,7,3,2,1]=>100111=>[1,2,3]
[2,4,3,1,5,7,6]=>[6,4,5,7,3,1,2]=>100110=>[1,2,2,1]
[2,4,3,1,6,5,7]=>[6,4,5,7,2,3,1]=>100101=>[1,2,1,1,1]
[2,4,3,1,6,7,5]=>[6,4,5,7,2,1,3]=>100110=>[1,2,2,1]
[2,4,3,1,7,5,6]=>[6,4,5,7,1,3,2]=>100101=>[1,2,1,1,1]
[2,4,3,1,7,6,5]=>[6,4,5,7,1,2,3]=>100100=>[1,2,1,2]
[2,4,3,5,1,6,7]=>[6,4,5,3,7,2,1]=>101011=>[1,1,1,1,2]
[2,4,3,5,1,7,6]=>[6,4,5,3,7,1,2]=>101010=>[1,1,1,1,1,1]
[2,4,3,5,6,1,7]=>[6,4,5,3,2,7,1]=>101101=>[1,1,2,1,1]
[2,4,3,5,6,7,1]=>[6,4,5,3,2,1,7]=>101110=>[1,1,3,1]
[2,4,3,5,7,1,6]=>[6,4,5,3,1,7,2]=>101101=>[1,1,2,1,1]
[2,4,3,5,7,6,1]=>[6,4,5,3,1,2,7]=>101100=>[1,1,2,2]
[2,4,3,6,1,5,7]=>[6,4,5,2,7,3,1]=>101011=>[1,1,1,1,2]
[2,4,3,6,1,7,5]=>[6,4,5,2,7,1,3]=>101010=>[1,1,1,1,1,1]
[2,4,3,6,5,1,7]=>[6,4,5,2,3,7,1]=>101001=>[1,1,1,2,1]
[2,4,3,6,5,7,1]=>[6,4,5,2,3,1,7]=>101010=>[1,1,1,1,1,1]
[2,4,3,6,7,1,5]=>[6,4,5,2,1,7,3]=>101101=>[1,1,2,1,1]
[2,4,3,6,7,5,1]=>[6,4,5,2,1,3,7]=>101100=>[1,1,2,2]
[2,4,3,7,1,5,6]=>[6,4,5,1,7,3,2]=>101011=>[1,1,1,1,2]
[2,4,3,7,1,6,5]=>[6,4,5,1,7,2,3]=>101010=>[1,1,1,1,1,1]
[2,4,3,7,5,1,6]=>[6,4,5,1,3,7,2]=>101001=>[1,1,1,2,1]
[2,4,3,7,5,6,1]=>[6,4,5,1,3,2,7]=>101010=>[1,1,1,1,1,1]
[2,4,3,7,6,1,5]=>[6,4,5,1,2,7,3]=>101001=>[1,1,1,2,1]
[2,4,3,7,6,5,1]=>[6,4,5,1,2,3,7]=>101000=>[1,1,1,3]
[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]=>110111=>[2,1,3]
[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]=>110110=>[2,1,2,1]
[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]=>110101=>[2,1,1,1,1]
[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]=>110110=>[2,1,2,1]
[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]=>110101=>[2,1,1,1,1]
[2,4,5,1,7,6,3]=>[6,4,3,7,1,2,5]=>110100=>[2,1,1,2]
[2,4,5,3,1,6,7]=>[6,4,3,5,7,2,1]=>110011=>[2,2,2]
[2,4,5,3,1,7,6]=>[6,4,3,5,7,1,2]=>110010=>[2,2,1,1]
[2,4,5,3,6,1,7]=>[6,4,3,5,2,7,1]=>110101=>[2,1,1,1,1]
[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>110110=>[2,1,2,1]
[2,4,5,3,7,1,6]=>[6,4,3,5,1,7,2]=>110101=>[2,1,1,1,1]
[2,4,5,3,7,6,1]=>[6,4,3,5,1,2,7]=>110100=>[2,1,1,2]
[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]=>111011=>[3,1,2]
[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]=>111010=>[3,1,1,1]
[2,4,5,6,3,1,7]=>[6,4,3,2,5,7,1]=>111001=>[3,2,1]
[2,4,5,6,3,7,1]=>[6,4,3,2,5,1,7]=>111010=>[3,1,1,1]
[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]=>111101=>[4,1,1]
[2,4,5,6,7,3,1]=>[6,4,3,2,1,5,7]=>111100=>[4,2]
[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]=>111011=>[3,1,2]
[2,4,5,7,1,6,3]=>[6,4,3,1,7,2,5]=>111010=>[3,1,1,1]
[2,4,5,7,3,1,6]=>[6,4,3,1,5,7,2]=>111001=>[3,2,1]
[2,4,5,7,3,6,1]=>[6,4,3,1,5,2,7]=>111010=>[3,1,1,1]
[2,4,5,7,6,1,3]=>[6,4,3,1,2,7,5]=>111001=>[3,2,1]
[2,4,5,7,6,3,1]=>[6,4,3,1,2,5,7]=>111000=>[3,3]
[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>110111=>[2,1,3]
[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]=>110110=>[2,1,2,1]
[2,4,6,1,5,3,7]=>[6,4,2,7,3,5,1]=>110101=>[2,1,1,1,1]
[2,4,6,1,5,7,3]=>[6,4,2,7,3,1,5]=>110110=>[2,1,2,1]
[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]=>110101=>[2,1,1,1,1]
[2,4,6,1,7,5,3]=>[6,4,2,7,1,3,5]=>110100=>[2,1,1,2]
[2,4,6,3,1,5,7]=>[6,4,2,5,7,3,1]=>110011=>[2,2,2]
[2,4,6,3,1,7,5]=>[6,4,2,5,7,1,3]=>110010=>[2,2,1,1]
[2,4,6,3,5,1,7]=>[6,4,2,5,3,7,1]=>110101=>[2,1,1,1,1]
[2,4,6,3,5,7,1]=>[6,4,2,5,3,1,7]=>110110=>[2,1,2,1]
[2,4,6,3,7,1,5]=>[6,4,2,5,1,7,3]=>110101=>[2,1,1,1,1]
[2,4,6,3,7,5,1]=>[6,4,2,5,1,3,7]=>110100=>[2,1,1,2]
[2,4,6,5,1,3,7]=>[6,4,2,3,7,5,1]=>110011=>[2,2,2]
[2,4,6,5,1,7,3]=>[6,4,2,3,7,1,5]=>110010=>[2,2,1,1]
[2,4,6,5,3,1,7]=>[6,4,2,3,5,7,1]=>110001=>[2,3,1]
[2,4,6,5,3,7,1]=>[6,4,2,3,5,1,7]=>110010=>[2,2,1,1]
[2,4,6,5,7,1,3]=>[6,4,2,3,1,7,5]=>110101=>[2,1,1,1,1]
[2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>110100=>[2,1,1,2]
[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>111011=>[3,1,2]
[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>111010=>[3,1,1,1]
[2,4,6,7,3,1,5]=>[6,4,2,1,5,7,3]=>111001=>[3,2,1]
[2,4,6,7,3,5,1]=>[6,4,2,1,5,3,7]=>111010=>[3,1,1,1]
[2,4,6,7,5,1,3]=>[6,4,2,1,3,7,5]=>111001=>[3,2,1]
[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>111000=>[3,3]
[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>110111=>[2,1,3]
[2,4,7,1,3,6,5]=>[6,4,1,7,5,2,3]=>110110=>[2,1,2,1]
[2,4,7,1,5,3,6]=>[6,4,1,7,3,5,2]=>110101=>[2,1,1,1,1]
[2,4,7,1,5,6,3]=>[6,4,1,7,3,2,5]=>110110=>[2,1,2,1]
[2,4,7,1,6,3,5]=>[6,4,1,7,2,5,3]=>110101=>[2,1,1,1,1]
[2,4,7,1,6,5,3]=>[6,4,1,7,2,3,5]=>110100=>[2,1,1,2]
[2,4,7,3,1,5,6]=>[6,4,1,5,7,3,2]=>110011=>[2,2,2]
[2,4,7,3,1,6,5]=>[6,4,1,5,7,2,3]=>110010=>[2,2,1,1]
[2,4,7,3,5,1,6]=>[6,4,1,5,3,7,2]=>110101=>[2,1,1,1,1]
[2,4,7,3,5,6,1]=>[6,4,1,5,3,2,7]=>110110=>[2,1,2,1]
[2,4,7,3,6,1,5]=>[6,4,1,5,2,7,3]=>110101=>[2,1,1,1,1]
[2,4,7,3,6,5,1]=>[6,4,1,5,2,3,7]=>110100=>[2,1,1,2]
[2,4,7,5,1,3,6]=>[6,4,1,3,7,5,2]=>110011=>[2,2,2]
[2,4,7,5,1,6,3]=>[6,4,1,3,7,2,5]=>110010=>[2,2,1,1]
[2,4,7,5,3,1,6]=>[6,4,1,3,5,7,2]=>110001=>[2,3,1]
[2,4,7,5,3,6,1]=>[6,4,1,3,5,2,7]=>110010=>[2,2,1,1]
[2,4,7,5,6,1,3]=>[6,4,1,3,2,7,5]=>110101=>[2,1,1,1,1]
[2,4,7,5,6,3,1]=>[6,4,1,3,2,5,7]=>110100=>[2,1,1,2]
[2,4,7,6,1,3,5]=>[6,4,1,2,7,5,3]=>110011=>[2,2,2]
[2,4,7,6,1,5,3]=>[6,4,1,2,7,3,5]=>110010=>[2,2,1,1]
[2,4,7,6,3,1,5]=>[6,4,1,2,5,7,3]=>110001=>[2,3,1]
[2,4,7,6,3,5,1]=>[6,4,1,2,5,3,7]=>110010=>[2,2,1,1]
[2,4,7,6,5,1,3]=>[6,4,1,2,3,7,5]=>110001=>[2,3,1]
[2,4,7,6,5,3,1]=>[6,4,1,2,3,5,7]=>110000=>[2,4]
[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>101111=>[1,1,4]
[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]=>101110=>[1,1,3,1]
[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]=>101101=>[1,1,2,1,1]
[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>101110=>[1,1,3,1]
[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>101101=>[1,1,2,1,1]
[2,5,1,3,7,6,4]=>[6,3,7,5,1,2,4]=>101100=>[1,1,2,2]
[2,5,1,4,3,6,7]=>[6,3,7,4,5,2,1]=>101011=>[1,1,1,1,2]
[2,5,1,4,3,7,6]=>[6,3,7,4,5,1,2]=>101010=>[1,1,1,1,1,1]
[2,5,1,4,6,3,7]=>[6,3,7,4,2,5,1]=>101101=>[1,1,2,1,1]
[2,5,1,4,6,7,3]=>[6,3,7,4,2,1,5]=>101110=>[1,1,3,1]
[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>101101=>[1,1,2,1,1]
[2,5,1,4,7,6,3]=>[6,3,7,4,1,2,5]=>101100=>[1,1,2,2]
[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]=>101011=>[1,1,1,1,2]
[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]=>101010=>[1,1,1,1,1,1]
[2,5,1,6,4,3,7]=>[6,3,7,2,4,5,1]=>101001=>[1,1,1,2,1]
[2,5,1,6,4,7,3]=>[6,3,7,2,4,1,5]=>101010=>[1,1,1,1,1,1]
[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]=>101101=>[1,1,2,1,1]
[2,5,1,6,7,4,3]=>[6,3,7,2,1,4,5]=>101100=>[1,1,2,2]
[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]=>101011=>[1,1,1,1,2]
[2,5,1,7,3,6,4]=>[6,3,7,1,5,2,4]=>101010=>[1,1,1,1,1,1]
[2,5,1,7,4,3,6]=>[6,3,7,1,4,5,2]=>101001=>[1,1,1,2,1]
[2,5,1,7,4,6,3]=>[6,3,7,1,4,2,5]=>101010=>[1,1,1,1,1,1]
[2,5,1,7,6,3,4]=>[6,3,7,1,2,5,4]=>101001=>[1,1,1,2,1]
[2,5,1,7,6,4,3]=>[6,3,7,1,2,4,5]=>101000=>[1,1,1,3]
[2,5,3,1,4,6,7]=>[6,3,5,7,4,2,1]=>100111=>[1,2,3]
[2,5,3,1,4,7,6]=>[6,3,5,7,4,1,2]=>100110=>[1,2,2,1]
[2,5,3,1,6,4,7]=>[6,3,5,7,2,4,1]=>100101=>[1,2,1,1,1]
[2,5,3,1,6,7,4]=>[6,3,5,7,2,1,4]=>100110=>[1,2,2,1]
[2,5,3,1,7,4,6]=>[6,3,5,7,1,4,2]=>100101=>[1,2,1,1,1]
[2,5,3,1,7,6,4]=>[6,3,5,7,1,2,4]=>100100=>[1,2,1,2]
[2,5,3,4,1,6,7]=>[6,3,5,4,7,2,1]=>101011=>[1,1,1,1,2]
[2,5,3,4,1,7,6]=>[6,3,5,4,7,1,2]=>101010=>[1,1,1,1,1,1]
[2,5,3,4,6,1,7]=>[6,3,5,4,2,7,1]=>101101=>[1,1,2,1,1]
[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>101110=>[1,1,3,1]
[2,5,3,4,7,1,6]=>[6,3,5,4,1,7,2]=>101101=>[1,1,2,1,1]
[2,5,3,4,7,6,1]=>[6,3,5,4,1,2,7]=>101100=>[1,1,2,2]
[2,5,3,6,1,4,7]=>[6,3,5,2,7,4,1]=>101011=>[1,1,1,1,2]
[2,5,3,6,1,7,4]=>[6,3,5,2,7,1,4]=>101010=>[1,1,1,1,1,1]
[2,5,3,6,4,1,7]=>[6,3,5,2,4,7,1]=>101001=>[1,1,1,2,1]
[2,5,3,6,4,7,1]=>[6,3,5,2,4,1,7]=>101010=>[1,1,1,1,1,1]
[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>101101=>[1,1,2,1,1]
[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>101100=>[1,1,2,2]
[2,5,3,7,1,4,6]=>[6,3,5,1,7,4,2]=>101011=>[1,1,1,1,2]
[2,5,3,7,1,6,4]=>[6,3,5,1,7,2,4]=>101010=>[1,1,1,1,1,1]
[2,5,3,7,4,1,6]=>[6,3,5,1,4,7,2]=>101001=>[1,1,1,2,1]
[2,5,3,7,4,6,1]=>[6,3,5,1,4,2,7]=>101010=>[1,1,1,1,1,1]
[2,5,3,7,6,1,4]=>[6,3,5,1,2,7,4]=>101001=>[1,1,1,2,1]
[2,5,3,7,6,4,1]=>[6,3,5,1,2,4,7]=>101000=>[1,1,1,3]
[2,5,4,1,3,6,7]=>[6,3,4,7,5,2,1]=>100111=>[1,2,3]
[2,5,4,1,3,7,6]=>[6,3,4,7,5,1,2]=>100110=>[1,2,2,1]
[2,5,4,1,6,3,7]=>[6,3,4,7,2,5,1]=>100101=>[1,2,1,1,1]
[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>100110=>[1,2,2,1]
[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>100101=>[1,2,1,1,1]
[2,5,4,1,7,6,3]=>[6,3,4,7,1,2,5]=>100100=>[1,2,1,2]
[2,5,4,3,1,6,7]=>[6,3,4,5,7,2,1]=>100011=>[1,3,2]
[2,5,4,3,1,7,6]=>[6,3,4,5,7,1,2]=>100010=>[1,3,1,1]
[2,5,4,3,6,1,7]=>[6,3,4,5,2,7,1]=>100101=>[1,2,1,1,1]
[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>100110=>[1,2,2,1]
[2,5,4,3,7,1,6]=>[6,3,4,5,1,7,2]=>100101=>[1,2,1,1,1]
[2,5,4,3,7,6,1]=>[6,3,4,5,1,2,7]=>100100=>[1,2,1,2]
[2,5,4,6,1,3,7]=>[6,3,4,2,7,5,1]=>101011=>[1,1,1,1,2]
[2,5,4,6,1,7,3]=>[6,3,4,2,7,1,5]=>101010=>[1,1,1,1,1,1]
[2,5,4,6,3,1,7]=>[6,3,4,2,5,7,1]=>101001=>[1,1,1,2,1]
[2,5,4,6,3,7,1]=>[6,3,4,2,5,1,7]=>101010=>[1,1,1,1,1,1]
[2,5,4,6,7,1,3]=>[6,3,4,2,1,7,5]=>101101=>[1,1,2,1,1]
[2,5,4,6,7,3,1]=>[6,3,4,2,1,5,7]=>101100=>[1,1,2,2]
[2,5,4,7,1,3,6]=>[6,3,4,1,7,5,2]=>101011=>[1,1,1,1,2]
[2,5,4,7,1,6,3]=>[6,3,4,1,7,2,5]=>101010=>[1,1,1,1,1,1]
[2,5,4,7,3,1,6]=>[6,3,4,1,5,7,2]=>101001=>[1,1,1,2,1]
[2,5,4,7,3,6,1]=>[6,3,4,1,5,2,7]=>101010=>[1,1,1,1,1,1]
[2,5,4,7,6,1,3]=>[6,3,4,1,2,7,5]=>101001=>[1,1,1,2,1]
[2,5,4,7,6,3,1]=>[6,3,4,1,2,5,7]=>101000=>[1,1,1,3]
[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>110111=>[2,1,3]
[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]=>110110=>[2,1,2,1]
[2,5,6,1,4,3,7]=>[6,3,2,7,4,5,1]=>110101=>[2,1,1,1,1]
[2,5,6,1,4,7,3]=>[6,3,2,7,4,1,5]=>110110=>[2,1,2,1]
[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]=>110101=>[2,1,1,1,1]
[2,5,6,1,7,4,3]=>[6,3,2,7,1,4,5]=>110100=>[2,1,1,2]
[2,5,6,3,1,4,7]=>[6,3,2,5,7,4,1]=>110011=>[2,2,2]
[2,5,6,3,1,7,4]=>[6,3,2,5,7,1,4]=>110010=>[2,2,1,1]
[2,5,6,3,4,1,7]=>[6,3,2,5,4,7,1]=>110101=>[2,1,1,1,1]
[2,5,6,3,4,7,1]=>[6,3,2,5,4,1,7]=>110110=>[2,1,2,1]
[2,5,6,3,7,1,4]=>[6,3,2,5,1,7,4]=>110101=>[2,1,1,1,1]
[2,5,6,3,7,4,1]=>[6,3,2,5,1,4,7]=>110100=>[2,1,1,2]
[2,5,6,4,1,3,7]=>[6,3,2,4,7,5,1]=>110011=>[2,2,2]
[2,5,6,4,1,7,3]=>[6,3,2,4,7,1,5]=>110010=>[2,2,1,1]
[2,5,6,4,3,1,7]=>[6,3,2,4,5,7,1]=>110001=>[2,3,1]
[2,5,6,4,3,7,1]=>[6,3,2,4,5,1,7]=>110010=>[2,2,1,1]
[2,5,6,4,7,1,3]=>[6,3,2,4,1,7,5]=>110101=>[2,1,1,1,1]
[2,5,6,4,7,3,1]=>[6,3,2,4,1,5,7]=>110100=>[2,1,1,2]
[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]=>111011=>[3,1,2]
[2,5,6,7,1,4,3]=>[6,3,2,1,7,4,5]=>111010=>[3,1,1,1]
[2,5,6,7,3,1,4]=>[6,3,2,1,5,7,4]=>111001=>[3,2,1]
[2,5,6,7,3,4,1]=>[6,3,2,1,5,4,7]=>111010=>[3,1,1,1]
[2,5,6,7,4,1,3]=>[6,3,2,1,4,7,5]=>111001=>[3,2,1]
[2,5,6,7,4,3,1]=>[6,3,2,1,4,5,7]=>111000=>[3,3]
[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>110111=>[2,1,3]
[2,5,7,1,3,6,4]=>[6,3,1,7,5,2,4]=>110110=>[2,1,2,1]
[2,5,7,1,4,3,6]=>[6,3,1,7,4,5,2]=>110101=>[2,1,1,1,1]
[2,5,7,1,4,6,3]=>[6,3,1,7,4,2,5]=>110110=>[2,1,2,1]
[2,5,7,1,6,3,4]=>[6,3,1,7,2,5,4]=>110101=>[2,1,1,1,1]
[2,5,7,1,6,4,3]=>[6,3,1,7,2,4,5]=>110100=>[2,1,1,2]
[2,5,7,3,1,4,6]=>[6,3,1,5,7,4,2]=>110011=>[2,2,2]
[2,5,7,3,1,6,4]=>[6,3,1,5,7,2,4]=>110010=>[2,2,1,1]
[2,5,7,3,4,1,6]=>[6,3,1,5,4,7,2]=>110101=>[2,1,1,1,1]
[2,5,7,3,4,6,1]=>[6,3,1,5,4,2,7]=>110110=>[2,1,2,1]
[2,5,7,3,6,1,4]=>[6,3,1,5,2,7,4]=>110101=>[2,1,1,1,1]
[2,5,7,3,6,4,1]=>[6,3,1,5,2,4,7]=>110100=>[2,1,1,2]
[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>110011=>[2,2,2]
[2,5,7,4,1,6,3]=>[6,3,1,4,7,2,5]=>110010=>[2,2,1,1]
[2,5,7,4,3,1,6]=>[6,3,1,4,5,7,2]=>110001=>[2,3,1]
[2,5,7,4,3,6,1]=>[6,3,1,4,5,2,7]=>110010=>[2,2,1,1]
[2,5,7,4,6,1,3]=>[6,3,1,4,2,7,5]=>110101=>[2,1,1,1,1]
[2,5,7,4,6,3,1]=>[6,3,1,4,2,5,7]=>110100=>[2,1,1,2]
[2,5,7,6,1,3,4]=>[6,3,1,2,7,5,4]=>110011=>[2,2,2]
[2,5,7,6,1,4,3]=>[6,3,1,2,7,4,5]=>110010=>[2,2,1,1]
[2,5,7,6,3,1,4]=>[6,3,1,2,5,7,4]=>110001=>[2,3,1]
[2,5,7,6,3,4,1]=>[6,3,1,2,5,4,7]=>110010=>[2,2,1,1]
[2,5,7,6,4,1,3]=>[6,3,1,2,4,7,5]=>110001=>[2,3,1]
[2,5,7,6,4,3,1]=>[6,3,1,2,4,5,7]=>110000=>[2,4]
[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>101111=>[1,1,4]
[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>101110=>[1,1,3,1]
[2,6,1,3,5,4,7]=>[6,2,7,5,3,4,1]=>101101=>[1,1,2,1,1]
[2,6,1,3,5,7,4]=>[6,2,7,5,3,1,4]=>101110=>[1,1,3,1]
[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]=>101101=>[1,1,2,1,1]
[2,6,1,3,7,5,4]=>[6,2,7,5,1,3,4]=>101100=>[1,1,2,2]
[2,6,1,4,3,5,7]=>[6,2,7,4,5,3,1]=>101011=>[1,1,1,1,2]
[2,6,1,4,3,7,5]=>[6,2,7,4,5,1,3]=>101010=>[1,1,1,1,1,1]
[2,6,1,4,5,3,7]=>[6,2,7,4,3,5,1]=>101101=>[1,1,2,1,1]
[2,6,1,4,5,7,3]=>[6,2,7,4,3,1,5]=>101110=>[1,1,3,1]
[2,6,1,4,7,3,5]=>[6,2,7,4,1,5,3]=>101101=>[1,1,2,1,1]
[2,6,1,4,7,5,3]=>[6,2,7,4,1,3,5]=>101100=>[1,1,2,2]
[2,6,1,5,3,4,7]=>[6,2,7,3,5,4,1]=>101011=>[1,1,1,1,2]
[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>101010=>[1,1,1,1,1,1]
[2,6,1,5,4,3,7]=>[6,2,7,3,4,5,1]=>101001=>[1,1,1,2,1]
[2,6,1,5,4,7,3]=>[6,2,7,3,4,1,5]=>101010=>[1,1,1,1,1,1]
[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>101101=>[1,1,2,1,1]
[2,6,1,5,7,4,3]=>[6,2,7,3,1,4,5]=>101100=>[1,1,2,2]
[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]=>101011=>[1,1,1,1,2]
[2,6,1,7,3,5,4]=>[6,2,7,1,5,3,4]=>101010=>[1,1,1,1,1,1]
[2,6,1,7,4,3,5]=>[6,2,7,1,4,5,3]=>101001=>[1,1,1,2,1]
[2,6,1,7,4,5,3]=>[6,2,7,1,4,3,5]=>101010=>[1,1,1,1,1,1]
[2,6,1,7,5,3,4]=>[6,2,7,1,3,5,4]=>101001=>[1,1,1,2,1]
[2,6,1,7,5,4,3]=>[6,2,7,1,3,4,5]=>101000=>[1,1,1,3]
[2,6,3,1,4,5,7]=>[6,2,5,7,4,3,1]=>100111=>[1,2,3]
[2,6,3,1,4,7,5]=>[6,2,5,7,4,1,3]=>100110=>[1,2,2,1]
[2,6,3,1,5,4,7]=>[6,2,5,7,3,4,1]=>100101=>[1,2,1,1,1]
[2,6,3,1,5,7,4]=>[6,2,5,7,3,1,4]=>100110=>[1,2,2,1]
[2,6,3,1,7,4,5]=>[6,2,5,7,1,4,3]=>100101=>[1,2,1,1,1]
[2,6,3,1,7,5,4]=>[6,2,5,7,1,3,4]=>100100=>[1,2,1,2]
[2,6,3,4,1,5,7]=>[6,2,5,4,7,3,1]=>101011=>[1,1,1,1,2]
[2,6,3,4,1,7,5]=>[6,2,5,4,7,1,3]=>101010=>[1,1,1,1,1,1]
[2,6,3,4,5,1,7]=>[6,2,5,4,3,7,1]=>101101=>[1,1,2,1,1]
[2,6,3,4,5,7,1]=>[6,2,5,4,3,1,7]=>101110=>[1,1,3,1]
[2,6,3,4,7,1,5]=>[6,2,5,4,1,7,3]=>101101=>[1,1,2,1,1]
[2,6,3,4,7,5,1]=>[6,2,5,4,1,3,7]=>101100=>[1,1,2,2]
[2,6,3,5,1,4,7]=>[6,2,5,3,7,4,1]=>101011=>[1,1,1,1,2]
[2,6,3,5,1,7,4]=>[6,2,5,3,7,1,4]=>101010=>[1,1,1,1,1,1]
[2,6,3,5,4,1,7]=>[6,2,5,3,4,7,1]=>101001=>[1,1,1,2,1]
[2,6,3,5,4,7,1]=>[6,2,5,3,4,1,7]=>101010=>[1,1,1,1,1,1]
[2,6,3,5,7,1,4]=>[6,2,5,3,1,7,4]=>101101=>[1,1,2,1,1]
[2,6,3,5,7,4,1]=>[6,2,5,3,1,4,7]=>101100=>[1,1,2,2]
[2,6,3,7,1,4,5]=>[6,2,5,1,7,4,3]=>101011=>[1,1,1,1,2]
[2,6,3,7,1,5,4]=>[6,2,5,1,7,3,4]=>101010=>[1,1,1,1,1,1]
[2,6,3,7,4,1,5]=>[6,2,5,1,4,7,3]=>101001=>[1,1,1,2,1]
[2,6,3,7,4,5,1]=>[6,2,5,1,4,3,7]=>101010=>[1,1,1,1,1,1]
[2,6,3,7,5,1,4]=>[6,2,5,1,3,7,4]=>101001=>[1,1,1,2,1]
[2,6,3,7,5,4,1]=>[6,2,5,1,3,4,7]=>101000=>[1,1,1,3]
[2,6,4,1,3,5,7]=>[6,2,4,7,5,3,1]=>100111=>[1,2,3]
[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>100110=>[1,2,2,1]
[2,6,4,1,5,3,7]=>[6,2,4,7,3,5,1]=>100101=>[1,2,1,1,1]
[2,6,4,1,5,7,3]=>[6,2,4,7,3,1,5]=>100110=>[1,2,2,1]
[2,6,4,1,7,3,5]=>[6,2,4,7,1,5,3]=>100101=>[1,2,1,1,1]
[2,6,4,1,7,5,3]=>[6,2,4,7,1,3,5]=>100100=>[1,2,1,2]
[2,6,4,3,1,5,7]=>[6,2,4,5,7,3,1]=>100011=>[1,3,2]
[2,6,4,3,1,7,5]=>[6,2,4,5,7,1,3]=>100010=>[1,3,1,1]
[2,6,4,3,5,1,7]=>[6,2,4,5,3,7,1]=>100101=>[1,2,1,1,1]
[2,6,4,3,5,7,1]=>[6,2,4,5,3,1,7]=>100110=>[1,2,2,1]
[2,6,4,3,7,1,5]=>[6,2,4,5,1,7,3]=>100101=>[1,2,1,1,1]
[2,6,4,3,7,5,1]=>[6,2,4,5,1,3,7]=>100100=>[1,2,1,2]
[2,6,4,5,1,3,7]=>[6,2,4,3,7,5,1]=>101011=>[1,1,1,1,2]
[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>101010=>[1,1,1,1,1,1]
[2,6,4,5,3,1,7]=>[6,2,4,3,5,7,1]=>101001=>[1,1,1,2,1]
[2,6,4,5,3,7,1]=>[6,2,4,3,5,1,7]=>101010=>[1,1,1,1,1,1]
[2,6,4,5,7,1,3]=>[6,2,4,3,1,7,5]=>101101=>[1,1,2,1,1]
[2,6,4,5,7,3,1]=>[6,2,4,3,1,5,7]=>101100=>[1,1,2,2]
[2,6,4,7,1,3,5]=>[6,2,4,1,7,5,3]=>101011=>[1,1,1,1,2]
[2,6,4,7,1,5,3]=>[6,2,4,1,7,3,5]=>101010=>[1,1,1,1,1,1]
[2,6,4,7,3,1,5]=>[6,2,4,1,5,7,3]=>101001=>[1,1,1,2,1]
[2,6,4,7,3,5,1]=>[6,2,4,1,5,3,7]=>101010=>[1,1,1,1,1,1]
[2,6,4,7,5,1,3]=>[6,2,4,1,3,7,5]=>101001=>[1,1,1,2,1]
[2,6,4,7,5,3,1]=>[6,2,4,1,3,5,7]=>101000=>[1,1,1,3]
[2,6,5,1,3,4,7]=>[6,2,3,7,5,4,1]=>100111=>[1,2,3]
[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>100110=>[1,2,2,1]
[2,6,5,1,4,3,7]=>[6,2,3,7,4,5,1]=>100101=>[1,2,1,1,1]
[2,6,5,1,4,7,3]=>[6,2,3,7,4,1,5]=>100110=>[1,2,2,1]
[2,6,5,1,7,3,4]=>[6,2,3,7,1,5,4]=>100101=>[1,2,1,1,1]
[2,6,5,1,7,4,3]=>[6,2,3,7,1,4,5]=>100100=>[1,2,1,2]
[2,6,5,3,1,4,7]=>[6,2,3,5,7,4,1]=>100011=>[1,3,2]
[2,6,5,3,1,7,4]=>[6,2,3,5,7,1,4]=>100010=>[1,3,1,1]
[2,6,5,3,4,1,7]=>[6,2,3,5,4,7,1]=>100101=>[1,2,1,1,1]
[2,6,5,3,4,7,1]=>[6,2,3,5,4,1,7]=>100110=>[1,2,2,1]
[2,6,5,3,7,1,4]=>[6,2,3,5,1,7,4]=>100101=>[1,2,1,1,1]
[2,6,5,3,7,4,1]=>[6,2,3,5,1,4,7]=>100100=>[1,2,1,2]
[2,6,5,4,1,3,7]=>[6,2,3,4,7,5,1]=>100011=>[1,3,2]
[2,6,5,4,1,7,3]=>[6,2,3,4,7,1,5]=>100010=>[1,3,1,1]
[2,6,5,4,3,1,7]=>[6,2,3,4,5,7,1]=>100001=>[1,4,1]
[2,6,5,4,3,7,1]=>[6,2,3,4,5,1,7]=>100010=>[1,3,1,1]
[2,6,5,4,7,1,3]=>[6,2,3,4,1,7,5]=>100101=>[1,2,1,1,1]
[2,6,5,4,7,3,1]=>[6,2,3,4,1,5,7]=>100100=>[1,2,1,2]
[2,6,5,7,1,3,4]=>[6,2,3,1,7,5,4]=>101011=>[1,1,1,1,2]
[2,6,5,7,1,4,3]=>[6,2,3,1,7,4,5]=>101010=>[1,1,1,1,1,1]
[2,6,5,7,3,1,4]=>[6,2,3,1,5,7,4]=>101001=>[1,1,1,2,1]
[2,6,5,7,3,4,1]=>[6,2,3,1,5,4,7]=>101010=>[1,1,1,1,1,1]
[2,6,5,7,4,1,3]=>[6,2,3,1,4,7,5]=>101001=>[1,1,1,2,1]
[2,6,5,7,4,3,1]=>[6,2,3,1,4,5,7]=>101000=>[1,1,1,3]
[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>110111=>[2,1,3]
[2,6,7,1,3,5,4]=>[6,2,1,7,5,3,4]=>110110=>[2,1,2,1]
[2,6,7,1,4,3,5]=>[6,2,1,7,4,5,3]=>110101=>[2,1,1,1,1]
[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>110110=>[2,1,2,1]
[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>110101=>[2,1,1,1,1]
[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>110100=>[2,1,1,2]
[2,6,7,3,1,4,5]=>[6,2,1,5,7,4,3]=>110011=>[2,2,2]
[2,6,7,3,1,5,4]=>[6,2,1,5,7,3,4]=>110010=>[2,2,1,1]
[2,6,7,3,4,1,5]=>[6,2,1,5,4,7,3]=>110101=>[2,1,1,1,1]
[2,6,7,3,4,5,1]=>[6,2,1,5,4,3,7]=>110110=>[2,1,2,1]
[2,6,7,3,5,1,4]=>[6,2,1,5,3,7,4]=>110101=>[2,1,1,1,1]
[2,6,7,3,5,4,1]=>[6,2,1,5,3,4,7]=>110100=>[2,1,1,2]
[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>110011=>[2,2,2]
[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>110010=>[2,2,1,1]
[2,6,7,4,3,1,5]=>[6,2,1,4,5,7,3]=>110001=>[2,3,1]
[2,6,7,4,3,5,1]=>[6,2,1,4,5,3,7]=>110010=>[2,2,1,1]
[2,6,7,4,5,1,3]=>[6,2,1,4,3,7,5]=>110101=>[2,1,1,1,1]
[2,6,7,4,5,3,1]=>[6,2,1,4,3,5,7]=>110100=>[2,1,1,2]
[2,6,7,5,1,3,4]=>[6,2,1,3,7,5,4]=>110011=>[2,2,2]
[2,6,7,5,1,4,3]=>[6,2,1,3,7,4,5]=>110010=>[2,2,1,1]
[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>110001=>[2,3,1]
[2,6,7,5,3,4,1]=>[6,2,1,3,5,4,7]=>110010=>[2,2,1,1]
[2,6,7,5,4,1,3]=>[6,2,1,3,4,7,5]=>110001=>[2,3,1]
[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>110000=>[2,4]
[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>101111=>[1,1,4]
[2,7,1,3,4,6,5]=>[6,1,7,5,4,2,3]=>101110=>[1,1,3,1]
[2,7,1,3,5,4,6]=>[6,1,7,5,3,4,2]=>101101=>[1,1,2,1,1]
[2,7,1,3,5,6,4]=>[6,1,7,5,3,2,4]=>101110=>[1,1,3,1]
[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>101101=>[1,1,2,1,1]
[2,7,1,3,6,5,4]=>[6,1,7,5,2,3,4]=>101100=>[1,1,2,2]
[2,7,1,4,3,5,6]=>[6,1,7,4,5,3,2]=>101011=>[1,1,1,1,2]
[2,7,1,4,3,6,5]=>[6,1,7,4,5,2,3]=>101010=>[1,1,1,1,1,1]
[2,7,1,4,5,3,6]=>[6,1,7,4,3,5,2]=>101101=>[1,1,2,1,1]
[2,7,1,4,5,6,3]=>[6,1,7,4,3,2,5]=>101110=>[1,1,3,1]
[2,7,1,4,6,3,5]=>[6,1,7,4,2,5,3]=>101101=>[1,1,2,1,1]
[2,7,1,4,6,5,3]=>[6,1,7,4,2,3,5]=>101100=>[1,1,2,2]
[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>101011=>[1,1,1,1,2]
[2,7,1,5,3,6,4]=>[6,1,7,3,5,2,4]=>101010=>[1,1,1,1,1,1]
[2,7,1,5,4,3,6]=>[6,1,7,3,4,5,2]=>101001=>[1,1,1,2,1]
[2,7,1,5,4,6,3]=>[6,1,7,3,4,2,5]=>101010=>[1,1,1,1,1,1]
[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>101101=>[1,1,2,1,1]
[2,7,1,5,6,4,3]=>[6,1,7,3,2,4,5]=>101100=>[1,1,2,2]
[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>101011=>[1,1,1,1,2]
[2,7,1,6,3,5,4]=>[6,1,7,2,5,3,4]=>101010=>[1,1,1,1,1,1]
[2,7,1,6,4,3,5]=>[6,1,7,2,4,5,3]=>101001=>[1,1,1,2,1]
[2,7,1,6,4,5,3]=>[6,1,7,2,4,3,5]=>101010=>[1,1,1,1,1,1]
[2,7,1,6,5,3,4]=>[6,1,7,2,3,5,4]=>101001=>[1,1,1,2,1]
[2,7,1,6,5,4,3]=>[6,1,7,2,3,4,5]=>101000=>[1,1,1,3]
[2,7,3,1,4,5,6]=>[6,1,5,7,4,3,2]=>100111=>[1,2,3]
[2,7,3,1,4,6,5]=>[6,1,5,7,4,2,3]=>100110=>[1,2,2,1]
[2,7,3,1,5,4,6]=>[6,1,5,7,3,4,2]=>100101=>[1,2,1,1,1]
[2,7,3,1,5,6,4]=>[6,1,5,7,3,2,4]=>100110=>[1,2,2,1]
[2,7,3,1,6,4,5]=>[6,1,5,7,2,4,3]=>100101=>[1,2,1,1,1]
[2,7,3,1,6,5,4]=>[6,1,5,7,2,3,4]=>100100=>[1,2,1,2]
[2,7,3,4,1,5,6]=>[6,1,5,4,7,3,2]=>101011=>[1,1,1,1,2]
[2,7,3,4,1,6,5]=>[6,1,5,4,7,2,3]=>101010=>[1,1,1,1,1,1]
[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>101101=>[1,1,2,1,1]
[2,7,3,4,5,6,1]=>[6,1,5,4,3,2,7]=>101110=>[1,1,3,1]
[2,7,3,4,6,1,5]=>[6,1,5,4,2,7,3]=>101101=>[1,1,2,1,1]
[2,7,3,4,6,5,1]=>[6,1,5,4,2,3,7]=>101100=>[1,1,2,2]
[2,7,3,5,1,4,6]=>[6,1,5,3,7,4,2]=>101011=>[1,1,1,1,2]
[2,7,3,5,1,6,4]=>[6,1,5,3,7,2,4]=>101010=>[1,1,1,1,1,1]
[2,7,3,5,4,1,6]=>[6,1,5,3,4,7,2]=>101001=>[1,1,1,2,1]
[2,7,3,5,4,6,1]=>[6,1,5,3,4,2,7]=>101010=>[1,1,1,1,1,1]
[2,7,3,5,6,1,4]=>[6,1,5,3,2,7,4]=>101101=>[1,1,2,1,1]
[2,7,3,5,6,4,1]=>[6,1,5,3,2,4,7]=>101100=>[1,1,2,2]
[2,7,3,6,1,4,5]=>[6,1,5,2,7,4,3]=>101011=>[1,1,1,1,2]
[2,7,3,6,1,5,4]=>[6,1,5,2,7,3,4]=>101010=>[1,1,1,1,1,1]
[2,7,3,6,4,1,5]=>[6,1,5,2,4,7,3]=>101001=>[1,1,1,2,1]
[2,7,3,6,4,5,1]=>[6,1,5,2,4,3,7]=>101010=>[1,1,1,1,1,1]
[2,7,3,6,5,1,4]=>[6,1,5,2,3,7,4]=>101001=>[1,1,1,2,1]
[2,7,3,6,5,4,1]=>[6,1,5,2,3,4,7]=>101000=>[1,1,1,3]
[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>100111=>[1,2,3]
[2,7,4,1,3,6,5]=>[6,1,4,7,5,2,3]=>100110=>[1,2,2,1]
[2,7,4,1,5,3,6]=>[6,1,4,7,3,5,2]=>100101=>[1,2,1,1,1]
[2,7,4,1,5,6,3]=>[6,1,4,7,3,2,5]=>100110=>[1,2,2,1]
[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>100101=>[1,2,1,1,1]
[2,7,4,1,6,5,3]=>[6,1,4,7,2,3,5]=>100100=>[1,2,1,2]
[2,7,4,3,1,5,6]=>[6,1,4,5,7,3,2]=>100011=>[1,3,2]
[2,7,4,3,1,6,5]=>[6,1,4,5,7,2,3]=>100010=>[1,3,1,1]
[2,7,4,3,5,1,6]=>[6,1,4,5,3,7,2]=>100101=>[1,2,1,1,1]
[2,7,4,3,5,6,1]=>[6,1,4,5,3,2,7]=>100110=>[1,2,2,1]
[2,7,4,3,6,1,5]=>[6,1,4,5,2,7,3]=>100101=>[1,2,1,1,1]
[2,7,4,3,6,5,1]=>[6,1,4,5,2,3,7]=>100100=>[1,2,1,2]
[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>101011=>[1,1,1,1,2]
[2,7,4,5,1,6,3]=>[6,1,4,3,7,2,5]=>101010=>[1,1,1,1,1,1]
[2,7,4,5,3,1,6]=>[6,1,4,3,5,7,2]=>101001=>[1,1,1,2,1]
[2,7,4,5,3,6,1]=>[6,1,4,3,5,2,7]=>101010=>[1,1,1,1,1,1]
[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>101101=>[1,1,2,1,1]
[2,7,4,5,6,3,1]=>[6,1,4,3,2,5,7]=>101100=>[1,1,2,2]
[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>101011=>[1,1,1,1,2]
[2,7,4,6,1,5,3]=>[6,1,4,2,7,3,5]=>101010=>[1,1,1,1,1,1]
[2,7,4,6,3,1,5]=>[6,1,4,2,5,7,3]=>101001=>[1,1,1,2,1]
[2,7,4,6,3,5,1]=>[6,1,4,2,5,3,7]=>101010=>[1,1,1,1,1,1]
[2,7,4,6,5,1,3]=>[6,1,4,2,3,7,5]=>101001=>[1,1,1,2,1]
[2,7,4,6,5,3,1]=>[6,1,4,2,3,5,7]=>101000=>[1,1,1,3]
[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>100111=>[1,2,3]
[2,7,5,1,3,6,4]=>[6,1,3,7,5,2,4]=>100110=>[1,2,2,1]
[2,7,5,1,4,3,6]=>[6,1,3,7,4,5,2]=>100101=>[1,2,1,1,1]
[2,7,5,1,4,6,3]=>[6,1,3,7,4,2,5]=>100110=>[1,2,2,1]
[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>100101=>[1,2,1,1,1]
[2,7,5,1,6,4,3]=>[6,1,3,7,2,4,5]=>100100=>[1,2,1,2]
[2,7,5,3,1,4,6]=>[6,1,3,5,7,4,2]=>100011=>[1,3,2]
[2,7,5,3,1,6,4]=>[6,1,3,5,7,2,4]=>100010=>[1,3,1,1]
[2,7,5,3,4,1,6]=>[6,1,3,5,4,7,2]=>100101=>[1,2,1,1,1]
[2,7,5,3,4,6,1]=>[6,1,3,5,4,2,7]=>100110=>[1,2,2,1]
[2,7,5,3,6,1,4]=>[6,1,3,5,2,7,4]=>100101=>[1,2,1,1,1]
[2,7,5,3,6,4,1]=>[6,1,3,5,2,4,7]=>100100=>[1,2,1,2]
[2,7,5,4,1,3,6]=>[6,1,3,4,7,5,2]=>100011=>[1,3,2]
[2,7,5,4,1,6,3]=>[6,1,3,4,7,2,5]=>100010=>[1,3,1,1]
[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>100001=>[1,4,1]
[2,7,5,4,3,6,1]=>[6,1,3,4,5,2,7]=>100010=>[1,3,1,1]
[2,7,5,4,6,1,3]=>[6,1,3,4,2,7,5]=>100101=>[1,2,1,1,1]
[2,7,5,4,6,3,1]=>[6,1,3,4,2,5,7]=>100100=>[1,2,1,2]
[2,7,5,6,1,3,4]=>[6,1,3,2,7,5,4]=>101011=>[1,1,1,1,2]
[2,7,5,6,1,4,3]=>[6,1,3,2,7,4,5]=>101010=>[1,1,1,1,1,1]
[2,7,5,6,3,1,4]=>[6,1,3,2,5,7,4]=>101001=>[1,1,1,2,1]
[2,7,5,6,3,4,1]=>[6,1,3,2,5,4,7]=>101010=>[1,1,1,1,1,1]
[2,7,5,6,4,1,3]=>[6,1,3,2,4,7,5]=>101001=>[1,1,1,2,1]
[2,7,5,6,4,3,1]=>[6,1,3,2,4,5,7]=>101000=>[1,1,1,3]
[2,7,6,1,3,4,5]=>[6,1,2,7,5,4,3]=>100111=>[1,2,3]
[2,7,6,1,3,5,4]=>[6,1,2,7,5,3,4]=>100110=>[1,2,2,1]
[2,7,6,1,4,3,5]=>[6,1,2,7,4,5,3]=>100101=>[1,2,1,1,1]
[2,7,6,1,4,5,3]=>[6,1,2,7,4,3,5]=>100110=>[1,2,2,1]
[2,7,6,1,5,3,4]=>[6,1,2,7,3,5,4]=>100101=>[1,2,1,1,1]
[2,7,6,1,5,4,3]=>[6,1,2,7,3,4,5]=>100100=>[1,2,1,2]
[2,7,6,3,1,4,5]=>[6,1,2,5,7,4,3]=>100011=>[1,3,2]
[2,7,6,3,1,5,4]=>[6,1,2,5,7,3,4]=>100010=>[1,3,1,1]
[2,7,6,3,4,1,5]=>[6,1,2,5,4,7,3]=>100101=>[1,2,1,1,1]
[2,7,6,3,4,5,1]=>[6,1,2,5,4,3,7]=>100110=>[1,2,2,1]
[2,7,6,3,5,1,4]=>[6,1,2,5,3,7,4]=>100101=>[1,2,1,1,1]
[2,7,6,3,5,4,1]=>[6,1,2,5,3,4,7]=>100100=>[1,2,1,2]
[2,7,6,4,1,3,5]=>[6,1,2,4,7,5,3]=>100011=>[1,3,2]
[2,7,6,4,1,5,3]=>[6,1,2,4,7,3,5]=>100010=>[1,3,1,1]
[2,7,6,4,3,1,5]=>[6,1,2,4,5,7,3]=>100001=>[1,4,1]
[2,7,6,4,3,5,1]=>[6,1,2,4,5,3,7]=>100010=>[1,3,1,1]
[2,7,6,4,5,1,3]=>[6,1,2,4,3,7,5]=>100101=>[1,2,1,1,1]
[2,7,6,4,5,3,1]=>[6,1,2,4,3,5,7]=>100100=>[1,2,1,2]
[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>100011=>[1,3,2]
[2,7,6,5,1,4,3]=>[6,1,2,3,7,4,5]=>100010=>[1,3,1,1]
[2,7,6,5,3,1,4]=>[6,1,2,3,5,7,4]=>100001=>[1,4,1]
[2,7,6,5,3,4,1]=>[6,1,2,3,5,4,7]=>100010=>[1,3,1,1]
[2,7,6,5,4,1,3]=>[6,1,2,3,4,7,5]=>100001=>[1,4,1]
[2,7,6,5,4,3,1]=>[6,1,2,3,4,5,7]=>100000=>[1,5]
[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>011111=>[1,5]
[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>011110=>[1,4,1]
[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>011101=>[1,3,1,1]
[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>011110=>[1,4,1]
[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>011101=>[1,3,1,1]
[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>011100=>[1,3,2]
[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>011011=>[1,2,1,2]
[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>011010=>[1,2,1,1,1]
[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]=>011101=>[1,3,1,1]
[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]=>011110=>[1,4,1]
[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]=>011101=>[1,3,1,1]
[3,1,2,5,7,6,4]=>[5,7,6,3,1,2,4]=>011100=>[1,3,2]
[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>011011=>[1,2,1,2]
[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]=>011010=>[1,2,1,1,1]
[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>011001=>[1,2,2,1]
[3,1,2,6,5,7,4]=>[5,7,6,2,3,1,4]=>011010=>[1,2,1,1,1]
[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]=>011101=>[1,3,1,1]
[3,1,2,6,7,5,4]=>[5,7,6,2,1,3,4]=>011100=>[1,3,2]
[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>011011=>[1,2,1,2]
[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>011010=>[1,2,1,1,1]
[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>011001=>[1,2,2,1]
[3,1,2,7,5,6,4]=>[5,7,6,1,3,2,4]=>011010=>[1,2,1,1,1]
[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>011001=>[1,2,2,1]
[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>011000=>[1,2,3]
[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]=>010111=>[1,1,1,3]
[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]=>010110=>[1,1,1,2,1]
[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]=>010101=>[1,1,1,1,1,1]
[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]=>010110=>[1,1,1,2,1]
[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]=>010101=>[1,1,1,1,1,1]
[3,1,4,2,7,6,5]=>[5,7,4,6,1,2,3]=>010100=>[1,1,1,1,2]
[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]=>011011=>[1,2,1,2]
[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]=>011010=>[1,2,1,1,1]
[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]=>011101=>[1,3,1,1]
[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>011110=>[1,4,1]
[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>011101=>[1,3,1,1]
[3,1,4,5,7,6,2]=>[5,7,4,3,1,2,6]=>011100=>[1,3,2]
[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]=>011011=>[1,2,1,2]
[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>011010=>[1,2,1,1,1]
[3,1,4,6,5,2,7]=>[5,7,4,2,3,6,1]=>011001=>[1,2,2,1]
[3,1,4,6,5,7,2]=>[5,7,4,2,3,1,6]=>011010=>[1,2,1,1,1]
[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]=>011101=>[1,3,1,1]
[3,1,4,6,7,5,2]=>[5,7,4,2,1,3,6]=>011100=>[1,3,2]
[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>011011=>[1,2,1,2]
[3,1,4,7,2,6,5]=>[5,7,4,1,6,2,3]=>011010=>[1,2,1,1,1]
[3,1,4,7,5,2,6]=>[5,7,4,1,3,6,2]=>011001=>[1,2,2,1]
[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>011010=>[1,2,1,1,1]
[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>011001=>[1,2,2,1]
[3,1,4,7,6,5,2]=>[5,7,4,1,2,3,6]=>011000=>[1,2,3]
[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]=>010111=>[1,1,1,3]
[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]=>010110=>[1,1,1,2,1]
[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]=>010101=>[1,1,1,1,1,1]
[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>010110=>[1,1,1,2,1]
[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>010101=>[1,1,1,1,1,1]
[3,1,5,2,7,6,4]=>[5,7,3,6,1,2,4]=>010100=>[1,1,1,1,2]
[3,1,5,4,2,6,7]=>[5,7,3,4,6,2,1]=>010011=>[1,1,2,2]
[3,1,5,4,2,7,6]=>[5,7,3,4,6,1,2]=>010010=>[1,1,2,1,1]
[3,1,5,4,6,2,7]=>[5,7,3,4,2,6,1]=>010101=>[1,1,1,1,1,1]
[3,1,5,4,6,7,2]=>[5,7,3,4,2,1,6]=>010110=>[1,1,1,2,1]
[3,1,5,4,7,2,6]=>[5,7,3,4,1,6,2]=>010101=>[1,1,1,1,1,1]
[3,1,5,4,7,6,2]=>[5,7,3,4,1,2,6]=>010100=>[1,1,1,1,2]
[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]=>011011=>[1,2,1,2]
[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]=>011010=>[1,2,1,1,1]
[3,1,5,6,4,2,7]=>[5,7,3,2,4,6,1]=>011001=>[1,2,2,1]
[3,1,5,6,4,7,2]=>[5,7,3,2,4,1,6]=>011010=>[1,2,1,1,1]
[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]=>011101=>[1,3,1,1]
[3,1,5,6,7,4,2]=>[5,7,3,2,1,4,6]=>011100=>[1,3,2]
[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]=>011011=>[1,2,1,2]
[3,1,5,7,2,6,4]=>[5,7,3,1,6,2,4]=>011010=>[1,2,1,1,1]
[3,1,5,7,4,2,6]=>[5,7,3,1,4,6,2]=>011001=>[1,2,2,1]
[3,1,5,7,4,6,2]=>[5,7,3,1,4,2,6]=>011010=>[1,2,1,1,1]
[3,1,5,7,6,2,4]=>[5,7,3,1,2,6,4]=>011001=>[1,2,2,1]
[3,1,5,7,6,4,2]=>[5,7,3,1,2,4,6]=>011000=>[1,2,3]
[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]=>010111=>[1,1,1,3]
[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>010110=>[1,1,1,2,1]
[3,1,6,2,5,4,7]=>[5,7,2,6,3,4,1]=>010101=>[1,1,1,1,1,1]
[3,1,6,2,5,7,4]=>[5,7,2,6,3,1,4]=>010110=>[1,1,1,2,1]
[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]=>010101=>[1,1,1,1,1,1]
[3,1,6,2,7,5,4]=>[5,7,2,6,1,3,4]=>010100=>[1,1,1,1,2]
[3,1,6,4,2,5,7]=>[5,7,2,4,6,3,1]=>010011=>[1,1,2,2]
[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>010010=>[1,1,2,1,1]
[3,1,6,4,5,2,7]=>[5,7,2,4,3,6,1]=>010101=>[1,1,1,1,1,1]
[3,1,6,4,5,7,2]=>[5,7,2,4,3,1,6]=>010110=>[1,1,1,2,1]
[3,1,6,4,7,2,5]=>[5,7,2,4,1,6,3]=>010101=>[1,1,1,1,1,1]
[3,1,6,4,7,5,2]=>[5,7,2,4,1,3,6]=>010100=>[1,1,1,1,2]
[3,1,6,5,2,4,7]=>[5,7,2,3,6,4,1]=>010011=>[1,1,2,2]
[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>010010=>[1,1,2,1,1]
[3,1,6,5,4,2,7]=>[5,7,2,3,4,6,1]=>010001=>[1,1,3,1]
[3,1,6,5,4,7,2]=>[5,7,2,3,4,1,6]=>010010=>[1,1,2,1,1]
[3,1,6,5,7,2,4]=>[5,7,2,3,1,6,4]=>010101=>[1,1,1,1,1,1]
[3,1,6,5,7,4,2]=>[5,7,2,3,1,4,6]=>010100=>[1,1,1,1,2]
[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]=>011011=>[1,2,1,2]
[3,1,6,7,2,5,4]=>[5,7,2,1,6,3,4]=>011010=>[1,2,1,1,1]
[3,1,6,7,4,2,5]=>[5,7,2,1,4,6,3]=>011001=>[1,2,2,1]
[3,1,6,7,4,5,2]=>[5,7,2,1,4,3,6]=>011010=>[1,2,1,1,1]
[3,1,6,7,5,2,4]=>[5,7,2,1,3,6,4]=>011001=>[1,2,2,1]
[3,1,6,7,5,4,2]=>[5,7,2,1,3,4,6]=>011000=>[1,2,3]
[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>010111=>[1,1,1,3]
[3,1,7,2,4,6,5]=>[5,7,1,6,4,2,3]=>010110=>[1,1,1,2,1]
[3,1,7,2,5,4,6]=>[5,7,1,6,3,4,2]=>010101=>[1,1,1,1,1,1]
[3,1,7,2,5,6,4]=>[5,7,1,6,3,2,4]=>010110=>[1,1,1,2,1]
[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>010101=>[1,1,1,1,1,1]
[3,1,7,2,6,5,4]=>[5,7,1,6,2,3,4]=>010100=>[1,1,1,1,2]
[3,1,7,4,2,5,6]=>[5,7,1,4,6,3,2]=>010011=>[1,1,2,2]
[3,1,7,4,2,6,5]=>[5,7,1,4,6,2,3]=>010010=>[1,1,2,1,1]
[3,1,7,4,5,2,6]=>[5,7,1,4,3,6,2]=>010101=>[1,1,1,1,1,1]
[3,1,7,4,5,6,2]=>[5,7,1,4,3,2,6]=>010110=>[1,1,1,2,1]
[3,1,7,4,6,2,5]=>[5,7,1,4,2,6,3]=>010101=>[1,1,1,1,1,1]
[3,1,7,4,6,5,2]=>[5,7,1,4,2,3,6]=>010100=>[1,1,1,1,2]
[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>010011=>[1,1,2,2]
[3,1,7,5,2,6,4]=>[5,7,1,3,6,2,4]=>010010=>[1,1,2,1,1]
[3,1,7,5,4,2,6]=>[5,7,1,3,4,6,2]=>010001=>[1,1,3,1]
[3,1,7,5,4,6,2]=>[5,7,1,3,4,2,6]=>010010=>[1,1,2,1,1]
[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>010101=>[1,1,1,1,1,1]
[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>010100=>[1,1,1,1,2]
[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>010011=>[1,1,2,2]
[3,1,7,6,2,5,4]=>[5,7,1,2,6,3,4]=>010010=>[1,1,2,1,1]
[3,1,7,6,4,2,5]=>[5,7,1,2,4,6,3]=>010001=>[1,1,3,1]
[3,1,7,6,4,5,2]=>[5,7,1,2,4,3,6]=>010010=>[1,1,2,1,1]
[3,1,7,6,5,2,4]=>[5,7,1,2,3,6,4]=>010001=>[1,1,3,1]
[3,1,7,6,5,4,2]=>[5,7,1,2,3,4,6]=>010000=>[1,1,4]
[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>001111=>[2,4]
[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>001110=>[2,3,1]
[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>001101=>[2,2,1,1]
[3,2,1,4,6,7,5]=>[5,6,7,4,2,1,3]=>001110=>[2,3,1]
[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>001101=>[2,2,1,1]
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>001100=>[2,2,2]
[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>001011=>[2,1,1,2]
[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>001010=>[2,1,1,1,1]
[3,2,1,5,6,4,7]=>[5,6,7,3,2,4,1]=>001101=>[2,2,1,1]
[3,2,1,5,6,7,4]=>[5,6,7,3,2,1,4]=>001110=>[2,3,1]
[3,2,1,5,7,4,6]=>[5,6,7,3,1,4,2]=>001101=>[2,2,1,1]
[3,2,1,5,7,6,4]=>[5,6,7,3,1,2,4]=>001100=>[2,2,2]
[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>001011=>[2,1,1,2]
[3,2,1,6,4,7,5]=>[5,6,7,2,4,1,3]=>001010=>[2,1,1,1,1]
[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>001001=>[2,1,2,1]
[3,2,1,6,5,7,4]=>[5,6,7,2,3,1,4]=>001010=>[2,1,1,1,1]
[3,2,1,6,7,4,5]=>[5,6,7,2,1,4,3]=>001101=>[2,2,1,1]
[3,2,1,6,7,5,4]=>[5,6,7,2,1,3,4]=>001100=>[2,2,2]
[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>001011=>[2,1,1,2]
[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>001010=>[2,1,1,1,1]
[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>001001=>[2,1,2,1]
[3,2,1,7,5,6,4]=>[5,6,7,1,3,2,4]=>001010=>[2,1,1,1,1]
[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>001001=>[2,1,2,1]
[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>001000=>[2,1,3]
[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>010111=>[1,1,1,3]
[3,2,4,1,5,7,6]=>[5,6,4,7,3,1,2]=>010110=>[1,1,1,2,1]
[3,2,4,1,6,5,7]=>[5,6,4,7,2,3,1]=>010101=>[1,1,1,1,1,1]
[3,2,4,1,6,7,5]=>[5,6,4,7,2,1,3]=>010110=>[1,1,1,2,1]
[3,2,4,1,7,5,6]=>[5,6,4,7,1,3,2]=>010101=>[1,1,1,1,1,1]
[3,2,4,1,7,6,5]=>[5,6,4,7,1,2,3]=>010100=>[1,1,1,1,2]
[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>011011=>[1,2,1,2]
[3,2,4,5,1,7,6]=>[5,6,4,3,7,1,2]=>011010=>[1,2,1,1,1]
[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>011101=>[1,3,1,1]
[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>011110=>[1,4,1]
[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>011101=>[1,3,1,1]
[3,2,4,5,7,6,1]=>[5,6,4,3,1,2,7]=>011100=>[1,3,2]
[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>011011=>[1,2,1,2]
[3,2,4,6,1,7,5]=>[5,6,4,2,7,1,3]=>011010=>[1,2,1,1,1]
[3,2,4,6,5,1,7]=>[5,6,4,2,3,7,1]=>011001=>[1,2,2,1]
[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>011010=>[1,2,1,1,1]
[3,2,4,6,7,1,5]=>[5,6,4,2,1,7,3]=>011101=>[1,3,1,1]
[3,2,4,6,7,5,1]=>[5,6,4,2,1,3,7]=>011100=>[1,3,2]
[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>011011=>[1,2,1,2]
[3,2,4,7,1,6,5]=>[5,6,4,1,7,2,3]=>011010=>[1,2,1,1,1]
[3,2,4,7,5,1,6]=>[5,6,4,1,3,7,2]=>011001=>[1,2,2,1]
[3,2,4,7,5,6,1]=>[5,6,4,1,3,2,7]=>011010=>[1,2,1,1,1]
[3,2,4,7,6,1,5]=>[5,6,4,1,2,7,3]=>011001=>[1,2,2,1]
[3,2,4,7,6,5,1]=>[5,6,4,1,2,3,7]=>011000=>[1,2,3]
[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>010111=>[1,1,1,3]
[3,2,5,1,4,7,6]=>[5,6,3,7,4,1,2]=>010110=>[1,1,1,2,1]
[3,2,5,1,6,4,7]=>[5,6,3,7,2,4,1]=>010101=>[1,1,1,1,1,1]
[3,2,5,1,6,7,4]=>[5,6,3,7,2,1,4]=>010110=>[1,1,1,2,1]
[3,2,5,1,7,4,6]=>[5,6,3,7,1,4,2]=>010101=>[1,1,1,1,1,1]
[3,2,5,1,7,6,4]=>[5,6,3,7,1,2,4]=>010100=>[1,1,1,1,2]
[3,2,5,4,1,6,7]=>[5,6,3,4,7,2,1]=>010011=>[1,1,2,2]
[3,2,5,4,1,7,6]=>[5,6,3,4,7,1,2]=>010010=>[1,1,2,1,1]
[3,2,5,4,6,1,7]=>[5,6,3,4,2,7,1]=>010101=>[1,1,1,1,1,1]
[3,2,5,4,6,7,1]=>[5,6,3,4,2,1,7]=>010110=>[1,1,1,2,1]
[3,2,5,4,7,1,6]=>[5,6,3,4,1,7,2]=>010101=>[1,1,1,1,1,1]
[3,2,5,4,7,6,1]=>[5,6,3,4,1,2,7]=>010100=>[1,1,1,1,2]
[3,2,5,6,1,4,7]=>[5,6,3,2,7,4,1]=>011011=>[1,2,1,2]
[3,2,5,6,1,7,4]=>[5,6,3,2,7,1,4]=>011010=>[1,2,1,1,1]
[3,2,5,6,4,1,7]=>[5,6,3,2,4,7,1]=>011001=>[1,2,2,1]
[3,2,5,6,4,7,1]=>[5,6,3,2,4,1,7]=>011010=>[1,2,1,1,1]
[3,2,5,6,7,1,4]=>[5,6,3,2,1,7,4]=>011101=>[1,3,1,1]
[3,2,5,6,7,4,1]=>[5,6,3,2,1,4,7]=>011100=>[1,3,2]
[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>011011=>[1,2,1,2]
[3,2,5,7,1,6,4]=>[5,6,3,1,7,2,4]=>011010=>[1,2,1,1,1]
[3,2,5,7,4,1,6]=>[5,6,3,1,4,7,2]=>011001=>[1,2,2,1]
[3,2,5,7,4,6,1]=>[5,6,3,1,4,2,7]=>011010=>[1,2,1,1,1]
[3,2,5,7,6,1,4]=>[5,6,3,1,2,7,4]=>011001=>[1,2,2,1]
[3,2,5,7,6,4,1]=>[5,6,3,1,2,4,7]=>011000=>[1,2,3]
[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>010111=>[1,1,1,3]
[3,2,6,1,4,7,5]=>[5,6,2,7,4,1,3]=>010110=>[1,1,1,2,1]
[3,2,6,1,5,4,7]=>[5,6,2,7,3,4,1]=>010101=>[1,1,1,1,1,1]
[3,2,6,1,5,7,4]=>[5,6,2,7,3,1,4]=>010110=>[1,1,1,2,1]
[3,2,6,1,7,4,5]=>[5,6,2,7,1,4,3]=>010101=>[1,1,1,1,1,1]
[3,2,6,1,7,5,4]=>[5,6,2,7,1,3,4]=>010100=>[1,1,1,1,2]
[3,2,6,4,1,5,7]=>[5,6,2,4,7,3,1]=>010011=>[1,1,2,2]
[3,2,6,4,1,7,5]=>[5,6,2,4,7,1,3]=>010010=>[1,1,2,1,1]
[3,2,6,4,5,1,7]=>[5,6,2,4,3,7,1]=>010101=>[1,1,1,1,1,1]
[3,2,6,4,5,7,1]=>[5,6,2,4,3,1,7]=>010110=>[1,1,1,2,1]
[3,2,6,4,7,1,5]=>[5,6,2,4,1,7,3]=>010101=>[1,1,1,1,1,1]
[3,2,6,4,7,5,1]=>[5,6,2,4,1,3,7]=>010100=>[1,1,1,1,2]
[3,2,6,5,1,4,7]=>[5,6,2,3,7,4,1]=>010011=>[1,1,2,2]
[3,2,6,5,1,7,4]=>[5,6,2,3,7,1,4]=>010010=>[1,1,2,1,1]
[3,2,6,5,4,1,7]=>[5,6,2,3,4,7,1]=>010001=>[1,1,3,1]
[3,2,6,5,4,7,1]=>[5,6,2,3,4,1,7]=>010010=>[1,1,2,1,1]
[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>010101=>[1,1,1,1,1,1]
[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>010100=>[1,1,1,1,2]
[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>011011=>[1,2,1,2]
[3,2,6,7,1,5,4]=>[5,6,2,1,7,3,4]=>011010=>[1,2,1,1,1]
[3,2,6,7,4,1,5]=>[5,6,2,1,4,7,3]=>011001=>[1,2,2,1]
[3,2,6,7,4,5,1]=>[5,6,2,1,4,3,7]=>011010=>[1,2,1,1,1]
[3,2,6,7,5,1,4]=>[5,6,2,1,3,7,4]=>011001=>[1,2,2,1]
[3,2,6,7,5,4,1]=>[5,6,2,1,3,4,7]=>011000=>[1,2,3]
[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>010111=>[1,1,1,3]
[3,2,7,1,4,6,5]=>[5,6,1,7,4,2,3]=>010110=>[1,1,1,2,1]
[3,2,7,1,5,4,6]=>[5,6,1,7,3,4,2]=>010101=>[1,1,1,1,1,1]
[3,2,7,1,5,6,4]=>[5,6,1,7,3,2,4]=>010110=>[1,1,1,2,1]
[3,2,7,1,6,4,5]=>[5,6,1,7,2,4,3]=>010101=>[1,1,1,1,1,1]
[3,2,7,1,6,5,4]=>[5,6,1,7,2,3,4]=>010100=>[1,1,1,1,2]
[3,2,7,4,1,5,6]=>[5,6,1,4,7,3,2]=>010011=>[1,1,2,2]
[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>010010=>[1,1,2,1,1]
[3,2,7,4,5,1,6]=>[5,6,1,4,3,7,2]=>010101=>[1,1,1,1,1,1]
[3,2,7,4,5,6,1]=>[5,6,1,4,3,2,7]=>010110=>[1,1,1,2,1]
[3,2,7,4,6,1,5]=>[5,6,1,4,2,7,3]=>010101=>[1,1,1,1,1,1]
[3,2,7,4,6,5,1]=>[5,6,1,4,2,3,7]=>010100=>[1,1,1,1,2]
[3,2,7,5,1,4,6]=>[5,6,1,3,7,4,2]=>010011=>[1,1,2,2]
[3,2,7,5,1,6,4]=>[5,6,1,3,7,2,4]=>010010=>[1,1,2,1,1]
[3,2,7,5,4,1,6]=>[5,6,1,3,4,7,2]=>010001=>[1,1,3,1]
[3,2,7,5,4,6,1]=>[5,6,1,3,4,2,7]=>010010=>[1,1,2,1,1]
[3,2,7,5,6,1,4]=>[5,6,1,3,2,7,4]=>010101=>[1,1,1,1,1,1]
[3,2,7,5,6,4,1]=>[5,6,1,3,2,4,7]=>010100=>[1,1,1,1,2]
[3,2,7,6,1,4,5]=>[5,6,1,2,7,4,3]=>010011=>[1,1,2,2]
[3,2,7,6,1,5,4]=>[5,6,1,2,7,3,4]=>010010=>[1,1,2,1,1]
[3,2,7,6,4,1,5]=>[5,6,1,2,4,7,3]=>010001=>[1,1,3,1]
[3,2,7,6,4,5,1]=>[5,6,1,2,4,3,7]=>010010=>[1,1,2,1,1]
[3,2,7,6,5,1,4]=>[5,6,1,2,3,7,4]=>010001=>[1,1,3,1]
[3,2,7,6,5,4,1]=>[5,6,1,2,3,4,7]=>010000=>[1,1,4]
[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>101111=>[1,1,4]
[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]=>101110=>[1,1,3,1]
[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]=>101101=>[1,1,2,1,1]
[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]=>101110=>[1,1,3,1]
[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]=>101101=>[1,1,2,1,1]
[3,4,1,2,7,6,5]=>[5,4,7,6,1,2,3]=>101100=>[1,1,2,2]
[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]=>101011=>[1,1,1,1,2]
[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]=>101010=>[1,1,1,1,1,1]
[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]=>101101=>[1,1,2,1,1]
[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]=>101110=>[1,1,3,1]
[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]=>101101=>[1,1,2,1,1]
[3,4,1,5,7,6,2]=>[5,4,7,3,1,2,6]=>101100=>[1,1,2,2]
[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]=>101011=>[1,1,1,1,2]
[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]=>101010=>[1,1,1,1,1,1]
[3,4,1,6,5,2,7]=>[5,4,7,2,3,6,1]=>101001=>[1,1,1,2,1]
[3,4,1,6,5,7,2]=>[5,4,7,2,3,1,6]=>101010=>[1,1,1,1,1,1]
[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]=>101101=>[1,1,2,1,1]
[3,4,1,6,7,5,2]=>[5,4,7,2,1,3,6]=>101100=>[1,1,2,2]
[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]=>101011=>[1,1,1,1,2]
[3,4,1,7,2,6,5]=>[5,4,7,1,6,2,3]=>101010=>[1,1,1,1,1,1]
[3,4,1,7,5,2,6]=>[5,4,7,1,3,6,2]=>101001=>[1,1,1,2,1]
[3,4,1,7,5,6,2]=>[5,4,7,1,3,2,6]=>101010=>[1,1,1,1,1,1]
[3,4,1,7,6,2,5]=>[5,4,7,1,2,6,3]=>101001=>[1,1,1,2,1]
[3,4,1,7,6,5,2]=>[5,4,7,1,2,3,6]=>101000=>[1,1,1,3]
[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>100111=>[1,2,3]
[3,4,2,1,5,7,6]=>[5,4,6,7,3,1,2]=>100110=>[1,2,2,1]
[3,4,2,1,6,5,7]=>[5,4,6,7,2,3,1]=>100101=>[1,2,1,1,1]
[3,4,2,1,6,7,5]=>[5,4,6,7,2,1,3]=>100110=>[1,2,2,1]
[3,4,2,1,7,5,6]=>[5,4,6,7,1,3,2]=>100101=>[1,2,1,1,1]
[3,4,2,1,7,6,5]=>[5,4,6,7,1,2,3]=>100100=>[1,2,1,2]
[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>101011=>[1,1,1,1,2]
[3,4,2,5,1,7,6]=>[5,4,6,3,7,1,2]=>101010=>[1,1,1,1,1,1]
[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>101101=>[1,1,2,1,1]
[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>101110=>[1,1,3,1]
[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>101101=>[1,1,2,1,1]
[3,4,2,5,7,6,1]=>[5,4,6,3,1,2,7]=>101100=>[1,1,2,2]
[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>101011=>[1,1,1,1,2]
[3,4,2,6,1,7,5]=>[5,4,6,2,7,1,3]=>101010=>[1,1,1,1,1,1]
[3,4,2,6,5,1,7]=>[5,4,6,2,3,7,1]=>101001=>[1,1,1,2,1]
[3,4,2,6,5,7,1]=>[5,4,6,2,3,1,7]=>101010=>[1,1,1,1,1,1]
[3,4,2,6,7,1,5]=>[5,4,6,2,1,7,3]=>101101=>[1,1,2,1,1]
[3,4,2,6,7,5,1]=>[5,4,6,2,1,3,7]=>101100=>[1,1,2,2]
[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>101011=>[1,1,1,1,2]
[3,4,2,7,1,6,5]=>[5,4,6,1,7,2,3]=>101010=>[1,1,1,1,1,1]
[3,4,2,7,5,1,6]=>[5,4,6,1,3,7,2]=>101001=>[1,1,1,2,1]
[3,4,2,7,5,6,1]=>[5,4,6,1,3,2,7]=>101010=>[1,1,1,1,1,1]
[3,4,2,7,6,1,5]=>[5,4,6,1,2,7,3]=>101001=>[1,1,1,2,1]
[3,4,2,7,6,5,1]=>[5,4,6,1,2,3,7]=>101000=>[1,1,1,3]
[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>110111=>[2,1,3]
[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]=>110110=>[2,1,2,1]
[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]=>110101=>[2,1,1,1,1]
[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]=>110110=>[2,1,2,1]
[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]=>110101=>[2,1,1,1,1]
[3,4,5,1,7,6,2]=>[5,4,3,7,1,2,6]=>110100=>[2,1,1,2]
[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>110011=>[2,2,2]
[3,4,5,2,1,7,6]=>[5,4,3,6,7,1,2]=>110010=>[2,2,1,1]
[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>110101=>[2,1,1,1,1]
[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>110110=>[2,1,2,1]
[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>110101=>[2,1,1,1,1]
[3,4,5,2,7,6,1]=>[5,4,3,6,1,2,7]=>110100=>[2,1,1,2]
[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>111011=>[3,1,2]
[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]=>111010=>[3,1,1,1]
[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>111001=>[3,2,1]
[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>111010=>[3,1,1,1]
[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>111101=>[4,1,1]
[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>111100=>[4,2]
[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>111011=>[3,1,2]
[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>111010=>[3,1,1,1]
[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>111001=>[3,2,1]
[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>111010=>[3,1,1,1]
[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>111001=>[3,2,1]
[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>111000=>[3,3]
[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>110111=>[2,1,3]
[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]=>110110=>[2,1,2,1]
[3,4,6,1,5,2,7]=>[5,4,2,7,3,6,1]=>110101=>[2,1,1,1,1]
[3,4,6,1,5,7,2]=>[5,4,2,7,3,1,6]=>110110=>[2,1,2,1]
[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]=>110101=>[2,1,1,1,1]
[3,4,6,1,7,5,2]=>[5,4,2,7,1,3,6]=>110100=>[2,1,1,2]
[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>110011=>[2,2,2]
[3,4,6,2,1,7,5]=>[5,4,2,6,7,1,3]=>110010=>[2,2,1,1]
[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>110101=>[2,1,1,1,1]
[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>110110=>[2,1,2,1]
[3,4,6,2,7,1,5]=>[5,4,2,6,1,7,3]=>110101=>[2,1,1,1,1]
[3,4,6,2,7,5,1]=>[5,4,2,6,1,3,7]=>110100=>[2,1,1,2]
[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>110011=>[2,2,2]
[3,4,6,5,1,7,2]=>[5,4,2,3,7,1,6]=>110010=>[2,2,1,1]
[3,4,6,5,2,1,7]=>[5,4,2,3,6,7,1]=>110001=>[2,3,1]
[3,4,6,5,2,7,1]=>[5,4,2,3,6,1,7]=>110010=>[2,2,1,1]
[3,4,6,5,7,1,2]=>[5,4,2,3,1,7,6]=>110101=>[2,1,1,1,1]
[3,4,6,5,7,2,1]=>[5,4,2,3,1,6,7]=>110100=>[2,1,1,2]
[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]=>111011=>[3,1,2]
[3,4,6,7,1,5,2]=>[5,4,2,1,7,3,6]=>111010=>[3,1,1,1]
[3,4,6,7,2,1,5]=>[5,4,2,1,6,7,3]=>111001=>[3,2,1]
[3,4,6,7,2,5,1]=>[5,4,2,1,6,3,7]=>111010=>[3,1,1,1]
[3,4,6,7,5,1,2]=>[5,4,2,1,3,7,6]=>111001=>[3,2,1]
[3,4,6,7,5,2,1]=>[5,4,2,1,3,6,7]=>111000=>[3,3]
[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>110111=>[2,1,3]
[3,4,7,1,2,6,5]=>[5,4,1,7,6,2,3]=>110110=>[2,1,2,1]
[3,4,7,1,5,2,6]=>[5,4,1,7,3,6,2]=>110101=>[2,1,1,1,1]
[3,4,7,1,5,6,2]=>[5,4,1,7,3,2,6]=>110110=>[2,1,2,1]
[3,4,7,1,6,2,5]=>[5,4,1,7,2,6,3]=>110101=>[2,1,1,1,1]
[3,4,7,1,6,5,2]=>[5,4,1,7,2,3,6]=>110100=>[2,1,1,2]
[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>110011=>[2,2,2]
[3,4,7,2,1,6,5]=>[5,4,1,6,7,2,3]=>110010=>[2,2,1,1]
[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>110101=>[2,1,1,1,1]
[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>110110=>[2,1,2,1]
[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>110101=>[2,1,1,1,1]
[3,4,7,2,6,5,1]=>[5,4,1,6,2,3,7]=>110100=>[2,1,1,2]
[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>110011=>[2,2,2]
[3,4,7,5,1,6,2]=>[5,4,1,3,7,2,6]=>110010=>[2,2,1,1]
[3,4,7,5,2,1,6]=>[5,4,1,3,6,7,2]=>110001=>[2,3,1]
[3,4,7,5,2,6,1]=>[5,4,1,3,6,2,7]=>110010=>[2,2,1,1]
[3,4,7,5,6,1,2]=>[5,4,1,3,2,7,6]=>110101=>[2,1,1,1,1]
[3,4,7,5,6,2,1]=>[5,4,1,3,2,6,7]=>110100=>[2,1,1,2]
[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>110011=>[2,2,2]
[3,4,7,6,1,5,2]=>[5,4,1,2,7,3,6]=>110010=>[2,2,1,1]
[3,4,7,6,2,1,5]=>[5,4,1,2,6,7,3]=>110001=>[2,3,1]
[3,4,7,6,2,5,1]=>[5,4,1,2,6,3,7]=>110010=>[2,2,1,1]
[3,4,7,6,5,1,2]=>[5,4,1,2,3,7,6]=>110001=>[2,3,1]
[3,4,7,6,5,2,1]=>[5,4,1,2,3,6,7]=>110000=>[2,4]
[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>101111=>[1,1,4]
[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]=>101110=>[1,1,3,1]
[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]=>101101=>[1,1,2,1,1]
[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]=>101110=>[1,1,3,1]
[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]=>101101=>[1,1,2,1,1]
[3,5,1,2,7,6,4]=>[5,3,7,6,1,2,4]=>101100=>[1,1,2,2]
[3,5,1,4,2,6,7]=>[5,3,7,4,6,2,1]=>101011=>[1,1,1,1,2]
[3,5,1,4,2,7,6]=>[5,3,7,4,6,1,2]=>101010=>[1,1,1,1,1,1]
[3,5,1,4,6,2,7]=>[5,3,7,4,2,6,1]=>101101=>[1,1,2,1,1]
[3,5,1,4,6,7,2]=>[5,3,7,4,2,1,6]=>101110=>[1,1,3,1]
[3,5,1,4,7,2,6]=>[5,3,7,4,1,6,2]=>101101=>[1,1,2,1,1]
[3,5,1,4,7,6,2]=>[5,3,7,4,1,2,6]=>101100=>[1,1,2,2]
[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]=>101011=>[1,1,1,1,2]
[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]=>101010=>[1,1,1,1,1,1]
[3,5,1,6,4,2,7]=>[5,3,7,2,4,6,1]=>101001=>[1,1,1,2,1]
[3,5,1,6,4,7,2]=>[5,3,7,2,4,1,6]=>101010=>[1,1,1,1,1,1]
[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]=>101101=>[1,1,2,1,1]
[3,5,1,6,7,4,2]=>[5,3,7,2,1,4,6]=>101100=>[1,1,2,2]
[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]=>101011=>[1,1,1,1,2]
[3,5,1,7,2,6,4]=>[5,3,7,1,6,2,4]=>101010=>[1,1,1,1,1,1]
[3,5,1,7,4,2,6]=>[5,3,7,1,4,6,2]=>101001=>[1,1,1,2,1]
[3,5,1,7,4,6,2]=>[5,3,7,1,4,2,6]=>101010=>[1,1,1,1,1,1]
[3,5,1,7,6,2,4]=>[5,3,7,1,2,6,4]=>101001=>[1,1,1,2,1]
[3,5,1,7,6,4,2]=>[5,3,7,1,2,4,6]=>101000=>[1,1,1,3]
[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>100111=>[1,2,3]
[3,5,2,1,4,7,6]=>[5,3,6,7,4,1,2]=>100110=>[1,2,2,1]
[3,5,2,1,6,4,7]=>[5,3,6,7,2,4,1]=>100101=>[1,2,1,1,1]
[3,5,2,1,6,7,4]=>[5,3,6,7,2,1,4]=>100110=>[1,2,2,1]
[3,5,2,1,7,4,6]=>[5,3,6,7,1,4,2]=>100101=>[1,2,1,1,1]
[3,5,2,1,7,6,4]=>[5,3,6,7,1,2,4]=>100100=>[1,2,1,2]
[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>101011=>[1,1,1,1,2]
[3,5,2,4,1,7,6]=>[5,3,6,4,7,1,2]=>101010=>[1,1,1,1,1,1]
[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>101101=>[1,1,2,1,1]
[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>101110=>[1,1,3,1]
[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>101101=>[1,1,2,1,1]
[3,5,2,4,7,6,1]=>[5,3,6,4,1,2,7]=>101100=>[1,1,2,2]
[3,5,2,6,1,4,7]=>[5,3,6,2,7,4,1]=>101011=>[1,1,1,1,2]
[3,5,2,6,1,7,4]=>[5,3,6,2,7,1,4]=>101010=>[1,1,1,1,1,1]
[3,5,2,6,4,1,7]=>[5,3,6,2,4,7,1]=>101001=>[1,1,1,2,1]
[3,5,2,6,4,7,1]=>[5,3,6,2,4,1,7]=>101010=>[1,1,1,1,1,1]
[3,5,2,6,7,1,4]=>[5,3,6,2,1,7,4]=>101101=>[1,1,2,1,1]
[3,5,2,6,7,4,1]=>[5,3,6,2,1,4,7]=>101100=>[1,1,2,2]
[3,5,2,7,1,4,6]=>[5,3,6,1,7,4,2]=>101011=>[1,1,1,1,2]
[3,5,2,7,1,6,4]=>[5,3,6,1,7,2,4]=>101010=>[1,1,1,1,1,1]
[3,5,2,7,4,1,6]=>[5,3,6,1,4,7,2]=>101001=>[1,1,1,2,1]
[3,5,2,7,4,6,1]=>[5,3,6,1,4,2,7]=>101010=>[1,1,1,1,1,1]
[3,5,2,7,6,1,4]=>[5,3,6,1,2,7,4]=>101001=>[1,1,1,2,1]
[3,5,2,7,6,4,1]=>[5,3,6,1,2,4,7]=>101000=>[1,1,1,3]
[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>100111=>[1,2,3]
[3,5,4,1,2,7,6]=>[5,3,4,7,6,1,2]=>100110=>[1,2,2,1]
[3,5,4,1,6,2,7]=>[5,3,4,7,2,6,1]=>100101=>[1,2,1,1,1]
[3,5,4,1,6,7,2]=>[5,3,4,7,2,1,6]=>100110=>[1,2,2,1]
[3,5,4,1,7,2,6]=>[5,3,4,7,1,6,2]=>100101=>[1,2,1,1,1]
[3,5,4,1,7,6,2]=>[5,3,4,7,1,2,6]=>100100=>[1,2,1,2]
[3,5,4,2,1,6,7]=>[5,3,4,6,7,2,1]=>100011=>[1,3,2]
[3,5,4,2,1,7,6]=>[5,3,4,6,7,1,2]=>100010=>[1,3,1,1]
[3,5,4,2,6,1,7]=>[5,3,4,6,2,7,1]=>100101=>[1,2,1,1,1]
[3,5,4,2,6,7,1]=>[5,3,4,6,2,1,7]=>100110=>[1,2,2,1]
[3,5,4,2,7,1,6]=>[5,3,4,6,1,7,2]=>100101=>[1,2,1,1,1]
[3,5,4,2,7,6,1]=>[5,3,4,6,1,2,7]=>100100=>[1,2,1,2]
[3,5,4,6,1,2,7]=>[5,3,4,2,7,6,1]=>101011=>[1,1,1,1,2]
[3,5,4,6,1,7,2]=>[5,3,4,2,7,1,6]=>101010=>[1,1,1,1,1,1]
[3,5,4,6,2,1,7]=>[5,3,4,2,6,7,1]=>101001=>[1,1,1,2,1]
[3,5,4,6,2,7,1]=>[5,3,4,2,6,1,7]=>101010=>[1,1,1,1,1,1]
[3,5,4,6,7,1,2]=>[5,3,4,2,1,7,6]=>101101=>[1,1,2,1,1]
[3,5,4,6,7,2,1]=>[5,3,4,2,1,6,7]=>101100=>[1,1,2,2]
[3,5,4,7,1,2,6]=>[5,3,4,1,7,6,2]=>101011=>[1,1,1,1,2]
[3,5,4,7,1,6,2]=>[5,3,4,1,7,2,6]=>101010=>[1,1,1,1,1,1]
[3,5,4,7,2,1,6]=>[5,3,4,1,6,7,2]=>101001=>[1,1,1,2,1]
[3,5,4,7,2,6,1]=>[5,3,4,1,6,2,7]=>101010=>[1,1,1,1,1,1]
[3,5,4,7,6,1,2]=>[5,3,4,1,2,7,6]=>101001=>[1,1,1,2,1]
[3,5,4,7,6,2,1]=>[5,3,4,1,2,6,7]=>101000=>[1,1,1,3]
[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>110111=>[2,1,3]
[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]=>110110=>[2,1,2,1]
[3,5,6,1,4,2,7]=>[5,3,2,7,4,6,1]=>110101=>[2,1,1,1,1]
[3,5,6,1,4,7,2]=>[5,3,2,7,4,1,6]=>110110=>[2,1,2,1]
[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]=>110101=>[2,1,1,1,1]
[3,5,6,1,7,4,2]=>[5,3,2,7,1,4,6]=>110100=>[2,1,1,2]
[3,5,6,2,1,4,7]=>[5,3,2,6,7,4,1]=>110011=>[2,2,2]
[3,5,6,2,1,7,4]=>[5,3,2,6,7,1,4]=>110010=>[2,2,1,1]
[3,5,6,2,4,1,7]=>[5,3,2,6,4,7,1]=>110101=>[2,1,1,1,1]
[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>110110=>[2,1,2,1]
[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>110101=>[2,1,1,1,1]
[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>110100=>[2,1,1,2]
[3,5,6,4,1,2,7]=>[5,3,2,4,7,6,1]=>110011=>[2,2,2]
[3,5,6,4,1,7,2]=>[5,3,2,4,7,1,6]=>110010=>[2,2,1,1]
[3,5,6,4,2,1,7]=>[5,3,2,4,6,7,1]=>110001=>[2,3,1]
[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>110010=>[2,2,1,1]
[3,5,6,4,7,1,2]=>[5,3,2,4,1,7,6]=>110101=>[2,1,1,1,1]
[3,5,6,4,7,2,1]=>[5,3,2,4,1,6,7]=>110100=>[2,1,1,2]
[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]=>111011=>[3,1,2]
[3,5,6,7,1,4,2]=>[5,3,2,1,7,4,6]=>111010=>[3,1,1,1]
[3,5,6,7,2,1,4]=>[5,3,2,1,6,7,4]=>111001=>[3,2,1]
[3,5,6,7,2,4,1]=>[5,3,2,1,6,4,7]=>111010=>[3,1,1,1]
[3,5,6,7,4,1,2]=>[5,3,2,1,4,7,6]=>111001=>[3,2,1]
[3,5,6,7,4,2,1]=>[5,3,2,1,4,6,7]=>111000=>[3,3]
[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>110111=>[2,1,3]
[3,5,7,1,2,6,4]=>[5,3,1,7,6,2,4]=>110110=>[2,1,2,1]
[3,5,7,1,4,2,6]=>[5,3,1,7,4,6,2]=>110101=>[2,1,1,1,1]
[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>110110=>[2,1,2,1]
[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>110101=>[2,1,1,1,1]
[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>110100=>[2,1,1,2]
[3,5,7,2,1,4,6]=>[5,3,1,6,7,4,2]=>110011=>[2,2,2]
[3,5,7,2,1,6,4]=>[5,3,1,6,7,2,4]=>110010=>[2,2,1,1]
[3,5,7,2,4,1,6]=>[5,3,1,6,4,7,2]=>110101=>[2,1,1,1,1]
[3,5,7,2,4,6,1]=>[5,3,1,6,4,2,7]=>110110=>[2,1,2,1]
[3,5,7,2,6,1,4]=>[5,3,1,6,2,7,4]=>110101=>[2,1,1,1,1]
[3,5,7,2,6,4,1]=>[5,3,1,6,2,4,7]=>110100=>[2,1,1,2]
[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>110011=>[2,2,2]
[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>110010=>[2,2,1,1]
[3,5,7,4,2,1,6]=>[5,3,1,4,6,7,2]=>110001=>[2,3,1]
[3,5,7,4,2,6,1]=>[5,3,1,4,6,2,7]=>110010=>[2,2,1,1]
[3,5,7,4,6,1,2]=>[5,3,1,4,2,7,6]=>110101=>[2,1,1,1,1]
[3,5,7,4,6,2,1]=>[5,3,1,4,2,6,7]=>110100=>[2,1,1,2]
[3,5,7,6,1,2,4]=>[5,3,1,2,7,6,4]=>110011=>[2,2,2]
[3,5,7,6,1,4,2]=>[5,3,1,2,7,4,6]=>110010=>[2,2,1,1]
[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>110001=>[2,3,1]
[3,5,7,6,2,4,1]=>[5,3,1,2,6,4,7]=>110010=>[2,2,1,1]
[3,5,7,6,4,1,2]=>[5,3,1,2,4,7,6]=>110001=>[2,3,1]
[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>110000=>[2,4]
[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>101111=>[1,1,4]
[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]=>101110=>[1,1,3,1]
[3,6,1,2,5,4,7]=>[5,2,7,6,3,4,1]=>101101=>[1,1,2,1,1]
[3,6,1,2,5,7,4]=>[5,2,7,6,3,1,4]=>101110=>[1,1,3,1]
[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]=>101101=>[1,1,2,1,1]
[3,6,1,2,7,5,4]=>[5,2,7,6,1,3,4]=>101100=>[1,1,2,2]
[3,6,1,4,2,5,7]=>[5,2,7,4,6,3,1]=>101011=>[1,1,1,1,2]
[3,6,1,4,2,7,5]=>[5,2,7,4,6,1,3]=>101010=>[1,1,1,1,1,1]
[3,6,1,4,5,2,7]=>[5,2,7,4,3,6,1]=>101101=>[1,1,2,1,1]
[3,6,1,4,5,7,2]=>[5,2,7,4,3,1,6]=>101110=>[1,1,3,1]
[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>101101=>[1,1,2,1,1]
[3,6,1,4,7,5,2]=>[5,2,7,4,1,3,6]=>101100=>[1,1,2,2]
[3,6,1,5,2,4,7]=>[5,2,7,3,6,4,1]=>101011=>[1,1,1,1,2]
[3,6,1,5,2,7,4]=>[5,2,7,3,6,1,4]=>101010=>[1,1,1,1,1,1]
[3,6,1,5,4,2,7]=>[5,2,7,3,4,6,1]=>101001=>[1,1,1,2,1]
[3,6,1,5,4,7,2]=>[5,2,7,3,4,1,6]=>101010=>[1,1,1,1,1,1]
[3,6,1,5,7,2,4]=>[5,2,7,3,1,6,4]=>101101=>[1,1,2,1,1]
[3,6,1,5,7,4,2]=>[5,2,7,3,1,4,6]=>101100=>[1,1,2,2]
[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]=>101011=>[1,1,1,1,2]
[3,6,1,7,2,5,4]=>[5,2,7,1,6,3,4]=>101010=>[1,1,1,1,1,1]
[3,6,1,7,4,2,5]=>[5,2,7,1,4,6,3]=>101001=>[1,1,1,2,1]
[3,6,1,7,4,5,2]=>[5,2,7,1,4,3,6]=>101010=>[1,1,1,1,1,1]
[3,6,1,7,5,2,4]=>[5,2,7,1,3,6,4]=>101001=>[1,1,1,2,1]
[3,6,1,7,5,4,2]=>[5,2,7,1,3,4,6]=>101000=>[1,1,1,3]
[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>100111=>[1,2,3]
[3,6,2,1,4,7,5]=>[5,2,6,7,4,1,3]=>100110=>[1,2,2,1]
[3,6,2,1,5,4,7]=>[5,2,6,7,3,4,1]=>100101=>[1,2,1,1,1]
[3,6,2,1,5,7,4]=>[5,2,6,7,3,1,4]=>100110=>[1,2,2,1]
[3,6,2,1,7,4,5]=>[5,2,6,7,1,4,3]=>100101=>[1,2,1,1,1]
[3,6,2,1,7,5,4]=>[5,2,6,7,1,3,4]=>100100=>[1,2,1,2]
[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>101011=>[1,1,1,1,2]
[3,6,2,4,1,7,5]=>[5,2,6,4,7,1,3]=>101010=>[1,1,1,1,1,1]
[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>101101=>[1,1,2,1,1]
[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>101110=>[1,1,3,1]
[3,6,2,4,7,1,5]=>[5,2,6,4,1,7,3]=>101101=>[1,1,2,1,1]
[3,6,2,4,7,5,1]=>[5,2,6,4,1,3,7]=>101100=>[1,1,2,2]
[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>101011=>[1,1,1,1,2]
[3,6,2,5,1,7,4]=>[5,2,6,3,7,1,4]=>101010=>[1,1,1,1,1,1]
[3,6,2,5,4,1,7]=>[5,2,6,3,4,7,1]=>101001=>[1,1,1,2,1]
[3,6,2,5,4,7,1]=>[5,2,6,3,4,1,7]=>101010=>[1,1,1,1,1,1]
[3,6,2,5,7,1,4]=>[5,2,6,3,1,7,4]=>101101=>[1,1,2,1,1]
[3,6,2,5,7,4,1]=>[5,2,6,3,1,4,7]=>101100=>[1,1,2,2]
[3,6,2,7,1,4,5]=>[5,2,6,1,7,4,3]=>101011=>[1,1,1,1,2]
[3,6,2,7,1,5,4]=>[5,2,6,1,7,3,4]=>101010=>[1,1,1,1,1,1]
[3,6,2,7,4,1,5]=>[5,2,6,1,4,7,3]=>101001=>[1,1,1,2,1]
[3,6,2,7,4,5,1]=>[5,2,6,1,4,3,7]=>101010=>[1,1,1,1,1,1]
[3,6,2,7,5,1,4]=>[5,2,6,1,3,7,4]=>101001=>[1,1,1,2,1]
[3,6,2,7,5,4,1]=>[5,2,6,1,3,4,7]=>101000=>[1,1,1,3]
[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>100111=>[1,2,3]
[3,6,4,1,2,7,5]=>[5,2,4,7,6,1,3]=>100110=>[1,2,2,1]
[3,6,4,1,5,2,7]=>[5,2,4,7,3,6,1]=>100101=>[1,2,1,1,1]
[3,6,4,1,5,7,2]=>[5,2,4,7,3,1,6]=>100110=>[1,2,2,1]
[3,6,4,1,7,2,5]=>[5,2,4,7,1,6,3]=>100101=>[1,2,1,1,1]
[3,6,4,1,7,5,2]=>[5,2,4,7,1,3,6]=>100100=>[1,2,1,2]
[3,6,4,2,1,5,7]=>[5,2,4,6,7,3,1]=>100011=>[1,3,2]
[3,6,4,2,1,7,5]=>[5,2,4,6,7,1,3]=>100010=>[1,3,1,1]
[3,6,4,2,5,1,7]=>[5,2,4,6,3,7,1]=>100101=>[1,2,1,1,1]
[3,6,4,2,5,7,1]=>[5,2,4,6,3,1,7]=>100110=>[1,2,2,1]
[3,6,4,2,7,1,5]=>[5,2,4,6,1,7,3]=>100101=>[1,2,1,1,1]
[3,6,4,2,7,5,1]=>[5,2,4,6,1,3,7]=>100100=>[1,2,1,2]
[3,6,4,5,1,2,7]=>[5,2,4,3,7,6,1]=>101011=>[1,1,1,1,2]
[3,6,4,5,1,7,2]=>[5,2,4,3,7,1,6]=>101010=>[1,1,1,1,1,1]
[3,6,4,5,2,1,7]=>[5,2,4,3,6,7,1]=>101001=>[1,1,1,2,1]
[3,6,4,5,2,7,1]=>[5,2,4,3,6,1,7]=>101010=>[1,1,1,1,1,1]
[3,6,4,5,7,1,2]=>[5,2,4,3,1,7,6]=>101101=>[1,1,2,1,1]
[3,6,4,5,7,2,1]=>[5,2,4,3,1,6,7]=>101100=>[1,1,2,2]
[3,6,4,7,1,2,5]=>[5,2,4,1,7,6,3]=>101011=>[1,1,1,1,2]
[3,6,4,7,1,5,2]=>[5,2,4,1,7,3,6]=>101010=>[1,1,1,1,1,1]
[3,6,4,7,2,1,5]=>[5,2,4,1,6,7,3]=>101001=>[1,1,1,2,1]
[3,6,4,7,2,5,1]=>[5,2,4,1,6,3,7]=>101010=>[1,1,1,1,1,1]
[3,6,4,7,5,1,2]=>[5,2,4,1,3,7,6]=>101001=>[1,1,1,2,1]
[3,6,4,7,5,2,1]=>[5,2,4,1,3,6,7]=>101000=>[1,1,1,3]
[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>100111=>[1,2,3]
[3,6,5,1,2,7,4]=>[5,2,3,7,6,1,4]=>100110=>[1,2,2,1]
[3,6,5,1,4,2,7]=>[5,2,3,7,4,6,1]=>100101=>[1,2,1,1,1]
[3,6,5,1,4,7,2]=>[5,2,3,7,4,1,6]=>100110=>[1,2,2,1]
[3,6,5,1,7,2,4]=>[5,2,3,7,1,6,4]=>100101=>[1,2,1,1,1]
[3,6,5,1,7,4,2]=>[5,2,3,7,1,4,6]=>100100=>[1,2,1,2]
[3,6,5,2,1,4,7]=>[5,2,3,6,7,4,1]=>100011=>[1,3,2]
[3,6,5,2,1,7,4]=>[5,2,3,6,7,1,4]=>100010=>[1,3,1,1]
[3,6,5,2,4,1,7]=>[5,2,3,6,4,7,1]=>100101=>[1,2,1,1,1]
[3,6,5,2,4,7,1]=>[5,2,3,6,4,1,7]=>100110=>[1,2,2,1]
[3,6,5,2,7,1,4]=>[5,2,3,6,1,7,4]=>100101=>[1,2,1,1,1]
[3,6,5,2,7,4,1]=>[5,2,3,6,1,4,7]=>100100=>[1,2,1,2]
[3,6,5,4,1,2,7]=>[5,2,3,4,7,6,1]=>100011=>[1,3,2]
[3,6,5,4,1,7,2]=>[5,2,3,4,7,1,6]=>100010=>[1,3,1,1]
[3,6,5,4,2,1,7]=>[5,2,3,4,6,7,1]=>100001=>[1,4,1]
[3,6,5,4,2,7,1]=>[5,2,3,4,6,1,7]=>100010=>[1,3,1,1]
[3,6,5,4,7,1,2]=>[5,2,3,4,1,7,6]=>100101=>[1,2,1,1,1]
[3,6,5,4,7,2,1]=>[5,2,3,4,1,6,7]=>100100=>[1,2,1,2]
[3,6,5,7,1,2,4]=>[5,2,3,1,7,6,4]=>101011=>[1,1,1,1,2]
[3,6,5,7,1,4,2]=>[5,2,3,1,7,4,6]=>101010=>[1,1,1,1,1,1]
[3,6,5,7,2,1,4]=>[5,2,3,1,6,7,4]=>101001=>[1,1,1,2,1]
[3,6,5,7,2,4,1]=>[5,2,3,1,6,4,7]=>101010=>[1,1,1,1,1,1]
[3,6,5,7,4,1,2]=>[5,2,3,1,4,7,6]=>101001=>[1,1,1,2,1]
[3,6,5,7,4,2,1]=>[5,2,3,1,4,6,7]=>101000=>[1,1,1,3]
[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>110111=>[2,1,3]
[3,6,7,1,2,5,4]=>[5,2,1,7,6,3,4]=>110110=>[2,1,2,1]
[3,6,7,1,4,2,5]=>[5,2,1,7,4,6,3]=>110101=>[2,1,1,1,1]
[3,6,7,1,4,5,2]=>[5,2,1,7,4,3,6]=>110110=>[2,1,2,1]
[3,6,7,1,5,2,4]=>[5,2,1,7,3,6,4]=>110101=>[2,1,1,1,1]
[3,6,7,1,5,4,2]=>[5,2,1,7,3,4,6]=>110100=>[2,1,1,2]
[3,6,7,2,1,4,5]=>[5,2,1,6,7,4,3]=>110011=>[2,2,2]
[3,6,7,2,1,5,4]=>[5,2,1,6,7,3,4]=>110010=>[2,2,1,1]
[3,6,7,2,4,1,5]=>[5,2,1,6,4,7,3]=>110101=>[2,1,1,1,1]
[3,6,7,2,4,5,1]=>[5,2,1,6,4,3,7]=>110110=>[2,1,2,1]
[3,6,7,2,5,1,4]=>[5,2,1,6,3,7,4]=>110101=>[2,1,1,1,1]
[3,6,7,2,5,4,1]=>[5,2,1,6,3,4,7]=>110100=>[2,1,1,2]
[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>110011=>[2,2,2]
[3,6,7,4,1,5,2]=>[5,2,1,4,7,3,6]=>110010=>[2,2,1,1]
[3,6,7,4,2,1,5]=>[5,2,1,4,6,7,3]=>110001=>[2,3,1]
[3,6,7,4,2,5,1]=>[5,2,1,4,6,3,7]=>110010=>[2,2,1,1]
[3,6,7,4,5,1,2]=>[5,2,1,4,3,7,6]=>110101=>[2,1,1,1,1]
[3,6,7,4,5,2,1]=>[5,2,1,4,3,6,7]=>110100=>[2,1,1,2]
[3,6,7,5,1,2,4]=>[5,2,1,3,7,6,4]=>110011=>[2,2,2]
[3,6,7,5,1,4,2]=>[5,2,1,3,7,4,6]=>110010=>[2,2,1,1]
[3,6,7,5,2,1,4]=>[5,2,1,3,6,7,4]=>110001=>[2,3,1]
[3,6,7,5,2,4,1]=>[5,2,1,3,6,4,7]=>110010=>[2,2,1,1]
[3,6,7,5,4,1,2]=>[5,2,1,3,4,7,6]=>110001=>[2,3,1]
[3,6,7,5,4,2,1]=>[5,2,1,3,4,6,7]=>110000=>[2,4]
[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>101111=>[1,1,4]
[3,7,1,2,4,6,5]=>[5,1,7,6,4,2,3]=>101110=>[1,1,3,1]
[3,7,1,2,5,4,6]=>[5,1,7,6,3,4,2]=>101101=>[1,1,2,1,1]
[3,7,1,2,5,6,4]=>[5,1,7,6,3,2,4]=>101110=>[1,1,3,1]
[3,7,1,2,6,4,5]=>[5,1,7,6,2,4,3]=>101101=>[1,1,2,1,1]
[3,7,1,2,6,5,4]=>[5,1,7,6,2,3,4]=>101100=>[1,1,2,2]
[3,7,1,4,2,5,6]=>[5,1,7,4,6,3,2]=>101011=>[1,1,1,1,2]
[3,7,1,4,2,6,5]=>[5,1,7,4,6,2,3]=>101010=>[1,1,1,1,1,1]
[3,7,1,4,5,2,6]=>[5,1,7,4,3,6,2]=>101101=>[1,1,2,1,1]
[3,7,1,4,5,6,2]=>[5,1,7,4,3,2,6]=>101110=>[1,1,3,1]
[3,7,1,4,6,2,5]=>[5,1,7,4,2,6,3]=>101101=>[1,1,2,1,1]
[3,7,1,4,6,5,2]=>[5,1,7,4,2,3,6]=>101100=>[1,1,2,2]
[3,7,1,5,2,4,6]=>[5,1,7,3,6,4,2]=>101011=>[1,1,1,1,2]
[3,7,1,5,2,6,4]=>[5,1,7,3,6,2,4]=>101010=>[1,1,1,1,1,1]
[3,7,1,5,4,2,6]=>[5,1,7,3,4,6,2]=>101001=>[1,1,1,2,1]
[3,7,1,5,4,6,2]=>[5,1,7,3,4,2,6]=>101010=>[1,1,1,1,1,1]
[3,7,1,5,6,2,4]=>[5,1,7,3,2,6,4]=>101101=>[1,1,2,1,1]
[3,7,1,5,6,4,2]=>[5,1,7,3,2,4,6]=>101100=>[1,1,2,2]
[3,7,1,6,2,4,5]=>[5,1,7,2,6,4,3]=>101011=>[1,1,1,1,2]
[3,7,1,6,2,5,4]=>[5,1,7,2,6,3,4]=>101010=>[1,1,1,1,1,1]
[3,7,1,6,4,2,5]=>[5,1,7,2,4,6,3]=>101001=>[1,1,1,2,1]
[3,7,1,6,4,5,2]=>[5,1,7,2,4,3,6]=>101010=>[1,1,1,1,1,1]
[3,7,1,6,5,2,4]=>[5,1,7,2,3,6,4]=>101001=>[1,1,1,2,1]
[3,7,1,6,5,4,2]=>[5,1,7,2,3,4,6]=>101000=>[1,1,1,3]
[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>100111=>[1,2,3]
[3,7,2,1,4,6,5]=>[5,1,6,7,4,2,3]=>100110=>[1,2,2,1]
[3,7,2,1,5,4,6]=>[5,1,6,7,3,4,2]=>100101=>[1,2,1,1,1]
[3,7,2,1,5,6,4]=>[5,1,6,7,3,2,4]=>100110=>[1,2,2,1]
[3,7,2,1,6,4,5]=>[5,1,6,7,2,4,3]=>100101=>[1,2,1,1,1]
[3,7,2,1,6,5,4]=>[5,1,6,7,2,3,4]=>100100=>[1,2,1,2]
[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>101011=>[1,1,1,1,2]
[3,7,2,4,1,6,5]=>[5,1,6,4,7,2,3]=>101010=>[1,1,1,1,1,1]
[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>101101=>[1,1,2,1,1]
[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>101110=>[1,1,3,1]
[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>101101=>[1,1,2,1,1]
[3,7,2,4,6,5,1]=>[5,1,6,4,2,3,7]=>101100=>[1,1,2,2]
[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>101011=>[1,1,1,1,2]
[3,7,2,5,1,6,4]=>[5,1,6,3,7,2,4]=>101010=>[1,1,1,1,1,1]
[3,7,2,5,4,1,6]=>[5,1,6,3,4,7,2]=>101001=>[1,1,1,2,1]
[3,7,2,5,4,6,1]=>[5,1,6,3,4,2,7]=>101010=>[1,1,1,1,1,1]
[3,7,2,5,6,1,4]=>[5,1,6,3,2,7,4]=>101101=>[1,1,2,1,1]
[3,7,2,5,6,4,1]=>[5,1,6,3,2,4,7]=>101100=>[1,1,2,2]
[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>101011=>[1,1,1,1,2]
[3,7,2,6,1,5,4]=>[5,1,6,2,7,3,4]=>101010=>[1,1,1,1,1,1]
[3,7,2,6,4,1,5]=>[5,1,6,2,4,7,3]=>101001=>[1,1,1,2,1]
[3,7,2,6,4,5,1]=>[5,1,6,2,4,3,7]=>101010=>[1,1,1,1,1,1]
[3,7,2,6,5,1,4]=>[5,1,6,2,3,7,4]=>101001=>[1,1,1,2,1]
[3,7,2,6,5,4,1]=>[5,1,6,2,3,4,7]=>101000=>[1,1,1,3]
[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>100111=>[1,2,3]
[3,7,4,1,2,6,5]=>[5,1,4,7,6,2,3]=>100110=>[1,2,2,1]
[3,7,4,1,5,2,6]=>[5,1,4,7,3,6,2]=>100101=>[1,2,1,1,1]
[3,7,4,1,5,6,2]=>[5,1,4,7,3,2,6]=>100110=>[1,2,2,1]
[3,7,4,1,6,2,5]=>[5,1,4,7,2,6,3]=>100101=>[1,2,1,1,1]
[3,7,4,1,6,5,2]=>[5,1,4,7,2,3,6]=>100100=>[1,2,1,2]
[3,7,4,2,1,5,6]=>[5,1,4,6,7,3,2]=>100011=>[1,3,2]
[3,7,4,2,1,6,5]=>[5,1,4,6,7,2,3]=>100010=>[1,3,1,1]
[3,7,4,2,5,1,6]=>[5,1,4,6,3,7,2]=>100101=>[1,2,1,1,1]
[3,7,4,2,5,6,1]=>[5,1,4,6,3,2,7]=>100110=>[1,2,2,1]
[3,7,4,2,6,1,5]=>[5,1,4,6,2,7,3]=>100101=>[1,2,1,1,1]
[3,7,4,2,6,5,1]=>[5,1,4,6,2,3,7]=>100100=>[1,2,1,2]
[3,7,4,5,1,2,6]=>[5,1,4,3,7,6,2]=>101011=>[1,1,1,1,2]
[3,7,4,5,1,6,2]=>[5,1,4,3,7,2,6]=>101010=>[1,1,1,1,1,1]
[3,7,4,5,2,1,6]=>[5,1,4,3,6,7,2]=>101001=>[1,1,1,2,1]
[3,7,4,5,2,6,1]=>[5,1,4,3,6,2,7]=>101010=>[1,1,1,1,1,1]
[3,7,4,5,6,1,2]=>[5,1,4,3,2,7,6]=>101101=>[1,1,2,1,1]
[3,7,4,5,6,2,1]=>[5,1,4,3,2,6,7]=>101100=>[1,1,2,2]
[3,7,4,6,1,2,5]=>[5,1,4,2,7,6,3]=>101011=>[1,1,1,1,2]
[3,7,4,6,1,5,2]=>[5,1,4,2,7,3,6]=>101010=>[1,1,1,1,1,1]
[3,7,4,6,2,1,5]=>[5,1,4,2,6,7,3]=>101001=>[1,1,1,2,1]
[3,7,4,6,2,5,1]=>[5,1,4,2,6,3,7]=>101010=>[1,1,1,1,1,1]
[3,7,4,6,5,1,2]=>[5,1,4,2,3,7,6]=>101001=>[1,1,1,2,1]
[3,7,4,6,5,2,1]=>[5,1,4,2,3,6,7]=>101000=>[1,1,1,3]
[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>100111=>[1,2,3]
[3,7,5,1,2,6,4]=>[5,1,3,7,6,2,4]=>100110=>[1,2,2,1]
[3,7,5,1,4,2,6]=>[5,1,3,7,4,6,2]=>100101=>[1,2,1,1,1]
[3,7,5,1,4,6,2]=>[5,1,3,7,4,2,6]=>100110=>[1,2,2,1]
[3,7,5,1,6,2,4]=>[5,1,3,7,2,6,4]=>100101=>[1,2,1,1,1]
[3,7,5,1,6,4,2]=>[5,1,3,7,2,4,6]=>100100=>[1,2,1,2]
[3,7,5,2,1,4,6]=>[5,1,3,6,7,4,2]=>100011=>[1,3,2]
[3,7,5,2,1,6,4]=>[5,1,3,6,7,2,4]=>100010=>[1,3,1,1]
[3,7,5,2,4,1,6]=>[5,1,3,6,4,7,2]=>100101=>[1,2,1,1,1]
[3,7,5,2,4,6,1]=>[5,1,3,6,4,2,7]=>100110=>[1,2,2,1]
[3,7,5,2,6,1,4]=>[5,1,3,6,2,7,4]=>100101=>[1,2,1,1,1]
[3,7,5,2,6,4,1]=>[5,1,3,6,2,4,7]=>100100=>[1,2,1,2]
[3,7,5,4,1,2,6]=>[5,1,3,4,7,6,2]=>100011=>[1,3,2]
[3,7,5,4,1,6,2]=>[5,1,3,4,7,2,6]=>100010=>[1,3,1,1]
[3,7,5,4,2,1,6]=>[5,1,3,4,6,7,2]=>100001=>[1,4,1]
[3,7,5,4,2,6,1]=>[5,1,3,4,6,2,7]=>100010=>[1,3,1,1]
[3,7,5,4,6,1,2]=>[5,1,3,4,2,7,6]=>100101=>[1,2,1,1,1]
[3,7,5,4,6,2,1]=>[5,1,3,4,2,6,7]=>100100=>[1,2,1,2]
[3,7,5,6,1,2,4]=>[5,1,3,2,7,6,4]=>101011=>[1,1,1,1,2]
[3,7,5,6,1,4,2]=>[5,1,3,2,7,4,6]=>101010=>[1,1,1,1,1,1]
[3,7,5,6,2,1,4]=>[5,1,3,2,6,7,4]=>101001=>[1,1,1,2,1]
[3,7,5,6,2,4,1]=>[5,1,3,2,6,4,7]=>101010=>[1,1,1,1,1,1]
[3,7,5,6,4,1,2]=>[5,1,3,2,4,7,6]=>101001=>[1,1,1,2,1]
[3,7,5,6,4,2,1]=>[5,1,3,2,4,6,7]=>101000=>[1,1,1,3]
[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>100111=>[1,2,3]
[3,7,6,1,2,5,4]=>[5,1,2,7,6,3,4]=>100110=>[1,2,2,1]
[3,7,6,1,4,2,5]=>[5,1,2,7,4,6,3]=>100101=>[1,2,1,1,1]
[3,7,6,1,4,5,2]=>[5,1,2,7,4,3,6]=>100110=>[1,2,2,1]
[3,7,6,1,5,2,4]=>[5,1,2,7,3,6,4]=>100101=>[1,2,1,1,1]
[3,7,6,1,5,4,2]=>[5,1,2,7,3,4,6]=>100100=>[1,2,1,2]
[3,7,6,2,1,4,5]=>[5,1,2,6,7,4,3]=>100011=>[1,3,2]
[3,7,6,2,1,5,4]=>[5,1,2,6,7,3,4]=>100010=>[1,3,1,1]
[3,7,6,2,4,1,5]=>[5,1,2,6,4,7,3]=>100101=>[1,2,1,1,1]
[3,7,6,2,4,5,1]=>[5,1,2,6,4,3,7]=>100110=>[1,2,2,1]
[3,7,6,2,5,1,4]=>[5,1,2,6,3,7,4]=>100101=>[1,2,1,1,1]
[3,7,6,2,5,4,1]=>[5,1,2,6,3,4,7]=>100100=>[1,2,1,2]
[3,7,6,4,1,2,5]=>[5,1,2,4,7,6,3]=>100011=>[1,3,2]
[3,7,6,4,1,5,2]=>[5,1,2,4,7,3,6]=>100010=>[1,3,1,1]
[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>100001=>[1,4,1]
[3,7,6,4,2,5,1]=>[5,1,2,4,6,3,7]=>100010=>[1,3,1,1]
[3,7,6,4,5,1,2]=>[5,1,2,4,3,7,6]=>100101=>[1,2,1,1,1]
[3,7,6,4,5,2,1]=>[5,1,2,4,3,6,7]=>100100=>[1,2,1,2]
[3,7,6,5,1,2,4]=>[5,1,2,3,7,6,4]=>100011=>[1,3,2]
[3,7,6,5,1,4,2]=>[5,1,2,3,7,4,6]=>100010=>[1,3,1,1]
[3,7,6,5,2,1,4]=>[5,1,2,3,6,7,4]=>100001=>[1,4,1]
[3,7,6,5,2,4,1]=>[5,1,2,3,6,4,7]=>100010=>[1,3,1,1]
[3,7,6,5,4,1,2]=>[5,1,2,3,4,7,6]=>100001=>[1,4,1]
[3,7,6,5,4,2,1]=>[5,1,2,3,4,6,7]=>100000=>[1,5]
[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>011111=>[1,5]
[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>011110=>[1,4,1]
[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>011101=>[1,3,1,1]
[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]=>011110=>[1,4,1]
[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>011101=>[1,3,1,1]
[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>011100=>[1,3,2]
[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]=>011011=>[1,2,1,2]
[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]=>011010=>[1,2,1,1,1]
[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]=>011101=>[1,3,1,1]
[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>011110=>[1,4,1]
[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>011101=>[1,3,1,1]
[4,1,2,5,7,6,3]=>[4,7,6,3,1,2,5]=>011100=>[1,3,2]
[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]=>011011=>[1,2,1,2]
[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>011010=>[1,2,1,1,1]
[4,1,2,6,5,3,7]=>[4,7,6,2,3,5,1]=>011001=>[1,2,2,1]
[4,1,2,6,5,7,3]=>[4,7,6,2,3,1,5]=>011010=>[1,2,1,1,1]
[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]=>011101=>[1,3,1,1]
[4,1,2,6,7,5,3]=>[4,7,6,2,1,3,5]=>011100=>[1,3,2]
[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>011011=>[1,2,1,2]
[4,1,2,7,3,6,5]=>[4,7,6,1,5,2,3]=>011010=>[1,2,1,1,1]
[4,1,2,7,5,3,6]=>[4,7,6,1,3,5,2]=>011001=>[1,2,2,1]
[4,1,2,7,5,6,3]=>[4,7,6,1,3,2,5]=>011010=>[1,2,1,1,1]
[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>011001=>[1,2,2,1]
[4,1,2,7,6,5,3]=>[4,7,6,1,2,3,5]=>011000=>[1,2,3]
[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>010111=>[1,1,1,3]
[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>010110=>[1,1,1,2,1]
[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>010101=>[1,1,1,1,1,1]
[4,1,3,2,6,7,5]=>[4,7,5,6,2,1,3]=>010110=>[1,1,1,2,1]
[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>010101=>[1,1,1,1,1,1]
[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>010100=>[1,1,1,1,2]
[4,1,3,5,2,6,7]=>[4,7,5,3,6,2,1]=>011011=>[1,2,1,2]
[4,1,3,5,2,7,6]=>[4,7,5,3,6,1,2]=>011010=>[1,2,1,1,1]
[4,1,3,5,6,2,7]=>[4,7,5,3,2,6,1]=>011101=>[1,3,1,1]
[4,1,3,5,6,7,2]=>[4,7,5,3,2,1,6]=>011110=>[1,4,1]
[4,1,3,5,7,2,6]=>[4,7,5,3,1,6,2]=>011101=>[1,3,1,1]
[4,1,3,5,7,6,2]=>[4,7,5,3,1,2,6]=>011100=>[1,3,2]
[4,1,3,6,2,5,7]=>[4,7,5,2,6,3,1]=>011011=>[1,2,1,2]
[4,1,3,6,2,7,5]=>[4,7,5,2,6,1,3]=>011010=>[1,2,1,1,1]
[4,1,3,6,5,2,7]=>[4,7,5,2,3,6,1]=>011001=>[1,2,2,1]
[4,1,3,6,5,7,2]=>[4,7,5,2,3,1,6]=>011010=>[1,2,1,1,1]
[4,1,3,6,7,2,5]=>[4,7,5,2,1,6,3]=>011101=>[1,3,1,1]
[4,1,3,6,7,5,2]=>[4,7,5,2,1,3,6]=>011100=>[1,3,2]
[4,1,3,7,2,5,6]=>[4,7,5,1,6,3,2]=>011011=>[1,2,1,2]
[4,1,3,7,2,6,5]=>[4,7,5,1,6,2,3]=>011010=>[1,2,1,1,1]
[4,1,3,7,5,2,6]=>[4,7,5,1,3,6,2]=>011001=>[1,2,2,1]
[4,1,3,7,5,6,2]=>[4,7,5,1,3,2,6]=>011010=>[1,2,1,1,1]
[4,1,3,7,6,2,5]=>[4,7,5,1,2,6,3]=>011001=>[1,2,2,1]
[4,1,3,7,6,5,2]=>[4,7,5,1,2,3,6]=>011000=>[1,2,3]
[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]=>010111=>[1,1,1,3]
[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]=>010110=>[1,1,1,2,1]
[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]=>010101=>[1,1,1,1,1,1]
[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]=>010110=>[1,1,1,2,1]
[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]=>010101=>[1,1,1,1,1,1]
[4,1,5,2,7,6,3]=>[4,7,3,6,1,2,5]=>010100=>[1,1,1,1,2]
[4,1,5,3,2,6,7]=>[4,7,3,5,6,2,1]=>010011=>[1,1,2,2]
[4,1,5,3,2,7,6]=>[4,7,3,5,6,1,2]=>010010=>[1,1,2,1,1]
[4,1,5,3,6,2,7]=>[4,7,3,5,2,6,1]=>010101=>[1,1,1,1,1,1]
[4,1,5,3,6,7,2]=>[4,7,3,5,2,1,6]=>010110=>[1,1,1,2,1]
[4,1,5,3,7,2,6]=>[4,7,3,5,1,6,2]=>010101=>[1,1,1,1,1,1]
[4,1,5,3,7,6,2]=>[4,7,3,5,1,2,6]=>010100=>[1,1,1,1,2]
[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]=>011011=>[1,2,1,2]
[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]=>011010=>[1,2,1,1,1]
[4,1,5,6,3,2,7]=>[4,7,3,2,5,6,1]=>011001=>[1,2,2,1]
[4,1,5,6,3,7,2]=>[4,7,3,2,5,1,6]=>011010=>[1,2,1,1,1]
[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]=>011101=>[1,3,1,1]
[4,1,5,6,7,3,2]=>[4,7,3,2,1,5,6]=>011100=>[1,3,2]
[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]=>011011=>[1,2,1,2]
[4,1,5,7,2,6,3]=>[4,7,3,1,6,2,5]=>011010=>[1,2,1,1,1]
[4,1,5,7,3,2,6]=>[4,7,3,1,5,6,2]=>011001=>[1,2,2,1]
[4,1,5,7,3,6,2]=>[4,7,3,1,5,2,6]=>011010=>[1,2,1,1,1]
[4,1,5,7,6,2,3]=>[4,7,3,1,2,6,5]=>011001=>[1,2,2,1]
[4,1,5,7,6,3,2]=>[4,7,3,1,2,5,6]=>011000=>[1,2,3]
[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]=>010111=>[1,1,1,3]
[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]=>010110=>[1,1,1,2,1]
[4,1,6,2,5,3,7]=>[4,7,2,6,3,5,1]=>010101=>[1,1,1,1,1,1]
[4,1,6,2,5,7,3]=>[4,7,2,6,3,1,5]=>010110=>[1,1,1,2,1]
[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]=>010101=>[1,1,1,1,1,1]
[4,1,6,2,7,5,3]=>[4,7,2,6,1,3,5]=>010100=>[1,1,1,1,2]
[4,1,6,3,2,5,7]=>[4,7,2,5,6,3,1]=>010011=>[1,1,2,2]
[4,1,6,3,2,7,5]=>[4,7,2,5,6,1,3]=>010010=>[1,1,2,1,1]
[4,1,6,3,5,2,7]=>[4,7,2,5,3,6,1]=>010101=>[1,1,1,1,1,1]
[4,1,6,3,5,7,2]=>[4,7,2,5,3,1,6]=>010110=>[1,1,1,2,1]
[4,1,6,3,7,2,5]=>[4,7,2,5,1,6,3]=>010101=>[1,1,1,1,1,1]
[4,1,6,3,7,5,2]=>[4,7,2,5,1,3,6]=>010100=>[1,1,1,1,2]
[4,1,6,5,2,3,7]=>[4,7,2,3,6,5,1]=>010011=>[1,1,2,2]
[4,1,6,5,2,7,3]=>[4,7,2,3,6,1,5]=>010010=>[1,1,2,1,1]
[4,1,6,5,3,2,7]=>[4,7,2,3,5,6,1]=>010001=>[1,1,3,1]
[4,1,6,5,3,7,2]=>[4,7,2,3,5,1,6]=>010010=>[1,1,2,1,1]
[4,1,6,5,7,2,3]=>[4,7,2,3,1,6,5]=>010101=>[1,1,1,1,1,1]
[4,1,6,5,7,3,2]=>[4,7,2,3,1,5,6]=>010100=>[1,1,1,1,2]
[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]=>011011=>[1,2,1,2]
[4,1,6,7,2,5,3]=>[4,7,2,1,6,3,5]=>011010=>[1,2,1,1,1]
[4,1,6,7,3,2,5]=>[4,7,2,1,5,6,3]=>011001=>[1,2,2,1]
[4,1,6,7,3,5,2]=>[4,7,2,1,5,3,6]=>011010=>[1,2,1,1,1]
[4,1,6,7,5,2,3]=>[4,7,2,1,3,6,5]=>011001=>[1,2,2,1]
[4,1,6,7,5,3,2]=>[4,7,2,1,3,5,6]=>011000=>[1,2,3]
[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]=>010111=>[1,1,1,3]
[4,1,7,2,3,6,5]=>[4,7,1,6,5,2,3]=>010110=>[1,1,1,2,1]
[4,1,7,2,5,3,6]=>[4,7,1,6,3,5,2]=>010101=>[1,1,1,1,1,1]
[4,1,7,2,5,6,3]=>[4,7,1,6,3,2,5]=>010110=>[1,1,1,2,1]
[4,1,7,2,6,3,5]=>[4,7,1,6,2,5,3]=>010101=>[1,1,1,1,1,1]
[4,1,7,2,6,5,3]=>[4,7,1,6,2,3,5]=>010100=>[1,1,1,1,2]
[4,1,7,3,2,5,6]=>[4,7,1,5,6,3,2]=>010011=>[1,1,2,2]
[4,1,7,3,2,6,5]=>[4,7,1,5,6,2,3]=>010010=>[1,1,2,1,1]
[4,1,7,3,5,2,6]=>[4,7,1,5,3,6,2]=>010101=>[1,1,1,1,1,1]
[4,1,7,3,5,6,2]=>[4,7,1,5,3,2,6]=>010110=>[1,1,1,2,1]
[4,1,7,3,6,2,5]=>[4,7,1,5,2,6,3]=>010101=>[1,1,1,1,1,1]
[4,1,7,3,6,5,2]=>[4,7,1,5,2,3,6]=>010100=>[1,1,1,1,2]
[4,1,7,5,2,3,6]=>[4,7,1,3,6,5,2]=>010011=>[1,1,2,2]
[4,1,7,5,2,6,3]=>[4,7,1,3,6,2,5]=>010010=>[1,1,2,1,1]
[4,1,7,5,3,2,6]=>[4,7,1,3,5,6,2]=>010001=>[1,1,3,1]
[4,1,7,5,3,6,2]=>[4,7,1,3,5,2,6]=>010010=>[1,1,2,1,1]
[4,1,7,5,6,2,3]=>[4,7,1,3,2,6,5]=>010101=>[1,1,1,1,1,1]
[4,1,7,5,6,3,2]=>[4,7,1,3,2,5,6]=>010100=>[1,1,1,1,2]
[4,1,7,6,2,3,5]=>[4,7,1,2,6,5,3]=>010011=>[1,1,2,2]
[4,1,7,6,2,5,3]=>[4,7,1,2,6,3,5]=>010010=>[1,1,2,1,1]
[4,1,7,6,3,2,5]=>[4,7,1,2,5,6,3]=>010001=>[1,1,3,1]
[4,1,7,6,3,5,2]=>[4,7,1,2,5,3,6]=>010010=>[1,1,2,1,1]
[4,1,7,6,5,2,3]=>[4,7,1,2,3,6,5]=>010001=>[1,1,3,1]
[4,1,7,6,5,3,2]=>[4,7,1,2,3,5,6]=>010000=>[1,1,4]
[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>001111=>[2,4]
[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>001110=>[2,3,1]
[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>001101=>[2,2,1,1]
[4,2,1,3,6,7,5]=>[4,6,7,5,2,1,3]=>001110=>[2,3,1]
[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>001101=>[2,2,1,1]
[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>001100=>[2,2,2]
[4,2,1,5,3,6,7]=>[4,6,7,3,5,2,1]=>001011=>[2,1,1,2]
[4,2,1,5,3,7,6]=>[4,6,7,3,5,1,2]=>001010=>[2,1,1,1,1]
[4,2,1,5,6,3,7]=>[4,6,7,3,2,5,1]=>001101=>[2,2,1,1]
[4,2,1,5,6,7,3]=>[4,6,7,3,2,1,5]=>001110=>[2,3,1]
[4,2,1,5,7,3,6]=>[4,6,7,3,1,5,2]=>001101=>[2,2,1,1]
[4,2,1,5,7,6,3]=>[4,6,7,3,1,2,5]=>001100=>[2,2,2]
[4,2,1,6,3,5,7]=>[4,6,7,2,5,3,1]=>001011=>[2,1,1,2]
[4,2,1,6,3,7,5]=>[4,6,7,2,5,1,3]=>001010=>[2,1,1,1,1]
[4,2,1,6,5,3,7]=>[4,6,7,2,3,5,1]=>001001=>[2,1,2,1]
[4,2,1,6,5,7,3]=>[4,6,7,2,3,1,5]=>001010=>[2,1,1,1,1]
[4,2,1,6,7,3,5]=>[4,6,7,2,1,5,3]=>001101=>[2,2,1,1]
[4,2,1,6,7,5,3]=>[4,6,7,2,1,3,5]=>001100=>[2,2,2]
[4,2,1,7,3,5,6]=>[4,6,7,1,5,3,2]=>001011=>[2,1,1,2]
[4,2,1,7,3,6,5]=>[4,6,7,1,5,2,3]=>001010=>[2,1,1,1,1]
[4,2,1,7,5,3,6]=>[4,6,7,1,3,5,2]=>001001=>[2,1,2,1]
[4,2,1,7,5,6,3]=>[4,6,7,1,3,2,5]=>001010=>[2,1,1,1,1]
[4,2,1,7,6,3,5]=>[4,6,7,1,2,5,3]=>001001=>[2,1,2,1]
[4,2,1,7,6,5,3]=>[4,6,7,1,2,3,5]=>001000=>[2,1,3]
[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>010111=>[1,1,1,3]
[4,2,3,1,5,7,6]=>[4,6,5,7,3,1,2]=>010110=>[1,1,1,2,1]
[4,2,3,1,6,5,7]=>[4,6,5,7,2,3,1]=>010101=>[1,1,1,1,1,1]
[4,2,3,1,6,7,5]=>[4,6,5,7,2,1,3]=>010110=>[1,1,1,2,1]
[4,2,3,1,7,5,6]=>[4,6,5,7,1,3,2]=>010101=>[1,1,1,1,1,1]
[4,2,3,1,7,6,5]=>[4,6,5,7,1,2,3]=>010100=>[1,1,1,1,2]
[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>011011=>[1,2,1,2]
[4,2,3,5,1,7,6]=>[4,6,5,3,7,1,2]=>011010=>[1,2,1,1,1]
[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>011101=>[1,3,1,1]
[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>011110=>[1,4,1]
[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>011101=>[1,3,1,1]
[4,2,3,5,7,6,1]=>[4,6,5,3,1,2,7]=>011100=>[1,3,2]
[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>011011=>[1,2,1,2]
[4,2,3,6,1,7,5]=>[4,6,5,2,7,1,3]=>011010=>[1,2,1,1,1]
[4,2,3,6,5,1,7]=>[4,6,5,2,3,7,1]=>011001=>[1,2,2,1]
[4,2,3,6,5,7,1]=>[4,6,5,2,3,1,7]=>011010=>[1,2,1,1,1]
[4,2,3,6,7,1,5]=>[4,6,5,2,1,7,3]=>011101=>[1,3,1,1]
[4,2,3,6,7,5,1]=>[4,6,5,2,1,3,7]=>011100=>[1,3,2]
[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>011011=>[1,2,1,2]
[4,2,3,7,1,6,5]=>[4,6,5,1,7,2,3]=>011010=>[1,2,1,1,1]
[4,2,3,7,5,1,6]=>[4,6,5,1,3,7,2]=>011001=>[1,2,2,1]
[4,2,3,7,5,6,1]=>[4,6,5,1,3,2,7]=>011010=>[1,2,1,1,1]
[4,2,3,7,6,1,5]=>[4,6,5,1,2,7,3]=>011001=>[1,2,2,1]
[4,2,3,7,6,5,1]=>[4,6,5,1,2,3,7]=>011000=>[1,2,3]
[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>010111=>[1,1,1,3]
[4,2,5,1,3,7,6]=>[4,6,3,7,5,1,2]=>010110=>[1,1,1,2,1]
[4,2,5,1,6,3,7]=>[4,6,3,7,2,5,1]=>010101=>[1,1,1,1,1,1]
[4,2,5,1,6,7,3]=>[4,6,3,7,2,1,5]=>010110=>[1,1,1,2,1]
[4,2,5,1,7,3,6]=>[4,6,3,7,1,5,2]=>010101=>[1,1,1,1,1,1]
[4,2,5,1,7,6,3]=>[4,6,3,7,1,2,5]=>010100=>[1,1,1,1,2]
[4,2,5,3,1,6,7]=>[4,6,3,5,7,2,1]=>010011=>[1,1,2,2]
[4,2,5,3,1,7,6]=>[4,6,3,5,7,1,2]=>010010=>[1,1,2,1,1]
[4,2,5,3,6,1,7]=>[4,6,3,5,2,7,1]=>010101=>[1,1,1,1,1,1]
[4,2,5,3,6,7,1]=>[4,6,3,5,2,1,7]=>010110=>[1,1,1,2,1]
[4,2,5,3,7,1,6]=>[4,6,3,5,1,7,2]=>010101=>[1,1,1,1,1,1]
[4,2,5,3,7,6,1]=>[4,6,3,5,1,2,7]=>010100=>[1,1,1,1,2]
[4,2,5,6,1,3,7]=>[4,6,3,2,7,5,1]=>011011=>[1,2,1,2]
[4,2,5,6,1,7,3]=>[4,6,3,2,7,1,5]=>011010=>[1,2,1,1,1]
[4,2,5,6,3,1,7]=>[4,6,3,2,5,7,1]=>011001=>[1,2,2,1]
[4,2,5,6,3,7,1]=>[4,6,3,2,5,1,7]=>011010=>[1,2,1,1,1]
[4,2,5,6,7,1,3]=>[4,6,3,2,1,7,5]=>011101=>[1,3,1,1]
[4,2,5,6,7,3,1]=>[4,6,3,2,1,5,7]=>011100=>[1,3,2]
[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>011011=>[1,2,1,2]
[4,2,5,7,1,6,3]=>[4,6,3,1,7,2,5]=>011010=>[1,2,1,1,1]
[4,2,5,7,3,1,6]=>[4,6,3,1,5,7,2]=>011001=>[1,2,2,1]
[4,2,5,7,3,6,1]=>[4,6,3,1,5,2,7]=>011010=>[1,2,1,1,1]
[4,2,5,7,6,1,3]=>[4,6,3,1,2,7,5]=>011001=>[1,2,2,1]
[4,2,5,7,6,3,1]=>[4,6,3,1,2,5,7]=>011000=>[1,2,3]
[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>010111=>[1,1,1,3]
[4,2,6,1,3,7,5]=>[4,6,2,7,5,1,3]=>010110=>[1,1,1,2,1]
[4,2,6,1,5,3,7]=>[4,6,2,7,3,5,1]=>010101=>[1,1,1,1,1,1]
[4,2,6,1,5,7,3]=>[4,6,2,7,3,1,5]=>010110=>[1,1,1,2,1]
[4,2,6,1,7,3,5]=>[4,6,2,7,1,5,3]=>010101=>[1,1,1,1,1,1]
[4,2,6,1,7,5,3]=>[4,6,2,7,1,3,5]=>010100=>[1,1,1,1,2]
[4,2,6,3,1,5,7]=>[4,6,2,5,7,3,1]=>010011=>[1,1,2,2]
[4,2,6,3,1,7,5]=>[4,6,2,5,7,1,3]=>010010=>[1,1,2,1,1]
[4,2,6,3,5,1,7]=>[4,6,2,5,3,7,1]=>010101=>[1,1,1,1,1,1]
[4,2,6,3,5,7,1]=>[4,6,2,5,3,1,7]=>010110=>[1,1,1,2,1]
[4,2,6,3,7,1,5]=>[4,6,2,5,1,7,3]=>010101=>[1,1,1,1,1,1]
[4,2,6,3,7,5,1]=>[4,6,2,5,1,3,7]=>010100=>[1,1,1,1,2]
[4,2,6,5,1,3,7]=>[4,6,2,3,7,5,1]=>010011=>[1,1,2,2]
[4,2,6,5,1,7,3]=>[4,6,2,3,7,1,5]=>010010=>[1,1,2,1,1]
[4,2,6,5,3,1,7]=>[4,6,2,3,5,7,1]=>010001=>[1,1,3,1]
[4,2,6,5,3,7,1]=>[4,6,2,3,5,1,7]=>010010=>[1,1,2,1,1]
[4,2,6,5,7,1,3]=>[4,6,2,3,1,7,5]=>010101=>[1,1,1,1,1,1]
[4,2,6,5,7,3,1]=>[4,6,2,3,1,5,7]=>010100=>[1,1,1,1,2]
[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>011011=>[1,2,1,2]
[4,2,6,7,1,5,3]=>[4,6,2,1,7,3,5]=>011010=>[1,2,1,1,1]
[4,2,6,7,3,1,5]=>[4,6,2,1,5,7,3]=>011001=>[1,2,2,1]
[4,2,6,7,3,5,1]=>[4,6,2,1,5,3,7]=>011010=>[1,2,1,1,1]
[4,2,6,7,5,1,3]=>[4,6,2,1,3,7,5]=>011001=>[1,2,2,1]
[4,2,6,7,5,3,1]=>[4,6,2,1,3,5,7]=>011000=>[1,2,3]
[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>010111=>[1,1,1,3]
[4,2,7,1,3,6,5]=>[4,6,1,7,5,2,3]=>010110=>[1,1,1,2,1]
[4,2,7,1,5,3,6]=>[4,6,1,7,3,5,2]=>010101=>[1,1,1,1,1,1]
[4,2,7,1,5,6,3]=>[4,6,1,7,3,2,5]=>010110=>[1,1,1,2,1]
[4,2,7,1,6,3,5]=>[4,6,1,7,2,5,3]=>010101=>[1,1,1,1,1,1]
[4,2,7,1,6,5,3]=>[4,6,1,7,2,3,5]=>010100=>[1,1,1,1,2]
[4,2,7,3,1,5,6]=>[4,6,1,5,7,3,2]=>010011=>[1,1,2,2]
[4,2,7,3,1,6,5]=>[4,6,1,5,7,2,3]=>010010=>[1,1,2,1,1]
[4,2,7,3,5,1,6]=>[4,6,1,5,3,7,2]=>010101=>[1,1,1,1,1,1]
[4,2,7,3,5,6,1]=>[4,6,1,5,3,2,7]=>010110=>[1,1,1,2,1]
[4,2,7,3,6,1,5]=>[4,6,1,5,2,7,3]=>010101=>[1,1,1,1,1,1]
[4,2,7,3,6,5,1]=>[4,6,1,5,2,3,7]=>010100=>[1,1,1,1,2]
[4,2,7,5,1,3,6]=>[4,6,1,3,7,5,2]=>010011=>[1,1,2,2]
[4,2,7,5,1,6,3]=>[4,6,1,3,7,2,5]=>010010=>[1,1,2,1,1]
[4,2,7,5,3,1,6]=>[4,6,1,3,5,7,2]=>010001=>[1,1,3,1]
[4,2,7,5,3,6,1]=>[4,6,1,3,5,2,7]=>010010=>[1,1,2,1,1]
[4,2,7,5,6,1,3]=>[4,6,1,3,2,7,5]=>010101=>[1,1,1,1,1,1]
[4,2,7,5,6,3,1]=>[4,6,1,3,2,5,7]=>010100=>[1,1,1,1,2]
[4,2,7,6,1,3,5]=>[4,6,1,2,7,5,3]=>010011=>[1,1,2,2]
[4,2,7,6,1,5,3]=>[4,6,1,2,7,3,5]=>010010=>[1,1,2,1,1]
[4,2,7,6,3,1,5]=>[4,6,1,2,5,7,3]=>010001=>[1,1,3,1]
[4,2,7,6,3,5,1]=>[4,6,1,2,5,3,7]=>010010=>[1,1,2,1,1]
[4,2,7,6,5,1,3]=>[4,6,1,2,3,7,5]=>010001=>[1,1,3,1]
[4,2,7,6,5,3,1]=>[4,6,1,2,3,5,7]=>010000=>[1,1,4]
[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>001111=>[2,4]
[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>001110=>[2,3,1]
[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>001101=>[2,2,1,1]
[4,3,1,2,6,7,5]=>[4,5,7,6,2,1,3]=>001110=>[2,3,1]
[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>001101=>[2,2,1,1]
[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>001100=>[2,2,2]
[4,3,1,5,2,6,7]=>[4,5,7,3,6,2,1]=>001011=>[2,1,1,2]
[4,3,1,5,2,7,6]=>[4,5,7,3,6,1,2]=>001010=>[2,1,1,1,1]
[4,3,1,5,6,2,7]=>[4,5,7,3,2,6,1]=>001101=>[2,2,1,1]
[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>001110=>[2,3,1]
[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>001101=>[2,2,1,1]
[4,3,1,5,7,6,2]=>[4,5,7,3,1,2,6]=>001100=>[2,2,2]
[4,3,1,6,2,5,7]=>[4,5,7,2,6,3,1]=>001011=>[2,1,1,2]
[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>001010=>[2,1,1,1,1]
[4,3,1,6,5,2,7]=>[4,5,7,2,3,6,1]=>001001=>[2,1,2,1]
[4,3,1,6,5,7,2]=>[4,5,7,2,3,1,6]=>001010=>[2,1,1,1,1]
[4,3,1,6,7,2,5]=>[4,5,7,2,1,6,3]=>001101=>[2,2,1,1]
[4,3,1,6,7,5,2]=>[4,5,7,2,1,3,6]=>001100=>[2,2,2]
[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>001011=>[2,1,1,2]
[4,3,1,7,2,6,5]=>[4,5,7,1,6,2,3]=>001010=>[2,1,1,1,1]
[4,3,1,7,5,2,6]=>[4,5,7,1,3,6,2]=>001001=>[2,1,2,1]
[4,3,1,7,5,6,2]=>[4,5,7,1,3,2,6]=>001010=>[2,1,1,1,1]
[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>001001=>[2,1,2,1]
[4,3,1,7,6,5,2]=>[4,5,7,1,2,3,6]=>001000=>[2,1,3]
[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>000111=>[3,3]
[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>000110=>[3,2,1]
[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>000101=>[3,1,1,1]
[4,3,2,1,6,7,5]=>[4,5,6,7,2,1,3]=>000110=>[3,2,1]
[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>000101=>[3,1,1,1]
[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>000100=>[3,1,2]
[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>001011=>[2,1,1,2]
[4,3,2,5,1,7,6]=>[4,5,6,3,7,1,2]=>001010=>[2,1,1,1,1]
[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>001101=>[2,2,1,1]
[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>001110=>[2,3,1]
[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>001101=>[2,2,1,1]
[4,3,2,5,7,6,1]=>[4,5,6,3,1,2,7]=>001100=>[2,2,2]
[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>001011=>[2,1,1,2]
[4,3,2,6,1,7,5]=>[4,5,6,2,7,1,3]=>001010=>[2,1,1,1,1]
[4,3,2,6,5,1,7]=>[4,5,6,2,3,7,1]=>001001=>[2,1,2,1]
[4,3,2,6,5,7,1]=>[4,5,6,2,3,1,7]=>001010=>[2,1,1,1,1]
[4,3,2,6,7,1,5]=>[4,5,6,2,1,7,3]=>001101=>[2,2,1,1]
[4,3,2,6,7,5,1]=>[4,5,6,2,1,3,7]=>001100=>[2,2,2]
[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>001011=>[2,1,1,2]
[4,3,2,7,1,6,5]=>[4,5,6,1,7,2,3]=>001010=>[2,1,1,1,1]
[4,3,2,7,5,1,6]=>[4,5,6,1,3,7,2]=>001001=>[2,1,2,1]
[4,3,2,7,5,6,1]=>[4,5,6,1,3,2,7]=>001010=>[2,1,1,1,1]
[4,3,2,7,6,1,5]=>[4,5,6,1,2,7,3]=>001001=>[2,1,2,1]
[4,3,2,7,6,5,1]=>[4,5,6,1,2,3,7]=>001000=>[2,1,3]
[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>010111=>[1,1,1,3]
[4,3,5,1,2,7,6]=>[4,5,3,7,6,1,2]=>010110=>[1,1,1,2,1]
[4,3,5,1,6,2,7]=>[4,5,3,7,2,6,1]=>010101=>[1,1,1,1,1,1]
[4,3,5,1,6,7,2]=>[4,5,3,7,2,1,6]=>010110=>[1,1,1,2,1]
[4,3,5,1,7,2,6]=>[4,5,3,7,1,6,2]=>010101=>[1,1,1,1,1,1]
[4,3,5,1,7,6,2]=>[4,5,3,7,1,2,6]=>010100=>[1,1,1,1,2]
[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>010011=>[1,1,2,2]
[4,3,5,2,1,7,6]=>[4,5,3,6,7,1,2]=>010010=>[1,1,2,1,1]
[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>010101=>[1,1,1,1,1,1]
[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>010110=>[1,1,1,2,1]
[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>010101=>[1,1,1,1,1,1]
[4,3,5,2,7,6,1]=>[4,5,3,6,1,2,7]=>010100=>[1,1,1,1,2]
[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>011011=>[1,2,1,2]
[4,3,5,6,1,7,2]=>[4,5,3,2,7,1,6]=>011010=>[1,2,1,1,1]
[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>011001=>[1,2,2,1]
[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>011010=>[1,2,1,1,1]
[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>011101=>[1,3,1,1]
[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>011100=>[1,3,2]
[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>011011=>[1,2,1,2]
[4,3,5,7,1,6,2]=>[4,5,3,1,7,2,6]=>011010=>[1,2,1,1,1]
[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>011001=>[1,2,2,1]
[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>011010=>[1,2,1,1,1]
[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>011001=>[1,2,2,1]
[4,3,5,7,6,2,1]=>[4,5,3,1,2,6,7]=>011000=>[1,2,3]
[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>010111=>[1,1,1,3]
[4,3,6,1,2,7,5]=>[4,5,2,7,6,1,3]=>010110=>[1,1,1,2,1]
[4,3,6,1,5,2,7]=>[4,5,2,7,3,6,1]=>010101=>[1,1,1,1,1,1]
[4,3,6,1,5,7,2]=>[4,5,2,7,3,1,6]=>010110=>[1,1,1,2,1]
[4,3,6,1,7,2,5]=>[4,5,2,7,1,6,3]=>010101=>[1,1,1,1,1,1]
[4,3,6,1,7,5,2]=>[4,5,2,7,1,3,6]=>010100=>[1,1,1,1,2]
[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>010011=>[1,1,2,2]
[4,3,6,2,1,7,5]=>[4,5,2,6,7,1,3]=>010010=>[1,1,2,1,1]
[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>010101=>[1,1,1,1,1,1]
[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>010110=>[1,1,1,2,1]
[4,3,6,2,7,1,5]=>[4,5,2,6,1,7,3]=>010101=>[1,1,1,1,1,1]
[4,3,6,2,7,5,1]=>[4,5,2,6,1,3,7]=>010100=>[1,1,1,1,2]
[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>010011=>[1,1,2,2]
[4,3,6,5,1,7,2]=>[4,5,2,3,7,1,6]=>010010=>[1,1,2,1,1]
[4,3,6,5,2,1,7]=>[4,5,2,3,6,7,1]=>010001=>[1,1,3,1]
[4,3,6,5,2,7,1]=>[4,5,2,3,6,1,7]=>010010=>[1,1,2,1,1]
[4,3,6,5,7,1,2]=>[4,5,2,3,1,7,6]=>010101=>[1,1,1,1,1,1]
[4,3,6,5,7,2,1]=>[4,5,2,3,1,6,7]=>010100=>[1,1,1,1,2]
[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>011011=>[1,2,1,2]
[4,3,6,7,1,5,2]=>[4,5,2,1,7,3,6]=>011010=>[1,2,1,1,1]
[4,3,6,7,2,1,5]=>[4,5,2,1,6,7,3]=>011001=>[1,2,2,1]
[4,3,6,7,2,5,1]=>[4,5,2,1,6,3,7]=>011010=>[1,2,1,1,1]
[4,3,6,7,5,1,2]=>[4,5,2,1,3,7,6]=>011001=>[1,2,2,1]
[4,3,6,7,5,2,1]=>[4,5,2,1,3,6,7]=>011000=>[1,2,3]
[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>010111=>[1,1,1,3]
[4,3,7,1,2,6,5]=>[4,5,1,7,6,2,3]=>010110=>[1,1,1,2,1]
[4,3,7,1,5,2,6]=>[4,5,1,7,3,6,2]=>010101=>[1,1,1,1,1,1]
[4,3,7,1,5,6,2]=>[4,5,1,7,3,2,6]=>010110=>[1,1,1,2,1]
[4,3,7,1,6,2,5]=>[4,5,1,7,2,6,3]=>010101=>[1,1,1,1,1,1]
[4,3,7,1,6,5,2]=>[4,5,1,7,2,3,6]=>010100=>[1,1,1,1,2]
[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>010011=>[1,1,2,2]
[4,3,7,2,1,6,5]=>[4,5,1,6,7,2,3]=>010010=>[1,1,2,1,1]
[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>010101=>[1,1,1,1,1,1]
[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>010110=>[1,1,1,2,1]
[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>010101=>[1,1,1,1,1,1]
[4,3,7,2,6,5,1]=>[4,5,1,6,2,3,7]=>010100=>[1,1,1,1,2]
[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>010011=>[1,1,2,2]
[4,3,7,5,1,6,2]=>[4,5,1,3,7,2,6]=>010010=>[1,1,2,1,1]
[4,3,7,5,2,1,6]=>[4,5,1,3,6,7,2]=>010001=>[1,1,3,1]
[4,3,7,5,2,6,1]=>[4,5,1,3,6,2,7]=>010010=>[1,1,2,1,1]
[4,3,7,5,6,1,2]=>[4,5,1,3,2,7,6]=>010101=>[1,1,1,1,1,1]
[4,3,7,5,6,2,1]=>[4,5,1,3,2,6,7]=>010100=>[1,1,1,1,2]
[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>010011=>[1,1,2,2]
[4,3,7,6,1,5,2]=>[4,5,1,2,7,3,6]=>010010=>[1,1,2,1,1]
[4,3,7,6,2,1,5]=>[4,5,1,2,6,7,3]=>010001=>[1,1,3,1]
[4,3,7,6,2,5,1]=>[4,5,1,2,6,3,7]=>010010=>[1,1,2,1,1]
[4,3,7,6,5,1,2]=>[4,5,1,2,3,7,6]=>010001=>[1,1,3,1]
[4,3,7,6,5,2,1]=>[4,5,1,2,3,6,7]=>010000=>[1,1,4]
[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>101111=>[1,1,4]
[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]=>101110=>[1,1,3,1]
[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]=>101101=>[1,1,2,1,1]
[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]=>101110=>[1,1,3,1]
[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]=>101101=>[1,1,2,1,1]
[4,5,1,2,7,6,3]=>[4,3,7,6,1,2,5]=>101100=>[1,1,2,2]
[4,5,1,3,2,6,7]=>[4,3,7,5,6,2,1]=>101011=>[1,1,1,1,2]
[4,5,1,3,2,7,6]=>[4,3,7,5,6,1,2]=>101010=>[1,1,1,1,1,1]
[4,5,1,3,6,2,7]=>[4,3,7,5,2,6,1]=>101101=>[1,1,2,1,1]
[4,5,1,3,6,7,2]=>[4,3,7,5,2,1,6]=>101110=>[1,1,3,1]
[4,5,1,3,7,2,6]=>[4,3,7,5,1,6,2]=>101101=>[1,1,2,1,1]
[4,5,1,3,7,6,2]=>[4,3,7,5,1,2,6]=>101100=>[1,1,2,2]
[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]=>101011=>[1,1,1,1,2]
[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]=>101010=>[1,1,1,1,1,1]
[4,5,1,6,3,2,7]=>[4,3,7,2,5,6,1]=>101001=>[1,1,1,2,1]
[4,5,1,6,3,7,2]=>[4,3,7,2,5,1,6]=>101010=>[1,1,1,1,1,1]
[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]=>101101=>[1,1,2,1,1]
[4,5,1,6,7,3,2]=>[4,3,7,2,1,5,6]=>101100=>[1,1,2,2]
[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]=>101011=>[1,1,1,1,2]
[4,5,1,7,2,6,3]=>[4,3,7,1,6,2,5]=>101010=>[1,1,1,1,1,1]
[4,5,1,7,3,2,6]=>[4,3,7,1,5,6,2]=>101001=>[1,1,1,2,1]
[4,5,1,7,3,6,2]=>[4,3,7,1,5,2,6]=>101010=>[1,1,1,1,1,1]
[4,5,1,7,6,2,3]=>[4,3,7,1,2,6,5]=>101001=>[1,1,1,2,1]
[4,5,1,7,6,3,2]=>[4,3,7,1,2,5,6]=>101000=>[1,1,1,3]
[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>100111=>[1,2,3]
[4,5,2,1,3,7,6]=>[4,3,6,7,5,1,2]=>100110=>[1,2,2,1]
[4,5,2,1,6,3,7]=>[4,3,6,7,2,5,1]=>100101=>[1,2,1,1,1]
[4,5,2,1,6,7,3]=>[4,3,6,7,2,1,5]=>100110=>[1,2,2,1]
[4,5,2,1,7,3,6]=>[4,3,6,7,1,5,2]=>100101=>[1,2,1,1,1]
[4,5,2,1,7,6,3]=>[4,3,6,7,1,2,5]=>100100=>[1,2,1,2]
[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>101011=>[1,1,1,1,2]
[4,5,2,3,1,7,6]=>[4,3,6,5,7,1,2]=>101010=>[1,1,1,1,1,1]
[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>101101=>[1,1,2,1,1]
[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>101110=>[1,1,3,1]
[4,5,2,3,7,1,6]=>[4,3,6,5,1,7,2]=>101101=>[1,1,2,1,1]
[4,5,2,3,7,6,1]=>[4,3,6,5,1,2,7]=>101100=>[1,1,2,2]
[4,5,2,6,1,3,7]=>[4,3,6,2,7,5,1]=>101011=>[1,1,1,1,2]
[4,5,2,6,1,7,3]=>[4,3,6,2,7,1,5]=>101010=>[1,1,1,1,1,1]
[4,5,2,6,3,1,7]=>[4,3,6,2,5,7,1]=>101001=>[1,1,1,2,1]
[4,5,2,6,3,7,1]=>[4,3,6,2,5,1,7]=>101010=>[1,1,1,1,1,1]
[4,5,2,6,7,1,3]=>[4,3,6,2,1,7,5]=>101101=>[1,1,2,1,1]
[4,5,2,6,7,3,1]=>[4,3,6,2,1,5,7]=>101100=>[1,1,2,2]
[4,5,2,7,1,3,6]=>[4,3,6,1,7,5,2]=>101011=>[1,1,1,1,2]
[4,5,2,7,1,6,3]=>[4,3,6,1,7,2,5]=>101010=>[1,1,1,1,1,1]
[4,5,2,7,3,1,6]=>[4,3,6,1,5,7,2]=>101001=>[1,1,1,2,1]
[4,5,2,7,3,6,1]=>[4,3,6,1,5,2,7]=>101010=>[1,1,1,1,1,1]
[4,5,2,7,6,1,3]=>[4,3,6,1,2,7,5]=>101001=>[1,1,1,2,1]
[4,5,2,7,6,3,1]=>[4,3,6,1,2,5,7]=>101000=>[1,1,1,3]
[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>100111=>[1,2,3]
[4,5,3,1,2,7,6]=>[4,3,5,7,6,1,2]=>100110=>[1,2,2,1]
[4,5,3,1,6,2,7]=>[4,3,5,7,2,6,1]=>100101=>[1,2,1,1,1]
[4,5,3,1,6,7,2]=>[4,3,5,7,2,1,6]=>100110=>[1,2,2,1]
[4,5,3,1,7,2,6]=>[4,3,5,7,1,6,2]=>100101=>[1,2,1,1,1]
[4,5,3,1,7,6,2]=>[4,3,5,7,1,2,6]=>100100=>[1,2,1,2]
[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>100011=>[1,3,2]
[4,5,3,2,1,7,6]=>[4,3,5,6,7,1,2]=>100010=>[1,3,1,1]
[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>100101=>[1,2,1,1,1]
[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>100110=>[1,2,2,1]
[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>100101=>[1,2,1,1,1]
[4,5,3,2,7,6,1]=>[4,3,5,6,1,2,7]=>100100=>[1,2,1,2]
[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>101011=>[1,1,1,1,2]
[4,5,3,6,1,7,2]=>[4,3,5,2,7,1,6]=>101010=>[1,1,1,1,1,1]
[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>101001=>[1,1,1,2,1]
[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>101010=>[1,1,1,1,1,1]
[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>101101=>[1,1,2,1,1]
[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>101100=>[1,1,2,2]
[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>101011=>[1,1,1,1,2]
[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>101010=>[1,1,1,1,1,1]
[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>101001=>[1,1,1,2,1]
[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>101010=>[1,1,1,1,1,1]
[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>101001=>[1,1,1,2,1]
[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>101000=>[1,1,1,3]
[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>110111=>[2,1,3]
[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]=>110110=>[2,1,2,1]
[4,5,6,1,3,2,7]=>[4,3,2,7,5,6,1]=>110101=>[2,1,1,1,1]
[4,5,6,1,3,7,2]=>[4,3,2,7,5,1,6]=>110110=>[2,1,2,1]
[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]=>110101=>[2,1,1,1,1]
[4,5,6,1,7,3,2]=>[4,3,2,7,1,5,6]=>110100=>[2,1,1,2]
[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>110011=>[2,2,2]
[4,5,6,2,1,7,3]=>[4,3,2,6,7,1,5]=>110010=>[2,2,1,1]
[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>110101=>[2,1,1,1,1]
[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>110110=>[2,1,2,1]
[4,5,6,2,7,1,3]=>[4,3,2,6,1,7,5]=>110101=>[2,1,1,1,1]
[4,5,6,2,7,3,1]=>[4,3,2,6,1,5,7]=>110100=>[2,1,1,2]
[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>110011=>[2,2,2]
[4,5,6,3,1,7,2]=>[4,3,2,5,7,1,6]=>110010=>[2,2,1,1]
[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>110001=>[2,3,1]
[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>110010=>[2,2,1,1]
[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>110101=>[2,1,1,1,1]
[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>110100=>[2,1,1,2]
[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>111011=>[3,1,2]
[4,5,6,7,1,3,2]=>[4,3,2,1,7,5,6]=>111010=>[3,1,1,1]
[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>111001=>[3,2,1]
[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>111010=>[3,1,1,1]
[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>111001=>[3,2,1]
[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>111000=>[3,3]
[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>110111=>[2,1,3]
[4,5,7,1,2,6,3]=>[4,3,1,7,6,2,5]=>110110=>[2,1,2,1]
[4,5,7,1,3,2,6]=>[4,3,1,7,5,6,2]=>110101=>[2,1,1,1,1]
[4,5,7,1,3,6,2]=>[4,3,1,7,5,2,6]=>110110=>[2,1,2,1]
[4,5,7,1,6,2,3]=>[4,3,1,7,2,6,5]=>110101=>[2,1,1,1,1]
[4,5,7,1,6,3,2]=>[4,3,1,7,2,5,6]=>110100=>[2,1,1,2]
[4,5,7,2,1,3,6]=>[4,3,1,6,7,5,2]=>110011=>[2,2,2]
[4,5,7,2,1,6,3]=>[4,3,1,6,7,2,5]=>110010=>[2,2,1,1]
[4,5,7,2,3,1,6]=>[4,3,1,6,5,7,2]=>110101=>[2,1,1,1,1]
[4,5,7,2,3,6,1]=>[4,3,1,6,5,2,7]=>110110=>[2,1,2,1]
[4,5,7,2,6,1,3]=>[4,3,1,6,2,7,5]=>110101=>[2,1,1,1,1]
[4,5,7,2,6,3,1]=>[4,3,1,6,2,5,7]=>110100=>[2,1,1,2]
[4,5,7,3,1,2,6]=>[4,3,1,5,7,6,2]=>110011=>[2,2,2]
[4,5,7,3,1,6,2]=>[4,3,1,5,7,2,6]=>110010=>[2,2,1,1]
[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>110001=>[2,3,1]
[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>110010=>[2,2,1,1]
[4,5,7,3,6,1,2]=>[4,3,1,5,2,7,6]=>110101=>[2,1,1,1,1]
[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>110100=>[2,1,1,2]
[4,5,7,6,1,2,3]=>[4,3,1,2,7,6,5]=>110011=>[2,2,2]
[4,5,7,6,1,3,2]=>[4,3,1,2,7,5,6]=>110010=>[2,2,1,1]
[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>110001=>[2,3,1]
[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>110010=>[2,2,1,1]
[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>110001=>[2,3,1]
[4,5,7,6,3,2,1]=>[4,3,1,2,5,6,7]=>110000=>[2,4]
[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>101111=>[1,1,4]
[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]=>101110=>[1,1,3,1]
[4,6,1,2,5,3,7]=>[4,2,7,6,3,5,1]=>101101=>[1,1,2,1,1]
[4,6,1,2,5,7,3]=>[4,2,7,6,3,1,5]=>101110=>[1,1,3,1]
[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]=>101101=>[1,1,2,1,1]
[4,6,1,2,7,5,3]=>[4,2,7,6,1,3,5]=>101100=>[1,1,2,2]
[4,6,1,3,2,5,7]=>[4,2,7,5,6,3,1]=>101011=>[1,1,1,1,2]
[4,6,1,3,2,7,5]=>[4,2,7,5,6,1,3]=>101010=>[1,1,1,1,1,1]
[4,6,1,3,5,2,7]=>[4,2,7,5,3,6,1]=>101101=>[1,1,2,1,1]
[4,6,1,3,5,7,2]=>[4,2,7,5,3,1,6]=>101110=>[1,1,3,1]
[4,6,1,3,7,2,5]=>[4,2,7,5,1,6,3]=>101101=>[1,1,2,1,1]
[4,6,1,3,7,5,2]=>[4,2,7,5,1,3,6]=>101100=>[1,1,2,2]
[4,6,1,5,2,3,7]=>[4,2,7,3,6,5,1]=>101011=>[1,1,1,1,2]
[4,6,1,5,2,7,3]=>[4,2,7,3,6,1,5]=>101010=>[1,1,1,1,1,1]
[4,6,1,5,3,2,7]=>[4,2,7,3,5,6,1]=>101001=>[1,1,1,2,1]
[4,6,1,5,3,7,2]=>[4,2,7,3,5,1,6]=>101010=>[1,1,1,1,1,1]
[4,6,1,5,7,2,3]=>[4,2,7,3,1,6,5]=>101101=>[1,1,2,1,1]
[4,6,1,5,7,3,2]=>[4,2,7,3,1,5,6]=>101100=>[1,1,2,2]
[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]=>101011=>[1,1,1,1,2]
[4,6,1,7,2,5,3]=>[4,2,7,1,6,3,5]=>101010=>[1,1,1,1,1,1]
[4,6,1,7,3,2,5]=>[4,2,7,1,5,6,3]=>101001=>[1,1,1,2,1]
[4,6,1,7,3,5,2]=>[4,2,7,1,5,3,6]=>101010=>[1,1,1,1,1,1]
[4,6,1,7,5,2,3]=>[4,2,7,1,3,6,5]=>101001=>[1,1,1,2,1]
[4,6,1,7,5,3,2]=>[4,2,7,1,3,5,6]=>101000=>[1,1,1,3]
[4,6,2,1,3,5,7]=>[4,2,6,7,5,3,1]=>100111=>[1,2,3]
[4,6,2,1,3,7,5]=>[4,2,6,7,5,1,3]=>100110=>[1,2,2,1]
[4,6,2,1,5,3,7]=>[4,2,6,7,3,5,1]=>100101=>[1,2,1,1,1]
[4,6,2,1,5,7,3]=>[4,2,6,7,3,1,5]=>100110=>[1,2,2,1]
[4,6,2,1,7,3,5]=>[4,2,6,7,1,5,3]=>100101=>[1,2,1,1,1]
[4,6,2,1,7,5,3]=>[4,2,6,7,1,3,5]=>100100=>[1,2,1,2]
[4,6,2,3,1,5,7]=>[4,2,6,5,7,3,1]=>101011=>[1,1,1,1,2]
[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>101010=>[1,1,1,1,1,1]
[4,6,2,3,5,1,7]=>[4,2,6,5,3,7,1]=>101101=>[1,1,2,1,1]
[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>101110=>[1,1,3,1]
[4,6,2,3,7,1,5]=>[4,2,6,5,1,7,3]=>101101=>[1,1,2,1,1]
[4,6,2,3,7,5,1]=>[4,2,6,5,1,3,7]=>101100=>[1,1,2,2]
[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>101011=>[1,1,1,1,2]
[4,6,2,5,1,7,3]=>[4,2,6,3,7,1,5]=>101010=>[1,1,1,1,1,1]
[4,6,2,5,3,1,7]=>[4,2,6,3,5,7,1]=>101001=>[1,1,1,2,1]
[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>101010=>[1,1,1,1,1,1]
[4,6,2,5,7,1,3]=>[4,2,6,3,1,7,5]=>101101=>[1,1,2,1,1]
[4,6,2,5,7,3,1]=>[4,2,6,3,1,5,7]=>101100=>[1,1,2,2]
[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>101011=>[1,1,1,1,2]
[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>101010=>[1,1,1,1,1,1]
[4,6,2,7,3,1,5]=>[4,2,6,1,5,7,3]=>101001=>[1,1,1,2,1]
[4,6,2,7,3,5,1]=>[4,2,6,1,5,3,7]=>101010=>[1,1,1,1,1,1]
[4,6,2,7,5,1,3]=>[4,2,6,1,3,7,5]=>101001=>[1,1,1,2,1]
[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>101000=>[1,1,1,3]
[4,6,3,1,2,5,7]=>[4,2,5,7,6,3,1]=>100111=>[1,2,3]
[4,6,3,1,2,7,5]=>[4,2,5,7,6,1,3]=>100110=>[1,2,2,1]
[4,6,3,1,5,2,7]=>[4,2,5,7,3,6,1]=>100101=>[1,2,1,1,1]
[4,6,3,1,5,7,2]=>[4,2,5,7,3,1,6]=>100110=>[1,2,2,1]
[4,6,3,1,7,2,5]=>[4,2,5,7,1,6,3]=>100101=>[1,2,1,1,1]
[4,6,3,1,7,5,2]=>[4,2,5,7,1,3,6]=>100100=>[1,2,1,2]
[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>100011=>[1,3,2]
[4,6,3,2,1,7,5]=>[4,2,5,6,7,1,3]=>100010=>[1,3,1,1]
[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>100101=>[1,2,1,1,1]
[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>100110=>[1,2,2,1]
[4,6,3,2,7,1,5]=>[4,2,5,6,1,7,3]=>100101=>[1,2,1,1,1]
[4,6,3,2,7,5,1]=>[4,2,5,6,1,3,7]=>100100=>[1,2,1,2]
[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>101011=>[1,1,1,1,2]
[4,6,3,5,1,7,2]=>[4,2,5,3,7,1,6]=>101010=>[1,1,1,1,1,1]
[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>101001=>[1,1,1,2,1]
[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>101010=>[1,1,1,1,1,1]
[4,6,3,5,7,1,2]=>[4,2,5,3,1,7,6]=>101101=>[1,1,2,1,1]
[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>101100=>[1,1,2,2]
[4,6,3,7,1,2,5]=>[4,2,5,1,7,6,3]=>101011=>[1,1,1,1,2]
[4,6,3,7,1,5,2]=>[4,2,5,1,7,3,6]=>101010=>[1,1,1,1,1,1]
[4,6,3,7,2,1,5]=>[4,2,5,1,6,7,3]=>101001=>[1,1,1,2,1]
[4,6,3,7,2,5,1]=>[4,2,5,1,6,3,7]=>101010=>[1,1,1,1,1,1]
[4,6,3,7,5,1,2]=>[4,2,5,1,3,7,6]=>101001=>[1,1,1,2,1]
[4,6,3,7,5,2,1]=>[4,2,5,1,3,6,7]=>101000=>[1,1,1,3]
[4,6,5,1,2,3,7]=>[4,2,3,7,6,5,1]=>100111=>[1,2,3]
[4,6,5,1,2,7,3]=>[4,2,3,7,6,1,5]=>100110=>[1,2,2,1]
[4,6,5,1,3,2,7]=>[4,2,3,7,5,6,1]=>100101=>[1,2,1,1,1]
[4,6,5,1,3,7,2]=>[4,2,3,7,5,1,6]=>100110=>[1,2,2,1]
[4,6,5,1,7,2,3]=>[4,2,3,7,1,6,5]=>100101=>[1,2,1,1,1]
[4,6,5,1,7,3,2]=>[4,2,3,7,1,5,6]=>100100=>[1,2,1,2]
[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>100011=>[1,3,2]
[4,6,5,2,1,7,3]=>[4,2,3,6,7,1,5]=>100010=>[1,3,1,1]
[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>100101=>[1,2,1,1,1]
[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>100110=>[1,2,2,1]
[4,6,5,2,7,1,3]=>[4,2,3,6,1,7,5]=>100101=>[1,2,1,1,1]
[4,6,5,2,7,3,1]=>[4,2,3,6,1,5,7]=>100100=>[1,2,1,2]
[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>100011=>[1,3,2]
[4,6,5,3,1,7,2]=>[4,2,3,5,7,1,6]=>100010=>[1,3,1,1]
[4,6,5,3,2,1,7]=>[4,2,3,5,6,7,1]=>100001=>[1,4,1]
[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>100010=>[1,3,1,1]
[4,6,5,3,7,1,2]=>[4,2,3,5,1,7,6]=>100101=>[1,2,1,1,1]
[4,6,5,3,7,2,1]=>[4,2,3,5,1,6,7]=>100100=>[1,2,1,2]
[4,6,5,7,1,2,3]=>[4,2,3,1,7,6,5]=>101011=>[1,1,1,1,2]
[4,6,5,7,1,3,2]=>[4,2,3,1,7,5,6]=>101010=>[1,1,1,1,1,1]
[4,6,5,7,2,1,3]=>[4,2,3,1,6,7,5]=>101001=>[1,1,1,2,1]
[4,6,5,7,2,3,1]=>[4,2,3,1,6,5,7]=>101010=>[1,1,1,1,1,1]
[4,6,5,7,3,1,2]=>[4,2,3,1,5,7,6]=>101001=>[1,1,1,2,1]
[4,6,5,7,3,2,1]=>[4,2,3,1,5,6,7]=>101000=>[1,1,1,3]
[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>110111=>[2,1,3]
[4,6,7,1,2,5,3]=>[4,2,1,7,6,3,5]=>110110=>[2,1,2,1]
[4,6,7,1,3,2,5]=>[4,2,1,7,5,6,3]=>110101=>[2,1,1,1,1]
[4,6,7,1,3,5,2]=>[4,2,1,7,5,3,6]=>110110=>[2,1,2,1]
[4,6,7,1,5,2,3]=>[4,2,1,7,3,6,5]=>110101=>[2,1,1,1,1]
[4,6,7,1,5,3,2]=>[4,2,1,7,3,5,6]=>110100=>[2,1,1,2]
[4,6,7,2,1,3,5]=>[4,2,1,6,7,5,3]=>110011=>[2,2,2]
[4,6,7,2,1,5,3]=>[4,2,1,6,7,3,5]=>110010=>[2,2,1,1]
[4,6,7,2,3,1,5]=>[4,2,1,6,5,7,3]=>110101=>[2,1,1,1,1]
[4,6,7,2,3,5,1]=>[4,2,1,6,5,3,7]=>110110=>[2,1,2,1]
[4,6,7,2,5,1,3]=>[4,2,1,6,3,7,5]=>110101=>[2,1,1,1,1]
[4,6,7,2,5,3,1]=>[4,2,1,6,3,5,7]=>110100=>[2,1,1,2]
[4,6,7,3,1,2,5]=>[4,2,1,5,7,6,3]=>110011=>[2,2,2]
[4,6,7,3,1,5,2]=>[4,2,1,5,7,3,6]=>110010=>[2,2,1,1]
[4,6,7,3,2,1,5]=>[4,2,1,5,6,7,3]=>110001=>[2,3,1]
[4,6,7,3,2,5,1]=>[4,2,1,5,6,3,7]=>110010=>[2,2,1,1]
[4,6,7,3,5,1,2]=>[4,2,1,5,3,7,6]=>110101=>[2,1,1,1,1]
[4,6,7,3,5,2,1]=>[4,2,1,5,3,6,7]=>110100=>[2,1,1,2]
[4,6,7,5,1,2,3]=>[4,2,1,3,7,6,5]=>110011=>[2,2,2]
[4,6,7,5,1,3,2]=>[4,2,1,3,7,5,6]=>110010=>[2,2,1,1]
[4,6,7,5,2,1,3]=>[4,2,1,3,6,7,5]=>110001=>[2,3,1]
[4,6,7,5,2,3,1]=>[4,2,1,3,6,5,7]=>110010=>[2,2,1,1]
[4,6,7,5,3,1,2]=>[4,2,1,3,5,7,6]=>110001=>[2,3,1]
[4,6,7,5,3,2,1]=>[4,2,1,3,5,6,7]=>110000=>[2,4]
[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>101111=>[1,1,4]
[4,7,1,2,3,6,5]=>[4,1,7,6,5,2,3]=>101110=>[1,1,3,1]
[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>101101=>[1,1,2,1,1]
[4,7,1,2,5,6,3]=>[4,1,7,6,3,2,5]=>101110=>[1,1,3,1]
[4,7,1,2,6,3,5]=>[4,1,7,6,2,5,3]=>101101=>[1,1,2,1,1]
[4,7,1,2,6,5,3]=>[4,1,7,6,2,3,5]=>101100=>[1,1,2,2]
[4,7,1,3,2,5,6]=>[4,1,7,5,6,3,2]=>101011=>[1,1,1,1,2]
[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>101010=>[1,1,1,1,1,1]
[4,7,1,3,5,2,6]=>[4,1,7,5,3,6,2]=>101101=>[1,1,2,1,1]
[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>101110=>[1,1,3,1]
[4,7,1,3,6,2,5]=>[4,1,7,5,2,6,3]=>101101=>[1,1,2,1,1]
[4,7,1,3,6,5,2]=>[4,1,7,5,2,3,6]=>101100=>[1,1,2,2]
[4,7,1,5,2,3,6]=>[4,1,7,3,6,5,2]=>101011=>[1,1,1,1,2]
[4,7,1,5,2,6,3]=>[4,1,7,3,6,2,5]=>101010=>[1,1,1,1,1,1]
[4,7,1,5,3,2,6]=>[4,1,7,3,5,6,2]=>101001=>[1,1,1,2,1]
[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>101010=>[1,1,1,1,1,1]
[4,7,1,5,6,2,3]=>[4,1,7,3,2,6,5]=>101101=>[1,1,2,1,1]
[4,7,1,5,6,3,2]=>[4,1,7,3,2,5,6]=>101100=>[1,1,2,2]
[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>101011=>[1,1,1,1,2]
[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>101010=>[1,1,1,1,1,1]
[4,7,1,6,3,2,5]=>[4,1,7,2,5,6,3]=>101001=>[1,1,1,2,1]
[4,7,1,6,3,5,2]=>[4,1,7,2,5,3,6]=>101010=>[1,1,1,1,1,1]
[4,7,1,6,5,2,3]=>[4,1,7,2,3,6,5]=>101001=>[1,1,1,2,1]
[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>101000=>[1,1,1,3]
[4,7,2,1,3,5,6]=>[4,1,6,7,5,3,2]=>100111=>[1,2,3]
[4,7,2,1,3,6,5]=>[4,1,6,7,5,2,3]=>100110=>[1,2,2,1]
[4,7,2,1,5,3,6]=>[4,1,6,7,3,5,2]=>100101=>[1,2,1,1,1]
[4,7,2,1,5,6,3]=>[4,1,6,7,3,2,5]=>100110=>[1,2,2,1]
[4,7,2,1,6,3,5]=>[4,1,6,7,2,5,3]=>100101=>[1,2,1,1,1]
[4,7,2,1,6,5,3]=>[4,1,6,7,2,3,5]=>100100=>[1,2,1,2]
[4,7,2,3,1,5,6]=>[4,1,6,5,7,3,2]=>101011=>[1,1,1,1,2]
[4,7,2,3,1,6,5]=>[4,1,6,5,7,2,3]=>101010=>[1,1,1,1,1,1]
[4,7,2,3,5,1,6]=>[4,1,6,5,3,7,2]=>101101=>[1,1,2,1,1]
[4,7,2,3,5,6,1]=>[4,1,6,5,3,2,7]=>101110=>[1,1,3,1]
[4,7,2,3,6,1,5]=>[4,1,6,5,2,7,3]=>101101=>[1,1,2,1,1]
[4,7,2,3,6,5,1]=>[4,1,6,5,2,3,7]=>101100=>[1,1,2,2]
[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>101011=>[1,1,1,1,2]
[4,7,2,5,1,6,3]=>[4,1,6,3,7,2,5]=>101010=>[1,1,1,1,1,1]
[4,7,2,5,3,1,6]=>[4,1,6,3,5,7,2]=>101001=>[1,1,1,2,1]
[4,7,2,5,3,6,1]=>[4,1,6,3,5,2,7]=>101010=>[1,1,1,1,1,1]
[4,7,2,5,6,1,3]=>[4,1,6,3,2,7,5]=>101101=>[1,1,2,1,1]
[4,7,2,5,6,3,1]=>[4,1,6,3,2,5,7]=>101100=>[1,1,2,2]
[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>101011=>[1,1,1,1,2]
[4,7,2,6,1,5,3]=>[4,1,6,2,7,3,5]=>101010=>[1,1,1,1,1,1]
[4,7,2,6,3,1,5]=>[4,1,6,2,5,7,3]=>101001=>[1,1,1,2,1]
[4,7,2,6,3,5,1]=>[4,1,6,2,5,3,7]=>101010=>[1,1,1,1,1,1]
[4,7,2,6,5,1,3]=>[4,1,6,2,3,7,5]=>101001=>[1,1,1,2,1]
[4,7,2,6,5,3,1]=>[4,1,6,2,3,5,7]=>101000=>[1,1,1,3]
[4,7,3,1,2,5,6]=>[4,1,5,7,6,3,2]=>100111=>[1,2,3]
[4,7,3,1,2,6,5]=>[4,1,5,7,6,2,3]=>100110=>[1,2,2,1]
[4,7,3,1,5,2,6]=>[4,1,5,7,3,6,2]=>100101=>[1,2,1,1,1]
[4,7,3,1,5,6,2]=>[4,1,5,7,3,2,6]=>100110=>[1,2,2,1]
[4,7,3,1,6,2,5]=>[4,1,5,7,2,6,3]=>100101=>[1,2,1,1,1]
[4,7,3,1,6,5,2]=>[4,1,5,7,2,3,6]=>100100=>[1,2,1,2]
[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>100011=>[1,3,2]
[4,7,3,2,1,6,5]=>[4,1,5,6,7,2,3]=>100010=>[1,3,1,1]
[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>100101=>[1,2,1,1,1]
[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>100110=>[1,2,2,1]
[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>100101=>[1,2,1,1,1]
[4,7,3,2,6,5,1]=>[4,1,5,6,2,3,7]=>100100=>[1,2,1,2]
[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>101011=>[1,1,1,1,2]
[4,7,3,5,1,6,2]=>[4,1,5,3,7,2,6]=>101010=>[1,1,1,1,1,1]
[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>101001=>[1,1,1,2,1]
[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>101010=>[1,1,1,1,1,1]
[4,7,3,5,6,1,2]=>[4,1,5,3,2,7,6]=>101101=>[1,1,2,1,1]
[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>101100=>[1,1,2,2]
[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>101011=>[1,1,1,1,2]
[4,7,3,6,1,5,2]=>[4,1,5,2,7,3,6]=>101010=>[1,1,1,1,1,1]
[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>101001=>[1,1,1,2,1]
[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>101010=>[1,1,1,1,1,1]
[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>101001=>[1,1,1,2,1]
[4,7,3,6,5,2,1]=>[4,1,5,2,3,6,7]=>101000=>[1,1,1,3]
[4,7,5,1,2,3,6]=>[4,1,3,7,6,5,2]=>100111=>[1,2,3]
[4,7,5,1,2,6,3]=>[4,1,3,7,6,2,5]=>100110=>[1,2,2,1]
[4,7,5,1,3,2,6]=>[4,1,3,7,5,6,2]=>100101=>[1,2,1,1,1]
[4,7,5,1,3,6,2]=>[4,1,3,7,5,2,6]=>100110=>[1,2,2,1]
[4,7,5,1,6,2,3]=>[4,1,3,7,2,6,5]=>100101=>[1,2,1,1,1]
[4,7,5,1,6,3,2]=>[4,1,3,7,2,5,6]=>100100=>[1,2,1,2]
[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>100011=>[1,3,2]
[4,7,5,2,1,6,3]=>[4,1,3,6,7,2,5]=>100010=>[1,3,1,1]
[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>100101=>[1,2,1,1,1]
[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>100110=>[1,2,2,1]
[4,7,5,2,6,1,3]=>[4,1,3,6,2,7,5]=>100101=>[1,2,1,1,1]
[4,7,5,2,6,3,1]=>[4,1,3,6,2,5,7]=>100100=>[1,2,1,2]
[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>100011=>[1,3,2]
[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>100010=>[1,3,1,1]
[4,7,5,3,2,1,6]=>[4,1,3,5,6,7,2]=>100001=>[1,4,1]
[4,7,5,3,2,6,1]=>[4,1,3,5,6,2,7]=>100010=>[1,3,1,1]
[4,7,5,3,6,1,2]=>[4,1,3,5,2,7,6]=>100101=>[1,2,1,1,1]
[4,7,5,3,6,2,1]=>[4,1,3,5,2,6,7]=>100100=>[1,2,1,2]
[4,7,5,6,1,2,3]=>[4,1,3,2,7,6,5]=>101011=>[1,1,1,1,2]
[4,7,5,6,1,3,2]=>[4,1,3,2,7,5,6]=>101010=>[1,1,1,1,1,1]
[4,7,5,6,2,1,3]=>[4,1,3,2,6,7,5]=>101001=>[1,1,1,2,1]
[4,7,5,6,2,3,1]=>[4,1,3,2,6,5,7]=>101010=>[1,1,1,1,1,1]
[4,7,5,6,3,1,2]=>[4,1,3,2,5,7,6]=>101001=>[1,1,1,2,1]
[4,7,5,6,3,2,1]=>[4,1,3,2,5,6,7]=>101000=>[1,1,1,3]
[4,7,6,1,2,3,5]=>[4,1,2,7,6,5,3]=>100111=>[1,2,3]
[4,7,6,1,2,5,3]=>[4,1,2,7,6,3,5]=>100110=>[1,2,2,1]
[4,7,6,1,3,2,5]=>[4,1,2,7,5,6,3]=>100101=>[1,2,1,1,1]
[4,7,6,1,3,5,2]=>[4,1,2,7,5,3,6]=>100110=>[1,2,2,1]
[4,7,6,1,5,2,3]=>[4,1,2,7,3,6,5]=>100101=>[1,2,1,1,1]
[4,7,6,1,5,3,2]=>[4,1,2,7,3,5,6]=>100100=>[1,2,1,2]
[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>100011=>[1,3,2]
[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>100010=>[1,3,1,1]
[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>100101=>[1,2,1,1,1]
[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>100110=>[1,2,2,1]
[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>100101=>[1,2,1,1,1]
[4,7,6,2,5,3,1]=>[4,1,2,6,3,5,7]=>100100=>[1,2,1,2]
[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>100011=>[1,3,2]
[4,7,6,3,1,5,2]=>[4,1,2,5,7,3,6]=>100010=>[1,3,1,1]
[4,7,6,3,2,1,5]=>[4,1,2,5,6,7,3]=>100001=>[1,4,1]
[4,7,6,3,2,5,1]=>[4,1,2,5,6,3,7]=>100010=>[1,3,1,1]
[4,7,6,3,5,1,2]=>[4,1,2,5,3,7,6]=>100101=>[1,2,1,1,1]
[4,7,6,3,5,2,1]=>[4,1,2,5,3,6,7]=>100100=>[1,2,1,2]
[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>100011=>[1,3,2]
[4,7,6,5,1,3,2]=>[4,1,2,3,7,5,6]=>100010=>[1,3,1,1]
[4,7,6,5,2,1,3]=>[4,1,2,3,6,7,5]=>100001=>[1,4,1]
[4,7,6,5,2,3,1]=>[4,1,2,3,6,5,7]=>100010=>[1,3,1,1]
[4,7,6,5,3,1,2]=>[4,1,2,3,5,7,6]=>100001=>[1,4,1]
[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>100000=>[1,5]
[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>011111=>[1,5]
[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>011110=>[1,4,1]
[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]=>011101=>[1,3,1,1]
[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>011110=>[1,4,1]
[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>011101=>[1,3,1,1]
[5,1,2,3,7,6,4]=>[3,7,6,5,1,2,4]=>011100=>[1,3,2]
[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>011011=>[1,2,1,2]
[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>011010=>[1,2,1,1,1]
[5,1,2,4,6,3,7]=>[3,7,6,4,2,5,1]=>011101=>[1,3,1,1]
[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>011110=>[1,4,1]
[5,1,2,4,7,3,6]=>[3,7,6,4,1,5,2]=>011101=>[1,3,1,1]
[5,1,2,4,7,6,3]=>[3,7,6,4,1,2,5]=>011100=>[1,3,2]
[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]=>011011=>[1,2,1,2]
[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]=>011010=>[1,2,1,1,1]
[5,1,2,6,4,3,7]=>[3,7,6,2,4,5,1]=>011001=>[1,2,2,1]
[5,1,2,6,4,7,3]=>[3,7,6,2,4,1,5]=>011010=>[1,2,1,1,1]
[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]=>011101=>[1,3,1,1]
[5,1,2,6,7,4,3]=>[3,7,6,2,1,4,5]=>011100=>[1,3,2]
[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]=>011011=>[1,2,1,2]
[5,1,2,7,3,6,4]=>[3,7,6,1,5,2,4]=>011010=>[1,2,1,1,1]
[5,1,2,7,4,3,6]=>[3,7,6,1,4,5,2]=>011001=>[1,2,2,1]
[5,1,2,7,4,6,3]=>[3,7,6,1,4,2,5]=>011010=>[1,2,1,1,1]
[5,1,2,7,6,3,4]=>[3,7,6,1,2,5,4]=>011001=>[1,2,2,1]
[5,1,2,7,6,4,3]=>[3,7,6,1,2,4,5]=>011000=>[1,2,3]
[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>010111=>[1,1,1,3]
[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>010110=>[1,1,1,2,1]
[5,1,3,2,6,4,7]=>[3,7,5,6,2,4,1]=>010101=>[1,1,1,1,1,1]
[5,1,3,2,6,7,4]=>[3,7,5,6,2,1,4]=>010110=>[1,1,1,2,1]
[5,1,3,2,7,4,6]=>[3,7,5,6,1,4,2]=>010101=>[1,1,1,1,1,1]
[5,1,3,2,7,6,4]=>[3,7,5,6,1,2,4]=>010100=>[1,1,1,1,2]
[5,1,3,4,2,6,7]=>[3,7,5,4,6,2,1]=>011011=>[1,2,1,2]
[5,1,3,4,2,7,6]=>[3,7,5,4,6,1,2]=>011010=>[1,2,1,1,1]
[5,1,3,4,6,2,7]=>[3,7,5,4,2,6,1]=>011101=>[1,3,1,1]
[5,1,3,4,6,7,2]=>[3,7,5,4,2,1,6]=>011110=>[1,4,1]
[5,1,3,4,7,2,6]=>[3,7,5,4,1,6,2]=>011101=>[1,3,1,1]
[5,1,3,4,7,6,2]=>[3,7,5,4,1,2,6]=>011100=>[1,3,2]
[5,1,3,6,2,4,7]=>[3,7,5,2,6,4,1]=>011011=>[1,2,1,2]
[5,1,3,6,2,7,4]=>[3,7,5,2,6,1,4]=>011010=>[1,2,1,1,1]
[5,1,3,6,4,2,7]=>[3,7,5,2,4,6,1]=>011001=>[1,2,2,1]
[5,1,3,6,4,7,2]=>[3,7,5,2,4,1,6]=>011010=>[1,2,1,1,1]
[5,1,3,6,7,2,4]=>[3,7,5,2,1,6,4]=>011101=>[1,3,1,1]
[5,1,3,6,7,4,2]=>[3,7,5,2,1,4,6]=>011100=>[1,3,2]
[5,1,3,7,2,4,6]=>[3,7,5,1,6,4,2]=>011011=>[1,2,1,2]
[5,1,3,7,2,6,4]=>[3,7,5,1,6,2,4]=>011010=>[1,2,1,1,1]
[5,1,3,7,4,2,6]=>[3,7,5,1,4,6,2]=>011001=>[1,2,2,1]
[5,1,3,7,4,6,2]=>[3,7,5,1,4,2,6]=>011010=>[1,2,1,1,1]
[5,1,3,7,6,2,4]=>[3,7,5,1,2,6,4]=>011001=>[1,2,2,1]
[5,1,3,7,6,4,2]=>[3,7,5,1,2,4,6]=>011000=>[1,2,3]
[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>010111=>[1,1,1,3]
[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>010110=>[1,1,1,2,1]
[5,1,4,2,6,3,7]=>[3,7,4,6,2,5,1]=>010101=>[1,1,1,1,1,1]
[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>010110=>[1,1,1,2,1]
[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>010101=>[1,1,1,1,1,1]
[5,1,4,2,7,6,3]=>[3,7,4,6,1,2,5]=>010100=>[1,1,1,1,2]
[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>010011=>[1,1,2,2]
[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>010010=>[1,1,2,1,1]
[5,1,4,3,6,2,7]=>[3,7,4,5,2,6,1]=>010101=>[1,1,1,1,1,1]
[5,1,4,3,6,7,2]=>[3,7,4,5,2,1,6]=>010110=>[1,1,1,2,1]
[5,1,4,3,7,2,6]=>[3,7,4,5,1,6,2]=>010101=>[1,1,1,1,1,1]
[5,1,4,3,7,6,2]=>[3,7,4,5,1,2,6]=>010100=>[1,1,1,1,2]
[5,1,4,6,2,3,7]=>[3,7,4,2,6,5,1]=>011011=>[1,2,1,2]
[5,1,4,6,2,7,3]=>[3,7,4,2,6,1,5]=>011010=>[1,2,1,1,1]
[5,1,4,6,3,2,7]=>[3,7,4,2,5,6,1]=>011001=>[1,2,2,1]
[5,1,4,6,3,7,2]=>[3,7,4,2,5,1,6]=>011010=>[1,2,1,1,1]
[5,1,4,6,7,2,3]=>[3,7,4,2,1,6,5]=>011101=>[1,3,1,1]
[5,1,4,6,7,3,2]=>[3,7,4,2,1,5,6]=>011100=>[1,3,2]
[5,1,4,7,2,3,6]=>[3,7,4,1,6,5,2]=>011011=>[1,2,1,2]
[5,1,4,7,2,6,3]=>[3,7,4,1,6,2,5]=>011010=>[1,2,1,1,1]
[5,1,4,7,3,2,6]=>[3,7,4,1,5,6,2]=>011001=>[1,2,2,1]
[5,1,4,7,3,6,2]=>[3,7,4,1,5,2,6]=>011010=>[1,2,1,1,1]
[5,1,4,7,6,2,3]=>[3,7,4,1,2,6,5]=>011001=>[1,2,2,1]
[5,1,4,7,6,3,2]=>[3,7,4,1,2,5,6]=>011000=>[1,2,3]
[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]=>010111=>[1,1,1,3]
[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]=>010110=>[1,1,1,2,1]
[5,1,6,2,4,3,7]=>[3,7,2,6,4,5,1]=>010101=>[1,1,1,1,1,1]
[5,1,6,2,4,7,3]=>[3,7,2,6,4,1,5]=>010110=>[1,1,1,2,1]
[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]=>010101=>[1,1,1,1,1,1]
[5,1,6,2,7,4,3]=>[3,7,2,6,1,4,5]=>010100=>[1,1,1,1,2]
[5,1,6,3,2,4,7]=>[3,7,2,5,6,4,1]=>010011=>[1,1,2,2]
[5,1,6,3,2,7,4]=>[3,7,2,5,6,1,4]=>010010=>[1,1,2,1,1]
[5,1,6,3,4,2,7]=>[3,7,2,5,4,6,1]=>010101=>[1,1,1,1,1,1]
[5,1,6,3,4,7,2]=>[3,7,2,5,4,1,6]=>010110=>[1,1,1,2,1]
[5,1,6,3,7,2,4]=>[3,7,2,5,1,6,4]=>010101=>[1,1,1,1,1,1]
[5,1,6,3,7,4,2]=>[3,7,2,5,1,4,6]=>010100=>[1,1,1,1,2]
[5,1,6,4,2,3,7]=>[3,7,2,4,6,5,1]=>010011=>[1,1,2,2]
[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>010010=>[1,1,2,1,1]
[5,1,6,4,3,2,7]=>[3,7,2,4,5,6,1]=>010001=>[1,1,3,1]
[5,1,6,4,3,7,2]=>[3,7,2,4,5,1,6]=>010010=>[1,1,2,1,1]
[5,1,6,4,7,2,3]=>[3,7,2,4,1,6,5]=>010101=>[1,1,1,1,1,1]
[5,1,6,4,7,3,2]=>[3,7,2,4,1,5,6]=>010100=>[1,1,1,1,2]
[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]=>011011=>[1,2,1,2]
[5,1,6,7,2,4,3]=>[3,7,2,1,6,4,5]=>011010=>[1,2,1,1,1]
[5,1,6,7,3,2,4]=>[3,7,2,1,5,6,4]=>011001=>[1,2,2,1]
[5,1,6,7,3,4,2]=>[3,7,2,1,5,4,6]=>011010=>[1,2,1,1,1]
[5,1,6,7,4,2,3]=>[3,7,2,1,4,6,5]=>011001=>[1,2,2,1]
[5,1,6,7,4,3,2]=>[3,7,2,1,4,5,6]=>011000=>[1,2,3]
[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]=>010111=>[1,1,1,3]
[5,1,7,2,3,6,4]=>[3,7,1,6,5,2,4]=>010110=>[1,1,1,2,1]
[5,1,7,2,4,3,6]=>[3,7,1,6,4,5,2]=>010101=>[1,1,1,1,1,1]
[5,1,7,2,4,6,3]=>[3,7,1,6,4,2,5]=>010110=>[1,1,1,2,1]
[5,1,7,2,6,3,4]=>[3,7,1,6,2,5,4]=>010101=>[1,1,1,1,1,1]
[5,1,7,2,6,4,3]=>[3,7,1,6,2,4,5]=>010100=>[1,1,1,1,2]
[5,1,7,3,2,4,6]=>[3,7,1,5,6,4,2]=>010011=>[1,1,2,2]
[5,1,7,3,2,6,4]=>[3,7,1,5,6,2,4]=>010010=>[1,1,2,1,1]
[5,1,7,3,4,2,6]=>[3,7,1,5,4,6,2]=>010101=>[1,1,1,1,1,1]
[5,1,7,3,4,6,2]=>[3,7,1,5,4,2,6]=>010110=>[1,1,1,2,1]
[5,1,7,3,6,2,4]=>[3,7,1,5,2,6,4]=>010101=>[1,1,1,1,1,1]
[5,1,7,3,6,4,2]=>[3,7,1,5,2,4,6]=>010100=>[1,1,1,1,2]
[5,1,7,4,2,3,6]=>[3,7,1,4,6,5,2]=>010011=>[1,1,2,2]
[5,1,7,4,2,6,3]=>[3,7,1,4,6,2,5]=>010010=>[1,1,2,1,1]
[5,1,7,4,3,2,6]=>[3,7,1,4,5,6,2]=>010001=>[1,1,3,1]
[5,1,7,4,3,6,2]=>[3,7,1,4,5,2,6]=>010010=>[1,1,2,1,1]
[5,1,7,4,6,2,3]=>[3,7,1,4,2,6,5]=>010101=>[1,1,1,1,1,1]
[5,1,7,4,6,3,2]=>[3,7,1,4,2,5,6]=>010100=>[1,1,1,1,2]
[5,1,7,6,2,3,4]=>[3,7,1,2,6,5,4]=>010011=>[1,1,2,2]
[5,1,7,6,2,4,3]=>[3,7,1,2,6,4,5]=>010010=>[1,1,2,1,1]
[5,1,7,6,3,2,4]=>[3,7,1,2,5,6,4]=>010001=>[1,1,3,1]
[5,1,7,6,3,4,2]=>[3,7,1,2,5,4,6]=>010010=>[1,1,2,1,1]
[5,1,7,6,4,2,3]=>[3,7,1,2,4,6,5]=>010001=>[1,1,3,1]
[5,1,7,6,4,3,2]=>[3,7,1,2,4,5,6]=>010000=>[1,1,4]
[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>001111=>[2,4]
[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>001110=>[2,3,1]
[5,2,1,3,6,4,7]=>[3,6,7,5,2,4,1]=>001101=>[2,2,1,1]
[5,2,1,3,6,7,4]=>[3,6,7,5,2,1,4]=>001110=>[2,3,1]
[5,2,1,3,7,4,6]=>[3,6,7,5,1,4,2]=>001101=>[2,2,1,1]
[5,2,1,3,7,6,4]=>[3,6,7,5,1,2,4]=>001100=>[2,2,2]
[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>001011=>[2,1,1,2]
[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>001010=>[2,1,1,1,1]
[5,2,1,4,6,3,7]=>[3,6,7,4,2,5,1]=>001101=>[2,2,1,1]
[5,2,1,4,6,7,3]=>[3,6,7,4,2,1,5]=>001110=>[2,3,1]
[5,2,1,4,7,3,6]=>[3,6,7,4,1,5,2]=>001101=>[2,2,1,1]
[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>001100=>[2,2,2]
[5,2,1,6,3,4,7]=>[3,6,7,2,5,4,1]=>001011=>[2,1,1,2]
[5,2,1,6,3,7,4]=>[3,6,7,2,5,1,4]=>001010=>[2,1,1,1,1]
[5,2,1,6,4,3,7]=>[3,6,7,2,4,5,1]=>001001=>[2,1,2,1]
[5,2,1,6,4,7,3]=>[3,6,7,2,4,1,5]=>001010=>[2,1,1,1,1]
[5,2,1,6,7,3,4]=>[3,6,7,2,1,5,4]=>001101=>[2,2,1,1]
[5,2,1,6,7,4,3]=>[3,6,7,2,1,4,5]=>001100=>[2,2,2]
[5,2,1,7,3,4,6]=>[3,6,7,1,5,4,2]=>001011=>[2,1,1,2]
[5,2,1,7,3,6,4]=>[3,6,7,1,5,2,4]=>001010=>[2,1,1,1,1]
[5,2,1,7,4,3,6]=>[3,6,7,1,4,5,2]=>001001=>[2,1,2,1]
[5,2,1,7,4,6,3]=>[3,6,7,1,4,2,5]=>001010=>[2,1,1,1,1]
[5,2,1,7,6,3,4]=>[3,6,7,1,2,5,4]=>001001=>[2,1,2,1]
[5,2,1,7,6,4,3]=>[3,6,7,1,2,4,5]=>001000=>[2,1,3]
[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>010111=>[1,1,1,3]
[5,2,3,1,4,7,6]=>[3,6,5,7,4,1,2]=>010110=>[1,1,1,2,1]
[5,2,3,1,6,4,7]=>[3,6,5,7,2,4,1]=>010101=>[1,1,1,1,1,1]
[5,2,3,1,6,7,4]=>[3,6,5,7,2,1,4]=>010110=>[1,1,1,2,1]
[5,2,3,1,7,4,6]=>[3,6,5,7,1,4,2]=>010101=>[1,1,1,1,1,1]
[5,2,3,1,7,6,4]=>[3,6,5,7,1,2,4]=>010100=>[1,1,1,1,2]
[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>011011=>[1,2,1,2]
[5,2,3,4,1,7,6]=>[3,6,5,4,7,1,2]=>011010=>[1,2,1,1,1]
[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>011101=>[1,3,1,1]
[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>011110=>[1,4,1]
[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>011101=>[1,3,1,1]
[5,2,3,4,7,6,1]=>[3,6,5,4,1,2,7]=>011100=>[1,3,2]
[5,2,3,6,1,4,7]=>[3,6,5,2,7,4,1]=>011011=>[1,2,1,2]
[5,2,3,6,1,7,4]=>[3,6,5,2,7,1,4]=>011010=>[1,2,1,1,1]
[5,2,3,6,4,1,7]=>[3,6,5,2,4,7,1]=>011001=>[1,2,2,1]
[5,2,3,6,4,7,1]=>[3,6,5,2,4,1,7]=>011010=>[1,2,1,1,1]
[5,2,3,6,7,1,4]=>[3,6,5,2,1,7,4]=>011101=>[1,3,1,1]
[5,2,3,6,7,4,1]=>[3,6,5,2,1,4,7]=>011100=>[1,3,2]
[5,2,3,7,1,4,6]=>[3,6,5,1,7,4,2]=>011011=>[1,2,1,2]
[5,2,3,7,1,6,4]=>[3,6,5,1,7,2,4]=>011010=>[1,2,1,1,1]
[5,2,3,7,4,1,6]=>[3,6,5,1,4,7,2]=>011001=>[1,2,2,1]
[5,2,3,7,4,6,1]=>[3,6,5,1,4,2,7]=>011010=>[1,2,1,1,1]
[5,2,3,7,6,1,4]=>[3,6,5,1,2,7,4]=>011001=>[1,2,2,1]
[5,2,3,7,6,4,1]=>[3,6,5,1,2,4,7]=>011000=>[1,2,3]
[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>010111=>[1,1,1,3]
[5,2,4,1,3,7,6]=>[3,6,4,7,5,1,2]=>010110=>[1,1,1,2,1]
[5,2,4,1,6,3,7]=>[3,6,4,7,2,5,1]=>010101=>[1,1,1,1,1,1]
[5,2,4,1,6,7,3]=>[3,6,4,7,2,1,5]=>010110=>[1,1,1,2,1]
[5,2,4,1,7,3,6]=>[3,6,4,7,1,5,2]=>010101=>[1,1,1,1,1,1]
[5,2,4,1,7,6,3]=>[3,6,4,7,1,2,5]=>010100=>[1,1,1,1,2]
[5,2,4,3,1,6,7]=>[3,6,4,5,7,2,1]=>010011=>[1,1,2,2]
[5,2,4,3,1,7,6]=>[3,6,4,5,7,1,2]=>010010=>[1,1,2,1,1]
[5,2,4,3,6,1,7]=>[3,6,4,5,2,7,1]=>010101=>[1,1,1,1,1,1]
[5,2,4,3,6,7,1]=>[3,6,4,5,2,1,7]=>010110=>[1,1,1,2,1]
[5,2,4,3,7,1,6]=>[3,6,4,5,1,7,2]=>010101=>[1,1,1,1,1,1]
[5,2,4,3,7,6,1]=>[3,6,4,5,1,2,7]=>010100=>[1,1,1,1,2]
[5,2,4,6,1,3,7]=>[3,6,4,2,7,5,1]=>011011=>[1,2,1,2]
[5,2,4,6,1,7,3]=>[3,6,4,2,7,1,5]=>011010=>[1,2,1,1,1]
[5,2,4,6,3,1,7]=>[3,6,4,2,5,7,1]=>011001=>[1,2,2,1]
[5,2,4,6,3,7,1]=>[3,6,4,2,5,1,7]=>011010=>[1,2,1,1,1]
[5,2,4,6,7,1,3]=>[3,6,4,2,1,7,5]=>011101=>[1,3,1,1]
[5,2,4,6,7,3,1]=>[3,6,4,2,1,5,7]=>011100=>[1,3,2]
[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>011011=>[1,2,1,2]
[5,2,4,7,1,6,3]=>[3,6,4,1,7,2,5]=>011010=>[1,2,1,1,1]
[5,2,4,7,3,1,6]=>[3,6,4,1,5,7,2]=>011001=>[1,2,2,1]
[5,2,4,7,3,6,1]=>[3,6,4,1,5,2,7]=>011010=>[1,2,1,1,1]
[5,2,4,7,6,1,3]=>[3,6,4,1,2,7,5]=>011001=>[1,2,2,1]
[5,2,4,7,6,3,1]=>[3,6,4,1,2,5,7]=>011000=>[1,2,3]
[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>010111=>[1,1,1,3]
[5,2,6,1,3,7,4]=>[3,6,2,7,5,1,4]=>010110=>[1,1,1,2,1]
[5,2,6,1,4,3,7]=>[3,6,2,7,4,5,1]=>010101=>[1,1,1,1,1,1]
[5,2,6,1,4,7,3]=>[3,6,2,7,4,1,5]=>010110=>[1,1,1,2,1]
[5,2,6,1,7,3,4]=>[3,6,2,7,1,5,4]=>010101=>[1,1,1,1,1,1]
[5,2,6,1,7,4,3]=>[3,6,2,7,1,4,5]=>010100=>[1,1,1,1,2]
[5,2,6,3,1,4,7]=>[3,6,2,5,7,4,1]=>010011=>[1,1,2,2]
[5,2,6,3,1,7,4]=>[3,6,2,5,7,1,4]=>010010=>[1,1,2,1,1]
[5,2,6,3,4,1,7]=>[3,6,2,5,4,7,1]=>010101=>[1,1,1,1,1,1]
[5,2,6,3,4,7,1]=>[3,6,2,5,4,1,7]=>010110=>[1,1,1,2,1]
[5,2,6,3,7,1,4]=>[3,6,2,5,1,7,4]=>010101=>[1,1,1,1,1,1]
[5,2,6,3,7,4,1]=>[3,6,2,5,1,4,7]=>010100=>[1,1,1,1,2]
[5,2,6,4,1,3,7]=>[3,6,2,4,7,5,1]=>010011=>[1,1,2,2]
[5,2,6,4,1,7,3]=>[3,6,2,4,7,1,5]=>010010=>[1,1,2,1,1]
[5,2,6,4,3,1,7]=>[3,6,2,4,5,7,1]=>010001=>[1,1,3,1]
[5,2,6,4,3,7,1]=>[3,6,2,4,5,1,7]=>010010=>[1,1,2,1,1]
[5,2,6,4,7,1,3]=>[3,6,2,4,1,7,5]=>010101=>[1,1,1,1,1,1]
[5,2,6,4,7,3,1]=>[3,6,2,4,1,5,7]=>010100=>[1,1,1,1,2]
[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>011011=>[1,2,1,2]
[5,2,6,7,1,4,3]=>[3,6,2,1,7,4,5]=>011010=>[1,2,1,1,1]
[5,2,6,7,3,1,4]=>[3,6,2,1,5,7,4]=>011001=>[1,2,2,1]
[5,2,6,7,3,4,1]=>[3,6,2,1,5,4,7]=>011010=>[1,2,1,1,1]
[5,2,6,7,4,1,3]=>[3,6,2,1,4,7,5]=>011001=>[1,2,2,1]
[5,2,6,7,4,3,1]=>[3,6,2,1,4,5,7]=>011000=>[1,2,3]
[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>010111=>[1,1,1,3]
[5,2,7,1,3,6,4]=>[3,6,1,7,5,2,4]=>010110=>[1,1,1,2,1]
[5,2,7,1,4,3,6]=>[3,6,1,7,4,5,2]=>010101=>[1,1,1,1,1,1]
[5,2,7,1,4,6,3]=>[3,6,1,7,4,2,5]=>010110=>[1,1,1,2,1]
[5,2,7,1,6,3,4]=>[3,6,1,7,2,5,4]=>010101=>[1,1,1,1,1,1]
[5,2,7,1,6,4,3]=>[3,6,1,7,2,4,5]=>010100=>[1,1,1,1,2]
[5,2,7,3,1,4,6]=>[3,6,1,5,7,4,2]=>010011=>[1,1,2,2]
[5,2,7,3,1,6,4]=>[3,6,1,5,7,2,4]=>010010=>[1,1,2,1,1]
[5,2,7,3,4,1,6]=>[3,6,1,5,4,7,2]=>010101=>[1,1,1,1,1,1]
[5,2,7,3,4,6,1]=>[3,6,1,5,4,2,7]=>010110=>[1,1,1,2,1]
[5,2,7,3,6,1,4]=>[3,6,1,5,2,7,4]=>010101=>[1,1,1,1,1,1]
[5,2,7,3,6,4,1]=>[3,6,1,5,2,4,7]=>010100=>[1,1,1,1,2]
[5,2,7,4,1,3,6]=>[3,6,1,4,7,5,2]=>010011=>[1,1,2,2]
[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>010010=>[1,1,2,1,1]
[5,2,7,4,3,1,6]=>[3,6,1,4,5,7,2]=>010001=>[1,1,3,1]
[5,2,7,4,3,6,1]=>[3,6,1,4,5,2,7]=>010010=>[1,1,2,1,1]
[5,2,7,4,6,1,3]=>[3,6,1,4,2,7,5]=>010101=>[1,1,1,1,1,1]
[5,2,7,4,6,3,1]=>[3,6,1,4,2,5,7]=>010100=>[1,1,1,1,2]
[5,2,7,6,1,3,4]=>[3,6,1,2,7,5,4]=>010011=>[1,1,2,2]
[5,2,7,6,1,4,3]=>[3,6,1,2,7,4,5]=>010010=>[1,1,2,1,1]
[5,2,7,6,3,1,4]=>[3,6,1,2,5,7,4]=>010001=>[1,1,3,1]
[5,2,7,6,3,4,1]=>[3,6,1,2,5,4,7]=>010010=>[1,1,2,1,1]
[5,2,7,6,4,1,3]=>[3,6,1,2,4,7,5]=>010001=>[1,1,3,1]
[5,2,7,6,4,3,1]=>[3,6,1,2,4,5,7]=>010000=>[1,1,4]
[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>001111=>[2,4]
[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>001110=>[2,3,1]
[5,3,1,2,6,4,7]=>[3,5,7,6,2,4,1]=>001101=>[2,2,1,1]
[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>001110=>[2,3,1]
[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>001101=>[2,2,1,1]
[5,3,1,2,7,6,4]=>[3,5,7,6,1,2,4]=>001100=>[2,2,2]
[5,3,1,4,2,6,7]=>[3,5,7,4,6,2,1]=>001011=>[2,1,1,2]
[5,3,1,4,2,7,6]=>[3,5,7,4,6,1,2]=>001010=>[2,1,1,1,1]
[5,3,1,4,6,2,7]=>[3,5,7,4,2,6,1]=>001101=>[2,2,1,1]
[5,3,1,4,6,7,2]=>[3,5,7,4,2,1,6]=>001110=>[2,3,1]
[5,3,1,4,7,2,6]=>[3,5,7,4,1,6,2]=>001101=>[2,2,1,1]
[5,3,1,4,7,6,2]=>[3,5,7,4,1,2,6]=>001100=>[2,2,2]
[5,3,1,6,2,4,7]=>[3,5,7,2,6,4,1]=>001011=>[2,1,1,2]
[5,3,1,6,2,7,4]=>[3,5,7,2,6,1,4]=>001010=>[2,1,1,1,1]
[5,3,1,6,4,2,7]=>[3,5,7,2,4,6,1]=>001001=>[2,1,2,1]
[5,3,1,6,4,7,2]=>[3,5,7,2,4,1,6]=>001010=>[2,1,1,1,1]
[5,3,1,6,7,2,4]=>[3,5,7,2,1,6,4]=>001101=>[2,2,1,1]
[5,3,1,6,7,4,2]=>[3,5,7,2,1,4,6]=>001100=>[2,2,2]
[5,3,1,7,2,4,6]=>[3,5,7,1,6,4,2]=>001011=>[2,1,1,2]
[5,3,1,7,2,6,4]=>[3,5,7,1,6,2,4]=>001010=>[2,1,1,1,1]
[5,3,1,7,4,2,6]=>[3,5,7,1,4,6,2]=>001001=>[2,1,2,1]
[5,3,1,7,4,6,2]=>[3,5,7,1,4,2,6]=>001010=>[2,1,1,1,1]
[5,3,1,7,6,2,4]=>[3,5,7,1,2,6,4]=>001001=>[2,1,2,1]
[5,3,1,7,6,4,2]=>[3,5,7,1,2,4,6]=>001000=>[2,1,3]
[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>000111=>[3,3]
[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>000110=>[3,2,1]
[5,3,2,1,6,4,7]=>[3,5,6,7,2,4,1]=>000101=>[3,1,1,1]
[5,3,2,1,6,7,4]=>[3,5,6,7,2,1,4]=>000110=>[3,2,1]
[5,3,2,1,7,4,6]=>[3,5,6,7,1,4,2]=>000101=>[3,1,1,1]
[5,3,2,1,7,6,4]=>[3,5,6,7,1,2,4]=>000100=>[3,1,2]
[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>001011=>[2,1,1,2]
[5,3,2,4,1,7,6]=>[3,5,6,4,7,1,2]=>001010=>[2,1,1,1,1]
[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>001101=>[2,2,1,1]
[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>001110=>[2,3,1]
[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>001101=>[2,2,1,1]
[5,3,2,4,7,6,1]=>[3,5,6,4,1,2,7]=>001100=>[2,2,2]
[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>001011=>[2,1,1,2]
[5,3,2,6,1,7,4]=>[3,5,6,2,7,1,4]=>001010=>[2,1,1,1,1]
[5,3,2,6,4,1,7]=>[3,5,6,2,4,7,1]=>001001=>[2,1,2,1]
[5,3,2,6,4,7,1]=>[3,5,6,2,4,1,7]=>001010=>[2,1,1,1,1]
[5,3,2,6,7,1,4]=>[3,5,6,2,1,7,4]=>001101=>[2,2,1,1]
[5,3,2,6,7,4,1]=>[3,5,6,2,1,4,7]=>001100=>[2,2,2]
[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>001011=>[2,1,1,2]
[5,3,2,7,1,6,4]=>[3,5,6,1,7,2,4]=>001010=>[2,1,1,1,1]
[5,3,2,7,4,1,6]=>[3,5,6,1,4,7,2]=>001001=>[2,1,2,1]
[5,3,2,7,4,6,1]=>[3,5,6,1,4,2,7]=>001010=>[2,1,1,1,1]
[5,3,2,7,6,1,4]=>[3,5,6,1,2,7,4]=>001001=>[2,1,2,1]
[5,3,2,7,6,4,1]=>[3,5,6,1,2,4,7]=>001000=>[2,1,3]
[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>010111=>[1,1,1,3]
[5,3,4,1,2,7,6]=>[3,5,4,7,6,1,2]=>010110=>[1,1,1,2,1]
[5,3,4,1,6,2,7]=>[3,5,4,7,2,6,1]=>010101=>[1,1,1,1,1,1]
[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>010110=>[1,1,1,2,1]
[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>010101=>[1,1,1,1,1,1]
[5,3,4,1,7,6,2]=>[3,5,4,7,1,2,6]=>010100=>[1,1,1,1,2]
[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>010011=>[1,1,2,2]
[5,3,4,2,1,7,6]=>[3,5,4,6,7,1,2]=>010010=>[1,1,2,1,1]
[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>010101=>[1,1,1,1,1,1]
[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>010110=>[1,1,1,2,1]
[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>010101=>[1,1,1,1,1,1]
[5,3,4,2,7,6,1]=>[3,5,4,6,1,2,7]=>010100=>[1,1,1,1,2]
[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>011011=>[1,2,1,2]
[5,3,4,6,1,7,2]=>[3,5,4,2,7,1,6]=>011010=>[1,2,1,1,1]
[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>011001=>[1,2,2,1]
[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>011010=>[1,2,1,1,1]
[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>011101=>[1,3,1,1]
[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>011100=>[1,3,2]
[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>011011=>[1,2,1,2]
[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>011010=>[1,2,1,1,1]
[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>011001=>[1,2,2,1]
[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>011010=>[1,2,1,1,1]
[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>011001=>[1,2,2,1]
[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>011000=>[1,2,3]
[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>010111=>[1,1,1,3]
[5,3,6,1,2,7,4]=>[3,5,2,7,6,1,4]=>010110=>[1,1,1,2,1]
[5,3,6,1,4,2,7]=>[3,5,2,7,4,6,1]=>010101=>[1,1,1,1,1,1]
[5,3,6,1,4,7,2]=>[3,5,2,7,4,1,6]=>010110=>[1,1,1,2,1]
[5,3,6,1,7,2,4]=>[3,5,2,7,1,6,4]=>010101=>[1,1,1,1,1,1]
[5,3,6,1,7,4,2]=>[3,5,2,7,1,4,6]=>010100=>[1,1,1,1,2]
[5,3,6,2,1,4,7]=>[3,5,2,6,7,4,1]=>010011=>[1,1,2,2]
[5,3,6,2,1,7,4]=>[3,5,2,6,7,1,4]=>010010=>[1,1,2,1,1]
[5,3,6,2,4,1,7]=>[3,5,2,6,4,7,1]=>010101=>[1,1,1,1,1,1]
[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>010110=>[1,1,1,2,1]
[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>010101=>[1,1,1,1,1,1]
[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>010100=>[1,1,1,1,2]
[5,3,6,4,1,2,7]=>[3,5,2,4,7,6,1]=>010011=>[1,1,2,2]
[5,3,6,4,1,7,2]=>[3,5,2,4,7,1,6]=>010010=>[1,1,2,1,1]
[5,3,6,4,2,1,7]=>[3,5,2,4,6,7,1]=>010001=>[1,1,3,1]
[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>010010=>[1,1,2,1,1]
[5,3,6,4,7,1,2]=>[3,5,2,4,1,7,6]=>010101=>[1,1,1,1,1,1]
[5,3,6,4,7,2,1]=>[3,5,2,4,1,6,7]=>010100=>[1,1,1,1,2]
[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>011011=>[1,2,1,2]
[5,3,6,7,1,4,2]=>[3,5,2,1,7,4,6]=>011010=>[1,2,1,1,1]
[5,3,6,7,2,1,4]=>[3,5,2,1,6,7,4]=>011001=>[1,2,2,1]
[5,3,6,7,2,4,1]=>[3,5,2,1,6,4,7]=>011010=>[1,2,1,1,1]
[5,3,6,7,4,1,2]=>[3,5,2,1,4,7,6]=>011001=>[1,2,2,1]
[5,3,6,7,4,2,1]=>[3,5,2,1,4,6,7]=>011000=>[1,2,3]
[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>010111=>[1,1,1,3]
[5,3,7,1,2,6,4]=>[3,5,1,7,6,2,4]=>010110=>[1,1,1,2,1]
[5,3,7,1,4,2,6]=>[3,5,1,7,4,6,2]=>010101=>[1,1,1,1,1,1]
[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>010110=>[1,1,1,2,1]
[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>010101=>[1,1,1,1,1,1]
[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>010100=>[1,1,1,1,2]
[5,3,7,2,1,4,6]=>[3,5,1,6,7,4,2]=>010011=>[1,1,2,2]
[5,3,7,2,1,6,4]=>[3,5,1,6,7,2,4]=>010010=>[1,1,2,1,1]
[5,3,7,2,4,1,6]=>[3,5,1,6,4,7,2]=>010101=>[1,1,1,1,1,1]
[5,3,7,2,4,6,1]=>[3,5,1,6,4,2,7]=>010110=>[1,1,1,2,1]
[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>010101=>[1,1,1,1,1,1]
[5,3,7,2,6,4,1]=>[3,5,1,6,2,4,7]=>010100=>[1,1,1,1,2]
[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>010011=>[1,1,2,2]
[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>010010=>[1,1,2,1,1]
[5,3,7,4,2,1,6]=>[3,5,1,4,6,7,2]=>010001=>[1,1,3,1]
[5,3,7,4,2,6,1]=>[3,5,1,4,6,2,7]=>010010=>[1,1,2,1,1]
[5,3,7,4,6,1,2]=>[3,5,1,4,2,7,6]=>010101=>[1,1,1,1,1,1]
[5,3,7,4,6,2,1]=>[3,5,1,4,2,6,7]=>010100=>[1,1,1,1,2]
[5,3,7,6,1,2,4]=>[3,5,1,2,7,6,4]=>010011=>[1,1,2,2]
[5,3,7,6,1,4,2]=>[3,5,1,2,7,4,6]=>010010=>[1,1,2,1,1]
[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>010001=>[1,1,3,1]
[5,3,7,6,2,4,1]=>[3,5,1,2,6,4,7]=>010010=>[1,1,2,1,1]
[5,3,7,6,4,1,2]=>[3,5,1,2,4,7,6]=>010001=>[1,1,3,1]
[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>010000=>[1,1,4]
[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>001111=>[2,4]
[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>001110=>[2,3,1]
[5,4,1,2,6,3,7]=>[3,4,7,6,2,5,1]=>001101=>[2,2,1,1]
[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>001110=>[2,3,1]
[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>001101=>[2,2,1,1]
[5,4,1,2,7,6,3]=>[3,4,7,6,1,2,5]=>001100=>[2,2,2]
[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>001011=>[2,1,1,2]
[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>001010=>[2,1,1,1,1]
[5,4,1,3,6,2,7]=>[3,4,7,5,2,6,1]=>001101=>[2,2,1,1]
[5,4,1,3,6,7,2]=>[3,4,7,5,2,1,6]=>001110=>[2,3,1]
[5,4,1,3,7,2,6]=>[3,4,7,5,1,6,2]=>001101=>[2,2,1,1]
[5,4,1,3,7,6,2]=>[3,4,7,5,1,2,6]=>001100=>[2,2,2]
[5,4,1,6,2,3,7]=>[3,4,7,2,6,5,1]=>001011=>[2,1,1,2]
[5,4,1,6,2,7,3]=>[3,4,7,2,6,1,5]=>001010=>[2,1,1,1,1]
[5,4,1,6,3,2,7]=>[3,4,7,2,5,6,1]=>001001=>[2,1,2,1]
[5,4,1,6,3,7,2]=>[3,4,7,2,5,1,6]=>001010=>[2,1,1,1,1]
[5,4,1,6,7,2,3]=>[3,4,7,2,1,6,5]=>001101=>[2,2,1,1]
[5,4,1,6,7,3,2]=>[3,4,7,2,1,5,6]=>001100=>[2,2,2]
[5,4,1,7,2,3,6]=>[3,4,7,1,6,5,2]=>001011=>[2,1,1,2]
[5,4,1,7,2,6,3]=>[3,4,7,1,6,2,5]=>001010=>[2,1,1,1,1]
[5,4,1,7,3,2,6]=>[3,4,7,1,5,6,2]=>001001=>[2,1,2,1]
[5,4,1,7,3,6,2]=>[3,4,7,1,5,2,6]=>001010=>[2,1,1,1,1]
[5,4,1,7,6,2,3]=>[3,4,7,1,2,6,5]=>001001=>[2,1,2,1]
[5,4,1,7,6,3,2]=>[3,4,7,1,2,5,6]=>001000=>[2,1,3]
[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>000111=>[3,3]
[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>000110=>[3,2,1]
[5,4,2,1,6,3,7]=>[3,4,6,7,2,5,1]=>000101=>[3,1,1,1]
[5,4,2,1,6,7,3]=>[3,4,6,7,2,1,5]=>000110=>[3,2,1]
[5,4,2,1,7,3,6]=>[3,4,6,7,1,5,2]=>000101=>[3,1,1,1]
[5,4,2,1,7,6,3]=>[3,4,6,7,1,2,5]=>000100=>[3,1,2]
[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>001011=>[2,1,1,2]
[5,4,2,3,1,7,6]=>[3,4,6,5,7,1,2]=>001010=>[2,1,1,1,1]
[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>001101=>[2,2,1,1]
[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>001110=>[2,3,1]
[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>001101=>[2,2,1,1]
[5,4,2,3,7,6,1]=>[3,4,6,5,1,2,7]=>001100=>[2,2,2]
[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>001011=>[2,1,1,2]
[5,4,2,6,1,7,3]=>[3,4,6,2,7,1,5]=>001010=>[2,1,1,1,1]
[5,4,2,6,3,1,7]=>[3,4,6,2,5,7,1]=>001001=>[2,1,2,1]
[5,4,2,6,3,7,1]=>[3,4,6,2,5,1,7]=>001010=>[2,1,1,1,1]
[5,4,2,6,7,1,3]=>[3,4,6,2,1,7,5]=>001101=>[2,2,1,1]
[5,4,2,6,7,3,1]=>[3,4,6,2,1,5,7]=>001100=>[2,2,2]
[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>001011=>[2,1,1,2]
[5,4,2,7,1,6,3]=>[3,4,6,1,7,2,5]=>001010=>[2,1,1,1,1]
[5,4,2,7,3,1,6]=>[3,4,6,1,5,7,2]=>001001=>[2,1,2,1]
[5,4,2,7,3,6,1]=>[3,4,6,1,5,2,7]=>001010=>[2,1,1,1,1]
[5,4,2,7,6,1,3]=>[3,4,6,1,2,7,5]=>001001=>[2,1,2,1]
[5,4,2,7,6,3,1]=>[3,4,6,1,2,5,7]=>001000=>[2,1,3]
[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>000111=>[3,3]
[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>000110=>[3,2,1]
[5,4,3,1,6,2,7]=>[3,4,5,7,2,6,1]=>000101=>[3,1,1,1]
[5,4,3,1,6,7,2]=>[3,4,5,7,2,1,6]=>000110=>[3,2,1]
[5,4,3,1,7,2,6]=>[3,4,5,7,1,6,2]=>000101=>[3,1,1,1]
[5,4,3,1,7,6,2]=>[3,4,5,7,1,2,6]=>000100=>[3,1,2]
[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>000011=>[4,2]
[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>000010=>[4,1,1]
[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>000101=>[3,1,1,1]
[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>000110=>[3,2,1]
[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>000101=>[3,1,1,1]
[5,4,3,2,7,6,1]=>[3,4,5,6,1,2,7]=>000100=>[3,1,2]
[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>001011=>[2,1,1,2]
[5,4,3,6,1,7,2]=>[3,4,5,2,7,1,6]=>001010=>[2,1,1,1,1]
[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>001001=>[2,1,2,1]
[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>001010=>[2,1,1,1,1]
[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>001101=>[2,2,1,1]
[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>001100=>[2,2,2]
[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>001011=>[2,1,1,2]
[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>001010=>[2,1,1,1,1]
[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>001001=>[2,1,2,1]
[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>001010=>[2,1,1,1,1]
[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>001001=>[2,1,2,1]
[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>001000=>[2,1,3]
[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>010111=>[1,1,1,3]
[5,4,6,1,2,7,3]=>[3,4,2,7,6,1,5]=>010110=>[1,1,1,2,1]
[5,4,6,1,3,2,7]=>[3,4,2,7,5,6,1]=>010101=>[1,1,1,1,1,1]
[5,4,6,1,3,7,2]=>[3,4,2,7,5,1,6]=>010110=>[1,1,1,2,1]
[5,4,6,1,7,2,3]=>[3,4,2,7,1,6,5]=>010101=>[1,1,1,1,1,1]
[5,4,6,1,7,3,2]=>[3,4,2,7,1,5,6]=>010100=>[1,1,1,1,2]
[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>010011=>[1,1,2,2]
[5,4,6,2,1,7,3]=>[3,4,2,6,7,1,5]=>010010=>[1,1,2,1,1]
[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>010101=>[1,1,1,1,1,1]
[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>010110=>[1,1,1,2,1]
[5,4,6,2,7,1,3]=>[3,4,2,6,1,7,5]=>010101=>[1,1,1,1,1,1]
[5,4,6,2,7,3,1]=>[3,4,2,6,1,5,7]=>010100=>[1,1,1,1,2]
[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>010011=>[1,1,2,2]
[5,4,6,3,1,7,2]=>[3,4,2,5,7,1,6]=>010010=>[1,1,2,1,1]
[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>010001=>[1,1,3,1]
[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>010010=>[1,1,2,1,1]
[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>010101=>[1,1,1,1,1,1]
[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>010100=>[1,1,1,1,2]
[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>011011=>[1,2,1,2]
[5,4,6,7,1,3,2]=>[3,4,2,1,7,5,6]=>011010=>[1,2,1,1,1]
[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>011001=>[1,2,2,1]
[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>011010=>[1,2,1,1,1]
[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>011001=>[1,2,2,1]
[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>011000=>[1,2,3]
[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>010111=>[1,1,1,3]
[5,4,7,1,2,6,3]=>[3,4,1,7,6,2,5]=>010110=>[1,1,1,2,1]
[5,4,7,1,3,2,6]=>[3,4,1,7,5,6,2]=>010101=>[1,1,1,1,1,1]
[5,4,7,1,3,6,2]=>[3,4,1,7,5,2,6]=>010110=>[1,1,1,2,1]
[5,4,7,1,6,2,3]=>[3,4,1,7,2,6,5]=>010101=>[1,1,1,1,1,1]
[5,4,7,1,6,3,2]=>[3,4,1,7,2,5,6]=>010100=>[1,1,1,1,2]
[5,4,7,2,1,3,6]=>[3,4,1,6,7,5,2]=>010011=>[1,1,2,2]
[5,4,7,2,1,6,3]=>[3,4,1,6,7,2,5]=>010010=>[1,1,2,1,1]
[5,4,7,2,3,1,6]=>[3,4,1,6,5,7,2]=>010101=>[1,1,1,1,1,1]
[5,4,7,2,3,6,1]=>[3,4,1,6,5,2,7]=>010110=>[1,1,1,2,1]
[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>010101=>[1,1,1,1,1,1]
[5,4,7,2,6,3,1]=>[3,4,1,6,2,5,7]=>010100=>[1,1,1,1,2]
[5,4,7,3,1,2,6]=>[3,4,1,5,7,6,2]=>010011=>[1,1,2,2]
[5,4,7,3,1,6,2]=>[3,4,1,5,7,2,6]=>010010=>[1,1,2,1,1]
[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>010001=>[1,1,3,1]
[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>010010=>[1,1,2,1,1]
[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>010101=>[1,1,1,1,1,1]
[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>010100=>[1,1,1,1,2]
[5,4,7,6,1,2,3]=>[3,4,1,2,7,6,5]=>010011=>[1,1,2,2]
[5,4,7,6,1,3,2]=>[3,4,1,2,7,5,6]=>010010=>[1,1,2,1,1]
[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>010001=>[1,1,3,1]
[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>010010=>[1,1,2,1,1]
[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>010001=>[1,1,3,1]
[5,4,7,6,3,2,1]=>[3,4,1,2,5,6,7]=>010000=>[1,1,4]
[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>101111=>[1,1,4]
[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>101110=>[1,1,3,1]
[5,6,1,2,4,3,7]=>[3,2,7,6,4,5,1]=>101101=>[1,1,2,1,1]
[5,6,1,2,4,7,3]=>[3,2,7,6,4,1,5]=>101110=>[1,1,3,1]
[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]=>101101=>[1,1,2,1,1]
[5,6,1,2,7,4,3]=>[3,2,7,6,1,4,5]=>101100=>[1,1,2,2]
[5,6,1,3,2,4,7]=>[3,2,7,5,6,4,1]=>101011=>[1,1,1,1,2]
[5,6,1,3,2,7,4]=>[3,2,7,5,6,1,4]=>101010=>[1,1,1,1,1,1]
[5,6,1,3,4,2,7]=>[3,2,7,5,4,6,1]=>101101=>[1,1,2,1,1]
[5,6,1,3,4,7,2]=>[3,2,7,5,4,1,6]=>101110=>[1,1,3,1]
[5,6,1,3,7,2,4]=>[3,2,7,5,1,6,4]=>101101=>[1,1,2,1,1]
[5,6,1,3,7,4,2]=>[3,2,7,5,1,4,6]=>101100=>[1,1,2,2]
[5,6,1,4,2,3,7]=>[3,2,7,4,6,5,1]=>101011=>[1,1,1,1,2]
[5,6,1,4,2,7,3]=>[3,2,7,4,6,1,5]=>101010=>[1,1,1,1,1,1]
[5,6,1,4,3,2,7]=>[3,2,7,4,5,6,1]=>101001=>[1,1,1,2,1]
[5,6,1,4,3,7,2]=>[3,2,7,4,5,1,6]=>101010=>[1,1,1,1,1,1]
[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>101101=>[1,1,2,1,1]
[5,6,1,4,7,3,2]=>[3,2,7,4,1,5,6]=>101100=>[1,1,2,2]
[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]=>101011=>[1,1,1,1,2]
[5,6,1,7,2,4,3]=>[3,2,7,1,6,4,5]=>101010=>[1,1,1,1,1,1]
[5,6,1,7,3,2,4]=>[3,2,7,1,5,6,4]=>101001=>[1,1,1,2,1]
[5,6,1,7,3,4,2]=>[3,2,7,1,5,4,6]=>101010=>[1,1,1,1,1,1]
[5,6,1,7,4,2,3]=>[3,2,7,1,4,6,5]=>101001=>[1,1,1,2,1]
[5,6,1,7,4,3,2]=>[3,2,7,1,4,5,6]=>101000=>[1,1,1,3]
[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>100111=>[1,2,3]
[5,6,2,1,3,7,4]=>[3,2,6,7,5,1,4]=>100110=>[1,2,2,1]
[5,6,2,1,4,3,7]=>[3,2,6,7,4,5,1]=>100101=>[1,2,1,1,1]
[5,6,2,1,4,7,3]=>[3,2,6,7,4,1,5]=>100110=>[1,2,2,1]
[5,6,2,1,7,3,4]=>[3,2,6,7,1,5,4]=>100101=>[1,2,1,1,1]
[5,6,2,1,7,4,3]=>[3,2,6,7,1,4,5]=>100100=>[1,2,1,2]
[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>101011=>[1,1,1,1,2]
[5,6,2,3,1,7,4]=>[3,2,6,5,7,1,4]=>101010=>[1,1,1,1,1,1]
[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>101101=>[1,1,2,1,1]
[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>101110=>[1,1,3,1]
[5,6,2,3,7,1,4]=>[3,2,6,5,1,7,4]=>101101=>[1,1,2,1,1]
[5,6,2,3,7,4,1]=>[3,2,6,5,1,4,7]=>101100=>[1,1,2,2]
[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>101011=>[1,1,1,1,2]
[5,6,2,4,1,7,3]=>[3,2,6,4,7,1,5]=>101010=>[1,1,1,1,1,1]
[5,6,2,4,3,1,7]=>[3,2,6,4,5,7,1]=>101001=>[1,1,1,2,1]
[5,6,2,4,3,7,1]=>[3,2,6,4,5,1,7]=>101010=>[1,1,1,1,1,1]
[5,6,2,4,7,1,3]=>[3,2,6,4,1,7,5]=>101101=>[1,1,2,1,1]
[5,6,2,4,7,3,1]=>[3,2,6,4,1,5,7]=>101100=>[1,1,2,2]
[5,6,2,7,1,3,4]=>[3,2,6,1,7,5,4]=>101011=>[1,1,1,1,2]
[5,6,2,7,1,4,3]=>[3,2,6,1,7,4,5]=>101010=>[1,1,1,1,1,1]
[5,6,2,7,3,1,4]=>[3,2,6,1,5,7,4]=>101001=>[1,1,1,2,1]
[5,6,2,7,3,4,1]=>[3,2,6,1,5,4,7]=>101010=>[1,1,1,1,1,1]
[5,6,2,7,4,1,3]=>[3,2,6,1,4,7,5]=>101001=>[1,1,1,2,1]
[5,6,2,7,4,3,1]=>[3,2,6,1,4,5,7]=>101000=>[1,1,1,3]
[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>100111=>[1,2,3]
[5,6,3,1,2,7,4]=>[3,2,5,7,6,1,4]=>100110=>[1,2,2,1]
[5,6,3,1,4,2,7]=>[3,2,5,7,4,6,1]=>100101=>[1,2,1,1,1]
[5,6,3,1,4,7,2]=>[3,2,5,7,4,1,6]=>100110=>[1,2,2,1]
[5,6,3,1,7,2,4]=>[3,2,5,7,1,6,4]=>100101=>[1,2,1,1,1]
[5,6,3,1,7,4,2]=>[3,2,5,7,1,4,6]=>100100=>[1,2,1,2]
[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>100011=>[1,3,2]
[5,6,3,2,1,7,4]=>[3,2,5,6,7,1,4]=>100010=>[1,3,1,1]
[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>100101=>[1,2,1,1,1]
[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>100110=>[1,2,2,1]
[5,6,3,2,7,1,4]=>[3,2,5,6,1,7,4]=>100101=>[1,2,1,1,1]
[5,6,3,2,7,4,1]=>[3,2,5,6,1,4,7]=>100100=>[1,2,1,2]
[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>101011=>[1,1,1,1,2]
[5,6,3,4,1,7,2]=>[3,2,5,4,7,1,6]=>101010=>[1,1,1,1,1,1]
[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>101001=>[1,1,1,2,1]
[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>101010=>[1,1,1,1,1,1]
[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>101101=>[1,1,2,1,1]
[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>101100=>[1,1,2,2]
[5,6,3,7,1,2,4]=>[3,2,5,1,7,6,4]=>101011=>[1,1,1,1,2]
[5,6,3,7,1,4,2]=>[3,2,5,1,7,4,6]=>101010=>[1,1,1,1,1,1]
[5,6,3,7,2,1,4]=>[3,2,5,1,6,7,4]=>101001=>[1,1,1,2,1]
[5,6,3,7,2,4,1]=>[3,2,5,1,6,4,7]=>101010=>[1,1,1,1,1,1]
[5,6,3,7,4,1,2]=>[3,2,5,1,4,7,6]=>101001=>[1,1,1,2,1]
[5,6,3,7,4,2,1]=>[3,2,5,1,4,6,7]=>101000=>[1,1,1,3]
[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>100111=>[1,2,3]
[5,6,4,1,2,7,3]=>[3,2,4,7,6,1,5]=>100110=>[1,2,2,1]
[5,6,4,1,3,2,7]=>[3,2,4,7,5,6,1]=>100101=>[1,2,1,1,1]
[5,6,4,1,3,7,2]=>[3,2,4,7,5,1,6]=>100110=>[1,2,2,1]
[5,6,4,1,7,2,3]=>[3,2,4,7,1,6,5]=>100101=>[1,2,1,1,1]
[5,6,4,1,7,3,2]=>[3,2,4,7,1,5,6]=>100100=>[1,2,1,2]
[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>100011=>[1,3,2]
[5,6,4,2,1,7,3]=>[3,2,4,6,7,1,5]=>100010=>[1,3,1,1]
[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>100101=>[1,2,1,1,1]
[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>100110=>[1,2,2,1]
[5,6,4,2,7,1,3]=>[3,2,4,6,1,7,5]=>100101=>[1,2,1,1,1]
[5,6,4,2,7,3,1]=>[3,2,4,6,1,5,7]=>100100=>[1,2,1,2]
[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>100011=>[1,3,2]
[5,6,4,3,1,7,2]=>[3,2,4,5,7,1,6]=>100010=>[1,3,1,1]
[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>100001=>[1,4,1]
[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>100010=>[1,3,1,1]
[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>100101=>[1,2,1,1,1]
[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>100100=>[1,2,1,2]
[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>101011=>[1,1,1,1,2]
[5,6,4,7,1,3,2]=>[3,2,4,1,7,5,6]=>101010=>[1,1,1,1,1,1]
[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>101001=>[1,1,1,2,1]
[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>101010=>[1,1,1,1,1,1]
[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>101001=>[1,1,1,2,1]
[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>101000=>[1,1,1,3]
[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>110111=>[2,1,3]
[5,6,7,1,2,4,3]=>[3,2,1,7,6,4,5]=>110110=>[2,1,2,1]
[5,6,7,1,3,2,4]=>[3,2,1,7,5,6,4]=>110101=>[2,1,1,1,1]
[5,6,7,1,3,4,2]=>[3,2,1,7,5,4,6]=>110110=>[2,1,2,1]
[5,6,7,1,4,2,3]=>[3,2,1,7,4,6,5]=>110101=>[2,1,1,1,1]
[5,6,7,1,4,3,2]=>[3,2,1,7,4,5,6]=>110100=>[2,1,1,2]
[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>110011=>[2,2,2]
[5,6,7,2,1,4,3]=>[3,2,1,6,7,4,5]=>110010=>[2,2,1,1]
[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>110101=>[2,1,1,1,1]
[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>110110=>[2,1,2,1]
[5,6,7,2,4,1,3]=>[3,2,1,6,4,7,5]=>110101=>[2,1,1,1,1]
[5,6,7,2,4,3,1]=>[3,2,1,6,4,5,7]=>110100=>[2,1,1,2]
[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>110011=>[2,2,2]
[5,6,7,3,1,4,2]=>[3,2,1,5,7,4,6]=>110010=>[2,2,1,1]
[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>110001=>[2,3,1]
[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>110010=>[2,2,1,1]
[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>110101=>[2,1,1,1,1]
[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>110100=>[2,1,1,2]
[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011=>[2,2,2]
[5,6,7,4,1,3,2]=>[3,2,1,4,7,5,6]=>110010=>[2,2,1,1]
[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>110001=>[2,3,1]
[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>110010=>[2,2,1,1]
[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>110001=>[2,3,1]
[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>110000=>[2,4]
[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>101111=>[1,1,4]
[5,7,1,2,3,6,4]=>[3,1,7,6,5,2,4]=>101110=>[1,1,3,1]
[5,7,1,2,4,3,6]=>[3,1,7,6,4,5,2]=>101101=>[1,1,2,1,1]
[5,7,1,2,4,6,3]=>[3,1,7,6,4,2,5]=>101110=>[1,1,3,1]
[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>101101=>[1,1,2,1,1]
[5,7,1,2,6,4,3]=>[3,1,7,6,2,4,5]=>101100=>[1,1,2,2]
[5,7,1,3,2,4,6]=>[3,1,7,5,6,4,2]=>101011=>[1,1,1,1,2]
[5,7,1,3,2,6,4]=>[3,1,7,5,6,2,4]=>101010=>[1,1,1,1,1,1]
[5,7,1,3,4,2,6]=>[3,1,7,5,4,6,2]=>101101=>[1,1,2,1,1]
[5,7,1,3,4,6,2]=>[3,1,7,5,4,2,6]=>101110=>[1,1,3,1]
[5,7,1,3,6,2,4]=>[3,1,7,5,2,6,4]=>101101=>[1,1,2,1,1]
[5,7,1,3,6,4,2]=>[3,1,7,5,2,4,6]=>101100=>[1,1,2,2]
[5,7,1,4,2,3,6]=>[3,1,7,4,6,5,2]=>101011=>[1,1,1,1,2]
[5,7,1,4,2,6,3]=>[3,1,7,4,6,2,5]=>101010=>[1,1,1,1,1,1]
[5,7,1,4,3,2,6]=>[3,1,7,4,5,6,2]=>101001=>[1,1,1,2,1]
[5,7,1,4,3,6,2]=>[3,1,7,4,5,2,6]=>101010=>[1,1,1,1,1,1]
[5,7,1,4,6,2,3]=>[3,1,7,4,2,6,5]=>101101=>[1,1,2,1,1]
[5,7,1,4,6,3,2]=>[3,1,7,4,2,5,6]=>101100=>[1,1,2,2]
[5,7,1,6,2,3,4]=>[3,1,7,2,6,5,4]=>101011=>[1,1,1,1,2]
[5,7,1,6,2,4,3]=>[3,1,7,2,6,4,5]=>101010=>[1,1,1,1,1,1]
[5,7,1,6,3,2,4]=>[3,1,7,2,5,6,4]=>101001=>[1,1,1,2,1]
[5,7,1,6,3,4,2]=>[3,1,7,2,5,4,6]=>101010=>[1,1,1,1,1,1]
[5,7,1,6,4,2,3]=>[3,1,7,2,4,6,5]=>101001=>[1,1,1,2,1]
[5,7,1,6,4,3,2]=>[3,1,7,2,4,5,6]=>101000=>[1,1,1,3]
[5,7,2,1,3,4,6]=>[3,1,6,7,5,4,2]=>100111=>[1,2,3]
[5,7,2,1,3,6,4]=>[3,1,6,7,5,2,4]=>100110=>[1,2,2,1]
[5,7,2,1,4,3,6]=>[3,1,6,7,4,5,2]=>100101=>[1,2,1,1,1]
[5,7,2,1,4,6,3]=>[3,1,6,7,4,2,5]=>100110=>[1,2,2,1]
[5,7,2,1,6,3,4]=>[3,1,6,7,2,5,4]=>100101=>[1,2,1,1,1]
[5,7,2,1,6,4,3]=>[3,1,6,7,2,4,5]=>100100=>[1,2,1,2]
[5,7,2,3,1,4,6]=>[3,1,6,5,7,4,2]=>101011=>[1,1,1,1,2]
[5,7,2,3,1,6,4]=>[3,1,6,5,7,2,4]=>101010=>[1,1,1,1,1,1]
[5,7,2,3,4,1,6]=>[3,1,6,5,4,7,2]=>101101=>[1,1,2,1,1]
[5,7,2,3,4,6,1]=>[3,1,6,5,4,2,7]=>101110=>[1,1,3,1]
[5,7,2,3,6,1,4]=>[3,1,6,5,2,7,4]=>101101=>[1,1,2,1,1]
[5,7,2,3,6,4,1]=>[3,1,6,5,2,4,7]=>101100=>[1,1,2,2]
[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>101011=>[1,1,1,1,2]
[5,7,2,4,1,6,3]=>[3,1,6,4,7,2,5]=>101010=>[1,1,1,1,1,1]
[5,7,2,4,3,1,6]=>[3,1,6,4,5,7,2]=>101001=>[1,1,1,2,1]
[5,7,2,4,3,6,1]=>[3,1,6,4,5,2,7]=>101010=>[1,1,1,1,1,1]
[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>101101=>[1,1,2,1,1]
[5,7,2,4,6,3,1]=>[3,1,6,4,2,5,7]=>101100=>[1,1,2,2]
[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>101011=>[1,1,1,1,2]
[5,7,2,6,1,4,3]=>[3,1,6,2,7,4,5]=>101010=>[1,1,1,1,1,1]
[5,7,2,6,3,1,4]=>[3,1,6,2,5,7,4]=>101001=>[1,1,1,2,1]
[5,7,2,6,3,4,1]=>[3,1,6,2,5,4,7]=>101010=>[1,1,1,1,1,1]
[5,7,2,6,4,1,3]=>[3,1,6,2,4,7,5]=>101001=>[1,1,1,2,1]
[5,7,2,6,4,3,1]=>[3,1,6,2,4,5,7]=>101000=>[1,1,1,3]
[5,7,3,1,2,4,6]=>[3,1,5,7,6,4,2]=>100111=>[1,2,3]
[5,7,3,1,2,6,4]=>[3,1,5,7,6,2,4]=>100110=>[1,2,2,1]
[5,7,3,1,4,2,6]=>[3,1,5,7,4,6,2]=>100101=>[1,2,1,1,1]
[5,7,3,1,4,6,2]=>[3,1,5,7,4,2,6]=>100110=>[1,2,2,1]
[5,7,3,1,6,2,4]=>[3,1,5,7,2,6,4]=>100101=>[1,2,1,1,1]
[5,7,3,1,6,4,2]=>[3,1,5,7,2,4,6]=>100100=>[1,2,1,2]
[5,7,3,2,1,4,6]=>[3,1,5,6,7,4,2]=>100011=>[1,3,2]
[5,7,3,2,1,6,4]=>[3,1,5,6,7,2,4]=>100010=>[1,3,1,1]
[5,7,3,2,4,1,6]=>[3,1,5,6,4,7,2]=>100101=>[1,2,1,1,1]
[5,7,3,2,4,6,1]=>[3,1,5,6,4,2,7]=>100110=>[1,2,2,1]
[5,7,3,2,6,1,4]=>[3,1,5,6,2,7,4]=>100101=>[1,2,1,1,1]
[5,7,3,2,6,4,1]=>[3,1,5,6,2,4,7]=>100100=>[1,2,1,2]
[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>101011=>[1,1,1,1,2]
[5,7,3,4,1,6,2]=>[3,1,5,4,7,2,6]=>101010=>[1,1,1,1,1,1]
[5,7,3,4,2,1,6]=>[3,1,5,4,6,7,2]=>101001=>[1,1,1,2,1]
[5,7,3,4,2,6,1]=>[3,1,5,4,6,2,7]=>101010=>[1,1,1,1,1,1]
[5,7,3,4,6,1,2]=>[3,1,5,4,2,7,6]=>101101=>[1,1,2,1,1]
[5,7,3,4,6,2,1]=>[3,1,5,4,2,6,7]=>101100=>[1,1,2,2]
[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>101011=>[1,1,1,1,2]
[5,7,3,6,1,4,2]=>[3,1,5,2,7,4,6]=>101010=>[1,1,1,1,1,1]
[5,7,3,6,2,1,4]=>[3,1,5,2,6,7,4]=>101001=>[1,1,1,2,1]
[5,7,3,6,2,4,1]=>[3,1,5,2,6,4,7]=>101010=>[1,1,1,1,1,1]
[5,7,3,6,4,1,2]=>[3,1,5,2,4,7,6]=>101001=>[1,1,1,2,1]
[5,7,3,6,4,2,1]=>[3,1,5,2,4,6,7]=>101000=>[1,1,1,3]
[5,7,4,1,2,3,6]=>[3,1,4,7,6,5,2]=>100111=>[1,2,3]
[5,7,4,1,2,6,3]=>[3,1,4,7,6,2,5]=>100110=>[1,2,2,1]
[5,7,4,1,3,2,6]=>[3,1,4,7,5,6,2]=>100101=>[1,2,1,1,1]
[5,7,4,1,3,6,2]=>[3,1,4,7,5,2,6]=>100110=>[1,2,2,1]
[5,7,4,1,6,2,3]=>[3,1,4,7,2,6,5]=>100101=>[1,2,1,1,1]
[5,7,4,1,6,3,2]=>[3,1,4,7,2,5,6]=>100100=>[1,2,1,2]
[5,7,4,2,1,3,6]=>[3,1,4,6,7,5,2]=>100011=>[1,3,2]
[5,7,4,2,1,6,3]=>[3,1,4,6,7,2,5]=>100010=>[1,3,1,1]
[5,7,4,2,3,1,6]=>[3,1,4,6,5,7,2]=>100101=>[1,2,1,1,1]
[5,7,4,2,3,6,1]=>[3,1,4,6,5,2,7]=>100110=>[1,2,2,1]
[5,7,4,2,6,1,3]=>[3,1,4,6,2,7,5]=>100101=>[1,2,1,1,1]
[5,7,4,2,6,3,1]=>[3,1,4,6,2,5,7]=>100100=>[1,2,1,2]
[5,7,4,3,1,2,6]=>[3,1,4,5,7,6,2]=>100011=>[1,3,2]
[5,7,4,3,1,6,2]=>[3,1,4,5,7,2,6]=>100010=>[1,3,1,1]
[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>100001=>[1,4,1]
[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>100010=>[1,3,1,1]
[5,7,4,3,6,1,2]=>[3,1,4,5,2,7,6]=>100101=>[1,2,1,1,1]
[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>100100=>[1,2,1,2]
[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>101011=>[1,1,1,1,2]
[5,7,4,6,1,3,2]=>[3,1,4,2,7,5,6]=>101010=>[1,1,1,1,1,1]
[5,7,4,6,2,1,3]=>[3,1,4,2,6,7,5]=>101001=>[1,1,1,2,1]
[5,7,4,6,2,3,1]=>[3,1,4,2,6,5,7]=>101010=>[1,1,1,1,1,1]
[5,7,4,6,3,1,2]=>[3,1,4,2,5,7,6]=>101001=>[1,1,1,2,1]
[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>101000=>[1,1,1,3]
[5,7,6,1,2,3,4]=>[3,1,2,7,6,5,4]=>100111=>[1,2,3]
[5,7,6,1,2,4,3]=>[3,1,2,7,6,4,5]=>100110=>[1,2,2,1]
[5,7,6,1,3,2,4]=>[3,1,2,7,5,6,4]=>100101=>[1,2,1,1,1]
[5,7,6,1,3,4,2]=>[3,1,2,7,5,4,6]=>100110=>[1,2,2,1]
[5,7,6,1,4,2,3]=>[3,1,2,7,4,6,5]=>100101=>[1,2,1,1,1]
[5,7,6,1,4,3,2]=>[3,1,2,7,4,5,6]=>100100=>[1,2,1,2]
[5,7,6,2,1,3,4]=>[3,1,2,6,7,5,4]=>100011=>[1,3,2]
[5,7,6,2,1,4,3]=>[3,1,2,6,7,4,5]=>100010=>[1,3,1,1]
[5,7,6,2,3,1,4]=>[3,1,2,6,5,7,4]=>100101=>[1,2,1,1,1]
[5,7,6,2,3,4,1]=>[3,1,2,6,5,4,7]=>100110=>[1,2,2,1]
[5,7,6,2,4,1,3]=>[3,1,2,6,4,7,5]=>100101=>[1,2,1,1,1]
[5,7,6,2,4,3,1]=>[3,1,2,6,4,5,7]=>100100=>[1,2,1,2]
[5,7,6,3,1,2,4]=>[3,1,2,5,7,6,4]=>100011=>[1,3,2]
[5,7,6,3,1,4,2]=>[3,1,2,5,7,4,6]=>100010=>[1,3,1,1]
[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>100001=>[1,4,1]
[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>100010=>[1,3,1,1]
[5,7,6,3,4,1,2]=>[3,1,2,5,4,7,6]=>100101=>[1,2,1,1,1]
[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>100100=>[1,2,1,2]
[5,7,6,4,1,2,3]=>[3,1,2,4,7,6,5]=>100011=>[1,3,2]
[5,7,6,4,1,3,2]=>[3,1,2,4,7,5,6]=>100010=>[1,3,1,1]
[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>100001=>[1,4,1]
[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>100010=>[1,3,1,1]
[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>100001=>[1,4,1]
[5,7,6,4,3,2,1]=>[3,1,2,4,5,6,7]=>100000=>[1,5]
[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>011111=>[1,5]
[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>011110=>[1,4,1]
[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>011101=>[1,3,1,1]
[6,1,2,3,5,7,4]=>[2,7,6,5,3,1,4]=>011110=>[1,4,1]
[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]=>011101=>[1,3,1,1]
[6,1,2,3,7,5,4]=>[2,7,6,5,1,3,4]=>011100=>[1,3,2]
[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>011011=>[1,2,1,2]
[6,1,2,4,3,7,5]=>[2,7,6,4,5,1,3]=>011010=>[1,2,1,1,1]
[6,1,2,4,5,3,7]=>[2,7,6,4,3,5,1]=>011101=>[1,3,1,1]
[6,1,2,4,5,7,3]=>[2,7,6,4,3,1,5]=>011110=>[1,4,1]
[6,1,2,4,7,3,5]=>[2,7,6,4,1,5,3]=>011101=>[1,3,1,1]
[6,1,2,4,7,5,3]=>[2,7,6,4,1,3,5]=>011100=>[1,3,2]
[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>011011=>[1,2,1,2]
[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>011010=>[1,2,1,1,1]
[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>011001=>[1,2,2,1]
[6,1,2,5,4,7,3]=>[2,7,6,3,4,1,5]=>011010=>[1,2,1,1,1]
[6,1,2,5,7,3,4]=>[2,7,6,3,1,5,4]=>011101=>[1,3,1,1]
[6,1,2,5,7,4,3]=>[2,7,6,3,1,4,5]=>011100=>[1,3,2]
[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]=>011011=>[1,2,1,2]
[6,1,2,7,3,5,4]=>[2,7,6,1,5,3,4]=>011010=>[1,2,1,1,1]
[6,1,2,7,4,3,5]=>[2,7,6,1,4,5,3]=>011001=>[1,2,2,1]
[6,1,2,7,4,5,3]=>[2,7,6,1,4,3,5]=>011010=>[1,2,1,1,1]
[6,1,2,7,5,3,4]=>[2,7,6,1,3,5,4]=>011001=>[1,2,2,1]
[6,1,2,7,5,4,3]=>[2,7,6,1,3,4,5]=>011000=>[1,2,3]
[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>010111=>[1,1,1,3]
[6,1,3,2,4,7,5]=>[2,7,5,6,4,1,3]=>010110=>[1,1,1,2,1]
[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>010101=>[1,1,1,1,1,1]
[6,1,3,2,5,7,4]=>[2,7,5,6,3,1,4]=>010110=>[1,1,1,2,1]
[6,1,3,2,7,4,5]=>[2,7,5,6,1,4,3]=>010101=>[1,1,1,1,1,1]
[6,1,3,2,7,5,4]=>[2,7,5,6,1,3,4]=>010100=>[1,1,1,1,2]
[6,1,3,4,2,5,7]=>[2,7,5,4,6,3,1]=>011011=>[1,2,1,2]
[6,1,3,4,2,7,5]=>[2,7,5,4,6,1,3]=>011010=>[1,2,1,1,1]
[6,1,3,4,5,2,7]=>[2,7,5,4,3,6,1]=>011101=>[1,3,1,1]
[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>011110=>[1,4,1]
[6,1,3,4,7,2,5]=>[2,7,5,4,1,6,3]=>011101=>[1,3,1,1]
[6,1,3,4,7,5,2]=>[2,7,5,4,1,3,6]=>011100=>[1,3,2]
[6,1,3,5,2,4,7]=>[2,7,5,3,6,4,1]=>011011=>[1,2,1,2]
[6,1,3,5,2,7,4]=>[2,7,5,3,6,1,4]=>011010=>[1,2,1,1,1]
[6,1,3,5,4,2,7]=>[2,7,5,3,4,6,1]=>011001=>[1,2,2,1]
[6,1,3,5,4,7,2]=>[2,7,5,3,4,1,6]=>011010=>[1,2,1,1,1]
[6,1,3,5,7,2,4]=>[2,7,5,3,1,6,4]=>011101=>[1,3,1,1]
[6,1,3,5,7,4,2]=>[2,7,5,3,1,4,6]=>011100=>[1,3,2]
[6,1,3,7,2,4,5]=>[2,7,5,1,6,4,3]=>011011=>[1,2,1,2]
[6,1,3,7,2,5,4]=>[2,7,5,1,6,3,4]=>011010=>[1,2,1,1,1]
[6,1,3,7,4,2,5]=>[2,7,5,1,4,6,3]=>011001=>[1,2,2,1]
[6,1,3,7,4,5,2]=>[2,7,5,1,4,3,6]=>011010=>[1,2,1,1,1]
[6,1,3,7,5,2,4]=>[2,7,5,1,3,6,4]=>011001=>[1,2,2,1]
[6,1,3,7,5,4,2]=>[2,7,5,1,3,4,6]=>011000=>[1,2,3]
[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>010111=>[1,1,1,3]
[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>010110=>[1,1,1,2,1]
[6,1,4,2,5,3,7]=>[2,7,4,6,3,5,1]=>010101=>[1,1,1,1,1,1]
[6,1,4,2,5,7,3]=>[2,7,4,6,3,1,5]=>010110=>[1,1,1,2,1]
[6,1,4,2,7,3,5]=>[2,7,4,6,1,5,3]=>010101=>[1,1,1,1,1,1]
[6,1,4,2,7,5,3]=>[2,7,4,6,1,3,5]=>010100=>[1,1,1,1,2]
[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>010011=>[1,1,2,2]
[6,1,4,3,2,7,5]=>[2,7,4,5,6,1,3]=>010010=>[1,1,2,1,1]
[6,1,4,3,5,2,7]=>[2,7,4,5,3,6,1]=>010101=>[1,1,1,1,1,1]
[6,1,4,3,5,7,2]=>[2,7,4,5,3,1,6]=>010110=>[1,1,1,2,1]
[6,1,4,3,7,2,5]=>[2,7,4,5,1,6,3]=>010101=>[1,1,1,1,1,1]
[6,1,4,3,7,5,2]=>[2,7,4,5,1,3,6]=>010100=>[1,1,1,1,2]
[6,1,4,5,2,3,7]=>[2,7,4,3,6,5,1]=>011011=>[1,2,1,2]
[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>011010=>[1,2,1,1,1]
[6,1,4,5,3,2,7]=>[2,7,4,3,5,6,1]=>011001=>[1,2,2,1]
[6,1,4,5,3,7,2]=>[2,7,4,3,5,1,6]=>011010=>[1,2,1,1,1]
[6,1,4,5,7,2,3]=>[2,7,4,3,1,6,5]=>011101=>[1,3,1,1]
[6,1,4,5,7,3,2]=>[2,7,4,3,1,5,6]=>011100=>[1,3,2]
[6,1,4,7,2,3,5]=>[2,7,4,1,6,5,3]=>011011=>[1,2,1,2]
[6,1,4,7,2,5,3]=>[2,7,4,1,6,3,5]=>011010=>[1,2,1,1,1]
[6,1,4,7,3,2,5]=>[2,7,4,1,5,6,3]=>011001=>[1,2,2,1]
[6,1,4,7,3,5,2]=>[2,7,4,1,5,3,6]=>011010=>[1,2,1,1,1]
[6,1,4,7,5,2,3]=>[2,7,4,1,3,6,5]=>011001=>[1,2,2,1]
[6,1,4,7,5,3,2]=>[2,7,4,1,3,5,6]=>011000=>[1,2,3]
[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>010111=>[1,1,1,3]
[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>010110=>[1,1,1,2,1]
[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>010101=>[1,1,1,1,1,1]
[6,1,5,2,4,7,3]=>[2,7,3,6,4,1,5]=>010110=>[1,1,1,2,1]
[6,1,5,2,7,3,4]=>[2,7,3,6,1,5,4]=>010101=>[1,1,1,1,1,1]
[6,1,5,2,7,4,3]=>[2,7,3,6,1,4,5]=>010100=>[1,1,1,1,2]
[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>010011=>[1,1,2,2]
[6,1,5,3,2,7,4]=>[2,7,3,5,6,1,4]=>010010=>[1,1,2,1,1]
[6,1,5,3,4,2,7]=>[2,7,3,5,4,6,1]=>010101=>[1,1,1,1,1,1]
[6,1,5,3,4,7,2]=>[2,7,3,5,4,1,6]=>010110=>[1,1,1,2,1]
[6,1,5,3,7,2,4]=>[2,7,3,5,1,6,4]=>010101=>[1,1,1,1,1,1]
[6,1,5,3,7,4,2]=>[2,7,3,5,1,4,6]=>010100=>[1,1,1,1,2]
[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>010011=>[1,1,2,2]
[6,1,5,4,2,7,3]=>[2,7,3,4,6,1,5]=>010010=>[1,1,2,1,1]
[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>010001=>[1,1,3,1]
[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>010010=>[1,1,2,1,1]
[6,1,5,4,7,2,3]=>[2,7,3,4,1,6,5]=>010101=>[1,1,1,1,1,1]
[6,1,5,4,7,3,2]=>[2,7,3,4,1,5,6]=>010100=>[1,1,1,1,2]
[6,1,5,7,2,3,4]=>[2,7,3,1,6,5,4]=>011011=>[1,2,1,2]
[6,1,5,7,2,4,3]=>[2,7,3,1,6,4,5]=>011010=>[1,2,1,1,1]
[6,1,5,7,3,2,4]=>[2,7,3,1,5,6,4]=>011001=>[1,2,2,1]
[6,1,5,7,3,4,2]=>[2,7,3,1,5,4,6]=>011010=>[1,2,1,1,1]
[6,1,5,7,4,2,3]=>[2,7,3,1,4,6,5]=>011001=>[1,2,2,1]
[6,1,5,7,4,3,2]=>[2,7,3,1,4,5,6]=>011000=>[1,2,3]
[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>010111=>[1,1,1,3]
[6,1,7,2,3,5,4]=>[2,7,1,6,5,3,4]=>010110=>[1,1,1,2,1]
[6,1,7,2,4,3,5]=>[2,7,1,6,4,5,3]=>010101=>[1,1,1,1,1,1]
[6,1,7,2,4,5,3]=>[2,7,1,6,4,3,5]=>010110=>[1,1,1,2,1]
[6,1,7,2,5,3,4]=>[2,7,1,6,3,5,4]=>010101=>[1,1,1,1,1,1]
[6,1,7,2,5,4,3]=>[2,7,1,6,3,4,5]=>010100=>[1,1,1,1,2]
[6,1,7,3,2,4,5]=>[2,7,1,5,6,4,3]=>010011=>[1,1,2,2]
[6,1,7,3,2,5,4]=>[2,7,1,5,6,3,4]=>010010=>[1,1,2,1,1]
[6,1,7,3,4,2,5]=>[2,7,1,5,4,6,3]=>010101=>[1,1,1,1,1,1]
[6,1,7,3,4,5,2]=>[2,7,1,5,4,3,6]=>010110=>[1,1,1,2,1]
[6,1,7,3,5,2,4]=>[2,7,1,5,3,6,4]=>010101=>[1,1,1,1,1,1]
[6,1,7,3,5,4,2]=>[2,7,1,5,3,4,6]=>010100=>[1,1,1,1,2]
[6,1,7,4,2,3,5]=>[2,7,1,4,6,5,3]=>010011=>[1,1,2,2]
[6,1,7,4,2,5,3]=>[2,7,1,4,6,3,5]=>010010=>[1,1,2,1,1]
[6,1,7,4,3,2,5]=>[2,7,1,4,5,6,3]=>010001=>[1,1,3,1]
[6,1,7,4,3,5,2]=>[2,7,1,4,5,3,6]=>010010=>[1,1,2,1,1]
[6,1,7,4,5,2,3]=>[2,7,1,4,3,6,5]=>010101=>[1,1,1,1,1,1]
[6,1,7,4,5,3,2]=>[2,7,1,4,3,5,6]=>010100=>[1,1,1,1,2]
[6,1,7,5,2,3,4]=>[2,7,1,3,6,5,4]=>010011=>[1,1,2,2]
[6,1,7,5,2,4,3]=>[2,7,1,3,6,4,5]=>010010=>[1,1,2,1,1]
[6,1,7,5,3,2,4]=>[2,7,1,3,5,6,4]=>010001=>[1,1,3,1]
[6,1,7,5,3,4,2]=>[2,7,1,3,5,4,6]=>010010=>[1,1,2,1,1]
[6,1,7,5,4,2,3]=>[2,7,1,3,4,6,5]=>010001=>[1,1,3,1]
[6,1,7,5,4,3,2]=>[2,7,1,3,4,5,6]=>010000=>[1,1,4]
[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>001111=>[2,4]
[6,2,1,3,4,7,5]=>[2,6,7,5,4,1,3]=>001110=>[2,3,1]
[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>001101=>[2,2,1,1]
[6,2,1,3,5,7,4]=>[2,6,7,5,3,1,4]=>001110=>[2,3,1]
[6,2,1,3,7,4,5]=>[2,6,7,5,1,4,3]=>001101=>[2,2,1,1]
[6,2,1,3,7,5,4]=>[2,6,7,5,1,3,4]=>001100=>[2,2,2]
[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>001011=>[2,1,1,2]
[6,2,1,4,3,7,5]=>[2,6,7,4,5,1,3]=>001010=>[2,1,1,1,1]
[6,2,1,4,5,3,7]=>[2,6,7,4,3,5,1]=>001101=>[2,2,1,1]
[6,2,1,4,5,7,3]=>[2,6,7,4,3,1,5]=>001110=>[2,3,1]
[6,2,1,4,7,3,5]=>[2,6,7,4,1,5,3]=>001101=>[2,2,1,1]
[6,2,1,4,7,5,3]=>[2,6,7,4,1,3,5]=>001100=>[2,2,2]
[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>001011=>[2,1,1,2]
[6,2,1,5,3,7,4]=>[2,6,7,3,5,1,4]=>001010=>[2,1,1,1,1]
[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>001001=>[2,1,2,1]
[6,2,1,5,4,7,3]=>[2,6,7,3,4,1,5]=>001010=>[2,1,1,1,1]
[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>001101=>[2,2,1,1]
[6,2,1,5,7,4,3]=>[2,6,7,3,1,4,5]=>001100=>[2,2,2]
[6,2,1,7,3,4,5]=>[2,6,7,1,5,4,3]=>001011=>[2,1,1,2]
[6,2,1,7,3,5,4]=>[2,6,7,1,5,3,4]=>001010=>[2,1,1,1,1]
[6,2,1,7,4,3,5]=>[2,6,7,1,4,5,3]=>001001=>[2,1,2,1]
[6,2,1,7,4,5,3]=>[2,6,7,1,4,3,5]=>001010=>[2,1,1,1,1]
[6,2,1,7,5,3,4]=>[2,6,7,1,3,5,4]=>001001=>[2,1,2,1]
[6,2,1,7,5,4,3]=>[2,6,7,1,3,4,5]=>001000=>[2,1,3]
[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>010111=>[1,1,1,3]
[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>010110=>[1,1,1,2,1]
[6,2,3,1,5,4,7]=>[2,6,5,7,3,4,1]=>010101=>[1,1,1,1,1,1]
[6,2,3,1,5,7,4]=>[2,6,5,7,3,1,4]=>010110=>[1,1,1,2,1]
[6,2,3,1,7,4,5]=>[2,6,5,7,1,4,3]=>010101=>[1,1,1,1,1,1]
[6,2,3,1,7,5,4]=>[2,6,5,7,1,3,4]=>010100=>[1,1,1,1,2]
[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>011011=>[1,2,1,2]
[6,2,3,4,1,7,5]=>[2,6,5,4,7,1,3]=>011010=>[1,2,1,1,1]
[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>011101=>[1,3,1,1]
[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>011110=>[1,4,1]
[6,2,3,4,7,1,5]=>[2,6,5,4,1,7,3]=>011101=>[1,3,1,1]
[6,2,3,4,7,5,1]=>[2,6,5,4,1,3,7]=>011100=>[1,3,2]
[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>011011=>[1,2,1,2]
[6,2,3,5,1,7,4]=>[2,6,5,3,7,1,4]=>011010=>[1,2,1,1,1]
[6,2,3,5,4,1,7]=>[2,6,5,3,4,7,1]=>011001=>[1,2,2,1]
[6,2,3,5,4,7,1]=>[2,6,5,3,4,1,7]=>011010=>[1,2,1,1,1]
[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>011101=>[1,3,1,1]
[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>011100=>[1,3,2]
[6,2,3,7,1,4,5]=>[2,6,5,1,7,4,3]=>011011=>[1,2,1,2]
[6,2,3,7,1,5,4]=>[2,6,5,1,7,3,4]=>011010=>[1,2,1,1,1]
[6,2,3,7,4,1,5]=>[2,6,5,1,4,7,3]=>011001=>[1,2,2,1]
[6,2,3,7,4,5,1]=>[2,6,5,1,4,3,7]=>011010=>[1,2,1,1,1]
[6,2,3,7,5,1,4]=>[2,6,5,1,3,7,4]=>011001=>[1,2,2,1]
[6,2,3,7,5,4,1]=>[2,6,5,1,3,4,7]=>011000=>[1,2,3]
[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>010111=>[1,1,1,3]
[6,2,4,1,3,7,5]=>[2,6,4,7,5,1,3]=>010110=>[1,1,1,2,1]
[6,2,4,1,5,3,7]=>[2,6,4,7,3,5,1]=>010101=>[1,1,1,1,1,1]
[6,2,4,1,5,7,3]=>[2,6,4,7,3,1,5]=>010110=>[1,1,1,2,1]
[6,2,4,1,7,3,5]=>[2,6,4,7,1,5,3]=>010101=>[1,1,1,1,1,1]
[6,2,4,1,7,5,3]=>[2,6,4,7,1,3,5]=>010100=>[1,1,1,1,2]
[6,2,4,3,1,5,7]=>[2,6,4,5,7,3,1]=>010011=>[1,1,2,2]
[6,2,4,3,1,7,5]=>[2,6,4,5,7,1,3]=>010010=>[1,1,2,1,1]
[6,2,4,3,5,1,7]=>[2,6,4,5,3,7,1]=>010101=>[1,1,1,1,1,1]
[6,2,4,3,5,7,1]=>[2,6,4,5,3,1,7]=>010110=>[1,1,1,2,1]
[6,2,4,3,7,1,5]=>[2,6,4,5,1,7,3]=>010101=>[1,1,1,1,1,1]
[6,2,4,3,7,5,1]=>[2,6,4,5,1,3,7]=>010100=>[1,1,1,1,2]
[6,2,4,5,1,3,7]=>[2,6,4,3,7,5,1]=>011011=>[1,2,1,2]
[6,2,4,5,1,7,3]=>[2,6,4,3,7,1,5]=>011010=>[1,2,1,1,1]
[6,2,4,5,3,1,7]=>[2,6,4,3,5,7,1]=>011001=>[1,2,2,1]
[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>011010=>[1,2,1,1,1]
[6,2,4,5,7,1,3]=>[2,6,4,3,1,7,5]=>011101=>[1,3,1,1]
[6,2,4,5,7,3,1]=>[2,6,4,3,1,5,7]=>011100=>[1,3,2]
[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>011011=>[1,2,1,2]
[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>011010=>[1,2,1,1,1]
[6,2,4,7,3,1,5]=>[2,6,4,1,5,7,3]=>011001=>[1,2,2,1]
[6,2,4,7,3,5,1]=>[2,6,4,1,5,3,7]=>011010=>[1,2,1,1,1]
[6,2,4,7,5,1,3]=>[2,6,4,1,3,7,5]=>011001=>[1,2,2,1]
[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>011000=>[1,2,3]
[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>010111=>[1,1,1,3]
[6,2,5,1,3,7,4]=>[2,6,3,7,5,1,4]=>010110=>[1,1,1,2,1]
[6,2,5,1,4,3,7]=>[2,6,3,7,4,5,1]=>010101=>[1,1,1,1,1,1]
[6,2,5,1,4,7,3]=>[2,6,3,7,4,1,5]=>010110=>[1,1,1,2,1]
[6,2,5,1,7,3,4]=>[2,6,3,7,1,5,4]=>010101=>[1,1,1,1,1,1]
[6,2,5,1,7,4,3]=>[2,6,3,7,1,4,5]=>010100=>[1,1,1,1,2]
[6,2,5,3,1,4,7]=>[2,6,3,5,7,4,1]=>010011=>[1,1,2,2]
[6,2,5,3,1,7,4]=>[2,6,3,5,7,1,4]=>010010=>[1,1,2,1,1]
[6,2,5,3,4,1,7]=>[2,6,3,5,4,7,1]=>010101=>[1,1,1,1,1,1]
[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>010110=>[1,1,1,2,1]
[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>010101=>[1,1,1,1,1,1]
[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>010100=>[1,1,1,1,2]
[6,2,5,4,1,3,7]=>[2,6,3,4,7,5,1]=>010011=>[1,1,2,2]
[6,2,5,4,1,7,3]=>[2,6,3,4,7,1,5]=>010010=>[1,1,2,1,1]
[6,2,5,4,3,1,7]=>[2,6,3,4,5,7,1]=>010001=>[1,1,3,1]
[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>010010=>[1,1,2,1,1]
[6,2,5,4,7,1,3]=>[2,6,3,4,1,7,5]=>010101=>[1,1,1,1,1,1]
[6,2,5,4,7,3,1]=>[2,6,3,4,1,5,7]=>010100=>[1,1,1,1,2]
[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>011011=>[1,2,1,2]
[6,2,5,7,1,4,3]=>[2,6,3,1,7,4,5]=>011010=>[1,2,1,1,1]
[6,2,5,7,3,1,4]=>[2,6,3,1,5,7,4]=>011001=>[1,2,2,1]
[6,2,5,7,3,4,1]=>[2,6,3,1,5,4,7]=>011010=>[1,2,1,1,1]
[6,2,5,7,4,1,3]=>[2,6,3,1,4,7,5]=>011001=>[1,2,2,1]
[6,2,5,7,4,3,1]=>[2,6,3,1,4,5,7]=>011000=>[1,2,3]
[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>010111=>[1,1,1,3]
[6,2,7,1,3,5,4]=>[2,6,1,7,5,3,4]=>010110=>[1,1,1,2,1]
[6,2,7,1,4,3,5]=>[2,6,1,7,4,5,3]=>010101=>[1,1,1,1,1,1]
[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>010110=>[1,1,1,2,1]
[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>010101=>[1,1,1,1,1,1]
[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>010100=>[1,1,1,1,2]
[6,2,7,3,1,4,5]=>[2,6,1,5,7,4,3]=>010011=>[1,1,2,2]
[6,2,7,3,1,5,4]=>[2,6,1,5,7,3,4]=>010010=>[1,1,2,1,1]
[6,2,7,3,4,1,5]=>[2,6,1,5,4,7,3]=>010101=>[1,1,1,1,1,1]
[6,2,7,3,4,5,1]=>[2,6,1,5,4,3,7]=>010110=>[1,1,1,2,1]
[6,2,7,3,5,1,4]=>[2,6,1,5,3,7,4]=>010101=>[1,1,1,1,1,1]
[6,2,7,3,5,4,1]=>[2,6,1,5,3,4,7]=>010100=>[1,1,1,1,2]
[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>010011=>[1,1,2,2]
[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>010010=>[1,1,2,1,1]
[6,2,7,4,3,1,5]=>[2,6,1,4,5,7,3]=>010001=>[1,1,3,1]
[6,2,7,4,3,5,1]=>[2,6,1,4,5,3,7]=>010010=>[1,1,2,1,1]
[6,2,7,4,5,1,3]=>[2,6,1,4,3,7,5]=>010101=>[1,1,1,1,1,1]
[6,2,7,4,5,3,1]=>[2,6,1,4,3,5,7]=>010100=>[1,1,1,1,2]
[6,2,7,5,1,3,4]=>[2,6,1,3,7,5,4]=>010011=>[1,1,2,2]
[6,2,7,5,1,4,3]=>[2,6,1,3,7,4,5]=>010010=>[1,1,2,1,1]
[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>010001=>[1,1,3,1]
[6,2,7,5,3,4,1]=>[2,6,1,3,5,4,7]=>010010=>[1,1,2,1,1]
[6,2,7,5,4,1,3]=>[2,6,1,3,4,7,5]=>010001=>[1,1,3,1]
[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>010000=>[1,1,4]
[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>001111=>[2,4]
[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>001110=>[2,3,1]
[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>001101=>[2,2,1,1]
[6,3,1,2,5,7,4]=>[2,5,7,6,3,1,4]=>001110=>[2,3,1]
[6,3,1,2,7,4,5]=>[2,5,7,6,1,4,3]=>001101=>[2,2,1,1]
[6,3,1,2,7,5,4]=>[2,5,7,6,1,3,4]=>001100=>[2,2,2]
[6,3,1,4,2,5,7]=>[2,5,7,4,6,3,1]=>001011=>[2,1,1,2]
[6,3,1,4,2,7,5]=>[2,5,7,4,6,1,3]=>001010=>[2,1,1,1,1]
[6,3,1,4,5,2,7]=>[2,5,7,4,3,6,1]=>001101=>[2,2,1,1]
[6,3,1,4,5,7,2]=>[2,5,7,4,3,1,6]=>001110=>[2,3,1]
[6,3,1,4,7,2,5]=>[2,5,7,4,1,6,3]=>001101=>[2,2,1,1]
[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>001100=>[2,2,2]
[6,3,1,5,2,4,7]=>[2,5,7,3,6,4,1]=>001011=>[2,1,1,2]
[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>001010=>[2,1,1,1,1]
[6,3,1,5,4,2,7]=>[2,5,7,3,4,6,1]=>001001=>[2,1,2,1]
[6,3,1,5,4,7,2]=>[2,5,7,3,4,1,6]=>001010=>[2,1,1,1,1]
[6,3,1,5,7,2,4]=>[2,5,7,3,1,6,4]=>001101=>[2,2,1,1]
[6,3,1,5,7,4,2]=>[2,5,7,3,1,4,6]=>001100=>[2,2,2]
[6,3,1,7,2,4,5]=>[2,5,7,1,6,4,3]=>001011=>[2,1,1,2]
[6,3,1,7,2,5,4]=>[2,5,7,1,6,3,4]=>001010=>[2,1,1,1,1]
[6,3,1,7,4,2,5]=>[2,5,7,1,4,6,3]=>001001=>[2,1,2,1]
[6,3,1,7,4,5,2]=>[2,5,7,1,4,3,6]=>001010=>[2,1,1,1,1]
[6,3,1,7,5,2,4]=>[2,5,7,1,3,6,4]=>001001=>[2,1,2,1]
[6,3,1,7,5,4,2]=>[2,5,7,1,3,4,6]=>001000=>[2,1,3]
[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>000111=>[3,3]
[6,3,2,1,4,7,5]=>[2,5,6,7,4,1,3]=>000110=>[3,2,1]
[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>000101=>[3,1,1,1]
[6,3,2,1,5,7,4]=>[2,5,6,7,3,1,4]=>000110=>[3,2,1]
[6,3,2,1,7,4,5]=>[2,5,6,7,1,4,3]=>000101=>[3,1,1,1]
[6,3,2,1,7,5,4]=>[2,5,6,7,1,3,4]=>000100=>[3,1,2]
[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>001011=>[2,1,1,2]
[6,3,2,4,1,7,5]=>[2,5,6,4,7,1,3]=>001010=>[2,1,1,1,1]
[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>001101=>[2,2,1,1]
[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>001110=>[2,3,1]
[6,3,2,4,7,1,5]=>[2,5,6,4,1,7,3]=>001101=>[2,2,1,1]
[6,3,2,4,7,5,1]=>[2,5,6,4,1,3,7]=>001100=>[2,2,2]
[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>001011=>[2,1,1,2]
[6,3,2,5,1,7,4]=>[2,5,6,3,7,1,4]=>001010=>[2,1,1,1,1]
[6,3,2,5,4,1,7]=>[2,5,6,3,4,7,1]=>001001=>[2,1,2,1]
[6,3,2,5,4,7,1]=>[2,5,6,3,4,1,7]=>001010=>[2,1,1,1,1]
[6,3,2,5,7,1,4]=>[2,5,6,3,1,7,4]=>001101=>[2,2,1,1]
[6,3,2,5,7,4,1]=>[2,5,6,3,1,4,7]=>001100=>[2,2,2]
[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>001011=>[2,1,1,2]
[6,3,2,7,1,5,4]=>[2,5,6,1,7,3,4]=>001010=>[2,1,1,1,1]
[6,3,2,7,4,1,5]=>[2,5,6,1,4,7,3]=>001001=>[2,1,2,1]
[6,3,2,7,4,5,1]=>[2,5,6,1,4,3,7]=>001010=>[2,1,1,1,1]
[6,3,2,7,5,1,4]=>[2,5,6,1,3,7,4]=>001001=>[2,1,2,1]
[6,3,2,7,5,4,1]=>[2,5,6,1,3,4,7]=>001000=>[2,1,3]
[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>010111=>[1,1,1,3]
[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>010110=>[1,1,1,2,1]
[6,3,4,1,5,2,7]=>[2,5,4,7,3,6,1]=>010101=>[1,1,1,1,1,1]
[6,3,4,1,5,7,2]=>[2,5,4,7,3,1,6]=>010110=>[1,1,1,2,1]
[6,3,4,1,7,2,5]=>[2,5,4,7,1,6,3]=>010101=>[1,1,1,1,1,1]
[6,3,4,1,7,5,2]=>[2,5,4,7,1,3,6]=>010100=>[1,1,1,1,2]
[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>010011=>[1,1,2,2]
[6,3,4,2,1,7,5]=>[2,5,4,6,7,1,3]=>010010=>[1,1,2,1,1]
[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>010101=>[1,1,1,1,1,1]
[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>010110=>[1,1,1,2,1]
[6,3,4,2,7,1,5]=>[2,5,4,6,1,7,3]=>010101=>[1,1,1,1,1,1]
[6,3,4,2,7,5,1]=>[2,5,4,6,1,3,7]=>010100=>[1,1,1,1,2]
[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>011011=>[1,2,1,2]
[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>011010=>[1,2,1,1,1]
[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>011001=>[1,2,2,1]
[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>011010=>[1,2,1,1,1]
[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>011101=>[1,3,1,1]
[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>011100=>[1,3,2]
[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>011011=>[1,2,1,2]
[6,3,4,7,1,5,2]=>[2,5,4,1,7,3,6]=>011010=>[1,2,1,1,1]
[6,3,4,7,2,1,5]=>[2,5,4,1,6,7,3]=>011001=>[1,2,2,1]
[6,3,4,7,2,5,1]=>[2,5,4,1,6,3,7]=>011010=>[1,2,1,1,1]
[6,3,4,7,5,1,2]=>[2,5,4,1,3,7,6]=>011001=>[1,2,2,1]
[6,3,4,7,5,2,1]=>[2,5,4,1,3,6,7]=>011000=>[1,2,3]
[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>010111=>[1,1,1,3]
[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>010110=>[1,1,1,2,1]
[6,3,5,1,4,2,7]=>[2,5,3,7,4,6,1]=>010101=>[1,1,1,1,1,1]
[6,3,5,1,4,7,2]=>[2,5,3,7,4,1,6]=>010110=>[1,1,1,2,1]
[6,3,5,1,7,2,4]=>[2,5,3,7,1,6,4]=>010101=>[1,1,1,1,1,1]
[6,3,5,1,7,4,2]=>[2,5,3,7,1,4,6]=>010100=>[1,1,1,1,2]
[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>010011=>[1,1,2,2]
[6,3,5,2,1,7,4]=>[2,5,3,6,7,1,4]=>010010=>[1,1,2,1,1]
[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>010101=>[1,1,1,1,1,1]
[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>010110=>[1,1,1,2,1]
[6,3,5,2,7,1,4]=>[2,5,3,6,1,7,4]=>010101=>[1,1,1,1,1,1]
[6,3,5,2,7,4,1]=>[2,5,3,6,1,4,7]=>010100=>[1,1,1,1,2]
[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>010011=>[1,1,2,2]
[6,3,5,4,1,7,2]=>[2,5,3,4,7,1,6]=>010010=>[1,1,2,1,1]
[6,3,5,4,2,1,7]=>[2,5,3,4,6,7,1]=>010001=>[1,1,3,1]
[6,3,5,4,2,7,1]=>[2,5,3,4,6,1,7]=>010010=>[1,1,2,1,1]
[6,3,5,4,7,1,2]=>[2,5,3,4,1,7,6]=>010101=>[1,1,1,1,1,1]
[6,3,5,4,7,2,1]=>[2,5,3,4,1,6,7]=>010100=>[1,1,1,1,2]
[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>011011=>[1,2,1,2]
[6,3,5,7,1,4,2]=>[2,5,3,1,7,4,6]=>011010=>[1,2,1,1,1]
[6,3,5,7,2,1,4]=>[2,5,3,1,6,7,4]=>011001=>[1,2,2,1]
[6,3,5,7,2,4,1]=>[2,5,3,1,6,4,7]=>011010=>[1,2,1,1,1]
[6,3,5,7,4,1,2]=>[2,5,3,1,4,7,6]=>011001=>[1,2,2,1]
[6,3,5,7,4,2,1]=>[2,5,3,1,4,6,7]=>011000=>[1,2,3]
[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>010111=>[1,1,1,3]
[6,3,7,1,2,5,4]=>[2,5,1,7,6,3,4]=>010110=>[1,1,1,2,1]
[6,3,7,1,4,2,5]=>[2,5,1,7,4,6,3]=>010101=>[1,1,1,1,1,1]
[6,3,7,1,4,5,2]=>[2,5,1,7,4,3,6]=>010110=>[1,1,1,2,1]
[6,3,7,1,5,2,4]=>[2,5,1,7,3,6,4]=>010101=>[1,1,1,1,1,1]
[6,3,7,1,5,4,2]=>[2,5,1,7,3,4,6]=>010100=>[1,1,1,1,2]
[6,3,7,2,1,4,5]=>[2,5,1,6,7,4,3]=>010011=>[1,1,2,2]
[6,3,7,2,1,5,4]=>[2,5,1,6,7,3,4]=>010010=>[1,1,2,1,1]
[6,3,7,2,4,1,5]=>[2,5,1,6,4,7,3]=>010101=>[1,1,1,1,1,1]
[6,3,7,2,4,5,1]=>[2,5,1,6,4,3,7]=>010110=>[1,1,1,2,1]
[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>010101=>[1,1,1,1,1,1]
[6,3,7,2,5,4,1]=>[2,5,1,6,3,4,7]=>010100=>[1,1,1,1,2]
[6,3,7,4,1,2,5]=>[2,5,1,4,7,6,3]=>010011=>[1,1,2,2]
[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>010010=>[1,1,2,1,1]
[6,3,7,4,2,1,5]=>[2,5,1,4,6,7,3]=>010001=>[1,1,3,1]
[6,3,7,4,2,5,1]=>[2,5,1,4,6,3,7]=>010010=>[1,1,2,1,1]
[6,3,7,4,5,1,2]=>[2,5,1,4,3,7,6]=>010101=>[1,1,1,1,1,1]
[6,3,7,4,5,2,1]=>[2,5,1,4,3,6,7]=>010100=>[1,1,1,1,2]
[6,3,7,5,1,2,4]=>[2,5,1,3,7,6,4]=>010011=>[1,1,2,2]
[6,3,7,5,1,4,2]=>[2,5,1,3,7,4,6]=>010010=>[1,1,2,1,1]
[6,3,7,5,2,1,4]=>[2,5,1,3,6,7,4]=>010001=>[1,1,3,1]
[6,3,7,5,2,4,1]=>[2,5,1,3,6,4,7]=>010010=>[1,1,2,1,1]
[6,3,7,5,4,1,2]=>[2,5,1,3,4,7,6]=>010001=>[1,1,3,1]
[6,3,7,5,4,2,1]=>[2,5,1,3,4,6,7]=>010000=>[1,1,4]
[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>001111=>[2,4]
[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>001110=>[2,3,1]
[6,4,1,2,5,3,7]=>[2,4,7,6,3,5,1]=>001101=>[2,2,1,1]
[6,4,1,2,5,7,3]=>[2,4,7,6,3,1,5]=>001110=>[2,3,1]
[6,4,1,2,7,3,5]=>[2,4,7,6,1,5,3]=>001101=>[2,2,1,1]
[6,4,1,2,7,5,3]=>[2,4,7,6,1,3,5]=>001100=>[2,2,2]
[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>001011=>[2,1,1,2]
[6,4,1,3,2,7,5]=>[2,4,7,5,6,1,3]=>001010=>[2,1,1,1,1]
[6,4,1,3,5,2,7]=>[2,4,7,5,3,6,1]=>001101=>[2,2,1,1]
[6,4,1,3,5,7,2]=>[2,4,7,5,3,1,6]=>001110=>[2,3,1]
[6,4,1,3,7,2,5]=>[2,4,7,5,1,6,3]=>001101=>[2,2,1,1]
[6,4,1,3,7,5,2]=>[2,4,7,5,1,3,6]=>001100=>[2,2,2]
[6,4,1,5,2,3,7]=>[2,4,7,3,6,5,1]=>001011=>[2,1,1,2]
[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>001010=>[2,1,1,1,1]
[6,4,1,5,3,2,7]=>[2,4,7,3,5,6,1]=>001001=>[2,1,2,1]
[6,4,1,5,3,7,2]=>[2,4,7,3,5,1,6]=>001010=>[2,1,1,1,1]
[6,4,1,5,7,2,3]=>[2,4,7,3,1,6,5]=>001101=>[2,2,1,1]
[6,4,1,5,7,3,2]=>[2,4,7,3,1,5,6]=>001100=>[2,2,2]
[6,4,1,7,2,3,5]=>[2,4,7,1,6,5,3]=>001011=>[2,1,1,2]
[6,4,1,7,2,5,3]=>[2,4,7,1,6,3,5]=>001010=>[2,1,1,1,1]
[6,4,1,7,3,2,5]=>[2,4,7,1,5,6,3]=>001001=>[2,1,2,1]
[6,4,1,7,3,5,2]=>[2,4,7,1,5,3,6]=>001010=>[2,1,1,1,1]
[6,4,1,7,5,2,3]=>[2,4,7,1,3,6,5]=>001001=>[2,1,2,1]
[6,4,1,7,5,3,2]=>[2,4,7,1,3,5,6]=>001000=>[2,1,3]
[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>000111=>[3,3]
[6,4,2,1,3,7,5]=>[2,4,6,7,5,1,3]=>000110=>[3,2,1]
[6,4,2,1,5,3,7]=>[2,4,6,7,3,5,1]=>000101=>[3,1,1,1]
[6,4,2,1,5,7,3]=>[2,4,6,7,3,1,5]=>000110=>[3,2,1]
[6,4,2,1,7,3,5]=>[2,4,6,7,1,5,3]=>000101=>[3,1,1,1]
[6,4,2,1,7,5,3]=>[2,4,6,7,1,3,5]=>000100=>[3,1,2]
[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>001011=>[2,1,1,2]
[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>001010=>[2,1,1,1,1]
[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>001101=>[2,2,1,1]
[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>001110=>[2,3,1]
[6,4,2,3,7,1,5]=>[2,4,6,5,1,7,3]=>001101=>[2,2,1,1]
[6,4,2,3,7,5,1]=>[2,4,6,5,1,3,7]=>001100=>[2,2,2]
[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>001011=>[2,1,1,2]
[6,4,2,5,1,7,3]=>[2,4,6,3,7,1,5]=>001010=>[2,1,1,1,1]
[6,4,2,5,3,1,7]=>[2,4,6,3,5,7,1]=>001001=>[2,1,2,1]
[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>001010=>[2,1,1,1,1]
[6,4,2,5,7,1,3]=>[2,4,6,3,1,7,5]=>001101=>[2,2,1,1]
[6,4,2,5,7,3,1]=>[2,4,6,3,1,5,7]=>001100=>[2,2,2]
[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>001011=>[2,1,1,2]
[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>001010=>[2,1,1,1,1]
[6,4,2,7,3,1,5]=>[2,4,6,1,5,7,3]=>001001=>[2,1,2,1]
[6,4,2,7,3,5,1]=>[2,4,6,1,5,3,7]=>001010=>[2,1,1,1,1]
[6,4,2,7,5,1,3]=>[2,4,6,1,3,7,5]=>001001=>[2,1,2,1]
[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>001000=>[2,1,3]
[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>000111=>[3,3]
[6,4,3,1,2,7,5]=>[2,4,5,7,6,1,3]=>000110=>[3,2,1]
[6,4,3,1,5,2,7]=>[2,4,5,7,3,6,1]=>000101=>[3,1,1,1]
[6,4,3,1,5,7,2]=>[2,4,5,7,3,1,6]=>000110=>[3,2,1]
[6,4,3,1,7,2,5]=>[2,4,5,7,1,6,3]=>000101=>[3,1,1,1]
[6,4,3,1,7,5,2]=>[2,4,5,7,1,3,6]=>000100=>[3,1,2]
[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>000011=>[4,2]
[6,4,3,2,1,7,5]=>[2,4,5,6,7,1,3]=>000010=>[4,1,1]
[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>000101=>[3,1,1,1]
[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>000110=>[3,2,1]
[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>000101=>[3,1,1,1]
[6,4,3,2,7,5,1]=>[2,4,5,6,1,3,7]=>000100=>[3,1,2]
[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>001011=>[2,1,1,2]
[6,4,3,5,1,7,2]=>[2,4,5,3,7,1,6]=>001010=>[2,1,1,1,1]
[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>001001=>[2,1,2,1]
[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>001010=>[2,1,1,1,1]
[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>001101=>[2,2,1,1]
[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>001100=>[2,2,2]
[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>001011=>[2,1,1,2]
[6,4,3,7,1,5,2]=>[2,4,5,1,7,3,6]=>001010=>[2,1,1,1,1]
[6,4,3,7,2,1,5]=>[2,4,5,1,6,7,3]=>001001=>[2,1,2,1]
[6,4,3,7,2,5,1]=>[2,4,5,1,6,3,7]=>001010=>[2,1,1,1,1]
[6,4,3,7,5,1,2]=>[2,4,5,1,3,7,6]=>001001=>[2,1,2,1]
[6,4,3,7,5,2,1]=>[2,4,5,1,3,6,7]=>001000=>[2,1,3]
[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>010111=>[1,1,1,3]
[6,4,5,1,2,7,3]=>[2,4,3,7,6,1,5]=>010110=>[1,1,1,2,1]
[6,4,5,1,3,2,7]=>[2,4,3,7,5,6,1]=>010101=>[1,1,1,1,1,1]
[6,4,5,1,3,7,2]=>[2,4,3,7,5,1,6]=>010110=>[1,1,1,2,1]
[6,4,5,1,7,2,3]=>[2,4,3,7,1,6,5]=>010101=>[1,1,1,1,1,1]
[6,4,5,1,7,3,2]=>[2,4,3,7,1,5,6]=>010100=>[1,1,1,1,2]
[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>010011=>[1,1,2,2]
[6,4,5,2,1,7,3]=>[2,4,3,6,7,1,5]=>010010=>[1,1,2,1,1]
[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>010101=>[1,1,1,1,1,1]
[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>010110=>[1,1,1,2,1]
[6,4,5,2,7,1,3]=>[2,4,3,6,1,7,5]=>010101=>[1,1,1,1,1,1]
[6,4,5,2,7,3,1]=>[2,4,3,6,1,5,7]=>010100=>[1,1,1,1,2]
[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>010011=>[1,1,2,2]
[6,4,5,3,1,7,2]=>[2,4,3,5,7,1,6]=>010010=>[1,1,2,1,1]
[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>010001=>[1,1,3,1]
[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>010010=>[1,1,2,1,1]
[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>010101=>[1,1,1,1,1,1]
[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>010100=>[1,1,1,1,2]
[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>011011=>[1,2,1,2]
[6,4,5,7,1,3,2]=>[2,4,3,1,7,5,6]=>011010=>[1,2,1,1,1]
[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>011001=>[1,2,2,1]
[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>011010=>[1,2,1,1,1]
[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>011001=>[1,2,2,1]
[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>011000=>[1,2,3]
[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>010111=>[1,1,1,3]
[6,4,7,1,2,5,3]=>[2,4,1,7,6,3,5]=>010110=>[1,1,1,2,1]
[6,4,7,1,3,2,5]=>[2,4,1,7,5,6,3]=>010101=>[1,1,1,1,1,1]
[6,4,7,1,3,5,2]=>[2,4,1,7,5,3,6]=>010110=>[1,1,1,2,1]
[6,4,7,1,5,2,3]=>[2,4,1,7,3,6,5]=>010101=>[1,1,1,1,1,1]
[6,4,7,1,5,3,2]=>[2,4,1,7,3,5,6]=>010100=>[1,1,1,1,2]
[6,4,7,2,1,3,5]=>[2,4,1,6,7,5,3]=>010011=>[1,1,2,2]
[6,4,7,2,1,5,3]=>[2,4,1,6,7,3,5]=>010010=>[1,1,2,1,1]
[6,4,7,2,3,1,5]=>[2,4,1,6,5,7,3]=>010101=>[1,1,1,1,1,1]
[6,4,7,2,3,5,1]=>[2,4,1,6,5,3,7]=>010110=>[1,1,1,2,1]
[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>010101=>[1,1,1,1,1,1]
[6,4,7,2,5,3,1]=>[2,4,1,6,3,5,7]=>010100=>[1,1,1,1,2]
[6,4,7,3,1,2,5]=>[2,4,1,5,7,6,3]=>010011=>[1,1,2,2]
[6,4,7,3,1,5,2]=>[2,4,1,5,7,3,6]=>010010=>[1,1,2,1,1]
[6,4,7,3,2,1,5]=>[2,4,1,5,6,7,3]=>010001=>[1,1,3,1]
[6,4,7,3,2,5,1]=>[2,4,1,5,6,3,7]=>010010=>[1,1,2,1,1]
[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>010101=>[1,1,1,1,1,1]
[6,4,7,3,5,2,1]=>[2,4,1,5,3,6,7]=>010100=>[1,1,1,1,2]
[6,4,7,5,1,2,3]=>[2,4,1,3,7,6,5]=>010011=>[1,1,2,2]
[6,4,7,5,1,3,2]=>[2,4,1,3,7,5,6]=>010010=>[1,1,2,1,1]
[6,4,7,5,2,1,3]=>[2,4,1,3,6,7,5]=>010001=>[1,1,3,1]
[6,4,7,5,2,3,1]=>[2,4,1,3,6,5,7]=>010010=>[1,1,2,1,1]
[6,4,7,5,3,1,2]=>[2,4,1,3,5,7,6]=>010001=>[1,1,3,1]
[6,4,7,5,3,2,1]=>[2,4,1,3,5,6,7]=>010000=>[1,1,4]
[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>001111=>[2,4]
[6,5,1,2,3,7,4]=>[2,3,7,6,5,1,4]=>001110=>[2,3,1]
[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>001101=>[2,2,1,1]
[6,5,1,2,4,7,3]=>[2,3,7,6,4,1,5]=>001110=>[2,3,1]
[6,5,1,2,7,3,4]=>[2,3,7,6,1,5,4]=>001101=>[2,2,1,1]
[6,5,1,2,7,4,3]=>[2,3,7,6,1,4,5]=>001100=>[2,2,2]
[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>001011=>[2,1,1,2]
[6,5,1,3,2,7,4]=>[2,3,7,5,6,1,4]=>001010=>[2,1,1,1,1]
[6,5,1,3,4,2,7]=>[2,3,7,5,4,6,1]=>001101=>[2,2,1,1]
[6,5,1,3,4,7,2]=>[2,3,7,5,4,1,6]=>001110=>[2,3,1]
[6,5,1,3,7,2,4]=>[2,3,7,5,1,6,4]=>001101=>[2,2,1,1]
[6,5,1,3,7,4,2]=>[2,3,7,5,1,4,6]=>001100=>[2,2,2]
[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>001011=>[2,1,1,2]
[6,5,1,4,2,7,3]=>[2,3,7,4,6,1,5]=>001010=>[2,1,1,1,1]
[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>001001=>[2,1,2,1]
[6,5,1,4,3,7,2]=>[2,3,7,4,5,1,6]=>001010=>[2,1,1,1,1]
[6,5,1,4,7,2,3]=>[2,3,7,4,1,6,5]=>001101=>[2,2,1,1]
[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>001100=>[2,2,2]
[6,5,1,7,2,3,4]=>[2,3,7,1,6,5,4]=>001011=>[2,1,1,2]
[6,5,1,7,2,4,3]=>[2,3,7,1,6,4,5]=>001010=>[2,1,1,1,1]
[6,5,1,7,3,2,4]=>[2,3,7,1,5,6,4]=>001001=>[2,1,2,1]
[6,5,1,7,3,4,2]=>[2,3,7,1,5,4,6]=>001010=>[2,1,1,1,1]
[6,5,1,7,4,2,3]=>[2,3,7,1,4,6,5]=>001001=>[2,1,2,1]
[6,5,1,7,4,3,2]=>[2,3,7,1,4,5,6]=>001000=>[2,1,3]
[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>000111=>[3,3]
[6,5,2,1,3,7,4]=>[2,3,6,7,5,1,4]=>000110=>[3,2,1]
[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>000101=>[3,1,1,1]
[6,5,2,1,4,7,3]=>[2,3,6,7,4,1,5]=>000110=>[3,2,1]
[6,5,2,1,7,3,4]=>[2,3,6,7,1,5,4]=>000101=>[3,1,1,1]
[6,5,2,1,7,4,3]=>[2,3,6,7,1,4,5]=>000100=>[3,1,2]
[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>001011=>[2,1,1,2]
[6,5,2,3,1,7,4]=>[2,3,6,5,7,1,4]=>001010=>[2,1,1,1,1]
[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>001101=>[2,2,1,1]
[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>001110=>[2,3,1]
[6,5,2,3,7,1,4]=>[2,3,6,5,1,7,4]=>001101=>[2,2,1,1]
[6,5,2,3,7,4,1]=>[2,3,6,5,1,4,7]=>001100=>[2,2,2]
[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>001011=>[2,1,1,2]
[6,5,2,4,1,7,3]=>[2,3,6,4,7,1,5]=>001010=>[2,1,1,1,1]
[6,5,2,4,3,1,7]=>[2,3,6,4,5,7,1]=>001001=>[2,1,2,1]
[6,5,2,4,3,7,1]=>[2,3,6,4,5,1,7]=>001010=>[2,1,1,1,1]
[6,5,2,4,7,1,3]=>[2,3,6,4,1,7,5]=>001101=>[2,2,1,1]
[6,5,2,4,7,3,1]=>[2,3,6,4,1,5,7]=>001100=>[2,2,2]
[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>001011=>[2,1,1,2]
[6,5,2,7,1,4,3]=>[2,3,6,1,7,4,5]=>001010=>[2,1,1,1,1]
[6,5,2,7,3,1,4]=>[2,3,6,1,5,7,4]=>001001=>[2,1,2,1]
[6,5,2,7,3,4,1]=>[2,3,6,1,5,4,7]=>001010=>[2,1,1,1,1]
[6,5,2,7,4,1,3]=>[2,3,6,1,4,7,5]=>001001=>[2,1,2,1]
[6,5,2,7,4,3,1]=>[2,3,6,1,4,5,7]=>001000=>[2,1,3]
[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>000111=>[3,3]
[6,5,3,1,2,7,4]=>[2,3,5,7,6,1,4]=>000110=>[3,2,1]
[6,5,3,1,4,2,7]=>[2,3,5,7,4,6,1]=>000101=>[3,1,1,1]
[6,5,3,1,4,7,2]=>[2,3,5,7,4,1,6]=>000110=>[3,2,1]
[6,5,3,1,7,2,4]=>[2,3,5,7,1,6,4]=>000101=>[3,1,1,1]
[6,5,3,1,7,4,2]=>[2,3,5,7,1,4,6]=>000100=>[3,1,2]
[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>000011=>[4,2]
[6,5,3,2,1,7,4]=>[2,3,5,6,7,1,4]=>000010=>[4,1,1]
[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>000101=>[3,1,1,1]
[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>000110=>[3,2,1]
[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>000101=>[3,1,1,1]
[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>000100=>[3,1,2]
[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>001011=>[2,1,1,2]
[6,5,3,4,1,7,2]=>[2,3,5,4,7,1,6]=>001010=>[2,1,1,1,1]
[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>001001=>[2,1,2,1]
[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>001010=>[2,1,1,1,1]
[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>001101=>[2,2,1,1]
[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>001100=>[2,2,2]
[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>001011=>[2,1,1,2]
[6,5,3,7,1,4,2]=>[2,3,5,1,7,4,6]=>001010=>[2,1,1,1,1]
[6,5,3,7,2,1,4]=>[2,3,5,1,6,7,4]=>001001=>[2,1,2,1]
[6,5,3,7,2,4,1]=>[2,3,5,1,6,4,7]=>001010=>[2,1,1,1,1]
[6,5,3,7,4,1,2]=>[2,3,5,1,4,7,6]=>001001=>[2,1,2,1]
[6,5,3,7,4,2,1]=>[2,3,5,1,4,6,7]=>001000=>[2,1,3]
[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>000111=>[3,3]
[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>000110=>[3,2,1]
[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>000101=>[3,1,1,1]
[6,5,4,1,3,7,2]=>[2,3,4,7,5,1,6]=>000110=>[3,2,1]
[6,5,4,1,7,2,3]=>[2,3,4,7,1,6,5]=>000101=>[3,1,1,1]
[6,5,4,1,7,3,2]=>[2,3,4,7,1,5,6]=>000100=>[3,1,2]
[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>000011=>[4,2]
[6,5,4,2,1,7,3]=>[2,3,4,6,7,1,5]=>000010=>[4,1,1]
[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>000101=>[3,1,1,1]
[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>000110=>[3,2,1]
[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>000101=>[3,1,1,1]
[6,5,4,2,7,3,1]=>[2,3,4,6,1,5,7]=>000100=>[3,1,2]
[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>000011=>[4,2]
[6,5,4,3,1,7,2]=>[2,3,4,5,7,1,6]=>000010=>[4,1,1]
[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>000001=>[5,1]
[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>000010=>[4,1,1]
[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>000101=>[3,1,1,1]
[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>000100=>[3,1,2]
[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>001011=>[2,1,1,2]
[6,5,4,7,1,3,2]=>[2,3,4,1,7,5,6]=>001010=>[2,1,1,1,1]
[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>001001=>[2,1,2,1]
[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>001010=>[2,1,1,1,1]
[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>001001=>[2,1,2,1]
[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>001000=>[2,1,3]
[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>010111=>[1,1,1,3]
[6,5,7,1,2,4,3]=>[2,3,1,7,6,4,5]=>010110=>[1,1,1,2,1]
[6,5,7,1,3,2,4]=>[2,3,1,7,5,6,4]=>010101=>[1,1,1,1,1,1]
[6,5,7,1,3,4,2]=>[2,3,1,7,5,4,6]=>010110=>[1,1,1,2,1]
[6,5,7,1,4,2,3]=>[2,3,1,7,4,6,5]=>010101=>[1,1,1,1,1,1]
[6,5,7,1,4,3,2]=>[2,3,1,7,4,5,6]=>010100=>[1,1,1,1,2]
[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>010011=>[1,1,2,2]
[6,5,7,2,1,4,3]=>[2,3,1,6,7,4,5]=>010010=>[1,1,2,1,1]
[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>010101=>[1,1,1,1,1,1]
[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>010110=>[1,1,1,2,1]
[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>010101=>[1,1,1,1,1,1]
[6,5,7,2,4,3,1]=>[2,3,1,6,4,5,7]=>010100=>[1,1,1,1,2]
[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>010011=>[1,1,2,2]
[6,5,7,3,1,4,2]=>[2,3,1,5,7,4,6]=>010010=>[1,1,2,1,1]
[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>010001=>[1,1,3,1]
[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>010010=>[1,1,2,1,1]
[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>010101=>[1,1,1,1,1,1]
[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>010100=>[1,1,1,1,2]
[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>010011=>[1,1,2,2]
[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>010010=>[1,1,2,1,1]
[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>010001=>[1,1,3,1]
[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>010010=>[1,1,2,1,1]
[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>010001=>[1,1,3,1]
[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>010000=>[1,1,4]
[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>101111=>[1,1,4]
[6,7,1,2,3,5,4]=>[2,1,7,6,5,3,4]=>101110=>[1,1,3,1]
[6,7,1,2,4,3,5]=>[2,1,7,6,4,5,3]=>101101=>[1,1,2,1,1]
[6,7,1,2,4,5,3]=>[2,1,7,6,4,3,5]=>101110=>[1,1,3,1]
[6,7,1,2,5,3,4]=>[2,1,7,6,3,5,4]=>101101=>[1,1,2,1,1]
[6,7,1,2,5,4,3]=>[2,1,7,6,3,4,5]=>101100=>[1,1,2,2]
[6,7,1,3,2,4,5]=>[2,1,7,5,6,4,3]=>101011=>[1,1,1,1,2]
[6,7,1,3,2,5,4]=>[2,1,7,5,6,3,4]=>101010=>[1,1,1,1,1,1]
[6,7,1,3,4,2,5]=>[2,1,7,5,4,6,3]=>101101=>[1,1,2,1,1]
[6,7,1,3,4,5,2]=>[2,1,7,5,4,3,6]=>101110=>[1,1,3,1]
[6,7,1,3,5,2,4]=>[2,1,7,5,3,6,4]=>101101=>[1,1,2,1,1]
[6,7,1,3,5,4,2]=>[2,1,7,5,3,4,6]=>101100=>[1,1,2,2]
[6,7,1,4,2,3,5]=>[2,1,7,4,6,5,3]=>101011=>[1,1,1,1,2]
[6,7,1,4,2,5,3]=>[2,1,7,4,6,3,5]=>101010=>[1,1,1,1,1,1]
[6,7,1,4,3,2,5]=>[2,1,7,4,5,6,3]=>101001=>[1,1,1,2,1]
[6,7,1,4,3,5,2]=>[2,1,7,4,5,3,6]=>101010=>[1,1,1,1,1,1]
[6,7,1,4,5,2,3]=>[2,1,7,4,3,6,5]=>101101=>[1,1,2,1,1]
[6,7,1,4,5,3,2]=>[2,1,7,4,3,5,6]=>101100=>[1,1,2,2]
[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>101011=>[1,1,1,1,2]
[6,7,1,5,2,4,3]=>[2,1,7,3,6,4,5]=>101010=>[1,1,1,1,1,1]
[6,7,1,5,3,2,4]=>[2,1,7,3,5,6,4]=>101001=>[1,1,1,2,1]
[6,7,1,5,3,4,2]=>[2,1,7,3,5,4,6]=>101010=>[1,1,1,1,1,1]
[6,7,1,5,4,2,3]=>[2,1,7,3,4,6,5]=>101001=>[1,1,1,2,1]
[6,7,1,5,4,3,2]=>[2,1,7,3,4,5,6]=>101000=>[1,1,1,3]
[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>100111=>[1,2,3]
[6,7,2,1,3,5,4]=>[2,1,6,7,5,3,4]=>100110=>[1,2,2,1]
[6,7,2,1,4,3,5]=>[2,1,6,7,4,5,3]=>100101=>[1,2,1,1,1]
[6,7,2,1,4,5,3]=>[2,1,6,7,4,3,5]=>100110=>[1,2,2,1]
[6,7,2,1,5,3,4]=>[2,1,6,7,3,5,4]=>100101=>[1,2,1,1,1]
[6,7,2,1,5,4,3]=>[2,1,6,7,3,4,5]=>100100=>[1,2,1,2]
[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>101011=>[1,1,1,1,2]
[6,7,2,3,1,5,4]=>[2,1,6,5,7,3,4]=>101010=>[1,1,1,1,1,1]
[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>101101=>[1,1,2,1,1]
[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>101110=>[1,1,3,1]
[6,7,2,3,5,1,4]=>[2,1,6,5,3,7,4]=>101101=>[1,1,2,1,1]
[6,7,2,3,5,4,1]=>[2,1,6,5,3,4,7]=>101100=>[1,1,2,2]
[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>101011=>[1,1,1,1,2]
[6,7,2,4,1,5,3]=>[2,1,6,4,7,3,5]=>101010=>[1,1,1,1,1,1]
[6,7,2,4,3,1,5]=>[2,1,6,4,5,7,3]=>101001=>[1,1,1,2,1]
[6,7,2,4,3,5,1]=>[2,1,6,4,5,3,7]=>101010=>[1,1,1,1,1,1]
[6,7,2,4,5,1,3]=>[2,1,6,4,3,7,5]=>101101=>[1,1,2,1,1]
[6,7,2,4,5,3,1]=>[2,1,6,4,3,5,7]=>101100=>[1,1,2,2]
[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>101011=>[1,1,1,1,2]
[6,7,2,5,1,4,3]=>[2,1,6,3,7,4,5]=>101010=>[1,1,1,1,1,1]
[6,7,2,5,3,1,4]=>[2,1,6,3,5,7,4]=>101001=>[1,1,1,2,1]
[6,7,2,5,3,4,1]=>[2,1,6,3,5,4,7]=>101010=>[1,1,1,1,1,1]
[6,7,2,5,4,1,3]=>[2,1,6,3,4,7,5]=>101001=>[1,1,1,2,1]
[6,7,2,5,4,3,1]=>[2,1,6,3,4,5,7]=>101000=>[1,1,1,3]
[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>100111=>[1,2,3]
[6,7,3,1,2,5,4]=>[2,1,5,7,6,3,4]=>100110=>[1,2,2,1]
[6,7,3,1,4,2,5]=>[2,1,5,7,4,6,3]=>100101=>[1,2,1,1,1]
[6,7,3,1,4,5,2]=>[2,1,5,7,4,3,6]=>100110=>[1,2,2,1]
[6,7,3,1,5,2,4]=>[2,1,5,7,3,6,4]=>100101=>[1,2,1,1,1]
[6,7,3,1,5,4,2]=>[2,1,5,7,3,4,6]=>100100=>[1,2,1,2]
[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>100011=>[1,3,2]
[6,7,3,2,1,5,4]=>[2,1,5,6,7,3,4]=>100010=>[1,3,1,1]
[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>100101=>[1,2,1,1,1]
[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>100110=>[1,2,2,1]
[6,7,3,2,5,1,4]=>[2,1,5,6,3,7,4]=>100101=>[1,2,1,1,1]
[6,7,3,2,5,4,1]=>[2,1,5,6,3,4,7]=>100100=>[1,2,1,2]
[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>101011=>[1,1,1,1,2]
[6,7,3,4,1,5,2]=>[2,1,5,4,7,3,6]=>101010=>[1,1,1,1,1,1]
[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>101001=>[1,1,1,2,1]
[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>101010=>[1,1,1,1,1,1]
[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101=>[1,1,2,1,1]
[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>101100=>[1,1,2,2]
[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>101011=>[1,1,1,1,2]
[6,7,3,5,1,4,2]=>[2,1,5,3,7,4,6]=>101010=>[1,1,1,1,1,1]
[6,7,3,5,2,1,4]=>[2,1,5,3,6,7,4]=>101001=>[1,1,1,2,1]
[6,7,3,5,2,4,1]=>[2,1,5,3,6,4,7]=>101010=>[1,1,1,1,1,1]
[6,7,3,5,4,1,2]=>[2,1,5,3,4,7,6]=>101001=>[1,1,1,2,1]
[6,7,3,5,4,2,1]=>[2,1,5,3,4,6,7]=>101000=>[1,1,1,3]
[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>100111=>[1,2,3]
[6,7,4,1,2,5,3]=>[2,1,4,7,6,3,5]=>100110=>[1,2,2,1]
[6,7,4,1,3,2,5]=>[2,1,4,7,5,6,3]=>100101=>[1,2,1,1,1]
[6,7,4,1,3,5,2]=>[2,1,4,7,5,3,6]=>100110=>[1,2,2,1]
[6,7,4,1,5,2,3]=>[2,1,4,7,3,6,5]=>100101=>[1,2,1,1,1]
[6,7,4,1,5,3,2]=>[2,1,4,7,3,5,6]=>100100=>[1,2,1,2]
[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>100011=>[1,3,2]
[6,7,4,2,1,5,3]=>[2,1,4,6,7,3,5]=>100010=>[1,3,1,1]
[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>100101=>[1,2,1,1,1]
[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>100110=>[1,2,2,1]
[6,7,4,2,5,1,3]=>[2,1,4,6,3,7,5]=>100101=>[1,2,1,1,1]
[6,7,4,2,5,3,1]=>[2,1,4,6,3,5,7]=>100100=>[1,2,1,2]
[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>100011=>[1,3,2]
[6,7,4,3,1,5,2]=>[2,1,4,5,7,3,6]=>100010=>[1,3,1,1]
[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>100001=>[1,4,1]
[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>100010=>[1,3,1,1]
[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>100101=>[1,2,1,1,1]
[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>100100=>[1,2,1,2]
[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>101011=>[1,1,1,1,2]
[6,7,4,5,1,3,2]=>[2,1,4,3,7,5,6]=>101010=>[1,1,1,1,1,1]
[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>101001=>[1,1,1,2,1]
[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>101010=>[1,1,1,1,1,1]
[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>101001=>[1,1,1,2,1]
[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>101000=>[1,1,1,3]
[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>100111=>[1,2,3]
[6,7,5,1,2,4,3]=>[2,1,3,7,6,4,5]=>100110=>[1,2,2,1]
[6,7,5,1,3,2,4]=>[2,1,3,7,5,6,4]=>100101=>[1,2,1,1,1]
[6,7,5,1,3,4,2]=>[2,1,3,7,5,4,6]=>100110=>[1,2,2,1]
[6,7,5,1,4,2,3]=>[2,1,3,7,4,6,5]=>100101=>[1,2,1,1,1]
[6,7,5,1,4,3,2]=>[2,1,3,7,4,5,6]=>100100=>[1,2,1,2]
[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>100011=>[1,3,2]
[6,7,5,2,1,4,3]=>[2,1,3,6,7,4,5]=>100010=>[1,3,1,1]
[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>100101=>[1,2,1,1,1]
[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>100110=>[1,2,2,1]
[6,7,5,2,4,1,3]=>[2,1,3,6,4,7,5]=>100101=>[1,2,1,1,1]
[6,7,5,2,4,3,1]=>[2,1,3,6,4,5,7]=>100100=>[1,2,1,2]
[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>100011=>[1,3,2]
[6,7,5,3,1,4,2]=>[2,1,3,5,7,4,6]=>100010=>[1,3,1,1]
[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>100001=>[1,4,1]
[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>100010=>[1,3,1,1]
[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>100101=>[1,2,1,1,1]
[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>100100=>[1,2,1,2]
[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>100011=>[1,3,2]
[6,7,5,4,1,3,2]=>[2,1,3,4,7,5,6]=>100010=>[1,3,1,1]
[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>100001=>[1,4,1]
[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>100010=>[1,3,1,1]
[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001=>[1,4,1]
[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>100000=>[1,5]
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111=>[1,5]
[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>011110=>[1,4,1]
[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>011101=>[1,3,1,1]
[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>011110=>[1,4,1]
[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>011101=>[1,3,1,1]
[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>011100=>[1,3,2]
[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>011011=>[1,2,1,2]
[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>011010=>[1,2,1,1,1]
[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>011101=>[1,3,1,1]
[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>011110=>[1,4,1]
[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>011101=>[1,3,1,1]
[7,1,2,4,6,5,3]=>[1,7,6,4,2,3,5]=>011100=>[1,3,2]
[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>011011=>[1,2,1,2]
[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>011010=>[1,2,1,1,1]
[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>011001=>[1,2,2,1]
[7,1,2,5,4,6,3]=>[1,7,6,3,4,2,5]=>011010=>[1,2,1,1,1]
[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>011101=>[1,3,1,1]
[7,1,2,5,6,4,3]=>[1,7,6,3,2,4,5]=>011100=>[1,3,2]
[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>011011=>[1,2,1,2]
[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>011010=>[1,2,1,1,1]
[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>011001=>[1,2,2,1]
[7,1,2,6,4,5,3]=>[1,7,6,2,4,3,5]=>011010=>[1,2,1,1,1]
[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>011001=>[1,2,2,1]
[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>011000=>[1,2,3]
[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>010111=>[1,1,1,3]
[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>010110=>[1,1,1,2,1]
[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>010101=>[1,1,1,1,1,1]
[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>010110=>[1,1,1,2,1]
[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>010101=>[1,1,1,1,1,1]
[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>010100=>[1,1,1,1,2]
[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>011011=>[1,2,1,2]
[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>011010=>[1,2,1,1,1]
[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>011101=>[1,3,1,1]
[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>011110=>[1,4,1]
[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>011101=>[1,3,1,1]
[7,1,3,4,6,5,2]=>[1,7,5,4,2,3,6]=>011100=>[1,3,2]
[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>011011=>[1,2,1,2]
[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>011010=>[1,2,1,1,1]
[7,1,3,5,4,2,6]=>[1,7,5,3,4,6,2]=>011001=>[1,2,2,1]
[7,1,3,5,4,6,2]=>[1,7,5,3,4,2,6]=>011010=>[1,2,1,1,1]
[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>011101=>[1,3,1,1]
[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>011100=>[1,3,2]
[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>011011=>[1,2,1,2]
[7,1,3,6,2,5,4]=>[1,7,5,2,6,3,4]=>011010=>[1,2,1,1,1]
[7,1,3,6,4,2,5]=>[1,7,5,2,4,6,3]=>011001=>[1,2,2,1]
[7,1,3,6,4,5,2]=>[1,7,5,2,4,3,6]=>011010=>[1,2,1,1,1]
[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>011001=>[1,2,2,1]
[7,1,3,6,5,4,2]=>[1,7,5,2,3,4,6]=>011000=>[1,2,3]
[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>010111=>[1,1,1,3]
[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>010110=>[1,1,1,2,1]
[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>010101=>[1,1,1,1,1,1]
[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>010110=>[1,1,1,2,1]
[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>010101=>[1,1,1,1,1,1]
[7,1,4,2,6,5,3]=>[1,7,4,6,2,3,5]=>010100=>[1,1,1,1,2]
[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>010011=>[1,1,2,2]
[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>010010=>[1,1,2,1,1]
[7,1,4,3,5,2,6]=>[1,7,4,5,3,6,2]=>010101=>[1,1,1,1,1,1]
[7,1,4,3,5,6,2]=>[1,7,4,5,3,2,6]=>010110=>[1,1,1,2,1]
[7,1,4,3,6,2,5]=>[1,7,4,5,2,6,3]=>010101=>[1,1,1,1,1,1]
[7,1,4,3,6,5,2]=>[1,7,4,5,2,3,6]=>010100=>[1,1,1,1,2]
[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>011011=>[1,2,1,2]
[7,1,4,5,2,6,3]=>[1,7,4,3,6,2,5]=>011010=>[1,2,1,1,1]
[7,1,4,5,3,2,6]=>[1,7,4,3,5,6,2]=>011001=>[1,2,2,1]
[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>011010=>[1,2,1,1,1]
[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>011101=>[1,3,1,1]
[7,1,4,5,6,3,2]=>[1,7,4,3,2,5,6]=>011100=>[1,3,2]
[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>011011=>[1,2,1,2]
[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>011010=>[1,2,1,1,1]
[7,1,4,6,3,2,5]=>[1,7,4,2,5,6,3]=>011001=>[1,2,2,1]
[7,1,4,6,3,5,2]=>[1,7,4,2,5,3,6]=>011010=>[1,2,1,1,1]
[7,1,4,6,5,2,3]=>[1,7,4,2,3,6,5]=>011001=>[1,2,2,1]
[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>011000=>[1,2,3]
[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>010111=>[1,1,1,3]
[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>010110=>[1,1,1,2,1]
[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>010101=>[1,1,1,1,1,1]
[7,1,5,2,4,6,3]=>[1,7,3,6,4,2,5]=>010110=>[1,1,1,2,1]
[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>010101=>[1,1,1,1,1,1]
[7,1,5,2,6,4,3]=>[1,7,3,6,2,4,5]=>010100=>[1,1,1,1,2]
[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>010011=>[1,1,2,2]
[7,1,5,3,2,6,4]=>[1,7,3,5,6,2,4]=>010010=>[1,1,2,1,1]
[7,1,5,3,4,2,6]=>[1,7,3,5,4,6,2]=>010101=>[1,1,1,1,1,1]
[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>010110=>[1,1,1,2,1]
[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>010101=>[1,1,1,1,1,1]
[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>010100=>[1,1,1,1,2]
[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>010011=>[1,1,2,2]
[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>010010=>[1,1,2,1,1]
[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>010001=>[1,1,3,1]
[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>010010=>[1,1,2,1,1]
[7,1,5,4,6,2,3]=>[1,7,3,4,2,6,5]=>010101=>[1,1,1,1,1,1]
[7,1,5,4,6,3,2]=>[1,7,3,4,2,5,6]=>010100=>[1,1,1,1,2]
[7,1,5,6,2,3,4]=>[1,7,3,2,6,5,4]=>011011=>[1,2,1,2]
[7,1,5,6,2,4,3]=>[1,7,3,2,6,4,5]=>011010=>[1,2,1,1,1]
[7,1,5,6,3,2,4]=>[1,7,3,2,5,6,4]=>011001=>[1,2,2,1]
[7,1,5,6,3,4,2]=>[1,7,3,2,5,4,6]=>011010=>[1,2,1,1,1]
[7,1,5,6,4,2,3]=>[1,7,3,2,4,6,5]=>011001=>[1,2,2,1]
[7,1,5,6,4,3,2]=>[1,7,3,2,4,5,6]=>011000=>[1,2,3]
[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>010111=>[1,1,1,3]
[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>010110=>[1,1,1,2,1]
[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>010101=>[1,1,1,1,1,1]
[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>010110=>[1,1,1,2,1]
[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>010101=>[1,1,1,1,1,1]
[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>010100=>[1,1,1,1,2]
[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>010011=>[1,1,2,2]
[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>010010=>[1,1,2,1,1]
[7,1,6,3,4,2,5]=>[1,7,2,5,4,6,3]=>010101=>[1,1,1,1,1,1]
[7,1,6,3,4,5,2]=>[1,7,2,5,4,3,6]=>010110=>[1,1,1,2,1]
[7,1,6,3,5,2,4]=>[1,7,2,5,3,6,4]=>010101=>[1,1,1,1,1,1]
[7,1,6,3,5,4,2]=>[1,7,2,5,3,4,6]=>010100=>[1,1,1,1,2]
[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>010011=>[1,1,2,2]
[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>010010=>[1,1,2,1,1]
[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>010001=>[1,1,3,1]
[7,1,6,4,3,5,2]=>[1,7,2,4,5,3,6]=>010010=>[1,1,2,1,1]
[7,1,6,4,5,2,3]=>[1,7,2,4,3,6,5]=>010101=>[1,1,1,1,1,1]
[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>010100=>[1,1,1,1,2]
[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>010011=>[1,1,2,2]
[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>010010=>[1,1,2,1,1]
[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>010001=>[1,1,3,1]
[7,1,6,5,3,4,2]=>[1,7,2,3,5,4,6]=>010010=>[1,1,2,1,1]
[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>010001=>[1,1,3,1]
[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>010000=>[1,1,4]
[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>001111=>[2,4]
[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>001110=>[2,3,1]
[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>001101=>[2,2,1,1]
[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>001110=>[2,3,1]
[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>001101=>[2,2,1,1]
[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>001100=>[2,2,2]
[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>001011=>[2,1,1,2]
[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>001010=>[2,1,1,1,1]
[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>001101=>[2,2,1,1]
[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>001110=>[2,3,1]
[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>001101=>[2,2,1,1]
[7,2,1,4,6,5,3]=>[1,6,7,4,2,3,5]=>001100=>[2,2,2]
[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>001011=>[2,1,1,2]
[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>001010=>[2,1,1,1,1]
[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>001001=>[2,1,2,1]
[7,2,1,5,4,6,3]=>[1,6,7,3,4,2,5]=>001010=>[2,1,1,1,1]
[7,2,1,5,6,3,4]=>[1,6,7,3,2,5,4]=>001101=>[2,2,1,1]
[7,2,1,5,6,4,3]=>[1,6,7,3,2,4,5]=>001100=>[2,2,2]
[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>001011=>[2,1,1,2]
[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>001010=>[2,1,1,1,1]
[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>001001=>[2,1,2,1]
[7,2,1,6,4,5,3]=>[1,6,7,2,4,3,5]=>001010=>[2,1,1,1,1]
[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>001001=>[2,1,2,1]
[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>001000=>[2,1,3]
[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>010111=>[1,1,1,3]
[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>010110=>[1,1,1,2,1]
[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>010101=>[1,1,1,1,1,1]
[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>010110=>[1,1,1,2,1]
[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>010101=>[1,1,1,1,1,1]
[7,2,3,1,6,5,4]=>[1,6,5,7,2,3,4]=>010100=>[1,1,1,1,2]
[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>011011=>[1,2,1,2]
[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>011010=>[1,2,1,1,1]
[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>011101=>[1,3,1,1]
[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110=>[1,4,1]
[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>011101=>[1,3,1,1]
[7,2,3,4,6,5,1]=>[1,6,5,4,2,3,7]=>011100=>[1,3,2]
[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>011011=>[1,2,1,2]
[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>011010=>[1,2,1,1,1]
[7,2,3,5,4,1,6]=>[1,6,5,3,4,7,2]=>011001=>[1,2,2,1]
[7,2,3,5,4,6,1]=>[1,6,5,3,4,2,7]=>011010=>[1,2,1,1,1]
[7,2,3,5,6,1,4]=>[1,6,5,3,2,7,4]=>011101=>[1,3,1,1]
[7,2,3,5,6,4,1]=>[1,6,5,3,2,4,7]=>011100=>[1,3,2]
[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>011011=>[1,2,1,2]
[7,2,3,6,1,5,4]=>[1,6,5,2,7,3,4]=>011010=>[1,2,1,1,1]
[7,2,3,6,4,1,5]=>[1,6,5,2,4,7,3]=>011001=>[1,2,2,1]
[7,2,3,6,4,5,1]=>[1,6,5,2,4,3,7]=>011010=>[1,2,1,1,1]
[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>011001=>[1,2,2,1]
[7,2,3,6,5,4,1]=>[1,6,5,2,3,4,7]=>011000=>[1,2,3]
[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>010111=>[1,1,1,3]
[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>010110=>[1,1,1,2,1]
[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>010101=>[1,1,1,1,1,1]
[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>010110=>[1,1,1,2,1]
[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>010101=>[1,1,1,1,1,1]
[7,2,4,1,6,5,3]=>[1,6,4,7,2,3,5]=>010100=>[1,1,1,1,2]
[7,2,4,3,1,5,6]=>[1,6,4,5,7,3,2]=>010011=>[1,1,2,2]
[7,2,4,3,1,6,5]=>[1,6,4,5,7,2,3]=>010010=>[1,1,2,1,1]
[7,2,4,3,5,1,6]=>[1,6,4,5,3,7,2]=>010101=>[1,1,1,1,1,1]
[7,2,4,3,5,6,1]=>[1,6,4,5,3,2,7]=>010110=>[1,1,1,2,1]
[7,2,4,3,6,1,5]=>[1,6,4,5,2,7,3]=>010101=>[1,1,1,1,1,1]
[7,2,4,3,6,5,1]=>[1,6,4,5,2,3,7]=>010100=>[1,1,1,1,2]
[7,2,4,5,1,3,6]=>[1,6,4,3,7,5,2]=>011011=>[1,2,1,2]
[7,2,4,5,1,6,3]=>[1,6,4,3,7,2,5]=>011010=>[1,2,1,1,1]
[7,2,4,5,3,1,6]=>[1,6,4,3,5,7,2]=>011001=>[1,2,2,1]
[7,2,4,5,3,6,1]=>[1,6,4,3,5,2,7]=>011010=>[1,2,1,1,1]
[7,2,4,5,6,1,3]=>[1,6,4,3,2,7,5]=>011101=>[1,3,1,1]
[7,2,4,5,6,3,1]=>[1,6,4,3,2,5,7]=>011100=>[1,3,2]
[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>011011=>[1,2,1,2]
[7,2,4,6,1,5,3]=>[1,6,4,2,7,3,5]=>011010=>[1,2,1,1,1]
[7,2,4,6,3,1,5]=>[1,6,4,2,5,7,3]=>011001=>[1,2,2,1]
[7,2,4,6,3,5,1]=>[1,6,4,2,5,3,7]=>011010=>[1,2,1,1,1]
[7,2,4,6,5,1,3]=>[1,6,4,2,3,7,5]=>011001=>[1,2,2,1]
[7,2,4,6,5,3,1]=>[1,6,4,2,3,5,7]=>011000=>[1,2,3]
[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>010111=>[1,1,1,3]
[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>010110=>[1,1,1,2,1]
[7,2,5,1,4,3,6]=>[1,6,3,7,4,5,2]=>010101=>[1,1,1,1,1,1]
[7,2,5,1,4,6,3]=>[1,6,3,7,4,2,5]=>010110=>[1,1,1,2,1]
[7,2,5,1,6,3,4]=>[1,6,3,7,2,5,4]=>010101=>[1,1,1,1,1,1]
[7,2,5,1,6,4,3]=>[1,6,3,7,2,4,5]=>010100=>[1,1,1,1,2]
[7,2,5,3,1,4,6]=>[1,6,3,5,7,4,2]=>010011=>[1,1,2,2]
[7,2,5,3,1,6,4]=>[1,6,3,5,7,2,4]=>010010=>[1,1,2,1,1]
[7,2,5,3,4,1,6]=>[1,6,3,5,4,7,2]=>010101=>[1,1,1,1,1,1]
[7,2,5,3,4,6,1]=>[1,6,3,5,4,2,7]=>010110=>[1,1,1,2,1]
[7,2,5,3,6,1,4]=>[1,6,3,5,2,7,4]=>010101=>[1,1,1,1,1,1]
[7,2,5,3,6,4,1]=>[1,6,3,5,2,4,7]=>010100=>[1,1,1,1,2]
[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>010011=>[1,1,2,2]
[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>010010=>[1,1,2,1,1]
[7,2,5,4,3,1,6]=>[1,6,3,4,5,7,2]=>010001=>[1,1,3,1]
[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>010010=>[1,1,2,1,1]
[7,2,5,4,6,1,3]=>[1,6,3,4,2,7,5]=>010101=>[1,1,1,1,1,1]
[7,2,5,4,6,3,1]=>[1,6,3,4,2,5,7]=>010100=>[1,1,1,1,2]
[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>011011=>[1,2,1,2]
[7,2,5,6,1,4,3]=>[1,6,3,2,7,4,5]=>011010=>[1,2,1,1,1]
[7,2,5,6,3,1,4]=>[1,6,3,2,5,7,4]=>011001=>[1,2,2,1]
[7,2,5,6,3,4,1]=>[1,6,3,2,5,4,7]=>011010=>[1,2,1,1,1]
[7,2,5,6,4,1,3]=>[1,6,3,2,4,7,5]=>011001=>[1,2,2,1]
[7,2,5,6,4,3,1]=>[1,6,3,2,4,5,7]=>011000=>[1,2,3]
[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>010111=>[1,1,1,3]
[7,2,6,1,3,5,4]=>[1,6,2,7,5,3,4]=>010110=>[1,1,1,2,1]
[7,2,6,1,4,3,5]=>[1,6,2,7,4,5,3]=>010101=>[1,1,1,1,1,1]
[7,2,6,1,4,5,3]=>[1,6,2,7,4,3,5]=>010110=>[1,1,1,2,1]
[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>010101=>[1,1,1,1,1,1]
[7,2,6,1,5,4,3]=>[1,6,2,7,3,4,5]=>010100=>[1,1,1,1,2]
[7,2,6,3,1,4,5]=>[1,6,2,5,7,4,3]=>010011=>[1,1,2,2]
[7,2,6,3,1,5,4]=>[1,6,2,5,7,3,4]=>010010=>[1,1,2,1,1]
[7,2,6,3,4,1,5]=>[1,6,2,5,4,7,3]=>010101=>[1,1,1,1,1,1]
[7,2,6,3,4,5,1]=>[1,6,2,5,4,3,7]=>010110=>[1,1,1,2,1]
[7,2,6,3,5,1,4]=>[1,6,2,5,3,7,4]=>010101=>[1,1,1,1,1,1]
[7,2,6,3,5,4,1]=>[1,6,2,5,3,4,7]=>010100=>[1,1,1,1,2]
[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>010011=>[1,1,2,2]
[7,2,6,4,1,5,3]=>[1,6,2,4,7,3,5]=>010010=>[1,1,2,1,1]
[7,2,6,4,3,1,5]=>[1,6,2,4,5,7,3]=>010001=>[1,1,3,1]
[7,2,6,4,3,5,1]=>[1,6,2,4,5,3,7]=>010010=>[1,1,2,1,1]
[7,2,6,4,5,1,3]=>[1,6,2,4,3,7,5]=>010101=>[1,1,1,1,1,1]
[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>010100=>[1,1,1,1,2]
[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>010011=>[1,1,2,2]
[7,2,6,5,1,4,3]=>[1,6,2,3,7,4,5]=>010010=>[1,1,2,1,1]
[7,2,6,5,3,1,4]=>[1,6,2,3,5,7,4]=>010001=>[1,1,3,1]
[7,2,6,5,3,4,1]=>[1,6,2,3,5,4,7]=>010010=>[1,1,2,1,1]
[7,2,6,5,4,1,3]=>[1,6,2,3,4,7,5]=>010001=>[1,1,3,1]
[7,2,6,5,4,3,1]=>[1,6,2,3,4,5,7]=>010000=>[1,1,4]
[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>001111=>[2,4]
[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>001110=>[2,3,1]
[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>001101=>[2,2,1,1]
[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>001110=>[2,3,1]
[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>001101=>[2,2,1,1]
[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>001100=>[2,2,2]
[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>001011=>[2,1,1,2]
[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>001010=>[2,1,1,1,1]
[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>001101=>[2,2,1,1]
[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>001110=>[2,3,1]
[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>001101=>[2,2,1,1]
[7,3,1,4,6,5,2]=>[1,5,7,4,2,3,6]=>001100=>[2,2,2]
[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>001011=>[2,1,1,2]
[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>001010=>[2,1,1,1,1]
[7,3,1,5,4,2,6]=>[1,5,7,3,4,6,2]=>001001=>[2,1,2,1]
[7,3,1,5,4,6,2]=>[1,5,7,3,4,2,6]=>001010=>[2,1,1,1,1]
[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>001101=>[2,2,1,1]
[7,3,1,5,6,4,2]=>[1,5,7,3,2,4,6]=>001100=>[2,2,2]
[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>001011=>[2,1,1,2]
[7,3,1,6,2,5,4]=>[1,5,7,2,6,3,4]=>001010=>[2,1,1,1,1]
[7,3,1,6,4,2,5]=>[1,5,7,2,4,6,3]=>001001=>[2,1,2,1]
[7,3,1,6,4,5,2]=>[1,5,7,2,4,3,6]=>001010=>[2,1,1,1,1]
[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>001001=>[2,1,2,1]
[7,3,1,6,5,4,2]=>[1,5,7,2,3,4,6]=>001000=>[2,1,3]
[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>000111=>[3,3]
[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>000110=>[3,2,1]
[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>000101=>[3,1,1,1]
[7,3,2,1,5,6,4]=>[1,5,6,7,3,2,4]=>000110=>[3,2,1]
[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>000101=>[3,1,1,1]
[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>000100=>[3,1,2]
[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>001011=>[2,1,1,2]
[7,3,2,4,1,6,5]=>[1,5,6,4,7,2,3]=>001010=>[2,1,1,1,1]
[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>001101=>[2,2,1,1]
[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>001110=>[2,3,1]
[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>001101=>[2,2,1,1]
[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>001100=>[2,2,2]
[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>001011=>[2,1,1,2]
[7,3,2,5,1,6,4]=>[1,5,6,3,7,2,4]=>001010=>[2,1,1,1,1]
[7,3,2,5,4,1,6]=>[1,5,6,3,4,7,2]=>001001=>[2,1,2,1]
[7,3,2,5,4,6,1]=>[1,5,6,3,4,2,7]=>001010=>[2,1,1,1,1]
[7,3,2,5,6,1,4]=>[1,5,6,3,2,7,4]=>001101=>[2,2,1,1]
[7,3,2,5,6,4,1]=>[1,5,6,3,2,4,7]=>001100=>[2,2,2]
[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>001011=>[2,1,1,2]
[7,3,2,6,1,5,4]=>[1,5,6,2,7,3,4]=>001010=>[2,1,1,1,1]
[7,3,2,6,4,1,5]=>[1,5,6,2,4,7,3]=>001001=>[2,1,2,1]
[7,3,2,6,4,5,1]=>[1,5,6,2,4,3,7]=>001010=>[2,1,1,1,1]
[7,3,2,6,5,1,4]=>[1,5,6,2,3,7,4]=>001001=>[2,1,2,1]
[7,3,2,6,5,4,1]=>[1,5,6,2,3,4,7]=>001000=>[2,1,3]
[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>010111=>[1,1,1,3]
[7,3,4,1,2,6,5]=>[1,5,4,7,6,2,3]=>010110=>[1,1,1,2,1]
[7,3,4,1,5,2,6]=>[1,5,4,7,3,6,2]=>010101=>[1,1,1,1,1,1]
[7,3,4,1,5,6,2]=>[1,5,4,7,3,2,6]=>010110=>[1,1,1,2,1]
[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>010101=>[1,1,1,1,1,1]
[7,3,4,1,6,5,2]=>[1,5,4,7,2,3,6]=>010100=>[1,1,1,1,2]
[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>010011=>[1,1,2,2]
[7,3,4,2,1,6,5]=>[1,5,4,6,7,2,3]=>010010=>[1,1,2,1,1]
[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>010101=>[1,1,1,1,1,1]
[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>010110=>[1,1,1,2,1]
[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>010101=>[1,1,1,1,1,1]
[7,3,4,2,6,5,1]=>[1,5,4,6,2,3,7]=>010100=>[1,1,1,1,2]
[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>011011=>[1,2,1,2]
[7,3,4,5,1,6,2]=>[1,5,4,3,7,2,6]=>011010=>[1,2,1,1,1]
[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>011001=>[1,2,2,1]
[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>011010=>[1,2,1,1,1]
[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>011101=>[1,3,1,1]
[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>011100=>[1,3,2]
[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>011011=>[1,2,1,2]
[7,3,4,6,1,5,2]=>[1,5,4,2,7,3,6]=>011010=>[1,2,1,1,1]
[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>011001=>[1,2,2,1]
[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>011010=>[1,2,1,1,1]
[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>011001=>[1,2,2,1]
[7,3,4,6,5,2,1]=>[1,5,4,2,3,6,7]=>011000=>[1,2,3]
[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>010111=>[1,1,1,3]
[7,3,5,1,2,6,4]=>[1,5,3,7,6,2,4]=>010110=>[1,1,1,2,1]
[7,3,5,1,4,2,6]=>[1,5,3,7,4,6,2]=>010101=>[1,1,1,1,1,1]
[7,3,5,1,4,6,2]=>[1,5,3,7,4,2,6]=>010110=>[1,1,1,2,1]
[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>010101=>[1,1,1,1,1,1]
[7,3,5,1,6,4,2]=>[1,5,3,7,2,4,6]=>010100=>[1,1,1,1,2]
[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>010011=>[1,1,2,2]
[7,3,5,2,1,6,4]=>[1,5,3,6,7,2,4]=>010010=>[1,1,2,1,1]
[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>010101=>[1,1,1,1,1,1]
[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>010110=>[1,1,1,2,1]
[7,3,5,2,6,1,4]=>[1,5,3,6,2,7,4]=>010101=>[1,1,1,1,1,1]
[7,3,5,2,6,4,1]=>[1,5,3,6,2,4,7]=>010100=>[1,1,1,1,2]
[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>010011=>[1,1,2,2]
[7,3,5,4,1,6,2]=>[1,5,3,4,7,2,6]=>010010=>[1,1,2,1,1]
[7,3,5,4,2,1,6]=>[1,5,3,4,6,7,2]=>010001=>[1,1,3,1]
[7,3,5,4,2,6,1]=>[1,5,3,4,6,2,7]=>010010=>[1,1,2,1,1]
[7,3,5,4,6,1,2]=>[1,5,3,4,2,7,6]=>010101=>[1,1,1,1,1,1]
[7,3,5,4,6,2,1]=>[1,5,3,4,2,6,7]=>010100=>[1,1,1,1,2]
[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>011011=>[1,2,1,2]
[7,3,5,6,1,4,2]=>[1,5,3,2,7,4,6]=>011010=>[1,2,1,1,1]
[7,3,5,6,2,1,4]=>[1,5,3,2,6,7,4]=>011001=>[1,2,2,1]
[7,3,5,6,2,4,1]=>[1,5,3,2,6,4,7]=>011010=>[1,2,1,1,1]
[7,3,5,6,4,1,2]=>[1,5,3,2,4,7,6]=>011001=>[1,2,2,1]
[7,3,5,6,4,2,1]=>[1,5,3,2,4,6,7]=>011000=>[1,2,3]
[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>010111=>[1,1,1,3]
[7,3,6,1,2,5,4]=>[1,5,2,7,6,3,4]=>010110=>[1,1,1,2,1]
[7,3,6,1,4,2,5]=>[1,5,2,7,4,6,3]=>010101=>[1,1,1,1,1,1]
[7,3,6,1,4,5,2]=>[1,5,2,7,4,3,6]=>010110=>[1,1,1,2,1]
[7,3,6,1,5,2,4]=>[1,5,2,7,3,6,4]=>010101=>[1,1,1,1,1,1]
[7,3,6,1,5,4,2]=>[1,5,2,7,3,4,6]=>010100=>[1,1,1,1,2]
[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>010011=>[1,1,2,2]
[7,3,6,2,1,5,4]=>[1,5,2,6,7,3,4]=>010010=>[1,1,2,1,1]
[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>010101=>[1,1,1,1,1,1]
[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>010110=>[1,1,1,2,1]
[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>010101=>[1,1,1,1,1,1]
[7,3,6,2,5,4,1]=>[1,5,2,6,3,4,7]=>010100=>[1,1,1,1,2]
[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>010011=>[1,1,2,2]
[7,3,6,4,1,5,2]=>[1,5,2,4,7,3,6]=>010010=>[1,1,2,1,1]
[7,3,6,4,2,1,5]=>[1,5,2,4,6,7,3]=>010001=>[1,1,3,1]
[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>010010=>[1,1,2,1,1]
[7,3,6,4,5,1,2]=>[1,5,2,4,3,7,6]=>010101=>[1,1,1,1,1,1]
[7,3,6,4,5,2,1]=>[1,5,2,4,3,6,7]=>010100=>[1,1,1,1,2]
[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>010011=>[1,1,2,2]
[7,3,6,5,1,4,2]=>[1,5,2,3,7,4,6]=>010010=>[1,1,2,1,1]
[7,3,6,5,2,1,4]=>[1,5,2,3,6,7,4]=>010001=>[1,1,3,1]
[7,3,6,5,2,4,1]=>[1,5,2,3,6,4,7]=>010010=>[1,1,2,1,1]
[7,3,6,5,4,1,2]=>[1,5,2,3,4,7,6]=>010001=>[1,1,3,1]
[7,3,6,5,4,2,1]=>[1,5,2,3,4,6,7]=>010000=>[1,1,4]
[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>001111=>[2,4]
[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>001110=>[2,3,1]
[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>001101=>[2,2,1,1]
[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>001110=>[2,3,1]
[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>001101=>[2,2,1,1]
[7,4,1,2,6,5,3]=>[1,4,7,6,2,3,5]=>001100=>[2,2,2]
[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>001011=>[2,1,1,2]
[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>001010=>[2,1,1,1,1]
[7,4,1,3,5,2,6]=>[1,4,7,5,3,6,2]=>001101=>[2,2,1,1]
[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>001110=>[2,3,1]
[7,4,1,3,6,2,5]=>[1,4,7,5,2,6,3]=>001101=>[2,2,1,1]
[7,4,1,3,6,5,2]=>[1,4,7,5,2,3,6]=>001100=>[2,2,2]
[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>001011=>[2,1,1,2]
[7,4,1,5,2,6,3]=>[1,4,7,3,6,2,5]=>001010=>[2,1,1,1,1]
[7,4,1,5,3,2,6]=>[1,4,7,3,5,6,2]=>001001=>[2,1,2,1]
[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>001010=>[2,1,1,1,1]
[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>001101=>[2,2,1,1]
[7,4,1,5,6,3,2]=>[1,4,7,3,2,5,6]=>001100=>[2,2,2]
[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>001011=>[2,1,1,2]
[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>001010=>[2,1,1,1,1]
[7,4,1,6,3,2,5]=>[1,4,7,2,5,6,3]=>001001=>[2,1,2,1]
[7,4,1,6,3,5,2]=>[1,4,7,2,5,3,6]=>001010=>[2,1,1,1,1]
[7,4,1,6,5,2,3]=>[1,4,7,2,3,6,5]=>001001=>[2,1,2,1]
[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>001000=>[2,1,3]
[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>000111=>[3,3]
[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>000110=>[3,2,1]
[7,4,2,1,5,3,6]=>[1,4,6,7,3,5,2]=>000101=>[3,1,1,1]
[7,4,2,1,5,6,3]=>[1,4,6,7,3,2,5]=>000110=>[3,2,1]
[7,4,2,1,6,3,5]=>[1,4,6,7,2,5,3]=>000101=>[3,1,1,1]
[7,4,2,1,6,5,3]=>[1,4,6,7,2,3,5]=>000100=>[3,1,2]
[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>001011=>[2,1,1,2]
[7,4,2,3,1,6,5]=>[1,4,6,5,7,2,3]=>001010=>[2,1,1,1,1]
[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>001101=>[2,2,1,1]
[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>001110=>[2,3,1]
[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>001101=>[2,2,1,1]
[7,4,2,3,6,5,1]=>[1,4,6,5,2,3,7]=>001100=>[2,2,2]
[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>001011=>[2,1,1,2]
[7,4,2,5,1,6,3]=>[1,4,6,3,7,2,5]=>001010=>[2,1,1,1,1]
[7,4,2,5,3,1,6]=>[1,4,6,3,5,7,2]=>001001=>[2,1,2,1]
[7,4,2,5,3,6,1]=>[1,4,6,3,5,2,7]=>001010=>[2,1,1,1,1]
[7,4,2,5,6,1,3]=>[1,4,6,3,2,7,5]=>001101=>[2,2,1,1]
[7,4,2,5,6,3,1]=>[1,4,6,3,2,5,7]=>001100=>[2,2,2]
[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>001011=>[2,1,1,2]
[7,4,2,6,1,5,3]=>[1,4,6,2,7,3,5]=>001010=>[2,1,1,1,1]
[7,4,2,6,3,1,5]=>[1,4,6,2,5,7,3]=>001001=>[2,1,2,1]
[7,4,2,6,3,5,1]=>[1,4,6,2,5,3,7]=>001010=>[2,1,1,1,1]
[7,4,2,6,5,1,3]=>[1,4,6,2,3,7,5]=>001001=>[2,1,2,1]
[7,4,2,6,5,3,1]=>[1,4,6,2,3,5,7]=>001000=>[2,1,3]
[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>000111=>[3,3]
[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>000110=>[3,2,1]
[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>000101=>[3,1,1,1]
[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>000110=>[3,2,1]
[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>000101=>[3,1,1,1]
[7,4,3,1,6,5,2]=>[1,4,5,7,2,3,6]=>000100=>[3,1,2]
[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>000011=>[4,2]
[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>000010=>[4,1,1]
[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>000101=>[3,1,1,1]
[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>000110=>[3,2,1]
[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>000101=>[3,1,1,1]
[7,4,3,2,6,5,1]=>[1,4,5,6,2,3,7]=>000100=>[3,1,2]
[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>001011=>[2,1,1,2]
[7,4,3,5,1,6,2]=>[1,4,5,3,7,2,6]=>001010=>[2,1,1,1,1]
[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>001001=>[2,1,2,1]
[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>001010=>[2,1,1,1,1]
[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>001101=>[2,2,1,1]
[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>001100=>[2,2,2]
[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>001011=>[2,1,1,2]
[7,4,3,6,1,5,2]=>[1,4,5,2,7,3,6]=>001010=>[2,1,1,1,1]
[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>001001=>[2,1,2,1]
[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>001010=>[2,1,1,1,1]
[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>001001=>[2,1,2,1]
[7,4,3,6,5,2,1]=>[1,4,5,2,3,6,7]=>001000=>[2,1,3]
[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>010111=>[1,1,1,3]
[7,4,5,1,2,6,3]=>[1,4,3,7,6,2,5]=>010110=>[1,1,1,2,1]
[7,4,5,1,3,2,6]=>[1,4,3,7,5,6,2]=>010101=>[1,1,1,1,1,1]
[7,4,5,1,3,6,2]=>[1,4,3,7,5,2,6]=>010110=>[1,1,1,2,1]
[7,4,5,1,6,2,3]=>[1,4,3,7,2,6,5]=>010101=>[1,1,1,1,1,1]
[7,4,5,1,6,3,2]=>[1,4,3,7,2,5,6]=>010100=>[1,1,1,1,2]
[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>010011=>[1,1,2,2]
[7,4,5,2,1,6,3]=>[1,4,3,6,7,2,5]=>010010=>[1,1,2,1,1]
[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>010101=>[1,1,1,1,1,1]
[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>010110=>[1,1,1,2,1]
[7,4,5,2,6,1,3]=>[1,4,3,6,2,7,5]=>010101=>[1,1,1,1,1,1]
[7,4,5,2,6,3,1]=>[1,4,3,6,2,5,7]=>010100=>[1,1,1,1,2]
[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>010011=>[1,1,2,2]
[7,4,5,3,1,6,2]=>[1,4,3,5,7,2,6]=>010010=>[1,1,2,1,1]
[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>010001=>[1,1,3,1]
[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>010010=>[1,1,2,1,1]
[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>010101=>[1,1,1,1,1,1]
[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>010100=>[1,1,1,1,2]
[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>011011=>[1,2,1,2]
[7,4,5,6,1,3,2]=>[1,4,3,2,7,5,6]=>011010=>[1,2,1,1,1]
[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>011001=>[1,2,2,1]
[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>011010=>[1,2,1,1,1]
[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>011001=>[1,2,2,1]
[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>011000=>[1,2,3]
[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>010111=>[1,1,1,3]
[7,4,6,1,2,5,3]=>[1,4,2,7,6,3,5]=>010110=>[1,1,1,2,1]
[7,4,6,1,3,2,5]=>[1,4,2,7,5,6,3]=>010101=>[1,1,1,1,1,1]
[7,4,6,1,3,5,2]=>[1,4,2,7,5,3,6]=>010110=>[1,1,1,2,1]
[7,4,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>010101=>[1,1,1,1,1,1]
[7,4,6,1,5,3,2]=>[1,4,2,7,3,5,6]=>010100=>[1,1,1,1,2]
[7,4,6,2,1,3,5]=>[1,4,2,6,7,5,3]=>010011=>[1,1,2,2]
[7,4,6,2,1,5,3]=>[1,4,2,6,7,3,5]=>010010=>[1,1,2,1,1]
[7,4,6,2,3,1,5]=>[1,4,2,6,5,7,3]=>010101=>[1,1,1,1,1,1]
[7,4,6,2,3,5,1]=>[1,4,2,6,5,3,7]=>010110=>[1,1,1,2,1]
[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>010101=>[1,1,1,1,1,1]
[7,4,6,2,5,3,1]=>[1,4,2,6,3,5,7]=>010100=>[1,1,1,1,2]
[7,4,6,3,1,2,5]=>[1,4,2,5,7,6,3]=>010011=>[1,1,2,2]
[7,4,6,3,1,5,2]=>[1,4,2,5,7,3,6]=>010010=>[1,1,2,1,1]
[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>010001=>[1,1,3,1]
[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>010010=>[1,1,2,1,1]
[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>010101=>[1,1,1,1,1,1]
[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>010100=>[1,1,1,1,2]
[7,4,6,5,1,2,3]=>[1,4,2,3,7,6,5]=>010011=>[1,1,2,2]
[7,4,6,5,1,3,2]=>[1,4,2,3,7,5,6]=>010010=>[1,1,2,1,1]
[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>010001=>[1,1,3,1]
[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>010010=>[1,1,2,1,1]
[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>010001=>[1,1,3,1]
[7,4,6,5,3,2,1]=>[1,4,2,3,5,6,7]=>010000=>[1,1,4]
[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>001111=>[2,4]
[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>001110=>[2,3,1]
[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>001101=>[2,2,1,1]
[7,5,1,2,4,6,3]=>[1,3,7,6,4,2,5]=>001110=>[2,3,1]
[7,5,1,2,6,3,4]=>[1,3,7,6,2,5,4]=>001101=>[2,2,1,1]
[7,5,1,2,6,4,3]=>[1,3,7,6,2,4,5]=>001100=>[2,2,2]
[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>001011=>[2,1,1,2]
[7,5,1,3,2,6,4]=>[1,3,7,5,6,2,4]=>001010=>[2,1,1,1,1]
[7,5,1,3,4,2,6]=>[1,3,7,5,4,6,2]=>001101=>[2,2,1,1]
[7,5,1,3,4,6,2]=>[1,3,7,5,4,2,6]=>001110=>[2,3,1]
[7,5,1,3,6,2,4]=>[1,3,7,5,2,6,4]=>001101=>[2,2,1,1]
[7,5,1,3,6,4,2]=>[1,3,7,5,2,4,6]=>001100=>[2,2,2]
[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>001011=>[2,1,1,2]
[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>001010=>[2,1,1,1,1]
[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>001001=>[2,1,2,1]
[7,5,1,4,3,6,2]=>[1,3,7,4,5,2,6]=>001010=>[2,1,1,1,1]
[7,5,1,4,6,2,3]=>[1,3,7,4,2,6,5]=>001101=>[2,2,1,1]
[7,5,1,4,6,3,2]=>[1,3,7,4,2,5,6]=>001100=>[2,2,2]
[7,5,1,6,2,3,4]=>[1,3,7,2,6,5,4]=>001011=>[2,1,1,2]
[7,5,1,6,2,4,3]=>[1,3,7,2,6,4,5]=>001010=>[2,1,1,1,1]
[7,5,1,6,3,2,4]=>[1,3,7,2,5,6,4]=>001001=>[2,1,2,1]
[7,5,1,6,3,4,2]=>[1,3,7,2,5,4,6]=>001010=>[2,1,1,1,1]
[7,5,1,6,4,2,3]=>[1,3,7,2,4,6,5]=>001001=>[2,1,2,1]
[7,5,1,6,4,3,2]=>[1,3,7,2,4,5,6]=>001000=>[2,1,3]
[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>000111=>[3,3]
[7,5,2,1,3,6,4]=>[1,3,6,7,5,2,4]=>000110=>[3,2,1]
[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>000101=>[3,1,1,1]
[7,5,2,1,4,6,3]=>[1,3,6,7,4,2,5]=>000110=>[3,2,1]
[7,5,2,1,6,3,4]=>[1,3,6,7,2,5,4]=>000101=>[3,1,1,1]
[7,5,2,1,6,4,3]=>[1,3,6,7,2,4,5]=>000100=>[3,1,2]
[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>001011=>[2,1,1,2]
[7,5,2,3,1,6,4]=>[1,3,6,5,7,2,4]=>001010=>[2,1,1,1,1]
[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>001101=>[2,2,1,1]
[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>001110=>[2,3,1]
[7,5,2,3,6,1,4]=>[1,3,6,5,2,7,4]=>001101=>[2,2,1,1]
[7,5,2,3,6,4,1]=>[1,3,6,5,2,4,7]=>001100=>[2,2,2]
[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>001011=>[2,1,1,2]
[7,5,2,4,1,6,3]=>[1,3,6,4,7,2,5]=>001010=>[2,1,1,1,1]
[7,5,2,4,3,1,6]=>[1,3,6,4,5,7,2]=>001001=>[2,1,2,1]
[7,5,2,4,3,6,1]=>[1,3,6,4,5,2,7]=>001010=>[2,1,1,1,1]
[7,5,2,4,6,1,3]=>[1,3,6,4,2,7,5]=>001101=>[2,2,1,1]
[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>001100=>[2,2,2]
[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>001011=>[2,1,1,2]
[7,5,2,6,1,4,3]=>[1,3,6,2,7,4,5]=>001010=>[2,1,1,1,1]
[7,5,2,6,3,1,4]=>[1,3,6,2,5,7,4]=>001001=>[2,1,2,1]
[7,5,2,6,3,4,1]=>[1,3,6,2,5,4,7]=>001010=>[2,1,1,1,1]
[7,5,2,6,4,1,3]=>[1,3,6,2,4,7,5]=>001001=>[2,1,2,1]
[7,5,2,6,4,3,1]=>[1,3,6,2,4,5,7]=>001000=>[2,1,3]
[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>000111=>[3,3]
[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>000110=>[3,2,1]
[7,5,3,1,4,2,6]=>[1,3,5,7,4,6,2]=>000101=>[3,1,1,1]
[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>000110=>[3,2,1]
[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>000101=>[3,1,1,1]
[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>000100=>[3,1,2]
[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>000011=>[4,2]
[7,5,3,2,1,6,4]=>[1,3,5,6,7,2,4]=>000010=>[4,1,1]
[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>000101=>[3,1,1,1]
[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>000110=>[3,2,1]
[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>000101=>[3,1,1,1]
[7,5,3,2,6,4,1]=>[1,3,5,6,2,4,7]=>000100=>[3,1,2]
[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>001011=>[2,1,1,2]
[7,5,3,4,1,6,2]=>[1,3,5,4,7,2,6]=>001010=>[2,1,1,1,1]
[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>001001=>[2,1,2,1]
[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>001010=>[2,1,1,1,1]
[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>001101=>[2,2,1,1]
[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>001100=>[2,2,2]
[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>001011=>[2,1,1,2]
[7,5,3,6,1,4,2]=>[1,3,5,2,7,4,6]=>001010=>[2,1,1,1,1]
[7,5,3,6,2,1,4]=>[1,3,5,2,6,7,4]=>001001=>[2,1,2,1]
[7,5,3,6,2,4,1]=>[1,3,5,2,6,4,7]=>001010=>[2,1,1,1,1]
[7,5,3,6,4,1,2]=>[1,3,5,2,4,7,6]=>001001=>[2,1,2,1]
[7,5,3,6,4,2,1]=>[1,3,5,2,4,6,7]=>001000=>[2,1,3]
[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>000111=>[3,3]
[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>000110=>[3,2,1]
[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>000101=>[3,1,1,1]
[7,5,4,1,3,6,2]=>[1,3,4,7,5,2,6]=>000110=>[3,2,1]
[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>000101=>[3,1,1,1]
[7,5,4,1,6,3,2]=>[1,3,4,7,2,5,6]=>000100=>[3,1,2]
[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>000011=>[4,2]
[7,5,4,2,1,6,3]=>[1,3,4,6,7,2,5]=>000010=>[4,1,1]
[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>000101=>[3,1,1,1]
[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>000110=>[3,2,1]
[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>000101=>[3,1,1,1]
[7,5,4,2,6,3,1]=>[1,3,4,6,2,5,7]=>000100=>[3,1,2]
[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>000011=>[4,2]
[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>000010=>[4,1,1]
[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>000001=>[5,1]
[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>000010=>[4,1,1]
[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>000101=>[3,1,1,1]
[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>000100=>[3,1,2]
[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>001011=>[2,1,1,2]
[7,5,4,6,1,3,2]=>[1,3,4,2,7,5,6]=>001010=>[2,1,1,1,1]
[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>001001=>[2,1,2,1]
[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>001010=>[2,1,1,1,1]
[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>001001=>[2,1,2,1]
[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>001000=>[2,1,3]
[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>010111=>[1,1,1,3]
[7,5,6,1,2,4,3]=>[1,3,2,7,6,4,5]=>010110=>[1,1,1,2,1]
[7,5,6,1,3,2,4]=>[1,3,2,7,5,6,4]=>010101=>[1,1,1,1,1,1]
[7,5,6,1,3,4,2]=>[1,3,2,7,5,4,6]=>010110=>[1,1,1,2,1]
[7,5,6,1,4,2,3]=>[1,3,2,7,4,6,5]=>010101=>[1,1,1,1,1,1]
[7,5,6,1,4,3,2]=>[1,3,2,7,4,5,6]=>010100=>[1,1,1,1,2]
[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>010011=>[1,1,2,2]
[7,5,6,2,1,4,3]=>[1,3,2,6,7,4,5]=>010010=>[1,1,2,1,1]
[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>010101=>[1,1,1,1,1,1]
[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>010110=>[1,1,1,2,1]
[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>010101=>[1,1,1,1,1,1]
[7,5,6,2,4,3,1]=>[1,3,2,6,4,5,7]=>010100=>[1,1,1,1,2]
[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>010011=>[1,1,2,2]
[7,5,6,3,1,4,2]=>[1,3,2,5,7,4,6]=>010010=>[1,1,2,1,1]
[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>010001=>[1,1,3,1]
[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>010010=>[1,1,2,1,1]
[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>010101=>[1,1,1,1,1,1]
[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>010100=>[1,1,1,1,2]
[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>010011=>[1,1,2,2]
[7,5,6,4,1,3,2]=>[1,3,2,4,7,5,6]=>010010=>[1,1,2,1,1]
[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>010001=>[1,1,3,1]
[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010=>[1,1,2,1,1]
[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>010001=>[1,1,3,1]
[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>010000=>[1,1,4]
[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>001111=>[2,4]
[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>001110=>[2,3,1]
[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>001101=>[2,2,1,1]
[7,6,1,2,4,5,3]=>[1,2,7,6,4,3,5]=>001110=>[2,3,1]
[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>001101=>[2,2,1,1]
[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>001100=>[2,2,2]
[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>001011=>[2,1,1,2]
[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>001010=>[2,1,1,1,1]
[7,6,1,3,4,2,5]=>[1,2,7,5,4,6,3]=>001101=>[2,2,1,1]
[7,6,1,3,4,5,2]=>[1,2,7,5,4,3,6]=>001110=>[2,3,1]
[7,6,1,3,5,2,4]=>[1,2,7,5,3,6,4]=>001101=>[2,2,1,1]
[7,6,1,3,5,4,2]=>[1,2,7,5,3,4,6]=>001100=>[2,2,2]
[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>001011=>[2,1,1,2]
[7,6,1,4,2,5,3]=>[1,2,7,4,6,3,5]=>001010=>[2,1,1,1,1]
[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>001001=>[2,1,2,1]
[7,6,1,4,3,5,2]=>[1,2,7,4,5,3,6]=>001010=>[2,1,1,1,1]
[7,6,1,4,5,2,3]=>[1,2,7,4,3,6,5]=>001101=>[2,2,1,1]
[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>001100=>[2,2,2]
[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>001011=>[2,1,1,2]
[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>001010=>[2,1,1,1,1]
[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>001001=>[2,1,2,1]
[7,6,1,5,3,4,2]=>[1,2,7,3,5,4,6]=>001010=>[2,1,1,1,1]
[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>001001=>[2,1,2,1]
[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>001000=>[2,1,3]
[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>000111=>[3,3]
[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>000110=>[3,2,1]
[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>000101=>[3,1,1,1]
[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>000110=>[3,2,1]
[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>000101=>[3,1,1,1]
[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>000100=>[3,1,2]
[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>001011=>[2,1,1,2]
[7,6,2,3,1,5,4]=>[1,2,6,5,7,3,4]=>001010=>[2,1,1,1,1]
[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>001101=>[2,2,1,1]
[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>001110=>[2,3,1]
[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>001101=>[2,2,1,1]
[7,6,2,3,5,4,1]=>[1,2,6,5,3,4,7]=>001100=>[2,2,2]
[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>001011=>[2,1,1,2]
[7,6,2,4,1,5,3]=>[1,2,6,4,7,3,5]=>001010=>[2,1,1,1,1]
[7,6,2,4,3,1,5]=>[1,2,6,4,5,7,3]=>001001=>[2,1,2,1]
[7,6,2,4,3,5,1]=>[1,2,6,4,5,3,7]=>001010=>[2,1,1,1,1]
[7,6,2,4,5,1,3]=>[1,2,6,4,3,7,5]=>001101=>[2,2,1,1]
[7,6,2,4,5,3,1]=>[1,2,6,4,3,5,7]=>001100=>[2,2,2]
[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>001011=>[2,1,1,2]
[7,6,2,5,1,4,3]=>[1,2,6,3,7,4,5]=>001010=>[2,1,1,1,1]
[7,6,2,5,3,1,4]=>[1,2,6,3,5,7,4]=>001001=>[2,1,2,1]
[7,6,2,5,3,4,1]=>[1,2,6,3,5,4,7]=>001010=>[2,1,1,1,1]
[7,6,2,5,4,1,3]=>[1,2,6,3,4,7,5]=>001001=>[2,1,2,1]
[7,6,2,5,4,3,1]=>[1,2,6,3,4,5,7]=>001000=>[2,1,3]
[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>000111=>[3,3]
[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>000110=>[3,2,1]
[7,6,3,1,4,2,5]=>[1,2,5,7,4,6,3]=>000101=>[3,1,1,1]
[7,6,3,1,4,5,2]=>[1,2,5,7,4,3,6]=>000110=>[3,2,1]
[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>000101=>[3,1,1,1]
[7,6,3,1,5,4,2]=>[1,2,5,7,3,4,6]=>000100=>[3,1,2]
[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>000011=>[4,2]
[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>000010=>[4,1,1]
[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>000101=>[3,1,1,1]
[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>000110=>[3,2,1]
[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>000101=>[3,1,1,1]
[7,6,3,2,5,4,1]=>[1,2,5,6,3,4,7]=>000100=>[3,1,2]
[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>001011=>[2,1,1,2]
[7,6,3,4,1,5,2]=>[1,2,5,4,7,3,6]=>001010=>[2,1,1,1,1]
[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>001001=>[2,1,2,1]
[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>001010=>[2,1,1,1,1]
[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>001101=>[2,2,1,1]
[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100=>[2,2,2]
[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>001011=>[2,1,1,2]
[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>001010=>[2,1,1,1,1]
[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>001001=>[2,1,2,1]
[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>001010=>[2,1,1,1,1]
[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>001001=>[2,1,2,1]
[7,6,3,5,4,2,1]=>[1,2,5,3,4,6,7]=>001000=>[2,1,3]
[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>000111=>[3,3]
[7,6,4,1,2,5,3]=>[1,2,4,7,6,3,5]=>000110=>[3,2,1]
[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>000101=>[3,1,1,1]
[7,6,4,1,3,5,2]=>[1,2,4,7,5,3,6]=>000110=>[3,2,1]
[7,6,4,1,5,2,3]=>[1,2,4,7,3,6,5]=>000101=>[3,1,1,1]
[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>000100=>[3,1,2]
[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>000011=>[4,2]
[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>000010=>[4,1,1]
[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>000101=>[3,1,1,1]
[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>000110=>[3,2,1]
[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>000101=>[3,1,1,1]
[7,6,4,2,5,3,1]=>[1,2,4,6,3,5,7]=>000100=>[3,1,2]
[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>000011=>[4,2]
[7,6,4,3,1,5,2]=>[1,2,4,5,7,3,6]=>000010=>[4,1,1]
[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>000001=>[5,1]
[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>000010=>[4,1,1]
[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>000101=>[3,1,1,1]
[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>000100=>[3,1,2]
[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>001011=>[2,1,1,2]
[7,6,4,5,1,3,2]=>[1,2,4,3,7,5,6]=>001010=>[2,1,1,1,1]
[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>001001=>[2,1,2,1]
[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>001010=>[2,1,1,1,1]
[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>001001=>[2,1,2,1]
[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>001000=>[2,1,3]
[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111=>[3,3]
[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>000110=>[3,2,1]
[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>000101=>[3,1,1,1]
[7,6,5,1,3,4,2]=>[1,2,3,7,5,4,6]=>000110=>[3,2,1]
[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>000101=>[3,1,1,1]
[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>000100=>[3,1,2]
[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>000011=>[4,2]
[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>000010=>[4,1,1]
[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>000101=>[3,1,1,1]
[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>000110=>[3,2,1]
[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>000101=>[3,1,1,1]
[7,6,5,2,4,3,1]=>[1,2,3,6,4,5,7]=>000100=>[3,1,2]
[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>000011=>[4,2]
[7,6,5,3,1,4,2]=>[1,2,3,5,7,4,6]=>000010=>[4,1,1]
[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>000001=>[5,1]
[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>000010=>[4,1,1]
[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>000101=>[3,1,1,1]
[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>000100=>[3,1,2]
[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>000011=>[4,2]
[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>000010=>[4,1,1]
[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>000001=>[5,1]
[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>000010=>[4,1,1]
[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>000001=>[5,1]
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000=>[6]
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000=>[7]
[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>1000000=>[1,6]
[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>0100000=>[1,1,5]
[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>0100000=>[1,1,5]
[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>1100000=>[2,5]
[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>0010000=>[2,1,4]
[7,8,5,6,4,3,2,1]=>[2,1,4,3,5,6,7,8]=>1010000=>[1,1,1,4]
[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>0010000=>[2,1,4]
[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>0110000=>[1,2,4]
[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>0010000=>[2,1,4]
[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>1010000=>[1,1,1,4]
[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>0110000=>[1,2,4]
[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>0110000=>[1,2,4]
[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>1110000=>[3,4]
[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000=>[3,1,3]
[8,6,7,4,5,3,2,1]=>[1,3,2,5,4,6,7,8]=>0101000=>[1,1,1,1,3]
[7,6,8,4,5,3,2,1]=>[2,3,1,5,4,6,7,8]=>0101000=>[1,1,1,1,3]
[6,7,8,4,5,3,2,1]=>[3,2,1,5,4,6,7,8]=>1101000=>[2,1,1,3]
[7,8,5,4,6,3,2,1]=>[2,1,4,5,3,6,7,8]=>1001000=>[1,2,1,3]
[8,7,4,5,6,3,2,1]=>[1,2,5,4,3,6,7,8]=>0011000=>[2,2,3]
[7,8,4,5,6,3,2,1]=>[2,1,5,4,3,6,7,8]=>1011000=>[1,1,2,3]
[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>0001000=>[3,1,3]
[8,6,4,5,7,3,2,1]=>[1,3,5,4,2,6,7,8]=>0011000=>[2,2,3]
[8,5,4,6,7,3,2,1]=>[1,4,5,3,2,6,7,8]=>0011000=>[2,2,3]
[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>0111000=>[1,3,3]
[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>0001000=>[3,1,3]
[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>1001000=>[1,2,1,3]
[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>0101000=>[1,1,1,1,3]
[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>0101000=>[1,1,1,1,3]
[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>1101000=>[2,1,1,3]
[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>0011000=>[2,2,3]
[6,7,4,5,8,3,2,1]=>[3,2,5,4,1,6,7,8]=>1011000=>[1,1,2,3]
[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>0011000=>[2,2,3]
[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>0111000=>[1,3,3]
[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>0011000=>[2,2,3]
[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>1011000=>[1,1,2,3]
[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>0111000=>[1,3,3]
[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>0111000=>[1,3,3]
[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>1111000=>[4,3]
[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>0000100=>[4,1,2]
[7,8,6,5,3,4,2,1]=>[2,1,3,4,6,5,7,8]=>1000100=>[1,3,1,2]
[8,6,7,5,3,4,2,1]=>[1,3,2,4,6,5,7,8]=>0100100=>[1,1,2,1,2]
[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100=>[2,1,1,1,2]
[7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,7,8]=>1010100=>[1,1,1,1,1,2]
[7,6,5,8,3,4,2,1]=>[2,3,4,1,6,5,7,8]=>0010100=>[2,1,1,1,2]
[6,7,5,8,3,4,2,1]=>[3,2,4,1,6,5,7,8]=>1010100=>[1,1,1,1,1,2]
[7,5,6,8,3,4,2,1]=>[2,4,3,1,6,5,7,8]=>0110100=>[1,2,1,1,2]
[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>1110100=>[3,1,1,2]
[8,7,6,4,3,5,2,1]=>[1,2,3,5,6,4,7,8]=>0000100=>[4,1,2]
[8,6,7,4,3,5,2,1]=>[1,3,2,5,6,4,7,8]=>0100100=>[1,1,2,1,2]
[7,6,8,4,3,5,2,1]=>[2,3,1,5,6,4,7,8]=>0100100=>[1,1,2,1,2]
[6,7,8,4,3,5,2,1]=>[3,2,1,5,6,4,7,8]=>1100100=>[2,2,1,2]
[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>0001100=>[3,2,2]
[8,6,7,3,4,5,2,1]=>[1,3,2,6,5,4,7,8]=>0101100=>[1,1,1,2,2]
[7,6,8,3,4,5,2,1]=>[2,3,1,6,5,4,7,8]=>0101100=>[1,1,1,2,2]
[6,7,8,3,4,5,2,1]=>[3,2,1,6,5,4,7,8]=>1101100=>[2,1,2,2]
[8,7,5,4,3,6,2,1]=>[1,2,4,5,6,3,7,8]=>0000100=>[4,1,2]
[8,7,5,3,4,6,2,1]=>[1,2,4,6,5,3,7,8]=>0001100=>[3,2,2]
[7,8,5,3,4,6,2,1]=>[2,1,4,6,5,3,7,8]=>1001100=>[1,2,2,2]
[8,7,4,3,5,6,2,1]=>[1,2,5,6,4,3,7,8]=>0001100=>[3,2,2]
[7,8,4,3,5,6,2,1]=>[2,1,5,6,4,3,7,8]=>1001100=>[1,2,2,2]
[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>0011100=>[2,3,2]
[8,6,5,4,3,7,2,1]=>[1,3,4,5,6,2,7,8]=>0000100=>[4,1,2]
[8,5,6,4,3,7,2,1]=>[1,4,3,5,6,2,7,8]=>0100100=>[1,1,2,1,2]
[8,6,4,5,3,7,2,1]=>[1,3,5,4,6,2,7,8]=>0010100=>[2,1,1,1,2]
[8,5,4,6,3,7,2,1]=>[1,4,5,3,6,2,7,8]=>0010100=>[2,1,1,1,2]
[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>0110100=>[1,2,1,1,2]
[8,5,6,3,4,7,2,1]=>[1,4,3,6,5,2,7,8]=>0101100=>[1,1,1,2,2]
[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>0001100=>[3,2,2]
[8,5,4,3,6,7,2,1]=>[1,4,5,6,3,2,7,8]=>0001100=>[3,2,2]
[8,4,5,3,6,7,2,1]=>[1,5,4,6,3,2,7,8]=>0101100=>[1,1,1,2,2]
[8,5,3,4,6,7,2,1]=>[1,4,6,5,3,2,7,8]=>0011100=>[2,3,2]
[8,4,3,5,6,7,2,1]=>[1,5,6,4,3,2,7,8]=>0011100=>[2,3,2]
[8,3,4,5,6,7,2,1]=>[1,6,5,4,3,2,7,8]=>0111100=>[1,4,2]
[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>0000100=>[4,1,2]
[6,7,5,4,3,8,2,1]=>[3,2,4,5,6,1,7,8]=>1000100=>[1,3,1,2]
[6,5,7,4,3,8,2,1]=>[3,4,2,5,6,1,7,8]=>0100100=>[1,1,2,1,2]
[5,6,7,4,3,8,2,1]=>[4,3,2,5,6,1,7,8]=>1100100=>[2,2,1,2]
[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>0010100=>[2,1,1,1,2]
[6,5,4,7,3,8,2,1]=>[3,4,5,2,6,1,7,8]=>0010100=>[2,1,1,1,2]
[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>1010100=>[1,1,1,1,1,2]
[6,4,5,7,3,8,2,1]=>[3,5,4,2,6,1,7,8]=>0110100=>[1,2,1,1,2]
[5,4,6,7,3,8,2,1]=>[4,5,3,2,6,1,7,8]=>0110100=>[1,2,1,1,2]
[4,5,6,7,3,8,2,1]=>[5,4,3,2,6,1,7,8]=>1110100=>[3,1,1,2]
[7,6,5,3,4,8,2,1]=>[2,3,4,6,5,1,7,8]=>0001100=>[3,2,2]
[7,5,6,3,4,8,2,1]=>[2,4,3,6,5,1,7,8]=>0101100=>[1,1,1,2,2]
[5,6,7,3,4,8,2,1]=>[4,3,2,6,5,1,7,8]=>1101100=>[2,1,2,2]
[7,6,4,3,5,8,2,1]=>[2,3,5,6,4,1,7,8]=>0001100=>[3,2,2]
[7,6,3,4,5,8,2,1]=>[2,3,6,5,4,1,7,8]=>0011100=>[2,3,2]
[7,5,4,3,6,8,2,1]=>[2,4,5,6,3,1,7,8]=>0001100=>[3,2,2]
[7,5,3,4,6,8,2,1]=>[2,4,6,5,3,1,7,8]=>0011100=>[2,3,2]
[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>0001100=>[3,2,2]
[4,5,6,3,7,8,2,1]=>[5,4,3,6,2,1,7,8]=>1101100=>[2,1,2,2]
[5,6,3,4,7,8,2,1]=>[4,3,6,5,2,1,7,8]=>1011100=>[1,1,3,2]
[6,3,4,5,7,8,2,1]=>[3,6,5,4,2,1,7,8]=>0111100=>[1,4,2]
[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>0011100=>[2,3,2]
[4,5,3,6,7,8,2,1]=>[5,4,6,3,2,1,7,8]=>1011100=>[1,1,3,2]
[4,3,5,6,7,8,2,1]=>[5,6,4,3,2,1,7,8]=>0111100=>[1,4,2]
[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>1111100=>[5,2]
[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>0000010=>[5,1,1]
[7,8,6,5,4,2,3,1]=>[2,1,3,4,5,7,6,8]=>1000010=>[1,4,1,1]
[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010=>[1,1,3,1,1]
[7,6,8,5,4,2,3,1]=>[2,3,1,4,5,7,6,8]=>0100010=>[1,1,3,1,1]
[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>0010010=>[2,1,2,1,1]
[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>0010010=>[2,1,2,1,1]
[8,5,6,7,4,2,3,1]=>[1,4,3,2,5,7,6,8]=>0110010=>[1,2,2,1,1]
[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>0010010=>[2,1,2,1,1]
[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>1010010=>[1,1,1,2,1,1]
[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>1110010=>[3,2,1,1]
[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>0001010=>[3,1,1,1,1]
[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>1101010=>[2,1,1,1,1,1]
[8,7,5,4,6,2,3,1]=>[1,2,4,5,3,7,6,8]=>0001010=>[3,1,1,1,1]
[7,8,4,5,6,2,3,1]=>[2,1,5,4,3,7,6,8]=>1011010=>[1,1,2,1,1,1]
[8,6,5,4,7,2,3,1]=>[1,3,4,5,2,7,6,8]=>0001010=>[3,1,1,1,1]
[8,5,6,4,7,2,3,1]=>[1,4,3,5,2,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>0011010=>[2,2,1,1,1]
[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>0011010=>[2,2,1,1,1]
[8,4,5,6,7,2,3,1]=>[1,5,4,3,2,7,6,8]=>0111010=>[1,3,1,1,1]
[7,6,5,4,8,2,3,1]=>[2,3,4,5,1,7,6,8]=>0001010=>[3,1,1,1,1]
[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[7,6,4,5,8,2,3,1]=>[2,3,5,4,1,7,6,8]=>0011010=>[2,2,1,1,1]
[6,7,4,5,8,2,3,1]=>[3,2,5,4,1,7,6,8]=>1011010=>[1,1,2,1,1,1]
[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>0011010=>[2,2,1,1,1]
[7,4,5,6,8,2,3,1]=>[2,5,4,3,1,7,6,8]=>0111010=>[1,3,1,1,1]
[6,5,4,7,8,2,3,1]=>[3,4,5,2,1,7,6,8]=>0011010=>[2,2,1,1,1]
[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>0111010=>[1,3,1,1,1]
[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>0111010=>[1,3,1,1,1]
[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>1111010=>[4,1,1,1]
[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>0000010=>[5,1,1]
[7,8,6,5,3,2,4,1]=>[2,1,3,4,6,7,5,8]=>1000010=>[1,4,1,1]
[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>0100010=>[1,1,3,1,1]
[8,7,5,6,3,2,4,1]=>[1,2,4,3,6,7,5,8]=>0010010=>[2,1,2,1,1]
[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>0010010=>[2,1,2,1,1]
[8,5,6,7,3,2,4,1]=>[1,4,3,2,6,7,5,8]=>0110010=>[1,2,2,1,1]
[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>0010010=>[2,1,2,1,1]
[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>1010010=>[1,1,1,2,1,1]
[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>1110010=>[3,2,1,1]
[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>0000110=>[4,2,1]
[8,6,7,5,2,3,4,1]=>[1,3,2,4,7,6,5,8]=>0100110=>[1,1,2,2,1]
[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>1100110=>[2,2,2,1]
[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110=>[1,2,1,2,1]
[7,6,5,8,2,3,4,1]=>[2,3,4,1,7,6,5,8]=>0010110=>[2,1,1,2,1]
[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>1010110=>[1,1,1,1,2,1]
[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>1110110=>[3,1,2,1]
[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>0000010=>[5,1,1]
[8,6,7,4,3,2,5,1]=>[1,3,2,5,6,7,4,8]=>0100010=>[1,1,3,1,1]
[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>0100010=>[1,1,3,1,1]
[6,7,8,4,3,2,5,1]=>[3,2,1,5,6,7,4,8]=>1100010=>[2,3,1,1]
[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>0001010=>[3,1,1,1,1]
[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,7,6,4,2,3,5,1]=>[1,2,3,5,7,6,4,8]=>0000110=>[4,2,1]
[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>0100110=>[1,1,2,2,1]
[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>1100110=>[2,2,2,1]
[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>0000110=>[4,2,1]
[7,8,6,3,2,4,5,1]=>[2,1,3,6,7,5,4,8]=>1000110=>[1,3,2,1]
[8,6,7,3,2,4,5,1]=>[1,3,2,6,7,5,4,8]=>0100110=>[1,1,2,2,1]
[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>0100110=>[1,1,2,2,1]
[6,7,8,3,2,4,5,1]=>[3,2,1,6,7,5,4,8]=>1100110=>[2,2,2,1]
[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>0001110=>[3,3,1]
[8,6,7,2,3,4,5,1]=>[1,3,2,7,6,5,4,8]=>0101110=>[1,1,1,3,1]
[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>1101110=>[2,1,3,1]
[8,7,5,4,3,2,6,1]=>[1,2,4,5,6,7,3,8]=>0000010=>[5,1,1]
[7,8,5,4,3,2,6,1]=>[2,1,4,5,6,7,3,8]=>1000010=>[1,4,1,1]
[8,7,4,5,3,2,6,1]=>[1,2,5,4,6,7,3,8]=>0010010=>[2,1,2,1,1]
[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>0001010=>[3,1,1,1,1]
[8,7,5,3,2,4,6,1]=>[1,2,4,6,7,5,3,8]=>0000110=>[4,2,1]
[7,8,5,3,2,4,6,1]=>[2,1,4,6,7,5,3,8]=>1000110=>[1,3,2,1]
[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>0000110=>[4,2,1]
[7,8,4,3,2,5,6,1]=>[2,1,5,6,7,4,3,8]=>1000110=>[1,3,2,1]
[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>0001110=>[3,3,1]
[8,7,3,2,4,5,6,1]=>[1,2,6,7,5,4,3,8]=>0001110=>[3,3,1]
[7,8,3,2,4,5,6,1]=>[2,1,6,7,5,4,3,8]=>1001110=>[1,2,3,1]
[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>0011110=>[2,4,1]
[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>1011110=>[1,1,4,1]
[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>0000010=>[5,1,1]
[8,6,4,5,3,2,7,1]=>[1,3,5,4,6,7,2,8]=>0010010=>[2,1,2,1,1]
[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>0010010=>[2,1,2,1,1]
[8,4,5,6,3,2,7,1]=>[1,5,4,3,6,7,2,8]=>0110010=>[1,2,2,1,1]
[8,6,5,3,4,2,7,1]=>[1,3,4,6,5,7,2,8]=>0001010=>[3,1,1,1,1]
[8,5,6,3,4,2,7,1]=>[1,4,3,6,5,7,2,8]=>0101010=>[1,1,1,1,1,1,1]
[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>0001010=>[3,1,1,1,1]
[8,6,3,4,5,2,7,1]=>[1,3,6,5,4,7,2,8]=>0011010=>[2,2,1,1,1]
[8,5,4,3,6,2,7,1]=>[1,4,5,6,3,7,2,8]=>0001010=>[3,1,1,1,1]
[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>0101010=>[1,1,1,1,1,1,1]
[8,6,5,4,2,3,7,1]=>[1,3,4,5,7,6,2,8]=>0000110=>[4,2,1]
[8,5,6,4,2,3,7,1]=>[1,4,3,5,7,6,2,8]=>0100110=>[1,1,2,2,1]
[8,6,4,5,2,3,7,1]=>[1,3,5,4,7,6,2,8]=>0010110=>[2,1,1,2,1]
[8,6,5,3,2,4,7,1]=>[1,3,4,6,7,5,2,8]=>0000110=>[4,2,1]
[8,6,4,3,2,5,7,1]=>[1,3,5,6,7,4,2,8]=>0000110=>[4,2,1]
[8,6,3,4,2,5,7,1]=>[1,3,6,5,7,4,2,8]=>0010110=>[2,1,1,2,1]
[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>0001110=>[3,3,1]
[8,6,2,3,4,5,7,1]=>[1,3,7,6,5,4,2,8]=>0011110=>[2,4,1]
[8,5,4,3,2,6,7,1]=>[1,4,5,6,7,3,2,8]=>0000110=>[4,2,1]
[8,4,5,3,2,6,7,1]=>[1,5,4,6,7,3,2,8]=>0100110=>[1,1,2,2,1]
[8,5,3,4,2,6,7,1]=>[1,4,6,5,7,3,2,8]=>0010110=>[2,1,1,2,1]
[8,4,3,5,2,6,7,1]=>[1,5,6,4,7,3,2,8]=>0010110=>[2,1,1,2,1]
[8,4,5,2,3,6,7,1]=>[1,5,4,7,6,3,2,8]=>0101110=>[1,1,1,3,1]
[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>0001110=>[3,3,1]
[8,5,2,3,4,6,7,1]=>[1,4,7,6,5,3,2,8]=>0011110=>[2,4,1]
[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>0001110=>[3,3,1]
[8,3,4,2,5,6,7,1]=>[1,6,5,7,4,3,2,8]=>0101110=>[1,1,1,3,1]
[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>0011110=>[2,4,1]
[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>0111110=>[1,5,1]
[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>0000010=>[5,1,1]
[6,7,5,4,3,2,8,1]=>[3,2,4,5,6,7,1,8]=>1000010=>[1,4,1,1]
[6,5,7,4,3,2,8,1]=>[3,4,2,5,6,7,1,8]=>0100010=>[1,1,3,1,1]
[5,6,7,4,3,2,8,1]=>[4,3,2,5,6,7,1,8]=>1100010=>[2,3,1,1]
[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>0010010=>[2,1,2,1,1]
[7,5,4,6,3,2,8,1]=>[2,4,5,3,6,7,1,8]=>0010010=>[2,1,2,1,1]
[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>0110010=>[1,2,2,1,1]
[6,5,4,7,3,2,8,1]=>[3,4,5,2,6,7,1,8]=>0010010=>[2,1,2,1,1]
[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>0110010=>[1,2,2,1,1]
[4,5,6,7,3,2,8,1]=>[5,4,3,2,6,7,1,8]=>1110010=>[3,2,1,1]
[7,6,5,3,4,2,8,1]=>[2,3,4,6,5,7,1,8]=>0001010=>[3,1,1,1,1]
[7,5,6,3,4,2,8,1]=>[2,4,3,6,5,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,3,4,2,8,1]=>[3,4,2,6,5,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,6,7,3,4,2,8,1]=>[4,3,2,6,5,7,1,8]=>1101010=>[2,1,1,1,1,1]
[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>0001010=>[3,1,1,1,1]
[6,7,3,4,5,2,8,1]=>[3,2,6,5,4,7,1,8]=>1011010=>[1,1,2,1,1,1]
[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>0001010=>[3,1,1,1,1]
[5,6,4,3,7,2,8,1]=>[4,3,5,6,2,7,1,8]=>1001010=>[1,2,1,1,1,1]
[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>1101010=>[2,1,1,1,1,1]
[6,5,3,4,7,2,8,1]=>[3,4,6,5,2,7,1,8]=>0011010=>[2,2,1,1,1]
[6,4,3,5,7,2,8,1]=>[3,5,6,4,2,7,1,8]=>0011010=>[2,2,1,1,1]
[6,3,4,5,7,2,8,1]=>[3,6,5,4,2,7,1,8]=>0111010=>[1,3,1,1,1]
[4,5,3,6,7,2,8,1]=>[5,4,6,3,2,7,1,8]=>1011010=>[1,1,2,1,1,1]
[4,3,5,6,7,2,8,1]=>[5,6,4,3,2,7,1,8]=>0111010=>[1,3,1,1,1]
[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>1111010=>[4,1,1,1]
[7,6,5,4,2,3,8,1]=>[2,3,4,5,7,6,1,8]=>0000110=>[4,2,1]
[6,5,7,4,2,3,8,1]=>[3,4,2,5,7,6,1,8]=>0100110=>[1,1,2,2,1]
[5,6,7,4,2,3,8,1]=>[4,3,2,5,7,6,1,8]=>1100110=>[2,2,2,1]
[6,7,4,5,2,3,8,1]=>[3,2,5,4,7,6,1,8]=>1010110=>[1,1,1,1,2,1]
[6,5,4,7,2,3,8,1]=>[3,4,5,2,7,6,1,8]=>0010110=>[2,1,1,2,1]
[5,6,4,7,2,3,8,1]=>[4,3,5,2,7,6,1,8]=>1010110=>[1,1,1,1,2,1]
[6,4,5,7,2,3,8,1]=>[3,5,4,2,7,6,1,8]=>0110110=>[1,2,1,2,1]
[5,4,6,7,2,3,8,1]=>[4,5,3,2,7,6,1,8]=>0110110=>[1,2,1,2,1]
[4,5,6,7,2,3,8,1]=>[5,4,3,2,7,6,1,8]=>1110110=>[3,1,2,1]
[7,6,5,3,2,4,8,1]=>[2,3,4,6,7,5,1,8]=>0000110=>[4,2,1]
[6,7,5,3,2,4,8,1]=>[3,2,4,6,7,5,1,8]=>1000110=>[1,3,2,1]
[6,5,7,3,2,4,8,1]=>[3,4,2,6,7,5,1,8]=>0100110=>[1,1,2,2,1]
[5,6,7,3,2,4,8,1]=>[4,3,2,6,7,5,1,8]=>1100110=>[2,2,2,1]
[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>0001110=>[3,3,1]
[6,5,7,2,3,4,8,1]=>[3,4,2,7,6,5,1,8]=>0101110=>[1,1,1,3,1]
[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>0000110=>[4,2,1]
[6,7,4,3,2,5,8,1]=>[3,2,5,6,7,4,1,8]=>1000110=>[1,3,2,1]
[7,6,3,4,2,5,8,1]=>[2,3,6,5,7,4,1,8]=>0010110=>[2,1,1,2,1]
[6,7,3,4,2,5,8,1]=>[3,2,6,5,7,4,1,8]=>1010110=>[1,1,1,1,2,1]
[7,6,4,2,3,5,8,1]=>[2,3,5,7,6,4,1,8]=>0001110=>[3,3,1]
[6,7,4,2,3,5,8,1]=>[3,2,5,7,6,4,1,8]=>1001110=>[1,2,3,1]
[7,6,3,2,4,5,8,1]=>[2,3,6,7,5,4,1,8]=>0001110=>[3,3,1]
[6,7,3,2,4,5,8,1]=>[3,2,6,7,5,4,1,8]=>1001110=>[1,2,3,1]
[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>0011110=>[2,4,1]
[6,7,2,3,4,5,8,1]=>[3,2,7,6,5,4,1,8]=>1011110=>[1,1,4,1]
[7,5,4,3,2,6,8,1]=>[2,4,5,6,7,3,1,8]=>0000110=>[4,2,1]
[7,4,5,3,2,6,8,1]=>[2,5,4,6,7,3,1,8]=>0100110=>[1,1,2,2,1]
[7,4,3,5,2,6,8,1]=>[2,5,6,4,7,3,1,8]=>0010110=>[2,1,1,2,1]
[7,4,5,2,3,6,8,1]=>[2,5,4,7,6,3,1,8]=>0101110=>[1,1,1,3,1]
[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>0001110=>[3,3,1]
[7,4,3,2,5,6,8,1]=>[2,5,6,7,4,3,1,8]=>0001110=>[3,3,1]
[7,4,2,3,5,6,8,1]=>[2,5,7,6,4,3,1,8]=>0011110=>[2,4,1]
[7,3,2,4,5,6,8,1]=>[2,6,7,5,4,3,1,8]=>0011110=>[2,4,1]
[7,2,3,4,5,6,8,1]=>[2,7,6,5,4,3,1,8]=>0111110=>[1,5,1]
[6,5,4,3,2,7,8,1]=>[3,4,5,6,7,2,1,8]=>0000110=>[4,2,1]
[4,5,6,3,2,7,8,1]=>[5,4,3,6,7,2,1,8]=>1100110=>[2,2,2,1]
[5,6,3,4,2,7,8,1]=>[4,3,6,5,7,2,1,8]=>1010110=>[1,1,1,1,2,1]
[6,4,3,5,2,7,8,1]=>[3,5,6,4,7,2,1,8]=>0010110=>[2,1,1,2,1]
[6,3,4,5,2,7,8,1]=>[3,6,5,4,7,2,1,8]=>0110110=>[1,2,1,2,1]
[4,5,3,6,2,7,8,1]=>[5,4,6,3,7,2,1,8]=>1010110=>[1,1,1,1,2,1]
[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>0110110=>[1,2,1,2,1]
[3,4,5,6,2,7,8,1]=>[6,5,4,3,7,2,1,8]=>1110110=>[3,1,2,1]
[5,6,4,2,3,7,8,1]=>[4,3,5,7,6,2,1,8]=>1001110=>[1,2,3,1]
[6,4,5,2,3,7,8,1]=>[3,5,4,7,6,2,1,8]=>0101110=>[1,1,1,3,1]
[5,4,6,2,3,7,8,1]=>[4,5,3,7,6,2,1,8]=>0101110=>[1,1,1,3,1]
[4,5,6,2,3,7,8,1]=>[5,4,3,7,6,2,1,8]=>1101110=>[2,1,3,1]
[6,5,2,3,4,7,8,1]=>[3,4,7,6,5,2,1,8]=>0011110=>[2,4,1]
[5,6,2,3,4,7,8,1]=>[4,3,7,6,5,2,1,8]=>1011110=>[1,1,4,1]
[6,4,3,2,5,7,8,1]=>[3,5,6,7,4,2,1,8]=>0001110=>[3,3,1]
[6,4,2,3,5,7,8,1]=>[3,5,7,6,4,2,1,8]=>0011110=>[2,4,1]
[5,4,3,2,6,7,8,1]=>[4,5,6,7,3,2,1,8]=>0001110=>[3,3,1]
[4,5,3,2,6,7,8,1]=>[5,4,6,7,3,2,1,8]=>1001110=>[1,2,3,1]
[5,3,4,2,6,7,8,1]=>[4,6,5,7,3,2,1,8]=>0101110=>[1,1,1,3,1]
[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>0101110=>[1,1,1,3,1]
[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>1101110=>[2,1,3,1]
[5,4,2,3,6,7,8,1]=>[4,5,7,6,3,2,1,8]=>0011110=>[2,4,1]
[4,5,2,3,6,7,8,1]=>[5,4,7,6,3,2,1,8]=>1011110=>[1,1,4,1]
[5,3,2,4,6,7,8,1]=>[4,6,7,5,3,2,1,8]=>0011110=>[2,4,1]
[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>0111110=>[1,5,1]
[4,3,2,5,6,7,8,1]=>[5,6,7,4,3,2,1,8]=>0011110=>[2,4,1]
[3,4,2,5,6,7,8,1]=>[6,5,7,4,3,2,1,8]=>1011110=>[1,1,4,1]
[4,2,3,5,6,7,8,1]=>[5,7,6,4,3,2,1,8]=>0111110=>[1,5,1]
[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>0111110=>[1,5,1]
[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>1111110=>[6,1]
[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>0000001=>[6,1]
[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001=>[1,5,1]
[8,6,7,5,4,3,1,2]=>[1,3,2,4,5,6,8,7]=>0100001=>[1,1,4,1]
[7,6,8,5,4,3,1,2]=>[2,3,1,4,5,6,8,7]=>0100001=>[1,1,4,1]
[6,7,8,5,4,3,1,2]=>[3,2,1,4,5,6,8,7]=>1100001=>[2,4,1]
[8,7,5,6,4,3,1,2]=>[1,2,4,3,5,6,8,7]=>0010001=>[2,1,3,1]
[7,8,5,6,4,3,1,2]=>[2,1,4,3,5,6,8,7]=>1010001=>[1,1,1,3,1]
[8,6,5,7,4,3,1,2]=>[1,3,4,2,5,6,8,7]=>0010001=>[2,1,3,1]
[8,5,6,7,4,3,1,2]=>[1,4,3,2,5,6,8,7]=>0110001=>[1,2,3,1]
[7,6,5,8,4,3,1,2]=>[2,3,4,1,5,6,8,7]=>0010001=>[2,1,3,1]
[6,7,5,8,4,3,1,2]=>[3,2,4,1,5,6,8,7]=>1010001=>[1,1,1,3,1]
[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>1110001=>[3,3,1]
[8,7,6,4,5,3,1,2]=>[1,2,3,5,4,6,8,7]=>0001001=>[3,1,2,1]
[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001=>[1,2,1,2,1]
[7,8,5,4,6,3,1,2]=>[2,1,4,5,3,6,8,7]=>1001001=>[1,2,1,2,1]
[8,7,4,5,6,3,1,2]=>[1,2,5,4,3,6,8,7]=>0011001=>[2,2,2,1]
[8,6,5,4,7,3,1,2]=>[1,3,4,5,2,6,8,7]=>0001001=>[3,1,2,1]
[8,6,4,5,7,3,1,2]=>[1,3,5,4,2,6,8,7]=>0011001=>[2,2,2,1]
[8,5,4,6,7,3,1,2]=>[1,4,5,3,2,6,8,7]=>0011001=>[2,2,2,1]
[7,6,5,4,8,3,1,2]=>[2,3,4,5,1,6,8,7]=>0001001=>[3,1,2,1]
[7,5,6,4,8,3,1,2]=>[2,4,3,5,1,6,8,7]=>0101001=>[1,1,1,1,2,1]
[7,6,4,5,8,3,1,2]=>[2,3,5,4,1,6,8,7]=>0011001=>[2,2,2,1]
[6,7,4,5,8,3,1,2]=>[3,2,5,4,1,6,8,7]=>1011001=>[1,1,2,2,1]
[7,5,4,6,8,3,1,2]=>[2,4,5,3,1,6,8,7]=>0011001=>[2,2,2,1]
[7,4,5,6,8,3,1,2]=>[2,5,4,3,1,6,8,7]=>0111001=>[1,3,2,1]
[6,5,4,7,8,3,1,2]=>[3,4,5,2,1,6,8,7]=>0011001=>[2,2,2,1]
[5,6,4,7,8,3,1,2]=>[4,3,5,2,1,6,8,7]=>1011001=>[1,1,2,2,1]
[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>0111001=>[1,3,2,1]
[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>1111001=>[4,2,1]
[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>0000101=>[4,1,1,1]
[7,8,6,5,3,4,1,2]=>[2,1,3,4,6,5,8,7]=>1000101=>[1,3,1,1,1]
[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>0100101=>[1,1,2,1,1,1]
[7,6,8,5,3,4,1,2]=>[2,3,1,4,6,5,8,7]=>0100101=>[1,1,2,1,1,1]
[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>0010101=>[2,1,1,1,1,1]
[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]
[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>0010101=>[2,1,1,1,1,1]
[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>0010101=>[2,1,1,1,1,1]
[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>0110101=>[1,2,1,1,1,1]
[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>0110101=>[1,2,1,1,1,1]
[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>1110101=>[3,1,1,1,1]
[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>0000101=>[4,1,1,1]
[7,8,6,4,3,5,1,2]=>[2,1,3,5,6,4,8,7]=>1000101=>[1,3,1,1,1]
[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>0100101=>[1,1,2,1,1,1]
[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>0001101=>[3,2,1,1]
[8,6,7,3,4,5,1,2]=>[1,3,2,6,5,4,8,7]=>0101101=>[1,1,1,2,1,1]
[7,6,8,3,4,5,1,2]=>[2,3,1,6,5,4,8,7]=>0101101=>[1,1,1,2,1,1]
[6,7,8,3,4,5,1,2]=>[3,2,1,6,5,4,8,7]=>1101101=>[2,1,2,1,1]
[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>0000101=>[4,1,1,1]
[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>1000101=>[1,3,1,1,1]
[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>1001101=>[1,2,2,1,1]
[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>1001101=>[1,2,2,1,1]
[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101=>[1,1,3,1,1]
[8,6,5,4,3,7,1,2]=>[1,3,4,5,6,2,8,7]=>0000101=>[4,1,1,1]
[8,6,3,4,5,7,1,2]=>[1,3,6,5,4,2,8,7]=>0011101=>[2,3,1,1]
[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>0101101=>[1,1,1,2,1,1]
[8,4,3,5,6,7,1,2]=>[1,5,6,4,3,2,8,7]=>0011101=>[2,3,1,1]
[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>0111101=>[1,4,1,1]
[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>0000101=>[4,1,1,1]
[7,5,6,4,3,8,1,2]=>[2,4,3,5,6,1,8,7]=>0100101=>[1,1,2,1,1,1]
[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>0100101=>[1,1,2,1,1,1]
[5,6,7,4,3,8,1,2]=>[4,3,2,5,6,1,8,7]=>1100101=>[2,2,1,1,1]
[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>0010101=>[2,1,1,1,1,1]
[7,4,5,6,3,8,1,2]=>[2,5,4,3,6,1,8,7]=>0110101=>[1,2,1,1,1,1]
[6,5,4,7,3,8,1,2]=>[3,4,5,2,6,1,8,7]=>0010101=>[2,1,1,1,1,1]
[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,4,5,7,3,8,1,2]=>[3,5,4,2,6,1,8,7]=>0110101=>[1,2,1,1,1,1]
[5,4,6,7,3,8,1,2]=>[4,5,3,2,6,1,8,7]=>0110101=>[1,2,1,1,1,1]
[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>1110101=>[3,1,1,1,1]
[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>0101101=>[1,1,1,2,1,1]
[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>0101101=>[1,1,1,2,1,1]
[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>1101101=>[2,1,2,1,1]
[7,6,4,3,5,8,1,2]=>[2,3,5,6,4,1,8,7]=>0001101=>[3,2,1,1]
[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>1001101=>[1,2,2,1,1]
[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>0011101=>[2,3,1,1]
[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>1011101=>[1,1,3,1,1]
[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>0011101=>[2,3,1,1]
[7,3,4,5,6,8,1,2]=>[2,6,5,4,3,1,8,7]=>0111101=>[1,4,1,1]
[6,5,4,3,7,8,1,2]=>[3,4,5,6,2,1,8,7]=>0001101=>[3,2,1,1]
[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>1001101=>[1,2,2,1,1]
[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>0101101=>[1,1,1,2,1,1]
[4,5,6,3,7,8,1,2]=>[5,4,3,6,2,1,8,7]=>1101101=>[2,1,2,1,1]
[6,5,3,4,7,8,1,2]=>[3,4,6,5,2,1,8,7]=>0011101=>[2,3,1,1]
[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>1011101=>[1,1,3,1,1]
[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>0011101=>[2,3,1,1]
[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>0111101=>[1,4,1,1]
[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>0011101=>[2,3,1,1]
[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>1011101=>[1,1,3,1,1]
[5,3,4,6,7,8,1,2]=>[4,6,5,3,2,1,8,7]=>0111101=>[1,4,1,1]
[4,3,5,6,7,8,1,2]=>[5,6,4,3,2,1,8,7]=>0111101=>[1,4,1,1]
[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>1111101=>[5,1,1]
[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>0000001=>[6,1]
[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>1000001=>[1,5,1]
[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>0100001=>[1,1,4,1]
[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>0100001=>[1,1,4,1]
[6,7,8,5,4,2,1,3]=>[3,2,1,4,5,7,8,6]=>1100001=>[2,4,1]
[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>0010001=>[2,1,3,1]
[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>1010001=>[1,1,1,3,1]
[8,6,5,7,4,2,1,3]=>[1,3,4,2,5,7,8,6]=>0010001=>[2,1,3,1]
[8,5,6,7,4,2,1,3]=>[1,4,3,2,5,7,8,6]=>0110001=>[1,2,3,1]
[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>0010001=>[2,1,3,1]
[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>1010001=>[1,1,1,3,1]
[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>1110001=>[3,3,1]
[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>0001001=>[3,1,2,1]
[7,8,6,4,5,2,1,3]=>[2,1,3,5,4,7,8,6]=>1001001=>[1,2,1,2,1]
[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>0101001=>[1,1,1,1,2,1]
[8,7,5,4,6,2,1,3]=>[1,2,4,5,3,7,8,6]=>0001001=>[3,1,2,1]
[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>0011001=>[2,2,2,1]
[8,6,5,4,7,2,1,3]=>[1,3,4,5,2,7,8,6]=>0001001=>[3,1,2,1]
[8,5,6,4,7,2,1,3]=>[1,4,3,5,2,7,8,6]=>0101001=>[1,1,1,1,2,1]
[8,6,4,5,7,2,1,3]=>[1,3,5,4,2,7,8,6]=>0011001=>[2,2,2,1]
[8,5,4,6,7,2,1,3]=>[1,4,5,3,2,7,8,6]=>0011001=>[2,2,2,1]
[8,4,5,6,7,2,1,3]=>[1,5,4,3,2,7,8,6]=>0111001=>[1,3,2,1]
[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>0001001=>[3,1,2,1]
[7,5,6,4,8,2,1,3]=>[2,4,3,5,1,7,8,6]=>0101001=>[1,1,1,1,2,1]
[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>0101001=>[1,1,1,1,2,1]
[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>1101001=>[2,1,1,2,1]
[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>1011001=>[1,1,2,2,1]
[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>0011001=>[2,2,2,1]
[7,4,5,6,8,2,1,3]=>[2,5,4,3,1,7,8,6]=>0111001=>[1,3,2,1]
[6,5,4,7,8,2,1,3]=>[3,4,5,2,1,7,8,6]=>0011001=>[2,2,2,1]
[6,4,5,7,8,2,1,3]=>[3,5,4,2,1,7,8,6]=>0111001=>[1,3,2,1]
[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>1111001=>[4,2,1]
[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>0000011=>[5,2]
[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>1000011=>[1,4,2]
[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>0100011=>[1,1,3,2]
[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011=>[2,3,2]
[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>0010011=>[2,1,2,2]
[7,8,5,6,4,1,2,3]=>[2,1,4,3,5,8,7,6]=>1010011=>[1,1,1,2,2]
[8,6,5,7,4,1,2,3]=>[1,3,4,2,5,8,7,6]=>0010011=>[2,1,2,2]
[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>0110011=>[1,2,2,2]
[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>0010011=>[2,1,2,2]
[6,7,5,8,4,1,2,3]=>[3,2,4,1,5,8,7,6]=>1010011=>[1,1,1,2,2]
[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>0110011=>[1,2,2,2]
[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>1110011=>[3,2,2]
[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>0001011=>[3,1,1,2]
[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>1001011=>[1,2,1,1,2]
[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>0101011=>[1,1,1,1,1,2]
[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>0001011=>[3,1,1,2]
[7,8,5,4,6,1,2,3]=>[2,1,4,5,3,8,7,6]=>1001011=>[1,2,1,1,2]
[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>0011011=>[2,2,1,2]
[7,8,4,5,6,1,2,3]=>[2,1,5,4,3,8,7,6]=>1011011=>[1,1,2,1,2]
[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>0001011=>[3,1,1,2]
[8,5,6,4,7,1,2,3]=>[1,4,3,5,2,8,7,6]=>0101011=>[1,1,1,1,1,2]
[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>0011011=>[2,2,1,2]
[8,4,5,6,7,1,2,3]=>[1,5,4,3,2,8,7,6]=>0111011=>[1,3,1,2]
[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>0001011=>[3,1,1,2]
[6,7,5,4,8,1,2,3]=>[3,2,4,5,1,8,7,6]=>1001011=>[1,2,1,1,2]
[7,5,6,4,8,1,2,3]=>[2,4,3,5,1,8,7,6]=>0101011=>[1,1,1,1,1,2]
[6,5,7,4,8,1,2,3]=>[3,4,2,5,1,8,7,6]=>0101011=>[1,1,1,1,1,2]
[5,6,7,4,8,1,2,3]=>[4,3,2,5,1,8,7,6]=>1101011=>[2,1,1,1,2]
[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>0011011=>[2,2,1,2]
[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>1011011=>[1,1,2,1,2]
[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>0011011=>[2,2,1,2]
[7,4,5,6,8,1,2,3]=>[2,5,4,3,1,8,7,6]=>0111011=>[1,3,1,2]
[6,5,4,7,8,1,2,3]=>[3,4,5,2,1,8,7,6]=>0011011=>[2,2,1,2]
[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>1011011=>[1,1,2,1,2]
[6,4,5,7,8,1,2,3]=>[3,5,4,2,1,8,7,6]=>0111011=>[1,3,1,2]
[5,4,6,7,8,1,2,3]=>[4,5,3,2,1,8,7,6]=>0111011=>[1,3,1,2]
[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>1111011=>[4,1,2]
[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>0000001=>[6,1]
[7,8,6,5,3,2,1,4]=>[2,1,3,4,6,7,8,5]=>1000001=>[1,5,1]
[8,6,7,5,3,2,1,4]=>[1,3,2,4,6,7,8,5]=>0100001=>[1,1,4,1]
[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>0100001=>[1,1,4,1]
[6,7,8,5,3,2,1,4]=>[3,2,1,4,6,7,8,5]=>1100001=>[2,4,1]
[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>0010001=>[2,1,3,1]
[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>1010001=>[1,1,1,3,1]
[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>0010001=>[2,1,3,1]
[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>0110001=>[1,2,3,1]
[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>0010001=>[2,1,3,1]
[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>1010001=>[1,1,1,3,1]
[7,5,6,8,3,2,1,4]=>[2,4,3,1,6,7,8,5]=>0110001=>[1,2,3,1]
[6,5,7,8,3,2,1,4]=>[3,4,2,1,6,7,8,5]=>0110001=>[1,2,3,1]
[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>1110001=>[3,3,1]
[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>0000101=>[4,1,1,1]
[7,8,6,5,2,3,1,4]=>[2,1,3,4,7,6,8,5]=>1000101=>[1,3,1,1,1]
[8,6,7,5,2,3,1,4]=>[1,3,2,4,7,6,8,5]=>0100101=>[1,1,2,1,1,1]
[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>0100101=>[1,1,2,1,1,1]
[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>0010101=>[2,1,1,1,1,1]
[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]
[8,6,5,7,2,3,1,4]=>[1,3,4,2,7,6,8,5]=>0010101=>[2,1,1,1,1,1]
[8,5,6,7,2,3,1,4]=>[1,4,3,2,7,6,8,5]=>0110101=>[1,2,1,1,1,1]
[7,6,5,8,2,3,1,4]=>[2,3,4,1,7,6,8,5]=>0010101=>[2,1,1,1,1,1]
[6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]
[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>0110101=>[1,2,1,1,1,1]
[6,5,7,8,2,3,1,4]=>[3,4,2,1,7,6,8,5]=>0110101=>[1,2,1,1,1,1]
[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>1110101=>[3,1,1,1,1]
[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>0000011=>[5,2]
[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>0100011=>[1,1,3,2]
[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>1100011=>[2,3,2]
[8,7,5,6,3,1,2,4]=>[1,2,4,3,6,8,7,5]=>0010011=>[2,1,2,2]
[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>1010011=>[1,1,1,2,2]
[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>0010011=>[2,1,2,2]
[8,5,6,7,3,1,2,4]=>[1,4,3,2,6,8,7,5]=>0110011=>[1,2,2,2]
[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>0010011=>[2,1,2,2]
[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>1010011=>[1,1,1,2,2]
[7,5,6,8,3,1,2,4]=>[2,4,3,1,6,8,7,5]=>0110011=>[1,2,2,2]
[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>0110011=>[1,2,2,2]
[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>1110011=>[3,2,2]
[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>0000011=>[5,2]
[7,8,6,5,2,1,3,4]=>[2,1,3,4,7,8,6,5]=>1000011=>[1,4,2]
[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>0100011=>[1,1,3,2]
[6,7,8,5,2,1,3,4]=>[3,2,1,4,7,8,6,5]=>1100011=>[2,3,2]
[8,7,5,6,2,1,3,4]=>[1,2,4,3,7,8,6,5]=>0010011=>[2,1,2,2]
[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>1010011=>[1,1,1,2,2]
[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>0010011=>[2,1,2,2]
[7,6,5,8,2,1,3,4]=>[2,3,4,1,7,8,6,5]=>0010011=>[2,1,2,2]
[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>1010011=>[1,1,1,2,2]
[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>0110011=>[1,2,2,2]
[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>0110011=>[1,2,2,2]
[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>1110011=>[3,2,2]
[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>0000111=>[4,3]
[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>1000111=>[1,3,3]
[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>0100111=>[1,1,2,3]
[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>0100111=>[1,1,2,3]
[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>1100111=>[2,2,3]
[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>0010111=>[2,1,1,3]
[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>1010111=>[1,1,1,1,3]
[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>0010111=>[2,1,1,3]
[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>0110111=>[1,2,1,3]
[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>0010111=>[2,1,1,3]
[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>1010111=>[1,1,1,1,3]
[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>0110111=>[1,2,1,3]
[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>0110111=>[1,2,1,3]
[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111=>[3,1,3]
[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>0000001=>[6,1]
[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>1000001=>[1,5,1]
[8,6,7,4,3,2,1,5]=>[1,3,2,5,6,7,8,4]=>0100001=>[1,1,4,1]
[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>0100001=>[1,1,4,1]
[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>1100001=>[2,4,1]
[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>0001001=>[3,1,2,1]
[8,6,7,3,4,2,1,5]=>[1,3,2,6,5,7,8,4]=>0101001=>[1,1,1,1,2,1]
[6,7,8,3,4,2,1,5]=>[3,2,1,6,5,7,8,4]=>1101001=>[2,1,1,2,1]
[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>0000101=>[4,1,1,1]
[7,8,6,4,2,3,1,5]=>[2,1,3,5,7,6,8,4]=>1000101=>[1,3,1,1,1]
[8,6,7,4,2,3,1,5]=>[1,3,2,5,7,6,8,4]=>0100101=>[1,1,2,1,1,1]
[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>0100101=>[1,1,2,1,1,1]
[6,7,8,4,2,3,1,5]=>[3,2,1,5,7,6,8,4]=>1100101=>[2,2,1,1,1]
[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>0000101=>[4,1,1,1]
[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>0100101=>[1,1,2,1,1,1]
[7,6,8,3,2,4,1,5]=>[2,3,1,6,7,5,8,4]=>0100101=>[1,1,2,1,1,1]
[6,7,8,3,2,4,1,5]=>[3,2,1,6,7,5,8,4]=>1100101=>[2,2,1,1,1]
[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>0001101=>[3,2,1,1]
[8,6,7,2,3,4,1,5]=>[1,3,2,7,6,5,8,4]=>0101101=>[1,1,1,2,1,1]
[7,6,8,2,3,4,1,5]=>[2,3,1,7,6,5,8,4]=>0101101=>[1,1,1,2,1,1]
[6,7,8,2,3,4,1,5]=>[3,2,1,7,6,5,8,4]=>1101101=>[2,1,2,1,1]
[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>0000011=>[5,2]
[8,6,7,4,3,1,2,5]=>[1,3,2,5,6,8,7,4]=>0100011=>[1,1,3,2]
[6,7,8,4,3,1,2,5]=>[3,2,1,5,6,8,7,4]=>1100011=>[2,3,2]
[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>0001011=>[3,1,1,2]
[7,8,6,3,4,1,2,5]=>[2,1,3,6,5,8,7,4]=>1001011=>[1,2,1,1,2]
[8,6,7,3,4,1,2,5]=>[1,3,2,6,5,8,7,4]=>0101011=>[1,1,1,1,1,2]
[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>0101011=>[1,1,1,1,1,2]
[6,7,8,3,4,1,2,5]=>[3,2,1,6,5,8,7,4]=>1101011=>[2,1,1,1,2]
[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>0000011=>[5,2]
[8,6,7,4,2,1,3,5]=>[1,3,2,5,7,8,6,4]=>0100011=>[1,1,3,2]
[7,6,8,4,2,1,3,5]=>[2,3,1,5,7,8,6,4]=>0100011=>[1,1,3,2]
[6,7,8,4,2,1,3,5]=>[3,2,1,5,7,8,6,4]=>1100011=>[2,3,2]
[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>0000111=>[4,3]
[8,6,7,4,1,2,3,5]=>[1,3,2,5,8,7,6,4]=>0100111=>[1,1,2,3]
[6,7,8,4,1,2,3,5]=>[3,2,1,5,8,7,6,4]=>1100111=>[2,2,3]
[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>0000011=>[5,2]
[7,8,6,3,2,1,4,5]=>[2,1,3,6,7,8,5,4]=>1000011=>[1,4,2]
[8,6,7,3,2,1,4,5]=>[1,3,2,6,7,8,5,4]=>0100011=>[1,1,3,2]
[7,6,8,3,2,1,4,5]=>[2,3,1,6,7,8,5,4]=>0100011=>[1,1,3,2]
[6,7,8,3,2,1,4,5]=>[3,2,1,6,7,8,5,4]=>1100011=>[2,3,2]
[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>0001011=>[3,1,1,2]
[8,6,7,2,3,1,4,5]=>[1,3,2,7,6,8,5,4]=>0101011=>[1,1,1,1,1,2]
[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,8,5,4]=>0101011=>[1,1,1,1,1,2]
[6,7,8,2,3,1,4,5]=>[3,2,1,7,6,8,5,4]=>1101011=>[2,1,1,1,2]
[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>0000111=>[4,3]
[7,8,6,3,1,2,4,5]=>[2,1,3,6,8,7,5,4]=>1000111=>[1,3,3]
[8,6,7,3,1,2,4,5]=>[1,3,2,6,8,7,5,4]=>0100111=>[1,1,2,3]
[7,6,8,3,1,2,4,5]=>[2,3,1,6,8,7,5,4]=>0100111=>[1,1,2,3]
[6,7,8,3,1,2,4,5]=>[3,2,1,6,8,7,5,4]=>1100111=>[2,2,3]
[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>0000111=>[4,3]
[7,8,6,2,1,3,4,5]=>[2,1,3,7,8,6,5,4]=>1000111=>[1,3,3]
[7,6,8,2,1,3,4,5]=>[2,3,1,7,8,6,5,4]=>0100111=>[1,1,2,3]
[6,7,8,2,1,3,4,5]=>[3,2,1,7,8,6,5,4]=>1100111=>[2,2,3]
[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>0001111=>[3,4]
[7,8,6,1,2,3,4,5]=>[2,1,3,8,7,6,5,4]=>1001111=>[1,2,4]
[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>0101111=>[1,1,1,4]
[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>0101111=>[1,1,1,4]
[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>1101111=>[2,1,4]
[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>0000001=>[6,1]
[7,8,5,4,3,2,1,6]=>[2,1,4,5,6,7,8,3]=>1000001=>[1,5,1]
[8,7,4,5,3,2,1,6]=>[1,2,5,4,6,7,8,3]=>0010001=>[2,1,3,1]
[7,8,4,5,3,2,1,6]=>[2,1,5,4,6,7,8,3]=>1010001=>[1,1,1,3,1]
[8,7,5,3,4,2,1,6]=>[1,2,4,6,5,7,8,3]=>0001001=>[3,1,2,1]
[8,7,4,3,5,2,1,6]=>[1,2,5,6,4,7,8,3]=>0001001=>[3,1,2,1]
[7,8,4,3,5,2,1,6]=>[2,1,5,6,4,7,8,3]=>1001001=>[1,2,1,2,1]
[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>0011001=>[2,2,2,1]
[8,7,4,5,2,3,1,6]=>[1,2,5,4,7,6,8,3]=>0010101=>[2,1,1,1,1,1]
[7,8,4,5,2,3,1,6]=>[2,1,5,4,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,3,2,4,1,6]=>[2,1,4,6,7,5,8,3]=>1000101=>[1,3,1,1,1]
[8,7,5,2,3,4,1,6]=>[1,2,4,7,6,5,8,3]=>0001101=>[3,2,1,1]
[7,8,5,2,3,4,1,6]=>[2,1,4,7,6,5,8,3]=>1001101=>[1,2,2,1,1]
[8,7,4,3,2,5,1,6]=>[1,2,5,6,7,4,8,3]=>0000101=>[4,1,1,1]
[7,8,4,3,2,5,1,6]=>[2,1,5,6,7,4,8,3]=>1000101=>[1,3,1,1,1]
[7,8,3,4,2,5,1,6]=>[2,1,6,5,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]
[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>0001101=>[3,2,1,1]
[7,8,4,2,3,5,1,6]=>[2,1,5,7,6,4,8,3]=>1001101=>[1,2,2,1,1]
[7,8,3,2,4,5,1,6]=>[2,1,6,7,5,4,8,3]=>1001101=>[1,2,2,1,1]
[8,7,2,3,4,5,1,6]=>[1,2,7,6,5,4,8,3]=>0011101=>[2,3,1,1]
[7,8,2,3,4,5,1,6]=>[2,1,7,6,5,4,8,3]=>1011101=>[1,1,3,1,1]
[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>0000011=>[5,2]
[7,8,5,4,3,1,2,6]=>[2,1,4,5,6,8,7,3]=>1000011=>[1,4,2]
[8,7,4,5,3,1,2,6]=>[1,2,5,4,6,8,7,3]=>0010011=>[2,1,2,2]
[7,8,4,5,3,1,2,6]=>[2,1,5,4,6,8,7,3]=>1010011=>[1,1,1,2,2]
[7,8,5,3,4,1,2,6]=>[2,1,4,6,5,8,7,3]=>1001011=>[1,2,1,1,2]
[7,8,4,3,5,1,2,6]=>[2,1,5,6,4,8,7,3]=>1001011=>[1,2,1,1,2]
[8,7,3,4,5,1,2,6]=>[1,2,6,5,4,8,7,3]=>0011011=>[2,2,1,2]
[7,8,3,4,5,1,2,6]=>[2,1,6,5,4,8,7,3]=>1011011=>[1,1,2,1,2]
[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>0000011=>[5,2]
[7,8,5,4,2,1,3,6]=>[2,1,4,5,7,8,6,3]=>1000011=>[1,4,2]
[7,8,4,5,2,1,3,6]=>[2,1,5,4,7,8,6,3]=>1010011=>[1,1,1,2,2]
[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>0000111=>[4,3]
[7,8,5,4,1,2,3,6]=>[2,1,4,5,8,7,6,3]=>1000111=>[1,3,3]
[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>0010111=>[2,1,1,3]
[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]=>1010111=>[1,1,1,1,3]
[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>0000011=>[5,2]
[7,8,5,3,2,1,4,6]=>[2,1,4,6,7,8,5,3]=>1000011=>[1,4,2]
[8,7,5,2,3,1,4,6]=>[1,2,4,7,6,8,5,3]=>0001011=>[3,1,1,2]
[7,8,5,2,3,1,4,6]=>[2,1,4,7,6,8,5,3]=>1001011=>[1,2,1,1,2]
[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>0000111=>[4,3]
[7,8,5,3,1,2,4,6]=>[2,1,4,6,8,7,5,3]=>1000111=>[1,3,3]
[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>0000111=>[4,3]
[7,8,5,2,1,3,4,6]=>[2,1,4,7,8,6,5,3]=>1000111=>[1,3,3]
[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>0001111=>[3,4]
[7,8,5,1,2,3,4,6]=>[2,1,4,8,7,6,5,3]=>1001111=>[1,2,4]
[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>0000011=>[5,2]
[7,8,4,3,2,1,5,6]=>[2,1,5,6,7,8,4,3]=>1000011=>[1,4,2]
[8,7,3,4,2,1,5,6]=>[1,2,6,5,7,8,4,3]=>0010011=>[2,1,2,2]
[7,8,3,4,2,1,5,6]=>[2,1,6,5,7,8,4,3]=>1010011=>[1,1,1,2,2]
[7,8,4,2,3,1,5,6]=>[2,1,5,7,6,8,4,3]=>1001011=>[1,2,1,1,2]
[7,8,3,2,4,1,5,6]=>[2,1,6,7,5,8,4,3]=>1001011=>[1,2,1,1,2]
[8,7,2,3,4,1,5,6]=>[1,2,7,6,5,8,4,3]=>0011011=>[2,2,1,2]
[7,8,2,3,4,1,5,6]=>[2,1,7,6,5,8,4,3]=>1011011=>[1,1,2,1,2]
[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>0000111=>[4,3]
[7,8,4,3,1,2,5,6]=>[2,1,5,6,8,7,4,3]=>1000111=>[1,3,3]
[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>0010111=>[2,1,1,3]
[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>1010111=>[1,1,1,1,3]
[7,8,4,2,1,3,5,6]=>[2,1,5,7,8,6,4,3]=>1000111=>[1,3,3]
[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>0001111=>[3,4]
[7,8,4,1,2,3,5,6]=>[2,1,5,8,7,6,4,3]=>1001111=>[1,2,4]
[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>0000111=>[4,3]
[7,8,3,2,1,4,5,6]=>[2,1,6,7,8,5,4,3]=>1000111=>[1,3,3]
[8,7,2,3,1,4,5,6]=>[1,2,7,6,8,5,4,3]=>0010111=>[2,1,1,3]
[7,8,2,3,1,4,5,6]=>[2,1,7,6,8,5,4,3]=>1010111=>[1,1,1,1,3]
[7,8,3,1,2,4,5,6]=>[2,1,6,8,7,5,4,3]=>1001111=>[1,2,4]
[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>0001111=>[3,4]
[7,8,2,1,3,4,5,6]=>[2,1,7,8,6,5,4,3]=>1001111=>[1,2,4]
[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>0011111=>[2,5]
[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>1011111=>[1,1,5]
[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>0000001=>[6,1]
[8,5,6,4,3,2,1,7]=>[1,4,3,5,6,7,8,2]=>0100001=>[1,1,4,1]
[8,6,4,5,3,2,1,7]=>[1,3,5,4,6,7,8,2]=>0010001=>[2,1,3,1]
[8,5,4,6,3,2,1,7]=>[1,4,5,3,6,7,8,2]=>0010001=>[2,1,3,1]
[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>0110001=>[1,2,3,1]
[8,6,5,3,4,2,1,7]=>[1,3,4,6,5,7,8,2]=>0001001=>[3,1,2,1]
[8,5,6,3,4,2,1,7]=>[1,4,3,6,5,7,8,2]=>0101001=>[1,1,1,1,2,1]
[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>0001001=>[3,1,2,1]
[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>0101001=>[1,1,1,1,2,1]
[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>0111001=>[1,3,2,1]
[8,6,5,4,2,3,1,7]=>[1,3,4,5,7,6,8,2]=>0000101=>[4,1,1,1]
[8,6,4,5,2,3,1,7]=>[1,3,5,4,7,6,8,2]=>0010101=>[2,1,1,1,1,1]
[8,6,5,3,2,4,1,7]=>[1,3,4,6,7,5,8,2]=>0000101=>[4,1,1,1]
[8,5,6,3,2,4,1,7]=>[1,4,3,6,7,5,8,2]=>0100101=>[1,1,2,1,1,1]
[8,6,5,2,3,4,1,7]=>[1,3,4,7,6,5,8,2]=>0001101=>[3,2,1,1]
[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>0000101=>[4,1,1,1]
[8,6,3,4,2,5,1,7]=>[1,3,6,5,7,4,8,2]=>0010101=>[2,1,1,1,1,1]
[8,6,4,2,3,5,1,7]=>[1,3,5,7,6,4,8,2]=>0001101=>[3,2,1,1]
[8,5,4,3,2,6,1,7]=>[1,4,5,6,7,3,8,2]=>0000101=>[4,1,1,1]
[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>0100101=>[1,1,2,1,1,1]
[8,5,3,4,2,6,1,7]=>[1,4,6,5,7,3,8,2]=>0010101=>[2,1,1,1,1,1]
[8,4,3,5,2,6,1,7]=>[1,5,6,4,7,3,8,2]=>0010101=>[2,1,1,1,1,1]
[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>0001101=>[3,2,1,1]
[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>0101101=>[1,1,1,2,1,1]
[8,3,2,4,5,6,1,7]=>[1,6,7,5,4,3,8,2]=>0011101=>[2,3,1,1]
[8,2,3,4,5,6,1,7]=>[1,7,6,5,4,3,8,2]=>0111101=>[1,4,1,1]
[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>0000011=>[5,2]
[8,5,4,6,3,1,2,7]=>[1,4,5,3,6,8,7,2]=>0010011=>[2,1,2,2]
[8,4,5,6,3,1,2,7]=>[1,5,4,3,6,8,7,2]=>0110011=>[1,2,2,2]
[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>0101011=>[1,1,1,1,1,2]
[8,6,3,4,5,1,2,7]=>[1,3,6,5,4,8,7,2]=>0011011=>[2,2,1,2]
[8,5,4,3,6,1,2,7]=>[1,4,5,6,3,8,7,2]=>0001011=>[3,1,1,2]
[8,5,3,4,6,1,2,7]=>[1,4,6,5,3,8,7,2]=>0011011=>[2,2,1,2]
[8,4,3,5,6,1,2,7]=>[1,5,6,4,3,8,7,2]=>0011011=>[2,2,1,2]
[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>0111011=>[1,3,1,2]
[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>0000011=>[5,2]
[8,5,6,4,2,1,3,7]=>[1,4,3,5,7,8,6,2]=>0100011=>[1,1,3,2]
[8,6,4,5,2,1,3,7]=>[1,3,5,4,7,8,6,2]=>0010011=>[2,1,2,2]
[8,5,4,6,2,1,3,7]=>[1,4,5,3,7,8,6,2]=>0010011=>[2,1,2,2]
[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>0000111=>[4,3]
[8,5,6,4,1,2,3,7]=>[1,4,3,5,8,7,6,2]=>0100111=>[1,1,2,3]
[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]=>0010111=>[2,1,1,3]
[8,5,4,6,1,2,3,7]=>[1,4,5,3,8,7,6,2]=>0010111=>[2,1,1,3]
[8,4,5,6,1,2,3,7]=>[1,5,4,3,8,7,6,2]=>0110111=>[1,2,1,3]
[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>0000011=>[5,2]
[8,5,6,3,2,1,4,7]=>[1,4,3,6,7,8,5,2]=>0100011=>[1,1,3,2]
[8,6,5,2,3,1,4,7]=>[1,3,4,7,6,8,5,2]=>0001011=>[3,1,1,2]
[8,5,6,2,3,1,4,7]=>[1,4,3,7,6,8,5,2]=>0101011=>[1,1,1,1,1,2]
[8,5,6,3,1,2,4,7]=>[1,4,3,6,8,7,5,2]=>0100111=>[1,1,2,3]
[8,5,6,2,1,3,4,7]=>[1,4,3,7,8,6,5,2]=>0100111=>[1,1,2,3]
[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>0001111=>[3,4]
[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>0101111=>[1,1,1,4]
[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>0000011=>[5,2]
[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>0010011=>[2,1,2,2]
[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>0001011=>[3,1,1,2]
[8,6,3,2,4,1,5,7]=>[1,3,6,7,5,8,4,2]=>0001011=>[3,1,1,2]
[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>0000111=>[4,3]
[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>0000111=>[4,3]
[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>0001111=>[3,4]
[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>0000111=>[4,3]
[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>0001111=>[3,4]
[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>0001111=>[3,4]
[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>0011111=>[2,5]
[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>0000011=>[5,2]
[8,4,5,3,2,1,6,7]=>[1,5,4,6,7,8,3,2]=>0100011=>[1,1,3,2]
[8,4,3,5,2,1,6,7]=>[1,5,6,4,7,8,3,2]=>0010011=>[2,1,2,2]
[8,3,4,5,2,1,6,7]=>[1,6,5,4,7,8,3,2]=>0110011=>[1,2,2,2]
[8,5,3,2,4,1,6,7]=>[1,4,6,7,5,8,3,2]=>0001011=>[3,1,1,2]
[8,5,2,3,4,1,6,7]=>[1,4,7,6,5,8,3,2]=>0011011=>[2,2,1,2]
[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>0111011=>[1,3,1,2]
[8,5,3,4,1,2,6,7]=>[1,4,6,5,8,7,3,2]=>0010111=>[2,1,1,3]
[8,3,4,5,1,2,6,7]=>[1,6,5,4,8,7,3,2]=>0110111=>[1,2,1,3]
[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>0000111=>[4,3]
[8,4,5,2,1,3,6,7]=>[1,5,4,7,8,6,3,2]=>0100111=>[1,1,2,3]
[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>0001111=>[3,4]
[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>0000111=>[4,3]
[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>0001111=>[3,4]
[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>0001111=>[3,4]
[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>0011111=>[2,5]
[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>0000111=>[4,3]
[8,3,4,2,1,5,6,7]=>[1,6,5,7,8,4,3,2]=>0100111=>[1,1,2,3]
[8,4,2,3,1,5,6,7]=>[1,5,7,6,8,4,3,2]=>0010111=>[2,1,1,3]
[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>0010111=>[2,1,1,3]
[8,2,3,4,1,5,6,7]=>[1,7,6,5,8,4,3,2]=>0110111=>[1,2,1,3]
[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>0101111=>[1,1,1,4]
[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>0011111=>[2,5]
[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>0001111=>[3,4]
[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>0101111=>[1,1,1,4]
[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>0011111=>[2,5]
[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>0011111=>[2,5]
[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>0111111=>[1,6]
[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>0000001=>[6,1]
[6,7,5,4,3,2,1,8]=>[3,2,4,5,6,7,8,1]=>1000001=>[1,5,1]
[7,5,6,4,3,2,1,8]=>[2,4,3,5,6,7,8,1]=>0100001=>[1,1,4,1]
[6,5,7,4,3,2,1,8]=>[3,4,2,5,6,7,8,1]=>0100001=>[1,1,4,1]
[5,6,7,4,3,2,1,8]=>[4,3,2,5,6,7,8,1]=>1100001=>[2,4,1]
[7,6,4,5,3,2,1,8]=>[2,3,5,4,6,7,8,1]=>0010001=>[2,1,3,1]
[6,7,4,5,3,2,1,8]=>[3,2,5,4,6,7,8,1]=>1010001=>[1,1,1,3,1]
[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>0010001=>[2,1,3,1]
[7,4,5,6,3,2,1,8]=>[2,5,4,3,6,7,8,1]=>0110001=>[1,2,3,1]
[6,5,4,7,3,2,1,8]=>[3,4,5,2,6,7,8,1]=>0010001=>[2,1,3,1]
[5,6,4,7,3,2,1,8]=>[4,3,5,2,6,7,8,1]=>1010001=>[1,1,1,3,1]
[6,4,5,7,3,2,1,8]=>[3,5,4,2,6,7,8,1]=>0110001=>[1,2,3,1]
[5,4,6,7,3,2,1,8]=>[4,5,3,2,6,7,8,1]=>0110001=>[1,2,3,1]
[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>1110001=>[3,3,1]
[7,6,5,3,4,2,1,8]=>[2,3,4,6,5,7,8,1]=>0001001=>[3,1,2,1]
[7,5,6,3,4,2,1,8]=>[2,4,3,6,5,7,8,1]=>0101001=>[1,1,1,1,2,1]
[6,5,7,3,4,2,1,8]=>[3,4,2,6,5,7,8,1]=>0101001=>[1,1,1,1,2,1]
[5,6,7,3,4,2,1,8]=>[4,3,2,6,5,7,8,1]=>1101001=>[2,1,1,2,1]
[7,6,4,3,5,2,1,8]=>[2,3,5,6,4,7,8,1]=>0001001=>[3,1,2,1]
[6,7,4,3,5,2,1,8]=>[3,2,5,6,4,7,8,1]=>1001001=>[1,2,1,2,1]
[7,6,3,4,5,2,1,8]=>[2,3,6,5,4,7,8,1]=>0011001=>[2,2,2,1]
[7,5,4,3,6,2,1,8]=>[2,4,5,6,3,7,8,1]=>0001001=>[3,1,2,1]
[7,4,5,3,6,2,1,8]=>[2,5,4,6,3,7,8,1]=>0101001=>[1,1,1,1,2,1]
[7,5,3,4,6,2,1,8]=>[2,4,6,5,3,7,8,1]=>0011001=>[2,2,2,1]
[7,4,3,5,6,2,1,8]=>[2,5,6,4,3,7,8,1]=>0011001=>[2,2,2,1]
[7,3,4,5,6,2,1,8]=>[2,6,5,4,3,7,8,1]=>0111001=>[1,3,2,1]
[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>0001001=>[3,1,2,1]
[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>1001001=>[1,2,1,2,1]
[6,4,5,3,7,2,1,8]=>[3,5,4,6,2,7,8,1]=>0101001=>[1,1,1,1,2,1]
[4,5,6,3,7,2,1,8]=>[5,4,3,6,2,7,8,1]=>1101001=>[2,1,1,2,1]
[6,5,3,4,7,2,1,8]=>[3,4,6,5,2,7,8,1]=>0011001=>[2,2,2,1]
[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>0011001=>[2,2,2,1]
[6,3,4,5,7,2,1,8]=>[3,6,5,4,2,7,8,1]=>0111001=>[1,3,2,1]
[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>0011001=>[2,2,2,1]
[4,5,3,6,7,2,1,8]=>[5,4,6,3,2,7,8,1]=>1011001=>[1,1,2,2,1]
[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>1111001=>[4,2,1]
[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>0000101=>[4,1,1,1]
[6,7,5,4,2,3,1,8]=>[3,2,4,5,7,6,8,1]=>1000101=>[1,3,1,1,1]
[7,5,6,4,2,3,1,8]=>[2,4,3,5,7,6,8,1]=>0100101=>[1,1,2,1,1,1]
[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>0100101=>[1,1,2,1,1,1]
[5,6,7,4,2,3,1,8]=>[4,3,2,5,7,6,8,1]=>1100101=>[2,2,1,1,1]
[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>0010101=>[2,1,1,1,1,1]
[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]
[7,4,5,6,2,3,1,8]=>[2,5,4,3,7,6,8,1]=>0110101=>[1,2,1,1,1,1]
[6,5,4,7,2,3,1,8]=>[3,4,5,2,7,6,8,1]=>0010101=>[2,1,1,1,1,1]
[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,4,5,7,2,3,1,8]=>[3,5,4,2,7,6,8,1]=>0110101=>[1,2,1,1,1,1]
[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>1110101=>[3,1,1,1,1]
[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>0000101=>[4,1,1,1]
[7,5,6,3,2,4,1,8]=>[2,4,3,6,7,5,8,1]=>0100101=>[1,1,2,1,1,1]
[6,5,7,3,2,4,1,8]=>[3,4,2,6,7,5,8,1]=>0100101=>[1,1,2,1,1,1]
[5,6,7,3,2,4,1,8]=>[4,3,2,6,7,5,8,1]=>1100101=>[2,2,1,1,1]
[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>0001101=>[3,2,1,1]
[6,7,5,2,3,4,1,8]=>[3,2,4,7,6,5,8,1]=>1001101=>[1,2,2,1,1]
[7,5,6,2,3,4,1,8]=>[2,4,3,7,6,5,8,1]=>0101101=>[1,1,1,2,1,1]
[6,5,7,2,3,4,1,8]=>[3,4,2,7,6,5,8,1]=>0101101=>[1,1,1,2,1,1]
[5,6,7,2,3,4,1,8]=>[4,3,2,7,6,5,8,1]=>1101101=>[2,1,2,1,1]
[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>0000101=>[4,1,1,1]
[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>1000101=>[1,3,1,1,1]
[6,7,3,4,2,5,1,8]=>[3,2,6,5,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[7,6,4,2,3,5,1,8]=>[2,3,5,7,6,4,8,1]=>0001101=>[3,2,1,1]
[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>1001101=>[1,2,2,1,1]
[6,7,3,2,4,5,1,8]=>[3,2,6,7,5,4,8,1]=>1001101=>[1,2,2,1,1]
[7,6,2,3,4,5,1,8]=>[2,3,7,6,5,4,8,1]=>0011101=>[2,3,1,1]
[6,7,2,3,4,5,1,8]=>[3,2,7,6,5,4,8,1]=>1011101=>[1,1,3,1,1]
[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>0000101=>[4,1,1,1]
[7,4,5,3,2,6,1,8]=>[2,5,4,6,7,3,8,1]=>0100101=>[1,1,2,1,1,1]
[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>0010101=>[2,1,1,1,1,1]
[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>0101101=>[1,1,1,2,1,1]
[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>0001101=>[3,2,1,1]
[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>0001101=>[3,2,1,1]
[7,3,4,2,5,6,1,8]=>[2,6,5,7,4,3,8,1]=>0101101=>[1,1,1,2,1,1]
[7,2,3,4,5,6,1,8]=>[2,7,6,5,4,3,8,1]=>0111101=>[1,4,1,1]
[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>0000101=>[4,1,1,1]
[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>0100101=>[1,1,2,1,1,1]
[5,4,6,3,2,7,1,8]=>[4,5,3,6,7,2,8,1]=>0100101=>[1,1,2,1,1,1]
[4,5,6,3,2,7,1,8]=>[5,4,3,6,7,2,8,1]=>1100101=>[2,2,1,1,1]
[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>0010101=>[2,1,1,1,1,1]
[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>0010101=>[2,1,1,1,1,1]
[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>0110101=>[1,2,1,1,1,1]
[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>0010101=>[2,1,1,1,1,1]
[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>0110101=>[1,2,1,1,1,1]
[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>1110101=>[3,1,1,1,1]
[6,5,4,2,3,7,1,8]=>[3,4,5,7,6,2,8,1]=>0001101=>[3,2,1,1]
[6,4,5,2,3,7,1,8]=>[3,5,4,7,6,2,8,1]=>0101101=>[1,1,1,2,1,1]
[5,4,6,2,3,7,1,8]=>[4,5,3,7,6,2,8,1]=>0101101=>[1,1,1,2,1,1]
[4,5,6,2,3,7,1,8]=>[5,4,3,7,6,2,8,1]=>1101101=>[2,1,2,1,1]
[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>0001101=>[3,2,1,1]
[5,6,3,2,4,7,1,8]=>[4,3,6,7,5,2,8,1]=>1001101=>[1,2,2,1,1]
[6,5,2,3,4,7,1,8]=>[3,4,7,6,5,2,8,1]=>0011101=>[2,3,1,1]
[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>1011101=>[1,1,3,1,1]
[6,4,3,2,5,7,1,8]=>[3,5,6,7,4,2,8,1]=>0001101=>[3,2,1,1]
[6,4,2,3,5,7,1,8]=>[3,5,7,6,4,2,8,1]=>0011101=>[2,3,1,1]
[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>0001101=>[3,2,1,1]
[5,3,4,2,6,7,1,8]=>[4,6,5,7,3,2,8,1]=>0101101=>[1,1,1,2,1,1]
[3,4,5,2,6,7,1,8]=>[6,5,4,7,3,2,8,1]=>1101101=>[2,1,2,1,1]
[5,3,2,4,6,7,1,8]=>[4,6,7,5,3,2,8,1]=>0011101=>[2,3,1,1]
[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>0111101=>[1,4,1,1]
[4,3,2,5,6,7,1,8]=>[5,6,7,4,3,2,8,1]=>0011101=>[2,3,1,1]
[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>1011101=>[1,1,3,1,1]
[4,2,3,5,6,7,1,8]=>[5,7,6,4,3,2,8,1]=>0111101=>[1,4,1,1]
[3,2,4,5,6,7,1,8]=>[6,7,5,4,3,2,8,1]=>0111101=>[1,4,1,1]
[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>1111101=>[5,1,1]
[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>0000011=>[5,2]
[6,7,5,4,3,1,2,8]=>[3,2,4,5,6,8,7,1]=>1000011=>[1,4,2]
[7,5,6,4,3,1,2,8]=>[2,4,3,5,6,8,7,1]=>0100011=>[1,1,3,2]
[6,5,7,4,3,1,2,8]=>[3,4,2,5,6,8,7,1]=>0100011=>[1,1,3,2]
[5,6,7,4,3,1,2,8]=>[4,3,2,5,6,8,7,1]=>1100011=>[2,3,2]
[6,7,4,5,3,1,2,8]=>[3,2,5,4,6,8,7,1]=>1010011=>[1,1,1,2,2]
[7,5,4,6,3,1,2,8]=>[2,4,5,3,6,8,7,1]=>0010011=>[2,1,2,2]
[7,4,5,6,3,1,2,8]=>[2,5,4,3,6,8,7,1]=>0110011=>[1,2,2,2]
[5,4,6,7,3,1,2,8]=>[4,5,3,2,6,8,7,1]=>0110011=>[1,2,2,2]
[4,5,6,7,3,1,2,8]=>[5,4,3,2,6,8,7,1]=>1110011=>[3,2,2]
[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>0001011=>[3,1,1,2]
[6,7,5,3,4,1,2,8]=>[3,2,4,6,5,8,7,1]=>1001011=>[1,2,1,1,2]
[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>0101011=>[1,1,1,1,1,2]
[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>1101011=>[2,1,1,1,2]
[7,6,4,3,5,1,2,8]=>[2,3,5,6,4,8,7,1]=>0001011=>[3,1,1,2]
[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>1011011=>[1,1,2,1,2]
[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>0001011=>[3,1,1,2]
[7,5,3,4,6,1,2,8]=>[2,4,6,5,3,8,7,1]=>0011011=>[2,2,1,2]
[7,3,4,5,6,1,2,8]=>[2,6,5,4,3,8,7,1]=>0111011=>[1,3,1,2]
[6,5,4,3,7,1,2,8]=>[3,4,5,6,2,8,7,1]=>0001011=>[3,1,1,2]
[6,4,5,3,7,1,2,8]=>[3,5,4,6,2,8,7,1]=>0101011=>[1,1,1,1,1,2]
[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>0101011=>[1,1,1,1,1,2]
[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>1101011=>[2,1,1,1,2]
[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>1011011=>[1,1,2,1,2]
[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>0011011=>[2,2,1,2]
[6,3,4,5,7,1,2,8]=>[3,6,5,4,2,8,7,1]=>0111011=>[1,3,1,2]
[5,4,3,6,7,1,2,8]=>[4,5,6,3,2,8,7,1]=>0011011=>[2,2,1,2]
[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>1011011=>[1,1,2,1,2]
[5,3,4,6,7,1,2,8]=>[4,6,5,3,2,8,7,1]=>0111011=>[1,3,1,2]
[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]=>1111011=>[4,1,2]
[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>0000011=>[5,2]
[6,7,5,4,2,1,3,8]=>[3,2,4,5,7,8,6,1]=>1000011=>[1,4,2]
[6,5,7,4,2,1,3,8]=>[3,4,2,5,7,8,6,1]=>0100011=>[1,1,3,2]
[5,6,7,4,2,1,3,8]=>[4,3,2,5,7,8,6,1]=>1100011=>[2,3,2]
[7,6,4,5,2,1,3,8]=>[2,3,5,4,7,8,6,1]=>0010011=>[2,1,2,2]
[6,7,4,5,2,1,3,8]=>[3,2,5,4,7,8,6,1]=>1010011=>[1,1,1,2,2]
[7,5,4,6,2,1,3,8]=>[2,4,5,3,7,8,6,1]=>0010011=>[2,1,2,2]
[7,4,5,6,2,1,3,8]=>[2,5,4,3,7,8,6,1]=>0110011=>[1,2,2,2]
[6,5,4,7,2,1,3,8]=>[3,4,5,2,7,8,6,1]=>0010011=>[2,1,2,2]
[4,5,6,7,2,1,3,8]=>[5,4,3,2,7,8,6,1]=>1110011=>[3,2,2]
[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>0000111=>[4,3]
[7,5,6,4,1,2,3,8]=>[2,4,3,5,8,7,6,1]=>0100111=>[1,1,2,3]
[6,5,7,4,1,2,3,8]=>[3,4,2,5,8,7,6,1]=>0100111=>[1,1,2,3]
[5,6,7,4,1,2,3,8]=>[4,3,2,5,8,7,6,1]=>1100111=>[2,2,3]
[7,6,4,5,1,2,3,8]=>[2,3,5,4,8,7,6,1]=>0010111=>[2,1,1,3]
[7,5,4,6,1,2,3,8]=>[2,4,5,3,8,7,6,1]=>0010111=>[2,1,1,3]
[7,4,5,6,1,2,3,8]=>[2,5,4,3,8,7,6,1]=>0110111=>[1,2,1,3]
[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]=>1110111=>[3,1,3]
[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>0000011=>[5,2]
[7,5,6,3,2,1,4,8]=>[2,4,3,6,7,8,5,1]=>0100011=>[1,1,3,2]
[7,6,5,2,3,1,4,8]=>[2,3,4,7,6,8,5,1]=>0001011=>[3,1,1,2]
[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>0000111=>[4,3]
[7,5,6,3,1,2,4,8]=>[2,4,3,6,8,7,5,1]=>0100111=>[1,1,2,3]
[7,6,5,2,1,3,4,8]=>[2,3,4,7,8,6,5,1]=>0000111=>[4,3]
[6,7,5,2,1,3,4,8]=>[3,2,4,7,8,6,5,1]=>1000111=>[1,3,3]
[6,5,7,2,1,3,4,8]=>[3,4,2,7,8,6,5,1]=>0100111=>[1,1,2,3]
[5,6,7,2,1,3,4,8]=>[4,3,2,7,8,6,5,1]=>1100111=>[2,2,3]
[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>0001111=>[3,4]
[6,7,5,1,2,3,4,8]=>[3,2,4,8,7,6,5,1]=>1001111=>[1,2,4]
[7,5,6,1,2,3,4,8]=>[2,4,3,8,7,6,5,1]=>0101111=>[1,1,1,4]
[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>0101111=>[1,1,1,4]
[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>1101111=>[2,1,4]
[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>0000011=>[5,2]
[6,7,4,3,2,1,5,8]=>[3,2,5,6,7,8,4,1]=>1000011=>[1,4,2]
[7,6,4,2,3,1,5,8]=>[2,3,5,7,6,8,4,1]=>0001011=>[3,1,1,2]
[6,7,4,2,3,1,5,8]=>[3,2,5,7,6,8,4,1]=>1001011=>[1,2,1,1,2]
[7,6,2,3,4,1,5,8]=>[2,3,7,6,5,8,4,1]=>0011011=>[2,2,1,2]
[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>0000111=>[4,3]
[7,6,3,4,1,2,5,8]=>[2,3,6,5,8,7,4,1]=>0010111=>[2,1,1,3]
[6,7,3,4,1,2,5,8]=>[3,2,6,5,8,7,4,1]=>1010111=>[1,1,1,1,3]
[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>0000111=>[4,3]
[6,7,4,2,1,3,5,8]=>[3,2,5,7,8,6,4,1]=>1000111=>[1,3,3]
[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>0000111=>[4,3]
[6,7,3,1,2,4,5,8]=>[3,2,6,8,7,5,4,1]=>1001111=>[1,2,4]
[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>0011111=>[2,5]
[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>1011111=>[1,1,5]
[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>0000011=>[5,2]
[7,4,5,3,2,1,6,8]=>[2,5,4,6,7,8,3,1]=>0100011=>[1,1,3,2]
[7,5,3,4,2,1,6,8]=>[2,4,6,5,7,8,3,1]=>0010011=>[2,1,2,2]
[7,4,3,5,2,1,6,8]=>[2,5,6,4,7,8,3,1]=>0010011=>[2,1,2,2]
[7,3,4,5,2,1,6,8]=>[2,6,5,4,7,8,3,1]=>0110011=>[1,2,2,2]
[7,4,5,2,3,1,6,8]=>[2,5,4,7,6,8,3,1]=>0101011=>[1,1,1,1,1,2]
[7,5,3,2,4,1,6,8]=>[2,4,6,7,5,8,3,1]=>0001011=>[3,1,1,2]
[7,5,2,3,4,1,6,8]=>[2,4,7,6,5,8,3,1]=>0011011=>[2,2,1,2]
[7,4,3,2,5,1,6,8]=>[2,5,6,7,4,8,3,1]=>0001011=>[3,1,1,2]
[7,3,2,4,5,1,6,8]=>[2,6,7,5,4,8,3,1]=>0011011=>[2,2,1,2]
[7,2,3,4,5,1,6,8]=>[2,7,6,5,4,8,3,1]=>0111011=>[1,3,1,2]
[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>0010111=>[2,1,1,3]
[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>0010111=>[2,1,1,3]
[7,3,4,5,1,2,6,8]=>[2,6,5,4,8,7,3,1]=>0110111=>[1,2,1,3]
[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>0000111=>[4,3]
[7,4,5,2,1,3,6,8]=>[2,5,4,7,8,6,3,1]=>0100111=>[1,1,2,3]
[7,4,5,1,2,3,6,8]=>[2,5,4,8,7,6,3,1]=>0101111=>[1,1,1,4]
[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>0000111=>[4,3]
[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>0001111=>[3,4]
[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>0001111=>[3,4]
[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>0011111=>[2,5]
[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>0000111=>[4,3]
[7,3,4,2,1,5,6,8]=>[2,6,5,7,8,4,3,1]=>0100111=>[1,1,2,3]
[7,3,2,4,1,5,6,8]=>[2,6,7,5,8,4,3,1]=>0010111=>[2,1,1,3]
[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>0011111=>[2,5]
[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>0001111=>[3,4]
[7,2,3,1,4,5,6,8]=>[2,7,6,8,5,4,3,1]=>0101111=>[1,1,1,4]
[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>0011111=>[2,5]
[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>0011111=>[2,5]
[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>0111111=>[1,6]
[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>0000011=>[5,2]
[5,6,4,3,2,1,7,8]=>[4,3,5,6,7,8,2,1]=>1000011=>[1,4,2]
[6,4,5,3,2,1,7,8]=>[3,5,4,6,7,8,2,1]=>0100011=>[1,1,3,2]
[4,5,6,3,2,1,7,8]=>[5,4,3,6,7,8,2,1]=>1100011=>[2,3,2]
[6,5,3,4,2,1,7,8]=>[3,4,6,5,7,8,2,1]=>0010011=>[2,1,2,2]
[5,6,3,4,2,1,7,8]=>[4,3,6,5,7,8,2,1]=>1010011=>[1,1,1,2,2]
[6,4,3,5,2,1,7,8]=>[3,5,6,4,7,8,2,1]=>0010011=>[2,1,2,2]
[6,3,4,5,2,1,7,8]=>[3,6,5,4,7,8,2,1]=>0110011=>[1,2,2,2]
[5,4,3,6,2,1,7,8]=>[4,5,6,3,7,8,2,1]=>0010011=>[2,1,2,2]
[3,4,5,6,2,1,7,8]=>[6,5,4,3,7,8,2,1]=>1110011=>[3,2,2]
[6,5,4,2,3,1,7,8]=>[3,4,5,7,6,8,2,1]=>0001011=>[3,1,1,2]
[5,6,4,2,3,1,7,8]=>[4,3,5,7,6,8,2,1]=>1001011=>[1,2,1,1,2]
[6,4,5,2,3,1,7,8]=>[3,5,4,7,6,8,2,1]=>0101011=>[1,1,1,1,1,2]
[5,4,6,2,3,1,7,8]=>[4,5,3,7,6,8,2,1]=>0101011=>[1,1,1,1,1,2]
[6,5,3,2,4,1,7,8]=>[3,4,6,7,5,8,2,1]=>0001011=>[3,1,1,2]
[6,5,2,3,4,1,7,8]=>[3,4,7,6,5,8,2,1]=>0011011=>[2,2,1,2]
[5,6,2,3,4,1,7,8]=>[4,3,7,6,5,8,2,1]=>1011011=>[1,1,2,1,2]
[6,4,3,2,5,1,7,8]=>[3,5,6,7,4,8,2,1]=>0001011=>[3,1,1,2]
[6,4,2,3,5,1,7,8]=>[3,5,7,6,4,8,2,1]=>0011011=>[2,2,1,2]
[6,2,3,4,5,1,7,8]=>[3,7,6,5,4,8,2,1]=>0111011=>[1,3,1,2]
[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>0001011=>[3,1,1,2]
[4,5,3,2,6,1,7,8]=>[5,4,6,7,3,8,2,1]=>1001011=>[1,2,1,1,2]
[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>1101011=>[2,1,1,1,2]
[4,5,2,3,6,1,7,8]=>[5,4,7,6,3,8,2,1]=>1011011=>[1,1,2,1,2]
[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>0111011=>[1,3,1,2]
[4,3,2,5,6,1,7,8]=>[5,6,7,4,3,8,2,1]=>0011011=>[2,2,1,2]
[3,4,2,5,6,1,7,8]=>[6,5,7,4,3,8,2,1]=>1011011=>[1,1,2,1,2]
[4,2,3,5,6,1,7,8]=>[5,7,6,4,3,8,2,1]=>0111011=>[1,3,1,2]
[3,2,4,5,6,1,7,8]=>[6,7,5,4,3,8,2,1]=>0111011=>[1,3,1,2]
[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>1111011=>[4,1,2]
[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>0000111=>[4,3]
[5,4,6,3,1,2,7,8]=>[4,5,3,6,8,7,2,1]=>0100111=>[1,1,2,3]
[4,5,6,3,1,2,7,8]=>[5,4,3,6,8,7,2,1]=>1100111=>[2,2,3]
[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>1010111=>[1,1,1,1,3]
[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>0010111=>[2,1,1,3]
[4,3,5,6,1,2,7,8]=>[5,6,4,3,8,7,2,1]=>0110111=>[1,2,1,3]
[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]=>1110111=>[3,1,3]
[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>0000111=>[4,3]
[6,4,5,2,1,3,7,8]=>[3,5,4,7,8,6,2,1]=>0100111=>[1,1,2,3]
[4,5,6,2,1,3,7,8]=>[5,4,3,7,8,6,2,1]=>1100111=>[2,2,3]
[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>0001111=>[3,4]
[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>1101111=>[2,1,4]
[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>0000111=>[4,3]
[5,6,3,2,1,4,7,8]=>[4,3,6,7,8,5,2,1]=>1000111=>[1,3,3]
[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>0011111=>[2,5]
[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>1011111=>[1,1,5]
[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>0000111=>[4,3]
[6,4,2,3,1,5,7,8]=>[3,5,7,6,8,4,2,1]=>0010111=>[2,1,1,3]
[6,3,2,4,1,5,7,8]=>[3,6,7,5,8,4,2,1]=>0010111=>[2,1,1,3]
[6,2,3,4,1,5,7,8]=>[3,7,6,5,8,4,2,1]=>0110111=>[1,2,1,3]
[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>0001111=>[3,4]
[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>0001111=>[3,4]
[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>0011111=>[2,5]
[6,2,3,1,4,5,7,8]=>[3,7,6,8,5,4,2,1]=>0101111=>[1,1,1,4]
[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>0011111=>[2,5]
[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>0011111=>[2,5]
[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>0111111=>[1,6]
[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>0000111=>[4,3]
[4,5,3,2,1,6,7,8]=>[5,4,6,7,8,3,2,1]=>1000111=>[1,3,3]
[5,3,4,2,1,6,7,8]=>[4,6,5,7,8,3,2,1]=>0100111=>[1,1,2,3]
[4,3,5,2,1,6,7,8]=>[5,6,4,7,8,3,2,1]=>0100111=>[1,1,2,3]
[3,4,5,2,1,6,7,8]=>[6,5,4,7,8,3,2,1]=>1100111=>[2,2,3]
[5,4,2,3,1,6,7,8]=>[4,5,7,6,8,3,2,1]=>0010111=>[2,1,1,3]
[4,5,2,3,1,6,7,8]=>[5,4,7,6,8,3,2,1]=>1010111=>[1,1,1,1,3]
[5,3,2,4,1,6,7,8]=>[4,6,7,5,8,3,2,1]=>0010111=>[2,1,1,3]
[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>0110111=>[1,2,1,3]
[4,3,2,5,1,6,7,8]=>[5,6,7,4,8,3,2,1]=>0010111=>[2,1,1,3]
[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>1010111=>[1,1,1,1,3]
[4,2,3,5,1,6,7,8]=>[5,7,6,4,8,3,2,1]=>0110111=>[1,2,1,3]
[3,2,4,5,1,6,7,8]=>[6,7,5,4,8,3,2,1]=>0110111=>[1,2,1,3]
[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>1110111=>[3,1,3]
[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>0001111=>[3,4]
[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>0101111=>[1,1,1,4]
[4,3,5,1,2,6,7,8]=>[5,6,4,8,7,3,2,1]=>0101111=>[1,1,1,4]
[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]=>1101111=>[2,1,4]
[5,4,2,1,3,6,7,8]=>[4,5,7,8,6,3,2,1]=>0001111=>[3,4]
[4,5,2,1,3,6,7,8]=>[5,4,7,8,6,3,2,1]=>1001111=>[1,2,4]
[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>0011111=>[2,5]
[5,3,2,1,4,6,7,8]=>[4,6,7,8,5,3,2,1]=>0001111=>[3,4]
[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>0101111=>[1,1,1,4]
[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>0011111=>[2,5]
[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>0011111=>[2,5]
[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>0111111=>[1,6]
[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>0001111=>[3,4]
[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>1001111=>[1,2,4]
[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>0101111=>[1,1,1,4]
[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>0101111=>[1,1,1,4]
[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>1101111=>[2,1,4]
[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>0011111=>[2,5]
[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>1011111=>[1,1,5]
[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>0011111=>[2,5]
[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>0111111=>[1,6]
[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>0011111=>[2,5]
[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>1011111=>[1,1,5]
[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>0111111=>[1,6]
[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>0111111=>[1,6]
[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111=>[7]
[6,8,7,5,4,3,2,1]=>[3,1,2,4,5,6,7,8]=>1000000=>[1,6]
[5,8,7,6,4,3,2,1]=>[4,1,2,3,5,6,7,8]=>1000000=>[1,6]
[5,7,8,6,4,3,2,1]=>[4,2,1,3,5,6,7,8]=>1100000=>[2,5]
[6,5,8,7,4,3,2,1]=>[3,4,1,2,5,6,7,8]=>0100000=>[1,1,5]
[5,6,8,7,4,3,2,1]=>[4,3,1,2,5,6,7,8]=>1100000=>[2,5]
[5,7,6,8,4,3,2,1]=>[4,2,3,1,5,6,7,8]=>1010000=>[1,1,1,4]
[4,8,7,6,5,3,2,1]=>[5,1,2,3,4,6,7,8]=>1000000=>[1,6]
[4,7,8,6,5,3,2,1]=>[5,2,1,3,4,6,7,8]=>1100000=>[2,5]
[4,6,8,7,5,3,2,1]=>[5,3,1,2,4,6,7,8]=>1100000=>[2,5]
[4,7,6,8,5,3,2,1]=>[5,2,3,1,4,6,7,8]=>1010000=>[1,1,1,4]
[4,6,7,8,5,3,2,1]=>[5,3,2,1,4,6,7,8]=>1110000=>[3,4]
[5,4,8,7,6,3,2,1]=>[4,5,1,2,3,6,7,8]=>0100000=>[1,1,5]
[5,4,7,8,6,3,2,1]=>[4,5,2,1,3,6,7,8]=>0110000=>[1,2,4]
[4,5,8,7,6,3,2,1]=>[5,4,1,2,3,6,7,8]=>1100000=>[2,5]
[4,5,7,8,6,3,2,1]=>[5,4,2,1,3,6,7,8]=>1110000=>[3,4]
[6,5,4,8,7,3,2,1]=>[3,4,5,1,2,6,7,8]=>0010000=>[2,1,4]
[5,6,4,8,7,3,2,1]=>[4,3,5,1,2,6,7,8]=>1010000=>[1,1,1,4]
[4,6,5,8,7,3,2,1]=>[5,3,4,1,2,6,7,8]=>1010000=>[1,1,1,4]
[4,5,6,8,7,3,2,1]=>[5,4,3,1,2,6,7,8]=>1110000=>[3,4]
[5,7,6,4,8,3,2,1]=>[4,2,3,5,1,6,7,8]=>1001000=>[1,2,1,3]
[4,7,6,5,8,3,2,1]=>[5,2,3,4,1,6,7,8]=>1001000=>[1,2,1,3]
[4,6,7,5,8,3,2,1]=>[5,3,2,4,1,6,7,8]=>1101000=>[2,1,1,3]
[5,4,7,6,8,3,2,1]=>[4,5,2,3,1,6,7,8]=>0101000=>[1,1,1,1,3]
[4,5,7,6,8,3,2,1]=>[5,4,2,3,1,6,7,8]=>1101000=>[2,1,1,3]
[4,6,5,7,8,3,2,1]=>[5,3,4,2,1,6,7,8]=>1011000=>[1,1,2,3]
[3,8,7,6,5,4,2,1]=>[6,1,2,3,4,5,7,8]=>1000000=>[1,6]
[3,7,8,6,5,4,2,1]=>[6,2,1,3,4,5,7,8]=>1100000=>[2,5]
[3,6,8,7,5,4,2,1]=>[6,3,1,2,4,5,7,8]=>1100000=>[2,5]
[3,7,6,8,5,4,2,1]=>[6,2,3,1,4,5,7,8]=>1010000=>[1,1,1,4]
[3,6,7,8,5,4,2,1]=>[6,3,2,1,4,5,7,8]=>1110000=>[3,4]
[3,5,8,7,6,4,2,1]=>[6,4,1,2,3,5,7,8]=>1100000=>[2,5]
[3,5,7,8,6,4,2,1]=>[6,4,2,1,3,5,7,8]=>1110000=>[3,4]
[3,5,6,8,7,4,2,1]=>[6,4,3,1,2,5,7,8]=>1110000=>[3,4]
[3,6,5,7,8,4,2,1]=>[6,3,4,2,1,5,7,8]=>1011000=>[1,1,2,3]
[3,5,6,7,8,4,2,1]=>[6,4,3,2,1,5,7,8]=>1111000=>[4,3]
[4,3,7,8,6,5,2,1]=>[5,6,2,1,3,4,7,8]=>0110000=>[1,2,4]
[4,3,6,7,8,5,2,1]=>[5,6,3,2,1,4,7,8]=>0111000=>[1,3,3]
[3,4,6,7,8,5,2,1]=>[6,5,3,2,1,4,7,8]=>1111000=>[4,3]
[5,4,3,8,7,6,2,1]=>[4,5,6,1,2,3,7,8]=>0010000=>[2,1,4]
[5,4,3,7,8,6,2,1]=>[4,5,6,2,1,3,7,8]=>0011000=>[2,2,3]
[3,5,4,7,8,6,2,1]=>[6,4,5,2,1,3,7,8]=>1011000=>[1,1,2,3]
[4,3,5,7,8,6,2,1]=>[5,6,4,2,1,3,7,8]=>0111000=>[1,3,3]
[3,4,5,8,7,6,2,1]=>[6,5,4,1,2,3,7,8]=>1110000=>[3,4]
[3,4,5,7,8,6,2,1]=>[6,5,4,2,1,3,7,8]=>1111000=>[4,3]
[6,5,4,3,8,7,2,1]=>[3,4,5,6,1,2,7,8]=>0001000=>[3,1,3]
[5,6,4,3,8,7,2,1]=>[4,3,5,6,1,2,7,8]=>1001000=>[1,2,1,3]
[4,5,6,3,8,7,2,1]=>[5,4,3,6,1,2,7,8]=>1101000=>[2,1,1,3]
[4,3,6,5,8,7,2,1]=>[5,6,3,4,1,2,7,8]=>0101000=>[1,1,1,1,3]
[4,5,3,6,8,7,2,1]=>[5,4,6,3,1,2,7,8]=>1011000=>[1,1,2,3]
[3,5,4,6,8,7,2,1]=>[6,4,5,3,1,2,7,8]=>1011000=>[1,1,2,3]
[3,4,5,6,8,7,2,1]=>[6,5,4,3,1,2,7,8]=>1111000=>[4,3]
[5,7,6,4,3,8,2,1]=>[4,2,3,5,6,1,7,8]=>1000100=>[1,3,1,2]
[4,7,6,5,3,8,2,1]=>[5,2,3,4,6,1,7,8]=>1000100=>[1,3,1,2]
[4,6,7,5,3,8,2,1]=>[5,3,2,4,6,1,7,8]=>1100100=>[2,2,1,2]
[3,7,6,5,4,8,2,1]=>[6,2,3,4,5,1,7,8]=>1000100=>[1,3,1,2]
[3,5,6,7,4,8,2,1]=>[6,4,3,2,5,1,7,8]=>1110100=>[3,1,1,2]
[4,3,7,6,5,8,2,1]=>[5,6,2,3,4,1,7,8]=>0100100=>[1,1,2,1,2]
[4,3,6,7,5,8,2,1]=>[5,6,3,2,4,1,7,8]=>0110100=>[1,2,1,1,2]
[3,4,7,6,5,8,2,1]=>[6,5,2,3,4,1,7,8]=>1100100=>[2,2,1,2]
[4,5,3,7,6,8,2,1]=>[5,4,6,2,3,1,7,8]=>1010100=>[1,1,1,1,1,2]
[4,3,6,5,7,8,2,1]=>[5,6,3,4,2,1,7,8]=>0101100=>[1,1,1,2,2]
[3,4,6,5,7,8,2,1]=>[6,5,3,4,2,1,7,8]=>1101100=>[2,1,2,2]
[2,8,7,6,5,4,3,1]=>[7,1,2,3,4,5,6,8]=>1000000=>[1,6]
[2,7,8,6,5,4,3,1]=>[7,2,1,3,4,5,6,8]=>1100000=>[2,5]
[2,6,8,7,5,4,3,1]=>[7,3,1,2,4,5,6,8]=>1100000=>[2,5]
[2,7,6,8,5,4,3,1]=>[7,2,3,1,4,5,6,8]=>1010000=>[1,1,1,4]
[2,6,7,8,5,4,3,1]=>[7,3,2,1,4,5,6,8]=>1110000=>[3,4]
[2,5,8,7,6,4,3,1]=>[7,4,1,2,3,5,6,8]=>1100000=>[2,5]
[2,6,5,8,7,4,3,1]=>[7,3,4,1,2,5,6,8]=>1010000=>[1,1,1,4]
[2,5,6,8,7,4,3,1]=>[7,4,3,1,2,5,6,8]=>1110000=>[3,4]
[2,7,6,5,8,4,3,1]=>[7,2,3,4,1,5,6,8]=>1001000=>[1,2,1,3]
[2,5,6,7,8,4,3,1]=>[7,4,3,2,1,5,6,8]=>1111000=>[4,3]
[2,4,8,7,6,5,3,1]=>[7,5,1,2,3,4,6,8]=>1100000=>[2,5]
[2,4,6,8,7,5,3,1]=>[7,5,3,1,2,4,6,8]=>1110000=>[3,4]
[2,4,7,6,8,5,3,1]=>[7,5,2,3,1,4,6,8]=>1101000=>[2,1,1,3]
[2,4,6,7,8,5,3,1]=>[7,5,3,2,1,4,6,8]=>1111000=>[4,3]
[2,5,4,8,7,6,3,1]=>[7,4,5,1,2,3,6,8]=>1010000=>[1,1,1,4]
[2,5,4,7,8,6,3,1]=>[7,4,5,2,1,3,6,8]=>1011000=>[1,1,2,3]
[2,4,6,5,8,7,3,1]=>[7,5,3,4,1,2,6,8]=>1101000=>[2,1,1,3]
[2,4,5,6,8,7,3,1]=>[7,5,4,3,1,2,6,8]=>1111000=>[4,3]
[2,7,6,5,4,8,3,1]=>[7,2,3,4,5,1,6,8]=>1000100=>[1,3,1,2]
[2,5,7,6,4,8,3,1]=>[7,4,2,3,5,1,6,8]=>1100100=>[2,2,1,2]
[2,4,7,6,5,8,3,1]=>[7,5,2,3,4,1,6,8]=>1100100=>[2,2,1,2]
[2,4,6,7,5,8,3,1]=>[7,5,3,2,4,1,6,8]=>1110100=>[3,1,1,2]
[2,4,5,7,6,8,3,1]=>[7,5,4,2,3,1,6,8]=>1110100=>[3,1,1,2]
[2,6,5,4,7,8,3,1]=>[7,3,4,5,2,1,6,8]=>1001100=>[1,2,2,2]
[2,5,6,4,7,8,3,1]=>[7,4,3,5,2,1,6,8]=>1101100=>[2,1,2,2]
[2,5,4,6,7,8,3,1]=>[7,4,5,3,2,1,6,8]=>1011100=>[1,1,3,2]
[2,4,5,6,7,8,3,1]=>[7,5,4,3,2,1,6,8]=>1111100=>[5,2]
[3,2,8,7,6,5,4,1]=>[6,7,1,2,3,4,5,8]=>0100000=>[1,1,5]
[3,2,6,8,7,5,4,1]=>[6,7,3,1,2,4,5,8]=>0110000=>[1,2,4]
[3,2,7,6,8,5,4,1]=>[6,7,2,3,1,4,5,8]=>0101000=>[1,1,1,1,3]
[3,2,6,7,8,5,4,1]=>[6,7,3,2,1,4,5,8]=>0111000=>[1,3,3]
[3,2,6,5,8,7,4,1]=>[6,7,3,4,1,2,5,8]=>0101000=>[1,1,1,1,3]
[3,2,7,6,5,8,4,1]=>[6,7,2,3,4,1,5,8]=>0100100=>[1,1,2,1,2]
[3,2,6,7,5,8,4,1]=>[6,7,3,2,4,1,5,8]=>0110100=>[1,2,1,1,2]
[3,2,5,6,7,8,4,1]=>[6,7,4,3,2,1,5,8]=>0111100=>[1,4,2]
[2,3,8,7,6,5,4,1]=>[7,6,1,2,3,4,5,8]=>1100000=>[2,5]
[2,3,7,6,8,5,4,1]=>[7,6,2,3,1,4,5,8]=>1101000=>[2,1,1,3]
[2,3,6,7,8,5,4,1]=>[7,6,3,2,1,4,5,8]=>1111000=>[4,3]
[2,3,5,7,8,6,4,1]=>[7,6,4,2,1,3,5,8]=>1111000=>[4,3]
[2,3,5,6,8,7,4,1]=>[7,6,4,3,1,2,5,8]=>1111000=>[4,3]
[2,3,7,6,5,8,4,1]=>[7,6,2,3,4,1,5,8]=>1100100=>[2,2,1,2]
[2,3,6,7,5,8,4,1]=>[7,6,3,2,4,1,5,8]=>1110100=>[3,1,1,2]
[2,3,6,5,7,8,4,1]=>[7,6,3,4,2,1,5,8]=>1101100=>[2,1,2,2]
[2,3,5,6,7,8,4,1]=>[7,6,4,3,2,1,5,8]=>1111100=>[5,2]
[4,3,2,8,7,6,5,1]=>[5,6,7,1,2,3,4,8]=>0010000=>[2,1,4]
[4,3,2,7,8,6,5,1]=>[5,6,7,2,1,3,4,8]=>0011000=>[2,2,3]
[4,3,2,7,6,8,5,1]=>[5,6,7,2,3,1,4,8]=>0010100=>[2,1,1,1,2]
[3,4,2,8,7,6,5,1]=>[6,5,7,1,2,3,4,8]=>1010000=>[1,1,1,4]
[3,4,2,7,6,8,5,1]=>[6,5,7,2,3,1,4,8]=>1010100=>[1,1,1,1,1,2]
[2,4,3,8,7,6,5,1]=>[7,5,6,1,2,3,4,8]=>1010000=>[1,1,1,4]
[2,4,3,7,8,6,5,1]=>[7,5,6,2,1,3,4,8]=>1011000=>[1,1,2,3]
[2,4,3,6,8,7,5,1]=>[7,5,6,3,1,2,4,8]=>1011000=>[1,1,2,3]
[2,4,3,7,6,8,5,1]=>[7,5,6,2,3,1,4,8]=>1010100=>[1,1,1,1,1,2]
[3,2,4,8,7,6,5,1]=>[6,7,5,1,2,3,4,8]=>0110000=>[1,2,4]
[3,2,4,7,8,6,5,1]=>[6,7,5,2,1,3,4,8]=>0111000=>[1,3,3]
[3,2,4,7,6,8,5,1]=>[6,7,5,2,3,1,4,8]=>0110100=>[1,2,1,1,2]
[2,3,4,8,7,6,5,1]=>[7,6,5,1,2,3,4,8]=>1110000=>[3,4]
[2,3,4,7,8,6,5,1]=>[7,6,5,2,1,3,4,8]=>1111000=>[4,3]
[2,3,4,7,6,8,5,1]=>[7,6,5,2,3,1,4,8]=>1110100=>[3,1,1,2]
[2,3,4,6,7,8,5,1]=>[7,6,5,3,2,1,4,8]=>1111100=>[5,2]
[5,4,3,2,8,7,6,1]=>[4,5,6,7,1,2,3,8]=>0001000=>[3,1,3]
[5,4,3,2,7,8,6,1]=>[4,5,6,7,2,1,3,8]=>0001100=>[3,2,2]
[4,5,3,2,8,7,6,1]=>[5,4,6,7,1,2,3,8]=>1001000=>[1,2,1,3]
[4,5,3,2,7,8,6,1]=>[5,4,6,7,2,1,3,8]=>1001100=>[1,2,2,2]
[2,5,4,3,8,7,6,1]=>[7,4,5,6,1,2,3,8]=>1001000=>[1,2,1,3]
[2,5,4,3,7,8,6,1]=>[7,4,5,6,2,1,3,8]=>1001100=>[1,2,2,2]
[2,4,5,3,8,7,6,1]=>[7,5,4,6,1,2,3,8]=>1101000=>[2,1,1,3]
[2,4,5,3,7,8,6,1]=>[7,5,4,6,2,1,3,8]=>1101100=>[2,1,2,2]
[2,3,5,4,8,7,6,1]=>[7,6,4,5,1,2,3,8]=>1101000=>[2,1,1,3]
[2,3,5,4,7,8,6,1]=>[7,6,4,5,2,1,3,8]=>1101100=>[2,1,2,2]
[4,3,2,5,8,7,6,1]=>[5,6,7,4,1,2,3,8]=>0011000=>[2,2,3]
[3,4,2,5,7,8,6,1]=>[6,5,7,4,2,1,3,8]=>1011100=>[1,1,3,2]
[2,4,3,5,8,7,6,1]=>[7,5,6,4,1,2,3,8]=>1011000=>[1,1,2,3]
[2,3,4,5,8,7,6,1]=>[7,6,5,4,1,2,3,8]=>1111000=>[4,3]
[2,3,4,5,7,8,6,1]=>[7,6,5,4,2,1,3,8]=>1111100=>[5,2]
[6,5,4,3,2,8,7,1]=>[3,4,5,6,7,1,2,8]=>0000100=>[4,1,2]
[3,6,5,4,2,8,7,1]=>[6,3,4,5,7,1,2,8]=>1000100=>[1,3,1,2]
[3,5,6,4,2,8,7,1]=>[6,4,3,5,7,1,2,8]=>1100100=>[2,2,1,2]
[4,3,6,5,2,8,7,1]=>[5,6,3,4,7,1,2,8]=>0100100=>[1,1,2,1,2]
[3,4,5,6,2,8,7,1]=>[6,5,4,3,7,1,2,8]=>1110100=>[3,1,1,2]
[2,4,6,5,3,8,7,1]=>[7,5,3,4,6,1,2,8]=>1100100=>[2,2,1,2]
[3,2,6,5,4,8,7,1]=>[6,7,3,4,5,1,2,8]=>0100100=>[1,1,2,1,2]
[2,4,3,6,5,8,7,1]=>[7,5,6,3,4,1,2,8]=>1010100=>[1,1,1,1,1,2]
[2,3,4,6,5,8,7,1]=>[7,6,5,3,4,1,2,8]=>1110100=>[3,1,1,2]
[5,4,3,2,6,8,7,1]=>[4,5,6,7,3,1,2,8]=>0001100=>[3,2,2]
[4,5,3,2,6,8,7,1]=>[5,4,6,7,3,1,2,8]=>1001100=>[1,2,2,2]
[2,5,4,3,6,8,7,1]=>[7,4,5,6,3,1,2,8]=>1001100=>[1,2,2,2]
[2,3,5,4,6,8,7,1]=>[7,6,4,5,3,1,2,8]=>1101100=>[2,1,2,2]
[2,4,3,5,6,8,7,1]=>[7,5,6,4,3,1,2,8]=>1011100=>[1,1,3,2]
[3,2,4,5,6,8,7,1]=>[6,7,5,4,3,1,2,8]=>0111100=>[1,4,2]
[2,3,4,5,6,8,7,1]=>[7,6,5,4,3,1,2,8]=>1111100=>[5,2]
[5,7,6,4,3,2,8,1]=>[4,2,3,5,6,7,1,8]=>1000010=>[1,4,1,1]
[4,7,6,5,3,2,8,1]=>[5,2,3,4,6,7,1,8]=>1000010=>[1,4,1,1]
[5,4,7,6,3,2,8,1]=>[4,5,2,3,6,7,1,8]=>0100010=>[1,1,3,1,1]
[4,5,7,6,3,2,8,1]=>[5,4,2,3,6,7,1,8]=>1100010=>[2,3,1,1]
[3,7,6,5,4,2,8,1]=>[6,2,3,4,5,7,1,8]=>1000010=>[1,4,1,1]
[3,6,7,5,4,2,8,1]=>[6,3,2,4,5,7,1,8]=>1100010=>[2,3,1,1]
[3,5,7,6,4,2,8,1]=>[6,4,2,3,5,7,1,8]=>1100010=>[2,3,1,1]
[3,4,6,7,5,2,8,1]=>[6,5,3,2,4,7,1,8]=>1110010=>[3,2,1,1]
[4,5,3,7,6,2,8,1]=>[5,4,6,2,3,7,1,8]=>1010010=>[1,1,1,2,1,1]
[4,6,5,3,7,2,8,1]=>[5,3,4,6,2,7,1,8]=>1001010=>[1,2,1,1,1,1]
[3,6,5,4,7,2,8,1]=>[6,3,4,5,2,7,1,8]=>1001010=>[1,2,1,1,1,1]
[4,3,6,5,7,2,8,1]=>[5,6,3,4,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[2,7,6,5,4,3,8,1]=>[7,2,3,4,5,6,1,8]=>1000010=>[1,4,1,1]
[2,5,7,6,4,3,8,1]=>[7,4,2,3,5,6,1,8]=>1100010=>[2,3,1,1]
[2,4,6,7,5,3,8,1]=>[7,5,3,2,4,6,1,8]=>1110010=>[3,2,1,1]
[2,5,4,7,6,3,8,1]=>[7,4,5,2,3,6,1,8]=>1010010=>[1,1,1,2,1,1]
[2,4,5,7,6,3,8,1]=>[7,5,4,2,3,6,1,8]=>1110010=>[3,2,1,1]
[2,5,6,4,7,3,8,1]=>[7,4,3,5,2,6,1,8]=>1101010=>[2,1,1,1,1,1]
[2,4,6,5,7,3,8,1]=>[7,5,3,4,2,6,1,8]=>1101010=>[2,1,1,1,1,1]
[2,5,4,6,7,3,8,1]=>[7,4,5,3,2,6,1,8]=>1011010=>[1,1,2,1,1,1]
[2,4,5,6,7,3,8,1]=>[7,5,4,3,2,6,1,8]=>1111010=>[4,1,1,1]
[3,2,7,6,5,4,8,1]=>[6,7,2,3,4,5,1,8]=>0100010=>[1,1,3,1,1]
[3,2,6,7,5,4,8,1]=>[6,7,3,2,4,5,1,8]=>0110010=>[1,2,2,1,1]
[3,2,5,7,6,4,8,1]=>[6,7,4,2,3,5,1,8]=>0110010=>[1,2,2,1,1]
[3,2,6,5,7,4,8,1]=>[6,7,3,4,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,6,7,4,8,1]=>[6,7,4,3,2,5,1,8]=>0111010=>[1,3,1,1,1]
[2,3,7,6,5,4,8,1]=>[7,6,2,3,4,5,1,8]=>1100010=>[2,3,1,1]
[2,3,6,7,5,4,8,1]=>[7,6,3,2,4,5,1,8]=>1110010=>[3,2,1,1]
[2,3,5,7,6,4,8,1]=>[7,6,4,2,3,5,1,8]=>1110010=>[3,2,1,1]
[2,3,5,6,7,4,8,1]=>[7,6,4,3,2,5,1,8]=>1111010=>[4,1,1,1]
[4,3,2,7,6,5,8,1]=>[5,6,7,2,3,4,1,8]=>0010010=>[2,1,2,1,1]
[4,3,2,6,7,5,8,1]=>[5,6,7,3,2,4,1,8]=>0011010=>[2,2,1,1,1]
[3,4,2,6,7,5,8,1]=>[6,5,7,3,2,4,1,8]=>1011010=>[1,1,2,1,1,1]
[2,4,3,7,6,5,8,1]=>[7,5,6,2,3,4,1,8]=>1010010=>[1,1,1,2,1,1]
[3,2,4,7,6,5,8,1]=>[6,7,5,2,3,4,1,8]=>0110010=>[1,2,2,1,1]
[2,3,4,7,6,5,8,1]=>[7,6,5,2,3,4,1,8]=>1110010=>[3,2,1,1]
[2,3,4,6,7,5,8,1]=>[7,6,5,3,2,4,1,8]=>1111010=>[4,1,1,1]
[5,4,3,2,7,6,8,1]=>[4,5,6,7,2,3,1,8]=>0001010=>[3,1,1,1,1]
[4,5,3,2,7,6,8,1]=>[5,4,6,7,2,3,1,8]=>1001010=>[1,2,1,1,1,1]
[4,3,5,2,7,6,8,1]=>[5,6,4,7,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,4,5,2,7,6,8,1]=>[6,5,4,7,2,3,1,8]=>1101010=>[2,1,1,1,1,1]
[2,5,4,3,7,6,8,1]=>[7,4,5,6,2,3,1,8]=>1001010=>[1,2,1,1,1,1]
[2,4,5,3,7,6,8,1]=>[7,5,4,6,2,3,1,8]=>1101010=>[2,1,1,1,1,1]
[3,2,5,4,7,6,8,1]=>[6,7,4,5,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]
[2,3,5,4,7,6,8,1]=>[7,6,4,5,2,3,1,8]=>1101010=>[2,1,1,1,1,1]
[4,3,2,5,7,6,8,1]=>[5,6,7,4,2,3,1,8]=>0011010=>[2,2,1,1,1]
[2,4,3,5,7,6,8,1]=>[7,5,6,4,2,3,1,8]=>1011010=>[1,1,2,1,1,1]
[3,2,4,5,7,6,8,1]=>[6,7,5,4,2,3,1,8]=>0111010=>[1,3,1,1,1]
[2,3,4,5,7,6,8,1]=>[7,6,5,4,2,3,1,8]=>1111010=>[4,1,1,1]
[2,6,5,4,3,7,8,1]=>[7,3,4,5,6,2,1,8]=>1000110=>[1,3,2,1]
[2,5,4,6,3,7,8,1]=>[7,4,5,3,6,2,1,8]=>1010110=>[1,1,1,1,2,1]
[2,4,5,6,3,7,8,1]=>[7,5,4,3,6,2,1,8]=>1110110=>[3,1,2,1]
[3,2,5,6,4,7,8,1]=>[6,7,4,3,5,2,1,8]=>0110110=>[1,2,1,2,1]
[2,3,6,5,4,7,8,1]=>[7,6,3,4,5,2,1,8]=>1100110=>[2,2,2,1]
[2,3,5,6,4,7,8,1]=>[7,6,4,3,5,2,1,8]=>1110110=>[3,1,2,1]
[4,3,2,6,5,7,8,1]=>[5,6,7,3,4,2,1,8]=>0010110=>[2,1,1,2,1]
[3,4,2,6,5,7,8,1]=>[6,5,7,3,4,2,1,8]=>1010110=>[1,1,1,1,2,1]
[2,4,3,6,5,7,8,1]=>[7,5,6,3,4,2,1,8]=>1010110=>[1,1,1,1,2,1]
[3,2,4,6,5,7,8,1]=>[6,7,5,3,4,2,1,8]=>0110110=>[1,2,1,2,1]
[2,3,4,6,5,7,8,1]=>[7,6,5,3,4,2,1,8]=>1110110=>[3,1,2,1]
[2,5,4,3,6,7,8,1]=>[7,4,5,6,3,2,1,8]=>1001110=>[1,2,3,1]
[2,4,5,3,6,7,8,1]=>[7,5,4,6,3,2,1,8]=>1101110=>[2,1,3,1]
[3,2,5,4,6,7,8,1]=>[6,7,4,5,3,2,1,8]=>0101110=>[1,1,1,3,1]
[2,3,5,4,6,7,8,1]=>[7,6,4,5,3,2,1,8]=>1101110=>[2,1,3,1]
[2,4,3,5,6,7,8,1]=>[7,5,6,4,3,2,1,8]=>1011110=>[1,1,4,1]
[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>1000000=>[1,6]
[1,7,8,6,5,4,3,2]=>[8,2,1,3,4,5,6,7]=>1100000=>[2,5]
[1,6,8,7,5,4,3,2]=>[8,3,1,2,4,5,6,7]=>1100000=>[2,5]
[1,7,6,8,5,4,3,2]=>[8,2,3,1,4,5,6,7]=>1010000=>[1,1,1,4]
[1,6,7,8,5,4,3,2]=>[8,3,2,1,4,5,6,7]=>1110000=>[3,4]
[1,5,8,7,6,4,3,2]=>[8,4,1,2,3,5,6,7]=>1100000=>[2,5]
[1,5,7,8,6,4,3,2]=>[8,4,2,1,3,5,6,7]=>1110000=>[3,4]
[1,6,5,8,7,4,3,2]=>[8,3,4,1,2,5,6,7]=>1010000=>[1,1,1,4]
[1,7,6,5,8,4,3,2]=>[8,2,3,4,1,5,6,7]=>1001000=>[1,2,1,3]
[1,5,7,6,8,4,3,2]=>[8,4,2,3,1,5,6,7]=>1101000=>[2,1,1,3]
[1,6,5,7,8,4,3,2]=>[8,3,4,2,1,5,6,7]=>1011000=>[1,1,2,3]
[1,5,6,7,8,4,3,2]=>[8,4,3,2,1,5,6,7]=>1111000=>[4,3]
[1,4,8,7,6,5,3,2]=>[8,5,1,2,3,4,6,7]=>1100000=>[2,5]
[1,4,7,8,6,5,3,2]=>[8,5,2,1,3,4,6,7]=>1110000=>[3,4]
[1,4,6,8,7,5,3,2]=>[8,5,3,1,2,4,6,7]=>1110000=>[3,4]
[1,4,6,7,8,5,3,2]=>[8,5,3,2,1,4,6,7]=>1111000=>[4,3]
[1,5,4,8,7,6,3,2]=>[8,4,5,1,2,3,6,7]=>1010000=>[1,1,1,4]
[1,4,5,8,7,6,3,2]=>[8,5,4,1,2,3,6,7]=>1110000=>[3,4]
[1,4,5,7,8,6,3,2]=>[8,5,4,2,1,3,6,7]=>1111000=>[4,3]
[1,6,5,4,8,7,3,2]=>[8,3,4,5,1,2,6,7]=>1001000=>[1,2,1,3]
[1,4,6,5,8,7,3,2]=>[8,5,3,4,1,2,6,7]=>1101000=>[2,1,1,3]
[1,7,6,5,4,8,3,2]=>[8,2,3,4,5,1,6,7]=>1000100=>[1,3,1,2]
[1,5,7,6,4,8,3,2]=>[8,4,2,3,5,1,6,7]=>1100100=>[2,2,1,2]
[1,4,7,6,5,8,3,2]=>[8,5,2,3,4,1,6,7]=>1100100=>[2,2,1,2]
[1,5,4,7,6,8,3,2]=>[8,4,5,2,3,1,6,7]=>1010100=>[1,1,1,1,1,2]
[1,6,5,4,7,8,3,2]=>[8,3,4,5,2,1,6,7]=>1001100=>[1,2,2,2]
[1,5,6,4,7,8,3,2]=>[8,4,3,5,2,1,6,7]=>1101100=>[2,1,2,2]
[1,5,4,6,7,8,3,2]=>[8,4,5,3,2,1,6,7]=>1011100=>[1,1,3,2]
[1,4,5,6,7,8,3,2]=>[8,5,4,3,2,1,6,7]=>1111100=>[5,2]
[1,3,8,7,6,5,4,2]=>[8,6,1,2,3,4,5,7]=>1100000=>[2,5]
[1,3,5,8,7,6,4,2]=>[8,6,4,1,2,3,5,7]=>1110000=>[3,4]
[1,3,5,7,8,6,4,2]=>[8,6,4,2,1,3,5,7]=>1111000=>[4,3]
[1,3,6,5,8,7,4,2]=>[8,6,3,4,1,2,5,7]=>1101000=>[2,1,1,3]
[1,3,5,6,8,7,4,2]=>[8,6,4,3,1,2,5,7]=>1111000=>[4,3]
[1,3,7,6,5,8,4,2]=>[8,6,2,3,4,1,5,7]=>1100100=>[2,2,1,2]
[1,3,6,7,5,8,4,2]=>[8,6,3,2,4,1,5,7]=>1110100=>[3,1,1,2]
[1,3,5,7,6,8,4,2]=>[8,6,4,2,3,1,5,7]=>1110100=>[3,1,1,2]
[1,3,6,5,7,8,4,2]=>[8,6,3,4,2,1,5,7]=>1101100=>[2,1,2,2]
[1,3,5,6,7,8,4,2]=>[8,6,4,3,2,1,5,7]=>1111100=>[5,2]
[1,4,3,8,7,6,5,2]=>[8,5,6,1,2,3,4,7]=>1010000=>[1,1,1,4]
[1,4,3,7,8,6,5,2]=>[8,5,6,2,1,3,4,7]=>1011000=>[1,1,2,3]
[1,4,3,6,8,7,5,2]=>[8,5,6,3,1,2,4,7]=>1011000=>[1,1,2,3]
[1,4,3,7,6,8,5,2]=>[8,5,6,2,3,1,4,7]=>1010100=>[1,1,1,1,1,2]
[1,4,3,6,7,8,5,2]=>[8,5,6,3,2,1,4,7]=>1011100=>[1,1,3,2]
[1,3,4,8,7,6,5,2]=>[8,6,5,1,2,3,4,7]=>1110000=>[3,4]
[1,3,4,7,8,6,5,2]=>[8,6,5,2,1,3,4,7]=>1111000=>[4,3]
[1,3,4,7,6,8,5,2]=>[8,6,5,2,3,1,4,7]=>1110100=>[3,1,1,2]
[1,3,4,6,7,8,5,2]=>[8,6,5,3,2,1,4,7]=>1111100=>[5,2]
[1,5,4,3,8,7,6,2]=>[8,4,5,6,1,2,3,7]=>1001000=>[1,2,1,3]
[1,5,4,3,7,8,6,2]=>[8,4,5,6,2,1,3,7]=>1001100=>[1,2,2,2]
[1,3,5,4,8,7,6,2]=>[8,6,4,5,1,2,3,7]=>1101000=>[2,1,1,3]
[1,3,5,4,7,8,6,2]=>[8,6,4,5,2,1,3,7]=>1101100=>[2,1,2,2]
[1,4,3,5,8,7,6,2]=>[8,5,6,4,1,2,3,7]=>1011000=>[1,1,2,3]
[1,4,3,5,7,8,6,2]=>[8,5,6,4,2,1,3,7]=>1011100=>[1,1,3,2]
[1,3,4,5,8,7,6,2]=>[8,6,5,4,1,2,3,7]=>1111000=>[4,3]
[1,3,4,5,7,8,6,2]=>[8,6,5,4,2,1,3,7]=>1111100=>[5,2]
[1,6,5,4,3,8,7,2]=>[8,3,4,5,6,1,2,7]=>1000100=>[1,3,1,2]
[1,5,6,4,3,8,7,2]=>[8,4,3,5,6,1,2,7]=>1100100=>[2,2,1,2]
[1,4,6,5,3,8,7,2]=>[8,5,3,4,6,1,2,7]=>1100100=>[2,2,1,2]
[1,5,4,6,3,8,7,2]=>[8,4,5,3,6,1,2,7]=>1010100=>[1,1,1,1,1,2]
[1,4,5,6,3,8,7,2]=>[8,5,4,3,6,1,2,7]=>1110100=>[3,1,1,2]
[1,3,6,5,4,8,7,2]=>[8,6,3,4,5,1,2,7]=>1100100=>[2,2,1,2]
[1,4,3,6,5,8,7,2]=>[8,5,6,3,4,1,2,7]=>1010100=>[1,1,1,1,1,2]
[1,3,4,6,5,8,7,2]=>[8,6,5,3,4,1,2,7]=>1110100=>[3,1,1,2]
[1,3,5,4,6,8,7,2]=>[8,6,4,5,3,1,2,7]=>1101100=>[2,1,2,2]
[1,3,4,5,6,8,7,2]=>[8,6,5,4,3,1,2,7]=>1111100=>[5,2]
[1,7,6,5,4,3,8,2]=>[8,2,3,4,5,6,1,7]=>1000010=>[1,4,1,1]
[1,6,7,5,4,3,8,2]=>[8,3,2,4,5,6,1,7]=>1100010=>[2,3,1,1]
[1,6,5,7,4,3,8,2]=>[8,3,4,2,5,6,1,7]=>1010010=>[1,1,1,2,1,1]
[1,4,7,6,5,3,8,2]=>[8,5,2,3,4,6,1,7]=>1100010=>[2,3,1,1]
[1,4,6,7,5,3,8,2]=>[8,5,3,2,4,6,1,7]=>1110010=>[3,2,1,1]
[1,5,4,7,6,3,8,2]=>[8,4,5,2,3,6,1,7]=>1010010=>[1,1,1,2,1,1]
[1,4,5,7,6,3,8,2]=>[8,5,4,2,3,6,1,7]=>1110010=>[3,2,1,1]
[1,5,6,4,7,3,8,2]=>[8,4,3,5,2,6,1,7]=>1101010=>[2,1,1,1,1,1]
[1,4,5,6,7,3,8,2]=>[8,5,4,3,2,6,1,7]=>1111010=>[4,1,1,1]
[1,3,6,7,5,4,8,2]=>[8,6,3,2,4,5,1,7]=>1110010=>[3,2,1,1]
[1,3,5,7,6,4,8,2]=>[8,6,4,2,3,5,1,7]=>1110010=>[3,2,1,1]
[1,3,5,6,7,4,8,2]=>[8,6,4,3,2,5,1,7]=>1111010=>[4,1,1,1]
[1,4,3,7,6,5,8,2]=>[8,5,6,2,3,4,1,7]=>1010010=>[1,1,1,2,1,1]
[1,3,4,7,6,5,8,2]=>[8,6,5,2,3,4,1,7]=>1110010=>[3,2,1,1]
[1,3,4,6,7,5,8,2]=>[8,6,5,3,2,4,1,7]=>1111010=>[4,1,1,1]
[1,5,4,3,7,6,8,2]=>[8,4,5,6,2,3,1,7]=>1001010=>[1,2,1,1,1,1]
[1,3,5,4,7,6,8,2]=>[8,6,4,5,2,3,1,7]=>1101010=>[2,1,1,1,1,1]
[1,4,3,5,7,6,8,2]=>[8,5,6,4,2,3,1,7]=>1011010=>[1,1,2,1,1,1]
[1,3,4,5,7,6,8,2]=>[8,6,5,4,2,3,1,7]=>1111010=>[4,1,1,1]
[1,6,5,4,3,7,8,2]=>[8,3,4,5,6,2,1,7]=>1000110=>[1,3,2,1]
[1,5,6,4,3,7,8,2]=>[8,4,3,5,6,2,1,7]=>1100110=>[2,2,2,1]
[1,5,4,6,3,7,8,2]=>[8,4,5,3,6,2,1,7]=>1010110=>[1,1,1,1,2,1]
[1,3,5,6,4,7,8,2]=>[8,6,4,3,5,2,1,7]=>1110110=>[3,1,2,1]
[1,4,3,6,5,7,8,2]=>[8,5,6,3,4,2,1,7]=>1010110=>[1,1,1,1,2,1]
[1,3,4,6,5,7,8,2]=>[8,6,5,3,4,2,1,7]=>1110110=>[3,1,2,1]
[1,5,4,3,6,7,8,2]=>[8,4,5,6,3,2,1,7]=>1001110=>[1,2,3,1]
[1,4,5,3,6,7,8,2]=>[8,5,4,6,3,2,1,7]=>1101110=>[2,1,3,1]
[1,3,5,4,6,7,8,2]=>[8,6,4,5,3,2,1,7]=>1101110=>[2,1,3,1]
[1,4,3,5,6,7,8,2]=>[8,5,6,4,3,2,1,7]=>1011110=>[1,1,4,1]
[1,3,4,5,6,7,8,2]=>[8,6,5,4,3,2,1,7]=>1111110=>[6,1]
[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>0100000=>[1,1,5]
[2,1,7,8,6,5,4,3]=>[7,8,2,1,3,4,5,6]=>0110000=>[1,2,4]
[2,1,6,8,7,5,4,3]=>[7,8,3,1,2,4,5,6]=>0110000=>[1,2,4]
[2,1,7,6,8,5,4,3]=>[7,8,2,3,1,4,5,6]=>0101000=>[1,1,1,1,3]
[2,1,6,7,8,5,4,3]=>[7,8,3,2,1,4,5,6]=>0111000=>[1,3,3]
[2,1,5,8,7,6,4,3]=>[7,8,4,1,2,3,5,6]=>0110000=>[1,2,4]
[2,1,5,7,8,6,4,3]=>[7,8,4,2,1,3,5,6]=>0111000=>[1,3,3]
[2,1,6,5,8,7,4,3]=>[7,8,3,4,1,2,5,6]=>0101000=>[1,1,1,1,3]
[2,1,5,6,8,7,4,3]=>[7,8,4,3,1,2,5,6]=>0111000=>[1,3,3]
[2,1,7,6,5,8,4,3]=>[7,8,2,3,4,1,5,6]=>0100100=>[1,1,2,1,2]
[2,1,6,7,5,8,4,3]=>[7,8,3,2,4,1,5,6]=>0110100=>[1,2,1,1,2]
[2,1,5,7,6,8,4,3]=>[7,8,4,2,3,1,5,6]=>0110100=>[1,2,1,1,2]
[2,1,6,5,7,8,4,3]=>[7,8,3,4,2,1,5,6]=>0101100=>[1,1,1,2,2]
[2,1,5,6,7,8,4,3]=>[7,8,4,3,2,1,5,6]=>0111100=>[1,4,2]
[2,1,4,8,7,6,5,3]=>[7,8,5,1,2,3,4,6]=>0110000=>[1,2,4]
[2,1,4,7,8,6,5,3]=>[7,8,5,2,1,3,4,6]=>0111000=>[1,3,3]
[2,1,4,6,8,7,5,3]=>[7,8,5,3,1,2,4,6]=>0111000=>[1,3,3]
[2,1,4,6,7,8,5,3]=>[7,8,5,3,2,1,4,6]=>0111100=>[1,4,2]
[2,1,5,4,8,7,6,3]=>[7,8,4,5,1,2,3,6]=>0101000=>[1,1,1,1,3]
[2,1,4,5,8,7,6,3]=>[7,8,5,4,1,2,3,6]=>0111000=>[1,3,3]
[2,1,4,5,7,8,6,3]=>[7,8,5,4,2,1,3,6]=>0111100=>[1,4,2]
[2,1,6,5,4,8,7,3]=>[7,8,3,4,5,1,2,6]=>0100100=>[1,1,2,1,2]
[2,1,4,6,5,8,7,3]=>[7,8,5,3,4,1,2,6]=>0110100=>[1,2,1,1,2]
[2,1,4,5,6,8,7,3]=>[7,8,5,4,3,1,2,6]=>0111100=>[1,4,2]
[2,1,7,6,5,4,8,3]=>[7,8,2,3,4,5,1,6]=>0100010=>[1,1,3,1,1]
[2,1,6,5,7,4,8,3]=>[7,8,3,4,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,6,7,4,8,3]=>[7,8,4,3,2,5,1,6]=>0111010=>[1,3,1,1,1]
[2,1,4,7,6,5,8,3]=>[7,8,5,2,3,4,1,6]=>0110010=>[1,2,2,1,1]
[2,1,5,4,7,6,8,3]=>[7,8,4,5,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,5,4,7,8,3]=>[7,8,3,4,5,2,1,6]=>0100110=>[1,1,2,2,1]
[2,1,5,4,6,7,8,3]=>[7,8,4,5,3,2,1,6]=>0101110=>[1,1,1,3,1]
[2,1,4,5,6,7,8,3]=>[7,8,5,4,3,2,1,6]=>0111110=>[1,5,1]
[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>1100000=>[2,5]
[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>1110000=>[3,4]
[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>1101000=>[2,1,1,3]
[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>1111000=>[4,3]
[1,2,5,8,7,6,4,3]=>[8,7,4,1,2,3,5,6]=>1110000=>[3,4]
[1,2,5,7,8,6,4,3]=>[8,7,4,2,1,3,5,6]=>1111000=>[4,3]
[1,2,6,5,8,7,4,3]=>[8,7,3,4,1,2,5,6]=>1101000=>[2,1,1,3]
[1,2,7,6,5,8,4,3]=>[8,7,2,3,4,1,5,6]=>1100100=>[2,2,1,2]
[1,2,6,7,5,8,4,3]=>[8,7,3,2,4,1,5,6]=>1110100=>[3,1,1,2]
[1,2,6,5,7,8,4,3]=>[8,7,3,4,2,1,5,6]=>1101100=>[2,1,2,2]
[1,2,5,6,7,8,4,3]=>[8,7,4,3,2,1,5,6]=>1111100=>[5,2]
[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>1110000=>[3,4]
[1,2,4,7,8,6,5,3]=>[8,7,5,2,1,3,4,6]=>1111000=>[4,3]
[1,2,4,6,8,7,5,3]=>[8,7,5,3,1,2,4,6]=>1111000=>[4,3]
[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>1110100=>[3,1,1,2]
[1,2,4,6,7,8,5,3]=>[8,7,5,3,2,1,4,6]=>1111100=>[5,2]
[1,2,5,4,8,7,6,3]=>[8,7,4,5,1,2,3,6]=>1101000=>[2,1,1,3]
[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>1111000=>[4,3]
[1,2,6,5,4,8,7,3]=>[8,7,3,4,5,1,2,6]=>1100100=>[2,2,1,2]
[1,2,4,6,5,8,7,3]=>[8,7,5,3,4,1,2,6]=>1110100=>[3,1,1,2]
[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>1111100=>[5,2]
[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>1100010=>[2,3,1,1]
[1,2,6,5,7,4,8,3]=>[8,7,3,4,2,5,1,6]=>1101010=>[2,1,1,1,1,1]
[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>1111010=>[4,1,1,1]
[1,2,4,6,7,5,8,3]=>[8,7,5,3,2,4,1,6]=>1111010=>[4,1,1,1]
[1,2,5,4,7,6,8,3]=>[8,7,4,5,2,3,1,6]=>1101010=>[2,1,1,1,1,1]
[1,2,6,5,4,7,8,3]=>[8,7,3,4,5,2,1,6]=>1100110=>[2,2,2,1]
[1,2,5,6,4,7,8,3]=>[8,7,4,3,5,2,1,6]=>1110110=>[3,1,2,1]
[1,2,4,6,5,7,8,3]=>[8,7,5,3,4,2,1,6]=>1110110=>[3,1,2,1]
[1,2,5,4,6,7,8,3]=>[8,7,4,5,3,2,1,6]=>1101110=>[2,1,3,1]
[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>1111110=>[6,1]
[3,2,1,8,7,6,5,4]=>[6,7,8,1,2,3,4,5]=>0010000=>[2,1,4]
[3,2,1,7,8,6,5,4]=>[6,7,8,2,1,3,4,5]=>0011000=>[2,2,3]
[3,2,1,6,8,7,5,4]=>[6,7,8,3,1,2,4,5]=>0011000=>[2,2,3]
[3,2,1,7,6,8,5,4]=>[6,7,8,2,3,1,4,5]=>0010100=>[2,1,1,1,2]
[3,2,1,6,7,8,5,4]=>[6,7,8,3,2,1,4,5]=>0011100=>[2,3,2]
[3,2,1,5,8,7,6,4]=>[6,7,8,4,1,2,3,5]=>0011000=>[2,2,3]
[3,2,1,5,7,8,6,4]=>[6,7,8,4,2,1,3,5]=>0011100=>[2,3,2]
[3,2,1,6,5,8,7,4]=>[6,7,8,3,4,1,2,5]=>0010100=>[2,1,1,1,2]
[3,2,1,5,6,8,7,4]=>[6,7,8,4,3,1,2,5]=>0011100=>[2,3,2]
[3,2,1,7,6,5,8,4]=>[6,7,8,2,3,4,1,5]=>0010010=>[2,1,2,1,1]
[3,2,1,6,7,5,8,4]=>[6,7,8,3,2,4,1,5]=>0011010=>[2,2,1,1,1]
[3,2,1,5,7,6,8,4]=>[6,7,8,4,2,3,1,5]=>0011010=>[2,2,1,1,1]
[3,2,1,6,5,7,8,4]=>[6,7,8,3,4,2,1,5]=>0010110=>[2,1,1,2,1]
[3,2,1,5,6,7,8,4]=>[6,7,8,4,3,2,1,5]=>0011110=>[2,4,1]
[2,3,1,8,7,6,5,4]=>[7,6,8,1,2,3,4,5]=>1010000=>[1,1,1,4]
[2,3,1,6,8,7,5,4]=>[7,6,8,3,1,2,4,5]=>1011000=>[1,1,2,3]
[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,1,4,5]=>1010100=>[1,1,1,1,1,2]
[2,3,1,6,7,8,5,4]=>[7,6,8,3,2,1,4,5]=>1011100=>[1,1,3,2]
[2,3,1,5,8,7,6,4]=>[7,6,8,4,1,2,3,5]=>1011000=>[1,1,2,3]
[2,3,1,7,6,5,8,4]=>[7,6,8,2,3,4,1,5]=>1010010=>[1,1,1,2,1,1]
[2,3,1,5,7,6,8,4]=>[7,6,8,4,2,3,1,5]=>1011010=>[1,1,2,1,1,1]
[2,3,1,5,6,7,8,4]=>[7,6,8,4,3,2,1,5]=>1011110=>[1,1,4,1]
[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>1010000=>[1,1,1,4]
[1,3,2,7,8,6,5,4]=>[8,6,7,2,1,3,4,5]=>1011000=>[1,1,2,3]
[1,3,2,6,8,7,5,4]=>[8,6,7,3,1,2,4,5]=>1011000=>[1,1,2,3]
[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>1010100=>[1,1,1,1,1,2]
[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>1011100=>[1,1,3,2]
[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>1011100=>[1,1,3,2]
[1,3,2,6,5,8,7,4]=>[8,6,7,3,4,1,2,5]=>1010100=>[1,1,1,1,1,2]
[1,3,2,7,6,5,8,4]=>[8,6,7,2,3,4,1,5]=>1010010=>[1,1,1,2,1,1]
[1,3,2,6,7,5,8,4]=>[8,6,7,3,2,4,1,5]=>1011010=>[1,1,2,1,1,1]
[1,3,2,5,7,6,8,4]=>[8,6,7,4,2,3,1,5]=>1011010=>[1,1,2,1,1,1]
[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>1011110=>[1,1,4,1]
[2,1,3,8,7,6,5,4]=>[7,8,6,1,2,3,4,5]=>0110000=>[1,2,4]
[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,4,5]=>0111000=>[1,3,3]
[2,1,3,6,8,7,5,4]=>[7,8,6,3,1,2,4,5]=>0111000=>[1,3,3]
[2,1,3,7,6,8,5,4]=>[7,8,6,2,3,1,4,5]=>0110100=>[1,2,1,1,2]
[2,1,3,6,7,8,5,4]=>[7,8,6,3,2,1,4,5]=>0111100=>[1,4,2]
[2,1,3,5,8,7,6,4]=>[7,8,6,4,1,2,3,5]=>0111000=>[1,3,3]
[2,1,3,5,7,8,6,4]=>[7,8,6,4,2,1,3,5]=>0111100=>[1,4,2]
[2,1,3,6,5,8,7,4]=>[7,8,6,3,4,1,2,5]=>0110100=>[1,2,1,1,2]
[2,1,3,6,5,7,8,4]=>[7,8,6,3,4,2,1,5]=>0110110=>[1,2,1,2,1]
[2,1,3,5,6,7,8,4]=>[7,8,6,4,3,2,1,5]=>0111110=>[1,5,1]
[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>1110000=>[3,4]
[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>1111000=>[4,3]
[1,2,3,6,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>1111000=>[4,3]
[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>1110100=>[3,1,1,2]
[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>1111100=>[5,2]
[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>1111000=>[4,3]
[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>1111100=>[5,2]
[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>1110100=>[3,1,1,2]
[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>1111100=>[5,2]
[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>1110010=>[3,2,1,1]
[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>1111010=>[4,1,1,1]
[1,2,3,5,7,6,8,4]=>[8,7,6,4,2,3,1,5]=>1111010=>[4,1,1,1]
[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>1110110=>[3,1,2,1]
[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>1111110=>[6,1]
[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>0001000=>[3,1,3]
[4,3,2,1,7,8,6,5]=>[5,6,7,8,2,1,3,4]=>0001100=>[3,2,2]
[4,3,2,1,6,8,7,5]=>[5,6,7,8,3,1,2,4]=>0001100=>[3,2,2]
[4,3,2,1,7,6,8,5]=>[5,6,7,8,2,3,1,4]=>0001010=>[3,1,1,1,1]
[4,3,2,1,6,7,8,5]=>[5,6,7,8,3,2,1,4]=>0001110=>[3,3,1]
[3,4,2,1,8,7,6,5]=>[6,5,7,8,1,2,3,4]=>1001000=>[1,2,1,3]
[3,4,2,1,7,8,6,5]=>[6,5,7,8,2,1,3,4]=>1001100=>[1,2,2,2]
[3,4,2,1,6,8,7,5]=>[6,5,7,8,3,1,2,4]=>1001100=>[1,2,2,2]
[3,4,2,1,7,6,8,5]=>[6,5,7,8,2,3,1,4]=>1001010=>[1,2,1,1,1,1]
[3,4,2,1,6,7,8,5]=>[6,5,7,8,3,2,1,4]=>1001110=>[1,2,3,1]
[2,4,3,1,8,7,6,5]=>[7,5,6,8,1,2,3,4]=>1001000=>[1,2,1,3]
[2,4,3,1,7,8,6,5]=>[7,5,6,8,2,1,3,4]=>1001100=>[1,2,2,2]
[2,4,3,1,6,8,7,5]=>[7,5,6,8,3,1,2,4]=>1001100=>[1,2,2,2]
[2,4,3,1,7,6,8,5]=>[7,5,6,8,2,3,1,4]=>1001010=>[1,2,1,1,1,1]
[2,4,3,1,6,7,8,5]=>[7,5,6,8,3,2,1,4]=>1001110=>[1,2,3,1]
[3,2,4,1,8,7,6,5]=>[6,7,5,8,1,2,3,4]=>0101000=>[1,1,1,1,3]
[3,2,4,1,7,8,6,5]=>[6,7,5,8,2,1,3,4]=>0101100=>[1,1,1,2,2]
[3,2,4,1,6,8,7,5]=>[6,7,5,8,3,1,2,4]=>0101100=>[1,1,1,2,2]
[3,2,4,1,7,6,8,5]=>[6,7,5,8,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,4,1,6,7,8,5]=>[6,7,5,8,3,2,1,4]=>0101110=>[1,1,1,3,1]
[2,3,4,1,8,7,6,5]=>[7,6,5,8,1,2,3,4]=>1101000=>[2,1,1,3]
[2,3,4,1,7,8,6,5]=>[7,6,5,8,2,1,3,4]=>1101100=>[2,1,2,2]
[2,3,4,1,6,8,7,5]=>[7,6,5,8,3,1,2,4]=>1101100=>[2,1,2,2]
[2,3,4,1,7,6,8,5]=>[7,6,5,8,2,3,1,4]=>1101010=>[2,1,1,1,1,1]
[2,3,4,1,6,7,8,5]=>[7,6,5,8,3,2,1,4]=>1101110=>[2,1,3,1]
[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>1001000=>[1,2,1,3]
[1,4,3,2,7,8,6,5]=>[8,5,6,7,2,1,3,4]=>1001100=>[1,2,2,2]
[1,4,3,2,7,6,8,5]=>[8,5,6,7,2,3,1,4]=>1001010=>[1,2,1,1,1,1]
[1,4,3,2,6,7,8,5]=>[8,5,6,7,3,2,1,4]=>1001110=>[1,2,3,1]
[1,3,4,2,8,7,6,5]=>[8,6,5,7,1,2,3,4]=>1101000=>[2,1,1,3]
[1,3,4,2,7,8,6,5]=>[8,6,5,7,2,1,3,4]=>1101100=>[2,1,2,2]
[1,3,4,2,7,6,8,5]=>[8,6,5,7,2,3,1,4]=>1101010=>[2,1,1,1,1,1]
[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>1101110=>[2,1,3,1]
[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>0101000=>[1,1,1,1,3]
[2,1,4,3,7,8,6,5]=>[7,8,5,6,2,1,3,4]=>0101100=>[1,1,1,2,2]
[2,1,4,3,6,8,7,5]=>[7,8,5,6,3,1,2,4]=>0101100=>[1,1,1,2,2]
[2,1,4,3,7,6,8,5]=>[7,8,5,6,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,4,3,6,7,8,5]=>[7,8,5,6,3,2,1,4]=>0101110=>[1,1,1,3,1]
[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>1101000=>[2,1,1,3]
[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>1101100=>[2,1,2,2]
[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>1101100=>[2,1,2,2]
[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>1101010=>[2,1,1,1,1,1]
[1,2,4,3,6,7,8,5]=>[8,7,5,6,3,2,1,4]=>1101110=>[2,1,3,1]
[3,2,1,4,8,7,6,5]=>[6,7,8,5,1,2,3,4]=>0011000=>[2,2,3]
[3,2,1,4,7,8,6,5]=>[6,7,8,5,2,1,3,4]=>0011100=>[2,3,2]
[3,2,1,4,7,6,8,5]=>[6,7,8,5,2,3,1,4]=>0011010=>[2,2,1,1,1]
[3,2,1,4,6,7,8,5]=>[6,7,8,5,3,2,1,4]=>0011110=>[2,4,1]
[2,3,1,4,8,7,6,5]=>[7,6,8,5,1,2,3,4]=>1011000=>[1,1,2,3]
[2,3,1,4,7,8,6,5]=>[7,6,8,5,2,1,3,4]=>1011100=>[1,1,3,2]
[2,3,1,4,6,8,7,5]=>[7,6,8,5,3,1,2,4]=>1011100=>[1,1,3,2]
[2,3,1,4,7,6,8,5]=>[7,6,8,5,2,3,1,4]=>1011010=>[1,1,2,1,1,1]
[2,3,1,4,6,7,8,5]=>[7,6,8,5,3,2,1,4]=>1011110=>[1,1,4,1]
[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>1011000=>[1,1,2,3]
[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>1011100=>[1,1,3,2]
[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>1011010=>[1,1,2,1,1,1]
[1,3,2,4,6,7,8,5]=>[8,6,7,5,3,2,1,4]=>1011110=>[1,1,4,1]
[2,1,3,4,8,7,6,5]=>[7,8,6,5,1,2,3,4]=>0111000=>[1,3,3]
[2,1,3,4,7,8,6,5]=>[7,8,6,5,2,1,3,4]=>0111100=>[1,4,2]
[2,1,3,4,6,8,7,5]=>[7,8,6,5,3,1,2,4]=>0111100=>[1,4,2]
[2,1,3,4,7,6,8,5]=>[7,8,6,5,2,3,1,4]=>0111010=>[1,3,1,1,1]
[2,1,3,4,6,7,8,5]=>[7,8,6,5,3,2,1,4]=>0111110=>[1,5,1]
[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>1111000=>[4,3]
[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>1111100=>[5,2]
[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>1111100=>[5,2]
[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>1111010=>[4,1,1,1]
[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>1111110=>[6,1]
[5,4,3,2,1,8,7,6]=>[4,5,6,7,8,1,2,3]=>0000100=>[4,1,2]
[5,4,3,2,1,7,8,6]=>[4,5,6,7,8,2,1,3]=>0000110=>[4,2,1]
[4,5,3,2,1,8,7,6]=>[5,4,6,7,8,1,2,3]=>1000100=>[1,3,1,2]
[4,5,3,2,1,7,8,6]=>[5,4,6,7,8,2,1,3]=>1000110=>[1,3,2,1]
[3,5,4,2,1,8,7,6]=>[6,4,5,7,8,1,2,3]=>1000100=>[1,3,1,2]
[4,3,5,2,1,8,7,6]=>[5,6,4,7,8,1,2,3]=>0100100=>[1,1,2,1,2]
[3,4,5,2,1,8,7,6]=>[6,5,4,7,8,1,2,3]=>1100100=>[2,2,1,2]
[2,5,4,3,1,8,7,6]=>[7,4,5,6,8,1,2,3]=>1000100=>[1,3,1,2]
[2,5,4,3,1,7,8,6]=>[7,4,5,6,8,2,1,3]=>1000110=>[1,3,2,1]
[2,4,5,3,1,8,7,6]=>[7,5,4,6,8,1,2,3]=>1100100=>[2,2,1,2]
[3,2,5,4,1,8,7,6]=>[6,7,4,5,8,1,2,3]=>0100100=>[1,1,2,1,2]
[2,3,5,4,1,8,7,6]=>[7,6,4,5,8,1,2,3]=>1100100=>[2,2,1,2]
[2,3,5,4,1,7,8,6]=>[7,6,4,5,8,2,1,3]=>1100110=>[2,2,2,1]
[4,3,2,5,1,8,7,6]=>[5,6,7,4,8,1,2,3]=>0010100=>[2,1,1,1,2]
[4,3,2,5,1,7,8,6]=>[5,6,7,4,8,2,1,3]=>0010110=>[2,1,1,2,1]
[3,4,2,5,1,8,7,6]=>[6,5,7,4,8,1,2,3]=>1010100=>[1,1,1,1,1,2]
[3,4,2,5,1,7,8,6]=>[6,5,7,4,8,2,1,3]=>1010110=>[1,1,1,1,2,1]
[2,4,3,5,1,8,7,6]=>[7,5,6,4,8,1,2,3]=>1010100=>[1,1,1,1,1,2]
[2,4,3,5,1,7,8,6]=>[7,5,6,4,8,2,1,3]=>1010110=>[1,1,1,1,2,1]
[3,2,4,5,1,8,7,6]=>[6,7,5,4,8,1,2,3]=>0110100=>[1,2,1,1,2]
[3,2,4,5,1,7,8,6]=>[6,7,5,4,8,2,1,3]=>0110110=>[1,2,1,2,1]
[2,3,4,5,1,8,7,6]=>[7,6,5,4,8,1,2,3]=>1110100=>[3,1,1,2]
[2,3,4,5,1,7,8,6]=>[7,6,5,4,8,2,1,3]=>1110110=>[3,1,2,1]
[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>1000100=>[1,3,1,2]
[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>1000110=>[1,3,2,1]
[1,4,5,3,2,8,7,6]=>[8,5,4,6,7,1,2,3]=>1100100=>[2,2,1,2]
[1,3,5,4,2,8,7,6]=>[8,6,4,5,7,1,2,3]=>1100100=>[2,2,1,2]
[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>1100110=>[2,2,2,1]
[1,4,3,5,2,8,7,6]=>[8,5,6,4,7,1,2,3]=>1010100=>[1,1,1,1,1,2]
[1,3,4,5,2,7,8,6]=>[8,6,5,4,7,2,1,3]=>1110110=>[3,1,2,1]
[2,1,5,4,3,8,7,6]=>[7,8,4,5,6,1,2,3]=>0100100=>[1,1,2,1,2]
[2,1,4,5,3,8,7,6]=>[7,8,5,4,6,1,2,3]=>0110100=>[1,2,1,1,2]
[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>1100100=>[2,2,1,2]
[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>1100110=>[2,2,2,1]
[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>1110100=>[3,1,1,2]
[3,2,1,5,4,8,7,6]=>[6,7,8,4,5,1,2,3]=>0010100=>[2,1,1,1,2]
[2,3,1,5,4,7,8,6]=>[7,6,8,4,5,2,1,3]=>1010110=>[1,1,1,1,2,1]
[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>1010100=>[1,1,1,1,1,2]
[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>1010110=>[1,1,1,1,2,1]
[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>1110100=>[3,1,1,2]
[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>1110110=>[3,1,2,1]
[4,3,2,1,5,8,7,6]=>[5,6,7,8,4,1,2,3]=>0001100=>[3,2,2]
[4,3,2,1,5,7,8,6]=>[5,6,7,8,4,2,1,3]=>0001110=>[3,3,1]
[3,4,2,1,5,8,7,6]=>[6,5,7,8,4,1,2,3]=>1001100=>[1,2,2,2]
[3,4,2,1,5,7,8,6]=>[6,5,7,8,4,2,1,3]=>1001110=>[1,2,3,1]
[2,4,3,1,5,8,7,6]=>[7,5,6,8,4,1,2,3]=>1001100=>[1,2,2,2]
[2,4,3,1,5,7,8,6]=>[7,5,6,8,4,2,1,3]=>1001110=>[1,2,3,1]
[3,2,4,1,5,8,7,6]=>[6,7,5,8,4,1,2,3]=>0101100=>[1,1,1,2,2]
[3,2,4,1,5,7,8,6]=>[6,7,5,8,4,2,1,3]=>0101110=>[1,1,1,3,1]
[2,3,4,1,5,8,7,6]=>[7,6,5,8,4,1,2,3]=>1101100=>[2,1,2,2]
[2,3,4,1,5,7,8,6]=>[7,6,5,8,4,2,1,3]=>1101110=>[2,1,3,1]
[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>1001100=>[1,2,2,2]
[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>1101100=>[2,1,2,2]
[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>1101110=>[2,1,3,1]
[2,1,4,3,5,8,7,6]=>[7,8,5,6,4,1,2,3]=>0101100=>[1,1,1,2,2]
[2,1,4,3,5,7,8,6]=>[7,8,5,6,4,2,1,3]=>0101110=>[1,1,1,3,1]
[1,2,4,3,5,7,8,6]=>[8,7,5,6,4,2,1,3]=>1101110=>[2,1,3,1]
[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>0011100=>[2,3,2]
[3,2,1,4,5,7,8,6]=>[6,7,8,5,4,2,1,3]=>0011110=>[2,4,1]
[2,3,1,4,5,8,7,6]=>[7,6,8,5,4,1,2,3]=>1011100=>[1,1,3,2]
[2,3,1,4,5,7,8,6]=>[7,6,8,5,4,2,1,3]=>1011110=>[1,1,4,1]
[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>1011110=>[1,1,4,1]
[2,1,3,4,5,8,7,6]=>[7,8,6,5,4,1,2,3]=>0111100=>[1,4,2]
[2,1,3,4,5,7,8,6]=>[7,8,6,5,4,2,1,3]=>0111110=>[1,5,1]
[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>1111100=>[5,2]
[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>1111110=>[6,1]
[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>0000010=>[5,1,1]
[5,6,4,3,2,1,8,7]=>[4,3,5,6,7,8,1,2]=>1000010=>[1,4,1,1]
[4,6,5,3,2,1,8,7]=>[5,3,4,6,7,8,1,2]=>1000010=>[1,4,1,1]
[5,4,6,3,2,1,8,7]=>[4,5,3,6,7,8,1,2]=>0100010=>[1,1,3,1,1]
[4,5,6,3,2,1,8,7]=>[5,4,3,6,7,8,1,2]=>1100010=>[2,3,1,1]
[3,6,5,4,2,1,8,7]=>[6,3,4,5,7,8,1,2]=>1000010=>[1,4,1,1]
[3,5,6,4,2,1,8,7]=>[6,4,3,5,7,8,1,2]=>1100010=>[2,3,1,1]
[4,3,6,5,2,1,8,7]=>[5,6,3,4,7,8,1,2]=>0100010=>[1,1,3,1,1]
[3,4,6,5,2,1,8,7]=>[6,5,3,4,7,8,1,2]=>1100010=>[2,3,1,1]
[5,4,3,6,2,1,8,7]=>[4,5,6,3,7,8,1,2]=>0010010=>[2,1,2,1,1]
[4,5,3,6,2,1,8,7]=>[5,4,6,3,7,8,1,2]=>1010010=>[1,1,1,2,1,1]
[4,3,5,6,2,1,8,7]=>[5,6,4,3,7,8,1,2]=>0110010=>[1,2,2,1,1]
[3,4,5,6,2,1,8,7]=>[6,5,4,3,7,8,1,2]=>1110010=>[3,2,1,1]
[2,6,5,4,3,1,8,7]=>[7,3,4,5,6,8,1,2]=>1000010=>[1,4,1,1]
[2,4,6,5,3,1,8,7]=>[7,5,3,4,6,8,1,2]=>1100010=>[2,3,1,1]
[2,4,5,6,3,1,8,7]=>[7,5,4,3,6,8,1,2]=>1110010=>[3,2,1,1]
[2,3,6,5,4,1,8,7]=>[7,6,3,4,5,8,1,2]=>1100010=>[2,3,1,1]
[2,3,5,6,4,1,8,7]=>[7,6,4,3,5,8,1,2]=>1110010=>[3,2,1,1]
[4,3,2,6,5,1,8,7]=>[5,6,7,3,4,8,1,2]=>0010010=>[2,1,2,1,1]
[2,4,3,6,5,1,8,7]=>[7,5,6,3,4,8,1,2]=>1010010=>[1,1,1,2,1,1]
[2,3,4,6,5,1,8,7]=>[7,6,5,3,4,8,1,2]=>1110010=>[3,2,1,1]
[5,4,3,2,6,1,8,7]=>[4,5,6,7,3,8,1,2]=>0001010=>[3,1,1,1,1]
[4,5,3,2,6,1,8,7]=>[5,4,6,7,3,8,1,2]=>1001010=>[1,2,1,1,1,1]
[4,3,5,2,6,1,8,7]=>[5,6,4,7,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,4,6,1,8,7]=>[6,7,4,5,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,3,2,5,6,1,8,7]=>[5,6,7,4,3,8,1,2]=>0011010=>[2,2,1,1,1]
[3,4,2,5,6,1,8,7]=>[6,5,7,4,3,8,1,2]=>1011010=>[1,1,2,1,1,1]
[2,4,3,5,6,1,8,7]=>[7,5,6,4,3,8,1,2]=>1011010=>[1,1,2,1,1,1]
[2,3,4,5,6,1,8,7]=>[7,6,5,4,3,8,1,2]=>1111010=>[4,1,1,1]
[1,6,5,4,3,2,8,7]=>[8,3,4,5,6,7,1,2]=>1000010=>[1,4,1,1]
[1,5,6,4,3,2,8,7]=>[8,4,3,5,6,7,1,2]=>1100010=>[2,3,1,1]
[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>1100010=>[2,3,1,1]
[1,4,5,6,3,2,8,7]=>[8,5,4,3,6,7,1,2]=>1110010=>[3,2,1,1]
[1,3,4,5,6,2,8,7]=>[8,6,5,4,3,7,1,2]=>1111010=>[4,1,1,1]
[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>0100010=>[1,1,3,1,1]
[2,1,5,6,4,3,8,7]=>[7,8,4,3,5,6,1,2]=>0110010=>[1,2,2,1,1]
[2,1,4,6,5,3,8,7]=>[7,8,5,3,4,6,1,2]=>0110010=>[1,2,2,1,1]
[2,1,5,4,6,3,8,7]=>[7,8,4,5,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[2,1,4,5,6,3,8,7]=>[7,8,5,4,3,6,1,2]=>0111010=>[1,3,1,1,1]
[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>1100010=>[2,3,1,1]
[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>1110010=>[3,2,1,1]
[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>1101010=>[2,1,1,1,1,1]
[3,2,1,5,6,4,8,7]=>[6,7,8,4,3,5,1,2]=>0011010=>[2,2,1,1,1]
[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>1010010=>[1,1,1,2,1,1]
[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>1110010=>[3,2,1,1]
[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>0001010=>[3,1,1,1,1]
[3,4,2,1,6,5,8,7]=>[6,5,7,8,3,4,1,2]=>1001010=>[1,2,1,1,1,1]
[2,4,3,1,6,5,8,7]=>[7,5,6,8,3,4,1,2]=>1001010=>[1,2,1,1,1,1]
[3,2,4,1,6,5,8,7]=>[6,7,5,8,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]
[2,3,4,1,6,5,8,7]=>[7,6,5,8,3,4,1,2]=>1101010=>[2,1,1,1,1,1]
[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>1001010=>[1,2,1,1,1,1]
[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]=>1101010=>[2,1,1,1,1,1]
[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]
[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>1101010=>[2,1,1,1,1,1]
[3,2,1,4,6,5,8,7]=>[6,7,8,5,3,4,1,2]=>0011010=>[2,2,1,1,1]
[2,3,1,4,6,5,8,7]=>[7,6,8,5,3,4,1,2]=>1011010=>[1,1,2,1,1,1]
[2,1,3,4,6,5,8,7]=>[7,8,6,5,3,4,1,2]=>0111010=>[1,3,1,1,1]
[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>1111010=>[4,1,1,1]
[5,4,3,2,1,6,8,7]=>[4,5,6,7,8,3,1,2]=>0000110=>[4,2,1]
[4,5,3,2,1,6,8,7]=>[5,4,6,7,8,3,1,2]=>1000110=>[1,3,2,1]
[4,3,5,2,1,6,8,7]=>[5,6,4,7,8,3,1,2]=>0100110=>[1,1,2,2,1]
[3,4,5,2,1,6,8,7]=>[6,5,4,7,8,3,1,2]=>1100110=>[2,2,2,1]
[3,2,5,4,1,6,8,7]=>[6,7,4,5,8,3,1,2]=>0100110=>[1,1,2,2,1]
[2,3,5,4,1,6,8,7]=>[7,6,4,5,8,3,1,2]=>1100110=>[2,2,2,1]
[3,4,2,5,1,6,8,7]=>[6,5,7,4,8,3,1,2]=>1010110=>[1,1,1,1,2,1]
[2,4,3,5,1,6,8,7]=>[7,5,6,4,8,3,1,2]=>1010110=>[1,1,1,1,2,1]
[2,3,4,5,1,6,8,7]=>[7,6,5,4,8,3,1,2]=>1110110=>[3,1,2,1]
[1,4,5,3,2,6,8,7]=>[8,5,4,6,7,3,1,2]=>1100110=>[2,2,2,1]
[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>1100110=>[2,2,2,1]
[1,4,3,5,2,6,8,7]=>[8,5,6,4,7,3,1,2]=>1010110=>[1,1,1,1,2,1]
[1,2,4,5,3,6,8,7]=>[8,7,5,4,6,3,1,2]=>1110110=>[3,1,2,1]
[3,2,1,5,4,6,8,7]=>[6,7,8,4,5,3,1,2]=>0010110=>[2,1,1,2,1]
[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>1010110=>[1,1,1,1,2,1]
[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>0110110=>[1,2,1,2,1]
[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>1110110=>[3,1,2,1]
[4,3,2,1,5,6,8,7]=>[5,6,7,8,4,3,1,2]=>0001110=>[3,3,1]
[3,4,2,1,5,6,8,7]=>[6,5,7,8,4,3,1,2]=>1001110=>[1,2,3,1]
[2,4,3,1,5,6,8,7]=>[7,5,6,8,4,3,1,2]=>1001110=>[1,2,3,1]
[3,2,4,1,5,6,8,7]=>[6,7,5,8,4,3,1,2]=>0101110=>[1,1,1,3,1]
[2,3,4,1,5,6,8,7]=>[7,6,5,8,4,3,1,2]=>1101110=>[2,1,3,1]
[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>1101110=>[2,1,3,1]
[2,1,4,3,5,6,8,7]=>[7,8,5,6,4,3,1,2]=>0101110=>[1,1,1,3,1]
[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>1101110=>[2,1,3,1]
[3,2,1,4,5,6,8,7]=>[6,7,8,5,4,3,1,2]=>0011110=>[2,4,1]
[2,3,1,4,5,6,8,7]=>[7,6,8,5,4,3,1,2]=>1011110=>[1,1,4,1]
[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>1011110=>[1,1,4,1]
[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>0111110=>[1,5,1]
[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>1111110=>[6,1]
[5,7,6,4,3,2,1,8]=>[4,2,3,5,6,7,8,1]=>1000001=>[1,5,1]
[4,7,6,5,3,2,1,8]=>[5,2,3,4,6,7,8,1]=>1000001=>[1,5,1]
[4,6,7,5,3,2,1,8]=>[5,3,2,4,6,7,8,1]=>1100001=>[2,4,1]
[5,4,7,6,3,2,1,8]=>[4,5,2,3,6,7,8,1]=>0100001=>[1,1,4,1]
[4,5,7,6,3,2,1,8]=>[5,4,2,3,6,7,8,1]=>1100001=>[2,4,1]
[4,6,5,7,3,2,1,8]=>[5,3,4,2,6,7,8,1]=>1010001=>[1,1,1,3,1]
[3,7,6,5,4,2,1,8]=>[6,2,3,4,5,7,8,1]=>1000001=>[1,5,1]
[3,4,7,6,5,2,1,8]=>[6,5,2,3,4,7,8,1]=>1100001=>[2,4,1]
[3,4,6,7,5,2,1,8]=>[6,5,3,2,4,7,8,1]=>1110001=>[3,3,1]
[5,4,3,7,6,2,1,8]=>[4,5,6,2,3,7,8,1]=>0010001=>[2,1,3,1]
[4,5,3,7,6,2,1,8]=>[5,4,6,2,3,7,8,1]=>1010001=>[1,1,1,3,1]
[3,5,4,7,6,2,1,8]=>[6,4,5,2,3,7,8,1]=>1010001=>[1,1,1,3,1]
[4,3,5,7,6,2,1,8]=>[5,6,4,2,3,7,8,1]=>0110001=>[1,2,3,1]
[3,4,5,7,6,2,1,8]=>[6,5,4,2,3,7,8,1]=>1110001=>[3,3,1]
[3,6,5,4,7,2,1,8]=>[6,3,4,5,2,7,8,1]=>1001001=>[1,2,1,2,1]
[3,4,6,5,7,2,1,8]=>[6,5,3,4,2,7,8,1]=>1101001=>[2,1,1,2,1]
[2,7,6,5,4,3,1,8]=>[7,2,3,4,5,6,8,1]=>1000001=>[1,5,1]
[2,6,7,5,4,3,1,8]=>[7,3,2,4,5,6,8,1]=>1100001=>[2,4,1]
[2,5,6,7,4,3,1,8]=>[7,4,3,2,5,6,8,1]=>1110001=>[3,3,1]
[2,4,7,6,5,3,1,8]=>[7,5,2,3,4,6,8,1]=>1100001=>[2,4,1]
[2,4,6,7,5,3,1,8]=>[7,5,3,2,4,6,8,1]=>1110001=>[3,3,1]
[2,5,4,7,6,3,1,8]=>[7,4,5,2,3,6,8,1]=>1010001=>[1,1,1,3,1]
[2,4,5,7,6,3,1,8]=>[7,5,4,2,3,6,8,1]=>1110001=>[3,3,1]
[2,5,6,4,7,3,1,8]=>[7,4,3,5,2,6,8,1]=>1101001=>[2,1,1,2,1]
[2,4,5,6,7,3,1,8]=>[7,5,4,3,2,6,8,1]=>1111001=>[4,2,1]
[3,2,7,6,5,4,1,8]=>[6,7,2,3,4,5,8,1]=>0100001=>[1,1,4,1]
[3,2,6,7,5,4,1,8]=>[6,7,3,2,4,5,8,1]=>0110001=>[1,2,3,1]
[3,2,5,6,7,4,1,8]=>[6,7,4,3,2,5,8,1]=>0111001=>[1,3,2,1]
[2,3,7,6,5,4,1,8]=>[7,6,2,3,4,5,8,1]=>1100001=>[2,4,1]
[2,3,6,7,5,4,1,8]=>[7,6,3,2,4,5,8,1]=>1110001=>[3,3,1]
[2,3,5,7,6,4,1,8]=>[7,6,4,2,3,5,8,1]=>1110001=>[3,3,1]
[4,3,2,7,6,5,1,8]=>[5,6,7,2,3,4,8,1]=>0010001=>[2,1,3,1]
[3,4,2,6,7,5,1,8]=>[6,5,7,3,2,4,8,1]=>1011001=>[1,1,2,2,1]
[2,4,3,7,6,5,1,8]=>[7,5,6,2,3,4,8,1]=>1010001=>[1,1,1,3,1]
[3,2,4,6,7,5,1,8]=>[6,7,5,3,2,4,8,1]=>0111001=>[1,3,2,1]
[2,3,4,7,6,5,1,8]=>[7,6,5,2,3,4,8,1]=>1110001=>[3,3,1]
[2,3,4,6,7,5,1,8]=>[7,6,5,3,2,4,8,1]=>1111001=>[4,2,1]
[5,4,3,2,7,6,1,8]=>[4,5,6,7,2,3,8,1]=>0001001=>[3,1,2,1]
[4,5,3,2,7,6,1,8]=>[5,4,6,7,2,3,8,1]=>1001001=>[1,2,1,2,1]
[3,5,4,2,7,6,1,8]=>[6,4,5,7,2,3,8,1]=>1001001=>[1,2,1,2,1]
[4,3,5,2,7,6,1,8]=>[5,6,4,7,2,3,8,1]=>0101001=>[1,1,1,1,2,1]
[3,4,5,2,7,6,1,8]=>[6,5,4,7,2,3,8,1]=>1101001=>[2,1,1,2,1]
[2,5,4,3,7,6,1,8]=>[7,4,5,6,2,3,8,1]=>1001001=>[1,2,1,2,1]
[2,4,5,3,7,6,1,8]=>[7,5,4,6,2,3,8,1]=>1101001=>[2,1,1,2,1]
[3,2,5,4,7,6,1,8]=>[6,7,4,5,2,3,8,1]=>0101001=>[1,1,1,1,2,1]
[2,3,5,4,7,6,1,8]=>[7,6,4,5,2,3,8,1]=>1101001=>[2,1,1,2,1]
[4,3,2,5,7,6,1,8]=>[5,6,7,4,2,3,8,1]=>0011001=>[2,2,2,1]
[3,4,2,5,7,6,1,8]=>[6,5,7,4,2,3,8,1]=>1011001=>[1,1,2,2,1]
[2,4,3,5,7,6,1,8]=>[7,5,6,4,2,3,8,1]=>1011001=>[1,1,2,2,1]
[3,2,4,5,7,6,1,8]=>[6,7,5,4,2,3,8,1]=>0111001=>[1,3,2,1]
[2,3,4,5,7,6,1,8]=>[7,6,5,4,2,3,8,1]=>1111001=>[4,2,1]
[3,6,5,4,2,7,1,8]=>[6,3,4,5,7,2,8,1]=>1000101=>[1,3,1,1,1]
[3,5,6,4,2,7,1,8]=>[6,4,3,5,7,2,8,1]=>1100101=>[2,2,1,1,1]
[4,3,6,5,2,7,1,8]=>[5,6,3,4,7,2,8,1]=>0100101=>[1,1,2,1,1,1]
[3,4,6,5,2,7,1,8]=>[6,5,3,4,7,2,8,1]=>1100101=>[2,2,1,1,1]
[3,5,4,6,2,7,1,8]=>[6,4,5,3,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,5,4,3,7,1,8]=>[7,3,4,5,6,2,8,1]=>1000101=>[1,3,1,1,1]
[2,4,6,5,3,7,1,8]=>[7,5,3,4,6,2,8,1]=>1100101=>[2,2,1,1,1]
[2,5,4,6,3,7,1,8]=>[7,4,5,3,6,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,5,6,3,7,1,8]=>[7,5,4,3,6,2,8,1]=>1110101=>[3,1,1,1,1]
[2,3,6,5,4,7,1,8]=>[7,6,3,4,5,2,8,1]=>1100101=>[2,2,1,1,1]
[2,3,5,6,4,7,1,8]=>[7,6,4,3,5,2,8,1]=>1110101=>[3,1,1,1,1]
[4,3,2,6,5,7,1,8]=>[5,6,7,3,4,2,8,1]=>0010101=>[2,1,1,1,1,1]
[3,4,2,6,5,7,1,8]=>[6,5,7,3,4,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,3,6,5,7,1,8]=>[7,5,6,3,4,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,3,4,6,5,7,1,8]=>[7,6,5,3,4,2,8,1]=>1110101=>[3,1,1,1,1]
[3,5,4,2,6,7,1,8]=>[6,4,5,7,3,2,8,1]=>1001101=>[1,2,2,1,1]
[2,5,4,3,6,7,1,8]=>[7,4,5,6,3,2,8,1]=>1001101=>[1,2,2,1,1]
[3,2,5,4,6,7,1,8]=>[6,7,4,5,3,2,8,1]=>0101101=>[1,1,1,2,1,1]
[2,3,5,4,6,7,1,8]=>[7,6,4,5,3,2,8,1]=>1101101=>[2,1,2,1,1]
[2,4,3,5,6,7,1,8]=>[7,5,6,4,3,2,8,1]=>1011101=>[1,1,3,1,1]
[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>1000001=>[1,5,1]
[1,6,7,5,4,3,2,8]=>[8,3,2,4,5,6,7,1]=>1100001=>[2,4,1]
[1,5,7,6,4,3,2,8]=>[8,4,2,3,5,6,7,1]=>1100001=>[2,4,1]
[1,6,5,7,4,3,2,8]=>[8,3,4,2,5,6,7,1]=>1010001=>[1,1,1,3,1]
[1,5,6,7,4,3,2,8]=>[8,4,3,2,5,6,7,1]=>1110001=>[3,3,1]
[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>1100001=>[2,4,1]
[1,5,4,7,6,3,2,8]=>[8,4,5,2,3,6,7,1]=>1010001=>[1,1,1,3,1]
[1,4,5,7,6,3,2,8]=>[8,5,4,2,3,6,7,1]=>1110001=>[3,3,1]
[1,6,5,4,7,3,2,8]=>[8,3,4,5,2,6,7,1]=>1001001=>[1,2,1,2,1]
[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>1101001=>[2,1,1,2,1]
[1,5,4,6,7,3,2,8]=>[8,4,5,3,2,6,7,1]=>1011001=>[1,1,2,2,1]
[1,4,5,6,7,3,2,8]=>[8,5,4,3,2,6,7,1]=>1111001=>[4,2,1]
[1,3,7,6,5,4,2,8]=>[8,6,2,3,4,5,7,1]=>1100001=>[2,4,1]
[1,3,5,7,6,4,2,8]=>[8,6,4,2,3,5,7,1]=>1110001=>[3,3,1]
[1,3,5,6,7,4,2,8]=>[8,6,4,3,2,5,7,1]=>1111001=>[4,2,1]
[1,3,4,6,7,5,2,8]=>[8,6,5,3,2,4,7,1]=>1111001=>[4,2,1]
[1,3,5,4,7,6,2,8]=>[8,6,4,5,2,3,7,1]=>1101001=>[2,1,1,2,1]
[1,4,3,5,7,6,2,8]=>[8,5,6,4,2,3,7,1]=>1011001=>[1,1,2,2,1]
[1,3,4,5,7,6,2,8]=>[8,6,5,4,2,3,7,1]=>1111001=>[4,2,1]
[1,6,5,4,3,7,2,8]=>[8,3,4,5,6,2,7,1]=>1000101=>[1,3,1,1,1]
[1,5,6,4,3,7,2,8]=>[8,4,3,5,6,2,7,1]=>1100101=>[2,2,1,1,1]
[1,5,4,6,3,7,2,8]=>[8,4,5,3,6,2,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>1110101=>[3,1,1,1,1]
[1,3,6,5,4,7,2,8]=>[8,6,3,4,5,2,7,1]=>1100101=>[2,2,1,1,1]
[1,3,5,6,4,7,2,8]=>[8,6,4,3,5,2,7,1]=>1110101=>[3,1,1,1,1]
[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,3,4,6,5,7,2,8]=>[8,6,5,3,4,2,7,1]=>1110101=>[3,1,1,1,1]
[1,4,5,3,6,7,2,8]=>[8,5,4,6,3,2,7,1]=>1101101=>[2,1,2,1,1]
[1,3,5,4,6,7,2,8]=>[8,6,4,5,3,2,7,1]=>1101101=>[2,1,2,1,1]
[1,4,3,5,6,7,2,8]=>[8,5,6,4,3,2,7,1]=>1011101=>[1,1,3,1,1]
[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]=>1111101=>[5,1,1]
[2,1,7,6,5,4,3,8]=>[7,8,2,3,4,5,6,1]=>0100001=>[1,1,4,1]
[2,1,6,7,5,4,3,8]=>[7,8,3,2,4,5,6,1]=>0110001=>[1,2,3,1]
[2,1,5,7,6,4,3,8]=>[7,8,4,2,3,5,6,1]=>0110001=>[1,2,3,1]
[2,1,6,5,7,4,3,8]=>[7,8,3,4,2,5,6,1]=>0101001=>[1,1,1,1,2,1]
[2,1,5,6,7,4,3,8]=>[7,8,4,3,2,5,6,1]=>0111001=>[1,3,2,1]
[2,1,4,6,5,7,3,8]=>[7,8,5,3,4,2,6,1]=>0110101=>[1,2,1,1,1,1]
[2,1,4,5,6,7,3,8]=>[7,8,5,4,3,2,6,1]=>0111101=>[1,4,1,1]
[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>1100001=>[2,4,1]
[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>1111001=>[4,2,1]
[1,2,4,6,7,5,3,8]=>[8,7,5,3,2,4,6,1]=>1111001=>[4,2,1]
[1,2,5,6,4,7,3,8]=>[8,7,4,3,5,2,6,1]=>1110101=>[3,1,1,1,1]
[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>1110101=>[3,1,1,1,1]
[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>1111101=>[5,1,1]
[3,2,1,7,6,5,4,8]=>[6,7,8,2,3,4,5,1]=>0010001=>[2,1,3,1]
[3,2,1,6,7,5,4,8]=>[6,7,8,3,2,4,5,1]=>0011001=>[2,2,2,1]
[3,2,1,5,7,6,4,8]=>[6,7,8,4,2,3,5,1]=>0011001=>[2,2,2,1]
[3,2,1,5,6,7,4,8]=>[6,7,8,4,3,2,5,1]=>0011101=>[2,3,1,1]
[2,3,1,7,6,5,4,8]=>[7,6,8,2,3,4,5,1]=>1010001=>[1,1,1,3,1]
[2,3,1,5,7,6,4,8]=>[7,6,8,4,2,3,5,1]=>1011001=>[1,1,2,2,1]
[2,3,1,6,5,7,4,8]=>[7,6,8,3,4,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[2,3,1,5,6,7,4,8]=>[7,6,8,4,3,2,5,1]=>1011101=>[1,1,3,1,1]
[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>1010001=>[1,1,1,3,1]
[1,3,2,6,7,5,4,8]=>[8,6,7,3,2,4,5,1]=>1011001=>[1,1,2,2,1]
[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>1011001=>[1,1,2,2,1]
[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>1011101=>[1,1,3,1,1]
[2,1,3,7,6,5,4,8]=>[7,8,6,2,3,4,5,1]=>0110001=>[1,2,3,1]
[2,1,3,6,7,5,4,8]=>[7,8,6,3,2,4,5,1]=>0111001=>[1,3,2,1]
[2,1,3,6,5,7,4,8]=>[7,8,6,3,4,2,5,1]=>0110101=>[1,2,1,1,1,1]
[2,1,3,5,6,7,4,8]=>[7,8,6,4,3,2,5,1]=>0111101=>[1,4,1,1]
[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>1110001=>[3,3,1]
[1,2,3,6,7,5,4,8]=>[8,7,6,3,2,4,5,1]=>1111001=>[4,2,1]
[1,2,3,5,7,6,4,8]=>[8,7,6,4,2,3,5,1]=>1111001=>[4,2,1]
[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>1110101=>[3,1,1,1,1]
[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>1111101=>[5,1,1]
[4,3,2,1,7,6,5,8]=>[5,6,7,8,2,3,4,1]=>0001001=>[3,1,2,1]
[4,3,2,1,6,7,5,8]=>[5,6,7,8,3,2,4,1]=>0001101=>[3,2,1,1]
[3,4,2,1,7,6,5,8]=>[6,5,7,8,2,3,4,1]=>1001001=>[1,2,1,2,1]
[3,2,4,1,7,6,5,8]=>[6,7,5,8,2,3,4,1]=>0101001=>[1,1,1,1,2,1]
[3,2,4,1,6,7,5,8]=>[6,7,5,8,3,2,4,1]=>0101101=>[1,1,1,2,1,1]
[2,3,4,1,7,6,5,8]=>[7,6,5,8,2,3,4,1]=>1101001=>[2,1,1,2,1]
[2,3,4,1,6,7,5,8]=>[7,6,5,8,3,2,4,1]=>1101101=>[2,1,2,1,1]
[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>1001001=>[1,2,1,2,1]
[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>1001101=>[1,2,2,1,1]
[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>1101101=>[2,1,2,1,1]
[2,1,4,3,7,6,5,8]=>[7,8,5,6,2,3,4,1]=>0101001=>[1,1,1,1,2,1]
[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>1101001=>[2,1,1,2,1]
[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>1101101=>[2,1,2,1,1]
[3,2,1,4,7,6,5,8]=>[6,7,8,5,2,3,4,1]=>0011001=>[2,2,2,1]
[3,2,1,4,6,7,5,8]=>[6,7,8,5,3,2,4,1]=>0011101=>[2,3,1,1]
[2,3,1,4,7,6,5,8]=>[7,6,8,5,2,3,4,1]=>1011001=>[1,1,2,2,1]
[2,3,1,4,6,7,5,8]=>[7,6,8,5,3,2,4,1]=>1011101=>[1,1,3,1,1]
[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>1011001=>[1,1,2,2,1]
[1,3,2,4,6,7,5,8]=>[8,6,7,5,3,2,4,1]=>1011101=>[1,1,3,1,1]
[2,1,3,4,6,7,5,8]=>[7,8,6,5,3,2,4,1]=>0111101=>[1,4,1,1]
[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>1111001=>[4,2,1]
[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>1111101=>[5,1,1]
[5,4,3,2,1,7,6,8]=>[4,5,6,7,8,2,3,1]=>0000101=>[4,1,1,1]
[3,2,5,4,1,7,6,8]=>[6,7,4,5,8,2,3,1]=>0100101=>[1,1,2,1,1,1]
[3,4,2,5,1,7,6,8]=>[6,5,7,4,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,3,5,1,7,6,8]=>[7,5,6,4,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[2,3,4,5,1,7,6,8]=>[7,6,5,4,8,2,3,1]=>1110101=>[3,1,1,1,1]
[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>1000101=>[1,3,1,1,1]
[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>1100101=>[2,2,1,1,1]
[1,4,3,5,2,7,6,8]=>[8,5,6,4,7,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>1110101=>[3,1,1,1,1]
[2,1,5,4,3,7,6,8]=>[7,8,4,5,6,2,3,1]=>0100101=>[1,1,2,1,1,1]
[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>1100101=>[2,2,1,1,1]
[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>1110101=>[3,1,1,1,1]
[2,3,1,5,4,7,6,8]=>[7,6,8,4,5,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>1110101=>[3,1,1,1,1]
[4,3,2,1,5,7,6,8]=>[5,6,7,8,4,2,3,1]=>0001101=>[3,2,1,1]
[2,4,3,1,5,7,6,8]=>[7,5,6,8,4,2,3,1]=>1001101=>[1,2,2,1,1]
[3,2,4,1,5,7,6,8]=>[6,7,5,8,4,2,3,1]=>0101101=>[1,1,1,2,1,1]
[2,3,4,1,5,7,6,8]=>[7,6,5,8,4,2,3,1]=>1101101=>[2,1,2,1,1]
[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>1001101=>[1,2,2,1,1]
[1,3,4,2,5,7,6,8]=>[8,6,5,7,4,2,3,1]=>1101101=>[2,1,2,1,1]
[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>1101101=>[2,1,2,1,1]
[2,3,1,4,5,7,6,8]=>[7,6,8,5,4,2,3,1]=>1011101=>[1,1,3,1,1]
[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>1011101=>[1,1,3,1,1]
[2,1,3,4,5,7,6,8]=>[7,8,6,5,4,2,3,1]=>0111101=>[1,4,1,1]
[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>1111101=>[5,1,1]
[4,6,5,3,2,1,7,8]=>[5,3,4,6,7,8,2,1]=>1000011=>[1,4,2]
[3,6,5,4,2,1,7,8]=>[6,3,4,5,7,8,2,1]=>1000011=>[1,4,2]
[3,4,6,5,2,1,7,8]=>[6,5,3,4,7,8,2,1]=>1100011=>[2,3,2]
[2,6,5,4,3,1,7,8]=>[7,3,4,5,6,8,2,1]=>1000011=>[1,4,2]
[2,4,6,5,3,1,7,8]=>[7,5,3,4,6,8,2,1]=>1100011=>[2,3,2]
[2,4,5,6,3,1,7,8]=>[7,5,4,3,6,8,2,1]=>1110011=>[3,2,2]
[2,3,6,5,4,1,7,8]=>[7,6,3,4,5,8,2,1]=>1100011=>[2,3,2]
[2,3,5,6,4,1,7,8]=>[7,6,4,3,5,8,2,1]=>1110011=>[3,2,2]
[2,3,4,6,5,1,7,8]=>[7,6,5,3,4,8,2,1]=>1110011=>[3,2,2]
[3,5,4,2,6,1,7,8]=>[6,4,5,7,3,8,2,1]=>1001011=>[1,2,1,1,2]
[2,5,4,3,6,1,7,8]=>[7,4,5,6,3,8,2,1]=>1001011=>[1,2,1,1,2]
[2,4,5,3,6,1,7,8]=>[7,5,4,6,3,8,2,1]=>1101011=>[2,1,1,1,2]
[3,2,5,4,6,1,7,8]=>[6,7,4,5,3,8,2,1]=>0101011=>[1,1,1,1,1,2]
[2,4,3,5,6,1,7,8]=>[7,5,6,4,3,8,2,1]=>1011011=>[1,1,2,1,2]
[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>1000011=>[1,4,2]
[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>1100011=>[2,3,2]
[1,4,6,5,3,2,7,8]=>[8,5,3,4,6,7,2,1]=>1100011=>[2,3,2]
[1,4,5,6,3,2,7,8]=>[8,5,4,3,6,7,2,1]=>1110011=>[3,2,2]
[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>1110011=>[3,2,2]
[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>1101011=>[2,1,1,1,2]
[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]=>1111011=>[4,1,2]
[2,1,6,5,4,3,7,8]=>[7,8,3,4,5,6,2,1]=>0100011=>[1,1,3,2]
[2,1,4,6,5,3,7,8]=>[7,8,5,3,4,6,2,1]=>0110011=>[1,2,2,2]
[2,1,4,5,6,3,7,8]=>[7,8,5,4,3,6,2,1]=>0111011=>[1,3,1,2]
[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>1100011=>[2,3,2]
[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>1110011=>[3,2,2]
[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>1110011=>[3,2,2]
[1,2,5,4,6,3,7,8]=>[8,7,4,5,3,6,2,1]=>1101011=>[2,1,1,1,2]
[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>1111011=>[4,1,2]
[3,2,1,6,5,4,7,8]=>[6,7,8,3,4,5,2,1]=>0010011=>[2,1,2,2]
[3,2,1,5,6,4,7,8]=>[6,7,8,4,3,5,2,1]=>0011011=>[2,2,1,2]
[2,3,1,6,5,4,7,8]=>[7,6,8,3,4,5,2,1]=>1010011=>[1,1,1,2,2]
[2,3,1,5,6,4,7,8]=>[7,6,8,4,3,5,2,1]=>1011011=>[1,1,2,1,2]
[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>1010011=>[1,1,1,2,2]
[1,3,2,5,6,4,7,8]=>[8,6,7,4,3,5,2,1]=>1011011=>[1,1,2,1,2]
[2,1,3,6,5,4,7,8]=>[7,8,6,3,4,5,2,1]=>0110011=>[1,2,2,2]
[2,1,3,5,6,4,7,8]=>[7,8,6,4,3,5,2,1]=>0111011=>[1,3,1,2]
[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>1110011=>[3,2,2]
[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>1111011=>[4,1,2]
[4,3,2,1,6,5,7,8]=>[5,6,7,8,3,4,2,1]=>0001011=>[3,1,1,2]
[3,4,2,1,6,5,7,8]=>[6,5,7,8,3,4,2,1]=>1001011=>[1,2,1,1,2]
[3,2,4,1,6,5,7,8]=>[6,7,5,8,3,4,2,1]=>0101011=>[1,1,1,1,1,2]
[2,3,4,1,6,5,7,8]=>[7,6,5,8,3,4,2,1]=>1101011=>[2,1,1,1,2]
[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>1001011=>[1,2,1,1,2]
[2,1,4,3,6,5,7,8]=>[7,8,5,6,3,4,2,1]=>0101011=>[1,1,1,1,1,2]
[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>1101011=>[2,1,1,1,2]
[2,3,1,4,6,5,7,8]=>[7,6,8,5,3,4,2,1]=>1011011=>[1,1,2,1,2]
[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>1011011=>[1,1,2,1,2]
[2,1,3,4,6,5,7,8]=>[7,8,6,5,3,4,2,1]=>0111011=>[1,3,1,2]
[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>1111011=>[4,1,2]
[3,5,4,2,1,6,7,8]=>[6,4,5,7,8,3,2,1]=>1000111=>[1,3,3]
[2,5,4,3,1,6,7,8]=>[7,4,5,6,8,3,2,1]=>1000111=>[1,3,3]
[2,4,5,3,1,6,7,8]=>[7,5,4,6,8,3,2,1]=>1100111=>[2,2,3]
[3,2,5,4,1,6,7,8]=>[6,7,4,5,8,3,2,1]=>0100111=>[1,1,2,3]
[2,3,5,4,1,6,7,8]=>[7,6,4,5,8,3,2,1]=>1100111=>[2,2,3]
[2,4,3,5,1,6,7,8]=>[7,5,6,4,8,3,2,1]=>1010111=>[1,1,1,1,3]
[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>1000111=>[1,3,3]
[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>1100111=>[2,2,3]
[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>1100111=>[2,2,3]
[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>1010111=>[1,1,1,1,3]
[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>1110111=>[3,1,3]
[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>1100111=>[2,2,3]
[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>1110111=>[3,1,3]
[2,3,1,5,4,6,7,8]=>[7,6,8,4,5,3,2,1]=>1010111=>[1,1,1,1,3]
[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>1010111=>[1,1,1,1,3]
[2,1,3,5,4,6,7,8]=>[7,8,6,4,5,3,2,1]=>0110111=>[1,2,1,3]
[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>1110111=>[3,1,3]
[2,4,3,1,5,6,7,8]=>[7,5,6,8,4,3,2,1]=>1001111=>[1,2,4]
[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>1001111=>[1,2,4]
[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>1101111=>[2,1,4]
[2,1,4,3,5,6,7,8]=>[7,8,5,6,4,3,2,1]=>0101111=>[1,1,1,4]
[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>1101111=>[2,1,4]
[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>1011111=>[1,1,5]
[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>1111010=>[4,1,1,1]
[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>1111010=>[4,1,1,1]
[1,2,3,7,5,6,8,4]=>[8,7,6,2,4,3,1,5]=>1110110=>[3,1,2,1]
[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>1110110=>[3,1,2,1]
[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>1110100=>[3,1,1,2]
[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>1110010=>[3,2,1,1]
[1,2,3,8,6,7,5,4]=>[8,7,6,1,3,2,4,5]=>1110100=>[3,1,1,2]
[1,2,4,5,8,6,7,3]=>[8,7,5,4,1,3,2,6]=>1111010=>[4,1,1,1]
[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>1110101=>[3,1,1,1,1]
[1,2,4,8,5,6,7,3]=>[8,7,5,1,4,3,2,6]=>1110110=>[3,1,2,1]
[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>1110100=>[3,1,1,2]
[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>1101010=>[2,1,1,1,1,1]
[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>1101011=>[2,1,1,1,2]
[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>1101101=>[2,1,2,1,1]
[1,2,6,4,5,7,8,3]=>[8,7,3,5,4,2,1,6]=>1101110=>[2,1,3,1]
[1,2,6,4,5,8,7,3]=>[8,7,3,5,4,1,2,6]=>1101100=>[2,1,2,2]
[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>1101101=>[2,1,2,1,1]
[1,2,7,4,5,6,8,3]=>[8,7,2,5,4,3,1,6]=>1101110=>[2,1,3,1]
[1,2,8,4,5,7,6,3]=>[8,7,1,5,4,2,3,6]=>1101100=>[2,1,2,2]
[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>1101000=>[2,1,1,3]
[1,2,7,5,4,6,3,8]=>[8,7,2,4,5,3,6,1]=>1100101=>[2,2,1,1,1]
[1,2,7,5,4,6,8,3]=>[8,7,2,4,5,3,1,6]=>1100110=>[2,2,2,1]
[1,2,8,5,4,6,7,3]=>[8,7,1,4,5,3,2,6]=>1100110=>[2,2,2,1]
[1,2,8,5,4,7,6,3]=>[8,7,1,4,5,2,3,6]=>1100100=>[2,2,1,2]
[1,2,7,5,6,4,3,8]=>[8,7,2,4,3,5,6,1]=>1101001=>[2,1,1,2,1]
[1,2,7,5,6,4,8,3]=>[8,7,2,4,3,5,1,6]=>1101010=>[2,1,1,1,1,1]
[1,2,8,5,6,4,7,3]=>[8,7,1,4,3,5,2,6]=>1101010=>[2,1,1,1,1,1]
[1,2,8,5,6,7,4,3]=>[8,7,1,4,3,2,5,6]=>1101100=>[2,1,2,2]
[1,2,8,5,7,6,4,3]=>[8,7,1,4,2,3,5,6]=>1101000=>[2,1,1,3]
[1,2,8,6,5,4,7,3]=>[8,7,1,3,4,5,2,6]=>1100010=>[2,3,1,1]
[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>1100100=>[2,2,1,2]
[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>1011010=>[1,1,2,1,1,1]
[1,3,2,8,5,6,7,4]=>[8,6,7,1,4,3,2,5]=>1010110=>[1,1,1,1,2,1]
[1,3,2,8,5,7,6,4]=>[8,6,7,1,4,2,3,5]=>1010100=>[1,1,1,1,1,2]
[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>1010010=>[1,1,1,2,1,1]
[1,3,4,2,8,6,7,5]=>[8,6,5,7,1,3,2,4]=>1101010=>[2,1,1,1,1,1]
[1,3,4,5,8,6,7,2]=>[8,6,5,4,1,3,2,7]=>1111010=>[4,1,1,1]
[1,3,4,7,5,6,2,8]=>[8,6,5,2,4,3,7,1]=>1110101=>[3,1,1,1,1]
[1,3,4,8,5,6,7,2]=>[8,6,5,1,4,3,2,7]=>1110110=>[3,1,2,1]
[1,3,4,8,6,5,7,2]=>[8,6,5,1,3,4,2,7]=>1110010=>[3,2,1,1]
[1,3,4,8,6,7,5,2]=>[8,6,5,1,3,2,4,7]=>1110100=>[3,1,1,2]
[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>1101011=>[2,1,1,1,2]
[1,3,6,4,5,7,2,8]=>[8,6,3,5,4,2,7,1]=>1101101=>[2,1,2,1,1]
[1,3,6,4,5,8,7,2]=>[8,6,3,5,4,1,2,7]=>1101100=>[2,1,2,2]
[1,3,7,4,5,6,2,8]=>[8,6,2,5,4,3,7,1]=>1101101=>[2,1,2,1,1]
[1,3,8,4,5,6,7,2]=>[8,6,1,5,4,3,2,7]=>1101110=>[2,1,3,1]
[1,3,7,4,6,5,2,8]=>[8,6,2,5,3,4,7,1]=>1101001=>[2,1,1,2,1]
[1,3,8,4,6,7,5,2]=>[8,6,1,5,3,2,4,7]=>1101100=>[2,1,2,2]
[1,3,8,4,7,6,5,2]=>[8,6,1,5,2,3,4,7]=>1101000=>[2,1,1,3]
[1,3,7,5,4,6,2,8]=>[8,6,2,4,5,3,7,1]=>1100101=>[2,2,1,1,1]
[1,3,7,5,4,6,8,2]=>[8,6,2,4,5,3,1,7]=>1100110=>[2,2,2,1]
[1,3,8,5,4,6,7,2]=>[8,6,1,4,5,3,2,7]=>1100110=>[2,2,2,1]
[1,3,8,5,4,7,6,2]=>[8,6,1,4,5,2,3,7]=>1100100=>[2,2,1,2]
[1,3,7,5,6,4,8,2]=>[8,6,2,4,3,5,1,7]=>1101010=>[2,1,1,1,1,1]
[1,3,8,5,6,4,7,2]=>[8,6,1,4,3,5,2,7]=>1101010=>[2,1,1,1,1,1]
[1,3,8,5,6,7,4,2]=>[8,6,1,4,3,2,5,7]=>1101100=>[2,1,2,2]
[1,3,8,5,7,6,4,2]=>[8,6,1,4,2,3,5,7]=>1101000=>[2,1,1,3]
[1,3,8,6,5,7,4,2]=>[8,6,1,3,4,2,5,7]=>1100100=>[2,2,1,2]
[1,3,8,7,5,6,4,2]=>[8,6,1,2,4,3,5,7]=>1100100=>[2,2,1,2]
[1,4,3,5,8,6,7,2]=>[8,5,6,4,1,3,2,7]=>1011010=>[1,1,2,1,1,1]
[1,4,3,7,5,6,2,8]=>[8,5,6,2,4,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,4,3,8,5,6,7,2]=>[8,5,6,1,4,3,2,7]=>1010110=>[1,1,1,1,2,1]
[1,4,3,8,5,7,6,2]=>[8,5,6,1,4,2,3,7]=>1010100=>[1,1,1,1,1,2]
[1,4,3,8,6,7,5,2]=>[8,5,6,1,3,2,4,7]=>1010100=>[1,1,1,1,1,2]
[1,5,3,4,2,7,6,8]=>[8,4,6,5,7,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[1,5,3,4,2,7,8,6]=>[8,4,6,5,7,2,1,3]=>1010110=>[1,1,1,1,2,1]
[1,5,3,4,2,8,7,6]=>[8,4,6,5,7,1,2,3]=>1010100=>[1,1,1,1,1,2]
[1,5,3,4,6,7,8,2]=>[8,4,6,5,3,2,1,7]=>1011110=>[1,1,4,1]
[1,5,3,4,8,6,7,2]=>[8,4,6,5,1,3,2,7]=>1011010=>[1,1,2,1,1,1]
[1,6,3,4,5,2,7,8]=>[8,3,6,5,4,7,2,1]=>1011011=>[1,1,2,1,2]
[1,6,3,4,5,7,2,8]=>[8,3,6,5,4,2,7,1]=>1011101=>[1,1,3,1,1]
[1,6,3,4,5,7,8,2]=>[8,3,6,5,4,2,1,7]=>1011110=>[1,1,4,1]
[1,6,3,4,5,8,7,2]=>[8,3,6,5,4,1,2,7]=>1011100=>[1,1,3,2]
[1,7,3,4,5,6,2,8]=>[8,2,6,5,4,3,7,1]=>1011101=>[1,1,3,1,1]
[1,7,3,4,5,6,8,2]=>[8,2,6,5,4,3,1,7]=>1011110=>[1,1,4,1]
[1,8,3,4,5,6,7,2]=>[8,1,6,5,4,3,2,7]=>1011110=>[1,1,4,1]
[1,8,3,4,7,6,5,2]=>[8,1,6,5,2,3,4,7]=>1011000=>[1,1,2,3]
[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>1010011=>[1,1,1,2,2]
[1,6,3,5,4,7,2,8]=>[8,3,6,4,5,2,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,3,5,4,7,8,2]=>[8,3,6,4,5,2,1,7]=>1010110=>[1,1,1,1,2,1]
[1,7,3,5,4,6,2,8]=>[8,2,6,4,5,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,5,4,6,7,2]=>[8,1,6,4,5,3,2,7]=>1010110=>[1,1,1,1,2,1]
[1,8,3,5,4,7,6,2]=>[8,1,6,4,5,2,3,7]=>1010100=>[1,1,1,1,1,2]
[1,7,3,5,6,4,8,2]=>[8,2,6,4,3,5,1,7]=>1011010=>[1,1,2,1,1,1]
[1,8,3,5,6,4,7,2]=>[8,1,6,4,3,5,2,7]=>1011010=>[1,1,2,1,1,1]
[1,8,3,5,7,6,4,2]=>[8,1,6,4,2,3,5,7]=>1011000=>[1,1,2,3]
[1,7,3,6,5,4,2,8]=>[8,2,6,3,4,5,7,1]=>1010001=>[1,1,1,3,1]
[1,7,3,6,5,4,8,2]=>[8,2,6,3,4,5,1,7]=>1010010=>[1,1,1,2,1,1]
[1,8,3,6,5,4,7,2]=>[8,1,6,3,4,5,2,7]=>1010010=>[1,1,1,2,1,1]
[1,8,3,6,5,7,4,2]=>[8,1,6,3,4,2,5,7]=>1010100=>[1,1,1,1,1,2]
[1,8,3,7,5,6,4,2]=>[8,1,6,2,4,3,5,7]=>1010100=>[1,1,1,1,1,2]
[1,8,3,7,6,5,4,2]=>[8,1,6,2,3,4,5,7]=>1010000=>[1,1,1,4]
[1,6,4,3,5,2,7,8]=>[8,3,5,6,4,7,2,1]=>1001011=>[1,2,1,1,2]
[1,7,4,3,5,6,8,2]=>[8,2,5,6,4,3,1,7]=>1001110=>[1,2,3,1]
[1,8,4,3,5,6,7,2]=>[8,1,5,6,4,3,2,7]=>1001110=>[1,2,3,1]
[1,8,4,3,5,7,6,2]=>[8,1,5,6,4,2,3,7]=>1001100=>[1,2,2,2]
[1,8,4,3,6,7,5,2]=>[8,1,5,6,3,2,4,7]=>1001100=>[1,2,2,2]
[1,6,4,5,3,2,7,8]=>[8,3,5,4,6,7,2,1]=>1010011=>[1,1,1,2,2]
[1,6,4,5,3,2,8,7]=>[8,3,5,4,6,7,1,2]=>1010010=>[1,1,1,2,1,1]
[1,6,4,5,3,8,7,2]=>[8,3,5,4,6,1,2,7]=>1010100=>[1,1,1,1,1,2]
[1,7,4,5,6,3,2,8]=>[8,2,5,4,3,6,7,1]=>1011001=>[1,1,2,2,1]
[1,8,4,5,6,3,7,2]=>[8,1,5,4,3,6,2,7]=>1011010=>[1,1,2,1,1,1]
[1,8,4,5,6,7,3,2]=>[8,1,5,4,3,2,6,7]=>1011100=>[1,1,3,2]
[1,8,4,5,7,6,3,2]=>[8,1,5,4,2,3,6,7]=>1011000=>[1,1,2,3]
[1,8,4,6,5,3,7,2]=>[8,1,5,3,4,6,2,7]=>1010010=>[1,1,1,2,1,1]
[1,8,4,6,5,7,3,2]=>[8,1,5,3,4,2,6,7]=>1010100=>[1,1,1,1,1,2]
[1,8,4,7,6,5,3,2]=>[8,1,5,2,3,4,6,7]=>1010000=>[1,1,1,4]
[1,7,5,4,3,6,2,8]=>[8,2,4,5,6,3,7,1]=>1000101=>[1,3,1,1,1]
[1,7,5,4,3,6,8,2]=>[8,2,4,5,6,3,1,7]=>1000110=>[1,3,2,1]
[1,8,5,4,3,6,7,2]=>[8,1,4,5,6,3,2,7]=>1000110=>[1,3,2,1]
[1,8,5,4,3,7,6,2]=>[8,1,4,5,6,2,3,7]=>1000100=>[1,3,1,2]
[1,8,5,4,6,3,7,2]=>[8,1,4,5,3,6,2,7]=>1001010=>[1,2,1,1,1,1]
[1,8,5,4,6,7,3,2]=>[8,1,4,5,3,2,6,7]=>1001100=>[1,2,2,2]
[1,8,5,4,7,6,3,2]=>[8,1,4,5,2,3,6,7]=>1001000=>[1,2,1,3]
[1,7,6,4,5,3,2,8]=>[8,2,3,5,4,6,7,1]=>1001001=>[1,2,1,2,1]
[1,8,6,4,5,3,7,2]=>[8,1,3,5,4,6,2,7]=>1001010=>[1,2,1,1,1,1]
[1,8,6,4,5,7,3,2]=>[8,1,3,5,4,2,6,7]=>1001100=>[1,2,2,2]
[1,8,7,4,5,6,3,2]=>[8,1,2,5,4,3,6,7]=>1001100=>[1,2,2,2]
[1,8,7,4,6,5,3,2]=>[8,1,2,5,3,4,6,7]=>1001000=>[1,2,1,3]
[1,8,6,5,4,7,3,2]=>[8,1,3,4,5,2,6,7]=>1000100=>[1,3,1,2]
[1,8,7,5,4,6,3,2]=>[8,1,2,4,5,3,6,7]=>1000100=>[1,3,1,2]
[1,8,7,5,6,4,3,2]=>[8,1,2,4,3,5,6,7]=>1001000=>[1,2,1,3]
[2,1,3,5,8,6,7,4]=>[7,8,6,4,1,3,2,5]=>0111010=>[1,3,1,1,1]
[2,1,3,8,5,6,7,4]=>[7,8,6,1,4,3,2,5]=>0110110=>[1,2,1,2,1]
[2,1,3,8,5,7,6,4]=>[7,8,6,1,4,2,3,5]=>0110100=>[1,2,1,1,2]
[2,1,3,8,6,7,5,4]=>[7,8,6,1,3,2,4,5]=>0110100=>[1,2,1,1,2]
[2,1,4,3,8,6,7,5]=>[7,8,5,6,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,4,5,8,6,7,3]=>[7,8,5,4,1,3,2,6]=>0111010=>[1,3,1,1,1]
[2,1,4,7,5,6,3,8]=>[7,8,5,2,4,3,6,1]=>0110101=>[1,2,1,1,1,1]
[2,1,4,8,6,5,7,3]=>[7,8,5,1,3,4,2,6]=>0110010=>[1,2,2,1,1]
[2,1,4,8,6,7,5,3]=>[7,8,5,1,3,2,4,6]=>0110100=>[1,2,1,1,2]
[2,1,5,4,8,6,7,3]=>[7,8,4,5,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,4,5,3,8,7]=>[7,8,3,5,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,4,5,7,8,3]=>[7,8,3,5,4,2,1,6]=>0101110=>[1,1,1,3,1]
[2,1,6,4,5,8,7,3]=>[7,8,3,5,4,1,2,6]=>0101100=>[1,1,1,2,2]
[2,1,7,4,5,6,3,8]=>[7,8,2,5,4,3,6,1]=>0101101=>[1,1,1,2,1,1]
[2,1,7,4,5,6,8,3]=>[7,8,2,5,4,3,1,6]=>0101110=>[1,1,1,3,1]
[2,1,8,4,5,7,6,3]=>[7,8,1,5,4,2,3,6]=>0101100=>[1,1,1,2,2]
[2,1,7,4,6,5,8,3]=>[7,8,2,5,3,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,4,6,7,5,3]=>[7,8,1,5,3,2,4,6]=>0101100=>[1,1,1,2,2]
[2,1,8,5,4,6,7,3]=>[7,8,1,4,5,3,2,6]=>0100110=>[1,1,2,2,1]
[2,1,8,5,4,7,6,3]=>[7,8,1,4,5,2,3,6]=>0100100=>[1,1,2,1,2]
[2,1,7,5,6,4,3,8]=>[7,8,2,4,3,5,6,1]=>0101001=>[1,1,1,1,2,1]
[2,1,7,5,6,4,8,3]=>[7,8,2,4,3,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,5,6,4,7,3]=>[7,8,1,4,3,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,5,6,7,4,3]=>[7,8,1,4,3,2,5,6]=>0101100=>[1,1,1,2,2]
[2,1,8,5,7,6,4,3]=>[7,8,1,4,2,3,5,6]=>0101000=>[1,1,1,1,3]
[2,1,8,6,5,4,7,3]=>[7,8,1,3,4,5,2,6]=>0100010=>[1,1,3,1,1]
[2,1,8,7,5,6,4,3]=>[7,8,1,2,4,3,5,6]=>0100100=>[1,1,2,1,2]
[2,3,1,4,8,6,7,5]=>[7,6,8,5,1,3,2,4]=>1011010=>[1,1,2,1,1,1]
[2,3,1,5,8,6,7,4]=>[7,6,8,4,1,3,2,5]=>1011010=>[1,1,2,1,1,1]
[2,3,1,7,5,6,4,8]=>[7,6,8,2,4,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[2,3,1,8,5,6,7,4]=>[7,6,8,1,4,3,2,5]=>1010110=>[1,1,1,1,2,1]
[2,3,1,8,5,7,6,4]=>[7,6,8,1,4,2,3,5]=>1010100=>[1,1,1,1,1,2]
[2,3,1,8,6,7,5,4]=>[7,6,8,1,3,2,4,5]=>1010100=>[1,1,1,1,1,2]
[2,3,4,1,8,6,7,5]=>[7,6,5,8,1,3,2,4]=>1101010=>[2,1,1,1,1,1]
[2,3,4,5,8,6,7,1]=>[7,6,5,4,1,3,2,8]=>1111010=>[4,1,1,1]
[2,3,4,7,5,6,1,8]=>[7,6,5,2,4,3,8,1]=>1110101=>[3,1,1,1,1]
[2,3,4,8,5,6,7,1]=>[7,6,5,1,4,3,2,8]=>1110110=>[3,1,2,1]
[2,3,4,8,5,7,6,1]=>[7,6,5,1,4,2,3,8]=>1110100=>[3,1,1,2]
[2,3,4,8,6,5,7,1]=>[7,6,5,1,3,4,2,8]=>1110010=>[3,2,1,1]
[2,3,4,8,6,7,5,1]=>[7,6,5,1,3,2,4,8]=>1110100=>[3,1,1,2]
[2,3,6,4,5,1,7,8]=>[7,6,3,5,4,8,2,1]=>1101011=>[2,1,1,1,2]
[2,3,6,4,5,1,8,7]=>[7,6,3,5,4,8,1,2]=>1101010=>[2,1,1,1,1,1]
[2,3,6,4,5,7,1,8]=>[7,6,3,5,4,2,8,1]=>1101101=>[2,1,2,1,1]
[2,3,6,4,5,7,8,1]=>[7,6,3,5,4,2,1,8]=>1101110=>[2,1,3,1]
[2,3,7,4,5,6,8,1]=>[7,6,2,5,4,3,1,8]=>1101110=>[2,1,3,1]
[2,3,7,4,6,5,8,1]=>[7,6,2,5,3,4,1,8]=>1101010=>[2,1,1,1,1,1]
[2,3,7,5,4,6,1,8]=>[7,6,2,4,5,3,8,1]=>1100101=>[2,2,1,1,1]
[2,3,7,5,4,6,8,1]=>[7,6,2,4,5,3,1,8]=>1100110=>[2,2,2,1]
[2,3,8,5,4,6,7,1]=>[7,6,1,4,5,3,2,8]=>1100110=>[2,2,2,1]
[2,3,7,5,6,4,8,1]=>[7,6,2,4,3,5,1,8]=>1101010=>[2,1,1,1,1,1]
[2,3,8,5,6,4,7,1]=>[7,6,1,4,3,5,2,8]=>1101010=>[2,1,1,1,1,1]
[2,3,8,5,6,7,4,1]=>[7,6,1,4,3,2,5,8]=>1101100=>[2,1,2,2]
[2,3,8,5,7,6,4,1]=>[7,6,1,4,2,3,5,8]=>1101000=>[2,1,1,3]
[2,3,8,6,5,7,4,1]=>[7,6,1,3,4,2,5,8]=>1100100=>[2,2,1,2]
[2,4,3,1,8,6,7,5]=>[7,5,6,8,1,3,2,4]=>1001010=>[1,2,1,1,1,1]
[2,4,3,5,8,6,7,1]=>[7,5,6,4,1,3,2,8]=>1011010=>[1,1,2,1,1,1]
[2,4,3,7,5,6,1,8]=>[7,5,6,2,4,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,3,8,5,6,7,1]=>[7,5,6,1,4,3,2,8]=>1010110=>[1,1,1,1,2,1]
[2,4,3,8,6,5,7,1]=>[7,5,6,1,3,4,2,8]=>1010010=>[1,1,1,2,1,1]
[2,4,3,8,6,7,5,1]=>[7,5,6,1,3,2,4,8]=>1010100=>[1,1,1,1,1,2]
[2,5,3,4,1,6,7,8]=>[7,4,6,5,8,3,2,1]=>1010111=>[1,1,1,1,3]
[2,5,3,4,1,7,6,8]=>[7,4,6,5,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[2,5,3,4,1,8,7,6]=>[7,4,6,5,8,1,2,3]=>1010100=>[1,1,1,1,1,2]
[2,5,3,4,6,7,1,8]=>[7,4,6,5,3,2,8,1]=>1011101=>[1,1,3,1,1]
[2,5,3,4,8,6,7,1]=>[7,4,6,5,1,3,2,8]=>1011010=>[1,1,2,1,1,1]
[2,5,3,4,8,7,6,1]=>[7,4,6,5,1,2,3,8]=>1011000=>[1,1,2,3]
[2,6,3,4,5,7,1,8]=>[7,3,6,5,4,2,8,1]=>1011101=>[1,1,3,1,1]
[2,6,3,4,5,7,8,1]=>[7,3,6,5,4,2,1,8]=>1011110=>[1,1,4,1]
[2,7,3,4,5,6,1,8]=>[7,2,6,5,4,3,8,1]=>1011101=>[1,1,3,1,1]
[2,7,3,4,5,6,8,1]=>[7,2,6,5,4,3,1,8]=>1011110=>[1,1,4,1]
[2,8,3,4,5,6,7,1]=>[7,1,6,5,4,3,2,8]=>1011110=>[1,1,4,1]
[2,8,3,4,5,7,6,1]=>[7,1,6,5,4,2,3,8]=>1011100=>[1,1,3,2]
[2,7,3,4,6,5,8,1]=>[7,2,6,5,3,4,1,8]=>1011010=>[1,1,2,1,1,1]
[2,6,3,5,4,1,7,8]=>[7,3,6,4,5,8,2,1]=>1010011=>[1,1,1,2,2]
[2,6,3,5,4,7,1,8]=>[7,3,6,4,5,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,3,5,4,7,8,1]=>[7,3,6,4,5,2,1,8]=>1010110=>[1,1,1,1,2,1]
[2,7,3,5,4,6,8,1]=>[7,2,6,4,5,3,1,8]=>1010110=>[1,1,1,1,2,1]
[2,8,3,5,4,7,6,1]=>[7,1,6,4,5,2,3,8]=>1010100=>[1,1,1,1,1,2]
[2,7,3,5,6,4,1,8]=>[7,2,6,4,3,5,8,1]=>1011001=>[1,1,2,2,1]
[2,8,3,5,7,6,4,1]=>[7,1,6,4,2,3,5,8]=>1011000=>[1,1,2,3]
[2,7,3,6,5,4,1,8]=>[7,2,6,3,4,5,8,1]=>1010001=>[1,1,1,3,1]
[2,7,3,6,5,4,8,1]=>[7,2,6,3,4,5,1,8]=>1010010=>[1,1,1,2,1,1]
[2,8,3,7,6,5,4,1]=>[7,1,6,2,3,4,5,8]=>1010000=>[1,1,1,4]
[2,5,4,3,8,6,7,1]=>[7,4,5,6,1,3,2,8]=>1001010=>[1,2,1,1,1,1]
[2,6,4,3,5,1,8,7]=>[7,3,5,6,4,8,1,2]=>1001010=>[1,2,1,1,1,1]
[2,6,4,3,5,7,1,8]=>[7,3,5,6,4,2,8,1]=>1001101=>[1,2,2,1,1]
[2,6,4,3,5,7,8,1]=>[7,3,5,6,4,2,1,8]=>1001110=>[1,2,3,1]
[2,6,4,3,5,8,7,1]=>[7,3,5,6,4,1,2,8]=>1001100=>[1,2,2,2]
[2,7,4,3,5,6,8,1]=>[7,2,5,6,4,3,1,8]=>1001110=>[1,2,3,1]
[2,8,4,3,5,6,7,1]=>[7,1,5,6,4,3,2,8]=>1001110=>[1,2,3,1]
[2,8,4,3,5,7,6,1]=>[7,1,5,6,4,2,3,8]=>1001100=>[1,2,2,2]
[2,7,4,3,6,5,1,8]=>[7,2,5,6,3,4,8,1]=>1001001=>[1,2,1,2,1]
[2,8,4,3,6,5,7,1]=>[7,1,5,6,3,4,2,8]=>1001010=>[1,2,1,1,1,1]
[2,8,4,3,6,7,5,1]=>[7,1,5,6,3,2,4,8]=>1001100=>[1,2,2,2]
[2,8,4,3,7,6,5,1]=>[7,1,5,6,2,3,4,8]=>1001000=>[1,2,1,3]
[2,6,4,5,3,1,7,8]=>[7,3,5,4,6,8,2,1]=>1010011=>[1,1,1,2,2]
[2,6,4,5,3,1,8,7]=>[7,3,5,4,6,8,1,2]=>1010010=>[1,1,1,2,1,1]
[2,6,4,5,3,7,1,8]=>[7,3,5,4,6,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,5,3,7,8,1]=>[7,3,5,4,6,2,1,8]=>1010110=>[1,1,1,1,2,1]
[2,6,4,5,3,8,7,1]=>[7,3,5,4,6,1,2,8]=>1010100=>[1,1,1,1,1,2]
[2,7,4,5,3,6,1,8]=>[7,2,5,4,6,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,5,3,6,7,1]=>[7,1,5,4,6,3,2,8]=>1010110=>[1,1,1,1,2,1]
[2,8,4,5,3,7,6,1]=>[7,1,5,4,6,2,3,8]=>1010100=>[1,1,1,1,1,2]
[2,7,4,5,6,3,8,1]=>[7,2,5,4,3,6,1,8]=>1011010=>[1,1,2,1,1,1]
[2,8,4,5,7,6,3,1]=>[7,1,5,4,2,3,6,8]=>1011000=>[1,1,2,3]
[2,7,4,6,5,3,8,1]=>[7,2,5,3,4,6,1,8]=>1010010=>[1,1,1,2,1,1]
[2,8,4,7,5,6,3,1]=>[7,1,5,2,4,3,6,8]=>1010100=>[1,1,1,1,1,2]
[2,7,5,4,6,3,1,8]=>[7,2,4,5,3,6,8,1]=>1001001=>[1,2,1,2,1]
[2,7,5,4,6,3,8,1]=>[7,2,4,5,3,6,1,8]=>1001010=>[1,2,1,1,1,1]
[2,8,5,4,6,3,7,1]=>[7,1,4,5,3,6,2,8]=>1001010=>[1,2,1,1,1,1]
[2,8,5,4,7,6,3,1]=>[7,1,4,5,2,3,6,8]=>1001000=>[1,2,1,3]
[2,7,6,4,5,3,8,1]=>[7,2,3,5,4,6,1,8]=>1001010=>[1,2,1,1,1,1]
[2,8,6,4,5,3,7,1]=>[7,1,3,5,4,6,2,8]=>1001010=>[1,2,1,1,1,1]
[2,8,7,4,6,5,3,1]=>[7,1,2,5,3,4,6,8]=>1001000=>[1,2,1,3]
[2,8,6,5,4,3,7,1]=>[7,1,3,4,5,6,2,8]=>1000010=>[1,4,1,1]
[2,8,7,5,6,4,3,1]=>[7,1,2,4,3,5,6,8]=>1001000=>[1,2,1,3]
[3,2,1,4,8,6,7,5]=>[6,7,8,5,1,3,2,4]=>0011010=>[2,2,1,1,1]
[3,2,1,5,8,6,7,4]=>[6,7,8,4,1,3,2,5]=>0011010=>[2,2,1,1,1]
[3,2,1,7,5,6,4,8]=>[6,7,8,2,4,3,5,1]=>0010101=>[2,1,1,1,1,1]
[3,2,1,7,5,6,8,4]=>[6,7,8,2,4,3,1,5]=>0010110=>[2,1,1,2,1]
[3,2,1,8,5,6,7,4]=>[6,7,8,1,4,3,2,5]=>0010110=>[2,1,1,2,1]
[3,2,1,8,5,7,6,4]=>[6,7,8,1,4,2,3,5]=>0010100=>[2,1,1,1,2]
[3,2,1,8,6,5,7,4]=>[6,7,8,1,3,4,2,5]=>0010010=>[2,1,2,1,1]
[3,2,1,8,6,7,5,4]=>[6,7,8,1,3,2,4,5]=>0010100=>[2,1,1,1,2]
[3,2,4,1,8,6,7,5]=>[6,7,5,8,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,4,8,5,6,7,1]=>[6,7,5,1,4,3,2,8]=>0110110=>[1,2,1,2,1]
[3,2,4,8,6,7,5,1]=>[6,7,5,1,3,2,4,8]=>0110100=>[1,2,1,1,2]
[3,2,5,4,8,6,7,1]=>[6,7,4,5,1,3,2,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,4,5,1,7,8]=>[6,7,3,5,4,8,2,1]=>0101011=>[1,1,1,1,1,2]
[3,2,6,4,5,1,8,7]=>[6,7,3,5,4,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,4,5,8,7,1]=>[6,7,3,5,4,1,2,8]=>0101100=>[1,1,1,2,2]
[3,2,7,4,6,5,8,1]=>[6,7,2,5,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,7,5,4,6,1,8]=>[6,7,2,4,5,3,8,1]=>0100101=>[1,1,2,1,1,1]
[3,2,7,5,4,6,8,1]=>[6,7,2,4,5,3,1,8]=>0100110=>[1,1,2,2,1]
[3,2,8,5,4,6,7,1]=>[6,7,1,4,5,3,2,8]=>0100110=>[1,1,2,2,1]
[3,2,7,5,6,4,1,8]=>[6,7,2,4,3,5,8,1]=>0101001=>[1,1,1,1,2,1]
[3,2,7,5,6,4,8,1]=>[6,7,2,4,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,5,6,4,7,1]=>[6,7,1,4,3,5,2,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,5,6,7,4,1]=>[6,7,1,4,3,2,5,8]=>0101100=>[1,1,1,2,2]
[3,2,8,5,7,6,4,1]=>[6,7,1,4,2,3,5,8]=>0101000=>[1,1,1,1,3]
[4,2,3,1,5,7,6,8]=>[5,7,6,8,4,2,3,1]=>0101101=>[1,1,1,2,1,1]
[4,2,3,1,5,7,8,6]=>[5,7,6,8,4,2,1,3]=>0101110=>[1,1,1,3,1]
[4,2,3,1,6,5,7,8]=>[5,7,6,8,3,4,2,1]=>0101011=>[1,1,1,1,1,2]
[4,2,3,1,6,5,8,7]=>[5,7,6,8,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,2,3,1,6,7,5,8]=>[5,7,6,8,3,2,4,1]=>0101101=>[1,1,1,2,1,1]
[4,2,3,1,6,7,8,5]=>[5,7,6,8,3,2,1,4]=>0101110=>[1,1,1,3,1]
[4,2,3,1,6,8,7,5]=>[5,7,6,8,3,1,2,4]=>0101100=>[1,1,1,2,2]
[4,2,3,1,7,6,8,5]=>[5,7,6,8,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,3,1,8,6,7,5]=>[5,7,6,8,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,3,1,8,7,6,5]=>[5,7,6,8,1,2,3,4]=>0101000=>[1,1,1,1,3]
[4,2,3,5,1,7,8,6]=>[5,7,6,4,8,2,1,3]=>0110110=>[1,2,1,2,1]
[4,2,3,5,1,8,7,6]=>[5,7,6,4,8,1,2,3]=>0110100=>[1,2,1,1,2]
[4,2,3,5,6,1,8,7]=>[5,7,6,4,3,8,1,2]=>0111010=>[1,3,1,1,1]
[4,2,3,5,7,6,8,1]=>[5,7,6,4,2,3,1,8]=>0111010=>[1,3,1,1,1]
[4,2,3,6,5,1,8,7]=>[5,7,6,3,4,8,1,2]=>0110010=>[1,2,2,1,1]
[4,2,3,6,5,7,1,8]=>[5,7,6,3,4,2,8,1]=>0110101=>[1,2,1,1,1,1]
[4,2,3,6,5,8,7,1]=>[5,7,6,3,4,1,2,8]=>0110100=>[1,2,1,1,2]
[4,2,3,7,5,6,8,1]=>[5,7,6,2,4,3,1,8]=>0110110=>[1,2,1,2,1]
[4,2,3,8,5,6,7,1]=>[5,7,6,1,4,3,2,8]=>0110110=>[1,2,1,2,1]
[4,2,3,7,6,5,8,1]=>[5,7,6,2,3,4,1,8]=>0110010=>[1,2,2,1,1]
[4,2,3,8,6,7,5,1]=>[5,7,6,1,3,2,4,8]=>0110100=>[1,2,1,1,2]
[4,2,3,8,7,6,5,1]=>[5,7,6,1,2,3,4,8]=>0110000=>[1,2,4]
[5,2,3,4,1,7,6,8]=>[4,7,6,5,8,2,3,1]=>0110101=>[1,2,1,1,1,1]
[5,2,3,4,1,7,8,6]=>[4,7,6,5,8,2,1,3]=>0110110=>[1,2,1,2,1]
[5,2,3,4,1,8,7,6]=>[4,7,6,5,8,1,2,3]=>0110100=>[1,2,1,1,2]
[5,2,3,4,6,8,7,1]=>[4,7,6,5,3,1,2,8]=>0111100=>[1,4,2]
[5,2,3,4,7,6,1,8]=>[4,7,6,5,2,3,8,1]=>0111001=>[1,3,2,1]
[8,2,3,4,5,7,6,1]=>[1,7,6,5,4,2,3,8]=>0111100=>[1,4,2]
[7,2,3,4,6,5,1,8]=>[2,7,6,5,3,4,8,1]=>0111001=>[1,3,2,1]
[8,2,3,4,6,7,5,1]=>[1,7,6,5,3,2,4,8]=>0111100=>[1,4,2]
[6,2,3,5,4,1,7,8]=>[3,7,6,4,5,8,2,1]=>0110011=>[1,2,2,2]
[6,2,3,5,4,1,8,7]=>[3,7,6,4,5,8,1,2]=>0110010=>[1,2,2,1,1]
[6,2,3,5,4,7,1,8]=>[3,7,6,4,5,2,8,1]=>0110101=>[1,2,1,1,1,1]
[6,2,3,5,4,8,7,1]=>[3,7,6,4,5,1,2,8]=>0110100=>[1,2,1,1,2]
[7,2,3,5,4,6,1,8]=>[2,7,6,4,5,3,8,1]=>0110101=>[1,2,1,1,1,1]
[8,2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2,8]=>0110110=>[1,2,1,2,1]
[8,2,3,5,7,6,4,1]=>[1,7,6,4,2,3,5,8]=>0111000=>[1,3,3]
[7,2,3,6,5,4,1,8]=>[2,7,6,3,4,5,8,1]=>0110001=>[1,2,3,1]
[7,2,3,6,5,4,8,1]=>[2,7,6,3,4,5,1,8]=>0110010=>[1,2,2,1,1]
[8,2,3,6,5,4,7,1]=>[1,7,6,3,4,5,2,8]=>0110010=>[1,2,2,1,1]
[8,2,3,6,5,7,4,1]=>[1,7,6,3,4,2,5,8]=>0110100=>[1,2,1,1,2]
[8,2,3,7,5,6,4,1]=>[1,7,6,2,4,3,5,8]=>0110100=>[1,2,1,1,2]
[8,2,3,7,6,5,4,1]=>[1,7,6,2,3,4,5,8]=>0110000=>[1,2,4]
[5,2,4,3,1,6,7,8]=>[4,7,5,6,8,3,2,1]=>0100111=>[1,1,2,3]
[5,2,4,3,1,6,8,7]=>[4,7,5,6,8,3,1,2]=>0100110=>[1,1,2,2,1]
[5,2,4,3,1,7,6,8]=>[4,7,5,6,8,2,3,1]=>0100101=>[1,1,2,1,1,1]
[5,2,4,3,1,8,7,6]=>[4,7,5,6,8,1,2,3]=>0100100=>[1,1,2,1,2]
[5,2,4,3,6,1,7,8]=>[4,7,5,6,3,8,2,1]=>0101011=>[1,1,1,1,1,2]
[5,2,4,3,6,1,8,7]=>[4,7,5,6,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,4,3,6,7,1,8]=>[4,7,5,6,3,2,8,1]=>0101101=>[1,1,1,2,1,1]
[5,2,4,3,6,7,8,1]=>[4,7,5,6,3,2,1,8]=>0101110=>[1,1,1,3,1]
[5,2,4,3,7,6,1,8]=>[4,7,5,6,2,3,8,1]=>0101001=>[1,1,1,1,2,1]
[5,2,4,3,7,6,8,1]=>[4,7,5,6,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,2,4,3,5,1,8,7]=>[3,7,5,6,4,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,2,4,3,5,7,1,8]=>[3,7,5,6,4,2,8,1]=>0101101=>[1,1,1,2,1,1]
[6,2,4,3,5,7,8,1]=>[3,7,5,6,4,2,1,8]=>0101110=>[1,1,1,3,1]
[7,2,4,3,5,6,1,8]=>[2,7,5,6,4,3,8,1]=>0101101=>[1,1,1,2,1,1]
[8,2,4,3,5,6,7,1]=>[1,7,5,6,4,3,2,8]=>0101110=>[1,1,1,3,1]
[7,2,4,3,6,5,8,1]=>[2,7,5,6,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,3,6,7,5,1]=>[1,7,5,6,3,2,4,8]=>0101100=>[1,1,1,2,2]
[8,2,4,3,7,6,5,1]=>[1,7,5,6,2,3,4,8]=>0101000=>[1,1,1,1,3]
[6,2,4,5,3,1,7,8]=>[3,7,5,4,6,8,2,1]=>0110011=>[1,2,2,2]
[6,2,4,5,3,1,8,7]=>[3,7,5,4,6,8,1,2]=>0110010=>[1,2,2,1,1]
[6,2,4,5,3,7,1,8]=>[3,7,5,4,6,2,8,1]=>0110101=>[1,2,1,1,1,1]
[6,2,4,5,3,8,7,1]=>[3,7,5,4,6,1,2,8]=>0110100=>[1,2,1,1,2]
[7,2,4,5,3,6,1,8]=>[2,7,5,4,6,3,8,1]=>0110101=>[1,2,1,1,1,1]
[8,2,4,5,3,7,6,1]=>[1,7,5,4,6,2,3,8]=>0110100=>[1,2,1,1,2]
[7,2,4,5,6,3,1,8]=>[2,7,5,4,3,6,8,1]=>0111001=>[1,3,2,1]
[8,2,4,5,6,3,7,1]=>[1,7,5,4,3,6,2,8]=>0111010=>[1,3,1,1,1]
[8,2,4,5,6,7,3,1]=>[1,7,5,4,3,2,6,8]=>0111100=>[1,4,2]
[8,2,4,7,6,5,3,1]=>[1,7,5,2,3,4,6,8]=>0110000=>[1,2,4]
[6,2,5,4,3,1,7,8]=>[3,7,4,5,6,8,2,1]=>0100011=>[1,1,3,2]
[6,2,5,4,3,1,8,7]=>[3,7,4,5,6,8,1,2]=>0100010=>[1,1,3,1,1]
[7,2,5,4,3,6,1,8]=>[2,7,4,5,6,3,8,1]=>0100101=>[1,1,2,1,1,1]
[7,2,5,4,3,6,8,1]=>[2,7,4,5,6,3,1,8]=>0100110=>[1,1,2,2,1]
[8,2,5,4,3,6,7,1]=>[1,7,4,5,6,3,2,8]=>0100110=>[1,1,2,2,1]
[8,2,5,4,6,7,3,1]=>[1,7,4,5,3,2,6,8]=>0101100=>[1,1,1,2,2]
[8,2,5,4,7,6,3,1]=>[1,7,4,5,2,3,6,8]=>0101000=>[1,1,1,1,3]
[7,2,6,4,5,3,1,8]=>[2,7,3,5,4,6,8,1]=>0101001=>[1,1,1,1,2,1]
[8,2,6,4,5,3,7,1]=>[1,7,3,5,4,6,2,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,4,5,7,3,1]=>[1,7,3,5,4,2,6,8]=>0101100=>[1,1,1,2,2]
[8,2,7,4,5,6,3,1]=>[1,7,2,5,4,3,6,8]=>0101100=>[1,1,1,2,2]
[8,2,7,4,6,5,3,1]=>[1,7,2,5,3,4,6,8]=>0101000=>[1,1,1,1,3]
[7,2,6,5,4,3,8,1]=>[2,7,3,4,5,6,1,8]=>0100010=>[1,1,3,1,1]
[8,2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2,8]=>0100010=>[1,1,3,1,1]
[8,2,7,5,4,6,3,1]=>[1,7,2,4,5,3,6,8]=>0100100=>[1,1,2,1,2]
[8,2,7,5,6,4,3,1]=>[1,7,2,4,3,5,6,8]=>0101000=>[1,1,1,1,3]
[8,2,7,6,5,4,3,1]=>[1,7,2,3,4,5,6,8]=>0100000=>[1,1,5]
[4,3,2,1,8,6,7,5]=>[5,6,7,8,1,3,2,4]=>0001010=>[3,1,1,1,1]
[4,3,2,7,5,6,8,1]=>[5,6,7,2,4,3,1,8]=>0010110=>[2,1,1,2,1]
[4,3,2,8,5,7,6,1]=>[5,6,7,1,4,2,3,8]=>0010100=>[2,1,1,1,2]
[4,3,2,8,6,7,5,1]=>[5,6,7,1,3,2,4,8]=>0010100=>[2,1,1,1,2]
[5,3,2,4,1,6,8,7]=>[4,6,7,5,8,3,1,2]=>0010110=>[2,1,1,2,1]
[5,3,2,4,1,7,6,8]=>[4,6,7,5,8,2,3,1]=>0010101=>[2,1,1,1,1,1]
[5,3,2,4,1,7,8,6]=>[4,6,7,5,8,2,1,3]=>0010110=>[2,1,1,2,1]
[5,3,2,4,1,8,7,6]=>[4,6,7,5,8,1,2,3]=>0010100=>[2,1,1,1,2]
[5,3,2,4,6,1,8,7]=>[4,6,7,5,3,8,1,2]=>0011010=>[2,2,1,1,1]
[5,3,2,4,7,6,8,1]=>[4,6,7,5,2,3,1,8]=>0011010=>[2,2,1,1,1]
[5,3,2,4,8,7,6,1]=>[4,6,7,5,1,2,3,8]=>0011000=>[2,2,3]
[6,3,2,4,5,1,8,7]=>[3,6,7,5,4,8,1,2]=>0011010=>[2,2,1,1,1]
[7,3,2,4,6,5,1,8]=>[2,6,7,5,3,4,8,1]=>0011001=>[2,2,2,1]
[7,3,2,4,6,5,8,1]=>[2,6,7,5,3,4,1,8]=>0011010=>[2,2,1,1,1]
[8,3,2,4,6,7,5,1]=>[1,6,7,5,3,2,4,8]=>0011100=>[2,3,2]
[6,3,2,5,4,1,7,8]=>[3,6,7,4,5,8,2,1]=>0010011=>[2,1,2,2]
[6,3,2,5,4,1,8,7]=>[3,6,7,4,5,8,1,2]=>0010010=>[2,1,2,1,1]
[7,3,2,5,4,6,8,1]=>[2,6,7,4,5,3,1,8]=>0010110=>[2,1,1,2,1]
[8,3,2,5,4,6,7,1]=>[1,6,7,4,5,3,2,8]=>0010110=>[2,1,1,2,1]
[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>0010100=>[2,1,1,1,2]
[8,3,2,5,6,4,7,1]=>[1,6,7,4,3,5,2,8]=>0011010=>[2,2,1,1,1]
[8,3,2,5,6,7,4,1]=>[1,6,7,4,3,2,5,8]=>0011100=>[2,3,2]
[7,3,2,6,5,4,8,1]=>[2,6,7,3,4,5,1,8]=>0010010=>[2,1,2,1,1]
[8,3,2,6,5,7,4,1]=>[1,6,7,3,4,2,5,8]=>0010100=>[2,1,1,1,2]
[8,3,2,7,5,6,4,1]=>[1,6,7,2,4,3,5,8]=>0010100=>[2,1,1,1,2]
[8,3,2,7,6,5,4,1]=>[1,6,7,2,3,4,5,8]=>0010000=>[2,1,4]
[5,3,4,2,1,7,8,6]=>[4,6,5,7,8,2,1,3]=>0100110=>[1,1,2,2,1]
[5,3,4,2,1,8,7,6]=>[4,6,5,7,8,1,2,3]=>0100100=>[1,1,2,1,2]
[5,3,4,2,6,1,8,7]=>[4,6,5,7,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,3,4,2,7,6,1,8]=>[4,6,5,7,2,3,8,1]=>0101001=>[1,1,1,1,2,1]
[5,3,4,2,7,6,8,1]=>[4,6,5,7,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,3,4,2,8,6,7,1]=>[4,6,5,7,1,3,2,8]=>0101010=>[1,1,1,1,1,1,1]
[5,3,4,2,8,7,6,1]=>[4,6,5,7,1,2,3,8]=>0101000=>[1,1,1,1,3]
[6,3,4,2,5,1,8,7]=>[3,6,5,7,4,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[8,3,4,2,5,7,6,1]=>[1,6,5,7,4,2,3,8]=>0101100=>[1,1,1,2,2]
[7,3,4,2,6,5,1,8]=>[2,6,5,7,3,4,8,1]=>0101001=>[1,1,1,1,2,1]
[7,3,4,2,6,5,8,1]=>[2,6,5,7,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,4,2,6,5,7,1]=>[1,6,5,7,3,4,2,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,4,2,7,6,5,1]=>[1,6,5,7,2,3,4,8]=>0101000=>[1,1,1,1,3]
[8,3,4,5,2,7,6,1]=>[1,6,5,4,7,2,3,8]=>0110100=>[1,2,1,1,2]
[7,3,4,6,5,2,1,8]=>[2,6,5,3,4,7,8,1]=>0110001=>[1,2,3,1]
[6,3,5,4,2,7,1,8]=>[3,6,4,5,7,2,8,1]=>0100101=>[1,1,2,1,1,1]
[7,3,5,4,2,6,1,8]=>[2,6,4,5,7,3,8,1]=>0100101=>[1,1,2,1,1,1]
[7,3,5,4,2,6,8,1]=>[2,6,4,5,7,3,1,8]=>0100110=>[1,1,2,2,1]
[8,3,5,4,2,6,7,1]=>[1,6,4,5,7,3,2,8]=>0100110=>[1,1,2,2,1]
[8,3,5,4,2,7,6,1]=>[1,6,4,5,7,2,3,8]=>0100100=>[1,1,2,1,2]
[7,3,5,4,6,2,1,8]=>[2,6,4,5,3,7,8,1]=>0101001=>[1,1,1,1,2,1]
[8,3,5,4,6,7,2,1]=>[1,6,4,5,3,2,7,8]=>0101100=>[1,1,1,2,2]
[8,3,5,4,7,6,2,1]=>[1,6,4,5,2,3,7,8]=>0101000=>[1,1,1,1,3]
[7,3,6,4,5,2,1,8]=>[2,6,3,5,4,7,8,1]=>0101001=>[1,1,1,1,2,1]
[8,3,6,4,5,7,2,1]=>[1,6,3,5,4,2,7,8]=>0101100=>[1,1,1,2,2]
[8,3,7,4,6,5,2,1]=>[1,6,2,5,3,4,7,8]=>0101000=>[1,1,1,1,3]
[7,3,6,5,4,2,1,8]=>[2,6,3,4,5,7,8,1]=>0100001=>[1,1,4,1]
[8,3,6,5,4,7,2,1]=>[1,6,3,4,5,2,7,8]=>0100100=>[1,1,2,1,2]
[8,3,7,5,4,6,2,1]=>[1,6,2,4,5,3,7,8]=>0100100=>[1,1,2,1,2]
[8,3,7,5,6,4,2,1]=>[1,6,2,4,3,5,7,8]=>0101000=>[1,1,1,1,3]
[8,3,7,6,5,4,2,1]=>[1,6,2,3,4,5,7,8]=>0100000=>[1,1,5]
[5,4,3,2,8,6,7,1]=>[4,5,6,7,1,3,2,8]=>0001010=>[3,1,1,1,1]
[8,4,3,2,5,7,6,1]=>[1,5,6,7,4,2,3,8]=>0001100=>[3,2,2]
[8,4,3,2,6,5,7,1]=>[1,5,6,7,3,4,2,8]=>0001010=>[3,1,1,1,1]
[8,4,3,2,6,7,5,1]=>[1,5,6,7,3,2,4,8]=>0001100=>[3,2,2]
[8,4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4,8]=>0001000=>[3,1,3]
[6,4,3,5,2,1,8,7]=>[3,5,6,4,7,8,1,2]=>0010010=>[2,1,2,1,1]
[8,4,3,5,2,7,6,1]=>[1,5,6,4,7,2,3,8]=>0010100=>[2,1,1,1,2]
[8,4,3,5,7,6,2,1]=>[1,5,6,4,2,3,7,8]=>0011000=>[2,2,3]
[7,4,3,6,5,2,1,8]=>[2,5,6,3,4,7,8,1]=>0010001=>[2,1,3,1]
[7,4,3,6,5,2,8,1]=>[2,5,6,3,4,7,1,8]=>0010010=>[2,1,2,1,1]
[8,4,3,6,5,2,7,1]=>[1,5,6,3,4,7,2,8]=>0010010=>[2,1,2,1,1]
[8,4,3,6,5,7,2,1]=>[1,5,6,3,4,2,7,8]=>0010100=>[2,1,1,1,2]
[8,4,3,7,6,5,2,1]=>[1,5,6,2,3,4,7,8]=>0010000=>[2,1,4]
[6,5,3,4,2,1,8,7]=>[3,4,6,5,7,8,1,2]=>0010010=>[2,1,2,1,1]
[6,5,3,4,2,8,7,1]=>[3,4,6,5,7,1,2,8]=>0010100=>[2,1,1,1,2]
[8,5,3,4,2,7,6,1]=>[1,4,6,5,7,2,3,8]=>0010100=>[2,1,1,1,2]
[8,7,3,4,6,5,2,1]=>[1,2,6,5,3,4,7,8]=>0011000=>[2,2,3]
[7,6,3,5,4,2,1,8]=>[2,3,6,4,5,7,8,1]=>0010001=>[2,1,3,1]
[8,6,3,5,4,2,7,1]=>[1,3,6,4,5,7,2,8]=>0010010=>[2,1,2,1,1]
[8,7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7,8]=>0010100=>[2,1,1,1,2]
[8,7,3,5,6,4,2,1]=>[1,2,6,4,3,5,7,8]=>0011000=>[2,2,3]
[8,7,3,6,5,4,2,1]=>[1,2,6,3,4,5,7,8]=>0010000=>[2,1,4]
[8,5,4,3,2,7,6,1]=>[1,4,5,6,7,2,3,8]=>0000100=>[4,1,2]
[8,5,4,3,7,6,2,1]=>[1,4,5,6,2,3,7,8]=>0001000=>[3,1,3]
[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>0001000=>[3,1,3]
[8,7,4,6,5,3,2,1]=>[1,2,5,3,4,6,7,8]=>0010000=>[2,1,4]
[2,4,1,3,6,5,8,7]=>[7,5,8,6,3,4,1,2]=>1011010=>[1,1,2,1,1,1]
[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>0110110=>[1,2,1,2,1]
[2,4,1,6,3,5,8,7]=>[7,5,8,3,6,4,1,2]=>1010110=>[1,1,1,1,2,1]
[2,4,6,1,3,5,8,7]=>[7,5,3,8,6,4,1,2]=>1101110=>[2,1,3,1]
[2,1,4,3,6,8,5,7]=>[7,8,5,6,3,1,4,2]=>0101101=>[1,1,1,2,1,1]
[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>1011101=>[1,1,3,1,1]
[2,1,4,6,3,8,5,7]=>[7,8,5,3,6,1,4,2]=>0110101=>[1,2,1,1,1,1]
[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,4,6,1,3,8,5,7]=>[7,5,3,8,6,1,4,2]=>1101101=>[2,1,2,1,1]
[2,1,4,6,8,3,5,7]=>[7,8,5,3,1,6,4,2]=>0111011=>[1,3,1,2]
[2,4,1,6,8,3,5,7]=>[7,5,8,3,1,6,4,2]=>1011011=>[1,1,2,1,2]
[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]=>1101011=>[2,1,1,1,2]
[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>1110111=>[3,1,3]
[2,4,1,3,6,5,7,8]=>[7,5,8,6,3,4,2,1]=>1011011=>[1,1,2,1,2]
[2,1,4,6,3,5,7,8]=>[7,8,5,3,6,4,2,1]=>0110111=>[1,2,1,3]
[2,4,1,6,3,5,7,8]=>[7,5,8,3,6,4,2,1]=>1010111=>[1,1,1,1,3]
[2,4,6,1,3,5,7,8]=>[7,5,3,8,6,4,2,1]=>1101111=>[2,1,4]
[2,4,1,3,6,7,5,8]=>[7,5,8,6,3,2,4,1]=>1011101=>[1,1,3,1,1]
[2,1,4,6,3,7,5,8]=>[7,8,5,3,6,2,4,1]=>0110101=>[1,2,1,1,1,1]
[2,4,1,6,3,7,5,8]=>[7,5,8,3,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,6,1,3,7,5,8]=>[7,5,3,8,6,2,4,1]=>1101101=>[2,1,2,1,1]
[2,1,4,6,7,3,5,8]=>[7,8,5,3,2,6,4,1]=>0111011=>[1,3,1,2]
[2,4,6,1,7,3,5,8]=>[7,5,3,8,2,6,4,1]=>1101011=>[2,1,1,1,2]
[2,4,6,7,1,3,5,8]=>[7,5,3,2,8,6,4,1]=>1110111=>[3,1,3]
[2,4,1,3,6,7,8,5]=>[7,5,8,6,3,2,1,4]=>1011110=>[1,1,4,1]
[2,1,4,6,3,7,8,5]=>[7,8,5,3,6,2,1,4]=>0110110=>[1,2,1,2,1]
[2,4,1,6,3,7,8,5]=>[7,5,8,3,6,2,1,4]=>1010110=>[1,1,1,1,2,1]
[2,4,6,1,3,7,8,5]=>[7,5,3,8,6,2,1,4]=>1101110=>[2,1,3,1]
[2,1,4,6,7,3,8,5]=>[7,8,5,3,2,6,1,4]=>0111010=>[1,3,1,1,1]
[2,4,1,6,7,3,8,5]=>[7,5,8,3,2,6,1,4]=>1011010=>[1,1,2,1,1,1]
[2,4,6,1,7,3,8,5]=>[7,5,3,8,2,6,1,4]=>1101010=>[2,1,1,1,1,1]
[2,4,6,7,1,3,8,5]=>[7,5,3,2,8,6,1,4]=>1110110=>[3,1,2,1]
[2,1,4,6,7,8,3,5]=>[7,8,5,3,2,1,6,4]=>0111101=>[1,4,1,1]
[2,4,1,6,7,8,3,5]=>[7,5,8,3,2,1,6,4]=>1011101=>[1,1,3,1,1]
[2,4,6,1,7,8,3,5]=>[7,5,3,8,2,1,6,4]=>1101101=>[2,1,2,1,1]
[2,4,6,7,1,8,3,5]=>[7,5,3,2,8,1,6,4]=>1110101=>[3,1,1,1,1]
[2,4,6,7,8,1,3,5]=>[7,5,3,2,1,8,6,4]=>1111011=>[4,1,2]
[2,1,4,3,7,5,8,6]=>[7,8,5,6,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,4,1,3,7,5,8,6]=>[7,5,8,6,2,4,1,3]=>1011010=>[1,1,2,1,1,1]
[2,4,1,7,3,5,8,6]=>[7,5,8,2,6,4,1,3]=>1010110=>[1,1,1,1,2,1]
[2,4,7,1,3,5,8,6]=>[7,5,2,8,6,4,1,3]=>1101110=>[2,1,3,1]
[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>0101101=>[1,1,1,2,1,1]
[2,4,1,3,7,8,5,6]=>[7,5,8,6,2,1,4,3]=>1011101=>[1,1,3,1,1]
[2,4,1,7,3,8,5,6]=>[7,5,8,2,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[2,4,7,1,3,8,5,6]=>[7,5,2,8,6,1,4,3]=>1101101=>[2,1,2,1,1]
[2,1,4,7,8,3,5,6]=>[7,8,5,2,1,6,4,3]=>0111011=>[1,3,1,2]
[2,4,1,7,8,3,5,6]=>[7,5,8,2,1,6,4,3]=>1011011=>[1,1,2,1,2]
[2,4,7,1,8,3,5,6]=>[7,5,2,8,1,6,4,3]=>1101011=>[2,1,1,1,2]
[2,4,7,8,1,3,5,6]=>[7,5,2,1,8,6,4,3]=>1110111=>[3,1,3]
[2,1,4,3,7,5,6,8]=>[7,8,5,6,2,4,3,1]=>0101011=>[1,1,1,1,1,2]
[2,1,4,7,3,5,6,8]=>[7,8,5,2,6,4,3,1]=>0110111=>[1,2,1,3]
[2,4,7,1,3,5,6,8]=>[7,5,2,8,6,4,3,1]=>1101111=>[2,1,4]
[2,4,1,5,3,7,6,8]=>[7,5,8,4,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[2,4,1,5,7,3,6,8]=>[7,5,8,4,2,6,3,1]=>1011011=>[1,1,2,1,2]
[2,4,5,1,7,3,6,8]=>[7,5,4,8,2,6,3,1]=>1101011=>[2,1,1,1,2]
[2,4,1,3,5,7,8,6]=>[7,5,8,6,4,2,1,3]=>1011110=>[1,1,4,1]
[2,4,5,1,3,7,8,6]=>[7,5,4,8,6,2,1,3]=>1101110=>[2,1,3,1]
[2,1,4,5,7,3,8,6]=>[7,8,5,4,2,6,1,3]=>0111010=>[1,3,1,1,1]
[2,4,1,5,7,3,8,6]=>[7,5,8,4,2,6,1,3]=>1011010=>[1,1,2,1,1,1]
[2,4,5,1,7,3,8,6]=>[7,5,4,8,2,6,1,3]=>1101010=>[2,1,1,1,1,1]
[2,4,5,7,1,3,8,6]=>[7,5,4,2,8,6,1,3]=>1110110=>[3,1,2,1]
[2,1,4,5,7,8,3,6]=>[7,8,5,4,2,1,6,3]=>0111101=>[1,4,1,1]
[2,4,1,5,7,8,3,6]=>[7,5,8,4,2,1,6,3]=>1011101=>[1,1,3,1,1]
[2,4,5,7,1,8,3,6]=>[7,5,4,2,8,1,6,3]=>1110101=>[3,1,1,1,1]
[2,4,5,7,8,1,3,6]=>[7,5,4,2,1,8,6,3]=>1111011=>[4,1,2]
[2,1,4,3,8,5,6,7]=>[7,8,5,6,1,4,3,2]=>0101011=>[1,1,1,1,1,2]
[2,4,1,3,8,5,6,7]=>[7,5,8,6,1,4,3,2]=>1011011=>[1,1,2,1,2]
[2,1,4,8,3,5,6,7]=>[7,8,5,1,6,4,3,2]=>0110111=>[1,2,1,3]
[2,4,1,8,3,5,6,7]=>[7,5,8,1,6,4,3,2]=>1010111=>[1,1,1,1,3]
[2,4,8,1,3,5,6,7]=>[7,5,1,8,6,4,3,2]=>1101111=>[2,1,4]
[2,1,4,3,5,8,6,7]=>[7,8,5,6,4,1,3,2]=>0101101=>[1,1,1,2,1,1]
[2,4,1,3,5,8,6,7]=>[7,5,8,6,4,1,3,2]=>1011101=>[1,1,3,1,1]
[2,4,1,5,3,8,6,7]=>[7,5,8,4,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[2,1,4,5,8,3,6,7]=>[7,8,5,4,1,6,3,2]=>0111011=>[1,3,1,2]
[2,4,1,5,8,3,6,7]=>[7,5,8,4,1,6,3,2]=>1011011=>[1,1,2,1,2]
[2,4,5,1,8,3,6,7]=>[7,5,4,8,1,6,3,2]=>1101011=>[2,1,1,1,2]
[2,4,5,8,1,3,6,7]=>[7,5,4,1,8,6,3,2]=>1110111=>[3,1,3]
[2,4,1,5,3,6,8,7]=>[7,5,8,4,6,3,1,2]=>1010110=>[1,1,1,1,2,1]
[2,4,5,1,3,6,8,7]=>[7,5,4,8,6,3,1,2]=>1101110=>[2,1,3,1]
[2,4,1,5,6,3,8,7]=>[7,5,8,4,3,6,1,2]=>1011010=>[1,1,2,1,1,1]
[2,1,4,5,6,8,3,7]=>[7,8,5,4,3,1,6,2]=>0111101=>[1,4,1,1]
[2,4,1,5,6,8,3,7]=>[7,5,8,4,3,1,6,2]=>1011101=>[1,1,3,1,1]
[2,4,5,6,1,8,3,7]=>[7,5,4,3,8,1,6,2]=>1110101=>[3,1,1,1,1]
[2,4,5,6,8,1,3,7]=>[7,5,4,3,1,8,6,2]=>1111011=>[4,1,2]
[2,4,1,3,5,6,7,8]=>[7,5,8,6,4,3,2,1]=>1011111=>[1,1,5]
[2,4,1,5,3,6,7,8]=>[7,5,8,4,6,3,2,1]=>1010111=>[1,1,1,1,3]
[2,4,5,1,3,6,7,8]=>[7,5,4,8,6,3,2,1]=>1101111=>[2,1,4]
[2,4,1,5,6,3,7,8]=>[7,5,8,4,3,6,2,1]=>1011011=>[1,1,2,1,2]
[2,4,5,1,6,3,7,8]=>[7,5,4,8,3,6,2,1]=>1101011=>[2,1,1,1,2]
[2,4,5,6,1,3,7,8]=>[7,5,4,3,8,6,2,1]=>1110111=>[3,1,3]
[2,4,1,5,6,7,3,8]=>[7,5,8,4,3,2,6,1]=>1011101=>[1,1,3,1,1]
[2,4,5,1,6,7,3,8]=>[7,5,4,8,3,2,6,1]=>1101101=>[2,1,2,1,1]
[2,4,5,6,1,7,3,8]=>[7,5,4,3,8,2,6,1]=>1110101=>[3,1,1,1,1]
[2,4,5,6,7,1,3,8]=>[7,5,4,3,2,8,6,1]=>1111011=>[4,1,2]
[2,4,1,5,6,7,8,3]=>[7,5,8,4,3,2,1,6]=>1011110=>[1,1,4,1]
[2,4,5,6,1,7,8,3]=>[7,5,4,3,8,2,1,6]=>1110110=>[3,1,2,1]
[2,4,5,6,7,1,8,3]=>[7,5,4,3,2,8,1,6]=>1111010=>[4,1,1,1]
[2,4,5,6,7,8,1,3]=>[7,5,4,3,2,1,8,6]=>1111101=>[5,1,1]
[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[2,5,1,3,6,4,8,7]=>[7,4,8,6,3,5,1,2]=>1011010=>[1,1,2,1,1,1]
[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>0110110=>[1,2,1,2,1]
[2,5,1,6,3,4,8,7]=>[7,4,8,3,6,5,1,2]=>1010110=>[1,1,1,1,2,1]
[2,5,1,3,6,8,4,7]=>[7,4,8,6,3,1,5,2]=>1011101=>[1,1,3,1,1]
[2,1,5,6,3,8,4,7]=>[7,8,4,3,6,1,5,2]=>0110101=>[1,2,1,1,1,1]
[2,5,1,6,3,8,4,7]=>[7,4,8,3,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[2,5,6,1,3,8,4,7]=>[7,4,3,8,6,1,5,2]=>1101101=>[2,1,2,1,1]
[2,5,1,6,8,3,4,7]=>[7,4,8,3,1,6,5,2]=>1011011=>[1,1,2,1,2]
[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]=>1101011=>[2,1,1,1,2]
[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>1110111=>[3,1,3]
[2,5,1,3,6,4,7,8]=>[7,4,8,6,3,5,2,1]=>1011011=>[1,1,2,1,2]
[2,1,5,6,3,4,7,8]=>[7,8,4,3,6,5,2,1]=>0110111=>[1,2,1,3]
[2,5,1,6,3,4,7,8]=>[7,4,8,3,6,5,2,1]=>1010111=>[1,1,1,1,3]
[2,5,1,3,6,7,4,8]=>[7,4,8,6,3,2,5,1]=>1011101=>[1,1,3,1,1]
[2,1,5,6,3,7,4,8]=>[7,8,4,3,6,2,5,1]=>0110101=>[1,2,1,1,1,1]
[2,5,1,6,3,7,4,8]=>[7,4,8,3,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[2,5,6,1,3,7,4,8]=>[7,4,3,8,6,2,5,1]=>1101101=>[2,1,2,1,1]
[2,1,5,6,7,3,4,8]=>[7,8,4,3,2,6,5,1]=>0111011=>[1,3,1,2]
[2,5,1,6,7,3,4,8]=>[7,4,8,3,2,6,5,1]=>1011011=>[1,1,2,1,2]
[2,5,6,1,7,3,4,8]=>[7,4,3,8,2,6,5,1]=>1101011=>[2,1,1,1,2]
[2,1,5,3,6,7,8,4]=>[7,8,4,6,3,2,1,5]=>0101110=>[1,1,1,3,1]
[2,1,5,6,3,7,8,4]=>[7,8,4,3,6,2,1,5]=>0110110=>[1,2,1,2,1]
[2,5,1,6,3,7,8,4]=>[7,4,8,3,6,2,1,5]=>1010110=>[1,1,1,1,2,1]
[2,5,6,1,3,7,8,4]=>[7,4,3,8,6,2,1,5]=>1101110=>[2,1,3,1]
[2,5,1,6,7,3,8,4]=>[7,4,8,3,2,6,1,5]=>1011010=>[1,1,2,1,1,1]
[2,5,6,1,7,3,8,4]=>[7,4,3,8,2,6,1,5]=>1101010=>[2,1,1,1,1,1]
[2,5,6,7,1,3,8,4]=>[7,4,3,2,8,6,1,5]=>1110110=>[3,1,2,1]
[2,1,5,6,7,8,3,4]=>[7,8,4,3,2,1,6,5]=>0111101=>[1,4,1,1]
[2,5,1,6,7,8,3,4]=>[7,4,8,3,2,1,6,5]=>1011101=>[1,1,3,1,1]
[2,5,6,1,7,8,3,4]=>[7,4,3,8,2,1,6,5]=>1101101=>[2,1,2,1,1]
[2,5,6,7,1,8,3,4]=>[7,4,3,2,8,1,6,5]=>1110101=>[3,1,1,1,1]
[2,5,6,7,8,1,3,4]=>[7,4,3,2,1,8,6,5]=>1111011=>[4,1,2]
[2,1,5,3,7,4,8,6]=>[7,8,4,6,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,7,3,4,8,6]=>[7,8,4,2,6,5,1,3]=>0110110=>[1,2,1,2,1]
[2,5,1,7,3,4,8,6]=>[7,4,8,2,6,5,1,3]=>1010110=>[1,1,1,1,2,1]
[2,5,7,1,3,4,8,6]=>[7,4,2,8,6,5,1,3]=>1101110=>[2,1,3,1]
[2,5,1,3,7,8,4,6]=>[7,4,8,6,2,1,5,3]=>1011101=>[1,1,3,1,1]
[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>0110101=>[1,2,1,1,1,1]
[2,5,1,7,3,8,4,6]=>[7,4,8,2,6,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,5,7,8,3,4,6]=>[7,8,4,2,1,6,5,3]=>0111011=>[1,3,1,2]
[2,5,7,1,8,3,4,6]=>[7,4,2,8,1,6,5,3]=>1101011=>[2,1,1,1,2]
[2,5,7,8,1,3,4,6]=>[7,4,2,1,8,6,5,3]=>1110111=>[3,1,3]
[2,5,1,3,7,4,6,8]=>[7,4,8,6,2,5,3,1]=>1011011=>[1,1,2,1,2]
[2,1,5,7,3,4,6,8]=>[7,8,4,2,6,5,3,1]=>0110111=>[1,2,1,3]
[2,5,1,7,3,4,6,8]=>[7,4,8,2,6,5,3,1]=>1010111=>[1,1,1,1,3]
[2,5,7,1,3,4,6,8]=>[7,4,2,8,6,5,3,1]=>1101111=>[2,1,4]
[2,5,1,3,4,7,6,8]=>[7,4,8,6,5,2,3,1]=>1011101=>[1,1,3,1,1]
[2,3,5,1,4,7,6,8]=>[7,6,4,8,5,2,3,1]=>1101101=>[2,1,2,1,1]
[2,1,3,5,7,4,6,8]=>[7,8,6,4,2,5,3,1]=>0111011=>[1,3,1,2]
[2,3,1,5,7,4,6,8]=>[7,6,8,4,2,5,3,1]=>1011011=>[1,1,2,1,2]
[2,3,5,7,1,4,6,8]=>[7,6,4,2,8,5,3,1]=>1110111=>[3,1,3]
[2,5,1,3,4,7,8,6]=>[7,4,8,6,5,2,1,3]=>1011110=>[1,1,4,1]
[2,3,5,1,4,7,8,6]=>[7,6,4,8,5,2,1,3]=>1101110=>[2,1,3,1]
[2,1,3,5,7,4,8,6]=>[7,8,6,4,2,5,1,3]=>0111010=>[1,3,1,1,1]
[2,3,5,1,7,4,8,6]=>[7,6,4,8,2,5,1,3]=>1101010=>[2,1,1,1,1,1]
[2,3,5,7,1,4,8,6]=>[7,6,4,2,8,5,1,3]=>1110110=>[3,1,2,1]
[2,3,5,1,7,8,4,6]=>[7,6,4,8,2,1,5,3]=>1101101=>[2,1,2,1,1]
[2,3,5,7,1,8,4,6]=>[7,6,4,2,8,1,5,3]=>1110101=>[3,1,1,1,1]
[2,5,1,3,8,4,6,7]=>[7,4,8,6,1,5,3,2]=>1011011=>[1,1,2,1,2]
[2,1,5,8,3,4,6,7]=>[7,8,4,1,6,5,3,2]=>0110111=>[1,2,1,3]
[2,5,1,8,3,4,6,7]=>[7,4,8,1,6,5,3,2]=>1010111=>[1,1,1,1,3]
[2,5,8,1,3,4,6,7]=>[7,4,1,8,6,5,3,2]=>1101111=>[2,1,4]
[2,5,1,3,4,8,6,7]=>[7,4,8,6,5,1,3,2]=>1011101=>[1,1,3,1,1]
[2,3,5,1,4,8,6,7]=>[7,6,4,8,5,1,3,2]=>1101101=>[2,1,2,1,1]
[2,3,1,5,8,4,6,7]=>[7,6,8,4,1,5,3,2]=>1011011=>[1,1,2,1,2]
[2,3,5,1,8,4,6,7]=>[7,6,4,8,1,5,3,2]=>1101011=>[2,1,1,1,2]
[2,3,5,8,1,4,6,7]=>[7,6,4,1,8,5,3,2]=>1110111=>[3,1,3]
[2,1,5,3,4,6,8,7]=>[7,8,4,6,5,3,1,2]=>0101110=>[1,1,1,3,1]
[2,5,1,3,4,6,8,7]=>[7,4,8,6,5,3,1,2]=>1011110=>[1,1,4,1]
[2,3,5,1,4,6,8,7]=>[7,6,4,8,5,3,1,2]=>1101110=>[2,1,3,1]
[2,3,5,6,1,4,8,7]=>[7,6,4,3,8,5,1,2]=>1110110=>[3,1,2,1]
[2,1,3,5,6,8,4,7]=>[7,8,6,4,3,1,5,2]=>0111101=>[1,4,1,1]
[2,3,1,5,6,8,4,7]=>[7,6,8,4,3,1,5,2]=>1011101=>[1,1,3,1,1]
[2,3,5,1,6,8,4,7]=>[7,6,4,8,3,1,5,2]=>1101101=>[2,1,2,1,1]
[2,3,5,6,1,8,4,7]=>[7,6,4,3,8,1,5,2]=>1110101=>[3,1,1,1,1]
[2,3,5,6,8,1,4,7]=>[7,6,4,3,1,8,5,2]=>1111011=>[4,1,2]
[2,5,1,3,4,6,7,8]=>[7,4,8,6,5,3,2,1]=>1011111=>[1,1,5]
[2,3,5,1,4,6,7,8]=>[7,6,4,8,5,3,2,1]=>1101111=>[2,1,4]
[2,3,5,1,6,4,7,8]=>[7,6,4,8,3,5,2,1]=>1101011=>[2,1,1,1,2]
[2,3,5,6,1,4,7,8]=>[7,6,4,3,8,5,2,1]=>1110111=>[3,1,3]
[2,3,5,1,6,7,4,8]=>[7,6,4,8,3,2,5,1]=>1101101=>[2,1,2,1,1]
[2,3,5,6,1,7,4,8]=>[7,6,4,3,8,2,5,1]=>1110101=>[3,1,1,1,1]
[2,3,5,6,7,1,4,8]=>[7,6,4,3,2,8,5,1]=>1111011=>[4,1,2]
[2,3,5,1,6,7,8,4]=>[7,6,4,8,3,2,1,5]=>1101110=>[2,1,3,1]
[2,3,5,6,1,7,8,4]=>[7,6,4,3,8,2,1,5]=>1110110=>[3,1,2,1]
[2,3,5,6,7,1,8,4]=>[7,6,4,3,2,8,1,5]=>1111010=>[4,1,1,1]
[2,3,5,6,7,8,1,4]=>[7,6,4,3,2,1,8,5]=>1111101=>[5,1,1]
[2,1,6,3,7,4,8,5]=>[7,8,3,6,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[2,6,1,3,7,4,8,5]=>[7,3,8,6,2,5,1,4]=>1011010=>[1,1,2,1,1,1]
[2,6,1,7,3,4,8,5]=>[7,3,8,2,6,5,1,4]=>1010110=>[1,1,1,1,2,1]
[2,6,7,1,3,4,8,5]=>[7,3,2,8,6,5,1,4]=>1101110=>[2,1,3,1]
[2,1,6,3,7,8,4,5]=>[7,8,3,6,2,1,5,4]=>0101101=>[1,1,1,2,1,1]
[2,6,1,7,3,8,4,5]=>[7,3,8,2,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,7,1,3,8,4,5]=>[7,3,2,8,6,1,5,4]=>1101101=>[2,1,2,1,1]
[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>0111011=>[1,3,1,2]
[2,6,1,7,8,3,4,5]=>[7,3,8,2,1,6,5,4]=>1011011=>[1,1,2,1,2]
[2,6,7,1,8,3,4,5]=>[7,3,2,8,1,6,5,4]=>1101011=>[2,1,1,1,2]
[2,6,7,8,1,3,4,5]=>[7,3,2,1,8,6,5,4]=>1110111=>[3,1,3]
[2,1,6,3,7,4,5,8]=>[7,8,3,6,2,5,4,1]=>0101011=>[1,1,1,1,1,2]
[2,1,6,7,3,4,5,8]=>[7,8,3,2,6,5,4,1]=>0110111=>[1,2,1,3]
[2,6,1,7,3,4,5,8]=>[7,3,8,2,6,5,4,1]=>1010111=>[1,1,1,1,3]
[2,6,7,1,3,4,5,8]=>[7,3,2,8,6,5,4,1]=>1101111=>[2,1,4]
[2,3,1,6,4,7,5,8]=>[7,6,8,3,5,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[2,1,3,6,7,4,5,8]=>[7,8,6,3,2,5,4,1]=>0111011=>[1,3,1,2]
[2,3,1,6,7,4,5,8]=>[7,6,8,3,2,5,4,1]=>1011011=>[1,1,2,1,2]
[2,3,6,7,1,4,5,8]=>[7,6,3,2,8,5,4,1]=>1110111=>[3,1,3]
[2,1,6,3,4,7,8,5]=>[7,8,3,6,5,2,1,4]=>0101110=>[1,1,1,3,1]
[2,6,1,3,4,7,8,5]=>[7,3,8,6,5,2,1,4]=>1011110=>[1,1,4,1]
[2,3,1,6,4,7,8,5]=>[7,6,8,3,5,2,1,4]=>1010110=>[1,1,1,1,2,1]
[2,3,6,1,4,7,8,5]=>[7,6,3,8,5,2,1,4]=>1101110=>[2,1,3,1]
[2,3,1,6,7,4,8,5]=>[7,6,8,3,2,5,1,4]=>1011010=>[1,1,2,1,1,1]
[2,3,6,1,7,4,8,5]=>[7,6,3,8,2,5,1,4]=>1101010=>[2,1,1,1,1,1]
[2,3,6,7,1,4,8,5]=>[7,6,3,2,8,5,1,4]=>1110110=>[3,1,2,1]
[2,1,3,6,7,8,4,5]=>[7,8,6,3,2,1,5,4]=>0111101=>[1,4,1,1]
[2,3,1,6,7,8,4,5]=>[7,6,8,3,2,1,5,4]=>1011101=>[1,1,3,1,1]
[2,3,6,1,7,8,4,5]=>[7,6,3,8,2,1,5,4]=>1101101=>[2,1,2,1,1]
[2,3,6,7,1,8,4,5]=>[7,6,3,2,8,1,5,4]=>1110101=>[3,1,1,1,1]
[2,3,6,7,8,1,4,5]=>[7,6,3,2,1,8,5,4]=>1111011=>[4,1,2]
[2,1,6,3,8,4,5,7]=>[7,8,3,6,1,5,4,2]=>0101011=>[1,1,1,1,1,2]
[2,6,1,3,8,4,5,7]=>[7,3,8,6,1,5,4,2]=>1011011=>[1,1,2,1,2]
[2,1,6,8,3,4,5,7]=>[7,8,3,1,6,5,4,2]=>0110111=>[1,2,1,3]
[2,6,1,8,3,4,5,7]=>[7,3,8,1,6,5,4,2]=>1010111=>[1,1,1,1,3]
[2,6,8,1,3,4,5,7]=>[7,3,1,8,6,5,4,2]=>1101111=>[2,1,4]
[2,6,1,3,4,8,5,7]=>[7,3,8,6,5,1,4,2]=>1011101=>[1,1,3,1,1]
[2,1,3,6,4,8,5,7]=>[7,8,6,3,5,1,4,2]=>0110101=>[1,2,1,1,1,1]
[2,3,1,6,4,8,5,7]=>[7,6,8,3,5,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,3,6,1,4,8,5,7]=>[7,6,3,8,5,1,4,2]=>1101101=>[2,1,2,1,1]
[2,1,3,6,8,4,5,7]=>[7,8,6,3,1,5,4,2]=>0111011=>[1,3,1,2]
[2,3,1,6,8,4,5,7]=>[7,6,8,3,1,5,4,2]=>1011011=>[1,1,2,1,2]
[2,3,6,1,8,4,5,7]=>[7,6,3,8,1,5,4,2]=>1101011=>[2,1,1,1,2]
[2,1,6,3,4,5,8,7]=>[7,8,3,6,5,4,1,2]=>0101110=>[1,1,1,3,1]
[2,6,1,3,4,5,8,7]=>[7,3,8,6,5,4,1,2]=>1011110=>[1,1,4,1]
[2,3,6,1,4,5,8,7]=>[7,6,3,8,5,4,1,2]=>1101110=>[2,1,3,1]
[2,3,4,6,1,5,8,7]=>[7,6,5,3,8,4,1,2]=>1110110=>[3,1,2,1]
[2,3,4,1,6,8,5,7]=>[7,6,5,8,3,1,4,2]=>1101101=>[2,1,2,1,1]
[2,3,4,6,8,1,5,7]=>[7,6,5,3,1,8,4,2]=>1111011=>[4,1,2]
[2,6,1,3,4,5,7,8]=>[7,3,8,6,5,4,2,1]=>1011111=>[1,1,5]
[2,1,3,6,4,5,7,8]=>[7,8,6,3,5,4,2,1]=>0110111=>[1,2,1,3]
[2,3,1,6,4,5,7,8]=>[7,6,8,3,5,4,2,1]=>1010111=>[1,1,1,1,3]
[2,3,6,1,4,5,7,8]=>[7,6,3,8,5,4,2,1]=>1101111=>[2,1,4]
[2,3,4,6,1,5,7,8]=>[7,6,5,3,8,4,2,1]=>1110111=>[3,1,3]
[2,3,4,6,1,7,5,8]=>[7,6,5,3,8,2,4,1]=>1110101=>[3,1,1,1,1]
[2,3,4,6,7,1,5,8]=>[7,6,5,3,2,8,4,1]=>1111011=>[4,1,2]
[2,3,4,6,7,8,1,5]=>[7,6,5,3,2,1,8,4]=>1111101=>[5,1,1]
[2,1,7,3,8,4,5,6]=>[7,8,2,6,1,5,4,3]=>0101011=>[1,1,1,1,1,2]
[2,1,7,8,3,4,5,6]=>[7,8,2,1,6,5,4,3]=>0110111=>[1,2,1,3]
[2,7,1,8,3,4,5,6]=>[7,2,8,1,6,5,4,3]=>1010111=>[1,1,1,1,3]
[2,7,8,1,3,4,5,6]=>[7,2,1,8,6,5,4,3]=>1101111=>[2,1,4]
[2,1,7,3,4,8,5,6]=>[7,8,2,6,5,1,4,3]=>0101101=>[1,1,1,2,1,1]
[2,7,1,3,4,8,5,6]=>[7,2,8,6,5,1,4,3]=>1011101=>[1,1,3,1,1]
[2,3,1,7,4,8,5,6]=>[7,6,8,2,5,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[2,3,7,1,4,8,5,6]=>[7,6,2,8,5,1,4,3]=>1101101=>[2,1,2,1,1]
[2,1,3,7,8,4,5,6]=>[7,8,6,2,1,5,4,3]=>0111011=>[1,3,1,2]
[2,3,7,8,1,4,5,6]=>[7,6,2,1,8,5,4,3]=>1110111=>[3,1,3]
[2,1,7,3,4,5,8,6]=>[7,8,2,6,5,4,1,3]=>0101110=>[1,1,1,3,1]
[2,7,1,3,4,5,8,6]=>[7,2,8,6,5,4,1,3]=>1011110=>[1,1,4,1]
[2,3,1,4,7,5,8,6]=>[7,6,8,5,2,4,1,3]=>1011010=>[1,1,2,1,1,1]
[2,3,4,1,7,5,8,6]=>[7,6,5,8,2,4,1,3]=>1101010=>[2,1,1,1,1,1]
[2,3,4,7,1,5,8,6]=>[7,6,5,2,8,4,1,3]=>1110110=>[3,1,2,1]
[2,1,3,4,7,8,5,6]=>[7,8,6,5,2,1,4,3]=>0111101=>[1,4,1,1]
[2,3,1,4,7,8,5,6]=>[7,6,8,5,2,1,4,3]=>1011101=>[1,1,3,1,1]
[2,3,4,1,7,8,5,6]=>[7,6,5,8,2,1,4,3]=>1101101=>[2,1,2,1,1]
[2,3,4,7,1,8,5,6]=>[7,6,5,2,8,1,4,3]=>1110101=>[3,1,1,1,1]
[2,3,4,7,8,1,5,6]=>[7,6,5,2,1,8,4,3]=>1111011=>[4,1,2]
[2,1,7,3,4,5,6,8]=>[7,8,2,6,5,4,3,1]=>0101111=>[1,1,1,4]
[2,7,1,3,4,5,6,8]=>[7,2,8,6,5,4,3,1]=>1011111=>[1,1,5]
[2,1,3,4,7,5,6,8]=>[7,8,6,5,2,4,3,1]=>0111011=>[1,3,1,2]
[2,3,1,4,7,5,6,8]=>[7,6,8,5,2,4,3,1]=>1011011=>[1,1,2,1,2]
[2,3,4,1,7,5,6,8]=>[7,6,5,8,2,4,3,1]=>1101011=>[2,1,1,1,2]
[2,3,4,7,1,5,6,8]=>[7,6,5,2,8,4,3,1]=>1110111=>[3,1,3]
[2,3,4,5,7,1,6,8]=>[7,6,5,4,2,8,3,1]=>1111011=>[4,1,2]
[2,3,4,5,7,1,8,6]=>[7,6,5,4,2,8,1,3]=>1111010=>[4,1,1,1]
[2,3,4,5,7,8,1,6]=>[7,6,5,4,2,1,8,3]=>1111101=>[5,1,1]
[2,1,8,3,4,5,6,7]=>[7,8,1,6,5,4,3,2]=>0101111=>[1,1,1,4]
[2,8,1,3,4,5,6,7]=>[7,1,8,6,5,4,3,2]=>1011111=>[1,1,5]
[2,1,3,8,4,5,6,7]=>[7,8,6,1,5,4,3,2]=>0110111=>[1,2,1,3]
[2,3,1,8,4,5,6,7]=>[7,6,8,1,5,4,3,2]=>1010111=>[1,1,1,1,3]
[2,3,8,1,4,5,6,7]=>[7,6,1,8,5,4,3,2]=>1101111=>[2,1,4]
[2,1,3,4,8,5,6,7]=>[7,8,6,5,1,4,3,2]=>0111011=>[1,3,1,2]
[2,3,1,4,8,5,6,7]=>[7,6,8,5,1,4,3,2]=>1011011=>[1,1,2,1,2]
[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>1101011=>[2,1,1,1,2]
[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>1110111=>[3,1,3]
[2,1,3,4,5,8,6,7]=>[7,8,6,5,4,1,3,2]=>0111101=>[1,4,1,1]
[2,3,1,4,5,8,6,7]=>[7,6,8,5,4,1,3,2]=>1011101=>[1,1,3,1,1]
[2,3,4,1,5,8,6,7]=>[7,6,5,8,4,1,3,2]=>1101101=>[2,1,2,1,1]
[2,3,4,5,1,8,6,7]=>[7,6,5,4,8,1,3,2]=>1110101=>[3,1,1,1,1]
[2,3,4,5,8,1,6,7]=>[7,6,5,4,1,8,3,2]=>1111011=>[4,1,2]
[2,3,4,5,6,8,1,7]=>[7,6,5,4,3,1,8,2]=>1111101=>[5,1,1]
[3,1,4,2,6,5,8,7]=>[6,8,5,7,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>1011010=>[1,1,2,1,1,1]
[3,4,1,6,2,5,8,7]=>[6,5,8,3,7,4,1,2]=>1010110=>[1,1,1,1,2,1]
[3,4,6,1,2,5,8,7]=>[6,5,3,8,7,4,1,2]=>1101110=>[2,1,3,1]
[3,1,4,2,6,8,5,7]=>[6,8,5,7,3,1,4,2]=>0101101=>[1,1,1,2,1,1]
[3,4,1,2,6,8,5,7]=>[6,5,8,7,3,1,4,2]=>1011101=>[1,1,3,1,1]
[3,4,1,6,2,8,5,7]=>[6,5,8,3,7,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[3,4,6,1,2,8,5,7]=>[6,5,3,8,7,1,4,2]=>1101101=>[2,1,2,1,1]
[3,1,4,6,8,2,5,7]=>[6,8,5,3,1,7,4,2]=>0111011=>[1,3,1,2]
[3,4,6,8,1,2,5,7]=>[6,5,3,1,8,7,4,2]=>1110111=>[3,1,3]
[3,4,1,2,6,5,7,8]=>[6,5,8,7,3,4,2,1]=>1011011=>[1,1,2,1,2]
[3,4,1,2,6,7,5,8]=>[6,5,8,7,3,2,4,1]=>1011101=>[1,1,3,1,1]
[3,1,4,6,2,7,5,8]=>[6,8,5,3,7,2,4,1]=>0110101=>[1,2,1,1,1,1]
[3,4,1,6,2,7,5,8]=>[6,5,8,3,7,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[3,4,6,1,2,7,5,8]=>[6,5,3,8,7,2,4,1]=>1101101=>[2,1,2,1,1]
[3,4,6,1,7,2,5,8]=>[6,5,3,8,2,7,4,1]=>1101011=>[2,1,1,1,2]
[3,4,6,7,1,2,5,8]=>[6,5,3,2,8,7,4,1]=>1110111=>[3,1,3]
[3,1,4,2,6,7,8,5]=>[6,8,5,7,3,2,1,4]=>0101110=>[1,1,1,3,1]
[3,4,1,2,6,7,8,5]=>[6,5,8,7,3,2,1,4]=>1011110=>[1,1,4,1]
[3,1,4,6,2,7,8,5]=>[6,8,5,3,7,2,1,4]=>0110110=>[1,2,1,2,1]
[3,4,1,6,2,7,8,5]=>[6,5,8,3,7,2,1,4]=>1010110=>[1,1,1,1,2,1]
[3,4,6,1,2,7,8,5]=>[6,5,3,8,7,2,1,4]=>1101110=>[2,1,3,1]
[3,1,4,6,7,2,8,5]=>[6,8,5,3,2,7,1,4]=>0111010=>[1,3,1,1,1]
[3,4,1,6,7,2,8,5]=>[6,5,8,3,2,7,1,4]=>1011010=>[1,1,2,1,1,1]
[3,4,6,1,7,2,8,5]=>[6,5,3,8,2,7,1,4]=>1101010=>[2,1,1,1,1,1]
[3,4,6,7,1,2,8,5]=>[6,5,3,2,8,7,1,4]=>1110110=>[3,1,2,1]
[3,4,1,6,7,8,2,5]=>[6,5,8,3,2,1,7,4]=>1011101=>[1,1,3,1,1]
[3,4,6,1,7,8,2,5]=>[6,5,3,8,2,1,7,4]=>1101101=>[2,1,2,1,1]
[3,4,6,7,1,8,2,5]=>[6,5,3,2,8,1,7,4]=>1110101=>[3,1,1,1,1]
[3,4,6,7,8,1,2,5]=>[6,5,3,2,1,8,7,4]=>1111011=>[4,1,2]
[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,4,1,2,7,5,8,6]=>[6,5,8,7,2,4,1,3]=>1011010=>[1,1,2,1,1,1]
[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>0110110=>[1,2,1,2,1]
[3,4,1,7,2,5,8,6]=>[6,5,8,2,7,4,1,3]=>1010110=>[1,1,1,1,2,1]
[3,1,4,2,7,8,5,6]=>[6,8,5,7,2,1,4,3]=>0101101=>[1,1,1,2,1,1]
[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>1011101=>[1,1,3,1,1]
[3,1,4,7,2,8,5,6]=>[6,8,5,2,7,1,4,3]=>0110101=>[1,2,1,1,1,1]
[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[3,4,7,1,2,8,5,6]=>[6,5,2,8,7,1,4,3]=>1101101=>[2,1,2,1,1]
[3,1,4,7,8,2,5,6]=>[6,8,5,2,1,7,4,3]=>0111011=>[1,3,1,2]
[3,4,1,7,8,2,5,6]=>[6,5,8,2,1,7,4,3]=>1011011=>[1,1,2,1,2]
[3,4,7,1,8,2,5,6]=>[6,5,2,8,1,7,4,3]=>1101011=>[2,1,1,1,2]
[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>1110111=>[3,1,3]
[3,4,1,2,7,5,6,8]=>[6,5,8,7,2,4,3,1]=>1011011=>[1,1,2,1,2]
[3,1,4,7,2,5,6,8]=>[6,8,5,2,7,4,3,1]=>0110111=>[1,2,1,3]
[3,4,7,1,2,5,6,8]=>[6,5,2,8,7,4,3,1]=>1101111=>[2,1,4]
[3,1,4,2,5,7,6,8]=>[6,8,5,7,4,2,3,1]=>0101101=>[1,1,1,2,1,1]
[3,4,1,2,5,7,6,8]=>[6,5,8,7,4,2,3,1]=>1011101=>[1,1,3,1,1]
[3,1,4,5,2,7,6,8]=>[6,8,5,4,7,2,3,1]=>0110101=>[1,2,1,1,1,1]
[3,4,1,5,2,7,6,8]=>[6,5,8,4,7,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[3,4,5,1,2,7,6,8]=>[6,5,4,8,7,2,3,1]=>1101101=>[2,1,2,1,1]
[3,1,4,5,7,2,6,8]=>[6,8,5,4,2,7,3,1]=>0111011=>[1,3,1,2]
[3,4,1,5,7,2,6,8]=>[6,5,8,4,2,7,3,1]=>1011011=>[1,1,2,1,2]
[3,4,5,1,7,2,6,8]=>[6,5,4,8,2,7,3,1]=>1101011=>[2,1,1,1,2]
[3,1,4,2,5,7,8,6]=>[6,8,5,7,4,2,1,3]=>0101110=>[1,1,1,3,1]
[3,4,1,2,5,7,8,6]=>[6,5,8,7,4,2,1,3]=>1011110=>[1,1,4,1]
[3,4,1,5,2,7,8,6]=>[6,5,8,4,7,2,1,3]=>1010110=>[1,1,1,1,2,1]
[3,4,5,1,2,7,8,6]=>[6,5,4,8,7,2,1,3]=>1101110=>[2,1,3,1]
[3,1,4,5,7,2,8,6]=>[6,8,5,4,2,7,1,3]=>0111010=>[1,3,1,1,1]
[3,4,5,1,7,2,8,6]=>[6,5,4,8,2,7,1,3]=>1101010=>[2,1,1,1,1,1]
[3,4,5,7,1,2,8,6]=>[6,5,4,2,8,7,1,3]=>1110110=>[3,1,2,1]
[3,1,4,5,7,8,2,6]=>[6,8,5,4,2,1,7,3]=>0111101=>[1,4,1,1]
[3,4,1,5,7,8,2,6]=>[6,5,8,4,2,1,7,3]=>1011101=>[1,1,3,1,1]
[3,4,5,1,7,8,2,6]=>[6,5,4,8,2,1,7,3]=>1101101=>[2,1,2,1,1]
[3,1,4,2,8,5,6,7]=>[6,8,5,7,1,4,3,2]=>0101011=>[1,1,1,1,1,2]
[3,4,1,2,8,5,6,7]=>[6,5,8,7,1,4,3,2]=>1011011=>[1,1,2,1,2]
[3,1,4,8,2,5,6,7]=>[6,8,5,1,7,4,3,2]=>0110111=>[1,2,1,3]
[3,4,1,8,2,5,6,7]=>[6,5,8,1,7,4,3,2]=>1010111=>[1,1,1,1,3]
[3,4,8,1,2,5,6,7]=>[6,5,1,8,7,4,3,2]=>1101111=>[2,1,4]
[3,4,1,2,5,8,6,7]=>[6,5,8,7,4,1,3,2]=>1011101=>[1,1,3,1,1]
[3,1,4,5,2,8,6,7]=>[6,8,5,4,7,1,3,2]=>0110101=>[1,2,1,1,1,1]
[3,4,1,5,2,8,6,7]=>[6,5,8,4,7,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[3,4,5,1,2,8,6,7]=>[6,5,4,8,7,1,3,2]=>1101101=>[2,1,2,1,1]
[3,4,1,5,8,2,6,7]=>[6,5,8,4,1,7,3,2]=>1011011=>[1,1,2,1,2]
[3,4,5,8,1,2,6,7]=>[6,5,4,1,8,7,3,2]=>1110111=>[3,1,3]
[3,4,1,2,5,6,8,7]=>[6,5,8,7,4,3,1,2]=>1011110=>[1,1,4,1]
[3,4,5,1,2,6,8,7]=>[6,5,4,8,7,3,1,2]=>1101110=>[2,1,3,1]
[3,1,4,5,6,2,8,7]=>[6,8,5,4,3,7,1,2]=>0111010=>[1,3,1,1,1]
[3,4,1,5,6,2,8,7]=>[6,5,8,4,3,7,1,2]=>1011010=>[1,1,2,1,1,1]
[3,4,5,1,6,2,8,7]=>[6,5,4,8,3,7,1,2]=>1101010=>[2,1,1,1,1,1]
[3,4,5,6,1,2,8,7]=>[6,5,4,3,8,7,1,2]=>1110110=>[3,1,2,1]
[3,1,4,5,6,8,2,7]=>[6,8,5,4,3,1,7,2]=>0111101=>[1,4,1,1]
[3,4,1,5,6,8,2,7]=>[6,5,8,4,3,1,7,2]=>1011101=>[1,1,3,1,1]
[3,4,5,6,1,8,2,7]=>[6,5,4,3,8,1,7,2]=>1110101=>[3,1,1,1,1]
[3,4,5,6,8,1,2,7]=>[6,5,4,3,1,8,7,2]=>1111011=>[4,1,2]
[3,1,4,2,5,6,7,8]=>[6,8,5,7,4,3,2,1]=>0101111=>[1,1,1,4]
[3,1,4,5,2,6,7,8]=>[6,8,5,4,7,3,2,1]=>0110111=>[1,2,1,3]
[3,4,1,5,2,6,7,8]=>[6,5,8,4,7,3,2,1]=>1010111=>[1,1,1,1,3]
[3,1,4,5,6,2,7,8]=>[6,8,5,4,3,7,2,1]=>0111011=>[1,3,1,2]
[3,4,1,5,6,2,7,8]=>[6,5,8,4,3,7,2,1]=>1011011=>[1,1,2,1,2]
[3,4,5,1,6,2,7,8]=>[6,5,4,8,3,7,2,1]=>1101011=>[2,1,1,1,2]
[3,1,4,5,6,7,2,8]=>[6,8,5,4,3,2,7,1]=>0111101=>[1,4,1,1]
[3,4,1,5,6,7,2,8]=>[6,5,8,4,3,2,7,1]=>1011101=>[1,1,3,1,1]
[3,4,5,1,6,7,2,8]=>[6,5,4,8,3,2,7,1]=>1101101=>[2,1,2,1,1]
[3,4,5,6,1,7,2,8]=>[6,5,4,3,8,2,7,1]=>1110101=>[3,1,1,1,1]
[3,1,4,5,6,7,8,2]=>[6,8,5,4,3,2,1,7]=>0111110=>[1,5,1]
[3,4,1,5,6,7,8,2]=>[6,5,8,4,3,2,1,7]=>1011110=>[1,1,4,1]
[3,4,5,1,6,7,8,2]=>[6,5,4,8,3,2,1,7]=>1101110=>[2,1,3,1]
[3,4,5,6,1,7,8,2]=>[6,5,4,3,8,2,1,7]=>1110110=>[3,1,2,1]
[3,4,5,6,7,1,8,2]=>[6,5,4,3,2,8,1,7]=>1111010=>[4,1,1,1]
[3,1,5,2,6,4,8,7]=>[6,8,4,7,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,5,1,2,6,4,8,7]=>[6,4,8,7,3,5,1,2]=>1011010=>[1,1,2,1,1,1]
[3,1,5,6,2,4,8,7]=>[6,8,4,3,7,5,1,2]=>0110110=>[1,2,1,2,1]
[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>1010110=>[1,1,1,1,2,1]
[3,5,6,1,2,4,8,7]=>[6,4,3,8,7,5,1,2]=>1101110=>[2,1,3,1]
[3,1,5,2,6,8,4,7]=>[6,8,4,7,3,1,5,2]=>0101101=>[1,1,1,2,1,1]
[3,5,1,2,6,8,4,7]=>[6,4,8,7,3,1,5,2]=>1011101=>[1,1,3,1,1]
[3,1,5,6,2,8,4,7]=>[6,8,4,3,7,1,5,2]=>0110101=>[1,2,1,1,1,1]
[3,5,1,6,2,8,4,7]=>[6,4,8,3,7,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[3,5,6,1,2,8,4,7]=>[6,4,3,8,7,1,5,2]=>1101101=>[2,1,2,1,1]
[3,1,5,6,8,2,4,7]=>[6,8,4,3,1,7,5,2]=>0111011=>[1,3,1,2]
[3,5,1,6,8,2,4,7]=>[6,4,8,3,1,7,5,2]=>1011011=>[1,1,2,1,2]
[3,5,6,1,8,2,4,7]=>[6,4,3,8,1,7,5,2]=>1101011=>[2,1,1,1,2]
[3,5,6,8,1,2,4,7]=>[6,4,3,1,8,7,5,2]=>1110111=>[3,1,3]
[3,1,5,2,6,4,7,8]=>[6,8,4,7,3,5,2,1]=>0101011=>[1,1,1,1,1,2]
[3,5,1,2,6,4,7,8]=>[6,4,8,7,3,5,2,1]=>1011011=>[1,1,2,1,2]
[3,1,5,6,2,4,7,8]=>[6,8,4,3,7,5,2,1]=>0110111=>[1,2,1,3]
[3,5,1,6,2,4,7,8]=>[6,4,8,3,7,5,2,1]=>1010111=>[1,1,1,1,3]
[3,1,5,2,6,7,4,8]=>[6,8,4,7,3,2,5,1]=>0101101=>[1,1,1,2,1,1]
[3,5,1,2,6,7,4,8]=>[6,4,8,7,3,2,5,1]=>1011101=>[1,1,3,1,1]
[3,5,1,6,2,7,4,8]=>[6,4,8,3,7,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[3,5,6,1,2,7,4,8]=>[6,4,3,8,7,2,5,1]=>1101101=>[2,1,2,1,1]
[3,1,5,6,7,2,4,8]=>[6,8,4,3,2,7,5,1]=>0111011=>[1,3,1,2]
[3,5,6,1,7,2,4,8]=>[6,4,3,8,2,7,5,1]=>1101011=>[2,1,1,1,2]
[3,5,6,7,1,2,4,8]=>[6,4,3,2,8,7,5,1]=>1110111=>[3,1,3]
[3,1,5,2,6,7,8,4]=>[6,8,4,7,3,2,1,5]=>0101110=>[1,1,1,3,1]
[3,5,1,2,6,7,8,4]=>[6,4,8,7,3,2,1,5]=>1011110=>[1,1,4,1]
[3,1,5,6,2,7,8,4]=>[6,8,4,3,7,2,1,5]=>0110110=>[1,2,1,2,1]
[3,5,1,6,2,7,8,4]=>[6,4,8,3,7,2,1,5]=>1010110=>[1,1,1,1,2,1]
[3,5,6,1,2,7,8,4]=>[6,4,3,8,7,2,1,5]=>1101110=>[2,1,3,1]
[3,1,5,6,7,2,8,4]=>[6,8,4,3,2,7,1,5]=>0111010=>[1,3,1,1,1]
[3,5,1,6,7,2,8,4]=>[6,4,8,3,2,7,1,5]=>1011010=>[1,1,2,1,1,1]
[3,5,6,1,7,2,8,4]=>[6,4,3,8,2,7,1,5]=>1101010=>[2,1,1,1,1,1]
[3,5,6,7,1,2,8,4]=>[6,4,3,2,8,7,1,5]=>1110110=>[3,1,2,1]
[3,1,5,6,7,8,2,4]=>[6,8,4,3,2,1,7,5]=>0111101=>[1,4,1,1]
[3,5,1,6,7,8,2,4]=>[6,4,8,3,2,1,7,5]=>1011101=>[1,1,3,1,1]
[3,5,6,1,7,8,2,4]=>[6,4,3,8,2,1,7,5]=>1101101=>[2,1,2,1,1]
[3,5,6,7,1,8,2,4]=>[6,4,3,2,8,1,7,5]=>1110101=>[3,1,1,1,1]
[3,5,6,7,8,1,2,4]=>[6,4,3,2,1,8,7,5]=>1111011=>[4,1,2]
[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,5,1,2,7,4,8,6]=>[6,4,8,7,2,5,1,3]=>1011010=>[1,1,2,1,1,1]
[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]=>0110110=>[1,2,1,2,1]
[3,5,1,7,2,4,8,6]=>[6,4,8,2,7,5,1,3]=>1010110=>[1,1,1,1,2,1]
[3,5,7,1,2,4,8,6]=>[6,4,2,8,7,5,1,3]=>1101110=>[2,1,3,1]
[3,1,5,2,7,8,4,6]=>[6,8,4,7,2,1,5,3]=>0101101=>[1,1,1,2,1,1]
[3,5,1,2,7,8,4,6]=>[6,4,8,7,2,1,5,3]=>1011101=>[1,1,3,1,1]
[3,1,5,7,2,8,4,6]=>[6,8,4,2,7,1,5,3]=>0110101=>[1,2,1,1,1,1]
[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[3,5,7,1,2,8,4,6]=>[6,4,2,8,7,1,5,3]=>1101101=>[2,1,2,1,1]
[3,1,5,7,8,2,4,6]=>[6,8,4,2,1,7,5,3]=>0111011=>[1,3,1,2]
[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>1110111=>[3,1,3]
[3,1,5,2,7,4,6,8]=>[6,8,4,7,2,5,3,1]=>0101011=>[1,1,1,1,1,2]
[3,5,1,2,7,4,6,8]=>[6,4,8,7,2,5,3,1]=>1011011=>[1,1,2,1,2]
[3,1,5,7,2,4,6,8]=>[6,8,4,2,7,5,3,1]=>0110111=>[1,2,1,3]
[3,5,1,7,2,4,6,8]=>[6,4,8,2,7,5,3,1]=>1010111=>[1,1,1,1,3]
[3,5,7,1,2,4,6,8]=>[6,4,2,8,7,5,3,1]=>1101111=>[2,1,4]
[3,1,5,2,4,7,6,8]=>[6,8,4,7,5,2,3,1]=>0101101=>[1,1,1,2,1,1]
[3,5,1,2,4,7,6,8]=>[6,4,8,7,5,2,3,1]=>1011101=>[1,1,3,1,1]
[3,1,2,5,4,7,6,8]=>[6,8,7,4,5,2,3,1]=>0110101=>[1,2,1,1,1,1]
[1,3,5,2,4,7,6,8]=>[8,6,4,7,5,2,3,1]=>1101101=>[2,1,2,1,1]
[3,1,2,5,7,4,6,8]=>[6,8,7,4,2,5,3,1]=>0111011=>[1,3,1,2]
[1,3,2,5,7,4,6,8]=>[8,6,7,4,2,5,3,1]=>1011011=>[1,1,2,1,2]
[1,3,5,2,7,4,6,8]=>[8,6,4,7,2,5,3,1]=>1101011=>[2,1,1,1,2]
[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>1110111=>[3,1,3]
[3,1,5,2,4,7,8,6]=>[6,8,4,7,5,2,1,3]=>0101110=>[1,1,1,3,1]
[3,5,1,2,4,7,8,6]=>[6,4,8,7,5,2,1,3]=>1011110=>[1,1,4,1]
[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>1101110=>[2,1,3,1]
[3,1,2,5,7,4,8,6]=>[6,8,7,4,2,5,1,3]=>0111010=>[1,3,1,1,1]
[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>1011010=>[1,1,2,1,1,1]
[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>1101010=>[2,1,1,1,1,1]
[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>1110110=>[3,1,2,1]
[3,1,2,5,7,8,4,6]=>[6,8,7,4,2,1,5,3]=>0111101=>[1,4,1,1]
[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>1011101=>[1,1,3,1,1]
[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>1101101=>[2,1,2,1,1]
[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>1110101=>[3,1,1,1,1]
[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>1111011=>[4,1,2]
[3,1,5,2,8,4,6,7]=>[6,8,4,7,1,5,3,2]=>0101011=>[1,1,1,1,1,2]
[3,1,5,8,2,4,6,7]=>[6,8,4,1,7,5,3,2]=>0110111=>[1,2,1,3]
[3,5,1,8,2,4,6,7]=>[6,4,8,1,7,5,3,2]=>1010111=>[1,1,1,1,3]
[3,5,8,1,2,4,6,7]=>[6,4,1,8,7,5,3,2]=>1101111=>[2,1,4]
[3,1,5,2,4,8,6,7]=>[6,8,4,7,5,1,3,2]=>0101101=>[1,1,1,2,1,1]
[3,1,2,5,4,8,6,7]=>[6,8,7,4,5,1,3,2]=>0110101=>[1,2,1,1,1,1]
[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>1101101=>[2,1,2,1,1]
[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>1011011=>[1,1,2,1,2]
[1,3,5,2,8,4,6,7]=>[8,6,4,7,1,5,3,2]=>1101011=>[2,1,1,1,2]
[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>1110111=>[3,1,3]
[3,1,5,2,4,6,8,7]=>[6,8,4,7,5,3,1,2]=>0101110=>[1,1,1,3,1]
[3,5,1,2,4,6,8,7]=>[6,4,8,7,5,3,1,2]=>1011110=>[1,1,4,1]
[3,1,2,5,4,6,8,7]=>[6,8,7,4,5,3,1,2]=>0110110=>[1,2,1,2,1]
[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>1101110=>[2,1,3,1]
[3,1,2,5,6,4,8,7]=>[6,8,7,4,3,5,1,2]=>0111010=>[1,3,1,1,1]
[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>1110110=>[3,1,2,1]
[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>1011101=>[1,1,3,1,1]
[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>1101101=>[2,1,2,1,1]
[1,3,5,6,2,8,4,7]=>[8,6,4,3,7,1,5,2]=>1110101=>[3,1,1,1,1]
[3,1,5,2,4,6,7,8]=>[6,8,4,7,5,3,2,1]=>0101111=>[1,1,1,4]
[3,5,1,2,4,6,7,8]=>[6,4,8,7,5,3,2,1]=>1011111=>[1,1,5]
[3,1,2,5,4,6,7,8]=>[6,8,7,4,5,3,2,1]=>0110111=>[1,2,1,3]
[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>1101111=>[2,1,4]
[3,1,2,5,6,4,7,8]=>[6,8,7,4,3,5,2,1]=>0111011=>[1,3,1,2]
[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>1101011=>[2,1,1,1,2]
[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>1110111=>[3,1,3]
[3,1,2,5,6,7,4,8]=>[6,8,7,4,3,2,5,1]=>0111101=>[1,4,1,1]
[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>1101101=>[2,1,2,1,1]
[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>1110101=>[3,1,1,1,1]
[1,3,5,6,7,2,4,8]=>[8,6,4,3,2,7,5,1]=>1111011=>[4,1,2]
[3,1,2,5,6,7,8,4]=>[6,8,7,4,3,2,1,5]=>0111110=>[1,5,1]
[1,3,5,2,6,7,8,4]=>[8,6,4,7,3,2,1,5]=>1101110=>[2,1,3,1]
[1,3,5,6,2,7,8,4]=>[8,6,4,3,7,2,1,5]=>1110110=>[3,1,2,1]
[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]=>1111010=>[4,1,1,1]
[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>1111101=>[5,1,1]
[3,1,6,2,7,4,8,5]=>[6,8,3,7,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,6,1,2,7,4,8,5]=>[6,3,8,7,2,5,1,4]=>1011010=>[1,1,2,1,1,1]
[3,1,6,7,2,4,8,5]=>[6,8,3,2,7,5,1,4]=>0110110=>[1,2,1,2,1]
[3,6,1,7,2,4,8,5]=>[6,3,8,2,7,5,1,4]=>1010110=>[1,1,1,1,2,1]
[3,6,7,1,2,4,8,5]=>[6,3,2,8,7,5,1,4]=>1101110=>[2,1,3,1]
[3,1,6,2,7,8,4,5]=>[6,8,3,7,2,1,5,4]=>0101101=>[1,1,1,2,1,1]
[3,6,1,2,7,8,4,5]=>[6,3,8,7,2,1,5,4]=>1011101=>[1,1,3,1,1]
[3,1,6,7,2,8,4,5]=>[6,8,3,2,7,1,5,4]=>0110101=>[1,2,1,1,1,1]
[3,6,1,7,2,8,4,5]=>[6,3,8,2,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[3,6,7,1,2,8,4,5]=>[6,3,2,8,7,1,5,4]=>1101101=>[2,1,2,1,1]
[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>1011011=>[1,1,2,1,2]
[3,6,7,1,8,2,4,5]=>[6,3,2,8,1,7,5,4]=>1101011=>[2,1,1,1,2]
[3,6,7,8,1,2,4,5]=>[6,3,2,1,8,7,5,4]=>1110111=>[3,1,3]
[3,1,6,2,7,4,5,8]=>[6,8,3,7,2,5,4,1]=>0101011=>[1,1,1,1,1,2]
[3,6,1,2,7,4,5,8]=>[6,3,8,7,2,5,4,1]=>1011011=>[1,1,2,1,2]
[3,1,6,7,2,4,5,8]=>[6,8,3,2,7,5,4,1]=>0110111=>[1,2,1,3]
[3,6,7,1,2,4,5,8]=>[6,3,2,8,7,5,4,1]=>1101111=>[2,1,4]
[3,1,6,2,4,7,5,8]=>[6,8,3,7,5,2,4,1]=>0101101=>[1,1,1,2,1,1]
[3,6,1,2,4,7,5,8]=>[6,3,8,7,5,2,4,1]=>1011101=>[1,1,3,1,1]
[3,1,2,6,4,7,5,8]=>[6,8,7,3,5,2,4,1]=>0110101=>[1,2,1,1,1,1]
[1,3,2,6,4,7,5,8]=>[8,6,7,3,5,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,3,6,2,4,7,5,8]=>[8,6,3,7,5,2,4,1]=>1101101=>[2,1,2,1,1]
[1,3,6,7,2,4,5,8]=>[8,6,3,2,7,5,4,1]=>1110111=>[3,1,3]
[3,1,6,2,4,7,8,5]=>[6,8,3,7,5,2,1,4]=>0101110=>[1,1,1,3,1]
[3,6,1,2,4,7,8,5]=>[6,3,8,7,5,2,1,4]=>1011110=>[1,1,4,1]
[3,1,2,6,4,7,8,5]=>[6,8,7,3,5,2,1,4]=>0110110=>[1,2,1,2,1]
[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>1010110=>[1,1,1,1,2,1]
[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>1101110=>[2,1,3,1]
[3,1,2,6,7,4,8,5]=>[6,8,7,3,2,5,1,4]=>0111010=>[1,3,1,1,1]
[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>1101010=>[2,1,1,1,1,1]
[1,3,6,7,2,4,8,5]=>[8,6,3,2,7,5,1,4]=>1110110=>[3,1,2,1]
[3,1,2,6,7,8,4,5]=>[6,8,7,3,2,1,5,4]=>0111101=>[1,4,1,1]
[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>1101101=>[2,1,2,1,1]
[1,3,6,7,2,8,4,5]=>[8,6,3,2,7,1,5,4]=>1110101=>[3,1,1,1,1]
[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]=>1111011=>[4,1,2]
[3,1,6,2,8,4,5,7]=>[6,8,3,7,1,5,4,2]=>0101011=>[1,1,1,1,1,2]
[3,6,1,2,8,4,5,7]=>[6,3,8,7,1,5,4,2]=>1011011=>[1,1,2,1,2]
[3,1,6,8,2,4,5,7]=>[6,8,3,1,7,5,4,2]=>0110111=>[1,2,1,3]
[3,6,1,8,2,4,5,7]=>[6,3,8,1,7,5,4,2]=>1010111=>[1,1,1,1,3]
[3,6,8,1,2,4,5,7]=>[6,3,1,8,7,5,4,2]=>1101111=>[2,1,4]
[3,1,6,2,4,8,5,7]=>[6,8,3,7,5,1,4,2]=>0101101=>[1,1,1,2,1,1]
[3,6,1,2,4,8,5,7]=>[6,3,8,7,5,1,4,2]=>1011101=>[1,1,3,1,1]
[3,1,2,6,4,8,5,7]=>[6,8,7,3,5,1,4,2]=>0110101=>[1,2,1,1,1,1]
[1,3,2,6,4,8,5,7]=>[8,6,7,3,5,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>1101101=>[2,1,2,1,1]
[3,1,2,6,8,4,5,7]=>[6,8,7,3,1,5,4,2]=>0111011=>[1,3,1,2]
[1,3,6,2,8,4,5,7]=>[8,6,3,7,1,5,4,2]=>1101011=>[2,1,1,1,2]
[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>1110111=>[3,1,3]
[3,1,6,2,4,5,8,7]=>[6,8,3,7,5,4,1,2]=>0101110=>[1,1,1,3,1]
[3,6,1,2,4,5,8,7]=>[6,3,8,7,5,4,1,2]=>1011110=>[1,1,4,1]
[3,1,2,4,6,5,8,7]=>[6,8,7,5,3,4,1,2]=>0111010=>[1,3,1,1,1]
[3,1,2,4,6,8,5,7]=>[6,8,7,5,3,1,4,2]=>0111101=>[1,4,1,1]
[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>1011101=>[1,1,3,1,1]
[3,6,1,2,4,5,7,8]=>[6,3,8,7,5,4,2,1]=>1011111=>[1,1,5]
[3,1,2,6,4,5,7,8]=>[6,8,7,3,5,4,2,1]=>0110111=>[1,2,1,3]
[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>1010111=>[1,1,1,1,3]
[3,1,2,4,6,5,7,8]=>[6,8,7,5,3,4,2,1]=>0111011=>[1,3,1,2]
[3,1,2,4,6,7,5,8]=>[6,8,7,5,3,2,4,1]=>0111101=>[1,4,1,1]
[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]=>1110101=>[3,1,1,1,1]
[3,1,2,4,6,7,8,5]=>[6,8,7,5,3,2,1,4]=>0111110=>[1,5,1]
[1,3,4,6,2,7,8,5]=>[8,6,5,3,7,2,1,4]=>1110110=>[3,1,2,1]
[1,3,4,6,7,2,8,5]=>[8,6,5,3,2,7,1,4]=>1111010=>[4,1,1,1]
[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]=>1111101=>[5,1,1]
[3,1,7,2,8,4,5,6]=>[6,8,2,7,1,5,4,3]=>0101011=>[1,1,1,1,1,2]
[3,7,1,2,8,4,5,6]=>[6,2,8,7,1,5,4,3]=>1011011=>[1,1,2,1,2]
[3,1,7,8,2,4,5,6]=>[6,8,2,1,7,5,4,3]=>0110111=>[1,2,1,3]
[3,7,1,8,2,4,5,6]=>[6,2,8,1,7,5,4,3]=>1010111=>[1,1,1,1,3]
[3,7,8,1,2,4,5,6]=>[6,2,1,8,7,5,4,3]=>1101111=>[2,1,4]
[3,1,7,2,4,8,5,6]=>[6,8,2,7,5,1,4,3]=>0101101=>[1,1,1,2,1,1]
[3,7,1,2,4,8,5,6]=>[6,2,8,7,5,1,4,3]=>1011101=>[1,1,3,1,1]
[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>1101101=>[2,1,2,1,1]
[3,1,2,7,8,4,5,6]=>[6,8,7,2,1,5,4,3]=>0111011=>[1,3,1,2]
[1,3,7,2,8,4,5,6]=>[8,6,2,7,1,5,4,3]=>1101011=>[2,1,1,1,2]
[3,1,7,2,4,5,8,6]=>[6,8,2,7,5,4,1,3]=>0101110=>[1,1,1,3,1]
[3,7,1,2,4,5,8,6]=>[6,2,8,7,5,4,1,3]=>1011110=>[1,1,4,1]
[3,1,2,7,4,5,8,6]=>[6,8,7,2,5,4,1,3]=>0110110=>[1,2,1,2,1]
[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>1101110=>[2,1,3,1]
[3,1,2,4,7,5,8,6]=>[6,8,7,5,2,4,1,3]=>0111010=>[1,3,1,1,1]
[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>1101010=>[2,1,1,1,1,1]
[3,1,2,4,7,8,5,6]=>[6,8,7,5,2,1,4,3]=>0111101=>[1,4,1,1]
[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>1011101=>[1,1,3,1,1]
[1,3,4,2,7,8,5,6]=>[8,6,5,7,2,1,4,3]=>1101101=>[2,1,2,1,1]
[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>1110101=>[3,1,1,1,1]
[1,3,4,7,8,2,5,6]=>[8,6,5,2,1,7,4,3]=>1111011=>[4,1,2]
[3,1,7,2,4,5,6,8]=>[6,8,2,7,5,4,3,1]=>0101111=>[1,1,1,4]
[3,7,1,2,4,5,6,8]=>[6,2,8,7,5,4,3,1]=>1011111=>[1,1,5]
[3,1,2,7,4,5,6,8]=>[6,8,7,2,5,4,3,1]=>0110111=>[1,2,1,3]
[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>1010111=>[1,1,1,1,3]
[1,3,7,2,4,5,6,8]=>[8,6,2,7,5,4,3,1]=>1101111=>[2,1,4]
[3,1,2,4,7,5,6,8]=>[6,8,7,5,2,4,3,1]=>0111011=>[1,3,1,2]
[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>1011011=>[1,1,2,1,2]
[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>1101011=>[2,1,1,1,2]
[1,3,4,7,2,5,6,8]=>[8,6,5,2,7,4,3,1]=>1110111=>[3,1,3]
[3,1,2,4,5,7,6,8]=>[6,8,7,5,4,2,3,1]=>0111101=>[1,4,1,1]
[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]=>1111011=>[4,1,2]
[3,1,2,4,5,7,8,6]=>[6,8,7,5,4,2,1,3]=>0111110=>[1,5,1]
[1,3,4,5,7,2,8,6]=>[8,6,5,4,2,7,1,3]=>1111010=>[4,1,1,1]
[1,3,4,5,7,8,2,6]=>[8,6,5,4,2,1,7,3]=>1111101=>[5,1,1]
[3,1,8,2,4,5,6,7]=>[6,8,1,7,5,4,3,2]=>0101111=>[1,1,1,4]
[3,8,1,2,4,5,6,7]=>[6,1,8,7,5,4,3,2]=>1011111=>[1,1,5]
[3,1,2,8,4,5,6,7]=>[6,8,7,1,5,4,3,2]=>0110111=>[1,2,1,3]
[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>1010111=>[1,1,1,1,3]
[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>1101111=>[2,1,4]
[3,1,2,4,8,5,6,7]=>[6,8,7,5,1,4,3,2]=>0111011=>[1,3,1,2]
[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>1011011=>[1,1,2,1,2]
[1,3,4,2,8,5,6,7]=>[8,6,5,7,1,4,3,2]=>1101011=>[2,1,1,1,2]
[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>1110111=>[3,1,3]
[3,1,2,4,5,8,6,7]=>[6,8,7,5,4,1,3,2]=>0111101=>[1,4,1,1]
[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>1011101=>[1,1,3,1,1]
[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>1101101=>[2,1,2,1,1]
[1,3,4,5,2,8,6,7]=>[8,6,5,4,7,1,3,2]=>1110101=>[3,1,1,1,1]
[3,1,2,4,5,6,8,7]=>[6,8,7,5,4,3,1,2]=>0111110=>[1,5,1]
[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>1111101=>[5,1,1]
[4,1,5,2,6,3,8,7]=>[5,8,4,7,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,5,1,2,6,3,8,7]=>[5,4,8,7,3,6,1,2]=>1011010=>[1,1,2,1,1,1]
[4,1,5,6,2,3,8,7]=>[5,8,4,3,7,6,1,2]=>0110110=>[1,2,1,2,1]
[4,5,1,6,2,3,8,7]=>[5,4,8,3,7,6,1,2]=>1010110=>[1,1,1,1,2,1]
[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>1101110=>[2,1,3,1]
[4,1,5,2,6,8,3,7]=>[5,8,4,7,3,1,6,2]=>0101101=>[1,1,1,2,1,1]
[4,1,5,6,2,8,3,7]=>[5,8,4,3,7,1,6,2]=>0110101=>[1,2,1,1,1,1]
[4,5,1,6,2,8,3,7]=>[5,4,8,3,7,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,6,1,2,8,3,7]=>[5,4,3,8,7,1,6,2]=>1101101=>[2,1,2,1,1]
[4,1,5,6,8,2,3,7]=>[5,8,4,3,1,7,6,2]=>0111011=>[1,3,1,2]
[4,5,1,6,8,2,3,7]=>[5,4,8,3,1,7,6,2]=>1011011=>[1,1,2,1,2]
[4,5,6,1,8,2,3,7]=>[5,4,3,8,1,7,6,2]=>1101011=>[2,1,1,1,2]
[4,5,6,8,1,2,3,7]=>[5,4,3,1,8,7,6,2]=>1110111=>[3,1,3]
[4,1,5,2,6,3,7,8]=>[5,8,4,7,3,6,2,1]=>0101011=>[1,1,1,1,1,2]
[4,5,1,2,6,3,7,8]=>[5,4,8,7,3,6,2,1]=>1011011=>[1,1,2,1,2]
[4,1,5,6,2,3,7,8]=>[5,8,4,3,7,6,2,1]=>0110111=>[1,2,1,3]
[4,1,5,2,6,7,3,8]=>[5,8,4,7,3,2,6,1]=>0101101=>[1,1,1,2,1,1]
[4,5,1,2,6,7,3,8]=>[5,4,8,7,3,2,6,1]=>1011101=>[1,1,3,1,1]
[4,1,5,6,2,7,3,8]=>[5,8,4,3,7,2,6,1]=>0110101=>[1,2,1,1,1,1]
[4,5,1,6,2,7,3,8]=>[5,4,8,3,7,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[4,1,5,6,7,2,3,8]=>[5,8,4,3,2,7,6,1]=>0111011=>[1,3,1,2]
[4,5,1,6,7,2,3,8]=>[5,4,8,3,2,7,6,1]=>1011011=>[1,1,2,1,2]
[4,5,6,1,7,2,3,8]=>[5,4,3,8,2,7,6,1]=>1101011=>[2,1,1,1,2]
[4,1,5,2,6,7,8,3]=>[5,8,4,7,3,2,1,6]=>0101110=>[1,1,1,3,1]
[4,5,1,2,6,7,8,3]=>[5,4,8,7,3,2,1,6]=>1011110=>[1,1,4,1]
[4,1,5,6,2,7,8,3]=>[5,8,4,3,7,2,1,6]=>0110110=>[1,2,1,2,1]
[4,5,1,6,2,7,8,3]=>[5,4,8,3,7,2,1,6]=>1010110=>[1,1,1,1,2,1]
[4,1,5,6,7,2,8,3]=>[5,8,4,3,2,7,1,6]=>0111010=>[1,3,1,1,1]
[4,5,1,6,7,2,8,3]=>[5,4,8,3,2,7,1,6]=>1011010=>[1,1,2,1,1,1]
[4,5,6,1,7,2,8,3]=>[5,4,3,8,2,7,1,6]=>1101010=>[2,1,1,1,1,1]
[4,5,6,7,1,2,8,3]=>[5,4,3,2,8,7,1,6]=>1110110=>[3,1,2,1]
[4,1,5,6,7,8,2,3]=>[5,8,4,3,2,1,7,6]=>0111101=>[1,4,1,1]
[4,5,1,6,7,8,2,3]=>[5,4,8,3,2,1,7,6]=>1011101=>[1,1,3,1,1]
[4,5,6,1,7,8,2,3]=>[5,4,3,8,2,1,7,6]=>1101101=>[2,1,2,1,1]
[4,5,6,7,1,8,2,3]=>[5,4,3,2,8,1,7,6]=>1110101=>[3,1,1,1,1]
[4,1,5,2,7,3,8,6]=>[5,8,4,7,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,5,1,2,7,3,8,6]=>[5,4,8,7,2,6,1,3]=>1011010=>[1,1,2,1,1,1]
[4,5,1,7,2,3,8,6]=>[5,4,8,2,7,6,1,3]=>1010110=>[1,1,1,1,2,1]
[4,5,7,1,2,3,8,6]=>[5,4,2,8,7,6,1,3]=>1101110=>[2,1,3,1]
[4,1,5,2,7,8,3,6]=>[5,8,4,7,2,1,6,3]=>0101101=>[1,1,1,2,1,1]
[4,1,5,7,2,8,3,6]=>[5,8,4,2,7,1,6,3]=>0110101=>[1,2,1,1,1,1]
[4,5,1,7,2,8,3,6]=>[5,4,8,2,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]
[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>1101101=>[2,1,2,1,1]
[4,1,5,7,8,2,3,6]=>[5,8,4,2,1,7,6,3]=>0111011=>[1,3,1,2]
[4,5,1,7,8,2,3,6]=>[5,4,8,2,1,7,6,3]=>1011011=>[1,1,2,1,2]
[4,5,7,1,8,2,3,6]=>[5,4,2,8,1,7,6,3]=>1101011=>[2,1,1,1,2]
[4,5,7,8,1,2,3,6]=>[5,4,2,1,8,7,6,3]=>1110111=>[3,1,3]
[4,1,5,2,7,3,6,8]=>[5,8,4,7,2,6,3,1]=>0101011=>[1,1,1,1,1,2]
[4,5,1,2,7,3,6,8]=>[5,4,8,7,2,6,3,1]=>1011011=>[1,1,2,1,2]
[4,5,1,7,2,3,6,8]=>[5,4,8,2,7,6,3,1]=>1010111=>[1,1,1,1,3]
[4,1,5,2,3,7,6,8]=>[5,8,4,7,6,2,3,1]=>0101101=>[1,1,1,2,1,1]
[4,5,1,2,3,7,6,8]=>[5,4,8,7,6,2,3,1]=>1011101=>[1,1,3,1,1]
[4,1,2,5,3,7,6,8]=>[5,8,7,4,6,2,3,1]=>0110101=>[1,2,1,1,1,1]
[1,4,2,5,3,7,6,8]=>[8,5,7,4,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[4,1,2,5,7,3,6,8]=>[5,8,7,4,2,6,3,1]=>0111011=>[1,3,1,2]
[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>1011011=>[1,1,2,1,2]
[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>1101011=>[2,1,1,1,2]
[1,4,5,7,2,3,6,8]=>[8,5,4,2,7,6,3,1]=>1110111=>[3,1,3]
[4,1,5,2,3,7,8,6]=>[5,8,4,7,6,2,1,3]=>0101110=>[1,1,1,3,1]
[4,5,1,2,3,7,8,6]=>[5,4,8,7,6,2,1,3]=>1011110=>[1,1,4,1]
[4,1,2,5,3,7,8,6]=>[5,8,7,4,6,2,1,3]=>0110110=>[1,2,1,2,1]
[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>1010110=>[1,1,1,1,2,1]
[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]=>1101110=>[2,1,3,1]
[4,1,2,5,7,3,8,6]=>[5,8,7,4,2,6,1,3]=>0111010=>[1,3,1,1,1]
[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>1011010=>[1,1,2,1,1,1]
[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>1101010=>[2,1,1,1,1,1]
[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>1110110=>[3,1,2,1]
[4,1,2,5,7,8,3,6]=>[5,8,7,4,2,1,6,3]=>0111101=>[1,4,1,1]
[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>1011101=>[1,1,3,1,1]
[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>1111011=>[4,1,2]
[4,1,5,2,8,3,6,7]=>[5,8,4,7,1,6,3,2]=>0101011=>[1,1,1,1,1,2]
[4,5,1,2,8,3,6,7]=>[5,4,8,7,1,6,3,2]=>1011011=>[1,1,2,1,2]
[4,1,5,8,2,3,6,7]=>[5,8,4,1,7,6,3,2]=>0110111=>[1,2,1,3]
[4,5,1,8,2,3,6,7]=>[5,4,8,1,7,6,3,2]=>1010111=>[1,1,1,1,3]
[4,5,8,1,2,3,6,7]=>[5,4,1,8,7,6,3,2]=>1101111=>[2,1,4]
[4,5,1,2,3,8,6,7]=>[5,4,8,7,6,1,3,2]=>1011101=>[1,1,3,1,1]
[4,1,2,5,3,8,6,7]=>[5,8,7,4,6,1,3,2]=>0110101=>[1,2,1,1,1,1]
[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[4,1,2,5,8,3,6,7]=>[5,8,7,4,1,6,3,2]=>0111011=>[1,3,1,2]
[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>1011011=>[1,1,2,1,2]
[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>1101011=>[2,1,1,1,2]
[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>1110111=>[3,1,3]
[4,1,5,2,3,6,8,7]=>[5,8,4,7,6,3,1,2]=>0101110=>[1,1,1,3,1]
[4,5,1,2,3,6,8,7]=>[5,4,8,7,6,3,1,2]=>1011110=>[1,1,4,1]
[4,1,2,5,3,6,8,7]=>[5,8,7,4,6,3,1,2]=>0110110=>[1,2,1,2,1]
[1,4,5,2,3,6,8,7]=>[8,5,4,7,6,3,1,2]=>1101110=>[2,1,3,1]
[4,1,2,5,6,3,8,7]=>[5,8,7,4,3,6,1,2]=>0111010=>[1,3,1,1,1]
[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>1011010=>[1,1,2,1,1,1]
[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>1101010=>[2,1,1,1,1,1]
[1,4,5,6,2,3,8,7]=>[8,5,4,3,7,6,1,2]=>1110110=>[3,1,2,1]
[4,1,2,5,6,8,3,7]=>[5,8,7,4,3,1,6,2]=>0111101=>[1,4,1,1]
[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>1011101=>[1,1,3,1,1]
[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>1111011=>[4,1,2]
[4,1,5,2,3,6,7,8]=>[5,8,4,7,6,3,2,1]=>0101111=>[1,1,1,4]
[4,1,2,5,3,6,7,8]=>[5,8,7,4,6,3,2,1]=>0110111=>[1,2,1,3]
[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>1010111=>[1,1,1,1,3]
[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>1101111=>[2,1,4]
[4,1,2,5,6,3,7,8]=>[5,8,7,4,3,6,2,1]=>0111011=>[1,3,1,2]
[1,4,2,5,6,3,7,8]=>[8,5,7,4,3,6,2,1]=>1011011=>[1,1,2,1,2]
[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>1101011=>[2,1,1,1,2]
[1,4,5,6,2,3,7,8]=>[8,5,4,3,7,6,2,1]=>1110111=>[3,1,3]
[1,4,2,5,6,7,3,8]=>[8,5,7,4,3,2,6,1]=>1011101=>[1,1,3,1,1]
[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>1110101=>[3,1,1,1,1]
[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>1111011=>[4,1,2]
[4,1,2,5,6,7,8,3]=>[5,8,7,4,3,2,1,6]=>0111110=>[1,5,1]
[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>1011110=>[1,1,4,1]
[1,4,5,2,6,7,8,3]=>[8,5,4,7,3,2,1,6]=>1101110=>[2,1,3,1]
[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]=>1110110=>[3,1,2,1]
[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>1111010=>[4,1,1,1]
[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>1111101=>[5,1,1]
[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,7,2,3,8,5]=>[5,8,3,2,7,6,1,4]=>0110110=>[1,2,1,2,1]
[4,6,1,7,2,3,8,5]=>[5,3,8,2,7,6,1,4]=>1010110=>[1,1,1,1,2,1]
[4,1,6,2,7,8,3,5]=>[5,8,3,7,2,1,6,4]=>0101101=>[1,1,1,2,1,1]
[4,6,1,2,7,8,3,5]=>[5,3,8,7,2,1,6,4]=>1011101=>[1,1,3,1,1]
[4,1,6,7,2,8,3,5]=>[5,8,3,2,7,1,6,4]=>0110101=>[1,2,1,1,1,1]
[4,6,1,7,2,8,3,5]=>[5,3,8,2,7,1,6,4]=>1010101=>[1,1,1,1,1,1,1]
[4,6,7,1,2,8,3,5]=>[5,3,2,8,7,1,6,4]=>1101101=>[2,1,2,1,1]
[4,1,6,7,8,2,3,5]=>[5,8,3,2,1,7,6,4]=>0111011=>[1,3,1,2]
[4,6,1,7,8,2,3,5]=>[5,3,8,2,1,7,6,4]=>1011011=>[1,1,2,1,2]
[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>1101011=>[2,1,1,1,2]
[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>1110111=>[3,1,3]
[4,1,6,2,7,3,5,8]=>[5,8,3,7,2,6,4,1]=>0101011=>[1,1,1,1,1,2]
[4,6,1,2,7,3,5,8]=>[5,3,8,7,2,6,4,1]=>1011011=>[1,1,2,1,2]
[4,1,6,7,2,3,5,8]=>[5,8,3,2,7,6,4,1]=>0110111=>[1,2,1,3]
[4,6,1,7,2,3,5,8]=>[5,3,8,2,7,6,4,1]=>1010111=>[1,1,1,1,3]
[4,6,7,1,2,3,5,8]=>[5,3,2,8,7,6,4,1]=>1101111=>[2,1,4]
[4,1,6,2,3,7,5,8]=>[5,8,3,7,6,2,4,1]=>0101101=>[1,1,1,2,1,1]
[4,6,1,2,3,7,5,8]=>[5,3,8,7,6,2,4,1]=>1011101=>[1,1,3,1,1]
[4,1,2,6,3,7,5,8]=>[5,8,7,3,6,2,4,1]=>0110101=>[1,2,1,1,1,1]
[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>1101101=>[2,1,2,1,1]
[4,1,2,6,7,3,5,8]=>[5,8,7,3,2,6,4,1]=>0111011=>[1,3,1,2]
[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>1101011=>[2,1,1,1,2]
[1,4,6,7,2,3,5,8]=>[8,5,3,2,7,6,4,1]=>1110111=>[3,1,3]
[4,1,6,2,3,7,8,5]=>[5,8,3,7,6,2,1,4]=>0101110=>[1,1,1,3,1]
[4,6,1,2,3,7,8,5]=>[5,3,8,7,6,2,1,4]=>1011110=>[1,1,4,1]
[4,1,2,6,7,3,8,5]=>[5,8,7,3,2,6,1,4]=>0111010=>[1,3,1,1,1]
[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>1011010=>[1,1,2,1,1,1]
[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>1101010=>[2,1,1,1,1,1]
[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>1110110=>[3,1,2,1]
[4,1,2,6,7,8,3,5]=>[5,8,7,3,2,1,6,4]=>0111101=>[1,4,1,1]
[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>1011101=>[1,1,3,1,1]
[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>1101101=>[2,1,2,1,1]
[1,4,6,7,2,8,3,5]=>[8,5,3,2,7,1,6,4]=>1110101=>[3,1,1,1,1]
[4,1,6,2,8,3,5,7]=>[5,8,3,7,1,6,4,2]=>0101011=>[1,1,1,1,1,2]
[4,6,1,2,8,3,5,7]=>[5,3,8,7,1,6,4,2]=>1011011=>[1,1,2,1,2]
[4,1,6,8,2,3,5,7]=>[5,8,3,1,7,6,4,2]=>0110111=>[1,2,1,3]
[4,6,1,8,2,3,5,7]=>[5,3,8,1,7,6,4,2]=>1010111=>[1,1,1,1,3]
[4,6,8,1,2,3,5,7]=>[5,3,1,8,7,6,4,2]=>1101111=>[2,1,4]
[4,1,6,2,3,8,5,7]=>[5,8,3,7,6,1,4,2]=>0101101=>[1,1,1,2,1,1]
[4,6,1,2,3,8,5,7]=>[5,3,8,7,6,1,4,2]=>1011101=>[1,1,3,1,1]
[4,1,2,6,3,8,5,7]=>[5,8,7,3,6,1,4,2]=>0110101=>[1,2,1,1,1,1]
[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>1101101=>[2,1,2,1,1]
[4,1,2,6,8,3,5,7]=>[5,8,7,3,1,6,4,2]=>0111011=>[1,3,1,2]
[1,4,2,6,8,3,5,7]=>[8,5,7,3,1,6,4,2]=>1011011=>[1,1,2,1,2]
[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>1101011=>[2,1,1,1,2]
[4,1,6,2,3,5,8,7]=>[5,8,3,7,6,4,1,2]=>0101110=>[1,1,1,3,1]
[4,6,1,2,3,5,8,7]=>[5,3,8,7,6,4,1,2]=>1011110=>[1,1,4,1]
[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>1010110=>[1,1,1,1,2,1]
[1,4,6,2,3,5,8,7]=>[8,5,3,7,6,4,1,2]=>1101110=>[2,1,3,1]
[4,1,2,3,6,5,8,7]=>[5,8,7,6,3,4,1,2]=>0111010=>[1,3,1,1,1]
[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>1011010=>[1,1,2,1,1,1]
[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>1110110=>[3,1,2,1]
[4,1,2,3,6,8,5,7]=>[5,8,7,6,3,1,4,2]=>0111101=>[1,4,1,1]
[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>1011101=>[1,1,3,1,1]
[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>1101101=>[2,1,2,1,1]
[1,2,4,6,8,3,5,7]=>[8,7,5,3,1,6,4,2]=>1111011=>[4,1,2]
[4,1,6,2,3,5,7,8]=>[5,8,3,7,6,4,2,1]=>0101111=>[1,1,1,4]
[4,6,1,2,3,5,7,8]=>[5,3,8,7,6,4,2,1]=>1011111=>[1,1,5]
[4,1,2,6,3,5,7,8]=>[5,8,7,3,6,4,2,1]=>0110111=>[1,2,1,3]
[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>1010111=>[1,1,1,1,3]
[4,1,2,3,6,5,7,8]=>[5,8,7,6,3,4,2,1]=>0111011=>[1,3,1,2]
[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>1110111=>[3,1,3]
[4,1,2,3,6,7,5,8]=>[5,8,7,6,3,2,4,1]=>0111101=>[1,4,1,1]
[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>1011101=>[1,1,3,1,1]
[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>1110101=>[3,1,1,1,1]
[1,2,4,6,7,3,5,8]=>[8,7,5,3,2,6,4,1]=>1111011=>[4,1,2]
[4,1,2,3,6,7,8,5]=>[5,8,7,6,3,2,1,4]=>0111110=>[1,5,1]
[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>1011110=>[1,1,4,1]
[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>1111010=>[4,1,1,1]
[1,2,4,6,7,8,3,5]=>[8,7,5,3,2,1,6,4]=>1111101=>[5,1,1]
[4,1,7,2,8,3,5,6]=>[5,8,2,7,1,6,4,3]=>0101011=>[1,1,1,1,1,2]
[4,7,1,2,8,3,5,6]=>[5,2,8,7,1,6,4,3]=>1011011=>[1,1,2,1,2]
[4,1,7,8,2,3,5,6]=>[5,8,2,1,7,6,4,3]=>0110111=>[1,2,1,3]
[4,7,1,8,2,3,5,6]=>[5,2,8,1,7,6,4,3]=>1010111=>[1,1,1,1,3]
[4,7,8,1,2,3,5,6]=>[5,2,1,8,7,6,4,3]=>1101111=>[2,1,4]
[4,1,7,2,3,8,5,6]=>[5,8,2,7,6,1,4,3]=>0101101=>[1,1,1,2,1,1]
[4,7,1,2,3,8,5,6]=>[5,2,8,7,6,1,4,3]=>1011101=>[1,1,3,1,1]
[4,1,2,7,3,8,5,6]=>[5,8,7,2,6,1,4,3]=>0110101=>[1,2,1,1,1,1]
[1,4,2,7,3,8,5,6]=>[8,5,7,2,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>1101101=>[2,1,2,1,1]
[4,1,2,7,8,3,5,6]=>[5,8,7,2,1,6,4,3]=>0111011=>[1,3,1,2]
[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>1011011=>[1,1,2,1,2]
[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>1101011=>[2,1,1,1,2]
[1,4,7,8,2,3,5,6]=>[8,5,2,1,7,6,4,3]=>1110111=>[3,1,3]
[4,1,7,2,3,5,8,6]=>[5,8,2,7,6,4,1,3]=>0101110=>[1,1,1,3,1]
[4,7,1,2,3,5,8,6]=>[5,2,8,7,6,4,1,3]=>1011110=>[1,1,4,1]
[4,1,2,7,3,5,8,6]=>[5,8,7,2,6,4,1,3]=>0110110=>[1,2,1,2,1]
[4,1,2,3,7,5,8,6]=>[5,8,7,6,2,4,1,3]=>0111010=>[1,3,1,1,1]
[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>1101010=>[2,1,1,1,1,1]
[4,1,2,3,7,8,5,6]=>[5,8,7,6,2,1,4,3]=>0111101=>[1,4,1,1]
[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>1011101=>[1,1,3,1,1]
[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>1101101=>[2,1,2,1,1]
[1,2,4,7,8,3,5,6]=>[8,7,5,2,1,6,4,3]=>1111011=>[4,1,2]
[4,1,7,2,3,5,6,8]=>[5,8,2,7,6,4,3,1]=>0101111=>[1,1,1,4]
[4,7,1,2,3,5,6,8]=>[5,2,8,7,6,4,3,1]=>1011111=>[1,1,5]
[4,1,2,7,3,5,6,8]=>[5,8,7,2,6,4,3,1]=>0110111=>[1,2,1,3]
[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>1010111=>[1,1,1,1,3]
[4,1,2,3,7,5,6,8]=>[5,8,7,6,2,4,3,1]=>0111011=>[1,3,1,2]
[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>1011011=>[1,1,2,1,2]
[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>1110111=>[3,1,3]
[4,1,2,3,5,7,6,8]=>[5,8,7,6,4,2,3,1]=>0111101=>[1,4,1,1]
[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>1011101=>[1,1,3,1,1]
[4,1,2,3,5,7,8,6]=>[5,8,7,6,4,2,1,3]=>0111110=>[1,5,1]
[1,4,2,3,5,7,8,6]=>[8,5,7,6,4,2,1,3]=>1011110=>[1,1,4,1]
[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>1111010=>[4,1,1,1]
[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>1111101=>[5,1,1]
[4,1,8,2,3,5,6,7]=>[5,8,1,7,6,4,3,2]=>0101111=>[1,1,1,4]
[4,8,1,2,3,5,6,7]=>[5,1,8,7,6,4,3,2]=>1011111=>[1,1,5]
[4,1,2,8,3,5,6,7]=>[5,8,7,1,6,4,3,2]=>0110111=>[1,2,1,3]
[1,4,2,8,3,5,6,7]=>[8,5,7,1,6,4,3,2]=>1010111=>[1,1,1,1,3]
[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>1101111=>[2,1,4]
[4,1,2,3,8,5,6,7]=>[5,8,7,6,1,4,3,2]=>0111011=>[1,3,1,2]
[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>1011011=>[1,1,2,1,2]
[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>1101011=>[2,1,1,1,2]
[1,2,4,8,3,5,6,7]=>[8,7,5,1,6,4,3,2]=>1110111=>[3,1,3]
[4,1,2,3,5,8,6,7]=>[5,8,7,6,4,1,3,2]=>0111101=>[1,4,1,1]
[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>1011101=>[1,1,3,1,1]
[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>1101101=>[2,1,2,1,1]
[1,2,4,5,3,8,6,7]=>[8,7,5,4,6,1,3,2]=>1110101=>[3,1,1,1,1]
[1,2,4,5,8,3,6,7]=>[8,7,5,4,1,6,3,2]=>1111011=>[4,1,2]
[4,1,2,3,5,6,8,7]=>[5,8,7,6,4,3,1,2]=>0111110=>[1,5,1]
[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>1011110=>[1,1,4,1]
[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>1111101=>[5,1,1]
[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>1011111=>[1,1,5]
[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,6,1,2,7,3,8,4]=>[4,3,8,7,2,6,1,5]=>1011010=>[1,1,2,1,1,1]
[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]=>0110110=>[1,2,1,2,1]
[5,6,1,7,2,3,8,4]=>[4,3,8,2,7,6,1,5]=>1010110=>[1,1,1,1,2,1]
[5,6,7,1,2,3,8,4]=>[4,3,2,8,7,6,1,5]=>1101110=>[2,1,3,1]
[5,1,6,2,7,8,3,4]=>[4,8,3,7,2,1,6,5]=>0101101=>[1,1,1,2,1,1]
[5,6,1,2,7,8,3,4]=>[4,3,8,7,2,1,6,5]=>1011101=>[1,1,3,1,1]
[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,6,7,1,2,8,3,4]=>[4,3,2,8,7,1,6,5]=>1101101=>[2,1,2,1,1]
[5,1,6,7,8,2,3,4]=>[4,8,3,2,1,7,6,5]=>0111011=>[1,3,1,2]
[5,6,7,1,8,2,3,4]=>[4,3,2,8,1,7,6,5]=>1101011=>[2,1,1,1,2]
[5,6,1,2,7,3,4,8]=>[4,3,8,7,2,6,5,1]=>1011011=>[1,1,2,1,2]
[5,1,6,7,2,3,4,8]=>[4,8,3,2,7,6,5,1]=>0110111=>[1,2,1,3]
[5,6,1,7,2,3,4,8]=>[4,3,8,2,7,6,5,1]=>1010111=>[1,1,1,1,3]
[5,1,6,2,3,7,4,8]=>[4,8,3,7,6,2,5,1]=>0101101=>[1,1,1,2,1,1]
[5,6,1,2,3,7,4,8]=>[4,3,8,7,6,2,5,1]=>1011101=>[1,1,3,1,1]
[5,1,2,6,3,7,4,8]=>[4,8,7,3,6,2,5,1]=>0110101=>[1,2,1,1,1,1]
[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[5,1,2,6,7,3,4,8]=>[4,8,7,3,2,6,5,1]=>0111011=>[1,3,1,2]
[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>1110111=>[3,1,3]
[5,6,1,2,3,7,8,4]=>[4,3,8,7,6,2,1,5]=>1011110=>[1,1,4,1]
[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>0110110=>[1,2,1,2,1]
[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>1010110=>[1,1,1,1,2,1]
[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>1101110=>[2,1,3,1]
[5,1,2,6,7,3,8,4]=>[4,8,7,3,2,6,1,5]=>0111010=>[1,3,1,1,1]
[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>1011010=>[1,1,2,1,1,1]
[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>1101010=>[2,1,1,1,1,1]
[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>1110110=>[3,1,2,1]
[5,1,2,6,7,8,3,4]=>[4,8,7,3,2,1,6,5]=>0111101=>[1,4,1,1]
[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>1101101=>[2,1,2,1,1]
[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>1110101=>[3,1,1,1,1]
[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>1111011=>[4,1,2]
[5,1,6,2,8,3,4,7]=>[4,8,3,7,1,6,5,2]=>0101011=>[1,1,1,1,1,2]
[5,6,1,2,8,3,4,7]=>[4,3,8,7,1,6,5,2]=>1011011=>[1,1,2,1,2]
[5,1,6,8,2,3,4,7]=>[4,8,3,1,7,6,5,2]=>0110111=>[1,2,1,3]
[5,6,1,8,2,3,4,7]=>[4,3,8,1,7,6,5,2]=>1010111=>[1,1,1,1,3]
[5,6,8,1,2,3,4,7]=>[4,3,1,8,7,6,5,2]=>1101111=>[2,1,4]
[5,1,6,2,3,8,4,7]=>[4,8,3,7,6,1,5,2]=>0101101=>[1,1,1,2,1,1]
[5,6,1,2,3,8,4,7]=>[4,3,8,7,6,1,5,2]=>1011101=>[1,1,3,1,1]
[5,1,2,6,3,8,4,7]=>[4,8,7,3,6,1,5,2]=>0110101=>[1,2,1,1,1,1]
[1,5,2,6,3,8,4,7]=>[8,4,7,3,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>1101101=>[2,1,2,1,1]
[5,1,2,6,8,3,4,7]=>[4,8,7,3,1,6,5,2]=>0111011=>[1,3,1,2]
[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>1011011=>[1,1,2,1,2]
[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>1101011=>[2,1,1,1,2]
[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>1110111=>[3,1,3]
[5,1,6,2,3,4,8,7]=>[4,8,3,7,6,5,1,2]=>0101110=>[1,1,1,3,1]
[5,6,1,2,3,4,8,7]=>[4,3,8,7,6,5,1,2]=>1011110=>[1,1,4,1]
[5,1,2,6,3,4,8,7]=>[4,8,7,3,6,5,1,2]=>0110110=>[1,2,1,2,1]
[1,5,2,6,3,4,8,7]=>[8,4,7,3,6,5,1,2]=>1010110=>[1,1,1,1,2,1]
[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>1101110=>[2,1,3,1]
[1,5,2,3,6,4,8,7]=>[8,4,7,6,3,5,1,2]=>1011010=>[1,1,2,1,1,1]
[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>1101010=>[2,1,1,1,1,1]
[1,2,5,6,3,4,8,7]=>[8,7,4,3,6,5,1,2]=>1110110=>[3,1,2,1]
[5,1,2,3,6,8,4,7]=>[4,8,7,6,3,1,5,2]=>0111101=>[1,4,1,1]
[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>1011101=>[1,1,3,1,1]
[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>1110101=>[3,1,1,1,1]
[5,1,6,2,3,4,7,8]=>[4,8,3,7,6,5,2,1]=>0101111=>[1,1,1,4]
[5,1,2,6,3,4,7,8]=>[4,8,7,3,6,5,2,1]=>0110111=>[1,2,1,3]
[1,5,2,6,3,4,7,8]=>[8,4,7,3,6,5,2,1]=>1010111=>[1,1,1,1,3]
[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>1101111=>[2,1,4]
[5,1,2,3,6,4,7,8]=>[4,8,7,6,3,5,2,1]=>0111011=>[1,3,1,2]
[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>1011011=>[1,1,2,1,2]
[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>1101011=>[2,1,1,1,2]
[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>1110111=>[3,1,3]
[5,1,2,3,6,7,4,8]=>[4,8,7,6,3,2,5,1]=>0111101=>[1,4,1,1]
[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>1101101=>[2,1,2,1,1]
[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>1110101=>[3,1,1,1,1]
[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>0111110=>[1,5,1]
[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>1011110=>[1,1,4,1]
[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>1101110=>[2,1,3,1]
[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]=>1110110=>[3,1,2,1]
[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>1111010=>[4,1,1,1]
[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>1111101=>[5,1,1]
[5,1,7,2,8,3,4,6]=>[4,8,2,7,1,6,5,3]=>0101011=>[1,1,1,1,1,2]
[5,7,1,2,8,3,4,6]=>[4,2,8,7,1,6,5,3]=>1011011=>[1,1,2,1,2]
[5,1,7,8,2,3,4,6]=>[4,8,2,1,7,6,5,3]=>0110111=>[1,2,1,3]
[5,7,1,8,2,3,4,6]=>[4,2,8,1,7,6,5,3]=>1010111=>[1,1,1,1,3]
[5,7,8,1,2,3,4,6]=>[4,2,1,8,7,6,5,3]=>1101111=>[2,1,4]
[5,1,7,2,3,8,4,6]=>[4,8,2,7,6,1,5,3]=>0101101=>[1,1,1,2,1,1]
[5,7,1,2,3,8,4,6]=>[4,2,8,7,6,1,5,3]=>1011101=>[1,1,3,1,1]
[5,1,2,7,3,8,4,6]=>[4,8,7,2,6,1,5,3]=>0110101=>[1,2,1,1,1,1]
[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>1101101=>[2,1,2,1,1]
[5,1,2,7,8,3,4,6]=>[4,8,7,2,1,6,5,3]=>0111011=>[1,3,1,2]
[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>1011011=>[1,1,2,1,2]
[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>1101011=>[2,1,1,1,2]
[1,5,7,8,2,3,4,6]=>[8,4,2,1,7,6,5,3]=>1110111=>[3,1,3]
[5,1,7,2,3,4,8,6]=>[4,8,2,7,6,5,1,3]=>0101110=>[1,1,1,3,1]
[5,7,1,2,3,4,8,6]=>[4,2,8,7,6,5,1,3]=>1011110=>[1,1,4,1]
[5,1,2,7,3,4,8,6]=>[4,8,7,2,6,5,1,3]=>0110110=>[1,2,1,2,1]
[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>1010110=>[1,1,1,1,2,1]
[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>1101110=>[2,1,3,1]
[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>1011010=>[1,1,2,1,1,1]
[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>1101010=>[2,1,1,1,1,1]
[1,2,5,7,3,4,8,6]=>[8,7,4,2,6,5,1,3]=>1110110=>[3,1,2,1]
[5,1,2,3,7,8,4,6]=>[4,8,7,6,2,1,5,3]=>0111101=>[1,4,1,1]
[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>1011101=>[1,1,3,1,1]
[1,2,5,3,7,8,4,6]=>[8,7,4,6,2,1,5,3]=>1101101=>[2,1,2,1,1]
[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>1110101=>[3,1,1,1,1]
[1,2,5,7,8,3,4,6]=>[8,7,4,2,1,6,5,3]=>1111011=>[4,1,2]
[5,1,7,2,3,4,6,8]=>[4,8,2,7,6,5,3,1]=>0101111=>[1,1,1,4]
[5,7,1,2,3,4,6,8]=>[4,2,8,7,6,5,3,1]=>1011111=>[1,1,5]
[5,1,2,7,3,4,6,8]=>[4,8,7,2,6,5,3,1]=>0110111=>[1,2,1,3]
[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>1010111=>[1,1,1,1,3]
[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>1101111=>[2,1,4]
[5,1,2,3,7,4,6,8]=>[4,8,7,6,2,5,3,1]=>0111011=>[1,3,1,2]
[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>1011011=>[1,1,2,1,2]
[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>1101011=>[2,1,1,1,2]
[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>1110111=>[3,1,3]
[5,1,2,3,4,7,6,8]=>[4,8,7,6,5,2,3,1]=>0111101=>[1,4,1,1]
[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>1011101=>[1,1,3,1,1]
[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>1101101=>[2,1,2,1,1]
[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>1111011=>[4,1,2]
[5,1,2,3,4,7,8,6]=>[4,8,7,6,5,2,1,3]=>0111110=>[1,5,1]
[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>1011110=>[1,1,4,1]
[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>1101110=>[2,1,3,1]
[1,2,3,5,7,4,8,6]=>[8,7,6,4,2,5,1,3]=>1111010=>[4,1,1,1]
[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>1111101=>[5,1,1]
[5,1,8,2,3,4,6,7]=>[4,8,1,7,6,5,3,2]=>0101111=>[1,1,1,4]
[5,8,1,2,3,4,6,7]=>[4,1,8,7,6,5,3,2]=>1011111=>[1,1,5]
[5,1,2,8,3,4,6,7]=>[4,8,7,1,6,5,3,2]=>0110111=>[1,2,1,3]
[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>1010111=>[1,1,1,1,3]
[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>1101111=>[2,1,4]
[5,1,2,3,8,4,6,7]=>[4,8,7,6,1,5,3,2]=>0111011=>[1,3,1,2]
[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>1101011=>[2,1,1,1,2]
[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>1110111=>[3,1,3]
[5,1,2,3,4,8,6,7]=>[4,8,7,6,5,1,3,2]=>0111101=>[1,4,1,1]
[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>1011101=>[1,1,3,1,1]
[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>1101101=>[2,1,2,1,1]
[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>1110101=>[3,1,1,1,1]
[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>1111011=>[4,1,2]
[5,1,2,3,4,6,8,7]=>[4,8,7,6,5,3,1,2]=>0111110=>[1,5,1]
[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>1011110=>[1,1,4,1]
[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>1101110=>[2,1,3,1]
[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>1111101=>[5,1,1]
[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>1011111=>[1,1,5]
[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>1101111=>[2,1,4]
[6,1,7,2,8,3,4,5]=>[3,8,2,7,1,6,5,4]=>0101011=>[1,1,1,1,1,2]
[6,7,1,2,8,3,4,5]=>[3,2,8,7,1,6,5,4]=>1011011=>[1,1,2,1,2]
[6,1,7,8,2,3,4,5]=>[3,8,2,1,7,6,5,4]=>0110111=>[1,2,1,3]
[6,7,1,8,2,3,4,5]=>[3,2,8,1,7,6,5,4]=>1010111=>[1,1,1,1,3]
[6,1,7,2,3,8,4,5]=>[3,8,2,7,6,1,5,4]=>0101101=>[1,1,1,2,1,1]
[6,7,1,2,3,8,4,5]=>[3,2,8,7,6,1,5,4]=>1011101=>[1,1,3,1,1]
[6,1,2,7,3,8,4,5]=>[3,8,7,2,6,1,5,4]=>0110101=>[1,2,1,1,1,1]
[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,6,7,2,3,8,4,5]=>[8,3,2,7,6,1,5,4]=>1101101=>[2,1,2,1,1]
[6,1,2,7,8,3,4,5]=>[3,8,7,2,1,6,5,4]=>0111011=>[1,3,1,2]
[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>1011011=>[1,1,2,1,2]
[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>1101011=>[2,1,1,1,2]
[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>1110111=>[3,1,3]
[6,1,7,2,3,4,8,5]=>[3,8,2,7,6,5,1,4]=>0101110=>[1,1,1,3,1]
[6,7,1,2,3,4,8,5]=>[3,2,8,7,6,5,1,4]=>1011110=>[1,1,4,1]
[6,1,2,7,3,4,8,5]=>[3,8,7,2,6,5,1,4]=>0110110=>[1,2,1,2,1]
[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>1010110=>[1,1,1,1,2,1]
[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>1101110=>[2,1,3,1]
[6,1,2,3,7,4,8,5]=>[3,8,7,6,2,5,1,4]=>0111010=>[1,3,1,1,1]
[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>1011010=>[1,1,2,1,1,1]
[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>1101010=>[2,1,1,1,1,1]
[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>1110110=>[3,1,2,1]
[6,1,2,3,7,8,4,5]=>[3,8,7,6,2,1,5,4]=>0111101=>[1,4,1,1]
[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>1011101=>[1,1,3,1,1]
[1,2,6,3,7,8,4,5]=>[8,7,3,6,2,1,5,4]=>1101101=>[2,1,2,1,1]
[1,2,6,7,3,8,4,5]=>[8,7,3,2,6,1,5,4]=>1110101=>[3,1,1,1,1]
[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>1111011=>[4,1,2]
[6,1,7,2,3,4,5,8]=>[3,8,2,7,6,5,4,1]=>0101111=>[1,1,1,4]
[6,1,2,7,3,4,5,8]=>[3,8,7,2,6,5,4,1]=>0110111=>[1,2,1,3]
[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>1010111=>[1,1,1,1,3]
[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>1101111=>[2,1,4]
[6,1,2,3,7,4,5,8]=>[3,8,7,6,2,5,4,1]=>0111011=>[1,3,1,2]
[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>1011011=>[1,1,2,1,2]
[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>1101011=>[2,1,1,1,2]
[6,1,2,3,4,7,5,8]=>[3,8,7,6,5,2,4,1]=>0111101=>[1,4,1,1]
[1,6,2,3,4,7,5,8]=>[8,3,7,6,5,2,4,1]=>1011101=>[1,1,3,1,1]
[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>1101101=>[2,1,2,1,1]
[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>1110101=>[3,1,1,1,1]
[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>1111011=>[4,1,2]
[6,1,2,3,4,7,8,5]=>[3,8,7,6,5,2,1,4]=>0111110=>[1,5,1]
[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>1101110=>[2,1,3,1]
[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>1110110=>[3,1,2,1]
[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>1111010=>[4,1,1,1]
[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>1111101=>[5,1,1]
[6,1,8,2,3,4,5,7]=>[3,8,1,7,6,5,4,2]=>0101111=>[1,1,1,4]
[6,8,1,2,3,4,5,7]=>[3,1,8,7,6,5,4,2]=>1011111=>[1,1,5]
[6,1,2,8,3,4,5,7]=>[3,8,7,1,6,5,4,2]=>0110111=>[1,2,1,3]
[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>1010111=>[1,1,1,1,3]
[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>1101111=>[2,1,4]
[6,1,2,3,8,4,5,7]=>[3,8,7,6,1,5,4,2]=>0111011=>[1,3,1,2]
[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>1011011=>[1,1,2,1,2]
[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>1101011=>[2,1,1,1,2]
[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>1110111=>[3,1,3]
[6,1,2,3,4,8,5,7]=>[3,8,7,6,5,1,4,2]=>0111101=>[1,4,1,1]
[1,6,2,3,4,8,5,7]=>[8,3,7,6,5,1,4,2]=>1011101=>[1,1,3,1,1]
[1,2,6,3,4,8,5,7]=>[8,7,3,6,5,1,4,2]=>1101101=>[2,1,2,1,1]
[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>1110101=>[3,1,1,1,1]
[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>1111011=>[4,1,2]
[6,1,2,3,4,5,8,7]=>[3,8,7,6,5,4,1,2]=>0111110=>[1,5,1]
[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>1110110=>[3,1,2,1]
[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>1111101=>[5,1,1]
[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>1011111=>[1,1,5]
[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>1101111=>[2,1,4]
[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>1110111=>[3,1,3]
[7,1,8,2,3,4,5,6]=>[2,8,1,7,6,5,4,3]=>0101111=>[1,1,1,4]
[7,1,2,8,3,4,5,6]=>[2,8,7,1,6,5,4,3]=>0110111=>[1,2,1,3]
[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>1010111=>[1,1,1,1,3]
[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>1101111=>[2,1,4]
[7,1,2,3,8,4,5,6]=>[2,8,7,6,1,5,4,3]=>0111011=>[1,3,1,2]
[1,7,2,3,8,4,5,6]=>[8,2,7,6,1,5,4,3]=>1011011=>[1,1,2,1,2]
[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>1101011=>[2,1,1,1,2]
[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>1110111=>[3,1,3]
[7,1,2,3,4,8,5,6]=>[2,8,7,6,5,1,4,3]=>0111101=>[1,4,1,1]
[1,7,2,3,4,8,5,6]=>[8,2,7,6,5,1,4,3]=>1011101=>[1,1,3,1,1]
[1,2,7,3,4,8,5,6]=>[8,7,2,6,5,1,4,3]=>1101101=>[2,1,2,1,1]
[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>1110101=>[3,1,1,1,1]
[7,1,2,3,4,5,8,6]=>[2,8,7,6,5,4,1,3]=>0111110=>[1,5,1]
[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>1011110=>[1,1,4,1]
[1,2,7,3,4,5,8,6]=>[8,7,2,6,5,4,1,3]=>1101110=>[2,1,3,1]
[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>1110110=>[3,1,2,1]
[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>1111010=>[4,1,1,1]
[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>1111101=>[5,1,1]
[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>1011111=>[1,1,5]
[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>1101111=>[2,1,4]
[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>1110111=>[3,1,3]
[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>1111011=>[4,1,2]
[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>1011111=>[1,1,5]
[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>1101111=>[2,1,4]
[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>1110111=>[3,1,3]
[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>1111011=>[4,1,2]
[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>1111101=>[5,1,1]
[5,3,2,6,1,4,8,7]=>[4,6,7,3,8,5,1,2]=>0010110=>[2,1,1,2,1]
[7,3,2,5,4,8,1,6]=>[2,6,7,4,5,1,8,3]=>0010101=>[2,1,1,1,1,1]
[8,4,5,2,3,7,6,1]=>[1,5,4,7,6,2,3,8]=>0101100=>[1,1,1,2,2]
[7,4,5,2,3,8,1,6]=>[2,5,4,7,6,1,8,3]=>0101101=>[1,1,1,2,1,1]
[6,4,5,2,3,1,8,7]=>[3,5,4,7,6,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,2,1,3,8,7]=>[4,5,3,7,8,6,1,2]=>0100110=>[1,1,2,2,1]
[3,6,1,5,4,2,8,7]=>[6,3,8,4,5,7,1,2]=>1010010=>[1,1,1,2,1,1]
[4,6,5,1,3,2,8,7]=>[5,3,4,8,6,7,1,2]=>1001010=>[1,2,1,1,1,1]
[5,6,4,3,1,2,8,7]=>[4,3,5,6,8,7,1,2]=>1000110=>[1,3,2,1]
[7,5,4,3,2,8,1,6]=>[2,4,5,6,7,1,8,3]=>0000101=>[4,1,1,1]
[8,6,4,3,7,2,5,1]=>[1,3,5,6,2,7,4,8]=>0001010=>[3,1,1,1,1]
[7,6,4,3,8,2,1,5]=>[2,3,5,6,1,7,8,4]=>0001001=>[3,1,2,1]
[6,7,4,3,8,1,2,5]=>[3,2,5,6,1,8,7,4]=>1001011=>[1,2,1,1,2]
[5,7,4,3,1,8,2,6]=>[4,2,5,6,8,1,7,3]=>1000101=>[1,3,1,1,1]
[4,7,5,1,3,8,2,6]=>[5,2,4,8,6,1,7,3]=>1001101=>[1,2,2,1,1]
[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,7,5,4,8,3,6]=>[7,8,2,4,5,1,6,3]=>0100101=>[1,1,2,1,1,1]
[3,8,1,5,4,7,6,2]=>[6,1,8,4,5,2,3,7]=>1010100=>[1,1,1,1,1,2]
[4,8,5,1,3,7,6,2]=>[5,1,4,8,6,2,3,7]=>1001100=>[1,2,2,2]
[5,8,4,3,1,7,6,2]=>[4,1,5,6,8,2,3,7]=>1000100=>[1,3,1,2]
[6,8,4,3,7,1,5,2]=>[3,1,5,6,2,8,4,7]=>1001010=>[1,2,1,1,1,1]
[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>1001001=>[1,2,1,2,1]
[6,8,5,7,3,1,4,2]=>[3,1,4,2,6,8,5,7]=>1010010=>[1,1,1,2,1,1]
[5,8,6,7,1,3,4,2]=>[4,1,3,2,8,6,5,7]=>1010110=>[1,1,1,1,2,1]
[4,8,6,1,7,3,5,2]=>[5,1,3,8,2,6,4,7]=>1001010=>[1,2,1,1,1,1]
[3,8,1,6,7,4,5,2]=>[6,1,8,3,2,5,4,7]=>1011010=>[1,1,2,1,1,1]
[2,1,8,6,7,4,5,3]=>[7,8,1,3,2,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,6,8,4,3,5]=>[7,8,2,3,1,5,6,4]=>0101001=>[1,1,1,1,2,1]
[3,7,1,6,8,4,2,5]=>[6,2,8,3,1,5,7,4]=>1011001=>[1,1,2,2,1]
[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>1001001=>[1,2,1,2,1]
[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,4,7,2,1,8,3,6]=>[4,5,2,7,8,1,6,3]=>0100101=>[1,1,2,1,1,1]
[6,4,7,2,8,1,3,5]=>[3,5,2,7,1,8,6,4]=>0101011=>[1,1,1,1,1,2]
[7,4,6,2,8,3,1,5]=>[2,5,3,7,1,6,8,4]=>0101001=>[1,1,1,1,2,1]
[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,2,6,7,4,5,1]=>[1,6,7,3,2,5,4,8]=>0011010=>[2,2,1,1,1]
[7,3,2,6,8,4,1,5]=>[2,6,7,3,1,5,8,4]=>0011001=>[2,2,2,1]
[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>0011011=>[2,2,1,2]
[5,3,2,7,1,8,4,6]=>[4,6,7,2,8,1,5,3]=>0010101=>[2,1,1,1,1,1]
[4,3,2,1,7,8,5,6]=>[5,6,7,8,2,1,4,3]=>0001101=>[3,2,1,1]
[3,4,1,2,8,7,6,5]=>[6,5,8,7,1,2,3,4]=>1011000=>[1,1,2,3]
[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>0010100=>[2,1,1,1,2]
[6,3,2,8,7,1,5,4]=>[3,6,7,1,2,8,4,5]=>0010010=>[2,1,2,1,1]
[7,3,2,8,6,5,1,4]=>[2,6,7,1,3,4,8,5]=>0010001=>[2,1,3,1]
[8,4,7,2,6,5,3,1]=>[1,5,2,7,3,4,6,8]=>0101000=>[1,1,1,1,3]
[7,4,8,2,6,5,1,3]=>[2,5,1,7,3,4,8,6]=>0101001=>[1,1,1,1,2,1]
[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[5,4,8,2,1,7,6,3]=>[4,5,1,7,8,2,3,6]=>0100100=>[1,1,2,1,2]
[4,5,8,1,2,7,6,3]=>[5,4,1,8,7,2,3,6]=>1101100=>[2,1,2,2]
[3,5,1,8,2,7,6,4]=>[6,4,8,1,7,2,3,5]=>1010100=>[1,1,1,1,1,2]
[2,1,5,8,3,7,6,4]=>[7,8,4,1,6,2,3,5]=>0110100=>[1,2,1,1,2]
[2,1,6,8,7,3,5,4]=>[7,8,3,1,2,6,4,5]=>0110010=>[1,2,2,1,1]
[3,6,1,8,7,2,5,4]=>[6,3,8,1,2,7,4,5]=>1010010=>[1,1,1,2,1,1]
[4,6,8,1,7,2,5,3]=>[5,3,1,8,2,7,4,6]=>1101010=>[2,1,1,1,1,1]
[5,6,8,7,1,2,4,3]=>[4,3,1,2,8,7,5,6]=>1100110=>[2,2,2,1]
[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>0100010=>[1,1,3,1,1]
[7,5,8,6,2,4,1,3]=>[2,4,1,3,7,5,8,6]=>0100101=>[1,1,2,1,1,1]
[8,5,7,6,2,4,3,1]=>[1,4,2,3,7,5,6,8]=>0100100=>[1,1,2,1,2]
[5,7,8,6,1,4,2,3]=>[4,2,1,3,8,5,7,6]=>1100101=>[2,2,1,1,1]
[4,7,8,1,6,5,2,3]=>[5,2,1,8,3,4,7,6]=>1101001=>[2,1,1,2,1]
[3,7,1,8,6,5,2,4]=>[6,2,8,1,3,4,7,5]=>1010001=>[1,1,1,3,1]
[2,1,7,8,6,5,3,4]=>[7,8,2,1,3,4,6,5]=>0110001=>[1,2,3,1]
[3,8,1,7,6,5,4,2]=>[6,1,8,2,3,4,5,7]=>1010000=>[1,1,1,4]
[4,8,7,1,6,5,3,2]=>[5,1,2,8,3,4,6,7]=>1001000=>[1,2,1,3]
[5,8,7,6,1,4,3,2]=>[4,1,2,3,8,5,6,7]=>1000100=>[1,3,1,2]
[6,8,7,5,4,1,3,2]=>[3,1,2,4,5,8,6,7]=>1000010=>[1,4,1,1]
[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>010101010=>[1,1,1,1,1,1,1,1,1]
[4,3,2,1,6,5,8,7,10,9]=>[7,8,9,10,5,6,3,4,1,2]=>000101010=>[3,1,1,1,1,1,1]
[6,3,2,5,4,1,8,7,10,9]=>[5,8,9,6,7,10,3,4,1,2]=>001001010=>[2,1,2,1,1,1,1]
[8,3,2,5,4,7,6,1,10,9]=>[3,8,9,6,7,4,5,10,1,2]=>001010010=>[2,1,1,1,2,1,1]
[10,3,2,5,4,7,6,9,8,1]=>[1,8,9,6,7,4,5,2,3,10]=>001010100=>[2,1,1,1,1,1,2]
[2,1,6,5,4,3,8,7,10,9]=>[9,10,5,6,7,8,3,4,1,2]=>010001010=>[1,1,3,1,1,1,1]
[6,5,4,3,2,1,8,7,10,9]=>[5,6,7,8,9,10,3,4,1,2]=>000001010=>[5,1,1,1,1]
[8,5,4,3,2,7,6,1,10,9]=>[3,6,7,8,9,4,5,10,1,2]=>000010010=>[4,1,2,1,1]
[10,5,4,3,2,7,6,9,8,1]=>[1,6,7,8,9,4,5,2,3,10]=>000010100=>[4,1,1,1,2]
[2,1,8,5,4,7,6,3,10,9]=>[9,10,3,6,7,4,5,8,1,2]=>010010010=>[1,1,2,1,2,1,1]
[8,7,4,3,6,5,2,1,10,9]=>[3,4,7,8,5,6,9,10,1,2]=>000100010=>[3,1,3,1,1]
[10,7,4,3,6,5,2,9,8,1]=>[1,4,7,8,5,6,9,2,3,10]=>000100100=>[3,1,2,1,2]
[2,1,10,5,4,7,6,9,8,3]=>[9,10,1,6,7,4,5,2,3,8]=>010010100=>[1,1,2,1,1,1,2]
[10,9,4,3,6,5,8,7,2,1]=>[1,2,7,8,5,6,3,4,9,10]=>000101000=>[3,1,1,1,3]
[8,9,5,6,3,4,10,1,2,7]=>[3,2,6,5,8,7,1,10,9,4]=>101011011=>[1,1,1,1,2,1,2]
[2,1,4,3,8,7,6,5,10,9]=>[9,10,7,8,3,4,5,6,1,2]=>010100010=>[1,1,1,1,3,1,1]
[4,3,2,1,8,7,6,5,10,9]=>[7,8,9,10,3,4,5,6,1,2]=>000100010=>[3,1,3,1,1]
[8,3,2,7,6,5,4,1,10,9]=>[3,8,9,4,5,6,7,10,1,2]=>001000010=>[2,1,4,1,1]
[10,3,2,7,6,5,4,9,8,1]=>[1,8,9,4,5,6,7,2,3,10]=>001000100=>[2,1,3,1,2]
[2,1,8,7,6,5,4,3,10,9]=>[9,10,3,4,5,6,7,8,1,2]=>010000010=>[1,1,5,1,1]
[8,7,6,5,4,3,2,1,10,9]=>[3,4,5,6,7,8,9,10,1,2]=>000000010=>[7,1,1]
[9,7,6,5,4,3,2,10,1,8]=>[2,4,5,6,7,8,9,1,10,3]=>000000101=>[6,1,1,1]
[10,7,6,5,4,3,2,9,8,1]=>[1,4,5,6,7,8,9,2,3,10]=>000000100=>[6,1,2]
[3,9,1,7,6,5,4,10,2,8]=>[8,2,10,4,5,6,7,1,9,3]=>101000101=>[1,1,1,3,1,1,1]
[2,1,10,7,6,5,4,9,8,3]=>[9,10,1,4,5,6,7,2,3,8]=>010000100=>[1,1,4,1,2]
[10,9,6,5,4,3,8,7,2,1]=>[1,2,5,6,7,8,3,4,9,10]=>000001000=>[5,1,3]
[2,1,4,3,10,7,6,9,8,5]=>[9,10,7,8,1,4,5,2,3,6]=>010100100=>[1,1,1,1,2,1,2]
[4,3,2,1,10,7,6,9,8,5]=>[7,8,9,10,1,4,5,2,3,6]=>000100100=>[3,1,2,1,2]
[10,3,2,9,6,5,8,7,4,1]=>[1,8,9,2,5,6,3,4,7,10]=>001001000=>[2,1,2,1,3]
[2,1,10,9,6,5,8,7,4,3]=>[9,10,1,2,5,6,3,4,7,8]=>010001000=>[1,1,3,1,3]
[10,9,8,5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5,8,9,10]=>000010000=>[4,1,4]
[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>010101010=>[1,1,1,1,1,1,1,1,1]
[9,8,7,6,10,4,3,2,1,5]=>[2,3,4,5,1,7,8,9,10,6]=>000100001=>[3,1,4,1]
[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>111101111=>[4,1,4]
[7,3,2,8,9,10,1,4,5,6]=>[4,8,9,3,2,1,10,7,6,5]=>001110111=>[2,3,1,3]
[8,5,4,3,2,9,10,1,6,7]=>[3,6,7,8,9,2,1,10,5,4]=>000011011=>[4,2,1,2]
[2,1,4,3,6,5,10,9,8,7]=>[9,10,7,8,5,6,1,2,3,4]=>010101000=>[1,1,1,1,1,1,3]
[4,3,2,1,6,5,10,9,8,7]=>[7,8,9,10,5,6,1,2,3,4]=>000101000=>[3,1,1,1,3]
[6,3,2,5,4,1,10,9,8,7]=>[5,8,9,6,7,10,1,2,3,4]=>001001000=>[2,1,2,1,3]
[10,3,2,5,4,9,8,7,6,1]=>[1,8,9,6,7,2,3,4,5,10]=>001010000=>[2,1,1,1,4]
[2,1,6,5,4,3,10,9,8,7]=>[9,10,5,6,7,8,1,2,3,4]=>010001000=>[1,1,3,1,3]
[6,5,4,3,2,1,10,9,8,7]=>[5,6,7,8,9,10,1,2,3,4]=>000001000=>[5,1,3]
[10,5,4,3,2,9,8,7,6,1]=>[1,6,7,8,9,2,3,4,5,10]=>000010000=>[4,1,4]
[2,1,10,5,4,9,8,7,6,3]=>[9,10,1,6,7,2,3,4,5,8]=>010010000=>[1,1,2,1,4]
[10,9,4,3,8,7,6,5,2,1]=>[1,2,7,8,3,4,5,6,9,10]=>000100000=>[3,1,5]
[7,10,5,9,3,8,1,6,4,2]=>[4,1,6,2,8,3,10,5,7,9]=>101010100=>[1,1,1,1,1,1,1,2]
[9,7,5,10,3,8,2,6,1,4]=>[2,4,6,1,8,3,9,5,10,7]=>001010101=>[2,1,1,1,1,1,1,1]
[5,6,7,10,1,2,3,9,8,4]=>[6,5,4,1,10,9,8,2,3,7]=>111011100=>[3,1,3,2]
[2,1,4,3,10,9,8,7,6,5]=>[9,10,7,8,1,2,3,4,5,6]=>010100000=>[1,1,1,1,5]
[4,3,2,1,10,9,8,7,6,5]=>[7,8,9,10,1,2,3,4,5,6]=>000100000=>[3,1,5]
[10,3,2,9,8,7,6,5,4,1]=>[1,8,9,2,3,4,5,6,7,10]=>001000000=>[2,1,6]
[4,5,10,1,2,9,8,7,6,3]=>[7,6,1,10,9,2,3,4,5,8]=>110110000=>[2,1,2,4]
[2,1,10,9,8,7,6,5,4,3]=>[9,10,1,2,3,4,5,6,7,8]=>010000000=>[1,1,7]
[3,10,1,9,8,7,6,5,4,2]=>[8,1,10,2,3,4,5,6,7,9]=>101000000=>[1,1,1,6]
[6,10,9,8,7,1,5,4,3,2]=>[5,1,2,3,4,10,6,7,8,9]=>100001000=>[1,4,1,3]
[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>100000001=>[1,7,1]
[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>000000000=>[9]
[3,2,5,1,4,6,7,8]=>[6,7,4,8,5,3,2,1]=>0101111=>[1,1,1,4]
[4,2,5,1,3,6,7,8]=>[5,7,4,8,6,3,2,1]=>0101111=>[1,1,1,4]
[5,2,4,1,3,6,7,8]=>[4,7,5,8,6,3,2,1]=>0101111=>[1,1,1,4]
[5,2,6,1,3,4,7,8]=>[4,7,3,8,6,5,2,1]=>0101111=>[1,1,1,4]
[5,3,6,1,2,4,7,8]=>[4,6,3,8,7,5,2,1]=>0101111=>[1,1,1,4]
[6,3,5,1,2,4,7,8]=>[3,6,4,8,7,5,2,1]=>0101111=>[1,1,1,4]
[4,2,7,1,3,5,6,8]=>[5,7,2,8,6,4,3,1]=>0101111=>[1,1,1,4]
[4,3,7,1,2,5,6,8]=>[5,6,2,8,7,4,3,1]=>0101111=>[1,1,1,4]
[5,3,7,1,2,4,6,8]=>[4,6,2,8,7,5,3,1]=>0101111=>[1,1,1,4]
[6,2,7,1,3,4,5,8]=>[3,7,2,8,6,5,4,1]=>0101111=>[1,1,1,4]
[6,3,7,1,2,4,5,8]=>[3,6,2,8,7,5,4,1]=>0101111=>[1,1,1,4]
[6,4,7,1,2,3,5,8]=>[3,5,2,8,7,6,4,1]=>0101111=>[1,1,1,4]
[7,2,5,1,3,4,6,8]=>[2,7,4,8,6,5,3,1]=>0101111=>[1,1,1,4]
[7,3,5,1,2,4,6,8]=>[2,6,4,8,7,5,3,1]=>0101111=>[1,1,1,4]
[7,3,6,1,2,4,5,8]=>[2,6,3,8,7,5,4,1]=>0101111=>[1,1,1,4]
[3,2,8,1,4,5,6,7]=>[6,7,1,8,5,4,3,2]=>0101111=>[1,1,1,4]
[5,2,8,1,3,4,6,7]=>[4,7,1,8,6,5,3,2]=>0101111=>[1,1,1,4]
[5,3,8,1,2,4,6,7]=>[4,6,1,8,7,5,3,2]=>0101111=>[1,1,1,4]
[5,4,8,1,2,3,6,7]=>[4,5,1,8,7,6,3,2]=>0101111=>[1,1,1,4]
[6,2,8,1,3,4,5,7]=>[3,7,1,8,6,5,4,2]=>0101111=>[1,1,1,4]
[6,3,8,1,2,4,5,7]=>[3,6,1,8,7,5,4,2]=>0101111=>[1,1,1,4]
[6,5,8,1,2,3,4,7]=>[3,4,1,8,7,6,5,2]=>0101111=>[1,1,1,4]
[7,2,8,1,3,4,5,6]=>[2,7,1,8,6,5,4,3]=>0101111=>[1,1,1,4]
[7,5,8,1,2,3,4,6]=>[2,4,1,8,7,6,5,3]=>0101111=>[1,1,1,4]
[8,2,4,1,3,5,6,7]=>[1,7,5,8,6,4,3,2]=>0101111=>[1,1,1,4]
[8,2,5,1,3,4,6,7]=>[1,7,4,8,6,5,3,2]=>0101111=>[1,1,1,4]
[8,3,5,1,2,4,6,7]=>[1,6,4,8,7,5,3,2]=>0101111=>[1,1,1,4]
[8,4,6,1,2,3,5,7]=>[1,5,3,8,7,6,4,2]=>0101111=>[1,1,1,4]
[8,3,7,1,2,4,5,6]=>[1,6,2,8,7,5,4,3]=>0101111=>[1,1,1,4]
[8,5,7,1,2,3,4,6]=>[1,4,2,8,7,6,5,3]=>0101111=>[1,1,1,4]
[3,2,5,7,1,4,6,8]=>[6,7,4,2,8,5,3,1]=>0110111=>[1,2,1,3]
[5,2,4,7,1,3,6,8]=>[4,7,5,2,8,6,3,1]=>0110111=>[1,2,1,3]
[5,3,4,7,1,2,6,8]=>[4,6,5,2,8,7,3,1]=>0110111=>[1,2,1,3]
[4,2,6,7,1,3,5,8]=>[5,7,3,2,8,6,4,1]=>0110111=>[1,2,1,3]
[5,2,6,7,1,3,4,8]=>[4,7,3,2,8,6,5,1]=>0110111=>[1,2,1,3]
[6,2,5,7,1,3,4,8]=>[3,7,4,2,8,6,5,1]=>0110111=>[1,2,1,3]
[6,3,5,7,1,2,4,8]=>[3,6,4,2,8,7,5,1]=>0110111=>[1,2,1,3]
[7,2,4,6,1,3,5,8]=>[2,7,5,3,8,6,4,1]=>0110111=>[1,2,1,3]
[7,3,5,6,1,2,4,8]=>[2,6,4,3,8,7,5,1]=>0110111=>[1,2,1,3]
[3,2,5,8,1,4,6,7]=>[6,7,4,1,8,5,3,2]=>0110111=>[1,2,1,3]
[4,2,5,8,1,3,6,7]=>[5,7,4,1,8,6,3,2]=>0110111=>[1,2,1,3]
[4,3,5,8,1,2,6,7]=>[5,6,4,1,8,7,3,2]=>0110111=>[1,2,1,3]
[5,2,4,8,1,3,6,7]=>[4,7,5,1,8,6,3,2]=>0110111=>[1,2,1,3]
[3,2,6,8,1,4,5,7]=>[6,7,3,1,8,5,4,2]=>0110111=>[1,2,1,3]
[4,2,6,8,1,3,5,7]=>[5,7,3,1,8,6,4,2]=>0110111=>[1,2,1,3]
[4,3,6,8,1,2,5,7]=>[5,6,3,1,8,7,4,2]=>0110111=>[1,2,1,3]
[5,2,6,8,1,3,4,7]=>[4,7,3,1,8,6,5,2]=>0110111=>[1,2,1,3]
[5,3,6,8,1,2,4,7]=>[4,6,3,1,8,7,5,2]=>0110111=>[1,2,1,3]
[5,4,6,8,1,2,3,7]=>[4,5,3,1,8,7,6,2]=>0110111=>[1,2,1,3]
[6,2,4,8,1,3,5,7]=>[3,7,5,1,8,6,4,2]=>0110111=>[1,2,1,3]
[6,3,4,8,1,2,5,7]=>[3,6,5,1,8,7,4,2]=>0110111=>[1,2,1,3]
[6,2,5,8,1,3,4,7]=>[3,7,4,1,8,6,5,2]=>0110111=>[1,2,1,3]
[6,3,5,8,1,2,4,7]=>[3,6,4,1,8,7,5,2]=>0110111=>[1,2,1,3]
[3,2,7,8,1,4,5,6]=>[6,7,2,1,8,5,4,3]=>0110111=>[1,2,1,3]
[5,2,7,8,1,3,4,6]=>[4,7,2,1,8,6,5,3]=>0110111=>[1,2,1,3]
[5,3,7,8,1,2,4,6]=>[4,6,2,1,8,7,5,3]=>0110111=>[1,2,1,3]
[5,4,7,8,1,2,3,6]=>[4,5,2,1,8,7,6,3]=>0110111=>[1,2,1,3]
[6,4,7,8,1,2,3,5]=>[3,5,2,1,8,7,6,4]=>0110111=>[1,2,1,3]
[7,3,4,8,1,2,5,6]=>[2,6,5,1,8,7,4,3]=>0110111=>[1,2,1,3]
[7,3,5,8,1,2,4,6]=>[2,6,4,1,8,7,5,3]=>0110111=>[1,2,1,3]
[7,4,5,8,1,2,3,6]=>[2,5,4,1,8,7,6,3]=>0110111=>[1,2,1,3]
[8,2,4,6,1,3,5,7]=>[1,7,5,3,8,6,4,2]=>0110111=>[1,2,1,3]
[8,3,5,6,1,2,4,7]=>[1,6,4,3,8,7,5,2]=>0110111=>[1,2,1,3]
[8,2,4,7,1,3,5,6]=>[1,7,5,2,8,6,4,3]=>0110111=>[1,2,1,3]
[8,3,4,7,1,2,5,6]=>[1,6,5,2,8,7,4,3]=>0110111=>[1,2,1,3]
[8,2,5,7,1,3,4,6]=>[1,7,4,2,8,6,5,3]=>0110111=>[1,2,1,3]
[8,3,5,7,1,2,4,6]=>[1,6,4,2,8,7,5,3]=>0110111=>[1,2,1,3]
[8,2,6,7,1,3,4,5]=>[1,7,3,2,8,6,5,4]=>0110111=>[1,2,1,3]
[8,4,6,7,1,2,3,5]=>[1,5,3,2,8,7,6,4]=>0110111=>[1,2,1,3]
[3,6,2,5,1,4,7,8]=>[6,3,7,4,8,5,2,1]=>1010111=>[1,1,1,1,3]
[4,6,2,5,1,3,7,8]=>[5,3,7,4,8,6,2,1]=>1010111=>[1,1,1,1,3]
[4,6,3,5,1,2,7,8]=>[5,3,6,4,8,7,2,1]=>1010111=>[1,1,1,1,3]
[3,7,2,5,1,4,6,8]=>[6,2,7,4,8,5,3,1]=>1010111=>[1,1,1,1,3]
[4,7,3,5,1,2,6,8]=>[5,2,6,4,8,7,3,1]=>1010111=>[1,1,1,1,3]
[5,7,2,4,1,3,6,8]=>[4,2,7,5,8,6,3,1]=>1010111=>[1,1,1,1,3]
[5,7,3,4,1,2,6,8]=>[4,2,6,5,8,7,3,1]=>1010111=>[1,1,1,1,3]
[3,7,2,6,1,4,5,8]=>[6,2,7,3,8,5,4,1]=>1010111=>[1,1,1,1,3]
[4,7,3,6,1,2,5,8]=>[5,2,6,3,8,7,4,1]=>1010111=>[1,1,1,1,3]
[5,7,3,6,1,2,4,8]=>[4,2,6,3,8,7,5,1]=>1010111=>[1,1,1,1,3]
[5,7,4,6,1,2,3,8]=>[4,2,5,3,8,7,6,1]=>1010111=>[1,1,1,1,3]
[6,7,2,4,1,3,5,8]=>[3,2,7,5,8,6,4,1]=>1010111=>[1,1,1,1,3]
[6,7,3,5,1,2,4,8]=>[3,2,6,4,8,7,5,1]=>1010111=>[1,1,1,1,3]
[3,8,2,5,1,4,6,7]=>[6,1,7,4,8,5,3,2]=>1010111=>[1,1,1,1,3]
[4,8,2,5,1,3,6,7]=>[5,1,7,4,8,6,3,2]=>1010111=>[1,1,1,1,3]
[5,8,2,4,1,3,6,7]=>[4,1,7,5,8,6,3,2]=>1010111=>[1,1,1,1,3]
[5,8,3,4,1,2,6,7]=>[4,1,6,5,8,7,3,2]=>1010111=>[1,1,1,1,3]
[3,8,2,6,1,4,5,7]=>[6,1,7,3,8,5,4,2]=>1010111=>[1,1,1,1,3]
[4,8,2,6,1,3,5,7]=>[5,1,7,3,8,6,4,2]=>1010111=>[1,1,1,1,3]
[5,8,3,6,1,2,4,7]=>[4,1,6,3,8,7,5,2]=>1010111=>[1,1,1,1,3]
[5,8,4,6,1,2,3,7]=>[4,1,5,3,8,7,6,2]=>1010111=>[1,1,1,1,3]
[6,8,2,4,1,3,5,7]=>[3,1,7,5,8,6,4,2]=>1010111=>[1,1,1,1,3]
[6,8,3,4,1,2,5,7]=>[3,1,6,5,8,7,4,2]=>1010111=>[1,1,1,1,3]
[6,8,2,5,1,3,4,7]=>[3,1,7,4,8,6,5,2]=>1010111=>[1,1,1,1,3]
[6,8,4,5,1,2,3,7]=>[3,1,5,4,8,7,6,2]=>1010111=>[1,1,1,1,3]
[3,8,2,7,1,4,5,6]=>[6,1,7,2,8,5,4,3]=>1010111=>[1,1,1,1,3]
[4,8,2,7,1,3,5,6]=>[5,1,7,2,8,6,4,3]=>1010111=>[1,1,1,1,3]
[4,8,3,7,1,2,5,6]=>[5,1,6,2,8,7,4,3]=>1010111=>[1,1,1,1,3]
[5,8,2,7,1,3,4,6]=>[4,1,7,2,8,6,5,3]=>1010111=>[1,1,1,1,3]
[5,8,3,7,1,2,4,6]=>[4,1,6,2,8,7,5,3]=>1010111=>[1,1,1,1,3]
[5,8,4,7,1,2,3,6]=>[4,1,5,2,8,7,6,3]=>1010111=>[1,1,1,1,3]
[6,8,3,7,1,2,4,5]=>[3,1,6,2,8,7,5,4]=>1010111=>[1,1,1,1,3]
[6,8,4,7,1,2,3,5]=>[3,1,5,2,8,7,6,4]=>1010111=>[1,1,1,1,3]
[6,8,5,7,1,2,3,4]=>[3,1,4,2,8,7,6,5]=>1010111=>[1,1,1,1,3]
[7,8,2,4,1,3,5,6]=>[2,1,7,5,8,6,4,3]=>1010111=>[1,1,1,1,3]
[7,8,3,5,1,2,4,6]=>[2,1,6,4,8,7,5,3]=>1010111=>[1,1,1,1,3]
[7,8,2,6,1,3,4,5]=>[2,1,7,3,8,6,5,4]=>1010111=>[1,1,1,1,3]
[7,8,4,6,1,2,3,5]=>[2,1,5,3,8,7,6,4]=>1010111=>[1,1,1,1,3]
[4,3,2,6,1,5,7,8]=>[5,6,7,3,8,4,2,1]=>0010111=>[2,1,1,3]
[5,3,2,6,1,4,7,8]=>[4,6,7,3,8,5,2,1]=>0010111=>[2,1,1,3]
[5,4,2,6,1,3,7,8]=>[4,5,7,3,8,6,2,1]=>0010111=>[2,1,1,3]
[6,3,2,5,1,4,7,8]=>[3,6,7,4,8,5,2,1]=>0010111=>[2,1,1,3]
[6,4,2,5,1,3,7,8]=>[3,5,7,4,8,6,2,1]=>0010111=>[2,1,1,3]
[6,5,2,4,1,3,7,8]=>[3,4,7,5,8,6,2,1]=>0010111=>[2,1,1,3]
[4,3,2,7,1,5,6,8]=>[5,6,7,2,8,4,3,1]=>0010111=>[2,1,1,3]
[5,3,2,7,1,4,6,8]=>[4,6,7,2,8,5,3,1]=>0010111=>[2,1,1,3]
[5,4,2,7,1,3,6,8]=>[4,5,7,2,8,6,3,1]=>0010111=>[2,1,1,3]
[5,4,3,7,1,2,6,8]=>[4,5,6,2,8,7,3,1]=>0010111=>[2,1,1,3]
[6,3,2,7,1,4,5,8]=>[3,6,7,2,8,5,4,1]=>0010111=>[2,1,1,3]
[6,4,2,7,1,3,5,8]=>[3,5,7,2,8,6,4,1]=>0010111=>[2,1,1,3]
[6,4,3,7,1,2,5,8]=>[3,5,6,2,8,7,4,1]=>0010111=>[2,1,1,3]
[6,5,3,7,1,2,4,8]=>[3,4,6,2,8,7,5,1]=>0010111=>[2,1,1,3]
[7,3,2,5,1,4,6,8]=>[2,6,7,4,8,5,3,1]=>0010111=>[2,1,1,3]
[7,4,2,5,1,3,6,8]=>[2,5,7,4,8,6,3,1]=>0010111=>[2,1,1,3]
[7,3,2,6,1,4,5,8]=>[2,6,7,3,8,5,4,1]=>0010111=>[2,1,1,3]
[7,4,2,6,1,3,5,8]=>[2,5,7,3,8,6,4,1]=>0010111=>[2,1,1,3]
[7,5,2,6,1,3,4,8]=>[2,4,7,3,8,6,5,1]=>0010111=>[2,1,1,3]
[7,5,3,6,1,2,4,8]=>[2,4,6,3,8,7,5,1]=>0010111=>[2,1,1,3]
[4,3,2,8,1,5,6,7]=>[5,6,7,1,8,4,3,2]=>0010111=>[2,1,1,3]
[5,3,2,8,1,4,6,7]=>[4,6,7,1,8,5,3,2]=>0010111=>[2,1,1,3]
[5,4,3,8,1,2,6,7]=>[4,5,6,1,8,7,3,2]=>0010111=>[2,1,1,3]
[6,3,2,8,1,4,5,7]=>[3,6,7,1,8,5,4,2]=>0010111=>[2,1,1,3]
[6,4,2,8,1,3,5,7]=>[3,5,7,1,8,6,4,2]=>0010111=>[2,1,1,3]
[6,4,3,8,1,2,5,7]=>[3,5,6,1,8,7,4,2]=>0010111=>[2,1,1,3]
[6,5,2,8,1,3,4,7]=>[3,4,7,1,8,6,5,2]=>0010111=>[2,1,1,3]
[6,5,3,8,1,2,4,7]=>[3,4,6,1,8,7,5,2]=>0010111=>[2,1,1,3]
[6,5,4,8,1,2,3,7]=>[3,4,5,1,8,7,6,2]=>0010111=>[2,1,1,3]
[7,4,2,8,1,3,5,6]=>[2,5,7,1,8,6,4,3]=>0010111=>[2,1,1,3]
[7,4,3,8,1,2,5,6]=>[2,5,6,1,8,7,4,3]=>0010111=>[2,1,1,3]
[7,5,3,8,1,2,4,6]=>[2,4,6,1,8,7,5,3]=>0010111=>[2,1,1,3]
[7,6,3,8,1,2,4,5]=>[2,3,6,1,8,7,5,4]=>0010111=>[2,1,1,3]
[7,6,4,8,1,2,3,5]=>[2,3,5,1,8,7,6,4]=>0010111=>[2,1,1,3]
[8,3,2,5,1,4,6,7]=>[1,6,7,4,8,5,3,2]=>0010111=>[2,1,1,3]
[8,4,2,5,1,3,6,7]=>[1,5,7,4,8,6,3,2]=>0010111=>[2,1,1,3]
[8,5,2,4,1,3,6,7]=>[1,4,7,5,8,6,3,2]=>0010111=>[2,1,1,3]
[8,3,2,6,1,4,5,7]=>[1,6,7,3,8,5,4,2]=>0010111=>[2,1,1,3]
[8,4,2,6,1,3,5,7]=>[1,5,7,3,8,6,4,2]=>0010111=>[2,1,1,3]
[8,5,3,6,1,2,4,7]=>[1,4,6,3,8,7,5,2]=>0010111=>[2,1,1,3]
[8,6,2,4,1,3,5,7]=>[1,3,7,5,8,6,4,2]=>0010111=>[2,1,1,3]
[8,6,3,5,1,2,4,7]=>[1,3,6,4,8,7,5,2]=>0010111=>[2,1,1,3]
[8,3,2,7,1,4,5,6]=>[1,6,7,2,8,5,4,3]=>0010111=>[2,1,1,3]
[8,4,2,7,1,3,5,6]=>[1,5,7,2,8,6,4,3]=>0010111=>[2,1,1,3]
[8,5,3,7,1,2,4,6]=>[1,4,6,2,8,7,5,3]=>0010111=>[2,1,1,3]
[8,5,4,7,1,2,3,6]=>[1,4,5,2,8,7,6,3]=>0010111=>[2,1,1,3]
[8,7,2,4,1,3,5,6]=>[1,2,7,5,8,6,4,3]=>0010111=>[2,1,1,3]
[8,7,2,5,1,3,4,6]=>[1,2,7,4,8,6,5,3]=>0010111=>[2,1,1,3]
[8,7,3,5,1,2,4,6]=>[1,2,6,4,8,7,5,3]=>0010111=>[2,1,1,3]
[8,7,2,6,1,3,4,5]=>[1,2,7,3,8,6,5,4]=>0010111=>[2,1,1,3]
[8,7,3,6,1,2,4,5]=>[1,2,6,3,8,7,5,4]=>0010111=>[2,1,1,3]
[8,7,4,6,1,2,3,5]=>[1,2,5,3,8,7,6,4]=>0010111=>[2,1,1,3]
[3,6,2,5,8,1,4,7]=>[6,3,7,4,1,8,5,2]=>1011011=>[1,1,2,1,2]
[4,6,2,5,8,1,3,7]=>[5,3,7,4,1,8,6,2]=>1011011=>[1,1,2,1,2]
[5,6,2,4,8,1,3,7]=>[4,3,7,5,1,8,6,2]=>1011011=>[1,1,2,1,2]
[5,6,3,4,8,1,2,7]=>[4,3,6,5,1,8,7,2]=>1011011=>[1,1,2,1,2]
[3,7,2,5,8,1,4,6]=>[6,2,7,4,1,8,5,3]=>1011011=>[1,1,2,1,2]
[4,7,2,5,8,1,3,6]=>[5,2,7,4,1,8,6,3]=>1011011=>[1,1,2,1,2]
[4,7,3,5,8,1,2,6]=>[5,2,6,4,1,8,7,3]=>1011011=>[1,1,2,1,2]
[5,7,2,4,8,1,3,6]=>[4,2,7,5,1,8,6,3]=>1011011=>[1,1,2,1,2]
[5,7,3,4,8,1,2,6]=>[4,2,6,5,1,8,7,3]=>1011011=>[1,1,2,1,2]
[3,7,2,6,8,1,4,5]=>[6,2,7,3,1,8,5,4]=>1011011=>[1,1,2,1,2]
[4,7,3,6,8,1,2,5]=>[5,2,6,3,1,8,7,4]=>1011011=>[1,1,2,1,2]
[5,7,3,6,8,1,2,4]=>[4,2,6,3,1,8,7,5]=>1011011=>[1,1,2,1,2]
[5,7,4,6,8,1,2,3]=>[4,2,5,3,1,8,7,6]=>1011011=>[1,1,2,1,2]
[6,7,2,4,8,1,3,5]=>[3,2,7,5,1,8,6,4]=>1011011=>[1,1,2,1,2]
[6,7,3,4,8,1,2,5]=>[3,2,6,5,1,8,7,4]=>1011011=>[1,1,2,1,2]
[6,7,3,5,8,1,2,4]=>[3,2,6,4,1,8,7,5]=>1011011=>[1,1,2,1,2]
[3,8,2,5,7,1,4,6]=>[6,1,7,4,2,8,5,3]=>1011011=>[1,1,2,1,2]
[4,8,2,5,7,1,3,6]=>[5,1,7,4,2,8,6,3]=>1011011=>[1,1,2,1,2]
[4,8,3,5,7,1,2,6]=>[5,1,6,4,2,8,7,3]=>1011011=>[1,1,2,1,2]
[5,8,2,4,7,1,3,6]=>[4,1,7,5,2,8,6,3]=>1011011=>[1,1,2,1,2]
[3,8,2,6,7,1,4,5]=>[6,1,7,3,2,8,5,4]=>1011011=>[1,1,2,1,2]
[4,8,3,6,7,1,2,5]=>[5,1,6,3,2,8,7,4]=>1011011=>[1,1,2,1,2]
[5,8,2,6,7,1,3,4]=>[4,1,7,3,2,8,6,5]=>1011011=>[1,1,2,1,2]
[5,8,4,6,7,1,2,3]=>[4,1,5,3,2,8,7,6]=>1011011=>[1,1,2,1,2]
[6,8,3,4,7,1,2,5]=>[3,1,6,5,2,8,7,4]=>1011011=>[1,1,2,1,2]
[6,8,2,5,7,1,3,4]=>[3,1,7,4,2,8,6,5]=>1011011=>[1,1,2,1,2]
[7,8,2,4,6,1,3,5]=>[2,1,7,5,3,8,6,4]=>1011011=>[1,1,2,1,2]
[7,8,3,4,6,1,2,5]=>[2,1,6,5,3,8,7,4]=>1011011=>[1,1,2,1,2]
[7,8,3,5,6,1,2,4]=>[2,1,6,4,3,8,7,5]=>1011011=>[1,1,2,1,2]
[4,3,2,6,8,1,5,7]=>[5,6,7,3,1,8,4,2]=>0011011=>[2,2,1,2]
[5,3,2,6,8,1,4,7]=>[4,6,7,3,1,8,5,2]=>0011011=>[2,2,1,2]
[5,4,2,6,8,1,3,7]=>[4,5,7,3,1,8,6,2]=>0011011=>[2,2,1,2]
[5,4,3,6,8,1,2,7]=>[4,5,6,3,1,8,7,2]=>0011011=>[2,2,1,2]
[6,3,2,5,8,1,4,7]=>[3,6,7,4,1,8,5,2]=>0011011=>[2,2,1,2]
[6,4,3,5,8,1,2,7]=>[3,5,6,4,1,8,7,2]=>0011011=>[2,2,1,2]
[6,5,2,4,8,1,3,7]=>[3,4,7,5,1,8,6,2]=>0011011=>[2,2,1,2]
[6,5,3,4,8,1,2,7]=>[3,4,6,5,1,8,7,2]=>0011011=>[2,2,1,2]
[4,3,2,7,8,1,5,6]=>[5,6,7,2,1,8,4,3]=>0011011=>[2,2,1,2]
[5,3,2,7,8,1,4,6]=>[4,6,7,2,1,8,5,3]=>0011011=>[2,2,1,2]
[5,4,2,7,8,1,3,6]=>[4,5,7,2,1,8,6,3]=>0011011=>[2,2,1,2]
[5,4,3,7,8,1,2,6]=>[4,5,6,2,1,8,7,3]=>0011011=>[2,2,1,2]
[6,4,2,7,8,1,3,5]=>[3,5,7,2,1,8,6,4]=>0011011=>[2,2,1,2]
[6,4,3,7,8,1,2,5]=>[3,5,6,2,1,8,7,4]=>0011011=>[2,2,1,2]
[6,5,2,7,8,1,3,4]=>[3,4,7,2,1,8,6,5]=>0011011=>[2,2,1,2]
[6,5,3,7,8,1,2,4]=>[3,4,6,2,1,8,7,5]=>0011011=>[2,2,1,2]
[7,3,2,5,8,1,4,6]=>[2,6,7,4,1,8,5,3]=>0011011=>[2,2,1,2]
[7,4,2,5,8,1,3,6]=>[2,5,7,4,1,8,6,3]=>0011011=>[2,2,1,2]
[7,5,2,4,8,1,3,6]=>[2,4,7,5,1,8,6,3]=>0011011=>[2,2,1,2]
[7,5,3,4,8,1,2,6]=>[2,4,6,5,1,8,7,3]=>0011011=>[2,2,1,2]
[7,3,2,6,8,1,4,5]=>[2,6,7,3,1,8,5,4]=>0011011=>[2,2,1,2]
[7,5,2,6,8,1,3,4]=>[2,4,7,3,1,8,6,5]=>0011011=>[2,2,1,2]
[7,5,3,6,8,1,2,4]=>[2,4,6,3,1,8,7,5]=>0011011=>[2,2,1,2]
[7,6,2,4,8,1,3,5]=>[2,3,7,5,1,8,6,4]=>0011011=>[2,2,1,2]
[7,6,3,4,8,1,2,5]=>[2,3,6,5,1,8,7,4]=>0011011=>[2,2,1,2]
[7,6,2,5,8,1,3,4]=>[2,3,7,4,1,8,6,5]=>0011011=>[2,2,1,2]
[7,6,3,5,8,1,2,4]=>[2,3,6,4,1,8,7,5]=>0011011=>[2,2,1,2]
[8,3,2,5,7,1,4,6]=>[1,6,7,4,2,8,5,3]=>0011011=>[2,2,1,2]
[8,4,2,5,7,1,3,6]=>[1,5,7,4,2,8,6,3]=>0011011=>[2,2,1,2]
[8,4,3,5,7,1,2,6]=>[1,5,6,4,2,8,7,3]=>0011011=>[2,2,1,2]
[8,5,2,4,7,1,3,6]=>[1,4,7,5,2,8,6,3]=>0011011=>[2,2,1,2]
[8,5,3,4,7,1,2,6]=>[1,4,6,5,2,8,7,3]=>0011011=>[2,2,1,2]
[8,3,2,6,7,1,4,5]=>[1,6,7,3,2,8,5,4]=>0011011=>[2,2,1,2]
[8,4,2,6,7,1,3,5]=>[1,5,7,3,2,8,6,4]=>0011011=>[2,2,1,2]
[8,4,3,6,7,1,2,5]=>[1,5,6,3,2,8,7,4]=>0011011=>[2,2,1,2]
[8,5,2,6,7,1,3,4]=>[1,4,7,3,2,8,6,5]=>0011011=>[2,2,1,2]
[8,5,3,6,7,1,2,4]=>[1,4,6,3,2,8,7,5]=>0011011=>[2,2,1,2]
[8,6,2,4,7,1,3,5]=>[1,3,7,5,2,8,6,4]=>0011011=>[2,2,1,2]
[8,7,2,4,6,1,3,5]=>[1,2,7,5,3,8,6,4]=>0011011=>[2,2,1,2]
[8,7,3,4,6,1,2,5]=>[1,2,6,5,3,8,7,4]=>0011011=>[2,2,1,2]
[8,7,2,5,6,1,3,4]=>[1,2,7,4,3,8,6,5]=>0011011=>[2,2,1,2]
[4,3,7,2,6,1,5,8]=>[5,6,2,7,3,8,4,1]=>0101011=>[1,1,1,1,1,2]
[5,3,7,2,6,1,4,8]=>[4,6,2,7,3,8,5,1]=>0101011=>[1,1,1,1,1,2]
[5,4,7,2,6,1,3,8]=>[4,5,2,7,3,8,6,1]=>0101011=>[1,1,1,1,1,2]
[6,3,7,2,5,1,4,8]=>[3,6,2,7,4,8,5,1]=>0101011=>[1,1,1,1,1,2]
[6,4,7,2,5,1,3,8]=>[3,5,2,7,4,8,6,1]=>0101011=>[1,1,1,1,1,2]
[6,4,7,3,5,1,2,8]=>[3,5,2,6,4,8,7,1]=>0101011=>[1,1,1,1,1,2]
[6,5,7,2,4,1,3,8]=>[3,4,2,7,5,8,6,1]=>0101011=>[1,1,1,1,1,2]
[7,3,6,2,5,1,4,8]=>[2,6,3,7,4,8,5,1]=>0101011=>[1,1,1,1,1,2]
[4,3,8,2,6,1,5,7]=>[5,6,1,7,3,8,4,2]=>0101011=>[1,1,1,1,1,2]
[5,3,8,2,6,1,4,7]=>[4,6,1,7,3,8,5,2]=>0101011=>[1,1,1,1,1,2]
[5,4,8,2,6,1,3,7]=>[4,5,1,7,3,8,6,2]=>0101011=>[1,1,1,1,1,2]
[6,4,8,2,5,1,3,7]=>[3,5,1,7,4,8,6,2]=>0101011=>[1,1,1,1,1,2]
[6,5,8,2,4,1,3,7]=>[3,4,1,7,5,8,6,2]=>0101011=>[1,1,1,1,1,2]
[6,5,8,3,4,1,2,7]=>[3,4,1,6,5,8,7,2]=>0101011=>[1,1,1,1,1,2]
[4,3,8,2,7,1,5,6]=>[5,6,1,7,2,8,4,3]=>0101011=>[1,1,1,1,1,2]
[5,4,8,2,7,1,3,6]=>[4,5,1,7,2,8,6,3]=>0101011=>[1,1,1,1,1,2]
[5,4,8,3,7,1,2,6]=>[4,5,1,6,2,8,7,3]=>0101011=>[1,1,1,1,1,2]
[6,4,8,2,7,1,3,5]=>[3,5,1,7,2,8,6,4]=>0101011=>[1,1,1,1,1,2]
[6,4,8,3,7,1,2,5]=>[3,5,1,6,2,8,7,4]=>0101011=>[1,1,1,1,1,2]
[6,5,8,3,7,1,2,4]=>[3,4,1,6,2,8,7,5]=>0101011=>[1,1,1,1,1,2]
[6,5,8,4,7,1,2,3]=>[3,4,1,5,2,8,7,6]=>0101011=>[1,1,1,1,1,2]
[7,3,8,2,5,1,4,6]=>[2,6,1,7,4,8,5,3]=>0101011=>[1,1,1,1,1,2]
[7,4,8,2,5,1,3,6]=>[2,5,1,7,4,8,6,3]=>0101011=>[1,1,1,1,1,2]
[7,5,8,2,4,1,3,6]=>[2,4,1,7,5,8,6,3]=>0101011=>[1,1,1,1,1,2]
[7,5,8,3,4,1,2,6]=>[2,4,1,6,5,8,7,3]=>0101011=>[1,1,1,1,1,2]
[7,4,8,2,6,1,3,5]=>[2,5,1,7,3,8,6,4]=>0101011=>[1,1,1,1,1,2]
[7,5,8,2,6,1,3,4]=>[2,4,1,7,3,8,6,5]=>0101011=>[1,1,1,1,1,2]
[7,5,8,3,6,1,2,4]=>[2,4,1,6,3,8,7,5]=>0101011=>[1,1,1,1,1,2]
[7,5,8,4,6,1,2,3]=>[2,4,1,5,3,8,7,6]=>0101011=>[1,1,1,1,1,2]
[7,6,8,2,4,1,3,5]=>[2,3,1,7,5,8,6,4]=>0101011=>[1,1,1,1,1,2]
[7,6,8,2,5,1,3,4]=>[2,3,1,7,4,8,6,5]=>0101011=>[1,1,1,1,1,2]
[8,3,6,2,5,1,4,7]=>[1,6,3,7,4,8,5,2]=>0101011=>[1,1,1,1,1,2]
[8,4,6,2,5,1,3,7]=>[1,5,3,7,4,8,6,2]=>0101011=>[1,1,1,1,1,2]
[8,3,7,2,5,1,4,6]=>[1,6,2,7,4,8,5,3]=>0101011=>[1,1,1,1,1,2]
[8,4,7,2,5,1,3,6]=>[1,5,2,7,4,8,6,3]=>0101011=>[1,1,1,1,1,2]
[8,4,7,3,5,1,2,6]=>[1,5,2,6,4,8,7,3]=>0101011=>[1,1,1,1,1,2]
[8,5,7,2,4,1,3,6]=>[1,4,2,7,5,8,6,3]=>0101011=>[1,1,1,1,1,2]
[8,5,7,3,4,1,2,6]=>[1,4,2,6,5,8,7,3]=>0101011=>[1,1,1,1,1,2]
[8,3,7,2,6,1,4,5]=>[1,6,2,7,3,8,5,4]=>0101011=>[1,1,1,1,1,2]
[8,4,7,2,6,1,3,5]=>[1,5,2,7,3,8,6,4]=>0101011=>[1,1,1,1,1,2]
[8,4,7,3,6,1,2,5]=>[1,5,2,6,3,8,7,4]=>0101011=>[1,1,1,1,1,2]
[8,5,7,2,6,1,3,4]=>[1,4,2,7,3,8,6,5]=>0101011=>[1,1,1,1,1,2]
[8,5,7,4,6,1,2,3]=>[1,4,2,5,3,8,7,6]=>0101011=>[1,1,1,1,1,2]
[8,6,7,2,4,1,3,5]=>[1,3,2,7,5,8,6,4]=>0101011=>[1,1,1,1,1,2]
[8,6,7,2,5,1,3,4]=>[1,3,2,7,4,8,6,5]=>0101011=>[1,1,1,1,1,2]
[8,6,7,3,5,1,2,4]=>[1,3,2,6,4,8,7,5]=>0101011=>[1,1,1,1,1,2]
[5,4,3,2,7,1,6,8]=>[4,5,6,7,2,8,3,1]=>0001011=>[3,1,1,2]
[6,4,3,2,7,1,5,8]=>[3,5,6,7,2,8,4,1]=>0001011=>[3,1,1,2]
[6,5,3,2,7,1,4,8]=>[3,4,6,7,2,8,5,1]=>0001011=>[3,1,1,2]
[6,5,4,2,7,1,3,8]=>[3,4,5,7,2,8,6,1]=>0001011=>[3,1,1,2]
[7,5,3,2,6,1,4,8]=>[2,4,6,7,3,8,5,1]=>0001011=>[3,1,1,2]
[7,5,4,2,6,1,3,8]=>[2,4,5,7,3,8,6,1]=>0001011=>[3,1,1,2]
[7,6,3,2,5,1,4,8]=>[2,3,6,7,4,8,5,1]=>0001011=>[3,1,1,2]
[7,6,4,2,5,1,3,8]=>[2,3,5,7,4,8,6,1]=>0001011=>[3,1,1,2]
[7,6,5,2,4,1,3,8]=>[2,3,4,7,5,8,6,1]=>0001011=>[3,1,1,2]
[5,4,3,2,8,1,6,7]=>[4,5,6,7,1,8,3,2]=>0001011=>[3,1,1,2]
[6,4,3,2,8,1,5,7]=>[3,5,6,7,1,8,4,2]=>0001011=>[3,1,1,2]
[6,5,3,2,8,1,4,7]=>[3,4,6,7,1,8,5,2]=>0001011=>[3,1,1,2]
[6,5,4,2,8,1,3,7]=>[3,4,5,7,1,8,6,2]=>0001011=>[3,1,1,2]
[6,5,4,3,8,1,2,7]=>[3,4,5,6,1,8,7,2]=>0001011=>[3,1,1,2]
[7,4,3,2,8,1,5,6]=>[2,5,6,7,1,8,4,3]=>0001011=>[3,1,1,2]
[7,5,3,2,8,1,4,6]=>[2,4,6,7,1,8,5,3]=>0001011=>[3,1,1,2]
[7,5,4,2,8,1,3,6]=>[2,4,5,7,1,8,6,3]=>0001011=>[3,1,1,2]
[7,5,4,3,8,1,2,6]=>[2,4,5,6,1,8,7,3]=>0001011=>[3,1,1,2]
[7,6,3,2,8,1,4,5]=>[2,3,6,7,1,8,5,4]=>0001011=>[3,1,1,2]
[7,6,5,2,8,1,3,4]=>[2,3,4,7,1,8,6,5]=>0001011=>[3,1,1,2]
[7,6,5,3,8,1,2,4]=>[2,3,4,6,1,8,7,5]=>0001011=>[3,1,1,2]
[8,5,3,2,6,1,4,7]=>[1,4,6,7,3,8,5,2]=>0001011=>[3,1,1,2]
[8,5,4,2,6,1,3,7]=>[1,4,5,7,3,8,6,2]=>0001011=>[3,1,1,2]
[8,6,3,2,5,1,4,7]=>[1,3,6,7,4,8,5,2]=>0001011=>[3,1,1,2]
[8,6,4,2,5,1,3,7]=>[1,3,5,7,4,8,6,2]=>0001011=>[3,1,1,2]
[8,6,5,2,4,1,3,7]=>[1,3,4,7,5,8,6,2]=>0001011=>[3,1,1,2]
[8,4,3,2,7,1,5,6]=>[1,5,6,7,2,8,4,3]=>0001011=>[3,1,1,2]
[8,5,3,2,7,1,4,6]=>[1,4,6,7,2,8,5,3]=>0001011=>[3,1,1,2]
[8,6,4,2,7,1,3,5]=>[1,3,5,7,2,8,6,4]=>0001011=>[3,1,1,2]
[8,7,3,2,5,1,4,6]=>[1,2,6,7,4,8,5,3]=>0001011=>[3,1,1,2]
[8,7,4,2,5,1,3,6]=>[1,2,5,7,4,8,6,3]=>0001011=>[3,1,1,2]
[8,7,5,2,4,1,3,6]=>[1,2,4,7,5,8,6,3]=>0001011=>[3,1,1,2]
[8,7,3,2,6,1,4,5]=>[1,2,6,7,3,8,5,4]=>0001011=>[3,1,1,2]
[8,7,4,2,6,1,3,5]=>[1,2,5,7,3,8,6,4]=>0001011=>[3,1,1,2]
[8,7,4,3,6,1,2,5]=>[1,2,5,6,3,8,7,4]=>0001011=>[3,1,1,2]
[8,7,5,2,6,1,3,4]=>[1,2,4,7,3,8,6,5]=>0001011=>[3,1,1,2]
[8,7,6,2,4,1,3,5]=>[1,2,3,7,5,8,6,4]=>0001011=>[3,1,1,2]
[8,7,6,2,5,1,3,4]=>[1,2,3,7,4,8,6,5]=>0001011=>[3,1,1,2]
[8,7,6,3,5,1,2,4]=>[1,2,3,6,4,8,7,5]=>0001011=>[3,1,1,2]
[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,7,2,6,1,3]=>[4,1,5,2,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,7,3,6,1,2]=>[4,1,5,2,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,7,2,5,1,4]=>[3,1,6,2,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,7,3,5,1,2]=>[3,1,5,2,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,5,7,3,4,1,2]=>[3,1,4,2,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,6,2,5,1,4]=>[2,1,6,3,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,6,2,5,1,3]=>[2,1,5,3,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,6,2,4,1,3]=>[2,1,4,3,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,4,3,8,2,7,1,6]=>[4,5,6,1,7,2,8,3]=>0010101=>[2,1,1,1,1,1]
[6,4,3,8,2,7,1,5]=>[3,5,6,1,7,2,8,4]=>0010101=>[2,1,1,1,1,1]
[6,5,3,8,2,7,1,4]=>[3,4,6,1,7,2,8,5]=>0010101=>[2,1,1,1,1,1]
[6,5,4,8,3,7,1,2]=>[3,4,5,1,6,2,8,7]=>0010101=>[2,1,1,1,1,1]
[7,5,3,8,2,6,1,4]=>[2,4,6,1,7,3,8,5]=>0010101=>[2,1,1,1,1,1]
[7,5,4,8,2,6,1,3]=>[2,4,5,1,7,3,8,6]=>0010101=>[2,1,1,1,1,1]
[7,5,4,8,3,6,1,2]=>[2,4,5,1,6,3,8,7]=>0010101=>[2,1,1,1,1,1]
[7,6,4,8,2,5,1,3]=>[2,3,5,1,7,4,8,6]=>0010101=>[2,1,1,1,1,1]
[7,6,4,8,3,5,1,2]=>[2,3,5,1,6,4,8,7]=>0010101=>[2,1,1,1,1,1]
[7,6,5,8,2,4,1,3]=>[2,3,4,1,7,5,8,6]=>0010101=>[2,1,1,1,1,1]
[8,5,3,7,2,6,1,4]=>[1,4,6,2,7,3,8,5]=>0010101=>[2,1,1,1,1,1]
[8,5,4,7,2,6,1,3]=>[1,4,5,2,7,3,8,6]=>0010101=>[2,1,1,1,1,1]
[8,5,4,7,3,6,1,2]=>[1,4,5,2,6,3,8,7]=>0010101=>[2,1,1,1,1,1]
[8,6,3,7,2,5,1,4]=>[1,3,6,2,7,4,8,5]=>0010101=>[2,1,1,1,1,1]
[8,6,4,7,2,5,1,3]=>[1,3,5,2,7,4,8,6]=>0010101=>[2,1,1,1,1,1]
[8,6,5,7,2,4,1,3]=>[1,3,4,2,7,5,8,6]=>0010101=>[2,1,1,1,1,1]
[8,7,3,6,2,5,1,4]=>[1,2,6,3,7,4,8,5]=>0010101=>[2,1,1,1,1,1]
[8,7,4,6,2,5,1,3]=>[1,2,5,3,7,4,8,6]=>0010101=>[2,1,1,1,1,1]
[8,7,4,6,3,5,1,2]=>[1,2,5,3,6,4,8,7]=>0010101=>[2,1,1,1,1,1]
[8,7,5,6,2,4,1,3]=>[1,2,4,3,7,5,8,6]=>0010101=>[2,1,1,1,1,1]
[6,5,4,3,2,8,1,7]=>[3,4,5,6,7,1,8,2]=>0000101=>[4,1,1,1]
[7,6,4,3,2,8,1,5]=>[2,3,5,6,7,1,8,4]=>0000101=>[4,1,1,1]
[7,6,5,4,2,8,1,3]=>[2,3,4,5,7,1,8,6]=>0000101=>[4,1,1,1]
[8,5,4,3,2,7,1,6]=>[1,4,5,6,7,2,8,3]=>0000101=>[4,1,1,1]
[8,6,4,3,2,7,1,5]=>[1,3,5,6,7,2,8,4]=>0000101=>[4,1,1,1]
[8,6,5,3,2,7,1,4]=>[1,3,4,6,7,2,8,5]=>0000101=>[4,1,1,1]
[8,6,5,4,2,7,1,3]=>[1,3,4,5,7,2,8,6]=>0000101=>[4,1,1,1]
[8,7,4,3,2,6,1,5]=>[1,2,5,6,7,3,8,4]=>0000101=>[4,1,1,1]
[8,7,5,3,2,6,1,4]=>[1,2,4,6,7,3,8,5]=>0000101=>[4,1,1,1]
[8,7,5,4,2,6,1,3]=>[1,2,4,5,7,3,8,6]=>0000101=>[4,1,1,1]
[8,7,6,3,2,5,1,4]=>[1,2,3,6,7,4,8,5]=>0000101=>[4,1,1,1]
[8,7,6,4,2,5,1,3]=>[1,2,3,5,7,4,8,6]=>0000101=>[4,1,1,1]
[8,7,6,5,2,4,1,3]=>[1,2,3,4,7,5,8,6]=>0000101=>[4,1,1,1]
[8,1,2,3,4,7,5,6]=>[1,8,7,6,5,2,4,3]=>0111101=>[1,4,1,1]
[8,1,2,3,7,4,5,6]=>[1,8,7,6,2,5,4,3]=>0111011=>[1,3,1,2]
[7,1,2,3,6,4,8,5]=>[2,8,7,6,3,5,1,4]=>0111010=>[1,3,1,1,1]
[5,1,2,3,8,7,4,6]=>[4,8,7,6,1,2,5,3]=>0111001=>[1,3,2,1]
[8,1,2,3,6,7,4,5]=>[1,8,7,6,3,2,5,4]=>0111101=>[1,4,1,1]
[4,1,2,8,3,7,5,6]=>[5,8,7,1,6,2,4,3]=>0110101=>[1,2,1,1,1,1]
[8,1,2,5,3,4,6,7]=>[1,8,7,4,6,5,3,2]=>0110111=>[1,2,1,3]
[8,1,2,6,3,4,5,7]=>[1,8,7,3,6,5,4,2]=>0110111=>[1,2,1,3]
[7,1,2,6,3,4,8,5]=>[2,8,7,3,6,5,1,4]=>0110110=>[1,2,1,2,1]
[8,1,2,6,3,7,4,5]=>[1,8,7,3,6,2,5,4]=>0110101=>[1,2,1,1,1,1]
[4,1,2,8,6,3,5,7]=>[5,8,7,1,3,6,4,2]=>0110011=>[1,2,2,2]
[4,1,2,8,7,3,5,6]=>[5,8,7,1,2,6,4,3]=>0110011=>[1,2,2,2]
[4,1,2,7,6,3,8,5]=>[5,8,7,2,3,6,1,4]=>0110010=>[1,2,2,1,1]
[8,1,2,5,6,3,4,7]=>[1,8,7,4,3,6,5,2]=>0111011=>[1,3,1,2]
[8,1,2,5,7,3,4,6]=>[1,8,7,4,2,6,5,3]=>0111011=>[1,3,1,2]
[8,1,2,7,6,3,4,5]=>[1,8,7,2,3,6,5,4]=>0110011=>[1,2,2,2]
[7,1,2,5,6,3,8,4]=>[2,8,7,4,3,6,1,5]=>0111010=>[1,3,1,1,1]
[4,1,2,5,8,7,3,6]=>[5,8,7,4,1,2,6,3]=>0111001=>[1,3,2,1]
[8,1,2,5,6,7,3,4]=>[1,8,7,4,3,2,6,5]=>0111101=>[1,4,1,1]
[3,1,8,2,4,7,5,6]=>[6,8,1,7,5,2,4,3]=>0101101=>[1,1,1,2,1,1]
[3,1,8,2,6,4,5,7]=>[6,8,1,7,3,5,4,2]=>0101011=>[1,1,1,1,1,2]
[3,1,8,2,7,4,5,6]=>[6,8,1,7,2,5,4,3]=>0101011=>[1,1,1,1,1,2]
[3,1,7,2,6,4,8,5]=>[6,8,2,7,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,2,6,7,4,5]=>[6,8,1,7,3,2,5,4]=>0101101=>[1,1,1,2,1,1]
[7,1,4,2,3,5,8,6]=>[2,8,5,7,6,4,1,3]=>0101110=>[1,1,1,3,1]
[8,1,4,2,3,7,5,6]=>[1,8,5,7,6,2,4,3]=>0101101=>[1,1,1,2,1,1]
[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]=>0101111=>[1,1,1,4]
[8,1,7,2,3,4,5,6]=>[1,8,2,7,6,5,4,3]=>0101111=>[1,1,1,4]
[6,1,5,2,3,8,4,7]=>[3,8,4,7,6,1,5,2]=>0101101=>[1,1,1,2,1,1]
[8,1,5,2,3,7,4,6]=>[1,8,4,7,6,2,5,3]=>0101101=>[1,1,1,2,1,1]
[6,1,8,2,3,7,4,5]=>[3,8,1,7,6,2,5,4]=>0101101=>[1,1,1,2,1,1]
[5,1,4,2,8,3,6,7]=>[4,8,5,7,1,6,3,2]=>0101011=>[1,1,1,1,1,2]
[5,1,4,2,7,3,8,6]=>[4,8,5,7,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,2,6,3,5,7]=>[1,8,5,7,3,6,4,2]=>0101011=>[1,1,1,1,1,2]
[7,1,4,2,6,3,8,5]=>[2,8,5,7,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,2,6,3,4,7]=>[1,8,4,7,3,6,5,2]=>0101011=>[1,1,1,1,1,2]
[8,1,5,2,7,3,4,6]=>[1,8,4,7,2,6,5,3]=>0101011=>[1,1,1,1,1,2]
[7,1,5,2,6,3,8,4]=>[2,8,4,7,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,1,4,2,6,8,3,7]=>[4,8,5,7,3,1,6,2]=>0101101=>[1,1,1,2,1,1]
[5,1,4,2,8,7,3,6]=>[4,8,5,7,1,2,6,3]=>0101001=>[1,1,1,1,2,1]
[8,1,5,2,6,7,3,4]=>[1,8,4,7,3,2,6,5]=>0101101=>[1,1,1,2,1,1]
[5,1,4,2,6,7,8,3]=>[4,8,5,7,3,2,1,6]=>0101110=>[1,1,1,3,1]
[3,1,4,8,2,7,5,6]=>[6,8,5,1,7,2,4,3]=>0110101=>[1,2,1,1,1,1]
[3,1,7,5,2,4,8,6]=>[6,8,2,4,7,5,1,3]=>0100110=>[1,1,2,2,1]
[3,1,8,6,2,4,5,7]=>[6,8,1,3,7,5,4,2]=>0100111=>[1,1,2,3]
[3,1,7,6,2,4,8,5]=>[6,8,2,3,7,5,1,4]=>0100110=>[1,1,2,2,1]
[3,1,6,5,2,8,4,7]=>[6,8,3,4,7,1,5,2]=>0100101=>[1,1,2,1,1,1]
[3,1,8,5,2,7,4,6]=>[6,8,1,4,7,2,5,3]=>0100101=>[1,1,2,1,1,1]
[3,1,8,6,2,7,4,5]=>[6,8,1,3,7,2,5,4]=>0100101=>[1,1,2,1,1,1]
[8,1,4,5,2,3,6,7]=>[1,8,5,4,7,6,3,2]=>0110111=>[1,2,1,3]
[7,1,4,5,2,3,8,6]=>[2,8,5,4,7,6,1,3]=>0110110=>[1,2,1,2,1]
[7,1,4,8,2,3,5,6]=>[2,8,5,1,7,6,4,3]=>0110111=>[1,2,1,3]
[7,1,8,5,2,3,4,6]=>[2,8,1,4,7,6,5,3]=>0100111=>[1,1,2,3]
[7,1,8,6,2,3,4,5]=>[2,8,1,3,7,6,5,4]=>0100111=>[1,1,2,3]
[7,1,6,5,2,3,8,4]=>[2,8,3,4,7,6,1,5]=>0100110=>[1,1,2,2,1]
[8,1,4,5,2,7,3,6]=>[1,8,5,4,7,2,6,3]=>0110101=>[1,2,1,1,1,1]
[8,1,4,6,2,7,3,5]=>[1,8,5,3,7,2,6,4]=>0110101=>[1,2,1,1,1,1]
[8,1,6,5,2,7,3,4]=>[1,8,3,4,7,2,6,5]=>0100101=>[1,1,2,1,1,1]
[6,1,4,5,2,7,8,3]=>[3,8,5,4,7,2,1,6]=>0110110=>[1,2,1,2,1]
[3,1,4,8,7,2,5,6]=>[6,8,5,1,2,7,4,3]=>0110011=>[1,2,2,2]
[3,1,8,5,6,2,4,7]=>[6,8,1,4,3,7,5,2]=>0101011=>[1,1,1,1,1,2]
[3,1,8,5,7,2,4,6]=>[6,8,1,4,2,7,5,3]=>0101011=>[1,1,1,1,1,2]
[3,1,7,5,6,2,8,4]=>[6,8,2,4,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,5,6,2,3,7]=>[1,8,5,4,3,7,6,2]=>0111011=>[1,3,1,2]
[8,1,4,5,7,2,3,6]=>[1,8,5,4,2,7,6,3]=>0111011=>[1,3,1,2]
[8,1,4,7,6,2,3,5]=>[1,8,5,2,3,7,6,4]=>0110011=>[1,2,2,2]
[8,1,7,5,6,2,3,4]=>[1,8,2,4,3,7,6,5]=>0101011=>[1,1,1,1,1,2]
[7,1,4,5,6,2,8,3]=>[2,8,5,4,3,7,1,6]=>0111010=>[1,3,1,1,1]
[3,1,4,5,8,7,2,6]=>[6,8,5,4,1,2,7,3]=>0111001=>[1,3,2,1]
[3,1,4,8,6,7,2,5]=>[6,8,5,1,3,2,7,4]=>0110101=>[1,2,1,1,1,1]
[3,1,8,5,6,7,2,4]=>[6,8,1,4,3,2,7,5]=>0101101=>[1,1,1,2,1,1]
[8,1,4,5,6,7,2,3]=>[1,8,5,4,3,2,7,6]=>0111101=>[1,4,1,1]
[2,8,1,3,4,7,5,6]=>[7,1,8,6,5,2,4,3]=>1011101=>[1,1,3,1,1]
[2,8,1,3,6,4,5,7]=>[7,1,8,6,3,5,4,2]=>1011011=>[1,1,2,1,2]
[2,8,1,3,7,4,5,6]=>[7,1,8,6,2,5,4,3]=>1011011=>[1,1,2,1,2]
[2,7,1,3,6,4,8,5]=>[7,2,8,6,3,5,1,4]=>1011010=>[1,1,2,1,1,1]
[2,5,1,3,8,7,4,6]=>[7,4,8,6,1,2,5,3]=>1011001=>[1,1,2,2,1]
[2,8,1,5,3,4,6,7]=>[7,1,8,4,6,5,3,2]=>1010111=>[1,1,1,1,3]
[2,7,1,5,3,4,8,6]=>[7,2,8,4,6,5,1,3]=>1010110=>[1,1,1,1,2,1]
[2,8,1,6,3,4,5,7]=>[7,1,8,3,6,5,4,2]=>1010111=>[1,1,1,1,3]
[2,7,1,6,3,4,8,5]=>[7,2,8,3,6,5,1,4]=>1010110=>[1,1,1,1,2,1]
[2,6,1,5,3,8,4,7]=>[7,3,8,4,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,1,6,3,7,4,5]=>[7,1,8,3,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,5,3,7,8,4]=>[7,3,8,4,6,2,1,5]=>1010110=>[1,1,1,1,2,1]
[2,4,1,8,6,3,5,7]=>[7,5,8,1,3,6,4,2]=>1010011=>[1,1,1,2,2]
[2,8,1,5,6,3,4,7]=>[7,1,8,4,3,6,5,2]=>1011011=>[1,1,2,1,2]
[2,8,1,5,7,3,4,6]=>[7,1,8,4,2,6,5,3]=>1011011=>[1,1,2,1,2]
[2,8,1,7,6,3,4,5]=>[7,1,8,2,3,6,5,4]=>1010011=>[1,1,1,2,2]
[2,7,1,5,6,3,8,4]=>[7,2,8,4,3,6,1,5]=>1011010=>[1,1,2,1,1,1]
[2,4,1,5,8,7,3,6]=>[7,5,8,4,1,2,6,3]=>1011001=>[1,1,2,2,1]
[2,8,1,5,6,7,3,4]=>[7,1,8,4,3,2,6,5]=>1011101=>[1,1,3,1,1]
[7,3,1,2,4,5,8,6]=>[2,6,8,7,5,4,1,3]=>0011110=>[2,4,1]
[8,3,1,2,4,7,5,6]=>[1,6,8,7,5,2,4,3]=>0011101=>[2,3,1,1]
[6,3,1,2,4,7,8,5]=>[3,6,8,7,5,2,1,4]=>0011110=>[2,4,1]
[8,3,1,2,6,4,5,7]=>[1,6,8,7,3,5,4,2]=>0011011=>[2,2,1,2]
[8,3,1,2,7,4,5,6]=>[1,6,8,7,2,5,4,3]=>0011011=>[2,2,1,2]
[7,3,1,2,6,4,8,5]=>[2,6,8,7,3,5,1,4]=>0011010=>[2,2,1,1,1]
[5,3,1,2,6,8,4,7]=>[4,6,8,7,3,1,5,2]=>0011101=>[2,3,1,1]
[5,3,1,2,6,7,8,4]=>[4,6,8,7,3,2,1,5]=>0011110=>[2,4,1]
[8,4,1,2,3,7,5,6]=>[1,5,8,7,6,2,4,3]=>0011101=>[2,3,1,1]
[7,6,1,2,3,4,8,5]=>[2,3,8,7,6,5,1,4]=>0011110=>[2,4,1]
[5,8,1,2,3,7,4,6]=>[4,1,8,7,6,2,5,3]=>1011101=>[1,1,3,1,1]
[8,6,1,2,3,7,4,5]=>[1,3,8,7,6,2,5,4]=>0011101=>[2,3,1,1]
[5,4,1,2,8,3,6,7]=>[4,5,8,7,1,6,3,2]=>0011011=>[2,2,1,2]
[5,4,1,2,7,3,8,6]=>[4,5,8,7,2,6,1,3]=>0011010=>[2,2,1,1,1]
[8,4,1,2,7,3,5,6]=>[1,5,8,7,2,6,4,3]=>0011011=>[2,2,1,2]
[7,4,1,2,6,3,8,5]=>[2,5,8,7,3,6,1,4]=>0011010=>[2,2,1,1,1]
[5,8,1,2,6,3,4,7]=>[4,1,8,7,3,6,5,2]=>1011011=>[1,1,2,1,2]
[5,8,1,2,7,3,4,6]=>[4,1,8,7,2,6,5,3]=>1011011=>[1,1,2,1,2]
[8,7,1,2,6,3,4,5]=>[1,2,8,7,3,6,5,4]=>0011011=>[2,2,1,2]
[5,7,1,2,6,3,8,4]=>[4,2,8,7,3,6,1,5]=>1011010=>[1,1,2,1,1,1]
[5,4,1,2,6,8,3,7]=>[4,5,8,7,3,1,6,2]=>0011101=>[2,3,1,1]
[5,4,1,2,8,7,3,6]=>[4,5,8,7,1,2,6,3]=>0011001=>[2,2,2,1]
[8,4,1,2,6,7,3,5]=>[1,5,8,7,3,2,6,4]=>0011101=>[2,3,1,1]
[5,8,1,2,6,7,3,4]=>[4,1,8,7,3,2,6,5]=>1011101=>[1,1,3,1,1]
[5,4,1,2,6,7,8,3]=>[4,5,8,7,3,2,1,6]=>0011110=>[2,4,1]
[4,3,1,8,2,5,6,7]=>[5,6,8,1,7,4,3,2]=>0010111=>[2,1,1,3]
[4,3,1,6,2,7,8,5]=>[5,6,8,3,7,2,1,4]=>0010110=>[2,1,1,2,1]
[8,3,1,5,2,4,6,7]=>[1,6,8,4,7,5,3,2]=>0010111=>[2,1,1,3]
[7,3,1,5,2,4,8,6]=>[2,6,8,4,7,5,1,3]=>0010110=>[2,1,1,2,1]
[7,3,1,8,2,4,5,6]=>[2,6,8,1,7,5,4,3]=>0010111=>[2,1,1,3]
[7,3,1,6,2,4,8,5]=>[2,6,8,3,7,5,1,4]=>0010110=>[2,1,1,2,1]
[6,3,1,5,2,8,4,7]=>[3,6,8,4,7,1,5,2]=>0010101=>[2,1,1,1,1,1]
[8,3,1,5,2,7,4,6]=>[1,6,8,4,7,2,5,3]=>0010101=>[2,1,1,1,1,1]
[8,3,1,6,2,7,4,5]=>[1,6,8,3,7,2,5,4]=>0010101=>[2,1,1,1,1,1]
[6,3,1,5,2,7,8,4]=>[3,6,8,4,7,2,1,5]=>0010110=>[2,1,1,2,1]
[8,4,1,5,2,3,6,7]=>[1,5,8,4,7,6,3,2]=>0010111=>[2,1,1,3]
[7,4,1,5,2,3,8,6]=>[2,5,8,4,7,6,1,3]=>0010110=>[2,1,1,2,1]
[8,4,1,6,2,3,5,7]=>[1,5,8,3,7,6,4,2]=>0010111=>[2,1,1,3]
[7,4,1,8,2,3,5,6]=>[2,5,8,1,7,6,4,3]=>0010111=>[2,1,1,3]
[7,4,1,6,2,3,8,5]=>[2,5,8,3,7,6,1,4]=>0010110=>[2,1,1,2,1]
[6,8,1,5,2,3,4,7]=>[3,1,8,4,7,6,5,2]=>1010111=>[1,1,1,1,3]
[8,7,1,5,2,3,4,6]=>[1,2,8,4,7,6,5,3]=>0010111=>[2,1,1,3]
[8,7,1,6,2,3,4,5]=>[1,2,8,3,7,6,5,4]=>0010111=>[2,1,1,3]
[6,7,1,5,2,3,8,4]=>[3,2,8,4,7,6,1,5]=>1010110=>[1,1,1,1,2,1]
[6,4,1,5,2,8,3,7]=>[3,5,8,4,7,1,6,2]=>0010101=>[2,1,1,1,1,1]
[8,4,1,5,2,7,3,6]=>[1,5,8,4,7,2,6,3]=>0010101=>[2,1,1,1,1,1]
[8,4,1,6,2,7,3,5]=>[1,5,8,3,7,2,6,4]=>0010101=>[2,1,1,1,1,1]
[6,8,1,5,2,7,3,4]=>[3,1,8,4,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,4,1,5,2,7,8,3]=>[3,5,8,4,7,2,1,6]=>0010110=>[2,1,1,2,1]
[4,3,1,5,8,2,6,7]=>[5,6,8,4,1,7,3,2]=>0011011=>[2,2,1,2]
[4,3,1,5,7,2,8,6]=>[5,6,8,4,2,7,1,3]=>0011010=>[2,2,1,1,1]
[4,3,1,8,7,2,5,6]=>[5,6,8,1,2,7,4,3]=>0010011=>[2,1,2,2]
[4,3,1,7,6,2,8,5]=>[5,6,8,2,3,7,1,4]=>0010010=>[2,1,2,1,1]
[8,3,1,5,6,2,4,7]=>[1,6,8,4,3,7,5,2]=>0011011=>[2,2,1,2]
[8,3,1,5,7,2,4,6]=>[1,6,8,4,2,7,5,3]=>0011011=>[2,2,1,2]
[8,3,1,7,6,2,4,5]=>[1,6,8,2,3,7,5,4]=>0010011=>[2,1,2,2]
[7,3,1,5,6,2,8,4]=>[2,6,8,4,3,7,1,5]=>0011010=>[2,2,1,1,1]
[8,4,1,5,6,2,3,7]=>[1,5,8,4,3,7,6,2]=>0011011=>[2,2,1,2]
[8,4,1,5,7,2,3,6]=>[1,5,8,4,2,7,6,3]=>0011011=>[2,2,1,2]
[8,4,1,7,6,2,3,5]=>[1,5,8,2,3,7,6,4]=>0010011=>[2,1,2,2]
[7,8,1,5,6,2,3,4]=>[2,1,8,4,3,7,6,5]=>1011011=>[1,1,2,1,2]
[7,4,1,5,6,2,8,3]=>[2,5,8,4,3,7,1,6]=>0011010=>[2,2,1,1,1]
[4,3,1,5,6,8,2,7]=>[5,6,8,4,3,1,7,2]=>0011101=>[2,3,1,1]
[4,3,1,5,8,7,2,6]=>[5,6,8,4,1,2,7,3]=>0011001=>[2,2,2,1]
[4,3,1,8,6,7,2,5]=>[5,6,8,1,3,2,7,4]=>0010101=>[2,1,1,1,1,1]
[8,3,1,5,6,7,2,4]=>[1,6,8,4,3,2,7,5]=>0011101=>[2,3,1,1]
[8,4,1,5,6,7,2,3]=>[1,5,8,4,3,2,7,6]=>0011101=>[2,3,1,1]
[4,3,1,5,6,7,8,2]=>[5,6,8,4,3,2,1,7]=>0011110=>[2,4,1]
[2,3,8,1,7,4,5,6]=>[7,6,1,8,2,5,4,3]=>1101011=>[2,1,1,1,2]
[2,3,7,1,6,4,8,5]=>[7,6,2,8,3,5,1,4]=>1101010=>[2,1,1,1,1,1]
[2,3,5,1,8,7,4,6]=>[7,6,4,8,1,2,5,3]=>1101001=>[2,1,1,2,1]
[2,3,8,1,6,7,4,5]=>[7,6,1,8,3,2,5,4]=>1101101=>[2,1,2,1,1]
[2,8,4,1,3,5,6,7]=>[7,1,5,8,6,4,3,2]=>1001111=>[1,2,4]
[2,7,4,1,3,5,8,6]=>[7,2,5,8,6,4,1,3]=>1001110=>[1,2,3,1]
[2,6,4,1,3,8,5,7]=>[7,3,5,8,6,1,4,2]=>1001101=>[1,2,2,1,1]
[2,6,4,1,3,7,8,5]=>[7,3,5,8,6,2,1,4]=>1001110=>[1,2,3,1]
[2,7,5,1,3,4,8,6]=>[7,2,4,8,6,5,1,3]=>1001110=>[1,2,3,1]
[2,8,7,1,3,4,5,6]=>[7,1,2,8,6,5,4,3]=>1001111=>[1,2,4]
[2,8,5,1,3,7,4,6]=>[7,1,4,8,6,2,5,3]=>1001101=>[1,2,2,1,1]
[2,6,8,1,3,7,4,5]=>[7,3,1,8,6,2,5,4]=>1101101=>[2,1,2,1,1]
[2,6,5,1,3,7,8,4]=>[7,3,4,8,6,2,1,5]=>1001110=>[1,2,3,1]
[2,5,4,1,8,3,6,7]=>[7,4,5,8,1,6,3,2]=>1001011=>[1,2,1,1,2]
[2,8,4,1,6,3,5,7]=>[7,1,5,8,3,6,4,2]=>1001011=>[1,2,1,1,2]
[2,8,4,1,7,3,5,6]=>[7,1,5,8,2,6,4,3]=>1001011=>[1,2,1,1,2]
[2,7,4,1,6,3,8,5]=>[7,2,5,8,3,6,1,4]=>1001010=>[1,2,1,1,1,1]
[2,8,5,1,6,3,4,7]=>[7,1,4,8,3,6,5,2]=>1001011=>[1,2,1,1,2]
[2,8,5,1,7,3,4,6]=>[7,1,4,8,2,6,5,3]=>1001011=>[1,2,1,1,2]
[2,7,8,1,6,3,4,5]=>[7,2,1,8,3,6,5,4]=>1101011=>[2,1,1,1,2]
[2,7,5,1,6,3,8,4]=>[7,2,4,8,3,6,1,5]=>1001010=>[1,2,1,1,1,1]
[2,5,4,1,8,7,3,6]=>[7,4,5,8,1,2,6,3]=>1001001=>[1,2,1,2,1]
[2,8,4,1,6,7,3,5]=>[7,1,5,8,3,2,6,4]=>1001101=>[1,2,2,1,1]
[2,8,5,1,6,7,3,4]=>[7,1,4,8,3,2,6,5]=>1001101=>[1,2,2,1,1]
[2,5,4,1,6,7,8,3]=>[7,4,5,8,3,2,1,6]=>1001110=>[1,2,3,1]
[6,3,4,1,2,8,5,7]=>[3,6,5,8,7,1,4,2]=>0101101=>[1,1,1,2,1,1]
[8,3,4,1,2,7,5,6]=>[1,6,5,8,7,2,4,3]=>0101101=>[1,1,1,2,1,1]
[6,3,4,1,2,7,8,5]=>[3,6,5,8,7,2,1,4]=>0101110=>[1,1,1,3,1]
[7,3,5,1,2,4,8,6]=>[2,6,4,8,7,5,1,3]=>0101110=>[1,1,1,3,1]
[6,3,7,1,2,4,8,5]=>[3,6,2,8,7,5,1,4]=>0101110=>[1,1,1,3,1]
[6,3,5,1,2,8,4,7]=>[3,6,4,8,7,1,5,2]=>0101101=>[1,1,1,2,1,1]
[8,3,5,1,2,7,4,6]=>[1,6,4,8,7,2,5,3]=>0101101=>[1,1,1,2,1,1]
[6,3,8,1,2,7,4,5]=>[3,6,1,8,7,2,5,4]=>0101101=>[1,1,1,2,1,1]
[6,3,5,1,2,7,8,4]=>[3,6,4,8,7,2,1,5]=>0101110=>[1,1,1,3,1]
[7,5,4,1,2,3,8,6]=>[2,4,5,8,7,6,1,3]=>0001110=>[3,3,1]
[6,7,4,1,2,3,8,5]=>[3,2,5,8,7,6,1,4]=>1001110=>[1,2,3,1]
[6,8,5,1,2,3,4,7]=>[3,1,4,8,7,6,5,2]=>1001111=>[1,2,4]
[6,7,5,1,2,3,8,4]=>[3,2,4,8,7,6,1,5]=>1001110=>[1,2,3,1]
[8,5,4,1,2,7,3,6]=>[1,4,5,8,7,2,6,3]=>0001101=>[3,2,1,1]
[6,8,4,1,2,7,3,5]=>[3,1,5,8,7,2,6,4]=>1001101=>[1,2,2,1,1]
[6,8,5,1,2,7,3,4]=>[3,1,4,8,7,2,6,5]=>1001101=>[1,2,2,1,1]
[6,5,4,1,2,7,8,3]=>[3,4,5,8,7,2,1,6]=>0001110=>[3,3,1]
[5,3,4,1,8,2,6,7]=>[4,6,5,8,1,7,3,2]=>0101011=>[1,1,1,1,1,2]
[8,3,4,1,6,2,5,7]=>[1,6,5,8,3,7,4,2]=>0101011=>[1,1,1,1,1,2]
[8,3,4,1,7,2,5,6]=>[1,6,5,8,2,7,4,3]=>0101011=>[1,1,1,1,1,2]
[7,3,4,1,6,2,8,5]=>[2,6,5,8,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,1,6,2,4,7]=>[1,6,4,8,3,7,5,2]=>0101011=>[1,1,1,1,1,2]
[8,3,5,1,7,2,4,6]=>[1,6,4,8,2,7,5,3]=>0101011=>[1,1,1,1,1,2]
[7,3,8,1,6,2,4,5]=>[2,6,1,8,3,7,5,4]=>0101011=>[1,1,1,1,1,2]
[7,3,5,1,6,2,8,4]=>[2,6,4,8,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[8,5,4,1,6,2,3,7]=>[1,4,5,8,3,7,6,2]=>0001011=>[3,1,1,2]
[8,5,4,1,7,2,3,6]=>[1,4,5,8,2,7,6,3]=>0001011=>[3,1,1,2]
[7,8,4,1,6,2,3,5]=>[2,1,5,8,3,7,6,4]=>1001011=>[1,2,1,1,2]
[7,8,5,1,6,2,3,4]=>[2,1,4,8,3,7,6,5]=>1001011=>[1,2,1,1,2]
[7,5,4,1,6,2,8,3]=>[2,4,5,8,3,7,1,6]=>0001010=>[3,1,1,1,1]
[5,3,4,1,6,8,2,7]=>[4,6,5,8,3,1,7,2]=>0101101=>[1,1,1,2,1,1]
[5,3,4,1,8,7,2,6]=>[4,6,5,8,1,2,7,3]=>0101001=>[1,1,1,1,2,1]
[8,3,4,1,6,7,2,5]=>[1,6,5,8,3,2,7,4]=>0101101=>[1,1,1,2,1,1]
[8,3,5,1,6,7,2,4]=>[1,6,4,8,3,2,7,5]=>0101101=>[1,1,1,2,1,1]
[8,5,4,1,6,7,2,3]=>[1,4,5,8,3,2,7,6]=>0001101=>[3,2,1,1]
[5,3,4,1,6,7,8,2]=>[4,6,5,8,3,2,1,7]=>0101110=>[1,1,1,3,1]
[2,3,4,8,1,7,5,6]=>[7,6,5,1,8,2,4,3]=>1110101=>[3,1,1,1,1]
[2,3,7,5,1,4,8,6]=>[7,6,2,4,8,5,1,3]=>1100110=>[2,2,2,1]
[2,3,8,6,1,4,5,7]=>[7,6,1,3,8,5,4,2]=>1100111=>[2,2,3]
[2,3,7,6,1,4,8,5]=>[7,6,2,3,8,5,1,4]=>1100110=>[2,2,2,1]
[2,3,8,5,1,7,4,6]=>[7,6,1,4,8,2,5,3]=>1100101=>[2,2,1,1,1]
[2,3,8,6,1,7,4,5]=>[7,6,1,3,8,2,5,4]=>1100101=>[2,2,1,1,1]
[2,3,6,5,1,7,8,4]=>[7,6,3,4,8,2,1,5]=>1100110=>[2,2,2,1]
[2,8,4,5,1,3,6,7]=>[7,1,5,4,8,6,3,2]=>1010111=>[1,1,1,1,3]
[2,7,4,5,1,3,8,6]=>[7,2,5,4,8,6,1,3]=>1010110=>[1,1,1,1,2,1]
[2,8,4,6,1,3,5,7]=>[7,1,5,3,8,6,4,2]=>1010111=>[1,1,1,1,3]
[2,7,4,8,1,3,5,6]=>[7,2,5,1,8,6,4,3]=>1010111=>[1,1,1,1,3]
[2,7,4,6,1,3,8,5]=>[7,2,5,3,8,6,1,4]=>1010110=>[1,1,1,1,2,1]
[2,8,6,5,1,3,4,7]=>[7,1,3,4,8,6,5,2]=>1000111=>[1,3,3]
[2,7,8,5,1,3,4,6]=>[7,2,1,4,8,6,5,3]=>1100111=>[2,2,3]
[2,7,8,6,1,3,4,5]=>[7,2,1,3,8,6,5,4]=>1100111=>[2,2,3]
[2,7,6,5,1,3,8,4]=>[7,2,3,4,8,6,1,5]=>1000110=>[1,3,2,1]
[2,6,4,5,1,8,3,7]=>[7,3,5,4,8,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,5,1,7,3,6]=>[7,1,5,4,8,2,6,3]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,6,1,7,3,5]=>[7,1,5,3,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,5,1,7,3,4]=>[7,1,3,4,8,2,6,5]=>1000101=>[1,3,1,1,1]
[2,6,4,5,1,7,8,3]=>[7,3,5,4,8,2,1,6]=>1010110=>[1,1,1,1,2,1]
[7,3,4,5,1,2,8,6]=>[2,6,5,4,8,7,1,3]=>0110110=>[1,2,1,2,1]
[7,3,4,6,1,2,8,5]=>[2,6,5,3,8,7,1,4]=>0110110=>[1,2,1,2,1]
[8,3,6,5,1,2,4,7]=>[1,6,3,4,8,7,5,2]=>0100111=>[1,1,2,3]
[7,3,8,5,1,2,4,6]=>[2,6,1,4,8,7,5,3]=>0100111=>[1,1,2,3]
[7,3,8,6,1,2,4,5]=>[2,6,1,3,8,7,5,4]=>0100111=>[1,1,2,3]
[7,3,6,5,1,2,8,4]=>[2,6,3,4,8,7,1,5]=>0100110=>[1,1,2,2,1]
[7,6,4,5,1,2,8,3]=>[2,3,5,4,8,7,1,6]=>0010110=>[2,1,1,2,1]
[6,3,4,5,1,8,2,7]=>[3,6,5,4,8,1,7,2]=>0110101=>[1,2,1,1,1,1]
[8,3,4,5,1,7,2,6]=>[1,6,5,4,8,2,7,3]=>0110101=>[1,2,1,1,1,1]
[8,3,4,6,1,7,2,5]=>[1,6,5,3,8,2,7,4]=>0110101=>[1,2,1,1,1,1]
[8,3,6,5,1,7,2,4]=>[1,6,3,4,8,2,7,5]=>0100101=>[1,1,2,1,1,1]
[8,6,4,5,1,7,2,3]=>[1,3,5,4,8,2,7,6]=>0010101=>[2,1,1,1,1,1]
[6,3,4,5,1,7,8,2]=>[3,6,5,4,8,2,1,7]=>0110110=>[1,2,1,2,1]
[2,3,4,8,6,1,5,7]=>[7,6,5,1,3,8,4,2]=>1110011=>[3,2,2]
[2,3,4,8,7,1,5,6]=>[7,6,5,1,2,8,4,3]=>1110011=>[3,2,2]
[2,3,4,7,6,1,8,5]=>[7,6,5,2,3,8,1,4]=>1110010=>[3,2,1,1]
[2,3,8,5,6,1,4,7]=>[7,6,1,4,3,8,5,2]=>1101011=>[2,1,1,1,2]
[2,3,8,5,7,1,4,6]=>[7,6,1,4,2,8,5,3]=>1101011=>[2,1,1,1,2]
[2,3,8,7,6,1,4,5]=>[7,6,1,2,3,8,5,4]=>1100011=>[2,3,2]
[2,3,7,5,6,1,8,4]=>[7,6,2,4,3,8,1,5]=>1101010=>[2,1,1,1,1,1]
[2,8,4,5,6,1,3,7]=>[7,1,5,4,3,8,6,2]=>1011011=>[1,1,2,1,2]
[2,8,4,5,7,1,3,6]=>[7,1,5,4,2,8,6,3]=>1011011=>[1,1,2,1,2]
[2,8,4,7,6,1,3,5]=>[7,1,5,2,3,8,6,4]=>1010011=>[1,1,1,2,2]
[2,8,7,5,6,1,3,4]=>[7,1,2,4,3,8,6,5]=>1001011=>[1,2,1,1,2]
[2,7,4,5,6,1,8,3]=>[7,2,5,4,3,8,1,6]=>1011010=>[1,1,2,1,1,1]
[8,3,4,5,7,1,2,6]=>[1,6,5,4,2,8,7,3]=>0111011=>[1,3,1,2]
[8,3,4,7,6,1,2,5]=>[1,6,5,2,3,8,7,4]=>0110011=>[1,2,2,2]
[8,3,7,5,6,1,2,4]=>[1,6,2,4,3,8,7,5]=>0101011=>[1,1,1,1,1,2]
[7,3,4,5,6,1,8,2]=>[2,6,5,4,3,8,1,7]=>0111010=>[1,3,1,1,1]
[2,3,4,5,8,7,1,6]=>[7,6,5,4,1,2,8,3]=>1111001=>[4,2,1]
[2,3,4,8,6,7,1,5]=>[7,6,5,1,3,2,8,4]=>1110101=>[3,1,1,1,1]
[2,3,8,5,6,7,1,4]=>[7,6,1,4,3,2,8,5]=>1101101=>[2,1,2,1,1]
[2,8,4,5,6,7,1,3]=>[7,1,5,4,3,2,8,6]=>1011101=>[1,1,3,1,1]
[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>01111111=>[1,7]
[8,1,2,3,4,5,6,9,7]=>[2,9,8,7,6,5,4,1,3]=>01111110=>[1,6,1]
[9,1,2,3,4,5,8,6,7]=>[1,9,8,7,6,5,2,4,3]=>01111101=>[1,5,1,1]
[7,1,2,3,4,5,8,9,6]=>[3,9,8,7,6,5,2,1,4]=>01111110=>[1,6,1]
[9,1,2,3,4,8,5,6,7]=>[1,9,8,7,6,2,5,4,3]=>01111011=>[1,4,1,2]
[6,1,2,3,4,9,8,5,7]=>[4,9,8,7,6,1,2,5,3]=>01111001=>[1,4,2,1]
[9,1,2,3,4,7,8,5,6]=>[1,9,8,7,6,3,2,5,4]=>01111101=>[1,5,1,1]
[6,1,2,3,4,7,8,9,5]=>[4,9,8,7,6,3,2,1,5]=>01111110=>[1,6,1]
[9,1,2,3,6,4,5,7,8]=>[1,9,8,7,4,6,5,3,2]=>01110111=>[1,3,1,3]
[8,1,2,3,9,4,5,6,7]=>[2,9,8,7,1,6,5,4,3]=>01110111=>[1,3,1,3]
[5,1,2,3,9,8,4,6,7]=>[5,9,8,7,1,2,6,4,3]=>01110011=>[1,3,2,2]
[9,1,2,3,6,8,4,5,7]=>[1,9,8,7,4,2,6,5,3]=>01111011=>[1,4,1,2]
[5,1,2,3,6,9,8,4,7]=>[5,9,8,7,4,1,2,6,3]=>01111001=>[1,4,2,1]
[5,1,2,3,6,7,8,9,4]=>[5,9,8,7,4,3,2,1,6]=>01111110=>[1,6,1]
[9,1,2,5,3,4,6,7,8]=>[1,9,8,5,7,6,4,3,2]=>01101111=>[1,2,1,4]
[9,1,2,8,3,4,5,6,7]=>[1,9,8,2,7,6,5,4,3]=>01101111=>[1,2,1,4]
[4,1,2,8,9,3,5,6,7]=>[6,9,8,2,1,7,5,4,3]=>01110111=>[1,3,1,3]
[8,1,2,5,9,3,4,6,7]=>[2,9,8,5,1,7,6,4,3]=>01110111=>[1,3,1,3]
[4,1,2,5,9,8,3,6,7]=>[6,9,8,5,1,2,7,4,3]=>01110011=>[1,3,2,2]
[4,1,2,5,6,7,8,9,3]=>[6,9,8,5,4,3,2,1,7]=>01111110=>[1,6,1]
[3,1,5,2,7,4,9,6,8]=>[7,9,5,8,3,6,1,4,2]=>01010101=>[1,1,1,1,1,1,1,1]
[9,1,8,2,3,4,5,6,7]=>[1,9,2,8,7,6,5,4,3]=>01011111=>[1,1,1,5]
[3,1,9,8,2,4,5,6,7]=>[7,9,1,2,8,6,5,4,3]=>01001111=>[1,1,2,4]
[9,1,4,8,2,3,5,6,7]=>[1,9,6,2,8,7,5,4,3]=>01101111=>[1,2,1,4]
[3,1,4,8,9,2,5,6,7]=>[7,9,6,2,1,8,5,4,3]=>01110111=>[1,3,1,3]
[7,1,4,5,6,2,8,9,3]=>[3,9,6,5,4,8,2,1,7]=>01110110=>[1,3,1,2,1]
[9,1,8,5,6,7,2,3,4]=>[1,9,2,5,4,3,8,7,6]=>01011011=>[1,1,1,2,1,2]
[8,1,4,5,6,7,2,9,3]=>[2,9,6,5,4,3,8,1,7]=>01111010=>[1,4,1,1,1]
[3,1,4,9,6,7,8,2,5]=>[7,9,6,1,4,3,2,8,5]=>01101101=>[1,2,1,2,1,1]
[3,1,9,5,6,7,8,2,4]=>[7,9,1,5,4,3,2,8,6]=>01011101=>[1,1,1,3,1,1]
[9,1,4,5,6,7,8,2,3]=>[1,9,6,5,4,3,2,8,7]=>01111101=>[1,5,1,1]
[3,1,4,5,6,7,8,9,2]=>[7,9,6,5,4,3,2,1,8]=>01111110=>[1,6,1]
[2,9,1,3,4,5,6,7,8]=>[8,1,9,7,6,5,4,3,2]=>10111111=>[1,1,6]
[2,4,1,6,3,8,5,9,7]=>[8,6,9,4,7,2,5,1,3]=>10101010=>[1,1,1,1,1,1,1,1]
[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]=>00111111=>[2,6]
[9,4,1,2,3,5,6,7,8]=>[1,6,9,8,7,5,4,3,2]=>00111111=>[2,6]
[5,9,1,2,3,4,6,7,8]=>[5,1,9,8,7,6,4,3,2]=>10111111=>[1,1,6]
[9,6,1,2,3,4,5,7,8]=>[1,4,9,8,7,6,5,3,2]=>00111111=>[2,6]
[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>00111111=>[2,6]
[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>10111111=>[1,1,6]
[8,7,1,2,3,4,5,9,6]=>[2,3,9,8,7,6,5,1,4]=>00111110=>[2,5,1]
[7,6,1,2,3,4,9,5,8]=>[3,4,9,8,7,6,1,5,2]=>00111101=>[2,4,1,1]
[9,7,1,2,3,4,8,5,6]=>[1,3,9,8,7,6,2,5,4]=>00111101=>[2,4,1,1]
[7,6,1,2,3,4,8,9,5]=>[3,4,9,8,7,6,2,1,5]=>00111110=>[2,5,1]
[5,6,1,2,3,9,4,7,8]=>[5,4,9,8,7,1,6,3,2]=>10111011=>[1,1,3,1,2]
[9,6,1,2,3,7,4,5,8]=>[1,4,9,8,7,3,6,5,2]=>00111011=>[2,3,1,2]
[5,6,1,2,3,7,9,4,8]=>[5,4,9,8,7,3,1,6,2]=>10111101=>[1,1,4,1,1]
[5,4,1,2,9,3,6,7,8]=>[5,6,9,8,1,7,4,3,2]=>00110111=>[2,2,1,3]
[5,9,1,2,6,3,4,7,8]=>[5,1,9,8,4,7,6,3,2]=>10110111=>[1,1,2,1,3]
[5,4,1,2,6,9,3,7,8]=>[5,6,9,8,4,1,7,3,2]=>00111011=>[2,3,1,2]
[4,3,1,9,2,5,6,7,8]=>[6,7,9,1,8,5,4,3,2]=>00101111=>[2,1,1,4]
[9,4,1,5,2,3,6,7,8]=>[1,6,9,5,8,7,4,3,2]=>00101111=>[2,1,1,4]
[4,3,1,5,9,2,6,7,8]=>[6,7,9,5,1,8,4,3,2]=>00110111=>[2,2,1,3]
[2,3,9,1,4,5,6,7,8]=>[8,7,1,9,6,5,4,3,2]=>11011111=>[2,1,5]
[2,9,8,1,3,4,5,6,7]=>[8,1,2,9,7,6,5,4,3]=>10011111=>[1,2,5]
[9,3,4,1,2,5,6,7,8]=>[1,7,6,9,8,5,4,3,2]=>01011111=>[1,1,1,5]
[9,3,8,1,2,4,5,6,7]=>[1,7,2,9,8,6,5,4,3]=>01011111=>[1,1,1,5]
[9,7,5,1,2,3,4,6,8]=>[1,3,5,9,8,7,6,4,2]=>00011111=>[3,5]
[9,7,8,1,2,3,4,5,6]=>[1,3,2,9,8,7,6,5,4]=>01011111=>[1,1,1,5]
[2,3,4,9,1,5,6,7,8]=>[8,7,6,1,9,5,4,3,2]=>11101111=>[3,1,4]
[2,3,9,8,1,4,5,6,7]=>[8,7,1,2,9,6,5,4,3]=>11001111=>[2,2,4]
[9,8,6,5,1,2,3,4,7]=>[1,2,4,5,9,8,7,6,3]=>00001111=>[4,4]
[6,3,4,5,1,7,9,2,8]=>[4,7,6,5,9,3,1,8,2]=>01101101=>[1,2,1,2,1,1]
[2,3,4,5,9,1,6,7,8]=>[8,7,6,5,1,9,4,3,2]=>11110111=>[4,1,3]
[9,7,4,5,6,1,2,3,8]=>[1,3,6,5,4,9,8,7,2]=>00110111=>[2,2,1,3]
[7,3,4,5,6,1,9,2,8]=>[3,7,6,5,4,9,1,8,2]=>01110101=>[1,3,1,1,1,1]
[2,3,4,5,6,9,1,7,8]=>[8,7,6,5,4,1,9,3,2]=>11111011=>[5,1,2]
[2,3,9,5,6,7,1,4,8]=>[8,7,1,5,4,3,9,6,2]=>11011011=>[2,1,2,1,2]
[2,9,4,5,6,7,1,3,8]=>[8,1,6,5,4,3,9,7,2]=>10111011=>[1,1,3,1,2]
[9,3,4,5,6,7,1,2,8]=>[1,7,6,5,4,3,9,8,2]=>01111011=>[1,4,1,2]
[2,3,4,5,6,7,9,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101=>[6,1,1]
[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]=>01111101=>[1,5,1,1]
[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]=>11111110=>[7,1]
[3,5,2,6,1,4,8,7]=>[6,4,7,3,8,5,1,2]=>1010110=>[1,1,1,1,2,1]
[3,5,2,6,4,1,8,7]=>[6,4,7,3,5,8,1,2]=>1010010=>[1,1,1,2,1,1]
[3,5,2,7,4,8,1,6]=>[6,4,7,2,5,1,8,3]=>1010101=>[1,1,1,1,1,1,1]
[3,5,2,7,4,8,6,1]=>[6,4,7,2,5,1,3,8]=>1010100=>[1,1,1,1,1,2]
[4,5,7,2,3,8,6,1]=>[5,4,2,7,6,1,3,8]=>1101100=>[2,1,2,2]
[4,5,7,2,3,8,1,6]=>[5,4,2,7,6,1,8,3]=>1101101=>[2,1,2,1,1]
[4,5,6,2,3,1,8,7]=>[5,4,3,7,6,8,1,2]=>1101010=>[2,1,1,1,1,1]
[4,5,6,2,1,3,8,7]=>[5,4,3,7,8,6,1,2]=>1100110=>[2,2,2,1]
[3,5,1,6,4,2,8,7]=>[6,4,8,3,5,7,1,2]=>1010010=>[1,1,1,2,1,1]
[4,5,6,1,3,2,8,7]=>[5,4,3,8,6,7,1,2]=>1101010=>[2,1,1,1,1,1]
[4,5,6,3,1,2,8,7]=>[5,4,3,6,8,7,1,2]=>1100110=>[2,2,2,1]
[4,5,7,3,2,8,1,6]=>[5,4,2,6,7,1,8,3]=>1100101=>[2,2,1,1,1]
[4,5,7,3,2,8,6,1]=>[5,4,2,6,7,1,3,8]=>1100100=>[2,2,1,2]
[4,6,7,3,8,2,5,1]=>[5,3,2,6,1,7,4,8]=>1101010=>[2,1,1,1,1,1]
[4,6,7,3,8,2,1,5]=>[5,3,2,6,1,7,8,4]=>1101001=>[2,1,1,2,1]
[4,6,7,3,8,1,2,5]=>[5,3,2,6,1,8,7,4]=>1101011=>[2,1,1,1,2]
[4,5,7,3,1,8,2,6]=>[5,4,2,6,8,1,7,3]=>1100101=>[2,2,1,1,1]
[4,5,7,1,3,8,2,6]=>[5,4,2,8,6,1,7,3]=>1101101=>[2,1,2,1,1]
[3,5,1,7,4,8,2,6]=>[6,4,8,2,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,5,7,4,8,3,6]=>[7,8,4,2,5,1,6,3]=>0110101=>[1,2,1,1,1,1]
[2,1,5,7,4,8,6,3]=>[7,8,4,2,5,1,3,6]=>0110100=>[1,2,1,1,2]
[3,5,1,7,4,8,6,2]=>[6,4,8,2,5,1,3,7]=>1010100=>[1,1,1,1,1,2]
[4,5,7,1,3,8,6,2]=>[5,4,2,8,6,1,3,7]=>1101100=>[2,1,2,2]
[4,5,7,3,1,8,6,2]=>[5,4,2,6,8,1,3,7]=>1100100=>[2,2,1,2]
[4,6,7,3,8,1,5,2]=>[5,3,2,6,1,8,4,7]=>1101010=>[2,1,1,1,1,1]
[4,6,7,3,8,5,1,2]=>[5,3,2,6,1,4,8,7]=>1101001=>[2,1,1,2,1]
[4,6,7,3,8,5,2,1]=>[5,3,2,6,1,4,7,8]=>1101000=>[2,1,1,3]
[5,6,7,8,3,1,4,2]=>[4,3,2,1,6,8,5,7]=>1110010=>[3,2,1,1]
[5,6,7,8,1,3,4,2]=>[4,3,2,1,8,6,5,7]=>1110110=>[3,1,2,1]
[4,6,7,1,8,3,5,2]=>[5,3,2,8,1,6,4,7]=>1101010=>[2,1,1,1,1,1]
[3,6,1,7,8,4,5,2]=>[6,3,8,2,1,5,4,7]=>1011010=>[1,1,2,1,1,1]
[2,1,6,7,8,4,5,3]=>[7,8,3,2,1,5,4,6]=>0111010=>[1,3,1,1,1]
[2,1,6,7,8,4,3,5]=>[7,8,3,2,1,5,6,4]=>0111001=>[1,3,2,1]
[3,6,1,7,8,4,2,5]=>[6,3,8,2,1,5,7,4]=>1011001=>[1,1,2,2,1]
[4,6,7,1,8,3,2,5]=>[5,3,2,8,1,6,7,4]=>1101001=>[2,1,1,2,1]
[5,6,7,8,1,3,2,4]=>[4,3,2,1,8,6,7,5]=>1110101=>[3,1,1,1,1]
[4,5,7,2,1,8,3,6]=>[5,4,2,7,8,1,6,3]=>1100101=>[2,2,1,1,1]
[4,6,7,2,8,1,3,5]=>[5,3,2,7,1,8,6,4]=>1101011=>[2,1,1,1,2]
[4,6,7,2,8,3,1,5]=>[5,3,2,7,1,6,8,4]=>1101001=>[2,1,1,2,1]
[4,6,7,2,8,3,5,1]=>[5,3,2,7,1,6,4,8]=>1101010=>[2,1,1,1,1,1]
[3,6,2,7,8,4,5,1]=>[6,3,7,2,1,5,4,8]=>1011010=>[1,1,2,1,1,1]
[3,6,2,7,8,4,1,5]=>[6,3,7,2,1,5,8,4]=>1011001=>[1,1,2,2,1]
[3,6,2,7,8,1,4,5]=>[6,3,7,2,1,8,5,4]=>1011011=>[1,1,2,1,2]
[3,5,2,7,1,8,4,6]=>[6,4,7,2,8,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[3,4,2,1,7,8,5,6]=>[6,5,7,8,2,1,4,3]=>1001101=>[1,2,2,1,1]
[3,4,1,2,7,8,6,5]=>[6,5,8,7,2,1,3,4]=>1011100=>[1,1,3,2]
[3,5,2,7,1,8,6,4]=>[6,4,7,2,8,1,3,5]=>1010100=>[1,1,1,1,1,2]
[3,6,2,7,8,1,5,4]=>[6,3,7,2,1,8,4,5]=>1011010=>[1,1,2,1,1,1]
[3,6,2,7,8,5,1,4]=>[6,3,7,2,1,4,8,5]=>1011001=>[1,1,2,2,1]
[3,6,2,7,8,5,4,1]=>[6,3,7,2,1,4,5,8]=>1011000=>[1,1,2,3]
[4,6,7,2,8,5,3,1]=>[5,3,2,7,1,4,6,8]=>1101000=>[2,1,1,3]
[4,6,7,2,8,5,1,3]=>[5,3,2,7,1,4,8,6]=>1101001=>[2,1,1,2,1]
[4,6,7,2,8,1,5,3]=>[5,3,2,7,1,8,4,6]=>1101010=>[2,1,1,1,1,1]
[4,5,7,2,1,8,6,3]=>[5,4,2,7,8,1,3,6]=>1100100=>[2,2,1,2]
[4,5,7,1,2,8,6,3]=>[5,4,2,8,7,1,3,6]=>1101100=>[2,1,2,2]
[3,5,1,7,2,8,6,4]=>[6,4,8,2,7,1,3,5]=>1010100=>[1,1,1,1,1,2]
[2,1,5,7,3,8,6,4]=>[7,8,4,2,6,1,3,5]=>0110100=>[1,2,1,1,2]
[2,1,6,7,8,3,5,4]=>[7,8,3,2,1,6,4,5]=>0111010=>[1,3,1,1,1]
[3,6,1,7,8,2,5,4]=>[6,3,8,2,1,7,4,5]=>1011010=>[1,1,2,1,1,1]
[4,6,7,1,8,2,5,3]=>[5,3,2,8,1,7,4,6]=>1101010=>[2,1,1,1,1,1]
[5,6,7,8,1,2,4,3]=>[4,3,2,1,8,7,5,6]=>1110110=>[3,1,2,1]
[5,6,7,8,2,1,4,3]=>[4,3,2,1,7,8,5,6]=>1110010=>[3,2,1,1]
[5,6,7,8,2,4,1,3]=>[4,3,2,1,7,5,8,6]=>1110101=>[3,1,1,1,1]
[5,6,7,8,2,4,3,1]=>[4,3,2,1,7,5,6,8]=>1110100=>[3,1,1,2]
[5,6,7,8,1,4,2,3]=>[4,3,2,1,8,5,7,6]=>1110101=>[3,1,1,1,1]
[4,6,7,1,8,5,2,3]=>[5,3,2,8,1,4,7,6]=>1101001=>[2,1,1,2,1]
[3,6,1,7,8,5,2,4]=>[6,3,8,2,1,4,7,5]=>1011001=>[1,1,2,2,1]
[2,1,6,7,8,5,3,4]=>[7,8,3,2,1,4,6,5]=>0111001=>[1,3,2,1]
[3,6,1,7,8,5,4,2]=>[6,3,8,2,1,4,5,7]=>1011000=>[1,1,2,3]
[4,6,7,1,8,5,3,2]=>[5,3,2,8,1,4,6,7]=>1101000=>[2,1,1,3]
[5,6,7,8,1,4,3,2]=>[4,3,2,1,8,5,6,7]=>1110100=>[3,1,1,2]
[5,6,7,8,4,1,3,2]=>[4,3,2,1,5,8,6,7]=>1110010=>[3,2,1,1]
[3,4,2,1,6,5,8,7,10,9]=>[8,7,9,10,5,6,3,4,1,2]=>100101010=>[1,2,1,1,1,1,1,1]
[3,5,2,6,4,1,8,7,10,9]=>[8,6,9,5,7,10,3,4,1,2]=>101001010=>[1,1,1,2,1,1,1,1]
[3,5,2,7,4,8,6,1,10,9]=>[8,6,9,4,7,3,5,10,1,2]=>101010010=>[1,1,1,1,1,2,1,1]
[3,5,2,7,4,9,6,10,8,1]=>[8,6,9,4,7,2,5,1,3,10]=>101010100=>[1,1,1,1,1,1,1,2]
[2,1,5,6,4,3,8,7,10,9]=>[9,10,6,5,7,8,3,4,1,2]=>011001010=>[1,2,2,1,1,1,1]
[4,5,6,3,2,1,8,7,10,9]=>[7,6,5,8,9,10,3,4,1,2]=>110001010=>[2,3,1,1,1,1]
[4,5,7,3,2,8,6,1,10,9]=>[7,6,4,8,9,3,5,10,1,2]=>110010010=>[2,2,1,2,1,1]
[4,5,7,3,2,9,6,10,8,1]=>[7,6,4,8,9,2,5,1,3,10]=>110010100=>[2,2,1,1,1,2]
[2,1,5,7,4,8,6,3,10,9]=>[9,10,6,4,7,3,5,8,1,2]=>011010010=>[1,2,1,1,2,1,1]
[4,6,7,3,8,5,2,1,10,9]=>[7,5,4,8,3,6,9,10,1,2]=>110100010=>[2,1,1,3,1,1]
[4,6,7,3,9,5,2,10,8,1]=>[7,5,4,8,2,6,9,1,3,10]=>110100100=>[2,1,1,2,1,2]
[2,1,5,7,4,9,6,10,8,3]=>[9,10,6,4,7,2,5,1,3,8]=>011010100=>[1,2,1,1,1,1,2]
[4,6,8,3,9,5,10,7,2,1]=>[7,5,3,8,2,6,1,4,9,10]=>110101000=>[2,1,1,1,1,3]
[2,1,4,3,7,8,6,5,10,9]=>[9,10,7,8,4,3,5,6,1,2]=>010110010=>[1,1,1,2,2,1,1]
[3,4,2,1,7,8,6,5,10,9]=>[8,7,9,10,4,3,5,6,1,2]=>100110010=>[1,2,2,2,1,1]
[3,6,2,7,8,5,4,1,10,9]=>[8,5,9,4,3,6,7,10,1,2]=>101100010=>[1,1,2,3,1,1]
[3,6,2,7,9,5,4,10,8,1]=>[8,5,9,4,2,6,7,1,3,10]=>101100100=>[1,1,2,2,1,2]
[2,1,6,7,8,5,4,3,10,9]=>[9,10,5,4,3,6,7,8,1,2]=>011100010=>[1,3,3,1,1]
[5,6,7,8,4,3,2,1,10,9]=>[6,5,4,3,7,8,9,10,1,2]=>111000010=>[3,4,1,1]
[5,6,7,9,4,3,2,10,8,1]=>[6,5,4,2,7,8,9,1,3,10]=>111000100=>[3,3,1,2]
[2,1,6,7,9,5,4,10,8,3]=>[9,10,5,4,2,6,7,1,3,8]=>011100100=>[1,3,2,1,2]
[5,6,8,9,4,3,10,7,2,1]=>[6,5,3,2,7,8,1,4,9,10]=>111001000=>[3,2,1,3]
[2,1,4,3,7,9,6,10,8,5]=>[9,10,7,8,4,2,5,1,3,6]=>010110100=>[1,1,1,2,1,1,2]
[3,4,2,1,7,9,6,10,8,5]=>[8,7,9,10,4,2,5,1,3,6]=>100110100=>[1,2,2,1,1,2]
[3,6,2,8,9,5,10,7,4,1]=>[8,5,9,3,2,6,1,4,7,10]=>101101000=>[1,1,2,1,1,3]
[2,1,6,8,9,5,10,7,4,3]=>[9,10,5,3,2,6,1,4,7,8]=>011101000=>[1,3,1,1,3]
[5,7,8,9,4,10,6,3,2,1]=>[6,4,3,2,7,1,5,8,9,10]=>111010000=>[3,1,1,4]
[6,7,8,9,10,2,3,4,5,1]=>[5,4,3,2,1,9,8,7,6,10]=>111101110=>[4,1,3,1]
[2,1,4,3,6,5,9,10,8,7]=>[9,10,7,8,5,6,2,1,3,4]=>010101100=>[1,1,1,1,1,2,2]
[3,4,2,1,6,5,9,10,8,7]=>[8,7,9,10,5,6,2,1,3,4]=>100101100=>[1,2,1,1,2,2]
[3,5,2,6,4,1,9,10,8,7]=>[8,6,9,5,7,10,2,1,3,4]=>101001100=>[1,1,1,2,2,2]
[3,5,2,8,4,9,10,7,6,1]=>[8,6,9,3,7,2,1,4,5,10]=>101011000=>[1,1,1,1,2,3]
[2,1,5,6,4,3,9,10,8,7]=>[9,10,6,5,7,8,2,1,3,4]=>011001100=>[1,2,2,2,2]
[4,5,6,3,2,1,9,10,8,7]=>[7,6,5,8,9,10,2,1,3,4]=>110001100=>[2,3,2,2]
[4,5,8,3,2,9,10,7,6,1]=>[7,6,3,8,9,2,1,4,5,10]=>110011000=>[2,2,2,3]
[2,1,5,8,4,9,10,7,6,3]=>[9,10,6,3,7,2,1,4,5,8]=>011011000=>[1,2,1,2,3]
[4,7,8,3,9,10,6,5,2,1]=>[7,4,3,8,2,1,5,6,9,10]=>110110000=>[2,1,2,4]
[2,1,4,3,8,9,10,7,6,5]=>[9,10,7,8,3,2,1,4,5,6]=>010111000=>[1,1,1,3,3]
[3,4,2,1,8,9,10,7,6,5]=>[8,7,9,10,3,2,1,4,5,6]=>100111000=>[1,2,3,3]
[3,7,2,8,9,10,6,5,4,1]=>[8,4,9,3,2,1,5,6,7,10]=>101110000=>[1,1,3,4]
[2,1,7,8,9,10,6,5,4,3]=>[9,10,4,3,2,1,5,6,7,8]=>011110000=>[1,4,4]
[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>111100000=>[4,5]
[6,5,8,7,3,4,1,2]=>[3,4,1,2,6,5,8,7]=>0100101=>[1,1,2,1,1,1]
[3,6,7,4,5,8,1,2]=>[6,3,2,5,4,1,8,7]=>1101101=>[2,1,2,1,1]
[2,6,7,4,5,1,8,3]=>[7,3,2,5,4,8,1,6]=>1101010=>[2,1,1,1,1,1]
[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>1101011=>[2,1,1,1,2]
[1,5,4,7,6,2,3,8]=>[8,4,5,2,3,7,6,1]=>1010011=>[1,1,1,2,2]
[2,5,4,7,6,1,8,3]=>[7,4,5,2,3,8,1,6]=>1010010=>[1,1,1,2,1,1]
[3,5,4,7,6,8,1,2]=>[6,4,5,2,3,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,7,8,6,1,2]=>[5,4,6,2,1,3,8,7]=>1011001=>[1,1,2,2,1]
[5,4,3,8,7,6,1,2]=>[4,5,6,1,2,3,8,7]=>0010001=>[2,1,3,1]
[6,4,8,3,7,5,1,2]=>[3,5,1,6,2,4,8,7]=>0101001=>[1,1,1,1,2,1]
[6,3,8,4,5,7,1,2]=>[3,6,1,5,4,2,8,7]=>0101101=>[1,1,1,2,1,1]
[5,3,4,8,6,7,1,2]=>[4,6,5,1,3,2,8,7]=>0110101=>[1,2,1,1,1,1]
[4,3,5,6,8,7,1,2]=>[5,6,4,3,1,2,8,7]=>0111001=>[1,3,2,1]
[3,2,5,6,1,8,7,4]=>[6,7,4,3,8,1,2,5]=>0110100=>[1,2,1,1,2]
[4,2,5,6,8,1,7,3]=>[5,7,4,3,1,8,2,6]=>0111010=>[1,3,1,1,1]
[5,2,4,8,6,1,7,3]=>[4,7,5,1,3,8,2,6]=>0110010=>[1,2,2,1,1]
[6,2,8,4,5,1,7,3]=>[3,7,1,5,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,8,2,4,5,1,6,3]=>[2,1,7,5,4,8,3,6]=>1011010=>[1,1,2,1,1,1]
[7,8,1,4,5,2,3,6]=>[2,1,8,5,4,7,6,3]=>1011011=>[1,1,2,1,2]
[6,1,8,4,5,2,3,7]=>[3,8,1,5,4,7,6,2]=>0101011=>[1,1,1,1,1,2]
[5,1,4,8,6,2,3,7]=>[4,8,5,1,3,7,6,2]=>0110011=>[1,2,2,2]
[4,1,3,2,8,6,5,7]=>[5,8,6,7,1,3,4,2]=>0101001=>[1,1,1,1,2,1]
[5,1,3,8,2,6,4,7]=>[4,8,6,1,7,3,5,2]=>0110101=>[1,2,1,1,1,1]
[6,1,8,3,2,5,4,7]=>[3,8,1,6,7,4,5,2]=>0100101=>[1,1,2,1,1,1]
[7,8,1,3,2,5,4,6]=>[2,1,8,6,7,4,5,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,3,1,5,6,4]=>[2,1,7,6,8,4,3,5]=>1010110=>[1,1,1,1,2,1]
[6,2,8,3,1,5,7,4]=>[3,7,1,6,8,4,2,5]=>0100110=>[1,1,2,2,1]
[5,2,3,8,1,6,7,4]=>[4,7,6,1,8,3,2,5]=>0110110=>[1,2,1,2,1]
[6,3,8,2,1,7,5,4]=>[3,6,1,7,8,2,4,5]=>0100100=>[1,1,2,1,2]
[7,8,3,2,1,6,5,4]=>[2,1,6,7,8,3,4,5]=>1000100=>[1,3,1,2]
[7,8,4,2,6,1,5,3]=>[2,1,5,7,3,8,4,6]=>1001010=>[1,2,1,1,1,1]
[5,4,2,8,7,1,6,3]=>[4,5,7,1,2,8,3,6]=>0010010=>[2,1,2,1,1]
[4,5,2,7,8,1,6,3]=>[5,4,7,2,1,8,3,6]=>1011010=>[1,1,2,1,1,1]
[2,5,3,7,1,6,8,4]=>[7,4,6,2,8,3,1,5]=>1010110=>[1,1,1,1,2,1]
[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>1100101=>[2,2,1,1,1]
[2,6,7,3,1,5,8,4]=>[7,3,2,6,8,4,1,5]=>1100110=>[2,2,2,1]
[3,6,7,2,1,8,5,4]=>[6,3,2,7,8,1,4,5]=>1100100=>[2,2,1,2]
[7,8,5,6,2,1,4,3]=>[2,1,4,3,7,8,5,6]=>1010010=>[1,1,1,2,1,1]
[6,5,8,7,1,2,3,4]=>[3,4,1,2,8,7,6,5]=>0100111=>[1,1,2,3]
[5,4,1,8,7,2,3,6]=>[4,5,8,1,2,7,6,3]=>0010011=>[2,1,2,2]
[6,4,8,1,7,2,3,5]=>[3,5,1,8,2,7,6,4]=>0101011=>[1,1,1,1,1,2]
[7,8,3,1,2,6,4,5]=>[2,1,6,8,7,3,5,4]=>1001101=>[1,2,2,1,1]
[5,3,1,8,2,7,4,6]=>[4,6,8,1,7,2,5,3]=>0010101=>[2,1,1,1,1,1]
[4,3,1,2,8,7,5,6]=>[5,6,8,7,1,2,4,3]=>0011001=>[2,2,2,1]
[4,2,1,3,8,5,7,6]=>[5,7,8,6,1,4,2,3]=>0011010=>[2,2,1,1,1]
[5,2,1,8,3,4,7,6]=>[4,7,8,1,6,5,2,3]=>0010110=>[2,1,1,2,1]
[6,2,8,1,3,4,7,5]=>[3,7,1,8,6,5,2,4]=>0101110=>[1,1,1,3,1]
[7,8,2,1,3,4,6,5]=>[2,1,7,8,6,5,3,4]=>1001110=>[1,2,3,1]
[4,3,1,2,6,5,8,7]=>[5,6,8,7,3,4,1,2]=>0011010=>[2,2,1,1,1]
[5,3,1,6,2,4,8,7]=>[4,6,8,3,7,5,1,2]=>0010110=>[2,1,1,2,1]
[6,3,1,5,2,4,8,7]=>[3,6,8,4,7,5,1,2]=>0010110=>[2,1,1,2,1]
[7,3,1,5,2,8,4,6]=>[2,6,8,4,7,1,5,3]=>0010101=>[2,1,1,1,1,1]
[8,4,5,1,2,7,3,6]=>[1,5,4,8,7,2,6,3]=>0101101=>[1,1,1,2,1,1]
[7,4,5,1,2,8,3,6]=>[2,5,4,8,7,1,6,3]=>0101101=>[1,1,1,2,1,1]
[6,4,5,1,2,3,8,7]=>[3,5,4,8,7,6,1,2]=>0101110=>[1,1,1,3,1]
[5,4,6,1,2,3,8,7]=>[4,5,3,8,7,6,1,2]=>0101110=>[1,1,1,3,1]
[2,1,6,5,3,4,8,7]=>[7,8,3,4,6,5,1,2]=>0100110=>[1,1,2,2,1]
[3,6,1,5,2,4,8,7]=>[6,3,8,4,7,5,1,2]=>1010110=>[1,1,1,1,2,1]
[4,6,5,1,2,3,8,7]=>[5,3,4,8,7,6,1,2]=>1001110=>[1,2,3,1]
[5,6,4,1,2,3,8,7]=>[4,3,5,8,7,6,1,2]=>1001110=>[1,2,3,1]
[6,5,4,1,2,3,8,7]=>[3,4,5,8,7,6,1,2]=>0001110=>[3,3,1]
[7,5,4,1,2,8,3,6]=>[2,4,5,8,7,1,6,3]=>0001101=>[3,2,1,1]
[8,6,4,1,7,2,3,5]=>[1,3,5,8,2,7,6,4]=>0001011=>[3,1,1,2]
[7,6,4,1,8,2,3,5]=>[2,3,5,8,1,7,6,4]=>0001011=>[3,1,1,2]
[6,7,4,1,8,2,3,5]=>[3,2,5,8,1,7,6,4]=>1001011=>[1,2,1,1,2]
[5,7,4,1,2,8,3,6]=>[4,2,5,8,7,1,6,3]=>1001101=>[1,2,2,1,1]
[4,7,5,1,2,8,3,6]=>[5,2,4,8,7,1,6,3]=>1001101=>[1,2,2,1,1]
[3,7,1,5,2,8,4,6]=>[6,2,8,4,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,7,5,3,8,4,6]=>[7,8,2,4,6,1,5,3]=>0100101=>[1,1,2,1,1,1]
[2,1,8,5,3,7,4,6]=>[7,8,1,4,6,2,5,3]=>0100101=>[1,1,2,1,1,1]
[3,8,1,5,2,7,4,6]=>[6,1,8,4,7,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[4,8,5,1,2,7,3,6]=>[5,1,4,8,7,2,6,3]=>1001101=>[1,2,2,1,1]
[5,8,4,1,2,7,3,6]=>[4,1,5,8,7,2,6,3]=>1001101=>[1,2,2,1,1]
[6,8,4,1,7,2,3,5]=>[3,1,5,8,2,7,6,4]=>1001011=>[1,2,1,1,2]
[8,7,4,1,6,2,3,5]=>[1,2,5,8,3,7,6,4]=>0001011=>[3,1,1,2]
[5,8,6,7,1,2,3,4]=>[4,1,3,2,8,7,6,5]=>1010111=>[1,1,1,1,3]
[4,8,6,1,7,2,3,5]=>[5,1,3,8,2,7,6,4]=>1001011=>[1,2,1,1,2]
[3,8,1,6,7,2,4,5]=>[6,1,8,3,2,7,5,4]=>1011011=>[1,1,2,1,2]
[2,1,8,6,7,3,4,5]=>[7,8,1,3,2,6,5,4]=>0101011=>[1,1,1,1,1,2]
[2,1,7,6,8,3,4,5]=>[7,8,2,3,1,6,5,4]=>0101011=>[1,1,1,1,1,2]
[3,7,1,6,8,2,4,5]=>[6,2,8,3,1,7,5,4]=>1011011=>[1,1,2,1,2]
[4,7,6,1,8,2,3,5]=>[5,2,3,8,1,7,6,4]=>1001011=>[1,2,1,1,2]
[5,7,6,8,1,2,3,4]=>[4,2,3,1,8,7,6,5]=>1010111=>[1,1,1,1,3]
[5,4,7,1,2,8,3,6]=>[4,5,2,8,7,1,6,3]=>0101101=>[1,1,1,2,1,1]
[6,4,7,1,8,2,3,5]=>[3,5,2,8,1,7,6,4]=>0101011=>[1,1,1,1,1,2]
[7,4,6,1,8,2,3,5]=>[2,5,3,8,1,7,6,4]=>0101011=>[1,1,1,1,1,2]
[8,4,6,1,7,2,3,5]=>[1,5,3,8,2,7,6,4]=>0101011=>[1,1,1,1,1,2]
[8,3,1,6,7,2,4,5]=>[1,6,8,3,2,7,5,4]=>0011011=>[2,2,1,2]
[7,3,1,6,8,2,4,5]=>[2,6,8,3,1,7,5,4]=>0011011=>[2,2,1,2]
[6,3,1,7,8,2,4,5]=>[3,6,8,2,1,7,5,4]=>0011011=>[2,2,1,2]
[5,3,1,7,2,8,4,6]=>[4,6,8,2,7,1,5,3]=>0010101=>[2,1,1,1,1,1]
[4,3,1,2,7,8,5,6]=>[5,6,8,7,2,1,4,3]=>0011101=>[2,3,1,1]
[2,1,4,3,8,7,5,6]=>[7,8,5,6,1,2,4,3]=>0101001=>[1,1,1,1,2,1]
[3,4,1,2,8,7,5,6]=>[6,5,8,7,1,2,4,3]=>1011001=>[1,1,2,2,1]
[6,3,1,8,7,2,4,5]=>[3,6,8,1,2,7,5,4]=>0010011=>[2,1,2,2]
[7,3,1,8,6,2,4,5]=>[2,6,8,1,3,7,5,4]=>0010011=>[2,1,2,2]
[8,4,7,1,6,2,3,5]=>[1,5,2,8,3,7,6,4]=>0101011=>[1,1,1,1,1,2]
[7,4,8,1,6,2,3,5]=>[2,5,1,8,3,7,6,4]=>0101011=>[1,1,1,1,1,2]
[5,4,8,1,2,7,3,6]=>[4,5,1,8,7,2,6,3]=>0101101=>[1,1,1,2,1,1]
[4,5,8,1,2,7,3,6]=>[5,4,1,8,7,2,6,3]=>1101101=>[2,1,2,1,1]
[3,5,1,8,2,7,4,6]=>[6,4,8,1,7,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,5,8,3,7,4,6]=>[7,8,4,1,6,2,5,3]=>0110101=>[1,2,1,1,1,1]
[2,1,6,8,7,3,4,5]=>[7,8,3,1,2,6,5,4]=>0110011=>[1,2,2,2]
[3,6,1,8,7,2,4,5]=>[6,3,8,1,2,7,5,4]=>1010011=>[1,1,1,2,2]
[4,6,8,1,7,2,3,5]=>[5,3,1,8,2,7,6,4]=>1101011=>[2,1,1,1,2]
[5,6,8,7,1,2,3,4]=>[4,3,1,2,8,7,6,5]=>1100111=>[2,2,3]
[7,5,8,6,1,2,3,4]=>[2,4,1,3,8,7,6,5]=>0100111=>[1,1,2,3]
[8,5,7,6,1,2,3,4]=>[1,4,2,3,8,7,6,5]=>0100111=>[1,1,2,3]
[5,7,8,6,1,2,3,4]=>[4,2,1,3,8,7,6,5]=>1100111=>[2,2,3]
[4,7,8,1,6,2,3,5]=>[5,2,1,8,3,7,6,4]=>1101011=>[2,1,1,1,2]
[3,7,1,8,6,2,4,5]=>[6,2,8,1,3,7,5,4]=>1010011=>[1,1,1,2,2]
[2,1,7,8,6,3,4,5]=>[7,8,2,1,3,6,5,4]=>0110011=>[1,2,2,2]
[2,1,8,7,6,3,4,5]=>[7,8,1,2,3,6,5,4]=>0100011=>[1,1,3,2]
[3,8,1,7,6,2,4,5]=>[6,1,8,2,3,7,5,4]=>1010011=>[1,1,1,2,2]
[4,8,7,1,6,2,3,5]=>[5,1,2,8,3,7,6,4]=>1001011=>[1,2,1,1,2]
[5,8,7,6,1,2,3,4]=>[4,1,2,3,8,7,6,5]=>1000111=>[1,3,3]
[6,8,7,5,1,2,3,4]=>[3,1,2,4,8,7,6,5]=>1000111=>[1,3,3]
[6,4,7,3,8,5,1,2]=>[3,5,2,6,1,4,8,7]=>0101001=>[1,1,1,1,2,1]
[6,4,7,3,5,8,1,2]=>[3,5,2,6,4,1,8,7]=>0101101=>[1,1,1,2,1,1]
[6,4,7,2,5,1,8,3]=>[3,5,2,7,4,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,4,2,7,6,1,3,8]=>[4,5,7,2,3,8,6,1]=>0010011=>[2,1,2,2]
[5,4,2,7,6,1,8,3]=>[4,5,7,2,3,8,1,6]=>0010010=>[2,1,2,1,1]
[5,4,3,7,6,8,1,2]=>[4,5,6,2,3,1,8,7]=>0010101=>[2,1,1,1,1,1]
[5,4,3,7,8,6,1,2]=>[4,5,6,2,1,3,8,7]=>0011001=>[2,2,2,1]
[6,4,8,3,5,7,1,2]=>[3,5,1,6,4,2,8,7]=>0101101=>[1,1,1,2,1,1]
[5,4,3,8,6,7,1,2]=>[4,5,6,1,3,2,8,7]=>0010101=>[2,1,1,1,1,1]
[5,4,3,6,8,7,1,2]=>[4,5,6,3,1,2,8,7]=>0011001=>[2,2,2,1]
[5,4,2,6,7,1,8,3]=>[4,5,7,3,2,8,1,6]=>0011010=>[2,2,1,1,1]
[5,4,2,6,7,1,3,8]=>[4,5,7,3,2,8,6,1]=>0011011=>[2,2,1,2]
[5,3,2,6,1,7,4,8]=>[4,6,7,3,8,2,5,1]=>0010101=>[2,1,1,1,1,1]
[5,3,2,6,1,7,8,4]=>[4,6,7,3,8,2,1,5]=>0010110=>[2,1,1,2,1]
[5,3,2,6,1,8,7,4]=>[4,6,7,3,8,1,2,5]=>0010100=>[2,1,1,1,2]
[5,4,2,6,8,1,7,3]=>[4,5,7,3,1,8,2,6]=>0011010=>[2,2,1,1,1]
[5,4,2,8,6,1,7,3]=>[4,5,7,1,3,8,2,6]=>0010010=>[2,1,2,1,1]
[6,4,8,2,5,1,7,3]=>[3,5,1,7,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,8,4,2,5,1,6,3]=>[2,1,5,7,4,8,3,6]=>1001010=>[1,2,1,1,1,1]
[7,8,4,2,5,1,3,6]=>[2,1,5,7,4,8,6,3]=>1001011=>[1,2,1,1,2]
[5,4,2,8,6,1,3,7]=>[4,5,7,1,3,8,6,2]=>0010011=>[2,1,2,2]
[5,3,2,6,1,8,4,7]=>[4,6,7,3,8,1,5,2]=>0010101=>[2,1,1,1,1,1]
[4,3,2,1,6,8,5,7]=>[5,6,7,8,3,1,4,2]=>0001101=>[3,2,1,1]
[4,3,2,1,8,6,5,7]=>[5,6,7,8,1,3,4,2]=>0001001=>[3,1,2,1]
[5,3,2,8,1,6,4,7]=>[4,6,7,1,8,3,5,2]=>0010101=>[2,1,1,1,1,1]
[6,3,8,2,1,5,4,7]=>[3,6,1,7,8,4,5,2]=>0100101=>[1,1,2,1,1,1]
[7,8,3,2,1,5,4,6]=>[2,1,6,7,8,4,5,3]=>1000101=>[1,3,1,1,1]
[7,8,3,2,1,5,6,4]=>[2,1,6,7,8,4,3,5]=>1000110=>[1,3,2,1]
[6,3,8,2,1,5,7,4]=>[3,6,1,7,8,4,2,5]=>0100110=>[1,1,2,2,1]
[5,3,2,8,1,6,7,4]=>[4,6,7,1,8,3,2,5]=>0010110=>[2,1,1,2,1]
[5,4,2,7,8,1,6,3]=>[4,5,7,2,1,8,3,6]=>0011010=>[2,2,1,1,1]
[5,3,2,7,1,8,6,4]=>[4,6,7,2,8,1,3,5]=>0010100=>[2,1,1,1,2]
[5,3,2,7,1,6,8,4]=>[4,6,7,2,8,3,1,5]=>0010110=>[2,1,1,2,1]
[5,3,2,7,1,6,4,8]=>[4,6,7,2,8,3,5,1]=>0010101=>[2,1,1,1,1,1]
[6,3,7,2,1,5,4,8]=>[3,6,2,7,8,4,5,1]=>0100101=>[1,1,2,1,1,1]
[6,3,7,2,1,5,8,4]=>[3,6,2,7,8,4,1,5]=>0100110=>[1,1,2,2,1]
[6,3,7,2,1,8,5,4]=>[3,6,2,7,8,1,4,5]=>0100100=>[1,1,2,1,2]
[6,4,7,2,8,1,5,3]=>[3,5,2,7,1,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,8,2,1,4,3]=>[3,4,2,1,7,8,5,6]=>0110010=>[1,2,2,1,1]
[6,5,8,7,2,1,3,4]=>[3,4,1,2,7,8,6,5]=>0100011=>[1,1,3,2]
[6,3,7,2,1,8,4,5]=>[3,6,2,7,8,1,5,4]=>0100101=>[1,1,2,1,1,1]
[6,3,7,2,1,4,8,5]=>[3,6,2,7,8,5,1,4]=>0100110=>[1,1,2,2,1]
[6,3,7,2,1,4,5,8]=>[3,6,2,7,8,5,4,1]=>0100111=>[1,1,2,3]
[5,3,2,7,1,4,8,6]=>[4,6,7,2,8,5,1,3]=>0010110=>[2,1,1,2,1]
[5,4,2,8,7,1,3,6]=>[4,5,7,1,2,8,6,3]=>0010011=>[2,1,2,2]
[7,8,4,2,6,1,3,5]=>[2,1,5,7,3,8,6,4]=>1001011=>[1,2,1,1,2]
[7,8,3,2,1,6,4,5]=>[2,1,6,7,8,3,5,4]=>1000101=>[1,3,1,1,1]
[6,3,8,2,1,7,4,5]=>[3,6,1,7,8,2,5,4]=>0100101=>[1,1,2,1,1,1]
[5,3,2,8,1,7,4,6]=>[4,6,7,1,8,2,5,3]=>0010101=>[2,1,1,1,1,1]
[4,3,2,1,8,7,5,6]=>[5,6,7,8,1,2,4,3]=>0001001=>[3,1,2,1]
[4,3,2,1,7,5,8,6]=>[5,6,7,8,2,4,1,3]=>0001010=>[3,1,1,1,1]
[4,3,2,1,7,5,6,8]=>[5,6,7,8,2,4,3,1]=>0001011=>[3,1,1,2]
[4,3,2,1,8,5,7,6]=>[5,6,7,8,1,4,2,3]=>0001010=>[3,1,1,1,1]
[5,3,2,8,1,4,7,6]=>[4,6,7,1,8,5,2,3]=>0010110=>[2,1,1,2,1]
[6,3,8,2,1,4,7,5]=>[3,6,1,7,8,5,2,4]=>0100110=>[1,1,2,2,1]
[7,8,3,2,1,4,6,5]=>[2,1,6,7,8,5,3,4]=>1000110=>[1,3,2,1]
[6,3,8,2,1,4,5,7]=>[3,6,1,7,8,5,4,2]=>0100111=>[1,1,2,3]
[4,3,2,1,8,5,6,7]=>[5,6,7,8,1,4,3,2]=>0001011=>[3,1,1,2]
[4,3,2,1,5,8,6,7]=>[5,6,7,8,4,1,3,2]=>0001101=>[3,2,1,1]
[7,8,5,6,1,2,4,3]=>[2,1,4,3,8,7,5,6]=>1010110=>[1,1,1,1,2,1]
[7,8,4,1,6,2,5,3]=>[2,1,5,8,3,7,4,6]=>1001010=>[1,2,1,1,1,1]
[7,8,1,4,6,2,5,3]=>[2,1,8,5,3,7,4,6]=>1011010=>[1,1,2,1,1,1]
[6,1,8,4,7,2,5,3]=>[3,8,1,5,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[1,6,8,4,7,2,5,3]=>[8,3,1,5,2,7,4,6]=>1101010=>[2,1,1,1,1,1]
[1,6,8,3,2,7,5,4]=>[8,3,1,6,7,2,4,5]=>1100100=>[2,2,1,2]
[6,1,8,3,2,7,5,4]=>[3,8,1,6,7,2,4,5]=>0100100=>[1,1,2,1,2]
[7,8,1,3,2,6,5,4]=>[2,1,8,6,7,3,4,5]=>1010100=>[1,1,1,1,1,2]
[7,8,3,1,2,6,5,4]=>[2,1,6,8,7,3,4,5]=>1001100=>[1,2,2,2]
[7,8,3,4,6,5,1,2]=>[2,1,6,5,3,4,8,7]=>1011001=>[1,1,2,2,1]
[7,8,2,4,6,1,5,3]=>[2,1,7,5,3,8,4,6]=>1011010=>[1,1,2,1,1,1]
[7,8,2,3,1,6,5,4]=>[2,1,7,6,8,3,4,5]=>1010100=>[1,1,1,1,1,2]
[7,8,2,1,3,6,5,4]=>[2,1,7,8,6,3,4,5]=>1001100=>[1,2,2,2]
[7,8,1,2,3,6,5,4]=>[2,1,8,7,6,3,4,5]=>1011100=>[1,1,3,2]
[6,1,8,2,3,7,5,4]=>[3,8,1,7,6,2,4,5]=>0101100=>[1,1,1,2,2]
[1,6,8,2,3,7,5,4]=>[8,3,1,7,6,2,4,5]=>1101100=>[2,1,2,2]
[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>1010100=>[1,1,1,1,1,2]
[5,1,2,8,3,7,6,4]=>[4,8,7,1,6,2,3,5]=>0110100=>[1,2,1,1,2]
[5,2,1,8,3,7,6,4]=>[4,7,8,1,6,2,3,5]=>0010100=>[2,1,1,1,2]
[6,2,8,1,3,7,5,4]=>[3,7,1,8,6,2,4,5]=>0101100=>[1,1,1,2,2]
[6,2,8,3,1,7,5,4]=>[3,7,1,6,8,2,4,5]=>0100100=>[1,1,2,1,2]
[6,2,8,4,7,1,5,3]=>[3,7,1,5,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[6,3,8,4,7,5,1,2]=>[3,6,1,5,2,4,8,7]=>0101001=>[1,1,1,1,2,1]
[3,6,8,4,7,5,1,2]=>[6,3,1,5,2,4,8,7]=>1101001=>[2,1,1,2,1]
[2,6,8,4,7,1,5,3]=>[7,3,1,5,2,8,4,6]=>1101010=>[2,1,1,1,1,1]
[2,6,8,3,1,7,5,4]=>[7,3,1,6,8,2,4,5]=>1100100=>[2,2,1,2]
[2,6,8,1,3,7,5,4]=>[7,3,1,8,6,2,4,5]=>1101100=>[2,1,2,2]
[2,5,1,8,3,7,6,4]=>[7,4,8,1,6,2,3,5]=>1010100=>[1,1,1,1,1,2]
[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>1110100=>[3,1,1,2]
[2,4,1,3,8,7,6,5]=>[7,5,8,6,1,2,3,4]=>1011000=>[1,1,2,3]
[2,5,3,8,1,7,6,4]=>[7,4,6,1,8,2,3,5]=>1010100=>[1,1,1,1,1,2]
[2,5,4,8,7,1,6,3]=>[7,4,5,1,2,8,3,6]=>1010010=>[1,1,1,2,1,1]
[3,5,4,8,7,6,1,2]=>[6,4,5,1,2,3,8,7]=>1010001=>[1,1,1,3,1]
[5,3,4,8,7,6,1,2]=>[4,6,5,1,2,3,8,7]=>0110001=>[1,2,3,1]
[5,2,4,8,7,1,6,3]=>[4,7,5,1,2,8,3,6]=>0110010=>[1,2,2,1,1]
[5,2,3,8,1,7,6,4]=>[4,7,6,1,8,2,3,5]=>0110100=>[1,2,1,1,2]
[4,2,1,3,8,7,6,5]=>[5,7,8,6,1,2,3,4]=>0011000=>[2,2,3]
[4,1,2,3,8,7,6,5]=>[5,8,7,6,1,2,3,4]=>0111000=>[1,3,3]
[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>1011000=>[1,1,2,3]
[4,1,3,2,8,7,6,5]=>[5,8,6,7,1,2,3,4]=>0101000=>[1,1,1,1,3]
[4,3,1,2,8,7,6,5]=>[5,6,8,7,1,2,3,4]=>0011000=>[2,2,3]
[6,3,8,1,2,7,5,4]=>[3,6,1,8,7,2,4,5]=>0101100=>[1,1,1,2,2]
[5,3,1,8,2,7,6,4]=>[4,6,8,1,7,2,3,5]=>0010100=>[2,1,1,1,2]
[5,1,3,8,2,7,6,4]=>[4,8,6,1,7,2,3,5]=>0110100=>[1,2,1,1,2]
[1,5,3,8,2,7,6,4]=>[8,4,6,1,7,2,3,5]=>1010100=>[1,1,1,1,1,2]
[1,5,4,8,7,2,6,3]=>[8,4,5,1,2,7,3,6]=>1010010=>[1,1,1,2,1,1]
[5,1,4,8,7,2,6,3]=>[4,8,5,1,2,7,3,6]=>0110010=>[1,2,2,1,1]
[5,4,1,8,7,2,6,3]=>[4,5,8,1,2,7,3,6]=>0010010=>[2,1,2,1,1]
[6,4,8,1,7,2,5,3]=>[3,5,1,8,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[6,5,8,7,1,2,4,3]=>[3,4,1,2,8,7,5,6]=>0100110=>[1,1,2,2,1]
[5,6,8,7,3,4,1,2]=>[4,3,1,2,6,5,8,7]=>1100101=>[2,2,1,1,1]
[5,6,8,7,2,1,4,3]=>[4,3,1,2,7,8,5,6]=>1100010=>[2,3,1,1]
[4,5,1,8,7,2,6,3]=>[5,4,8,1,2,7,3,6]=>1010010=>[1,1,1,2,1,1]
[4,1,5,8,7,2,6,3]=>[5,8,4,1,2,7,3,6]=>0110010=>[1,2,2,1,1]
[1,4,5,8,7,2,6,3]=>[8,5,4,1,2,7,3,6]=>1110010=>[3,2,1,1]
[1,3,5,8,2,7,6,4]=>[8,6,4,1,7,2,3,5]=>1110100=>[3,1,1,2]
[3,1,5,8,2,7,6,4]=>[6,8,4,1,7,2,3,5]=>0110100=>[1,2,1,1,2]
[3,6,8,1,2,7,5,4]=>[6,3,1,8,7,2,4,5]=>1101100=>[2,1,2,2]
[3,6,8,2,1,7,5,4]=>[6,3,1,7,8,2,4,5]=>1100100=>[2,2,1,2]
[4,6,8,2,7,1,5,3]=>[5,3,1,7,2,8,4,6]=>1101010=>[2,1,1,1,1,1]
[4,6,8,3,7,5,1,2]=>[5,3,1,6,2,4,8,7]=>1101001=>[2,1,1,2,1]
[4,5,3,8,7,6,1,2]=>[5,4,6,1,2,3,8,7]=>1010001=>[1,1,1,3,1]
[4,5,2,8,7,1,6,3]=>[5,4,7,1,2,8,3,6]=>1010010=>[1,1,1,2,1,1]
[3,5,2,8,1,7,6,4]=>[6,4,7,1,8,2,3,5]=>1010100=>[1,1,1,1,1,2]
[3,1,4,2,8,7,6,5]=>[6,8,5,7,1,2,3,4]=>0101000=>[1,1,1,1,3]
[3,1,2,4,8,7,6,5]=>[6,8,7,5,1,2,3,4]=>0111000=>[1,3,3]
[3,2,5,8,1,7,6,4]=>[6,7,4,1,8,2,3,5]=>0110100=>[1,2,1,1,2]
[4,2,5,8,7,1,6,3]=>[5,7,4,1,2,8,3,6]=>0110010=>[1,2,2,1,1]
[4,3,5,8,7,6,1,2]=>[5,6,4,1,2,3,8,7]=>0110001=>[1,2,3,1]
[3,4,5,8,7,6,1,2]=>[6,5,4,1,2,3,8,7]=>1110001=>[3,3,1]
[2,4,5,8,7,1,6,3]=>[7,5,4,1,2,8,3,6]=>1110010=>[3,2,1,1]
[2,3,5,8,1,7,6,4]=>[7,6,4,1,8,2,3,5]=>1110100=>[3,1,1,2]
[4,1,3,2,6,5,8,7]=>[5,8,6,7,3,4,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,1,3,2,6,4,8,7]=>[4,8,6,7,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,1,3,2,5,4,8,7]=>[3,8,6,7,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[7,1,3,2,5,4,8,6]=>[2,8,6,7,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[8,1,3,2,5,4,7,6]=>[1,8,6,7,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,2,5,3,7,6]=>[1,8,5,7,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[7,1,4,2,5,3,8,6]=>[2,8,5,7,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[6,1,4,2,5,3,8,7]=>[3,8,5,7,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,1,4,2,6,3,8,7]=>[4,8,5,7,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,3,5,4,8,7]=>[7,8,3,6,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,2,5,4,8,7]=>[6,8,3,7,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,2,5,3,8,7]=>[5,8,3,7,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,2,5,1,4,3,8,7]=>[3,7,4,8,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,1,4,3,8,7]=>[4,7,3,8,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,7,1,4,3,8,6]=>[4,7,2,8,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[5,2,8,1,4,3,7,6]=>[4,7,1,8,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[6,2,8,1,4,3,7,5]=>[3,7,1,8,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,1,4,3,8,5]=>[3,7,2,8,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[7,2,6,1,4,3,8,5]=>[2,7,3,8,5,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[7,2,5,1,4,3,8,6]=>[2,7,4,8,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,2,5,3,8,6]=>[5,8,2,7,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,7,2,5,4,8,6]=>[6,8,2,7,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,3,5,4,8,6]=>[7,8,2,6,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,3,5,4,7,6]=>[7,8,1,6,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,2,5,4,7,6]=>[6,8,1,7,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,2,5,3,7,6]=>[5,8,1,7,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,2,5,1,4,3,7,6]=>[1,7,4,8,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,1,4,3,7,5]=>[1,7,3,8,5,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,1,4,3,8,2,6,5]=>[2,8,5,6,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,3,7,2,6,5]=>[1,8,5,6,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,3,7,2,6,4]=>[1,8,4,6,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,1,5,3,8,2,6,4]=>[2,8,4,6,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,1,5,3,7,4]=>[1,7,3,8,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,2,6,3,7,4]=>[4,8,1,7,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,2,6,3,7,5]=>[5,8,1,7,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,2,6,4,7,5]=>[6,8,1,7,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,3,6,4,7,5]=>[7,8,1,6,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,3,6,4,8,5]=>[7,8,2,6,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,2,6,3,8,5]=>[5,8,2,7,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,7,2,6,3,8,4]=>[4,8,2,7,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[7,2,6,1,5,3,8,4]=>[2,7,3,8,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,1,5,3,8,4]=>[3,7,2,8,4,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,8,1,5,3,7,4]=>[3,7,1,8,4,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,2,6,3,7,4]=>[1,8,4,7,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,2,7,3,8,4]=>[3,8,4,7,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,1,4,2,7,3,8,5]=>[3,8,5,7,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,2,6,3,7,5]=>[1,8,5,7,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,3,2,6,4,7,5]=>[1,8,6,7,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,1,3,2,6,4,8,5]=>[2,8,6,7,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[6,1,3,2,7,4,8,5]=>[3,8,6,7,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,3,2,7,4,8,6]=>[4,8,6,7,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,3,2,7,5,8,6]=>[5,8,6,7,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,4,3,8,5,7,6]=>[7,8,5,6,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,4,2,8,5,7,6]=>[6,8,5,7,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,3,2,8,5,7,6]=>[5,8,6,7,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,1,3,2,8,4,7,6]=>[4,8,6,7,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[6,1,3,2,8,4,7,5]=>[3,8,6,7,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,1,3,2,6,5]=>[1,5,2,8,6,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[7,4,8,1,3,2,6,5]=>[2,5,1,8,6,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,1,4,2,6,5]=>[2,6,1,8,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,1,4,2,6,5]=>[1,6,2,8,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[6,1,4,2,8,3,7,5]=>[3,8,5,7,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,4,2,8,3,7,6]=>[4,8,5,7,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,5,2,8,3,7,6]=>[5,8,4,7,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,2,8,4,7,6]=>[6,8,4,7,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,3,8,4,7,6]=>[7,8,4,6,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,3,8,4,7,5]=>[7,8,3,6,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,2,8,4,7,5]=>[6,8,3,7,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,2,8,3,7,5]=>[5,8,3,7,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,2,8,3,7,4]=>[4,8,3,7,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,2,8,3,7,4]=>[3,8,4,7,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,1,5,2,6,4]=>[1,6,2,8,4,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,1,5,2,6,4]=>[2,6,1,8,4,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,3,8,1,5,4]=>[3,7,2,6,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,8,3,7,1,5,4]=>[3,7,1,6,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,2,6,1,5,4]=>[1,6,2,7,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,3,7,2,6,4]=>[4,8,1,6,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,3,7,2,6,5]=>[5,8,1,6,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,4,7,2,6,5]=>[6,8,1,5,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,4,7,3,6,5]=>[7,8,1,5,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,4,8,3,6,5]=>[7,8,2,5,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,7,4,8,2,6,5]=>[6,8,2,5,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,3,8,2,6,5]=>[5,8,2,6,1,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,7,3,8,2,6,4]=>[4,8,2,6,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,2,6,1,5,4]=>[2,6,1,7,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,3,7,1,5,4]=>[1,7,3,6,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[7,2,6,3,8,1,5,4]=>[2,7,3,6,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[3,4,2,6,8,1,5,7]=>[6,5,7,3,1,8,4,2]=>1011011=>[1,1,2,1,2]
[5,3,6,2,8,1,4,7]=>[4,6,3,7,1,8,5,2]=>0101011=>[1,1,1,1,1,2]
[5,3,6,2,4,8,1,7]=>[4,6,3,7,5,1,8,2]=>0101101=>[1,1,1,2,1,1]
[5,7,3,8,2,4,1,6]=>[4,2,6,1,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,8,2,4,6,1]=>[4,2,6,1,7,5,3,8]=>1010110=>[1,1,1,1,2,1]
[7,4,2,5,8,3,6,1]=>[2,5,7,4,1,6,3,8]=>0011010=>[2,2,1,1,1]
[7,4,2,5,8,3,1,6]=>[2,5,7,4,1,6,8,3]=>0011001=>[2,2,2,1]
[4,5,2,6,3,8,1,7]=>[5,4,7,3,6,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,2,1,6,8,3,7]=>[5,4,7,8,3,1,6,2]=>1001101=>[1,2,2,1,1]
[5,3,1,6,8,2,4,7]=>[4,6,8,3,1,7,5,2]=>0011011=>[2,2,1,2]
[5,6,2,8,1,3,4,7]=>[4,3,7,1,8,6,5,2]=>1010111=>[1,1,1,1,3]
[3,5,6,1,4,8,2,7]=>[6,4,3,8,5,1,7,2]=>1101101=>[2,1,2,1,1]
[4,1,5,6,3,8,2,7]=>[5,8,4,3,6,1,7,2]=>0110101=>[1,2,1,1,1,1]
[4,5,1,6,3,8,2,7]=>[5,4,8,3,6,1,7,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,6,3,2,8,1,7]=>[5,4,3,6,7,1,8,2]=>1100101=>[2,2,1,1,1]
[7,4,5,3,8,2,1,6]=>[2,5,4,6,1,7,8,3]=>0101001=>[1,1,1,1,2,1]
[7,4,5,3,8,2,6,1]=>[2,5,4,6,1,7,3,8]=>0101010=>[1,1,1,1,1,1,1]
[6,7,4,8,3,2,5,1]=>[3,2,5,1,6,7,4,8]=>1010010=>[1,1,1,2,1,1]
[6,7,4,8,3,2,1,5]=>[3,2,5,1,6,7,8,4]=>1010001=>[1,1,1,3,1]
[6,7,4,1,8,3,2,5]=>[3,2,5,8,1,6,7,4]=>1001001=>[1,2,1,2,1]
[7,4,5,3,1,8,2,6]=>[2,5,4,6,8,1,7,3]=>0100101=>[1,1,2,1,1,1]
[4,7,1,5,8,3,2,6]=>[5,2,8,4,1,6,7,3]=>1011001=>[1,1,2,2,1]
[5,3,7,8,1,4,2,6]=>[4,6,2,1,8,5,7,3]=>0110101=>[1,2,1,1,1,1]
[7,5,8,2,4,6,1,3]=>[2,4,1,7,5,3,8,6]=>0101101=>[1,1,1,2,1,1]
[7,3,5,8,1,4,6,2]=>[2,6,4,1,8,5,3,7]=>0110110=>[1,2,1,2,1]
[4,5,1,7,8,3,6,2]=>[5,4,8,2,1,6,3,7]=>1011010=>[1,1,2,1,1,1]
[7,4,1,5,8,3,6,2]=>[2,5,8,4,1,6,3,7]=>0011010=>[2,2,1,1,1]
[6,7,4,3,8,1,5,2]=>[3,2,5,6,1,8,4,7]=>1001010=>[1,2,1,1,1,1]
[6,7,4,8,3,1,5,2]=>[3,2,5,1,6,8,4,7]=>1010010=>[1,1,1,2,1,1]
[6,7,4,8,3,5,2,1]=>[3,2,5,1,6,4,7,8]=>1010100=>[1,1,1,1,1,2]
[5,6,7,3,8,4,2,1]=>[4,3,2,6,1,5,7,8]=>1101000=>[2,1,1,3]
[5,6,7,3,1,8,4,2]=>[4,3,2,6,8,1,5,7]=>1100100=>[2,2,1,2]
[5,6,1,7,3,8,4,2]=>[4,3,8,2,6,1,5,7]=>1010100=>[1,1,1,1,1,2]
[5,1,6,7,3,8,4,2]=>[4,8,3,2,6,1,5,7]=>0110100=>[1,2,1,1,2]
[6,4,7,1,8,3,5,2]=>[3,5,2,8,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[6,7,8,3,1,4,5,2]=>[3,2,1,6,8,5,4,7]=>1100110=>[2,2,2,1]
[6,7,2,8,4,5,1,3]=>[3,2,7,1,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,7,2,8,4,1,3,5]=>[3,2,7,1,5,8,6,4]=>1010011=>[1,1,1,2,2]
[6,1,7,4,8,3,2,5]=>[3,8,2,5,1,6,7,4]=>0101001=>[1,1,1,1,2,1]
[5,1,6,7,3,2,8,4]=>[4,8,3,2,6,7,1,5]=>0110010=>[1,2,2,1,1]
[5,6,1,7,3,2,8,4]=>[4,3,8,2,6,7,1,5]=>1010010=>[1,1,1,2,1,1]
[5,6,7,3,2,1,8,4]=>[4,3,2,6,7,8,1,5]=>1100010=>[2,3,1,1]
[5,6,7,3,2,8,4,1]=>[4,3,2,6,7,1,5,8]=>1100100=>[2,2,1,2]
[5,6,2,7,3,8,4,1]=>[4,3,7,2,6,1,5,8]=>1010100=>[1,1,1,1,1,2]
[5,6,2,7,3,1,8,4]=>[4,3,7,2,6,8,1,5]=>1010010=>[1,1,1,2,1,1]
[5,6,2,1,7,3,8,4]=>[4,3,7,8,2,6,1,5]=>1001010=>[1,2,1,1,1,1]
[6,1,7,4,2,8,3,5]=>[3,8,2,5,7,1,6,4]=>0100101=>[1,1,2,1,1,1]
[6,7,2,1,8,3,4,5]=>[3,2,7,8,1,6,5,4]=>1001011=>[1,2,1,1,2]
[7,5,8,2,1,3,4,6]=>[2,4,1,7,8,6,5,3]=>0100111=>[1,1,2,3]
[5,7,3,1,8,2,4,6]=>[4,2,6,8,1,7,5,3]=>1001011=>[1,2,1,1,2]
[4,7,1,5,2,8,3,6]=>[5,2,8,4,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]
[7,4,2,5,1,8,3,6]=>[2,5,7,4,8,1,6,3]=>0010101=>[2,1,1,1,1,1]
[6,7,4,2,1,8,3,5]=>[3,2,5,7,8,1,6,4]=>1000101=>[1,3,1,1,1]
[6,7,4,2,8,3,1,5]=>[3,2,5,7,1,6,8,4]=>1001001=>[1,2,1,2,1]
[6,7,4,2,8,3,5,1]=>[3,2,5,7,1,6,4,8]=>1001010=>[1,2,1,1,1,1]
[3,6,7,2,8,4,5,1]=>[6,3,2,7,1,5,4,8]=>1101010=>[2,1,1,1,1,1]
[3,6,7,2,8,4,1,5]=>[6,3,2,7,1,5,8,4]=>1101001=>[2,1,1,2,1]
[3,6,7,2,1,8,4,5]=>[6,3,2,7,8,1,5,4]=>1100101=>[2,2,1,1,1]
[5,7,3,8,2,1,4,6]=>[4,2,6,1,7,8,5,3]=>1010011=>[1,1,1,2,2]
[3,4,7,8,2,1,5,6]=>[6,5,2,1,7,8,4,3]=>1110011=>[3,2,2]
[3,7,8,1,4,6,2,5]=>[6,2,1,8,5,3,7,4]=>1101101=>[2,1,2,1,1]
[3,4,7,8,2,6,1,5]=>[6,5,2,1,7,3,8,4]=>1110101=>[3,1,1,1,1]
[5,7,3,8,2,6,1,4]=>[4,2,6,1,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[3,6,7,2,8,5,1,4]=>[6,3,2,7,1,4,8,5]=>1101001=>[2,1,1,2,1]
[3,6,7,8,5,2,1,4]=>[6,3,2,1,4,7,8,5]=>1110001=>[3,3,1]
[3,6,7,8,5,2,4,1]=>[6,3,2,1,4,7,5,8]=>1110010=>[3,2,1,1]
[6,4,7,8,2,5,3,1]=>[3,5,2,1,7,4,6,8]=>0110100=>[1,2,1,1,2]
[6,4,7,8,2,1,5,3]=>[3,5,2,1,7,8,4,6]=>0110010=>[1,2,2,1,1]
[4,1,5,7,8,2,6,3]=>[5,8,4,2,1,7,3,6]=>0111010=>[1,3,1,1,1]
[5,3,7,8,1,6,2,4]=>[4,6,2,1,8,3,7,5]=>0110101=>[1,2,1,1,1,1]
[6,7,2,8,5,1,3,4]=>[3,2,7,1,4,8,6,5]=>1010011=>[1,1,1,2,2]
[6,4,1,7,8,2,5,3]=>[3,5,8,2,1,7,4,6]=>0011010=>[2,2,1,1,1]
[5,1,6,2,7,8,4,3]=>[4,8,3,7,2,1,5,6]=>0101100=>[1,1,1,2,2]
[5,6,2,1,7,8,4,3]=>[4,3,7,8,2,1,5,6]=>1001100=>[1,2,2,2]
[5,6,2,7,1,8,4,3]=>[4,3,7,2,8,1,5,6]=>1010100=>[1,1,1,1,1,2]
[5,6,2,7,8,4,3,1]=>[4,3,7,2,1,5,6,8]=>1011000=>[1,1,2,3]
[5,6,7,2,8,4,3,1]=>[4,3,2,7,1,5,6,8]=>1101000=>[2,1,1,3]
[5,6,7,2,1,8,4,3]=>[4,3,2,7,8,1,5,6]=>1100100=>[2,2,1,2]
[5,6,1,7,2,8,4,3]=>[4,3,8,2,7,1,5,6]=>1010100=>[1,1,1,1,1,2]
[5,1,6,7,2,8,4,3]=>[4,8,3,2,7,1,5,6]=>0110100=>[1,2,1,1,2]
[6,4,7,1,8,2,5,3]=>[3,5,2,8,1,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[3,6,7,1,8,5,2,4]=>[6,3,2,8,1,4,7,5]=>1101001=>[2,1,1,2,1]
[6,7,8,5,2,4,1,3]=>[3,2,1,4,7,5,8,6]=>1100101=>[2,2,1,1,1]
[6,7,8,3,5,1,4,2]=>[3,2,1,6,4,8,5,7]=>1101010=>[2,1,1,1,1,1]
[4,6,7,8,1,5,3,2]=>[5,3,2,1,8,4,6,7]=>1110100=>[3,1,1,2]
[5,1,6,7,8,4,3,2]=>[4,8,3,2,1,5,6,7]=>0111000=>[1,3,3]
[5,6,1,7,8,4,3,2]=>[4,3,8,2,1,5,6,7]=>1011000=>[1,1,2,3]
[5,6,7,1,8,4,3,2]=>[4,3,2,8,1,5,6,7]=>1101000=>[2,1,1,3]
[8,6,1,3,4,2,5,7]=>[1,3,8,6,5,7,4,2]=>0011011=>[2,2,1,2]
[8,3,2,5,1,6,4,7]=>[1,6,7,4,8,3,5,2]=>0010101=>[2,1,1,1,1,1]
[8,5,3,6,2,4,1,7]=>[1,4,6,3,7,5,8,2]=>0010101=>[2,1,1,1,1,1]
[5,3,2,7,4,1,8,6]=>[4,6,7,2,5,8,1,3]=>0010010=>[2,1,2,1,1]
[7,5,3,8,2,4,6,1]=>[2,4,6,1,7,5,3,8]=>0010110=>[2,1,1,2,1]
[7,2,4,5,8,3,6,1]=>[2,7,5,4,1,6,3,8]=>0111010=>[1,3,1,1,1]
[2,4,5,3,7,1,8,6]=>[7,5,4,6,2,8,1,3]=>1101010=>[2,1,1,1,1,1]
[8,2,4,5,6,3,1,7]=>[1,7,5,4,3,6,8,2]=>0111001=>[1,3,2,1]
[8,2,4,5,6,1,3,7]=>[1,7,5,4,3,8,6,2]=>0111011=>[1,3,1,2]
[8,1,2,4,5,6,3,7]=>[1,8,7,5,4,3,6,2]=>0111101=>[1,4,1,1]
[8,2,5,1,3,6,4,7]=>[1,7,4,8,6,3,5,2]=>0101101=>[1,1,1,2,1,1]
[8,5,6,2,1,4,3,7]=>[1,4,3,7,8,5,6,2]=>0100101=>[1,1,2,1,1,1]
[8,5,3,6,4,1,2,7]=>[1,4,6,3,5,8,7,2]=>0010011=>[2,1,2,2]
[8,4,1,5,6,3,2,7]=>[1,5,8,4,3,6,7,2]=>0011001=>[2,2,2,1]
[8,1,4,5,6,3,2,7]=>[1,8,5,4,3,6,7,2]=>0111001=>[1,3,2,1]
[4,5,3,7,2,1,8,6]=>[5,4,6,2,7,8,1,3]=>1010010=>[1,1,1,2,1,1]
[7,4,5,8,3,2,6,1]=>[2,5,4,1,6,7,3,8]=>0110010=>[1,2,2,1,1]
[4,3,6,7,2,8,5,1]=>[5,6,3,2,7,1,4,8]=>0110100=>[1,2,1,1,2]
[4,3,6,7,2,8,1,5]=>[5,6,3,2,7,1,8,4]=>0110101=>[1,2,1,1,1,1]
[1,4,3,6,7,2,8,5]=>[8,5,6,3,2,7,1,4]=>1011010=>[1,1,2,1,1,1]
[4,5,3,7,1,8,2,6]=>[5,4,6,2,8,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,1,5,3,7,2,8,6]=>[5,8,4,6,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[5,3,4,7,1,2,8,6]=>[4,6,5,2,8,7,1,3]=>0110110=>[1,2,1,2,1]
[7,5,8,2,1,4,6,3]=>[2,4,1,7,8,5,3,6]=>0100110=>[1,1,2,2,1]
[7,5,3,8,4,1,6,2]=>[2,4,6,1,5,8,3,7]=>0010010=>[2,1,2,1,1]
[7,4,5,8,3,6,1,2]=>[2,5,4,1,6,3,8,7]=>0110101=>[1,2,1,1,1,1]
[4,3,6,7,8,1,5,2]=>[5,6,3,2,1,8,4,7]=>0111010=>[1,3,1,1,1]
[1,6,4,7,8,3,5,2]=>[8,3,5,2,1,6,4,7]=>1011010=>[1,1,2,1,1,1]
[6,4,7,8,3,5,2,1]=>[3,5,2,1,6,4,7,8]=>0110100=>[1,2,1,1,2]
[3,5,6,7,8,4,1,2]=>[6,4,3,2,1,5,8,7]=>1111001=>[4,2,1]
[3,1,5,6,7,8,4,2]=>[6,8,4,3,2,1,5,7]=>0111100=>[1,4,2]
[4,6,1,7,8,3,5,2]=>[5,3,8,2,1,6,4,7]=>1011010=>[1,1,2,1,1,1]
[3,6,7,1,4,8,5,2]=>[6,3,2,8,5,1,4,7]=>1101100=>[2,1,2,2]
[6,2,4,1,7,8,5,3]=>[3,7,5,8,2,1,4,6]=>0101100=>[1,1,1,2,2]
[2,6,7,1,4,8,3,5]=>[7,3,2,8,5,1,6,4]=>1101101=>[2,1,2,1,1]
[4,3,6,7,8,1,2,5]=>[5,6,3,2,1,8,7,4]=>0111011=>[1,3,1,2]
[1,5,3,6,7,8,2,4]=>[8,4,6,3,2,1,7,5]=>1011101=>[1,1,3,1,1]
[3,5,6,7,8,2,1,4]=>[6,4,3,2,1,7,8,5]=>1111001=>[4,2,1]
[3,5,6,7,8,2,4,1]=>[6,4,3,2,1,7,5,8]=>1111010=>[4,1,1,1]
[5,2,7,1,3,8,4,6]=>[4,7,2,8,6,1,5,3]=>0101101=>[1,1,1,2,1,1]
[5,3,1,7,8,2,4,6]=>[4,6,8,2,1,7,5,3]=>0011011=>[2,2,1,2]
[4,5,2,7,8,1,3,6]=>[5,4,7,2,1,8,6,3]=>1011011=>[1,1,2,1,2]
[4,2,6,7,8,3,1,5]=>[5,7,3,2,1,6,8,4]=>0111001=>[1,3,2,1]
[4,2,6,7,8,3,5,1]=>[5,7,3,2,1,6,4,8]=>0111010=>[1,3,1,1,1]
[3,6,2,7,4,8,5,1]=>[6,3,7,2,5,1,4,8]=>1010100=>[1,1,1,1,1,2]
[3,6,2,7,4,8,1,5]=>[6,3,7,2,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,2,1,6,4,7,8,5]=>[6,7,8,3,5,2,1,4]=>0010110=>[2,1,1,2,1]
[3,7,4,2,1,5,8,6]=>[6,2,5,7,8,4,1,3]=>1000110=>[1,3,2,1]
[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>1010110=>[1,1,1,1,2,1]
[4,7,2,1,3,5,8,6]=>[5,2,7,8,6,4,1,3]=>1001110=>[1,2,3,1]
[7,8,4,2,1,3,6,5]=>[2,1,5,7,8,6,3,4]=>1000110=>[1,3,2,1]
[7,8,1,3,4,2,6,5]=>[2,1,8,6,5,7,3,4]=>1011010=>[1,1,2,1,1,1]
[7,8,3,4,2,1,6,5]=>[2,1,6,5,7,8,3,4]=>1010010=>[1,1,1,2,1,1]
[6,3,2,7,1,8,5,4]=>[3,6,7,2,8,1,4,5]=>0010100=>[2,1,1,1,2]
[3,6,2,7,1,8,5,4]=>[6,3,7,2,8,1,4,5]=>1010100=>[1,1,1,1,1,2]
[6,7,3,8,2,5,4,1]=>[3,2,6,1,7,4,5,8]=>1010100=>[1,1,1,1,1,2]
[6,4,7,8,5,2,3,1]=>[3,5,2,1,4,7,6,8]=>0110010=>[1,2,2,1,1]
[2,6,4,7,8,1,5,3]=>[7,3,5,2,1,8,4,6]=>1011010=>[1,1,2,1,1,1]
[4,6,2,7,8,1,5,3]=>[5,3,7,2,1,8,4,6]=>1011010=>[1,1,2,1,1,1]
[7,4,5,8,6,2,1,3]=>[2,5,4,1,3,7,8,6]=>0110001=>[1,2,3,1]
[7,4,1,5,8,6,2,3]=>[2,5,8,4,1,3,7,6]=>0011001=>[2,2,2,1]
[7,5,3,8,6,1,2,4]=>[2,4,6,1,3,8,7,5]=>0010011=>[2,1,2,2]
[7,5,8,2,1,6,3,4]=>[2,4,1,7,8,3,6,5]=>0100101=>[1,1,2,1,1,1]
[6,2,7,1,3,8,5,4]=>[3,7,2,8,6,1,4,5]=>0101100=>[1,1,1,2,2]
[6,3,1,7,8,2,5,4]=>[3,6,8,2,1,7,4,5]=>0011010=>[2,2,1,1,1]
[4,6,1,7,8,5,2,3]=>[5,3,8,2,1,4,7,6]=>1011001=>[1,1,2,2,1]
[5,1,2,6,7,8,4,3]=>[4,8,7,3,2,1,5,6]=>0111100=>[1,4,2]
[5,2,6,7,8,4,1,3]=>[4,7,3,2,1,5,8,6]=>0111001=>[1,3,2,1]
[5,2,6,7,8,4,3,1]=>[4,7,3,2,1,5,6,8]=>0111000=>[1,3,3]
[2,5,6,7,8,4,1,3]=>[7,4,3,2,1,5,8,6]=>1111001=>[4,2,1]
[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>1011100=>[1,1,3,2]
[1,6,4,7,8,5,2,3]=>[8,3,5,2,1,4,7,6]=>1011001=>[1,1,2,2,1]
[2,6,7,1,3,8,5,4]=>[7,3,2,8,6,1,4,5]=>1101100=>[2,1,2,2]
[6,7,8,2,1,5,4,3]=>[3,2,1,7,8,4,5,6]=>1100100=>[2,2,1,2]
[6,7,3,8,5,1,4,2]=>[3,2,6,1,4,8,5,7]=>1010010=>[1,1,1,2,1,1]
[6,4,7,8,5,3,1,2]=>[3,5,2,1,4,6,8,7]=>0110001=>[1,2,3,1]
[4,5,2,3,7,6,1,8]=>[5,4,7,6,2,3,8,1]=>1011001=>[1,1,2,2,1]
[6,4,3,7,2,5,1,8]=>[3,5,6,2,7,4,8,1]=>0010101=>[2,1,1,1,1,1]
[8,4,3,6,5,1,2,7]=>[1,5,6,3,4,8,7,2]=>0010011=>[2,1,2,2]
[1,5,6,3,4,8,7,2]=>[8,4,3,6,5,1,2,7]=>1101100=>[2,1,2,2]
[4,6,2,7,3,5,1,8]=>[5,3,7,2,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[3,2,6,7,4,5,1,8]=>[6,7,3,2,5,4,8,1]=>0110101=>[1,2,1,1,1,1]
[4,7,2,6,5,3,1,8]=>[5,2,7,3,4,6,8,1]=>1010001=>[1,1,1,3,1]
[5,7,6,2,4,3,1,8]=>[4,2,3,7,5,6,8,1]=>1001001=>[1,2,1,2,1]
[1,7,5,4,8,3,6,2]=>[8,2,4,5,1,6,3,7]=>1001010=>[1,2,1,1,1,1]
[8,7,5,4,1,3,2,6]=>[1,2,4,5,8,6,7,3]=>0000101=>[4,1,1,1]
[6,8,5,4,2,1,3,7]=>[3,1,4,5,7,8,6,2]=>1000011=>[1,4,2]
[5,8,6,2,4,1,3,7]=>[4,1,3,7,5,8,6,2]=>1001011=>[1,2,1,1,2]
[4,8,2,6,5,1,3,7]=>[5,1,7,3,4,8,6,2]=>1010011=>[1,1,1,2,2]
[3,2,8,6,5,1,4,7]=>[6,7,1,3,4,8,5,2]=>0100011=>[1,1,3,2]
[4,1,2,6,5,8,7,3]=>[5,8,7,3,4,1,2,6]=>0110100=>[1,2,1,1,2]
[5,1,6,2,4,8,7,3]=>[4,8,3,7,5,1,2,6]=>0101100=>[1,1,1,2,2]
[6,1,5,4,2,8,7,3]=>[3,8,4,5,7,1,2,6]=>0100100=>[1,1,2,1,2]
[7,1,5,4,8,2,6,3]=>[2,8,4,5,1,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,4,7,6,2,3]=>[1,8,4,5,2,3,7,6]=>0101001=>[1,1,1,1,2,1]
[1,8,6,7,4,5,3,2]=>[8,1,3,2,5,4,6,7]=>1010100=>[1,1,1,1,1,2]
[8,1,6,7,4,5,2,3]=>[1,8,3,2,5,4,7,6]=>0110101=>[1,2,1,1,1,1]
[7,1,6,8,4,2,5,3]=>[2,8,3,1,5,7,4,6]=>0110010=>[1,2,2,1,1]
[6,1,7,8,2,4,5,3]=>[3,8,2,1,7,5,4,6]=>0110110=>[1,2,1,2,1]
[5,1,7,2,8,4,6,3]=>[4,8,2,7,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,2,7,8,5,6,3]=>[5,8,7,2,1,4,3,6]=>0111010=>[1,3,1,1,1]
[3,2,1,7,8,5,6,4]=>[6,7,8,2,1,4,3,5]=>0011010=>[2,2,1,1,1]
[3,2,8,7,1,5,4,6]=>[6,7,1,2,8,4,5,3]=>0100101=>[1,1,2,1,1,1]
[4,8,2,7,1,5,3,6]=>[5,1,7,2,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[5,8,7,2,1,4,3,6]=>[4,1,2,7,8,5,6,3]=>1000101=>[1,3,1,1,1]
[6,8,7,1,2,4,3,5]=>[3,1,2,8,7,5,6,4]=>1001101=>[1,2,2,1,1]
[7,8,6,1,4,2,3,5]=>[2,1,3,8,5,7,6,4]=>1001011=>[1,2,1,1,2]
[8,7,6,1,4,3,2,5]=>[1,2,3,8,5,6,7,4]=>0001001=>[3,1,2,1]
[1,7,6,8,4,3,5,2]=>[8,2,3,1,5,6,4,7]=>1010010=>[1,1,1,2,1,1]
[1,6,7,8,3,4,5,2]=>[8,3,2,1,6,5,4,7]=>1110110=>[3,1,2,1]
[8,6,7,1,3,4,2,5]=>[1,3,2,8,6,5,7,4]=>0101101=>[1,1,1,2,1,1]
[7,6,8,1,3,2,4,5]=>[2,3,1,8,6,7,5,4]=>0101011=>[1,1,1,1,1,2]
[5,7,8,2,1,3,4,6]=>[4,2,1,7,8,6,5,3]=>1100111=>[2,2,3]
[4,7,2,8,1,3,5,6]=>[5,2,7,1,8,6,4,3]=>1010111=>[1,1,1,1,3]
[3,2,6,8,4,1,5,7]=>[6,7,3,1,5,8,4,2]=>0110011=>[1,2,2,2]
[4,6,2,8,3,1,5,7]=>[5,3,7,1,6,8,4,2]=>1010011=>[1,1,1,2,2]
[5,6,8,2,3,1,4,7]=>[4,3,1,7,6,8,5,2]=>1101011=>[2,1,1,1,2]
[6,5,8,3,2,1,4,7]=>[3,4,1,6,7,8,5,2]=>0100011=>[1,1,3,2]
[7,5,8,3,1,2,4,6]=>[2,4,1,6,8,7,5,3]=>0100111=>[1,1,2,3]
[8,5,7,3,1,4,2,6]=>[1,4,2,6,8,5,7,3]=>0100101=>[1,1,2,1,1,1]
[1,5,7,3,8,4,6,2]=>[8,4,2,6,1,5,3,7]=>1101010=>[2,1,1,1,1,1]
[1,4,3,7,8,5,6,2]=>[8,5,6,2,1,4,3,7]=>1011010=>[1,1,2,1,1,1]
[8,4,3,7,1,5,2,6]=>[1,5,6,2,8,4,7,3]=>0010101=>[2,1,1,1,1,1]
[6,4,3,8,2,1,5,7]=>[3,5,6,1,7,8,4,2]=>0010011=>[2,1,2,2]
[4,5,2,3,8,1,6,7]=>[5,4,7,6,1,8,3,2]=>1011011=>[1,1,2,1,2]
[3,2,5,4,8,1,6,7]=>[6,7,4,5,1,8,3,2]=>0101011=>[1,1,1,1,1,2]
[4,5,2,3,1,8,7,6]=>[5,4,7,6,8,1,2,3]=>1010100=>[1,1,1,1,1,2]
[6,4,3,1,2,8,7,5]=>[3,5,6,8,7,1,2,4]=>0001100=>[3,2,2]
[7,4,3,1,8,2,6,5]=>[2,5,6,8,1,7,3,4]=>0001010=>[3,1,1,1,1]
[8,4,3,1,7,6,2,5]=>[1,5,6,8,2,3,7,4]=>0001001=>[3,1,2,1]
[1,5,8,3,7,6,4,2]=>[8,4,1,6,2,3,5,7]=>1101000=>[2,1,1,3]
[8,5,1,3,7,6,2,4]=>[1,4,8,6,2,3,7,5]=>0011001=>[2,2,2,1]
[7,5,1,3,8,2,6,4]=>[2,4,8,6,1,7,3,5]=>0011010=>[2,2,1,1,1]
[6,5,1,3,2,8,7,4]=>[3,4,8,6,7,1,2,5]=>0010100=>[2,1,1,1,2]
[5,6,1,2,3,8,7,4]=>[4,3,8,7,6,1,2,5]=>1011100=>[1,1,3,2]
[4,6,2,1,3,8,7,5]=>[5,3,7,8,6,1,2,4]=>1001100=>[1,2,2,2]
[3,2,6,1,4,8,7,5]=>[6,7,3,8,5,1,2,4]=>0101100=>[1,1,1,2,2]
[3,2,7,1,8,4,6,5]=>[6,7,2,8,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[4,7,2,1,8,3,6,5]=>[5,2,7,8,1,6,3,4]=>1001010=>[1,2,1,1,1,1]
[5,7,1,2,8,3,6,4]=>[4,2,8,7,1,6,3,5]=>1011010=>[1,1,2,1,1,1]
[6,7,1,8,2,3,5,4]=>[3,2,8,1,7,6,4,5]=>1010110=>[1,1,1,1,2,1]
[7,6,1,8,3,2,5,4]=>[2,3,8,1,6,7,4,5]=>0010010=>[2,1,2,1,1]
[8,6,1,7,3,5,2,4]=>[1,3,8,2,6,4,7,5]=>0010101=>[2,1,1,1,1,1]
[1,6,8,7,3,5,4,2]=>[8,3,1,2,6,4,5,7]=>1100100=>[2,2,1,2]
[1,7,8,6,5,3,4,2]=>[8,2,1,3,4,6,5,7]=>1100010=>[2,3,1,1]
[8,7,1,6,5,3,2,4]=>[1,2,8,3,4,6,7,5]=>0010001=>[2,1,3,1]
[7,8,1,6,5,2,3,4]=>[2,1,8,3,4,7,6,5]=>1010011=>[1,1,1,2,2]
[6,8,1,7,2,5,3,4]=>[3,1,8,2,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,2,7,6,3,4]=>[4,1,8,7,2,3,6,5]=>1011001=>[1,1,2,2,1]
[4,8,2,1,7,6,3,5]=>[5,1,7,8,2,3,6,4]=>1001001=>[1,2,1,2,1]
[3,2,8,1,7,6,4,5]=>[6,7,1,8,2,3,5,4]=>0101001=>[1,1,1,1,2,1]
[4,1,2,8,7,6,5,3]=>[5,8,7,1,2,3,4,6]=>0110000=>[1,2,4]
[5,1,8,2,7,6,4,3]=>[4,8,1,7,2,3,5,6]=>0101000=>[1,1,1,1,3]
[6,1,8,7,2,5,4,3]=>[3,8,1,2,7,4,5,6]=>0100100=>[1,1,2,1,2]
[7,1,8,6,5,2,4,3]=>[2,8,1,3,4,7,5,6]=>0100010=>[1,1,3,1,1]
[8,1,7,6,5,4,2,3]=>[1,8,2,3,4,5,7,6]=>0100001=>[1,1,4,1]
[3,1,2,6,5,8,7,4]=>[6,8,7,3,4,1,2,5]=>0110100=>[1,2,1,1,2]
[3,1,6,2,4,8,7,5]=>[6,8,3,7,5,1,2,4]=>0101100=>[1,1,1,2,2]
[3,1,5,2,4,8,7,6]=>[6,8,4,7,5,1,2,3]=>0101100=>[1,1,1,2,2]
[4,5,1,2,3,8,7,6]=>[5,4,8,7,6,1,2,3]=>1011100=>[1,1,3,2]
[4,6,1,2,3,8,7,5]=>[5,3,8,7,6,1,2,4]=>1011100=>[1,1,3,2]
[1,6,5,3,4,8,7,2]=>[8,3,4,6,5,1,2,7]=>1001100=>[1,2,2,2]
[6,1,5,2,4,8,7,3]=>[3,8,4,7,5,1,2,6]=>0101100=>[1,1,1,2,2]
[6,5,1,2,3,8,7,4]=>[3,4,8,7,6,1,2,5]=>0011100=>[2,3,2]
[6,4,1,2,3,8,7,5]=>[3,5,8,7,6,1,2,4]=>0011100=>[2,3,2]
[5,4,1,2,3,8,7,6]=>[4,5,8,7,6,1,2,3]=>0011100=>[2,3,2]
[5,4,1,2,7,3,6,8]=>[4,5,8,7,2,6,3,1]=>0011011=>[2,2,1,2]
[6,4,1,7,2,3,5,8]=>[3,5,8,2,7,6,4,1]=>0010111=>[2,1,1,3]
[6,4,1,8,2,3,5,7]=>[3,5,8,1,7,6,4,2]=>0010111=>[2,1,1,3]
[7,4,1,2,8,3,6,5]=>[2,5,8,7,1,6,3,4]=>0011010=>[2,2,1,1,1]
[7,5,1,2,8,3,6,4]=>[2,4,8,7,1,6,3,5]=>0011010=>[2,2,1,1,1]
[7,1,5,2,8,4,6,3]=>[2,8,4,7,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[1,7,5,3,8,4,6,2]=>[8,2,4,6,1,5,3,7]=>1001010=>[1,2,1,1,1,1]
[1,8,5,3,7,4,6,2]=>[8,1,4,6,2,5,3,7]=>1001010=>[1,2,1,1,1,1]
[8,1,5,2,7,4,6,3]=>[1,8,4,7,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[8,5,1,2,7,3,6,4]=>[1,4,8,7,2,6,3,5]=>0011010=>[2,2,1,1,1]
[8,4,1,2,7,3,6,5]=>[1,5,8,7,2,6,3,4]=>0011010=>[2,2,1,1,1]
[8,4,1,7,2,3,5,6]=>[1,5,8,2,7,6,4,3]=>0010111=>[2,1,1,3]
[7,4,1,6,2,3,5,8]=>[2,5,8,3,7,6,4,1]=>0010111=>[2,1,1,3]
[8,6,1,7,2,3,5,4]=>[1,3,8,2,7,6,4,5]=>0010110=>[2,1,1,2,1]
[8,1,6,7,2,4,5,3]=>[1,8,3,2,7,5,4,6]=>0110110=>[1,2,1,2,1]
[1,8,6,7,3,4,5,2]=>[8,1,3,2,6,5,4,7]=>1010110=>[1,1,1,1,2,1]
[1,7,6,8,3,4,5,2]=>[8,2,3,1,6,5,4,7]=>1010110=>[1,1,1,1,2,1]
[7,1,6,8,2,4,5,3]=>[2,8,3,1,7,5,4,6]=>0110110=>[1,2,1,2,1]
[7,6,1,8,2,3,5,4]=>[2,3,8,1,7,6,4,5]=>0010110=>[2,1,1,2,1]
[4,7,1,2,8,3,6,5]=>[5,2,8,7,1,6,3,4]=>1011010=>[1,1,2,1,1,1]
[3,1,7,2,8,4,6,5]=>[6,8,2,7,1,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,2,7,8,5,6,4]=>[6,8,7,2,1,4,3,5]=>0111010=>[1,3,1,1,1]
[1,4,3,8,7,5,6,2]=>[8,5,6,1,2,4,3,7]=>1010010=>[1,1,1,2,1,1]
[4,1,2,8,7,5,6,3]=>[5,8,7,1,2,4,3,6]=>0110010=>[1,2,2,1,1]
[3,1,2,8,7,5,6,4]=>[6,8,7,1,2,4,3,5]=>0110010=>[1,2,2,1,1]
[3,1,8,2,7,4,6,5]=>[6,8,1,7,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,7,2,4,5,6]=>[6,8,1,2,7,5,4,3]=>0100111=>[1,1,2,3]
[3,1,7,6,2,4,5,8]=>[6,8,2,3,7,5,4,1]=>0100111=>[1,1,2,3]
[4,7,1,6,2,3,5,8]=>[5,2,8,3,7,6,4,1]=>1010111=>[1,1,1,1,3]
[4,8,1,6,2,3,5,7]=>[5,1,8,3,7,6,4,2]=>1010111=>[1,1,1,1,3]
[4,8,1,7,2,3,5,6]=>[5,1,8,2,7,6,4,3]=>1010111=>[1,1,1,1,3]
[4,8,1,2,7,3,6,5]=>[5,1,8,7,2,6,3,4]=>1011010=>[1,1,2,1,1,1]
[5,8,1,2,7,3,6,4]=>[4,1,8,7,2,6,3,5]=>1011010=>[1,1,2,1,1,1]
[5,1,8,2,7,4,6,3]=>[4,8,1,7,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[1,5,8,3,7,4,6,2]=>[8,4,1,6,2,5,3,7]=>1101010=>[2,1,1,1,1,1]
[1,6,8,7,3,4,5,2]=>[8,3,1,2,6,5,4,7]=>1100110=>[2,2,2,1]
[6,1,8,7,2,4,5,3]=>[3,8,1,2,7,5,4,6]=>0100110=>[1,1,2,2,1]
[6,8,1,7,2,3,5,4]=>[3,1,8,2,7,6,4,5]=>1010110=>[1,1,1,1,2,1]
[6,8,7,1,2,3,4,5]=>[3,1,2,8,7,6,5,4]=>1001111=>[1,2,4]
[5,8,7,1,2,3,4,6]=>[4,1,2,8,7,6,5,3]=>1001111=>[1,2,4]
[5,8,6,1,2,3,4,7]=>[4,1,3,8,7,6,5,2]=>1001111=>[1,2,4]
[5,7,6,1,2,3,4,8]=>[4,2,3,8,7,6,5,1]=>1001111=>[1,2,4]
[7,8,1,6,2,3,5,4]=>[2,1,8,3,7,6,4,5]=>1010110=>[1,1,1,1,2,1]
[7,1,8,6,2,4,5,3]=>[2,8,1,3,7,5,4,6]=>0100110=>[1,1,2,2,1]
[1,7,8,6,3,4,5,2]=>[8,2,1,3,6,5,4,7]=>1100110=>[2,2,2,1]
[1,8,7,6,3,4,5,2]=>[8,1,2,3,6,5,4,7]=>1000110=>[1,3,2,1]
[8,1,7,6,2,4,5,3]=>[1,8,2,3,7,5,4,6]=>0100110=>[1,1,2,2,1]
[8,7,1,6,2,3,5,4]=>[1,2,8,3,7,6,4,5]=>0010110=>[2,1,1,2,1]
[3,2,5,1,6,4,8,7]=>[6,7,4,8,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,4,7,1,8,6]=>[6,7,4,5,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,3,7,6,8,1]=>[5,7,4,6,2,3,1,8]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,3,7,1,8,6]=>[5,7,4,6,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,3,6,1,8,7]=>[5,7,4,6,3,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,1,6,3,8,7]=>[5,7,4,8,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,4,6,2,8,7]=>[6,8,4,5,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,1,5,3,6,2,8,7]=>[5,8,4,6,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,3,5,1,6,2,8,7]=>[5,6,4,8,3,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,3,5,2,7,1,8,6]=>[5,6,4,7,2,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,2,7,5,8,1]=>[5,6,3,7,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,2,7,1,8,5]=>[5,6,3,7,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,1,7,2,8,5]=>[5,6,3,8,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,3,5,1,7,2,8,6]=>[5,6,4,8,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,4,7,2,8,6]=>[6,8,4,5,2,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,4,7,3,8,6]=>[7,8,4,5,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,4,7,6,8,2]=>[6,8,4,5,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,5,3,7,6,8,2]=>[5,8,4,6,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,5,1,7,6,8,2]=>[5,6,4,8,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,1,7,5,8,2]=>[5,6,3,8,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,5,7,1,8,2]=>[5,6,3,4,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,4,7,2,8,1]=>[4,6,3,5,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,4,7,1,8,2]=>[4,6,3,5,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,1,7,4,8,2]=>[4,6,3,8,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,3,7,4,8,2]=>[4,8,3,6,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,3,7,5,8,2]=>[5,8,3,6,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,4,7,5,8,2]=>[6,8,3,5,2,4,1,7]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,4,7,5,8,3]=>[7,8,3,5,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,4,7,3,8,5]=>[7,8,3,5,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,4,7,2,8,5]=>[6,8,3,5,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,3,7,2,8,5]=>[5,8,3,6,2,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,3,7,2,8,4]=>[4,8,3,6,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,1,7,2,8,4]=>[4,6,3,8,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,2,7,1,8,4]=>[4,6,3,7,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,2,7,4,8,1]=>[4,6,3,7,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,3,7,4,8,1]=>[4,7,3,6,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,3,7,1,8,4]=>[4,7,3,6,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,1,7,3,8,4]=>[4,7,3,8,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,1,7,3,8,6]=>[5,7,4,8,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,1,7,3,8,5]=>[5,7,3,8,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,3,7,1,8,5]=>[5,7,3,6,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,3,7,5,8,1]=>[5,7,3,6,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,4,7,5,8,1]=>[6,7,3,5,2,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,4,7,1,8,5]=>[6,7,3,5,2,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,1,7,4,8,5]=>[6,7,3,8,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,1,7,4,8,6]=>[6,7,4,8,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,2,4,1,7,5,8,6]=>[6,7,5,8,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,4,2,7,6,8,5]=>[6,8,5,7,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,1,7,6,8,4]=>[6,7,4,8,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,1,7,5,8,4]=>[6,7,3,8,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,5,7,1,8,4]=>[6,7,3,4,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,5,7,3,8,1]=>[5,7,3,4,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,5,7,1,8,3]=>[5,7,3,4,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,1,7,5,8,3]=>[5,7,3,8,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[4,2,5,1,7,6,8,3]=>[5,7,4,8,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,5,2,7,6,8,3]=>[5,8,4,7,2,3,1,6]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,2,7,6,8,4]=>[6,8,4,7,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,3,7,6,8,4]=>[7,8,4,6,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,3,7,5,8,4]=>[7,8,3,6,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,2,7,5,8,4]=>[6,8,3,7,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,2,7,5,8,3]=>[5,8,3,7,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,2,7,4,8,3]=>[4,8,3,7,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,1,7,4,8,3]=>[4,7,3,8,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,4,7,1,8,3]=>[4,7,3,5,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,4,7,3,8,1]=>[4,7,3,5,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,2,7,3,8,1]=>[4,5,3,7,2,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,2,7,1,8,3]=>[4,5,3,7,2,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,1,7,2,8,3]=>[4,5,3,8,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,4,7,2,8,3]=>[4,8,3,5,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,5,7,2,8,3]=>[5,8,3,4,2,7,1,6]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,5,7,2,8,4]=>[6,8,3,4,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,5,7,3,8,4]=>[7,8,3,4,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,5,7,4,8,2]=>[6,8,3,4,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,5,7,3,8,2]=>[5,8,3,4,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,4,7,3,8,2]=>[4,8,3,5,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,1,7,3,8,2]=>[4,5,3,8,2,6,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,3,7,1,8,2]=>[4,5,3,6,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,2,1,6,4,7]=>[1,6,4,7,8,3,5,2]=>0100101=>[1,1,2,1,1,1]
[8,6,3,5,2,4,1,7]=>[1,3,6,4,7,5,8,2]=>0010101=>[2,1,1,1,1,1]
[3,7,5,2,4,1,8,6]=>[6,2,4,7,5,8,1,3]=>1001010=>[1,2,1,1,1,1]
[8,3,7,5,2,4,6,1]=>[1,6,2,4,7,5,3,8]=>0100110=>[1,1,2,2,1]
[8,2,4,5,7,3,6,1]=>[1,7,5,4,2,6,3,8]=>0111010=>[1,3,1,1,1]
[2,4,5,7,3,1,8,6]=>[7,5,4,2,6,8,1,3]=>1110010=>[3,2,1,1]
[8,2,4,6,5,3,1,7]=>[1,7,5,3,4,6,8,2]=>0110001=>[1,2,3,1]
[8,2,5,4,6,1,3,7]=>[1,7,4,5,3,8,6,2]=>0101011=>[1,1,1,1,1,2]
[8,6,3,5,1,4,2,7]=>[1,3,6,4,8,5,7,2]=>0010101=>[2,1,1,1,1,1]
[8,6,1,4,5,3,2,7]=>[1,3,8,5,4,6,7,2]=>0011001=>[2,2,2,1]
[8,1,5,6,4,3,2,7]=>[1,8,4,3,5,6,7,2]=>0110001=>[1,2,3,1]
[5,7,4,3,2,1,8,6]=>[4,2,5,6,7,8,1,3]=>1000010=>[1,4,1,1]
[8,5,7,4,3,2,6,1]=>[1,4,2,5,6,7,3,8]=>0100010=>[1,1,3,1,1]
[4,6,8,3,2,7,5,1]=>[5,3,1,6,7,2,4,8]=>1100100=>[2,2,1,2]
[4,7,6,3,2,8,1,5]=>[5,2,3,6,7,1,8,4]=>1000101=>[1,3,1,1,1]
[1,4,6,7,3,2,8,5]=>[8,5,3,2,6,7,1,4]=>1110010=>[3,2,1,1]
[5,4,7,3,1,8,2,6]=>[4,5,2,6,8,1,7,3]=>0100101=>[1,1,2,1,1,1]
[1,7,4,5,3,2,8,6]=>[8,2,5,4,6,7,1,3]=>1010010=>[1,1,1,2,1,1]
[3,7,5,1,4,2,8,6]=>[6,2,4,8,5,7,1,3]=>1001010=>[1,2,1,1,1,1]
[5,7,4,2,1,3,8,6]=>[4,2,5,7,8,6,1,3]=>1000110=>[1,3,2,1]
[8,5,7,4,2,1,6,3]=>[1,4,2,5,7,8,3,6]=>0100010=>[1,1,3,1,1]
[8,3,7,5,1,4,6,2]=>[1,6,2,4,8,5,3,7]=>0100110=>[1,1,2,2,1]
[8,4,1,7,5,3,6,2]=>[1,5,8,2,4,6,3,7]=>0010010=>[2,1,2,1,1]
[4,6,3,8,7,1,5,2]=>[5,3,6,1,2,8,4,7]=>1010010=>[1,1,1,2,1,1]
[1,7,4,8,6,3,5,2]=>[8,2,5,1,3,6,4,7]=>1010010=>[1,1,1,2,1,1]
[8,4,7,6,3,5,2,1]=>[1,5,2,3,6,4,7,8]=>0100100=>[1,1,2,1,2]
[3,6,5,8,7,4,1,2]=>[6,3,4,1,2,5,8,7]=>1010001=>[1,1,1,3,1]
[3,1,5,8,6,7,4,2]=>[6,8,4,1,3,2,5,7]=>0110100=>[1,2,1,1,2]
[4,8,1,6,7,3,5,2]=>[5,1,8,3,2,6,4,7]=>1011010=>[1,1,2,1,1,1]
[3,6,4,1,8,7,5,2]=>[6,3,5,8,1,2,4,7]=>1001000=>[1,2,1,3]
[8,2,6,1,4,7,5,3]=>[1,7,3,8,5,2,4,6]=>0101100=>[1,1,1,2,2]
[2,7,6,8,1,4,3,5]=>[7,2,3,1,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,6,4,8,2,5]=>[6,2,8,3,5,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,5,6,8,2,4]=>[8,2,6,4,3,1,7,5]=>1011101=>[1,1,3,1,1]
[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>1110101=>[3,1,1,1,1]
[3,7,6,5,8,2,1,4]=>[6,2,3,4,1,7,8,5]=>1001001=>[1,2,1,2,1]
[3,6,8,5,7,2,4,1]=>[6,3,1,4,2,7,5,8]=>1101010=>[2,1,1,1,1,1]
[2,3,5,7,6,8,1,4]=>[7,6,4,2,3,1,8,5]=>1110101=>[3,1,1,1,1]
[2,1,6,5,7,8,3,4]=>[7,8,3,4,2,1,6,5]=>0101101=>[1,1,1,2,1,1]
[4,2,7,6,8,3,1,5]=>[5,7,2,3,1,6,8,4]=>0101001=>[1,1,1,1,2,1]
[4,2,6,8,7,3,5,1]=>[5,7,3,1,2,6,4,8]=>0110010=>[1,2,2,1,1]
[3,8,2,4,6,7,5,1]=>[6,1,7,5,3,2,4,8]=>1011100=>[1,1,3,2]
[3,7,2,6,4,8,1,5]=>[6,2,7,3,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,2,6,1,4,7,8,5]=>[6,7,3,8,5,2,1,4]=>0101110=>[1,1,1,3,1]
[5,3,7,2,1,8,4,6]=>[4,6,2,7,8,1,5,3]=>0100101=>[1,1,2,1,1,1]
[4,7,3,2,1,5,8,6]=>[5,2,6,7,8,4,1,3]=>1000110=>[1,3,2,1]
[8,7,6,1,3,4,2,5]=>[1,2,3,8,6,5,7,4]=>0001101=>[3,2,1,1]
[8,5,7,3,2,1,6,4]=>[1,4,2,6,7,8,3,5]=>0100010=>[1,1,3,1,1]
[8,3,6,7,2,1,5,4]=>[1,6,3,2,7,8,4,5]=>0110010=>[1,2,2,1,1]
[3,7,8,6,2,1,5,4]=>[6,2,1,3,7,8,4,5]=>1100010=>[2,3,1,1]
[8,7,6,3,5,2,4,1]=>[1,2,3,6,4,7,5,8]=>0001010=>[3,1,1,1,1]
[2,7,4,8,1,6,5,3]=>[7,2,5,1,8,3,4,6]=>1010100=>[1,1,1,1,1,2]
[4,6,8,2,1,7,5,3]=>[5,3,1,7,8,2,4,6]=>1100100=>[2,2,1,2]
[8,4,1,5,7,2,6,3]=>[1,5,8,4,2,7,3,6]=>0011010=>[2,2,1,1,1]
[8,5,3,7,1,6,2,4]=>[1,4,6,2,8,3,7,5]=>0010101=>[2,1,1,1,1,1]
[8,5,7,2,1,3,6,4]=>[1,4,2,7,8,6,3,5]=>0100110=>[1,1,2,2,1]
[8,2,6,7,1,3,5,4]=>[1,7,3,2,8,6,4,5]=>0110110=>[1,2,1,2,1]
[8,3,6,1,7,5,2,4]=>[1,6,3,8,2,4,7,5]=>0101001=>[1,1,1,1,2,1]
[4,6,1,8,7,2,5,3]=>[5,3,8,1,2,7,4,6]=>1010010=>[1,1,1,2,1,1]
[8,1,2,5,6,7,4,3]=>[1,8,7,4,3,2,5,6]=>0111100=>[1,4,2]
[8,2,6,5,7,4,1,3]=>[1,7,3,4,2,5,8,6]=>0101001=>[1,1,1,1,2,1]
[2,1,7,8,5,6,4,3]=>[7,8,2,1,4,3,5,6]=>0110100=>[1,2,1,1,2]
[8,2,5,7,6,4,3,1]=>[1,7,4,2,3,5,6,8]=>0110000=>[1,2,4]
[2,7,6,8,5,4,1,3]=>[7,2,3,1,4,5,8,6]=>1010001=>[1,1,1,3,1]
[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>1011000=>[1,1,2,3]
[1,7,4,8,2,6,5,3]=>[8,2,5,1,7,3,4,6]=>1010100=>[1,1,1,1,1,2]
[3,7,8,1,6,5,2,4]=>[6,2,1,8,3,4,7,5]=>1101001=>[2,1,1,2,1]
[2,7,8,6,1,3,5,4]=>[7,2,1,3,8,6,4,5]=>1100110=>[2,2,2,1]
[8,7,6,3,5,1,4,2]=>[1,2,3,6,4,8,5,7]=>0001010=>[3,1,1,1,1]
[8,4,7,6,5,1,3,2]=>[1,5,2,3,4,8,6,7]=>0100010=>[1,1,3,1,1]
[8,7,1,5,6,4,3,2]=>[1,2,8,4,3,5,6,7]=>0011000=>[2,2,3]
[8,1,6,7,5,4,3,2]=>[1,8,3,2,4,5,6,7]=>0110000=>[1,2,4]
[6,5,3,1,2,4,8,7]=>[3,4,6,8,7,5,1,2]=>0001110=>[3,3,1]
[4,6,3,5,1,2,8,7]=>[5,3,6,4,8,7,1,2]=>1010110=>[1,1,1,1,2,1]
[8,5,3,7,2,1,4,6]=>[1,4,6,2,7,8,5,3]=>0010011=>[2,1,2,2]
[6,8,1,4,5,7,3,2]=>[3,1,8,5,4,2,6,7]=>1011100=>[1,1,3,2]
[8,7,2,4,5,1,3,6]=>[1,2,7,5,4,8,6,3]=>0011011=>[2,2,1,2]
[3,6,2,4,5,1,8,7]=>[6,3,7,5,4,8,1,2]=>1011010=>[1,1,2,1,1,1]
[2,6,1,4,5,3,8,7]=>[7,3,8,5,4,6,1,2]=>1011010=>[1,1,2,1,1,1]
[6,1,2,4,5,3,8,7]=>[3,8,7,5,4,6,1,2]=>0111010=>[1,3,1,1,1]
[5,6,3,2,1,4,8,7]=>[4,3,6,7,8,5,1,2]=>1000110=>[1,3,2,1]
[5,4,3,6,1,2,8,7]=>[4,5,6,3,8,7,1,2]=>0010110=>[2,1,1,2,1]
[6,3,1,4,5,2,8,7]=>[3,6,8,5,4,7,1,2]=>0011010=>[2,2,1,1,1]
[3,1,6,4,5,2,8,7]=>[6,8,3,5,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,4,5,1,2,6]=>[1,6,2,5,4,8,7,3]=>0101011=>[1,1,1,1,1,2]
[5,8,7,4,2,6,3,1]=>[4,1,2,5,7,3,6,8]=>1000100=>[1,3,1,2]
[2,8,7,4,1,6,3,5]=>[7,1,2,5,8,3,6,4]=>1000101=>[1,3,1,1,1]
[8,1,7,4,2,6,3,5]=>[1,8,2,5,7,3,6,4]=>0100101=>[1,1,2,1,1,1]
[3,7,8,4,5,1,2,6]=>[6,2,1,5,4,8,7,3]=>1101011=>[2,1,1,1,2]
[2,1,8,7,5,3,4,6]=>[7,8,1,2,4,6,5,3]=>0100011=>[1,1,3,2]
[2,1,6,8,5,7,3,4]=>[7,8,3,1,4,2,6,5]=>0110101=>[1,2,1,1,1,1]
[5,6,3,8,1,7,2,4]=>[4,3,6,1,8,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[7,6,1,4,5,8,3,2]=>[2,3,8,5,4,1,6,7]=>0011100=>[2,3,2]
[3,7,6,4,5,8,2,1]=>[6,2,3,5,4,1,7,8]=>1001100=>[1,2,2,2]
[8,5,7,4,1,6,3,2]=>[1,4,2,5,8,3,6,7]=>0100100=>[1,1,2,1,2]
[5,1,8,4,7,6,2,3]=>[4,8,1,5,2,3,7,6]=>0101001=>[1,1,1,1,2,1]
[2,5,8,4,7,6,1,3]=>[7,4,1,5,2,3,8,6]=>1101001=>[2,1,1,2,1]
[2,4,8,3,5,6,7,1]=>[7,5,1,6,4,3,2,8]=>1101110=>[2,1,3,1]
[4,1,8,3,5,6,7,2]=>[5,8,1,6,4,3,2,7]=>0101110=>[1,1,1,3,1]
[3,8,4,2,5,6,7,1]=>[6,1,5,7,4,3,2,8]=>1001110=>[1,2,3,1]
[8,4,1,3,5,6,7,2]=>[1,5,8,6,4,3,2,7]=>0011110=>[2,4,1]
[7,5,8,4,3,6,1,2]=>[2,4,1,5,6,3,8,7]=>0100101=>[1,1,2,1,1,1]
[6,5,3,8,4,1,7,2]=>[3,4,6,1,5,8,2,7]=>0010010=>[2,1,2,1,1]
[2,1,5,8,4,6,7,3]=>[7,8,4,1,5,3,2,6]=>0110110=>[1,2,1,2,1]
[2,1,4,8,3,6,7,5]=>[7,8,5,1,6,3,2,4]=>0110110=>[1,2,1,2,1]
[6,4,3,8,2,1,7,5]=>[3,5,6,1,7,8,2,4]=>0010010=>[2,1,2,1,1]
[7,3,8,4,2,6,1,5]=>[2,6,1,5,7,3,8,4]=>0100101=>[1,1,2,1,1,1]
[8,3,1,2,5,6,7,4]=>[1,6,8,7,4,3,2,5]=>0011110=>[2,4,1]
[3,1,8,2,5,6,7,4]=>[6,8,1,7,4,3,2,5]=>0101110=>[1,1,1,3,1]
[2,3,8,1,5,6,7,4]=>[7,6,1,8,4,3,2,5]=>1101110=>[2,1,3,1]
[4,3,8,2,5,6,7,1]=>[5,6,1,7,4,3,2,8]=>0101110=>[1,1,1,3,1]
[4,8,2,3,5,6,7,1]=>[5,1,7,6,4,3,2,8]=>1011110=>[1,1,4,1]
[3,8,2,1,5,6,7,4]=>[6,1,7,8,4,3,2,5]=>1001110=>[1,2,3,1]
[2,8,1,3,5,6,7,4]=>[7,1,8,6,4,3,2,5]=>1011110=>[1,1,4,1]
[8,1,2,3,5,6,7,4]=>[1,8,7,6,4,3,2,5]=>0111110=>[1,5,1]
[7,8,2,4,3,6,1,5]=>[2,1,7,5,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,2,4,1,7,5]=>[3,1,6,7,5,8,2,4]=>1001010=>[1,2,1,1,1,1]
[2,1,8,3,4,6,7,5]=>[7,8,1,6,5,3,2,4]=>0101110=>[1,1,1,3,1]
[2,1,7,8,5,4,3,6]=>[7,8,2,1,4,5,6,3]=>0110001=>[1,2,3,1]
[5,7,3,8,1,4,2,6]=>[4,2,6,1,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]
[7,1,8,4,5,3,2,6]=>[2,8,1,5,4,6,7,3]=>0101001=>[1,1,1,1,2,1]
[2,7,8,4,5,3,1,6]=>[7,2,1,5,4,6,8,3]=>1101001=>[2,1,1,2,1]
[8,7,1,4,3,6,2,5]=>[1,2,8,5,6,3,7,4]=>0010101=>[2,1,1,1,1,1]
[3,8,7,4,2,6,1,5]=>[6,1,2,5,7,3,8,4]=>1000101=>[1,3,1,1,1]
[5,7,8,4,3,6,2,1]=>[4,2,1,5,6,3,7,8]=>1100100=>[2,2,1,2]
[5,6,3,8,4,2,7,1]=>[4,3,6,1,5,7,2,8]=>1010010=>[1,1,1,2,1,1]
[4,8,3,6,2,1,7,5]=>[5,1,6,3,7,8,2,4]=>1010010=>[1,1,1,2,1,1]
[8,6,3,1,4,2,7,5]=>[1,3,6,8,5,7,2,4]=>0001010=>[3,1,1,1,1]
[7,5,3,8,2,4,1,6]=>[2,4,6,1,7,5,8,3]=>0010101=>[2,1,1,1,1,1]
[2,4,3,1,8,5,7,6]=>[7,5,6,8,1,4,2,3]=>1001010=>[1,2,1,1,1,1]
[4,1,3,2,6,8,7,5]=>[5,8,6,7,3,1,2,4]=>0101100=>[1,1,1,2,2]
[7,5,3,6,2,8,1,4]=>[2,4,6,3,7,1,8,5]=>0010101=>[2,1,1,1,1,1]
[8,6,3,5,1,2,7,4]=>[1,3,6,4,8,7,2,5]=>0010110=>[2,1,1,2,1]
[5,8,3,2,6,1,7,4]=>[4,1,6,7,3,8,2,5]=>1001010=>[1,2,1,1,1,1]
[4,5,3,8,6,2,7,1]=>[5,4,6,1,3,7,2,8]=>1010010=>[1,1,1,2,1,1]
[3,5,8,4,7,6,2,1]=>[6,4,1,5,2,3,7,8]=>1101000=>[2,1,1,3]
[5,8,2,4,7,6,1,3]=>[4,1,7,5,2,3,8,6]=>1011001=>[1,1,2,2,1]
[8,7,5,4,1,6,2,3]=>[1,2,4,5,8,3,7,6]=>0000101=>[4,1,1,1]
[2,7,6,4,5,8,1,3]=>[7,2,3,5,4,1,8,6]=>1001101=>[1,2,2,1,1]
[7,1,6,4,5,8,2,3]=>[2,8,3,5,4,1,7,6]=>0101101=>[1,1,1,2,1,1]
[5,7,3,6,1,8,2,4]=>[4,2,6,3,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,1,7,6,5,8,3,4]=>[7,8,2,3,4,1,6,5]=>0100101=>[1,1,2,1,1,1]
[2,1,8,5,3,6,7,4]=>[7,8,1,4,6,3,2,5]=>0100110=>[1,1,2,2,1]
[6,8,3,5,2,1,7,4]=>[3,1,6,4,7,8,2,5]=>1010010=>[1,1,1,2,1,1]
[7,8,5,4,2,6,1,3]=>[2,1,4,5,7,3,8,6]=>1000101=>[1,3,1,1,1]
[8,1,4,2,5,6,7,3]=>[1,8,5,7,4,3,2,6]=>0101110=>[1,1,1,3,1]
[2,8,4,1,5,6,7,3]=>[7,1,5,8,4,3,2,6]=>1001110=>[1,2,3,1]
[4,8,1,2,5,6,7,3]=>[5,1,8,7,4,3,2,6]=>1011110=>[1,1,4,1]
[3,4,8,1,5,6,7,2]=>[6,5,1,8,4,3,2,7]=>1101110=>[2,1,3,1]
[3,4,2,8,5,6,7,1]=>[6,5,7,1,4,3,2,8]=>1010110=>[1,1,1,1,2,1]
[2,4,1,8,5,6,7,3]=>[7,5,8,1,4,3,2,6]=>1010110=>[1,1,1,1,2,1]
[4,1,2,8,5,6,7,3]=>[5,8,7,1,4,3,2,6]=>0110110=>[1,2,1,2,1]
[8,4,2,1,5,6,7,3]=>[1,5,7,8,4,3,2,6]=>0001110=>[3,3,1]
[7,5,2,4,8,6,1,3]=>[2,4,7,5,1,3,8,6]=>0011001=>[2,2,2,1]
[6,5,3,2,8,1,7,4]=>[3,4,6,7,1,8,2,5]=>0001010=>[3,1,1,1,1]
[2,1,5,3,8,6,7,4]=>[7,8,4,6,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,4,3,5,8,1,7,2]=>[3,5,6,4,1,8,2,7]=>0011010=>[2,2,1,1,1]
[7,3,5,4,8,6,1,2]=>[2,6,4,5,1,3,8,7]=>0101001=>[1,1,1,1,2,1]
[8,3,4,1,5,6,7,2]=>[1,6,5,8,4,3,2,7]=>0101110=>[1,1,1,3,1]
[4,3,1,8,5,6,7,2]=>[5,6,8,1,4,3,2,7]=>0010110=>[2,1,1,2,1]
[3,1,4,8,5,6,7,2]=>[6,8,5,1,4,3,2,7]=>0110110=>[1,2,1,2,1]
[6,5,3,7,2,8,4,1]=>[3,4,6,2,7,1,5,8]=>0010100=>[2,1,1,1,2]
[6,3,7,4,5,8,2,1]=>[3,6,2,5,4,1,7,8]=>0101100=>[1,1,1,2,2]
[6,7,2,4,5,8,3,1]=>[3,2,7,5,4,1,6,8]=>1011100=>[1,1,3,2]
[5,1,7,4,8,6,3,2]=>[4,8,2,5,1,3,6,7]=>0101000=>[1,1,1,1,3]
[2,5,7,4,8,6,3,1]=>[7,4,2,5,1,3,6,8]=>1101000=>[2,1,1,3]
[5,6,3,7,1,8,4,2]=>[4,3,6,2,8,1,5,7]=>1010100=>[1,1,1,1,1,2]
[3,8,7,4,5,2,1,6]=>[6,1,2,5,4,7,8,3]=>1001001=>[1,2,1,2,1]
[3,7,5,4,8,6,2,1]=>[6,2,4,5,1,3,7,8]=>1001000=>[1,2,1,3]
[5,7,1,4,8,6,2,3]=>[4,2,8,5,1,3,7,6]=>1011001=>[1,1,2,2,1]
[5,6,3,1,8,2,7,4]=>[4,3,6,8,1,7,2,5]=>1001010=>[1,2,1,1,1,1]
[4,6,3,5,8,2,7,1]=>[5,3,6,4,1,7,2,8]=>1011010=>[1,1,2,1,1,1]
[4,6,3,8,1,2,7,5]=>[5,3,6,1,8,7,2,4]=>1010110=>[1,1,1,1,2,1]
[3,7,8,4,1,6,2,5]=>[6,2,1,5,8,3,7,4]=>1100101=>[2,2,1,1,1]
[3,2,5,1,6,8,4,7]=>[6,7,4,8,3,1,5,2]=>0101101=>[1,1,1,2,1,1]
[3,6,2,5,4,8,1,7]=>[6,3,7,4,5,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[3,5,2,4,7,1,8,6]=>[6,4,7,5,2,8,1,3]=>1011010=>[1,1,2,1,1,1]
[3,5,8,2,4,7,6,1]=>[6,4,1,7,5,2,3,8]=>1101100=>[2,1,2,2]
[4,2,5,8,3,7,6,1]=>[5,7,4,1,6,2,3,8]=>0110100=>[1,2,1,1,2]
[4,2,6,5,3,8,1,7]=>[5,7,3,4,6,1,8,2]=>0100101=>[1,1,2,1,1,1]
[5,4,2,1,6,8,3,7]=>[4,5,7,8,3,1,6,2]=>0001101=>[3,2,1,1]
[6,3,5,1,4,8,2,7]=>[3,6,4,8,5,1,7,2]=>0101101=>[1,1,1,2,1,1]
[4,6,1,5,3,8,2,7]=>[5,3,8,4,6,1,7,2]=>1010101=>[1,1,1,1,1,1,1]
[5,1,6,4,3,8,2,7]=>[4,8,3,5,6,1,7,2]=>0100101=>[1,1,2,1,1,1]
[5,4,3,2,7,1,8,6]=>[4,5,6,7,2,8,1,3]=>0001010=>[3,1,1,1,1]
[5,4,3,8,2,7,6,1]=>[4,5,6,1,7,2,3,8]=>0010100=>[2,1,1,1,2]
[4,3,6,2,8,7,5,1]=>[5,6,3,7,1,2,4,8]=>0101000=>[1,1,1,1,3]
[4,3,7,6,2,1,8,5]=>[5,6,2,3,7,8,1,4]=>0100010=>[1,1,3,1,1]
[6,4,3,1,7,2,8,5]=>[3,5,6,8,2,7,1,4]=>0001010=>[3,1,1,1,1]
[7,5,4,3,1,8,2,6]=>[2,4,5,6,8,1,7,3]=>0000101=>[4,1,1,1]
[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>1101001=>[2,1,1,2,1]
[7,2,5,8,4,1,3,6]=>[2,7,4,1,5,8,6,3]=>0110011=>[1,2,2,2]
[2,8,5,7,4,6,1,3]=>[7,1,4,2,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[3,5,8,7,1,4,6,2]=>[6,4,1,2,8,5,3,7]=>1100110=>[2,2,2,1]
[1,4,5,8,7,3,6,2]=>[8,5,4,1,2,6,3,7]=>1110010=>[3,2,1,1]
[1,5,4,8,7,3,6,2]=>[8,4,5,1,2,6,3,7]=>1010010=>[1,1,1,2,1,1]
[6,4,3,8,1,7,5,2]=>[3,5,6,1,8,2,4,7]=>0010100=>[2,1,1,1,2]
[4,3,7,1,8,6,5,2]=>[5,6,2,8,1,3,4,7]=>0101000=>[1,1,1,1,3]
[4,8,3,7,6,5,2,1]=>[5,1,6,2,3,4,7,8]=>1010000=>[1,1,1,4]
[5,3,8,7,6,4,2,1]=>[4,6,1,2,3,5,7,8]=>0100000=>[1,1,5]
[7,5,3,1,8,6,4,2]=>[2,4,6,8,1,3,5,7]=>0001000=>[3,1,3]
[1,8,6,5,3,7,4,2]=>[8,1,3,4,6,2,5,7]=>1000100=>[1,3,1,2]
[1,5,8,6,3,7,4,2]=>[8,4,1,3,6,2,5,7]=>1100100=>[2,2,1,2]
[4,6,1,8,7,3,5,2]=>[5,3,8,1,2,6,4,7]=>1010010=>[1,1,1,2,1,1]
[6,8,7,3,1,4,5,2]=>[3,1,2,6,8,5,4,7]=>1000110=>[1,3,2,1]
[6,2,8,7,4,5,1,3]=>[3,7,1,2,5,4,8,6]=>0100101=>[1,1,2,1,1,1]
[7,6,2,8,4,1,3,5]=>[2,3,7,1,5,8,6,4]=>0010011=>[2,1,2,2]
[7,3,1,6,8,4,2,5]=>[2,6,8,3,1,5,7,4]=>0011001=>[2,2,2,1]
[1,7,6,4,8,3,2,5]=>[8,2,3,5,1,6,7,4]=>1001001=>[1,2,1,2,1]
[5,7,1,6,3,2,8,4]=>[4,2,8,3,6,7,1,5]=>1010010=>[1,1,1,2,1,1]
[6,1,7,5,3,2,8,4]=>[3,8,2,4,6,7,1,5]=>0100010=>[1,1,3,1,1]
[7,6,5,3,2,1,8,4]=>[2,3,4,6,7,8,1,5]=>0000010=>[5,1,1]
[6,5,3,2,8,7,4,1]=>[3,4,6,7,1,2,5,8]=>0001000=>[3,1,3]
[5,2,6,3,8,7,4,1]=>[4,7,3,6,1,2,5,8]=>0101000=>[1,1,1,1,3]
[5,2,7,6,3,1,8,4]=>[4,7,2,3,6,8,1,5]=>0100010=>[1,1,3,1,1]
[6,5,2,1,7,3,8,4]=>[3,4,7,8,2,6,1,5]=>0001010=>[3,1,1,1,1]
[5,2,7,4,1,8,3,6]=>[4,7,2,5,8,1,6,3]=>0100101=>[1,1,2,1,1,1]
[4,7,2,6,3,1,8,5]=>[5,2,7,3,6,8,1,4]=>1010010=>[1,1,1,2,1,1]
[2,4,8,6,3,7,5,1]=>[7,5,1,3,6,2,4,8]=>1100100=>[2,2,1,2]
[3,8,6,2,4,7,5,1]=>[6,1,3,7,5,2,4,8]=>1001100=>[1,2,2,2]
[7,3,6,2,4,1,8,5]=>[2,6,3,7,5,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,6,7,2,1,4,8,5]=>[6,3,2,7,8,5,1,4]=>1100110=>[2,2,2,1]
[4,3,7,8,2,1,5,6]=>[5,6,2,1,7,8,4,3]=>0110011=>[1,2,2,2]
[8,3,7,1,4,6,2,5]=>[1,6,2,8,5,3,7,4]=>0101101=>[1,1,1,2,1,1]
[3,8,2,5,7,1,6,4]=>[6,1,7,4,2,8,3,5]=>1011010=>[1,1,2,1,1,1]
[7,8,3,6,2,1,5,4]=>[2,1,6,3,7,8,4,5]=>1010010=>[1,1,1,2,1,1]
[8,7,3,6,2,5,4,1]=>[1,2,6,3,7,4,5,8]=>0010100=>[2,1,1,1,2]
[4,7,8,2,1,6,5,3]=>[5,2,1,7,8,3,4,6]=>1100100=>[2,2,1,2]
[4,2,6,8,1,7,5,3]=>[5,7,3,1,8,2,4,6]=>0110100=>[1,2,1,1,2]
[5,4,8,2,7,1,6,3]=>[4,5,1,7,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]
[4,8,1,5,7,2,6,3]=>[5,1,8,4,2,7,3,6]=>1011010=>[1,1,2,1,1,1]
[5,8,3,7,1,6,2,4]=>[4,1,6,2,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,7,2,6,1,3,4]=>[4,1,2,7,3,8,6,5]=>1001011=>[1,2,1,1,2]
[8,6,2,7,5,1,3,4]=>[1,3,7,2,4,8,6,5]=>0010011=>[2,1,2,2]
[3,6,8,1,7,5,2,4]=>[6,3,1,8,2,4,7,5]=>1101001=>[2,1,1,2,1]
[5,1,6,8,2,7,4,3]=>[4,8,3,1,7,2,5,6]=>0110100=>[1,2,1,1,2]
[6,5,2,8,1,7,4,3]=>[3,4,7,1,8,2,5,6]=>0010100=>[2,1,1,1,2]
[5,2,7,1,8,6,4,3]=>[4,7,2,8,1,3,5,6]=>0101000=>[1,1,1,1,3]
[5,8,2,7,6,4,3,1]=>[4,1,7,2,3,5,6,8]=>1010000=>[1,1,1,4]
[6,2,8,7,5,4,3,1]=>[3,7,1,2,4,5,6,8]=>0100000=>[1,1,5]
[7,6,2,1,8,5,4,3]=>[2,3,7,8,1,4,5,6]=>0001000=>[3,1,3]
[6,1,7,2,8,5,4,3]=>[3,8,2,7,1,4,5,6]=>0101000=>[1,1,1,1,3]
[7,5,1,8,2,6,4,3]=>[2,4,8,1,7,3,5,6]=>0010100=>[2,1,1,1,2]
[4,7,1,8,6,2,5,3]=>[5,2,8,1,3,7,4,6]=>1010010=>[1,1,1,2,1,1]
[7,8,3,1,6,5,2,4]=>[2,1,6,8,3,4,7,5]=>1001001=>[1,2,1,2,1]
[8,7,4,6,1,5,3,2]=>[1,2,5,3,8,4,6,7]=>0010100=>[2,1,1,1,2]
[8,5,7,1,6,4,3,2]=>[1,4,2,8,3,5,6,7]=>0101000=>[1,1,1,1,3]
[6,8,1,7,5,4,3,2]=>[3,1,8,2,4,5,6,7]=>1010000=>[1,1,1,4]
[7,1,8,6,5,4,3,2]=>[2,8,1,3,4,5,6,7]=>0100000=>[1,1,5]
[5,4,2,3,7,6,1,8]=>[4,5,7,6,2,3,8,1]=>0011001=>[2,2,2,1]
[6,4,2,7,3,5,1,8]=>[3,5,7,2,6,4,8,1]=>0010101=>[2,1,1,1,1,1]
[7,4,2,6,3,5,1,8]=>[2,5,7,3,6,4,8,1]=>0010101=>[2,1,1,1,1,1]
[8,4,2,6,3,1,5,7]=>[1,5,7,3,6,8,4,2]=>0010011=>[2,1,2,2]
[3,2,7,6,4,5,1,8]=>[6,7,2,3,5,4,8,1]=>0100101=>[1,1,2,1,1,1]
[4,7,2,6,3,5,1,8]=>[5,2,7,3,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[5,7,6,2,3,4,1,8]=>[4,2,3,7,6,5,8,1]=>1001101=>[1,2,2,1,1]
[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>1001101=>[1,2,2,1,1]
[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>1001011=>[1,2,1,1,2]
[6,8,5,2,3,1,4,7]=>[3,1,4,7,6,8,5,2]=>1001011=>[1,2,1,1,2]
[5,8,6,2,3,1,4,7]=>[4,1,3,7,6,8,5,2]=>1001011=>[1,2,1,1,2]
[4,8,2,6,3,1,5,7]=>[5,1,7,3,6,8,4,2]=>1010011=>[1,1,1,2,2]
[3,2,8,6,4,1,5,7]=>[6,7,1,3,5,8,4,2]=>0100011=>[1,1,3,2]
[3,2,1,6,4,8,5,7]=>[6,7,8,3,5,1,4,2]=>0010101=>[2,1,1,1,1,1]
[7,1,5,2,8,3,4,6]=>[2,8,4,7,1,6,5,3]=>0101011=>[1,1,1,1,1,2]
[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>1001011=>[1,2,1,1,2]
[1,8,6,7,2,3,4,5]=>[8,1,3,2,7,6,5,4]=>1010111=>[1,1,1,1,3]
[8,1,6,7,2,3,4,5]=>[1,8,3,2,7,6,5,4]=>0110111=>[1,2,1,3]
[7,1,6,8,2,3,4,5]=>[2,8,3,1,7,6,5,4]=>0110111=>[1,2,1,3]
[3,2,1,7,8,4,5,6]=>[6,7,8,2,1,5,4,3]=>0011011=>[2,2,1,2]
[3,2,8,7,1,4,5,6]=>[6,7,1,2,8,5,4,3]=>0100111=>[1,1,2,3]
[5,8,7,2,1,3,4,6]=>[4,1,2,7,8,6,5,3]=>1000111=>[1,3,3]
[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>1010111=>[1,1,1,1,3]
[6,5,8,2,3,1,4,7]=>[3,4,1,7,6,8,5,2]=>0101011=>[1,1,1,1,1,2]
[8,5,7,2,1,3,4,6]=>[1,4,2,7,8,6,5,3]=>0100111=>[1,1,2,3]
[6,4,2,8,3,1,5,7]=>[3,5,7,1,6,8,4,2]=>0010011=>[2,1,2,2]
[5,4,2,3,8,1,6,7]=>[4,5,7,6,1,8,3,2]=>0011011=>[2,2,1,2]
[3,2,5,4,1,8,6,7]=>[6,7,4,5,8,1,3,2]=>0100101=>[1,1,2,1,1,1]
[4,5,2,3,1,8,6,7]=>[5,4,7,6,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[5,4,2,3,1,8,6,7]=>[4,5,7,6,8,1,3,2]=>0010101=>[2,1,1,1,1,1]
[6,4,2,1,3,8,5,7]=>[3,5,7,8,6,1,4,2]=>0001101=>[3,2,1,1]
[7,4,2,1,8,3,5,6]=>[2,5,7,8,1,6,4,3]=>0001011=>[3,1,1,2]
[8,4,2,1,7,3,5,6]=>[1,5,7,8,2,6,4,3]=>0001011=>[3,1,1,2]
[1,4,2,8,7,3,5,6]=>[8,5,7,1,2,6,4,3]=>1010011=>[1,1,1,2,2]
[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>1101011=>[2,1,1,1,2]
[8,5,1,2,7,3,4,6]=>[1,4,8,7,2,6,5,3]=>0011011=>[2,2,1,2]
[7,5,1,2,8,3,4,6]=>[2,4,8,7,1,6,5,3]=>0011011=>[2,2,1,2]
[6,5,1,2,3,8,4,7]=>[3,4,8,7,6,1,5,2]=>0011101=>[2,3,1,1]
[4,6,2,1,3,8,5,7]=>[5,3,7,8,6,1,4,2]=>1001101=>[1,2,2,1,1]
[3,2,6,1,4,8,5,7]=>[6,7,3,8,5,1,4,2]=>0101101=>[1,1,1,2,1,1]
[3,2,7,1,8,4,5,6]=>[6,7,2,8,1,5,4,3]=>0101011=>[1,1,1,1,1,2]
[4,7,2,1,8,3,5,6]=>[5,2,7,8,1,6,4,3]=>1001011=>[1,2,1,1,2]
[7,6,1,8,2,3,4,5]=>[2,3,8,1,7,6,5,4]=>0010111=>[2,1,1,3]
[8,6,1,7,2,3,4,5]=>[1,3,8,2,7,6,5,4]=>0010111=>[2,1,1,3]
[1,6,8,7,2,3,4,5]=>[8,3,1,2,7,6,5,4]=>1100111=>[2,2,3]
[1,7,8,6,2,3,4,5]=>[8,2,1,3,7,6,5,4]=>1100111=>[2,2,3]
[7,8,1,6,2,3,4,5]=>[2,1,8,3,7,6,5,4]=>1010111=>[1,1,1,1,3]
[6,8,1,7,2,3,4,5]=>[3,1,8,2,7,6,5,4]=>1010111=>[1,1,1,1,3]
[4,8,2,1,7,3,5,6]=>[5,1,7,8,2,6,4,3]=>1001011=>[1,2,1,1,2]
[3,2,8,1,7,4,5,6]=>[6,7,1,8,2,5,4,3]=>0101011=>[1,1,1,1,1,2]
[3,2,1,8,7,4,5,6]=>[6,7,8,1,2,5,4,3]=>0010011=>[2,1,2,2]
[5,1,8,2,7,3,4,6]=>[4,8,1,7,2,6,5,3]=>0101011=>[1,1,1,1,1,2]
[6,1,8,7,2,3,4,5]=>[3,8,1,2,7,6,5,4]=>0100111=>[1,1,2,3]
[8,1,7,6,2,3,4,5]=>[1,8,2,3,7,6,5,4]=>0100111=>[1,1,2,3]
[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>1000111=>[1,3,3]
[6,3,5,1,2,4,8,7]=>[3,6,4,8,7,5,1,2]=>0101110=>[1,1,1,3,1]
[4,3,5,6,1,2,8,7]=>[5,6,4,3,8,7,1,2]=>0110110=>[1,2,1,2,1]
[8,3,7,5,2,1,4,6]=>[1,6,2,4,7,8,5,3]=>0100011=>[1,1,3,2]
[6,3,7,5,1,8,4,2]=>[3,6,2,4,8,1,5,7]=>0100100=>[1,1,2,1,2]
[6,5,2,7,1,8,3,4]=>[3,4,7,2,8,1,6,5]=>0010101=>[2,1,1,1,1,1]
[8,5,2,7,4,1,3,6]=>[1,4,7,2,5,8,6,3]=>0010011=>[2,1,2,2]
[2,6,1,5,4,3,8,7]=>[7,3,8,4,5,6,1,2]=>1010010=>[1,1,1,2,1,1]
[6,4,3,5,1,2,8,7]=>[3,5,6,4,8,7,1,2]=>0010110=>[2,1,1,2,1]
[5,3,1,4,6,2,8,7]=>[4,6,8,5,3,7,1,2]=>0011010=>[2,2,1,1,1]
[3,1,4,6,5,2,8,7]=>[6,8,5,3,4,7,1,2]=>0110010=>[1,2,2,1,1]
[5,7,4,6,2,8,3,1]=>[4,2,5,3,7,1,6,8]=>1010100=>[1,1,1,1,1,2]
[8,1,4,7,2,6,3,5]=>[1,8,5,2,7,3,6,4]=>0110101=>[1,2,1,1,1,1]
[3,4,7,8,5,2,1,6]=>[6,5,2,1,4,7,8,3]=>1110001=>[3,3,1]
[2,1,8,5,7,3,4,6]=>[7,8,1,4,2,6,5,3]=>0101011=>[1,1,1,1,1,2]
[8,6,3,5,1,7,4,2]=>[1,3,6,4,8,2,5,7]=>0010100=>[2,1,1,1,2]
[5,8,2,4,6,7,3,1]=>[4,1,7,5,3,2,6,8]=>1011100=>[1,1,3,2]
[3,4,8,6,5,7,1,2]=>[6,5,1,3,4,2,8,7]=>1100101=>[2,2,1,1,1]
[7,5,4,8,1,6,3,2]=>[2,4,5,1,8,3,6,7]=>0010100=>[2,1,1,1,2]
[5,1,4,6,8,2,7,3]=>[4,8,5,3,1,7,2,6]=>0111010=>[1,3,1,1,1]
[2,5,4,6,7,1,8,3]=>[7,4,5,3,2,8,1,6]=>1011010=>[1,1,2,1,1,1]
[2,4,6,3,7,5,8,1]=>[7,5,3,6,2,4,1,8]=>1101010=>[2,1,1,1,1,1]
[4,1,6,3,8,5,7,2]=>[5,8,3,6,1,4,2,7]=>0101010=>[1,1,1,1,1,1,1]
[3,7,4,2,8,6,5,1]=>[6,2,5,7,1,3,4,8]=>1001000=>[1,2,1,3]
[7,4,1,3,5,8,6,2]=>[2,5,8,6,4,1,3,7]=>0011100=>[2,3,2]
[6,5,8,4,1,7,3,2]=>[3,4,1,5,8,2,6,7]=>0100100=>[1,1,2,1,2]
[8,5,3,7,4,1,6,2]=>[1,4,6,2,5,8,3,7]=>0010010=>[2,1,2,1,1]
[2,1,4,8,3,7,6,5]=>[7,8,5,1,6,2,3,4]=>0110100=>[1,2,1,1,2]
[7,4,3,8,2,1,6,5]=>[2,5,6,1,7,8,3,4]=>0010010=>[2,1,2,1,1]
[6,3,7,4,1,8,2,5]=>[3,6,2,5,8,1,7,4]=>0100101=>[1,1,2,1,1,1]
[8,3,1,2,5,7,6,4]=>[1,6,8,7,4,2,3,5]=>0011100=>[2,3,2]
[3,1,8,2,7,6,5,4]=>[6,8,1,7,2,3,4,5]=>0101000=>[1,1,1,1,3]
[2,3,8,1,6,7,5,4]=>[7,6,1,8,3,2,4,5]=>1101100=>[2,1,2,2]
[4,3,7,2,6,8,5,1]=>[5,6,2,7,3,1,4,8]=>0101100=>[1,1,1,2,2]
[4,7,2,3,8,5,6,1]=>[5,2,7,6,1,4,3,8]=>1011010=>[1,1,2,1,1,1]
[3,8,2,1,7,5,6,4]=>[6,1,7,8,2,4,3,5]=>1001010=>[1,2,1,1,1,1]
[2,8,1,3,6,5,7,4]=>[7,1,8,6,3,4,2,5]=>1011010=>[1,1,2,1,1,1]
[2,7,8,5,4,3,1,6]=>[7,2,1,4,5,6,8,3]=>1100001=>[2,4,1]
[8,7,1,6,3,4,2,5]=>[1,2,8,3,6,5,7,4]=>0010101=>[2,1,1,1,1,1]
[3,8,6,7,2,4,1,5]=>[6,1,3,2,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,3,8,7,4,2,6,1]=>[4,6,1,2,5,7,3,8]=>0100010=>[1,1,3,1,1]
[4,3,8,7,2,1,6,5]=>[5,6,1,2,7,8,3,4]=>0100010=>[1,1,3,1,1]
[8,3,6,1,4,2,7,5]=>[1,6,3,8,5,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,3,5,8,2,4,1,6]=>[2,6,4,1,7,5,8,3]=>0110101=>[1,2,1,1,1,1]
[2,3,4,1,8,5,7,6]=>[7,6,5,8,1,4,2,3]=>1101010=>[2,1,1,1,1,1]
[4,1,3,2,6,7,8,5]=>[5,8,6,7,3,2,1,4]=>0101110=>[1,1,1,3,1]
[8,3,5,6,2,7,1,4]=>[1,6,4,3,7,2,8,5]=>0110101=>[1,2,1,1,1,1]
[5,3,6,1,8,7,2,4]=>[4,6,3,8,1,2,7,5]=>0101001=>[1,1,1,1,2,1]
[5,6,2,8,7,4,1,3]=>[4,3,7,1,2,5,8,6]=>1010001=>[1,1,1,3,1]
[7,8,5,6,1,4,2,3]=>[2,1,4,3,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,5,4,7,1,3]=>[7,1,3,4,5,2,8,6]=>1000101=>[1,3,1,1,1]
[8,1,6,4,5,7,2,3]=>[1,8,3,5,4,2,7,6]=>0101101=>[1,1,1,2,1,1]
[5,8,3,6,1,7,2,4]=>[4,1,6,3,8,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,1,8,6,5,7,3,4]=>[7,8,1,3,4,2,6,5]=>0100101=>[1,1,2,1,1,1]
[2,1,7,5,3,6,8,4]=>[7,8,2,4,6,3,1,5]=>0100110=>[1,1,2,2,1]
[6,7,3,5,2,1,8,4]=>[3,2,6,4,7,8,1,5]=>1010010=>[1,1,1,2,1,1]
[7,1,4,2,5,6,8,3]=>[2,8,5,7,4,3,1,6]=>0101110=>[1,1,1,3,1]
[2,7,4,1,6,5,8,3]=>[7,2,5,8,3,4,1,6]=>1001010=>[1,2,1,1,1,1]
[4,6,1,2,8,7,3,5]=>[5,3,8,7,1,2,6,4]=>1011001=>[1,1,2,2,1]
[2,4,1,5,8,7,6,3]=>[7,5,8,4,1,2,3,6]=>1011000=>[1,1,2,3]
[4,1,2,5,8,6,7,3]=>[5,8,7,4,1,3,2,6]=>0111010=>[1,3,1,1,1]
[6,4,2,1,5,8,7,3]=>[3,5,7,8,4,1,2,6]=>0001100=>[3,2,2]
[8,5,2,4,6,1,7,3]=>[1,4,7,5,3,8,2,6]=>0011010=>[2,2,1,1,1]
[7,5,3,2,6,8,1,4]=>[2,4,6,7,3,1,8,5]=>0001101=>[3,2,1,1]
[2,1,5,3,6,8,7,4]=>[7,8,4,6,3,1,2,5]=>0101100=>[1,1,1,2,2]
[7,3,5,4,6,1,8,2]=>[2,6,4,5,3,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[6,3,4,1,5,7,8,2]=>[3,6,5,8,4,2,1,7]=>0101110=>[1,1,1,3,1]
[4,3,1,5,7,6,8,2]=>[5,6,8,4,2,3,1,7]=>0011010=>[2,2,1,1,1]
[3,1,4,5,6,8,7,2]=>[6,8,5,4,3,1,2,7]=>0111100=>[1,4,2]
[4,5,2,6,3,1,8,7]=>[5,4,7,3,6,8,1,2]=>1010010=>[1,1,1,2,1,1]
[6,5,2,1,4,3,8,7]=>[3,4,7,8,5,6,1,2]=>0001010=>[3,1,1,1,1]
[6,5,2,7,4,8,3,1]=>[3,4,7,2,5,1,6,8]=>0010100=>[2,1,1,1,2]
[8,5,2,7,4,1,6,3]=>[1,4,7,2,5,8,3,6]=>0010010=>[2,1,2,1,1]
[8,3,7,5,2,1,6,4]=>[1,6,2,4,7,8,3,5]=>0100010=>[1,1,3,1,1]
[6,3,7,5,2,8,4,1]=>[3,6,2,4,7,1,5,8]=>0100100=>[1,1,2,1,2]
[3,1,6,5,4,2,8,7]=>[6,8,3,4,5,7,1,2]=>0100010=>[1,1,3,1,1]
[5,6,3,2,4,1,8,7]=>[4,3,6,7,5,8,1,2]=>1001010=>[1,2,1,1,1,1]
[3,6,2,4,1,5,8,7]=>[6,3,7,5,8,4,1,2]=>1010110=>[1,1,1,1,2,1]
[2,6,1,3,5,4,8,7]=>[7,3,8,6,4,5,1,2]=>1011010=>[1,1,2,1,1,1]
[6,7,2,3,4,8,5,1]=>[3,2,7,6,5,1,4,8]=>1011100=>[1,1,3,2]
[8,7,2,3,4,1,6,5]=>[1,2,7,6,5,8,3,4]=>0011010=>[2,2,1,1,1]
[5,1,7,3,8,4,6,2]=>[4,8,2,6,1,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[2,5,7,3,8,6,4,1]=>[7,4,2,6,1,3,5,8]=>1101000=>[2,1,1,3]
[7,6,1,3,5,8,4,2]=>[2,3,8,6,4,1,5,7]=>0011100=>[2,3,2]
[3,6,7,4,1,8,5,2]=>[6,3,2,5,8,1,4,7]=>1100100=>[2,2,1,2]
[5,6,3,7,4,8,1,2]=>[4,3,6,2,5,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[2,1,6,7,4,8,5,3]=>[7,8,3,2,5,1,4,6]=>0110100=>[1,2,1,1,2]
[2,1,8,7,4,3,6,5]=>[7,8,1,2,5,6,3,4]=>0100010=>[1,1,3,1,1]
[5,8,3,7,4,2,6,1]=>[4,1,6,2,5,7,3,8]=>1010010=>[1,1,1,2,1,1]
[3,8,7,4,1,2,6,5]=>[6,1,2,5,8,7,3,4]=>1000110=>[1,3,2,1]
[7,8,1,3,5,2,6,4]=>[2,1,8,6,4,7,3,5]=>1011010=>[1,1,2,1,1,1]
[5,8,7,3,2,6,1,4]=>[4,1,2,6,7,3,8,5]=>1000101=>[1,3,1,1,1]
[2,8,6,3,1,5,7,4]=>[7,1,3,6,8,4,2,5]=>1000110=>[1,3,2,1]
[8,1,6,3,2,5,4,7]=>[1,8,3,6,7,4,5,2]=>0100101=>[1,1,2,1,1,1]
[2,8,4,1,6,3,7,5]=>[7,1,5,8,3,6,2,4]=>1001010=>[1,2,1,1,1,1]
[4,8,1,2,7,6,3,5]=>[5,1,8,7,2,3,6,4]=>1011001=>[1,1,2,2,1]
[3,8,4,2,5,7,1,6]=>[6,1,5,7,4,2,8,3]=>1001101=>[1,2,2,1,1]
[6,8,3,5,2,7,4,1]=>[3,1,6,4,7,2,5,8]=>1010100=>[1,1,1,1,1,2]
[2,1,5,3,8,7,6,4]=>[7,8,4,6,1,2,3,5]=>0101000=>[1,1,1,1,3]
[6,5,3,2,8,7,1,4]=>[3,4,6,7,1,2,8,5]=>0001001=>[3,1,2,1]
[7,5,2,4,8,1,6,3]=>[2,4,7,5,1,8,3,6]=>0011010=>[2,2,1,1,1]
[3,4,2,8,5,7,6,1]=>[6,5,7,1,4,2,3,8]=>1010100=>[1,1,1,1,1,2]
[2,4,1,8,7,6,5,3]=>[7,5,8,1,2,3,4,6]=>1010000=>[1,1,1,4]
[8,4,2,1,7,5,3,6]=>[1,5,7,8,2,4,6,3]=>0001001=>[3,1,2,1]
[4,3,1,8,6,7,5,2]=>[5,6,8,1,3,2,4,7]=>0010100=>[2,1,1,1,2]
[3,1,4,8,6,5,7,2]=>[6,8,5,1,3,4,2,7]=>0110010=>[1,2,2,1,1]
[7,1,6,5,4,8,2,3]=>[2,8,3,4,5,1,7,6]=>0100101=>[1,1,2,1,1,1]
[3,7,5,6,8,4,2,1]=>[6,2,4,3,1,5,7,8]=>1011000=>[1,1,2,3]
[5,7,1,6,8,2,4,3]=>[4,2,8,3,1,7,5,6]=>1011010=>[1,1,2,1,1,1]
[8,6,2,5,1,7,4,3]=>[1,3,7,4,8,2,5,6]=>0010100=>[2,1,1,1,2]
[5,6,2,1,8,7,3,4]=>[4,3,7,8,1,2,6,5]=>1001001=>[1,2,1,2,1]
[4,6,2,5,8,3,7,1]=>[5,3,7,4,1,6,2,8]=>1011010=>[1,1,2,1,1,1]
[7,5,2,6,3,8,1,4]=>[2,4,7,3,6,1,8,5]=>0010101=>[2,1,1,1,1,1]
[4,1,2,3,6,8,7,5]=>[5,8,7,6,3,1,2,4]=>0111100=>[1,4,2]
[2,4,3,1,8,5,6,7]=>[7,5,6,8,1,4,3,2]=>1001011=>[1,2,1,1,2]
[7,5,2,8,3,4,6,1]=>[2,4,7,1,6,5,3,8]=>0010110=>[2,1,1,2,1]
[5,6,2,8,4,3,1,7]=>[4,3,7,1,5,6,8,2]=>1010001=>[1,1,1,3,1]
[4,7,2,8,1,5,3,6]=>[5,2,7,1,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[8,7,2,1,4,5,6,3]=>[1,2,7,8,5,4,3,6]=>0001110=>[3,3,1]
[3,6,8,7,1,5,4,2]=>[6,3,1,2,8,4,5,7]=>1100100=>[2,2,1,2]
[5,7,8,6,3,4,1,2]=>[4,2,1,3,6,5,8,7]=>1100101=>[2,2,1,1,1]
[7,1,8,5,4,3,6,2]=>[2,8,1,4,5,6,3,7]=>0100010=>[1,1,3,1,1]
[2,7,8,4,5,3,6,1]=>[7,2,1,5,4,6,3,8]=>1101010=>[2,1,1,1,1,1]
[5,7,3,8,1,4,6,2]=>[4,2,6,1,8,5,3,7]=>1010110=>[1,1,1,1,2,1]
[2,1,7,8,5,4,6,3]=>[7,8,2,1,4,5,3,6]=>0110010=>[1,2,2,1,1]
[2,1,5,8,4,6,3,7]=>[7,8,4,1,5,3,6,2]=>0110101=>[1,2,1,1,1,1]
[6,5,3,8,4,1,2,7]=>[3,4,6,1,5,8,7,2]=>0010011=>[2,1,2,2]
[7,5,8,4,3,6,2,1]=>[2,4,1,5,6,3,7,8]=>0100100=>[1,1,2,1,2]
[2,4,8,3,5,6,1,7]=>[7,5,1,6,4,3,8,2]=>1101101=>[2,1,2,1,1]
[4,1,8,3,6,5,2,7]=>[5,8,1,6,3,4,7,2]=>0101001=>[1,1,1,1,2,1]
[3,4,8,1,7,2,5,6]=>[6,5,1,8,2,7,4,3]=>1101011=>[2,1,1,1,2]
[8,4,1,3,7,2,6,5]=>[1,5,8,6,2,7,3,4]=>0011010=>[2,2,1,1,1]
[3,1,8,2,4,7,6,5]=>[6,8,1,7,5,2,3,4]=>0101100=>[1,1,1,2,2]
[2,3,8,1,4,6,7,5]=>[7,6,1,8,5,3,2,4]=>1101110=>[2,1,3,1]
[4,3,8,2,5,1,7,6]=>[5,6,1,7,4,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[6,3,8,4,2,5,7,1]=>[3,6,1,5,7,4,2,8]=>0100110=>[1,1,2,2,1]
[7,4,3,8,2,5,1,6]=>[2,5,6,1,7,4,8,3]=>0010101=>[2,1,1,1,1,1]
[2,1,4,8,3,5,7,6]=>[7,8,5,1,6,4,2,3]=>0110110=>[1,2,1,2,1]
[6,8,2,4,3,5,1,7]=>[3,1,7,5,6,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,3,5,1,6,7]=>[5,1,7,6,4,8,3,2]=>1011011=>[1,1,2,1,2]
[3,8,2,1,4,6,5,7]=>[6,1,7,8,5,3,4,2]=>1001101=>[1,2,2,1,1]
[2,8,1,3,4,5,7,6]=>[7,1,8,6,5,4,2,3]=>1011110=>[1,1,4,1]
[2,8,4,1,6,5,3,7]=>[7,1,5,8,3,4,6,2]=>1001001=>[1,2,1,2,1]
[2,8,4,1,6,5,7,3]=>[7,1,5,8,3,4,2,6]=>1001010=>[1,2,1,1,1,1]
[2,8,7,6,1,4,3,5]=>[7,1,2,3,8,5,6,4]=>1000101=>[1,3,1,1,1]
[2,8,5,6,7,4,3,1]=>[7,1,4,3,2,5,6,8]=>1011000=>[1,1,2,3]
[7,5,8,6,1,4,2,3]=>[2,4,1,3,8,5,7,6]=>0100101=>[1,1,2,1,1,1]
[3,5,7,6,1,4,2,8]=>[6,4,2,3,8,5,7,1]=>1100101=>[2,2,1,1,1]
[3,5,7,2,4,1,6,8]=>[6,4,2,7,5,8,3,1]=>1101011=>[2,1,1,1,2]
[7,5,8,2,4,1,6,3]=>[2,4,1,7,5,8,3,6]=>0101010=>[1,1,1,1,1,1,1]
[2,8,5,3,4,7,6,1]=>[7,1,4,6,5,2,3,8]=>1001100=>[1,2,2,2]
[2,8,5,3,4,1,7,6]=>[7,1,4,6,5,8,2,3]=>1001010=>[1,2,1,1,1,1]
[2,8,5,3,4,1,6,7]=>[7,1,4,6,5,8,3,2]=>1001011=>[1,2,1,1,2]
[2,8,7,6,1,4,5,3]=>[7,1,2,3,8,5,4,6]=>1000110=>[1,3,2,1]
[2,8,5,3,6,1,7,4]=>[7,1,4,6,3,8,2,5]=>1001010=>[1,2,1,1,1,1]
[2,8,5,6,7,4,1,3]=>[7,1,4,3,2,5,8,6]=>1011001=>[1,1,2,2,1]
[2,8,5,3,4,7,1,6]=>[7,1,4,6,5,2,8,3]=>1001101=>[1,2,2,1,1]
[2,8,5,3,4,6,1,7]=>[7,1,4,6,5,3,8,2]=>1001101=>[1,2,2,1,1]
[2,8,5,3,4,6,7,1]=>[7,1,4,6,5,3,2,8]=>1001110=>[1,2,3,1]
[3,5,7,2,4,6,1,8]=>[6,4,2,7,5,3,8,1]=>1101101=>[2,1,2,1,1]
[6,5,2,7,3,1,4,8]=>[3,4,7,2,6,8,5,1]=>0010011=>[2,1,2,2]
[6,5,2,8,3,1,7,4]=>[3,4,7,1,6,8,2,5]=>0010010=>[2,1,2,1,1]
[6,5,2,8,3,1,4,7]=>[3,4,7,1,6,8,5,2]=>0010011=>[2,1,2,2]
[7,5,8,2,4,6,3,1]=>[2,4,1,7,5,3,6,8]=>0101100=>[1,1,1,2,2]
[7,5,8,6,1,4,3,2]=>[2,4,1,3,8,5,6,7]=>0100100=>[1,1,2,1,2]
[6,5,8,2,1,3,7,4]=>[3,4,1,7,8,6,2,5]=>0100110=>[1,1,2,2,1]
[3,5,6,2,1,8,7,4]=>[6,4,3,7,8,1,2,5]=>1100100=>[2,2,1,2]
[3,5,7,6,1,4,8,2]=>[6,4,2,3,8,5,1,7]=>1100110=>[2,2,2,1]
[3,5,7,2,4,1,8,6]=>[6,4,2,7,5,8,1,3]=>1101010=>[2,1,1,1,1,1]
[3,5,7,2,4,6,8,1]=>[6,4,2,7,5,3,1,8]=>1101110=>[2,1,3,1]
[6,5,2,7,3,1,8,4]=>[3,4,7,2,6,8,1,5]=>0010010=>[2,1,2,1,1]
[4,5,2,6,3,1,7,8]=>[5,4,7,3,6,8,2,1]=>1010011=>[1,1,1,2,2]
[4,1,2,3,7,6,8,5]=>[5,8,7,6,2,3,1,4]=>0111010=>[1,3,1,1,1]
[6,5,2,7,3,4,8,1]=>[3,4,7,2,6,5,1,8]=>0010110=>[2,1,1,2,1]
[5,1,6,7,4,3,8,2]=>[4,8,3,2,5,6,1,7]=>0110010=>[1,2,2,1,1]
[5,1,2,6,4,8,7,3]=>[4,8,7,3,5,1,2,6]=>0110100=>[1,2,1,1,2]
[5,1,2,8,6,4,7,3]=>[4,8,7,1,3,5,2,6]=>0110010=>[1,2,2,1,1]
[5,1,6,8,7,3,4,2]=>[4,8,3,1,2,6,5,7]=>0110010=>[1,2,2,1,1]
[6,5,2,8,3,7,4,1]=>[3,4,7,1,6,2,5,8]=>0010100=>[2,1,1,1,2]
[4,1,2,3,8,7,5,6]=>[5,8,7,6,1,2,4,3]=>0111001=>[1,3,2,1]
[4,1,2,3,8,6,5,7]=>[5,8,7,6,1,3,4,2]=>0111001=>[1,3,2,1]
[4,1,2,3,8,6,7,5]=>[5,8,7,6,1,3,2,4]=>0111010=>[1,3,1,1,1]
[4,1,2,3,7,6,5,8]=>[5,8,7,6,2,3,4,1]=>0111001=>[1,3,2,1]
[4,1,2,3,8,5,7,6]=>[5,8,7,6,1,4,2,3]=>0111010=>[1,3,1,1,1]
[7,1,6,8,4,3,5,2]=>[2,8,3,1,5,6,4,7]=>0110010=>[1,2,2,1,1]
[6,1,2,8,4,5,7,3]=>[3,8,7,1,5,4,2,6]=>0110110=>[1,2,1,2,1]
[5,6,8,2,3,1,7,4]=>[4,3,1,7,6,8,2,5]=>1101010=>[2,1,1,1,1,1]
[6,5,8,2,4,3,1,7]=>[3,4,1,7,5,6,8,2]=>0101001=>[1,1,1,1,2,1]
[6,5,8,2,4,3,7,1]=>[3,4,1,7,5,6,2,8]=>0101010=>[1,1,1,1,1,1,1]
[7,5,2,8,3,4,1,6]=>[2,4,7,1,6,5,8,3]=>0010101=>[2,1,1,1,1,1]
[6,5,2,8,3,7,1,4]=>[3,4,7,1,6,2,8,5]=>0010101=>[2,1,1,1,1,1]
[6,5,2,7,3,4,1,8]=>[3,4,7,2,6,5,8,1]=>0010101=>[2,1,1,1,1,1]
[5,1,6,7,4,3,2,8]=>[4,8,3,2,5,6,7,1]=>0110001=>[1,2,3,1]
[5,1,6,8,7,3,2,4]=>[4,8,3,1,2,6,7,5]=>0110001=>[1,2,3,1]
[7,1,6,8,4,3,2,5]=>[2,8,3,1,5,6,7,4]=>0110001=>[1,2,3,1]
[5,7,8,6,3,4,2,1]=>[4,2,1,3,6,5,7,8]=>1100100=>[2,2,1,2]
[4,1,8,3,6,5,7,2]=>[5,8,1,6,3,4,2,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,3,6,2,7,5]=>[5,8,1,6,3,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,4,8,6,2,7,5]=>[6,8,5,1,3,7,2,4]=>0110010=>[1,2,2,1,1]
[3,1,4,8,6,5,2,7]=>[6,8,5,1,3,4,7,2]=>0110001=>[1,2,3,1]
[7,1,6,5,8,3,2,4]=>[2,8,3,4,1,6,7,5]=>0101001=>[1,1,1,1,2,1]
[4,1,6,7,8,3,2,5]=>[5,8,3,2,1,6,7,4]=>0111001=>[1,3,2,1]
[4,1,6,5,7,3,2,8]=>[5,8,3,4,2,6,7,1]=>0101001=>[1,1,1,1,2,1]
[4,5,2,6,3,7,1,8]=>[5,4,7,3,6,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,2,7,3,8,1,6]=>[5,4,7,2,6,1,8,3]=>1010101=>[1,1,1,1,1,1,1]
[3,5,6,2,4,8,7,1]=>[6,4,3,7,5,1,2,8]=>1101100=>[2,1,2,2]
[3,5,6,2,4,8,1,7]=>[6,4,3,7,5,1,8,2]=>1101101=>[2,1,2,1,1]
[3,7,5,6,8,4,1,2]=>[6,2,4,3,1,5,8,7]=>1011001=>[1,1,2,2,1]
[3,6,5,2,8,1,7,4]=>[6,3,4,7,1,8,2,5]=>1001010=>[1,2,1,1,1,1]
[6,1,2,5,8,4,7,3]=>[3,8,7,4,1,5,2,6]=>0111010=>[1,3,1,1,1]
[7,1,6,5,8,3,4,2]=>[2,8,3,4,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,2,6,3,8,4,1]=>[2,4,7,3,6,1,5,8]=>0010100=>[2,1,1,1,2]
[4,1,2,3,5,8,7,6]=>[5,8,7,6,4,1,2,3]=>0111100=>[1,4,2]
[4,1,2,3,7,8,6,5]=>[5,8,7,6,2,1,3,4]=>0111100=>[1,4,2]
[4,5,2,7,3,8,6,1]=>[5,4,7,2,6,1,3,8]=>1010100=>[1,1,1,1,1,2]
[4,1,6,7,8,3,5,2]=>[5,8,3,2,1,6,4,7]=>0111010=>[1,3,1,1,1]
[4,1,2,6,8,5,7,3]=>[5,8,7,3,1,4,2,6]=>0111010=>[1,3,1,1,1]
[4,1,2,5,6,8,7,3]=>[5,8,7,4,3,1,2,6]=>0111100=>[1,4,2]
[4,5,2,6,3,7,8,1]=>[5,4,7,3,6,2,1,8]=>1010110=>[1,1,1,1,2,1]
[7,8,5,6,1,4,3,2]=>[2,1,4,3,8,5,6,7]=>1010100=>[1,1,1,1,1,2]
[7,8,4,2,1,5,3,6]=>[2,1,5,7,8,4,6,3]=>1000101=>[1,3,1,1,1]
[7,8,2,1,6,5,3,4]=>[2,1,7,8,3,4,6,5]=>1001001=>[1,2,1,2,1]
[2,4,8,1,5,7,3,6]=>[7,5,1,8,4,2,6,3]=>1101101=>[2,1,2,1,1]
[4,3,8,1,7,2,5,6]=>[5,6,1,8,2,7,4,3]=>0101011=>[1,1,1,1,1,2]
[6,3,1,4,7,2,5,8]=>[3,6,8,5,2,7,4,1]=>0011011=>[2,2,1,2]
[7,8,3,4,5,1,6,2]=>[2,1,6,5,4,8,3,7]=>1011010=>[1,1,2,1,1,1]
[7,8,3,5,4,2,1,6]=>[2,1,6,4,5,7,8,3]=>1010001=>[1,1,1,3,1]
[7,8,4,1,2,3,6,5]=>[2,1,5,8,7,6,3,4]=>1001110=>[1,2,3,1]
[7,8,3,6,5,4,1,2]=>[2,1,6,3,4,5,8,7]=>1010001=>[1,1,1,3,1]
[7,8,2,1,5,3,4,6]=>[2,1,7,8,4,6,5,3]=>1001011=>[1,2,1,1,2]
[7,8,2,6,4,1,3,5]=>[2,1,7,3,5,8,6,4]=>1010011=>[1,1,1,2,2]
[7,8,2,5,6,4,1,3]=>[2,1,7,4,3,5,8,6]=>1011001=>[1,1,2,2,1]
[7,8,1,6,5,4,3,2]=>[2,1,8,3,4,5,6,7]=>1010000=>[1,1,1,4]
[6,2,1,7,5,4,3,8]=>[3,7,8,2,4,5,6,1]=>0010001=>[2,1,3,1]
[2,1,8,7,5,4,3,6]=>[7,8,1,2,4,5,6,3]=>0100001=>[1,1,4,1]
[1,3,8,2,6,4,7,5]=>[8,6,1,7,3,5,2,4]=>1101010=>[2,1,1,1,1,1]
[5,3,7,1,6,4,8,2]=>[4,6,2,8,3,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,2,7,4,1,8]=>[4,6,3,7,2,5,8,1]=>0101001=>[1,1,1,1,2,1]
[6,3,1,8,4,2,7,5]=>[3,6,8,1,5,7,2,4]=>0010010=>[2,1,2,1,1]
[6,4,2,1,5,3,8,7]=>[3,5,7,8,4,6,1,2]=>0001010=>[3,1,1,1,1]
[6,4,3,7,5,8,1,2]=>[3,5,6,2,4,1,8,7]=>0010101=>[2,1,1,1,1,1]
[4,3,8,7,5,6,1,2]=>[5,6,1,2,4,3,8,7]=>0100101=>[1,1,2,1,1,1]
[2,4,7,1,5,3,6,8]=>[7,5,2,8,4,6,3,1]=>1101011=>[2,1,1,1,2]
[2,1,7,5,6,8,4,3]=>[7,8,2,4,3,1,5,6]=>0101100=>[1,1,1,2,2]
[1,8,5,7,3,6,4,2]=>[8,1,4,2,6,3,5,7]=>1010100=>[1,1,1,1,1,2]
[1,5,6,8,2,4,7,3]=>[8,4,3,1,7,5,2,6]=>1110110=>[3,1,2,1]
[2,6,8,5,3,1,4,7]=>[7,3,1,4,6,8,5,2]=>1100011=>[2,3,2]
[5,6,7,3,8,4,1,2]=>[4,3,2,6,1,5,8,7]=>1101001=>[2,1,1,2,1]
[5,2,8,1,4,7,3,6]=>[4,7,1,8,5,2,6,3]=>0101101=>[1,1,1,2,1,1]
[4,5,6,7,2,8,1,3]=>[5,4,3,2,7,1,8,6]=>1110101=>[3,1,1,1,1]
[4,5,7,6,1,8,3,2]=>[5,4,2,3,8,1,6,7]=>1100100=>[2,2,1,2]
[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>1100101=>[2,2,1,1,1]
[1,6,5,8,3,2,7,4]=>[8,3,4,1,6,7,2,5]=>1010010=>[1,1,1,2,1,1]
[4,7,5,6,3,1,8,2]=>[5,2,4,3,6,8,1,7]=>1010010=>[1,1,1,2,1,1]
[5,1,6,3,4,2,8,7]=>[4,8,3,6,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,7,1,4,2,3,8,6]=>[4,2,8,5,7,6,1,3]=>1010110=>[1,1,1,1,2,1]
[5,7,6,4,3,8,1,2]=>[4,2,3,5,6,1,8,7]=>1000101=>[1,3,1,1,1]
[6,3,4,5,8,7,1,2]=>[3,6,5,4,1,2,8,7]=>0111001=>[1,3,2,1]
[6,2,4,1,8,3,7,5]=>[3,7,5,8,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[6,2,3,5,4,8,1,7]=>[3,7,6,4,5,1,8,2]=>0110101=>[1,2,1,1,1,1]
[6,1,3,4,5,8,7,2]=>[3,8,6,5,4,1,2,7]=>0111100=>[1,4,2]
[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>1011101=>[1,1,3,1,1]
[5,7,2,4,1,6,3,8]=>[4,2,7,5,8,3,6,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,5,8,1,4,3,2]=>[3,2,4,1,8,5,6,7]=>1010100=>[1,1,1,1,1,2]
[5,8,7,6,3,4,1,2]=>[4,1,2,3,6,5,8,7]=>1000101=>[1,3,1,1,1]
[5,8,7,6,2,3,1,4]=>[4,1,2,3,7,6,8,5]=>1000101=>[1,3,1,1,1]
[4,1,7,2,6,5,3,8]=>[5,8,2,7,3,4,6,1]=>0101001=>[1,1,1,1,2,1]
[4,8,2,1,5,6,3,7]=>[5,1,7,8,4,3,6,2]=>1001101=>[1,2,2,1,1]
[4,2,7,8,1,6,3,5]=>[5,7,2,1,8,3,6,4]=>0110101=>[1,2,1,1,1,1]
[2,1,8,7,6,5,3,4]=>[7,8,1,2,3,4,6,5]=>0100001=>[1,1,4,1]
[4,3,7,5,6,8,1,2]=>[5,6,2,4,3,1,8,7]=>0101101=>[1,1,1,2,1,1]
[3,8,5,6,1,4,7,2]=>[6,1,4,3,8,5,2,7]=>1010110=>[1,1,1,1,2,1]
[5,3,7,8,2,1,6,4]=>[4,6,2,1,7,8,3,5]=>0110010=>[1,2,2,1,1]
[5,2,8,7,1,6,4,3]=>[4,7,1,2,8,3,5,6]=>0100100=>[1,1,2,1,2]
[1,6,8,7,5,2,4,3]=>[8,3,1,2,4,7,5,6]=>1100010=>[2,3,1,1]
[3,6,7,8,5,1,4,2]=>[6,3,2,1,4,8,5,7]=>1110010=>[3,2,1,1]
[3,7,6,8,5,2,1,4]=>[6,2,3,1,4,7,8,5]=>1010001=>[1,1,1,3,1]
[4,1,8,6,2,3,5,7]=>[5,8,1,3,7,6,4,2]=>0100111=>[1,1,2,3]
[4,7,8,6,3,5,1,2]=>[5,2,1,3,6,4,8,7]=>1100101=>[2,2,1,1,1]
[3,8,7,6,5,4,1,2]=>[6,1,2,3,4,5,8,7]=>1000001=>[1,5,1]
[2,1,7,6,5,3,4,8]=>[7,8,2,3,4,6,5,1]=>0100011=>[1,1,3,2]
[2,8,1,6,4,5,3,7]=>[7,1,8,3,5,4,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,7,5,1,4,3,6]=>[7,1,2,4,8,5,6,3]=>1000101=>[1,3,1,1,1]
[2,7,8,6,5,4,1,3]=>[7,2,1,3,4,5,8,6]=>1100001=>[2,4,1]
[6,4,2,7,1,3,8,5]=>[3,5,7,2,8,6,1,4]=>0010110=>[2,1,1,2,1]
[7,4,2,5,1,3,8,6]=>[2,5,7,4,8,6,1,3]=>0010110=>[2,1,1,2,1]
[7,5,3,6,1,8,2,4]=>[2,4,6,3,8,1,7,5]=>0010101=>[2,1,1,1,1,1]
[7,3,6,2,4,8,1,5]=>[2,6,3,7,5,1,8,4]=>0101101=>[1,1,1,2,1,1]
[4,3,7,1,2,5,8,6]=>[5,6,2,8,7,4,1,3]=>0101110=>[1,1,1,3,1]
[3,6,2,7,1,4,8,5]=>[6,3,7,2,8,5,1,4]=>1010110=>[1,1,1,1,2,1]
[5,3,6,7,1,2,8,4]=>[4,6,3,2,8,7,1,5]=>0110110=>[1,2,1,2,1]
[6,3,7,4,1,2,8,5]=>[3,6,2,5,8,7,1,4]=>0100110=>[1,1,2,2,1]
[4,7,1,5,2,3,8,6]=>[5,2,8,4,7,6,1,3]=>1010110=>[1,1,1,1,2,1]
[3,7,5,1,2,4,8,6]=>[6,2,4,8,7,5,1,3]=>1001110=>[1,2,3,1]
[8,6,4,2,3,7,1,5]=>[1,3,5,7,6,2,8,4]=>0001101=>[3,2,1,1]
[5,7,4,2,3,8,1,6]=>[4,2,5,7,6,1,8,3]=>1001101=>[1,2,2,1,1]
[3,7,6,1,4,8,2,5]=>[6,2,3,8,5,1,7,4]=>1001101=>[1,2,2,1,1]
[5,7,2,6,1,8,3,4]=>[4,2,7,3,8,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,4,7,5,2,8,1,3]=>[3,5,2,4,7,1,8,6]=>0100101=>[1,1,2,1,1,1]
[7,4,8,5,2,6,1,3]=>[2,5,1,4,7,3,8,6]=>0100101=>[1,1,2,1,1,1]
[5,8,2,6,3,7,1,4]=>[4,1,7,3,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,6,1,2,7,4,5]=>[6,1,3,8,7,2,5,4]=>1001101=>[1,2,2,1,1]
[3,8,6,2,4,7,1,5]=>[6,1,3,7,5,2,8,4]=>1001101=>[1,2,2,1,1]
[6,8,4,3,7,1,2,5]=>[3,1,5,6,2,8,7,4]=>1001011=>[1,2,1,1,2]
[6,8,5,3,7,1,2,4]=>[3,1,4,6,2,8,7,5]=>1001011=>[1,2,1,1,2]
[3,8,5,7,1,2,4,6]=>[6,1,4,2,8,7,5,3]=>1010111=>[1,1,1,1,3]
[2,8,5,7,1,3,4,6]=>[7,1,4,2,8,6,5,3]=>1010111=>[1,1,1,1,3]
[2,7,6,4,8,1,3,5]=>[7,2,3,5,1,8,6,4]=>1001011=>[1,2,1,1,2]
[2,5,7,4,8,1,3,6]=>[7,4,2,5,1,8,6,3]=>1101011=>[2,1,1,1,2]
[5,4,6,7,2,8,1,3]=>[4,5,3,2,7,1,8,6]=>0110101=>[1,2,1,1,1,1]
[4,6,3,7,1,8,2,5]=>[5,3,6,2,8,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[3,5,7,1,4,8,2,6]=>[6,4,2,8,5,1,7,3]=>1101101=>[2,1,2,1,1]
[5,3,7,2,4,8,1,6]=>[4,6,2,7,5,1,8,3]=>0101101=>[1,1,1,2,1,1]
[7,4,6,3,8,1,2,5]=>[2,5,3,6,1,8,7,4]=>0101011=>[1,1,1,1,1,2]
[8,4,6,3,7,1,2,5]=>[1,5,3,6,2,8,7,4]=>0101011=>[1,1,1,1,1,2]
[8,4,1,6,7,2,3,5]=>[1,5,8,3,2,7,6,4]=>0011011=>[2,2,1,2]
[5,4,1,7,8,2,3,6]=>[4,5,8,2,1,7,6,3]=>0011011=>[2,2,1,2]
[6,5,3,7,1,8,2,4]=>[3,4,6,2,8,1,7,5]=>0010101=>[2,1,1,1,1,1]
[6,5,1,2,7,8,3,4]=>[3,4,8,7,2,1,6,5]=>0011101=>[2,3,1,1]
[5,3,6,4,7,8,1,2]=>[4,6,3,5,2,1,8,7]=>0101101=>[1,1,1,2,1,1]
[6,3,7,4,8,5,1,2]=>[3,6,2,5,1,4,8,7]=>0101001=>[1,1,1,1,2,1]
[4,7,1,5,8,6,2,3]=>[5,2,8,4,1,3,7,6]=>1011001=>[1,1,2,2,1]
[7,5,1,2,8,6,3,4]=>[2,4,8,7,1,3,6,5]=>0011001=>[2,2,2,1]
[7,5,3,8,1,6,2,4]=>[2,4,6,1,8,3,7,5]=>0010101=>[2,1,1,1,1,1]
[8,6,1,7,5,2,3,4]=>[1,3,8,2,4,7,6,5]=>0010011=>[2,1,2,2]
[5,7,2,8,1,6,3,4]=>[4,2,7,1,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,3,7,8,5,1,2,4]=>[3,6,2,1,4,8,7,5]=>0110011=>[1,2,2,2]
[3,6,8,2,7,1,4,5]=>[6,3,1,7,2,8,5,4]=>1101011=>[2,1,1,1,2]
[2,4,8,7,1,3,5,6]=>[7,5,1,2,8,6,4,3]=>1100111=>[2,2,3]
[4,3,8,7,1,2,5,6]=>[5,6,1,2,8,7,4,3]=>0100111=>[1,1,2,3]
[8,4,7,6,1,2,3,5]=>[1,5,2,3,8,7,6,4]=>0100111=>[1,1,2,3]
[5,4,8,7,1,2,3,6]=>[4,5,1,2,8,7,6,3]=>0100111=>[1,1,2,3]
[3,5,8,7,1,2,4,6]=>[6,4,1,2,8,7,5,3]=>1100111=>[2,2,3]
[4,6,8,2,7,1,3,5]=>[5,3,1,7,2,8,6,4]=>1101011=>[2,1,1,1,2]
[4,7,1,8,6,2,3,5]=>[5,2,8,1,3,7,6,4]=>1010011=>[1,1,1,2,2]
[7,5,8,6,4,1,2,3]=>[2,4,1,3,5,8,7,6]=>0100011=>[1,1,3,2]
[6,8,4,7,5,1,2,3]=>[3,1,5,2,4,8,7,6]=>1010011=>[1,1,1,2,2]
[2,8,7,6,1,3,4,5]=>[7,1,2,3,8,6,5,4]=>1000111=>[1,3,3]
[3,8,7,6,1,2,4,5]=>[6,1,2,3,8,7,5,4]=>1000111=>[1,3,3]
[4,8,7,6,1,2,3,5]=>[5,1,2,3,8,7,6,4]=>1000111=>[1,3,3]
[5,6,3,1,4,2,8,7]=>[4,3,6,8,5,7,1,2]=>1001010=>[1,2,1,1,1,1]
[7,5,3,8,2,1,6,4]=>[2,4,6,1,7,8,3,5]=>0010010=>[2,1,2,1,1]
[3,8,7,4,5,1,6,2]=>[6,1,2,5,4,8,3,7]=>1001010=>[1,2,1,1,1,1]
[6,7,1,4,5,8,2,3]=>[3,2,8,5,4,1,7,6]=>1011101=>[1,1,3,1,1]
[2,1,7,8,5,3,6,4]=>[7,8,2,1,4,6,3,5]=>0110010=>[1,2,2,1,1]
[5,7,3,8,1,2,6,4]=>[4,2,6,1,8,7,3,5]=>1010110=>[1,1,1,1,2,1]
[8,7,1,4,5,3,2,6]=>[1,2,8,5,4,6,7,3]=>0011001=>[2,2,2,1]
[2,7,8,4,1,6,5,3]=>[7,2,1,5,8,3,4,6]=>1100100=>[2,2,1,2]
[7,1,8,4,2,6,5,3]=>[2,8,1,5,7,3,4,6]=>0100100=>[1,1,2,1,2]
[7,5,1,4,8,6,3,2]=>[2,4,8,5,1,3,6,7]=>0011000=>[2,2,3]
[6,5,3,1,8,4,7,2]=>[3,4,6,8,1,5,2,7]=>0001010=>[3,1,1,1,1]
[6,4,3,8,1,5,7,2]=>[3,5,6,1,8,4,2,7]=>0010110=>[2,1,1,2,1]
[8,6,3,1,2,5,7,4]=>[1,3,6,8,7,4,2,5]=>0001110=>[3,3,1]
[8,7,1,4,2,6,5,3]=>[1,2,8,5,7,3,4,6]=>0010100=>[2,1,1,1,2]
[7,3,8,4,1,6,5,2]=>[2,6,1,5,8,3,4,7]=>0100100=>[1,1,2,1,2]
[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,9,1]=>11111101=>[6,1,1]
[2,3,4,5,6,8,9,1,7]=>[8,7,6,5,4,2,1,9,3]=>11111101=>[6,1,1]
[2,3,4,5,7,8,9,1,6]=>[8,7,6,5,3,2,1,9,4]=>11111101=>[6,1,1]
[2,3,4,6,7,8,9,1,5]=>[8,7,6,4,3,2,1,9,5]=>11111101=>[6,1,1]
[2,3,5,6,7,8,9,1,4]=>[8,7,5,4,3,2,1,9,6]=>11111101=>[6,1,1]
[2,4,5,6,7,8,9,1,3]=>[8,6,5,4,3,2,1,9,7]=>11111101=>[6,1,1]
[3,4,5,6,7,8,9,1,2]=>[7,6,5,4,3,2,1,9,8]=>11111101=>[6,1,1]
[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]=>111111110=>[8,1]
[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,10,1]=>111111101=>[7,1,1]
[2,3,4,5,6,7,1,8,9]=>[8,7,6,5,4,3,9,2,1]=>11111011=>[5,1,2]
[2,3,4,5,6,7,8,10,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101=>[7,1,1]
[2,3,4,5,6,1,9,7,8]=>[8,7,6,5,4,9,1,3,2]=>11110101=>[4,1,1,1,1]
[2,3,4,5,6,7,9,10,1,8]=>[9,8,7,6,5,4,2,1,10,3]=>111111101=>[7,1,1]
[2,3,4,5,1,8,9,6,7]=>[8,7,6,5,9,2,1,4,3]=>11101101=>[3,1,2,1,1]
[2,3,4,5,6,8,9,10,1,7]=>[9,8,7,6,5,3,2,1,10,4]=>111111101=>[7,1,1]
[2,3,4,1,7,8,9,5,6]=>[8,7,6,9,3,2,1,5,4]=>11011101=>[2,1,3,1,1]
[2,3,4,5,7,8,9,10,1,6]=>[9,8,7,6,4,3,2,1,10,5]=>111111101=>[7,1,1]
[2,3,1,6,7,8,9,4,5]=>[8,7,9,4,3,2,1,6,5]=>10111101=>[1,1,4,1,1]
[2,3,4,6,7,8,9,10,1,5]=>[9,8,7,5,4,3,2,1,10,6]=>111111101=>[7,1,1]
[2,1,5,6,7,8,9,3,4]=>[8,9,5,4,3,2,1,7,6]=>01111101=>[1,5,1,1]
[2,3,5,6,7,8,9,10,1,4]=>[9,8,6,5,4,3,2,1,10,7]=>111111101=>[7,1,1]
[1,4,5,6,7,8,9,2,3]=>[9,6,5,4,3,2,1,8,7]=>11111101=>[6,1,1]
[2,4,5,6,7,8,9,10,1,3]=>[9,7,6,5,4,3,2,1,10,8]=>111111101=>[7,1,1]
[3,4,5,6,7,8,9,10,1,2]=>[8,7,6,5,4,3,2,1,10,9]=>111111101=>[7,1,1]
[3,6,4,5,7,2,8,1]=>[6,3,5,4,2,7,1,8]=>1011010=>[1,1,2,1,1,1]
[5,3,2,7,4,6,8,1]=>[4,6,7,2,5,3,1,8]=>0010110=>[2,1,1,2,1]
[7,5,3,6,2,4,8,1]=>[2,4,6,3,7,5,1,8]=>0010110=>[2,1,1,2,1]
[8,5,3,6,2,7,1,4]=>[1,4,6,3,7,2,8,5]=>0010101=>[2,1,1,1,1,1]
[8,2,6,3,4,7,1,5]=>[1,7,3,6,5,2,8,4]=>0101101=>[1,1,1,2,1,1]
[7,2,6,3,4,5,8,1]=>[2,7,3,6,5,4,1,8]=>0101110=>[1,1,1,3,1]
[6,2,7,3,4,5,8,1]=>[3,7,2,6,5,4,1,8]=>0101110=>[1,1,1,3,1]
[3,6,2,7,4,5,8,1]=>[6,3,7,2,5,4,1,8]=>1010110=>[1,1,1,1,2,1]
[4,2,5,7,3,6,8,1]=>[5,7,4,2,6,3,1,8]=>0110110=>[1,2,1,2,1]
[5,4,7,6,2,3,8,1]=>[4,5,2,3,7,6,1,8]=>0100110=>[1,1,2,2,1]
[6,7,3,5,2,4,8,1]=>[3,2,6,4,7,5,1,8]=>1010110=>[1,1,1,1,2,1]
[3,7,6,2,4,5,8,1]=>[6,2,3,7,5,4,1,8]=>1001110=>[1,2,3,1]
[2,7,6,3,4,5,8,1]=>[7,2,3,6,5,4,1,8]=>1001110=>[1,2,3,1]
[6,5,3,1,2,8,4,7]=>[3,4,6,8,7,1,5,2]=>0001101=>[3,2,1,1]
[8,6,5,2,3,7,1,4]=>[1,3,4,7,6,2,8,5]=>0001101=>[3,2,1,1]
[7,5,2,1,8,3,4,6]=>[2,4,7,8,1,6,5,3]=>0001011=>[3,1,1,2]
[1,6,3,2,8,4,5,7]=>[8,3,6,7,1,5,4,2]=>1001011=>[1,2,1,1,2]
[5,7,3,1,2,8,4,6]=>[4,2,6,8,7,1,5,3]=>1001101=>[1,2,2,1,1]
[5,6,2,3,1,8,4,7]=>[4,3,7,6,8,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[4,2,6,5,1,8,3,7]=>[5,7,3,4,8,1,6,2]=>0100101=>[1,1,2,1,1,1]
[5,4,8,6,2,7,1,3]=>[4,5,1,3,7,2,8,6]=>0100101=>[1,1,2,1,1,1]
[6,8,3,5,2,7,1,4]=>[3,1,6,4,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,2,3,6,1,4]=>[2,1,4,7,6,3,8,5]=>1001101=>[1,2,2,1,1]
[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>1001011=>[1,2,1,1,2]
[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>1010111=>[1,1,1,1,3]
[2,8,1,7,3,4,5,6]=>[7,1,8,2,6,5,4,3]=>1010111=>[1,1,1,1,3]
[4,8,1,5,7,2,3,6]=>[5,1,8,4,2,7,6,3]=>1011011=>[1,1,2,1,2]
[4,2,8,3,7,1,5,6]=>[5,7,1,6,2,8,4,3]=>0101011=>[1,1,1,1,1,2]
[4,1,7,5,8,2,3,6]=>[5,8,2,4,1,7,6,3]=>0101011=>[1,1,1,1,1,2]
[8,1,2,7,3,4,5,6]=>[1,8,7,2,6,5,4,3]=>0110111=>[1,2,1,3]
[3,6,2,7,1,8,4,5]=>[6,3,7,2,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[6,3,7,1,2,8,4,5]=>[3,6,2,8,7,1,5,4]=>0101101=>[1,1,1,2,1,1]
[7,2,6,1,8,3,4,5]=>[2,7,3,8,1,6,5,4]=>0101011=>[1,1,1,1,1,2]
[7,3,1,5,8,2,4,6]=>[2,6,8,4,1,7,5,3]=>0011011=>[2,2,1,2]
[3,2,1,5,8,4,6,7]=>[6,7,8,4,1,5,3,2]=>0011011=>[2,2,1,2]
[1,5,3,4,6,8,2,7]=>[8,4,6,5,3,1,7,2]=>1011101=>[1,1,3,1,1]
[5,4,6,3,8,7,1,2]=>[4,5,3,6,1,2,8,7]=>0101001=>[1,1,1,1,2,1]
[3,6,4,5,8,7,1,2]=>[6,3,5,4,1,2,8,7]=>1011001=>[1,1,2,2,1]
[6,5,3,4,8,7,1,2]=>[3,4,6,5,1,2,8,7]=>0011001=>[2,2,2,1]
[5,3,2,8,7,1,4,6]=>[4,6,7,1,2,8,5,3]=>0010011=>[2,1,2,2]
[5,3,1,8,7,2,4,6]=>[4,6,8,1,2,7,5,3]=>0010011=>[2,1,2,2]
[8,5,3,7,6,1,2,4]=>[1,4,6,2,3,8,7,5]=>0010011=>[2,1,2,2]
[6,1,8,3,7,2,4,5]=>[3,8,1,6,2,7,5,4]=>0101011=>[1,1,1,1,1,2]
[6,3,8,1,7,2,4,5]=>[3,6,1,8,2,7,5,4]=>0101011=>[1,1,1,1,1,2]
[7,6,8,2,3,5,1,4]=>[2,3,1,7,6,4,8,5]=>0101101=>[1,1,1,2,1,1]
[3,7,8,2,4,6,1,5]=>[6,2,1,7,5,3,8,4]=>1101101=>[2,1,2,1,1]
[6,7,3,8,2,5,1,4]=>[3,2,6,1,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,4,7,8,2,6,1,3]=>[4,5,2,1,7,3,8,6]=>0110101=>[1,2,1,1,1,1]
[4,2,5,8,7,1,3,6]=>[5,7,4,1,2,8,6,3]=>0110011=>[1,2,2,2]
[3,6,2,8,7,1,4,5]=>[6,3,7,1,2,8,5,4]=>1010011=>[1,1,1,2,2]
[2,3,8,7,1,4,5,6]=>[7,6,1,2,8,5,4,3]=>1100111=>[2,2,3]
[7,2,8,6,1,3,4,5]=>[2,7,1,3,8,6,5,4]=>0100111=>[1,1,2,3]
[2,1,8,7,3,4,5,6]=>[7,8,1,2,6,5,4,3]=>0100111=>[1,1,2,3]
[8,2,7,6,1,3,4,5]=>[1,7,2,3,8,6,5,4]=>0100111=>[1,1,2,3]
[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>1100111=>[2,2,3]
[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>1100111=>[2,2,3]
[1,7,8,3,6,2,4,5]=>[8,2,1,6,3,7,5,4]=>1101011=>[2,1,1,1,2]
[4,1,5,8,7,2,3,6]=>[5,8,4,1,2,7,6,3]=>0110011=>[1,2,2,2]
[5,4,8,7,6,1,2,3]=>[4,5,1,2,3,8,7,6]=>0100011=>[1,1,3,2]
[6,8,3,7,5,1,2,4]=>[3,1,6,2,4,8,7,5]=>1010011=>[1,1,1,2,2]
[7,8,6,2,5,1,3,4]=>[2,1,3,7,4,8,6,5]=>1001011=>[1,2,1,1,2]
[8,1,6,7,3,2,5,4]=>[1,8,3,2,6,7,4,5]=>0110010=>[1,2,2,1,1]
[8,1,6,7,3,2,4,5]=>[1,8,3,2,6,7,5,4]=>0110011=>[1,2,2,2]
[8,1,5,3,7,2,4,6]=>[1,8,4,6,2,7,5,3]=>0101011=>[1,1,1,1,1,2]
[8,1,5,3,6,2,4,7]=>[1,8,4,6,3,7,5,2]=>0101011=>[1,1,1,1,1,2]
[7,5,1,3,6,2,4,8]=>[2,4,8,6,3,7,5,1]=>0011011=>[2,2,1,2]
[7,5,8,3,6,2,4,1]=>[2,4,1,6,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[7,4,8,3,2,6,5,1]=>[2,5,1,6,7,3,4,8]=>0100100=>[1,1,2,1,2]
[7,4,1,3,2,6,5,8]=>[2,5,8,6,7,3,4,1]=>0010101=>[2,1,1,1,1,1]
[8,1,4,3,2,6,5,7]=>[1,8,5,6,7,3,4,2]=>0100101=>[1,1,2,1,1,1]
[8,1,4,3,2,7,5,6]=>[1,8,5,6,7,2,4,3]=>0100101=>[1,1,2,1,1,1]
[8,1,4,3,2,7,6,5]=>[1,8,5,6,7,2,3,4]=>0100100=>[1,1,2,1,2]
[8,1,5,4,6,7,2,3]=>[1,8,4,5,3,2,7,6]=>0101101=>[1,1,1,2,1,1]
[8,1,5,3,6,2,7,4]=>[1,8,4,6,3,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,3,2,6,7,5]=>[1,8,5,6,7,3,2,4]=>0100110=>[1,1,2,2,1]
[8,1,4,3,2,5,7,6]=>[1,8,5,6,7,4,2,3]=>0100110=>[1,1,2,2,1]
[8,1,4,3,2,5,6,7]=>[1,8,5,6,7,4,3,2]=>0100111=>[1,1,2,3]
[7,4,1,3,2,5,6,8]=>[2,5,8,6,7,4,3,1]=>0010111=>[2,1,1,3]
[7,4,8,3,2,5,6,1]=>[2,5,1,6,7,4,3,8]=>0100110=>[1,1,2,2,1]
[6,4,3,8,2,5,7,1]=>[3,5,6,1,7,4,2,8]=>0010110=>[2,1,1,2,1]
[6,4,3,1,2,5,8,7]=>[3,5,6,8,7,4,1,2]=>0001110=>[3,3,1]
[7,4,1,3,2,5,8,6]=>[2,5,8,6,7,4,1,3]=>0010110=>[2,1,1,2,1]
[7,4,1,3,2,6,8,5]=>[2,5,8,6,7,3,1,4]=>0010110=>[2,1,1,2,1]
[7,5,1,3,6,2,8,4]=>[2,4,8,6,3,7,1,5]=>0011010=>[2,2,1,1,1]
[7,5,1,4,6,8,2,3]=>[2,4,8,5,3,1,7,6]=>0011101=>[2,3,1,1]
[7,5,8,3,6,2,1,4]=>[2,4,1,6,3,7,8,5]=>0101001=>[1,1,1,1,2,1]
[7,4,8,3,2,6,1,5]=>[2,5,1,6,7,3,8,4]=>0100101=>[1,1,2,1,1,1]
[7,4,8,3,2,5,1,6]=>[2,5,1,6,7,4,8,3]=>0100101=>[1,1,2,1,1,1]
[6,4,3,8,2,5,1,7]=>[3,5,6,1,7,4,8,2]=>0010101=>[2,1,1,1,1,1]
[6,4,3,7,2,5,8,1]=>[3,5,6,2,7,4,1,8]=>0010110=>[2,1,1,2,1]
[5,4,3,2,8,6,1,7]=>[4,5,6,7,1,3,8,2]=>0001001=>[3,1,2,1]
[5,4,3,2,8,7,1,6]=>[4,5,6,7,1,2,8,3]=>0001001=>[3,1,2,1]
[6,5,3,8,7,2,1,4]=>[3,4,6,1,2,7,8,5]=>0010001=>[2,1,3,1]
[6,5,4,8,7,1,2,3]=>[3,4,5,1,2,8,7,6]=>0010011=>[2,1,2,2]
[6,5,4,1,7,8,2,3]=>[3,4,5,8,2,1,7,6]=>0001101=>[3,2,1,1]
[6,5,3,1,7,2,8,4]=>[3,4,6,8,2,7,1,5]=>0001010=>[3,1,1,1,1]
[6,4,3,1,2,7,8,5]=>[3,5,6,8,7,2,1,4]=>0001110=>[3,3,1]
[5,4,3,2,1,8,6,7]=>[4,5,6,7,8,1,3,2]=>0000101=>[4,1,1,1]
[6,5,3,1,8,2,7,4]=>[3,4,6,8,1,7,2,5]=>0001010=>[3,1,1,1,1]
[6,5,4,1,8,7,2,3]=>[3,4,5,8,1,2,7,6]=>0001001=>[3,1,2,1]
[7,5,1,4,8,6,2,3]=>[2,4,8,5,1,3,7,6]=>0011001=>[2,2,2,1]
[7,4,1,3,2,8,6,5]=>[2,5,8,6,7,1,3,4]=>0010100=>[2,1,1,1,2]
[7,4,1,3,2,8,5,6]=>[2,5,8,6,7,1,4,3]=>0010101=>[2,1,1,1,1,1]
[6,4,3,1,2,8,5,7]=>[3,5,6,8,7,1,4,2]=>0001101=>[3,2,1,1]
[6,4,3,1,2,7,5,8]=>[3,5,6,8,7,2,4,1]=>0001101=>[3,2,1,1]
[6,4,3,8,2,7,5,1]=>[3,5,6,1,7,2,4,8]=>0010100=>[2,1,1,1,2]
[6,5,3,8,7,2,4,1]=>[3,4,6,1,2,7,5,8]=>0010010=>[2,1,2,1,1]
[6,5,3,1,7,2,4,8]=>[3,4,6,8,2,7,5,1]=>0001011=>[3,1,1,2]
[6,5,3,1,8,2,4,7]=>[3,4,6,8,1,7,5,2]=>0001011=>[3,1,1,2]
[7,5,1,3,8,2,4,6]=>[2,4,8,6,1,7,5,3]=>0011011=>[2,2,1,2]
[7,6,1,8,3,2,4,5]=>[2,3,8,1,6,7,5,4]=>0010011=>[2,1,2,2]
[7,6,1,8,4,5,2,3]=>[2,3,8,1,5,4,7,6]=>0010101=>[2,1,1,1,1,1]
[7,6,8,1,4,5,2,3]=>[2,3,1,8,5,4,7,6]=>0101101=>[1,1,1,2,1,1]
[7,6,8,1,3,2,5,4]=>[2,3,1,8,6,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[6,5,3,7,8,2,4,1]=>[3,4,6,2,1,7,5,8]=>0011010=>[2,2,1,1,1]
[6,4,3,7,2,8,5,1]=>[3,5,6,2,7,1,4,8]=>0010100=>[2,1,1,1,2]
[6,4,3,7,2,1,5,8]=>[3,5,6,2,7,8,4,1]=>0010011=>[2,1,2,2]
[7,4,8,3,2,1,5,6]=>[2,5,1,6,7,8,4,3]=>0100011=>[1,1,3,2]
[7,4,8,3,2,1,6,5]=>[2,5,1,6,7,8,3,4]=>0100010=>[1,1,3,1,1]
[7,5,8,3,1,2,6,4]=>[2,4,1,6,8,7,3,5]=>0100110=>[1,1,2,2,1]
[7,5,8,4,1,6,2,3]=>[2,4,1,5,8,3,7,6]=>0100101=>[1,1,2,1,1,1]
[6,5,4,8,1,7,2,3]=>[3,4,5,1,8,2,7,6]=>0010101=>[2,1,1,1,1,1]
[6,5,3,8,1,2,7,4]=>[3,4,6,1,8,7,2,5]=>0010110=>[2,1,1,2,1]
[5,4,3,2,8,1,7,6]=>[4,5,6,7,1,8,2,3]=>0001010=>[3,1,1,1,1]
[6,4,3,7,2,1,8,5]=>[3,5,6,2,7,8,1,4]=>0010010=>[2,1,2,1,1]
[6,5,3,7,1,2,8,4]=>[3,4,6,2,8,7,1,5]=>0010110=>[2,1,1,2,1]
[6,5,4,7,1,8,2,3]=>[3,4,5,2,8,1,7,6]=>0010101=>[2,1,1,1,1,1]
[6,5,3,7,8,2,1,4]=>[3,4,6,2,1,7,8,5]=>0011001=>[2,2,2,1]
[6,4,3,7,2,8,1,5]=>[3,5,6,2,7,1,8,4]=>0010101=>[2,1,1,1,1,1]
[5,4,3,2,7,8,1,6]=>[4,5,6,7,2,1,8,3]=>0001101=>[3,2,1,1]
[5,4,3,2,6,8,1,7]=>[4,5,6,7,3,1,8,2]=>0001101=>[3,2,1,1]
[5,6,2,1,3,4,8,7]=>[4,3,7,8,6,5,1,2]=>1001110=>[1,2,3,1]
[5,8,2,7,4,1,3,6]=>[4,1,7,2,5,8,6,3]=>1010011=>[1,1,1,2,2]
[5,3,7,8,2,1,4,6]=>[4,6,2,1,7,8,5,3]=>0110011=>[1,2,2,2]
[7,6,1,2,5,8,3,4]=>[2,3,8,7,4,1,6,5]=>0011101=>[2,3,1,1]
[2,1,7,8,4,3,5,6]=>[7,8,2,1,5,6,4,3]=>0110011=>[1,2,2,2]
[8,3,7,4,1,5,6,2]=>[1,6,2,5,8,4,3,7]=>0100110=>[1,1,2,2,1]
[7,8,1,2,5,4,6,3]=>[2,1,8,7,4,5,3,6]=>1011010=>[1,1,2,1,1,1]
[2,6,8,3,1,4,7,5]=>[7,3,1,6,8,5,2,4]=>1100110=>[2,2,2,1]
[6,1,8,3,2,4,5,7]=>[3,8,1,6,7,5,4,2]=>0100111=>[1,1,2,3]
[8,4,1,3,7,6,2,5]=>[1,5,8,6,2,3,7,4]=>0011001=>[2,2,2,1]
[5,8,7,4,2,1,6,3]=>[4,1,2,5,7,8,3,6]=>1000010=>[1,4,1,1]
[7,5,1,6,8,3,4,2]=>[2,4,8,3,1,6,5,7]=>0011010=>[2,2,1,1,1]
[6,5,2,1,8,7,4,3]=>[3,4,7,8,1,2,5,6]=>0001000=>[3,1,3]
[4,7,2,8,1,3,6,5]=>[5,2,7,1,8,6,3,4]=>1010110=>[1,1,1,1,2,1]
[7,3,8,6,1,2,5,4]=>[2,6,1,3,8,7,4,5]=>0100110=>[1,1,2,2,1]
[3,4,7,1,8,2,6,5]=>[6,5,2,8,1,7,3,4]=>1101010=>[2,1,1,1,1,1]
[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>1010111=>[1,1,1,1,3]
[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>1010111=>[1,1,1,1,3]
[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>1010111=>[1,1,1,1,3]
[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>1010111=>[1,1,1,1,3]
[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>1010111=>[1,1,1,1,3]
[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>1010111=>[1,1,1,1,3]
[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>1010111=>[1,1,1,1,3]
[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>1010111=>[1,1,1,1,3]
[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>1010111=>[1,1,1,1,3]
[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,8,3,5,4,6]=>[8,2,7,1,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>1110101=>[3,1,1,1,1]
[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>1110101=>[3,1,1,1,1]
[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,5,3,6,4,7]=>[8,1,7,4,6,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,5,3,6,4,8]=>[8,2,7,4,6,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>1011101=>[1,1,3,1,1]
[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>1011101=>[1,1,3,1,1]
[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>1011101=>[1,1,3,1,1]
[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>1110101=>[3,1,1,1,1]
[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,8,3,7,4,6]=>[8,4,7,1,6,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,7,2,5,1,8]=>[5,3,6,2,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,7,5,2,1,8]=>[5,3,6,2,4,7,8,1]=>1010001=>[1,1,1,3,1]
[4,6,3,8,5,1,7,2]=>[5,3,6,1,4,8,2,7]=>1010010=>[1,1,1,2,1,1]
[4,6,3,8,5,1,2,7]=>[5,3,6,1,4,8,7,2]=>1010011=>[1,1,1,2,2]
[5,6,8,3,4,1,2,7]=>[4,3,1,6,5,8,7,2]=>1101011=>[2,1,1,1,2]
[5,6,8,3,4,1,7,2]=>[4,3,1,6,5,8,2,7]=>1101010=>[2,1,1,1,1,1]
[4,6,2,7,5,3,1,8]=>[5,3,7,2,4,6,8,1]=>1010001=>[1,1,1,3,1]
[5,6,7,2,4,3,1,8]=>[4,3,2,7,5,6,8,1]=>1101001=>[2,1,1,2,1]
[5,6,8,4,3,1,7,2]=>[4,3,1,5,6,8,2,7]=>1100010=>[2,3,1,1]
[5,6,8,4,3,1,2,7]=>[4,3,1,5,6,8,7,2]=>1100011=>[2,3,2]
[5,7,8,4,1,6,2,3]=>[4,2,1,5,8,3,7,6]=>1100101=>[2,2,1,1,1]
[5,7,8,4,1,6,3,2]=>[4,2,1,5,8,3,6,7]=>1100100=>[2,2,1,2]
[5,7,8,4,1,3,6,2]=>[4,2,1,5,8,6,3,7]=>1100110=>[2,2,2,1]
[5,6,8,4,2,1,7,3]=>[4,3,1,5,7,8,2,6]=>1100010=>[2,3,1,1]
[5,6,8,2,4,1,7,3]=>[4,3,1,7,5,8,2,6]=>1101010=>[2,1,1,1,1,1]
[4,6,2,8,5,1,7,3]=>[5,3,7,1,4,8,2,6]=>1010010=>[1,1,1,2,1,1]
[3,2,6,8,5,1,7,4]=>[6,7,3,1,4,8,2,5]=>0110010=>[1,2,2,1,1]
[3,2,6,8,5,1,4,7]=>[6,7,3,1,4,8,5,2]=>0110011=>[1,2,2,2]
[4,6,2,8,5,1,3,7]=>[5,3,7,1,4,8,6,2]=>1010011=>[1,1,1,2,2]
[5,6,8,2,4,1,3,7]=>[4,3,1,7,5,8,6,2]=>1101011=>[2,1,1,1,2]
[5,6,8,4,2,1,3,7]=>[4,3,1,5,7,8,6,2]=>1100011=>[2,3,2]
[5,7,8,4,1,3,2,6]=>[4,2,1,5,8,6,7,3]=>1100101=>[2,2,1,1,1]
[5,7,8,4,1,2,6,3]=>[4,2,1,5,8,7,3,6]=>1100110=>[2,2,2,1]
[5,7,8,4,1,2,3,6]=>[4,2,1,5,8,7,6,3]=>1100111=>[2,2,3]
[6,7,8,1,5,2,3,4]=>[3,2,1,8,4,7,6,5]=>1101011=>[2,1,1,1,2]
[6,7,8,1,5,2,4,3]=>[3,2,1,8,4,7,5,6]=>1101010=>[2,1,1,1,1,1]
[6,7,8,1,5,3,2,4]=>[3,2,1,8,4,6,7,5]=>1101001=>[2,1,1,2,1]
[6,7,8,1,3,5,2,4]=>[3,2,1,8,6,4,7,5]=>1101101=>[2,1,2,1,1]
[5,7,8,2,1,6,3,4]=>[4,2,1,7,8,3,6,5]=>1100101=>[2,2,1,1,1]
[4,7,2,8,1,6,3,5]=>[5,2,7,1,8,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,2,7,8,1,6,4,5]=>[6,7,2,1,8,3,5,4]=>0110101=>[1,2,1,1,1,1]
[3,2,7,8,1,6,5,4]=>[6,7,2,1,8,3,4,5]=>0110100=>[1,2,1,1,2]
[4,7,2,8,1,6,5,3]=>[5,2,7,1,8,3,4,6]=>1010100=>[1,1,1,1,1,2]
[5,7,8,2,1,6,4,3]=>[4,2,1,7,8,3,5,6]=>1100100=>[2,2,1,2]
[6,7,8,1,3,5,4,2]=>[3,2,1,8,6,4,5,7]=>1101100=>[2,1,2,2]
[6,7,8,1,5,3,4,2]=>[3,2,1,8,4,6,5,7]=>1101010=>[2,1,1,1,1,1]
[6,7,8,1,5,4,3,2]=>[3,2,1,8,4,5,6,7]=>1101000=>[2,1,1,3]
[6,7,8,1,5,4,2,3]=>[3,2,1,8,4,5,7,6]=>1101001=>[2,1,1,2,1]
[6,7,8,1,4,5,2,3]=>[3,2,1,8,5,4,7,6]=>1101101=>[2,1,2,1,1]
[6,7,8,1,4,5,3,2]=>[3,2,1,8,5,4,6,7]=>1101100=>[2,1,2,2]
[6,7,8,1,4,3,5,2]=>[3,2,1,8,5,6,4,7]=>1101010=>[2,1,1,1,1,1]
[6,7,8,1,3,4,5,2]=>[3,2,1,8,6,5,4,7]=>1101110=>[2,1,3,1]
[5,7,8,2,1,4,6,3]=>[4,2,1,7,8,5,3,6]=>1100110=>[2,2,2,1]
[4,7,2,8,1,5,6,3]=>[5,2,7,1,8,4,3,6]=>1010110=>[1,1,1,1,2,1]
[3,2,7,8,1,5,6,4]=>[6,7,2,1,8,4,3,5]=>0110110=>[1,2,1,2,1]
[3,2,6,8,4,1,7,5]=>[6,7,3,1,5,8,2,4]=>0110010=>[1,2,2,1,1]
[4,6,2,8,3,1,7,5]=>[5,3,7,1,6,8,2,4]=>1010010=>[1,1,1,2,1,1]
[5,6,8,3,2,1,7,4]=>[4,3,1,6,7,8,2,5]=>1100010=>[2,3,1,1]
[5,7,8,3,1,4,6,2]=>[4,2,1,6,8,5,3,7]=>1100110=>[2,2,2,1]
[5,7,8,3,1,6,4,2]=>[4,2,1,6,8,3,5,7]=>1100100=>[2,2,1,2]
[5,7,8,3,1,6,2,4]=>[4,2,1,6,8,3,7,5]=>1100101=>[2,2,1,1,1]
[4,7,3,8,1,6,2,5]=>[5,2,6,1,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,8,1,6,5,2]=>[5,2,6,1,8,3,4,7]=>1010100=>[1,1,1,1,1,2]
[4,7,3,8,1,5,6,2]=>[5,2,6,1,8,4,3,7]=>1010110=>[1,1,1,1,2,1]
[4,6,3,8,2,1,7,5]=>[5,3,6,1,7,8,2,4]=>1010010=>[1,1,1,2,1,1]
[4,5,3,2,8,1,7,6]=>[5,4,6,7,1,8,2,3]=>1001010=>[1,2,1,1,1,1]
[4,5,2,3,8,1,7,6]=>[5,4,7,6,1,8,2,3]=>1011010=>[1,1,2,1,1,1]
[3,2,5,4,8,1,7,6]=>[6,7,4,5,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,5,3,2,8,1,6,7]=>[5,4,6,7,1,8,3,2]=>1001011=>[1,2,1,1,2]
[4,6,3,8,2,1,5,7]=>[5,3,6,1,7,8,4,2]=>1010011=>[1,1,1,2,2]
[4,7,3,8,1,5,2,6]=>[5,2,6,1,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,8,1,2,6,5]=>[5,2,6,1,8,7,3,4]=>1010110=>[1,1,1,1,2,1]
[4,7,3,8,1,2,5,6]=>[5,2,6,1,8,7,4,3]=>1010111=>[1,1,1,1,3]
[5,7,8,3,1,2,4,6]=>[4,2,1,6,8,7,5,3]=>1100111=>[2,2,3]
[5,7,8,3,1,2,6,4]=>[4,2,1,6,8,7,3,5]=>1100110=>[2,2,2,1]
[5,7,8,3,1,4,2,6]=>[4,2,1,6,8,5,7,3]=>1100101=>[2,2,1,1,1]
[5,6,8,3,2,1,4,7]=>[4,3,1,6,7,8,5,2]=>1100011=>[2,3,2]
[3,2,7,8,1,5,4,6]=>[6,7,2,1,8,4,5,3]=>0110101=>[1,2,1,1,1,1]
[5,7,8,2,1,4,3,6]=>[4,2,1,7,8,5,6,3]=>1100101=>[2,2,1,1,1]
[6,7,8,1,3,4,2,5]=>[3,2,1,8,6,5,7,4]=>1101101=>[2,1,2,1,1]
[6,7,8,1,4,3,2,5]=>[3,2,1,8,5,6,7,4]=>1101001=>[2,1,1,2,1]
[6,7,8,1,4,2,5,3]=>[3,2,1,8,5,7,4,6]=>1101010=>[2,1,1,1,1,1]
[6,7,8,1,4,2,3,5]=>[3,2,1,8,5,7,6,4]=>1101011=>[2,1,1,1,2]
[6,7,8,1,2,5,3,4]=>[3,2,1,8,7,4,6,5]=>1101101=>[2,1,2,1,1]
[6,7,8,1,2,5,4,3]=>[3,2,1,8,7,4,5,6]=>1101100=>[2,1,2,2]
[6,7,8,1,2,4,5,3]=>[3,2,1,8,7,5,4,6]=>1101110=>[2,1,3,1]
[6,7,8,1,3,2,5,4]=>[3,2,1,8,6,7,4,5]=>1101010=>[2,1,1,1,1,1]
[5,7,8,2,1,3,6,4]=>[4,2,1,7,8,6,3,5]=>1100110=>[2,2,2,1]
[3,2,7,8,1,4,6,5]=>[6,7,2,1,8,5,3,4]=>0110110=>[1,2,1,2,1]
[6,7,8,1,3,2,4,5]=>[3,2,1,8,6,7,5,4]=>1101011=>[2,1,1,1,2]
[6,7,8,1,2,4,3,5]=>[3,2,1,8,7,5,6,4]=>1101101=>[2,1,2,1,1]
[6,7,8,1,2,3,5,4]=>[3,2,1,8,7,6,4,5]=>1101110=>[2,1,3,1]
[7,2,8,5,1,6,4,3]=>[2,7,1,4,8,3,5,6]=>0100100=>[1,1,2,1,2]
[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>1100101=>[2,2,1,1,1]
[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>1100011=>[2,3,2]
[7,2,8,5,4,1,6,3]=>[2,7,1,4,5,8,3,6]=>0100010=>[1,1,3,1,1]
[2,8,5,4,3,1,7,6]=>[7,1,4,5,6,8,2,3]=>1000010=>[1,4,1,1]
[2,8,4,5,6,1,7,3]=>[7,1,5,4,3,8,2,6]=>1011010=>[1,1,2,1,1,1]
[2,8,6,5,7,3,1,4]=>[7,1,3,4,2,6,8,5]=>1001001=>[1,2,1,2,1]
[2,8,4,5,3,7,1,6]=>[7,1,5,4,6,2,8,3]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,3,5,6,1,7]=>[7,1,5,6,4,3,8,2]=>1001101=>[1,2,2,1,1]
[7,2,8,4,5,6,1,3]=>[2,7,1,5,4,3,8,6]=>0101101=>[1,1,1,2,1,1]
[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>1010011=>[1,1,1,2,2]
[6,2,3,8,5,1,7,4]=>[3,7,6,1,4,8,2,5]=>0110010=>[1,2,2,1,1]
[6,3,2,8,5,1,4,7]=>[3,6,7,1,4,8,5,2]=>0010011=>[2,1,2,2]
[7,4,8,2,5,6,3,1]=>[2,5,1,7,4,3,6,8]=>0101100=>[1,1,1,2,2]
[7,4,8,5,2,1,3,6]=>[2,5,1,4,7,8,6,3]=>0100011=>[1,1,3,2]
[6,4,8,5,1,3,7,2]=>[3,5,1,4,8,6,2,7]=>0100110=>[1,1,2,2,1]
[6,3,7,5,2,1,8,4]=>[3,6,2,4,7,8,1,5]=>0100010=>[1,1,3,1,1]
[4,3,7,5,1,2,8,6]=>[5,6,2,4,8,7,1,3]=>0100110=>[1,1,2,2,1]
[4,3,7,1,5,6,8,2]=>[5,6,2,8,4,3,1,7]=>0101110=>[1,1,1,3,1]
[3,6,1,7,5,2,8,4]=>[6,3,8,2,4,7,1,5]=>1010010=>[1,1,1,2,1,1]
[3,4,1,2,7,6,8,5]=>[6,5,8,7,2,3,1,4]=>1011010=>[1,1,2,1,1,1]
[3,4,2,1,7,5,8,6]=>[6,5,7,8,2,4,1,3]=>1001010=>[1,2,1,1,1,1]
[3,6,5,7,1,4,8,2]=>[6,3,4,2,8,5,1,7]=>1010110=>[1,1,1,1,2,1]
[6,5,2,7,4,1,8,3]=>[3,4,7,2,5,8,1,6]=>0010010=>[2,1,2,1,1]
[3,5,2,6,4,8,7,1]=>[6,4,7,3,5,1,2,8]=>1010100=>[1,1,1,1,1,2]
[5,3,1,8,6,4,7,2]=>[4,6,8,1,3,5,2,7]=>0010010=>[2,1,2,1,1]
[5,6,1,8,7,2,4,3]=>[4,3,8,1,2,7,5,6]=>1010010=>[1,1,1,2,1,1]
[6,3,5,8,2,7,4,1]=>[3,6,4,1,7,2,5,8]=>0110100=>[1,2,1,1,2]
[6,5,8,4,2,3,7,1]=>[3,4,1,5,7,6,2,8]=>0100110=>[1,1,2,2,1]
[6,2,5,8,3,7,1,4]=>[3,7,4,1,6,2,8,5]=>0110101=>[1,2,1,1,1,1]
[1,6,5,7,3,4,2,8]=>[8,3,4,2,6,5,7,1]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,7,4,6,3,8]=>[8,4,7,2,5,3,6,1]=>1010101=>[1,1,1,1,1,1,1]
[5,2,1,8,7,6,3,4]=>[4,7,8,1,2,3,6,5]=>0010001=>[2,1,3,1]
[7,1,3,8,4,6,2,5]=>[2,8,6,1,5,3,7,4]=>0110101=>[1,2,1,1,1,1]
[2,3,4,8,6,1,7,5]=>[7,6,5,1,3,8,2,4]=>1110010=>[3,2,1,1]
[2,3,4,8,6,5,1,7]=>[7,6,5,1,3,4,8,2]=>1110001=>[3,3,1]
[2,7,3,5,8,6,1,4]=>[7,2,6,4,1,3,8,5]=>1011001=>[1,1,2,2,1]
[3,2,4,7,8,6,1,5]=>[6,7,5,2,1,3,8,4]=>0111001=>[1,3,2,1]
[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[5,2,4,7,1,8,3,6]=>[4,7,5,2,8,1,6,3]=>0110101=>[1,2,1,1,1,1]
[5,3,6,4,1,8,7,2]=>[4,6,3,5,8,1,2,7]=>0100100=>[1,1,2,1,2]
[5,3,6,1,4,8,2,7]=>[4,6,3,8,5,1,7,2]=>0101101=>[1,1,1,2,1,1]
[7,3,5,6,8,4,2,1]=>[2,6,4,3,1,5,7,8]=>0111000=>[1,3,3]
[6,3,5,1,8,2,7,4]=>[3,6,4,8,1,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[2,6,1,5,8,4,7,3]=>[7,3,8,4,1,5,2,6]=>1011010=>[1,1,2,1,1,1]
[2,7,6,5,8,3,4,1]=>[7,2,3,4,1,6,5,8]=>1001010=>[1,2,1,1,1,1]
[5,7,1,6,3,8,4,2]=>[4,2,8,3,6,1,5,7]=>1010100=>[1,1,1,1,1,2]
[3,2,4,1,7,8,5,6]=>[6,7,5,8,2,1,4,3]=>0101101=>[1,1,1,2,1,1]
[3,1,4,2,7,8,6,5]=>[6,8,5,7,2,1,3,4]=>0101100=>[1,1,1,2,2]
[5,1,4,7,2,8,6,3]=>[4,8,5,2,7,1,3,6]=>0110100=>[1,2,1,1,2]
[3,6,4,7,8,2,5,1]=>[6,3,5,2,1,7,4,8]=>1011010=>[1,1,2,1,1,1]
[3,1,4,6,8,5,7,2]=>[6,8,5,3,1,4,2,7]=>0111010=>[1,3,1,1,1]
[6,3,4,5,7,1,8,2]=>[3,6,5,4,2,8,1,7]=>0111010=>[1,3,1,1,1]
[2,5,4,6,1,7,8,3]=>[7,4,5,3,8,2,1,6]=>1010110=>[1,1,1,1,2,1]
[7,2,1,4,3,6,5,8]=>[2,7,8,5,6,3,4,1]=>0010101=>[2,1,1,1,1,1]
[7,3,4,1,2,6,5,8]=>[2,6,5,8,7,3,4,1]=>0101101=>[1,1,1,2,1,1]
[7,4,3,2,1,6,5,8]=>[2,5,6,7,8,3,4,1]=>0000101=>[4,1,1,1]
[7,6,3,2,5,4,1,8]=>[2,3,6,7,4,5,8,1]=>0001001=>[3,1,2,1]
[6,7,3,2,5,4,8,1]=>[3,2,6,7,4,5,1,8]=>1001010=>[1,2,1,1,1,1]
[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>1001010=>[1,2,1,1,1,1]
[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>1010110=>[1,1,1,1,2,1]
[7,3,5,1,6,2,4,8]=>[2,6,4,8,3,7,5,1]=>0101011=>[1,1,1,1,1,2]
[7,2,1,5,6,3,4,8]=>[2,7,8,4,3,6,5,1]=>0011011=>[2,2,1,2]
[7,2,1,6,5,4,3,8]=>[2,7,8,3,4,5,6,1]=>0010001=>[2,1,3,1]
[7,3,6,1,5,4,2,8]=>[2,6,3,8,4,5,7,1]=>0101001=>[1,1,1,1,2,1]
[7,4,6,5,1,3,2,8]=>[2,5,3,4,8,6,7,1]=>0100101=>[1,1,2,1,1,1]
[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>1000010=>[1,4,1,1]
[1,8,6,4,3,7,2,5]=>[8,1,3,5,6,2,7,4]=>1000101=>[1,3,1,1,1]
[6,5,7,4,3,1,8,2]=>[3,4,2,5,6,8,1,7]=>0100010=>[1,1,3,1,1]
[6,4,7,5,1,3,8,2]=>[3,5,2,4,8,6,1,7]=>0100110=>[1,1,2,2,1]
[6,3,7,1,5,4,8,2]=>[3,6,2,8,4,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[6,2,1,7,5,4,8,3]=>[3,7,8,2,4,5,1,6]=>0010010=>[2,1,2,1,1]
[3,2,1,8,5,4,7,6]=>[6,7,8,1,4,5,2,3]=>0010010=>[2,1,2,1,1]
[2,3,8,1,5,4,7,6]=>[7,6,1,8,4,5,2,3]=>1101010=>[2,1,1,1,1,1]
[2,4,8,5,1,3,7,6]=>[7,5,1,4,8,6,2,3]=>1100110=>[2,2,2,1]
[2,5,8,4,3,1,7,6]=>[7,4,1,5,6,8,2,3]=>1100010=>[2,3,1,1]
[2,6,8,4,3,7,1,5]=>[7,3,1,5,6,2,8,4]=>1100101=>[2,2,1,1,1]
[2,7,8,4,3,6,5,1]=>[7,2,1,5,6,3,4,8]=>1100100=>[2,2,1,2]
[1,8,7,4,3,6,5,2]=>[8,1,2,5,6,3,4,7]=>1000100=>[1,3,1,2]
[1,8,7,5,6,3,4,2]=>[8,1,2,4,3,6,5,7]=>1001010=>[1,2,1,1,1,1]
[2,7,8,5,6,3,4,1]=>[7,2,1,4,3,6,5,8]=>1101010=>[2,1,1,1,1,1]
[2,6,8,5,7,3,1,4]=>[7,3,1,4,2,6,8,5]=>1101001=>[2,1,1,2,1]
[2,5,8,6,7,1,3,4]=>[7,4,1,3,2,8,6,5]=>1101011=>[2,1,1,1,2]
[2,4,8,6,1,7,3,5]=>[7,5,1,3,8,2,6,4]=>1100101=>[2,2,1,1,1]
[3,2,1,8,6,7,4,5]=>[6,7,8,1,3,2,5,4]=>0010101=>[2,1,1,1,1,1]
[5,2,1,7,6,8,4,3]=>[4,7,8,2,3,1,5,6]=>0010100=>[2,1,1,1,2]
[5,3,7,1,6,8,4,2]=>[4,6,2,8,3,1,5,7]=>0101100=>[1,1,1,2,2]
[5,4,7,6,1,8,3,2]=>[4,5,2,3,8,1,6,7]=>0100100=>[1,1,2,1,2]
[4,5,7,6,8,1,3,2]=>[5,4,2,3,1,8,6,7]=>1101010=>[2,1,1,1,1,1]
[4,6,7,5,8,3,1,2]=>[5,3,2,4,1,6,8,7]=>1101001=>[2,1,1,2,1]
[1,8,6,5,7,3,2,4]=>[8,1,3,4,2,6,7,5]=>1001001=>[1,2,1,2,1]
[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>1011011=>[1,1,2,1,2]
[4,7,5,6,8,2,3,1]=>[5,2,4,3,1,7,6,8]=>1011010=>[1,1,2,1,1,1]
[4,6,5,7,8,2,1,3]=>[5,3,4,2,1,7,8,6]=>1011001=>[1,1,2,2,1]
[5,4,6,7,1,8,2,3]=>[4,5,3,2,8,1,7,6]=>0110101=>[1,2,1,1,1,1]
[5,3,6,1,7,8,2,4]=>[4,6,3,8,2,1,7,5]=>0101101=>[1,1,1,2,1,1]
[5,2,1,6,7,8,3,4]=>[4,7,8,3,2,1,6,5]=>0011101=>[2,3,1,1]
[6,2,1,5,7,3,8,4]=>[3,7,8,4,2,6,1,5]=>0011010=>[2,2,1,1,1]
[6,3,5,1,7,2,8,4]=>[3,6,4,8,2,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,4,5,7,1,2,8,3]=>[3,5,4,2,8,7,1,6]=>0110110=>[1,2,1,2,1]
[6,5,4,7,2,1,8,3]=>[3,4,5,2,7,8,1,6]=>0010010=>[2,1,2,1,1]
[5,6,4,7,2,8,1,3]=>[4,3,5,2,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>1001101=>[1,2,2,1,1]
[5,7,3,2,6,8,4,1]=>[4,2,6,7,3,1,5,8]=>1001100=>[1,2,2,2]
[5,6,3,2,7,8,1,4]=>[4,3,6,7,2,1,8,5]=>1001101=>[1,2,2,1,1]
[6,5,3,2,7,1,8,4]=>[3,4,6,7,2,8,1,5]=>0001010=>[3,1,1,1,1]
[6,4,3,2,1,7,8,5]=>[3,5,6,7,8,2,1,4]=>0000110=>[4,2,1]
[6,2,1,4,3,7,8,5]=>[3,7,8,5,6,2,1,4]=>0010110=>[2,1,1,2,1]
[5,2,1,4,3,8,7,6]=>[4,7,8,5,6,1,2,3]=>0010100=>[2,1,1,1,2]
[5,3,4,1,2,8,7,6]=>[4,6,5,8,7,1,2,3]=>0101100=>[1,1,1,2,2]
[4,6,3,2,8,7,1,5]=>[5,3,6,7,1,2,8,4]=>1001001=>[1,2,1,2,1]
[4,7,3,2,8,6,5,1]=>[5,2,6,7,1,3,4,8]=>1001000=>[1,2,1,3]
[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>1001000=>[1,2,1,3]
[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>1010100=>[1,1,1,1,1,2]
[3,7,4,8,2,6,5,1]=>[6,2,5,1,7,3,4,8]=>1010100=>[1,1,1,1,1,2]
[3,6,4,8,2,7,1,5]=>[6,3,5,1,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,5,4,8,2,1,7,6]=>[6,4,5,1,7,8,2,3]=>1010010=>[1,1,1,2,1,1]
[3,4,5,8,1,2,7,6]=>[6,5,4,1,8,7,2,3]=>1110110=>[3,1,2,1]
[4,3,5,1,8,2,7,6]=>[5,6,4,8,1,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,1,5,8,3,7,6]=>[5,7,8,4,1,6,2,3]=>0011010=>[2,2,1,1,1]
[4,2,1,6,8,7,3,5]=>[5,7,8,3,1,2,6,4]=>0011001=>[2,2,2,1]
[4,3,6,1,8,7,2,5]=>[5,6,3,8,1,2,7,4]=>0101001=>[1,1,1,1,2,1]
[3,4,6,8,1,7,2,5]=>[6,5,3,1,8,2,7,4]=>1110101=>[3,1,1,1,1]
[3,5,6,8,7,1,2,4]=>[6,4,3,1,2,8,7,5]=>1110011=>[3,2,2]
[3,6,5,8,7,2,1,4]=>[6,3,4,1,2,7,8,5]=>1010001=>[1,1,1,3,1]
[3,7,5,8,6,2,4,1]=>[6,2,4,1,3,7,5,8]=>1010010=>[1,1,1,2,1,1]
[1,8,5,7,6,2,4,3]=>[8,1,4,2,3,7,5,6]=>1010010=>[1,1,1,2,1,1]
[1,8,6,7,5,4,2,3]=>[8,1,3,2,4,5,7,6]=>1010001=>[1,1,1,3,1]
[3,6,7,8,5,4,1,2]=>[6,3,2,1,4,5,8,7]=>1110001=>[3,3,1]
[3,5,7,8,6,1,4,2]=>[6,4,2,1,3,8,5,7]=>1110010=>[3,2,1,1]
[3,4,7,8,1,6,5,2]=>[6,5,2,1,8,3,4,7]=>1110100=>[3,1,1,2]
[4,2,1,7,8,6,5,3]=>[5,7,8,2,1,3,4,6]=>0011000=>[2,2,3]
[2,3,8,1,7,6,5,4]=>[7,6,1,8,2,3,4,5]=>1101000=>[2,1,1,3]
[2,4,8,7,1,6,5,3]=>[7,5,1,2,8,3,4,6]=>1100100=>[2,2,1,2]
[2,5,8,7,6,1,4,3]=>[7,4,1,2,3,8,5,6]=>1100010=>[2,3,1,1]
[2,6,8,7,5,4,1,3]=>[7,3,1,2,4,5,8,6]=>1100001=>[2,4,1]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010=>[1,1,1,1,1,1,1,1,1,1,1]
[2,1,4,3,6,5,10,9,8,7,12,11]=>[11,12,9,10,7,8,3,4,5,6,1,2]=>01010100010=>[1,1,1,1,1,1,3,1,1]
[2,1,4,3,6,5,12,9,8,11,10,7]=>[11,12,9,10,7,8,1,4,5,2,3,6]=>01010100100=>[1,1,1,1,1,1,2,1,2]
[2,1,4,3,8,7,6,5,10,9,12,11]=>[11,12,9,10,5,6,7,8,3,4,1,2]=>01010001010=>[1,1,1,1,3,1,1,1,1]
[2,1,4,3,8,7,6,5,12,11,10,9]=>[11,12,9,10,5,6,7,8,1,2,3,4]=>01010001000=>[1,1,1,1,3,1,3]
[2,1,4,3,10,7,6,9,8,5,12,11]=>[11,12,9,10,3,6,7,4,5,8,1,2]=>01010010010=>[1,1,1,1,2,1,2,1,1]
[2,1,4,3,12,7,6,9,8,11,10,5]=>[11,12,9,10,1,6,7,4,5,2,3,8]=>01010010100=>[1,1,1,1,2,1,1,1,2]
[2,1,4,3,12,9,8,7,6,11,10,5]=>[11,12,9,10,1,4,5,6,7,2,3,8]=>01010000100=>[1,1,1,1,4,1,2]
[2,1,4,3,12,11,8,7,10,9,6,5]=>[11,12,9,10,1,2,5,6,3,4,7,8]=>01010001000=>[1,1,1,1,3,1,3]
[2,1,6,5,4,3,8,7,10,9,12,11]=>[11,12,7,8,9,10,5,6,3,4,1,2]=>01000101010=>[1,1,3,1,1,1,1,1,1]
[2,1,6,5,4,3,8,7,12,11,10,9]=>[11,12,7,8,9,10,5,6,1,2,3,4]=>01000101000=>[1,1,3,1,1,1,3]
[2,1,6,5,4,3,10,9,8,7,12,11]=>[11,12,7,8,9,10,3,4,5,6,1,2]=>01000100010=>[1,1,3,1,3,1,1]
[2,1,6,5,4,3,12,9,8,11,10,7]=>[11,12,7,8,9,10,1,4,5,2,3,6]=>01000100100=>[1,1,3,1,2,1,2]
[2,1,8,5,4,7,6,3,10,9,12,11]=>[11,12,5,8,9,6,7,10,3,4,1,2]=>01001001010=>[1,1,2,1,2,1,1,1,1]
[2,1,8,5,4,7,6,3,12,11,10,9]=>[11,12,5,8,9,6,7,10,1,2,3,4]=>01001001000=>[1,1,2,1,2,1,3]
[2,1,10,5,4,7,6,9,8,3,12,11]=>[11,12,3,8,9,6,7,4,5,10,1,2]=>01001010010=>[1,1,2,1,1,1,2,1,1]
[2,1,12,5,4,7,6,9,8,11,10,3]=>[11,12,1,8,9,6,7,4,5,2,3,10]=>01001010100=>[1,1,2,1,1,1,1,1,2]
[2,1,10,5,4,9,8,7,6,3,12,11]=>[11,12,3,8,9,4,5,6,7,10,1,2]=>01001000010=>[1,1,2,1,4,1,1]
[2,1,12,5,4,9,8,7,6,11,10,3]=>[11,12,1,8,9,4,5,6,7,2,3,10]=>01001000100=>[1,1,2,1,3,1,2]
[2,1,12,5,4,11,8,7,10,9,6,3]=>[11,12,1,8,9,2,5,6,3,4,7,10]=>01001001000=>[1,1,2,1,2,1,3]
[2,1,8,7,6,5,4,3,12,11,10,9]=>[11,12,5,6,7,8,9,10,1,2,3,4]=>01000001000=>[1,1,5,1,3]
[2,1,10,7,6,5,4,9,8,3,12,11]=>[11,12,3,6,7,8,9,4,5,10,1,2]=>01000010010=>[1,1,4,1,2,1,1]
[2,1,12,7,6,5,4,9,8,11,10,3]=>[11,12,1,6,7,8,9,4,5,2,3,10]=>01000010100=>[1,1,4,1,1,1,2]
[2,1,12,7,6,5,4,11,10,9,8,3]=>[11,12,1,6,7,8,9,2,3,4,5,10]=>01000010000=>[1,1,4,1,4]
[2,1,10,9,6,5,8,7,4,3,12,11]=>[11,12,3,4,7,8,5,6,9,10,1,2]=>01000100010=>[1,1,3,1,3,1,1]
[2,1,12,9,6,5,8,7,4,11,10,3]=>[11,12,1,4,7,8,5,6,9,2,3,10]=>01000100100=>[1,1,3,1,2,1,2]
[2,1,12,11,6,5,8,7,10,9,4,3]=>[11,12,1,2,7,8,5,6,3,4,9,10]=>01000101000=>[1,1,3,1,1,1,3]
[2,1,12,11,8,7,6,5,10,9,4,3]=>[11,12,1,2,5,6,7,8,3,4,9,10]=>01000001000=>[1,1,5,1,3]
[2,1,12,11,10,7,6,9,8,5,4,3]=>[11,12,1,2,3,6,7,4,5,8,9,10]=>01000010000=>[1,1,4,1,4]
[2,1,12,11,10,9,8,7,6,5,4,3]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>01000000000=>[1,1,9]
[4,3,2,1,6,5,8,7,12,11,10,9]=>[9,10,11,12,7,8,5,6,1,2,3,4]=>00010101000=>[3,1,1,1,1,1,3]
[4,3,2,1,6,5,10,9,8,7,12,11]=>[9,10,11,12,7,8,3,4,5,6,1,2]=>00010100010=>[3,1,1,1,3,1,1]
[4,3,2,1,6,5,12,9,8,11,10,7]=>[9,10,11,12,7,8,1,4,5,2,3,6]=>00010100100=>[3,1,1,1,2,1,2]
[4,3,2,1,8,7,6,5,10,9,12,11]=>[9,10,11,12,5,6,7,8,3,4,1,2]=>00010001010=>[3,1,3,1,1,1,1]
[4,3,2,1,8,7,6,5,12,11,10,9]=>[9,10,11,12,5,6,7,8,1,2,3,4]=>00010001000=>[3,1,3,1,3]
[4,3,2,1,10,7,6,9,8,5,12,11]=>[9,10,11,12,3,6,7,4,5,8,1,2]=>00010010010=>[3,1,2,1,2,1,1]
[4,3,2,1,12,7,6,9,8,11,10,5]=>[9,10,11,12,1,6,7,4,5,2,3,8]=>00010010100=>[3,1,2,1,1,1,2]
[4,3,2,1,12,7,6,11,10,9,8,5]=>[9,10,11,12,1,6,7,2,3,4,5,8]=>00010010000=>[3,1,2,1,4]
[4,3,2,1,10,9,8,7,6,5,12,11]=>[9,10,11,12,3,4,5,6,7,8,1,2]=>00010000010=>[3,1,5,1,1]
[4,3,2,1,12,9,8,7,6,11,10,5]=>[9,10,11,12,1,4,5,6,7,2,3,8]=>00010000100=>[3,1,4,1,2]
[4,3,2,1,12,11,8,7,10,9,6,5]=>[9,10,11,12,1,2,5,6,3,4,7,8]=>00010001000=>[3,1,3,1,3]
[6,3,2,5,4,1,8,7,10,9,12,11]=>[7,10,11,8,9,12,5,6,3,4,1,2]=>00100101010=>[2,1,2,1,1,1,1,1,1]
[6,3,2,5,4,1,8,7,12,11,10,9]=>[7,10,11,8,9,12,5,6,1,2,3,4]=>00100101000=>[2,1,2,1,1,1,3]
[6,3,2,5,4,1,10,9,8,7,12,11]=>[7,10,11,8,9,12,3,4,5,6,1,2]=>00100100010=>[2,1,2,1,3,1,1]
[6,3,2,5,4,1,12,9,8,11,10,7]=>[7,10,11,8,9,12,1,4,5,2,3,6]=>00100100100=>[2,1,2,1,2,1,2]
[8,3,2,5,4,7,6,1,10,9,12,11]=>[5,10,11,8,9,6,7,12,3,4,1,2]=>00101001010=>[2,1,1,1,2,1,1,1,1]
[8,3,2,5,4,7,6,1,12,11,10,9]=>[5,10,11,8,9,6,7,12,1,2,3,4]=>00101001000=>[2,1,1,1,2,1,3]
[10,3,2,5,4,7,6,9,8,1,12,11]=>[3,10,11,8,9,6,7,4,5,12,1,2]=>00101010010=>[2,1,1,1,1,1,2,1,1]
[12,3,2,5,4,7,6,9,8,11,10,1]=>[1,10,11,8,9,6,7,4,5,2,3,12]=>00101010100=>[2,1,1,1,1,1,1,1,2]
[10,3,2,5,4,9,8,7,6,1,12,11]=>[3,10,11,8,9,4,5,6,7,12,1,2]=>00101000010=>[2,1,1,1,4,1,1]
[12,3,2,5,4,9,8,7,6,11,10,1]=>[1,10,11,8,9,4,5,6,7,2,3,12]=>00101000100=>[2,1,1,1,3,1,2]
[12,3,2,5,4,11,8,7,10,9,6,1]=>[1,10,11,8,9,2,5,6,3,4,7,12]=>00101001000=>[2,1,1,1,2,1,3]
[8,3,2,7,6,5,4,1,10,9,12,11]=>[5,10,11,6,7,8,9,12,3,4,1,2]=>00100001010=>[2,1,4,1,1,1,1]
[8,3,2,7,6,5,4,1,12,11,10,9]=>[5,10,11,6,7,8,9,12,1,2,3,4]=>00100001000=>[2,1,4,1,3]
[10,3,2,7,6,5,4,9,8,1,12,11]=>[3,10,11,6,7,8,9,4,5,12,1,2]=>00100010010=>[2,1,3,1,2,1,1]
[12,3,2,7,6,5,4,9,8,11,10,1]=>[1,10,11,6,7,8,9,4,5,2,3,12]=>00100010100=>[2,1,3,1,1,1,2]
[12,3,2,7,6,5,4,11,10,9,8,1]=>[1,10,11,6,7,8,9,2,3,4,5,12]=>00100010000=>[2,1,3,1,4]
[10,3,2,9,6,5,8,7,4,1,12,11]=>[3,10,11,4,7,8,5,6,9,12,1,2]=>00100100010=>[2,1,2,1,3,1,1]
[12,3,2,9,6,5,8,7,4,11,10,1]=>[1,10,11,4,7,8,5,6,9,2,3,12]=>00100100100=>[2,1,2,1,2,1,2]
[12,3,2,11,6,5,8,7,10,9,4,1]=>[1,10,11,2,7,8,5,6,3,4,9,12]=>00100101000=>[2,1,2,1,1,1,3]
[12,3,2,9,8,7,6,5,4,11,10,1]=>[1,10,11,4,5,6,7,8,9,2,3,12]=>00100000100=>[2,1,5,1,2]
[12,3,2,11,8,7,6,5,10,9,4,1]=>[1,10,11,2,5,6,7,8,3,4,9,12]=>00100001000=>[2,1,4,1,3]
[12,3,2,11,10,7,6,9,8,5,4,1]=>[1,10,11,2,3,6,7,4,5,8,9,12]=>00100010000=>[2,1,3,1,4]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>00000100000=>[5,1,5]
[8,5,4,3,2,7,6,1,12,11,10,9]=>[5,8,9,10,11,6,7,12,1,2,3,4]=>00001001000=>[4,1,2,1,3]
[12,5,4,3,2,7,6,11,10,9,8,1]=>[1,8,9,10,11,6,7,2,3,4,5,12]=>00001010000=>[4,1,1,1,4]
[10,5,4,3,2,9,8,7,6,1,12,11]=>[3,8,9,10,11,4,5,6,7,12,1,2]=>00001000010=>[4,1,4,1,1]
[12,5,4,3,2,9,8,7,6,11,10,1]=>[1,8,9,10,11,4,5,6,7,2,3,12]=>00001000100=>[4,1,3,1,2]
[12,5,4,3,2,11,8,7,10,9,6,1]=>[1,8,9,10,11,2,5,6,3,4,7,12]=>00001001000=>[4,1,2,1,3]
[8,7,4,3,6,5,2,1,10,9,12,11]=>[5,6,9,10,7,8,11,12,3,4,1,2]=>00010001010=>[3,1,3,1,1,1,1]
[8,7,4,3,6,5,2,1,12,11,10,9]=>[5,6,9,10,7,8,11,12,1,2,3,4]=>00010001000=>[3,1,3,1,3]
[10,7,4,3,6,5,2,9,8,1,12,11]=>[3,6,9,10,7,8,11,4,5,12,1,2]=>00010010010=>[3,1,2,1,2,1,1]
[12,7,4,3,6,5,2,9,8,11,10,1]=>[1,6,9,10,7,8,11,4,5,2,3,12]=>00010010100=>[3,1,2,1,1,1,2]
[12,7,4,3,6,5,2,11,10,9,8,1]=>[1,6,9,10,7,8,11,2,3,4,5,12]=>00010010000=>[3,1,2,1,4]
[10,9,4,3,6,5,8,7,2,1,12,11]=>[3,4,9,10,7,8,5,6,11,12,1,2]=>00010100010=>[3,1,1,1,3,1,1]
[12,9,4,3,6,5,8,7,2,11,10,1]=>[1,4,9,10,7,8,5,6,11,2,3,12]=>00010100100=>[3,1,1,1,2,1,2]
[12,11,4,3,6,5,8,7,10,9,2,1]=>[1,2,9,10,7,8,5,6,3,4,11,12]=>00010101000=>[3,1,1,1,1,1,3]
[10,9,4,3,8,7,6,5,2,1,12,11]=>[3,4,9,10,5,6,7,8,11,12,1,2]=>00010000010=>[3,1,5,1,1]
[12,9,4,3,8,7,6,5,2,11,10,1]=>[1,4,9,10,5,6,7,8,11,2,3,12]=>00010000100=>[3,1,4,1,2]
[12,11,4,3,8,7,6,5,10,9,2,1]=>[1,2,9,10,5,6,7,8,3,4,11,12]=>00010001000=>[3,1,3,1,3]
[12,11,4,3,10,7,6,9,8,5,2,1]=>[1,2,9,10,3,6,7,4,5,8,11,12]=>00010010000=>[3,1,2,1,4]
[12,11,6,5,4,3,10,9,8,7,2,1]=>[1,2,7,8,9,10,3,4,5,6,11,12]=>00000100000=>[5,1,5]
[10,9,8,5,4,7,6,3,2,1,12,11]=>[3,4,5,8,9,6,7,10,11,12,1,2]=>00001000010=>[4,1,4,1,1]
[12,9,8,5,4,7,6,3,2,11,10,1]=>[1,4,5,8,9,6,7,10,11,2,3,12]=>00001000100=>[4,1,3,1,2]
[12,11,8,5,4,7,6,3,10,9,2,1]=>[1,2,5,8,9,6,7,10,3,4,11,12]=>00001001000=>[4,1,2,1,3]
[12,11,10,5,4,7,6,9,8,3,2,1]=>[1,2,3,8,9,6,7,4,5,10,11,12]=>00001010000=>[4,1,1,1,4]
[10,9,8,7,6,5,4,3,2,1,12,11]=>[3,4,5,6,7,8,9,10,11,12,1,2]=>00000000010=>[9,1,1]
[12,11,10,9,6,5,8,7,4,3,2,1]=>[1,2,3,4,7,8,5,6,9,10,11,12]=>00000100000=>[5,1,5]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000=>[11]
[7,4,6,1,8,3,5,2]=>[2,5,3,8,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,1,7,4,6,2]=>[1,6,4,8,2,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,4,1,7,5,6,2]=>[1,6,5,8,2,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,8,3,1,7,5,6,2]=>[5,1,6,8,2,4,3,7]=>1001010=>[1,2,1,1,1,1]
[4,6,2,1,7,5,8,3]=>[5,3,7,8,2,4,1,6]=>1001010=>[1,2,1,1,1,1]
[1,4,6,2,7,5,8,3]=>[8,5,3,7,2,4,1,6]=>1101010=>[2,1,1,1,1,1]
[1,7,5,2,6,8,4,3]=>[8,2,4,7,3,1,5,6]=>1001100=>[1,2,2,2]
[7,5,2,1,6,8,4,3]=>[2,4,7,8,3,1,5,6]=>0001100=>[3,2,2]
[6,8,4,3,1,7,5,2]=>[3,1,5,6,8,2,4,7]=>1000100=>[1,3,1,2]
[3,6,8,4,1,7,5,2]=>[6,3,1,5,8,2,4,7]=>1100100=>[2,2,1,2]
[3,6,7,5,1,8,4,2]=>[6,3,2,4,8,1,5,7]=>1100100=>[2,2,1,2]
[7,5,6,1,8,3,4,2]=>[2,4,3,8,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[3,4,6,5,7,1,8,2]=>[6,5,3,4,2,8,1,7]=>1101010=>[2,1,1,1,1,1]
[4,7,5,6,1,8,3,2]=>[5,2,4,3,8,1,6,7]=>1010100=>[1,1,1,1,1,2]
[6,7,5,1,8,4,3,2]=>[3,2,4,8,1,5,6,7]=>1001000=>[1,2,1,3]
[6,8,4,1,7,5,3,2]=>[3,1,5,8,2,4,6,7]=>1001000=>[1,2,1,3]
[6,7,5,3,1,8,4,2]=>[3,2,4,6,8,1,5,7]=>1000100=>[1,3,1,2]
[8,4,2,1,6,7,5,3]=>[1,5,7,8,3,2,4,6]=>0001100=>[3,2,2]
[1,8,4,2,6,7,5,3]=>[8,1,5,7,3,2,4,6]=>1001100=>[1,2,2,2]
[1,5,3,2,7,6,8,4]=>[8,4,6,7,2,3,1,5]=>1001010=>[1,2,1,1,1,1]
[5,3,2,1,7,6,8,4]=>[4,6,7,8,2,3,1,5]=>0001010=>[3,1,1,1,1]
[2,5,3,1,7,6,8,4]=>[7,4,6,8,2,3,1,5]=>1001010=>[1,2,1,1,1,1]
[2,8,4,1,6,7,5,3]=>[7,1,5,8,3,2,4,6]=>1001100=>[1,2,2,2]
[2,7,5,1,6,8,4,3]=>[7,2,4,8,3,1,5,6]=>1001100=>[1,2,2,2]
[2,4,6,1,7,5,8,3]=>[7,5,3,8,2,4,1,6]=>1101010=>[2,1,1,1,1,1]
[4,7,1,6,5,8,2,3]=>[5,2,8,3,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,6,5,7,1,3]=>[5,1,7,3,4,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,6,1,2,7,5,8,3]=>[5,3,8,7,2,4,1,6]=>1011010=>[1,1,2,1,1,1]
[7,5,1,2,6,8,4,3]=>[2,4,8,7,3,1,5,6]=>0011100=>[2,3,2]
[8,4,1,2,6,7,5,3]=>[1,5,8,7,3,2,4,6]=>0011100=>[2,3,2]
[5,3,1,2,7,6,8,4]=>[4,6,8,7,2,3,1,5]=>0011010=>[2,2,1,1,1]
[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>1101010=>[2,1,1,1,1,1]
[4,3,1,2,7,6,8,5]=>[5,6,8,7,2,3,1,4]=>0011010=>[2,2,1,1,1]
[3,5,1,2,7,6,8,4]=>[6,4,8,7,2,3,1,5]=>1011010=>[1,1,2,1,1,1]
[6,7,1,5,8,2,3,4]=>[3,2,8,4,1,7,6,5]=>1011011=>[1,1,2,1,2]
[2,7,6,1,5,8,3,4]=>[7,2,3,8,4,1,6,5]=>1001101=>[1,2,2,1,1]
[2,3,5,1,7,6,8,4]=>[7,6,4,8,2,3,1,5]=>1101010=>[2,1,1,1,1,1]
[7,6,1,5,8,3,2,4]=>[2,3,8,4,1,6,7,5]=>0011001=>[2,2,2,1]
[3,6,7,1,5,8,2,4]=>[6,3,2,8,4,1,7,5]=>1101101=>[2,1,2,1,1]
[7,1,6,5,8,2,4,3]=>[2,8,3,4,1,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[7,5,1,6,8,4,2,3]=>[2,4,8,3,1,5,7,6]=>0011001=>[2,2,2,1]
[8,4,1,6,7,5,2,3]=>[1,5,8,3,2,4,7,6]=>0011001=>[2,2,2,1]
[5,2,3,1,7,6,8,4]=>[4,7,6,8,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,5,2,1,7,6,8,4]=>[6,4,7,8,2,3,1,5]=>1001010=>[1,2,1,1,1,1]
[1,3,5,2,7,6,8,4]=>[8,6,4,7,2,3,1,5]=>1101010=>[2,1,1,1,1,1]
[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>1001101=>[1,2,2,1,1]
[7,6,2,1,5,8,3,4]=>[2,3,7,8,4,1,6,5]=>0001101=>[3,2,1,1]
[8,3,1,5,7,6,2,4]=>[1,6,8,4,2,3,7,5]=>0011001=>[2,2,2,1]
[6,2,4,1,7,5,8,3]=>[3,7,5,8,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[6,2,5,1,7,4,8,3]=>[3,7,4,8,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[7,1,6,4,8,2,5,3]=>[2,8,3,5,1,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,4,7,1,5,3]=>[1,7,3,5,2,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,2,7,4,8,3]=>[3,8,4,7,2,5,1,6]=>0101010=>[1,1,1,1,1,1,1]
[7,6,2,5,8,3,1,4]=>[2,3,7,4,1,6,8,5]=>0011001=>[2,2,2,1]
[8,3,5,7,6,2,1,4]=>[1,6,4,2,3,7,8,5]=>0110001=>[1,2,3,1]
[1,8,3,5,7,6,2,4]=>[8,1,6,4,2,3,7,5]=>1011001=>[1,1,2,2,1]
[1,5,2,3,7,6,8,4]=>[8,4,7,6,2,3,1,5]=>1011010=>[1,1,2,1,1,1]
[5,2,1,3,7,6,8,4]=>[4,7,8,6,2,3,1,5]=>0011010=>[2,2,1,1,1]
[7,5,2,6,8,4,1,3]=>[2,4,7,3,1,5,8,6]=>0011001=>[2,2,2,1]
[8,4,2,6,7,5,1,3]=>[1,5,7,3,2,4,8,6]=>0011001=>[2,2,2,1]
[6,1,4,2,7,5,8,3]=>[3,8,5,7,2,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,5,7,1,4,3]=>[1,7,3,4,2,8,5,6]=>0101010=>[1,1,1,1,1,1,1]
[3,6,8,2,5,7,1,4]=>[6,3,1,7,4,2,8,5]=>1101101=>[2,1,2,1,1]
[8,3,2,5,7,6,1,4]=>[1,6,7,4,2,3,8,5]=>0011001=>[2,2,2,1]
[5,1,3,2,7,6,8,4]=>[4,8,6,7,2,3,1,5]=>0101010=>[1,1,1,1,1,1,1]
[4,1,3,2,7,6,8,5]=>[5,8,6,7,2,3,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,1,3,7,6,8,5]=>[5,7,8,6,2,3,1,4]=>0011010=>[2,2,1,1,1]
[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>1011010=>[1,1,2,1,1,1]
[2,4,1,3,7,6,8,5]=>[7,5,8,6,2,3,1,4]=>1011010=>[1,1,2,1,1,1]
[2,5,1,3,7,6,8,4]=>[7,4,8,6,2,3,1,5]=>1011010=>[1,1,2,1,1,1]
[2,8,3,5,7,6,1,4]=>[7,1,6,4,2,3,8,5]=>1011001=>[1,1,2,2,1]
[6,8,2,3,5,7,1,4]=>[3,1,7,6,4,2,8,5]=>1011101=>[1,1,3,1,1]
[6,7,1,3,5,8,2,4]=>[3,2,8,6,4,1,7,5]=>1011101=>[1,1,3,1,1]
[8,3,5,7,6,1,2,4]=>[1,6,4,2,3,8,7,5]=>0110011=>[1,2,2,2]
[5,1,2,3,7,6,8,4]=>[4,8,7,6,2,3,1,5]=>0111010=>[1,3,1,1,1]
[3,1,2,4,7,6,8,5]=>[6,8,7,5,2,3,1,4]=>0111010=>[1,3,1,1,1]
[10,8,9,5,6,7,1,2,3,4]=>[1,3,2,6,5,4,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[10,8,9,4,5,6,1,2,3,7]=>[1,3,2,7,6,5,10,9,8,4]=>010110111=>[1,1,1,2,1,3]
[10,7,8,5,6,9,1,2,3,4]=>[1,4,3,6,5,2,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[10,7,8,4,5,9,1,2,3,6]=>[1,4,3,7,6,2,10,9,8,5]=>010110111=>[1,1,1,2,1,3]
[10,6,7,4,5,8,1,2,3,9]=>[1,5,4,7,6,3,10,9,8,2]=>010110111=>[1,1,1,2,1,3]
[10,7,8,3,4,9,1,2,5,6]=>[1,4,3,8,7,2,10,9,6,5]=>010110111=>[1,1,1,2,1,3]
[10,6,7,3,4,8,1,2,5,9]=>[1,5,4,8,7,3,10,9,6,2]=>010110111=>[1,1,1,2,1,3]
[9,8,10,5,6,7,1,2,3,4]=>[2,3,1,6,5,4,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[9,8,10,4,5,6,1,2,3,7]=>[2,3,1,7,6,5,10,9,8,4]=>010110111=>[1,1,1,2,1,3]
[9,7,10,5,6,8,1,2,3,4]=>[2,4,1,6,5,3,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[9,7,10,4,5,8,1,2,3,6]=>[2,4,1,7,6,3,10,9,8,5]=>010110111=>[1,1,1,2,1,3]
[9,6,10,4,5,7,1,2,3,8]=>[2,5,1,7,6,4,10,9,8,3]=>010110111=>[1,1,1,2,1,3]
[9,7,10,3,4,8,1,2,5,6]=>[2,4,1,8,7,3,10,9,6,5]=>010110111=>[1,1,1,2,1,3]
[9,6,10,3,4,7,1,2,5,8]=>[2,5,1,8,7,4,10,9,6,3]=>010110111=>[1,1,1,2,1,3]
[8,7,9,5,6,10,1,2,3,4]=>[3,4,2,6,5,1,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[8,7,9,4,5,10,1,2,3,6]=>[3,4,2,7,6,1,10,9,8,5]=>010110111=>[1,1,1,2,1,3]
[8,6,9,4,5,10,1,2,3,7]=>[3,5,2,7,6,1,10,9,8,4]=>010110111=>[1,1,1,2,1,3]
[7,6,8,4,5,9,1,2,3,10]=>[4,5,3,7,6,2,10,9,8,1]=>010110111=>[1,1,1,2,1,3]
[8,7,9,3,4,10,1,2,5,6]=>[3,4,2,8,7,1,10,9,6,5]=>010110111=>[1,1,1,2,1,3]
[8,6,9,3,4,10,1,2,5,7]=>[3,5,2,8,7,1,10,9,6,4]=>010110111=>[1,1,1,2,1,3]
[7,6,8,3,4,9,1,2,5,10]=>[4,5,3,8,7,2,10,9,6,1]=>010110111=>[1,1,1,2,1,3]
[9,6,10,5,7,8,1,2,3,4]=>[2,5,1,6,4,3,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[9,6,10,4,7,8,1,2,3,5]=>[2,5,1,7,4,3,10,9,8,6]=>010110111=>[1,1,1,2,1,3]
[9,5,10,4,6,7,1,2,3,8]=>[2,6,1,7,5,4,10,9,8,3]=>010110111=>[1,1,1,2,1,3]
[9,6,10,3,7,8,1,2,4,5]=>[2,5,1,8,4,3,10,9,7,6]=>010110111=>[1,1,1,2,1,3]
[9,5,10,3,6,7,1,2,4,8]=>[2,6,1,8,5,4,10,9,7,3]=>010110111=>[1,1,1,2,1,3]
[8,6,9,5,7,10,1,2,3,4]=>[3,5,2,6,4,1,10,9,8,7]=>010110111=>[1,1,1,2,1,3]
[8,6,9,4,7,10,1,2,3,5]=>[3,5,2,7,4,1,10,9,8,6]=>010110111=>[1,1,1,2,1,3]
[8,5,9,4,6,10,1,2,3,7]=>[3,6,2,7,5,1,10,9,8,4]=>010110111=>[1,1,1,2,1,3]
[7,5,8,4,6,9,1,2,3,10]=>[4,6,3,7,5,2,10,9,8,1]=>010110111=>[1,1,1,2,1,3]
[8,6,9,3,7,10,1,2,4,5]=>[3,5,2,8,4,1,10,9,7,6]=>010110111=>[1,1,1,2,1,3]
[8,5,9,3,6,10,1,2,4,7]=>[3,6,2,8,5,1,10,9,7,4]=>010110111=>[1,1,1,2,1,3]
[7,5,8,3,6,9,1,2,4,10]=>[4,6,3,8,5,2,10,9,7,1]=>010110111=>[1,1,1,2,1,3]
[8,4,9,3,5,10,1,2,6,7]=>[3,7,2,8,6,1,10,9,5,4]=>010110111=>[1,1,1,2,1,3]
[7,4,8,3,5,9,1,2,6,10]=>[4,7,3,8,6,2,10,9,5,1]=>010110111=>[1,1,1,2,1,3]
[9,6,10,2,7,8,1,3,4,5]=>[2,5,1,9,4,3,10,8,7,6]=>010110111=>[1,1,1,2,1,3]
[9,5,10,2,6,7,1,3,4,8]=>[2,6,1,9,5,4,10,8,7,3]=>010110111=>[1,1,1,2,1,3]
[8,6,9,2,7,10,1,3,4,5]=>[3,5,2,9,4,1,10,8,7,6]=>010110111=>[1,1,1,2,1,3]
[8,5,9,2,6,10,1,3,4,7]=>[3,6,2,9,5,1,10,8,7,4]=>010110111=>[1,1,1,2,1,3]
[7,5,8,2,6,9,1,3,4,10]=>[4,6,3,9,5,2,10,8,7,1]=>010110111=>[1,1,1,2,1,3]
[8,4,9,2,5,10,1,3,6,7]=>[3,7,2,9,6,1,10,8,5,4]=>010110111=>[1,1,1,2,1,3]
[7,4,8,2,5,9,1,3,6,10]=>[4,7,3,9,6,2,10,8,5,1]=>010110111=>[1,1,1,2,1,3]
[8,1,2,4,3,6,5,7]=>[1,8,7,5,6,3,4,2]=>0110101=>[1,2,1,1,1,1]
[8,1,3,5,6,2,7,4]=>[1,8,6,4,3,7,2,5]=>0111010=>[1,3,1,1,1]
[8,1,3,4,2,6,7,5]=>[1,8,6,5,7,3,2,4]=>0110110=>[1,2,1,2,1]
[8,1,3,2,4,5,7,6]=>[1,8,6,7,5,4,2,3]=>0101110=>[1,1,1,3,1]
[2,7,8,3,4,5,6,1]=>[7,2,1,6,5,4,3,8]=>1101110=>[2,1,3,1]
[2,6,3,8,4,5,7,1]=>[7,3,6,1,5,4,2,8]=>1010110=>[1,1,1,1,2,1]
[6,3,2,1,4,5,8,7]=>[3,6,7,8,5,4,1,2]=>0001110=>[3,3,1]
[7,3,1,4,2,6,8,5]=>[2,6,8,5,7,3,1,4]=>0010110=>[2,1,1,2,1]
[7,4,1,5,6,8,2,3]=>[2,5,8,4,3,1,7,6]=>0011101=>[2,3,1,1]
[4,7,8,5,6,1,2,3]=>[5,2,1,4,3,8,7,6]=>1101011=>[2,1,1,1,2]
[3,7,8,5,6,2,1,4]=>[6,2,1,4,3,7,8,5]=>1101001=>[2,1,1,2,1]
[3,7,8,4,2,6,1,5]=>[6,2,1,5,7,3,8,4]=>1100101=>[2,2,1,1,1]
[3,7,8,2,4,5,1,6]=>[6,2,1,7,5,4,8,3]=>1101101=>[2,1,2,1,1]
[3,6,2,8,4,5,1,7]=>[6,3,7,1,5,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[2,3,6,7,4,5,8,1]=>[7,6,3,2,5,4,1,8]=>1110110=>[3,1,2,1]
[3,5,2,4,8,6,1,7]=>[6,4,7,5,1,3,8,2]=>1011001=>[1,1,2,2,1]
[3,5,4,2,8,7,1,6]=>[6,4,5,7,1,2,8,3]=>1001001=>[1,2,1,2,1]
[4,6,5,8,7,1,2,3]=>[5,3,4,1,2,8,7,6]=>1010011=>[1,1,1,2,2]
[6,4,5,1,7,8,2,3]=>[3,5,4,8,2,1,7,6]=>0101101=>[1,1,1,2,1,1]
[7,4,1,2,3,8,5,6]=>[2,5,8,7,6,1,4,3]=>0011101=>[2,3,1,1]
[6,2,4,1,3,7,5,8]=>[3,7,5,8,6,2,4,1]=>0101101=>[1,1,1,2,1,1]
[2,6,4,8,3,7,5,1]=>[7,3,5,1,6,2,4,8]=>1010100=>[1,1,1,1,1,2]
[2,6,5,8,7,3,4,1]=>[7,3,4,1,2,6,5,8]=>1010010=>[1,1,1,2,1,1]
[6,2,5,1,7,3,4,8]=>[3,7,4,8,2,6,5,1]=>0101011=>[1,1,1,1,1,2]
[6,5,2,1,8,3,4,7]=>[3,4,7,8,1,6,5,2]=>0001011=>[3,1,1,2]
[2,5,6,7,8,3,4,1]=>[7,4,3,2,1,6,5,8]=>1111010=>[4,1,1,1]
[2,4,6,7,3,8,5,1]=>[7,5,3,2,6,1,4,8]=>1110100=>[3,1,1,2]
[4,2,6,7,3,1,5,8]=>[5,7,3,2,6,8,4,1]=>0110011=>[1,2,2,2]
[4,7,8,2,3,1,5,6]=>[5,2,1,7,6,8,4,3]=>1101011=>[2,1,1,1,2]
[4,7,8,3,2,1,6,5]=>[5,2,1,6,7,8,3,4]=>1100010=>[2,3,1,1]
[5,6,4,8,1,7,2,3]=>[4,3,5,1,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,8,1,2,7,4]=>[4,3,6,1,8,7,2,5]=>1010110=>[1,1,1,1,2,1]
[4,2,5,3,7,1,6,8]=>[5,7,4,6,2,8,3,1]=>0101011=>[1,1,1,1,1,2]
[4,3,6,7,2,1,8,5]=>[5,6,3,2,7,8,1,4]=>0110010=>[1,2,2,1,1]
[3,4,6,7,2,8,1,5]=>[6,5,3,2,7,1,8,4]=>1110101=>[3,1,1,1,1]
[3,4,5,2,7,8,1,6]=>[6,5,4,7,2,1,8,3]=>1101101=>[2,1,2,1,1]
[3,4,2,5,6,8,1,7]=>[6,5,7,4,3,1,8,2]=>1011101=>[1,1,3,1,1]
[5,2,7,8,6,4,1,3]=>[4,7,2,1,3,5,8,6]=>0110001=>[1,2,3,1]
[5,1,2,7,8,6,4,3]=>[4,8,7,2,1,3,5,6]=>0111000=>[1,3,3]
[4,7,1,8,6,5,2,3]=>[5,2,8,1,3,4,7,6]=>1010001=>[1,1,1,3,1]
[4,7,1,2,8,6,5,3]=>[5,2,8,7,1,3,4,6]=>1011000=>[1,1,2,3]
[4,6,8,1,2,7,5,3]=>[5,3,1,8,7,2,4,6]=>1101100=>[2,1,2,2]
[6,8,7,1,5,3,2,4]=>[3,1,2,8,4,6,7,5]=>1001001=>[1,2,1,2,1]
[6,8,7,3,5,1,2,4]=>[3,1,2,6,4,8,7,5]=>1001011=>[1,2,1,1,2]
[7,8,1,6,3,5,2,4]=>[2,1,8,3,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,3,6,5,2,4]=>[2,1,8,6,3,4,7,5]=>1011001=>[1,1,2,2,1]
[7,8,3,6,5,2,1,4]=>[2,1,6,3,4,7,8,5]=>1010001=>[1,1,1,3,1]
[4,7,2,8,6,1,5,3]=>[5,2,7,1,3,8,4,6]=>1010010=>[1,1,1,2,1,1]
[1,7,3,4,8,6,5,2]=>[8,2,6,5,1,3,4,7]=>1011000=>[1,1,2,3]
[4,2,7,1,8,6,5,3]=>[5,7,2,8,1,3,4,6]=>0101000=>[1,1,1,1,3]
[7,8,2,3,6,5,1,4]=>[2,1,7,6,3,4,8,5]=>1011001=>[1,1,2,2,1]
[8,5,7,1,6,2,3,4]=>[1,4,2,8,3,7,6,5]=>0101011=>[1,1,1,1,1,2]
[8,5,7,1,2,6,3,4]=>[1,4,2,8,7,3,6,5]=>0101101=>[1,1,1,2,1,1]
[6,8,2,7,1,3,5,4]=>[3,1,7,2,8,6,4,5]=>1010110=>[1,1,1,1,2,1]
[6,8,7,2,5,3,1,4]=>[3,1,2,7,4,6,8,5]=>1001001=>[1,2,1,2,1]
[6,2,4,8,7,1,5,3]=>[3,7,5,1,2,8,4,6]=>0110010=>[1,2,2,1,1]
[1,6,8,3,7,4,5,2]=>[8,3,1,6,2,5,4,7]=>1101010=>[2,1,1,1,1,1]
[1,6,8,3,4,7,5,2]=>[8,3,1,6,5,2,4,7]=>1101100=>[2,1,2,2]
[6,2,4,8,1,7,5,3]=>[3,7,5,1,8,2,4,6]=>0110100=>[1,2,1,1,2]
[6,8,7,2,3,5,1,4]=>[3,1,2,7,6,4,8,5]=>1001101=>[1,2,2,1,1]
[6,8,2,1,7,3,5,4]=>[3,1,7,8,2,6,4,5]=>1001010=>[1,2,1,1,1,1]
[8,5,7,2,1,6,3,4]=>[1,4,2,7,8,3,6,5]=>0100101=>[1,1,2,1,1,1]
[8,5,7,1,2,3,6,4]=>[1,4,2,8,7,6,3,5]=>0101110=>[1,1,1,3,1]
[8,7,6,2,1,4,3,5]=>[1,2,3,7,8,5,6,4]=>0000101=>[4,1,1,1]
[8,5,7,2,3,1,6,4]=>[1,4,2,7,6,8,3,5]=>0101010=>[1,1,1,1,1,1,1]
[5,8,4,2,7,1,6,3]=>[4,1,5,7,2,8,3,6]=>1001010=>[1,2,1,1,1,1]
[1,8,7,5,3,4,6,2]=>[8,1,2,4,6,5,3,7]=>1000110=>[1,3,2,1]
[1,8,7,3,5,4,6,2]=>[8,1,2,6,4,5,3,7]=>1001010=>[1,2,1,1,1,1]
[8,2,5,4,7,1,6,3]=>[1,7,4,5,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]
[8,5,2,7,3,1,6,4]=>[1,4,7,2,6,8,3,5]=>0010010=>[2,1,2,1,1]
[8,7,6,2,4,3,1,5]=>[1,2,3,7,5,6,8,4]=>0001001=>[3,1,2,1]
[8,7,6,1,2,4,3,5]=>[1,2,3,8,7,5,6,4]=>0001101=>[3,2,1,1]
[8,7,6,1,4,2,3,5]=>[1,2,3,8,5,7,6,4]=>0001011=>[3,1,1,2]
[8,7,6,4,1,3,2,5]=>[1,2,3,5,8,6,7,4]=>0000101=>[4,1,1,1]
[5,8,4,7,2,1,6,3]=>[4,1,5,2,7,8,3,6]=>1010010=>[1,1,1,2,1,1]
[1,8,7,5,4,3,6,2]=>[8,1,2,4,5,6,3,7]=>1000010=>[1,4,1,1]
[1,6,8,4,3,7,5,2]=>[8,3,1,5,6,2,4,7]=>1100100=>[2,2,1,2]
[6,8,7,3,2,5,1,4]=>[3,1,2,6,7,4,8,5]=>1000101=>[1,3,1,1,1]
[6,8,1,7,3,2,5,4]=>[3,1,8,2,6,7,4,5]=>1010010=>[1,1,1,2,1,1]
[8,5,7,3,1,6,2,4]=>[1,4,2,6,8,3,7,5]=>0100101=>[1,1,2,1,1,1]
[8,5,7,1,3,2,6,4]=>[1,4,2,8,6,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,3,1,2,6,4]=>[1,4,2,6,8,7,3,5]=>0100110=>[1,1,2,2,1]
[5,8,4,7,1,2,6,3]=>[4,1,5,2,8,7,3,6]=>1010110=>[1,1,1,1,2,1]
[5,8,4,1,7,2,6,3]=>[4,1,5,8,2,7,3,6]=>1001010=>[1,2,1,1,1,1]
[5,8,4,7,1,6,2,3]=>[4,1,5,2,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[8,1,2,6,5,7,4,3]=>[1,8,7,3,4,2,5,6]=>0110100=>[1,2,1,1,2]
[8,2,5,6,7,4,1,3]=>[1,7,4,3,2,5,8,6]=>0111001=>[1,3,2,1]
[4,8,5,7,1,6,2,3]=>[5,1,4,2,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,5,7,1,2,6,3]=>[5,1,4,2,8,7,3,6]=>1010110=>[1,1,1,1,2,1]
[4,8,5,1,7,2,6,3]=>[5,1,4,8,2,7,3,6]=>1001010=>[1,2,1,1,1,1]
[8,5,3,1,7,2,6,4]=>[1,4,6,8,2,7,3,5]=>0001010=>[3,1,1,1,1]
[8,5,3,7,1,2,6,4]=>[1,4,6,2,8,7,3,5]=>0010110=>[2,1,1,2,1]
[6,8,1,3,7,2,5,4]=>[3,1,8,6,2,7,4,5]=>1011010=>[1,1,2,1,1,1]
[4,6,2,8,1,7,5,3]=>[5,3,7,1,8,2,4,6]=>1010100=>[1,1,1,1,1,2]
[1,6,4,8,3,7,5,2]=>[8,3,5,1,6,2,4,7]=>1010100=>[1,1,1,1,1,2]
[1,8,7,4,5,3,6,2]=>[8,1,2,5,4,6,3,7]=>1001010=>[1,2,1,1,1,1]
[4,8,5,7,2,1,6,3]=>[5,1,4,2,7,8,3,6]=>1010010=>[1,1,1,2,1,1]
[8,5,3,7,2,1,6,4]=>[1,4,6,2,7,8,3,5]=>0010010=>[2,1,2,1,1]
[8,7,6,3,1,4,2,5]=>[1,2,3,6,8,5,7,4]=>0000101=>[4,1,1,1]
[8,7,6,1,3,2,4,5]=>[1,2,3,8,6,7,5,4]=>0001011=>[3,1,1,2]
[8,5,3,2,7,1,6,4]=>[1,4,6,7,2,8,3,5]=>0001010=>[3,1,1,1,1]
[4,8,5,2,7,1,6,3]=>[5,1,4,7,2,8,3,6]=>1001010=>[1,2,1,1,1,1]
[1,8,7,4,3,5,6,2]=>[8,1,2,5,6,4,3,7]=>1000110=>[1,3,2,1]
[1,8,7,3,4,5,6,2]=>[8,1,2,6,5,4,3,7]=>1001110=>[1,2,3,1]
[8,2,4,5,7,1,6,3]=>[1,7,5,4,2,8,3,6]=>0111010=>[1,3,1,1,1]
[8,5,2,3,7,1,6,4]=>[1,4,7,6,2,8,3,5]=>0011010=>[2,2,1,1,1]
[6,3,1,5,4,2,8,7]=>[3,6,8,4,5,7,1,2]=>0010010=>[2,1,2,1,1]
[8,3,1,5,2,7,6,4]=>[1,6,8,4,7,2,3,5]=>0010100=>[2,1,1,1,2]
[8,5,4,2,1,7,3,6]=>[1,4,5,7,8,2,6,3]=>0000101=>[4,1,1,1]
[8,5,4,2,1,7,6,3]=>[1,4,5,7,8,2,3,6]=>0000100=>[4,1,2]
[6,5,4,2,1,3,8,7]=>[3,4,5,7,8,6,1,2]=>0000110=>[4,2,1]
[6,5,4,2,3,1,8,7]=>[3,4,5,7,6,8,1,2]=>0001010=>[3,1,1,1,1]
[6,3,2,5,1,4,8,7]=>[3,6,7,4,8,5,1,2]=>0010110=>[2,1,1,2,1]
[6,5,4,3,1,2,8,7]=>[3,4,5,6,8,7,1,2]=>0000110=>[4,2,1]
[6,5,4,1,3,2,8,7]=>[3,4,5,8,6,7,1,2]=>0001010=>[3,1,1,1,1]
[8,5,4,1,2,7,6,3]=>[1,4,5,8,7,2,3,6]=>0001100=>[3,2,2]
[8,7,4,1,6,3,2,5]=>[1,2,5,8,3,6,7,4]=>0001001=>[3,1,2,1]
[8,7,4,1,6,3,5,2]=>[1,2,5,8,3,6,4,7]=>0001010=>[3,1,1,1,1]
[8,7,4,1,6,5,3,2]=>[1,2,5,8,3,4,6,7]=>0001000=>[3,1,3]
[8,5,4,1,3,7,6,2]=>[1,4,5,8,6,2,3,7]=>0001100=>[3,2,2]
[8,5,4,3,1,7,6,2]=>[1,4,5,6,8,2,3,7]=>0000100=>[4,1,2]
[8,3,2,5,1,7,6,4]=>[1,6,7,4,8,2,3,5]=>0010100=>[2,1,1,1,2]
[2,1,8,5,3,7,6,4]=>[7,8,1,4,6,2,3,5]=>0100100=>[1,1,2,1,2]
[8,3,2,5,1,7,4,6]=>[1,6,7,4,8,2,5,3]=>0010101=>[2,1,1,1,1,1]
[8,5,4,3,1,7,2,6]=>[1,4,5,6,8,2,7,3]=>0000101=>[4,1,1,1]
[8,5,4,1,3,7,2,6]=>[1,4,5,8,6,2,7,3]=>0001101=>[3,2,1,1]
[8,7,4,1,6,5,2,3]=>[1,2,5,8,3,4,7,6]=>0001001=>[3,1,2,1]
[8,7,4,1,6,2,5,3]=>[1,2,5,8,3,7,4,6]=>0001010=>[3,1,1,1,1]
[8,7,6,5,2,1,4,3]=>[1,2,3,4,7,8,5,6]=>0000010=>[5,1,1]
[8,7,4,3,6,2,1,5]=>[1,2,5,6,3,7,8,4]=>0001001=>[3,1,2,1]
[8,3,2,7,6,4,1,5]=>[1,6,7,2,3,5,8,4]=>0010001=>[2,1,3,1]
[2,1,8,7,6,4,3,5]=>[7,8,1,2,3,5,6,4]=>0100001=>[1,1,4,1]
[2,1,8,7,6,4,5,3]=>[7,8,1,2,3,5,4,6]=>0100010=>[1,1,3,1,1]
[8,3,2,7,6,4,5,1]=>[1,6,7,2,3,5,4,8]=>0010010=>[2,1,2,1,1]
[8,7,4,3,6,2,5,1]=>[1,2,5,6,3,7,4,8]=>0001010=>[3,1,1,1,1]
[8,7,6,5,2,4,3,1]=>[1,2,3,4,7,5,6,8]=>0000100=>[4,1,2]
[8,5,4,2,3,7,6,1]=>[1,4,5,7,6,2,3,8]=>0001100=>[3,2,2]
[8,7,4,2,6,5,3,1]=>[1,2,5,7,3,4,6,8]=>0001000=>[3,1,3]
[8,7,4,2,6,3,5,1]=>[1,2,5,7,3,6,4,8]=>0001010=>[3,1,1,1,1]
[8,7,4,2,6,3,1,5]=>[1,2,5,7,3,6,8,4]=>0001001=>[3,1,2,1]
[8,3,1,7,6,4,2,5]=>[1,6,8,2,3,5,7,4]=>0010001=>[2,1,3,1]
[8,3,1,7,6,4,5,2]=>[1,6,8,2,3,5,4,7]=>0010010=>[2,1,2,1,1]
[8,3,1,7,6,5,4,2]=>[1,6,8,2,3,4,5,7]=>0010000=>[2,1,4]
[8,3,1,5,4,7,6,2]=>[1,6,8,4,5,2,3,7]=>0010100=>[2,1,1,1,2]
[8,3,1,5,4,7,2,6]=>[1,6,8,4,5,2,7,3]=>0010101=>[2,1,1,1,1,1]
[8,3,1,7,6,5,2,4]=>[1,6,8,2,3,4,7,5]=>0010001=>[2,1,3,1]
[8,3,1,7,6,2,5,4]=>[1,6,8,2,3,7,4,5]=>0010010=>[2,1,2,1,1]
[8,7,4,2,6,1,5,3]=>[1,2,5,7,3,8,4,6]=>0001010=>[3,1,1,1,1]
[8,7,4,2,6,5,1,3]=>[1,2,5,7,3,4,8,6]=>0001001=>[3,1,2,1]
[8,5,4,2,3,7,1,6]=>[1,4,5,7,6,2,8,3]=>0001101=>[3,2,1,1]
[8,3,2,5,4,7,1,6]=>[1,6,7,4,5,2,8,3]=>0010101=>[2,1,1,1,1,1]
[2,1,8,5,4,7,3,6]=>[7,8,1,4,5,2,6,3]=>0100101=>[1,1,2,1,1,1]
[8,3,2,7,6,5,1,4]=>[1,6,7,2,3,4,8,5]=>0010001=>[2,1,3,1]
[8,7,4,3,6,5,1,2]=>[1,2,5,6,3,4,8,7]=>0001001=>[3,1,2,1]
[8,7,6,5,3,1,4,2]=>[1,2,3,4,6,8,5,7]=>0000010=>[5,1,1]
[8,7,6,5,1,3,2,4]=>[1,2,3,4,8,6,7,5]=>0000101=>[4,1,1,1]
[8,7,6,5,1,3,4,2]=>[1,2,3,4,8,6,5,7]=>0000110=>[4,2,1]
[8,7,6,5,1,4,3,2]=>[1,2,3,4,8,5,6,7]=>0000100=>[4,1,2]
[8,7,6,5,4,1,3,2]=>[1,2,3,4,5,8,6,7]=>0000010=>[5,1,1]
[8,7,4,3,6,1,5,2]=>[1,2,5,6,3,8,4,7]=>0001010=>[3,1,1,1,1]
[8,3,2,7,6,1,5,4]=>[1,6,7,2,3,8,4,5]=>0010010=>[2,1,2,1,1]
[2,1,8,7,6,3,5,4]=>[7,8,1,2,3,6,4,5]=>0100010=>[1,1,3,1,1]
[8,3,2,7,6,1,4,5]=>[1,6,7,2,3,8,5,4]=>0010011=>[2,1,2,2]
[8,7,6,5,1,4,2,3]=>[1,2,3,4,8,5,7,6]=>0000101=>[4,1,1,1]
[8,7,6,5,1,2,4,3]=>[1,2,3,4,8,7,5,6]=>0000110=>[4,2,1]
[7,3,5,1,8,4,6,2]=>[2,6,4,8,1,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[7,3,4,1,8,5,6,2]=>[2,6,5,8,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,5,6,2,1,8,7,3]=>[5,4,3,7,8,1,2,6]=>1100100=>[2,2,1,2]
[1,6,5,2,7,4,3,8]=>[8,3,4,7,2,5,6,1]=>1001001=>[1,2,1,2,1]
[7,4,3,1,8,6,5,2]=>[2,5,6,8,1,3,4,7]=>0001000=>[3,1,3]
[7,6,5,1,8,4,3,2]=>[2,3,4,8,1,5,6,7]=>0001000=>[3,1,3]
[7,6,4,1,8,5,3,2]=>[2,3,5,8,1,4,6,7]=>0001000=>[3,1,3]
[6,4,2,1,8,7,5,3]=>[3,5,7,8,1,2,4,6]=>0001000=>[3,1,3]
[1,6,4,2,7,5,3,8]=>[8,3,5,7,2,4,6,1]=>1001001=>[1,2,1,2,1]
[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>1001001=>[1,2,1,2,1]
[5,3,2,1,8,7,6,4]=>[4,6,7,8,1,2,3,5]=>0001000=>[3,1,3]
[2,5,3,1,7,8,6,4]=>[7,4,6,8,2,1,3,5]=>1001100=>[1,2,2,2]
[2,6,4,1,7,8,5,3]=>[7,3,5,8,2,1,4,6]=>1001100=>[1,2,2,2]
[2,6,5,1,7,8,4,3]=>[7,3,4,8,2,1,5,6]=>1001100=>[1,2,2,2]
[4,5,7,1,6,8,2,3]=>[5,4,2,8,3,1,7,6]=>1101101=>[2,1,2,1,1]
[6,5,1,2,8,4,3,7]=>[3,4,8,7,1,5,6,2]=>0011001=>[2,2,2,1]
[6,4,1,2,8,5,3,7]=>[3,5,8,7,1,4,6,2]=>0011001=>[2,2,2,1]
[5,3,1,2,8,6,4,7]=>[4,6,8,7,1,3,5,2]=>0011001=>[2,2,2,1]
[4,3,1,2,8,6,5,7]=>[5,6,8,7,1,3,4,2]=>0011001=>[2,2,2,1]
[6,1,2,5,8,3,4,7]=>[3,8,7,4,1,6,5,2]=>0111011=>[1,3,1,2]
[7,1,3,4,8,2,5,6]=>[2,8,6,5,1,7,4,3]=>0111011=>[1,3,1,2]
[7,1,5,6,8,2,3,4]=>[2,8,4,3,1,7,6,5]=>0111011=>[1,3,1,2]
[2,6,1,5,7,8,3,4]=>[7,3,8,4,2,1,6,5]=>1011101=>[1,1,3,1,1]
[7,4,1,6,8,5,2,3]=>[2,5,8,3,1,4,7,6]=>0011001=>[2,2,2,1]
[5,2,3,1,8,6,7,4]=>[4,7,6,8,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]
[3,5,2,1,6,8,7,4]=>[6,4,7,8,3,1,2,5]=>1001100=>[1,2,2,2]
[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>1011011=>[1,1,2,1,2]
[6,2,1,5,8,7,3,4]=>[3,7,8,4,1,2,6,5]=>0011001=>[2,2,2,1]
[7,3,1,5,8,6,2,4]=>[2,6,8,4,1,3,7,5]=>0011001=>[2,2,2,1]
[6,2,4,1,8,5,7,3]=>[3,7,5,8,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]
[6,2,5,1,8,4,7,3]=>[3,7,4,8,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,3,1,4,8,6,2,5]=>[2,6,8,5,1,3,7,4]=>0011001=>[2,2,2,1]
[6,2,1,4,8,7,3,5]=>[3,7,8,5,1,2,6,4]=>0011001=>[2,2,2,1]
[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>1011011=>[1,1,2,1,2]
[5,2,1,3,8,7,4,6]=>[4,7,8,6,1,2,5,3]=>0011001=>[2,2,2,1]
[7,4,1,3,8,5,2,6]=>[2,5,8,6,1,4,7,3]=>0011001=>[2,2,2,1]
[7,5,1,3,8,4,2,6]=>[2,4,8,6,1,5,7,3]=>0011001=>[2,2,2,1]
[3,6,7,1,4,8,2,5]=>[6,3,2,8,5,1,7,4]=>1101101=>[2,1,2,1,1]
[7,6,1,4,8,3,2,5]=>[2,3,8,5,1,6,7,4]=>0011001=>[2,2,2,1]
[4,2,1,3,8,7,5,6]=>[5,7,8,6,1,2,4,3]=>0011001=>[2,2,2,1]
[2,6,1,4,7,8,3,5]=>[7,3,8,5,2,1,6,4]=>1011101=>[1,1,3,1,1]
[7,1,4,6,8,2,3,5]=>[2,8,5,3,1,7,6,4]=>0111011=>[1,3,1,2]
[7,1,3,5,8,2,4,6]=>[2,8,6,4,1,7,5,3]=>0111011=>[1,3,1,2]
[6,1,2,4,8,3,5,7]=>[3,8,7,5,1,6,4,2]=>0111011=>[1,3,1,2]
[5,2,3,1,6,4,8,7]=>[4,7,6,8,3,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[7,4,5,2,3,1,8,6]=>[2,5,4,7,6,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,3,5,2,4,1]=>[1,3,2,6,4,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[7,3,5,2,4,1,8,6]=>[2,6,4,7,5,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[6,3,5,2,4,1,8,7]=>[3,6,4,7,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,4,1,6,3,8,7]=>[4,7,5,8,3,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,3,5,2,8,7]=>[5,8,3,6,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,3,4,1,5,2,8,7]=>[3,6,5,8,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,3,4,1,8,7]=>[4,7,3,6,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,7,3,4,1,8,6]=>[4,7,2,6,5,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[5,2,8,6,7,3,4,1]=>[4,7,1,3,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[6,2,8,5,7,3,4,1]=>[3,7,1,4,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,3,4,1,8,5]=>[3,7,2,6,5,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[7,3,4,1,5,2,8,6]=>[2,6,5,8,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,3,5,2,8,6]=>[5,8,2,6,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,7,4,5,2,8,6]=>[6,8,2,5,4,7,1,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,4,5,3,8,6]=>[7,8,2,5,4,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,6,7,4,5,2]=>[6,8,1,3,2,5,4,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,6,7,3,5,2]=>[5,8,1,3,2,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,3,4,1,5,2]=>[1,3,2,6,5,8,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,3,4,1,6,2]=>[1,4,2,6,5,8,3,7]=>0101010=>[1,1,1,1,1,1,1]
[8,5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,3,5,1,6,2]=>[1,5,2,6,4,8,3,7]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,4,7,3,6,2]=>[4,8,1,5,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,5,7,3,6,2]=>[5,8,1,4,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,5,7,4,6,2]=>[6,8,1,4,2,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,5,7,4,6,3]=>[7,8,1,4,2,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,4,6,3,8,5]=>[7,8,2,5,3,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[3,1,7,4,6,2,8,5]=>[6,8,2,5,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,3,6,2,8,5]=>[5,8,2,6,3,7,1,4]=>0101010=>[1,1,1,1,1,1,1]
[5,1,7,3,6,2,8,4]=>[4,8,2,6,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,3,5,1,8,4]=>[3,7,2,6,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,8,4,7,3,5,1]=>[3,7,1,5,2,6,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[7,3,6,2,5,1,8,4]=>[2,6,3,7,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,5,1,7,3,8,4]=>[3,7,4,8,2,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[5,2,4,1,7,3,8,6]=>[4,7,5,8,2,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[6,2,4,1,7,3,8,5]=>[3,7,5,8,2,6,1,4]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,4,6,2,3,1]=>[1,4,2,5,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[7,4,6,2,3,1,8,5]=>[2,5,3,7,6,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[6,2,3,1,7,4,8,5]=>[3,7,6,8,2,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[5,2,3,1,7,4,8,6]=>[4,7,6,8,2,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,3,1,7,5,8,6]=>[5,7,6,8,2,4,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,1,4,2,8,6,7,5]=>[6,8,5,7,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]
[6,2,3,1,8,5,7,4]=>[3,7,6,8,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,5,6,2,3,1,7,4]=>[1,4,3,7,6,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[7,4,8,5,6,2,3,1]=>[2,5,1,4,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,5,6,2,4,1]=>[2,6,1,4,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,5,6,2,4,1,7,3]=>[1,4,3,7,5,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,4,1,8,6,7,3]=>[4,7,5,8,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,5,2,8,6,7,3]=>[5,8,4,7,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]
[3,1,5,2,8,6,7,4]=>[6,8,4,7,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,3,8,5,7,4]=>[7,8,3,6,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,2,8,5,7,4]=>[6,8,3,7,1,4,2,5]=>0101010=>[1,1,1,1,1,1,1]
[4,1,6,2,8,5,7,3]=>[5,8,3,7,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]
[5,1,6,2,8,4,7,3]=>[4,8,3,7,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[8,4,6,2,5,1,7,3]=>[1,5,3,7,4,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,4,6,2,5,1]=>[2,6,1,5,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,3,8,4,5,1]=>[3,7,2,6,1,5,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,5,1,6,2,7,3]=>[1,5,4,8,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,4,6,2,7,3]=>[4,8,1,5,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,5,6,2,7,3]=>[5,8,1,4,3,7,2,6]=>0101010=>[1,1,1,1,1,1,1]
[3,1,8,5,6,2,7,4]=>[6,8,1,4,3,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,5,6,3,7,4]=>[7,8,1,4,3,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,4,8,5,6,3]=>[7,8,2,5,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]
[3,1,7,4,8,5,6,2]=>[6,8,2,5,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,3,8,5,6,2]=>[5,8,2,6,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,4,5,1,6,2]=>[2,6,1,5,4,8,3,7]=>0101010=>[1,1,1,1,1,1,1]
[8,4,5,1,7,3,6,2]=>[1,5,4,8,2,6,3,7]=>0101010=>[1,1,1,1,1,1,1]
[7,3,6,2,8,4,5,1]=>[2,6,3,7,1,5,4,8]=>0101010=>[1,1,1,1,1,1,1]
[7,8,5,6,1,3,4,2]=>[2,1,4,3,8,6,5,7]=>1010110=>[1,1,1,1,2,1]
[7,8,1,3,6,2,5,4]=>[2,1,8,6,3,7,4,5]=>1011010=>[1,1,2,1,1,1]
[1,3,8,4,7,2,5,6]=>[8,6,1,5,2,7,4,3]=>1101011=>[2,1,1,1,2]
[3,6,1,4,7,2,5,8]=>[6,3,8,5,2,7,4,1]=>1011011=>[1,1,2,1,2]
[4,6,1,2,5,7,3,8]=>[5,3,8,7,4,2,6,1]=>1011101=>[1,1,3,1,1]
[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>1101101=>[2,1,2,1,1]
[7,8,2,4,5,6,1,3]=>[2,1,7,5,4,3,8,6]=>1011101=>[1,1,3,1,1]
[7,8,2,1,6,3,4,5]=>[2,1,7,8,3,6,5,4]=>1001011=>[1,2,1,1,2]
[7,8,3,5,6,4,1,2]=>[2,1,6,4,3,5,8,7]=>1011001=>[1,1,2,2,1]
[7,8,5,1,4,2,6,3]=>[2,1,4,8,5,7,3,6]=>1001010=>[1,2,1,1,1,1]
[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>1100010=>[2,3,1,1]
[5,6,1,4,3,2,7,8]=>[4,3,8,5,6,7,2,1]=>1010011=>[1,1,1,2,2]
[2,6,4,8,3,7,1,5]=>[7,3,5,1,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[1,4,6,8,3,7,5,2]=>[8,5,3,1,6,2,4,7]=>1110100=>[3,1,1,2]
[2,5,8,1,4,7,6,3]=>[7,4,1,8,5,2,3,6]=>1101100=>[2,1,2,2]
[3,5,8,4,7,6,1,2]=>[6,4,1,5,2,3,8,7]=>1101001=>[2,1,1,2,1]
[1,6,2,4,7,3,8,5]=>[8,3,7,5,2,6,1,4]=>1011010=>[1,1,2,1,1,1]
[5,6,2,1,4,7,8,3]=>[4,3,7,8,5,2,1,6]=>1001110=>[1,2,3,1]
[4,6,2,5,3,1,8,7]=>[5,3,7,4,6,8,1,2]=>1010010=>[1,1,1,2,1,1]
[7,5,3,6,2,4,1,8]=>[2,4,6,3,7,5,8,1]=>0010101=>[2,1,1,1,1,1]
[5,7,3,6,1,4,8,2]=>[4,2,6,3,8,5,1,7]=>1010110=>[1,1,1,1,2,1]
[4,6,7,8,3,5,1,2]=>[5,3,2,1,6,4,8,7]=>1110101=>[3,1,1,1,1]
[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>1101010=>[2,1,1,1,1,1]
[3,5,6,7,8,1,4,2]=>[6,4,3,2,1,8,5,7]=>1111010=>[4,1,1,1]
[3,6,5,7,8,2,1,4]=>[6,3,4,2,1,7,8,5]=>1011001=>[1,1,2,2,1]
[5,2,7,6,1,4,3,8]=>[4,7,2,3,8,5,6,1]=>0100101=>[1,1,2,1,1,1]
[2,1,6,8,4,5,3,7]=>[7,8,3,1,5,4,6,2]=>0110101=>[1,2,1,1,1,1]
[2,7,1,8,5,3,4,6]=>[7,2,8,1,4,6,5,3]=>1010011=>[1,1,1,2,2]
[3,7,6,8,5,4,1,2]=>[6,2,3,1,4,5,8,7]=>1010001=>[1,1,1,3,1]
[3,1,8,5,4,6,7,2]=>[6,8,1,4,5,3,2,7]=>0100110=>[1,1,2,2,1]
[3,4,7,1,5,2,6,8]=>[6,5,2,8,4,7,3,1]=>1101011=>[2,1,1,1,2]
[4,3,7,8,1,2,6,5]=>[5,6,2,1,8,7,3,4]=>0110110=>[1,2,1,2,1]
[1,7,3,8,5,2,6,4]=>[8,2,6,1,4,7,3,5]=>1010010=>[1,1,1,2,1,1]
[5,7,8,6,3,2,1,4]=>[4,2,1,3,6,7,8,5]=>1100001=>[2,4,1]
[5,7,8,6,1,3,4,2]=>[4,2,1,3,8,6,5,7]=>1100110=>[2,2,2,1]
[7,6,5,8,1,3,4,2]=>[2,3,4,1,8,6,5,7]=>0010110=>[2,1,1,2,1]
[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>1001011=>[1,2,1,1,2]
[7,1,3,4,8,2,6,5]=>[2,8,6,5,1,7,3,4]=>0111010=>[1,3,1,1,1]
[3,6,5,4,1,2,7,8]=>[6,3,4,5,8,7,2,1]=>1000111=>[1,3,3]
[7,2,5,6,3,8,1,4]=>[2,7,4,3,6,1,8,5]=>0110101=>[1,2,1,1,1,1]
[6,5,2,7,1,8,4,3]=>[3,4,7,2,8,1,5,6]=>0010100=>[2,1,1,1,2]
[5,6,2,7,3,1,4,8]=>[4,3,7,2,6,8,5,1]=>1010011=>[1,1,1,2,2]
[5,7,6,4,1,8,3,2]=>[4,2,3,5,8,1,6,7]=>1000100=>[1,3,1,2]
[6,1,5,2,8,3,4,7]=>[3,8,4,7,1,6,5,2]=>0101011=>[1,1,1,1,1,2]
[6,7,5,3,8,4,1,2]=>[3,2,4,6,1,5,8,7]=>1001001=>[1,2,1,2,1]
[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>1000110=>[1,3,2,1]
[6,7,5,4,3,1,8,2]=>[3,2,4,5,6,8,1,7]=>1000010=>[1,4,1,1]
[7,5,2,4,3,1,6,8]=>[2,4,7,5,6,8,3,1]=>0010011=>[2,1,2,2]
[7,4,6,1,2,5,3,8]=>[2,5,3,8,7,4,6,1]=>0101101=>[1,1,1,2,1,1]
[7,1,4,2,5,3,6,8]=>[2,8,5,7,4,6,3,1]=>0101011=>[1,1,1,1,1,2]
[6,8,1,4,2,5,7,3]=>[3,1,8,5,7,4,2,6]=>1010110=>[1,1,1,1,2,1]
[1,6,4,2,5,7,3,8]=>[8,3,5,7,4,2,6,1]=>1001101=>[1,2,2,1,1]
[1,6,3,7,5,4,2,8]=>[8,3,6,2,4,5,7,1]=>1010001=>[1,1,1,3,1]
[6,8,1,3,7,5,4,2]=>[3,1,8,6,2,4,5,7]=>1011000=>[1,1,2,3]
[7,1,3,5,6,4,2,8]=>[2,8,6,4,3,5,7,1]=>0111001=>[1,3,2,1]
[7,3,1,6,4,5,2,8]=>[2,6,8,3,5,4,7,1]=>0010101=>[2,1,1,1,1,1]
[7,4,2,6,5,1,3,8]=>[2,5,7,3,4,8,6,1]=>0010011=>[2,1,2,2]
[7,4,6,3,1,5,2,8]=>[2,5,3,6,8,4,7,1]=>0100101=>[1,1,2,1,1,1]
[7,2,4,1,5,3,6,8]=>[2,7,5,8,4,6,3,1]=>0101011=>[1,1,1,1,1,2]
[7,2,3,5,4,1,6,8]=>[2,7,6,4,5,8,3,1]=>0110011=>[1,2,2,2]
[6,8,1,2,3,4,7,5]=>[3,1,8,7,6,5,2,4]=>1011110=>[1,1,4,1]
[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>1101100=>[2,1,2,2]
[5,1,8,2,3,6,7,4]=>[4,8,1,7,6,3,2,5]=>0101110=>[1,1,1,3,1]
[5,8,2,3,7,6,4,1]=>[4,1,7,6,2,3,5,8]=>1011000=>[1,1,2,3]
[6,2,8,1,3,7,4,5]=>[3,7,1,8,6,2,5,4]=>0101101=>[1,1,1,2,1,1]
[6,8,2,3,5,4,7,1]=>[3,1,7,6,4,5,2,8]=>1011010=>[1,1,2,1,1,1]
[6,8,2,4,1,5,7,3]=>[3,1,7,5,8,4,2,6]=>1010110=>[1,1,1,1,2,1]
[6,8,3,1,2,4,7,5]=>[3,1,6,8,7,5,2,4]=>1001110=>[1,2,3,1]
[2,6,4,1,5,7,3,8]=>[7,3,5,8,4,2,6,1]=>1001101=>[1,2,2,1,1]
[2,6,3,5,7,1,4,8]=>[7,3,6,4,2,8,5,1]=>1011011=>[1,1,2,1,2]
[2,5,1,7,8,3,6,4]=>[7,4,8,2,1,6,3,5]=>1011010=>[1,1,2,1,1,1]
[2,5,3,6,8,4,7,1]=>[7,4,6,3,1,5,2,8]=>1011010=>[1,1,2,1,1,1]
[2,1,4,7,8,5,6,3]=>[7,8,5,2,1,4,3,6]=>0111010=>[1,3,1,1,1]
[2,4,7,6,8,5,1,3]=>[7,5,2,3,1,4,8,6]=>1101001=>[2,1,1,2,1]
[2,5,3,7,6,1,8,4]=>[7,4,6,2,3,8,1,5]=>1010010=>[1,1,1,2,1,1]
[2,5,7,8,1,4,6,3]=>[7,4,2,1,8,5,3,6]=>1110110=>[3,1,2,1]
[3,5,7,4,1,6,2,8]=>[6,4,2,5,8,3,7,1]=>1100101=>[2,2,1,1,1]
[5,3,4,1,8,6,7,2]=>[4,6,5,8,1,3,2,7]=>0101010=>[1,1,1,1,1,1,1]
[5,2,8,4,6,1,7,3]=>[4,7,1,5,3,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,1,8,6,3,7,4]=>[4,7,8,1,3,6,2,5]=>0010010=>[2,1,2,1,1]
[4,2,8,6,5,3,7,1]=>[5,7,1,3,4,6,2,8]=>0100010=>[1,1,3,1,1]
[4,2,8,5,7,6,3,1]=>[5,7,1,4,2,3,6,8]=>0101000=>[1,1,1,1,3]
[1,4,2,7,5,8,6,3]=>[8,5,7,2,4,1,3,6]=>1010100=>[1,1,1,1,1,2]
[4,1,8,6,7,5,3,2]=>[5,8,1,3,2,4,6,7]=>0101000=>[1,1,1,1,3]
[5,3,8,7,6,2,4,1]=>[4,6,1,2,3,7,5,8]=>0100010=>[1,1,3,1,1]
[5,8,4,7,6,2,1,3]=>[4,1,5,2,3,7,8,6]=>1010001=>[1,1,1,3,1]
[5,8,7,4,3,6,1,2]=>[4,1,2,5,6,3,8,7]=>1000101=>[1,3,1,1,1]
[6,4,8,3,1,7,2,5]=>[3,5,1,6,8,2,7,4]=>0100101=>[1,1,2,1,1,1]
[6,4,2,8,7,1,3,5]=>[3,5,7,1,2,8,6,4]=>0010011=>[2,1,2,2]
[6,3,8,7,2,5,1,4]=>[3,6,1,2,7,4,8,5]=>0100101=>[1,1,2,1,1,1]
[5,8,3,7,1,6,4,2]=>[4,1,6,2,8,3,5,7]=>1010100=>[1,1,1,1,1,2]
[5,1,3,8,6,7,2,4]=>[4,8,6,1,3,2,7,5]=>0110101=>[1,2,1,1,1,1]
[1,5,3,7,8,6,2,4]=>[8,4,6,2,1,3,7,5]=>1011001=>[1,1,2,2,1]
[1,5,7,6,4,2,8,3]=>[8,4,2,3,5,7,1,6]=>1100010=>[2,3,1,1]
[5,8,7,4,1,6,2,3]=>[4,1,2,5,8,3,7,6]=>1000101=>[1,3,1,1,1]
[6,4,8,1,2,7,3,5]=>[3,5,1,8,7,2,6,4]=>0101101=>[1,1,1,2,1,1]
[6,8,5,1,2,3,7,4]=>[3,1,4,8,7,6,2,5]=>1001110=>[1,2,3,1]
[6,8,5,2,4,3,7,1]=>[3,1,4,7,5,6,2,8]=>1001010=>[1,2,1,1,1,1]
[6,8,5,3,1,2,7,4]=>[3,1,4,6,8,7,2,5]=>1000110=>[1,3,2,1]
[4,5,1,2,7,6,3,8]=>[5,4,8,7,2,3,6,1]=>1011001=>[1,1,2,2,1]
[4,5,1,2,6,8,7,3]=>[5,4,8,7,3,1,2,6]=>1011100=>[1,1,3,2]
[3,5,6,1,8,4,7,2]=>[6,4,3,8,1,5,2,7]=>1101010=>[2,1,1,1,1,1]
[3,5,7,1,2,8,6,4]=>[6,4,2,8,7,1,3,5]=>1101100=>[2,1,2,2]
[3,6,2,7,5,1,4,8]=>[6,3,7,2,4,8,5,1]=>1010011=>[1,1,1,2,2]
[4,2,6,1,7,3,5,8]=>[5,7,3,8,2,6,4,1]=>0101011=>[1,1,1,1,1,2]
[4,6,3,1,2,7,5,8]=>[5,3,6,8,7,2,4,1]=>1001101=>[1,2,2,1,1]
[4,5,3,1,7,6,2,8]=>[5,4,6,8,2,3,7,1]=>1001001=>[1,2,1,2,1]
[4,2,5,7,1,6,3,8]=>[5,7,4,2,8,3,6,1]=>0110101=>[1,2,1,1,1,1]
[3,5,2,7,8,1,6,4]=>[6,4,7,2,1,8,3,5]=>1011010=>[1,1,2,1,1,1]
[3,1,4,7,5,6,2,8]=>[6,8,5,2,4,3,7,1]=>0110101=>[1,2,1,1,1,1]
[3,4,6,5,8,7,1,2]=>[6,5,3,4,1,2,8,7]=>1101001=>[2,1,1,2,1]
[3,1,4,5,8,6,7,2]=>[6,8,5,4,1,3,2,7]=>0111010=>[1,3,1,1,1]
[3,4,6,8,5,2,7,1]=>[6,5,3,1,4,7,2,8]=>1110010=>[3,2,1,1]
[3,5,6,2,8,4,7,1]=>[6,4,3,7,1,5,2,8]=>1101010=>[2,1,1,1,1,1]
[4,2,5,6,1,8,7,3]=>[5,7,4,3,8,1,2,6]=>0110100=>[1,2,1,1,2]
[4,5,3,1,6,8,7,2]=>[5,4,6,8,3,1,2,7]=>1001100=>[1,2,2,2]
[2,1,7,5,8,6,4,3]=>[7,8,2,4,1,3,5,6]=>0101000=>[1,1,1,1,3]
[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>1100100=>[2,2,1,2]
[4,1,2,7,3,8,6,5]=>[5,8,7,2,6,1,3,4]=>0110100=>[1,2,1,1,2]
[6,4,1,7,5,2,3,8]=>[3,5,8,2,4,7,6,1]=>0010011=>[2,1,2,2]
[6,1,3,7,5,2,4,8]=>[3,8,6,2,4,7,5,1]=>0110011=>[1,2,2,2]
[3,1,2,6,8,5,4,7]=>[6,8,7,3,1,4,5,2]=>0111001=>[1,3,2,1]
[3,7,1,2,5,4,8,6]=>[6,2,8,7,4,5,1,3]=>1011010=>[1,1,2,1,1,1]
[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>1101100=>[2,1,2,2]
[2,4,1,7,8,6,5,3]=>[7,5,8,2,1,3,4,6]=>1011000=>[1,1,2,3]
[3,4,7,5,1,8,6,2]=>[6,5,2,4,8,1,3,7]=>1100100=>[2,2,1,2]
[2,7,4,1,5,8,6,3]=>[7,2,5,8,4,1,3,6]=>1001100=>[1,2,2,2]
[2,3,7,1,5,8,6,4]=>[7,6,2,8,4,1,3,5]=>1101100=>[2,1,2,2]
[5,2,8,1,3,7,4,6]=>[4,7,1,8,6,2,5,3]=>0101101=>[1,1,1,2,1,1]
[2,1,6,8,3,4,7,5]=>[7,8,3,1,6,5,2,4]=>0110110=>[1,2,1,2,1]
[2,6,8,3,1,5,7,4]=>[7,3,1,6,8,4,2,5]=>1100110=>[2,2,2,1]
[2,8,6,4,1,5,7,3]=>[7,1,3,5,8,4,2,6]=>1000110=>[1,3,2,1]
[3,6,4,8,5,1,7,2]=>[6,3,5,1,4,8,2,7]=>1010010=>[1,1,1,2,1,1]
[6,3,7,4,5,1,8,2]=>[3,6,2,5,4,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[2,6,3,7,5,8,1,4]=>[7,3,6,2,4,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,2,1,7,8,3,4,6]=>[4,7,8,2,1,6,5,3]=>0011011=>[2,2,1,2]
[4,7,2,3,6,8,1,5]=>[5,2,7,6,3,1,8,4]=>1011101=>[1,1,3,1,1]
[5,2,7,3,6,8,1,4]=>[4,7,2,6,3,1,8,5]=>0101101=>[1,1,1,2,1,1]
[5,7,4,6,2,8,1,3]=>[4,2,5,3,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,4,6,1,8,2]=>[4,2,6,5,3,8,1,7]=>1011010=>[1,1,2,1,1,1]
[5,3,8,4,6,1,7,2]=>[4,6,1,5,3,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[8,5,2,4,1,6,7,3]=>[1,4,7,5,8,3,2,6]=>0010110=>[2,1,1,2,1]
[8,2,3,5,1,6,7,4]=>[1,7,6,4,8,3,2,5]=>0110110=>[1,2,1,2,1]
[4,2,8,3,6,7,1,5]=>[5,7,1,6,3,2,8,4]=>0101101=>[1,1,1,2,1,1]
[2,4,8,1,7,3,5,6]=>[7,5,1,8,2,6,4,3]=>1101011=>[2,1,1,1,2]
[8,4,1,3,6,2,5,7]=>[1,5,8,6,3,7,4,2]=>0011011=>[2,2,1,2]
[4,8,3,1,7,2,5,6]=>[5,1,6,8,2,7,4,3]=>1001011=>[1,2,1,1,2]
[5,2,8,4,7,1,6,3]=>[4,7,1,5,2,8,3,6]=>0101010=>[1,1,1,1,1,1,1]
[5,8,4,7,3,1,6,2]=>[4,1,5,2,6,8,3,7]=>1010010=>[1,1,1,2,1,1]
[4,6,8,3,1,7,5,2]=>[5,3,1,6,8,2,4,7]=>1100100=>[2,2,1,2]
[6,3,8,2,7,1,5,4]=>[3,6,1,7,2,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[6,3,1,8,2,4,7,5]=>[3,6,8,1,7,5,2,4]=>0010110=>[2,1,1,2,1]
[5,3,8,1,2,6,4,7]=>[4,6,1,8,7,3,5,2]=>0101101=>[1,1,1,2,1,1]
[5,7,4,1,6,2,3,8]=>[4,2,5,8,3,7,6,1]=>1001011=>[1,2,1,1,2]
[8,5,4,1,2,6,3,7]=>[1,4,5,8,7,3,6,2]=>0001101=>[3,2,1,1]
[5,1,8,4,2,7,3,6]=>[4,8,1,5,7,2,6,3]=>0100101=>[1,1,2,1,1,1]
[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>1010010=>[1,1,1,2,1,1]
[6,8,5,3,1,7,4,2]=>[3,1,4,6,8,2,5,7]=>1000100=>[1,3,1,2]
[8,4,5,1,2,6,3,7]=>[1,5,4,8,7,3,6,2]=>0101101=>[1,1,1,2,1,1]
[5,6,3,7,1,2,4,8]=>[4,3,6,2,8,7,5,1]=>1010111=>[1,1,1,1,3]
[1,6,3,7,2,8,4,5]=>[8,3,6,2,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[6,3,2,7,8,5,1,4]=>[3,6,7,2,1,4,8,5]=>0011001=>[2,2,2,1]
[4,5,7,8,3,1,6,2]=>[5,4,2,1,6,8,3,7]=>1110010=>[3,2,1,1]
[4,7,2,5,8,1,6,3]=>[5,2,7,4,1,8,3,6]=>1011010=>[1,1,2,1,1,1]
[8,1,3,4,6,2,5,7]=>[1,8,6,5,3,7,4,2]=>0111011=>[1,3,1,2]
[3,8,2,4,6,7,1,5]=>[6,1,7,5,3,2,8,4]=>1011101=>[1,1,3,1,1]
[3,5,6,8,2,7,1,4]=>[6,4,3,1,7,2,8,5]=>1110101=>[3,1,1,1,1]
[2,4,5,6,8,1,7,3]=>[7,5,4,3,1,8,2,6]=>1111010=>[4,1,1,1]
[4,8,3,5,6,1,7,2]=>[5,1,6,4,3,8,2,7]=>1011010=>[1,1,2,1,1,1]
[5,6,2,3,7,8,1,4]=>[4,3,7,6,2,1,8,5]=>1011101=>[1,1,3,1,1]
[5,8,7,3,4,1,2,6]=>[4,1,2,6,5,8,7,3]=>1001011=>[1,2,1,1,2]
[6,8,7,3,4,1,2,5]=>[3,1,2,6,5,8,7,4]=>1001011=>[1,2,1,1,2]
[6,8,4,7,1,5,3,2]=>[3,1,5,2,8,4,6,7]=>1010100=>[1,1,1,1,1,2]
[6,8,4,7,2,5,3,1]=>[3,1,5,2,7,4,6,8]=>1010100=>[1,1,1,1,1,2]
[5,4,8,7,2,6,3,1]=>[4,5,1,2,7,3,6,8]=>0100100=>[1,1,2,1,2]
[5,4,8,7,1,6,3,2]=>[4,5,1,2,8,3,6,7]=>0100100=>[1,1,2,1,2]
[5,3,8,7,6,1,2,4]=>[4,6,1,2,3,8,7,5]=>0100011=>[1,1,3,2]
[4,3,8,7,6,1,2,5]=>[5,6,1,2,3,8,7,4]=>0100011=>[1,1,3,2]
[4,8,3,7,5,1,2,6]=>[5,1,6,2,4,8,7,3]=>1010011=>[1,1,1,2,2]
[8,3,4,6,5,1,2,7]=>[1,6,5,3,4,8,7,2]=>0110011=>[1,2,2,2]
[3,8,4,7,5,1,2,6]=>[6,1,5,2,4,8,7,3]=>1010011=>[1,1,1,2,2]
[3,4,8,7,6,1,2,5]=>[6,5,1,2,3,8,7,4]=>1100011=>[2,3,2]
[3,5,8,7,6,1,2,4]=>[6,4,1,2,3,8,7,5]=>1100011=>[2,3,2]
[4,5,8,7,6,1,2,3]=>[5,4,1,2,3,8,7,6]=>1100011=>[2,3,2]
[4,5,8,7,1,6,3,2]=>[5,4,1,2,8,3,6,7]=>1100100=>[2,2,1,2]
[4,5,8,7,2,6,3,1]=>[5,4,1,2,7,3,6,8]=>1100100=>[2,2,1,2]
[3,5,8,2,7,6,4,1]=>[6,4,1,7,2,3,5,8]=>1101000=>[2,1,1,3]
[3,5,8,1,7,6,4,2]=>[6,4,1,8,2,3,5,7]=>1101000=>[2,1,1,3]
[2,5,8,1,7,6,4,3]=>[7,4,1,8,2,3,5,6]=>1101000=>[2,1,1,3]
[2,5,8,7,1,6,3,4]=>[7,4,1,2,8,3,6,5]=>1100101=>[2,2,1,1,1]
[2,4,8,7,1,6,3,5]=>[7,5,1,2,8,3,6,4]=>1100101=>[2,2,1,1,1]
[2,8,4,7,1,5,3,6]=>[7,1,5,2,8,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[8,2,4,6,1,5,3,7]=>[1,7,5,3,8,4,6,2]=>0110101=>[1,2,1,1,1,1]
[8,1,4,6,2,5,3,7]=>[1,8,5,3,7,4,6,2]=>0110101=>[1,2,1,1,1,1]
[1,8,4,7,2,5,3,6]=>[8,1,5,2,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>1100101=>[2,2,1,1,1]
[1,5,8,7,2,6,3,4]=>[8,4,1,2,7,3,6,5]=>1100101=>[2,2,1,1,1]
[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>1101000=>[2,1,1,3]
[2,5,8,3,7,6,4,1]=>[7,4,1,6,2,3,5,8]=>1101000=>[2,1,1,3]
[1,4,2,8,7,6,5,3]=>[8,5,7,1,2,3,4,6]=>1010000=>[1,1,1,4]
[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>1101001=>[2,1,1,2,1]
[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>1001001=>[1,2,1,2,1]
[8,1,3,2,6,5,4,7]=>[1,8,6,7,3,4,5,2]=>0101001=>[1,1,1,1,2,1]
[8,2,3,1,6,5,4,7]=>[1,7,6,8,3,4,5,2]=>0101001=>[1,1,1,1,2,1]
[2,8,3,1,7,5,4,6]=>[7,1,6,8,2,4,5,3]=>1001001=>[1,2,1,2,1]
[2,3,8,1,7,6,4,5]=>[7,6,1,8,2,3,5,4]=>1101001=>[2,1,1,2,1]
[3,4,1,8,7,6,5,2]=>[6,5,8,1,2,3,4,7]=>1010000=>[1,1,1,4]
[4,3,1,8,7,6,5,2]=>[5,6,8,1,2,3,4,7]=>0010000=>[2,1,4]
[4,2,1,8,7,6,5,3]=>[5,7,8,1,2,3,4,6]=>0010000=>[2,1,4]
[3,8,2,1,7,5,4,6]=>[6,1,7,8,2,4,5,3]=>1001001=>[1,2,1,2,1]
[8,3,2,1,6,5,4,7]=>[1,6,7,8,3,4,5,2]=>0001001=>[3,1,2,1]
[8,4,2,6,1,5,3,7]=>[1,5,7,3,8,4,6,2]=>0010101=>[2,1,1,1,1,1]
[4,2,8,7,1,6,3,5]=>[5,7,1,2,8,3,6,4]=>0100101=>[1,1,2,1,1,1]
[5,2,8,7,1,6,3,4]=>[4,7,1,2,8,3,6,5]=>0100101=>[1,1,2,1,1,1]
[5,2,8,1,7,6,4,3]=>[4,7,1,8,2,3,5,6]=>0101000=>[1,1,1,1,3]
[5,3,8,1,7,6,4,2]=>[4,6,1,8,2,3,5,7]=>0101000=>[1,1,1,1,3]
[5,3,8,2,7,6,4,1]=>[4,6,1,7,2,3,5,8]=>0101000=>[1,1,1,1,3]
[6,8,3,2,7,5,4,1]=>[3,1,6,7,2,4,5,8]=>1001000=>[1,2,1,3]
[6,8,3,1,7,5,4,2]=>[3,1,6,8,2,4,5,7]=>1001000=>[1,2,1,3]
[6,8,2,1,7,5,4,3]=>[3,1,7,8,2,4,5,6]=>1001000=>[1,2,1,3]
[6,8,2,7,1,5,3,4]=>[3,1,7,2,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,7,2,1,4,3,5]=>[3,1,2,7,8,5,6,4]=>1000101=>[1,3,1,1,1]
[8,5,6,1,2,4,3,7]=>[1,4,3,8,7,5,6,2]=>0101101=>[1,1,1,2,1,1]
[5,8,7,1,2,4,3,6]=>[4,1,2,8,7,5,6,3]=>1001101=>[1,2,2,1,1]
[6,8,1,2,7,5,4,3]=>[3,1,8,7,2,4,5,6]=>1011000=>[1,1,2,3]
[6,8,2,3,7,5,4,1]=>[3,1,7,6,2,4,5,8]=>1011000=>[1,1,2,3]
[5,2,8,3,7,6,4,1]=>[4,7,1,6,2,3,5,8]=>0101000=>[1,1,1,1,3]
[5,1,8,3,7,6,4,2]=>[4,8,1,6,2,3,5,7]=>0101000=>[1,1,1,1,3]
[5,1,8,7,2,6,3,4]=>[4,8,1,2,7,3,6,5]=>0100101=>[1,1,2,1,1,1]
[4,1,8,7,2,6,3,5]=>[5,8,1,2,7,3,6,4]=>0100101=>[1,1,2,1,1,1]
[4,8,1,7,2,5,3,6]=>[5,1,8,2,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[8,4,1,6,2,5,3,7]=>[1,5,8,3,7,4,6,2]=>0010101=>[2,1,1,1,1,1]
[8,3,1,2,6,5,4,7]=>[1,6,8,7,3,4,5,2]=>0011001=>[2,2,2,1]
[3,8,1,2,7,5,4,6]=>[6,1,8,7,2,4,5,3]=>1011001=>[1,1,2,2,1]
[3,1,8,2,7,6,4,5]=>[6,8,1,7,2,3,5,4]=>0101001=>[1,1,1,1,2,1]
[3,1,2,8,7,6,5,4]=>[6,8,7,1,2,3,4,5]=>0110000=>[1,2,4]
[4,1,3,8,7,6,5,2]=>[5,8,6,1,2,3,4,7]=>0110000=>[1,2,4]
[3,1,4,8,7,6,5,2]=>[6,8,5,1,2,3,4,7]=>0110000=>[1,2,4]
[2,1,8,3,7,6,4,5]=>[7,8,1,6,2,3,5,4]=>0101001=>[1,1,1,1,2,1]
[2,8,1,3,7,5,4,6]=>[7,1,8,6,2,4,5,3]=>1011001=>[1,1,2,2,1]
[8,2,1,3,6,5,4,7]=>[1,7,8,6,3,4,5,2]=>0011001=>[2,2,2,1]
[8,1,2,3,6,5,4,7]=>[1,8,7,6,3,4,5,2]=>0111001=>[1,3,2,1]
[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>1011001=>[1,1,2,2,1]
[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>1101001=>[2,1,1,2,1]
[1,4,3,6,8,2,5,7]=>[8,5,6,3,1,7,4,2]=>1011011=>[1,1,2,1,2]
[3,1,6,2,5,8,4,7]=>[6,8,3,7,4,1,5,2]=>0101101=>[1,1,1,2,1,1]
[3,5,1,8,2,4,7,6]=>[6,4,8,1,7,5,2,3]=>1010110=>[1,1,1,1,2,1]
[1,4,5,2,8,3,7,6]=>[8,5,4,7,1,6,2,3]=>1101010=>[2,1,1,1,1,1]
[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,4,2,6,8,3,7]=>[8,4,5,7,3,1,6,2]=>1001101=>[1,2,2,1,1]
[3,1,6,5,8,2,4,7]=>[6,8,3,4,1,7,5,2]=>0101011=>[1,1,1,1,1,2]
[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>1001101=>[1,2,2,1,1]
[1,5,2,6,4,8,3,7]=>[8,4,7,3,5,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>1100101=>[2,2,1,1,1]
[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>1101010=>[2,1,1,1,1,1]
[4,1,2,6,3,8,7,5]=>[5,8,7,3,6,1,2,4]=>0110100=>[1,2,1,1,2]
[7,1,5,4,2,8,3,6]=>[2,8,4,5,7,1,6,3]=>0100101=>[1,1,2,1,1,1]
[1,4,7,5,2,8,3,6]=>[8,5,2,4,7,1,6,3]=>1100101=>[2,2,1,1,1]
[7,1,3,5,2,8,4,6]=>[2,8,6,4,7,1,5,3]=>0110101=>[1,2,1,1,1,1]
[7,2,5,1,8,3,4,6]=>[2,7,4,8,1,6,5,3]=>0101011=>[1,1,1,1,1,2]
[1,4,5,2,8,7,3,6]=>[8,5,4,7,1,2,6,3]=>1101001=>[2,1,1,2,1]
[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>1001010=>[1,2,1,1,1,1]
[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>1010100=>[1,1,1,1,1,2]
[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>1101000=>[2,1,1,3]
[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>1100010=>[2,3,1,1]
[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>1010010=>[1,1,1,2,1,1]
[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>1001001=>[1,2,1,2,1]
[6,2,1,8,7,3,4,5]=>[3,7,8,1,2,6,5,4]=>0010011=>[2,1,2,2]
[7,3,1,6,2,8,4,5]=>[2,6,8,3,7,1,5,4]=>0010101=>[2,1,1,1,1,1]
[1,7,6,4,2,8,3,5]=>[8,2,3,5,7,1,6,4]=>1000101=>[1,3,1,1,1]
[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>1001010=>[1,2,1,1,1,1]
[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>1010010=>[1,1,1,2,1,1]
[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>1100010=>[2,3,1,1]
[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>1100100=>[2,2,1,2]
[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>1010100=>[1,1,1,1,1,2]
[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>1010010=>[1,1,1,2,1,1]
[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>1001010=>[1,2,1,1,1,1]
[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>1100101=>[2,2,1,1,1]
[4,1,2,8,6,3,7,5]=>[5,8,7,1,3,6,2,4]=>0110010=>[1,2,2,1,1]
[3,1,8,6,2,4,7,5]=>[6,8,1,3,7,5,2,4]=>0100110=>[1,1,2,2,1]
[4,3,7,1,8,2,5,6]=>[5,6,2,8,1,7,4,3]=>0101011=>[1,1,1,1,1,2]
[8,3,1,6,2,4,7,5]=>[1,6,8,3,7,5,2,4]=>0010110=>[2,1,1,2,1]
[7,1,8,3,2,4,6,5]=>[2,8,1,6,7,5,3,4]=>0100110=>[1,1,2,2,1]
[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>1000110=>[1,3,2,1]
[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>1010010=>[1,1,1,2,1,1]
[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>1001010=>[1,2,1,1,1,1]
[8,1,5,4,2,7,3,6]=>[1,8,4,5,7,2,6,3]=>0100101=>[1,1,2,1,1,1]
[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>1100101=>[2,2,1,1,1]
[8,5,3,1,7,2,4,6]=>[1,4,6,8,2,7,5,3]=>0001011=>[3,1,1,2]
[8,6,2,1,7,3,4,5]=>[1,3,7,8,2,6,5,4]=>0001011=>[3,1,1,2]
[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>1000101=>[1,3,1,1,1]
[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>1001010=>[1,2,1,1,1,1]
[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>1010100=>[1,1,1,1,1,2]
[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>1100100=>[2,2,1,2]
[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>1101000=>[2,1,1,3]
[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>1100100=>[2,2,1,2]
[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>1010100=>[1,1,1,1,1,2]
[1,7,2,8,5,3,6,4]=>[8,2,7,1,4,6,3,5]=>1010010=>[1,1,1,2,1,1]
[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>1001001=>[1,2,1,2,1]
[7,1,8,3,2,6,4,5]=>[2,8,1,6,7,3,5,4]=>0100101=>[1,1,2,1,1,1]
[7,2,1,8,6,3,4,5]=>[2,7,8,1,3,6,5,4]=>0010011=>[2,1,2,2]
[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>1000101=>[1,3,1,1,1]
[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>1010001=>[1,1,1,3,1]
[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>1100010=>[2,3,1,1]
[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>1100100=>[2,2,1,2]
[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>1101000=>[2,1,1,3]
[4,1,7,3,6,5,8,2]=>[5,8,2,6,3,4,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,7,6,2,4,3]=>[4,8,1,2,3,7,5,6]=>0100010=>[1,1,3,1,1]
[8,1,7,6,3,4,5,2]=>[1,8,2,3,6,5,4,7]=>0100110=>[1,1,2,2,1]
[5,7,8,6,2,4,1,3]=>[4,2,1,3,7,5,8,6]=>1100101=>[2,2,1,1,1]
[5,7,1,6,2,4,3,8]=>[4,2,8,3,7,5,6,1]=>1010101=>[1,1,1,1,1,1,1]
[6,4,1,5,2,7,3,8]=>[3,5,8,4,7,2,6,1]=>0010101=>[2,1,1,1,1,1]
[8,1,4,5,3,7,6,2]=>[1,8,5,4,6,2,3,7]=>0110100=>[1,2,1,1,2]
[6,1,4,5,3,8,7,2]=>[3,8,5,4,6,1,2,7]=>0110100=>[1,2,1,1,2]
[6,1,4,5,3,7,8,2]=>[3,8,5,4,6,2,1,7]=>0110110=>[1,2,1,2,1]
[5,1,7,8,6,2,4,3]=>[4,8,2,1,3,7,5,6]=>0110010=>[1,2,2,1,1]
[6,1,4,8,3,5,7,2]=>[3,8,5,1,6,4,2,7]=>0110110=>[1,2,1,2,1]
[7,1,8,6,3,4,5,2]=>[2,8,1,3,6,5,4,7]=>0100110=>[1,1,2,2,1]
[7,1,4,5,3,8,6,2]=>[2,8,5,4,6,1,3,7]=>0110100=>[1,2,1,1,2]
[7,1,4,5,3,6,8,2]=>[2,8,5,4,6,3,1,7]=>0110110=>[1,2,1,2,1]
[8,1,4,5,3,6,7,2]=>[1,8,5,4,6,3,2,7]=>0110110=>[1,2,1,2,1]
[7,4,1,5,2,6,3,8]=>[2,5,8,4,7,3,6,1]=>0010101=>[2,1,1,1,1,1]
[6,3,5,7,2,1,4,8]=>[3,6,4,2,7,8,5,1]=>0110011=>[1,2,2,2]
[6,3,5,8,2,1,7,4]=>[3,6,4,1,7,8,2,5]=>0110010=>[1,2,2,1,1]
[6,3,5,7,2,1,8,4]=>[3,6,4,2,7,8,1,5]=>0110010=>[1,2,2,1,1]
[8,4,5,7,3,6,1,2]=>[1,5,4,2,6,3,8,7]=>0110101=>[1,2,1,1,1,1]
[6,4,5,8,3,7,2,1]=>[3,5,4,1,6,2,7,8]=>0110100=>[1,2,1,1,2]
[5,8,7,6,2,4,1,3]=>[4,1,2,3,7,5,8,6]=>1000101=>[1,3,1,1,1]
[5,4,8,6,3,1,7,2]=>[4,5,1,3,6,8,2,7]=>0100010=>[1,1,3,1,1]
[5,4,1,8,2,3,7,6]=>[4,5,8,1,7,6,2,3]=>0010110=>[2,1,1,2,1]
[5,8,1,6,2,4,3,7]=>[4,1,8,3,7,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[8,4,1,5,2,6,3,7]=>[1,5,8,4,7,3,6,2]=>0010101=>[2,1,1,1,1,1]
[6,3,5,8,2,1,4,7]=>[3,6,4,1,7,8,5,2]=>0110011=>[1,2,2,2]
[2,3,4,1,8,6,5,7]=>[7,6,5,8,1,3,4,2]=>1101001=>[2,1,1,2,1]
[8,3,5,6,2,1,4,7]=>[1,6,4,3,7,8,5,2]=>0110011=>[1,2,2,2]
[2,3,8,5,1,4,7,6]=>[7,6,1,4,8,5,2,3]=>1100110=>[2,2,2,1]
[2,3,8,6,1,5,7,4]=>[7,6,1,3,8,4,2,5]=>1100110=>[2,2,2,1]
[2,8,6,7,1,3,5,4]=>[7,1,3,2,8,6,4,5]=>1010110=>[1,1,1,1,2,1]
[8,3,5,7,2,1,6,4]=>[1,6,4,2,7,8,3,5]=>0110010=>[1,2,2,1,1]
[2,3,8,5,6,1,7,4]=>[7,6,1,4,3,8,2,5]=>1101010=>[2,1,1,1,1,1]
[7,4,5,6,3,1,8,2]=>[2,5,4,3,6,8,1,7]=>0110010=>[1,2,2,1,1]
[8,4,5,6,3,1,7,2]=>[1,5,4,3,6,8,2,7]=>0110010=>[1,2,2,1,1]
[7,3,5,6,2,8,1,4]=>[2,6,4,3,7,1,8,5]=>0110101=>[1,2,1,1,1,1]
[7,3,5,8,2,1,6,4]=>[2,6,4,1,7,8,3,5]=>0110010=>[1,2,2,1,1]
[7,3,5,6,2,1,4,8]=>[2,6,4,3,7,8,5,1]=>0110011=>[1,2,2,2]
[2,7,6,5,1,3,4,8]=>[7,2,3,4,8,6,5,1]=>1000111=>[1,3,3]
[2,7,6,8,1,3,5,4]=>[7,2,3,1,8,6,4,5]=>1010110=>[1,1,1,1,2,1]
[2,7,6,5,8,3,1,4]=>[7,2,3,4,1,6,8,5]=>1001001=>[1,2,1,2,1]
[8,7,5,6,1,4,2,3]=>[1,2,4,3,8,5,7,6]=>0010101=>[2,1,1,1,1,1]
[2,6,4,1,8,5,7,3]=>[7,3,5,8,1,4,2,6]=>1001010=>[1,2,1,1,1,1]
[2,6,1,3,8,5,7,4]=>[7,3,8,6,1,4,2,5]=>1011010=>[1,1,2,1,1,1]
[2,7,1,3,6,5,8,4]=>[7,2,8,6,3,4,1,5]=>1011010=>[1,1,2,1,1,1]
[2,7,6,8,4,3,1,5]=>[7,2,3,1,5,6,8,4]=>1010001=>[1,1,1,3,1]
[2,7,6,1,8,3,4,5]=>[7,2,3,8,1,6,5,4]=>1001011=>[1,2,1,1,2]
[2,7,6,1,4,3,5,8]=>[7,2,3,8,5,6,4,1]=>1001011=>[1,2,1,1,2]
[7,3,5,1,2,8,4,6]=>[2,6,4,8,7,1,5,3]=>0101101=>[1,1,1,2,1,1]
[8,4,1,5,2,3,7,6]=>[1,5,8,4,7,6,2,3]=>0010110=>[2,1,1,2,1]
[7,8,1,6,3,4,2,5]=>[2,1,8,3,6,5,7,4]=>1010101=>[1,1,1,1,1,1,1]
[6,4,1,8,3,2,7,5]=>[3,5,8,1,6,7,2,4]=>0010010=>[2,1,2,1,1]
[2,3,8,6,4,1,7,5]=>[7,6,1,3,5,8,2,4]=>1100010=>[2,3,1,1]
[2,8,6,7,4,3,1,5]=>[7,1,3,2,5,6,8,4]=>1010001=>[1,1,1,3,1]
[8,3,5,7,2,4,1,6]=>[1,6,4,2,7,5,8,3]=>0110101=>[1,2,1,1,1,1]
[2,3,4,1,8,7,5,6]=>[7,6,5,8,1,2,4,3]=>1101001=>[2,1,1,2,1]
[2,8,6,1,7,3,4,5]=>[7,1,3,8,2,6,5,4]=>1001011=>[1,2,1,1,2]
[2,3,8,1,6,4,7,5]=>[7,6,1,8,3,5,2,4]=>1101010=>[2,1,1,1,1,1]
[2,3,8,1,4,5,7,6]=>[7,6,1,8,5,4,2,3]=>1101110=>[2,1,3,1]
[2,8,6,1,4,3,5,7]=>[7,1,3,8,5,6,4,2]=>1001011=>[1,2,1,1,2]
[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>11111110=>[7,1]
[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>01111111=>[1,7]
[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>111111110=>[8,1]
[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>011111111=>[1,8]
[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110=>[9,1]
[9,1,2,3,4,5,6,7,10,8]=>[2,10,9,8,7,6,5,4,1,3]=>011111110=>[1,7,1]
[1,8,2,3,4,5,6,9,7]=>[9,2,8,7,6,5,4,1,3]=>10111110=>[1,1,5,1]
[7,1,2,3,4,5,6,9,8]=>[3,9,8,7,6,5,4,1,2]=>01111110=>[1,6,1]
[2,1,9,3,4,5,6,7,8]=>[8,9,1,7,6,5,4,3,2]=>01011111=>[1,1,1,5]
[2,8,1,3,4,5,6,7,9]=>[8,2,9,7,6,5,4,3,1]=>10111111=>[1,1,6]
[2,10,1,3,4,5,6,7,8,9]=>[9,1,10,8,7,6,5,4,3,2]=>101111111=>[1,1,7]
[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>0111111111=>[1,9]
[8,4,3,6,5,1,7,2]=>[1,5,6,3,4,8,2,7]=>0010010=>[2,1,2,1,1]
[8,5,6,3,4,1,7,2]=>[1,4,3,6,5,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[8,6,5,4,3,1,7,2]=>[1,3,4,5,6,8,2,7]=>0000010=>[5,1,1]
[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>1000011=>[1,4,2]
[1,8,6,5,2,7,3,4]=>[8,1,3,4,7,2,6,5]=>1000101=>[1,3,1,1,1]
[8,7,5,4,1,6,3,2]=>[1,2,4,5,8,3,6,7]=>0000100=>[4,1,2]
[7,8,5,4,1,3,6,2]=>[2,1,4,5,8,6,3,7]=>1000110=>[1,3,2,1]
[6,8,5,4,2,1,7,3]=>[3,1,4,5,7,8,2,6]=>1000010=>[1,4,1,1]
[5,8,6,2,4,1,7,3]=>[4,1,3,7,5,8,2,6]=>1001010=>[1,2,1,1,1,1]
[4,8,2,6,5,1,7,3]=>[5,1,7,3,4,8,2,6]=>1010010=>[1,1,1,2,1,1]
[3,2,8,6,5,1,7,4]=>[6,7,1,3,4,8,2,5]=>0100010=>[1,1,3,1,1]
[3,2,1,7,6,4,5,8]=>[6,7,8,2,3,5,4,1]=>0010011=>[2,1,2,2]
[4,1,3,7,6,2,5,8]=>[5,8,6,2,3,7,4,1]=>0110011=>[1,2,2,2]
[5,1,7,3,6,2,4,8]=>[4,8,2,6,3,7,5,1]=>0101011=>[1,1,1,1,1,2]
[6,1,7,5,3,2,4,8]=>[3,8,2,4,6,7,5,1]=>0100011=>[1,1,3,2]
[7,1,6,5,2,4,3,8]=>[2,8,3,4,7,5,6,1]=>0100101=>[1,1,2,1,1,1]
[8,1,6,5,2,3,7,4]=>[1,8,3,4,7,6,2,5]=>0100110=>[1,1,2,2,1]
[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>1100111=>[2,2,3]
[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>1101011=>[2,1,1,1,2]
[8,1,7,2,6,3,5,4]=>[1,8,2,7,3,6,4,5]=>0101010=>[1,1,1,1,1,1,1]
[7,1,8,2,6,4,3,5]=>[2,8,1,7,3,5,6,4]=>0101001=>[1,1,1,1,2,1]
[6,1,8,2,4,7,3,5]=>[3,8,1,7,5,2,6,4]=>0101101=>[1,1,1,2,1,1]
[5,1,8,3,2,7,4,6]=>[4,8,1,6,7,2,5,3]=>0100101=>[1,1,2,1,1,1]
[4,1,3,8,2,7,5,6]=>[5,8,6,1,7,2,4,3]=>0110101=>[1,2,1,1,1,1]
[3,2,1,8,4,7,5,6]=>[6,7,8,1,5,2,4,3]=>0010101=>[2,1,1,1,1,1]
[3,2,8,7,1,6,5,4]=>[6,7,1,2,8,3,4,5]=>0100100=>[1,1,2,1,2]
[4,8,2,7,1,6,5,3]=>[5,1,7,2,8,3,4,6]=>1010100=>[1,1,1,1,1,2]
[5,8,7,2,1,6,4,3]=>[4,1,2,7,8,3,5,6]=>1000100=>[1,3,1,2]
[6,8,7,1,3,5,4,2]=>[3,1,2,8,6,4,5,7]=>1001100=>[1,2,2,2]
[7,8,6,1,5,3,4,2]=>[2,1,3,8,4,6,5,7]=>1001010=>[1,2,1,1,1,1]
[8,7,6,1,5,4,3,2]=>[1,2,3,8,4,5,6,7]=>0001000=>[3,1,3]
[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>1001001=>[1,2,1,2,1]
[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>1101101=>[2,1,2,1,1]
[8,6,7,1,4,5,3,2]=>[1,3,2,8,5,4,6,7]=>0101100=>[1,1,1,2,2]
[7,6,8,1,4,3,5,2]=>[2,3,1,8,5,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[6,5,8,3,2,1,7,4]=>[3,4,1,6,7,8,2,5]=>0100010=>[1,1,3,1,1]
[7,5,8,3,1,4,6,2]=>[2,4,1,6,8,5,3,7]=>0100110=>[1,1,2,2,1]
[8,5,7,3,1,6,4,2]=>[1,4,2,6,8,3,5,7]=>0100100=>[1,1,2,1,2]
[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>1100101=>[2,2,1,1,1]
[1,5,4,8,2,7,3,6]=>[8,4,5,1,7,2,6,3]=>1010101=>[1,1,1,1,1,1,1]
[8,4,3,7,1,6,5,2]=>[1,5,6,2,8,3,4,7]=>0010100=>[2,1,1,1,2]
[7,4,3,8,1,5,6,2]=>[2,5,6,1,8,4,3,7]=>0010110=>[2,1,1,2,1]
[6,4,3,1,5,2,7,8]=>[3,5,6,8,4,7,2,1]=>0001011=>[3,1,1,2]
[7,4,3,1,2,6,5,8]=>[2,5,6,8,7,3,4,1]=>0001101=>[3,2,1,1]
[8,4,3,1,2,5,7,6]=>[1,5,6,8,7,4,2,3]=>0001110=>[3,3,1]
[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>1001111=>[1,2,4]
[8,5,1,4,2,3,7,6]=>[1,4,8,5,7,6,2,3]=>0010110=>[2,1,1,2,1]
[7,5,1,4,2,6,3,8]=>[2,4,8,5,7,3,6,1]=>0010101=>[2,1,1,1,1,1]
[6,5,1,4,3,2,7,8]=>[3,4,8,5,6,7,2,1]=>0010011=>[2,1,2,2]
[5,6,1,3,4,2,7,8]=>[4,3,8,6,5,7,2,1]=>1011011=>[1,1,2,1,2]
[4,6,2,1,5,3,7,8]=>[5,3,7,8,4,6,2,1]=>1001011=>[1,2,1,1,2]
[3,2,6,1,5,4,7,8]=>[6,7,3,8,4,5,2,1]=>0101011=>[1,1,1,1,1,2]
[3,2,7,1,4,6,5,8]=>[6,7,2,8,5,3,4,1]=>0101101=>[1,1,1,2,1,1]
[4,7,2,1,3,6,5,8]=>[5,2,7,8,6,3,4,1]=>1001101=>[1,2,2,1,1]
[5,7,1,3,2,6,4,8]=>[4,2,8,6,7,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,1,2,4,5,3,8]=>[3,2,8,7,5,4,6,1]=>1011101=>[1,1,3,1,1]
[7,6,1,2,5,4,3,8]=>[2,3,8,7,4,5,6,1]=>0011001=>[2,2,2,1]
[8,6,1,2,5,3,7,4]=>[1,3,8,7,4,6,2,5]=>0011010=>[2,2,1,1,1]
[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>1011011=>[1,1,2,1,2]
[8,7,1,2,3,6,5,4]=>[1,2,8,7,6,3,4,5]=>0011100=>[2,3,2]
[7,8,1,2,3,5,6,4]=>[2,1,8,7,6,4,3,5]=>1011110=>[1,1,4,1]
[6,8,1,2,4,3,7,5]=>[3,1,8,7,5,6,2,4]=>1011010=>[1,1,2,1,1,1]
[5,8,1,3,2,4,7,6]=>[4,1,8,6,7,5,2,3]=>1010110=>[1,1,1,1,2,1]
[4,8,2,1,3,5,7,6]=>[5,1,7,8,6,4,2,3]=>1001110=>[1,2,3,1]
[3,2,8,1,4,5,7,6]=>[6,7,1,8,5,4,2,3]=>0101110=>[1,1,1,3,1]
[4,1,3,2,5,6,7,8]=>[5,8,6,7,4,3,2,1]=>0101111=>[1,1,1,4]
[5,1,2,4,3,6,7,8]=>[4,8,7,5,6,3,2,1]=>0110111=>[1,2,1,3]
[6,1,2,3,5,4,7,8]=>[3,8,7,6,4,5,2,1]=>0111011=>[1,3,1,2]
[7,1,2,3,4,6,5,8]=>[2,8,7,6,5,3,4,1]=>0111101=>[1,4,1,1]
[8,1,2,3,4,5,7,6]=>[1,8,7,6,5,4,2,3]=>0111110=>[1,5,1]
[6,7,3,8,5,1,2,4]=>[3,2,6,1,4,8,7,5]=>1010011=>[1,1,1,2,2]
[6,7,4,5,1,8,3,2]=>[3,2,5,4,8,1,6,7]=>1010100=>[1,1,1,1,1,2]
[5,4,7,6,8,1,2,3]=>[4,5,2,3,1,8,7,6]=>0101011=>[1,1,1,1,1,2]
[3,8,4,5,7,1,2,6]=>[6,1,5,4,2,8,7,3]=>1011011=>[1,1,2,1,2]
[4,5,6,7,1,8,3,2]=>[5,4,3,2,8,1,6,7]=>1110100=>[3,1,1,2]
[3,5,6,2,7,4,8,1]=>[6,4,3,7,2,5,1,8]=>1101010=>[2,1,1,1,1,1]
[3,5,6,1,7,8,4,2]=>[6,4,3,8,2,1,5,7]=>1101100=>[2,1,2,2]
[2,5,6,1,8,7,4,3]=>[7,4,3,8,1,2,5,6]=>1101000=>[2,1,1,3]
[2,5,6,8,1,7,3,4]=>[7,4,3,1,8,2,6,5]=>1110101=>[3,1,1,1,1]
[8,2,4,5,1,6,3,7]=>[1,7,5,4,8,3,6,2]=>0110101=>[1,2,1,1,1,1]
[1,4,8,6,2,3,7,5]=>[8,5,1,3,7,6,2,4]=>1100110=>[2,2,2,1]
[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>1110110=>[3,1,2,1]
[1,5,6,2,8,4,7,3]=>[8,4,3,7,1,5,2,6]=>1101010=>[2,1,1,1,1,1]
[2,5,6,3,4,7,8,1]=>[7,4,3,6,5,2,1,8]=>1101110=>[2,1,3,1]
[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>1011010=>[1,1,2,1,1,1]
[8,1,3,2,5,4,6,7]=>[1,8,6,7,4,5,3,2]=>0101011=>[1,1,1,1,1,2]
[8,2,3,1,5,6,4,7]=>[1,7,6,8,4,3,5,2]=>0101101=>[1,1,1,2,1,1]
[2,8,3,1,5,7,4,6]=>[7,1,6,8,4,2,5,3]=>1001101=>[1,2,2,1,1]
[2,4,1,6,8,7,5,3]=>[7,5,8,3,1,2,4,6]=>1011000=>[1,1,2,3]
[3,4,1,6,7,8,5,2]=>[6,5,8,3,2,1,4,7]=>1011100=>[1,1,3,2]
[4,3,1,7,6,8,5,2]=>[5,6,8,2,3,1,4,7]=>0010100=>[2,1,1,1,2]
[5,2,7,8,1,6,3,4]=>[4,7,2,1,8,3,6,5]=>0110101=>[1,2,1,1,1,1]
[5,3,7,2,6,4,8,1]=>[4,6,2,7,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,7,3,1,5,8,4,2]=>[3,2,6,8,4,1,5,7]=>1001100=>[1,2,2,2]
[6,7,2,1,8,5,4,3]=>[3,2,7,8,1,4,5,6]=>1001000=>[1,2,1,3]
[6,7,2,8,1,5,3,4]=>[3,2,7,1,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,8,2,1,4,3,5]=>[3,2,1,7,8,5,6,4]=>1100101=>[2,2,1,1,1]
[6,7,1,2,8,4,5,3]=>[3,2,8,7,1,5,4,6]=>1011010=>[1,1,2,1,1,1]
[6,7,1,3,4,8,5,2]=>[3,2,8,6,5,1,4,7]=>1011100=>[1,1,3,2]
[5,2,7,3,4,6,8,1]=>[4,7,2,6,5,3,1,8]=>0101110=>[1,1,1,3,1]
[5,1,7,3,4,8,6,2]=>[4,8,2,6,5,1,3,7]=>0101100=>[1,1,1,2,2]
[5,1,7,8,2,3,6,4]=>[4,8,2,1,7,6,3,5]=>0110110=>[1,2,1,2,1]
[4,1,8,7,2,3,6,5]=>[5,8,1,2,7,6,3,4]=>0100110=>[1,1,2,2,1]
[3,8,1,2,7,4,5,6]=>[6,1,8,7,2,5,4,3]=>1011011=>[1,1,2,1,2]
[4,1,3,7,5,8,6,2]=>[5,8,6,2,4,1,3,7]=>0110100=>[1,2,1,1,2]
[3,1,4,5,7,8,6,2]=>[6,8,5,4,2,1,3,7]=>0111100=>[1,4,2]
[2,1,8,3,4,7,6,5]=>[7,8,1,6,5,2,3,4]=>0101100=>[1,1,1,2,2]
[8,2,1,3,4,6,5,7]=>[1,7,8,6,5,3,4,2]=>0011101=>[2,3,1,1]
[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>1011110=>[1,1,4,1]
[1,2,8,3,4,6,7,5]=>[8,7,1,6,5,3,2,4]=>1101110=>[2,1,3,1]
[4,2,1,6,5,8,7,3]=>[5,7,8,3,4,1,2,6]=>0010100=>[2,1,1,1,2]
[5,2,6,1,4,8,7,3]=>[4,7,3,8,5,1,2,6]=>0101100=>[1,1,1,2,2]
[5,2,6,4,1,8,7,3]=>[4,7,3,5,8,1,2,6]=>0100100=>[1,1,2,1,2]
[5,2,7,4,8,1,6,3]=>[4,7,2,5,1,8,3,6]=>0101010=>[1,1,1,1,1,1,1]
[5,2,7,4,8,6,1,3]=>[4,7,2,5,1,3,8,6]=>0101001=>[1,1,1,1,2,1]
[5,7,2,3,8,6,1,4]=>[4,2,7,6,1,3,8,5]=>1011001=>[1,1,2,2,1]
[5,7,2,3,8,1,6,4]=>[4,2,7,6,1,8,3,5]=>1011010=>[1,1,2,1,1,1]
[5,6,2,3,1,8,7,4]=>[4,3,7,6,8,1,2,5]=>1010100=>[1,1,1,1,1,2]
[5,6,2,1,3,8,7,4]=>[4,3,7,8,6,1,2,5]=>1001100=>[1,2,2,2]
[5,1,6,4,2,8,7,3]=>[4,8,3,5,7,1,2,6]=>0100100=>[1,1,2,1,2]
[5,6,1,3,2,8,7,4]=>[4,3,8,6,7,1,2,5]=>1010100=>[1,1,1,1,1,2]
[5,6,3,1,2,8,7,4]=>[4,3,6,8,7,1,2,5]=>1001100=>[1,2,2,2]
[5,6,3,2,1,8,7,4]=>[4,3,6,7,8,1,2,5]=>1000100=>[1,3,1,2]
[5,7,3,2,8,1,6,4]=>[4,2,6,7,1,8,3,5]=>1001010=>[1,2,1,1,1,1]
[5,7,3,2,8,6,1,4]=>[4,2,6,7,1,3,8,5]=>1001001=>[1,2,1,2,1]
[6,7,3,8,2,1,5,4]=>[3,2,6,1,7,8,4,5]=>1010010=>[1,1,1,2,1,1]
[6,7,3,8,1,2,5,4]=>[3,2,6,1,8,7,4,5]=>1010110=>[1,1,1,1,2,1]
[5,7,3,1,8,2,6,4]=>[4,2,6,8,1,7,3,5]=>1001010=>[1,2,1,1,1,1]
[5,7,1,3,8,2,6,4]=>[4,2,8,6,1,7,3,5]=>1011010=>[1,1,2,1,1,1]
[5,1,7,4,8,2,6,3]=>[4,8,2,5,1,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[1,5,7,4,8,3,6,2]=>[8,4,2,5,1,6,3,7]=>1101010=>[2,1,1,1,1,1]
[1,5,7,4,8,6,3,2]=>[8,4,2,5,1,3,6,7]=>1101000=>[2,1,1,3]
[5,1,7,4,8,6,2,3]=>[4,8,2,5,1,3,7,6]=>0101001=>[1,1,1,1,2,1]
[5,7,1,3,8,6,2,4]=>[4,2,8,6,1,3,7,5]=>1011001=>[1,1,2,2,1]
[5,7,3,1,8,6,2,4]=>[4,2,6,8,1,3,7,5]=>1001001=>[1,2,1,2,1]
[6,7,3,8,1,5,2,4]=>[3,2,6,1,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,8,5,2,1,4]=>[3,2,6,1,4,7,8,5]=>1010001=>[1,1,1,3,1]
[6,7,8,3,1,4,2,5]=>[3,2,1,6,8,5,7,4]=>1100101=>[2,2,1,1,1]
[6,7,1,8,3,5,2,4]=>[3,2,8,1,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,1,7,8,4,5,2,3]=>[3,8,2,1,5,4,7,6]=>0110101=>[1,2,1,1,1,1]
[1,6,7,8,4,5,3,2]=>[8,3,2,1,5,4,6,7]=>1110100=>[3,1,1,2]
[1,6,7,8,4,3,5,2]=>[8,3,2,1,5,6,4,7]=>1110010=>[3,2,1,1]
[6,1,7,8,4,2,5,3]=>[3,8,2,1,5,7,4,6]=>0110010=>[1,2,2,1,1]
[6,7,1,8,3,2,5,4]=>[3,2,8,1,6,7,4,5]=>1010010=>[1,1,1,2,1,1]
[5,7,2,1,8,3,6,4]=>[4,2,7,8,1,6,3,5]=>1001010=>[1,2,1,1,1,1]
[6,7,2,8,1,3,5,4]=>[3,2,7,1,8,6,4,5]=>1010110=>[1,1,1,1,2,1]
[6,7,2,8,3,1,5,4]=>[3,2,7,1,6,8,4,5]=>1010010=>[1,1,1,2,1,1]
[6,7,2,8,3,5,1,4]=>[3,2,7,1,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,2,7,8,4,5,1,3]=>[3,7,2,1,5,4,8,6]=>0110101=>[1,2,1,1,1,1]
[6,2,7,8,4,1,5,3]=>[3,7,2,1,5,8,4,6]=>0110010=>[1,2,2,1,1]
[6,2,7,8,1,4,5,3]=>[3,7,2,1,8,5,4,6]=>0110110=>[1,2,1,2,1]
[5,2,7,1,8,4,6,3]=>[4,7,2,8,1,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[4,2,1,7,8,5,6,3]=>[5,7,8,2,1,4,3,6]=>0011010=>[2,2,1,1,1]
[4,1,2,7,8,6,5,3]=>[5,8,7,2,1,3,4,6]=>0111000=>[1,3,3]
[6,2,7,8,1,5,4,3]=>[3,7,2,1,8,4,5,6]=>0110100=>[1,2,1,1,2]
[6,2,7,8,5,1,4,3]=>[3,7,2,1,4,8,5,6]=>0110010=>[1,2,2,1,1]
[6,2,7,8,5,4,1,3]=>[3,7,2,1,4,5,8,6]=>0110001=>[1,2,3,1]
[6,7,2,8,5,3,1,4]=>[3,2,7,1,4,6,8,5]=>1010001=>[1,1,1,3,1]
[5,7,2,1,8,6,3,4]=>[4,2,7,8,1,3,6,5]=>1001001=>[1,2,1,2,1]
[5,7,1,2,8,6,3,4]=>[4,2,8,7,1,3,6,5]=>1011001=>[1,1,2,2,1]
[5,1,7,2,8,6,4,3]=>[4,8,2,7,1,3,5,6]=>0101000=>[1,1,1,1,3]
[1,5,7,3,8,6,4,2]=>[8,4,2,6,1,3,5,7]=>1101000=>[2,1,1,3]
[1,6,7,8,3,5,4,2]=>[8,3,2,1,6,4,5,7]=>1110100=>[3,1,1,2]
[6,1,7,8,2,5,4,3]=>[3,8,2,1,7,4,5,6]=>0110100=>[1,2,1,1,2]
[6,7,1,8,2,5,3,4]=>[3,2,8,1,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,8,2,4,1,3,5]=>[3,2,1,7,5,8,6,4]=>1101011=>[2,1,1,1,2]
[6,7,8,2,4,3,1,5]=>[3,2,1,7,5,6,8,4]=>1101001=>[2,1,1,2,1]
[6,7,1,8,5,2,3,4]=>[3,2,8,1,4,7,6,5]=>1010011=>[1,1,1,2,2]
[6,1,7,8,5,2,4,3]=>[3,8,2,1,4,7,5,6]=>0110010=>[1,2,2,1,1]
[1,6,7,8,5,3,4,2]=>[8,3,2,1,4,6,5,7]=>1110010=>[3,2,1,1]
[6,1,7,8,5,4,2,3]=>[3,8,2,1,4,5,7,6]=>0110001=>[1,2,3,1]
[6,7,1,8,5,3,2,4]=>[3,2,8,1,4,6,7,5]=>1010001=>[1,1,1,3,1]
[6,7,8,4,1,3,2,5]=>[3,2,1,5,8,6,7,4]=>1100101=>[2,2,1,1,1]
[6,3,8,5,2,7,4,1]=>[3,6,1,4,7,2,5,8]=>0100100=>[1,1,2,1,2]
[6,5,2,8,4,7,3,1]=>[3,4,7,1,5,2,6,8]=>0010100=>[2,1,1,1,2]
[6,3,4,5,8,7,2,1]=>[3,6,5,4,1,2,7,8]=>0111000=>[1,3,3]
[5,8,1,4,7,2,3,6]=>[4,1,8,5,2,7,6,3]=>1011011=>[1,1,2,1,2]
[5,6,1,4,8,7,3,2]=>[4,3,8,5,1,2,6,7]=>1011000=>[1,1,2,3]
[3,6,4,8,5,7,1,2]=>[6,3,5,1,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,1,4,8,6,3,7,2]=>[4,8,5,1,3,6,2,7]=>0110010=>[1,2,2,1,1]
[3,4,7,1,8,6,5,2]=>[6,5,2,8,1,3,4,7]=>1101000=>[2,1,1,3]
[6,3,8,4,2,7,1,5]=>[3,6,1,5,7,2,8,4]=>0100101=>[1,1,2,1,1,1]
[3,6,8,7,1,4,2,5]=>[6,3,1,2,8,5,7,4]=>1100101=>[2,2,1,1,1]
[5,3,7,1,6,8,2,4]=>[4,6,2,8,3,1,7,5]=>0101101=>[1,1,1,2,1,1]
[4,3,8,5,6,7,2,1]=>[5,6,1,4,3,2,7,8]=>0101100=>[1,1,1,2,2]
[5,8,1,7,6,2,4,3]=>[4,1,8,2,3,7,5,6]=>1010010=>[1,1,1,2,1,1]
[4,6,1,2,7,8,5,3]=>[5,3,8,7,2,1,4,6]=>1011100=>[1,1,3,2]
[3,6,4,2,8,7,5,1]=>[6,3,5,7,1,2,4,8]=>1001000=>[1,2,1,3]
[6,3,7,5,2,8,1,4]=>[3,6,2,4,7,1,8,5]=>0100101=>[1,1,2,1,1,1]
[6,5,2,7,4,8,1,3]=>[3,4,7,2,5,1,8,6]=>0010101=>[2,1,1,1,1,1]
[5,7,1,4,8,3,2,6]=>[4,2,8,5,1,6,7,3]=>1011001=>[1,1,2,2,1]
[7,8,3,5,1,4,6,2]=>[2,1,6,4,8,5,3,7]=>1010110=>[1,1,1,1,2,1]
[5,8,1,4,6,7,2,3]=>[4,1,8,5,3,2,7,6]=>1011101=>[1,1,3,1,1]
[6,5,8,4,3,7,2,1]=>[3,4,1,5,6,2,7,8]=>0100100=>[1,1,2,1,2]
[6,3,7,4,2,8,5,1]=>[3,6,2,5,7,1,4,8]=>0100100=>[1,1,2,1,2]
[8,7,1,6,2,4,5,3]=>[1,2,8,3,7,5,4,6]=>0010110=>[2,1,1,2,1]
[3,8,6,7,1,4,5,2]=>[6,1,3,2,8,5,4,7]=>1010110=>[1,1,1,1,2,1]
[5,3,8,7,4,1,2,6]=>[4,6,1,2,5,8,7,3]=>0100011=>[1,1,3,2]
[4,3,8,7,1,5,6,2]=>[5,6,1,2,8,4,3,7]=>0100110=>[1,1,2,2,1]
[8,3,6,1,2,5,7,4]=>[1,6,3,8,7,4,2,5]=>0101110=>[1,1,1,3,1]
[5,6,1,8,7,3,2,4]=>[4,3,8,1,2,6,7,5]=>1010001=>[1,1,1,3,1]
[7,5,3,6,4,2,8,1]=>[2,4,6,3,5,7,1,8]=>0010010=>[2,1,2,1,1]
[8,5,2,6,4,7,3,1]=>[1,4,7,3,5,2,6,8]=>0010100=>[2,1,1,1,2]
[8,2,6,3,4,7,5,1]=>[1,7,3,6,5,2,4,8]=>0101100=>[1,1,1,2,2]
[7,2,6,3,5,4,8,1]=>[2,7,3,6,4,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,4,3,5,8,1]=>[3,7,2,5,6,4,1,8]=>0100110=>[1,1,2,2,1]
[5,7,3,6,4,2,8,1]=>[4,2,6,3,5,7,1,8]=>1010010=>[1,1,1,2,1,1]
[3,7,6,4,5,2,8,1]=>[6,2,3,5,4,7,1,8]=>1001010=>[1,2,1,1,1,1]
[2,7,6,5,3,4,8,1]=>[7,2,3,4,6,5,1,8]=>1000110=>[1,3,2,1]
[6,5,4,3,1,8,2,7]=>[3,4,5,6,8,1,7,2]=>0000101=>[4,1,1,1]
[8,6,5,4,2,7,3,1]=>[1,3,4,5,7,2,6,8]=>0000100=>[4,1,2]
[7,5,4,1,8,3,2,6]=>[2,4,5,8,1,6,7,3]=>0001001=>[3,1,2,1]
[5,4,6,3,1,8,2,7]=>[4,5,3,6,8,1,7,2]=>0100101=>[1,1,2,1,1,1]
[6,5,8,4,2,7,3,1]=>[3,4,1,5,7,2,6,8]=>0100100=>[1,1,2,1,2]
[3,8,6,2,5,7,4,1]=>[6,1,3,7,4,2,5,8]=>1001100=>[1,2,2,2]
[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>1001001=>[1,2,1,2,1]
[8,7,5,2,6,4,3,1]=>[1,2,4,7,3,5,6,8]=>0001000=>[3,1,3]
[8,7,1,6,2,5,4,3]=>[1,2,8,3,7,4,5,6]=>0010100=>[2,1,1,1,2]
[7,8,1,6,3,2,5,4]=>[2,1,8,3,6,7,4,5]=>1010010=>[1,1,1,2,1,1]
[2,8,1,7,3,5,6,4]=>[7,1,8,2,6,4,3,5]=>1010110=>[1,1,1,1,2,1]
[4,8,1,3,7,2,6,5]=>[5,1,8,6,2,7,3,4]=>1011010=>[1,1,2,1,1,1]
[4,2,8,5,7,3,6,1]=>[5,7,1,4,2,6,3,8]=>0101010=>[1,1,1,1,1,1,1]
[3,7,1,5,8,4,2,6]=>[6,2,8,4,1,5,7,3]=>1011001=>[1,1,2,2,1]
[6,7,3,1,8,4,2,5]=>[3,2,6,8,1,5,7,4]=>1001001=>[1,2,1,2,1]
[1,7,3,8,4,5,2,6]=>[8,2,6,1,5,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>1010011=>[1,1,1,2,2]
[7,6,1,8,4,3,2,5]=>[2,3,8,1,5,6,7,4]=>0010001=>[2,1,3,1]
[8,6,1,7,4,2,5,3]=>[1,3,8,2,5,7,4,6]=>0010010=>[2,1,2,1,1]
[8,1,2,7,3,4,6,5]=>[1,8,7,2,6,5,3,4]=>0110110=>[1,2,1,2,1]
[7,1,2,8,3,5,4,6]=>[2,8,7,1,6,4,5,3]=>0110101=>[1,2,1,1,1,1]
[7,2,6,1,8,4,3,5]=>[2,7,3,8,1,5,6,4]=>0101001=>[1,1,1,1,2,1]
[8,2,6,1,7,3,5,4]=>[1,7,3,8,2,6,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,1,4,7,5,6,2]=>[1,6,8,5,2,4,3,7]=>0011010=>[2,2,1,1,1]
[7,3,1,5,8,4,2,6]=>[2,6,8,4,1,5,7,3]=>0011001=>[2,2,2,1]
[4,2,1,5,8,3,6,7]=>[5,7,8,4,1,6,3,2]=>0011011=>[2,2,1,2]
[5,4,2,7,1,8,3,6]=>[4,5,7,2,8,1,6,3]=>0010101=>[2,1,1,1,1,1]
[4,7,5,6,8,3,2,1]=>[5,2,4,3,1,6,7,8]=>1011000=>[1,1,2,3]
[6,5,1,8,7,4,2,3]=>[3,4,8,1,2,5,7,6]=>0010001=>[2,1,3,1]
[8,6,4,7,5,3,2,1]=>[1,3,5,2,4,6,7,8]=>0010000=>[2,1,4]
[5,4,8,1,7,2,6,3]=>[4,5,1,8,2,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[3,6,8,2,4,7,5,1]=>[6,3,1,7,5,2,4,8]=>1101100=>[2,1,2,2]
[5,7,3,8,2,6,4,1]=>[4,2,6,1,7,3,5,8]=>1010100=>[1,1,1,1,1,2]
[5,4,6,8,2,7,3,1]=>[4,5,3,1,7,2,6,8]=>0110100=>[1,2,1,1,2]
[3,6,8,1,7,2,5,4]=>[6,3,1,8,2,7,4,5]=>1101010=>[2,1,1,1,1,1]
[2,3,8,7,4,5,6,1]=>[7,6,1,2,5,4,3,8]=>1100110=>[2,2,2,1]
[7,2,8,6,4,3,5,1]=>[2,7,1,3,5,6,4,8]=>0100010=>[1,1,3,1,1]
[2,1,8,7,5,6,3,4]=>[7,8,1,2,4,3,6,5]=>0100101=>[1,1,2,1,1,1]
[8,2,7,6,3,5,4,1]=>[1,7,2,3,6,4,5,8]=>0100100=>[1,1,2,1,2]
[8,1,7,6,5,2,4,3]=>[1,8,2,3,4,7,5,6]=>0100010=>[1,1,3,1,1]
[7,1,8,6,5,3,2,4]=>[2,8,1,3,4,6,7,5]=>0100001=>[1,1,4,1]
[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>1100011=>[2,3,2]
[1,3,8,7,4,6,2,5]=>[8,6,1,2,5,3,7,4]=>1100101=>[2,2,1,1,1]
[1,5,8,3,7,6,2,4]=>[8,4,1,6,2,3,7,5]=>1101001=>[2,1,1,2,1]
[6,8,4,7,5,3,2,1]=>[3,1,5,2,4,6,7,8]=>1010000=>[1,1,1,4]
[3,8,7,6,4,5,2,1]=>[6,1,2,3,5,4,7,8]=>1000100=>[1,3,1,2]
[2,8,7,6,5,3,4,1]=>[7,1,2,3,4,6,5,8]=>1000010=>[1,4,1,1]
[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>1000001=>[1,5,1]
[5,8,6,7,3,4,1,2]=>[4,1,3,2,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,8,6,7,3,5,1,2]=>[5,1,3,2,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,8,6,7,4,5,1,2]=>[6,1,3,2,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,7,4,5,1,3]=>[7,1,3,2,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,6,7,4,5,2,3]=>[8,1,3,2,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,5,7,4,6,2,3]=>[8,1,4,2,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,8,5,7,4,6,1,2]=>[6,1,4,2,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,8,5,7,3,6,1,2]=>[5,1,4,2,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,6,4,5,1,2]=>[2,1,6,3,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,7,4,5,1,2]=>[3,1,6,2,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,7,4,6,1,2]=>[4,1,6,2,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,7,4,8,5,6,1,2]=>[6,2,5,1,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,8,5,6,1,2]=>[5,2,6,1,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,7,2,8,5,6,1,3]=>[5,2,7,1,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,1,8,5,6,2,3]=>[5,2,8,1,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,8,5,6,2,4]=>[6,2,8,1,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,8,5,6,1,4]=>[6,2,7,1,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,7,3,8,5,6,1,4]=>[7,2,6,1,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,7,4,8,5,6,1,3]=>[7,2,5,1,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,7,4,6,1,3]=>[4,1,7,2,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,7,4,5,1,3]=>[3,1,7,2,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,6,4,5,1,3]=>[2,1,7,3,5,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,6,4,5,2,3]=>[2,1,8,3,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,1,7,4,5,2,3]=>[3,1,8,2,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,7,4,6,2,3]=>[4,1,8,2,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,7,4,8,5,6,2,3]=>[8,2,5,1,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,8,5,6,2,4]=>[8,2,6,1,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,5,6,1,7,3,4]=>[7,1,4,3,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,7,3,6,2,5]=>[5,1,8,2,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,7,3,6,2,4]=>[4,1,8,2,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,1,7,3,5,2,4]=>[3,1,8,2,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,6,3,5,1,4]=>[2,1,7,3,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,7,3,5,1,4]=>[3,1,7,2,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,7,3,6,1,4]=>[4,1,7,2,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,7,3,6,1,5]=>[5,1,7,2,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[2,7,3,8,4,6,1,5]=>[7,2,6,1,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,8,4,6,1,5]=>[6,2,7,1,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,8,4,6,2,5]=>[6,2,8,1,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,7,3,6,1,5]=>[7,1,5,2,6,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,7,2,6,1,5]=>[6,1,5,2,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,5,7,2,6,1,3]=>[5,1,4,2,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[3,8,5,7,2,6,1,4]=>[6,1,4,2,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,5,7,3,6,1,4]=>[7,1,4,2,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,6,7,3,5,2,4]=>[8,1,3,2,6,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,7,3,5,1,4]=>[7,1,3,2,6,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,6,7,2,5,1,4]=>[6,1,3,2,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,6,7,2,5,1,3]=>[5,1,3,2,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,6,7,2,4,1,3]=>[4,1,3,2,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,5,7,1,4,2,3]=>[3,1,4,2,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,6,7,1,4,2,3]=>[4,1,3,2,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,6,7,1,5,2,3]=>[5,1,3,2,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,8,6,7,1,5,2,4]=>[6,1,3,2,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,5,1,8,6,7,3,4]=>[7,4,8,1,3,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,8,5,7,3,4]=>[7,3,8,1,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,8,5,7,3,4]=>[8,3,7,1,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,5,7,1,6,2,4]=>[6,1,4,2,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,7,1,5,2,3]=>[3,1,5,2,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,6,1,5,2,3]=>[2,1,5,3,8,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,6,1,5,2,4]=>[2,1,6,3,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,7,1,5,2,4]=>[3,1,6,2,8,4,7,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,7,1,6,2,5]=>[5,1,6,2,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,7,1,6,2,5]=>[6,1,5,2,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,8,4,7,3,5]=>[7,3,8,1,5,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,6,1,8,4,5]=>[6,2,7,3,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,6,2,8,4,5]=>[6,2,8,3,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,6,2,7,3,5]=>[5,1,8,3,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,6,2,7,3,4]=>[4,1,8,3,7,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,5,2,6,3,4]=>[2,1,8,4,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,5,1,6,3,4]=>[2,1,7,4,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,5,1,7,3,4]=>[3,1,7,4,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,6,1,7,3,4]=>[4,1,7,3,8,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,6,1,7,3,5]=>[5,1,7,3,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,6,2,8,4,5]=>[8,2,6,3,7,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[2,7,3,6,1,8,4,5]=>[7,2,6,3,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>11111111=>[8]
[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>11111110=>[7,1]
[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>11111110=>[7,1]
[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>11111110=>[7,1]
[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>11111110=>[7,1]
[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>11111110=>[7,1]
[1,3,4,5,6,7,8,9,2]=>[9,7,6,5,4,3,2,1,8]=>11111110=>[7,1]
[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>111111111=>[9]
[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>11111100=>[6,2]
[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>111111110=>[8,1]
[1,2,3,4,5,8,7,9,6]=>[9,8,7,6,5,2,3,1,4]=>11111010=>[5,1,1,1]
[1,2,3,4,5,6,8,9,10,7]=>[10,9,8,7,6,5,3,2,1,4]=>111111110=>[8,1]
[1,2,3,4,7,6,8,9,5]=>[9,8,7,6,3,4,2,1,5]=>11110110=>[4,1,2,1]
[1,2,3,4,5,7,8,9,10,6]=>[10,9,8,7,6,4,3,2,1,5]=>111111110=>[8,1]
[1,2,3,6,5,7,8,9,4]=>[9,8,7,4,5,3,2,1,6]=>11101110=>[3,1,3,1]
[1,2,3,4,6,7,8,9,10,5]=>[10,9,8,7,5,4,3,2,1,6]=>111111110=>[8,1]
[1,2,5,4,6,7,8,9,3]=>[9,8,5,6,4,3,2,1,7]=>11011110=>[2,1,4,1]
[1,2,3,5,6,7,8,9,10,4]=>[10,9,8,6,5,4,3,2,1,7]=>111111110=>[8,1]
[1,4,3,5,6,7,8,9,2]=>[9,6,7,5,4,3,2,1,8]=>10111110=>[1,1,5,1]
[1,2,4,5,6,7,8,9,10,3]=>[10,9,7,6,5,4,3,2,1,8]=>111111110=>[8,1]
[3,2,4,5,6,7,8,9,1]=>[7,8,6,5,4,3,2,1,9]=>01111110=>[1,6,1]
[1,3,4,5,6,7,8,9,10,2]=>[10,8,7,6,5,4,3,2,1,9]=>111111110=>[8,1]
[6,7,4,8,3,5,1,2]=>[3,2,5,1,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,7,4,5,2,8,1,3]=>[3,2,5,4,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,7,4,6,2,3,1,8]=>[4,2,5,3,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]
[5,7,4,6,3,8,1,2]=>[4,2,5,3,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,7,4,8,3,6,1,2]=>[4,2,5,1,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,5,3,7,1,2]=>[3,1,5,4,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,6,3,7,1,2]=>[4,1,5,3,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,6,4,8,3,7,1,2]=>[4,3,5,1,6,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,7,2,4,1,8]=>[4,3,6,2,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,7,2,8,1,4]=>[4,3,6,2,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,8,2,7,1,4]=>[4,3,6,1,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,6,4,8,2,7,1,3]=>[4,3,5,1,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,6,2,7,1,3]=>[4,1,5,3,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,5,2,7,1,3]=>[3,1,5,4,7,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,5,2,6,1,3]=>[2,1,5,4,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,5,2,3,1,7]=>[3,1,5,4,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,6,2,3,1,7]=>[4,1,5,3,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,4,8,2,3,1,7]=>[4,3,5,1,7,6,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,8,2,4,1,7]=>[4,3,6,1,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,4,2,8,1,7]=>[4,3,6,5,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,5,2,7,1,8]=>[5,3,6,4,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,5,2,8,1,7]=>[5,3,6,4,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,8,2,5,1,7]=>[5,3,6,1,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,6,2,5,1,7]=>[5,1,6,3,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,6,2,4,1,7]=>[4,1,6,3,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,5,2,4,1,7]=>[3,1,6,4,7,5,8,2]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,5,2,4,1,6]=>[2,1,6,4,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,5,2,6,1,4]=>[2,1,6,4,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,6,2,7,1,4]=>[4,1,6,3,7,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,6,2,7,1,5]=>[5,1,6,3,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,8,2,7,1,5]=>[5,3,6,1,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,7,2,8,1,5]=>[5,3,6,2,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,6,2,5,1,8]=>[5,2,6,3,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,6,2,8,1,5]=>[5,2,6,3,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,8,2,6,1,5]=>[5,2,6,1,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,7,4,8,2,6,1,3]=>[4,2,5,1,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,6,2,8,1,4]=>[4,2,6,3,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,6,2,4,1,8]=>[4,2,6,3,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,5,2,4,1,8]=>[3,2,6,4,7,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,5,2,8,1,4]=>[3,2,6,4,7,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,4,8,2,5,1,3]=>[3,2,5,1,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,7,5,8,2,4,1,3]=>[3,2,4,1,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,5,7,2,3,1,4]=>[3,1,4,2,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,4,8,2,3,1,5]=>[3,2,5,1,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,8,2,4,1,5]=>[3,2,6,1,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,4,2,8,1,5]=>[3,2,6,5,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,4,2,6,1,8]=>[4,2,6,5,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,4,2,8,1,6]=>[4,2,6,5,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]
[5,7,4,8,2,3,1,6]=>[4,2,5,1,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,7,2,3,1,6]=>[4,1,5,2,7,6,8,3]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,7,2,3,1,5]=>[3,1,5,2,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,6,2,3,1,5]=>[2,1,5,3,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,6,2,4,1,5]=>[2,1,6,3,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,7,2,4,1,5]=>[3,1,6,2,7,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,7,2,4,1,6]=>[4,1,6,2,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,7,2,5,1,6]=>[5,1,6,2,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,8,2,5,1,6]=>[5,2,6,1,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,5,2,8,1,6]=>[5,2,6,4,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,5,2,6,1,8]=>[5,2,6,4,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,7,2,6,1,8]=>[5,4,6,2,7,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,7,2,8,1,6]=>[5,4,6,2,7,1,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,8,2,7,1,6]=>[5,4,6,1,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,5,2,7,1,6]=>[5,1,6,4,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,4,2,7,1,6]=>[4,1,6,5,7,2,8,3]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,4,2,7,1,5]=>[3,1,6,5,7,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,4,2,6,1,5]=>[2,1,6,5,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,4,2,5,1,7]=>[3,1,6,5,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,4,2,6,1,7]=>[4,1,6,5,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,5,2,6,1,7]=>[5,1,6,4,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,8,2,6,1,7]=>[5,4,6,1,7,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,6,2,8,1,7]=>[5,4,6,3,7,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,2,1,8,3,6]=>[5,2,4,7,8,1,6,3]=>1000101=>[1,3,1,1,1]
[4,8,5,2,1,7,6,3]=>[5,1,4,7,8,2,3,6]=>1000100=>[1,3,1,2]
[4,6,5,2,1,3,8,7]=>[5,3,4,7,8,6,1,2]=>1000110=>[1,3,2,1]
[5,6,4,2,3,1,8,7]=>[4,3,5,7,6,8,1,2]=>1001010=>[1,2,1,1,1,1]
[6,4,5,3,1,2,8,7]=>[3,5,4,6,8,7,1,2]=>0100110=>[1,1,2,2,1]
[5,4,6,1,3,2,8,7]=>[4,5,3,8,6,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,6,8,1,7,3,2,5]=>[5,3,1,8,2,6,7,4]=>1101001=>[2,1,1,2,1]
[4,7,8,1,6,3,5,2]=>[5,2,1,8,3,6,4,7]=>1101010=>[2,1,1,1,1,1]
[7,4,8,1,6,5,3,2]=>[2,5,1,8,3,4,6,7]=>0101000=>[1,1,1,1,3]
[5,4,8,1,3,7,6,2]=>[4,5,1,8,6,2,3,7]=>0101100=>[1,1,1,2,2]
[8,4,5,3,1,7,6,2]=>[1,5,4,6,8,2,3,7]=>0100100=>[1,1,2,1,2]
[5,4,7,1,3,8,2,6]=>[4,5,2,8,6,1,7,3]=>0101101=>[1,1,1,2,1,1]
[6,4,8,1,7,5,2,3]=>[3,5,1,8,2,4,7,6]=>0101001=>[1,1,1,1,2,1]
[5,6,8,7,2,1,3,4]=>[4,3,1,2,7,8,6,5]=>1100011=>[2,3,2]
[8,5,7,6,4,2,1,3]=>[1,4,2,3,5,7,8,6]=>0100001=>[1,1,4,1]
[8,4,6,3,7,2,1,5]=>[1,5,3,6,2,7,8,4]=>0101001=>[1,1,1,1,2,1]
[6,3,2,8,7,4,1,5]=>[3,6,7,1,2,5,8,4]=>0010001=>[2,1,3,1]
[2,1,6,8,7,4,3,5]=>[7,8,3,1,2,5,6,4]=>0110001=>[1,2,3,1]
[2,1,7,8,6,4,5,3]=>[7,8,2,1,3,5,4,6]=>0110010=>[1,2,2,1,1]
[7,3,2,8,6,4,5,1]=>[2,6,7,1,3,5,4,8]=>0010010=>[2,1,2,1,1]
[7,6,8,5,2,4,3,1]=>[2,3,1,4,7,5,6,8]=>0100100=>[1,1,2,1,2]
[5,7,8,6,2,3,1,4]=>[4,2,1,3,7,6,8,5]=>1100101=>[2,2,1,1,1]
[5,8,7,6,3,2,1,4]=>[4,1,2,3,6,7,8,5]=>1000001=>[1,5,1]
[6,8,7,5,3,2,4,1]=>[3,1,2,4,6,7,5,8]=>1000010=>[1,4,1,1]
[5,8,4,2,3,7,6,1]=>[4,1,5,7,6,2,3,8]=>1001100=>[1,2,2,2]
[7,8,4,2,6,5,3,1]=>[2,1,5,7,3,4,6,8]=>1001000=>[1,2,1,3]
[4,8,7,2,6,3,5,1]=>[5,1,2,7,3,6,4,8]=>1001010=>[1,2,1,1,1,1]
[4,8,6,2,7,3,1,5]=>[5,1,3,7,2,6,8,4]=>1001001=>[1,2,1,2,1]
[3,6,1,8,7,4,2,5]=>[6,3,8,1,2,5,7,4]=>1010001=>[1,1,1,3,1]
[3,7,1,8,6,4,5,2]=>[6,2,8,1,3,5,4,7]=>1010010=>[1,1,1,2,1,1]
[3,8,1,6,7,5,2,4]=>[6,1,8,3,2,4,7,5]=>1011001=>[1,1,2,2,1]
[3,7,1,6,8,2,5,4]=>[6,2,8,3,1,7,4,5]=>1011010=>[1,1,2,1,1,1]
[4,7,6,2,8,1,3,5]=>[5,2,3,7,1,8,6,4]=>1001011=>[1,2,1,1,2]
[6,7,4,2,8,1,5,3]=>[3,2,5,7,1,8,4,6]=>1001010=>[1,2,1,1,1,1]
[6,8,4,2,7,5,1,3]=>[3,1,5,7,2,4,8,6]=>1001001=>[1,2,1,2,1]
[2,1,8,6,7,5,3,4]=>[7,8,1,3,2,4,6,5]=>0101001=>[1,1,1,1,2,1]
[8,3,2,6,7,5,1,4]=>[1,6,7,3,2,4,8,5]=>0011001=>[2,2,2,1]
[8,6,4,3,7,5,1,2]=>[1,3,5,6,2,4,8,7]=>0001001=>[3,1,2,1]
[5,8,6,7,3,1,2,4]=>[4,1,3,2,6,8,7,5]=>1010011=>[1,1,1,2,2]
[6,7,5,8,1,3,4,2]=>[3,2,4,1,8,6,5,7]=>1010110=>[1,1,1,1,2,1]
[7,6,5,8,1,4,3,2]=>[2,3,4,1,8,5,6,7]=>0010100=>[2,1,1,1,2]
[8,6,5,7,4,1,3,2]=>[1,3,4,2,5,8,6,7]=>0010010=>[2,1,2,1,1]
[7,6,4,3,8,1,5,2]=>[2,3,5,6,1,8,4,7]=>0001010=>[3,1,1,1,1]
[7,3,2,6,8,1,5,4]=>[2,6,7,3,1,8,4,5]=>0011010=>[2,2,1,1,1]
[2,1,7,6,8,3,5,4]=>[7,8,2,3,1,6,4,5]=>0101010=>[1,1,1,1,1,1,1]
[7,5,6,8,1,4,2,3]=>[2,4,3,1,8,5,7,6]=>0110101=>[1,2,1,1,1,1]
[6,5,7,8,1,2,4,3]=>[3,4,2,1,8,7,5,6]=>0110110=>[1,2,1,2,1]
[8,1,3,7,4,6,5,2]=>[1,8,6,2,5,3,4,7]=>0110100=>[1,2,1,1,2]
[5,2,8,7,4,6,1,3]=>[4,7,1,2,5,3,8,6]=>0100101=>[1,1,2,1,1,1]
[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[6,2,7,5,4,8,3,1]=>[3,7,2,4,5,1,6,8]=>0100100=>[1,1,2,1,2]
[8,1,3,5,4,7,6,2]=>[1,8,6,4,5,2,3,7]=>0110100=>[1,2,1,1,2]
[6,1,5,4,3,8,7,2]=>[3,8,4,5,6,1,2,7]=>0100100=>[1,1,2,1,2]
[6,1,8,3,4,5,7,2]=>[3,8,1,6,5,4,2,7]=>0101110=>[1,1,1,3,1]
[7,1,5,3,4,8,6,2]=>[2,8,4,6,5,1,3,7]=>0101100=>[1,1,1,2,2]
[7,1,4,3,5,6,8,2]=>[2,8,5,6,4,3,1,7]=>0101110=>[1,1,1,3,1]
[8,1,3,4,5,6,7,2]=>[1,8,6,5,4,3,2,7]=>0111110=>[1,5,1]
[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>1011101=>[1,1,3,1,1]
[6,3,2,7,5,1,8,4]=>[3,6,7,2,4,8,1,5]=>0010010=>[2,1,2,1,1]
[8,4,7,2,5,6,1,3]=>[1,5,2,7,4,3,8,6]=>0101101=>[1,1,1,2,1,1]
[6,5,8,2,4,7,3,1]=>[3,4,1,7,5,2,6,8]=>0101100=>[1,1,1,2,2]
[8,5,2,1,4,3,7,6]=>[1,4,7,8,5,6,2,3]=>0001010=>[3,1,1,1,1]
[6,5,2,8,4,1,3,7]=>[3,4,7,1,5,8,6,2]=>0010011=>[2,1,2,2]
[5,6,2,1,4,8,3,7]=>[4,3,7,8,5,1,6,2]=>1001101=>[1,2,2,1,1]
[3,6,1,8,5,2,4,7]=>[6,3,8,1,4,7,5,2]=>1010011=>[1,1,1,2,2]
[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>1101011=>[2,1,1,1,2]
[3,4,1,2,8,6,5,7]=>[6,5,8,7,1,3,4,2]=>1011001=>[1,1,2,2,1]
[4,3,1,2,6,8,5,7]=>[5,6,8,7,3,1,4,2]=>0011101=>[2,3,1,1]
[5,8,1,6,3,2,4,7]=>[4,1,8,3,6,7,5,2]=>1010011=>[1,1,1,2,2]
[6,3,8,5,2,1,4,7]=>[3,6,1,4,7,8,5,2]=>0100011=>[1,1,3,2]
[8,3,1,5,2,4,7,6]=>[1,6,8,4,7,5,2,3]=>0010110=>[2,1,1,2,1]
[3,8,2,6,1,5,7,4]=>[6,1,7,3,8,4,2,5]=>1010110=>[1,1,1,1,2,1]
[3,8,6,7,2,1,5,4]=>[6,1,3,2,7,8,4,5]=>1010010=>[1,1,1,2,1,1]
[8,5,6,4,2,1,7,3]=>[1,4,3,5,7,8,2,6]=>0100010=>[1,1,3,1,1]
[7,2,5,8,3,1,6,4]=>[2,7,4,1,6,8,3,5]=>0110010=>[1,2,2,1,1]
[1,7,5,6,3,2,4,8]=>[8,2,4,3,6,7,5,1]=>1010011=>[1,1,1,2,2]
[6,1,2,3,8,5,7,4]=>[3,8,7,6,1,4,2,5]=>0111010=>[1,3,1,1,1]
[7,1,2,3,6,5,8,4]=>[2,8,7,6,3,4,1,5]=>0111010=>[1,3,1,1,1]
[7,2,1,3,8,6,4,5]=>[2,7,8,6,1,3,5,4]=>0011001=>[2,2,2,1]
[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>1100111=>[2,2,3]
[5,2,7,3,1,8,4,6]=>[4,7,2,6,8,1,5,3]=>0100101=>[1,1,2,1,1,1]
[5,8,2,4,1,3,7,6]=>[4,1,7,5,8,6,2,3]=>1010110=>[1,1,1,1,2,1]
[8,7,2,6,3,4,1,5]=>[1,2,7,3,6,5,8,4]=>0010101=>[2,1,1,1,1,1]
[4,8,1,6,3,2,7,5]=>[5,1,8,3,6,7,2,4]=>1010010=>[1,1,1,2,1,1]
[3,1,8,6,4,2,7,5]=>[6,8,1,3,5,7,2,4]=>0100010=>[1,1,3,1,1]
[8,1,6,7,4,3,2,5]=>[1,8,3,2,5,6,7,4]=>0110001=>[1,2,3,1]
[3,5,8,7,2,4,1,6]=>[6,4,1,2,7,5,8,3]=>1100101=>[2,2,1,1,1]
[4,2,1,3,7,8,5,6]=>[5,7,8,6,2,1,4,3]=>0011101=>[2,3,1,1]
[2,4,1,3,8,7,5,6]=>[7,5,8,6,1,2,4,3]=>1011001=>[1,1,2,2,1]
[2,5,8,3,1,7,4,6]=>[7,4,1,6,8,2,5,3]=>1100101=>[2,2,1,1,1]
[8,6,1,3,7,2,4,5]=>[1,3,8,6,2,7,5,4]=>0011011=>[2,2,1,2]
[2,8,1,3,6,4,7,5]=>[7,1,8,6,3,5,2,4]=>1011010=>[1,1,2,1,1,1]
[6,8,2,3,4,1,5,7]=>[3,1,7,6,5,8,4,2]=>1011011=>[1,1,2,1,2]
[5,1,8,3,2,4,6,7]=>[4,8,1,6,7,5,3,2]=>0100111=>[1,1,2,3]
[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>00000000=>[8]
[8,9,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9]=>10000000=>[1,7]
[8,7,9,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9]=>01000000=>[1,1,6]
[8,7,6,9,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9]=>00100000=>[2,1,5]
[8,7,6,5,9,4,3,2,1]=>[2,3,4,5,1,6,7,8,9]=>00010000=>[3,1,4]
[8,7,6,5,4,9,3,2,1]=>[2,3,4,5,6,1,7,8,9]=>00001000=>[4,1,3]
[8,7,6,5,4,3,9,2,1]=>[2,3,4,5,6,7,1,8,9]=>00000100=>[5,1,2]
[8,7,6,5,4,3,2,9,1]=>[2,3,4,5,6,7,8,1,9]=>00000010=>[6,1,1]
[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>00000001=>[7,1]
[9,10,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10]=>100000000=>[1,8]
[7,8,9,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9]=>11000000=>[2,6]
[9,8,10,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10]=>010000000=>[1,1,7]
[8,6,7,9,5,4,3,2,1]=>[2,4,3,1,5,6,7,8,9]=>01100000=>[1,2,5]
[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9,10]=>001000000=>[2,1,6]
[8,7,5,6,9,4,3,2,1]=>[2,3,5,4,1,6,7,8,9]=>00110000=>[2,2,4]
[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,1,6,7,8,9,10]=>000100000=>[3,1,5]
[8,7,6,4,5,9,3,2,1]=>[2,3,4,6,5,1,7,8,9]=>00011000=>[3,2,3]
[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,5,6,1,7,8,9,10]=>000010000=>[4,1,4]
[8,7,6,5,3,4,9,2,1]=>[2,3,4,5,7,6,1,8,9]=>00001100=>[4,2,2]
[9,8,7,6,5,4,10,3,2,1]=>[2,3,4,5,6,7,1,8,9,10]=>000001000=>[5,1,3]
[8,7,6,5,4,2,3,9,1]=>[2,3,4,5,6,8,7,1,9]=>00000110=>[5,2,1]
[9,8,7,6,5,4,3,10,2,1]=>[2,3,4,5,6,7,8,1,9,10]=>000000100=>[6,1,2]
[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>00000011=>[6,2]
[9,8,7,6,5,4,3,2,10,1]=>[2,3,4,5,6,7,8,9,1,10]=>000000010=>[7,1,1]
[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>000000001=>[8,1]
[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>1011001=>[1,1,2,2,1]
[1,6,2,4,8,5,3,7]=>[8,3,7,5,1,4,6,2]=>1011001=>[1,1,2,2,1]
[1,6,2,4,7,5,3,8]=>[8,3,7,5,2,4,6,1]=>1011001=>[1,1,2,2,1]
[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>1010011=>[1,1,1,2,2]
[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>1001001=>[1,2,1,2,1]
[4,2,5,7,8,6,1,3]=>[5,7,4,2,1,3,8,6]=>0111001=>[1,3,2,1]
[7,2,3,1,8,5,6,4]=>[2,7,6,8,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,5,1,7,3,4,6]=>[1,7,4,8,2,6,5,3]=>0101011=>[1,1,1,1,1,2]
[6,2,1,8,3,4,7,5]=>[3,7,8,1,6,5,2,4]=>0010110=>[2,1,1,2,1]
[6,2,8,3,5,1,7,4]=>[3,7,1,6,4,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,2,4,8,5,7,1,3]=>[3,7,5,1,4,2,8,6]=>0110101=>[1,2,1,1,1,1]
[1,3,6,4,8,5,7,2]=>[8,6,3,5,1,4,2,7]=>1101010=>[2,1,1,1,1,1]
[1,3,6,4,7,5,8,2]=>[8,6,3,5,2,4,1,7]=>1101010=>[2,1,1,1,1,1]
[6,2,4,7,5,8,1,3]=>[3,7,5,2,4,1,8,6]=>0110101=>[1,2,1,1,1,1]
[6,2,1,3,7,8,4,5]=>[3,7,8,6,2,1,5,4]=>0011101=>[2,3,1,1]
[7,8,2,1,4,3,5,6]=>[2,1,7,8,5,6,4,3]=>1001011=>[1,2,1,1,2]
[7,6,4,2,3,1,8,5]=>[2,3,5,7,6,8,1,4]=>0001010=>[3,1,1,1,1]
[5,7,2,3,1,6,8,4]=>[4,2,7,6,8,3,1,5]=>1010110=>[1,1,1,1,2,1]
[7,5,4,2,6,8,1,3]=>[2,4,5,7,3,1,8,6]=>0001101=>[3,2,1,1]
[1,7,5,3,4,6,8,2]=>[8,2,4,6,5,3,1,7]=>1001110=>[1,2,3,1]
[8,2,5,4,6,7,1,3]=>[1,7,4,5,3,2,8,6]=>0101101=>[1,1,1,2,1,1]
[5,2,6,3,1,8,7,4]=>[4,7,3,6,8,1,2,5]=>0100100=>[1,1,2,1,2]
[8,2,6,4,3,1,7,5]=>[1,7,3,5,6,8,2,4]=>0100010=>[1,1,3,1,1]
[8,2,7,4,1,3,5,6]=>[1,7,2,5,8,6,4,3]=>0100111=>[1,1,2,3]
[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>1100111=>[2,2,3]
[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>1001111=>[1,2,4]
[6,8,4,1,3,2,5,7]=>[3,1,5,8,6,7,4,2]=>1001011=>[1,2,1,1,2]
[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>1000011=>[1,4,2]
[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>1010110=>[1,1,1,1,2,1]
[5,3,8,1,2,7,4,6]=>[4,6,1,8,7,2,5,3]=>0101101=>[1,1,1,2,1,1]
[5,1,8,3,2,6,4,7]=>[4,8,1,6,7,3,5,2]=>0100101=>[1,1,2,1,1,1]
[5,7,3,1,2,6,4,8]=>[4,2,6,8,7,3,5,1]=>1001101=>[1,2,2,1,1]
[1,7,5,4,2,6,3,8]=>[8,2,4,5,7,3,6,1]=>1000101=>[1,3,1,1,1]
[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>1101101=>[2,1,2,1,1]
[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>1100101=>[2,2,1,1,1]
[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>1101010=>[2,1,1,1,1,1]
[5,3,1,6,7,2,4,8]=>[4,6,8,3,2,7,5,1]=>0011011=>[2,2,1,2]
[5,3,6,1,2,8,4,7]=>[4,6,3,8,7,1,5,2]=>0101101=>[1,1,1,2,1,1]
[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>1001101=>[1,2,2,1,1]
[1,7,4,5,3,8,6,2]=>[8,2,5,4,6,1,3,7]=>1010100=>[1,1,1,1,1,2]
[6,3,4,1,2,5,8,7]=>[3,6,5,8,7,4,1,2]=>0101110=>[1,1,1,3,1]
[6,3,1,4,2,7,5,8]=>[3,6,8,5,7,2,4,1]=>0010101=>[2,1,1,1,1,1]
[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>1001111=>[1,2,4]
[8,6,3,2,4,1,7,5]=>[1,3,6,7,5,8,2,4]=>0001010=>[3,1,1,1,1]
[8,5,3,2,6,7,1,4]=>[1,4,6,7,3,2,8,5]=>0001101=>[3,2,1,1]
[4,5,2,6,8,1,7,3]=>[5,4,7,3,1,8,2,6]=>1011010=>[1,1,2,1,1,1]
[4,2,5,6,7,8,1,3]=>[5,7,4,3,2,1,8,6]=>0111101=>[1,4,1,1]
[5,2,3,6,7,1,8,4]=>[4,7,6,3,2,8,1,5]=>0111010=>[1,3,1,1,1]
[6,2,3,4,1,7,8,5]=>[3,7,6,5,8,2,1,4]=>0110110=>[1,2,1,2,1]
[7,2,3,1,4,5,8,6]=>[2,7,6,8,5,4,1,3]=>0101110=>[1,1,1,3,1]
[8,6,1,4,3,2,5,7]=>[1,3,8,5,6,7,4,2]=>0010011=>[2,1,2,2]
[8,3,1,6,5,2,4,7]=>[1,6,8,3,4,7,5,2]=>0010011=>[2,1,2,2]
[3,7,5,1,8,2,4,6]=>[6,2,4,8,1,7,5,3]=>1001011=>[1,2,1,1,2]
[4,1,5,2,8,7,3,6]=>[5,8,4,7,1,2,6,3]=>0101001=>[1,1,1,1,2,1]
[8,1,2,4,6,5,3,7]=>[1,8,7,5,3,4,6,2]=>0111001=>[1,3,2,1]
[8,1,2,5,4,6,3,7]=>[1,8,7,4,5,3,6,2]=>0110101=>[1,2,1,1,1,1]
[8,2,6,5,1,3,4,7]=>[1,7,3,4,8,6,5,2]=>0100111=>[1,1,2,3]
[8,3,1,6,2,5,4,7]=>[1,6,8,3,7,4,5,2]=>0010101=>[2,1,1,1,1,1]
[8,1,2,6,4,5,3,7]=>[1,8,7,3,5,4,6,2]=>0110101=>[1,2,1,1,1,1]
[8,1,2,5,6,4,3,7]=>[1,8,7,4,3,5,6,2]=>0111001=>[1,3,2,1]
[8,1,2,6,5,4,3,7]=>[1,8,7,3,4,5,6,2]=>0110001=>[1,2,3,1]
[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>1000101=>[1,3,1,1,1]
[5,1,4,8,2,7,3,6]=>[4,8,5,1,7,2,6,3]=>0110101=>[1,2,1,1,1,1]
[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>1110101=>[3,1,1,1,1]
[1,4,7,6,2,8,3,5]=>[8,5,2,3,7,1,6,4]=>1100101=>[2,2,1,1,1]
[5,1,4,7,2,8,3,6]=>[4,8,5,2,7,1,6,3]=>0110101=>[1,2,1,1,1,1]
[1,7,4,5,2,8,3,6]=>[8,2,5,4,7,1,6,3]=>1010101=>[1,1,1,1,1,1,1]
[3,7,5,1,2,8,4,6]=>[6,2,4,8,7,1,5,3]=>1001101=>[1,2,2,1,1]
[5,7,2,8,1,3,4,6]=>[4,2,7,1,8,6,5,3]=>1010111=>[1,1,1,1,3]
[5,2,8,7,1,3,4,6]=>[4,7,1,2,8,6,5,3]=>0100111=>[1,1,2,3]
[4,1,5,8,2,7,3,6]=>[5,8,4,1,7,2,6,3]=>0110101=>[1,2,1,1,1,1]
[1,4,6,2,8,7,3,5]=>[8,5,3,7,1,2,6,4]=>1101001=>[2,1,1,2,1]
[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,1,2,6,4,8,7,5]=>[6,8,7,3,5,1,2,4]=>0110100=>[1,2,1,1,2]
[2,1,7,6,3,4,8,5]=>[7,8,2,3,6,5,1,4]=>0100110=>[1,1,2,2,1]
[3,1,2,7,4,6,8,5]=>[6,8,7,2,5,3,1,4]=>0110110=>[1,2,1,2,1]
[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>1101101=>[2,1,2,1,1]
[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>1111010=>[4,1,1,1]
[5,1,4,2,7,8,3,6]=>[4,8,5,7,2,1,6,3]=>0101101=>[1,1,1,2,1,1]
[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,4,2,6,8,7,3,5]=>[8,5,7,3,1,2,6,4]=>1011001=>[1,1,2,2,1]
[3,1,2,8,4,6,7,5]=>[6,8,7,1,5,3,2,4]=>0110110=>[1,2,1,2,1]
[3,1,2,7,6,4,8,5]=>[6,8,7,2,3,5,1,4]=>0110010=>[1,2,2,1,1]
[5,3,7,1,8,2,4,6]=>[4,6,2,8,1,7,5,3]=>0101011=>[1,1,1,1,1,2]
[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>1000110=>[1,3,2,1]
[4,8,7,2,1,3,5,6]=>[5,1,2,7,8,6,4,3]=>1000111=>[1,3,3]
[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>1001011=>[1,2,1,1,2]
[3,1,7,8,2,6,4,5]=>[6,8,2,1,7,3,5,4]=>0110101=>[1,2,1,1,1,1]
[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>1011010=>[1,1,2,1,1,1]
[5,2,8,1,3,4,7,6]=>[4,7,1,8,6,5,2,3]=>0101110=>[1,1,1,3,1]
[2,1,8,6,3,4,7,5]=>[7,8,1,3,6,5,2,4]=>0100110=>[1,1,2,2,1]
[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>1011010=>[1,1,2,1,1,1]
[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>1111010=>[4,1,1,1]
[1,2,3,7,5,8,6,4]=>[8,7,6,2,4,1,3,5]=>1110100=>[3,1,1,2]
[1,4,2,7,3,8,6,5]=>[8,5,7,2,6,1,3,4]=>1010100=>[1,1,1,1,1,2]
[3,1,7,2,8,6,4,5]=>[6,8,2,7,1,3,5,4]=>0101001=>[1,1,1,1,2,1]
[2,1,7,8,3,4,6,5]=>[7,8,2,1,6,5,3,4]=>0110110=>[1,2,1,2,1]
[1,2,3,8,7,5,6,4]=>[8,7,6,1,2,4,3,5]=>1110010=>[3,2,1,1]
[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>011111111=>[1,8]
[10,1,2,3,4,5,6,9,7,8]=>[1,10,9,8,7,6,5,2,4,3]=>011111101=>[1,6,1,1]
[10,1,2,3,4,5,9,6,7,8]=>[1,10,9,8,7,6,2,5,4,3]=>011111011=>[1,5,1,2]
[9,1,2,3,4,10,5,6,7,8]=>[2,10,9,8,7,1,6,5,4,3]=>011110111=>[1,4,1,3]
[10,1,2,3,9,4,5,6,7,8]=>[1,10,9,8,2,7,6,5,4,3]=>011101111=>[1,3,1,4]
[10,1,2,9,3,4,5,6,7,8]=>[1,10,9,2,8,7,6,5,4,3]=>011011111=>[1,2,1,5]
[9,1,10,2,3,4,5,6,7,8]=>[2,10,1,9,8,7,6,5,4,3]=>010111111=>[1,1,1,6]
[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>001111111=>[2,7]
[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>[1,9]
[10,1,2,3,4,5,6,7,8,11,9]=>[2,11,10,9,8,7,6,5,4,1,3]=>0111111110=>[1,8,1]
[8,1,2,3,4,5,6,9,10,7]=>[3,10,9,8,7,6,5,2,1,4]=>011111110=>[1,7,1]
[11,1,2,3,4,5,6,7,10,8,9]=>[1,11,10,9,8,7,6,5,2,4,3]=>0111111101=>[1,7,1,1]
[7,1,2,3,4,5,10,9,6,8]=>[4,10,9,8,7,6,1,2,5,3]=>011111001=>[1,5,2,1]
[11,1,2,3,4,5,6,10,7,8,9]=>[1,11,10,9,8,7,6,2,5,4,3]=>0111111011=>[1,6,1,2]
[6,1,2,3,4,10,9,5,7,8]=>[5,10,9,8,7,1,2,6,4,3]=>011110011=>[1,4,2,2]
[10,1,2,3,4,5,11,6,7,8,9]=>[2,11,10,9,8,7,1,6,5,4,3]=>0111110111=>[1,5,1,3]
[5,1,2,3,9,10,4,6,7,8]=>[6,10,9,8,2,1,7,5,4,3]=>011110111=>[1,4,1,3]
[11,1,2,3,4,10,5,6,7,8,9]=>[1,11,10,9,8,2,7,6,5,4,3]=>0111101111=>[1,4,1,4]
[4,1,2,10,9,3,5,6,7,8]=>[7,10,9,1,2,8,6,5,4,3]=>011001111=>[1,2,2,4]
[11,1,2,3,10,4,5,6,7,8,9]=>[1,11,10,9,2,8,7,6,5,4,3]=>0111011111=>[1,3,1,5]
[3,1,10,9,2,4,5,6,7,8]=>[8,10,1,2,9,7,6,5,4,3]=>010011111=>[1,1,2,5]
[10,1,2,11,3,4,5,6,7,8,9]=>[2,11,10,1,9,8,7,6,5,4,3]=>0110111111=>[1,2,1,6]
[2,9,10,1,3,4,5,6,7,8]=>[9,2,1,10,8,7,6,5,4,3]=>110111111=>[2,1,6]
[11,1,10,2,3,4,5,6,7,8,9]=>[1,11,2,10,9,8,7,6,5,4,3]=>0101111111=>[1,1,1,7]
[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,11,10,9,8,7,6,5,4,3]=>0011111111=>[2,8]
[4,7,8,5,6,2,1,3]=>[5,2,1,4,3,7,8,6]=>1101001=>[2,1,1,2,1]
[5,7,8,4,2,6,1,3]=>[4,2,1,5,7,3,8,6]=>1100101=>[2,2,1,1,1]
[6,7,8,4,2,5,1,3]=>[3,2,1,5,7,4,8,6]=>1100101=>[2,2,1,1,1]
[8,6,3,7,2,1,5,4]=>[1,3,6,2,7,8,4,5]=>0010010=>[2,1,2,1,1]
[7,6,3,8,2,1,5,4]=>[2,3,6,1,7,8,4,5]=>0010010=>[2,1,2,1,1]
[6,7,8,3,2,1,5,4]=>[3,2,1,6,7,8,4,5]=>1100010=>[2,3,1,1]
[5,7,8,3,2,1,6,4]=>[4,2,1,6,7,8,3,5]=>1100010=>[2,3,1,1]
[2,7,8,4,3,5,6,1]=>[7,2,1,5,6,4,3,8]=>1100110=>[2,2,2,1]
[3,7,8,4,2,5,1,6]=>[6,2,1,5,7,4,8,3]=>1100101=>[2,2,1,1,1]
[4,7,8,3,2,1,5,6]=>[5,2,1,6,7,8,4,3]=>1100011=>[2,3,2]
[5,7,8,3,2,1,4,6]=>[4,2,1,6,7,8,5,3]=>1100011=>[2,3,2]
[7,6,3,8,2,1,4,5]=>[2,3,6,1,7,8,5,4]=>0010011=>[2,1,2,2]
[8,6,3,7,2,1,4,5]=>[1,3,6,2,7,8,5,4]=>0010011=>[2,1,2,2]
[5,6,3,8,2,1,4,7]=>[4,3,6,1,7,8,5,2]=>1010011=>[1,1,1,2,2]
[3,6,4,8,2,5,1,7]=>[6,3,5,1,7,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,8,3,5,7,1]=>[7,3,5,1,6,4,2,8]=>1010110=>[1,1,1,1,2,1]
[2,6,4,7,3,5,8,1]=>[7,3,5,2,6,4,1,8]=>1010110=>[1,1,1,1,2,1]
[3,6,4,7,2,5,1,8]=>[6,3,5,2,7,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,3,7,2,1,5,8]=>[5,3,6,2,7,8,4,1]=>1010011=>[1,1,1,2,2]
[5,6,3,7,2,1,4,8]=>[4,3,6,2,7,8,5,1]=>1010011=>[1,1,1,2,2]
[8,4,3,2,1,6,5,7]=>[1,5,6,7,8,3,4,2]=>0000101=>[4,1,1,1]
[6,4,3,2,1,7,5,8]=>[3,5,6,7,8,2,4,1]=>0000101=>[4,1,1,1]
[4,5,3,2,7,1,6,8]=>[5,4,6,7,2,8,3,1]=>1001011=>[1,2,1,1,2]
[3,5,4,2,8,6,1,7]=>[6,4,5,7,1,3,8,2]=>1001001=>[1,2,1,2,1]
[6,4,3,2,1,8,5,7]=>[3,5,6,7,8,1,4,2]=>0000101=>[4,1,1,1]
[7,4,3,2,1,8,5,6]=>[2,5,6,7,8,1,4,3]=>0000101=>[4,1,1,1]
[8,4,3,2,1,7,5,6]=>[1,5,6,7,8,2,4,3]=>0000101=>[4,1,1,1]
[8,4,3,2,1,7,6,5]=>[1,5,6,7,8,2,3,4]=>0000100=>[4,1,2]
[7,4,3,2,1,8,6,5]=>[2,5,6,7,8,1,3,4]=>0000100=>[4,1,2]
[6,4,3,2,1,8,7,5]=>[3,5,6,7,8,1,2,4]=>0000100=>[4,1,2]
[5,6,3,8,2,1,7,4]=>[4,3,6,1,7,8,2,5]=>1010010=>[1,1,1,2,1,1]
[7,5,3,2,8,1,6,4]=>[2,4,6,7,1,8,3,5]=>0001010=>[3,1,1,1,1]
[8,5,4,2,7,6,1,3]=>[1,4,5,7,2,3,8,6]=>0001001=>[3,1,2,1]
[7,5,4,2,8,6,1,3]=>[2,4,5,7,1,3,8,6]=>0001001=>[3,1,2,1]
[6,5,4,2,8,7,1,3]=>[3,4,5,7,1,2,8,6]=>0001001=>[3,1,2,1]
[4,6,5,8,7,2,1,3]=>[5,3,4,1,2,7,8,6]=>1010001=>[1,1,1,3,1]
[2,6,5,7,8,3,4,1]=>[7,3,4,2,1,6,5,8]=>1011010=>[1,1,2,1,1,1]
[6,5,4,2,7,8,1,3]=>[3,4,5,7,2,1,8,6]=>0001101=>[3,2,1,1]
[8,5,4,2,6,7,1,3]=>[1,4,5,7,3,2,8,6]=>0001101=>[3,2,1,1]
[8,5,3,2,6,1,7,4]=>[1,4,6,7,3,8,2,5]=>0001010=>[3,1,1,1,1]
[7,5,3,2,6,1,8,4]=>[2,4,6,7,3,8,1,5]=>0001010=>[3,1,1,1,1]
[5,6,3,7,2,1,8,4]=>[4,3,6,2,7,8,1,5]=>1010010=>[1,1,1,2,1,1]
[3,6,4,7,2,8,1,5]=>[6,3,5,2,7,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,7,3,8,5,1]=>[7,3,5,2,6,1,4,8]=>1010100=>[1,1,1,1,1,2]
[3,5,4,2,7,8,1,6]=>[6,4,5,7,2,1,8,3]=>1001101=>[1,2,2,1,1]
[4,5,3,2,7,1,8,6]=>[5,4,6,7,2,8,1,3]=>1001010=>[1,2,1,1,1,1]
[7,4,3,2,1,6,8,5]=>[2,5,6,7,8,3,1,4]=>0000110=>[4,2,1]
[8,4,3,2,1,6,7,5]=>[1,5,6,7,8,3,2,4]=>0000110=>[4,2,1]
[8,4,3,2,1,5,7,6]=>[1,5,6,7,8,4,2,3]=>0000110=>[4,2,1]
[7,4,3,2,1,5,8,6]=>[2,5,6,7,8,4,1,3]=>0000110=>[4,2,1]
[6,4,3,2,1,5,8,7]=>[3,5,6,7,8,4,1,2]=>0000110=>[4,2,1]
[3,5,4,2,6,8,1,7]=>[6,4,5,7,3,1,8,2]=>1001101=>[1,2,2,1,1]
[5,6,3,4,1,2,8,7]=>[4,3,6,5,8,7,1,2]=>1010110=>[1,1,1,1,2,1]
[8,5,3,7,2,6,4,1]=>[1,4,6,2,7,3,5,8]=>0010100=>[2,1,1,1,2]
[8,5,7,4,2,6,3,1]=>[1,4,2,5,7,3,6,8]=>0100100=>[1,1,2,1,2]
[7,5,8,4,2,6,1,3]=>[2,4,1,5,7,3,8,6]=>0100101=>[1,1,2,1,1,1]
[2,1,7,8,5,6,3,4]=>[7,8,2,1,4,3,6,5]=>0110101=>[1,2,1,1,1,1]
[6,8,3,7,5,1,4,2]=>[3,1,6,2,4,8,5,7]=>1010010=>[1,1,1,2,1,1]
[5,7,3,8,1,6,2,4]=>[4,2,6,1,8,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[3,2,6,4,8,5,1,7]=>[6,7,3,5,1,4,8,2]=>0101001=>[1,1,1,1,2,1]
[3,2,5,8,4,6,1,7]=>[6,7,4,1,5,3,8,2]=>0110101=>[1,2,1,1,1,1]
[3,5,2,4,1,7,6,8]=>[6,4,7,5,8,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[4,2,1,5,7,3,6,8]=>[5,7,8,4,2,6,3,1]=>0011011=>[2,2,1,2]
[4,2,5,3,8,1,6,7]=>[5,7,4,6,1,8,3,2]=>0101011=>[1,1,1,1,1,2]
[4,2,5,8,3,1,6,7]=>[5,7,4,1,6,8,3,2]=>0110011=>[1,2,2,2]
[4,1,5,3,8,2,6,7]=>[5,8,4,6,1,7,3,2]=>0101011=>[1,1,1,1,1,2]
[4,1,5,8,3,2,6,7]=>[5,8,4,1,6,7,3,2]=>0110011=>[1,2,2,2]
[4,3,8,5,2,1,6,7]=>[5,6,1,4,7,8,3,2]=>0100011=>[1,1,3,2]
[4,3,6,2,5,1,7,8]=>[5,6,3,7,4,8,2,1]=>0101011=>[1,1,1,1,1,2]
[4,6,3,2,5,1,7,8]=>[5,3,6,7,4,8,2,1]=>1001011=>[1,2,1,1,2]
[4,6,7,1,3,2,5,8]=>[5,3,2,8,6,7,4,1]=>1101011=>[2,1,1,1,2]
[4,5,1,7,3,2,6,8]=>[5,4,8,2,6,7,3,1]=>1010011=>[1,1,1,2,2]
[2,5,1,4,3,7,8,6]=>[7,4,8,5,6,2,1,3]=>1010110=>[1,1,1,1,2,1]
[5,2,1,4,3,7,8,6]=>[4,7,8,5,6,2,1,3]=>0010110=>[2,1,1,2,1]
[4,3,1,5,7,2,6,8]=>[5,6,8,4,2,7,3,1]=>0011011=>[2,2,1,2]
[4,3,6,1,5,2,7,8]=>[5,6,3,8,4,7,2,1]=>0101011=>[1,1,1,1,1,2]
[4,6,3,1,5,2,7,8]=>[5,3,6,8,4,7,2,1]=>1001011=>[1,2,1,1,2]
[4,3,6,1,7,2,5,8]=>[5,6,3,8,2,7,4,1]=>0101011=>[1,1,1,1,1,2]
[6,2,4,1,3,7,8,5]=>[3,7,5,8,6,2,1,4]=>0101110=>[1,1,1,3,1]
[3,6,4,1,2,7,5,8]=>[6,3,5,8,7,2,4,1]=>1001101=>[1,2,2,1,1]
[5,6,2,7,1,3,4,8]=>[4,3,7,2,8,6,5,1]=>1010111=>[1,1,1,1,3]
[4,6,2,1,7,3,5,8]=>[5,3,7,8,2,6,4,1]=>1001011=>[1,2,1,1,2]
[3,2,6,1,4,7,5,8]=>[6,7,3,8,5,2,4,1]=>0101101=>[1,1,1,2,1,1]
[3,7,2,4,8,5,1,6]=>[6,2,7,5,1,4,8,3]=>1011001=>[1,1,2,2,1]
[7,3,1,4,6,8,2,5]=>[2,6,8,5,3,1,7,4]=>0011101=>[2,3,1,1]
[3,2,6,1,5,7,4,8]=>[6,7,3,8,4,2,5,1]=>0101101=>[1,1,1,2,1,1]
[6,3,2,1,5,7,4,8]=>[3,6,7,8,4,2,5,1]=>0001101=>[3,2,1,1]
[6,4,2,1,5,3,7,8]=>[3,5,7,8,4,6,2,1]=>0001011=>[3,1,1,2]
[4,2,6,1,5,3,7,8]=>[5,7,3,8,4,6,2,1]=>0101011=>[1,1,1,1,1,2]
[4,2,1,7,5,3,6,8]=>[5,7,8,2,4,6,3,1]=>0010011=>[2,1,2,2]
[7,4,1,5,6,2,3,8]=>[2,5,8,4,3,7,6,1]=>0011011=>[2,2,1,2]
[7,2,1,5,3,6,8,4]=>[2,7,8,4,6,3,1,5]=>0010110=>[2,1,1,2,1]
[6,2,5,1,3,7,8,4]=>[3,7,4,8,6,2,1,5]=>0101110=>[1,1,1,3,1]
[6,3,5,1,2,7,4,8]=>[3,6,4,8,7,2,5,1]=>0101101=>[1,1,1,2,1,1]
[6,4,5,1,7,2,3,8]=>[3,5,4,8,2,7,6,1]=>0101011=>[1,1,1,1,1,2]
[5,2,6,4,1,3,7,8]=>[4,7,3,5,8,6,2,1]=>0100111=>[1,1,2,3]
[4,6,5,1,7,2,3,8]=>[5,3,4,8,2,7,6,1]=>1001011=>[1,2,1,1,2]
[3,6,5,1,2,7,4,8]=>[6,3,4,8,7,2,5,1]=>1001101=>[1,2,2,1,1]
[6,5,2,1,4,7,8,3]=>[3,4,7,8,5,2,1,6]=>0001110=>[3,3,1]
[6,5,3,1,4,7,2,8]=>[3,4,6,8,5,2,7,1]=>0001101=>[3,2,1,1]
[2,3,1,8,5,4,7,6]=>[7,6,8,1,4,5,2,3]=>1010010=>[1,1,1,2,1,1]
[2,4,1,5,8,3,7,6]=>[7,5,8,4,1,6,2,3]=>1011010=>[1,1,2,1,1,1]
[2,4,1,5,3,8,7,6]=>[7,5,8,4,6,1,2,3]=>1010100=>[1,1,1,1,1,2]
[3,4,5,1,2,8,7,6]=>[6,5,4,8,7,1,2,3]=>1101100=>[2,1,2,2]
[3,4,5,1,8,2,7,6]=>[6,5,4,8,1,7,2,3]=>1101010=>[2,1,1,1,1,1]
[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>1010010=>[1,1,1,2,1,1]
[2,4,8,5,3,1,7,6]=>[7,5,1,4,6,8,2,3]=>1100010=>[2,3,1,1]
[3,4,5,8,2,1,7,6]=>[6,5,4,1,7,8,2,3]=>1110010=>[3,2,1,1]
[3,4,5,2,8,1,7,6]=>[6,5,4,7,1,8,2,3]=>1101010=>[2,1,1,1,1,1]
[3,4,6,2,1,7,8,5]=>[6,5,3,7,8,2,1,4]=>1100110=>[2,2,2,1]
[3,4,6,2,1,7,5,8]=>[6,5,3,7,8,2,4,1]=>1100101=>[2,2,1,1,1]
[3,5,6,2,7,1,4,8]=>[6,4,3,7,2,8,5,1]=>1101011=>[2,1,1,1,2]
[3,5,6,2,7,1,8,4]=>[6,4,3,7,2,8,1,5]=>1101010=>[2,1,1,1,1,1]
[3,5,6,2,7,8,1,4]=>[6,4,3,7,2,1,8,5]=>1101101=>[2,1,2,1,1]
[3,4,6,2,8,7,1,5]=>[6,5,3,7,1,2,8,4]=>1101001=>[2,1,1,2,1]
[3,4,6,8,2,7,1,5]=>[6,5,3,1,7,2,8,4]=>1110101=>[3,1,1,1,1]
[2,4,8,6,3,7,1,5]=>[7,5,1,3,6,2,8,4]=>1100101=>[2,2,1,1,1]
[1,8,4,6,3,7,2,5]=>[8,1,5,3,6,2,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,6,3,7,5,2]=>[8,1,5,3,6,2,4,7]=>1010100=>[1,1,1,1,1,2]
[3,4,6,8,2,7,5,1]=>[6,5,3,1,7,2,4,8]=>1110100=>[3,1,1,2]
[3,4,6,2,8,7,5,1]=>[6,5,3,7,1,2,4,8]=>1101000=>[2,1,1,3]
[3,5,6,2,7,8,4,1]=>[6,4,3,7,2,1,5,8]=>1101100=>[2,1,2,2]
[3,5,6,2,7,4,1,8]=>[6,4,3,7,2,5,8,1]=>1101001=>[2,1,1,2,1]
[4,5,6,7,2,8,3,1]=>[5,4,3,2,7,1,6,8]=>1110100=>[3,1,1,2]
[3,5,6,8,7,2,4,1]=>[6,4,3,1,2,7,5,8]=>1110010=>[3,2,1,1]
[2,5,8,6,7,3,4,1]=>[7,4,1,3,2,6,5,8]=>1101010=>[2,1,1,1,1,1]
[1,8,5,6,7,3,4,2]=>[8,1,4,3,2,6,5,7]=>1011010=>[1,1,2,1,1,1]
[1,8,5,6,7,3,2,4]=>[8,1,4,3,2,6,7,5]=>1011001=>[1,1,2,2,1]
[2,5,8,6,7,3,1,4]=>[7,4,1,3,2,6,8,5]=>1101001=>[2,1,1,2,1]
[3,5,6,8,7,2,1,4]=>[6,4,3,1,2,7,8,5]=>1110001=>[3,3,1]
[4,5,6,7,2,1,8,3]=>[5,4,3,2,7,8,1,6]=>1110010=>[3,2,1,1]
[3,4,6,1,8,7,2,5]=>[6,5,3,8,1,2,7,4]=>1101001=>[2,1,1,2,1]
[2,4,1,6,8,7,3,5]=>[7,5,8,3,1,2,6,4]=>1011001=>[1,1,2,2,1]
[2,3,1,8,6,7,4,5]=>[7,6,8,1,3,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,2,6,7,5,4]=>[8,1,6,7,3,2,4,5]=>1001100=>[1,2,2,2]
[2,5,1,6,7,8,4,3]=>[7,4,8,3,2,1,5,6]=>1011100=>[1,1,3,2]
[2,5,1,6,7,4,8,3]=>[7,4,8,3,2,5,1,6]=>1011010=>[1,1,2,1,1,1]
[2,5,1,6,7,4,3,8]=>[7,4,8,3,2,5,6,1]=>1011001=>[1,1,2,2,1]
[3,5,6,1,7,4,2,8]=>[6,4,3,8,2,5,7,1]=>1101001=>[2,1,1,2,1]
[3,5,6,1,7,4,8,2]=>[6,4,3,8,2,5,1,7]=>1101010=>[2,1,1,1,1,1]
[3,4,6,1,8,7,5,2]=>[6,5,3,8,1,2,4,7]=>1101000=>[2,1,1,3]
[3,4,6,8,1,7,5,2]=>[6,5,3,1,8,2,4,7]=>1110100=>[3,1,1,2]
[2,4,8,6,1,7,5,3]=>[7,5,1,3,8,2,4,6]=>1100100=>[2,2,1,2]
[1,8,4,6,2,7,5,3]=>[8,1,5,3,7,2,4,6]=>1010100=>[1,1,1,1,1,2]
[1,8,5,6,7,2,4,3]=>[8,1,4,3,2,7,5,6]=>1011010=>[1,1,2,1,1,1]
[2,5,8,6,7,1,4,3]=>[7,4,1,3,2,8,5,6]=>1101010=>[2,1,1,1,1,1]
[3,5,6,8,7,1,4,2]=>[6,4,3,1,2,8,5,7]=>1110010=>[3,2,1,1]
[4,5,6,7,8,1,3,2]=>[5,4,3,2,1,8,6,7]=>1111010=>[4,1,1,1]
[4,5,6,7,1,3,8,2]=>[5,4,3,2,8,6,1,7]=>1110110=>[3,1,2,1]
[4,5,6,7,1,3,2,8]=>[5,4,3,2,8,6,7,1]=>1110101=>[3,1,1,1,1]
[4,5,6,7,3,1,8,2]=>[5,4,3,2,6,8,1,7]=>1110010=>[3,2,1,1]
[3,5,6,8,7,4,1,2]=>[6,4,3,1,2,5,8,7]=>1110001=>[3,3,1]
[2,5,8,6,7,4,1,3]=>[7,4,1,3,2,5,8,6]=>1101001=>[2,1,1,2,1]
[1,8,5,6,7,4,2,3]=>[8,1,4,3,2,5,7,6]=>1011001=>[1,1,2,2,1]
[1,8,5,6,7,4,3,2]=>[8,1,4,3,2,5,6,7]=>1011000=>[1,1,2,3]
[2,5,8,6,7,4,3,1]=>[7,4,1,3,2,5,6,8]=>1101000=>[2,1,1,3]
[8,2,5,3,7,1,6,4]=>[1,7,4,6,2,8,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,3,7,1,6,5]=>[1,7,5,6,2,8,3,4]=>0101010=>[1,1,1,1,1,1,1]
[5,8,2,4,3,7,1,6]=>[4,1,7,5,6,2,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,2,5,6,1,8,3,7]=>[5,7,4,3,8,1,6,2]=>0110101=>[1,2,1,1,1,1]
[4,2,5,6,1,7,3,8]=>[5,7,4,3,8,2,6,1]=>0110101=>[1,2,1,1,1,1]
[6,1,5,7,3,2,4,8]=>[3,8,4,2,6,7,5,1]=>0110011=>[1,2,2,2]
[6,1,5,8,3,2,4,7]=>[3,8,4,1,6,7,5,2]=>0110011=>[1,2,2,2]
[3,8,2,4,7,1,5,6]=>[6,1,7,5,2,8,4,3]=>1011011=>[1,1,2,1,2]
[3,6,8,2,4,7,1,5]=>[6,3,1,7,5,2,8,4]=>1101101=>[2,1,2,1,1]
[4,3,5,6,7,1,8,2]=>[5,6,4,3,2,8,1,7]=>0111010=>[1,3,1,1,1]
[3,7,1,5,6,8,2,4]=>[6,2,8,4,3,1,7,5]=>1011101=>[1,1,3,1,1]
[3,7,1,5,8,2,4,6]=>[6,2,8,4,1,7,5,3]=>1011011=>[1,1,2,1,2]
[8,3,2,4,6,1,5,7]=>[1,6,7,5,3,8,4,2]=>0011011=>[2,2,1,2]
[7,3,2,4,6,1,5,8]=>[2,6,7,5,3,8,4,1]=>0011011=>[2,2,1,2]
[3,2,5,1,7,4,6,8]=>[6,7,4,8,2,5,3,1]=>0101011=>[1,1,1,1,1,2]
[3,2,5,1,8,4,6,7]=>[6,7,4,8,1,5,3,2]=>0101011=>[1,1,1,1,1,2]
[3,2,5,1,7,8,4,6]=>[6,7,4,8,2,1,5,3]=>0101101=>[1,1,1,2,1,1]
[7,8,3,2,4,6,1,5]=>[2,1,6,7,5,3,8,4]=>1001101=>[1,2,2,1,1]
[6,1,5,7,8,3,2,4]=>[3,8,4,2,1,6,7,5]=>0111001=>[1,3,2,1]
[4,2,5,6,1,7,8,3]=>[5,7,4,3,8,2,1,6]=>0110110=>[1,2,1,2,1]
[5,7,6,1,8,3,4,2]=>[4,2,3,8,1,6,5,7]=>1001010=>[1,2,1,1,1,1]
[5,8,6,1,7,3,4,2]=>[4,1,3,8,2,6,5,7]=>1001010=>[1,2,1,1,1,1]
[6,1,5,8,7,3,2,4]=>[3,8,4,1,2,6,7,5]=>0110001=>[1,2,3,1]
[8,7,3,2,4,6,1,5]=>[1,2,6,7,5,3,8,4]=>0001101=>[3,2,1,1]
[3,2,5,1,8,7,4,6]=>[6,7,4,8,1,2,5,3]=>0101001=>[1,1,1,1,2,1]
[3,2,5,1,6,4,7,8]=>[6,7,4,8,3,5,2,1]=>0101011=>[1,1,1,1,1,2]
[3,2,4,1,8,7,5,6]=>[6,7,5,8,1,2,4,3]=>0101001=>[1,1,1,1,2,1]
[3,2,5,1,6,8,7,4]=>[6,7,4,8,3,1,2,5]=>0101100=>[1,1,1,2,2]
[3,8,6,5,1,7,4,2]=>[6,1,3,4,8,2,5,7]=>1000100=>[1,3,1,2]
[3,7,6,5,1,8,4,2]=>[6,2,3,4,8,1,5,7]=>1000100=>[1,3,1,2]
[6,5,1,7,8,4,2,3]=>[3,4,8,2,1,5,7,6]=>0011001=>[2,2,2,1]
[3,2,5,1,6,7,8,4]=>[6,7,4,8,3,2,1,5]=>0101110=>[1,1,1,3,1]
[3,2,4,1,8,5,6,7]=>[6,7,5,8,1,4,3,2]=>0101011=>[1,1,1,1,1,2]
[3,2,4,1,7,5,6,8]=>[6,7,5,8,2,4,3,1]=>0101011=>[1,1,1,1,1,2]
[3,2,4,1,6,8,5,7]=>[6,7,5,8,3,1,4,2]=>0101101=>[1,1,1,2,1,1]
[3,2,4,1,8,5,7,6]=>[6,7,5,8,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,3,2,4,7,6,1,5]=>[1,6,7,5,2,3,8,4]=>0011001=>[2,2,2,1]
[3,2,5,1,8,4,7,6]=>[6,7,4,8,1,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[3,2,5,1,6,7,4,8]=>[6,7,4,8,3,2,5,1]=>0101101=>[1,1,1,2,1,1]
[6,5,1,7,4,2,3,8]=>[3,4,8,2,5,7,6,1]=>0010011=>[2,1,2,2]
[6,5,1,8,4,2,3,7]=>[3,4,8,1,5,7,6,2]=>0010011=>[2,1,2,2]
[8,4,2,3,7,5,1,6]=>[1,5,7,6,2,4,8,3]=>0011001=>[2,2,2,1]
[4,2,6,1,8,3,7,5]=>[5,7,3,8,1,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,1,8,3,7,4]=>[4,7,3,8,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,4,6,1,7,3,5,2]=>[1,5,3,8,2,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[5,2,6,1,8,4,7,3]=>[4,7,3,8,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,4,2,3,8,5,1,6]=>[2,5,7,6,1,4,8,3]=>0011001=>[2,2,2,1]
[8,5,1,6,4,2,3,7]=>[1,4,8,3,5,7,6,2]=>0010011=>[2,1,2,2]
[7,5,1,6,4,2,3,8]=>[2,4,8,3,5,7,6,1]=>0010011=>[2,1,2,2]
[3,2,5,1,7,6,4,8]=>[6,7,4,8,2,3,5,1]=>0101001=>[1,1,1,1,2,1]
[3,2,5,1,8,6,4,7]=>[6,7,4,8,1,3,5,2]=>0101001=>[1,1,1,1,2,1]
[7,3,2,4,8,6,1,5]=>[2,6,7,5,1,3,8,4]=>0011001=>[2,2,2,1]
[8,6,1,5,7,3,2,4]=>[1,3,8,4,2,6,7,5]=>0011001=>[2,2,2,1]
[4,2,6,1,8,5,7,3]=>[5,7,3,8,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]
[8,5,6,1,7,3,4,2]=>[1,4,3,8,2,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[3,6,8,5,1,7,4,2]=>[6,3,1,4,8,2,5,7]=>1100100=>[2,2,1,2]
[8,5,1,6,7,4,2,3]=>[1,4,8,3,2,5,7,6]=>0011001=>[2,2,2,1]
[3,2,5,1,8,6,7,4]=>[6,7,4,8,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,4,1,8,6,5,7]=>[6,7,5,8,1,3,4,2]=>0101001=>[1,1,1,1,2,1]
[3,2,4,1,5,8,6,7]=>[6,7,5,8,4,1,3,2]=>0101101=>[1,1,1,2,1,1]
[3,2,5,1,7,8,6,4]=>[6,7,4,8,2,1,3,5]=>0101100=>[1,1,1,2,2]
[7,8,5,1,6,4,2,3]=>[2,1,4,8,3,5,7,6]=>1001001=>[1,2,1,2,1]
[3,8,5,1,7,6,4,2]=>[6,1,4,8,2,3,5,7]=>1001000=>[1,2,1,3]
[3,7,5,1,8,6,4,2]=>[6,2,4,8,1,3,5,7]=>1001000=>[1,2,1,3]
[8,7,5,1,6,4,2,3]=>[1,2,4,8,3,5,7,6]=>0001001=>[3,1,2,1]
[3,2,5,1,8,7,6,4]=>[6,7,4,8,1,2,3,5]=>0101000=>[1,1,1,1,3]
[6,5,7,3,1,8,4,2]=>[3,4,2,6,8,1,5,7]=>0100100=>[1,1,2,1,2]
[4,6,3,7,1,8,5,2]=>[5,3,6,2,8,1,4,7]=>1010100=>[1,1,1,1,1,2]
[4,6,3,7,5,1,8,2]=>[5,3,6,2,4,8,1,7]=>1010010=>[1,1,1,2,1,1]
[4,2,6,1,7,5,3,8]=>[5,7,3,8,2,4,6,1]=>0101001=>[1,1,1,1,2,1]
[2,5,7,4,1,6,3,8]=>[7,4,2,5,8,3,6,1]=>1100101=>[2,2,1,1,1]
[2,5,7,4,1,6,8,3]=>[7,4,2,5,8,3,1,6]=>1100110=>[2,2,2,1]
[5,4,7,3,6,1,8,2]=>[4,5,2,6,3,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,7,8,3,1,6,2]=>[4,5,2,1,6,8,3,7]=>0110010=>[1,2,2,1,1]
[4,3,7,5,1,8,6,2]=>[5,6,2,4,8,1,3,7]=>0100100=>[1,1,2,1,2]
[6,4,3,8,5,1,7,2]=>[3,5,6,1,4,8,2,7]=>0010010=>[2,1,2,1,1]
[5,8,4,3,6,1,7,2]=>[4,1,5,6,3,8,2,7]=>1001010=>[1,2,1,1,1,1]
[5,4,8,3,6,1,7,2]=>[4,5,1,6,3,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,3,6,7,1,8,2]=>[4,5,6,3,2,8,1,7]=>0011010=>[2,2,1,1,1]
[2,5,4,6,1,7,3,8]=>[7,4,5,3,8,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[3,2,5,8,1,6,7,4]=>[6,7,4,1,8,3,2,5]=>0110110=>[1,2,1,2,1]
[2,5,4,6,8,1,7,3]=>[7,4,5,3,1,8,2,6]=>1011010=>[1,1,2,1,1,1]
[5,2,8,4,1,6,7,3]=>[4,7,1,5,8,3,2,6]=>0100110=>[1,1,2,2,1]
[4,6,2,1,8,5,7,3]=>[5,3,7,8,1,4,2,6]=>1001010=>[1,2,1,1,1,1]
[2,4,1,7,5,8,6,3]=>[7,5,8,2,4,1,3,6]=>1010100=>[1,1,1,1,1,2]
[2,4,1,7,5,3,8,6]=>[7,5,8,2,4,6,1,3]=>1010010=>[1,1,1,2,1,1]
[2,6,4,1,8,5,3,7]=>[7,3,5,8,1,4,6,2]=>1001001=>[1,2,1,2,1]
[5,4,8,2,1,6,3,7]=>[4,5,1,7,8,3,6,2]=>0100101=>[1,1,2,1,1,1]
[2,5,8,4,1,6,3,7]=>[7,4,1,5,8,3,6,2]=>1100101=>[2,2,1,1,1]
[3,2,5,6,1,8,4,7]=>[6,7,4,3,8,1,5,2]=>0110101=>[1,2,1,1,1,1]
[4,8,3,2,6,1,5,7]=>[5,1,6,7,3,8,4,2]=>1001011=>[1,2,1,1,2]
[3,5,2,8,1,6,4,7]=>[6,4,7,1,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[3,2,1,6,8,5,4,7]=>[6,7,8,3,1,4,5,2]=>0011001=>[2,2,2,1]
[3,2,7,1,5,4,8,6]=>[6,7,2,8,4,5,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,2,7,1,5,8,6,4]=>[6,7,2,8,4,1,3,5]=>0101100=>[1,1,1,2,2]
[3,8,2,5,1,6,7,4]=>[6,1,7,4,8,3,2,5]=>1010110=>[1,1,1,1,2,1]
[4,8,3,2,6,7,1,5]=>[5,1,6,7,3,2,8,4]=>1001101=>[1,2,2,1,1]
[4,3,8,2,6,7,1,5]=>[5,6,1,7,3,2,8,4]=>0101101=>[1,1,1,2,1,1]
[4,3,2,6,7,8,1,5]=>[5,6,7,3,2,1,8,4]=>0011101=>[2,3,1,1]
[4,3,2,6,7,1,5,8]=>[5,6,7,3,2,8,4,1]=>0011011=>[2,2,1,2]
[4,3,7,2,6,8,1,5]=>[5,6,2,7,3,1,8,4]=>0101101=>[1,1,1,2,1,1]
[4,3,7,8,2,6,1,5]=>[5,6,2,1,7,3,8,4]=>0110101=>[1,2,1,1,1,1]
[2,5,7,4,8,1,6,3]=>[7,4,2,5,1,8,3,6]=>1101010=>[2,1,1,1,1,1]
[3,2,5,7,8,1,6,4]=>[6,7,4,2,1,8,3,5]=>0111010=>[1,3,1,1,1]
[3,2,5,7,1,6,8,4]=>[6,7,4,2,8,3,1,5]=>0110110=>[1,2,1,2,1]
[3,2,5,7,1,6,4,8]=>[6,7,4,2,8,3,5,1]=>0110101=>[1,2,1,1,1,1]
[6,3,2,7,1,5,4,8]=>[3,6,7,2,8,4,5,1]=>0010101=>[2,1,1,1,1,1]
[6,3,2,7,1,5,8,4]=>[3,6,7,2,8,4,1,5]=>0010110=>[2,1,1,2,1]
[6,3,2,7,8,1,5,4]=>[3,6,7,2,1,8,4,5]=>0011010=>[2,2,1,1,1]
[4,2,6,1,7,8,5,3]=>[5,7,3,8,2,1,4,6]=>0101100=>[1,1,1,2,2]
[6,5,2,1,7,8,4,3]=>[3,4,7,8,2,1,5,6]=>0001100=>[3,2,2]
[2,1,7,5,3,8,6,4]=>[7,8,2,4,6,1,3,5]=>0100100=>[1,1,2,1,2]
[6,2,1,8,5,3,7,4]=>[3,7,8,1,4,6,2,5]=>0010010=>[2,1,2,1,1]
[6,3,2,7,1,4,8,5]=>[3,6,7,2,8,5,1,4]=>0010110=>[2,1,1,2,1]
[6,3,2,1,4,7,8,5]=>[3,6,7,8,5,2,1,4]=>0001110=>[3,3,1]
[6,3,2,1,4,7,5,8]=>[3,6,7,8,5,2,4,1]=>0001101=>[3,2,1,1]
[3,5,2,1,7,4,6,8]=>[6,4,7,8,2,5,3,1]=>1001011=>[1,2,1,1,2]
[3,5,2,1,7,8,4,6]=>[6,4,7,8,2,1,5,3]=>1001101=>[1,2,2,1,1]
[5,8,4,2,1,7,3,6]=>[4,1,5,7,8,2,6,3]=>1000101=>[1,3,1,1,1]
[4,6,2,1,8,3,7,5]=>[5,3,7,8,1,6,2,4]=>1001010=>[1,2,1,1,1,1]
[2,4,1,7,3,8,6,5]=>[7,5,8,2,6,1,3,4]=>1010100=>[1,1,1,1,1,2]
[3,2,7,1,4,8,6,5]=>[6,7,2,8,5,1,3,4]=>0101100=>[1,1,1,2,2]
[3,5,8,2,1,7,4,6]=>[6,4,1,7,8,2,5,3]=>1100101=>[2,2,1,1,1]
[4,8,3,7,2,1,5,6]=>[5,1,6,2,7,8,4,3]=>1010011=>[1,1,1,2,2]
[4,3,7,2,8,1,5,6]=>[5,6,2,7,1,8,4,3]=>0101011=>[1,1,1,1,1,2]
[4,8,3,2,7,1,5,6]=>[5,1,6,7,2,8,4,3]=>1001011=>[1,2,1,1,2]
[3,5,2,8,1,7,4,6]=>[6,4,7,1,8,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[6,3,2,8,1,4,7,5]=>[3,6,7,1,8,5,2,4]=>0010110=>[2,1,1,2,1]
[3,2,1,4,7,5,8,6]=>[6,7,8,5,2,4,1,3]=>0011010=>[2,2,1,1,1]
[5,3,2,1,8,4,6,7]=>[4,6,7,8,1,5,3,2]=>0001011=>[3,1,1,2]
[4,8,3,2,1,5,6,7]=>[5,1,6,7,8,4,3,2]=>1000111=>[1,3,3]
[4,3,8,2,1,5,6,7]=>[5,6,1,7,8,4,3,2]=>0100111=>[1,1,2,3]
[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>10000000=>[1,7]
[8,7,6,4,5,3,2,1,9]=>[2,3,4,6,5,7,8,9,1]=>00010001=>[3,1,3,1]
[1,9,8,7,5,6,4,3,2]=>[9,1,2,3,5,4,6,7,8]=>10001000=>[1,3,1,3]
[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>100000000=>[1,8]
[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001=>[9,1]
[9,8,7,5,6,4,3,2,1,10]=>[2,3,4,6,5,7,8,9,10,1]=>000100001=>[3,1,4,1]
[8,7,5,4,6,3,2,1,9]=>[2,3,5,6,4,7,8,9,1]=>00010001=>[3,1,3,1]
[8,7,4,6,5,3,2,1,9]=>[2,3,6,4,5,7,8,9,1]=>00100001=>[2,1,4,1]
[1,9,8,6,5,7,4,3,2]=>[9,1,2,4,5,3,6,7,8]=>10001000=>[1,3,1,3]
[1,9,8,5,7,6,4,3,2]=>[9,1,2,5,3,4,6,7,8]=>10010000=>[1,2,1,4]
[1,10,9,8,6,7,5,4,3,2]=>[10,1,2,3,5,4,6,7,8,9]=>100010000=>[1,3,1,4]
[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000=>[1,9]
[6,2,3,1,5,4,8,7]=>[3,7,6,8,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[8,4,5,2,3,1,7,6]=>[1,5,4,7,6,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,2,5,3,4,1]=>[1,3,2,7,4,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,5,3,4,1,7,6]=>[1,7,4,6,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[6,2,5,3,4,1,8,7]=>[3,7,4,6,5,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,2,4,3,8,7]=>[3,8,4,7,5,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,4,5,1,3,2,8,7]=>[3,5,4,8,6,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,3,4,2,8,7]=>[3,8,4,6,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[6,3,5,1,4,2,8,7]=>[3,6,4,8,5,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,2,4,1,7,6]=>[1,6,4,7,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,5,6,2,4,1]=>[1,6,2,4,3,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,2,4,1,6,5]=>[1,6,2,7,5,8,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,1,4,2,7,6]=>[1,6,4,8,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,3,4,2,7,6]=>[1,8,4,6,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,4,5,1,3,2,7,6]=>[1,5,4,8,6,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,4,5,3,7,6]=>[7,8,1,5,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,4,5,1,3,2]=>[1,3,2,5,4,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,1,5,3,4,2]=>[1,3,2,8,4,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,3,5,1,4,2]=>[1,3,2,6,4,8,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,5,6,1,4,2]=>[1,6,2,4,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,3,6,1,4,2]=>[1,4,2,6,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,4,6,2,5,1]=>[1,6,2,5,3,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,4,6,1,5,2]=>[1,6,2,5,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,1,6,4,5,2]=>[1,6,2,8,3,5,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,3,6,4,5,2]=>[1,8,2,6,3,5,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,5,6,3,4,2]=>[1,8,2,4,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,5,6,1,3,2]=>[1,5,2,4,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,4,7,5,6,3]=>[7,8,1,5,2,4,3,6]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,3,4,2,6,5]=>[1,8,2,6,5,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,3,6,2,5,4]=>[1,8,2,6,3,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,1,6,2,5,4]=>[1,6,2,8,3,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,7,2,6,4,5,1]=>[1,6,2,7,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,3,6,4,5,1]=>[1,7,2,6,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,3,6,1,5,4]=>[1,7,2,6,3,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,1,6,3,5,4]=>[1,7,2,8,3,6,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,2,4,3,6,5]=>[1,8,2,7,5,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,3,2,7,4,6,5]=>[1,8,6,7,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,3,7,4,6,5]=>[7,8,1,6,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,2,4,3,7,6]=>[1,8,4,7,5,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,1,4,3,6,5]=>[1,7,2,8,5,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,3,4,1,6,5]=>[1,7,2,6,5,8,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,5,6,3,4,1]=>[1,7,2,4,3,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,5,6,2,3,1]=>[1,5,2,4,3,7,6,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,2,3,1,6,5]=>[1,5,2,7,6,8,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,3,1,7,4,6,5]=>[1,7,6,8,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,3,1,5,4,7,6]=>[1,7,6,8,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,2,3,1,8,5,7,6]=>[5,7,6,8,1,4,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,1,3,2,8,6,7,5]=>[5,8,6,7,1,3,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,2,3,1,5,4]=>[1,3,2,7,6,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,3,1,7,5,6,4]=>[1,7,6,8,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,2,6,3,4,1]=>[1,4,2,7,3,6,5,8]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,2,6,1,4,3]=>[1,4,2,7,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,5,6,1,4,3]=>[1,7,2,4,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,2,5,1,4,3]=>[1,3,2,7,4,8,5,6]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,1,5,2,4,3]=>[1,3,2,8,4,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[8,6,7,1,3,2,5,4]=>[1,3,2,8,6,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,6,7,3,5,4]=>[7,8,1,3,2,6,4,5]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,3,7,5,6,4]=>[7,8,1,6,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,3,2,7,5,6,4]=>[1,8,6,7,2,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,5,6,2,4,3]=>[1,8,2,4,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,2,6,4,5,3]=>[1,8,2,7,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,1,6,4,5,3]=>[1,7,2,8,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,4,6,1,5,3]=>[1,7,2,5,3,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,4,6,3,5,1]=>[1,7,2,5,3,6,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,2,6,3,5,1]=>[1,5,2,7,3,6,4,8]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,2,6,1,5,3]=>[1,5,2,7,3,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,1,6,2,5,3]=>[1,5,2,8,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,4,6,2,5,3]=>[1,8,2,5,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,1,6,2,4,3]=>[1,4,2,8,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,5,7,3,6,4]=>[7,8,1,4,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,4,6,1,3,2]=>[1,4,2,5,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[8,5,7,1,6,3,4,2]=>[1,4,2,8,3,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,4,6,3,5,2]=>[1,8,2,5,3,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,1,6,3,5,2]=>[1,5,2,8,3,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[8,4,7,3,6,1,5,2]=>[1,5,2,6,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]
[2,4,8,3,6,1,7,5]=>[7,5,1,6,3,8,2,4]=>1101010=>[2,1,1,1,1,1]
[6,5,8,1,3,2,7,4]=>[3,4,1,8,6,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[4,5,8,6,3,2,7,1]=>[5,4,1,3,6,7,2,8]=>1100010=>[2,3,1,1]
[6,5,8,7,3,1,2,4]=>[3,4,1,2,6,8,7,5]=>0100011=>[1,1,3,2]
[1,5,8,7,3,6,2,4]=>[8,4,1,2,6,3,7,5]=>1100101=>[2,2,1,1,1]
[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>1010100=>[1,1,1,1,1,2]
[6,7,2,8,4,1,5,3]=>[3,2,7,1,5,8,4,6]=>1010010=>[1,1,1,2,1,1]
[3,6,2,8,4,5,7,1]=>[6,3,7,1,5,4,2,8]=>1010110=>[1,1,1,1,2,1]
[2,6,1,8,4,5,7,3]=>[7,3,8,1,5,4,2,6]=>1010110=>[1,1,1,1,2,1]
[2,8,4,6,1,5,7,3]=>[7,1,5,3,8,4,2,6]=>1010110=>[1,1,1,1,2,1]
[6,3,1,8,4,5,7,2]=>[3,6,8,1,5,4,2,7]=>0010110=>[2,1,1,2,1]
[3,1,6,8,4,5,7,2]=>[6,8,3,1,5,4,2,7]=>0110110=>[1,2,1,2,1]
[2,3,6,8,4,5,7,1]=>[7,6,3,1,5,4,2,8]=>1110110=>[3,1,2,1]
[6,3,7,8,4,1,5,2]=>[3,6,2,1,5,8,4,7]=>0110010=>[1,2,2,1,1]
[1,3,7,8,4,6,5,2]=>[8,6,2,1,5,3,4,7]=>1110100=>[3,1,1,2]
[1,5,7,8,2,4,6,3]=>[8,4,2,1,7,5,3,6]=>1110110=>[3,1,2,1]
[5,1,7,8,2,4,6,3]=>[4,8,2,1,7,5,3,6]=>0110110=>[1,2,1,2,1]
[3,6,7,8,4,2,5,1]=>[6,3,2,1,5,7,4,8]=>1110010=>[3,2,1,1]
[7,6,1,8,4,2,5,3]=>[2,3,8,1,5,7,4,6]=>0010010=>[2,1,2,1,1]
[5,6,8,7,3,2,1,4]=>[4,3,1,2,6,7,8,5]=>1100001=>[2,4,1]
[2,8,3,7,1,6,5,4]=>[7,1,6,2,8,3,4,5]=>1010100=>[1,1,1,1,1,2]
[5,2,8,7,3,6,1,4]=>[4,7,1,2,6,3,8,5]=>0100101=>[1,1,2,1,1,1]
[7,2,1,8,4,6,5,3]=>[2,7,8,1,5,3,4,6]=>0010100=>[2,1,1,1,2]
[3,2,7,8,4,6,5,1]=>[6,7,2,1,5,3,4,8]=>0110100=>[1,2,1,1,2]
[5,2,7,8,1,4,6,3]=>[4,7,2,1,8,5,3,6]=>0110110=>[1,2,1,2,1]
[1,2,7,8,5,4,6,3]=>[8,7,2,1,4,5,3,6]=>1110010=>[3,2,1,1]
[4,2,1,3,8,5,6,7]=>[5,7,8,6,1,4,3,2]=>0011011=>[2,2,1,2]
[7,2,5,8,3,4,6,1]=>[2,7,4,1,6,5,3,8]=>0110110=>[1,2,1,2,1]
[6,2,8,5,4,3,1,7]=>[3,7,1,4,5,6,8,2]=>0100001=>[1,1,4,1]
[2,8,3,5,4,1,6,7]=>[7,1,6,4,5,8,3,2]=>1010011=>[1,1,1,2,2]
[2,8,4,5,3,1,6,7]=>[7,1,5,4,6,8,3,2]=>1010011=>[1,1,1,2,2]
[6,4,8,5,2,3,1,7]=>[3,5,1,4,7,6,8,2]=>0100101=>[1,1,2,1,1,1]
[7,3,5,8,2,4,6,1]=>[2,6,4,1,7,5,3,8]=>0110110=>[1,2,1,2,1]
[4,3,1,2,8,5,6,7]=>[5,6,8,7,1,4,3,2]=>0011011=>[2,2,1,2]
[3,4,2,1,8,5,6,7]=>[6,5,7,8,1,4,3,2]=>1001011=>[1,2,1,1,2]
[2,7,6,8,4,3,5,1]=>[7,2,3,1,5,6,4,8]=>1010010=>[1,1,1,2,1,1]
[5,7,1,8,3,4,6,2]=>[4,2,8,1,6,5,3,7]=>1010110=>[1,1,1,1,2,1]
[3,7,5,8,1,4,6,2]=>[6,2,4,1,8,5,3,7]=>1010110=>[1,1,1,1,2,1]
[1,7,5,8,3,4,6,2]=>[8,2,4,1,6,5,3,7]=>1010110=>[1,1,1,1,2,1]
[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>1100001=>[2,4,1]
[4,6,8,5,1,3,2,7]=>[5,3,1,4,8,6,7,2]=>1100101=>[2,2,1,1,1]
[5,6,8,1,4,3,2,7]=>[4,3,1,8,5,6,7,2]=>1101001=>[2,1,1,2,1]
[7,5,8,6,3,4,2,1]=>[2,4,1,3,6,5,7,8]=>0100100=>[1,1,2,1,2]
[2,4,8,3,6,5,1,7]=>[7,5,1,6,3,4,8,2]=>1101001=>[2,1,1,2,1]
[2,8,4,1,5,6,3,7]=>[7,1,5,8,4,3,6,2]=>1001101=>[1,2,2,1,1]
[4,1,8,3,5,6,2,7]=>[5,8,1,6,4,3,7,2]=>0101101=>[1,1,1,2,1,1]
[5,6,8,4,1,3,2,7]=>[4,3,1,5,8,6,7,2]=>1100101=>[2,2,1,1,1]
[4,6,8,1,5,3,2,7]=>[5,3,1,8,4,6,7,2]=>1101001=>[2,1,1,2,1]
[1,6,8,4,5,3,2,7]=>[8,3,1,5,4,6,7,2]=>1101001=>[2,1,1,2,1]
[1,7,3,8,5,4,6,2]=>[8,2,6,1,4,5,3,7]=>1010010=>[1,1,1,2,1,1]
[3,7,1,8,5,4,6,2]=>[6,2,8,1,4,5,3,7]=>1010010=>[1,1,1,2,1,1]
[2,7,3,8,4,6,5,1]=>[7,2,6,1,5,3,4,8]=>1010100=>[1,1,1,1,1,2]
[7,1,3,8,4,6,5,2]=>[2,8,6,1,5,3,4,7]=>0110100=>[1,2,1,1,2]
[5,7,8,4,3,6,1,2]=>[4,2,1,5,6,3,8,7]=>1100101=>[2,2,1,1,1]
[2,8,7,4,1,6,5,3]=>[7,1,2,5,8,3,4,6]=>1000100=>[1,3,1,2]
[2,8,5,4,3,1,6,7]=>[7,1,4,5,6,8,3,2]=>1000011=>[1,4,2]
[6,5,8,4,2,3,1,7]=>[3,4,1,5,7,6,8,2]=>0100101=>[1,1,2,1,1,1]
[4,1,3,2,8,5,6,7]=>[5,8,6,7,1,4,3,2]=>0101011=>[1,1,1,1,1,2]
[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>1001011=>[1,2,1,1,2]
[7,3,2,8,5,4,6,1]=>[2,6,7,1,4,5,3,8]=>0010010=>[2,1,2,1,1]
[6,4,8,2,5,3,1,7]=>[3,5,1,7,4,6,8,2]=>0101001=>[1,1,1,1,2,1]
[2,8,4,3,5,1,6,7]=>[7,1,5,6,4,8,3,2]=>1001011=>[1,2,1,1,2]
[2,8,3,4,5,1,6,7]=>[7,1,6,5,4,8,3,2]=>1011011=>[1,1,2,1,2]
[6,2,8,4,5,3,1,7]=>[3,7,1,5,4,6,8,2]=>0101001=>[1,1,1,1,2,1]
[7,2,3,8,5,4,6,1]=>[2,7,6,1,4,5,3,8]=>0110010=>[1,2,2,1,1]
[4,2,3,1,8,5,6,7]=>[5,7,6,8,1,4,3,2]=>0101011=>[1,1,1,1,1,2]
[3,2,1,4,8,5,6,7]=>[6,7,8,5,1,4,3,2]=>0011011=>[2,2,1,2]
[5,1,3,2,4,8,6,7]=>[4,8,6,7,5,1,3,2]=>0101101=>[1,1,1,2,1,1]
[2,8,1,5,3,4,7,6]=>[7,1,8,4,6,5,2,3]=>1010110=>[1,1,1,1,2,1]
[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>1101010=>[2,1,1,1,1,1]
[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>1010011=>[1,1,1,2,2]
[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>1001011=>[1,2,1,1,2]
[8,1,5,3,2,4,6,7]=>[1,8,4,6,7,5,3,2]=>0100111=>[1,1,2,3]
[3,8,1,5,2,4,6,7]=>[6,1,8,4,7,5,3,2]=>1010111=>[1,1,1,1,3]
[3,5,1,4,8,2,6,7]=>[6,4,8,5,1,7,3,2]=>1011011=>[1,1,2,1,2]
[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>1010011=>[1,1,1,2,2]
[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>1100011=>[2,3,2]
[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>1100101=>[2,2,1,1,1]
[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>1110010=>[3,2,1,1]
[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>1101001=>[2,1,1,2,1]
[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>1011001=>[1,1,2,2,1]
[5,1,2,7,4,8,3,6]=>[4,8,7,2,5,1,6,3]=>0110101=>[1,2,1,1,1,1]
[8,3,5,1,4,7,2,6]=>[1,6,4,8,5,2,7,3]=>0101101=>[1,1,1,2,1,1]
[2,8,1,5,4,7,3,6]=>[7,1,8,4,5,2,6,3]=>1010101=>[1,1,1,1,1,1,1]
[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>1101001=>[2,1,1,2,1]
[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>1110001=>[3,3,1]
[2,8,1,4,3,7,6,5]=>[7,1,8,5,6,2,3,4]=>1010100=>[1,1,1,1,1,2]
[6,1,2,8,7,4,3,5]=>[3,8,7,1,2,5,6,4]=>0110001=>[1,2,3,1]
[6,4,1,2,8,7,3,5]=>[3,5,8,7,1,2,6,4]=>0011001=>[2,2,2,1]
[3,6,4,8,1,7,2,5]=>[6,3,5,1,8,2,7,4]=>1010101=>[1,1,1,1,1,1,1]
[7,6,1,4,2,8,3,5]=>[2,3,8,5,7,1,6,4]=>0010101=>[2,1,1,1,1,1]
[7,1,6,2,8,4,3,5]=>[2,8,3,7,1,5,6,4]=>0101001=>[1,1,1,1,2,1]
[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>1101001=>[2,1,1,2,1]
[6,7,1,4,2,8,3,5]=>[3,2,8,5,7,1,6,4]=>1010101=>[1,1,1,1,1,1,1]
[6,3,7,1,4,8,2,5]=>[3,6,2,8,5,1,7,4]=>0101101=>[1,1,1,2,1,1]
[3,7,8,1,5,2,4,6]=>[6,2,1,8,4,7,5,3]=>1101011=>[2,1,1,1,2]
[7,1,2,8,5,3,4,6]=>[2,8,7,1,4,6,5,3]=>0110011=>[1,2,2,2]
[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>1011001=>[1,1,2,2,1]
[6,1,2,8,4,3,7,5]=>[3,8,7,1,5,6,2,4]=>0110010=>[1,2,2,1,1]
[6,4,1,2,8,3,7,5]=>[3,5,8,7,1,6,2,4]=>0011010=>[2,2,1,1,1]
[7,6,1,3,2,4,8,5]=>[2,3,8,6,7,5,1,4]=>0010110=>[2,1,1,2,1]
[6,7,1,3,2,4,8,5]=>[3,2,8,6,7,5,1,4]=>1010110=>[1,1,1,1,2,1]
[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>1101101=>[2,1,2,1,1]
[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>1101011=>[2,1,1,1,2]
[5,8,1,3,7,2,4,6]=>[4,1,8,6,2,7,5,3]=>1011011=>[1,1,2,1,2]
[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>1110011=>[3,2,2]
[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>1110101=>[3,1,1,1,1]
[2,8,1,7,3,5,4,6]=>[7,1,8,2,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]
[8,6,1,3,2,4,7,5]=>[1,3,8,6,7,5,2,4]=>0010110=>[2,1,1,2,1]
[4,2,8,1,7,3,6,5]=>[5,7,1,8,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[2,8,1,7,4,3,6,5]=>[7,1,8,2,5,6,3,4]=>1010010=>[1,1,1,2,1,1]
[7,1,2,8,4,3,6,5]=>[2,8,7,1,5,6,3,4]=>0110010=>[1,2,2,1,1]
[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>1101001=>[2,1,1,2,1]
[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>1100101=>[2,2,1,1,1]
[2,8,1,7,5,3,4,6]=>[7,1,8,2,4,6,5,3]=>1010011=>[1,1,1,2,2]
[8,3,7,1,5,2,4,6]=>[1,6,2,8,4,7,5,3]=>0101011=>[1,1,1,1,1,2]
[3,8,6,1,4,7,2,5]=>[6,1,3,8,5,2,7,4]=>1001101=>[1,2,2,1,1]
[8,6,1,4,2,7,3,5]=>[1,3,8,5,7,2,6,4]=>0010101=>[2,1,1,1,1,1]
[8,1,6,2,7,4,3,5]=>[1,8,3,7,2,5,6,4]=>0101001=>[1,1,1,1,2,1]
[7,1,2,8,6,4,3,5]=>[2,8,7,1,3,5,6,4]=>0110001=>[1,2,3,1]
[7,4,1,2,8,6,3,5]=>[2,5,8,7,1,3,6,4]=>0011001=>[2,2,2,1]
[3,7,4,8,1,6,2,5]=>[6,2,5,1,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[3,4,8,7,1,6,2,5]=>[6,5,1,2,8,3,7,4]=>1100101=>[2,2,1,1,1]
[4,2,8,1,7,6,3,5]=>[5,7,1,8,2,3,6,4]=>0101001=>[1,1,1,1,2,1]
[2,8,1,7,6,4,3,5]=>[7,1,8,2,3,5,6,4]=>1010001=>[1,1,1,3,1]
[7,8,3,4,1,5,2,6]=>[2,1,6,5,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,4,1,6,2,5]=>[2,1,6,5,8,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,4,1,8,2,5]=>[3,2,6,5,8,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,4,1,8,2,6]=>[4,2,6,5,8,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,4,1,6,2,7]=>[4,1,6,5,8,3,7,2]=>1010101=>[1,1,1,1,1,1,1]
[6,7,3,4,1,5,2,8]=>[3,2,6,5,8,4,7,1]=>1010101=>[1,1,1,1,1,1,1]
[5,7,3,4,1,6,2,8]=>[4,2,6,5,8,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,8,3,4,1,7]=>[4,3,7,1,6,5,8,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,7,3,4,1,8]=>[4,3,7,2,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,2,8,3,5,1,7]=>[5,3,7,1,6,4,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,5,1,6,2,8]=>[5,2,6,4,8,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,3,1,7,4,8]=>[4,3,7,6,8,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,4,1,7,3,8]=>[4,3,7,5,8,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,2,5,1,7,3,8]=>[5,3,7,4,8,2,6,1]=>1010101=>[1,1,1,1,1,1,1]
[4,6,2,5,1,8,3,7]=>[5,3,7,4,8,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,8,3,7,2,6]=>[5,4,8,1,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,7,3,8,2,6]=>[5,4,8,2,6,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,6,2,7,3,8,1,5]=>[5,3,7,2,6,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,7,4,8,1,3]=>[4,3,7,2,5,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,8,4,7,1,2]=>[4,3,6,1,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,8,4,7,1,3]=>[4,3,7,1,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,6,2,8,3,7,1,5]=>[5,3,7,1,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,7,3,6,2,8]=>[5,4,8,2,6,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,8,3,6,2,7]=>[5,4,8,1,6,3,7,2]=>1010101=>[1,1,1,1,1,1,1]
[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>00111111=>[2,6]
[10,2,1,3,4,5,6,7,8,9]=>[1,9,10,8,7,6,5,4,3,2]=>001111111=>[2,7]
[9,2,3,1,4,5,6,7,8]=>[1,8,7,9,6,5,4,3,2]=>01011111=>[1,1,1,5]
[4,2,3,5,6,7,8,9,1]=>[6,8,7,5,4,3,2,1,9]=>01111110=>[1,6,1]
[3,4,2,5,6,7,8,9,1]=>[7,6,8,5,4,3,2,1,9]=>10111110=>[1,1,5,1]
[3,2,4,5,6,7,8,9,10,1]=>[8,9,7,6,5,4,3,2,1,10]=>011111110=>[1,7,1]
[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>[9,1]
[6,5,3,2,1,4,8,7]=>[3,4,6,7,8,5,1,2]=>0000110=>[4,2,1]
[4,6,3,5,2,1,8,7]=>[5,3,6,4,7,8,1,2]=>1010010=>[1,1,1,2,1,1]
[8,7,3,5,2,4,1,6]=>[1,2,6,4,7,5,8,3]=>0010101=>[2,1,1,1,1,1]
[6,8,2,4,5,7,3,1]=>[3,1,7,5,4,2,6,8]=>1011100=>[1,1,3,2]
[8,7,2,4,5,3,1,6]=>[1,2,7,5,4,6,8,3]=>0011001=>[2,2,2,1]
[3,6,1,4,5,2,8,7]=>[6,3,8,5,4,7,1,2]=>1011010=>[1,1,2,1,1,1]
[8,3,7,4,5,2,1,6]=>[1,6,2,5,4,7,8,3]=>0101001=>[1,1,1,1,2,1]
[6,3,8,4,5,7,2,1]=>[3,6,1,5,4,2,7,8]=>0101100=>[1,1,1,2,2]
[5,8,7,4,3,6,2,1]=>[4,1,2,5,6,3,7,8]=>1000100=>[1,3,1,2]
[2,8,7,4,3,6,1,5]=>[7,1,2,5,6,3,8,4]=>1000101=>[1,3,1,1,1]
[8,1,7,4,3,6,2,5]=>[1,8,2,5,6,3,7,4]=>0100101=>[1,1,2,1,1,1]
[8,7,3,5,1,4,2,6]=>[1,2,6,4,8,5,7,3]=>0010101=>[2,1,1,1,1,1]
[2,1,6,8,5,7,4,3]=>[7,8,3,1,4,2,5,6]=>0110100=>[1,2,1,1,2]
[6,8,3,5,1,7,4,2]=>[3,1,6,4,8,2,5,7]=>1010100=>[1,1,1,1,1,2]
[5,1,8,4,7,6,3,2]=>[4,8,1,5,2,3,6,7]=>0101000=>[1,1,1,1,3]
[2,5,8,4,7,6,3,1]=>[7,4,1,5,2,3,6,8]=>1101000=>[2,1,1,3]
[4,3,8,1,5,6,7,2]=>[5,6,1,8,4,3,2,7]=>0101110=>[1,1,1,3,1]
[4,8,1,3,5,6,7,2]=>[5,1,8,6,4,3,2,7]=>1011110=>[1,1,4,1]
[5,8,7,4,1,6,3,2]=>[4,1,2,5,8,3,6,7]=>1000100=>[1,3,1,2]
[5,8,3,6,1,4,7,2]=>[4,1,6,3,8,5,2,7]=>1010110=>[1,1,1,1,2,1]
[4,8,3,6,1,2,7,5]=>[5,1,6,3,8,7,2,4]=>1010110=>[1,1,1,1,2,1]
[3,8,7,4,1,6,2,5]=>[6,1,2,5,8,3,7,4]=>1000101=>[1,3,1,1,1]
[3,8,1,2,5,6,7,4]=>[6,1,8,7,4,3,2,5]=>1011110=>[1,1,4,1]
[8,7,1,4,2,6,3,5]=>[1,2,8,5,7,3,6,4]=>0010101=>[2,1,1,1,1,1]
[8,6,3,1,2,4,7,5]=>[1,3,6,8,7,5,2,4]=>0001110=>[3,3,1]
[8,1,7,4,5,2,3,6]=>[1,8,2,5,4,7,6,3]=>0101011=>[1,1,1,1,1,2]
[2,8,7,4,5,1,3,6]=>[7,1,2,5,4,8,6,3]=>1001011=>[1,2,1,1,2]
[8,7,2,4,1,6,3,5]=>[1,2,7,5,8,3,6,4]=>0010101=>[2,1,1,1,1,1]
[5,8,3,6,2,4,7,1]=>[4,1,6,3,7,5,2,8]=>1010110=>[1,1,1,1,2,1]
[8,6,3,2,1,4,7,5]=>[1,3,6,7,8,5,2,4]=>0000110=>[4,2,1]
[8,7,3,5,2,1,4,6]=>[1,2,6,4,7,8,5,3]=>0010011=>[2,1,2,2]
[5,8,3,6,2,1,7,4]=>[4,1,6,3,7,8,2,5]=>1010010=>[1,1,1,2,1,1]
[5,8,7,4,2,6,1,3]=>[4,1,2,5,7,3,8,6]=>1000101=>[1,3,1,1,1]
[2,6,8,4,5,7,1,3]=>[7,3,1,5,4,2,8,6]=>1101101=>[2,1,2,1,1]
[6,1,8,4,5,7,2,3]=>[3,8,1,5,4,2,7,6]=>0101101=>[1,1,1,2,1,1]
[6,8,3,5,1,7,2,4]=>[3,1,6,4,8,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,1,5,8,3,6,7,4]=>[7,8,4,1,6,3,2,5]=>0110110=>[1,2,1,2,1]
[5,8,3,6,1,2,7,4]=>[4,1,6,3,8,7,2,5]=>1010110=>[1,1,1,1,2,1]
[4,1,8,2,5,6,7,3]=>[5,8,1,7,4,3,2,6]=>0101110=>[1,1,1,3,1]
[2,4,8,1,5,6,7,3]=>[7,5,1,8,4,3,2,6]=>1101110=>[2,1,3,1]
[4,8,2,1,5,6,7,3]=>[5,1,7,8,4,3,2,6]=>1001110=>[1,2,3,1]
[3,4,8,2,5,6,7,1]=>[6,5,1,7,4,3,2,8]=>1101110=>[2,1,3,1]
[5,8,1,4,7,6,2,3]=>[4,1,8,5,2,3,7,6]=>1011001=>[1,1,2,2,1]
[5,8,3,1,6,2,7,4]=>[4,1,6,8,3,7,2,5]=>1001010=>[1,2,1,1,1,1]
[4,5,3,8,6,1,7,2]=>[5,4,6,1,3,8,2,7]=>1010010=>[1,1,1,2,1,1]
[3,4,1,8,5,6,7,2]=>[6,5,8,1,4,3,2,7]=>1010110=>[1,1,1,1,2,1]
[2,4,6,8,10,1,3,5,7,9]=>[9,7,5,3,1,10,8,6,4,2]=>111101111=>[4,1,4]
[2,4,6,9,10,1,3,5,7,8]=>[9,7,5,2,1,10,8,6,4,3]=>111101111=>[4,1,4]
[2,4,7,8,10,1,3,5,6,9]=>[9,7,4,3,1,10,8,6,5,2]=>111101111=>[4,1,4]
[2,4,7,9,10,1,3,5,6,8]=>[9,7,4,2,1,10,8,6,5,3]=>111101111=>[4,1,4]
[2,4,8,9,10,1,3,5,6,7]=>[9,7,3,2,1,10,8,6,5,4]=>111101111=>[4,1,4]
[2,5,6,8,10,1,3,4,7,9]=>[9,6,5,3,1,10,8,7,4,2]=>111101111=>[4,1,4]
[2,5,6,9,10,1,3,4,7,8]=>[9,6,5,2,1,10,8,7,4,3]=>111101111=>[4,1,4]
[2,5,7,8,10,1,3,4,6,9]=>[9,6,4,3,1,10,8,7,5,2]=>111101111=>[4,1,4]
[2,5,7,9,10,1,3,4,6,8]=>[9,6,4,2,1,10,8,7,5,3]=>111101111=>[4,1,4]
[2,5,8,9,10,1,3,4,6,7]=>[9,6,3,2,1,10,8,7,5,4]=>111101111=>[4,1,4]
[2,6,7,8,10,1,3,4,5,9]=>[9,5,4,3,1,10,8,7,6,2]=>111101111=>[4,1,4]
[2,6,7,9,10,1,3,4,5,8]=>[9,5,4,2,1,10,8,7,6,3]=>111101111=>[4,1,4]
[2,6,8,9,10,1,3,4,5,7]=>[9,5,3,2,1,10,8,7,6,4]=>111101111=>[4,1,4]
[2,7,8,9,10,1,3,4,5,6]=>[9,4,3,2,1,10,8,7,6,5]=>111101111=>[4,1,4]
[3,4,6,8,10,1,2,5,7,9]=>[8,7,5,3,1,10,9,6,4,2]=>111101111=>[4,1,4]
[3,4,6,9,10,1,2,5,7,8]=>[8,7,5,2,1,10,9,6,4,3]=>111101111=>[4,1,4]
[3,4,7,8,10,1,2,5,6,9]=>[8,7,4,3,1,10,9,6,5,2]=>111101111=>[4,1,4]
[3,4,7,9,10,1,2,5,6,8]=>[8,7,4,2,1,10,9,6,5,3]=>111101111=>[4,1,4]
[3,4,8,9,10,1,2,5,6,7]=>[8,7,3,2,1,10,9,6,5,4]=>111101111=>[4,1,4]
[3,5,6,8,10,1,2,4,7,9]=>[8,6,5,3,1,10,9,7,4,2]=>111101111=>[4,1,4]
[3,5,6,9,10,1,2,4,7,8]=>[8,6,5,2,1,10,9,7,4,3]=>111101111=>[4,1,4]
[3,5,7,8,10,1,2,4,6,9]=>[8,6,4,3,1,10,9,7,5,2]=>111101111=>[4,1,4]
[3,5,7,9,10,1,2,4,6,8]=>[8,6,4,2,1,10,9,7,5,3]=>111101111=>[4,1,4]
[3,5,8,9,10,1,2,4,6,7]=>[8,6,3,2,1,10,9,7,5,4]=>111101111=>[4,1,4]
[3,6,7,8,10,1,2,4,5,9]=>[8,5,4,3,1,10,9,7,6,2]=>111101111=>[4,1,4]
[3,6,7,9,10,1,2,4,5,8]=>[8,5,4,2,1,10,9,7,6,3]=>111101111=>[4,1,4]
[3,6,8,9,10,1,2,4,5,7]=>[8,5,3,2,1,10,9,7,6,4]=>111101111=>[4,1,4]
[3,7,8,9,10,1,2,4,5,6]=>[8,4,3,2,1,10,9,7,6,5]=>111101111=>[4,1,4]
[4,5,6,8,10,1,2,3,7,9]=>[7,6,5,3,1,10,9,8,4,2]=>111101111=>[4,1,4]
[4,5,6,9,10,1,2,3,7,8]=>[7,6,5,2,1,10,9,8,4,3]=>111101111=>[4,1,4]
[4,5,7,8,10,1,2,3,6,9]=>[7,6,4,3,1,10,9,8,5,2]=>111101111=>[4,1,4]
[4,5,7,9,10,1,2,3,6,8]=>[7,6,4,2,1,10,9,8,5,3]=>111101111=>[4,1,4]
[4,5,8,9,10,1,2,3,6,7]=>[7,6,3,2,1,10,9,8,5,4]=>111101111=>[4,1,4]
[4,6,7,8,10,1,2,3,5,9]=>[7,5,4,3,1,10,9,8,6,2]=>111101111=>[4,1,4]
[4,6,7,9,10,1,2,3,5,8]=>[7,5,4,2,1,10,9,8,6,3]=>111101111=>[4,1,4]
[4,6,8,9,10,1,2,3,5,7]=>[7,5,3,2,1,10,9,8,6,4]=>111101111=>[4,1,4]
[4,7,8,9,10,1,2,3,5,6]=>[7,4,3,2,1,10,9,8,6,5]=>111101111=>[4,1,4]
[5,6,7,8,10,1,2,3,4,9]=>[6,5,4,3,1,10,9,8,7,2]=>111101111=>[4,1,4]
[5,6,7,9,10,1,2,3,4,8]=>[6,5,4,2,1,10,9,8,7,3]=>111101111=>[4,1,4]
[5,6,8,9,10,1,2,3,4,7]=>[6,5,3,2,1,10,9,8,7,4]=>111101111=>[4,1,4]
[5,7,8,9,10,1,2,3,4,6]=>[6,4,3,2,1,10,9,8,7,5]=>111101111=>[4,1,4]
[4,5,7,6,2,3,8,1]=>[5,4,2,3,7,6,1,8]=>1100110=>[2,2,2,1]
[3,5,7,2,6,4,8,1]=>[6,4,2,7,3,5,1,8]=>1101010=>[2,1,1,1,1,1]
[2,5,7,3,6,4,8,1]=>[7,4,2,6,3,5,1,8]=>1101010=>[2,1,1,1,1,1]
[1,5,7,3,6,8,4,2]=>[8,4,2,6,3,1,5,7]=>1101100=>[2,1,2,2]
[8,4,3,7,6,1,5,2]=>[1,5,6,2,3,8,4,7]=>0010010=>[2,1,2,1,1]
[6,7,2,3,5,4,8,1]=>[3,2,7,6,4,5,1,8]=>1011010=>[1,1,2,1,1,1]
[5,2,7,3,6,4,8,1]=>[4,7,2,6,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[8,3,4,7,6,1,5,2]=>[1,6,5,2,3,8,4,7]=>0110010=>[1,2,2,1,1]
[8,2,4,7,1,6,5,3]=>[1,7,5,2,8,3,4,6]=>0110100=>[1,2,1,1,2]
[3,1,4,7,6,8,5,2]=>[6,8,5,2,3,1,4,7]=>0110100=>[1,2,1,1,2]
[4,1,3,7,6,8,5,2]=>[5,8,6,2,3,1,4,7]=>0110100=>[1,2,1,1,2]
[5,1,7,3,6,8,4,2]=>[4,8,2,6,3,1,5,7]=>0101100=>[1,1,1,2,2]
[6,7,1,3,5,8,4,2]=>[3,2,8,6,4,1,5,7]=>1011100=>[1,1,3,2]
[5,8,7,3,6,1,4,2]=>[4,1,2,6,3,8,5,7]=>1001010=>[1,2,1,1,1,1]
[4,8,3,7,6,1,5,2]=>[5,1,6,2,3,8,4,7]=>1010010=>[1,1,1,2,1,1]
[3,8,4,7,6,1,5,2]=>[6,1,5,2,3,8,4,7]=>1010010=>[1,1,1,2,1,1]
[2,8,4,7,1,6,5,3]=>[7,1,5,2,8,3,4,6]=>1010100=>[1,1,1,1,1,2]
[8,1,4,7,2,6,5,3]=>[1,8,5,2,7,3,4,6]=>0110100=>[1,2,1,1,2]
[8,1,3,2,7,6,5,4]=>[1,8,6,7,2,3,4,5]=>0101000=>[1,1,1,1,3]
[2,8,3,1,7,6,5,4]=>[7,1,6,8,2,3,4,5]=>1001000=>[1,2,1,3]
[3,8,2,1,7,6,5,4]=>[6,1,7,8,2,3,4,5]=>1001000=>[1,2,1,3]
[6,7,1,2,8,5,4,3]=>[3,2,8,7,1,4,5,6]=>1011000=>[1,1,2,3]
[8,2,3,1,7,6,5,4]=>[1,7,6,8,2,3,4,5]=>0101000=>[1,1,1,1,3]
[8,3,2,1,7,6,5,4]=>[1,6,7,8,2,3,4,5]=>0001000=>[3,1,3]
[3,4,1,7,6,8,5,2]=>[6,5,8,2,3,1,4,7]=>1010100=>[1,1,1,1,1,2]
[1,4,2,7,8,6,5,3]=>[8,5,7,2,1,3,4,6]=>1011000=>[1,1,2,3]
[8,4,2,7,1,6,5,3]=>[1,5,7,2,8,3,4,6]=>0010100=>[2,1,1,1,2]
[8,5,7,2,1,6,4,3]=>[1,4,2,7,8,3,5,6]=>0100100=>[1,1,2,1,2]
[1,5,7,2,8,6,4,3]=>[8,4,2,7,1,3,5,6]=>1101000=>[2,1,1,3]
[3,5,7,1,6,8,4,2]=>[6,4,2,8,3,1,5,7]=>1101100=>[2,1,2,2]
[6,7,4,5,8,1,3,2]=>[3,2,5,4,1,8,6,7]=>1011010=>[1,1,2,1,1,1]
[5,4,7,6,8,1,3,2]=>[4,5,2,3,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[2,5,7,8,1,6,4,3]=>[7,4,2,1,8,3,5,6]=>1110100=>[3,1,1,2]
[1,5,7,8,2,6,4,3]=>[8,4,2,1,7,3,5,6]=>1110100=>[3,1,1,2]
[8,5,7,1,2,6,4,3]=>[1,4,2,8,7,3,5,6]=>0101100=>[1,1,1,2,2]
[8,4,1,7,2,6,5,3]=>[1,5,8,2,7,3,4,6]=>0010100=>[2,1,1,1,2]
[1,4,8,7,2,6,5,3]=>[8,5,1,2,7,3,4,6]=>1100100=>[2,2,1,2]
[3,4,8,7,6,1,5,2]=>[6,5,1,2,3,8,4,7]=>1100010=>[2,3,1,1]
[4,3,8,7,6,1,5,2]=>[5,6,1,2,3,8,4,7]=>0100010=>[1,1,3,1,1]
[5,3,7,8,6,1,4,2]=>[4,6,2,1,3,8,5,7]=>0110010=>[1,2,2,1,1]
[6,7,2,8,1,5,4,3]=>[3,2,7,1,8,4,5,6]=>1010100=>[1,1,1,1,1,2]
[5,2,7,8,1,6,4,3]=>[4,7,2,1,8,3,5,6]=>0110100=>[1,2,1,1,2]
[4,2,8,7,1,6,5,3]=>[5,7,1,2,8,3,4,6]=>0100100=>[1,1,2,1,2]
[3,2,8,1,7,6,5,4]=>[6,7,1,8,2,3,4,5]=>0101000=>[1,1,1,1,3]
[1,3,8,2,7,6,5,4]=>[8,6,1,7,2,3,4,5]=>1101000=>[2,1,1,3]
[8,3,1,2,7,6,5,4]=>[1,6,8,7,2,3,4,5]=>0011000=>[2,2,3]
[8,2,1,3,7,6,5,4]=>[1,7,8,6,2,3,4,5]=>0011000=>[2,2,3]
[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>1101000=>[2,1,1,3]
[2,1,8,3,7,6,5,4]=>[7,8,1,6,2,3,4,5]=>0101000=>[1,1,1,1,3]
[5,1,7,8,2,6,4,3]=>[4,8,2,1,7,3,5,6]=>0110100=>[1,2,1,1,2]
[6,7,1,8,2,5,4,3]=>[3,2,8,1,7,4,5,6]=>1010100=>[1,1,1,1,1,2]
[5,8,7,1,2,6,4,3]=>[4,1,2,8,7,3,5,6]=>1001100=>[1,2,2,2]
[4,8,1,7,2,6,5,3]=>[5,1,8,2,7,3,4,6]=>1010100=>[1,1,1,1,1,2]
[3,8,1,2,7,6,5,4]=>[6,1,8,7,2,3,4,5]=>1011000=>[1,1,2,3]
[2,8,1,3,7,6,5,4]=>[7,1,8,6,2,3,4,5]=>1011000=>[1,1,2,3]
[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>1011000=>[1,1,2,3]
[8,1,2,3,7,6,5,4]=>[1,8,7,6,2,3,4,5]=>0111000=>[1,3,3]
[3,1,4,5,6,7,8,9,10,2]=>[8,10,7,6,5,4,3,2,1,9]=>011111110=>[1,7,1]
[2,3,4,5,6,7,8,9,11,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>1111111101=>[8,1,1]
[10,3,4,5,6,7,8,1,2,9]=>[1,8,7,6,5,4,3,10,9,2]=>011111011=>[1,5,1,2]
[10,1,4,5,6,7,8,9,2,3]=>[1,10,7,6,5,4,3,2,9,8]=>011111101=>[1,6,1,1]
[3,1,4,5,6,7,8,9,10,11,2]=>[9,11,8,7,6,5,4,3,2,1,10]=>0111111110=>[1,8,1]
[2,3,4,5,6,7,8,9,10,12,1,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>11111111101=>[9,1,1]
[11,3,4,5,6,7,8,9,1,2,10]=>[1,9,8,7,6,5,4,3,11,10,2]=>0111111011=>[1,6,1,2]
[2,10,4,5,6,7,8,1,3,9]=>[9,1,7,6,5,4,3,10,8,2]=>101111011=>[1,1,4,1,2]
[8,3,4,5,6,7,1,10,2,9]=>[3,8,7,6,5,4,10,1,9,2]=>011110101=>[1,4,1,1,1,1]
[3,1,10,5,6,7,8,9,2,4]=>[8,10,1,6,5,4,3,2,9,7]=>010111101=>[1,1,1,4,1,1]
[9,1,4,5,6,7,8,2,10,3]=>[2,10,7,6,5,4,3,9,1,8]=>011111010=>[1,5,1,1,1]
[11,1,4,5,6,7,8,9,10,2,3]=>[1,11,8,7,6,5,4,3,2,10,9]=>0111111101=>[1,7,1,1]
[3,1,4,5,6,7,8,9,10,11,12,2]=>[10,12,9,8,7,6,5,4,3,2,1,11]=>01111111110=>[1,9,1]
[6,7,1,8,4,5,2,3]=>[3,2,8,1,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,5,8,2,6,4]=>[6,2,8,4,1,7,3,5]=>1011010=>[1,1,2,1,1,1]
[2,7,1,5,8,3,6,4]=>[7,2,8,4,1,6,3,5]=>1011010=>[1,1,2,1,1,1]
[2,6,5,1,8,3,7,4]=>[7,3,4,8,1,6,2,5]=>1001010=>[1,2,1,1,1,1]
[3,6,5,1,8,2,7,4]=>[6,3,4,8,1,7,2,5]=>1001010=>[1,2,1,1,1,1]
[4,6,5,1,8,7,2,3]=>[5,3,4,8,1,2,7,6]=>1001001=>[1,2,1,2,1]
[5,6,4,1,8,7,2,3]=>[4,3,5,8,1,2,7,6]=>1001001=>[1,2,1,2,1]
[8,1,4,5,7,6,2,3]=>[1,8,5,4,2,3,7,6]=>0111001=>[1,3,2,1]
[6,4,5,1,8,7,2,3]=>[3,5,4,8,1,2,7,6]=>0101001=>[1,1,1,1,2,1]
[5,4,6,1,8,7,2,3]=>[4,5,3,8,1,2,7,6]=>0101001=>[1,1,1,1,2,1]
[4,5,6,1,8,7,2,3]=>[5,4,3,8,1,2,7,6]=>1101001=>[2,1,1,2,1]
[3,5,6,1,8,2,7,4]=>[6,4,3,8,1,7,2,5]=>1101010=>[2,1,1,1,1,1]
[2,5,6,1,8,3,7,4]=>[7,4,3,8,1,6,2,5]=>1101010=>[2,1,1,1,1,1]
[2,4,6,1,3,8,7,5]=>[7,5,3,8,6,1,2,4]=>1101100=>[2,1,2,2]
[3,4,6,1,2,8,7,5]=>[6,5,3,8,7,1,2,4]=>1101100=>[2,1,2,2]
[4,3,6,1,2,8,7,5]=>[5,6,3,8,7,1,2,4]=>0101100=>[1,1,1,2,2]
[5,3,6,1,8,2,7,4]=>[4,6,3,8,1,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[7,3,1,5,8,2,6,4]=>[2,6,8,4,1,7,3,5]=>0011010=>[2,2,1,1,1]
[8,1,3,5,7,2,6,4]=>[1,8,6,4,2,7,3,5]=>0111010=>[1,3,1,1,1]
[8,1,2,5,7,3,6,4]=>[1,8,7,4,2,6,3,5]=>0111010=>[1,3,1,1,1]
[7,2,1,5,8,3,6,4]=>[2,7,8,4,1,6,3,5]=>0011010=>[2,2,1,1,1]
[6,2,5,1,8,3,7,4]=>[3,7,4,8,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,1,3,8,7,5]=>[5,7,3,8,6,1,2,4]=>0101100=>[1,1,1,2,2]
[2,3,6,1,4,8,7,5]=>[7,6,3,8,5,1,2,4]=>1101100=>[2,1,2,2]
[4,2,5,3,1,8,7,6]=>[5,7,4,6,8,1,2,3]=>0100100=>[1,1,2,1,2]
[6,2,4,1,3,8,7,5]=>[3,7,5,8,6,1,2,4]=>0101100=>[1,1,1,2,2]
[7,2,1,4,3,8,6,5]=>[2,7,8,5,6,1,3,4]=>0010100=>[2,1,1,1,2]
[8,1,2,4,3,7,6,5]=>[1,8,7,5,6,2,3,4]=>0110100=>[1,2,1,1,2]
[8,1,3,4,2,7,6,5]=>[1,8,6,5,7,2,3,4]=>0110100=>[1,2,1,1,2]
[7,3,1,4,2,8,6,5]=>[2,6,8,5,7,1,3,4]=>0010100=>[2,1,1,1,2]
[6,3,4,1,2,8,7,5]=>[3,6,5,8,7,1,2,4]=>0101100=>[1,1,1,2,2]
[4,6,3,1,2,8,7,5]=>[5,3,6,8,7,1,2,4]=>1001100=>[1,2,2,2]
[3,6,4,1,2,8,7,5]=>[6,3,5,8,7,1,2,4]=>1001100=>[1,2,2,2]
[2,6,4,1,3,8,7,5]=>[7,3,5,8,6,1,2,4]=>1001100=>[1,2,2,2]
[2,7,1,4,3,8,6,5]=>[7,2,8,5,6,1,3,4]=>1010100=>[1,1,1,1,1,2]
[3,7,1,4,2,8,6,5]=>[6,2,8,5,7,1,3,4]=>1010100=>[1,1,1,1,1,2]
[4,7,1,3,2,8,6,5]=>[5,2,8,6,7,1,3,4]=>1010100=>[1,1,1,1,1,2]
[8,1,6,7,2,3,5,4]=>[1,8,3,2,7,6,4,5]=>0110110=>[1,2,1,2,1]
[4,7,1,2,3,8,6,5]=>[5,2,8,7,6,1,3,4]=>1011100=>[1,1,3,2]
[3,7,1,2,4,8,6,5]=>[6,2,8,7,5,1,3,4]=>1011100=>[1,1,3,2]
[2,7,1,3,4,8,6,5]=>[7,2,8,6,5,1,3,4]=>1011100=>[1,1,3,2]
[2,6,3,1,4,8,7,5]=>[7,3,6,8,5,1,2,4]=>1001100=>[1,2,2,2]
[3,6,2,1,4,8,7,5]=>[6,3,7,8,5,1,2,4]=>1001100=>[1,2,2,2]
[5,6,2,1,8,3,7,4]=>[4,3,7,8,1,6,2,5]=>1001010=>[1,2,1,1,1,1]
[6,5,2,1,8,3,7,4]=>[3,4,7,8,1,6,2,5]=>0001010=>[3,1,1,1,1]
[8,1,5,2,7,3,6,4]=>[1,8,4,7,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,4,2,3,7,6,5]=>[1,8,5,7,6,2,3,4]=>0101100=>[1,1,1,2,2]
[7,4,1,2,3,8,6,5]=>[2,5,8,7,6,1,3,4]=>0011100=>[2,3,2]
[6,4,2,1,3,8,7,5]=>[3,5,7,8,6,1,2,4]=>0001100=>[3,2,2]
[5,4,2,3,1,8,7,6]=>[4,5,7,6,8,1,2,3]=>0010100=>[2,1,1,1,2]
[3,5,2,4,1,8,7,6]=>[6,4,7,5,8,1,2,3]=>1010100=>[1,1,1,1,1,2]
[6,3,2,1,4,8,7,5]=>[3,6,7,8,5,1,2,4]=>0001100=>[3,2,2]
[7,3,1,2,4,8,6,5]=>[2,6,8,7,5,1,3,4]=>0011100=>[2,3,2]
[8,1,3,2,4,7,6,5]=>[1,8,6,7,5,2,3,4]=>0101100=>[1,1,1,2,2]
[8,1,2,3,4,7,6,5]=>[1,8,7,6,5,2,3,4]=>0111100=>[1,4,2]
[7,2,1,3,4,8,6,5]=>[2,7,8,6,5,1,3,4]=>0011100=>[2,3,2]
[6,2,3,1,4,8,7,5]=>[3,7,6,8,5,1,2,4]=>0101100=>[1,1,1,2,2]
[2,4,3,6,1,5,8,7]=>[7,5,6,3,8,4,1,2]=>1010110=>[1,1,1,1,2,1]
[2,4,3,6,5,8,1,7]=>[7,5,6,3,4,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[2,4,6,3,5,8,7,1]=>[7,5,3,6,4,1,2,8]=>1101100=>[2,1,2,2]
[2,4,6,3,5,8,1,7]=>[7,5,3,6,4,1,8,2]=>1101101=>[2,1,2,1,1]
[2,4,6,3,5,1,8,7]=>[7,5,3,6,4,8,1,2]=>1101010=>[2,1,1,1,1,1]
[2,4,6,3,1,5,8,7]=>[7,5,3,6,8,4,1,2]=>1100110=>[2,2,2,1]
[2,4,1,6,5,3,8,7]=>[7,5,8,3,4,6,1,2]=>1010010=>[1,1,1,2,1,1]
[2,4,6,1,5,3,8,7]=>[7,5,3,8,4,6,1,2]=>1101010=>[2,1,1,1,1,1]
[4,2,6,5,3,1,8,7]=>[5,7,3,4,6,8,1,2]=>0100010=>[1,1,3,1,1]
[4,2,6,5,1,3,8,7]=>[5,7,3,4,8,6,1,2]=>0100110=>[1,1,2,2,1]
[4,2,6,5,1,8,7,3]=>[5,7,3,4,8,1,2,6]=>0100100=>[1,1,2,1,2]
[4,2,6,5,8,1,7,3]=>[5,7,3,4,1,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[4,2,6,5,8,1,3,7]=>[5,7,3,4,1,8,6,2]=>0101011=>[1,1,1,1,1,2]
[4,2,6,5,8,3,1,7]=>[5,7,3,4,1,6,8,2]=>0101001=>[1,1,1,1,2,1]
[2,4,6,1,5,8,3,7]=>[7,5,3,8,4,1,6,2]=>1101101=>[2,1,2,1,1]
[2,4,1,6,5,8,3,7]=>[7,5,8,3,4,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,1,4,6,5,8,3,7]=>[7,8,5,3,4,1,6,2]=>0110101=>[1,2,1,1,1,1]
[2,4,1,6,5,8,7,3]=>[7,5,8,3,4,1,2,6]=>1010100=>[1,1,1,1,1,2]
[2,4,6,1,5,8,7,3]=>[7,5,3,8,4,1,2,6]=>1101100=>[2,1,2,2]
[4,2,6,5,3,8,7,1]=>[5,7,3,4,6,1,2,8]=>0100100=>[1,1,2,1,2]
[4,2,6,5,8,3,7,1]=>[5,7,3,4,1,6,2,8]=>0101010=>[1,1,1,1,1,1,1]
[2,6,4,3,8,7,1,5]=>[7,3,5,6,1,2,8,4]=>1001001=>[1,2,1,2,1]
[2,6,4,3,8,7,5,1]=>[7,3,5,6,1,2,4,8]=>1001000=>[1,2,1,3]
[4,2,6,8,5,3,7,1]=>[5,7,3,1,4,6,2,8]=>0110010=>[1,2,2,1,1]
[2,4,6,8,1,5,7,3]=>[7,5,3,1,8,4,2,6]=>1110110=>[3,1,2,1]
[2,4,6,1,8,5,7,3]=>[7,5,3,8,1,4,2,6]=>1101010=>[2,1,1,1,1,1]
[2,4,1,6,8,5,7,3]=>[7,5,8,3,1,4,2,6]=>1011010=>[1,1,2,1,1,1]
[2,1,4,6,8,5,7,3]=>[7,8,5,3,1,4,2,6]=>0111010=>[1,3,1,1,1]
[2,1,4,6,8,5,3,7]=>[7,8,5,3,1,4,6,2]=>0111001=>[1,3,2,1]
[2,4,1,6,8,5,3,7]=>[7,5,8,3,1,4,6,2]=>1011001=>[1,1,2,2,1]
[2,4,6,1,8,5,3,7]=>[7,5,3,8,1,4,6,2]=>1101001=>[2,1,1,2,1]
[2,4,6,8,1,5,3,7]=>[7,5,3,1,8,4,6,2]=>1110101=>[3,1,1,1,1]
[4,2,6,8,5,3,1,7]=>[5,7,3,1,4,6,8,2]=>0110001=>[1,2,3,1]
[4,2,6,8,5,1,3,7]=>[5,7,3,1,4,8,6,2]=>0110011=>[1,2,2,2]
[4,2,6,8,5,1,7,3]=>[5,7,3,1,4,8,2,6]=>0110010=>[1,2,2,1,1]
[2,4,6,8,3,5,7,1]=>[7,5,3,1,6,4,2,8]=>1110110=>[3,1,2,1]
[2,4,6,8,3,5,1,7]=>[7,5,3,1,6,4,8,2]=>1110101=>[3,1,1,1,1]
[2,4,6,8,3,1,5,7]=>[7,5,3,1,6,8,4,2]=>1110011=>[3,2,2]
[2,4,6,3,1,8,5,7]=>[7,5,3,6,8,1,4,2]=>1100101=>[2,2,1,1,1]
[2,4,6,3,8,1,5,7]=>[7,5,3,6,1,8,4,2]=>1101011=>[2,1,1,1,2]
[2,4,6,3,8,5,1,7]=>[7,5,3,6,1,4,8,2]=>1101001=>[2,1,1,2,1]
[2,4,6,3,8,5,7,1]=>[7,5,3,6,1,4,2,8]=>1101010=>[2,1,1,1,1,1]
[2,4,3,6,8,5,7,1]=>[7,5,6,3,1,4,2,8]=>1011010=>[1,1,2,1,1,1]
[2,4,3,6,8,5,1,7]=>[7,5,6,3,1,4,8,2]=>1011001=>[1,1,2,2,1]
[2,4,3,6,8,1,5,7]=>[7,5,6,3,1,8,4,2]=>1011011=>[1,1,2,1,2]
[2,4,3,6,1,8,5,7]=>[7,5,6,3,8,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,4,3,1,6,8,5,7]=>[7,5,6,8,3,1,4,2]=>1001101=>[1,2,2,1,1]
[2,4,1,3,6,8,7,5]=>[7,5,8,6,3,1,2,4]=>1011100=>[1,1,3,2]
[2,4,3,6,1,8,7,5]=>[7,5,6,3,8,1,2,4]=>1010100=>[1,1,1,1,1,2]
[2,4,3,6,8,1,7,5]=>[7,5,6,3,1,8,2,4]=>1011010=>[1,1,2,1,1,1]
[4,6,5,2,8,7,3,1]=>[5,3,4,7,1,2,6,8]=>1001000=>[1,2,1,3]
[4,6,5,2,8,7,1,3]=>[5,3,4,7,1,2,8,6]=>1001001=>[1,2,1,2,1]
[4,6,2,5,8,7,1,3]=>[5,3,7,4,1,2,8,6]=>1011001=>[1,1,2,2,1]
[4,6,2,5,8,7,3,1]=>[5,3,7,4,1,2,6,8]=>1011000=>[1,1,2,3]
[2,4,6,3,8,1,7,5]=>[7,5,3,6,1,8,2,4]=>1101010=>[2,1,1,1,1,1]
[2,4,6,3,1,8,7,5]=>[7,5,3,6,8,1,2,4]=>1100100=>[2,2,1,2]
[2,4,1,6,3,8,7,5]=>[7,5,8,3,6,1,2,4]=>1010100=>[1,1,1,1,1,2]
[2,1,4,6,3,8,7,5]=>[7,8,5,3,6,1,2,4]=>0110100=>[1,2,1,1,2]
[2,1,4,6,8,3,7,5]=>[7,8,5,3,1,6,2,4]=>0111010=>[1,3,1,1,1]
[2,4,1,6,8,3,7,5]=>[7,5,8,3,1,6,2,4]=>1011010=>[1,1,2,1,1,1]
[2,4,6,1,8,3,7,5]=>[7,5,3,8,1,6,2,4]=>1101010=>[2,1,1,1,1,1]
[2,4,6,8,1,3,7,5]=>[7,5,3,1,8,6,2,4]=>1110110=>[3,1,2,1]
[2,4,6,8,3,1,7,5]=>[7,5,3,1,6,8,2,4]=>1110010=>[3,2,1,1]
[4,6,2,8,5,7,3,1]=>[5,3,7,1,4,2,6,8]=>1010100=>[1,1,1,1,1,2]
[4,6,2,8,5,7,1,3]=>[5,3,7,1,4,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,2,4,8,7,1,3,5]=>[3,7,5,1,2,8,6,4]=>0110011=>[1,2,2,2]
[6,4,2,8,7,5,3,1]=>[3,5,7,1,2,4,6,8]=>0010000=>[2,1,4]
[2,6,4,8,1,7,5,3]=>[7,3,5,1,8,2,4,6]=>1010100=>[1,1,1,1,1,2]
[2,6,4,1,8,7,5,3]=>[7,3,5,8,1,2,4,6]=>1001000=>[1,2,1,3]
[2,6,1,4,8,7,5,3]=>[7,3,8,5,1,2,4,6]=>1011000=>[1,1,2,3]
[2,1,6,4,8,7,5,3]=>[7,8,3,5,1,2,4,6]=>0101000=>[1,1,1,1,3]
[2,1,6,4,8,7,3,5]=>[7,8,3,5,1,2,6,4]=>0101001=>[1,1,1,1,2,1]
[2,6,1,4,8,7,3,5]=>[7,3,8,5,1,2,6,4]=>1011001=>[1,1,2,2,1]
[2,6,4,1,8,7,3,5]=>[7,3,5,8,1,2,6,4]=>1001001=>[1,2,1,2,1]
[2,6,4,8,1,7,3,5]=>[7,3,5,1,8,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[6,4,2,8,7,5,1,3]=>[3,5,7,1,2,4,8,6]=>0010001=>[2,1,3,1]
[6,2,4,8,7,3,5,1]=>[3,7,5,1,2,6,4,8]=>0110010=>[1,2,2,1,1]
[6,2,4,8,7,3,1,5]=>[3,7,5,1,2,6,8,4]=>0110001=>[1,2,3,1]
[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>1101101=>[2,1,2,1,1]
[5,2,4,7,3,6,8,1]=>[4,7,5,2,6,3,1,8]=>0110110=>[1,2,1,2,1]
[1,7,6,3,4,8,2,5]=>[8,2,3,6,5,1,7,4]=>1001101=>[1,2,2,1,1]
[8,1,6,3,7,2,4,5]=>[1,8,3,6,2,7,5,4]=>0101011=>[1,1,1,1,1,2]
[7,1,6,3,8,2,4,5]=>[2,8,3,6,1,7,5,4]=>0101011=>[1,1,1,1,1,2]
[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>1101011=>[2,1,1,1,2]
[6,1,7,3,4,8,2,5]=>[3,8,2,6,5,1,7,4]=>0101101=>[1,1,1,2,1,1]
[2,1,7,4,5,8,3,6]=>[7,8,2,5,4,1,6,3]=>0101101=>[1,1,1,2,1,1]
[5,1,4,7,3,8,2,6]=>[4,8,5,2,6,1,7,3]=>0110101=>[1,2,1,1,1,1]
[4,3,1,7,5,8,2,6]=>[5,6,8,2,4,1,7,3]=>0010101=>[2,1,1,1,1,1]
[2,8,6,3,7,1,4,5]=>[7,1,3,6,2,8,5,4]=>1001011=>[1,2,1,1,2]
[6,8,1,3,7,2,4,5]=>[3,1,8,6,2,7,5,4]=>1011011=>[1,1,2,1,2]
[5,8,2,1,7,3,4,6]=>[4,1,7,8,2,6,5,3]=>1001011=>[1,2,1,1,2]
[5,7,2,1,8,3,4,6]=>[4,2,7,8,1,6,5,3]=>1001011=>[1,2,1,1,2]
[6,7,1,3,8,2,4,5]=>[3,2,8,6,1,7,5,4]=>1011011=>[1,1,2,1,2]
[5,1,2,4,8,3,6,7]=>[4,8,7,5,1,6,3,2]=>0111011=>[1,3,1,2]
[4,3,6,1,5,8,2,7]=>[5,6,3,8,4,1,7,2]=>0101101=>[1,1,1,2,1,1]
[2,6,1,4,5,8,3,7]=>[7,3,8,5,4,1,6,2]=>1011101=>[1,1,3,1,1]
[6,5,1,3,4,8,2,7]=>[3,4,8,6,5,1,7,2]=>0011101=>[2,3,1,1]
[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>1011011=>[1,1,2,1,2]
[8,5,1,3,7,2,4,6]=>[1,4,8,6,2,7,5,3]=>0011011=>[2,2,1,2]
[1,5,3,2,8,4,6,7]=>[8,4,6,7,1,5,3,2]=>1001011=>[1,2,1,1,2]
[6,4,2,1,5,8,3,7]=>[3,5,7,8,4,1,6,2]=>0001101=>[3,2,1,1]
[2,5,3,4,1,8,6,7]=>[7,4,6,5,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[4,3,5,2,1,8,6,7]=>[5,6,4,7,8,1,3,2]=>0100101=>[1,1,2,1,1,1]
[2,6,4,8,7,1,3,5]=>[7,3,5,1,2,8,6,4]=>1010011=>[1,1,1,2,2]
[1,6,4,8,7,2,3,5]=>[8,3,5,1,2,7,6,4]=>1010011=>[1,1,1,2,2]
[2,7,8,3,6,1,4,5]=>[7,2,1,6,3,8,5,4]=>1101011=>[2,1,1,1,2]
[4,3,2,8,7,1,5,6]=>[5,6,7,1,2,8,4,3]=>0010011=>[2,1,2,2]
[5,2,4,8,7,1,3,6]=>[4,7,5,1,2,8,6,3]=>0110011=>[1,2,2,2]
[6,2,8,3,7,1,4,5]=>[3,7,1,6,2,8,5,4]=>0101011=>[1,1,1,1,1,2]
[5,1,4,8,7,2,3,6]=>[4,8,5,1,2,7,6,3]=>0110011=>[1,2,2,2]
[4,8,2,5,1,3,7,6]=>[5,1,7,4,8,6,2,3]=>1010110=>[1,1,1,1,2,1]
[4,7,2,5,1,3,8,6]=>[5,2,7,4,8,6,1,3]=>1010110=>[1,1,1,1,2,1]
[3,7,2,1,5,4,8,6]=>[6,2,7,8,4,5,1,3]=>1001010=>[1,2,1,1,1,1]
[3,8,2,1,5,4,7,6]=>[6,1,7,8,4,5,2,3]=>1001010=>[1,2,1,1,1,1]
[8,3,2,1,5,4,6,7]=>[1,6,7,8,4,5,3,2]=>0001011=>[3,1,1,2]
[8,3,2,1,6,4,5,7]=>[1,6,7,8,3,5,4,2]=>0001011=>[3,1,1,2]
[8,4,2,5,1,6,3,7]=>[1,5,7,4,8,3,6,2]=>0010101=>[2,1,1,1,1,1]
[8,3,2,1,5,6,4,7]=>[1,6,7,8,4,3,5,2]=>0001101=>[3,2,1,1]
[8,3,2,1,4,6,5,7]=>[1,6,7,8,5,3,4,2]=>0001101=>[3,2,1,1]
[3,8,2,1,4,5,7,6]=>[6,1,7,8,5,4,2,3]=>1001110=>[1,2,3,1]
[3,7,2,1,4,5,8,6]=>[6,2,7,8,5,4,1,3]=>1001110=>[1,2,3,1]
[3,2,7,1,4,6,8,5]=>[6,7,2,8,5,3,1,4]=>0101110=>[1,1,1,3,1]
[3,2,8,1,4,6,7,5]=>[6,7,1,8,5,3,2,4]=>0101110=>[1,1,1,3,1]
[3,2,8,1,4,7,6,5]=>[6,7,1,8,5,2,3,4]=>0101100=>[1,1,1,2,2]
[3,8,2,1,4,7,5,6]=>[6,1,7,8,5,2,4,3]=>1001101=>[1,2,2,1,1]
[3,8,2,1,5,7,4,6]=>[6,1,7,8,4,2,5,3]=>1001101=>[1,2,2,1,1]
[4,8,2,5,1,7,3,6]=>[5,1,7,4,8,2,6,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,2,5,1,8,3,6]=>[5,2,7,4,8,1,6,3]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,1,5,8,4,6]=>[6,2,7,8,4,1,5,3]=>1001101=>[1,2,2,1,1]
[3,7,2,1,4,8,5,6]=>[6,2,7,8,5,1,4,3]=>1001101=>[1,2,2,1,1]
[3,2,1,7,5,8,6,4]=>[6,7,8,2,4,1,3,5]=>0010100=>[2,1,1,1,2]
[3,2,7,1,6,8,4,5]=>[6,7,2,8,3,1,5,4]=>0101101=>[1,1,1,2,1,1]
[4,2,7,6,1,8,3,5]=>[5,7,2,3,8,1,6,4]=>0100101=>[1,1,2,1,1,1]
[4,3,7,6,8,1,2,5]=>[5,6,2,3,1,8,7,4]=>0101011=>[1,1,1,1,1,2]
[4,3,8,6,7,1,2,5]=>[5,6,1,3,2,8,7,4]=>0101011=>[1,1,1,1,1,2]
[4,2,8,6,1,7,3,5]=>[5,7,1,3,8,2,6,4]=>0100101=>[1,1,2,1,1,1]
[3,2,8,1,6,7,4,5]=>[6,7,1,8,3,2,5,4]=>0101101=>[1,1,1,2,1,1]
[3,2,1,8,7,5,6,4]=>[6,7,8,1,2,4,3,5]=>0010010=>[2,1,2,1,1]
[3,8,2,1,7,4,5,6]=>[6,1,7,8,2,5,4,3]=>1001011=>[1,2,1,1,2]
[3,2,8,1,7,4,6,5]=>[6,7,1,8,2,5,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,1,6,4,7,5]=>[6,7,1,8,3,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,7,1,6,4,8,5]=>[6,7,2,8,3,5,1,4]=>0101010=>[1,1,1,1,1,1,1]
[4,2,7,6,1,3,8,5]=>[5,7,2,3,8,6,1,4]=>0100110=>[1,1,2,2,1]
[4,2,8,6,1,3,7,5]=>[5,7,1,3,8,6,2,4]=>0100110=>[1,1,2,2,1]
[4,2,8,7,1,3,6,5]=>[5,7,1,2,8,6,3,4]=>0100110=>[1,1,2,2,1]
[5,7,8,3,4,1,2,6]=>[4,2,1,6,5,8,7,3]=>1101011=>[2,1,1,1,2]
[4,2,7,8,1,3,6,5]=>[5,7,2,1,8,6,3,4]=>0110110=>[1,2,1,2,1]
[4,2,6,8,1,3,7,5]=>[5,7,3,1,8,6,2,4]=>0110110=>[1,2,1,2,1]
[4,2,6,7,1,3,8,5]=>[5,7,3,2,8,6,1,4]=>0110110=>[1,2,1,2,1]
[3,2,6,1,8,4,7,5]=>[6,7,3,8,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,7,2,1,8,4,5,6]=>[6,2,7,8,1,5,4,3]=>1001011=>[1,2,1,1,2]
[3,7,2,1,8,5,4,6]=>[6,2,7,8,1,4,5,3]=>1001001=>[1,2,1,2,1]
[4,7,3,8,5,1,2,6]=>[5,2,6,1,4,8,7,3]=>1010011=>[1,1,1,2,2]
[4,3,7,8,6,1,2,5]=>[5,6,2,1,3,8,7,4]=>0110011=>[1,2,2,2]
[3,2,7,1,8,6,4,5]=>[6,7,2,8,1,3,5,4]=>0101001=>[1,1,1,1,2,1]
[3,2,1,6,8,5,7,4]=>[6,7,8,3,1,4,2,5]=>0011010=>[2,2,1,1,1]
[3,2,6,1,8,7,4,5]=>[6,7,3,8,1,2,5,4]=>0101001=>[1,1,1,1,2,1]
[4,2,6,8,1,7,3,5]=>[5,7,3,1,8,2,6,4]=>0110101=>[1,2,1,1,1,1]
[4,3,6,8,7,1,2,5]=>[5,6,3,1,2,8,7,4]=>0110011=>[1,2,2,2]
[4,2,6,7,1,8,3,5]=>[5,7,3,2,8,1,6,4]=>0110101=>[1,2,1,1,1,1]
[3,2,6,1,7,8,4,5]=>[6,7,3,8,2,1,5,4]=>0101101=>[1,1,1,2,1,1]
[3,4,6,8,7,5,1,2]=>[6,5,3,1,2,4,8,7]=>1110001=>[3,3,1]
[5,3,6,4,8,7,1,2]=>[4,6,3,5,1,2,8,7]=>0101001=>[1,1,1,1,2,1]
[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>1101100=>[2,1,2,2]
[3,1,8,5,4,2,6,7]=>[6,8,1,4,5,7,3,2]=>0100011=>[1,1,3,2]
[1,2,7,5,4,8,6,3]=>[8,7,2,4,5,1,3,6]=>1100100=>[2,2,1,2]
[6,3,7,5,4,8,1,2]=>[3,6,2,4,5,1,8,7]=>0100101=>[1,1,2,1,1,1]
[7,3,8,5,4,6,1,2]=>[2,6,1,4,5,3,8,7]=>0100101=>[1,1,2,1,1,1]
[3,8,7,5,4,6,1,2]=>[6,1,2,4,5,3,8,7]=>1000101=>[1,3,1,1,1]
[4,3,6,7,8,5,1,2]=>[5,6,3,2,1,4,8,7]=>0111001=>[1,3,2,1]
[4,5,6,3,8,7,1,2]=>[5,4,3,6,1,2,8,7]=>1101001=>[2,1,1,2,1]
[3,6,8,5,4,7,1,2]=>[6,3,1,4,5,2,8,7]=>1100101=>[2,2,1,1,1]
[6,8,3,5,4,7,1,2]=>[3,1,6,4,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[7,6,3,5,4,8,1,2]=>[2,3,6,4,5,1,8,7]=>0010101=>[2,1,1,1,1,1]
[1,6,2,5,4,8,7,3]=>[8,3,7,4,5,1,2,6]=>1010100=>[1,1,1,1,1,2]
[7,1,2,5,8,3,6,4]=>[2,8,7,4,1,6,3,5]=>0111010=>[1,3,1,1,1]
[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>1011010=>[1,1,2,1,1,1]
[6,2,1,5,4,8,7,3]=>[3,7,8,4,5,1,2,6]=>0010100=>[2,1,1,1,2]
[4,1,6,2,8,7,5,3]=>[5,8,3,7,1,2,4,6]=>0101000=>[1,1,1,1,3]
[7,8,1,2,4,6,5,3]=>[2,1,8,7,5,3,4,6]=>1011100=>[1,1,3,2]
[7,8,3,1,4,2,6,5]=>[2,1,6,8,5,7,3,4]=>1001010=>[1,2,1,1,1,1]
[4,3,6,1,8,2,7,5]=>[5,6,3,8,1,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[2,3,8,5,4,1,6,7]=>[7,6,1,4,5,8,3,2]=>1100011=>[2,3,2]
[4,8,1,5,2,3,7,6]=>[5,1,8,4,7,6,2,3]=>1010110=>[1,1,1,1,2,1]
[5,8,1,6,4,3,2,7]=>[4,1,8,3,5,6,7,2]=>1010001=>[1,1,1,3,1]
[6,1,5,7,4,3,2,8]=>[3,8,4,2,5,6,7,1]=>0110001=>[1,2,3,1]
[1,5,8,6,4,3,2,7]=>[8,4,1,3,5,6,7,2]=>1100001=>[2,4,1]
[3,4,6,1,5,8,2,7]=>[6,5,3,8,4,1,7,2]=>1101101=>[2,1,2,1,1]
[7,8,4,1,5,3,2,6]=>[2,1,5,8,4,6,7,3]=>1001001=>[1,2,1,2,1]
[7,8,5,1,6,3,2,4]=>[2,1,4,8,3,6,7,5]=>1001001=>[1,2,1,2,1]
[2,6,1,5,7,3,8,4]=>[7,3,8,4,2,6,1,5]=>1011010=>[1,1,2,1,1,1]
[1,6,8,7,4,3,2,5]=>[8,3,1,2,5,6,7,4]=>1100001=>[2,4,1]
[6,8,1,7,4,3,2,5]=>[3,1,8,2,5,6,7,4]=>1010001=>[1,1,1,3,1]
[5,1,7,6,4,3,2,8]=>[4,8,2,3,5,6,7,1]=>0100001=>[1,1,4,1]
[6,1,7,8,4,3,2,5]=>[3,8,2,1,5,6,7,4]=>0110001=>[1,2,3,1]
[7,1,8,6,4,3,2,5]=>[2,8,1,3,5,6,7,4]=>0100001=>[1,1,4,1]
[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>1000001=>[1,5,1]
[2,1,7,5,6,3,8,4]=>[7,8,2,4,3,6,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,1,6,7,5,8,2,4]=>[6,8,3,2,4,1,7,5]=>0110101=>[1,2,1,1,1,1]
[7,8,1,6,5,3,2,4]=>[2,1,8,3,4,6,7,5]=>1010001=>[1,1,1,3,1]
[7,8,2,1,4,5,6,3]=>[2,1,7,8,5,4,3,6]=>1001110=>[1,2,3,1]
[2,8,1,5,4,6,7,3]=>[7,1,8,4,5,3,2,6]=>1010110=>[1,1,1,1,2,1]
[7,2,1,5,4,6,8,3]=>[2,7,8,4,5,3,1,6]=>0010110=>[2,1,1,2,1]
[1,2,8,5,6,3,7,4]=>[8,7,1,4,3,6,2,5]=>1101010=>[2,1,1,1,1,1]
[6,1,2,5,7,3,8,4]=>[3,8,7,4,2,6,1,5]=>0111010=>[1,3,1,1,1]
[4,2,1,5,6,3,7,8]=>[5,7,8,4,3,6,2,1]=>0011011=>[2,2,1,2]
[4,3,6,1,5,7,2,8]=>[5,6,3,8,4,2,7,1]=>0101101=>[1,1,1,2,1,1]
[5,1,6,3,7,8,2,4]=>[4,8,3,6,2,1,7,5]=>0101101=>[1,1,1,2,1,1]
[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>1110101=>[3,1,1,1,1]
[2,4,6,3,7,1,8,5]=>[7,5,3,6,2,8,1,4]=>1101010=>[2,1,1,1,1,1]
[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>1101001=>[2,1,1,2,1]
[4,1,6,7,3,8,2,5]=>[5,8,3,2,6,1,7,4]=>0110101=>[1,2,1,1,1,1]
[5,4,6,1,3,7,2,8]=>[4,5,3,8,6,2,7,1]=>0101101=>[1,1,1,2,1,1]
[6,4,1,5,2,3,7,8]=>[3,5,8,4,7,6,2,1]=>0010111=>[2,1,1,3]
[4,1,7,5,2,3,8,6]=>[5,8,2,4,7,6,1,3]=>0100110=>[1,1,2,2,1]
[1,2,4,5,8,3,7,6]=>[8,7,5,4,1,6,2,3]=>1111010=>[4,1,1,1]
[7,2,3,5,4,1,8,6]=>[2,7,6,4,5,8,1,3]=>0110010=>[1,2,2,1,1]
[2,8,3,5,4,1,7,6]=>[7,1,6,4,5,8,2,3]=>1010010=>[1,1,1,2,1,1]
[4,2,6,3,8,1,7,5]=>[5,7,3,6,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,8,2,3,4,1,6,5]=>[2,1,7,6,5,8,3,4]=>1011010=>[1,1,2,1,1,1]
[7,8,1,4,6,3,2,5]=>[2,1,8,5,3,6,7,4]=>1011001=>[1,1,2,2,1]
[3,1,6,4,7,8,2,5]=>[6,8,3,5,2,1,7,4]=>0101101=>[1,1,1,2,1,1]
[1,8,5,7,4,3,2,6]=>[8,1,4,2,5,6,7,3]=>1010001=>[1,1,1,3,1]
[7,1,5,8,4,3,2,6]=>[2,8,4,1,5,6,7,3]=>0110001=>[1,2,3,1]
[5,1,8,7,4,3,2,6]=>[4,8,1,2,5,6,7,3]=>0100001=>[1,1,4,1]
[6,5,1,8,4,3,2,7]=>[3,4,8,1,5,6,7,2]=>0010001=>[2,1,3,1]
[6,5,7,1,4,3,2,8]=>[3,4,2,8,5,6,7,1]=>0101001=>[1,1,1,1,2,1]
[7,5,8,1,4,3,2,6]=>[2,4,1,8,5,6,7,3]=>0101001=>[1,1,1,1,2,1]
[5,8,7,1,4,3,2,6]=>[4,1,2,8,5,6,7,3]=>1001001=>[1,2,1,2,1]
[1,5,7,8,4,3,2,6]=>[8,4,2,1,5,6,7,3]=>1110001=>[3,3,1]
[2,4,7,5,1,3,8,6]=>[7,5,2,4,8,6,1,3]=>1100110=>[2,2,2,1]
[7,8,4,6,1,3,2,5]=>[2,1,5,3,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,4,1,3,2,6]=>[2,1,4,5,8,6,7,3]=>1000101=>[1,3,1,1,1]
[3,5,6,4,1,8,2,7]=>[6,4,3,5,8,1,7,2]=>1100101=>[2,2,1,1,1]
[2,6,4,5,1,3,8,7]=>[7,3,5,4,8,6,1,2]=>1010110=>[1,1,1,1,2,1]
[1,6,5,8,4,3,2,7]=>[8,3,4,1,5,6,7,2]=>1010001=>[1,1,1,3,1]
[6,8,5,1,4,3,2,7]=>[3,1,4,8,5,6,7,2]=>1001001=>[1,2,1,2,1]
[7,6,5,1,4,3,2,8]=>[2,3,4,8,5,6,7,1]=>0001001=>[3,1,2,1]
[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>11111101=>[6,1,1]
[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>11111010=>[5,1,1,1]
[1,2,3,4,7,5,8,9,6]=>[9,8,7,6,3,5,2,1,4]=>11110110=>[4,1,2,1]
[1,2,3,6,4,7,8,9,5]=>[9,8,7,4,6,3,2,1,5]=>11101110=>[3,1,3,1]
[1,2,5,3,6,7,8,9,4]=>[9,8,5,7,4,3,2,1,6]=>11011110=>[2,1,4,1]
[1,4,2,5,6,7,8,9,3]=>[9,6,8,5,4,3,2,1,7]=>10111110=>[1,1,5,1]
[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>00111111=>[2,6]
[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>11011111=>[2,1,5]
[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>00011111=>[3,5]
[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>11101111=>[3,1,4]
[9,6,7,8,1,2,3,4,5]=>[1,4,3,2,9,8,7,6,5]=>01101111=>[1,2,1,4]
[8,9,6,7,1,2,3,4,5]=>[2,1,4,3,9,8,7,6,5]=>10101111=>[1,1,1,1,4]
[9,8,6,7,1,2,3,4,5]=>[1,2,4,3,9,8,7,6,5]=>00101111=>[2,1,1,4]
[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111=>[4,4]
[9,5,6,7,8,1,2,3,4]=>[1,5,4,3,2,9,8,7,6]=>01110111=>[1,3,1,3]
[8,9,5,6,7,1,2,3,4]=>[2,1,5,4,3,9,8,7,6]=>10110111=>[1,1,2,1,3]
[9,8,5,6,7,1,2,3,4]=>[1,2,5,4,3,9,8,7,6]=>00110111=>[2,2,1,3]
[9,7,8,5,6,1,2,3,4]=>[1,3,2,5,4,9,8,7,6]=>01010111=>[1,1,1,1,1,3]
[9,8,7,5,6,1,2,3,4]=>[1,2,3,5,4,9,8,7,6]=>00010111=>[3,1,1,3]
[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>00000111=>[5,3]
[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>11011011=>[2,1,2,1,2]
[9,7,8,4,5,6,1,2,3]=>[1,3,2,6,5,4,9,8,7]=>01011011=>[1,1,1,2,1,2]
[9,8,7,4,5,6,1,2,3]=>[1,2,3,6,5,4,9,8,7]=>00011011=>[3,2,1,2]
[8,9,6,7,4,5,1,2,3]=>[2,1,4,3,6,5,9,8,7]=>10101011=>[1,1,1,1,1,1,2]
[9,8,6,7,4,5,1,2,3]=>[1,2,4,3,6,5,9,8,7]=>00101011=>[2,1,1,1,1,2]
[9,8,7,6,4,5,1,2,3]=>[1,2,3,4,6,5,9,8,7]=>00001011=>[4,1,1,2]
[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>00000011=>[6,2]
[9,7,8,5,6,3,4,1,2]=>[1,3,2,5,4,7,6,9,8]=>01010101=>[1,1,1,1,1,1,1,1]
[9,8,7,5,6,3,4,1,2]=>[1,2,3,5,4,7,6,9,8]=>00010101=>[3,1,1,1,1,1]
[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,7,6,9,8]=>00000101=>[5,1,1,1]
[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>00000001=>[7,1]
[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>101111111=>[1,1,7]
[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>110111111=>[2,1,6]
[10,8,9,1,2,3,4,5,6,7]=>[1,3,2,10,9,8,7,6,5,4]=>010111111=>[1,1,1,6]
[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>000111111=>[3,6]
[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>111011111=>[3,1,5]
[10,7,8,9,1,2,3,4,5,6]=>[1,4,3,2,10,9,8,7,6,5]=>011011111=>[1,2,1,5]
[9,10,7,8,1,2,3,4,5,6]=>[2,1,4,3,10,9,8,7,6,5]=>101011111=>[1,1,1,1,5]
[10,9,7,8,1,2,3,4,5,6]=>[1,2,4,3,10,9,8,7,6,5]=>001011111=>[2,1,1,5]
[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>000011111=>[4,5]
[10,6,7,8,9,1,2,3,4,5]=>[1,5,4,3,2,10,9,8,7,6]=>011101111=>[1,3,1,4]
[9,10,6,7,8,1,2,3,4,5]=>[2,1,5,4,3,10,9,8,7,6]=>101101111=>[1,1,2,1,4]
[10,9,6,7,8,1,2,3,4,5]=>[1,2,5,4,3,10,9,8,7,6]=>001101111=>[2,2,1,4]
[10,8,9,6,7,1,2,3,4,5]=>[1,3,2,5,4,10,9,8,7,6]=>010101111=>[1,1,1,1,1,4]
[10,9,8,6,7,1,2,3,4,5]=>[1,2,3,5,4,10,9,8,7,6]=>000101111=>[3,1,1,4]
[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>000001111=>[5,4]
[9,10,5,6,7,8,1,2,3,4]=>[2,1,6,5,4,3,10,9,8,7]=>101110111=>[1,1,3,1,3]
[10,9,5,6,7,8,1,2,3,4]=>[1,2,6,5,4,3,10,9,8,7]=>001110111=>[2,3,1,3]
[8,9,10,5,6,7,1,2,3,4]=>[3,2,1,6,5,4,10,9,8,7]=>110110111=>[2,1,2,1,3]
[10,9,8,5,6,7,1,2,3,4]=>[1,2,3,6,5,4,10,9,8,7]=>000110111=>[3,2,1,3]
[9,10,7,8,5,6,1,2,3,4]=>[2,1,4,3,6,5,10,9,8,7]=>101010111=>[1,1,1,1,1,1,3]
[10,9,7,8,5,6,1,2,3,4]=>[1,2,4,3,6,5,10,9,8,7]=>001010111=>[2,1,1,1,1,3]
[10,9,8,7,5,6,1,2,3,4]=>[1,2,3,4,6,5,10,9,8,7]=>000010111=>[4,1,1,3]
[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>000000111=>[6,3]
[10,7,8,9,4,5,6,1,2,3]=>[1,4,3,2,7,6,5,10,9,8]=>011011011=>[1,2,1,2,1,2]
[9,10,7,8,4,5,6,1,2,3]=>[2,1,4,3,7,6,5,10,9,8]=>101011011=>[1,1,1,1,2,1,2]
[10,9,7,8,4,5,6,1,2,3]=>[1,2,4,3,7,6,5,10,9,8]=>001011011=>[2,1,1,2,1,2]
[10,9,8,7,4,5,6,1,2,3]=>[1,2,3,4,7,6,5,10,9,8]=>000011011=>[4,2,1,2]
[10,8,9,6,7,4,5,1,2,3]=>[1,3,2,5,4,7,6,10,9,8]=>010101011=>[1,1,1,1,1,1,1,2]
[10,9,8,6,7,4,5,1,2,3]=>[1,2,3,5,4,7,6,10,9,8]=>000101011=>[3,1,1,1,1,2]
[10,9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,7,6,10,9,8]=>000001011=>[5,1,1,2]
[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>000000011=>[7,2]
[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>101010101=>[1,1,1,1,1,1,1,1,1]
[10,9,7,8,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7,10,9]=>001010101=>[2,1,1,1,1,1,1,1]
[10,9,8,7,5,6,3,4,1,2]=>[1,2,3,4,6,5,8,7,10,9]=>000010101=>[4,1,1,1,1,1]
[10,9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,8,7,10,9]=>000000101=>[6,1,1,1]
[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>000000001=>[8,1]
[3,4,6,2,7,1,5,8]=>[6,5,3,7,2,8,4,1]=>1101011=>[2,1,1,1,2]
[3,6,2,5,4,1,7,8]=>[6,3,7,4,5,8,2,1]=>1010011=>[1,1,1,2,2]
[3,2,7,5,4,1,6,8]=>[6,7,2,4,5,8,3,1]=>0100011=>[1,1,3,2]
[4,3,6,2,8,1,5,7]=>[5,6,3,7,1,8,4,2]=>0101011=>[1,1,1,1,1,2]
[6,1,2,5,4,7,8,3]=>[3,8,7,4,5,2,1,6]=>0110110=>[1,2,1,2,1]
[6,2,4,5,1,3,7,8]=>[3,7,5,4,8,6,2,1]=>0110111=>[1,2,1,3]
[4,2,8,5,1,3,7,6]=>[5,7,1,4,8,6,2,3]=>0100110=>[1,1,2,2,1]
[4,3,6,8,1,7,2,5]=>[5,6,3,1,8,2,7,4]=>0110101=>[1,2,1,1,1,1]
[5,3,6,4,1,7,2,8]=>[4,6,3,5,8,2,7,1]=>0100101=>[1,1,2,1,1,1]
[6,2,1,5,8,3,7,4]=>[3,7,8,4,1,6,2,5]=>0011010=>[2,2,1,1,1]
[1,6,7,4,8,3,5,2]=>[8,3,2,5,1,6,4,7]=>1101010=>[2,1,1,1,1,1]
[1,4,6,3,7,5,8,2]=>[8,5,3,6,2,4,1,7]=>1101010=>[2,1,1,1,1,1]
[4,6,7,2,5,8,1,3]=>[5,3,2,7,4,1,8,6]=>1101101=>[2,1,2,1,1]
[2,4,6,1,7,5,3,8]=>[7,5,3,8,2,4,6,1]=>1101001=>[2,1,1,2,1]
[7,5,4,6,2,8,1,3]=>[2,4,5,3,7,1,8,6]=>0010101=>[2,1,1,1,1,1]
[1,7,5,4,3,8,6,2]=>[8,2,4,5,6,1,3,7]=>1000100=>[1,3,1,2]
[1,4,6,3,5,8,7,2]=>[8,5,3,6,4,1,2,7]=>1101100=>[2,1,2,2]
[1,5,8,4,3,6,7,2]=>[8,4,1,5,6,3,2,7]=>1100110=>[2,2,2,1]
[5,4,6,2,7,8,1,3]=>[4,5,3,7,2,1,8,6]=>0101101=>[1,1,1,2,1,1]
[2,5,4,1,6,7,3,8]=>[7,4,5,8,3,2,6,1]=>1001101=>[1,2,2,1,1]
[5,6,3,2,7,1,4,8]=>[4,3,6,7,2,8,5,1]=>1001011=>[1,2,1,1,2]
[5,6,3,2,7,1,8,4]=>[4,3,6,7,2,8,1,5]=>1001010=>[1,2,1,1,1,1]
[8,5,6,3,2,7,1,4]=>[1,4,3,6,7,2,8,5]=>0100101=>[1,1,2,1,1,1]
[5,4,6,2,8,1,7,3]=>[4,5,3,7,1,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[2,4,1,7,8,5,3,6]=>[7,5,8,2,1,4,6,3]=>1011001=>[1,1,2,2,1]
[2,5,4,1,6,3,8,7]=>[7,4,5,8,3,6,1,2]=>1001010=>[1,2,1,1,1,1]
[5,6,3,2,1,8,4,7]=>[4,3,6,7,8,1,5,2]=>1000101=>[1,3,1,1,1]
[3,5,2,1,6,4,7,8]=>[6,4,7,8,3,5,2,1]=>1001011=>[1,2,1,1,2]
[6,8,4,3,2,1,5,7]=>[3,1,5,6,7,8,4,2]=>1000011=>[1,4,2]
[5,3,8,2,1,6,4,7]=>[4,6,1,7,8,3,5,2]=>0100101=>[1,1,2,1,1,1]
[3,7,5,8,2,1,4,6]=>[6,2,4,1,7,8,5,3]=>1010011=>[1,1,1,2,2]
[7,3,2,8,5,1,6,4]=>[2,6,7,1,4,8,3,5]=>0010010=>[2,1,2,1,1]
[8,4,6,3,2,1,7,5]=>[1,5,3,6,7,8,2,4]=>0100010=>[1,1,3,1,1]
[8,6,4,3,2,1,7,5]=>[1,3,5,6,7,8,2,4]=>0000010=>[5,1,1]
[7,6,4,3,2,1,8,5]=>[2,3,5,6,7,8,1,4]=>0000010=>[5,1,1]
[7,8,4,3,2,1,6,5]=>[2,1,5,6,7,8,3,4]=>1000010=>[1,4,1,1]
[5,4,7,2,1,8,6,3]=>[4,5,2,7,8,1,3,6]=>0100100=>[1,1,2,1,2]
[7,5,8,3,2,6,1,4]=>[2,4,1,6,7,3,8,5]=>0100101=>[1,1,2,1,1,1]
[5,7,3,2,1,6,8,4]=>[4,2,6,7,8,3,1,5]=>1000110=>[1,3,2,1]
[5,7,3,2,1,6,4,8]=>[4,2,6,7,8,3,5,1]=>1000101=>[1,3,1,1,1]
[6,3,7,2,5,1,8,4]=>[3,6,2,7,4,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,7,8,3,5,2,1,4]=>[3,2,1,6,4,7,8,5]=>1101001=>[2,1,1,2,1]
[6,2,5,7,8,4,1,3]=>[3,7,4,2,1,5,8,6]=>0111001=>[1,3,2,1]
[2,1,5,7,8,6,3,4]=>[7,8,4,2,1,3,6,5]=>0111001=>[1,3,2,1]
[3,6,7,2,8,1,4,5]=>[6,3,2,7,1,8,5,4]=>1101011=>[2,1,1,1,2]
[6,3,7,2,8,1,4,5]=>[3,6,2,7,1,8,5,4]=>0101011=>[1,1,1,1,1,2]
[3,2,6,1,7,4,5,8]=>[6,7,3,8,2,5,4,1]=>0101011=>[1,1,1,1,1,2]
[3,5,2,1,4,7,6,8]=>[6,4,7,8,5,2,3,1]=>1001101=>[1,2,2,1,1]
[7,3,5,2,1,8,4,6]=>[2,6,4,7,8,1,5,3]=>0100101=>[1,1,2,1,1,1]
[2,5,4,1,3,7,8,6]=>[7,4,5,8,6,2,1,3]=>1001110=>[1,2,3,1]
[2,5,8,4,1,3,7,6]=>[7,4,1,5,8,6,2,3]=>1100110=>[2,2,2,1]
[2,4,1,7,8,3,6,5]=>[7,5,8,2,1,6,3,4]=>1011010=>[1,1,2,1,1,1]
[3,7,2,8,6,1,4,5]=>[6,2,7,1,3,8,5,4]=>1010011=>[1,1,1,2,2]
[3,6,8,2,1,7,4,5]=>[6,3,1,7,8,2,5,4]=>1100101=>[2,2,1,1,1]
[5,3,8,2,1,4,7,6]=>[4,6,1,7,8,5,2,3]=>0100110=>[1,1,2,2,1]
[4,8,7,3,2,1,5,6]=>[5,1,2,6,7,8,4,3]=>1000011=>[1,4,2]
[4,7,3,2,1,5,6,8]=>[5,2,6,7,8,4,3,1]=>1000111=>[1,3,3]
[8,4,7,3,2,1,5,6]=>[1,5,2,6,7,8,4,3]=>0100011=>[1,1,3,2]
[8,3,5,2,1,4,7,6]=>[1,6,4,7,8,5,2,3]=>0100110=>[1,1,2,2,1]
[7,3,2,8,6,1,4,5]=>[2,6,7,1,3,8,5,4]=>0010011=>[2,1,2,2]
[7,8,6,5,4,3,2,1,9]=>[3,2,4,5,6,7,8,9,1]=>10000001=>[1,6,1]
[1,8,9,7,6,5,4,3,2]=>[9,2,1,3,4,5,6,7,8]=>11000000=>[2,6]
[8,9,7,6,5,4,3,2,1,10]=>[3,2,4,5,6,7,8,9,10,1]=>100000001=>[1,7,1]
[7,6,8,5,4,3,2,1,9]=>[3,4,2,5,6,7,8,9,1]=>01000001=>[1,1,5,1]
[6,8,7,5,4,3,2,1,9]=>[4,2,3,5,6,7,8,9,1]=>10000001=>[1,6,1]
[1,8,7,9,6,5,4,3,2]=>[9,2,3,1,4,5,6,7,8]=>10100000=>[1,1,1,5]
[1,7,9,8,6,5,4,3,2]=>[9,3,1,2,4,5,6,7,8]=>11000000=>[2,6]
[1,9,10,8,7,6,5,4,3,2]=>[10,2,1,3,4,5,6,7,8,9]=>110000000=>[2,7]
[7,8,3,5,4,6,1,2]=>[2,1,6,4,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[8,6,3,7,5,2,4,1]=>[1,3,6,2,4,7,5,8]=>0010010=>[2,1,2,1,1]
[5,4,1,6,3,2,8,7]=>[4,5,8,3,6,7,1,2]=>0010010=>[2,1,2,1,1]
[5,4,1,6,2,3,8,7]=>[4,5,8,3,7,6,1,2]=>0010110=>[2,1,1,2,1]
[5,7,1,6,2,8,3,4]=>[4,2,8,3,7,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,7,1,6,2,8,4,3]=>[4,2,8,3,7,1,5,6]=>1010100=>[1,1,1,1,1,2]
[2,7,6,5,1,8,3,4]=>[7,2,3,4,8,1,6,5]=>1000101=>[1,3,1,1,1]
[2,7,6,5,1,8,4,3]=>[7,2,3,4,8,1,5,6]=>1000100=>[1,3,1,2]
[2,3,6,5,1,4,8,7]=>[7,6,3,4,8,5,1,2]=>1100110=>[2,2,2,1]
[2,3,6,4,1,5,8,7]=>[7,6,3,5,8,4,1,2]=>1100110=>[2,2,2,1]
[2,3,6,1,5,4,8,7]=>[7,6,3,8,4,5,1,2]=>1101010=>[2,1,1,1,1,1]
[2,7,6,1,4,8,5,3]=>[7,2,3,8,5,1,4,6]=>1001100=>[1,2,2,2]
[2,7,6,1,4,8,3,5]=>[7,2,3,8,5,1,6,4]=>1001101=>[1,2,2,1,1]
[7,3,5,1,8,4,2,6]=>[2,6,4,8,1,5,7,3]=>0101001=>[1,1,1,1,2,1]
[7,3,5,1,8,6,4,2]=>[2,6,4,8,1,3,5,7]=>0101000=>[1,1,1,1,3]
[2,7,6,1,5,8,4,3]=>[7,2,3,8,4,1,5,6]=>1001100=>[1,2,2,2]
[2,7,6,4,1,8,5,3]=>[7,2,3,5,8,1,4,6]=>1000100=>[1,3,1,2]
[2,1,7,6,3,8,5,4]=>[7,8,2,3,6,1,4,5]=>0100100=>[1,1,2,1,2]
[2,1,7,6,3,8,4,5]=>[7,8,2,3,6,1,5,4]=>0100101=>[1,1,2,1,1,1]
[5,7,3,6,2,8,4,1]=>[4,2,6,3,7,1,5,8]=>1010100=>[1,1,1,1,1,2]
[2,7,6,4,1,8,3,5]=>[7,2,3,5,8,1,6,4]=>1000101=>[1,3,1,1,1]
[7,3,5,1,8,6,2,4]=>[2,6,4,8,1,3,7,5]=>0101001=>[1,1,1,1,2,1]
[6,3,5,1,8,2,4,7]=>[3,6,4,8,1,7,5,2]=>0101011=>[1,1,1,1,1,2]
[2,3,4,8,7,6,1,5]=>[7,6,5,1,2,3,8,4]=>1110001=>[3,3,1]
[2,3,4,8,5,7,1,6]=>[7,6,5,1,4,2,8,3]=>1110101=>[3,1,1,1,1]
[7,3,5,4,8,1,2,6]=>[2,6,4,5,1,8,7,3]=>0101011=>[1,1,1,1,1,2]
[6,4,3,5,8,7,2,1]=>[3,5,6,4,1,2,7,8]=>0011000=>[2,2,3]
[2,1,4,5,8,7,3,6]=>[7,8,5,4,1,2,6,3]=>0111001=>[1,3,2,1]
[6,4,3,5,8,7,1,2]=>[3,5,6,4,1,2,8,7]=>0011001=>[2,2,2,1]
[7,3,5,4,8,1,6,2]=>[2,6,4,5,1,8,3,7]=>0101010=>[1,1,1,1,1,1,1]
[2,3,4,8,7,5,6,1]=>[7,6,5,1,2,4,3,8]=>1110010=>[3,2,1,1]
[2,3,4,8,7,5,1,6]=>[7,6,5,1,2,4,8,3]=>1110001=>[3,3,1]
[2,7,6,5,4,8,1,3]=>[7,2,3,4,5,1,8,6]=>1000101=>[1,3,1,1,1]
[7,3,5,6,8,4,1,2]=>[2,6,4,3,1,5,8,7]=>0111001=>[1,3,2,1]
[7,3,5,6,8,1,4,2]=>[2,6,4,3,1,8,5,7]=>0111010=>[1,3,1,1,1]
[7,3,5,6,8,1,2,4]=>[2,6,4,3,1,8,7,5]=>0111011=>[1,3,1,2]
[6,4,1,5,8,7,2,3]=>[3,5,8,4,1,2,7,6]=>0011001=>[2,2,2,1]
[6,4,1,5,8,7,3,2]=>[3,5,8,4,1,2,6,7]=>0011000=>[2,2,3]
[6,4,1,5,8,3,7,2]=>[3,5,8,4,1,6,2,7]=>0011010=>[2,2,1,1,1]
[5,7,1,6,3,8,2,4]=>[4,2,8,3,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,4,1,5,8,3,2,7]=>[3,5,8,4,1,6,7,2]=>0011001=>[2,2,2,1]
[7,4,1,5,8,2,3,6]=>[2,5,8,4,1,7,6,3]=>0011011=>[2,2,1,2]
[7,4,1,5,8,2,6,3]=>[2,5,8,4,1,7,3,6]=>0011010=>[2,2,1,1,1]
[6,3,5,7,8,2,1,4]=>[3,6,4,2,1,7,8,5]=>0111001=>[1,3,2,1]
[6,3,5,7,8,2,4,1]=>[3,6,4,2,1,7,5,8]=>0111010=>[1,3,1,1,1]
[2,7,6,4,5,8,3,1]=>[7,2,3,5,4,1,6,8]=>1001100=>[1,2,2,2]
[5,7,3,6,1,8,4,2]=>[4,2,6,3,8,1,5,7]=>1010100=>[1,1,1,1,1,2]
[2,1,4,5,8,6,3,7]=>[7,8,5,4,1,3,6,2]=>0111001=>[1,3,2,1]
[7,3,5,4,8,6,2,1]=>[2,6,4,5,1,3,7,8]=>0101000=>[1,1,1,1,3]
[2,3,4,8,5,6,1,7]=>[7,6,5,1,4,3,8,2]=>1110101=>[3,1,1,1,1]
[2,3,4,8,7,1,6,5]=>[7,6,5,1,2,8,3,4]=>1110010=>[3,2,1,1]
[2,3,4,8,1,7,6,5]=>[7,6,5,1,8,2,3,4]=>1110100=>[3,1,1,2]
[2,3,4,8,1,6,7,5]=>[7,6,5,1,8,3,2,4]=>1110110=>[3,1,2,1]
[2,3,4,8,5,1,7,6]=>[7,6,5,1,4,8,2,3]=>1110010=>[3,2,1,1]
[6,3,5,4,8,2,7,1]=>[3,6,4,5,1,7,2,8]=>0101010=>[1,1,1,1,1,1,1]
[7,4,3,5,8,2,1,6]=>[2,5,6,4,1,7,8,3]=>0011001=>[2,2,2,1]
[2,1,4,5,8,3,7,6]=>[7,8,5,4,1,6,2,3]=>0111010=>[1,3,1,1,1]
[7,4,3,5,8,2,6,1]=>[2,5,6,4,1,7,3,8]=>0011010=>[2,2,1,1,1]
[6,3,5,4,8,2,1,7]=>[3,6,4,5,1,7,8,2]=>0101001=>[1,1,1,1,2,1]
[2,3,4,8,5,1,6,7]=>[7,6,5,1,4,8,3,2]=>1110011=>[3,2,2]
[2,3,4,8,1,6,5,7]=>[7,6,5,1,8,3,4,2]=>1110101=>[3,1,1,1,1]
[2,3,4,8,1,5,7,6]=>[7,6,5,1,8,4,2,3]=>1110110=>[3,1,2,1]
[7,8,2,6,1,5,3,4]=>[2,1,7,3,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,6,2,5,3,4]=>[2,1,8,3,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,6,7,2,5,3,4]=>[8,1,3,2,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,5,7,2,6,3,4]=>[8,1,4,2,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,7,2,6,3,4]=>[4,1,8,2,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,7,1,6,3,4]=>[4,1,7,2,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,7,1,5,3,4]=>[7,1,3,2,8,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,5,7,1,6,3,4]=>[7,1,4,2,8,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,1,7,5,6,3,4]=>[7,1,8,2,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,7,5,6,3,4]=>[8,1,7,2,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,1,7,4,6,3,5]=>[7,1,8,2,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,7,1,6,3,5]=>[7,1,5,2,8,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,7,1,6,3,5]=>[5,1,7,2,8,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,7,2,6,3,5]=>[5,1,8,2,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,7,5,6,2,3]=>[5,1,8,2,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,7,5,6,2,3]=>[8,1,5,2,4,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,1,7,5,6,2,4]=>[6,1,8,2,4,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,1,7,4,6,2,5]=>[6,1,8,2,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,1,7,2,6,4,5]=>[6,1,8,2,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,2,7,1,6,4,5]=>[6,1,7,2,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,2,7,4,6,1,5]=>[6,1,7,2,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,2,7,5,6,1,4]=>[6,1,7,2,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,7,5,6,1,3]=>[5,1,7,2,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,7,5,6,1,2]=>[5,1,6,2,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,7,5,6,1,2]=>[6,1,5,2,4,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,7,5,6,1,3]=>[7,1,5,2,4,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[2,8,3,7,5,6,1,4]=>[7,1,6,2,4,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,8,3,7,4,6,1,5]=>[7,1,6,2,5,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,3,7,1,6,4,5]=>[7,1,6,2,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,1,7,3,6,4,5]=>[7,1,8,2,6,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[7,5,2,8,6,4,1,3]=>[2,4,7,1,3,5,8,6]=>0010001=>[2,1,3,1]
[7,5,1,8,6,2,3,4]=>[2,4,8,1,3,7,6,5]=>0010011=>[2,1,2,2]
[7,4,8,6,1,5,2,3]=>[2,5,1,3,8,4,7,6]=>0100101=>[1,1,2,1,1,1]
[7,1,8,4,5,2,6,3]=>[2,8,1,5,4,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[6,8,1,7,4,2,5,3]=>[3,1,8,2,5,7,4,6]=>1010010=>[1,1,1,2,1,1]
[1,6,7,4,2,8,5,3]=>[8,3,2,5,7,1,4,6]=>1100100=>[2,2,1,2]
[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>1101001=>[2,1,1,2,1]
[7,1,8,3,5,6,2,4]=>[2,8,1,6,4,3,7,5]=>0101101=>[1,1,1,2,1,1]
[7,3,8,6,2,5,1,4]=>[2,6,1,3,7,4,8,5]=>0100101=>[1,1,2,1,1,1]
[7,4,2,8,6,1,3,5]=>[2,5,7,1,3,8,6,4]=>0010011=>[2,1,2,2]
[7,3,1,8,4,2,5,6]=>[2,6,8,1,5,7,4,3]=>0010011=>[2,1,2,2]
[7,2,8,4,1,5,3,6]=>[2,7,1,5,8,4,6,3]=>0100101=>[1,1,2,1,1,1]
[7,2,8,3,5,1,6,4]=>[2,7,1,6,4,8,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,2,8,3,4,6,1,5]=>[2,7,1,6,5,3,8,4]=>0101101=>[1,1,1,2,1,1]
[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>1110101=>[3,1,1,1,1]
[6,2,3,8,5,7,4,1]=>[3,7,6,1,4,2,5,8]=>0110100=>[1,2,1,1,2]
[6,2,4,8,5,3,1,7]=>[3,7,5,1,4,6,8,2]=>0110001=>[1,2,3,1]
[6,3,1,4,8,5,2,7]=>[3,6,8,5,1,4,7,2]=>0011001=>[2,2,2,1]
[2,6,3,7,8,5,4,1]=>[7,3,6,2,1,4,5,8]=>1011000=>[1,1,2,3]
[2,6,3,7,8,4,5,1]=>[7,3,6,2,1,5,4,8]=>1011010=>[1,1,2,1,1,1]
[2,4,7,3,5,6,8,1]=>[7,5,2,6,4,3,1,8]=>1101110=>[2,1,3,1]
[2,4,7,3,6,8,5,1]=>[7,5,2,6,3,1,4,8]=>1101100=>[2,1,2,2]
[2,5,3,7,8,1,6,4]=>[7,4,6,2,1,8,3,5]=>1011010=>[1,1,2,1,1,1]
[3,1,5,4,7,8,2,6]=>[6,8,4,5,2,1,7,3]=>0101101=>[1,1,1,2,1,1]
[5,3,1,4,8,2,6,7]=>[4,6,8,5,1,7,3,2]=>0011011=>[2,2,1,2]
[5,2,4,8,6,1,3,7]=>[4,7,5,1,3,8,6,2]=>0110011=>[1,2,2,2]
[5,2,3,8,4,6,7,1]=>[4,7,6,1,5,3,2,8]=>0110110=>[1,2,1,2,1]
[4,8,2,3,6,1,7,5]=>[5,1,7,6,3,8,2,4]=>1011010=>[1,1,2,1,1,1]
[4,8,2,3,5,7,1,6]=>[5,1,7,6,4,2,8,3]=>1011101=>[1,1,3,1,1]
[1,4,7,8,3,6,2,5]=>[8,5,2,1,6,3,7,4]=>1110101=>[3,1,1,1,1]
[4,8,1,3,6,7,2,5]=>[5,1,8,6,3,2,7,4]=>1011101=>[1,1,3,1,1]
[5,3,8,2,4,7,1,6]=>[4,6,1,7,5,2,8,3]=>0101101=>[1,1,1,2,1,1]
[5,4,3,8,1,2,7,6]=>[4,5,6,1,8,7,2,3]=>0010110=>[2,1,1,2,1]
[6,4,2,8,1,3,7,5]=>[3,5,7,1,8,6,2,4]=>0010110=>[2,1,1,2,1]
[6,3,8,2,5,1,7,4]=>[3,6,1,7,4,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,3,8,1,4,7,2,5]=>[3,6,1,8,5,2,7,4]=>0101101=>[1,1,1,2,1,1]
[5,8,1,3,6,2,7,4]=>[4,1,8,6,3,7,2,5]=>1011010=>[1,1,2,1,1,1]
[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>1100110=>[2,2,2,1]
[5,8,1,4,2,6,3,7]=>[4,1,8,5,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,1,2,7,6,3]=>[4,1,5,8,7,2,3,6]=>1001100=>[1,2,2,2]
[6,5,1,2,8,7,3,4]=>[3,4,8,7,1,2,6,5]=>0011001=>[2,2,2,1]
[6,5,3,1,4,2,8,7]=>[3,4,6,8,5,7,1,2]=>0001010=>[3,1,1,1,1]
[5,3,1,6,4,2,7,8]=>[4,6,8,3,5,7,2,1]=>0010011=>[2,1,2,2]
[4,6,1,7,5,2,8,3]=>[5,3,8,2,4,7,1,6]=>1010010=>[1,1,1,2,1,1]
[4,5,1,7,2,6,3,8]=>[5,4,8,2,7,3,6,1]=>1010101=>[1,1,1,1,1,1,1]
[3,5,6,1,2,8,7,4]=>[6,4,3,8,7,1,2,5]=>1101100=>[2,1,2,2]
[3,5,7,1,8,6,2,4]=>[6,4,2,8,1,3,7,5]=>1101001=>[2,1,1,2,1]
[3,6,2,7,5,1,8,4]=>[6,3,7,2,4,8,1,5]=>1010010=>[1,1,1,2,1,1]
[4,2,5,7,1,8,6,3]=>[5,7,4,2,8,1,3,6]=>0110100=>[1,2,1,1,2]
[3,4,7,2,8,6,1,5]=>[6,5,2,7,1,3,8,4]=>1101001=>[2,1,1,2,1]
[3,4,5,8,2,7,1,6]=>[6,5,4,1,7,2,8,3]=>1110101=>[3,1,1,1,1]
[3,4,6,2,8,1,5,7]=>[6,5,3,7,1,8,4,2]=>1101011=>[2,1,1,1,2]
[3,5,2,6,8,1,7,4]=>[6,4,7,3,1,8,2,5]=>1011010=>[1,1,2,1,1,1]
[4,2,5,6,1,3,8,7]=>[5,7,4,3,8,6,1,2]=>0110110=>[1,2,1,2,1]
[4,3,1,2,5,6,8,7]=>[5,6,8,7,4,3,1,2]=>0011110=>[2,4,1]
[5,3,6,8,4,7,2,1]=>[4,6,3,1,5,2,7,8]=>0110100=>[1,2,1,1,2]
[3,7,2,5,4,8,6,1]=>[6,2,7,4,5,1,3,8]=>1010100=>[1,1,1,1,1,2]
[8,4,2,5,7,3,6,1]=>[1,5,7,4,2,6,3,8]=>0011010=>[2,2,1,1,1]
[4,7,2,5,8,3,6,1]=>[5,2,7,4,1,6,3,8]=>1011010=>[1,1,2,1,1,1]
[5,2,6,8,4,3,7,1]=>[4,7,3,1,5,6,2,8]=>0110010=>[1,2,2,1,1]
[3,1,6,5,4,8,2,7]=>[6,8,3,4,5,1,7,2]=>0100101=>[1,1,2,1,1,1]
[4,1,6,5,8,3,2,7]=>[5,8,3,4,1,6,7,2]=>0101001=>[1,1,1,1,2,1]
[5,1,6,8,4,3,2,7]=>[4,8,3,1,5,6,7,2]=>0110001=>[1,2,3,1]
[8,5,4,7,6,3,2,1]=>[1,4,5,2,3,6,7,8]=>0010000=>[2,1,4]
[5,7,1,8,4,3,2,6]=>[4,2,8,1,5,6,7,3]=>1010001=>[1,1,1,3,1]
[2,7,1,5,4,3,8,6]=>[7,2,8,4,5,6,1,3]=>1010010=>[1,1,1,2,1,1]
[8,2,1,5,4,3,7,6]=>[1,7,8,4,5,6,2,3]=>0010010=>[2,1,2,1,1]
[8,4,1,5,7,3,2,6]=>[1,5,8,4,2,6,7,3]=>0011001=>[2,2,2,1]
[8,4,6,1,7,3,2,5]=>[1,5,3,8,2,6,7,4]=>0101001=>[1,1,1,1,2,1]
[8,3,6,1,4,7,2,5]=>[1,6,3,8,5,2,7,4]=>0101101=>[1,1,1,2,1,1]
[2,7,6,1,4,3,8,5]=>[7,2,3,8,5,6,1,4]=>1001010=>[1,2,1,1,1,1]
[6,7,8,5,1,3,2,4]=>[3,2,1,4,8,6,7,5]=>1100101=>[2,2,1,1,1]
[5,7,2,8,4,3,6,1]=>[4,2,7,1,5,6,3,8]=>1010010=>[1,1,1,2,1,1]
[8,3,6,2,4,7,5,1]=>[1,6,3,7,5,2,4,8]=>0101100=>[1,1,1,2,2]
[3,7,6,2,4,8,5,1]=>[6,2,3,7,5,1,4,8]=>1001100=>[1,2,2,2]
[5,7,3,8,4,6,2,1]=>[4,2,6,1,5,3,7,8]=>1010100=>[1,1,1,1,1,2]
[4,7,3,5,8,6,2,1]=>[5,2,6,4,1,3,7,8]=>1011000=>[1,1,2,3]
[8,7,2,1,4,3,6,5]=>[1,2,7,8,5,6,3,4]=>0001010=>[3,1,1,1,1]
[8,7,3,1,4,6,2,5]=>[1,2,6,8,5,3,7,4]=>0001101=>[3,2,1,1]
[8,7,6,3,2,5,4,1]=>[1,2,3,6,7,4,5,8]=>0000100=>[4,1,2]
[8,7,3,5,1,6,2,4]=>[1,2,6,4,8,3,7,5]=>0010101=>[2,1,1,1,1,1]
[8,7,2,5,1,3,6,4]=>[1,2,7,4,8,6,3,5]=>0010110=>[2,1,1,2,1]
[8,2,6,5,1,3,7,4]=>[1,7,3,4,8,6,2,5]=>0100110=>[1,1,2,2,1]
[8,4,6,5,7,1,2,3]=>[1,5,3,4,2,8,7,6]=>0101011=>[1,1,1,1,1,2]
[4,7,6,5,8,1,2,3]=>[5,2,3,4,1,8,7,6]=>1001011=>[1,2,1,1,2]
[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>01111111=>[1,7]
[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>10111111=>[1,1,6]
[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>011111111=>[1,8]
[7,8,1,2,3,4,5,6,9]=>[3,2,9,8,7,6,5,4,1]=>10111111=>[1,1,6]
[1,8,9,2,3,4,5,6,7]=>[9,2,1,8,7,6,5,4,3]=>11011111=>[2,1,5]
[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>101111111=>[1,1,7]
[10,1,2,3,4,5,6,7,8,9,11]=>[2,11,10,9,8,7,6,5,4,3,1]=>0111111111=>[1,9]
[8,9,1,2,3,4,5,6,7,10]=>[3,2,10,9,8,7,6,5,4,1]=>101111111=>[1,1,7]
[7,1,8,2,3,4,5,6,9]=>[3,9,2,8,7,6,5,4,1]=>01011111=>[1,1,1,5]
[6,8,1,2,3,4,5,7,9]=>[4,2,9,8,7,6,5,3,1]=>10111111=>[1,1,6]
[1,8,2,9,3,4,5,6,7]=>[9,2,8,1,7,6,5,4,3]=>10101111=>[1,1,1,1,4]
[1,7,9,2,3,4,5,6,8]=>[9,3,1,8,7,6,5,4,2]=>11011111=>[2,1,5]
[1,9,10,2,3,4,5,6,7,8]=>[10,2,1,9,8,7,6,5,4,3]=>110111111=>[2,1,6]
[1,11,2,3,4,5,6,7,8,9,10]=>[11,1,10,9,8,7,6,5,4,3,2]=>1011111111=>[1,1,8]
[3,6,4,8,7,5,1,2]=>[6,3,5,1,2,4,8,7]=>1010001=>[1,1,1,3,1]
[5,6,4,3,8,7,1,2]=>[4,3,5,6,1,2,8,7]=>1001001=>[1,2,1,2,1]
[1,6,2,4,7,8,5,3]=>[8,3,7,5,2,1,4,6]=>1011100=>[1,1,3,2]
[3,6,2,4,8,1,5,7]=>[6,3,7,5,1,8,4,2]=>1011011=>[1,1,2,1,2]
[3,4,7,2,8,1,6,5]=>[6,5,2,7,1,8,3,4]=>1101010=>[2,1,1,1,1,1]
[1,4,7,2,5,8,6,3]=>[8,5,2,7,4,1,3,6]=>1101100=>[2,1,2,2]
[7,3,8,4,5,6,1,2]=>[2,6,1,5,4,3,8,7]=>0101101=>[1,1,1,2,1,1]
[3,5,6,4,8,7,1,2]=>[6,4,3,5,1,2,8,7]=>1101001=>[2,1,1,2,1]
[4,6,8,5,3,7,1,2]=>[5,3,1,4,6,2,8,7]=>1100101=>[2,2,1,1,1]
[6,8,5,3,4,7,1,2]=>[3,1,4,6,5,2,8,7]=>1001101=>[1,2,2,1,1]
[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>1000100=>[1,3,1,2]
[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>1001010=>[1,2,1,1,1,1]
[4,2,7,5,1,8,6,3]=>[5,7,2,4,8,1,3,6]=>0100100=>[1,1,2,1,2]
[7,8,1,4,2,6,5,3]=>[2,1,8,5,7,3,4,6]=>1010100=>[1,1,1,1,1,2]
[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>1101011=>[2,1,1,1,2]
[6,5,1,3,4,2,8,7]=>[3,4,8,6,5,7,1,2]=>0011010=>[2,2,1,1,1]
[4,8,5,3,1,7,2,6]=>[5,1,4,6,8,2,7,3]=>1000101=>[1,3,1,1,1]
[7,4,5,3,2,8,1,6]=>[2,5,4,6,7,1,8,3]=>0100101=>[1,1,2,1,1,1]
[5,8,3,6,1,4,2,7]=>[4,1,6,3,8,5,7,2]=>1010101=>[1,1,1,1,1,1,1]
[2,5,8,6,4,1,3,7]=>[7,4,1,3,5,8,6,2]=>1100011=>[2,3,2]
[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>1101101=>[2,1,2,1,1]
[3,6,2,5,8,1,7,4]=>[6,3,7,4,1,8,2,5]=>1011010=>[1,1,2,1,1,1]
[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>1100011=>[2,3,2]
[6,1,7,8,2,4,3,5]=>[3,8,2,1,7,5,6,4]=>0110101=>[1,2,1,1,1,1]
[7,1,8,6,3,4,2,5]=>[2,8,1,3,6,5,7,4]=>0100101=>[1,1,2,1,1,1]
[7,2,1,4,5,6,8,3]=>[2,7,8,5,4,3,1,6]=>0011110=>[2,4,1]
[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>1101010=>[2,1,1,1,1,1]
[6,1,3,2,7,5,8,4]=>[3,8,6,7,2,4,1,5]=>0101010=>[1,1,1,1,1,1,1]
[1,6,3,8,5,7,2,4]=>[8,3,6,1,4,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,1,7,5,8,3]=>[7,3,5,8,2,4,1,6]=>1001010=>[1,2,1,1,1,1]
[7,6,5,8,1,4,2,3]=>[2,3,4,1,8,5,7,6]=>0010101=>[2,1,1,1,1,1]
[5,8,6,7,3,2,1,4]=>[4,1,3,2,6,7,8,5]=>1010001=>[1,1,1,3,1]
[1,6,4,3,7,2,8,5]=>[8,3,5,6,2,7,1,4]=>1001010=>[1,2,1,1,1,1]
[2,6,3,4,8,7,1,5]=>[7,3,6,5,1,2,8,4]=>1011001=>[1,1,2,2,1]
[7,1,3,4,5,2,8,6]=>[2,8,6,5,4,7,1,3]=>0111010=>[1,3,1,1,1]
[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>1010010=>[1,1,1,2,1,1]
[4,1,6,3,8,2,7,5]=>[5,8,3,6,1,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,8,2,4,6,3,1,5]=>[2,1,7,5,3,6,8,4]=>1011001=>[1,1,2,2,1]
[3,2,6,4,7,8,1,5]=>[6,7,3,5,2,1,8,4]=>0101101=>[1,1,1,2,1,1]
[2,8,5,7,4,3,1,6]=>[7,1,4,2,5,6,8,3]=>1010001=>[1,1,1,3,1]
[7,2,5,8,3,4,1,6]=>[2,7,4,1,6,5,8,3]=>0110101=>[1,2,1,1,1,1]
[5,3,8,7,1,2,6,4]=>[4,6,1,2,8,7,3,5]=>0100110=>[1,1,2,2,1]
[6,5,3,8,2,1,7,4]=>[3,4,6,1,7,8,2,5]=>0010010=>[2,1,2,1,1]
[7,5,8,4,1,2,3,6]=>[2,4,1,5,8,7,6,3]=>0100111=>[1,1,2,3]
[5,8,7,4,1,3,2,6]=>[4,1,2,5,8,6,7,3]=>1000101=>[1,3,1,1,1]
[3,5,7,8,4,1,2,6]=>[6,4,2,1,5,8,7,3]=>1110011=>[3,2,2]
[1,4,7,5,3,8,2,6]=>[8,5,2,4,6,1,7,3]=>1100101=>[2,2,1,1,1]
[2,4,6,7,3,1,8,5]=>[7,5,3,2,6,8,1,4]=>1110010=>[3,2,1,1]
[7,8,4,6,3,1,2,5]=>[2,1,5,3,6,8,7,4]=>1010011=>[1,1,1,2,2]
[2,6,4,5,3,8,1,7]=>[7,3,5,4,6,1,8,2]=>1010101=>[1,1,1,1,1,1,1]
[3,6,5,8,4,2,1,7]=>[6,3,4,1,5,7,8,2]=>1010001=>[1,1,1,3,1]
[5,6,8,4,2,3,1,7]=>[4,3,1,5,7,6,8,2]=>1100101=>[2,2,1,1,1]
[6,8,5,4,3,1,2,7]=>[3,1,4,5,6,8,7,2]=>1000011=>[1,4,2]
[6,1,4,2,8,5,7,3]=>[3,8,5,7,1,4,2,6]=>0101010=>[1,1,1,1,1,1,1]
[4,8,6,5,3,2,7,1]=>[5,1,3,4,6,7,2,8]=>1000010=>[1,4,1,1]
[8,6,5,1,2,4,7,3]=>[1,3,4,8,7,5,2,6]=>0001110=>[3,3,1]
[6,7,5,8,2,1,4,3]=>[3,2,4,1,7,8,5,6]=>1010010=>[1,1,1,2,1,1]
[1,7,5,8,2,6,4,3]=>[8,2,4,1,7,3,5,6]=>1010100=>[1,1,1,1,1,2]
[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>1101001=>[2,1,1,2,1]
[6,3,8,5,7,1,2,4]=>[3,6,1,4,2,8,7,5]=>0101011=>[1,1,1,1,1,2]
[8,3,1,5,6,2,7,4]=>[1,6,8,4,3,7,2,5]=>0011010=>[2,2,1,1,1]
[6,8,5,2,1,4,7,3]=>[3,1,4,7,8,5,2,6]=>1000110=>[1,3,2,1]
[3,8,2,5,6,1,7,4]=>[6,1,7,4,3,8,2,5]=>1011010=>[1,1,2,1,1,1]
[2,8,1,5,6,3,7,4]=>[7,1,8,4,3,6,2,5]=>1011010=>[1,1,2,1,1,1]
[8,1,2,5,6,3,7,4]=>[1,8,7,4,3,6,2,5]=>0111010=>[1,3,1,1,1]
[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>1011001=>[1,1,2,2,1]
[5,1,8,6,2,7,3,4]=>[4,8,1,3,7,2,6,5]=>0100101=>[1,1,2,1,1,1]
[2,5,8,6,1,7,3,4]=>[7,4,1,3,8,2,6,5]=>1100101=>[2,2,1,1,1]
[8,6,1,5,7,2,3,4]=>[1,3,8,4,2,7,6,5]=>0011011=>[2,2,1,2]
[3,8,6,5,7,1,2,4]=>[6,1,3,4,2,8,7,5]=>1001011=>[1,2,1,1,2]
[7,6,5,8,1,2,4,3]=>[2,3,4,1,8,7,5,6]=>0010110=>[2,1,1,2,1]
[5,1,7,6,8,4,2,3]=>[4,8,2,3,1,5,7,6]=>0101001=>[1,1,1,1,2,1]
[5,1,3,7,8,6,2,4]=>[4,8,6,2,1,3,7,5]=>0111001=>[1,3,2,1]
[7,2,5,8,1,6,4,3]=>[2,7,4,1,8,3,5,6]=>0110100=>[1,2,1,1,2]
[3,2,8,5,7,6,1,4]=>[6,7,1,4,2,3,8,5]=>0101001=>[1,1,1,1,2,1]
[8,2,1,5,7,6,3,4]=>[1,7,8,4,2,3,6,5]=>0011001=>[2,2,2,1]
[5,2,8,6,1,7,3,4]=>[4,7,1,3,8,2,6,5]=>0100101=>[1,1,2,1,1,1]
[1,2,8,6,5,7,3,4]=>[8,7,1,3,4,2,6,5]=>1100101=>[2,2,1,1,1]
[4,2,1,3,6,7,8,5]=>[5,7,8,6,3,2,1,4]=>0011110=>[2,4,1]
[8,2,5,6,3,7,1,4]=>[1,7,4,3,6,2,8,5]=>0110101=>[1,2,1,1,1,1]
[7,2,6,5,4,1,8,3]=>[2,7,3,4,5,8,1,6]=>0100010=>[1,1,3,1,1]
[6,1,3,5,4,7,8,2]=>[3,8,6,4,5,2,1,7]=>0110110=>[1,2,1,2,1]
[6,1,5,3,4,7,8,2]=>[3,8,4,6,5,2,1,7]=>0101110=>[1,1,1,3,1]
[7,5,6,2,4,1,8,3]=>[2,4,3,7,5,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[8,5,2,6,3,7,1,4]=>[1,4,7,3,6,2,8,5]=>0010101=>[2,1,1,1,1,1]
[4,3,1,2,6,7,8,5]=>[5,6,8,7,3,2,1,4]=>0011110=>[2,4,1]
[8,1,6,5,7,3,2,4]=>[1,8,3,4,2,6,7,5]=>0101001=>[1,1,1,1,2,1]
[3,5,8,6,2,7,1,4]=>[6,4,1,3,7,2,8,5]=>1100101=>[2,2,1,1,1]
[5,8,1,6,3,7,2,4]=>[4,1,8,3,6,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,5,6,3,7,2,4]=>[8,1,4,3,6,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,6,5,4,2,8,3]=>[8,2,3,4,5,7,1,6]=>1000010=>[1,4,1,1]
[5,7,6,1,4,2,8,3]=>[4,2,3,8,5,7,1,6]=>1001010=>[1,2,1,1,1,1]
[7,1,4,2,6,5,8,3]=>[2,8,5,7,3,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[4,1,7,3,5,6,8,2]=>[5,8,2,6,4,3,1,7]=>0101110=>[1,1,1,3,1]
[2,7,4,1,5,6,8,3]=>[7,2,5,8,4,3,1,6]=>1001110=>[1,2,3,1]
[5,7,6,4,1,2,8,3]=>[4,2,3,5,8,7,1,6]=>1000110=>[1,3,2,1]
[4,7,6,1,5,2,8,3]=>[5,2,3,8,4,7,1,6]=>1001010=>[1,2,1,1,1,1]
[1,7,6,4,5,2,8,3]=>[8,2,3,5,4,7,1,6]=>1001010=>[1,2,1,1,1,1]
[1,8,3,6,5,7,2,4]=>[8,1,6,3,4,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[3,8,1,6,5,7,2,4]=>[6,1,8,3,4,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[8,1,3,5,7,6,2,4]=>[1,8,6,4,2,3,7,5]=>0111001=>[1,3,2,1]
[7,8,5,4,1,6,2,3]=>[2,1,4,5,8,3,7,6]=>1000101=>[1,3,1,1,1]
[6,1,5,4,3,7,8,2]=>[3,8,4,5,6,2,1,7]=>0100110=>[1,1,2,2,1]
[7,5,6,4,2,1,8,3]=>[2,4,3,5,7,8,1,6]=>0100010=>[1,1,3,1,1]
[8,3,2,6,5,7,1,4]=>[1,6,7,3,4,2,8,5]=>0010101=>[2,1,1,1,1,1]
[7,4,6,2,5,1,8,3]=>[2,5,3,7,4,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[6,1,4,3,5,7,8,2]=>[3,8,5,6,4,2,1,7]=>0101110=>[1,1,1,3,1]
[6,1,3,4,5,7,8,2]=>[3,8,6,5,4,2,1,7]=>0111110=>[1,5,1]
[7,2,6,4,5,1,8,3]=>[2,7,3,5,4,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,3,6,5,7,1,4]=>[1,7,6,3,4,2,8,5]=>0110101=>[1,2,1,1,1,1]
[5,4,7,3,6,8,1,2]=>[4,5,2,6,3,1,8,7]=>0101101=>[1,1,1,2,1,1]
[3,4,7,8,5,6,1,2]=>[6,5,2,1,4,3,8,7]=>1110101=>[3,1,1,1,1]
[3,4,7,2,5,1,6,8]=>[6,5,2,7,4,8,3,1]=>1101011=>[2,1,1,1,2]
[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>1101101=>[2,1,2,1,1]
[3,6,2,4,7,1,5,8]=>[6,3,7,5,2,8,4,1]=>1011011=>[1,1,2,1,2]
[6,8,3,4,5,7,1,2]=>[3,1,6,5,4,2,8,7]=>1011101=>[1,1,3,1,1]
[4,3,6,7,5,8,1,2]=>[5,6,3,2,4,1,8,7]=>0110101=>[1,2,1,1,1,1]
[6,3,7,5,8,4,1,2]=>[3,6,2,4,1,5,8,7]=>0101001=>[1,1,1,1,2,1]
[7,3,8,6,4,5,1,2]=>[2,6,1,3,5,4,8,7]=>0100101=>[1,1,2,1,1,1]
[3,2,7,6,5,1,4,8]=>[6,7,2,3,4,8,5,1]=>0100011=>[1,1,3,2]
[1,2,7,6,5,8,3,4]=>[8,7,2,3,4,1,6,5]=>1100101=>[2,2,1,1,1]
[4,8,2,6,1,5,3,7]=>[5,1,7,3,8,4,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,3,8,6,4,1,5,7]=>[7,6,1,3,5,8,4,2]=>1100011=>[2,3,2]
[4,3,6,2,5,1,8,7]=>[5,6,3,7,4,8,1,2]=>0101010=>[1,1,1,1,1,1,1]
[7,8,3,2,5,1,4,6]=>[2,1,6,7,4,8,5,3]=>1001011=>[1,2,1,1,2]
[7,8,1,2,5,6,3,4]=>[2,1,8,7,4,3,6,5]=>1011101=>[1,1,3,1,1]
[4,1,6,2,5,7,3,8]=>[5,8,3,7,4,2,6,1]=>0101101=>[1,1,1,2,1,1]
[6,1,2,5,8,7,3,4]=>[3,8,7,4,1,2,6,5]=>0111001=>[1,3,2,1]
[2,1,8,6,4,7,3,5]=>[7,8,1,3,5,2,6,4]=>0100101=>[1,1,2,1,1,1]
[7,1,3,6,8,4,2,5]=>[2,8,6,3,1,5,7,4]=>0111001=>[1,3,2,1]
[1,8,3,6,7,4,5,2]=>[8,1,6,3,2,5,4,7]=>1011010=>[1,1,2,1,1,1]
[7,1,5,8,3,6,2,4]=>[2,8,4,1,6,3,7,5]=>0110101=>[1,2,1,1,1,1]
[5,1,8,7,2,3,6,4]=>[4,8,1,2,7,6,3,5]=>0100110=>[1,1,2,2,1]
[6,1,5,7,4,2,8,3]=>[3,8,4,2,5,7,1,6]=>0110010=>[1,2,2,1,1]
[3,1,6,4,7,2,5,8]=>[6,8,3,5,2,7,4,1]=>0101011=>[1,1,1,1,1,2]
[2,4,7,5,1,8,3,6]=>[7,5,2,4,8,1,6,3]=>1100101=>[2,2,1,1,1]
[6,5,7,1,4,2,3,8]=>[3,4,2,8,5,7,6,1]=>0101011=>[1,1,1,1,1,2]
[5,6,8,1,3,2,4,7]=>[4,3,1,8,6,7,5,2]=>1101011=>[2,1,1,1,2]
[6,8,5,1,3,4,2,7]=>[3,1,4,8,6,5,7,2]=>1001101=>[1,2,2,1,1]
[2,8,3,4,5,1,7,6]=>[7,1,6,5,4,8,2,3]=>1011010=>[1,1,2,1,1,1]
[6,2,4,3,1,5,7,8]=>[3,7,5,6,8,4,2,1]=>0100111=>[1,1,2,3]
[4,2,8,3,1,7,5,6]=>[5,7,1,6,8,2,4,3]=>0100101=>[1,1,2,1,1,1]
[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>1101011=>[2,1,1,1,2]
[5,3,7,4,1,6,2,8]=>[4,6,2,5,8,3,7,1]=>0100101=>[1,1,2,1,1,1]
[2,4,7,3,6,1,8,5]=>[7,5,2,6,3,8,1,4]=>1101010=>[2,1,1,1,1,1]
[5,8,7,6,3,1,2,4]=>[4,1,2,3,6,8,7,5]=>1000011=>[1,4,2]
[7,5,6,8,1,4,3,2]=>[2,4,3,1,8,5,6,7]=>0110100=>[1,2,1,1,2]
[2,4,7,1,6,5,3,8]=>[7,5,2,8,3,4,6,1]=>1101001=>[2,1,1,2,1]
[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>1110001=>[3,3,1]
[6,3,1,2,8,4,5,7]=>[3,6,8,7,1,5,4,2]=>0011011=>[2,2,1,2]
[4,2,1,3,6,5,8,7]=>[5,7,8,6,3,4,1,2]=>0011010=>[2,2,1,1,1]
[2,8,1,4,5,6,3,7]=>[7,1,8,5,4,3,6,2]=>1011101=>[1,1,3,1,1]
[7,2,1,5,4,6,3,8]=>[2,7,8,4,5,3,6,1]=>0010101=>[2,1,1,1,1,1]
[4,2,6,1,8,5,3,7]=>[5,7,3,8,1,4,6,2]=>0101001=>[1,1,1,1,2,1]
[7,8,2,1,4,5,3,6]=>[2,1,7,8,5,4,6,3]=>1001101=>[1,2,2,1,1]
[7,8,4,1,5,3,6,2]=>[2,1,5,8,4,6,3,7]=>1001010=>[1,2,1,1,1,1]
[3,4,6,1,5,8,7,2]=>[6,5,3,8,4,1,2,7]=>1101100=>[2,1,2,2]
[7,5,1,6,4,3,8,2]=>[2,4,8,3,5,6,1,7]=>0010010=>[2,1,2,1,1]
[5,8,1,6,3,4,7,2]=>[4,1,8,3,6,5,2,7]=>1010110=>[1,1,1,1,2,1]
[6,5,1,8,2,7,4,3]=>[3,4,8,1,7,2,5,6]=>0010100=>[2,1,1,1,2]
[6,8,1,7,5,2,3,4]=>[3,1,8,2,4,7,6,5]=>1010011=>[1,1,1,2,2]
[7,6,1,8,5,3,2,4]=>[2,3,8,1,4,6,7,5]=>0010001=>[2,1,3,1]
[5,6,1,7,4,8,2,3]=>[4,3,8,2,5,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,6,1,5,7,4,2,8]=>[6,3,8,4,2,5,7,1]=>1011001=>[1,1,2,2,1]
[2,5,6,1,7,4,8,3]=>[7,4,3,8,2,5,1,6]=>1101010=>[2,1,1,1,1,1]
[3,1,7,5,6,4,8,2]=>[6,8,2,4,3,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,1,7,6,4,8,3,2]=>[4,8,2,3,5,1,6,7]=>0100100=>[1,1,2,1,2]
[6,1,7,8,5,3,4,2]=>[3,8,2,1,4,6,5,7]=>0110010=>[1,2,2,1,1]
[7,1,8,6,5,4,2,3]=>[2,8,1,3,4,5,7,6]=>0100001=>[1,1,4,1]
[2,6,5,7,3,4,8,1]=>[7,3,4,2,6,5,1,8]=>1010110=>[1,1,1,1,2,1]
[1,6,4,7,5,8,2,3]=>[8,3,5,2,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[8,5,3,6,2,7,4,1]=>[1,4,6,3,7,2,5,8]=>0010100=>[2,1,1,1,2]
[1,3,7,4,6,8,2,5]=>[8,6,2,5,3,1,7,4]=>1101101=>[2,1,2,1,1]
[4,7,5,6,3,2,8,1]=>[5,2,4,3,6,7,1,8]=>1010010=>[1,1,1,2,1,1]
[1,7,6,5,4,8,2,3]=>[8,2,3,4,5,1,7,6]=>1000101=>[1,3,1,1,1]
[8,1,6,5,7,2,4,3]=>[1,8,3,4,2,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>1101011=>[2,1,1,1,2]
[6,1,7,5,3,8,2,4]=>[3,8,2,4,6,1,7,5]=>0100101=>[1,1,2,1,1,1]
[2,1,7,5,6,8,3,4]=>[7,8,2,4,3,1,6,5]=>0101101=>[1,1,1,2,1,1]
[5,4,1,7,6,8,2,3]=>[4,5,8,2,3,1,7,6]=>0010101=>[2,1,1,1,1,1]
[4,8,5,6,2,7,3,1]=>[5,1,4,3,7,2,6,8]=>1010100=>[1,1,1,1,1,2]
[3,8,6,4,2,7,5,1]=>[6,1,3,5,7,2,4,8]=>1000100=>[1,3,1,2]
[7,8,5,2,4,6,3,1]=>[2,1,4,7,5,3,6,8]=>1001100=>[1,2,2,2]
[2,8,6,3,7,4,5,1]=>[7,1,3,6,2,5,4,8]=>1001010=>[1,2,1,1,1,1]
[7,8,1,6,2,4,5,3]=>[2,1,8,3,7,5,4,6]=>1010110=>[1,1,1,1,2,1]
[6,8,1,4,7,2,5,3]=>[3,1,8,5,2,7,4,6]=>1011010=>[1,1,2,1,1,1]
[3,8,4,1,7,2,6,5]=>[6,1,5,8,2,7,3,4]=>1001010=>[1,2,1,1,1,1]
[5,4,7,1,8,3,2,6]=>[4,5,2,8,1,6,7,3]=>0101001=>[1,1,1,1,2,1]
[3,7,4,1,8,5,2,6]=>[6,2,5,8,1,4,7,3]=>1001001=>[1,2,1,2,1]
[6,7,1,4,8,3,2,5]=>[3,2,8,5,1,6,7,4]=>1011001=>[1,1,2,2,1]
[2,7,1,8,4,5,3,6]=>[7,2,8,1,5,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[6,1,2,8,4,3,5,7]=>[3,8,7,1,5,6,4,2]=>0110011=>[1,2,2,2]
[6,5,1,4,3,8,2,7]=>[3,4,8,5,6,1,7,2]=>0010101=>[2,1,1,1,1,1]
[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>1011011=>[1,1,2,1,2]
[8,5,1,3,7,2,6,4]=>[1,4,8,6,2,7,3,5]=>0011010=>[2,2,1,1,1]
[8,4,2,1,7,3,6,5]=>[1,5,7,8,2,6,3,4]=>0001010=>[3,1,1,1,1]
[7,4,2,1,8,5,3,6]=>[2,5,7,8,1,4,6,3]=>0001001=>[3,1,2,1]
[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>1001011=>[1,2,1,1,2]
[6,4,3,1,5,8,2,7]=>[3,5,6,8,4,1,7,2]=>0001101=>[3,2,1,1]
[3,7,6,8,4,5,2,1]=>[6,2,3,1,5,4,7,8]=>1010100=>[1,1,1,1,1,2]
[2,7,6,8,5,3,4,1]=>[7,2,3,1,4,6,5,8]=>1010010=>[1,1,1,2,1,1]
[1,7,6,8,5,4,2,3]=>[8,2,3,1,4,5,7,6]=>1010001=>[1,1,1,3,1]
[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>1101001=>[2,1,1,2,1]
[2,4,8,6,7,3,5,1]=>[7,5,1,3,2,6,4,8]=>1101010=>[2,1,1,1,1,1]
[7,3,8,5,4,6,2,1]=>[2,6,1,4,5,3,7,8]=>0100100=>[1,1,2,1,2]
[3,4,8,5,6,7,2,1]=>[6,5,1,4,3,2,7,8]=>1101100=>[2,1,2,2]
[6,3,5,8,4,7,2,1]=>[3,6,4,1,5,2,7,8]=>0110100=>[1,2,1,1,2]
[5,4,3,8,6,7,2,1]=>[4,5,6,1,3,2,7,8]=>0010100=>[2,1,1,1,2]
[5,4,2,8,7,3,6,1]=>[4,5,7,1,2,6,3,8]=>0010010=>[2,1,2,1,1]
[6,2,5,8,7,3,4,1]=>[3,7,4,1,2,6,5,8]=>0110010=>[1,2,2,1,1]
[3,2,8,5,7,4,6,1]=>[6,7,1,4,2,5,3,8]=>0101010=>[1,1,1,1,1,1,1]
[1,3,8,7,5,6,2,4]=>[8,6,1,2,4,3,7,5]=>1100101=>[2,2,1,1,1]
[2,1,8,7,4,6,3,5]=>[7,8,1,2,5,3,6,4]=>0100101=>[1,1,2,1,1,1]
[3,1,8,5,7,6,2,4]=>[6,8,1,4,2,3,7,5]=>0101001=>[1,1,1,1,2,1]
[6,1,5,8,7,4,2,3]=>[3,8,4,1,2,5,7,6]=>0110001=>[1,2,3,1]
[5,4,1,8,7,6,2,3]=>[4,5,8,1,2,3,7,6]=>0010001=>[2,1,3,1]
[5,8,6,7,4,3,2,1]=>[4,1,3,2,5,6,7,8]=>1010000=>[1,1,1,4]
[4,8,7,5,6,3,2,1]=>[5,1,2,4,3,6,7,8]=>1001000=>[1,2,1,3]
[4,2,1,6,3,5,8,7]=>[5,7,8,3,6,4,1,2]=>0010110=>[2,1,1,2,1]
[6,2,1,4,3,5,8,7]=>[3,7,8,5,6,4,1,2]=>0010110=>[2,1,1,2,1]
[6,2,1,4,3,8,5,7]=>[3,7,8,5,6,1,4,2]=>0010101=>[2,1,1,1,1,1]
[8,2,1,4,3,6,5,7]=>[1,7,8,5,6,3,4,2]=>0010101=>[2,1,1,1,1,1]
[8,2,4,1,3,6,5,7]=>[1,7,5,8,6,3,4,2]=>0101101=>[1,1,1,2,1,1]
[6,2,4,1,3,8,5,7]=>[3,7,5,8,6,1,4,2]=>0101101=>[1,1,1,2,1,1]
[6,2,4,1,3,5,8,7]=>[3,7,5,8,6,4,1,2]=>0101110=>[1,1,1,3,1]
[4,2,6,1,3,5,8,7]=>[5,7,3,8,6,4,1,2]=>0101110=>[1,1,1,3,1]
[2,1,6,4,3,5,8,7]=>[7,8,3,5,6,4,1,2]=>0100110=>[1,1,2,2,1]
[2,6,1,4,3,5,8,7]=>[7,3,8,5,6,4,1,2]=>1010110=>[1,1,1,1,2,1]
[2,6,4,1,3,5,8,7]=>[7,3,5,8,6,4,1,2]=>1001110=>[1,2,3,1]
[4,6,2,1,3,5,8,7]=>[5,3,7,8,6,4,1,2]=>1001110=>[1,2,3,1]
[6,4,2,1,3,5,8,7]=>[3,5,7,8,6,4,1,2]=>0001110=>[3,3,1]
[8,4,2,1,3,6,5,7]=>[1,5,7,8,6,3,4,2]=>0001101=>[3,2,1,1]
[8,4,2,1,6,3,5,7]=>[1,5,7,8,3,6,4,2]=>0001011=>[3,1,1,2]
[6,4,2,1,8,3,5,7]=>[3,5,7,8,1,6,4,2]=>0001011=>[3,1,1,2]
[4,6,2,1,8,3,5,7]=>[5,3,7,8,1,6,4,2]=>1001011=>[1,2,1,1,2]
[2,6,1,4,3,8,5,7]=>[7,3,8,5,6,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,1,6,4,3,8,5,7]=>[7,8,3,5,6,1,4,2]=>0100101=>[1,1,2,1,1,1]
[2,1,8,4,3,6,5,7]=>[7,8,1,5,6,3,4,2]=>0100101=>[1,1,2,1,1,1]
[2,8,1,4,3,6,5,7]=>[7,1,8,5,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,4,1,3,6,5,7]=>[7,1,5,8,6,3,4,2]=>1001101=>[1,2,2,1,1]
[4,8,2,1,3,6,5,7]=>[5,1,7,8,6,3,4,2]=>1001101=>[1,2,2,1,1]
[4,8,2,1,6,3,5,7]=>[5,1,7,8,3,6,4,2]=>1001011=>[1,2,1,1,2]
[6,8,2,1,4,3,5,7]=>[3,1,7,8,5,6,4,2]=>1001011=>[1,2,1,1,2]
[8,6,2,1,4,3,5,7]=>[1,3,7,8,5,6,4,2]=>0001011=>[3,1,1,2]
[2,8,1,4,6,3,5,7]=>[7,1,8,5,3,6,4,2]=>1011011=>[1,1,2,1,2]
[2,1,8,4,6,3,5,7]=>[7,8,1,5,3,6,4,2]=>0101011=>[1,1,1,1,1,2]
[2,1,6,4,8,3,5,7]=>[7,8,3,5,1,6,4,2]=>0101011=>[1,1,1,1,1,2]
[2,6,1,4,8,3,5,7]=>[7,3,8,5,1,6,4,2]=>1011011=>[1,1,2,1,2]
[2,6,4,1,8,3,5,7]=>[7,3,5,8,1,6,4,2]=>1001011=>[1,2,1,1,2]
[2,6,4,8,1,3,5,7]=>[7,3,5,1,8,6,4,2]=>1010111=>[1,1,1,1,3]
[4,6,2,8,1,3,5,7]=>[5,3,7,1,8,6,4,2]=>1010111=>[1,1,1,1,3]
[4,2,6,1,3,8,5,7]=>[5,7,3,8,6,1,4,2]=>0101101=>[1,1,1,2,1,1]
[4,2,6,1,8,3,5,7]=>[5,7,3,8,1,6,4,2]=>0101011=>[1,1,1,1,1,2]
[6,2,4,1,8,3,5,7]=>[3,7,5,8,1,6,4,2]=>0101011=>[1,1,1,1,1,2]
[8,2,4,1,6,3,5,7]=>[1,7,5,8,3,6,4,2]=>0101011=>[1,1,1,1,1,2]
[8,2,1,4,6,3,5,7]=>[1,7,8,5,3,6,4,2]=>0011011=>[2,2,1,2]
[6,2,1,4,8,3,5,7]=>[3,7,8,5,1,6,4,2]=>0011011=>[2,2,1,2]
[4,2,1,6,8,3,5,7]=>[5,7,8,3,1,6,4,2]=>0011011=>[2,2,1,2]
[4,2,1,6,3,8,5,7]=>[5,7,8,3,6,1,4,2]=>0010101=>[2,1,1,1,1,1]
[4,2,1,3,6,8,5,7]=>[5,7,8,6,3,1,4,2]=>0011101=>[2,3,1,1]
[2,1,4,3,8,6,5,7]=>[7,8,5,6,1,3,4,2]=>0101001=>[1,1,1,1,2,1]
[2,4,1,3,8,6,5,7]=>[7,5,8,6,1,3,4,2]=>1011001=>[1,1,2,2,1]
[4,2,1,3,8,6,5,7]=>[5,7,8,6,1,3,4,2]=>0011001=>[2,2,2,1]
[4,2,1,8,3,6,5,7]=>[5,7,8,1,6,3,4,2]=>0010101=>[2,1,1,1,1,1]
[4,2,1,8,6,3,5,7]=>[5,7,8,1,3,6,4,2]=>0010011=>[2,1,2,2]
[6,2,1,8,4,3,5,7]=>[3,7,8,1,5,6,4,2]=>0010011=>[2,1,2,2]
[8,2,1,6,4,3,5,7]=>[1,7,8,3,5,6,4,2]=>0010011=>[2,1,2,2]
[8,2,6,1,4,3,5,7]=>[1,7,3,8,5,6,4,2]=>0101011=>[1,1,1,1,1,2]
[6,2,8,1,4,3,5,7]=>[3,7,1,8,5,6,4,2]=>0101011=>[1,1,1,1,1,2]
[4,2,8,1,6,3,5,7]=>[5,7,1,8,3,6,4,2]=>0101011=>[1,1,1,1,1,2]
[4,2,8,1,3,6,5,7]=>[5,7,1,8,6,3,4,2]=>0101101=>[1,1,1,2,1,1]
[2,4,8,1,3,6,5,7]=>[7,5,1,8,6,3,4,2]=>1101101=>[2,1,2,1,1]
[2,4,1,8,3,6,5,7]=>[7,5,8,1,6,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[2,1,4,8,3,6,5,7]=>[7,8,5,1,6,3,4,2]=>0110101=>[1,2,1,1,1,1]
[2,1,4,8,6,3,5,7]=>[7,8,5,1,3,6,4,2]=>0110011=>[1,2,2,2]
[2,4,8,1,6,3,5,7]=>[7,5,1,8,3,6,4,2]=>1101011=>[2,1,1,1,2]
[2,4,8,6,1,3,5,7]=>[7,5,1,3,8,6,4,2]=>1100111=>[2,2,3]
[4,2,8,6,1,3,5,7]=>[5,7,1,3,8,6,4,2]=>0100111=>[1,1,2,3]
[6,2,8,4,1,3,5,7]=>[3,7,1,5,8,6,4,2]=>0100111=>[1,1,2,3]
[8,2,6,4,1,3,5,7]=>[1,7,3,5,8,6,4,2]=>0100111=>[1,1,2,3]
[8,4,6,2,1,3,5,7]=>[1,5,3,7,8,6,4,2]=>0100111=>[1,1,2,3]
[6,4,8,2,1,3,5,7]=>[3,5,1,7,8,6,4,2]=>0100111=>[1,1,2,3]
[4,6,8,2,1,3,5,7]=>[5,3,1,7,8,6,4,2]=>1100111=>[2,2,3]
[2,6,8,4,1,3,5,7]=>[7,3,1,5,8,6,4,2]=>1100111=>[2,2,3]
[2,6,8,1,4,3,5,7]=>[7,3,1,8,5,6,4,2]=>1101011=>[2,1,1,1,2]
[2,6,1,8,4,3,5,7]=>[7,3,8,1,5,6,4,2]=>1010011=>[1,1,1,2,2]
[2,1,6,8,4,3,5,7]=>[7,8,3,1,5,6,4,2]=>0110011=>[1,2,2,2]
[2,1,8,6,4,3,5,7]=>[7,8,1,3,5,6,4,2]=>0100011=>[1,1,3,2]
[2,8,1,6,4,3,5,7]=>[7,1,8,3,5,6,4,2]=>1010011=>[1,1,1,2,2]
[2,8,6,4,1,3,5,7]=>[7,1,3,5,8,6,4,2]=>1000111=>[1,3,3]
[4,8,6,2,1,3,5,7]=>[5,1,3,7,8,6,4,2]=>1000111=>[1,3,3]
[6,8,4,2,1,3,5,7]=>[3,1,5,7,8,6,4,2]=>1000111=>[1,3,3]
[3,2,6,1,5,4,8,7]=>[6,7,3,8,4,5,1,2]=>0101010=>[1,1,1,1,1,1,1]
[5,2,4,3,8,1,7,6]=>[4,7,5,6,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[6,2,4,1,5,3,8,7]=>[3,7,5,8,4,6,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,1,5,2,8,7]=>[5,6,3,8,4,7,1,2]=>0101010=>[1,1,1,1,1,1,1]
[4,3,5,2,8,1,7,6]=>[5,6,4,7,1,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,3,7,2,6,5,8,1]=>[5,6,2,7,3,4,1,8]=>0101010=>[1,1,1,1,1,1,1]
[4,3,8,2,6,1,7,5]=>[5,6,1,7,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[4,3,8,1,7,2,6,5]=>[5,6,1,8,2,7,3,4]=>0101010=>[1,1,1,1,1,1,1]
[4,3,8,1,5,2,7,6]=>[5,6,1,8,4,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,1,8,3,4,2,7,6]=>[4,8,1,6,5,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,4,8,1,3,2,7,6]=>[4,5,1,8,6,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[2,1,5,4,8,3,7,6]=>[7,8,4,5,1,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,1,7,6,8,3,4,2]=>[4,8,2,3,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,7,6,8,1,5,2]=>[5,6,2,3,1,8,4,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,7,1,8,5,6,2]=>[5,6,2,8,1,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,3,6,5,8,1,7,2]=>[5,6,3,4,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[6,3,5,4,7,2,8,1]=>[3,6,4,5,2,7,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,3,5,4,8,1,7,2]=>[3,6,4,5,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[7,1,6,3,8,4,5,2]=>[2,8,3,6,1,5,4,7]=>0101010=>[1,1,1,1,1,1,1]
[7,4,6,5,8,1,3,2]=>[2,5,3,4,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[2,1,8,4,6,3,7,5]=>[7,8,1,5,3,6,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,4,6,1,3,2,7,5]=>[1,5,3,8,6,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,6,3,4,2,7,5]=>[1,8,3,6,5,7,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,1,6,3,7,2,5,4]=>[1,8,3,6,2,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,1,7,2,6,4]=>[1,6,4,8,2,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,3,5,2,6,1,7,4]=>[1,6,4,7,3,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[7,3,5,2,6,4,8,1]=>[2,6,4,7,3,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[8,2,6,3,5,1,7,4]=>[1,7,3,6,4,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,7,1,5,3,6,4]=>[1,7,2,8,4,6,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,1,5,3,7,6]=>[1,7,5,8,4,6,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,1,7,3,6,5]=>[1,7,5,8,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,3,6,1,7,5]=>[1,7,5,6,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,4,6,1,7,5]=>[6,7,1,5,3,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,1,5,4,7,6]=>[6,7,1,8,4,5,2,3]=>0101010=>[1,1,1,1,1,1,1]
[3,2,7,6,8,1,5,4]=>[6,7,2,3,1,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,7,1,8,5,6,4]=>[6,7,2,8,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,5,8,1,7,4]=>[6,7,3,4,1,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,2,4,3,8,1]=>[3,4,2,7,5,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[6,5,8,2,4,1,7,3]=>[3,4,1,7,5,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[7,2,4,1,8,5,6,3]=>[2,7,5,8,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]
[7,6,8,2,4,1,5,3]=>[2,3,1,7,5,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[7,6,8,1,5,2,4,3]=>[2,3,1,8,4,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,7,3,8,5,6,4]=>[7,8,2,6,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,1,3,2,8,5,6,4]=>[2,8,6,7,1,4,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,1,8,5,6,2,4,3]=>[2,8,1,4,3,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[7,1,8,2,6,4,5,3]=>[2,8,1,7,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[7,2,8,1,5,4,6,3]=>[2,7,1,8,4,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[6,2,7,4,5,3,8,1]=>[3,7,2,5,4,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,4,7,2,6,3,8,1]=>[4,5,2,7,3,6,1,8]=>0101010=>[1,1,1,1,1,1,1]
[5,4,8,2,6,1,7,3]=>[4,5,1,7,3,8,2,6]=>0101010=>[1,1,1,1,1,1,1]
[6,5,8,1,7,2,4,3]=>[3,4,1,8,2,7,5,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,6,5,8,3,7,4]=>[7,8,3,4,1,6,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,4,8,1,3,2]=>[3,4,2,5,1,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[6,5,7,1,8,3,4,2]=>[3,4,2,8,1,6,5,7]=>0101010=>[1,1,1,1,1,1,1]
[6,1,7,4,8,3,5,2]=>[3,8,2,5,1,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,7,1,8,3,6,2]=>[4,5,2,8,1,6,3,7]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,3,8,1,7,2]=>[4,5,3,6,1,8,2,7]=>0101010=>[1,1,1,1,1,1,1]
[2,1,4,3,9,10,11,12,8,7,6,5]=>[11,12,9,10,4,3,2,1,5,6,7,8]=>01011110000=>[1,1,1,4,4]
[2,1,5,6,4,3,8,7,10,9,12,11]=>[11,12,8,7,9,10,5,6,3,4,1,2]=>01100101010=>[1,2,2,1,1,1,1,1,1]
[2,1,5,7,4,8,6,3,10,9,12,11]=>[11,12,8,6,9,5,7,10,3,4,1,2]=>01101001010=>[1,2,1,1,2,1,1,1,1]
[2,1,5,7,4,9,6,10,8,3,12,11]=>[11,12,8,6,9,4,7,3,5,10,1,2]=>01101010010=>[1,2,1,1,1,1,2,1,1]
[2,1,5,7,4,9,6,11,8,12,10,3]=>[11,12,8,6,9,4,7,2,5,1,3,10]=>01101010100=>[1,2,1,1,1,1,1,1,2]
[2,1,5,9,4,10,11,12,8,7,6,3]=>[11,12,8,4,9,3,2,1,5,6,7,10]=>01101110000=>[1,2,1,3,4]
[2,1,6,9,10,5,11,12,8,7,4,3]=>[11,12,7,4,3,8,2,1,5,6,9,10]=>01110110000=>[1,3,1,2,4]
[2,1,8,9,10,11,12,7,6,5,4,3]=>[11,12,5,4,3,2,1,6,7,8,9,10]=>01111100000=>[1,5,5]
[3,4,2,1,6,5,8,7,10,9,12,11]=>[10,9,11,12,7,8,5,6,3,4,1,2]=>10010101010=>[1,2,1,1,1,1,1,1,1,1]
[3,5,2,6,4,1,8,7,10,9,12,11]=>[10,8,11,7,9,12,5,6,3,4,1,2]=>10100101010=>[1,1,1,2,1,1,1,1,1,1]
[3,5,2,7,4,8,6,1,10,9,12,11]=>[10,8,11,6,9,5,7,12,3,4,1,2]=>10101001010=>[1,1,1,1,1,2,1,1,1,1]
[3,5,2,7,4,9,6,10,8,1,12,11]=>[10,8,11,6,9,4,7,3,5,12,1,2]=>10101010010=>[1,1,1,1,1,1,1,2,1,1]
[3,8,2,9,10,11,12,7,6,5,4,1]=>[10,5,11,4,3,2,1,6,7,8,9,12]=>10111100000=>[1,1,4,5]
[6,7,8,9,10,5,4,3,2,1,12,11]=>[7,6,5,4,3,8,9,10,11,12,1,2]=>11110000010=>[4,5,1,1]
[2,8,3,1,5,4,6,7]=>[7,1,6,8,4,5,3,2]=>1001011=>[1,2,1,1,2]
[2,5,3,4,7,1,8,6]=>[7,4,6,5,2,8,1,3]=>1011010=>[1,1,2,1,1,1]
[2,4,8,3,5,7,6,1]=>[7,5,1,6,4,2,3,8]=>1101100=>[2,1,2,2]
[4,2,5,3,1,8,6,7]=>[5,7,4,6,8,1,3,2]=>0100101=>[1,1,2,1,1,1]
[4,2,1,8,5,3,6,7]=>[5,7,8,1,4,6,3,2]=>0010011=>[2,1,2,2]
[5,4,1,3,8,2,6,7]=>[4,5,8,6,1,7,3,2]=>0011011=>[2,2,1,2]
[5,1,4,8,3,2,6,7]=>[4,8,5,1,6,7,3,2]=>0110011=>[1,2,2,2]
[1,5,8,4,3,2,6,7]=>[8,4,1,5,6,7,3,2]=>1100011=>[2,3,2]
[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>1000011=>[1,4,2]
[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>1001001=>[1,2,1,2,1]
[1,5,7,3,8,4,2,6]=>[8,4,2,6,1,5,7,3]=>1101001=>[2,1,1,2,1]
[5,1,4,7,8,3,2,6]=>[4,8,5,2,1,6,7,3]=>0111001=>[1,3,2,1]
[4,8,1,5,7,3,6,2]=>[5,1,8,4,2,6,3,7]=>1011010=>[1,1,2,1,1,1]
[8,1,5,3,7,4,6,2]=>[1,8,4,6,2,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[3,8,4,7,6,5,2,1]=>[6,1,5,2,3,4,7,8]=>1010000=>[1,1,1,4]
[1,6,8,5,3,7,4,2]=>[8,3,1,4,6,2,5,7]=>1100100=>[2,2,1,2]
[6,8,1,7,4,3,5,2]=>[3,1,8,2,5,6,4,7]=>1010010=>[1,1,1,2,1,1]
[6,4,8,1,7,3,5,2]=>[3,5,1,8,2,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[6,4,8,7,1,5,2,3]=>[3,5,1,2,8,4,7,6]=>0100101=>[1,1,2,1,1,1]
[7,6,4,1,3,8,2,5]=>[2,3,5,8,6,1,7,4]=>0001101=>[3,2,1,1]
[1,7,5,6,3,2,8,4]=>[8,2,4,3,6,7,1,5]=>1010010=>[1,1,1,2,1,1]
[4,2,1,7,8,5,3,6]=>[5,7,8,2,1,4,6,3]=>0011001=>[2,2,2,1]
[2,7,4,6,3,1,8,5]=>[7,2,5,3,6,8,1,4]=>1010010=>[1,1,1,2,1,1]
[2,6,8,4,3,7,5,1]=>[7,3,1,5,6,2,4,8]=>1100100=>[2,2,1,2]
[6,2,4,8,3,7,5,1]=>[3,7,5,1,6,2,4,8]=>0110100=>[1,2,1,1,2]
[7,2,6,3,4,1,8,5]=>[2,7,3,6,5,8,1,4]=>0101010=>[1,1,1,1,1,1,1]
[2,6,7,3,1,4,8,5]=>[7,3,2,6,8,5,1,4]=>1100110=>[2,2,2,1]
[2,7,1,8,3,5,4,6]=>[7,2,8,1,6,4,5,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,7,3,5,8,4,6]=>[7,8,2,6,4,1,5,3]=>0101101=>[1,1,1,2,1,1]
[8,7,1,3,6,2,4,5]=>[1,2,8,6,3,7,5,4]=>0011011=>[2,2,1,2]
[8,2,1,7,3,5,6,4]=>[1,7,8,2,6,4,3,5]=>0010110=>[2,1,1,2,1]
[7,8,2,6,3,1,5,4]=>[2,1,7,3,6,8,4,5]=>1010010=>[1,1,1,2,1,1]
[8,7,2,6,3,5,4,1]=>[1,2,7,3,6,4,5,8]=>0010100=>[2,1,1,1,2]
[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>1100110=>[2,2,2,1]
[8,3,7,1,5,6,2,4]=>[1,6,2,8,4,3,7,5]=>0101101=>[1,1,1,2,1,1]
[8,6,1,2,7,5,3,4]=>[1,3,8,7,2,4,6,5]=>0011001=>[2,2,2,1]
[8,1,6,2,7,4,5,3]=>[1,8,3,7,2,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[1,8,5,2,6,7,4,3]=>[8,1,4,7,3,2,5,6]=>1001100=>[1,2,2,2]
[5,2,1,8,6,7,4,3]=>[4,7,8,1,3,2,5,6]=>0010100=>[2,1,1,1,2]
[2,8,5,7,6,4,3,1]=>[7,1,4,2,3,5,6,8]=>1010000=>[1,1,1,4]
[1,7,8,5,2,6,4,3]=>[8,2,1,4,7,3,5,6]=>1100100=>[2,2,1,2]
[7,8,1,6,4,2,5,3]=>[2,1,8,3,5,7,4,6]=>1010010=>[1,1,1,2,1,1]
[7,8,6,1,5,3,2,4]=>[2,1,3,8,4,6,7,5]=>1001001=>[1,2,1,2,1]
[7,3,8,6,1,5,2,4]=>[2,6,1,3,8,4,7,5]=>0100101=>[1,1,2,1,1,1]
[8,7,6,1,5,3,4,2]=>[1,2,3,8,4,6,5,7]=>0001010=>[3,1,1,1,1]
[8,7,1,6,4,5,3,2]=>[1,2,8,3,5,4,6,7]=>0010100=>[2,1,1,1,2]
[8,1,7,5,6,4,3,2]=>[1,8,2,4,3,5,6,7]=>0101000=>[1,1,1,1,3]
[1,8,6,7,5,4,3,2]=>[8,1,3,2,4,5,6,7]=>1010000=>[1,1,1,4]
[6,3,5,2,1,4,8,7]=>[3,6,4,7,8,5,1,2]=>0100110=>[1,1,2,2,1]
[6,3,5,7,2,8,4,1]=>[3,6,4,2,7,1,5,8]=>0110100=>[1,2,1,1,2]
[8,5,2,7,4,3,1,6]=>[1,4,7,2,5,6,8,3]=>0010001=>[2,1,3,1]
[4,5,3,6,1,2,8,7]=>[5,4,6,3,8,7,1,2]=>1010110=>[1,1,1,1,2,1]
[3,5,1,4,6,2,8,7]=>[6,4,8,5,3,7,1,2]=>1011010=>[1,1,2,1,1,1]
[8,3,4,5,7,2,1,6]=>[1,6,5,4,2,7,8,3]=>0111001=>[1,3,2,1]
[5,7,4,6,3,8,2,1]=>[4,2,5,3,6,1,7,8]=>1010100=>[1,1,1,1,1,2]
[2,8,4,6,3,7,1,5]=>[7,1,5,3,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[8,1,4,7,3,6,2,5]=>[1,8,5,2,6,3,7,4]=>0110101=>[1,2,1,1,1,1]
[8,3,4,7,5,1,2,6]=>[1,6,5,2,4,8,7,3]=>0110011=>[1,2,2,2]
[8,5,1,4,7,3,2,6]=>[1,4,8,5,2,6,7,3]=>0011001=>[2,2,2,1]
[8,5,3,7,1,4,2,6]=>[1,4,6,2,8,5,7,3]=>0010101=>[2,1,1,1,1,1]
[2,1,8,5,7,4,3,6]=>[7,8,1,4,2,5,6,3]=>0101001=>[1,1,1,1,2,1]
[6,5,3,7,1,8,4,2]=>[3,4,6,2,8,1,5,7]=>0010100=>[2,1,1,1,2]
[6,5,1,4,7,8,3,2]=>[3,4,8,5,2,1,6,7]=>0011100=>[2,3,2]
[6,3,4,7,5,8,1,2]=>[3,6,5,2,4,1,8,7]=>0110101=>[1,2,1,1,1,1]
[5,1,4,6,8,3,7,2]=>[4,8,5,3,1,6,2,7]=>0111010=>[1,3,1,1,1]
[4,7,1,3,5,8,6,2]=>[5,2,8,6,4,1,3,7]=>1011100=>[1,1,3,2]
[4,8,3,7,1,2,6,5]=>[5,1,6,2,8,7,3,4]=>1010110=>[1,1,1,1,2,1]
[3,8,6,4,1,7,2,5]=>[6,1,3,5,8,2,7,4]=>1000101=>[1,3,1,1,1]
[3,8,1,2,5,7,6,4]=>[6,1,8,7,4,2,3,5]=>1011100=>[1,1,3,2]
[2,8,7,5,4,1,3,6]=>[7,1,2,4,5,8,6,3]=>1000011=>[1,4,2]
[8,7,2,6,4,1,3,5]=>[1,2,7,3,5,8,6,4]=>0010011=>[2,1,2,2]
[3,8,6,7,4,2,1,5]=>[6,1,3,2,5,7,8,4]=>1010001=>[1,1,1,3,1]
[5,7,6,8,4,2,3,1]=>[4,2,3,1,5,7,6,8]=>1010010=>[1,1,1,2,1,1]
[5,3,7,8,2,4,6,1]=>[4,6,2,1,7,5,3,8]=>0110110=>[1,2,1,2,1]
[8,3,6,2,1,4,7,5]=>[1,6,3,7,8,5,2,4]=>0100110=>[1,1,2,2,1]
[5,3,7,6,2,1,8,4]=>[4,6,2,3,7,8,1,5]=>0100010=>[1,1,3,1,1]
[5,3,6,2,8,7,1,4]=>[4,6,3,7,1,2,8,5]=>0101001=>[1,1,1,1,2,1]
[5,7,8,6,4,2,1,3]=>[4,2,1,3,5,7,8,6]=>1100001=>[2,4,1]
[2,6,7,5,4,8,1,3]=>[7,3,2,4,5,1,8,6]=>1100101=>[2,2,1,1,1]
[6,1,7,4,5,8,2,3]=>[3,8,2,5,4,1,7,6]=>0101101=>[1,1,1,2,1,1]
[6,7,3,5,1,8,2,4]=>[3,2,6,4,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,1,6,7,5,8,3,4]=>[7,8,3,2,4,1,6,5]=>0110101=>[1,2,1,1,1,1]
[2,1,5,7,3,6,8,4]=>[7,8,4,2,6,3,1,5]=>0110110=>[1,2,1,2,1]
[5,7,3,6,1,2,8,4]=>[4,2,6,3,8,7,1,5]=>1010110=>[1,1,1,1,2,1]
[4,1,7,2,5,6,8,3]=>[5,8,2,7,4,3,1,6]=>0101110=>[1,1,1,3,1]
[2,4,7,1,6,5,8,3]=>[7,5,2,8,3,4,1,6]=>1101010=>[2,1,1,1,1,1]
[4,6,2,1,8,7,5,3]=>[5,3,7,8,1,2,4,6]=>1001000=>[1,2,1,3]
[3,4,6,2,7,8,5,1]=>[6,5,3,7,2,1,4,8]=>1101100=>[2,1,2,2]
[4,6,1,2,5,8,7,3]=>[5,3,8,7,4,1,2,6]=>1011100=>[1,1,3,2]
[5,6,1,4,8,2,7,3]=>[4,3,8,5,1,7,2,6]=>1011010=>[1,1,2,1,1,1]
[5,6,3,1,8,7,2,4]=>[4,3,6,8,1,2,7,5]=>1001001=>[1,2,1,2,1]
[3,5,6,4,7,1,8,2]=>[6,4,3,5,2,8,1,7]=>1101010=>[2,1,1,1,1,1]
[3,4,6,1,5,7,8,2]=>[6,5,3,8,4,2,1,7]=>1101110=>[2,1,3,1]
[3,4,1,5,7,6,8,2]=>[6,5,8,4,2,3,1,7]=>1011010=>[1,1,2,1,1,1]
[3,8,2,7,1,6,5,4]=>[6,1,7,2,8,3,4,5]=>1010100=>[1,1,1,1,1,2]
[3,8,2,7,6,1,5,4]=>[6,1,7,2,3,8,4,5]=>1010010=>[1,1,1,2,1,1]
[3,8,2,7,6,5,1,4]=>[6,1,7,2,3,4,8,5]=>1010001=>[1,1,1,3,1]
[3,8,2,7,6,5,4,1]=>[6,1,7,2,3,4,5,8]=>1010000=>[1,1,1,4]
[4,8,7,2,6,5,3,1]=>[5,1,2,7,3,4,6,8]=>1001000=>[1,2,1,3]
[4,8,7,2,6,5,1,3]=>[5,1,2,7,3,4,8,6]=>1001001=>[1,2,1,2,1]
[4,8,7,2,6,1,5,3]=>[5,1,2,7,3,8,4,6]=>1001010=>[1,2,1,1,1,1]
[4,8,7,2,1,6,5,3]=>[5,1,2,7,8,3,4,6]=>1000100=>[1,3,1,2]
[4,8,7,3,1,6,5,2]=>[5,1,2,6,8,3,4,7]=>1000100=>[1,3,1,2]
[4,8,7,3,2,1,6,5]=>[5,1,2,6,7,8,3,4]=>1000010=>[1,4,1,1]
[4,8,7,3,2,6,1,5]=>[5,1,2,6,7,3,8,4]=>1000101=>[1,3,1,1,1]
[4,8,7,3,2,6,5,1]=>[5,1,2,6,7,3,4,8]=>1000100=>[1,3,1,2]
[4,8,7,3,6,2,5,1]=>[5,1,2,6,3,7,4,8]=>1001010=>[1,2,1,1,1,1]
[4,8,7,3,6,2,1,5]=>[5,1,2,6,3,7,8,4]=>1001001=>[1,2,1,2,1]
[4,8,7,3,6,1,5,2]=>[5,1,2,6,3,8,4,7]=>1001010=>[1,2,1,1,1,1]
[4,8,7,3,6,5,1,2]=>[5,1,2,6,3,4,8,7]=>1001001=>[1,2,1,2,1]
[4,8,7,3,6,5,2,1]=>[5,1,2,6,3,4,7,8]=>1001000=>[1,2,1,3]
[5,8,7,6,3,4,2,1]=>[4,1,2,3,6,5,7,8]=>1000100=>[1,3,1,2]
[5,8,7,6,3,1,4,2]=>[4,1,2,3,6,8,5,7]=>1000010=>[1,4,1,1]
[5,8,7,6,3,2,4,1]=>[4,1,2,3,6,7,5,8]=>1000010=>[1,4,1,1]
[5,8,7,6,2,4,3,1]=>[4,1,2,3,7,5,6,8]=>1000100=>[1,3,1,2]
[5,8,7,6,2,1,4,3]=>[4,1,2,3,7,8,5,6]=>1000010=>[1,4,1,1]
[5,8,7,6,4,2,3,1]=>[4,1,2,3,5,7,6,8]=>1000010=>[1,4,1,1]
[5,8,7,6,4,2,1,3]=>[4,1,2,3,5,7,8,6]=>1000001=>[1,5,1]
[5,8,7,6,4,1,3,2]=>[4,1,2,3,5,8,6,7]=>1000010=>[1,4,1,1]
[5,8,7,6,4,3,1,2]=>[4,1,2,3,5,6,8,7]=>1000001=>[1,5,1]
[7,3,4,2,1,6,5,8]=>[2,6,5,7,8,3,4,1]=>0100101=>[1,1,2,1,1,1]
[7,3,5,2,6,1,4,8]=>[2,6,4,7,3,8,5,1]=>0101011=>[1,1,1,1,1,2]
[7,3,5,2,6,4,1,8]=>[2,6,4,7,3,5,8,1]=>0101001=>[1,1,1,1,2,1]
[6,3,5,2,7,4,8,1]=>[3,6,4,7,2,5,1,8]=>0101010=>[1,1,1,1,1,1,1]
[7,2,1,5,6,4,3,8]=>[2,7,8,4,3,5,6,1]=>0011001=>[2,2,2,1]
[7,3,5,1,6,4,2,8]=>[2,6,4,8,3,5,7,1]=>0101001=>[1,1,1,1,2,1]
[7,4,5,6,1,3,2,8]=>[2,5,4,3,8,6,7,1]=>0110101=>[1,2,1,1,1,1]
[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>1110010=>[3,2,1,1]
[1,4,6,7,3,8,2,5]=>[8,5,3,2,6,1,7,4]=>1110101=>[3,1,1,1,1]
[6,4,5,7,3,1,8,2]=>[3,5,4,2,6,8,1,7]=>0110010=>[1,2,2,1,1]
[6,4,5,7,1,3,8,2]=>[3,5,4,2,8,6,1,7]=>0110110=>[1,2,1,2,1]
[6,3,5,1,7,4,8,2]=>[3,6,4,8,2,5,1,7]=>0101010=>[1,1,1,1,1,1,1]
[6,2,1,5,7,4,8,3]=>[3,7,8,4,2,5,1,6]=>0011010=>[2,2,1,1,1]
[3,2,1,5,7,4,8,6]=>[6,7,8,4,2,5,1,3]=>0011010=>[2,2,1,1,1]
[2,4,6,7,3,8,1,5]=>[7,5,3,2,6,1,8,4]=>1110101=>[3,1,1,1,1]
[1,4,6,7,3,8,5,2]=>[8,5,3,2,6,1,4,7]=>1110100=>[3,1,1,2]
[1,5,6,7,8,3,4,2]=>[8,4,3,2,1,6,5,7]=>1111010=>[4,1,1,1]
[2,5,6,7,8,3,1,4]=>[7,4,3,2,1,6,8,5]=>1111001=>[4,2,1]
[3,2,1,6,7,8,4,5]=>[6,7,8,3,2,1,5,4]=>0011101=>[2,3,1,1]
[5,2,1,6,7,8,4,3]=>[4,7,8,3,2,1,5,6]=>0011100=>[2,3,2]
[5,3,6,1,7,8,4,2]=>[4,6,3,8,2,1,5,7]=>0101100=>[1,1,1,2,2]
[5,4,6,7,1,8,3,2]=>[4,5,3,2,8,1,6,7]=>0110100=>[1,2,1,1,2]
[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>1111001=>[4,2,1]
[6,4,5,7,2,1,8,3]=>[3,5,4,2,7,8,1,6]=>0110010=>[1,2,2,1,1]
[5,4,6,7,2,8,3,1]=>[4,5,3,2,7,1,6,8]=>0110100=>[1,2,1,1,2]
[5,3,6,2,7,8,4,1]=>[4,6,3,7,2,1,5,8]=>0101100=>[1,1,1,2,2]
[5,3,6,2,7,8,1,4]=>[4,6,3,7,2,1,8,5]=>0101101=>[1,1,1,2,1,1]
[6,3,5,2,7,1,8,4]=>[3,6,4,7,2,8,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,3,4,2,1,7,8,5]=>[3,6,5,7,8,2,1,4]=>0100110=>[1,1,2,2,1]
[5,3,4,1,2,7,8,6]=>[4,6,5,8,7,2,1,3]=>0101110=>[1,1,1,3,1]
[4,3,6,2,7,8,1,5]=>[5,6,3,7,2,1,8,4]=>0101101=>[1,1,1,2,1,1]
[4,3,6,2,7,8,5,1]=>[5,6,3,7,2,1,4,8]=>0101100=>[1,1,1,2,2]
[1,3,6,2,7,8,5,4]=>[8,6,3,7,2,1,4,5]=>1101100=>[2,1,2,2]
[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>1110100=>[3,1,1,2]
[3,4,6,7,2,8,5,1]=>[6,5,3,2,7,1,4,8]=>1110100=>[3,1,1,2]
[3,4,5,7,2,1,8,6]=>[6,5,4,2,7,8,1,3]=>1110010=>[3,2,1,1]
[4,2,1,5,7,3,8,6]=>[5,7,8,4,2,6,1,3]=>0011010=>[2,2,1,1,1]
[4,2,1,6,7,8,3,5]=>[5,7,8,3,2,1,6,4]=>0011101=>[2,3,1,1]
[4,3,6,1,7,8,2,5]=>[5,6,3,8,2,1,7,4]=>0101101=>[1,1,1,2,1,1]
[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>1111010=>[4,1,1,1]
[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>1111001=>[4,2,1]
[3,4,6,7,1,8,5,2]=>[6,5,3,2,8,1,4,7]=>1110100=>[3,1,1,2]
[4,3,6,1,7,8,5,2]=>[5,6,3,8,2,1,4,7]=>0101100=>[1,1,1,2,2]
[4,2,1,6,7,8,5,3]=>[5,7,8,3,2,1,4,6]=>0011100=>[2,3,2]
[2,3,6,1,7,8,5,4]=>[7,6,3,8,2,1,4,5]=>1101100=>[2,1,2,2]
[2,4,6,7,1,8,5,3]=>[7,5,3,2,8,1,4,6]=>1110100=>[3,1,1,2]
[2,5,6,7,8,1,4,3]=>[7,4,3,2,1,8,5,6]=>1111010=>[4,1,1,1]
[2,1,4,3,6,5,8,7,9]=>[8,9,6,7,4,5,2,3,1]=>01010101=>[1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,9]=>[8,6,9,7,4,5,2,3,1]=>10110101=>[1,1,2,1,1,1,1]
[2,4,1,6,3,5,8,7,9]=>[8,6,9,4,7,5,2,3,1]=>10101101=>[1,1,1,1,2,1,1]
[2,4,1,6,3,8,5,7,9]=>[8,6,9,4,7,2,5,3,1]=>10101011=>[1,1,1,1,1,1,2]
[2,4,1,6,3,7,5,9,8]=>[8,6,9,4,7,3,5,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[2,4,1,5,3,7,6,9,8]=>[8,6,9,5,7,3,4,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[2,3,1,5,4,7,6,9,8]=>[8,7,9,5,6,3,4,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,9,8]=>[9,7,8,5,6,3,4,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[2,4,1,3,6,5,8,7,10,9]=>[9,7,10,8,5,6,3,4,1,2]=>101101010=>[1,1,2,1,1,1,1,1]
[2,4,6,1,3,5,8,7,9]=>[8,6,4,9,7,5,2,3,1]=>11011101=>[2,1,3,1,1]
[2,4,1,6,3,5,8,7,10,9]=>[9,7,10,5,8,6,3,4,1,2]=>101011010=>[1,1,1,1,2,1,1,1]
[2,4,1,6,8,3,5,7,9]=>[8,6,9,4,2,7,5,3,1]=>10110111=>[1,1,2,1,3]
[2,4,1,6,3,8,5,7,10,9]=>[9,7,10,5,8,3,6,4,1,2]=>101010110=>[1,1,1,1,1,1,2,1]
[2,4,1,6,3,8,9,5,7]=>[8,6,9,4,7,2,1,5,3]=>10101101=>[1,1,1,1,2,1,1]
[2,4,1,6,3,8,5,10,7,9]=>[9,7,10,5,8,3,6,1,4,2]=>101010101=>[1,1,1,1,1,1,1,1,1]
[2,4,1,6,3,7,5,8,9]=>[8,6,9,4,7,3,5,2,1]=>10101011=>[1,1,1,1,1,1,2]
[2,4,1,6,3,8,5,9,7,10]=>[9,7,10,5,8,3,6,2,4,1]=>101010101=>[1,1,1,1,1,1,1,1,1]
[2,4,1,5,3,8,6,9,7]=>[8,6,9,5,7,2,4,1,3]=>10101010=>[1,1,1,1,1,1,1,1]
[2,4,1,6,3,7,5,9,8,10]=>[9,7,10,5,8,4,6,2,3,1]=>101010101=>[1,1,1,1,1,1,1,1,1]
[2,3,1,6,4,7,5,9,8]=>[8,7,9,4,6,3,5,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[2,4,1,5,3,7,6,9,8,10]=>[9,7,10,6,8,4,5,2,3,1]=>101010101=>[1,1,1,1,1,1,1,1,1]
[1,4,2,5,3,7,6,9,8]=>[9,6,8,5,7,3,4,1,2]=>10101010=>[1,1,1,1,1,1,1,1]
[2,3,1,5,4,7,6,9,8,10]=>[9,8,10,6,7,4,5,2,3,1]=>101010101=>[1,1,1,1,1,1,1,1,1]
[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>101010101=>[1,1,1,1,1,1,1,1,1]
[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>01111111=>[1,7]
[1,4,3,6,2,5,7,8]=>[8,5,6,3,7,4,2,1]=>1010111=>[1,1,1,1,3]
[1,4,3,7,2,5,6,8]=>[8,5,6,2,7,4,3,1]=>1010111=>[1,1,1,1,3]
[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,4,3,7,5,8,2,6]=>[8,5,6,2,4,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]
[1,5,4,8,3,7,2,6]=>[8,4,5,1,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]
[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>1110101=>[3,1,1,1,1]
[6,8,2,4,5,7,1,3]=>[3,1,7,5,4,2,8,6]=>1011101=>[1,1,3,1,1]
[3,7,8,4,5,2,6,1]=>[6,2,1,5,4,7,3,8]=>1101010=>[2,1,1,1,1,1]
[7,8,1,4,5,3,6,2]=>[2,1,8,5,4,6,3,7]=>1011010=>[1,1,2,1,1,1]
[3,8,7,4,1,6,5,2]=>[6,1,2,5,8,3,4,7]=>1000100=>[1,3,1,2]
[4,8,3,6,1,5,7,2]=>[5,1,6,3,8,4,2,7]=>1010110=>[1,1,1,1,2,1]
[5,8,3,1,6,4,7,2]=>[4,1,6,8,3,5,2,7]=>1001010=>[1,2,1,1,1,1]
[5,8,1,4,7,6,3,2]=>[4,1,8,5,2,3,6,7]=>1011000=>[1,1,2,3]
[7,5,1,8,6,2,4,3]=>[2,4,8,1,3,7,5,6]=>0010010=>[2,1,2,1,1]
[7,4,1,8,2,6,3,5]=>[2,5,8,1,7,3,6,4]=>0010101=>[2,1,1,1,1,1]
[6,1,3,8,5,2,4,7]=>[3,8,6,1,4,7,5,2]=>0110011=>[1,2,2,2]
[7,2,8,4,1,6,5,3]=>[2,7,1,5,8,3,4,6]=>0100100=>[1,1,2,1,2]
[7,2,8,3,6,5,1,4]=>[2,7,1,6,3,4,8,5]=>0101001=>[1,1,1,1,2,1]
[7,1,8,2,3,6,5,4]=>[2,8,1,7,6,3,4,5]=>0101100=>[1,1,1,2,2]
[6,1,2,8,3,5,4,7]=>[3,8,7,1,6,4,5,2]=>0110101=>[1,2,1,1,1,1]
[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>1011010=>[1,1,2,1,1,1]
[5,1,2,3,8,4,7,6]=>[4,8,7,6,1,5,2,3]=>0111010=>[1,3,1,1,1]
[6,2,8,1,3,5,4,7]=>[3,7,1,8,6,4,5,2]=>0101101=>[1,1,1,2,1,1]
[6,2,4,1,8,7,3,5]=>[3,7,5,8,1,2,6,4]=>0101001=>[1,1,1,1,2,1]
[2,6,3,8,7,1,5,4]=>[7,3,6,1,2,8,4,5]=>1010010=>[1,1,1,2,1,1]
[2,5,1,8,3,4,7,6]=>[7,4,8,1,6,5,2,3]=>1010110=>[1,1,1,1,2,1]
[2,5,1,3,8,4,7,6]=>[7,4,8,6,1,5,2,3]=>1011010=>[1,1,2,1,1,1]
[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>1101010=>[2,1,1,1,1,1]
[1,2,4,8,3,7,6,5]=>[8,7,5,1,6,2,3,4]=>1110100=>[3,1,1,2]
[2,4,8,1,3,7,6,5]=>[7,5,1,8,6,2,3,4]=>1101100=>[2,1,2,2]
[2,4,8,3,7,1,6,5]=>[7,5,1,6,2,8,3,4]=>1101010=>[2,1,1,1,1,1]
[2,4,8,3,7,6,1,5]=>[7,5,1,6,2,3,8,4]=>1101001=>[2,1,1,2,1]
[2,5,4,1,3,8,7,6]=>[7,4,5,8,6,1,2,3]=>1001100=>[1,2,2,2]
[3,1,5,4,8,2,7,6]=>[6,8,4,5,1,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,2,3,8,4,7,1,6]=>[4,7,6,1,5,2,8,3]=>0110101=>[1,2,1,1,1,1]
[4,8,1,2,3,7,6,5]=>[5,1,8,7,6,2,3,4]=>1011100=>[1,1,3,2]
[1,4,8,3,7,2,6,5]=>[8,5,1,6,2,7,3,4]=>1101010=>[2,1,1,1,1,1]
[5,3,8,1,2,4,7,6]=>[4,6,1,8,7,5,2,3]=>0101110=>[1,1,1,3,1]
[5,1,3,8,2,4,7,6]=>[4,8,6,1,7,5,2,3]=>0110110=>[1,2,1,2,1]
[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>1010100=>[1,1,1,1,1,2]
[5,4,8,1,2,7,6,3]=>[4,5,1,8,7,2,3,6]=>0101100=>[1,1,1,2,2]
[6,5,1,2,8,7,4,3]=>[3,4,8,7,1,2,5,6]=>0011000=>[2,2,3]
[5,3,1,6,4,2,8,7]=>[4,6,8,3,5,7,1,2]=>0010010=>[2,1,2,1,1]
[5,1,6,2,8,7,4,3]=>[4,8,3,7,1,2,5,6]=>0101000=>[1,1,1,1,3]
[4,1,2,5,8,7,6,3]=>[5,8,7,4,1,2,3,6]=>0111000=>[1,3,3]
[1,4,2,5,8,7,6,3]=>[8,5,7,4,1,2,3,6]=>1011000=>[1,1,2,3]
[3,5,1,2,8,7,4,6]=>[6,4,8,7,1,2,5,3]=>1011001=>[1,1,2,2,1]
[3,6,2,8,7,5,1,4]=>[6,3,7,1,2,4,8,5]=>1010001=>[1,1,1,3,1]
[4,2,6,1,8,7,3,5]=>[5,7,3,8,1,2,6,4]=>0101001=>[1,1,1,1,2,1]
[4,3,1,5,8,2,7,6]=>[5,6,8,4,1,7,2,3]=>0011010=>[2,2,1,1,1]
[3,4,8,7,2,6,1,5]=>[6,5,1,2,7,3,8,4]=>1100101=>[2,2,1,1,1]
[3,4,8,7,1,2,6,5]=>[6,5,1,2,8,7,3,4]=>1100110=>[2,2,2,1]
[3,4,8,1,7,2,6,5]=>[6,5,1,8,2,7,3,4]=>1101010=>[2,1,1,1,1,1]
[3,4,8,2,7,1,6,5]=>[6,5,1,7,2,8,3,4]=>1101010=>[2,1,1,1,1,1]
[3,4,8,2,7,6,1,5]=>[6,5,1,7,2,3,8,4]=>1101001=>[2,1,1,2,1]
[4,3,1,2,5,8,7,6]=>[5,6,8,7,4,1,2,3]=>0011100=>[2,3,2]
[3,1,4,2,5,8,7,6]=>[6,8,5,7,4,1,2,3]=>0101100=>[1,1,1,2,2]
[6,4,1,2,7,3,5,8]=>[3,5,8,7,2,6,4,1]=>0011011=>[2,2,1,2]
[2,3,7,5,4,1,8,6]=>[7,6,2,4,5,8,1,3]=>1100010=>[2,3,1,1]
[6,3,1,5,4,2,7,8]=>[3,6,8,4,5,7,2,1]=>0010011=>[2,1,2,2]
[7,8,1,5,4,2,6,3]=>[2,1,8,4,5,7,3,6]=>1010010=>[1,1,1,2,1,1]
[7,8,3,5,4,1,6,2]=>[2,1,6,4,5,8,3,7]=>1010010=>[1,1,1,2,1,1]
[7,8,2,5,4,1,3,6]=>[2,1,7,4,5,8,6,3]=>1010011=>[1,1,1,2,2]
[7,8,2,5,4,6,1,3]=>[2,1,7,4,5,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,2,1,5,4,7,3,8]=>[3,7,8,4,5,2,6,1]=>0010101=>[2,1,1,1,1,1]
[5,3,6,1,4,7,8,2]=>[4,6,3,8,5,2,1,7]=>0101110=>[1,1,1,3,1]
[5,3,6,2,4,7,1,8]=>[4,6,3,7,5,2,8,1]=>0101101=>[1,1,1,2,1,1]
[6,4,2,1,7,3,8,5]=>[3,5,7,8,2,6,1,4]=>0001010=>[3,1,1,1,1]
[4,2,7,1,8,3,6,5]=>[5,7,2,8,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,7,4,8,1,5]=>[6,7,3,2,5,1,8,4]=>0110101=>[1,2,1,1,1,1]
[3,1,6,7,4,8,5,2]=>[6,8,3,2,5,1,4,7]=>0110100=>[1,2,1,1,2]
[2,7,6,5,3,1,4,8]=>[7,2,3,4,6,8,5,1]=>1000011=>[1,4,2]
[2,7,1,4,8,3,5,6]=>[7,2,8,5,1,6,4,3]=>1011011=>[1,1,2,1,2]
[3,7,6,4,8,5,1,2]=>[6,2,3,5,1,4,8,7]=>1001001=>[1,2,1,2,1]
[5,7,6,3,8,4,1,2]=>[4,2,3,6,1,5,8,7]=>1001001=>[1,2,1,2,1]
[5,1,6,2,4,8,3,7]=>[4,8,3,7,5,1,6,2]=>0101101=>[1,1,1,2,1,1]
[4,7,6,5,2,8,1,3]=>[5,2,3,4,7,1,8,6]=>1000101=>[1,3,1,1,1]
[4,7,6,5,1,8,3,2]=>[5,2,3,4,8,1,6,7]=>1000100=>[1,3,1,2]
[1,7,6,5,3,2,8,4]=>[8,2,3,4,6,7,1,5]=>1000010=>[1,4,1,1]
[4,7,6,5,1,2,8,3]=>[5,2,3,4,8,7,1,6]=>1000110=>[1,3,2,1]
[4,7,6,5,3,1,8,2]=>[5,2,3,4,6,8,1,7]=>1000010=>[1,4,1,1]
[6,1,3,5,4,8,7,2]=>[3,8,6,4,5,1,2,7]=>0110100=>[1,2,1,1,2]
[5,1,6,2,4,7,8,3]=>[4,8,3,7,5,2,1,6]=>0101110=>[1,1,1,3,1]
[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>1101100=>[2,1,2,2]
[6,1,4,2,8,3,5,7]=>[3,8,5,7,1,6,4,2]=>0101011=>[1,1,1,1,1,2]
[4,1,8,2,6,3,5,7]=>[5,8,1,7,3,6,4,2]=>0101011=>[1,1,1,1,1,2]
[4,7,2,1,5,3,6,8]=>[5,2,7,8,4,6,3,1]=>1001011=>[1,2,1,1,2]
[4,7,1,6,2,3,8,5]=>[5,2,8,3,7,6,1,4]=>1010110=>[1,1,1,1,2,1]
[1,7,2,6,8,3,5,4]=>[8,2,7,3,1,6,4,5]=>1011010=>[1,1,2,1,1,1]
[3,2,8,5,4,6,1,7]=>[6,7,1,4,5,3,8,2]=>0100101=>[1,1,2,1,1,1]
[4,7,6,3,5,8,1,2]=>[5,2,3,6,4,1,8,7]=>1001101=>[1,2,2,1,1]
[4,7,1,2,5,3,8,6]=>[5,2,8,7,4,6,1,3]=>1011010=>[1,1,2,1,1,1]
[3,7,6,5,1,4,8,2]=>[6,2,3,4,8,5,1,7]=>1000110=>[1,3,2,1]
[3,7,6,5,2,1,8,4]=>[6,2,3,4,7,8,1,5]=>1000010=>[1,4,1,1]
[3,7,6,5,8,1,4,2]=>[6,2,3,4,1,8,5,7]=>1001010=>[1,2,1,1,1,1]
[4,7,6,8,3,5,1,2]=>[5,2,3,1,6,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[2,7,6,5,1,4,3,8]=>[7,2,3,4,8,5,6,1]=>1000101=>[1,3,1,1,1]
[2,7,6,5,8,1,3,4]=>[7,2,3,4,1,8,6,5]=>1001011=>[1,2,1,1,2]
[2,7,6,5,8,4,1,3]=>[7,2,3,4,1,5,8,6]=>1001001=>[1,2,1,2,1]
[4,2,1,7,3,5,8,6]=>[5,7,8,2,6,4,1,3]=>0010110=>[2,1,1,2,1]
[7,3,1,5,4,2,8,6]=>[2,6,8,4,5,7,1,3]=>0010010=>[2,1,2,1,1]
[8,4,1,5,2,7,6,3]=>[1,5,8,4,7,2,3,6]=>0010100=>[2,1,1,1,2]
[8,2,5,1,3,7,6,4]=>[1,7,4,8,6,2,3,5]=>0101100=>[1,1,1,2,2]
[4,3,7,2,1,5,8,6]=>[5,6,2,7,8,4,1,3]=>0100110=>[1,1,2,2,1]
[6,3,7,4,2,1,8,5]=>[3,6,2,5,7,8,1,4]=>0100010=>[1,1,3,1,1]
[4,7,2,5,3,1,8,6]=>[5,2,7,4,6,8,1,3]=>1010010=>[1,1,1,2,1,1]
[7,5,4,3,2,1,8,6]=>[2,4,5,6,7,8,1,3]=>0000010=>[5,1,1]
[8,5,3,2,1,7,6,4]=>[1,4,6,7,8,2,3,5]=>0000100=>[4,1,2]
[6,5,2,1,8,4,3,7]=>[3,4,7,8,1,5,6,2]=>0001001=>[3,1,2,1]
[4,6,3,2,8,1,5,7]=>[5,3,6,7,1,8,4,2]=>1001011=>[1,2,1,1,2]
[5,7,4,3,2,8,1,6]=>[4,2,5,6,7,1,8,3]=>1000101=>[1,3,1,1,1]
[6,2,7,5,3,8,1,4]=>[3,7,2,4,6,1,8,5]=>0100101=>[1,1,2,1,1,1]
[7,1,8,5,3,6,4,2]=>[2,8,1,4,6,3,5,7]=>0100100=>[1,1,2,1,2]
[5,8,1,6,2,7,4,3]=>[4,1,8,3,7,2,5,6]=>1010100=>[1,1,1,1,1,2]
[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>1001100=>[1,2,2,2]
[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>1000100=>[1,3,1,2]
[8,7,3,1,6,5,4,2]=>[1,2,6,8,3,4,5,7]=>0001000=>[3,1,3]
[8,7,2,6,1,5,4,3]=>[1,2,7,3,8,4,5,6]=>0010100=>[2,1,1,1,2]
[1,8,5,7,4,3,6,2]=>[8,1,4,2,5,6,3,7]=>1010010=>[1,1,1,2,1,1]
[1,8,5,7,2,4,6,3]=>[8,1,4,2,7,5,3,6]=>1010110=>[1,1,1,1,2,1]
[3,8,6,1,7,2,5,4]=>[6,1,3,8,2,7,4,5]=>1001010=>[1,2,1,1,1,1]
[5,8,4,6,7,1,3,2]=>[4,1,5,3,2,8,6,7]=>1011010=>[1,1,2,1,1,1]
[7,2,8,5,6,1,4,3]=>[2,7,1,4,3,8,5,6]=>0101010=>[1,1,1,1,1,1,1]
[2,6,5,8,4,1,3,7]=>[7,3,4,1,5,8,6,2]=>1010011=>[1,1,1,2,2]
[6,5,4,8,3,2,1,7]=>[3,4,5,1,6,7,8,2]=>0010001=>[2,1,3,1]
[8,4,3,7,2,1,6,5]=>[1,5,6,2,7,8,3,4]=>0010010=>[2,1,2,1,1]
[8,2,4,7,1,3,6,5]=>[1,7,5,2,8,6,3,4]=>0110110=>[1,2,1,2,1]
[6,2,5,8,1,4,3,7]=>[3,7,4,1,8,5,6,2]=>0110101=>[1,2,1,1,1,1]
[4,3,6,8,2,1,5,7]=>[5,6,3,1,7,8,4,2]=>0110011=>[1,2,2,2]
[6,3,5,1,8,4,2,7]=>[3,6,4,8,1,5,7,2]=>0101001=>[1,1,1,1,2,1]
[8,4,1,5,7,3,6,2]=>[1,5,8,4,2,6,3,7]=>0011010=>[2,2,1,1,1]
[6,4,2,5,8,3,1,7]=>[3,5,7,4,1,6,8,2]=>0011001=>[2,2,2,1]
[5,4,1,6,8,2,3,7]=>[4,5,8,3,1,7,6,2]=>0011011=>[2,2,1,2]
[6,5,2,1,7,8,3,4]=>[3,4,7,8,2,1,6,5]=>0001101=>[3,2,1,1]
[6,3,7,4,8,5,2,1]=>[3,6,2,5,1,4,7,8]=>0101000=>[1,1,1,1,3]
[4,7,2,5,8,6,3,1]=>[5,2,7,4,1,3,6,8]=>1011000=>[1,1,2,3]
[6,3,1,8,4,7,5,2]=>[3,6,8,1,5,2,4,7]=>0010100=>[2,1,1,1,2]
[6,4,2,8,7,3,5,1]=>[3,5,7,1,2,6,4,8]=>0010010=>[2,1,2,1,1]
[6,5,3,8,7,4,1,2]=>[3,4,6,1,2,5,8,7]=>0010001=>[2,1,3,1]
[8,5,3,7,6,4,2,1]=>[1,4,6,2,3,5,7,8]=>0010000=>[2,1,4]
[5,4,8,1,7,6,2,3]=>[4,5,1,8,2,3,7,6]=>0101001=>[1,1,1,1,2,1]
[5,2,8,1,7,3,6,4]=>[4,7,1,8,2,6,3,5]=>0101010=>[1,1,1,1,1,1,1]
[6,4,8,2,1,7,5,3]=>[3,5,1,7,8,2,4,6]=>0100100=>[1,1,2,1,2]
[5,7,3,8,1,6,4,2]=>[4,2,6,1,8,3,5,7]=>1010100=>[1,1,1,1,1,2]
[2,5,8,7,1,3,6,4]=>[7,4,1,2,8,6,3,5]=>1100110=>[2,2,2,1]
[5,3,8,7,2,1,6,4]=>[4,6,1,2,7,8,3,5]=>0100010=>[1,1,3,1,1]
[8,3,7,6,1,5,4,2]=>[1,6,2,3,8,4,5,7]=>0100100=>[1,1,2,1,2]
[8,2,7,6,5,1,4,3]=>[1,7,2,3,4,8,5,6]=>0100010=>[1,1,3,1,1]
[4,3,8,7,6,2,1,5]=>[5,6,1,2,3,7,8,4]=>0100001=>[1,1,4,1]
[2,4,8,7,6,1,3,5]=>[7,5,1,2,3,8,6,4]=>1100011=>[2,3,2]
[3,5,8,7,2,6,1,4]=>[6,4,1,2,7,3,8,5]=>1100101=>[2,2,1,1,1]
[4,7,3,8,6,5,1,2]=>[5,2,6,1,3,4,8,7]=>1010001=>[1,1,1,3,1]
[7,5,8,6,4,3,2,1]=>[2,4,1,3,5,6,7,8]=>0100000=>[1,1,5]
[3,8,7,6,5,1,4,2]=>[6,1,2,3,4,8,5,7]=>1000010=>[1,4,1,1]
[2,8,7,6,5,4,1,3]=>[7,1,2,3,4,5,8,6]=>1000001=>[1,5,1]
[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>10111111=>[1,1,6]
[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>00111111=>[2,6]
[4,5,6,1,2,3,7,8,9]=>[6,5,4,9,8,7,3,2,1]=>11011111=>[2,1,5]
[4,2,5,1,3,6,7,8,9]=>[6,8,5,9,7,4,3,2,1]=>01011111=>[1,1,1,5]
[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>00011111=>[3,5]
[5,6,7,8,1,2,3,4,9]=>[5,4,3,2,9,8,7,6,1]=>11101111=>[3,1,4]
[5,2,6,7,1,3,4,8,9]=>[5,8,4,3,9,7,6,2,1]=>01101111=>[1,2,1,4]
[5,6,3,4,1,2,7,8,9]=>[5,4,7,6,9,8,3,2,1]=>10101111=>[1,1,1,1,4]
[5,3,2,6,1,4,7,8,9]=>[5,7,8,4,9,6,3,2,1]=>00101111=>[2,1,1,4]
[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>00001111=>[4,4]
[6,2,7,8,9,1,3,4,5]=>[4,8,3,2,1,9,7,6,5]=>01110111=>[1,3,1,3]
[6,7,3,4,8,1,2,5,9]=>[4,3,7,6,2,9,8,5,1]=>10110111=>[1,1,2,1,3]
[6,3,2,7,8,1,4,5,9]=>[4,7,8,3,2,9,6,5,1]=>00110111=>[2,2,1,3]
[6,4,7,2,5,1,3,8,9]=>[4,6,3,8,5,9,7,2,1]=>01010111=>[1,1,1,1,1,3]
[6,4,3,2,7,1,5,8,9]=>[4,6,7,8,3,9,5,2,1]=>00010111=>[3,1,1,3]
[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>00000111=>[5,3]
[7,4,8,2,5,9,1,3,6]=>[3,6,2,8,5,1,9,7,4]=>01011011=>[1,1,1,2,1,2]
[7,4,3,2,8,9,1,5,6]=>[3,6,7,8,2,1,9,5,4]=>00011011=>[3,2,1,2]
[7,8,5,6,3,4,1,2,9]=>[3,2,5,4,7,6,9,8,1]=>10101011=>[1,1,1,1,1,1,2]
[7,5,3,8,2,6,1,4,9]=>[3,5,7,2,8,4,9,6,1]=>00101011=>[2,1,1,1,1,2]
[7,5,4,3,2,8,1,6,9]=>[3,5,6,7,8,2,9,4,1]=>00001011=>[4,1,1,2]
[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>00000011=>[6,2]
[8,6,9,4,7,2,5,1,3]=>[2,4,1,6,3,8,5,9,7]=>01010101=>[1,1,1,1,1,1,1,1]
[8,6,4,3,9,2,7,1,5]=>[2,4,6,7,1,8,3,9,5]=>00010101=>[3,1,1,1,1,1]
[8,6,5,4,3,2,9,1,7]=>[2,4,5,6,7,8,1,9,3]=>00000101=>[5,1,1,1]
[3,4,1,2,5,6,7,8,9,10]=>[8,7,10,9,6,5,4,3,2,1]=>101111111=>[1,1,7]
[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>001111111=>[2,7]
[4,5,6,1,2,3,7,8,9,10]=>[7,6,5,10,9,8,4,3,2,1]=>110111111=>[2,1,6]
[4,2,5,1,3,6,7,8,9,10]=>[7,9,6,10,8,5,4,3,2,1]=>010111111=>[1,1,1,6]
[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>000111111=>[3,6]
[5,6,7,8,1,2,3,4,9,10]=>[6,5,4,3,10,9,8,7,2,1]=>111011111=>[3,1,5]
[5,2,6,7,1,3,4,8,9,10]=>[6,9,5,4,10,8,7,3,2,1]=>011011111=>[1,2,1,5]
[5,6,3,4,1,2,7,8,9,10]=>[6,5,8,7,10,9,4,3,2,1]=>101011111=>[1,1,1,1,5]
[5,3,2,6,1,4,7,8,9,10]=>[6,8,9,5,10,7,4,3,2,1]=>001011111=>[2,1,1,5]
[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>000011111=>[4,5]
[6,2,7,8,9,1,3,4,5,10]=>[5,9,4,3,2,10,8,7,6,1]=>011101111=>[1,3,1,4]
[6,7,3,4,8,1,2,5,9,10]=>[5,4,8,7,3,10,9,6,2,1]=>101101111=>[1,1,2,1,4]
[6,3,2,7,8,1,4,5,9,10]=>[5,8,9,4,3,10,7,6,2,1]=>001101111=>[2,2,1,4]
[6,4,7,2,5,1,3,8,9,10]=>[5,7,4,9,6,10,8,3,2,1]=>010101111=>[1,1,1,1,1,4]
[6,4,3,2,7,1,5,8,9,10]=>[5,7,8,9,4,10,6,3,2,1]=>000101111=>[3,1,1,4]
[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>000001111=>[5,4]
[7,8,3,4,9,10,1,2,5,6]=>[4,3,8,7,2,1,10,9,6,5]=>101110111=>[1,1,3,1,3]
[7,8,9,4,5,6,1,2,3,10]=>[4,3,2,7,6,5,10,9,8,1]=>110110111=>[2,1,2,1,3]
[7,4,3,2,8,9,1,5,6,10]=>[4,7,8,9,3,2,10,6,5,1]=>000110111=>[3,2,1,3]
[7,8,5,6,3,4,1,2,9,10]=>[4,3,6,5,8,7,10,9,2,1]=>101010111=>[1,1,1,1,1,1,3]
[7,5,3,8,2,6,1,4,9,10]=>[4,6,8,3,9,5,10,7,2,1]=>001010111=>[2,1,1,1,1,3]
[7,5,4,3,2,8,1,6,9,10]=>[4,6,7,8,9,3,10,5,2,1]=>000010111=>[4,1,1,3]
[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>000000111=>[6,3]
[8,5,9,10,2,6,7,1,3,4]=>[3,6,2,1,9,5,4,10,8,7]=>011011011=>[1,2,1,2,1,2]
[8,5,3,9,2,6,10,1,4,7]=>[3,6,8,2,9,5,1,10,7,4]=>001011011=>[2,1,1,2,1,2]
[8,6,9,4,7,2,5,1,3,10]=>[3,5,2,7,4,9,6,10,8,1]=>010101011=>[1,1,1,1,1,1,1,2]
[8,6,4,3,9,2,7,1,5,10]=>[3,5,7,8,2,9,4,10,6,1]=>000101011=>[3,1,1,1,1,2]
[8,6,5,4,3,2,9,1,7,10]=>[3,5,6,7,8,9,2,10,4,1]=>000001011=>[5,1,1,2]
[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>000000011=>[7,2]
[9,7,5,4,3,10,2,8,1,6]=>[2,4,6,7,8,1,9,3,10,5]=>000010101=>[4,1,1,1,1,1]
[3,6,5,1,2,4,8,7]=>[6,3,4,8,7,5,1,2]=>1001110=>[1,2,3,1]
[3,7,5,8,2,4,1,6]=>[6,2,4,1,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[3,8,5,7,2,4,1,6]=>[6,1,4,2,7,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[5,1,7,8,4,3,2,6]=>[4,8,2,1,5,6,7,3]=>0110001=>[1,2,3,1]
[5,1,2,6,4,3,8,7]=>[4,8,7,3,5,6,1,2]=>0110010=>[1,2,2,1,1]
[6,1,2,5,4,3,8,7]=>[3,8,7,4,5,6,1,2]=>0110010=>[1,2,2,1,1]
[5,1,2,4,6,3,8,7]=>[4,8,7,5,3,6,1,2]=>0111010=>[1,3,1,1,1]
[4,1,2,6,5,3,8,7]=>[5,8,7,3,4,6,1,2]=>0110010=>[1,2,2,1,1]
[4,1,5,7,8,3,2,6]=>[5,8,4,2,1,6,7,3]=>0111001=>[1,3,2,1]
[4,1,5,8,7,3,2,6]=>[5,8,4,1,2,6,7,3]=>0110001=>[1,2,3,1]
[4,7,1,8,3,6,2,5]=>[5,2,8,1,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[4,1,7,8,5,2,3,6]=>[5,8,2,1,4,7,6,3]=>0110011=>[1,2,2,2]
[5,1,7,4,8,2,3,6]=>[4,8,2,5,1,7,6,3]=>0101011=>[1,1,1,1,1,2]
[7,5,3,8,1,4,2,6]=>[2,4,6,1,8,5,7,3]=>0010101=>[2,1,1,1,1,1]
[2,1,5,8,7,3,4,6]=>[7,8,4,1,2,6,5,3]=>0110011=>[1,2,2,2]
[5,1,8,4,7,2,3,6]=>[4,8,1,5,2,7,6,3]=>0101011=>[1,1,1,1,1,2]
[4,1,8,7,5,2,3,6]=>[5,8,1,2,4,7,6,3]=>0100011=>[1,1,3,2]
[4,7,1,6,3,2,8,5]=>[5,2,8,3,6,7,1,4]=>1010010=>[1,1,1,2,1,1]
[6,1,2,3,7,5,8,4]=>[3,8,7,6,2,4,1,5]=>0111010=>[1,3,1,1,1]
[7,1,2,3,8,6,5,4]=>[2,8,7,6,1,3,4,5]=>0111000=>[1,3,3]
[7,1,2,3,5,8,6,4]=>[2,8,7,6,4,1,3,5]=>0111100=>[1,4,2]
[6,8,1,4,3,7,2,5]=>[3,1,8,5,6,2,7,4]=>1010101=>[1,1,1,1,1,1,1]
[8,7,3,2,4,1,6,5]=>[1,2,6,7,5,8,3,4]=>0001010=>[3,1,1,1,1]
[2,1,7,3,4,8,6,5]=>[7,8,2,6,5,1,3,4]=>0101100=>[1,1,1,2,2]
[7,8,3,2,4,1,6,5]=>[2,1,6,7,5,8,3,4]=>1001010=>[1,2,1,1,1,1]
[6,7,1,4,3,8,2,5]=>[3,2,8,5,6,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[8,1,2,3,5,7,6,4]=>[1,8,7,6,4,2,3,5]=>0111100=>[1,4,2]
[8,1,2,3,6,7,5,4]=>[1,8,7,6,3,2,4,5]=>0111100=>[1,4,2]
[7,1,2,3,6,8,5,4]=>[2,8,7,6,3,1,4,5]=>0111100=>[1,4,2]
[7,1,2,3,8,5,6,4]=>[2,8,7,6,1,4,3,5]=>0111010=>[1,3,1,1,1]
[8,1,2,3,7,5,6,4]=>[1,8,7,6,2,4,3,5]=>0111010=>[1,3,1,1,1]
[8,1,2,3,6,5,7,4]=>[1,8,7,6,3,4,2,5]=>0111010=>[1,3,1,1,1]
[7,1,8,5,4,3,2,6]=>[2,8,1,4,5,6,7,3]=>0100001=>[1,1,4,1]
[7,8,2,6,3,4,1,5]=>[2,1,7,3,6,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,7,3,4,1,5]=>[3,1,7,2,6,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[6,7,2,8,3,4,1,5]=>[3,2,7,1,6,5,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,8,7,1,4,2,6,5]=>[6,1,2,8,5,7,3,4]=>1001010=>[1,2,1,1,1,1]
[3,7,8,1,4,2,6,5]=>[6,2,1,8,5,7,3,4]=>1101010=>[2,1,1,1,1,1]
[3,6,8,1,4,2,7,5]=>[6,3,1,8,5,7,2,4]=>1101010=>[2,1,1,1,1,1]
[3,5,7,8,2,4,1,6]=>[6,4,2,1,7,5,8,3]=>1110101=>[3,1,1,1,1]
[3,6,7,1,4,2,8,5]=>[6,3,2,8,5,7,1,4]=>1101010=>[2,1,1,1,1,1]
[7,6,2,8,3,1,4,5]=>[2,3,7,1,6,8,5,4]=>0010011=>[2,1,2,2]
[8,6,2,7,3,1,4,5]=>[1,3,7,2,6,8,5,4]=>0010011=>[2,1,2,2]
[8,1,7,5,4,3,2,6]=>[1,8,2,4,5,6,7,3]=>0100001=>[1,1,4,1]
[8,1,7,4,5,3,2,6]=>[1,8,2,5,4,6,7,3]=>0101001=>[1,1,1,1,2,1]
[5,8,3,7,1,4,2,6]=>[4,1,6,2,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]
[2,1,7,3,4,6,8,5]=>[7,8,2,6,5,3,1,4]=>0101110=>[1,1,1,3,1]
[6,7,3,2,4,1,8,5]=>[3,2,6,7,5,8,1,4]=>1001010=>[1,2,1,1,1,1]
[8,7,2,4,3,6,1,5]=>[1,2,7,5,6,3,8,4]=>0010101=>[2,1,1,1,1,1]
[7,1,2,3,5,6,8,4]=>[2,8,7,6,4,3,1,5]=>0111110=>[1,5,1]
[6,1,2,3,8,7,4,5]=>[3,8,7,6,1,2,5,4]=>0111001=>[1,3,2,1]
[5,1,2,3,7,8,6,4]=>[4,8,7,6,2,1,3,5]=>0111100=>[1,4,2]
[5,1,2,3,8,7,6,4]=>[4,8,7,6,1,2,3,5]=>0111000=>[1,3,3]
[5,1,2,3,8,6,7,4]=>[4,8,7,6,1,3,2,5]=>0111010=>[1,3,1,1,1]
[6,1,2,3,5,8,7,4]=>[3,8,7,6,4,1,2,5]=>0111100=>[1,4,2]
[8,6,2,4,3,1,7,5]=>[1,3,7,5,6,8,2,4]=>0010010=>[2,1,2,1,1]
[7,6,3,2,4,8,1,5]=>[2,3,6,7,5,1,8,4]=>0001101=>[3,2,1,1]
[2,1,6,3,4,8,7,5]=>[7,8,3,6,5,1,2,4]=>0101100=>[1,1,1,2,2]
[8,6,3,2,4,7,1,5]=>[1,3,6,7,5,2,8,4]=>0001101=>[3,2,1,1]
[7,6,2,4,3,1,8,5]=>[2,3,7,5,6,8,1,4]=>0010010=>[2,1,2,1,1]
[6,1,2,3,5,7,8,4]=>[3,8,7,6,4,2,1,5]=>0111110=>[1,5,1]
[5,1,2,3,6,8,7,4]=>[4,8,7,6,3,1,2,5]=>0111100=>[1,4,2]
[7,8,1,2,6,3,5,4]=>[2,1,8,7,3,6,4,5]=>1011010=>[1,1,2,1,1,1]
[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>1100101=>[2,2,1,1,1]
[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>1100010=>[2,3,1,1]
[1,3,6,8,4,7,5,2]=>[8,6,3,1,5,2,4,7]=>1110100=>[3,1,1,2]
[3,4,8,5,7,6,1,2]=>[6,5,1,4,2,3,8,7]=>1101001=>[2,1,1,2,1]
[1,2,6,8,4,5,7,3]=>[8,7,3,1,5,4,2,6]=>1110110=>[3,1,2,1]
[7,5,1,2,4,3,6,8]=>[2,4,8,7,5,6,3,1]=>0011011=>[2,2,1,2]
[7,4,6,1,5,2,3,8]=>[2,5,3,8,4,7,6,1]=>0101011=>[1,1,1,1,1,2]
[7,1,4,2,6,3,5,8]=>[2,8,5,7,3,6,4,1]=>0101011=>[1,1,1,1,1,2]
[6,8,1,4,7,2,3,5]=>[3,1,8,5,2,7,6,4]=>1011011=>[1,1,2,1,2]
[6,8,1,7,3,5,4,2]=>[3,1,8,2,6,4,5,7]=>1010100=>[1,1,1,1,1,2]
[7,1,3,6,5,4,2,8]=>[2,8,6,3,4,5,7,1]=>0110001=>[1,2,3,1]
[7,1,2,3,6,5,4,8]=>[2,8,7,6,3,4,5,1]=>0111001=>[1,3,2,1]
[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>1011001=>[1,1,2,2,1]
[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>1101001=>[2,1,1,2,1]
[6,8,2,1,7,4,3,5]=>[3,1,7,8,2,5,6,4]=>1001001=>[1,2,1,2,1]
[2,5,3,8,7,4,6,1]=>[7,4,6,1,2,5,3,8]=>1010010=>[1,1,1,2,1,1]
[2,4,8,7,6,5,1,3]=>[7,5,1,2,3,4,8,6]=>1100001=>[2,4,1]
[2,5,8,4,1,7,6,3]=>[7,4,1,5,8,2,3,6]=>1100100=>[2,2,1,2]
[5,3,8,4,1,7,6,2]=>[4,6,1,5,8,2,3,7]=>0100100=>[1,1,2,1,2]
[4,2,8,7,6,5,3,1]=>[5,7,1,2,3,4,6,8]=>0100000=>[1,1,5]
[4,1,8,7,6,5,3,2]=>[5,8,1,2,3,4,6,7]=>0100000=>[1,1,5]
[4,3,8,7,6,5,1,2]=>[5,6,1,2,3,4,8,7]=>0100001=>[1,1,4,1]
[5,8,3,7,6,1,4,2]=>[4,1,6,2,3,8,5,7]=>1010010=>[1,1,1,2,1,1]
[1,5,8,4,7,2,6,3]=>[8,4,1,5,2,7,3,6]=>1101010=>[2,1,1,1,1,1]
[5,1,8,4,7,2,6,3]=>[4,8,1,5,2,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[5,8,7,4,6,1,2,3]=>[4,1,2,5,3,8,7,6]=>1001011=>[1,2,1,1,2]
[5,6,3,1,2,4,8,7]=>[4,3,6,8,7,5,1,2]=>1001110=>[1,2,3,1]
[5,6,2,4,3,1,8,7]=>[4,3,7,5,6,8,1,2]=>1010010=>[1,1,1,2,1,1]
[5,6,1,2,4,3,8,7]=>[4,3,8,7,5,6,1,2]=>1011010=>[1,1,2,1,1,1]
[4,5,8,1,7,2,3,6]=>[5,4,1,8,2,7,6,3]=>1101011=>[2,1,1,1,2]
[3,5,1,8,7,4,6,2]=>[6,4,8,1,2,5,3,7]=>1010010=>[1,1,1,2,1,1]
[3,5,1,8,7,2,6,4]=>[6,4,8,1,2,7,3,5]=>1010010=>[1,1,1,2,1,1]
[4,5,8,3,1,7,2,6]=>[5,4,1,6,8,2,7,3]=>1100101=>[2,2,1,1,1]
[4,5,2,8,7,1,3,6]=>[5,4,7,1,2,8,6,3]=>1010011=>[1,1,1,2,2]
[3,2,5,8,7,1,6,4]=>[6,7,4,1,2,8,3,5]=>0110010=>[1,2,2,1,1]
[3,4,8,7,6,2,1,5]=>[6,5,1,2,3,7,8,4]=>1100001=>[2,4,1]
[3,1,4,8,7,6,2,5]=>[6,8,5,1,2,3,7,4]=>0110001=>[1,2,3,1]
[3,4,8,7,6,5,1,2]=>[6,5,1,2,3,4,8,7]=>1100001=>[2,4,1]
[3,2,5,8,7,4,6,1]=>[6,7,4,1,2,5,3,8]=>0110010=>[1,2,2,1,1]
[4,5,8,3,1,7,6,2]=>[5,4,1,6,8,2,3,7]=>1100100=>[2,2,1,2]
[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>1101000=>[2,1,1,3]
[7,1,4,8,2,6,5,3]=>[2,8,5,1,7,3,4,6]=>0110100=>[1,2,1,1,2]
[6,8,1,3,7,5,2,4]=>[3,1,8,6,2,4,7,5]=>1011001=>[1,1,2,2,1]
[3,7,8,1,2,6,5,4]=>[6,2,1,8,7,3,4,5]=>1101100=>[2,1,2,2]
[1,3,7,8,2,6,5,4]=>[8,6,2,1,7,3,4,5]=>1110100=>[3,1,1,2]
[2,3,7,8,1,6,5,4]=>[7,6,2,1,8,3,4,5]=>1110100=>[3,1,1,2]
[2,7,8,1,3,6,5,4]=>[7,2,1,8,6,3,4,5]=>1101100=>[2,1,2,2]
[8,1,2,6,7,3,5,4]=>[1,8,7,3,2,6,4,5]=>0111010=>[1,3,1,1,1]
[8,1,2,6,7,5,3,4]=>[1,8,7,3,2,4,6,5]=>0111001=>[1,3,2,1]
[8,2,5,7,1,3,6,4]=>[1,7,4,2,8,6,3,5]=>0110110=>[1,2,1,2,1]
[2,8,1,6,7,3,5,4]=>[7,1,8,3,2,6,4,5]=>1011010=>[1,1,2,1,1,1]
[2,6,8,3,7,1,5,4]=>[7,3,1,6,2,8,4,5]=>1101010=>[2,1,1,1,1,1]
[2,8,6,4,7,1,5,3]=>[7,1,3,5,2,8,4,6]=>1001010=>[1,2,1,1,1,1]
[6,8,3,4,1,7,5,2]=>[3,1,6,5,8,2,4,7]=>1010100=>[1,1,1,1,1,2]
[6,8,3,7,4,1,5,2]=>[3,1,6,2,5,8,4,7]=>1010010=>[1,1,1,2,1,1]
[2,6,8,3,7,5,1,4]=>[7,3,1,6,2,4,8,5]=>1101001=>[2,1,1,2,1]
[2,8,1,6,7,5,3,4]=>[7,1,8,3,2,4,6,5]=>1011001=>[1,1,2,2,1]
[8,2,5,7,1,6,3,4]=>[1,7,4,2,8,3,6,5]=>0110101=>[1,2,1,1,1,1]
[8,4,7,2,3,6,1,5]=>[1,5,2,7,6,3,8,4]=>0101101=>[1,1,1,2,1,1]
[8,5,7,4,2,6,1,3]=>[1,4,2,5,7,3,8,6]=>0100101=>[1,1,2,1,1,1]
[8,3,5,7,4,1,6,2]=>[1,6,4,2,5,8,3,7]=>0110010=>[1,2,2,1,1]
[8,5,2,4,7,1,6,3]=>[1,4,7,5,2,8,3,6]=>0011010=>[2,2,1,1,1]
[8,2,3,5,7,1,6,4]=>[1,7,6,4,2,8,3,5]=>0111010=>[1,3,1,1,1]
[8,2,4,7,3,6,1,5]=>[1,7,5,2,6,3,8,4]=>0110101=>[1,2,1,1,1,1]
[8,2,7,1,4,6,3,5]=>[1,7,2,8,5,3,6,4]=>0101101=>[1,1,1,2,1,1]
[8,7,1,2,4,6,3,5]=>[1,2,8,7,5,3,6,4]=>0011101=>[2,3,1,1]
[8,7,1,4,6,2,3,5]=>[1,2,8,5,3,7,6,4]=>0011011=>[2,2,1,2]
[8,4,7,1,3,6,2,5]=>[1,5,2,8,6,3,7,4]=>0101101=>[1,1,1,2,1,1]
[1,6,8,3,7,2,5,4]=>[8,3,1,6,2,7,4,5]=>1101010=>[2,1,1,1,1,1]
[8,3,5,7,1,2,6,4]=>[1,6,4,2,8,7,3,5]=>0110110=>[1,2,1,2,1]
[5,8,7,1,3,6,2,4]=>[4,1,2,8,6,3,7,5]=>1001101=>[1,2,2,1,1]
[8,5,4,7,1,6,2,3]=>[1,4,5,2,8,3,7,6]=>0010101=>[2,1,1,1,1,1]
[8,5,1,4,7,2,6,3]=>[1,4,8,5,2,7,3,6]=>0011010=>[2,2,1,1,1]
[1,4,6,8,2,7,5,3]=>[8,5,3,1,7,2,4,6]=>1110100=>[3,1,1,2]
[1,6,5,8,2,7,4,3]=>[8,3,4,1,7,2,5,6]=>1010100=>[1,1,1,1,1,2]
[8,5,6,3,1,7,4,2]=>[1,4,3,6,8,2,5,7]=>0100100=>[1,1,2,1,2]
[5,6,2,8,1,7,4,3]=>[4,3,7,1,8,2,5,6]=>1010100=>[1,1,1,1,1,2]
[1,8,4,5,7,2,6,3]=>[8,1,5,4,2,7,3,6]=>1011010=>[1,1,2,1,1,1]
[5,8,7,3,6,1,2,4]=>[4,1,2,6,3,8,7,5]=>1001011=>[1,2,1,1,2]
[8,3,5,7,1,6,2,4]=>[1,6,4,2,8,3,7,5]=>0110101=>[1,2,1,1,1,1]
[1,6,8,3,7,5,2,4]=>[8,3,1,6,2,4,7,5]=>1101001=>[2,1,1,2,1]
[6,3,8,2,7,5,1,4]=>[3,6,1,7,2,4,8,5]=>0101001=>[1,1,1,1,2,1]
[6,8,4,2,7,1,5,3]=>[3,1,5,7,2,8,4,6]=>1001010=>[1,2,1,1,1,1]
[8,6,4,7,3,1,5,2]=>[1,3,5,2,6,8,4,7]=>0010010=>[2,1,2,1,1]
[8,4,5,7,3,1,6,2]=>[1,5,4,2,6,8,3,7]=>0110010=>[1,2,2,1,1]
[8,4,2,5,7,1,6,3]=>[1,5,7,4,2,8,3,6]=>0011010=>[2,2,1,1,1]
[8,3,4,7,2,6,1,5]=>[1,6,5,2,7,3,8,4]=>0110101=>[1,2,1,1,1,1]
[8,7,1,3,4,6,2,5]=>[1,2,8,6,5,3,7,4]=>0011101=>[2,3,1,1]
[8,3,7,2,4,6,1,5]=>[1,6,2,7,5,3,8,4]=>0101101=>[1,1,1,2,1,1]
[2,8,4,5,7,1,6,3]=>[7,1,5,4,2,8,3,6]=>1011010=>[1,1,2,1,1,1]
[8,7,3,4,5,1,6,2]=>[1,2,6,5,4,8,3,7]=>0011010=>[2,2,1,1,1]
[8,7,4,5,2,6,1,3]=>[1,2,5,4,7,3,8,6]=>0010101=>[2,1,1,1,1,1]
[5,8,7,2,3,6,1,4]=>[4,1,2,7,6,3,8,5]=>1001101=>[1,2,2,1,1]
[8,7,2,3,4,6,1,5]=>[1,2,7,6,5,3,8,4]=>0011101=>[2,3,1,1]
[8,7,2,3,6,1,4,5]=>[1,2,7,6,3,8,5,4]=>0011011=>[2,2,1,2]
[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>1010010=>[1,1,1,2,1,1]
[4,2,8,5,3,7,1,6]=>[5,7,1,4,6,2,8,3]=>0100101=>[1,1,2,1,1,1]
[5,2,1,8,4,3,7,6]=>[4,7,8,1,5,6,2,3]=>0010010=>[2,1,2,1,1]
[7,3,4,8,2,1,6,5]=>[2,6,5,1,7,8,3,4]=>0110010=>[1,2,2,1,1]
[6,3,4,8,2,7,5,1]=>[3,6,5,1,7,2,4,8]=>0110100=>[1,2,1,1,2]
[5,3,4,1,8,2,7,6]=>[4,6,5,8,1,7,2,3]=>0101010=>[1,1,1,1,1,1,1]
[8,1,5,4,3,2,7,6]=>[1,8,4,5,6,7,2,3]=>0100010=>[1,1,3,1,1]
[3,5,4,2,8,1,7,6]=>[6,4,5,7,1,8,2,3]=>1001010=>[1,2,1,1,1,1]
[4,5,3,2,8,7,1,6]=>[5,4,6,7,1,2,8,3]=>1001001=>[1,2,1,2,1]
[6,4,3,2,8,7,5,1]=>[3,5,6,7,1,2,4,8]=>0001000=>[3,1,3]
[6,5,3,2,1,7,8,4]=>[3,4,6,7,8,2,1,5]=>0000110=>[4,2,1]
[5,6,3,2,7,8,4,1]=>[4,3,6,7,2,1,5,8]=>1001100=>[1,2,2,2]
[4,1,6,3,2,7,8,5]=>[5,8,3,6,7,2,1,4]=>0100110=>[1,1,2,2,1]
[3,6,4,2,7,8,1,5]=>[6,3,5,7,2,1,8,4]=>1001101=>[1,2,2,1,1]
[8,1,6,4,3,7,2,5]=>[1,8,3,5,6,2,7,4]=>0100101=>[1,1,2,1,1,1]
[8,1,7,4,3,6,5,2]=>[1,8,2,5,6,3,4,7]=>0100100=>[1,1,2,1,2]
[5,7,3,2,6,4,8,1]=>[4,2,6,7,3,5,1,8]=>1001010=>[1,2,1,1,1,1]
[4,7,5,6,2,3,8,1]=>[5,2,4,3,7,6,1,8]=>1010110=>[1,1,1,1,2,1]
[3,1,7,5,6,2,4,8]=>[6,8,2,4,3,7,5,1]=>0101011=>[1,1,1,1,1,2]
[4,6,5,7,2,8,1,3]=>[5,3,4,2,7,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,6,4,7,2,8,3,1]=>[4,3,5,2,7,1,6,8]=>1010100=>[1,1,1,1,1,2]
[6,5,4,1,7,2,8,3]=>[3,4,5,8,2,7,1,6]=>0001010=>[3,1,1,1,1]
[6,4,5,7,1,8,2,3]=>[3,5,4,2,8,1,7,6]=>0110101=>[1,2,1,1,1,1]
[5,4,6,1,7,8,2,3]=>[4,5,3,8,2,1,7,6]=>0101101=>[1,1,1,2,1,1]
[8,1,5,6,7,2,3,4]=>[1,8,4,3,2,7,6,5]=>0111011=>[1,3,1,2]
[2,1,4,6,8,7,3,5]=>[7,8,5,3,1,2,6,4]=>0111001=>[1,3,2,1]
[4,3,1,6,8,7,2,5]=>[5,6,8,3,1,2,7,4]=>0011001=>[2,2,2,1]
[5,3,6,8,7,2,4,1]=>[4,6,3,1,2,7,5,8]=>0110010=>[1,2,2,1,1]
[7,3,5,8,6,2,1,4]=>[2,6,4,1,3,7,8,5]=>0110001=>[1,2,3,1]
[7,2,8,5,6,3,1,4]=>[2,7,1,4,3,6,8,5]=>0101001=>[1,1,1,1,2,1]
[4,2,1,8,6,7,3,5]=>[5,7,8,1,3,2,6,4]=>0010101=>[2,1,1,1,1,1]
[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[4,2,8,7,6,1,5,3]=>[5,7,1,2,3,8,4,6]=>0100010=>[1,1,3,1,1]
[5,2,8,7,6,4,1,3]=>[4,7,1,2,3,5,8,6]=>0100001=>[1,1,4,1]
[7,2,1,8,6,5,4,3]=>[2,7,8,1,3,4,5,6]=>0010000=>[2,1,4]
[7,3,6,1,8,5,4,2]=>[2,6,3,8,1,4,5,7]=>0101000=>[1,1,1,1,3]
[5,3,7,8,6,4,1,2]=>[4,6,2,1,3,5,8,7]=>0110001=>[1,2,3,1]
[4,3,1,7,8,6,5,2]=>[5,6,8,2,1,3,4,7]=>0011000=>[2,2,3]
[3,4,7,8,6,1,5,2]=>[6,5,2,1,3,8,4,7]=>1110010=>[3,2,1,1]
[8,1,5,7,6,2,4,3]=>[1,8,4,2,3,7,5,6]=>0110010=>[1,2,2,1,1]
[4,5,7,6,8,3,1,2]=>[5,4,2,3,1,6,8,7]=>1101001=>[2,1,1,2,1]
[5,4,1,7,6,8,3,2]=>[4,5,8,2,3,1,6,7]=>0010100=>[2,1,1,1,2]
[6,4,7,5,8,3,2,1]=>[3,5,2,4,1,6,7,8]=>0101000=>[1,1,1,1,3]
[7,5,6,4,3,1,8,2]=>[2,4,3,5,6,8,1,7]=>0100010=>[1,1,3,1,1]
[6,5,1,7,4,3,8,2]=>[3,4,8,2,5,6,1,7]=>0010010=>[2,1,2,1,1]
[4,6,7,5,3,8,1,2]=>[5,3,2,4,6,1,8,7]=>1100101=>[2,2,1,1,1]
[3,6,7,5,1,4,8,2]=>[6,3,2,4,8,5,1,7]=>1100110=>[2,2,2,1]
[8,1,6,7,5,4,2,3]=>[1,8,3,2,4,5,7,6]=>0110001=>[1,2,3,1]
[8,1,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>0100000=>[1,1,5]
[2,7,6,1,5,4,3,8]=>[7,2,3,8,4,5,6,1]=>1001001=>[1,2,1,2,1]
[8,6,4,3,1,5,7,2]=>[1,3,5,6,8,4,2,7]=>0000110=>[4,2,1]
[8,6,4,1,5,2,7,3]=>[1,3,5,8,4,7,2,6]=>0001010=>[3,1,1,1,1]
[8,6,3,1,7,2,4,5]=>[1,3,6,8,2,7,5,4]=>0001011=>[3,1,1,2]
[8,7,3,1,5,2,4,6]=>[1,2,6,8,4,7,5,3]=>0001011=>[3,1,1,2]
[5,3,1,7,2,4,6,8]=>[4,6,8,2,7,5,3,1]=>0010111=>[2,1,1,3]
[8,7,1,2,4,5,3,6]=>[1,2,8,7,5,4,6,3]=>0011101=>[2,3,1,1]
[8,5,1,3,6,4,7,2]=>[1,4,8,6,3,5,2,7]=>0011010=>[2,2,1,1,1]
[8,6,1,5,2,4,7,3]=>[1,3,8,4,7,5,2,6]=>0010110=>[2,1,1,2,1]
[8,6,1,2,5,7,3,4]=>[1,3,8,7,4,2,6,5]=>0011101=>[2,3,1,1]
[8,6,1,2,7,4,3,5]=>[1,3,8,7,2,5,6,4]=>0011001=>[2,2,2,1]
[8,7,1,2,5,4,3,6]=>[1,2,8,7,4,5,6,3]=>0011001=>[2,2,2,1]
[5,1,4,2,3,8,6,7]=>[4,8,5,7,6,1,3,2]=>0101101=>[1,1,1,2,1,1]
[5,1,4,2,7,3,6,8]=>[4,8,5,7,2,6,3,1]=>0101011=>[1,1,1,1,1,2]
[5,7,8,1,3,4,6,2]=>[4,2,1,8,6,5,3,7]=>1101110=>[2,1,3,1]
[5,8,1,7,3,4,6,2]=>[4,1,8,2,6,5,3,7]=>1010110=>[1,1,1,1,2,1]
[8,1,5,7,2,4,6,3]=>[1,8,4,2,7,5,3,6]=>0110110=>[1,2,1,2,1]
[8,4,1,2,7,6,3,5]=>[1,5,8,7,2,3,6,4]=>0011001=>[2,2,2,1]
[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>1011001=>[1,1,2,2,1]
[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>1010011=>[1,1,1,2,2]
[6,1,2,8,7,5,3,4]=>[3,8,7,1,2,4,6,5]=>0110001=>[1,2,3,1]
[6,1,2,4,8,7,5,3]=>[3,8,7,5,1,2,4,6]=>0111000=>[1,3,3]
[3,1,8,4,6,7,5,2]=>[6,8,1,5,3,2,4,7]=>0101100=>[1,1,1,2,2]
[7,1,2,4,6,8,5,3]=>[2,8,7,5,3,1,4,6]=>0111100=>[1,4,2]
[7,1,2,6,8,5,3,4]=>[2,8,7,3,1,4,6,5]=>0111001=>[1,3,2,1]
[6,1,2,7,8,5,3,4]=>[3,8,7,2,1,4,6,5]=>0111001=>[1,3,2,1]
[6,1,2,7,4,8,5,3]=>[3,8,7,2,5,1,4,6]=>0110100=>[1,2,1,1,2]
[5,7,1,3,8,4,6,2]=>[4,2,8,6,1,5,3,7]=>1011010=>[1,1,2,1,1,1]
[5,7,1,8,4,2,6,3]=>[4,2,8,1,5,7,3,6]=>1010010=>[1,1,1,2,1,1]
[7,1,5,3,2,8,6,4]=>[2,8,4,6,7,1,3,5]=>0100100=>[1,1,2,1,2]
[7,1,4,5,2,8,6,3]=>[2,8,5,4,7,1,3,6]=>0110100=>[1,2,1,1,2]
[4,7,3,1,5,8,6,2]=>[5,2,6,8,4,1,3,7]=>1001100=>[1,2,2,2]
[4,8,7,3,1,5,6,2]=>[5,1,2,6,8,4,3,7]=>1000110=>[1,3,2,1]
[8,1,7,4,5,2,6,3]=>[1,8,2,5,4,7,3,6]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,5,3,2,6,4]=>[1,8,2,4,6,7,3,5]=>0100010=>[1,1,3,1,1]
[8,3,7,1,2,6,4,5]=>[1,6,2,8,7,3,5,4]=>0101101=>[1,1,1,2,1,1]
[3,1,2,8,6,4,5,7]=>[6,8,7,1,3,5,4,2]=>0110011=>[1,2,2,2]
[3,1,7,2,6,4,5,8]=>[6,8,2,7,3,5,4,1]=>0101011=>[1,1,1,1,1,2]
[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>1011010=>[1,1,2,1,1,1]
[5,8,1,7,2,4,6,3]=>[4,1,8,2,7,5,3,6]=>1010110=>[1,1,1,1,2,1]
[8,1,2,6,7,4,5,3]=>[1,8,7,3,2,5,4,6]=>0111010=>[1,3,1,1,1]
[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>1111010=>[4,1,1,1]
[7,1,2,8,3,6,5,4]=>[2,8,7,1,6,3,4,5]=>0110100=>[1,2,1,1,2]
[3,1,7,8,4,6,5,2]=>[6,8,2,1,5,3,4,7]=>0110100=>[1,2,1,1,2]
[8,1,2,7,4,6,5,3]=>[1,8,7,2,5,3,4,6]=>0110100=>[1,2,1,1,2]
[8,1,2,7,3,6,5,4]=>[1,8,7,2,6,3,4,5]=>0110100=>[1,2,1,1,2]
[1,2,3,5,8,7,4,6]=>[8,7,6,4,1,2,5,3]=>1111001=>[4,2,1]
[7,8,5,6,3,1,4,2]=>[2,1,4,3,6,8,5,7]=>1010010=>[1,1,1,2,1,1]
[7,8,5,3,6,1,2,4]=>[2,1,4,6,3,8,7,5]=>1001011=>[1,2,1,1,2]
[7,5,6,3,1,4,2,8]=>[2,4,3,6,8,5,7,1]=>0100101=>[1,1,2,1,1,1]
[7,5,8,3,1,4,2,6]=>[2,4,1,6,8,5,7,3]=>0100101=>[1,1,2,1,1,1]
[7,8,5,3,1,4,2,6]=>[2,1,4,6,8,5,7,3]=>1000101=>[1,3,1,1,1]
[7,8,5,3,1,6,2,4]=>[2,1,4,6,8,3,7,5]=>1000101=>[1,3,1,1,1]
[7,8,5,3,1,6,4,2]=>[2,1,4,6,8,3,5,7]=>1000100=>[1,3,1,2]
[7,8,5,3,6,1,4,2]=>[2,1,4,6,3,8,5,7]=>1001010=>[1,2,1,1,1,1]
[7,8,5,3,6,4,1,2]=>[2,1,4,6,3,5,8,7]=>1001001=>[1,2,1,2,1]
[7,8,5,3,4,1,6,2]=>[2,1,4,6,5,8,3,7]=>1001010=>[1,2,1,1,1,1]
[7,8,5,3,1,4,6,2]=>[2,1,4,6,8,5,3,7]=>1000110=>[1,3,2,1]
[7,8,5,3,1,2,6,4]=>[2,1,4,6,8,7,3,5]=>1000110=>[1,3,2,1]
[7,5,3,8,1,2,6,4]=>[2,4,6,1,8,7,3,5]=>0010110=>[2,1,1,2,1]
[7,5,8,3,4,1,6,2]=>[2,4,1,6,5,8,3,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,8,3,4,6,1,2]=>[2,4,1,6,5,3,8,7]=>0101101=>[1,1,1,2,1,1]
[7,5,6,3,4,1,8,2]=>[2,4,3,6,5,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,6,3,1,4,8,2]=>[2,4,3,6,8,5,1,7]=>0100110=>[1,1,2,2,1]
[7,5,6,3,1,2,8,4]=>[2,4,3,6,8,7,1,5]=>0100110=>[1,1,2,2,1]
[7,5,3,6,1,2,8,4]=>[2,4,6,3,8,7,1,5]=>0010110=>[2,1,1,2,1]
[7,5,3,4,1,2,8,6]=>[2,4,6,5,8,7,1,3]=>0010110=>[2,1,1,2,1]
[7,5,3,1,4,2,6,8]=>[2,4,6,8,5,7,3,1]=>0001011=>[3,1,1,2]
[7,5,3,1,4,2,8,6]=>[2,4,6,8,5,7,1,3]=>0001010=>[3,1,1,1,1]
[7,5,3,1,6,2,8,4]=>[2,4,6,8,3,7,1,5]=>0001010=>[3,1,1,1,1]
[7,5,3,1,6,4,8,2]=>[2,4,6,8,3,5,1,7]=>0001010=>[3,1,1,1,1]
[7,5,3,6,1,4,8,2]=>[2,4,6,3,8,5,1,7]=>0010110=>[2,1,1,2,1]
[7,5,3,6,4,1,8,2]=>[2,4,6,3,5,8,1,7]=>0010010=>[2,1,2,1,1]
[7,5,3,6,4,8,1,2]=>[2,4,6,3,5,1,8,7]=>0010101=>[2,1,1,1,1,1]
[7,5,3,8,4,6,1,2]=>[2,4,6,1,5,3,8,7]=>0010101=>[2,1,1,1,1,1]
[7,5,3,8,1,4,6,2]=>[2,4,6,1,8,5,3,7]=>0010110=>[2,1,1,2,1]
[7,5,3,1,8,4,6,2]=>[2,4,6,8,1,5,3,7]=>0001010=>[3,1,1,1,1]
[7,5,3,1,8,2,6,4]=>[2,4,6,8,1,7,3,5]=>0001010=>[3,1,1,1,1]
[7,5,3,1,8,2,4,6]=>[2,4,6,8,1,7,5,3]=>0001011=>[3,1,1,2]
[7,5,3,1,6,2,4,8]=>[2,4,6,8,3,7,5,1]=>0001011=>[3,1,1,2]
[7,5,3,1,6,4,2,8]=>[2,4,6,8,3,5,7,1]=>0001001=>[3,1,2,1]
[7,5,3,1,8,4,2,6]=>[2,4,6,8,1,5,7,3]=>0001001=>[3,1,2,1]
[7,5,3,1,8,6,2,4]=>[2,4,6,8,1,3,7,5]=>0001001=>[3,1,2,1]
[7,5,3,8,1,6,4,2]=>[2,4,6,1,8,3,5,7]=>0010100=>[2,1,1,1,2]
[7,5,3,8,6,1,4,2]=>[2,4,6,1,3,8,5,7]=>0010010=>[2,1,2,1,1]
[7,5,3,8,6,4,1,2]=>[2,4,6,1,3,5,8,7]=>0010001=>[2,1,3,1]
[7,5,8,3,6,4,1,2]=>[2,4,1,6,3,5,8,7]=>0101001=>[1,1,1,1,2,1]
[7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,8,3,1,6,4,2]=>[2,4,1,6,8,3,5,7]=>0100100=>[1,1,2,1,2]
[7,5,8,3,1,6,2,4]=>[2,4,1,6,8,3,7,5]=>0100101=>[1,1,2,1,1,1]
[7,5,3,6,1,4,2,8]=>[2,4,6,3,8,5,7,1]=>0010101=>[2,1,1,1,1,1]
[7,5,3,6,4,1,2,8]=>[2,4,6,3,5,8,7,1]=>0010011=>[2,1,2,2]
[7,5,3,8,4,1,2,6]=>[2,4,6,1,5,8,7,3]=>0010011=>[2,1,2,2]
[7,5,8,6,3,1,2,4]=>[2,4,1,3,6,8,7,5]=>0100011=>[1,1,3,2]
[7,5,8,6,3,1,4,2]=>[2,4,1,3,6,8,5,7]=>0100010=>[1,1,3,1,1]
[7,5,8,6,3,4,1,2]=>[2,4,1,3,6,5,8,7]=>0100101=>[1,1,2,1,1,1]
[7,5,6,8,3,1,4,2]=>[2,4,3,1,6,8,5,7]=>0110010=>[1,2,2,1,1]
[7,5,6,3,8,1,2,4]=>[2,4,3,6,1,8,7,5]=>0101011=>[1,1,1,1,1,2]
[7,5,3,4,1,6,2,8]=>[2,4,6,5,8,3,7,1]=>0010101=>[2,1,1,1,1,1]
[7,5,3,4,1,8,2,6]=>[2,4,6,5,8,1,7,3]=>0010101=>[2,1,1,1,1,1]
[7,5,6,3,1,8,2,4]=>[2,4,3,6,8,1,7,5]=>0100101=>[1,1,2,1,1,1]
[7,5,6,3,1,8,4,2]=>[2,4,3,6,8,1,5,7]=>0100100=>[1,1,2,1,2]
[7,5,6,3,8,1,4,2]=>[2,4,3,6,1,8,5,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,6,3,8,4,1,2]=>[2,4,3,6,1,5,8,7]=>0101001=>[1,1,1,1,2,1]
[7,5,3,6,8,4,1,2]=>[2,4,6,3,1,5,8,7]=>0011001=>[2,2,2,1]
[7,5,3,6,8,1,4,2]=>[2,4,6,3,1,8,5,7]=>0011010=>[2,2,1,1,1]
[7,5,3,6,1,8,4,2]=>[2,4,6,3,8,1,5,7]=>0010100=>[2,1,1,1,2]
[7,5,3,1,6,8,4,2]=>[2,4,6,8,3,1,5,7]=>0001100=>[3,2,2]
[7,5,3,1,6,8,2,4]=>[2,4,6,8,3,1,7,5]=>0001101=>[3,2,1,1]
[7,5,3,1,4,8,2,6]=>[2,4,6,8,5,1,7,3]=>0001101=>[3,2,1,1]
[7,5,3,1,4,6,2,8]=>[2,4,6,8,5,3,7,1]=>0001101=>[3,2,1,1]
[7,5,3,1,2,6,4,8]=>[2,4,6,8,7,3,5,1]=>0001101=>[3,2,1,1]
[7,5,3,1,2,8,4,6]=>[2,4,6,8,7,1,5,3]=>0001101=>[3,2,1,1]
[7,5,3,1,2,8,6,4]=>[2,4,6,8,7,1,3,5]=>0001100=>[3,2,2]
[7,5,3,1,4,8,6,2]=>[2,4,6,8,5,1,3,7]=>0001100=>[3,2,2]
[7,5,3,4,1,8,6,2]=>[2,4,6,5,8,1,3,7]=>0010100=>[2,1,1,1,2]
[7,5,3,4,8,1,6,2]=>[2,4,6,5,1,8,3,7]=>0011010=>[2,2,1,1,1]
[7,5,3,4,8,6,1,2]=>[2,4,6,5,1,3,8,7]=>0011001=>[2,2,2,1]
[7,5,3,4,6,1,8,2]=>[2,4,6,5,3,8,1,7]=>0011010=>[2,2,1,1,1]
[7,5,3,4,1,6,8,2]=>[2,4,6,5,8,3,1,7]=>0010110=>[2,1,1,2,1]
[7,5,3,1,4,6,8,2]=>[2,4,6,8,5,3,1,7]=>0001110=>[3,3,1]
[7,5,3,1,2,6,8,4]=>[2,4,6,8,7,3,1,5]=>0001110=>[3,3,1]
[7,5,3,1,2,4,8,6]=>[2,4,6,8,7,5,1,3]=>0001110=>[3,3,1]
[3,6,2,5,4,1,8,7]=>[6,3,7,4,5,8,1,2]=>1010010=>[1,1,1,2,1,1]
[3,5,2,8,4,7,6,1]=>[6,4,7,1,5,2,3,8]=>1010100=>[1,1,1,1,1,2]
[5,4,7,3,2,8,6,1]=>[4,5,2,6,7,1,3,8]=>0100100=>[1,1,2,1,2]
[5,4,8,3,2,7,6,1]=>[4,5,1,6,7,2,3,8]=>0100100=>[1,1,2,1,2]
[6,4,5,3,2,1,8,7]=>[3,5,4,6,7,8,1,2]=>0100010=>[1,1,3,1,1]
[5,3,2,6,4,1,8,7]=>[4,6,7,3,5,8,1,2]=>0010010=>[2,1,2,1,1]
[4,5,8,3,2,7,6,1]=>[5,4,1,6,7,2,3,8]=>1100100=>[2,2,1,2]
[4,7,6,3,8,5,2,1]=>[5,2,3,6,1,4,7,8]=>1001000=>[1,2,1,3]
[4,8,6,3,7,5,2,1]=>[5,1,3,6,2,4,7,8]=>1001000=>[1,2,1,3]
[4,8,5,3,2,7,6,1]=>[5,1,4,6,7,2,3,8]=>1000100=>[1,3,1,2]
[5,8,4,3,2,7,6,1]=>[4,1,5,6,7,2,3,8]=>1000100=>[1,3,1,2]
[5,3,2,8,4,7,6,1]=>[4,6,7,1,5,2,3,8]=>0010100=>[2,1,1,1,2]
[2,1,5,8,4,7,6,3]=>[7,8,4,1,5,2,3,6]=>0110100=>[1,2,1,1,2]
[5,3,2,7,4,8,6,1]=>[4,6,7,2,5,1,3,8]=>0010100=>[2,1,1,1,2]
[5,7,4,3,2,8,6,1]=>[4,2,5,6,7,1,3,8]=>1000100=>[1,3,1,2]
[4,7,5,3,2,8,6,1]=>[5,2,4,6,7,1,3,8]=>1000100=>[1,3,1,2]
[4,7,8,3,6,5,2,1]=>[5,2,1,6,3,4,7,8]=>1101000=>[2,1,1,3]
[4,6,8,3,7,5,2,1]=>[5,3,1,6,2,4,7,8]=>1101000=>[2,1,1,3]
[7,6,4,3,8,5,2,1]=>[2,3,5,6,1,4,7,8]=>0001000=>[3,1,3]
[7,3,2,6,8,5,4,1]=>[2,6,7,3,1,4,5,8]=>0011000=>[2,2,3]
[2,1,8,6,7,5,4,3]=>[7,8,1,3,2,4,5,6]=>0101000=>[1,1,1,1,3]
[8,3,2,6,7,5,4,1]=>[1,6,7,3,2,4,5,8]=>0011000=>[2,2,3]
[8,6,4,3,7,5,2,1]=>[1,3,5,6,2,4,7,8]=>0001000=>[3,1,3]
[8,5,7,6,4,3,2,1]=>[1,4,2,3,5,6,7,8]=>0100000=>[1,1,5]
[8,4,5,3,2,7,6,1]=>[1,5,4,6,7,2,3,8]=>0100100=>[1,1,2,1,2]
[8,4,7,3,6,5,2,1]=>[1,5,2,6,3,4,7,8]=>0101000=>[1,1,1,1,3]
[8,4,6,3,7,5,2,1]=>[1,5,3,6,2,4,7,8]=>0101000=>[1,1,1,1,3]
[7,4,6,3,8,5,2,1]=>[2,5,3,6,1,4,7,8]=>0101000=>[1,1,1,1,3]
[3,7,2,6,8,5,4,1]=>[6,2,7,3,1,4,5,8]=>1011000=>[1,1,2,3]
[3,8,2,6,7,5,4,1]=>[6,1,7,3,2,4,5,8]=>1011000=>[1,1,2,3]
[3,8,2,5,4,7,6,1]=>[6,1,7,4,5,2,3,8]=>1010100=>[1,1,1,1,1,2]
[3,7,2,8,6,5,4,1]=>[6,2,7,1,3,4,5,8]=>1010000=>[1,1,1,4]
[3,6,2,8,7,5,4,1]=>[6,3,7,1,2,4,5,8]=>1010000=>[1,1,1,4]
[6,4,7,3,8,5,2,1]=>[3,5,2,6,1,4,7,8]=>0101000=>[1,1,1,1,3]
[6,4,8,3,7,5,2,1]=>[3,5,1,6,2,4,7,8]=>0101000=>[1,1,1,1,3]
[7,4,8,3,6,5,2,1]=>[2,5,1,6,3,4,7,8]=>0101000=>[1,1,1,1,3]
[7,4,5,3,2,8,6,1]=>[2,5,4,6,7,1,3,8]=>0100100=>[1,1,2,1,2]
[7,5,4,3,2,8,6,1]=>[2,4,5,6,7,1,3,8]=>0000100=>[4,1,2]
[7,3,2,5,4,8,6,1]=>[2,6,7,4,5,1,3,8]=>0010100=>[2,1,1,1,2]
[2,1,7,5,4,8,6,3]=>[7,8,2,4,5,1,3,6]=>0100100=>[1,1,2,1,2]
[7,3,2,8,6,5,4,1]=>[2,6,7,1,3,4,5,8]=>0010000=>[2,1,4]
[7,8,4,3,6,5,2,1]=>[2,1,5,6,3,4,7,8]=>1001000=>[1,2,1,3]
[6,8,5,7,4,3,2,1]=>[3,1,4,2,5,6,7,8]=>1010000=>[1,1,1,4]
[6,8,4,3,7,5,2,1]=>[3,1,5,6,2,4,7,8]=>1001000=>[1,2,1,3]
[6,3,2,8,7,5,4,1]=>[3,6,7,1,2,4,5,8]=>0010000=>[2,1,4]
[6,3,2,7,8,5,4,1]=>[3,6,7,2,1,4,5,8]=>0011000=>[2,2,3]
[6,7,4,3,8,5,2,1]=>[3,2,5,6,1,4,7,8]=>1001000=>[1,2,1,3]
[2,3,1,4,5,6,7,8,9]=>[8,7,9,6,5,4,3,2,1]=>10111111=>[1,1,6]
[2,3,4,1,5,6,7,8,9]=>[8,7,6,9,5,4,3,2,1]=>11011111=>[2,1,5]
[2,3,4,5,1,6,7,8,9]=>[8,7,6,5,9,4,3,2,1]=>11101111=>[3,1,4]
[2,3,4,5,6,1,7,8,9]=>[8,7,6,5,4,9,3,2,1]=>11110111=>[4,1,3]
[2,3,1,4,5,6,7,8,9,10]=>[9,8,10,7,6,5,4,3,2,1]=>101111111=>[1,1,7]
[2,4,3,1,5,6,7,8,9]=>[8,6,7,9,5,4,3,2,1]=>10011111=>[1,2,5]
[2,3,4,1,5,6,7,8,9,10]=>[9,8,7,10,6,5,4,3,2,1]=>110111111=>[2,1,6]
[2,3,5,4,1,6,7,8,9]=>[8,7,5,6,9,4,3,2,1]=>11001111=>[2,2,4]
[2,3,4,5,1,6,7,8,9,10]=>[9,8,7,6,10,5,4,3,2,1]=>111011111=>[3,1,5]
[2,3,4,6,5,1,7,8,9]=>[8,7,6,4,5,9,3,2,1]=>11100111=>[3,2,3]
[2,3,4,5,6,1,7,8,9,10]=>[9,8,7,6,5,10,4,3,2,1]=>111101111=>[4,1,4]
[2,3,4,5,7,6,1,8,9]=>[8,7,6,5,3,4,9,2,1]=>11110011=>[4,2,2]
[2,3,4,5,6,7,1,8,9,10]=>[9,8,7,6,5,4,10,3,2,1]=>111110111=>[5,1,3]
[2,3,4,5,6,8,7,1,9]=>[8,7,6,5,4,2,3,9,1]=>11111001=>[5,2,1]
[2,3,4,5,6,7,8,1,9,10]=>[9,8,7,6,5,4,3,10,2,1]=>111111011=>[6,1,2]
[2,3,4,5,6,7,9,8,1]=>[8,7,6,5,4,3,1,2,9]=>11111100=>[6,2]
[4,6,8,3,5,7,1,2]=>[5,3,1,6,4,2,8,7]=>1101101=>[2,1,2,1,1]
[6,8,1,2,4,5,7,3]=>[3,1,8,7,5,4,2,6]=>1011110=>[1,1,4,1]
[3,5,8,2,4,7,1,6]=>[6,4,1,7,5,2,8,3]=>1101101=>[2,1,2,1,1]
[4,2,5,7,3,6,1,8]=>[5,7,4,2,6,3,8,1]=>0110101=>[1,2,1,1,1,1]
[4,5,2,8,3,1,6,7]=>[5,4,7,1,6,8,3,2]=>1010011=>[1,1,1,2,2]
[4,2,5,8,3,7,1,6]=>[5,7,4,1,6,2,8,3]=>0110101=>[1,2,1,1,1,1]
[1,2,5,8,3,6,7,4]=>[8,7,4,1,6,3,2,5]=>1110110=>[3,1,2,1]
[5,3,6,8,4,7,1,2]=>[4,6,3,1,5,2,8,7]=>0110101=>[1,2,1,1,1,1]
[3,1,2,6,8,5,7,4]=>[6,8,7,3,1,4,2,5]=>0111010=>[1,3,1,1,1]
[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>1010110=>[1,1,1,1,2,1]
[5,4,8,3,2,1,6,7]=>[4,5,1,6,7,8,3,2]=>0100011=>[1,1,3,2]
[5,4,3,7,2,6,1,8]=>[4,5,6,2,7,3,8,1]=>0010101=>[2,1,1,1,1,1]
[4,3,6,2,7,5,1,8]=>[5,6,3,7,2,4,8,1]=>0101001=>[1,1,1,1,2,1]
[4,6,3,2,1,8,5,7]=>[5,3,6,7,8,1,4,2]=>1000101=>[1,3,1,1,1]
[7,5,1,4,8,2,6,3]=>[2,4,8,5,1,7,3,6]=>0011010=>[2,2,1,1,1]
[5,4,7,3,8,6,1,2]=>[4,5,2,6,1,3,8,7]=>0101001=>[1,1,1,1,2,1]
[8,3,5,1,2,7,6,4]=>[1,6,4,8,7,2,3,5]=>0101100=>[1,1,1,2,2]
[1,8,4,3,5,2,7,6]=>[8,1,5,6,4,7,2,3]=>1001010=>[1,2,1,1,1,1]
[4,6,3,1,5,2,8,7]=>[5,3,6,8,4,7,1,2]=>1001010=>[1,2,1,1,1,1]
[1,8,3,6,2,7,5,4]=>[8,1,6,3,7,2,4,5]=>1010100=>[1,1,1,1,1,2]
[1,6,8,7,4,2,5,3]=>[8,3,1,2,5,7,4,6]=>1100010=>[2,3,1,1]
[6,4,8,7,5,3,1,2]=>[3,5,1,2,4,6,8,7]=>0100001=>[1,1,4,1]
[7,6,4,3,8,5,1,2]=>[2,3,5,6,1,4,8,7]=>0001001=>[3,1,2,1]
[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>1001010=>[1,2,1,1,1,1]
[6,3,2,1,8,5,4,7]=>[3,6,7,8,1,4,5,2]=>0001001=>[3,1,2,1]
[6,5,3,2,7,4,1,8]=>[3,4,6,7,2,5,8,1]=>0001001=>[3,1,2,1]
[5,2,6,3,7,4,1,8]=>[4,7,3,6,2,5,8,1]=>0101001=>[1,1,1,1,2,1]
[2,8,5,3,1,6,4,7]=>[7,1,4,6,8,3,5,2]=>1000101=>[1,3,1,1,1]
[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>1011100=>[1,1,3,2]
[5,7,1,8,2,4,6,3]=>[4,2,8,1,7,5,3,6]=>1010110=>[1,1,1,1,2,1]
[5,1,2,7,8,3,6,4]=>[4,8,7,2,1,6,3,5]=>0111010=>[1,3,1,1,1]
[4,2,1,7,3,8,5,6]=>[5,7,8,2,6,1,4,3]=>0010101=>[2,1,1,1,1,1]
[7,3,2,1,8,4,5,6]=>[2,6,7,8,1,5,4,3]=>0001011=>[3,1,1,2]
[7,8,3,2,5,6,1,4]=>[2,1,6,7,4,3,8,5]=>1001101=>[1,2,2,1,1]
[7,1,8,2,4,5,6,3]=>[2,8,1,7,5,4,3,6]=>0101110=>[1,1,1,3,1]
[8,7,6,1,2,4,5,3]=>[1,2,3,8,7,5,4,6]=>0001110=>[3,3,1]
[8,3,7,6,2,1,4,5]=>[1,6,2,3,7,8,5,4]=>0100011=>[1,1,3,2]
[3,2,8,7,5,1,4,6]=>[6,7,1,2,4,8,5,3]=>0100011=>[1,1,3,2]
[8,3,6,5,2,1,4,7]=>[1,6,3,4,7,8,5,2]=>0100011=>[1,1,3,2]
[7,6,3,5,2,4,1,8]=>[2,3,6,4,7,5,8,1]=>0010101=>[2,1,1,1,1,1]
[8,2,4,1,6,5,3,7]=>[1,7,5,8,3,4,6,2]=>0101001=>[1,1,1,1,2,1]
[4,2,8,1,7,5,3,6]=>[5,7,1,8,2,4,6,3]=>0101001=>[1,1,1,1,2,1]
[8,2,4,1,7,6,3,5]=>[1,7,5,8,2,3,6,4]=>0101001=>[1,1,1,1,2,1]
[8,7,1,5,6,2,4,3]=>[1,2,8,4,3,7,5,6]=>0011010=>[2,2,1,1,1]
[8,5,7,3,6,4,1,2]=>[1,4,2,6,3,5,8,7]=>0101001=>[1,1,1,1,2,1]
[6,8,3,7,5,4,1,2]=>[3,1,6,2,4,5,8,7]=>1010001=>[1,1,1,3,1]
[8,1,6,7,5,2,4,3]=>[1,8,3,2,4,7,5,6]=>0110010=>[1,2,2,1,1]
[8,1,2,6,4,3,7,5]=>[1,8,7,3,5,6,2,4]=>0110010=>[1,2,2,1,1]
[2,8,1,7,5,4,3,6]=>[7,1,8,2,4,5,6,3]=>1010001=>[1,1,1,3,1]
[2,1,8,6,5,4,3,7]=>[7,8,1,3,4,5,6,2]=>0100001=>[1,1,4,1]
[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>1010100=>[1,1,1,1,1,2]
[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>1010100=>[1,1,1,1,1,2]
[1,7,8,6,5,2,4,3]=>[8,2,1,3,4,7,5,6]=>1100010=>[2,3,1,1]
[7,3,8,6,5,4,1,2]=>[2,6,1,3,4,5,8,7]=>0100001=>[1,1,4,1]
[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>1000010=>[1,4,1,1]
[8,1,7,3,2,6,5,4]=>[1,8,2,6,7,3,4,5]=>0100100=>[1,1,2,1,2]
[5,1,4,3,2,8,7,6]=>[4,8,5,6,7,1,2,3]=>0100100=>[1,1,2,1,2]
[8,6,5,3,2,1,7,4]=>[1,3,4,6,7,8,2,5]=>0000010=>[5,1,1]
[8,6,5,4,1,7,2,3]=>[1,3,4,5,8,2,7,6]=>0000101=>[4,1,1,1]
[8,6,1,7,4,3,2,5]=>[1,3,8,2,5,6,7,4]=>0010001=>[2,1,3,1]
[4,6,3,2,7,5,1,8]=>[5,3,6,7,2,4,8,1]=>1001001=>[1,2,1,2,1]
[7,4,8,3,1,6,2,5]=>[2,5,1,6,8,3,7,4]=>0100101=>[1,1,2,1,1,1]
[7,1,5,8,3,2,6,4]=>[2,8,4,1,6,7,3,5]=>0110010=>[1,2,2,1,1]
[5,7,4,1,8,2,6,3]=>[4,2,5,8,1,7,3,6]=>1001010=>[1,2,1,1,1,1]
[1,8,7,2,5,4,6,3]=>[8,1,2,7,4,5,3,6]=>1001010=>[1,2,1,1,1,1]
[1,8,5,3,7,2,6,4]=>[8,1,4,6,2,7,3,5]=>1001010=>[1,2,1,1,1,1]
[4,3,1,8,7,5,2,6]=>[5,6,8,1,2,4,7,3]=>0010001=>[2,1,3,1]
[1,4,8,6,3,5,2,7]=>[8,5,1,3,6,4,7,2]=>1100101=>[2,2,1,1,1]
[7,4,6,3,5,2,1,8]=>[2,5,3,6,4,7,8,1]=>0101001=>[1,1,1,1,2,1]
[1,3,5,6,8,4,2,7]=>[8,6,4,3,1,5,7,2]=>1111001=>[4,2,1]
[3,5,4,8,7,1,2,6]=>[6,4,5,1,2,8,7,3]=>1010011=>[1,1,1,2,2]
[3,1,4,6,8,7,2,5]=>[6,8,5,3,1,2,7,4]=>0111001=>[1,3,2,1]
[1,6,3,8,7,2,5,4]=>[8,3,6,1,2,7,4,5]=>1010010=>[1,1,1,2,1,1]
[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>1011000=>[1,1,2,3]
[8,4,1,6,7,5,3,2]=>[1,5,8,3,2,4,6,7]=>0011000=>[2,2,3]
[7,3,6,8,5,1,2,4]=>[2,6,3,1,4,8,7,5]=>0110011=>[1,2,2,2]
[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>1101101=>[2,1,2,1,1]
[3,6,5,2,8,1,4,7]=>[6,3,4,7,1,8,5,2]=>1001011=>[1,2,1,1,2]
[4,2,6,3,8,1,5,7]=>[5,7,3,6,1,8,4,2]=>0101011=>[1,1,1,1,1,2]
[4,2,6,7,3,5,1,8]=>[5,7,3,2,6,4,8,1]=>0110101=>[1,2,1,1,1,1]
[3,6,2,4,7,5,1,8]=>[6,3,7,5,2,4,8,1]=>1011001=>[1,1,2,2,1]
[8,7,6,4,3,1,5,2]=>[1,2,3,5,6,8,4,7]=>0000010=>[5,1,1]
[8,7,6,4,1,5,2,3]=>[1,2,3,5,8,4,7,6]=>0000101=>[4,1,1,1]
[3,8,7,2,1,4,6,5]=>[6,1,2,7,8,5,3,4]=>1000110=>[1,3,2,1]
[3,6,8,2,1,5,4,7]=>[6,3,1,7,8,4,5,2]=>1100101=>[2,2,1,1,1]
[2,4,8,1,6,5,3,7]=>[7,5,1,8,3,4,6,2]=>1101001=>[2,1,1,2,1]
[4,2,8,1,5,7,3,6]=>[5,7,1,8,4,2,6,3]=>0101101=>[1,1,1,2,1,1]
[8,5,7,6,1,4,2,3]=>[1,4,2,3,8,5,7,6]=>0100101=>[1,1,2,1,1,1]
[8,6,1,7,3,5,4,2]=>[1,3,8,2,6,4,5,7]=>0010100=>[2,1,1,1,2]
[8,6,1,7,5,4,2,3]=>[1,3,8,2,4,5,7,6]=>0010001=>[2,1,3,1]
[1,6,2,8,7,3,5,4]=>[8,3,7,1,2,6,4,5]=>1010010=>[1,1,1,2,1,1]
[1,8,2,4,6,7,3,5]=>[8,1,7,5,3,2,6,4]=>1011101=>[1,1,3,1,1]
[2,8,5,4,7,1,3,6]=>[7,1,4,5,2,8,6,3]=>1001011=>[1,2,1,1,2]
[2,1,5,8,6,4,3,7]=>[7,8,4,1,3,5,6,2]=>0110001=>[1,2,3,1]
[7,2,5,6,4,3,1,8]=>[2,7,4,3,5,6,8,1]=>0110001=>[1,2,3,1]
[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>1111001=>[4,2,1]
[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>1101001=>[2,1,1,2,1]
[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>1110100=>[3,1,1,2]
[7,1,8,6,3,5,4,2]=>[2,8,1,3,6,4,5,7]=>0100100=>[1,1,2,1,2]
[1,8,7,6,3,5,2,4]=>[8,1,2,3,6,4,7,5]=>1000101=>[1,3,1,1,1]
[1,8,7,4,6,3,2,5]=>[8,1,2,5,3,6,7,4]=>1001001=>[1,2,1,2,1]
[7,1,5,8,3,4,6,2]=>[2,8,4,1,6,5,3,7]=>0110110=>[1,2,1,2,1]
[7,1,6,4,2,3,5,8]=>[2,8,3,5,7,6,4,1]=>0100111=>[1,1,2,3]
[8,6,2,4,7,3,5,1]=>[1,3,7,5,2,6,4,8]=>0011010=>[2,2,1,1,1]
[8,6,2,4,5,7,3,1]=>[1,3,7,5,4,2,6,8]=>0011100=>[2,3,2]
[2,7,1,4,5,8,3,6]=>[7,2,8,5,4,1,6,3]=>1011101=>[1,1,3,1,1]
[7,1,6,4,5,2,3,8]=>[2,8,3,5,4,7,6,1]=>0101011=>[1,1,1,1,1,2]
[7,1,4,5,6,8,2,3]=>[2,8,5,4,3,1,7,6]=>0111101=>[1,4,1,1]
[7,1,4,6,5,8,3,2]=>[2,8,5,3,4,1,6,7]=>0110100=>[1,2,1,1,2]
[7,1,2,3,8,5,4,6]=>[2,8,7,6,1,4,5,3]=>0111001=>[1,3,2,1]
[7,1,5,4,3,8,2,6]=>[2,8,4,5,6,1,7,3]=>0100101=>[1,1,2,1,1,1]
[7,1,3,4,2,6,8,5]=>[2,8,6,5,7,3,1,4]=>0110110=>[1,2,1,2,1]
[7,1,5,4,6,2,8,3]=>[2,8,4,5,3,7,1,6]=>0101010=>[1,1,1,1,1,1,1]
[7,1,5,6,4,3,8,2]=>[2,8,4,3,5,6,1,7]=>0110010=>[1,2,2,1,1]
[7,1,6,5,4,3,2,8]=>[2,8,3,4,5,6,7,1]=>0100001=>[1,1,4,1]
[8,6,2,5,4,3,7,1]=>[1,3,7,4,5,6,2,8]=>0010010=>[2,1,2,1,1]
[2,5,1,4,7,8,6,3]=>[7,4,8,5,2,1,3,6]=>1011100=>[1,1,3,2]
[3,5,1,4,8,6,2,7]=>[6,4,8,5,1,3,7,2]=>1011001=>[1,1,2,2,1]
[3,6,2,4,7,8,1,5]=>[6,3,7,5,2,1,8,4]=>1011101=>[1,1,3,1,1]
[5,6,2,4,8,7,1,3]=>[4,3,7,5,1,2,8,6]=>1011001=>[1,1,2,2,1]
[6,3,8,2,4,7,1,5]=>[3,6,1,7,5,2,8,4]=>0101101=>[1,1,1,2,1,1]
[6,5,8,7,2,3,1,4]=>[3,4,1,2,7,6,8,5]=>0100101=>[1,1,2,1,1,1]
[6,5,7,8,2,4,1,3]=>[3,4,2,1,7,5,8,6]=>0110101=>[1,2,1,1,1,1]
[6,3,4,2,8,5,1,7]=>[3,6,5,7,1,4,8,2]=>0101001=>[1,1,1,1,2,1]
[3,4,7,2,5,8,1,6]=>[6,5,2,7,4,1,8,3]=>1101101=>[2,1,2,1,1]
[4,6,8,1,3,5,2,7]=>[5,3,1,8,6,4,7,2]=>1101101=>[2,1,2,1,1]
[4,3,8,1,2,7,5,6]=>[5,6,1,8,7,2,4,3]=>0101101=>[1,1,1,2,1,1]
[3,6,4,1,7,2,5,8]=>[6,3,5,8,2,7,4,1]=>1001011=>[1,2,1,1,2]
[2,8,3,1,5,6,4,7]=>[7,1,6,8,4,3,5,2]=>1001101=>[1,2,2,1,1]
[3,8,7,1,5,4,2,6]=>[6,1,2,8,4,5,7,3]=>1001001=>[1,2,1,2,1]
[4,3,1,7,6,8,2,5]=>[5,6,8,2,3,1,7,4]=>0010101=>[2,1,1,1,1,1]
[3,4,1,7,5,6,8,2]=>[6,5,8,2,4,3,1,7]=>1010110=>[1,1,1,1,2,1]
[3,4,1,5,7,6,2,8]=>[6,5,8,4,2,3,7,1]=>1011001=>[1,1,2,2,1]
[3,7,4,1,6,2,8,5]=>[6,2,5,8,3,7,1,4]=>1001010=>[1,2,1,1,1,1]
[8,4,7,2,5,3,6,1]=>[1,5,2,7,4,6,3,8]=>0101010=>[1,1,1,1,1,1,1]
[4,7,8,1,2,3,6,5]=>[5,2,1,8,7,6,3,4]=>1101110=>[2,1,3,1]
[2,8,6,1,5,3,7,4]=>[7,1,3,8,4,6,2,5]=>1001010=>[1,2,1,1,1,1]
[7,6,5,1,3,8,2,4]=>[2,3,4,8,6,1,7,5]=>0001101=>[3,2,1,1]
[7,6,5,1,3,4,8,2]=>[2,3,4,8,6,5,1,7]=>0001110=>[3,3,1]
[7,2,6,4,1,3,8,5]=>[2,7,3,5,8,6,1,4]=>0100110=>[1,1,2,2,1]
[6,7,5,2,1,3,8,4]=>[3,2,4,7,8,6,1,5]=>1000110=>[1,3,2,1]
[8,4,5,3,7,2,6,1]=>[1,5,4,6,2,7,3,8]=>0101010=>[1,1,1,1,1,1,1]
[4,7,5,2,8,1,6,3]=>[5,2,4,7,1,8,3,6]=>1001010=>[1,2,1,1,1,1]
[2,6,4,3,1,5,7,8]=>[7,3,5,6,8,4,2,1]=>1000111=>[1,3,3]
[7,3,8,4,1,5,2,6]=>[2,6,1,5,8,4,7,3]=>0100101=>[1,1,2,1,1,1]
[7,2,3,4,1,6,5,8]=>[2,7,6,5,8,3,4,1]=>0110101=>[1,2,1,1,1,1]
[4,2,8,3,6,1,5,7]=>[5,7,1,6,3,8,4,2]=>0101011=>[1,1,1,1,1,2]
[6,8,5,7,2,1,3,4]=>[3,1,4,2,7,8,6,5]=>1010011=>[1,1,1,2,2]
[4,8,5,2,7,1,3,6]=>[5,1,4,7,2,8,6,3]=>1001011=>[1,2,1,1,2]
[6,3,5,2,1,7,4,8]=>[3,6,4,7,8,2,5,1]=>0100101=>[1,1,2,1,1,1]
[3,6,5,4,2,8,1,7]=>[6,3,4,5,7,1,8,2]=>1000101=>[1,3,1,1,1]
[1,6,4,7,2,5,3,8]=>[8,3,5,2,7,4,6,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,4,8,2,5,3,7]=>[8,3,5,1,7,4,6,2]=>1010101=>[1,1,1,1,1,1,1]
[1,6,5,8,2,4,3,7]=>[8,3,4,1,7,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>1101010=>[2,1,1,1,1,1]
[1,6,2,4,3,7,8,5]=>[8,3,7,5,6,2,1,4]=>1010110=>[1,1,1,1,2,1]
[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>1101101=>[2,1,2,1,1]
[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>1101110=>[2,1,3,1]
[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>1101101=>[2,1,2,1,1]
[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>1101101=>[2,1,2,1,1]
[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>1010101=>[1,1,1,1,1,1,1]
[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>1101010=>[2,1,1,1,1,1]
[1,5,6,7,2,4,8,3]=>[8,4,3,2,7,5,1,6]=>1110110=>[3,1,2,1]
[1,5,8,2,4,6,7,3]=>[8,4,1,7,5,3,2,6]=>1101110=>[2,1,3,1]
[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>1101110=>[2,1,3,1]
[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>1110011=>[3,2,2]
[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>1100111=>[2,2,3]
[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>1101101=>[2,1,2,1,1]
[1,7,6,2,8,3,4,5]=>[8,2,3,7,1,6,5,4]=>1001011=>[1,2,1,1,2]
[1,7,3,4,2,8,6,5]=>[8,2,6,5,7,1,3,4]=>1010100=>[1,1,1,1,1,2]
[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>1010100=>[1,1,1,1,1,2]
[1,5,6,2,4,8,7,3]=>[8,4,3,7,5,1,2,6]=>1101100=>[2,1,2,2]
[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>1100011=>[2,3,2]
[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>1011100=>[1,1,3,2]
[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>1011100=>[1,1,3,2]
[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>1001100=>[1,2,2,2]
[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>1001000=>[1,2,1,3]
[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>1000100=>[1,3,1,2]
[1,6,7,5,2,3,8,4]=>[8,3,2,4,7,6,1,5]=>1100110=>[2,2,2,1]
[1,7,5,2,8,4,3,6]=>[8,2,4,7,1,5,6,3]=>1001001=>[1,2,1,2,1]
[1,7,5,6,2,8,3,4]=>[8,2,4,3,7,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,5,7,6,2,4,8,3]=>[8,4,2,3,7,5,1,6]=>1100110=>[2,2,2,1]
[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>1100110=>[2,2,2,1]
[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>1001101=>[1,2,2,1,1]
[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>1001110=>[1,2,3,1]
[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>1100110=>[2,2,2,1]
[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,6,8,5,2,3,7,4]=>[8,3,1,4,7,6,2,5]=>1100110=>[2,2,2,1]
[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>1001110=>[1,2,3,1]
[1,6,4,2,3,7,5,8]=>[8,3,5,7,6,2,4,1]=>1001101=>[1,2,2,1,1]
[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>1100110=>[2,2,2,1]
[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>1100110=>[2,2,2,1]
[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>1001001=>[1,2,1,2,1]
[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>1100110=>[2,2,2,1]
[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>1001101=>[1,2,2,1,1]
[1,7,6,4,2,8,5,3]=>[8,2,3,5,7,1,4,6]=>1000100=>[1,3,1,2]
[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>1001000=>[1,2,1,3]
[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>1001100=>[1,2,2,2]
[7,3,5,6,1,4,8,2]=>[2,6,4,3,8,5,1,7]=>0110110=>[1,2,1,2,1]
[3,7,5,6,1,4,8,2]=>[6,2,4,3,8,5,1,7]=>1010110=>[1,1,1,1,2,1]
[3,6,1,4,2,8,5,7]=>[6,3,8,5,7,1,4,2]=>1010101=>[1,1,1,1,1,1,1]
[4,7,1,6,3,5,8,2]=>[5,2,8,3,6,4,1,7]=>1010110=>[1,1,1,1,2,1]
[3,1,4,7,6,5,8,2]=>[6,8,5,2,3,4,1,7]=>0110010=>[1,2,2,1,1]
[7,1,6,4,3,5,8,2]=>[2,8,3,5,6,4,1,7]=>0100110=>[1,1,2,2,1]
[8,1,6,4,2,7,5,3]=>[1,8,3,5,7,2,4,6]=>0100100=>[1,1,2,1,2]
[8,4,1,3,7,2,5,6]=>[1,5,8,6,2,7,4,3]=>0011011=>[2,2,1,2]
[7,4,1,3,8,2,5,6]=>[2,5,8,6,1,7,4,3]=>0011011=>[2,2,1,2]
[4,7,8,1,2,6,5,3]=>[5,2,1,8,7,3,4,6]=>1101100=>[2,1,2,2]
[6,8,1,4,2,7,5,3]=>[3,1,8,5,7,2,4,6]=>1010100=>[1,1,1,1,1,2]
[1,8,6,4,2,7,5,3]=>[8,1,3,5,7,2,4,6]=>1000100=>[1,3,1,2]
[4,8,1,3,7,2,5,6]=>[5,1,8,6,2,7,4,3]=>1011011=>[1,1,2,1,2]
[8,7,1,3,6,2,5,4]=>[1,2,8,6,3,7,4,5]=>0011010=>[2,2,1,1,1]
[6,8,5,7,3,2,1,4]=>[3,1,4,2,6,7,8,5]=>1010001=>[1,1,1,3,1]
[2,8,3,4,7,6,1,5]=>[7,1,6,5,2,3,8,4]=>1011001=>[1,1,2,2,1]
[3,7,8,4,6,2,1,5]=>[6,2,1,5,3,7,8,4]=>1101001=>[2,1,1,2,1]
[2,4,3,7,8,6,1,5]=>[7,5,6,2,1,3,8,4]=>1011001=>[1,1,2,2,1]
[5,7,6,8,3,2,1,4]=>[4,2,3,1,6,7,8,5]=>1010001=>[1,1,1,3,1]
[3,7,5,4,8,2,1,6]=>[6,2,4,5,1,7,8,3]=>1001001=>[1,2,1,2,1]
[7,1,3,4,2,8,5,6]=>[2,8,6,5,7,1,4,3]=>0110101=>[1,2,1,1,1,1]
[6,1,4,3,8,2,5,7]=>[3,8,5,6,1,7,4,2]=>0101011=>[1,1,1,1,1,2]
[4,1,7,3,8,2,5,6]=>[5,8,2,6,1,7,4,3]=>0101011=>[1,1,1,1,1,2]
[8,1,4,3,7,2,5,6]=>[1,8,5,6,2,7,4,3]=>0101011=>[1,1,1,1,1,2]
[4,2,3,7,8,6,1,5]=>[5,7,6,2,1,3,8,4]=>0111001=>[1,3,2,1]
[2,7,5,6,3,8,1,4]=>[7,2,4,3,6,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,7,2,6,3,8,1,4]=>[4,2,7,3,6,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[5,2,3,8,7,6,1,4]=>[4,7,6,1,2,3,8,5]=>0110001=>[1,2,3,1]
[8,2,3,7,5,6,1,4]=>[1,7,6,2,4,3,8,5]=>0110101=>[1,2,1,1,1,1]
[1,7,8,4,2,6,5,3]=>[8,2,1,5,7,3,4,6]=>1100100=>[2,2,1,2]
[4,7,1,8,2,5,6,3]=>[5,2,8,1,7,4,3,6]=>1010110=>[1,1,1,1,2,1]
[2,4,3,8,5,6,1,7]=>[7,5,6,1,4,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[7,5,8,6,3,2,1,4]=>[2,4,1,3,6,7,8,5]=>0100001=>[1,1,4,1]
[6,5,8,7,3,2,1,4]=>[3,4,1,2,6,7,8,5]=>0100001=>[1,1,4,1]
[8,5,7,6,3,2,1,4]=>[1,4,2,3,6,7,8,5]=>0100001=>[1,1,4,1]
[2,5,3,8,7,6,1,4]=>[7,4,6,1,2,3,8,5]=>1010001=>[1,1,1,3,1]
[3,7,5,8,6,2,1,4]=>[6,2,4,1,3,7,8,5]=>1010001=>[1,1,1,3,1]
[3,7,8,6,5,2,1,4]=>[6,2,1,3,4,7,8,5]=>1100001=>[2,4,1]
[1,8,7,3,6,2,5,4]=>[8,1,2,6,3,7,4,5]=>1001010=>[1,2,1,1,1,1]
[6,8,7,5,3,2,1,4]=>[3,1,2,4,6,7,8,5]=>1000001=>[1,5,1]
[5,7,6,8,3,4,1,2]=>[4,2,3,1,6,5,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,7,6,8,4,5,1,2]=>[6,2,3,1,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[1,5,4,7,6,8,2,3]=>[8,4,5,2,3,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[3,7,4,6,5,8,1,2]=>[6,2,5,3,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,5,4,8,6,7,1,2]=>[6,4,5,1,3,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,6,5,7,1,2]=>[6,1,5,3,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,6,4,7,5,8,1,2]=>[6,3,5,2,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,6,4,8,5,7,2,3]=>[8,3,5,1,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,8,4,6,5,7,2,3]=>[8,1,5,3,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,5,4,8,6,7,2,3]=>[8,4,5,1,3,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,5,4,6,2,3]=>[2,1,8,4,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,5,2,4,3,6]=>[2,1,8,4,7,5,6,3]=>1010101=>[1,1,1,1,1,1,1]
[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,6,5,8,3,4]=>[8,2,7,3,4,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,6,8,2,5,3,4]=>[8,2,3,1,7,4,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,7,6,8,1,4,2,3]=>[4,2,3,1,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,5,6,1,3,2,4]=>[2,1,4,3,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,6,7,1,3,2,4]=>[4,1,3,2,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,3,2,7,6,8,4,5]=>[8,6,7,2,3,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,3,2,6,4,5]=>[2,1,8,6,7,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,6,2,4,3,5]=>[2,1,8,3,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,4,2,6,3,5]=>[2,1,8,5,7,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,4,2,5,3,6]=>[2,1,8,5,7,4,6,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,1,4,3,6,5]=>[2,1,7,8,5,6,3,4]=>1001010=>[1,2,1,1,1,1]
[7,8,1,2,4,3,5,6]=>[2,1,8,7,5,6,4,3]=>1011011=>[1,1,2,1,2]
[4,3,6,5,8,7,1,2]=>[5,6,3,4,1,2,8,7]=>0101001=>[1,1,1,1,2,1]
[3,4,6,5,7,8,1,2]=>[6,5,3,4,2,1,8,7]=>1101101=>[2,1,2,1,1]
[3,4,1,5,6,7,8,9,2]=>[7,6,9,5,4,3,2,1,8]=>10111110=>[1,1,5,1]
[3,4,5,1,6,7,8,9,2]=>[7,6,5,9,4,3,2,1,8]=>11011110=>[2,1,4,1]
[3,4,5,6,1,7,8,9,2]=>[7,6,5,4,9,3,2,1,8]=>11101110=>[3,1,3,1]
[3,4,5,6,7,1,8,9,2]=>[7,6,5,4,3,9,2,1,8]=>11110110=>[4,1,2,1]
[3,4,5,6,7,8,1,9,2]=>[7,6,5,4,3,2,9,1,8]=>11111010=>[5,1,1,1]
[3,1,2,5,6,7,8,9,4]=>[7,9,8,5,4,3,2,1,6]=>01111110=>[1,6,1]
[3,4,1,5,6,7,8,9,10,2]=>[8,7,10,6,5,4,3,2,1,9]=>101111110=>[1,1,6,1]
[3,4,1,2,6,7,8,9,5]=>[7,6,9,8,4,3,2,1,5]=>10111110=>[1,1,5,1]
[3,4,5,1,6,7,8,9,10,2]=>[8,7,6,10,5,4,3,2,1,9]=>110111110=>[2,1,5,1]
[3,4,5,1,2,7,8,9,6]=>[7,6,5,9,8,3,2,1,4]=>11011110=>[2,1,4,1]
[3,4,5,6,1,7,8,9,10,2]=>[8,7,6,5,10,4,3,2,1,9]=>111011110=>[3,1,4,1]
[3,4,5,6,1,2,8,9,7]=>[7,6,5,4,9,8,2,1,3]=>11101110=>[3,1,3,1]
[3,4,5,6,7,1,8,9,10,2]=>[8,7,6,5,4,10,3,2,1,9]=>111101110=>[4,1,3,1]
[3,4,5,6,7,1,2,9,8]=>[7,6,5,4,3,9,8,1,2]=>11110110=>[4,1,2,1]
[3,4,5,6,7,8,1,9,10,2]=>[8,7,6,5,4,3,10,2,1,9]=>111110110=>[5,1,2,1]
[3,4,5,6,7,8,1,2,9]=>[7,6,5,4,3,2,9,8,1]=>11111011=>[5,1,2]
[3,4,5,6,7,8,9,1,10,2]=>[8,7,6,5,4,3,2,10,1,9]=>111111010=>[6,1,1,1]
[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>1011001=>[1,1,2,2,1]
[1,7,4,3,2,8,6,5]=>[8,2,5,6,7,1,3,4]=>1000100=>[1,3,1,2]
[1,4,7,6,2,5,8,3]=>[8,5,2,3,7,4,1,6]=>1100110=>[2,2,2,1]
[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>1100101=>[2,2,1,1,1]
[1,2,6,5,3,7,8,4]=>[8,7,3,4,6,2,1,5]=>1100110=>[2,2,2,1]
[1,3,7,5,2,6,8,4]=>[8,6,2,4,7,3,1,5]=>1100110=>[2,2,2,1]
[1,3,7,4,2,6,8,5]=>[8,6,2,5,7,3,1,4]=>1100110=>[2,2,2,1]
[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>1100110=>[2,2,2,1]
[1,2,6,4,3,7,5,8]=>[8,7,3,5,6,2,4,1]=>1100101=>[2,2,1,1,1]
[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>1100110=>[2,2,2,1]
[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>1001101=>[1,2,2,1,1]
[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>1001101=>[1,2,2,1,1]
[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>1000100=>[1,3,1,2]
[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>1001100=>[1,2,2,2]
[7,6,5,4,3,1,8,2]=>[2,3,4,5,6,8,1,7]=>0000010=>[5,1,1]
[6,8,5,4,3,2,1,7]=>[3,1,4,5,6,7,8,2]=>1000001=>[1,5,1]
[8,7,6,5,4,3,1,9,2]=>[2,3,4,5,6,7,9,1,8]=>00000010=>[6,1,1]
[7,9,6,5,4,3,2,1,8]=>[3,1,4,5,6,7,8,9,2]=>10000001=>[1,6,1]
[9,8,7,6,5,4,3,1,10,2]=>[2,3,4,5,6,7,8,10,1,9]=>000000010=>[7,1,1]
[1,7,6,5,4,3,9,8,2]=>[9,3,4,5,6,7,1,2,8]=>10000100=>[1,4,1,2]
[7,1,5,4,3,8,6,2]=>[2,8,4,5,6,1,3,7]=>0100100=>[1,1,2,1,2]
[3,6,5,4,8,1,7,2]=>[6,3,4,5,1,8,2,7]=>1001010=>[1,2,1,1,1,1]
[6,8,1,4,3,2,7,5]=>[3,1,8,5,6,7,2,4]=>1010010=>[1,1,1,2,1,1]
[2,8,5,4,3,7,1,6]=>[7,1,4,5,6,2,8,3]=>1000101=>[1,3,1,1,1]
[8,10,7,6,5,4,3,2,1,9]=>[3,1,4,5,6,7,8,9,10,2]=>100000001=>[1,7,1]
[10,9,8,7,6,5,4,3,1,11,2]=>[2,3,4,5,6,7,8,9,11,1,10]=>0000000010=>[8,1,1]
[1,8,7,6,5,4,3,10,9,2]=>[10,3,4,5,6,7,8,1,2,9]=>100000100=>[1,5,1,2]
[7,6,1,4,3,8,5,2]=>[2,3,8,5,6,1,4,7]=>0010100=>[2,1,1,1,2]
[4,6,5,8,3,1,7,2]=>[5,3,4,1,6,8,2,7]=>1010010=>[1,1,1,2,1,1]
[6,8,5,1,3,2,7,4]=>[3,1,4,8,6,7,2,5]=>1001010=>[1,2,1,1,1,1]
[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>1010100=>[1,1,1,1,1,2]
[3,8,5,4,7,2,1,6]=>[6,1,4,5,2,7,8,3]=>1001001=>[1,2,1,2,1]
[9,11,8,7,6,5,4,3,2,1,10]=>[3,1,4,5,6,7,8,9,10,11,2]=>1000000001=>[1,8,1]
[11,10,9,8,7,6,5,4,3,1,12,2]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000010=>[9,1,1]
[7,6,5,1,3,8,4,2]=>[2,3,4,8,6,1,5,7]=>0001100=>[3,2,2]
[1,6,3,4,8,7,5,2]=>[8,3,6,5,1,2,4,7]=>1011000=>[1,1,2,3]
[1,4,5,8,3,7,6,2]=>[8,5,4,1,6,2,3,7]=>1110100=>[3,1,1,2]
[6,8,5,4,1,2,7,3]=>[3,1,4,5,8,7,2,6]=>1000110=>[1,3,2,1]
[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>1001100=>[1,2,2,2]
[6,8,2,4,3,7,1,5]=>[3,1,7,5,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>1011010=>[1,1,2,1,1,1]
[7,5,8,4,3,2,1,6]=>[2,4,1,5,6,7,8,3]=>0100001=>[1,1,4,1]
[4,8,5,7,3,2,1,6]=>[5,1,4,2,6,7,8,3]=>1010001=>[1,1,1,3,1]
[10,12,9,8,7,6,5,4,3,2,1,11]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>10000000001=>[1,9,1]
[5,1,7,6,8,4,3,2]=>[4,8,2,3,1,5,6,7]=>0101000=>[1,1,1,1,3]
[6,4,8,5,2,7,1,3]=>[3,5,1,4,7,2,8,6]=>0100101=>[1,1,2,1,1,1]
[8,4,7,5,2,6,1,3]=>[1,5,2,4,7,3,8,6]=>0100101=>[1,1,2,1,1,1]
[5,4,6,8,2,1,7,3]=>[4,5,3,1,7,8,2,6]=>0110010=>[1,2,2,1,1]
[6,4,5,8,1,2,7,3]=>[3,5,4,1,8,7,2,6]=>0110110=>[1,2,1,2,1]
[8,4,6,5,2,1,7,3]=>[1,5,3,4,7,8,2,6]=>0100010=>[1,1,3,1,1]
[2,7,5,1,8,4,3,6]=>[7,2,4,8,1,5,6,3]=>1001001=>[1,2,1,2,1]
[2,8,6,7,4,3,5,1]=>[7,1,3,2,5,6,4,8]=>1010010=>[1,1,1,2,1,1]
[3,6,5,2,4,1,8,7]=>[6,3,4,7,5,8,1,2]=>1001010=>[1,2,1,1,1,1]
[5,2,3,6,4,1,8,7]=>[4,7,6,3,5,8,1,2]=>0110010=>[1,2,2,1,1]
[3,8,7,1,4,6,5,2]=>[6,1,2,8,5,3,4,7]=>1001100=>[1,2,2,2]
[4,3,7,6,8,2,5,1]=>[5,6,2,3,1,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[5,3,6,8,1,7,2,4]=>[4,6,3,1,8,2,7,5]=>0110101=>[1,2,1,1,1,1]
[3,2,6,8,5,7,1,4]=>[6,7,3,1,4,2,8,5]=>0110101=>[1,2,1,1,1,1]
[6,3,7,2,4,8,5,1]=>[3,6,2,7,5,1,4,8]=>0101100=>[1,1,1,2,2]
[3,6,4,7,5,1,8,2]=>[6,3,5,2,4,8,1,7]=>1010010=>[1,1,1,2,1,1]
[8,4,7,6,2,3,1,5]=>[1,5,2,3,7,6,8,4]=>0100101=>[1,1,2,1,1,1]
[8,4,7,1,2,5,6,3]=>[1,5,2,8,7,4,3,6]=>0101110=>[1,1,1,3,1]
[7,4,3,8,2,5,6,1]=>[2,5,6,1,7,4,3,8]=>0010110=>[2,1,1,2,1]
[6,4,1,5,8,2,7,3]=>[3,5,8,4,1,7,2,6]=>0011010=>[2,2,1,1,1]
[2,5,8,7,3,6,1,4]=>[7,4,1,2,6,3,8,5]=>1100101=>[2,2,1,1,1]
[2,1,5,8,7,4,6,3]=>[7,8,4,1,2,5,3,6]=>0110010=>[1,2,2,1,1]
[4,2,7,1,8,5,6,3]=>[5,7,2,8,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]
[3,4,7,2,8,5,6,1]=>[6,5,2,7,1,4,3,8]=>1101010=>[2,1,1,1,1,1]
[7,2,3,4,8,5,6,1]=>[2,7,6,5,1,4,3,8]=>0111010=>[1,3,1,1,1]
[6,1,8,5,2,7,4,3]=>[3,8,1,4,7,2,5,6]=>0100100=>[1,1,2,1,2]
[2,1,7,4,5,8,6,3]=>[7,8,2,5,4,1,3,6]=>0101100=>[1,1,1,2,2]
[8,2,1,6,4,7,5,3]=>[1,7,8,3,5,2,4,6]=>0010100=>[2,1,1,1,2]
[7,8,2,6,4,1,5,3]=>[2,1,7,3,5,8,4,6]=>1010010=>[1,1,1,2,1,1]
[5,1,6,8,4,7,2,3]=>[4,8,3,1,5,2,7,6]=>0110101=>[1,2,1,1,1,1]
[3,6,8,7,5,2,1,4]=>[6,3,1,2,4,7,8,5]=>1100001=>[2,4,1]
[8,1,6,4,7,3,2,5]=>[1,8,3,5,2,6,7,4]=>0101001=>[1,1,1,1,2,1]
[7,3,5,8,4,2,1,6]=>[2,6,4,1,5,7,8,3]=>0110001=>[1,2,3,1]
[4,8,7,5,6,1,2,3]=>[5,1,2,4,3,8,7,6]=>1001011=>[1,2,1,1,2]
[3,1,8,7,2,5,6,4]=>[6,8,1,2,7,4,3,5]=>0100110=>[1,1,2,2,1]
[8,2,3,7,1,5,6,4]=>[1,7,6,2,8,4,3,5]=>0110110=>[1,2,1,2,1]
[2,8,4,6,7,3,1,5]=>[7,1,5,3,2,6,8,4]=>1011001=>[1,1,2,2,1]
[4,3,8,2,7,6,1,5]=>[5,6,1,7,2,3,8,4]=>0101001=>[1,1,1,1,2,1]
[6,8,4,2,1,3,7,5]=>[3,1,5,7,8,6,2,4]=>1000110=>[1,3,2,1]
[2,8,3,7,1,5,6,4]=>[7,1,6,2,8,4,3,5]=>1010110=>[1,1,1,1,2,1]
[6,4,1,3,2,8,5,7]=>[3,5,8,6,7,1,4,2]=>0010101=>[2,1,1,1,1,1]
[5,3,8,6,2,1,4,7]=>[4,6,1,3,7,8,5,2]=>0100011=>[1,1,3,2]
[7,2,5,4,3,8,1,6]=>[2,7,4,5,6,1,8,3]=>0100101=>[1,1,2,1,1,1]
[3,6,8,1,4,5,2,7]=>[6,3,1,8,5,4,7,2]=>1101101=>[2,1,2,1,1]
[3,8,6,1,2,5,4,7]=>[6,1,3,8,7,4,5,2]=>1001101=>[1,2,2,1,1]
[4,1,6,5,8,2,3,7]=>[5,8,3,4,1,7,6,2]=>0101011=>[1,1,1,1,1,2]
[2,3,6,8,4,5,1,7]=>[7,6,3,1,5,4,8,2]=>1110101=>[3,1,1,1,1]
[5,8,4,3,7,6,1,2]=>[4,1,5,6,2,3,8,7]=>1001001=>[1,2,1,2,1]
[8,7,4,3,1,6,2,5]=>[1,2,5,6,8,3,7,4]=>0000101=>[4,1,1,1]
[7,1,5,3,4,8,2,6]=>[2,8,4,6,5,1,7,3]=>0101101=>[1,1,1,2,1,1]
[2,8,6,1,7,4,5,3]=>[7,1,3,8,2,5,4,6]=>1001010=>[1,2,1,1,1,1]
[4,8,6,5,7,2,1,3]=>[5,1,3,4,2,7,8,6]=>1001001=>[1,2,1,2,1]
[4,7,6,8,2,1,5,3]=>[5,2,3,1,7,8,4,6]=>1010010=>[1,1,1,2,1,1]
[6,1,8,7,4,3,5,2]=>[3,8,1,2,5,6,4,7]=>0100010=>[1,1,3,1,1]
[8,5,4,3,1,6,7,2]=>[1,4,5,6,8,3,2,7]=>0000110=>[4,2,1]
[1,5,8,6,3,4,7,2]=>[8,4,1,3,6,5,2,7]=>1100110=>[2,2,2,1]
[2,5,8,6,3,4,7,1]=>[7,4,1,3,6,5,2,8]=>1100110=>[2,2,2,1]
[4,1,3,8,5,6,7,2]=>[5,8,6,1,4,3,2,7]=>0110110=>[1,2,1,2,1]
[6,5,8,4,3,1,7,2]=>[3,4,1,5,6,8,2,7]=>0100010=>[1,1,3,1,1]
[7,2,8,1,3,6,4,5]=>[2,7,1,8,6,3,5,4]=>0101101=>[1,1,1,2,1,1]
[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>1001110=>[1,2,3,1]
[1,8,3,2,5,6,7,4]=>[8,1,6,7,4,3,2,5]=>1001110=>[1,2,3,1]
[2,8,3,1,5,6,7,4]=>[7,1,6,8,4,3,2,5]=>1001110=>[1,2,3,1]
[4,8,3,2,5,6,7,1]=>[5,1,6,7,4,3,2,8]=>1001110=>[1,2,3,1]
[8,2,3,1,5,6,7,4]=>[1,7,6,8,4,3,2,5]=>0101110=>[1,1,1,3,1]
[4,5,8,1,2,3,7,6]=>[5,4,1,8,7,6,2,3]=>1101110=>[2,1,3,1]
[4,2,7,1,8,6,3,5]=>[5,7,2,8,1,3,6,4]=>0101001=>[1,1,1,1,2,1]
[3,8,4,1,2,6,7,5]=>[6,1,5,8,7,3,2,4]=>1001110=>[1,2,3,1]
[5,4,8,2,3,6,7,1]=>[4,5,1,7,6,3,2,8]=>0101110=>[1,1,1,3,1]
[5,8,3,6,7,4,1,2]=>[4,1,6,3,2,5,8,7]=>1011001=>[1,1,2,2,1]
[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>1100101=>[2,2,1,1,1]
[2,7,1,4,3,8,5,6]=>[7,2,8,5,6,1,4,3]=>1010101=>[1,1,1,1,1,1,1]
[2,4,1,8,6,3,7,5]=>[7,5,8,1,3,6,2,4]=>1010010=>[1,1,1,2,1,1]
[7,6,3,5,8,2,1,4]=>[2,3,6,4,1,7,8,5]=>0011001=>[2,2,2,1]
[8,2,5,6,1,4,7,3]=>[1,7,4,3,8,5,2,6]=>0110110=>[1,2,1,2,1]
[8,6,5,4,1,2,7,3]=>[1,3,4,5,8,7,2,6]=>0000110=>[4,2,1]
[2,6,1,8,3,7,5,4]=>[7,3,8,1,6,2,4,5]=>1010100=>[1,1,1,1,1,2]
[4,7,1,6,2,8,5,3]=>[5,2,8,3,7,1,4,6]=>1010100=>[1,1,1,1,1,2]
[2,8,6,3,7,1,5,4]=>[7,1,3,6,2,8,4,5]=>1001010=>[1,2,1,1,1,1]
[7,6,1,5,8,2,3,4]=>[2,3,8,4,1,7,6,5]=>0011011=>[2,2,1,2]
[4,8,2,5,1,6,7,3]=>[5,1,7,4,8,3,2,6]=>1010110=>[1,1,1,1,2,1]
[3,4,8,5,2,6,7,1]=>[6,5,1,4,7,3,2,8]=>1100110=>[2,2,2,1]
[7,2,1,5,8,6,3,4]=>[2,7,8,4,1,3,6,5]=>0011001=>[2,2,2,1]
[2,8,4,5,1,6,7,3]=>[7,1,5,4,8,3,2,6]=>1010110=>[1,1,1,1,2,1]
[5,4,8,3,7,6,1,2]=>[4,5,1,6,2,3,8,7]=>0101001=>[1,1,1,1,2,1]
[3,1,5,8,6,2,7,4]=>[6,8,4,1,3,7,2,5]=>0110010=>[1,2,2,1,1]
[6,3,4,8,5,1,7,2]=>[3,6,5,1,4,8,2,7]=>0110010=>[1,2,2,1,1]
[7,6,1,2,8,3,5,4]=>[2,3,8,7,1,6,4,5]=>0011010=>[2,2,1,1,1]
[7,5,8,4,1,2,6,3]=>[2,4,1,5,8,7,3,6]=>0100110=>[1,1,2,2,1]
[7,5,8,4,6,1,3,2]=>[2,4,1,5,3,8,6,7]=>0101010=>[1,1,1,1,1,1,1]
[6,5,4,8,7,1,3,2]=>[3,4,5,1,2,8,6,7]=>0010010=>[2,1,2,1,1]
[6,5,4,8,1,2,7,3]=>[3,4,5,1,8,7,2,6]=>0010110=>[2,1,1,2,1]
[7,5,1,6,2,3,8,4]=>[2,4,8,3,7,6,1,5]=>0010110=>[2,1,1,2,1]
[7,5,1,6,8,2,4,3]=>[2,4,8,3,1,7,5,6]=>0011010=>[2,2,1,1,1]
[6,5,4,1,8,2,7,3]=>[3,4,5,8,1,7,2,6]=>0001010=>[3,1,1,1,1]
[6,5,4,7,1,2,8,3]=>[3,4,5,2,8,7,1,6]=>0010110=>[2,1,1,2,1]
[6,5,4,7,8,1,3,2]=>[3,4,5,2,1,8,6,7]=>0011010=>[2,2,1,1,1]
[6,5,3,7,1,4,2,8]=>[3,4,6,2,8,5,7,1]=>0010101=>[2,1,1,1,1,1]
[6,5,3,1,8,4,2,7]=>[3,4,6,8,1,5,7,2]=>0001001=>[3,1,2,1]
[7,5,1,4,8,3,2,6]=>[2,4,8,5,1,6,7,3]=>0011001=>[2,2,2,1]
[8,1,6,4,7,3,5,2]=>[1,8,3,5,2,6,4,7]=>0101010=>[1,1,1,1,1,1,1]
[7,5,1,4,8,3,6,2]=>[2,4,8,5,1,6,3,7]=>0011010=>[2,2,1,1,1]
[6,5,3,7,1,4,8,2]=>[3,4,6,2,8,5,1,7]=>0010110=>[2,1,1,2,1]
[6,4,3,1,5,8,7,2]=>[3,5,6,8,4,1,2,7]=>0001100=>[3,2,2]
[7,4,1,5,3,8,6,2]=>[2,5,8,4,6,1,3,7]=>0010100=>[2,1,1,1,2]
[8,1,5,4,3,7,6,2]=>[1,8,4,5,6,2,3,7]=>0100100=>[1,1,2,1,2]
[8,1,5,4,3,7,2,6]=>[1,8,4,5,6,2,7,3]=>0100101=>[1,1,2,1,1,1]
[7,4,1,5,3,8,2,6]=>[2,5,8,4,6,1,7,3]=>0010101=>[2,1,1,1,1,1]
[7,4,1,5,3,2,6,8]=>[2,5,8,4,6,7,3,1]=>0010011=>[2,1,2,2]
[8,1,5,4,3,2,6,7]=>[1,8,4,5,6,7,3,2]=>0100011=>[1,1,3,2]
[8,1,6,4,2,5,3,7]=>[1,8,3,5,7,4,6,2]=>0100101=>[1,1,2,1,1,1]
[6,5,3,1,2,7,4,8]=>[3,4,6,8,7,2,5,1]=>0001101=>[3,2,1,1]
[6,5,3,8,1,4,2,7]=>[3,4,6,1,8,5,7,2]=>0010101=>[2,1,1,1,1,1]
[7,6,8,1,4,3,2,5]=>[2,3,1,8,5,6,7,4]=>0101001=>[1,1,1,1,2,1]
[8,1,7,2,5,4,3,6]=>[1,8,2,7,4,5,6,3]=>0101001=>[1,1,1,1,2,1]
[8,1,7,2,5,4,6,3]=>[1,8,2,7,4,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[7,6,1,2,5,4,8,3]=>[2,3,8,7,4,5,1,6]=>0011010=>[2,2,1,1,1]
[6,5,3,8,1,4,7,2]=>[3,4,6,1,8,5,2,7]=>0010110=>[2,1,1,2,1]
[6,5,3,1,2,7,8,4]=>[3,4,6,8,7,2,1,5]=>0001110=>[3,3,1]
[7,5,1,4,2,6,8,3]=>[2,4,8,5,7,3,1,6]=>0010110=>[2,1,1,2,1]
[8,1,6,4,2,5,7,3]=>[1,8,3,5,7,4,2,6]=>0100110=>[1,1,2,2,1]
[7,4,1,5,3,2,8,6]=>[2,5,8,4,6,7,1,3]=>0010010=>[2,1,2,1,1]
[6,4,3,1,5,2,8,7]=>[3,5,6,8,4,7,1,2]=>0001010=>[3,1,1,1,1]
[6,4,3,1,5,7,2,8]=>[3,5,6,8,4,2,7,1]=>0001101=>[3,2,1,1]
[7,4,1,5,3,6,2,8]=>[2,5,8,4,6,3,7,1]=>0010101=>[2,1,1,1,1,1]
[8,1,5,4,3,6,2,7]=>[1,8,4,5,6,3,7,2]=>0100101=>[1,1,2,1,1,1]
[8,1,5,4,3,6,7,2]=>[1,8,4,5,6,3,2,7]=>0100110=>[1,1,2,2,1]
[7,4,1,5,3,6,8,2]=>[2,5,8,4,6,3,1,7]=>0010110=>[2,1,1,2,1]
[6,4,3,1,5,7,8,2]=>[3,5,6,8,4,2,1,7]=>0001110=>[3,3,1]
[6,7,3,8,4,5,1,2]=>[3,2,6,1,5,4,8,7]=>1010101=>[1,1,1,1,1,1,1]
[6,7,4,5,1,8,2,3]=>[3,2,5,4,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,6,2,3,1,8]=>[5,2,4,3,7,6,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,6,1,8,2,3]=>[5,2,4,3,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,6,3,8,1,2]=>[5,2,4,3,6,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,7,5,8,4,6,1,2]=>[6,2,4,1,5,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,8,6,7,1,2]=>[5,4,6,1,3,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,6,5,7,1,2]=>[5,1,6,3,4,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,6,4,7,1,8,2,3]=>[4,3,5,2,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,6,1,7,3,8,2,4]=>[4,3,8,2,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,6,1,8,4,7,2,3]=>[4,3,8,1,5,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,6,5,7,2,3]=>[5,1,8,3,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,8,6,7,2,3]=>[5,4,8,1,3,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[7,8,4,5,1,6,2,3]=>[2,1,5,4,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,3,1,6,5,7]=>[5,1,7,6,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,2,8,1,4,3,7]=>[4,3,7,1,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,4,1,8,2,7]=>[4,3,6,5,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]
[3,6,4,5,2,7,1,8]=>[6,3,5,4,7,2,8,1]=>1010101=>[1,1,1,1,1,1,1]
[3,6,4,5,1,8,2,7]=>[6,3,5,4,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,8,1,5,3,7]=>[7,3,5,1,8,4,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,3,6,1,5,4,7]=>[7,1,6,3,8,4,5,2]=>1010101=>[1,1,1,1,1,1,1]
[2,8,3,4,1,6,5,7]=>[7,1,6,5,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,5,3,4,1,6]=>[2,1,7,4,6,5,8,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,5,3,6,2,4]=>[2,1,8,4,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,5,3,8,6,7,2,4]=>[8,4,6,1,3,2,7,5]=>1010101=>[1,1,1,1,1,1,1]
[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>1010101=>[1,1,1,1,1,1,1]
[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,7,3,5,1,8]=>[7,3,5,2,6,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[2,7,3,6,4,5,1,8]=>[7,2,6,3,5,4,8,1]=>1010101=>[1,1,1,1,1,1,1]
[1,7,3,6,4,8,2,5]=>[8,2,6,3,5,1,7,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>1010101=>[1,1,1,1,1,1,1]
[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>1010101=>[1,1,1,1,1,1,1]
[1,7,5,6,3,8,2,4]=>[8,2,4,3,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[2,7,5,6,3,4,1,8]=>[7,2,4,3,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,2,5,3,4,1,8]=>[3,2,7,4,6,5,8,1]=>1010101=>[1,1,1,1,1,1,1]
[6,7,1,5,3,8,2,4]=>[3,2,8,4,6,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,5,8,1,4,2,3]=>[3,2,4,1,8,5,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,6,7,2,3,1,4]=>[4,1,3,2,7,6,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,2,3,1,8,4,5]=>[3,2,7,6,8,1,5,4]=>1010101=>[1,1,1,1,1,1,1]
[6,7,2,8,1,4,3,5]=>[3,2,7,1,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,4,2,7,5,6,1,8]=>[6,5,7,2,4,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[3,4,1,7,5,8,2,6]=>[6,5,8,2,4,1,7,3]=>1010101=>[1,1,1,1,1,1,1]
[2,7,5,8,1,4,3,6]=>[7,2,4,1,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]
[2,3,1,7,5,8,4,6]=>[7,6,8,2,4,1,5,3]=>1010101=>[1,1,1,1,1,1,1]
[2,3,1,8,4,7,5,6]=>[7,6,8,1,5,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,3,1,6,4,5]=>[2,1,7,6,8,3,5,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,6,1,4,3,5]=>[2,1,7,3,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,6,7,1,4,3,5]=>[7,1,3,2,8,5,6,4]=>1010101=>[1,1,1,1,1,1,1]
[2,8,1,4,3,7,5,6]=>[7,1,8,5,6,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,5,4,6,1,8]=>[6,2,7,4,5,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,2,7,3,6,1,8]=>[5,4,7,2,6,3,8,1]=>1010101=>[1,1,1,1,1,1,1]
[4,5,1,8,2,7,3,6]=>[5,4,8,1,7,2,6,3]=>1010101=>[1,1,1,1,1,1,1]
[3,4,1,8,2,7,5,6]=>[6,5,8,1,7,2,4,3]=>1010101=>[1,1,1,1,1,1,1]
[3,4,1,8,6,7,2,5]=>[6,5,8,1,3,2,7,4]=>1010101=>[1,1,1,1,1,1,1]
[3,4,2,5,1,8,6,7]=>[6,5,7,4,8,1,3,2]=>1010101=>[1,1,1,1,1,1,1]
[3,4,2,8,1,6,5,7]=>[6,5,7,1,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[3,8,2,5,1,6,4,7]=>[6,1,7,4,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,2,8,1,6,3,7]=>[5,4,7,1,8,3,6,2]=>1010101=>[1,1,1,1,1,1,1]
[4,5,3,6,1,8,2,7]=>[5,4,6,3,8,1,7,2]=>1010101=>[1,1,1,1,1,1,1]
[7,1,5,8,4,6,2,3]=>[2,8,4,1,5,3,7,6]=>0110101=>[1,2,1,1,1,1]
[8,6,7,1,4,2,5,3]=>[1,3,2,8,5,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,6,3,7,5,1,2,4]=>[1,3,6,2,4,8,7,5]=>0010011=>[2,1,2,2]
[8,6,1,7,3,2,5,4]=>[1,3,8,2,6,7,4,5]=>0010010=>[2,1,2,1,1]
[7,6,1,8,3,5,2,4]=>[2,3,8,1,6,4,7,5]=>0010101=>[2,1,1,1,1,1]
[7,6,2,8,3,5,1,4]=>[2,3,7,1,6,4,8,5]=>0010101=>[2,1,1,1,1,1]
[7,6,2,3,8,5,1,4]=>[2,3,7,6,1,4,8,5]=>0011001=>[2,2,2,1]
[8,7,1,5,2,6,3,4]=>[1,2,8,4,7,3,6,5]=>0010101=>[2,1,1,1,1,1]
[8,5,2,3,1,7,6,4]=>[1,4,7,6,8,2,3,5]=>0010100=>[2,1,1,1,2]
[8,6,2,3,7,1,5,4]=>[1,3,7,6,2,8,4,5]=>0011010=>[2,2,1,1,1]
[8,6,2,7,3,1,5,4]=>[1,3,7,2,6,8,4,5]=>0010010=>[2,1,2,1,1]
[8,6,7,2,4,1,5,3]=>[1,3,2,7,5,8,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,7,2,5,1,6,3,4]=>[1,2,7,4,8,3,6,5]=>0010101=>[2,1,1,1,1,1]
[8,4,2,1,7,6,3,5]=>[1,5,7,8,2,3,6,4]=>0001001=>[3,1,2,1]
[5,8,7,3,1,4,2,6]=>[4,1,2,6,8,5,7,3]=>1000101=>[1,3,1,1,1]
[5,8,7,3,1,4,6,2]=>[4,1,2,6,8,5,3,7]=>1000110=>[1,3,2,1]
[8,5,7,2,1,4,6,3]=>[1,4,2,7,8,5,3,6]=>0100110=>[1,1,2,2,1]
[8,4,2,1,3,7,6,5]=>[1,5,7,8,6,2,3,4]=>0001100=>[3,2,2]
[8,7,4,1,2,3,6,5]=>[1,2,5,8,7,6,3,4]=>0001110=>[3,3,1]
[8,6,1,3,7,2,5,4]=>[1,3,8,6,2,7,4,5]=>0011010=>[2,2,1,1,1]
[8,5,1,3,2,7,6,4]=>[1,4,8,6,7,2,3,5]=>0010100=>[2,1,1,1,2]
[8,5,7,4,1,6,2,3]=>[1,4,2,5,8,3,7,6]=>0100101=>[1,1,2,1,1,1]
[8,1,6,4,7,2,5,3]=>[1,8,3,5,2,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[6,1,5,8,4,2,7,3]=>[3,8,4,1,5,7,2,6]=>0110010=>[1,2,2,1,1]
[5,8,3,6,4,1,2,7]=>[4,1,6,3,5,8,7,2]=>1010011=>[1,1,1,2,2]
[5,2,8,6,4,1,3,7]=>[4,7,1,3,5,8,6,2]=>0100011=>[1,1,3,2]
[8,4,7,5,1,6,2,3]=>[1,5,2,4,8,3,7,6]=>0100101=>[1,1,2,1,1,1]
[8,4,7,5,1,2,6,3]=>[1,5,2,4,8,7,3,6]=>0100110=>[1,1,2,2,1]
[8,4,7,5,1,2,3,6]=>[1,5,2,4,8,7,6,3]=>0100111=>[1,1,2,3]
[8,7,3,5,1,2,6,4]=>[1,2,6,4,8,7,3,5]=>0010110=>[2,1,1,2,1]
[8,3,2,6,5,1,4,7]=>[1,6,7,3,4,8,5,2]=>0010011=>[2,1,2,2]
[8,4,7,2,1,5,3,6]=>[1,5,2,7,8,4,6,3]=>0100101=>[1,1,2,1,1,1]
[8,3,2,7,1,5,4,6]=>[1,6,7,2,8,4,5,3]=>0010101=>[2,1,1,1,1,1]
[8,3,2,1,7,6,4,5]=>[1,6,7,8,2,3,5,4]=>0001001=>[3,1,2,1]
[8,7,3,1,2,4,6,5]=>[1,2,6,8,7,5,3,4]=>0001110=>[3,3,1]
[8,3,2,1,4,7,6,5]=>[1,6,7,8,5,2,3,4]=>0001100=>[3,2,2]
[8,3,2,1,7,4,6,5]=>[1,6,7,8,2,5,3,4]=>0001010=>[3,1,1,1,1]
[8,3,2,7,1,5,6,4]=>[1,6,7,2,8,4,3,5]=>0010110=>[2,1,1,2,1]
[8,4,7,2,1,5,6,3]=>[1,5,2,7,8,4,3,6]=>0100110=>[1,1,2,2,1]
[3,8,7,4,1,2,5,6]=>[6,1,2,5,8,7,4,3]=>1000111=>[1,3,3]
[8,7,2,1,6,3,4,5]=>[1,2,7,8,3,6,5,4]=>0001011=>[3,1,1,2]
[8,7,2,1,3,6,4,5]=>[1,2,7,8,6,3,5,4]=>0001101=>[3,2,1,1]
[8,7,2,1,3,4,6,5]=>[1,2,7,8,6,5,3,4]=>0001110=>[3,3,1]
[3,6,5,4,1,2,8,7]=>[6,3,4,5,8,7,1,2]=>1000110=>[1,3,2,1]
[4,7,5,8,6,2,1,3]=>[5,2,4,1,3,7,8,6]=>1010001=>[1,1,1,3,1]
[5,8,1,3,7,6,4,2]=>[4,1,8,6,2,3,5,7]=>1011000=>[1,1,2,3]
[4,2,6,8,5,7,3,1]=>[5,7,3,1,4,2,6,8]=>0110100=>[1,2,1,1,2]
[6,4,2,7,3,8,5,1]=>[3,5,7,2,6,1,4,8]=>0010100=>[2,1,1,1,2]
[2,1,5,8,7,6,3,4]=>[7,8,4,1,2,3,6,5]=>0110001=>[1,2,3,1]
[2,1,4,7,6,3,8,5]=>[7,8,5,2,3,6,1,4]=>0110010=>[1,2,2,1,1]
[6,4,7,8,5,3,2,1]=>[3,5,2,1,4,6,7,8]=>0110000=>[1,2,4]
[6,3,7,1,5,2,8,4]=>[3,6,2,8,4,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[3,2,6,8,4,7,5,1]=>[6,7,3,1,5,2,4,8]=>0110100=>[1,2,1,1,2]
[8,4,6,1,3,2,5,7]=>[1,5,3,8,6,7,4,2]=>0101011=>[1,1,1,1,1,2]
[4,2,8,6,7,3,1,5]=>[5,7,1,3,2,6,8,4]=>0101001=>[1,1,1,1,2,1]
[7,4,3,8,2,1,5,6]=>[2,5,6,1,7,8,4,3]=>0010011=>[2,1,2,2]
[4,7,5,8,1,6,3,2]=>[5,2,4,1,8,3,6,7]=>1010100=>[1,1,1,1,1,2]
[4,2,5,1,6,7,8,3]=>[5,7,4,8,3,2,1,6]=>0101110=>[1,1,1,3,1]
[2,4,8,5,7,1,3,6]=>[7,5,1,4,2,8,6,3]=>1101011=>[2,1,1,1,2]
[7,8,2,5,6,1,4,3]=>[2,1,7,4,3,8,5,6]=>1011010=>[1,1,2,1,1,1]
[2,6,7,3,5,1,8,4]=>[7,3,2,6,4,8,1,5]=>1101010=>[2,1,1,1,1,1]
[2,7,6,1,4,5,8,3]=>[7,2,3,8,5,4,1,6]=>1001110=>[1,2,3,1]
[7,4,3,5,1,6,8,2]=>[2,5,6,4,8,3,1,7]=>0010110=>[2,1,1,2,1]
[6,2,5,8,4,3,7,1]=>[3,7,4,1,5,6,2,8]=>0110010=>[1,2,2,1,1]
[8,6,7,1,5,4,3,2]=>[1,3,2,8,4,5,6,7]=>0101000=>[1,1,1,1,3]
[2,1,6,5,8,4,7,3]=>[7,8,3,4,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[2,6,4,8,7,3,5,1]=>[7,3,5,1,2,6,4,8]=>1010010=>[1,1,1,2,1,1]
[4,8,2,7,6,1,3,5]=>[5,1,7,2,3,8,6,4]=>1010011=>[1,1,1,2,2]
[5,8,4,3,2,7,1,6]=>[4,1,5,6,7,2,8,3]=>1000101=>[1,3,1,1,1]
[6,3,8,2,4,5,7,1]=>[3,6,1,7,5,4,2,8]=>0101110=>[1,1,1,3,1]
[5,8,4,2,3,6,1,7]=>[4,1,5,7,6,3,8,2]=>1001101=>[1,2,2,1,1]
[5,8,2,4,3,1,6,7]=>[4,1,7,5,6,8,3,2]=>1010011=>[1,1,1,2,2]
[8,2,1,3,4,7,5,6]=>[1,7,8,6,5,2,4,3]=>0011101=>[2,3,1,1]
[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>1101010=>[2,1,1,1,1,1]
[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>1110110=>[3,1,2,1]
[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>1101011=>[2,1,1,1,2]
[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>1011010=>[1,1,2,1,1,1]
[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>1101110=>[2,1,3,1]
[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>1110110=>[3,1,2,1]
[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>1011011=>[1,1,2,1,2]
[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>1101101=>[2,1,2,1,1]
[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>1101010=>[2,1,1,1,1,1]
[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>1101011=>[2,1,1,1,2]
[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>1011011=>[1,1,2,1,2]
[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>1101011=>[2,1,1,1,2]
[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>1011010=>[1,1,2,1,1,1]
[1,3,2,8,4,6,7,5]=>[8,6,7,1,5,3,2,4]=>1010110=>[1,1,1,1,2,1]
[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>1011110=>[1,1,4,1]
[1,7,8,2,4,3,6,5]=>[8,2,1,7,5,6,3,4]=>1101010=>[2,1,1,1,1,1]
[7,6,3,1,5,2,4,8]=>[2,3,6,8,4,7,5,1]=>0001011=>[3,1,1,2]
[6,7,3,1,5,2,8,4]=>[3,2,6,8,4,7,1,5]=>1001010=>[1,2,1,1,1,1]
[6,8,3,1,5,2,7,4]=>[3,1,6,8,4,7,2,5]=>1001010=>[1,2,1,1,1,1]
[6,8,4,5,1,2,7,3]=>[3,1,5,4,8,7,2,6]=>1010110=>[1,1,1,1,2,1]
[6,7,4,5,1,2,8,3]=>[3,2,5,4,8,7,1,6]=>1010110=>[1,1,1,1,2,1]
[7,2,1,6,5,3,4,8]=>[2,7,8,3,4,6,5,1]=>0010011=>[2,1,2,2]
[7,3,6,1,5,2,4,8]=>[2,6,3,8,4,7,5,1]=>0101011=>[1,1,1,1,1,2]
[7,4,6,5,1,2,3,8]=>[2,5,3,4,8,7,6,1]=>0100111=>[1,1,2,3]
[6,7,5,4,1,2,8,3]=>[3,2,4,5,8,7,1,6]=>1000110=>[1,3,2,1]
[5,8,6,4,1,7,2,3]=>[4,1,3,5,8,2,7,6]=>1000101=>[1,3,1,1,1]
[5,7,6,4,1,8,2,3]=>[4,2,3,5,8,1,7,6]=>1000101=>[1,3,1,1,1]
[5,6,7,4,1,8,2,3]=>[4,3,2,5,8,1,7,6]=>1100101=>[2,2,1,1,1]
[6,5,7,4,1,2,8,3]=>[3,4,2,5,8,7,1,6]=>0100110=>[1,1,2,2,1]
[6,4,7,5,1,2,8,3]=>[3,5,2,4,8,7,1,6]=>0100110=>[1,1,2,2,1]
[6,2,1,7,5,3,8,4]=>[3,7,8,2,4,6,1,5]=>0010010=>[2,1,2,1,1]
[6,3,8,1,5,2,7,4]=>[3,6,1,8,4,7,2,5]=>0101010=>[1,1,1,1,1,1,1]
[6,4,8,5,1,2,7,3]=>[3,5,1,4,8,7,2,6]=>0100110=>[1,1,2,2,1]
[5,6,8,4,1,7,2,3]=>[4,3,1,5,8,2,7,6]=>1100101=>[2,2,1,1,1]
[4,6,8,5,7,1,2,3]=>[5,3,1,4,2,8,7,6]=>1101011=>[2,1,1,1,2]
[4,5,8,6,7,1,2,3]=>[5,4,1,3,2,8,7,6]=>1101011=>[2,1,1,1,2]
[5,4,8,6,1,7,2,3]=>[4,5,1,3,8,2,7,6]=>0100101=>[1,1,2,1,1,1]
[5,3,8,1,6,7,2,4]=>[4,6,1,8,3,2,7,5]=>0101101=>[1,1,1,2,1,1]
[5,2,1,8,6,7,3,4]=>[4,7,8,1,3,2,6,5]=>0010101=>[2,1,1,1,1,1]
[5,2,1,7,6,8,3,4]=>[4,7,8,2,3,1,6,5]=>0010101=>[2,1,1,1,1,1]
[5,4,7,6,1,8,2,3]=>[4,5,2,3,8,1,7,6]=>0100101=>[1,1,2,1,1,1]
[4,5,7,6,8,1,2,3]=>[5,4,2,3,1,8,7,6]=>1101011=>[2,1,1,1,2]
[4,6,7,5,8,1,2,3]=>[5,3,2,4,1,8,7,6]=>1101011=>[2,1,1,1,2]
[4,8,6,5,7,1,2,3]=>[5,1,3,4,2,8,7,6]=>1001011=>[1,2,1,1,2]
[4,8,5,6,7,1,2,3]=>[5,1,4,3,2,8,7,6]=>1011011=>[1,1,2,1,2]
[4,7,5,6,8,1,2,3]=>[5,2,4,3,1,8,7,6]=>1011011=>[1,1,2,1,2]
[4,6,5,7,8,1,2,3]=>[5,3,4,2,1,8,7,6]=>1011011=>[1,1,2,1,2]
[5,7,4,6,1,8,2,3]=>[4,2,5,3,8,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,6,1,7,2,3]=>[4,1,5,3,8,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,1,6,7,2,4]=>[4,1,6,8,3,2,7,5]=>1001101=>[1,2,2,1,1]
[5,7,3,1,6,8,2,4]=>[4,2,6,8,3,1,7,5]=>1001101=>[1,2,2,1,1]
[5,6,3,1,7,8,2,4]=>[4,3,6,8,2,1,7,5]=>1001101=>[1,2,2,1,1]
[6,2,1,4,3,8,7,5]=>[3,7,8,5,6,1,2,4]=>0010100=>[2,1,1,1,2]
[5,8,3,1,7,6,2,4]=>[4,1,6,8,2,3,7,5]=>1001001=>[1,2,1,2,1]
[5,7,4,8,1,6,2,3]=>[4,2,5,1,8,3,7,6]=>1010101=>[1,1,1,1,1,1,1]
[5,2,1,6,8,7,3,4]=>[4,7,8,3,1,2,6,5]=>0011001=>[2,2,2,1]
[5,4,6,8,1,7,2,3]=>[4,5,3,1,8,2,7,6]=>0110101=>[1,2,1,1,1,1]
[4,5,6,8,7,1,2,3]=>[5,4,3,1,2,8,7,6]=>1110011=>[3,2,2]
[4,7,5,8,6,1,2,3]=>[5,2,4,1,3,8,7,6]=>1010011=>[1,1,1,2,2]
[4,8,6,7,5,1,2,3]=>[5,1,3,2,4,8,7,6]=>1010011=>[1,1,1,2,2]
[4,7,6,8,5,1,2,3]=>[5,2,3,1,4,8,7,6]=>1010011=>[1,1,1,2,2]
[4,6,7,8,5,1,2,3]=>[5,3,2,1,4,8,7,6]=>1110011=>[3,2,2]
[4,5,7,8,6,1,2,3]=>[5,4,2,1,3,8,7,6]=>1110011=>[3,2,2]
[5,4,7,8,1,6,2,3]=>[4,5,2,1,8,3,7,6]=>0110101=>[1,2,1,1,1,1]
[5,3,7,1,8,6,2,4]=>[4,6,2,8,1,3,7,5]=>0101001=>[1,1,1,1,2,1]
[5,2,1,7,8,6,3,4]=>[4,7,8,2,1,3,6,5]=>0011001=>[2,2,2,1]
[5,3,8,1,7,6,2,4]=>[4,6,1,8,2,3,7,5]=>0101001=>[1,1,1,1,2,1]
[5,4,8,7,1,6,2,3]=>[4,5,1,2,8,3,7,6]=>0100101=>[1,1,2,1,1,1]
[4,6,8,7,5,1,2,3]=>[5,3,1,2,4,8,7,6]=>1100011=>[2,3,2]
[4,7,8,6,5,1,2,3]=>[5,2,1,3,4,8,7,6]=>1100011=>[2,3,2]
[4,8,7,6,5,1,2,3]=>[5,1,2,3,4,8,7,6]=>1000011=>[1,4,2]
[2,4,6,3,7,5,1,8]=>[7,5,3,6,2,4,8,1]=>1101001=>[2,1,1,2,1]
[4,2,7,3,6,5,1,8]=>[5,7,2,6,3,4,8,1]=>0101001=>[1,1,1,1,2,1]
[2,5,3,1,6,4,8,7]=>[7,4,6,8,3,5,1,2]=>1001010=>[1,2,1,1,1,1]
[2,5,3,7,6,4,1,8]=>[7,4,6,2,3,5,8,1]=>1010001=>[1,1,1,3,1]
[4,2,7,6,3,5,1,8]=>[5,7,2,3,6,4,8,1]=>0100101=>[1,1,2,1,1,1]
[2,6,3,7,5,4,1,8]=>[7,3,6,2,4,5,8,1]=>1010001=>[1,1,1,3,1]
[2,3,1,8,6,5,4,7]=>[7,6,8,1,3,4,5,2]=>1010001=>[1,1,1,3,1]
[3,6,8,2,1,4,5,7]=>[6,3,1,7,8,5,4,2]=>1100111=>[2,2,3]
[1,2,6,3,8,7,4,5]=>[8,7,3,6,1,2,5,4]=>1101001=>[2,1,1,2,1]
[2,1,3,8,7,5,4,6]=>[7,8,6,1,2,4,5,3]=>0110001=>[1,2,3,1]
[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>1110010=>[3,2,1,1]
[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>1110100=>[3,1,1,2]
[1,2,7,6,3,8,4,5]=>[8,7,2,3,6,1,5,4]=>1100101=>[2,2,1,1,1]
[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>1110100=>[3,1,1,2]
[2,1,3,8,5,4,7,6]=>[7,8,6,1,4,5,2,3]=>0110010=>[1,2,2,1,1]
[2,1,8,4,3,5,7,6]=>[7,8,1,5,6,4,2,3]=>0100110=>[1,1,2,2,1]
[5,4,2,8,3,1,6,7]=>[4,5,7,1,6,8,3,2]=>0010011=>[2,1,2,2]
[3,5,8,2,4,1,6,7]=>[6,4,1,7,5,8,3,2]=>1101011=>[2,1,1,1,2]
[2,5,4,8,3,1,6,7]=>[7,4,5,1,6,8,3,2]=>1010011=>[1,1,1,2,2]
[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>1010011=>[1,1,1,2,2]
[1,2,7,3,6,4,8,5]=>[8,7,2,6,3,5,1,4]=>1101010=>[2,1,1,1,1,1]
[1,2,8,6,3,7,4,5]=>[8,7,1,3,6,2,5,4]=>1100101=>[2,2,1,1,1]
[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>1110100=>[3,1,1,2]
[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>1101100=>[2,1,2,2]
[1,2,6,3,8,4,7,5]=>[8,7,3,6,1,5,2,4]=>1101010=>[2,1,1,1,1,1]
[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>1011001=>[1,1,2,2,1]
[4,2,1,8,3,7,5,6]=>[5,7,8,1,6,2,4,3]=>0010101=>[2,1,1,1,1,1]
[1,8,4,2,7,3,5,6]=>[8,1,5,7,2,6,4,3]=>1001011=>[1,2,1,1,2]
[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>1100110=>[2,2,2,1]
[1,2,7,3,8,4,6,5]=>[8,7,2,6,1,5,3,4]=>1101010=>[2,1,1,1,1,1]
[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>1110010=>[3,2,1,1]
[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>1110001=>[3,3,1]
[2,5,3,8,1,6,4,7]=>[7,4,6,1,8,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,7,1,5,3,8]=>[7,3,5,2,8,4,6,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,5,7,1,4,3,8]=>[7,3,4,2,8,5,6,1]=>1010101=>[1,1,1,1,1,1,1]
[3,8,5,7,1,2,6,4]=>[6,1,4,2,8,7,3,5]=>1010110=>[1,1,1,1,2,1]
[3,4,8,6,1,2,5,7]=>[6,5,1,3,8,7,4,2]=>1100111=>[2,2,3]
[2,5,7,1,4,8,6,3]=>[7,4,2,8,5,1,3,6]=>1101100=>[2,1,2,2]
[2,4,3,8,1,6,5,7]=>[7,5,6,1,8,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[3,5,7,6,1,2,4,8]=>[6,4,2,3,8,7,5,1]=>1100111=>[2,2,3]
[3,8,5,7,1,6,4,2]=>[6,1,4,2,8,3,5,7]=>1010100=>[1,1,1,1,1,2]
[3,2,8,5,6,1,7,4]=>[6,7,1,4,3,8,2,5]=>0101010=>[1,1,1,1,1,1,1]
[3,8,5,7,2,1,6,4]=>[6,1,4,2,7,8,3,5]=>1010010=>[1,1,1,2,1,1]
[3,4,8,6,2,1,5,7]=>[6,5,1,3,7,8,4,2]=>1100011=>[2,3,2]
[3,5,7,6,2,1,4,8]=>[6,4,2,3,7,8,5,1]=>1100011=>[2,3,2]
[4,8,6,7,2,1,3,5]=>[5,1,3,2,7,8,6,4]=>1010011=>[1,1,1,2,2]
[5,8,6,7,2,1,4,3]=>[4,1,3,2,7,8,5,6]=>1010010=>[1,1,1,2,1,1]
[4,8,6,7,2,1,5,3]=>[5,1,3,2,7,8,4,6]=>1010010=>[1,1,1,2,1,1]
[4,3,8,5,1,6,7,2]=>[5,6,1,4,8,3,2,7]=>0100110=>[1,1,2,2,1]
[5,8,6,7,1,4,3,2]=>[4,1,3,2,8,5,6,7]=>1010100=>[1,1,1,1,1,2]
[5,8,6,7,1,2,4,3]=>[4,1,3,2,8,7,5,6]=>1010110=>[1,1,1,1,2,1]
[4,2,8,5,1,7,6,3]=>[5,7,1,4,8,2,3,6]=>0100100=>[1,1,2,1,2]
[3,4,2,8,5,6,1,7]=>[6,5,7,1,4,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[3,2,5,7,6,1,4,8]=>[6,7,4,2,3,8,5,1]=>0110011=>[1,2,2,2]
[4,8,6,7,1,3,2,5]=>[5,1,3,2,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,6,7,1,2,5,3]=>[5,1,3,2,8,7,4,6]=>1010110=>[1,1,1,1,2,1]
[4,8,6,7,2,5,3,1]=>[5,1,3,2,7,4,6,8]=>1010100=>[1,1,1,1,1,2]
[4,3,8,5,1,2,6,7]=>[5,6,1,4,8,7,3,2]=>0100111=>[1,1,2,3]
[4,2,6,7,5,1,3,8]=>[5,7,3,2,4,8,6,1]=>0110011=>[1,2,2,2]
[3,8,5,7,1,4,2,6]=>[6,1,4,2,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,7,1,5,2,6]=>[6,1,5,2,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[3,5,2,8,4,6,1,7]=>[6,4,7,1,5,3,8,2]=>1010101=>[1,1,1,1,1,1,1]
[3,5,1,7,4,6,2,8]=>[6,4,8,2,5,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[3,8,4,7,2,5,1,6]=>[6,1,5,2,7,4,8,3]=>1010101=>[1,1,1,1,1,1,1]
[4,1,2,6,7,5,3,8]=>[5,8,7,3,2,4,6,1]=>0111001=>[1,3,2,1]
[4,2,6,7,5,3,8,1]=>[5,7,3,2,4,6,1,8]=>0110010=>[1,2,2,1,1]
[4,8,6,7,3,1,2,5]=>[5,1,3,2,6,8,7,4]=>1010011=>[1,1,1,2,2]
[3,1,5,7,6,2,4,8]=>[6,8,4,2,3,7,5,1]=>0110011=>[1,2,2,2]
[3,4,1,7,5,6,2,8]=>[6,5,8,2,4,3,7,1]=>1010101=>[1,1,1,1,1,1,1]
[4,1,7,5,2,8,6,3]=>[5,8,2,4,7,1,3,6]=>0100100=>[1,1,2,1,2]
[4,1,6,7,5,2,3,8]=>[5,8,3,2,4,7,6,1]=>0110011=>[1,2,2,2]
[4,8,6,7,2,3,1,5]=>[5,1,3,2,7,6,8,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,6,7,4,2,3,1]=>[4,1,3,2,5,7,6,8]=>1010010=>[1,1,1,2,1,1]
[4,8,6,7,3,1,5,2]=>[5,1,3,2,6,8,4,7]=>1010010=>[1,1,1,2,1,1]
[4,1,6,7,5,3,8,2]=>[5,8,3,2,4,6,1,7]=>0110010=>[1,2,2,1,1]
[4,1,7,5,3,2,8,6]=>[5,8,2,4,6,7,1,3]=>0100010=>[1,1,3,1,1]
[4,2,8,5,3,1,7,6]=>[5,7,1,4,6,8,2,3]=>0100010=>[1,1,3,1,1]
[4,2,1,6,7,5,3,8]=>[5,7,8,3,2,4,6,1]=>0011001=>[2,2,2,1]
[4,8,6,7,3,2,1,5]=>[5,1,3,2,6,7,8,4]=>1010001=>[1,1,1,3,1]
[5,8,6,7,4,2,1,3]=>[4,1,3,2,5,7,8,6]=>1010001=>[1,1,1,3,1]
[7,3,5,8,1,4,2,6]=>[2,6,4,1,8,5,7,3]=>0110101=>[1,2,1,1,1,1]
[3,8,7,6,1,4,2,5]=>[6,1,2,3,8,5,7,4]=>1000101=>[1,3,1,1,1]
[5,1,8,3,6,7,2,4]=>[4,8,1,6,3,2,7,5]=>0101101=>[1,1,1,2,1,1]
[1,4,7,8,5,6,2,3]=>[8,5,2,1,4,3,7,6]=>1110101=>[3,1,1,1,1]
[3,4,7,1,5,8,6,2]=>[6,5,2,8,4,1,3,7]=>1101100=>[2,1,2,2]
[3,6,1,4,7,8,5,2]=>[6,3,8,5,2,1,4,7]=>1011100=>[1,1,3,2]
[1,6,8,4,7,5,2,3]=>[8,3,1,5,2,4,7,6]=>1101001=>[2,1,1,2,1]
[6,8,1,3,5,7,2,4]=>[3,1,8,6,4,2,7,5]=>1011101=>[1,1,3,1,1]
[7,6,1,4,3,8,2,5]=>[2,3,8,5,6,1,7,4]=>0010101=>[2,1,1,1,1,1]
[3,8,1,6,5,4,2,7]=>[6,1,8,3,4,5,7,2]=>1010001=>[1,1,1,3,1]
[4,1,3,7,5,8,2,6]=>[5,8,6,2,4,1,7,3]=>0110101=>[1,2,1,1,1,1]
[6,1,7,3,8,4,2,5]=>[3,8,2,6,1,5,7,4]=>0101001=>[1,1,1,1,2,1]
[7,1,8,6,3,5,2,4]=>[2,8,1,3,6,4,7,5]=>0100101=>[1,1,2,1,1,1]
[3,1,7,6,5,8,4,2]=>[6,8,2,3,4,1,5,7]=>0100100=>[1,1,2,1,2]
[8,2,7,6,5,3,4,1]=>[1,7,2,3,4,6,5,8]=>0100010=>[1,1,3,1,1]
[8,4,2,6,7,5,3,1]=>[1,5,7,3,2,4,6,8]=>0011000=>[2,2,3]
[4,8,1,6,7,5,3,2]=>[5,1,8,3,2,4,6,7]=>1011000=>[1,1,2,3]
[7,4,1,6,8,2,5,3]=>[2,5,8,3,1,7,4,6]=>0011010=>[2,2,1,1,1]
[1,3,8,6,2,7,5,4]=>[8,6,1,3,7,2,4,5]=>1100100=>[2,2,1,2]
[6,1,3,2,7,8,4,5]=>[3,8,6,7,2,1,5,4]=>0101101=>[1,1,1,2,1,1]
[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>1001011=>[1,2,1,1,2]
[4,7,2,6,8,1,5,3]=>[5,2,7,3,1,8,4,6]=>1011010=>[1,1,2,1,1,1]
[8,7,3,6,4,5,2,1]=>[1,2,6,3,5,4,7,8]=>0010100=>[2,1,1,1,2]
[5,7,8,6,2,1,4,3]=>[4,2,1,3,7,8,5,6]=>1100010=>[2,3,1,1]
[2,7,4,1,6,8,3,5]=>[7,2,5,8,3,1,6,4]=>1001101=>[1,2,2,1,1]
[3,7,2,4,5,1,6,8]=>[6,2,7,5,4,8,3,1]=>1011011=>[1,1,2,1,2]
[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>1001011=>[1,2,1,1,2]
[2,8,4,6,5,1,3,7]=>[7,1,5,3,4,8,6,2]=>1010011=>[1,1,1,2,2]
[3,4,1,7,5,2,6,8]=>[6,5,8,2,4,7,3,1]=>1010011=>[1,1,1,2,2]
[7,5,8,6,1,2,4,3]=>[2,4,1,3,8,7,5,6]=>0100110=>[1,1,2,2,1]
[5,6,8,7,3,1,4,2]=>[4,3,1,2,6,8,5,7]=>1100010=>[2,3,1,1]
[2,5,4,3,6,8,1,7]=>[7,4,5,6,3,1,8,2]=>1001101=>[1,2,2,1,1]
[3,8,5,4,6,2,1,7]=>[6,1,4,5,3,7,8,2]=>1001001=>[1,2,1,2,1]
[4,8,2,1,3,7,5,6]=>[5,1,7,8,6,2,4,3]=>1001101=>[1,2,2,1,1]
[6,4,1,2,7,5,8,3]=>[3,5,8,7,2,4,1,6]=>0011010=>[2,2,1,1,1]
[4,1,8,3,6,7,5,2]=>[5,8,1,6,3,2,4,7]=>0101100=>[1,1,1,2,2]
[8,3,7,4,5,2,6,1]=>[1,6,2,5,4,7,3,8]=>0101010=>[1,1,1,1,1,1,1]
[4,3,7,8,5,1,6,2]=>[5,6,2,1,4,8,3,7]=>0110010=>[1,2,2,1,1]
[5,4,8,2,7,6,1,3]=>[4,5,1,7,2,3,8,6]=>0101001=>[1,1,1,1,2,1]
[1,2,7,3,6,5,8,4]=>[8,7,2,6,3,4,1,5]=>1101010=>[2,1,1,1,1,1]
[2,8,7,6,3,4,1,5]=>[7,1,2,3,6,5,8,4]=>1000101=>[1,3,1,1,1]
[5,8,2,6,3,4,1,7]=>[4,1,7,3,6,5,8,2]=>1010101=>[1,1,1,1,1,1,1]
[4,1,7,5,8,6,2,3]=>[5,8,2,4,1,3,7,6]=>0101001=>[1,1,1,1,2,1]
[5,1,7,8,4,3,6,2]=>[4,8,2,1,5,6,3,7]=>0110010=>[1,2,2,1,1]
[8,2,7,5,4,3,6,1]=>[1,7,2,4,5,6,3,8]=>0100010=>[1,1,3,1,1]
[6,3,8,1,4,7,5,2]=>[3,6,1,8,5,2,4,7]=>0101100=>[1,1,1,2,2]
[3,8,4,5,6,1,2,7]=>[6,1,5,4,3,8,7,2]=>1011011=>[1,1,2,1,2]
[1,4,3,5,7,8,2,6]=>[8,5,6,4,2,1,7,3]=>1011101=>[1,1,3,1,1]
[6,5,8,7,1,3,4,2]=>[3,4,1,2,8,6,5,7]=>0100110=>[1,1,2,2,1]
[3,6,7,2,4,8,1,5]=>[6,3,2,7,5,1,8,4]=>1101101=>[2,1,2,1,1]
[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>1010010=>[1,1,1,2,1,1]
[2,8,5,6,4,3,1,7]=>[7,1,4,3,5,6,8,2]=>1010001=>[1,1,1,3,1]
[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>1000001=>[1,5,1]
[6,1,5,2,8,4,7,3]=>[3,8,4,7,1,5,2,6]=>0101010=>[1,1,1,1,1,1,1]
[4,6,1,8,5,7,2,3]=>[5,3,8,1,4,2,7,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,1,2,8,5,6,3]=>[5,2,8,7,1,4,3,6]=>1011010=>[1,1,2,1,1,1]
[1,4,7,2,8,5,6,3]=>[8,5,2,7,1,4,3,6]=>1101010=>[2,1,1,1,1,1]
[1,7,3,5,8,6,2,4]=>[8,2,6,4,1,3,7,5]=>1011001=>[1,1,2,2,1]
[7,3,5,8,6,1,2,4]=>[2,6,4,1,3,8,7,5]=>0110011=>[1,2,2,2]
[3,6,8,1,5,7,2,4]=>[6,3,1,8,4,2,7,5]=>1101101=>[2,1,2,1,1]
[3,4,6,5,8,1,7,2]=>[6,5,3,4,1,8,2,7]=>1101010=>[2,1,1,1,1,1]
[6,8,1,5,7,2,3,4]=>[3,1,8,4,2,7,6,5]=>1011011=>[1,1,2,1,2]
[7,1,2,5,8,6,3,4]=>[2,8,7,4,1,3,6,5]=>0111001=>[1,3,2,1]
[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>1011001=>[1,1,2,2,1]
[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>1010110=>[1,1,1,1,2,1]
[7,6,8,1,2,3,5,4]=>[2,3,1,8,7,6,4,5]=>0101110=>[1,1,1,3,1]
[2,7,1,5,8,6,3,4]=>[7,2,8,4,1,3,6,5]=>1011001=>[1,1,2,2,1]
[2,4,7,1,8,5,6,3]=>[7,5,2,8,1,4,3,6]=>1101010=>[2,1,1,1,1,1]
[4,7,5,8,3,1,6,2]=>[5,2,4,1,6,8,3,7]=>1010010=>[1,1,1,2,1,1]
[4,7,2,1,8,5,6,3]=>[5,2,7,8,1,4,3,6]=>1001010=>[1,2,1,1,1,1]
[7,6,8,2,1,3,5,4]=>[2,3,1,7,8,6,4,5]=>0100110=>[1,1,2,2,1]
[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>1101010=>[2,1,1,1,1,1]
[3,7,6,8,2,1,5,4]=>[6,2,3,1,7,8,4,5]=>1010010=>[1,1,1,2,1,1]
[7,4,2,1,6,8,5,3]=>[2,5,7,8,3,1,4,6]=>0001100=>[3,2,2]
[6,7,4,1,8,5,3,2]=>[3,2,5,8,1,4,6,7]=>1001000=>[1,2,1,3]
[6,7,4,3,1,8,5,2]=>[3,2,5,6,8,1,4,7]=>1000100=>[1,3,1,2]
[2,7,4,1,6,8,5,3]=>[7,2,5,8,3,1,4,6]=>1001100=>[1,2,2,2]
[2,3,7,6,8,1,5,4]=>[7,6,2,3,1,8,4,5]=>1101010=>[2,1,1,1,1,1]
[7,4,2,6,8,5,1,3]=>[2,5,7,3,1,4,8,6]=>0011001=>[2,2,2,1]
[7,3,2,5,8,6,1,4]=>[2,6,7,4,1,3,8,5]=>0011001=>[2,2,2,1]
[3,1,7,6,8,2,5,4]=>[6,8,2,3,1,7,4,5]=>0101010=>[1,1,1,1,1,1,1]
[3,7,6,8,1,2,5,4]=>[6,2,3,1,8,7,4,5]=>1010110=>[1,1,1,1,2,1]
[1,3,7,6,8,2,5,4]=>[8,6,2,3,1,7,4,5]=>1101010=>[2,1,1,1,1,1]
[1,7,4,2,6,8,5,3]=>[8,2,5,7,3,1,4,6]=>1001100=>[1,2,2,2]
[7,4,1,2,6,8,5,3]=>[2,5,8,7,3,1,4,6]=>0011100=>[2,3,2]
[7,1,4,2,8,5,6,3]=>[2,8,5,7,1,4,3,6]=>0101010=>[1,1,1,1,1,1,1]
[7,1,8,2,5,4,6,3]=>[2,8,1,7,4,5,3,6]=>0101010=>[1,1,1,1,1,1,1]
[7,3,8,4,6,1,5,2]=>[2,6,1,5,3,8,4,7]=>0101010=>[1,1,1,1,1,1,1]
[7,2,8,1,6,4,5,3]=>[2,7,1,8,3,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[7,1,6,8,5,4,2,3]=>[2,8,3,1,4,5,7,6]=>0110001=>[1,2,3,1]
[7,1,2,6,8,5,4,3]=>[2,8,7,3,1,4,5,6]=>0111000=>[1,3,3]
[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>1011000=>[1,1,2,3]
[1,7,6,8,3,2,5,4]=>[8,2,3,1,6,7,4,5]=>1010010=>[1,1,1,2,1,1]
[7,6,8,3,1,2,5,4]=>[2,3,1,6,8,7,4,5]=>0100110=>[1,1,2,2,1]
[7,1,5,8,6,3,2,4]=>[2,8,4,1,3,6,7,5]=>0110001=>[1,2,3,1]
[7,2,5,8,6,3,1,4]=>[2,7,4,1,3,6,8,5]=>0110001=>[1,2,3,1]
[3,6,7,1,8,5,4,2]=>[6,3,2,8,1,4,5,7]=>1101000=>[2,1,1,3]
[7,2,6,8,5,4,1,3]=>[2,7,3,1,4,5,8,6]=>0110001=>[1,2,3,1]
[7,6,8,2,3,1,5,4]=>[2,3,1,7,6,8,4,5]=>0101010=>[1,1,1,1,1,1,1]
[2,7,6,8,3,1,5,4]=>[7,2,3,1,6,8,4,5]=>1010010=>[1,1,1,2,1,1]
[2,7,1,6,8,5,4,3]=>[7,2,8,3,1,4,5,6]=>1011000=>[1,1,2,3]
[6,7,3,1,8,5,4,2]=>[3,2,6,8,1,4,5,7]=>1001000=>[1,2,1,3]
[6,7,1,8,5,4,3,2]=>[3,2,8,1,4,5,6,7]=>1010000=>[1,1,1,4]
[7,2,1,6,8,5,4,3]=>[2,7,8,3,1,4,5,6]=>0011000=>[2,2,3]
[7,6,8,3,2,1,5,4]=>[2,3,1,6,7,8,4,5]=>0100010=>[1,1,3,1,1]
[4,7,8,5,6,1,3,2]=>[5,2,1,4,3,8,6,7]=>1101010=>[2,1,1,1,1,1]
[4,6,5,8,7,1,3,2]=>[5,3,4,1,2,8,6,7]=>1010010=>[1,1,1,2,1,1]
[5,6,4,8,1,2,7,3]=>[4,3,5,1,8,7,2,6]=>1010110=>[1,1,1,1,2,1]
[8,1,5,6,7,2,4,3]=>[1,8,4,3,2,7,5,6]=>0111010=>[1,3,1,1,1]
[6,4,5,1,8,2,7,3]=>[3,5,4,8,1,7,2,6]=>0101010=>[1,1,1,1,1,1,1]
[5,4,6,7,1,2,8,3]=>[4,5,3,2,8,7,1,6]=>0110110=>[1,2,1,2,1]
[4,3,6,7,2,1,5,8]=>[5,6,3,2,7,8,4,1]=>0110011=>[1,2,2,2]
[5,3,6,7,1,4,2,8]=>[4,6,3,2,8,5,7,1]=>0110101=>[1,2,1,1,1,1]
[8,1,4,6,7,3,2,5]=>[1,8,5,3,2,6,7,4]=>0111001=>[1,3,2,1]
[8,1,3,6,7,4,5,2]=>[1,8,6,3,2,5,4,7]=>0111010=>[1,3,1,1,1]
[7,2,1,6,8,4,5,3]=>[2,7,8,3,1,5,4,6]=>0011010=>[2,2,1,1,1]
[5,2,6,7,1,4,8,3]=>[4,7,3,2,8,5,1,6]=>0110110=>[1,2,1,2,1]
[4,2,6,7,3,1,8,5]=>[5,7,3,2,6,8,1,4]=>0110010=>[1,2,2,1,1]
[6,2,4,1,5,8,7,3]=>[3,7,5,8,4,1,2,6]=>0101100=>[1,1,1,2,2]
[7,2,1,5,4,8,6,3]=>[2,7,8,4,5,1,3,6]=>0010100=>[2,1,1,1,2]
[8,1,4,5,3,7,2,6]=>[1,8,5,4,6,2,7,3]=>0110101=>[1,2,1,1,1,1]
[7,3,1,5,4,8,2,6]=>[2,6,8,4,5,1,7,3]=>0010101=>[2,1,1,1,1,1]
[6,3,4,1,5,8,2,7]=>[3,6,5,8,4,1,7,2]=>0101101=>[1,1,1,2,1,1]
[5,3,4,2,1,8,6,7]=>[4,6,5,7,8,1,3,2]=>0100101=>[1,1,2,1,1,1]
[4,3,5,2,7,1,6,8]=>[5,6,4,7,2,8,3,1]=>0101011=>[1,1,1,1,1,2]
[5,6,3,8,1,4,2,7]=>[4,3,6,1,8,5,7,2]=>1010101=>[1,1,1,1,1,1,1]
[8,1,7,2,4,5,6,3]=>[1,8,2,7,5,4,3,6]=>0101110=>[1,1,1,3,1]
[7,6,1,2,4,5,8,3]=>[2,3,8,7,5,4,1,6]=>0011110=>[2,4,1]
[4,7,8,2,3,1,6,5]=>[5,2,1,7,6,8,3,4]=>1101010=>[2,1,1,1,1,1]
[5,6,2,8,1,4,7,3]=>[4,3,7,1,8,5,2,6]=>1010110=>[1,1,1,1,2,1]
[6,5,2,1,3,7,8,4]=>[3,4,7,8,6,2,1,5]=>0001110=>[3,3,1]
[7,5,1,3,2,6,8,4]=>[2,4,8,6,7,3,1,5]=>0010110=>[2,1,1,2,1]
[8,1,6,3,2,5,7,4]=>[1,8,3,6,7,4,2,5]=>0100110=>[1,1,2,2,1]
[7,4,1,3,5,2,8,6]=>[2,5,8,6,4,7,1,3]=>0011010=>[2,2,1,1,1]
[5,4,2,3,1,6,8,7]=>[4,5,7,6,8,3,1,2]=>0010110=>[2,1,1,2,1]
[7,3,1,4,5,6,2,8]=>[2,6,8,5,4,3,7,1]=>0011101=>[2,3,1,1]
[8,1,4,3,5,6,2,7]=>[1,8,5,6,4,3,7,2]=>0101101=>[1,1,1,2,1,1]
[6,2,3,1,5,7,8,4]=>[3,7,6,8,4,2,1,5]=>0101110=>[1,1,1,3,1]
[7,8,4,2,1,6,5,3]=>[2,1,5,7,8,3,4,6]=>1000100=>[1,3,1,2]
[7,8,4,2,1,5,6,3]=>[2,1,5,7,8,4,3,6]=>1000110=>[1,3,2,1]
[6,2,3,4,8,7,1,5]=>[3,7,6,5,1,2,8,4]=>0111001=>[1,3,2,1]
[6,2,3,4,7,8,1,5]=>[3,7,6,5,2,1,8,4]=>0111101=>[1,4,1,1]
[7,8,3,4,6,2,1,5]=>[2,1,6,5,3,7,8,4]=>1011001=>[1,1,2,2,1]
[7,8,3,6,4,2,1,5]=>[2,1,6,3,5,7,8,4]=>1010001=>[1,1,1,3,1]
[7,8,3,5,6,2,1,4]=>[2,1,6,4,3,7,8,5]=>1011001=>[1,1,2,2,1]
[6,2,3,8,7,5,1,4]=>[3,7,6,1,2,4,8,5]=>0110001=>[1,2,3,1]
[6,2,3,7,8,5,1,4]=>[3,7,6,2,1,4,8,5]=>0111001=>[1,3,2,1]
[6,3,2,5,8,7,1,4]=>[3,6,7,4,1,2,8,5]=>0011001=>[2,2,2,1]
[6,3,2,8,4,7,1,5]=>[3,6,7,1,5,2,8,4]=>0010101=>[2,1,1,1,1,1]
[6,4,3,8,7,5,1,2]=>[3,5,6,1,2,4,8,7]=>0010001=>[2,1,3,1]
[6,4,3,7,8,5,1,2]=>[3,5,6,2,1,4,8,7]=>0011001=>[2,2,2,1]
[6,2,4,1,7,3,5,8]=>[3,7,5,8,2,6,4,1]=>0101011=>[1,1,1,1,1,2]
[6,3,2,7,4,8,1,5]=>[3,6,7,2,5,1,8,4]=>0010101=>[2,1,1,1,1,1]
[5,7,2,3,6,1,8,4]=>[4,2,7,6,3,8,1,5]=>1011010=>[1,1,2,1,1,1]
[5,8,2,3,6,1,7,4]=>[4,1,7,6,3,8,2,5]=>1011010=>[1,1,2,1,1,1]
[4,7,5,8,3,2,1,6]=>[5,2,4,1,6,7,8,3]=>1010001=>[1,1,1,3,1]
[4,5,6,8,3,2,1,7]=>[5,4,3,1,6,7,8,2]=>1110001=>[3,3,1]
[4,6,8,5,3,2,1,7]=>[5,3,1,4,6,7,8,2]=>1100001=>[2,4,1]
[5,6,1,4,2,3,7,8]=>[4,3,8,5,7,6,2,1]=>1010111=>[1,1,1,1,3]
[5,6,8,4,3,7,1,2]=>[4,3,1,5,6,2,8,7]=>1100101=>[2,2,1,1,1]
[5,6,1,4,2,3,8,7]=>[4,3,8,5,7,6,1,2]=>1010110=>[1,1,1,1,2,1]
[5,2,8,3,4,1,7,6]=>[4,7,1,6,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[4,5,8,6,3,2,1,7]=>[5,4,1,3,6,7,8,2]=>1100001=>[2,4,1]
[4,6,5,8,3,2,1,7]=>[5,3,4,1,6,7,8,2]=>1010001=>[1,1,1,3,1]
[6,2,3,4,5,8,1,7]=>[3,7,6,5,4,1,8,2]=>0111101=>[1,4,1,1]
[5,6,2,4,1,7,8,3]=>[4,3,7,5,8,2,1,6]=>1010110=>[1,1,1,1,2,1]
[5,7,2,4,1,8,6,3]=>[4,2,7,5,8,1,3,6]=>1010100=>[1,1,1,1,1,2]
[6,1,4,2,8,7,5,3]=>[3,8,5,7,1,2,4,6]=>0101000=>[1,1,1,1,3]
[5,2,7,4,1,6,8,3]=>[4,7,2,5,8,3,1,6]=>0100110=>[1,1,2,2,1]
[5,4,1,3,7,2,6,8]=>[4,5,8,6,2,7,3,1]=>0011011=>[2,2,1,2]
[5,8,6,4,3,7,1,2]=>[4,1,3,5,6,2,8,7]=>1000101=>[1,3,1,1,1]
[5,8,1,4,2,3,7,6]=>[4,1,8,5,7,6,2,3]=>1010110=>[1,1,1,1,2,1]
[4,8,6,5,3,2,1,7]=>[5,1,3,4,6,7,8,2]=>1000001=>[1,5,1]
[5,4,7,8,3,2,1,6]=>[4,5,2,1,6,7,8,3]=>0110001=>[1,2,3,1]
[5,4,8,7,3,2,1,6]=>[4,5,1,2,6,7,8,3]=>0100001=>[1,1,4,1]
[4,6,8,7,3,2,1,5]=>[5,3,1,2,6,7,8,4]=>1100001=>[2,4,1]
[4,6,7,8,3,2,1,5]=>[5,3,2,1,6,7,8,4]=>1110001=>[3,3,1]
[4,7,6,8,3,2,1,5]=>[5,2,3,1,6,7,8,4]=>1010001=>[1,1,1,3,1]
[4,7,8,5,3,2,1,6]=>[5,2,1,4,6,7,8,3]=>1100001=>[2,4,1]
[5,7,1,3,4,2,6,8]=>[4,2,8,6,5,7,3,1]=>1011011=>[1,1,2,1,2]
[5,1,8,4,2,3,6,7]=>[4,8,1,5,7,6,3,2]=>0100111=>[1,1,2,3]
[5,1,7,4,2,3,6,8]=>[4,8,2,5,7,6,3,1]=>0100111=>[1,1,2,3]
[4,8,7,5,3,2,1,6]=>[5,1,2,4,6,7,8,3]=>1000001=>[1,5,1]
[4,7,8,6,3,2,1,5]=>[5,2,1,3,6,7,8,4]=>1100001=>[2,4,1]
[4,8,7,6,3,2,1,5]=>[5,1,2,3,6,7,8,4]=>1000001=>[1,5,1]
[4,8,2,6,3,7,5,1]=>[5,1,7,3,6,2,4,8]=>1010100=>[1,1,1,1,1,2]
[4,3,8,7,2,5,1,6]=>[5,6,1,2,7,4,8,3]=>0100101=>[1,1,2,1,1,1]
[5,8,4,3,7,1,6,2]=>[4,1,5,6,2,8,3,7]=>1001010=>[1,2,1,1,1,1]
[6,8,1,2,4,3,5,7]=>[3,1,8,7,5,6,4,2]=>1011011=>[1,1,2,1,2]
[4,8,7,6,3,1,2,5]=>[5,1,2,3,6,8,7,4]=>1000011=>[1,4,2]
[5,8,4,7,3,1,2,6]=>[4,1,5,2,6,8,7,3]=>1010011=>[1,1,1,2,2]
[4,3,8,2,7,5,6,1]=>[5,6,1,7,2,4,3,8]=>0101010=>[1,1,1,1,1,1,1]
[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[4,3,2,8,1,6,5,7]=>[5,6,7,1,8,3,4,2]=>0010101=>[2,1,1,1,1,1]
[4,1,3,8,2,6,5,7]=>[5,8,6,1,7,3,4,2]=>0110101=>[1,2,1,1,1,1]
[4,1,8,3,7,5,6,2]=>[5,8,1,6,2,4,3,7]=>0101010=>[1,1,1,1,1,1,1]
[4,1,8,7,3,5,2,6]=>[5,8,1,2,6,4,7,3]=>0100101=>[1,1,2,1,1,1]
[7,3,8,1,5,4,6,2]=>[2,6,1,8,4,5,3,7]=>0101010=>[1,1,1,1,1,1,1]
[3,4,8,7,2,5,1,6]=>[6,5,1,2,7,4,8,3]=>1100101=>[2,2,1,1,1]
[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>1101001=>[2,1,1,2,1]
[3,4,2,1,8,6,5,7]=>[6,5,7,8,1,3,4,2]=>1001001=>[1,2,1,2,1]
[3,4,1,8,2,6,5,7]=>[6,5,8,1,7,3,4,2]=>1010101=>[1,1,1,1,1,1,1]
[4,1,7,8,5,3,2,6]=>[5,8,2,1,4,6,7,3]=>0110001=>[1,2,3,1]
[4,2,3,1,8,6,5,7]=>[5,7,6,8,1,3,4,2]=>0101001=>[1,1,1,1,2,1]
[3,7,6,8,4,2,1,5]=>[6,2,3,1,5,7,8,4]=>1010001=>[1,1,1,3,1]
[3,7,8,6,2,4,1,5]=>[6,2,1,3,7,5,8,4]=>1100101=>[2,2,1,1,1]
[4,2,3,8,1,6,5,7]=>[5,7,6,1,8,3,4,2]=>0110101=>[1,2,1,1,1,1]
[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>1110001=>[3,3,1]
[4,3,7,8,5,2,1,6]=>[5,6,2,1,4,7,8,3]=>0110001=>[1,2,3,1]
[7,3,8,2,6,4,5,1]=>[2,6,1,7,3,5,4,8]=>0101010=>[1,1,1,1,1,1,1]
[2,4,8,3,6,1,5,7]=>[7,5,1,6,3,8,4,2]=>1101011=>[2,1,1,1,2]
[2,4,3,1,8,6,5,7]=>[7,5,6,8,1,3,4,2]=>1001001=>[1,2,1,2,1]
[3,1,2,4,8,6,5,7]=>[6,8,7,5,1,3,4,2]=>0111001=>[1,3,2,1]
[3,1,4,8,2,6,5,7]=>[6,8,5,1,7,3,4,2]=>0110101=>[1,2,1,1,1,1]
[7,3,4,8,5,1,6,2]=>[2,6,5,1,4,8,3,7]=>0110010=>[1,2,2,1,1]
[6,7,2,8,3,5,4,1]=>[3,2,7,1,6,4,5,8]=>1010100=>[1,1,1,1,1,2]
[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>1111001=>[4,2,1]
[4,8,3,6,2,1,5,7]=>[5,1,6,3,7,8,4,2]=>1010011=>[1,1,1,2,2]
[3,5,8,2,6,1,4,7]=>[6,4,1,7,3,8,5,2]=>1101011=>[2,1,1,1,2]
[5,3,8,7,2,4,6,1]=>[4,6,1,2,7,5,3,8]=>0100110=>[1,1,2,2,1]
[2,8,4,5,7,3,6,1]=>[7,1,5,4,2,6,3,8]=>1011010=>[1,1,2,1,1,1]
[2,4,5,7,3,8,1,6]=>[7,5,4,2,6,1,8,3]=>1110101=>[3,1,1,1,1]
[6,2,4,5,8,3,1,7]=>[3,7,5,4,1,6,8,2]=>0111001=>[1,3,2,1]
[4,8,1,2,5,6,3,7]=>[5,1,8,7,4,3,6,2]=>1011101=>[1,1,3,1,1]
[5,2,1,6,3,8,4,7]=>[4,7,8,3,6,1,5,2]=>0010101=>[2,1,1,1,1,1]
[5,6,4,8,1,3,2,7]=>[4,3,5,1,8,6,7,2]=>1010101=>[1,1,1,1,1,1,1]
[6,5,4,3,8,2,1,7]=>[3,4,5,6,1,7,8,2]=>0001001=>[3,1,2,1]
[5,4,3,7,2,8,1,6]=>[4,5,6,2,7,1,8,3]=>0010101=>[2,1,1,1,1,1]
[4,6,8,3,7,2,5,1]=>[5,3,1,6,2,7,4,8]=>1101010=>[2,1,1,1,1,1]
[1,4,3,6,2,7,8,5]=>[8,5,6,3,7,2,1,4]=>1010110=>[1,1,1,1,2,1]
[5,7,3,4,1,2,8,6]=>[4,2,6,5,8,7,1,3]=>1010110=>[1,1,1,1,2,1]
[8,5,4,7,6,2,1,3]=>[1,4,5,2,3,7,8,6]=>0010001=>[2,1,3,1]
[4,7,8,3,6,1,5,2]=>[5,2,1,6,3,8,4,7]=>1101010=>[2,1,1,1,1,1]
[1,3,8,6,4,7,5,2]=>[8,6,1,3,5,2,4,7]=>1100100=>[2,2,1,2]
[8,6,2,7,4,1,5,3]=>[1,3,7,2,5,8,4,6]=>0010010=>[2,1,2,1,1]
[7,6,2,1,4,3,8,5]=>[2,3,7,8,5,6,1,4]=>0001010=>[3,1,1,1,1]
[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>1100110=>[2,2,2,1]
[3,2,6,8,5,7,4,1]=>[6,7,3,1,4,2,5,8]=>0110100=>[1,2,1,1,2]
[7,5,2,3,1,6,8,4]=>[2,4,7,6,8,3,1,5]=>0010110=>[2,1,1,2,1]
[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>1010110=>[1,1,1,1,2,1]
[3,1,7,5,2,8,4,6]=>[6,8,2,4,7,1,5,3]=>0100101=>[1,1,2,1,1,1]
[2,5,7,4,1,8,3,6]=>[7,4,2,5,8,1,6,3]=>1100101=>[2,2,1,1,1]
[4,2,6,1,7,8,3,5]=>[5,7,3,8,2,1,6,4]=>0101101=>[1,1,1,2,1,1]
[4,2,7,6,3,8,1,5]=>[5,7,2,3,6,1,8,4]=>0100101=>[1,1,2,1,1,1]
[3,7,1,8,4,2,5,6]=>[6,2,8,1,5,7,4,3]=>1010011=>[1,1,1,2,2]
[4,2,1,3,7,5,8,6]=>[5,7,8,6,2,4,1,3]=>0011010=>[2,2,1,1,1]
[8,1,3,7,4,2,6,5]=>[1,8,6,2,5,7,3,4]=>0110010=>[1,2,2,1,1]
[8,4,3,7,6,2,1,5]=>[1,5,6,2,3,7,8,4]=>0010001=>[2,1,3,1]
[3,6,2,8,7,1,5,4]=>[6,3,7,1,2,8,4,5]=>1010010=>[1,1,1,2,1,1]
[7,3,2,8,1,6,5,4]=>[2,6,7,1,8,3,4,5]=>0010100=>[2,1,1,1,2]
[3,8,7,2,6,5,4,1]=>[6,1,2,7,3,4,5,8]=>1001000=>[1,2,1,3]
[4,2,7,8,6,1,5,3]=>[5,7,2,1,3,8,4,6]=>0110010=>[1,2,2,1,1]
[6,8,2,4,7,1,5,3]=>[3,1,7,5,2,8,4,6]=>1011010=>[1,1,2,1,1,1]
[5,2,1,8,7,3,6,4]=>[4,7,8,1,2,6,3,5]=>0010010=>[2,1,2,1,1]
[8,2,1,6,3,7,5,4]=>[1,7,8,3,6,2,4,5]=>0010100=>[2,1,1,1,2]
[6,8,3,1,7,5,2,4]=>[3,1,6,8,2,4,7,5]=>1001001=>[1,2,1,2,1]
[6,2,8,1,5,7,4,3]=>[3,7,1,8,4,2,5,6]=>0101100=>[1,1,1,2,2]
[5,7,8,2,6,1,4,3]=>[4,2,1,7,3,8,5,6]=>1101010=>[2,1,1,1,1,1]
[8,7,2,5,6,4,3,1]=>[1,2,7,4,3,5,6,8]=>0011000=>[2,2,3]
[7,2,6,8,1,5,4,3]=>[2,7,3,1,8,4,5,6]=>0110100=>[1,2,1,1,2]
[1,2,7,8,5,6,4,3]=>[8,7,2,1,4,3,5,6]=>1110100=>[3,1,1,2]
[7,4,8,1,6,2,5,3]=>[2,5,1,8,3,7,4,6]=>0101010=>[1,1,1,1,1,1,1]
[8,2,1,7,6,5,4,3]=>[1,7,8,2,3,4,5,6]=>0010000=>[2,1,4]
[8,6,7,5,1,4,3,2]=>[1,3,2,4,8,5,6,7]=>0100100=>[1,1,2,1,2]
[7,8,6,5,4,1,3,2]=>[2,1,3,4,5,8,6,7]=>1000010=>[1,4,1,1]
[5,8,4,3,2,1,6,7]=>[4,1,5,6,7,8,3,2]=>1000011=>[1,4,2]
[6,4,7,3,2,1,8,5]=>[3,5,2,6,7,8,1,4]=>0100010=>[1,1,3,1,1]
[5,4,7,3,2,1,6,8]=>[4,5,2,6,7,8,3,1]=>0100011=>[1,1,3,2]
[6,5,3,7,2,1,4,8]=>[3,4,6,2,7,8,5,1]=>0010011=>[2,1,2,2]
[5,8,3,6,2,1,4,7]=>[4,1,6,3,7,8,5,2]=>1010011=>[1,1,1,2,2]
[6,3,7,8,2,1,4,5]=>[3,6,2,1,7,8,5,4]=>0110011=>[1,2,2,2]
[5,3,7,6,2,1,4,8]=>[4,6,2,3,7,8,5,1]=>0100011=>[1,1,3,2]
[3,8,7,6,2,1,4,5]=>[6,1,2,3,7,8,5,4]=>1000011=>[1,4,2]
[5,8,4,2,6,1,3,7]=>[4,1,5,7,3,8,6,2]=>1001011=>[1,2,1,1,2]
[4,8,7,2,5,1,3,6]=>[5,1,2,7,4,8,6,3]=>1001011=>[1,2,1,1,2]
[5,8,3,2,6,1,4,7]=>[4,1,6,7,3,8,5,2]=>1001011=>[1,2,1,1,2]
[4,8,3,2,5,1,7,6]=>[5,1,6,7,4,8,2,3]=>1001010=>[1,2,1,1,1,1]
[4,3,7,2,5,1,8,6]=>[5,6,2,7,4,8,1,3]=>0101010=>[1,1,1,1,1,1,1]
[3,8,7,2,5,1,4,6]=>[6,1,2,7,4,8,5,3]=>1001011=>[1,2,1,1,2]
[6,4,2,7,5,1,3,8]=>[3,5,7,2,4,8,6,1]=>0010011=>[2,1,2,2]
[6,3,2,7,5,1,4,8]=>[3,6,7,2,4,8,5,1]=>0010011=>[2,1,2,2]
[5,3,2,6,7,1,4,8]=>[4,6,7,3,2,8,5,1]=>0011011=>[2,2,1,2]
[3,8,2,6,5,1,4,7]=>[6,1,7,3,4,8,5,2]=>1010011=>[1,1,1,2,2]
[6,2,7,8,5,1,3,4]=>[3,7,2,1,4,8,6,5]=>0110011=>[1,2,2,2]
[5,2,7,6,8,1,3,4]=>[4,7,2,3,1,8,6,5]=>0101011=>[1,1,1,1,1,2]
[4,2,7,6,5,1,3,8]=>[5,7,2,3,4,8,6,1]=>0100011=>[1,1,3,2]
[2,8,7,6,5,1,3,4]=>[7,1,2,3,4,8,6,5]=>1000011=>[1,4,2]
[6,5,4,3,1,7,8,2]=>[3,4,5,6,8,2,1,7]=>0000110=>[4,2,1]
[6,4,7,3,1,5,8,2]=>[3,5,2,6,8,4,1,7]=>0100110=>[1,1,2,2,1]
[5,4,7,3,1,8,6,2]=>[4,5,2,6,8,1,3,7]=>0100100=>[1,1,2,1,2]
[6,4,3,7,1,5,8,2]=>[3,5,6,2,8,4,1,7]=>0010110=>[2,1,1,2,1]
[5,4,3,6,1,8,7,2]=>[4,5,6,3,8,1,2,7]=>0010100=>[2,1,1,1,2]
[6,3,7,8,1,4,5,2]=>[3,6,2,1,8,5,4,7]=>0110110=>[1,2,1,2,1]
[5,3,7,6,1,4,8,2]=>[4,6,2,3,8,5,1,7]=>0100110=>[1,1,2,2,1]
[4,3,7,6,1,5,8,2]=>[5,6,2,3,8,4,1,7]=>0100110=>[1,1,2,2,1]
[3,8,7,6,1,4,5,2]=>[6,1,2,3,8,5,4,7]=>1000110=>[1,3,2,1]
[6,5,4,2,1,7,3,8]=>[3,4,5,7,8,2,6,1]=>0000101=>[4,1,1,1]
[6,4,7,2,1,5,3,8]=>[3,5,2,7,8,4,6,1]=>0100101=>[1,1,2,1,1,1]
[4,8,7,2,1,5,3,6]=>[5,1,2,7,8,4,6,3]=>1000101=>[1,3,1,1,1]
[5,8,3,2,1,4,7,6]=>[4,1,6,7,8,5,2,3]=>1000110=>[1,3,2,1]
[4,8,3,2,1,5,7,6]=>[5,1,6,7,8,4,2,3]=>1000110=>[1,3,2,1]
[5,3,7,2,1,4,8,6]=>[4,6,2,7,8,5,1,3]=>0100110=>[1,1,2,2,1]
[3,8,7,2,1,4,5,6]=>[6,1,2,7,8,5,4,3]=>1000111=>[1,3,3]
[6,5,2,7,1,4,3,8]=>[3,4,7,2,8,5,6,1]=>0010101=>[2,1,1,1,1,1]
[5,8,2,6,1,4,3,7]=>[4,1,7,3,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[6,4,2,7,1,5,3,8]=>[3,5,7,2,8,4,6,1]=>0010101=>[2,1,1,1,1,1]
[5,4,2,6,1,8,3,7]=>[4,5,7,3,8,1,6,2]=>0010101=>[2,1,1,1,1,1]
[4,3,2,6,1,5,8,7]=>[5,6,7,3,8,4,1,2]=>0010110=>[2,1,1,2,1]
[6,2,7,8,1,4,3,5]=>[3,7,2,1,8,5,6,4]=>0110101=>[1,2,1,1,1,1]
[3,2,7,6,1,4,5,8]=>[6,7,2,3,8,5,4,1]=>0100111=>[1,1,2,3]
[6,5,4,1,8,7,3,2]=>[3,4,5,8,1,2,6,7]=>0001000=>[3,1,3]
[5,8,4,1,6,7,3,2]=>[4,1,5,8,3,2,6,7]=>1001100=>[1,2,2,2]
[6,4,7,1,5,8,3,2]=>[3,5,2,8,4,1,6,7]=>0101100=>[1,1,1,2,2]
[5,4,7,1,6,8,3,2]=>[4,5,2,8,3,1,6,7]=>0101100=>[1,1,1,2,2]
[4,8,7,1,5,6,3,2]=>[5,1,2,8,4,3,6,7]=>1001100=>[1,2,2,2]
[5,4,3,1,6,8,7,2]=>[4,5,6,8,3,1,2,7]=>0001100=>[3,2,2]
[4,8,3,1,5,6,7,2]=>[5,1,6,8,4,3,2,7]=>1001110=>[1,2,3,1]
[3,8,7,1,5,4,6,2]=>[6,1,2,8,4,5,3,7]=>1001010=>[1,2,1,1,1,1]
[5,8,2,1,6,4,3,7]=>[4,1,7,8,3,5,6,2]=>1001001=>[1,2,1,2,1]
[6,3,2,1,5,4,8,7]=>[3,6,7,8,4,5,1,2]=>0001010=>[3,1,1,1,1]
[5,3,2,1,6,4,8,7]=>[4,6,7,8,3,5,1,2]=>0001010=>[3,1,1,1,1]
[3,8,2,1,5,4,6,7]=>[6,1,7,8,4,5,3,2]=>1001011=>[1,2,1,1,2]
[6,2,7,1,5,4,3,8]=>[3,7,2,8,4,5,6,1]=>0101001=>[1,1,1,1,2,1]
[5,2,7,1,6,4,3,8]=>[4,7,2,8,3,5,6,1]=>0101001=>[1,1,1,1,2,1]
[4,2,7,1,5,6,3,8]=>[5,7,2,8,4,3,6,1]=>0101101=>[1,1,1,2,1,1]
[3,2,7,1,5,4,6,8]=>[6,7,2,8,4,5,3,1]=>0101011=>[1,1,1,1,1,2]
[2,8,7,1,5,4,3,6]=>[7,1,2,8,4,5,6,3]=>1001001=>[1,2,1,2,1]
[6,5,1,7,8,4,3,2]=>[3,4,8,2,1,5,6,7]=>0011000=>[2,2,3]
[5,8,1,6,7,4,3,2]=>[4,1,8,3,2,5,6,7]=>1011000=>[1,1,2,3]
[6,4,1,7,5,8,3,2]=>[3,5,8,2,4,1,6,7]=>0010100=>[2,1,1,1,2]
[5,4,1,6,7,8,3,2]=>[4,5,8,3,2,1,6,7]=>0011100=>[2,3,2]
[4,8,1,6,5,7,3,2]=>[5,1,8,3,4,2,6,7]=>1010100=>[1,1,1,1,1,2]
[6,3,1,7,5,4,8,2]=>[3,6,8,2,4,5,1,7]=>0010010=>[2,1,2,1,1]
[5,3,1,6,7,4,8,2]=>[4,6,8,3,2,5,1,7]=>0011010=>[2,2,1,1,1]
[4,3,1,6,5,7,8,2]=>[5,6,8,3,4,2,1,7]=>0010110=>[2,1,1,2,1]
[3,8,1,6,5,4,7,2]=>[6,1,8,3,4,5,2,7]=>1010010=>[1,1,1,2,1,1]
[5,2,1,6,7,4,3,8]=>[4,7,8,3,2,5,6,1]=>0011001=>[2,2,2,1]
[4,2,1,6,5,7,3,8]=>[5,7,8,3,4,2,6,1]=>0010101=>[2,1,1,1,1,1]
[2,8,1,6,5,4,3,7]=>[7,1,8,3,4,5,6,2]=>1010001=>[1,1,1,3,1]
[6,1,7,8,5,4,3,2]=>[3,8,2,1,4,5,6,7]=>0110000=>[1,2,4]
[4,1,7,6,5,8,3,2]=>[5,8,2,3,4,1,6,7]=>0100100=>[1,1,2,1,2]
[3,1,7,6,5,4,8,2]=>[6,8,2,3,4,5,1,7]=>0100010=>[1,1,3,1,1]
[4,5,8,1,2,6,3,7]=>[5,4,1,8,7,3,6,2]=>1101101=>[2,1,2,1,1]
[1,4,5,7,2,6,3,8]=>[8,5,4,2,7,3,6,1]=>1110101=>[3,1,1,1,1]
[1,7,3,5,6,2,4,8]=>[8,2,6,4,3,7,5,1]=>1011011=>[1,1,2,1,2]
[8,1,3,5,7,2,4,6]=>[1,8,6,4,2,7,5,3]=>0111011=>[1,3,1,2]
[3,6,8,1,7,2,4,5]=>[6,3,1,8,2,7,5,4]=>1101011=>[2,1,1,1,2]
[3,4,5,6,8,1,7,2]=>[6,5,4,3,1,8,2,7]=>1111010=>[4,1,1,1]
[4,5,8,2,6,7,1,3]=>[5,4,1,7,3,2,8,6]=>1101101=>[2,1,2,1,1]
[8,2,3,5,6,7,1,4]=>[1,7,6,4,3,2,8,5]=>0111101=>[1,4,1,1]
[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>1011011=>[1,1,2,1,2]
[8,1,2,3,5,4,6,7]=>[1,8,7,6,4,5,3,2]=>0111011=>[1,3,1,2]
[2,7,8,1,3,5,4,6]=>[7,2,1,8,6,4,5,3]=>1101101=>[2,1,2,1,1]
[2,7,8,3,5,6,1,4]=>[7,2,1,6,4,3,8,5]=>1101101=>[2,1,2,1,1]
[2,4,5,7,8,1,6,3]=>[7,5,4,2,1,8,3,6]=>1111010=>[4,1,1,1]
[4,5,8,1,7,6,3,2]=>[5,4,1,8,2,3,6,7]=>1101000=>[2,1,1,3]
[4,5,8,7,2,1,6,3]=>[5,4,1,2,7,8,3,6]=>1100010=>[2,3,1,1]
[8,7,3,5,6,2,1,4]=>[1,2,6,4,3,7,8,5]=>0011001=>[2,2,2,1]
[8,7,2,1,3,5,4,6]=>[1,2,7,8,6,4,5,3]=>0001101=>[3,2,1,1]
[3,6,8,7,2,1,5,4]=>[6,3,1,2,7,8,4,5]=>1100010=>[2,3,1,1]
[8,6,4,1,7,5,3,2]=>[1,3,5,8,2,4,6,7]=>0001000=>[3,1,3]
[7,6,4,3,1,8,5,2]=>[2,3,5,6,8,1,4,7]=>0000100=>[4,1,2]
[2,3,6,7,8,1,5,4]=>[7,6,3,2,1,8,4,5]=>1111010=>[4,1,1,1]
[3,6,8,1,2,5,4,7]=>[6,3,1,8,7,4,5,2]=>1101101=>[2,1,2,1,1]
[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>1110101=>[3,1,1,1,1]
[7,4,1,8,5,2,3,6]=>[2,5,8,1,4,7,6,3]=>0010011=>[2,1,2,2]
[7,1,4,2,8,3,6,5]=>[2,8,5,7,1,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[7,1,8,2,5,3,6,4]=>[2,8,1,7,4,6,3,5]=>0101010=>[1,1,1,1,1,1,1]
[8,1,7,5,4,2,3,6]=>[1,8,2,4,5,7,6,3]=>0100011=>[1,1,3,2]
[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>1010001=>[1,1,1,3,1]
[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>1000101=>[1,3,1,1,1]
[8,6,3,1,2,5,4,7]=>[1,3,6,8,7,4,5,2]=>0001101=>[3,2,1,1]
[8,1,7,6,3,2,4,5]=>[1,8,2,3,6,7,5,4]=>0100011=>[1,1,3,2]
[8,2,5,7,6,3,1,4]=>[1,7,4,2,3,6,8,5]=>0110001=>[1,2,3,1]
[3,6,8,1,7,5,4,2]=>[6,3,1,8,2,4,5,7]=>1101000=>[2,1,1,3]
[8,2,6,7,5,4,1,3]=>[1,7,3,2,4,5,8,6]=>0110001=>[1,2,3,1]
[2,7,8,6,3,1,5,4]=>[7,2,1,3,6,8,4,5]=>1100010=>[2,3,1,1]
[2,7,8,1,6,5,4,3]=>[7,2,1,8,3,4,5,6]=>1101000=>[2,1,1,3]
[7,3,1,8,6,5,4,2]=>[2,6,8,1,3,4,5,7]=>0010000=>[2,1,4]
[8,7,2,1,6,5,4,3]=>[1,2,7,8,3,4,5,6]=>0001000=>[3,1,3]
[8,7,6,3,2,1,5,4]=>[1,2,3,6,7,8,4,5]=>0000010=>[5,1,1]
[2,1,8,6,3,7,4,5]=>[7,8,1,3,6,2,5,4]=>0100101=>[1,1,2,1,1,1]
[8,6,1,5,2,7,4,3]=>[1,3,8,4,7,2,5,6]=>0010100=>[2,1,1,1,2]
[8,5,1,7,4,2,6,3]=>[1,4,8,2,5,7,3,6]=>0010010=>[2,1,2,1,1]
[2,1,7,5,4,3,8,6]=>[7,8,2,4,5,6,1,3]=>0100010=>[1,1,3,1,1]
[2,1,8,4,5,3,6,7]=>[7,8,1,5,4,6,3,2]=>0101011=>[1,1,1,1,1,2]
[2,1,7,8,3,6,5,4]=>[7,8,2,1,6,3,4,5]=>0110100=>[1,2,1,1,2]
[2,1,8,5,7,6,3,4]=>[7,8,1,4,2,3,6,5]=>0101001=>[1,1,1,1,2,1]
[2,1,4,8,5,7,3,6]=>[7,8,5,1,4,2,6,3]=>0110101=>[1,2,1,1,1,1]
[2,1,5,4,6,8,3,7]=>[7,8,4,5,3,1,6,2]=>0101101=>[1,1,1,2,1,1]
[8,5,3,1,6,2,4,7]=>[1,4,6,8,3,7,5,2]=>0001011=>[3,1,1,2]
[7,5,1,4,6,8,3,2]=>[2,4,8,5,3,1,6,7]=>0011100=>[2,3,2]
[6,4,1,5,2,3,8,7]=>[3,5,8,4,7,6,1,2]=>0010110=>[2,1,1,2,1]
[8,3,7,5,2,6,1,4]=>[1,6,2,4,7,3,8,5]=>0100101=>[1,1,2,1,1,1]
[5,3,7,4,6,8,1,2]=>[4,6,2,5,3,1,8,7]=>0101101=>[1,1,1,2,1,1]
[5,8,3,7,6,2,1,4]=>[4,1,6,2,3,7,8,5]=>1010001=>[1,1,1,3,1]
[5,2,4,8,6,3,1,7]=>[4,7,5,1,3,6,8,2]=>0110001=>[1,2,3,1]
[4,2,6,3,8,5,1,7]=>[5,7,3,6,1,4,8,2]=>0101001=>[1,1,1,1,2,1]
[4,6,3,2,7,8,1,5]=>[5,3,6,7,2,1,8,4]=>1001101=>[1,2,2,1,1]
[3,6,8,7,5,4,1,2]=>[6,3,1,2,4,5,8,7]=>1100001=>[2,4,1]
[8,5,2,7,4,6,1,3]=>[1,4,7,2,5,3,8,6]=>0010101=>[2,1,1,1,1,1]
[5,8,2,1,7,6,4,3]=>[4,1,7,8,2,3,5,6]=>1001000=>[1,2,1,3]
[6,3,8,1,5,7,4,2]=>[3,6,1,8,4,2,5,7]=>0101100=>[1,1,1,2,2]
[8,3,2,4,1,7,5,6]=>[1,6,7,5,8,2,4,3]=>0010101=>[2,1,1,1,1,1]
[7,4,2,3,1,8,6,5]=>[2,5,7,6,8,1,3,4]=>0010100=>[2,1,1,1,2]
[7,2,4,3,1,5,8,6]=>[2,7,5,6,8,4,1,3]=>0100110=>[1,1,2,2,1]
[7,8,3,1,5,4,6,2]=>[2,1,6,8,4,5,3,7]=>1001010=>[1,2,1,1,1,1]
[7,2,8,1,4,6,5,3]=>[2,7,1,8,5,3,4,6]=>0101100=>[1,1,1,2,2]
[6,2,3,1,4,5,8,7]=>[3,7,6,8,5,4,1,2]=>0101110=>[1,1,1,3,1]
[5,6,1,4,3,2,8,7]=>[4,3,8,5,6,7,1,2]=>1010010=>[1,1,1,2,1,1]
[5,7,1,8,3,6,2,4]=>[4,2,8,1,6,3,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,1,4,5,3,2,7]=>[3,1,8,5,4,6,7,2]=>1011001=>[1,1,2,2,1]
[6,7,1,5,4,3,8,2]=>[3,2,8,4,5,6,1,7]=>1010010=>[1,1,1,2,1,1]
[8,7,5,1,3,4,2,6]=>[1,2,4,8,6,5,7,3]=>0001101=>[3,2,1,1]
[6,5,7,1,3,8,2,4]=>[3,4,2,8,6,1,7,5]=>0101101=>[1,1,1,2,1,1]
[8,2,6,1,4,7,3,5]=>[1,7,3,8,5,2,6,4]=>0101101=>[1,1,1,2,1,1]
[5,8,1,6,3,7,4,2]=>[4,1,8,3,6,2,5,7]=>1010100=>[1,1,1,1,1,2]
[8,3,5,6,1,7,4,2]=>[1,6,4,3,8,2,5,7]=>0110100=>[1,2,1,1,2]
[7,5,4,8,2,1,3,6]=>[2,4,5,1,7,8,6,3]=>0010011=>[2,1,2,2]
[7,3,6,5,4,1,8,2]=>[2,6,3,4,5,8,1,7]=>0100010=>[1,1,3,1,1]
[8,3,6,4,5,1,2,7]=>[1,6,3,5,4,8,7,2]=>0101011=>[1,1,1,1,1,2]
[7,3,5,8,1,6,2,4]=>[2,6,4,1,8,3,7,5]=>0110101=>[1,2,1,1,1,1]
[6,3,5,4,1,2,8,7]=>[3,6,4,5,8,7,1,2]=>0100110=>[1,1,2,2,1]
[2,6,3,5,1,4,8,7]=>[7,3,6,4,8,5,1,2]=>1010110=>[1,1,1,1,2,1]
[2,7,8,5,1,6,4,3]=>[7,2,1,4,8,3,5,6]=>1100100=>[2,2,1,2]
[8,7,3,6,5,1,4,2]=>[1,2,6,3,4,8,5,7]=>0010010=>[2,1,2,1,1]
[2,8,3,4,6,1,5,7]=>[7,1,6,5,3,8,4,2]=>1011011=>[1,1,2,1,2]
[2,7,4,3,6,1,8,5]=>[7,2,5,6,3,8,1,4]=>1001010=>[1,2,1,1,1,1]
[3,4,7,2,8,1,5,6]=>[6,5,2,7,1,8,4,3]=>1101011=>[2,1,1,1,2]
[4,3,2,5,7,1,8,6]=>[5,6,7,4,2,8,1,3]=>0011010=>[2,2,1,1,1]
[4,2,3,5,8,1,6,7]=>[5,7,6,4,1,8,3,2]=>0111011=>[1,3,1,2]
[3,2,8,4,7,1,6,5]=>[6,7,1,5,2,8,3,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,4,7,5,1,6,3]=>[1,7,5,2,4,8,3,6]=>0110010=>[1,2,2,1,1]
[3,8,4,7,1,6,5,2]=>[6,1,5,2,8,3,4,7]=>1010100=>[1,1,1,1,1,2]
[3,2,4,6,1,5,8,7]=>[6,7,5,3,8,4,1,2]=>0110110=>[1,2,1,2,1]
[8,3,4,5,7,6,1,2]=>[1,6,5,4,2,3,8,7]=>0111001=>[1,3,2,1]
[2,8,4,6,5,7,1,3]=>[7,1,5,3,4,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[2,3,8,4,6,7,1,5]=>[7,6,1,5,3,2,8,4]=>1101101=>[2,1,2,1,1]
[2,4,3,5,8,7,1,6]=>[7,5,6,4,1,2,8,3]=>1011001=>[1,1,2,2,1]
[3,2,4,5,6,8,1,7]=>[6,7,5,4,3,1,8,2]=>0111101=>[1,4,1,1]
[5,6,8,1,4,2,7,3]=>[4,3,1,8,5,7,2,6]=>1101010=>[2,1,1,1,1,1]
[1,5,7,8,4,6,2,3]=>[8,4,2,1,5,3,7,6]=>1110101=>[3,1,1,1,1]
[1,3,5,7,8,6,2,4]=>[8,6,4,2,1,3,7,5]=>1111001=>[4,2,1]
[3,5,7,8,6,1,2,4]=>[6,4,2,1,3,8,7,5]=>1110011=>[3,2,2]
[3,5,1,6,8,2,7,4]=>[6,4,8,3,1,7,2,5]=>1011010=>[1,1,2,1,1,1]
[3,1,5,6,8,2,7,4]=>[6,8,4,3,1,7,2,5]=>0111010=>[1,3,1,1,1]
[2,3,5,6,8,1,7,4]=>[7,6,4,3,1,8,2,5]=>1111010=>[4,1,1,1]
[5,6,4,8,2,1,7,3]=>[4,3,5,1,7,8,2,6]=>1010010=>[1,1,1,2,1,1]
[5,1,6,3,8,4,7,2]=>[4,8,3,6,1,5,2,7]=>0101010=>[1,1,1,1,1,1,1]
[2,5,1,6,8,3,7,4]=>[7,4,8,3,1,6,2,5]=>1011010=>[1,1,2,1,1,1]
[5,1,2,6,8,3,7,4]=>[4,8,7,3,1,6,2,5]=>0111010=>[1,3,1,1,1]
[5,7,1,8,6,2,3,4]=>[4,2,8,1,3,7,6,5]=>1010011=>[1,1,1,2,2]
[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>1011001=>[1,1,2,2,1]
[1,6,7,5,2,8,3,4]=>[8,3,2,4,7,1,6,5]=>1100101=>[2,2,1,1,1]
[6,1,7,5,2,8,3,4]=>[3,8,2,4,7,1,6,5]=>0100101=>[1,1,2,1,1,1]
[2,6,7,5,1,8,3,4]=>[7,3,2,4,8,1,6,5]=>1100101=>[2,2,1,1,1]
[5,7,2,8,6,1,3,4]=>[4,2,7,1,3,8,6,5]=>1010011=>[1,1,1,2,2]
[3,5,7,8,6,2,1,4]=>[6,4,2,1,3,7,8,5]=>1110001=>[3,3,1]
[5,1,7,8,6,3,4,2]=>[4,8,2,1,3,6,5,7]=>0110010=>[1,2,2,1,1]
[5,1,3,7,8,6,4,2]=>[4,8,6,2,1,3,5,7]=>0111000=>[1,3,3]
[5,2,7,8,4,6,1,3]=>[4,7,2,1,5,3,8,6]=>0110101=>[1,2,1,1,1,1]
[3,2,5,7,8,6,1,4]=>[6,7,4,2,1,3,8,5]=>0111001=>[1,3,2,1]
[6,2,7,5,1,8,3,4]=>[3,7,2,4,8,1,6,5]=>0100101=>[1,1,2,1,1,1]
[1,2,6,7,5,8,3,4]=>[8,7,3,2,4,1,6,5]=>1110101=>[3,1,1,1,1]
[6,2,7,5,4,1,8,3]=>[3,7,2,4,5,8,1,6]=>0100010=>[1,1,3,1,1]
[6,7,5,2,4,1,8,3]=>[3,2,4,7,5,8,1,6]=>1001010=>[1,2,1,1,1,1]
[6,7,2,5,3,8,1,4]=>[3,2,7,4,6,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,7,4,5,2,1,8,3]=>[3,2,5,4,7,8,1,6]=>1010010=>[1,1,1,2,1,1]
[5,1,7,8,6,4,3,2]=>[4,8,2,1,3,5,6,7]=>0110000=>[1,2,4]
[2,5,7,8,6,3,1,4]=>[7,4,2,1,3,6,8,5]=>1110001=>[3,3,1]
[5,1,7,8,6,3,2,4]=>[4,8,2,1,3,6,7,5]=>0110001=>[1,2,3,1]
[6,3,7,5,1,8,2,4]=>[3,6,2,4,8,1,7,5]=>0100101=>[1,1,2,1,1,1]
[1,6,7,5,3,8,2,4]=>[8,3,2,4,6,1,7,5]=>1100101=>[2,2,1,1,1]
[1,6,7,5,4,2,8,3]=>[8,3,2,4,5,7,1,6]=>1100010=>[2,3,1,1]
[6,7,5,1,4,2,8,3]=>[3,2,4,8,5,7,1,6]=>1001010=>[1,2,1,1,1,1]
[5,7,8,6,4,1,2,3]=>[4,2,1,3,5,8,7,6]=>1100011=>[2,3,2]
[4,1,7,2,6,5,8,3]=>[5,8,2,7,3,4,1,6]=>0101010=>[1,1,1,1,1,1,1]
[2,4,7,1,5,6,8,3]=>[7,5,2,8,4,3,1,6]=>1101110=>[2,1,3,1]
[6,7,4,1,5,2,8,3]=>[3,2,5,8,4,7,1,6]=>1001010=>[1,2,1,1,1,1]
[1,6,7,4,5,2,8,3]=>[8,3,2,5,4,7,1,6]=>1101010=>[2,1,1,1,1,1]
[1,6,3,7,5,8,2,4]=>[8,3,6,2,4,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[6,3,1,7,5,8,2,4]=>[3,6,8,2,4,1,7,5]=>0010101=>[2,1,1,1,1,1]
[2,5,3,7,8,6,1,4]=>[7,4,6,2,1,3,8,5]=>1011001=>[1,1,2,2,1]
[6,7,5,4,2,1,8,3]=>[3,2,4,5,7,8,1,6]=>1000010=>[1,4,1,1]
[6,3,2,7,5,8,1,4]=>[3,6,7,2,4,1,8,5]=>0010101=>[2,1,1,1,1,1]
[6,7,4,2,5,1,8,3]=>[3,2,5,7,4,8,1,6]=>1001010=>[1,2,1,1,1,1]
[6,2,7,4,5,1,8,3]=>[3,7,2,5,4,8,1,6]=>0101010=>[1,1,1,1,1,1,1]
[6,2,3,7,5,8,1,4]=>[3,7,6,2,4,1,8,5]=>0110101=>[1,2,1,1,1,1]
[4,5,1,6,3,2,8,7]=>[5,4,8,3,6,7,1,2]=>1010010=>[1,1,1,2,1,1]
[7,5,1,6,3,8,2,4]=>[2,4,8,3,6,1,7,5]=>0010101=>[2,1,1,1,1,1]
[7,5,1,6,3,8,4,2]=>[2,4,8,3,6,1,5,7]=>0010100=>[2,1,1,1,2]
[2,7,6,1,3,8,4,5]=>[7,2,3,8,6,1,5,4]=>1001101=>[1,2,2,1,1]
[7,3,5,1,8,2,6,4]=>[2,6,4,8,1,7,3,5]=>0101010=>[1,1,1,1,1,1,1]
[7,3,5,1,8,2,4,6]=>[2,6,4,8,1,7,5,3]=>0101011=>[1,1,1,1,1,2]
[2,1,6,7,3,8,5,4]=>[7,8,3,2,6,1,4,5]=>0110100=>[1,2,1,1,2]
[3,7,5,4,8,1,6,2]=>[6,2,4,5,1,8,3,7]=>1001010=>[1,2,1,1,1,1]
[3,7,5,4,8,1,2,6]=>[6,2,4,5,1,8,7,3]=>1001011=>[1,2,1,1,2]
[4,6,1,5,8,7,3,2]=>[5,3,8,4,1,2,6,7]=>1011000=>[1,1,2,3]
[4,6,1,5,8,7,2,3]=>[5,3,8,4,1,2,7,6]=>1011001=>[1,1,2,2,1]
[4,6,1,5,8,2,7,3]=>[5,3,8,4,1,7,2,6]=>1011010=>[1,1,2,1,1,1]
[7,5,1,6,2,8,3,4]=>[2,4,8,3,7,1,6,5]=>0010101=>[2,1,1,1,1,1]
[7,5,1,6,2,8,4,3]=>[2,4,8,3,7,1,5,6]=>0010100=>[2,1,1,1,2]
[4,6,1,5,8,2,3,7]=>[5,3,8,4,1,7,6,2]=>1011011=>[1,1,2,1,2]
[4,7,1,5,8,3,6,2]=>[5,2,8,4,1,6,3,7]=>1011010=>[1,1,2,1,1,1]
[6,8,5,4,3,2,7,1]=>[3,1,4,5,6,7,2,8]=>1000010=>[1,4,1,1]
[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>[1,9]
[7,9,6,5,4,3,2,8,1]=>[3,1,4,5,6,7,8,2,9]=>10000010=>[1,5,1,1]
[8,9,6,5,4,3,2,1,7]=>[2,1,4,5,6,7,8,9,3]=>10000001=>[1,6,1]
[6,8,5,4,3,7,2,1]=>[3,1,4,5,6,2,7,8]=>1000100=>[1,3,1,2]
[5,8,4,3,2,1,7,6]=>[4,1,5,6,7,8,2,3]=>1000010=>[1,4,1,1]
[6,5,4,3,1,8,7,2]=>[3,4,5,6,8,1,2,7]=>0000100=>[4,1,2]
[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>00000101=>[5,1,1,1]
[8,7,5,4,3,1,6,2]=>[1,2,4,5,6,8,3,7]=>0000010=>[5,1,1]
[9,7,6,5,4,3,1,8,2]=>[1,3,4,5,6,7,9,2,8]=>00000010=>[6,1,1]
[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>[9,1]
[3,5,2,6,8,4,1,7]=>[6,4,7,3,1,5,8,2]=>1011001=>[1,1,2,2,1]
[7,5,3,2,8,4,1,6]=>[2,4,6,7,1,5,8,3]=>0001001=>[3,1,2,1]
[2,4,5,7,3,8,6,1]=>[7,5,4,2,6,1,3,8]=>1110100=>[3,1,1,2]
[2,5,6,1,8,4,3,7]=>[7,4,3,8,1,5,6,2]=>1101001=>[2,1,1,2,1]
[5,3,6,8,1,4,2,7]=>[4,6,3,1,8,5,7,2]=>0110101=>[1,2,1,1,1,1]
[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>1111001=>[4,2,1]
[4,5,6,3,8,2,1,7]=>[5,4,3,6,1,7,8,2]=>1101001=>[2,1,1,2,1]
[6,1,4,7,3,2,8,5]=>[3,8,5,2,6,7,1,4]=>0110010=>[1,2,2,1,1]
[5,1,7,3,8,4,2,6]=>[4,8,2,6,1,5,7,3]=>0101001=>[1,1,1,1,2,1]
[2,5,1,7,4,3,8,6]=>[7,4,8,2,5,6,1,3]=>1010010=>[1,1,1,2,1,1]
[2,5,7,4,1,8,6,3]=>[7,4,2,5,8,1,3,6]=>1100100=>[2,2,1,2]
[5,3,7,1,4,8,6,2]=>[4,6,2,8,5,1,3,7]=>0101100=>[1,1,1,2,2]
[6,4,3,1,7,8,5,2]=>[3,5,6,8,2,1,4,7]=>0001100=>[3,2,2]
[6,4,1,7,3,8,5,2]=>[3,5,8,2,6,1,4,7]=>0010100=>[2,1,1,1,2]
[5,1,6,3,7,8,4,2]=>[4,8,3,6,2,1,5,7]=>0101100=>[1,1,1,2,2]
[5,6,1,7,8,3,4,2]=>[4,3,8,2,1,6,5,7]=>1011010=>[1,1,2,1,1,1]
[1,6,3,7,4,8,5,2]=>[8,3,6,2,5,1,4,7]=>1010100=>[1,1,1,1,1,2]
[6,7,2,1,4,3,8,5]=>[3,2,7,8,5,6,1,4]=>1001010=>[1,2,1,1,1,1]
[5,6,1,3,2,7,8,4]=>[4,3,8,6,7,2,1,5]=>1010110=>[1,1,1,1,2,1]
[2,5,6,3,7,8,4,1]=>[7,4,3,6,2,1,5,8]=>1101100=>[2,1,2,2]
[2,5,6,3,1,7,8,4]=>[7,4,3,6,8,2,1,5]=>1100110=>[2,2,2,1]
[2,6,4,7,3,1,8,5]=>[7,3,5,2,6,8,1,4]=>1010010=>[1,1,1,2,1,1]
[6,3,7,2,8,4,1,5]=>[3,6,2,7,1,5,8,4]=>0101001=>[1,1,1,1,2,1]
[6,3,2,7,1,8,4,5]=>[3,6,7,2,8,1,5,4]=>0010101=>[2,1,1,1,1,1]
[7,5,3,2,1,8,4,6]=>[2,4,6,7,8,1,5,3]=>0000101=>[4,1,1,1]
[7,3,8,4,2,1,5,6]=>[2,6,1,5,7,8,4,3]=>0100011=>[1,1,3,2]
[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>1110001=>[3,3,1]
[7,3,8,4,6,2,1,5]=>[2,6,1,5,3,7,8,4]=>0101001=>[1,1,1,1,2,1]
[5,7,3,8,2,1,6,4]=>[4,2,6,1,7,8,3,5]=>1010010=>[1,1,1,2,1,1]
[6,3,7,8,5,2,1,4]=>[3,6,2,1,4,7,8,5]=>0110001=>[1,2,3,1]
[4,6,2,7,8,5,3,1]=>[5,3,7,2,1,4,6,8]=>1011000=>[1,1,2,3]
[4,6,2,1,7,8,5,3]=>[5,3,7,8,2,1,4,6]=>1001100=>[1,2,2,2]
[7,4,5,8,1,2,6,3]=>[2,5,4,1,8,7,3,6]=>0110110=>[1,2,1,2,1]
[2,5,1,7,3,8,6,4]=>[7,4,8,2,6,1,3,5]=>1010100=>[1,1,1,1,1,2]
[6,7,2,1,3,8,5,4]=>[3,2,7,8,6,1,4,5]=>1001100=>[1,2,2,2]
[5,1,6,7,8,2,4,3]=>[4,8,3,2,1,7,5,6]=>0111010=>[1,3,1,1,1]
[6,2,1,7,3,8,5,4]=>[3,7,8,2,6,1,4,5]=>0010100=>[2,1,1,1,2]
[6,2,7,1,8,5,4,3]=>[3,7,2,8,1,4,5,6]=>0101000=>[1,1,1,1,3]
[6,3,1,7,8,5,4,2]=>[3,6,8,2,1,4,5,7]=>0011000=>[2,2,3]
[4,1,3,6,8,2,5,7]=>[5,8,6,3,1,7,4,2]=>0111011=>[1,3,1,2]
[4,2,3,6,8,1,5,7]=>[5,7,6,3,1,8,4,2]=>0111011=>[1,3,1,2]
[5,3,2,1,8,4,7,6]=>[4,6,7,8,1,5,2,3]=>0001010=>[3,1,1,1,1]
[2,4,6,5,8,1,3,7]=>[7,5,3,4,1,8,6,2]=>1101011=>[2,1,1,1,2]
[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>1011101=>[1,1,3,1,1]
[5,3,2,1,6,8,4,7]=>[4,6,7,8,3,1,5,2]=>0001101=>[3,2,1,1]
[6,2,4,5,8,1,3,7]=>[3,7,5,4,1,8,6,2]=>0111011=>[1,3,1,2]
[2,8,4,1,7,6,3,5]=>[7,1,5,8,2,3,6,4]=>1001001=>[1,2,1,2,1]
[8,1,4,2,7,3,6,5]=>[1,8,5,7,2,6,3,4]=>0101010=>[1,1,1,1,1,1,1]
[1,5,3,2,8,7,4,6]=>[8,4,6,7,1,2,5,3]=>1001001=>[1,2,1,2,1]
[8,2,1,7,5,3,4,6]=>[1,7,8,2,4,6,5,3]=>0010011=>[2,1,2,2]
[5,8,7,4,1,2,6,3]=>[4,1,2,5,8,7,3,6]=>1000110=>[1,3,2,1]
[5,8,7,4,6,2,1,3]=>[4,1,2,5,3,7,8,6]=>1001001=>[1,2,1,2,1]
[3,4,2,5,8,6,7,1]=>[6,5,7,4,1,3,2,8]=>1011010=>[1,1,2,1,1,1]
[4,3,6,2,8,1,7,5]=>[5,6,3,7,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[2,3,5,8,6,7,1,4]=>[7,6,4,1,3,2,8,5]=>1110101=>[3,1,1,1,1]
[1,2,8,3,5,6,7,4]=>[8,7,1,6,4,3,2,5]=>1101110=>[2,1,3,1]
[3,2,6,4,8,1,7,5]=>[6,7,3,5,1,8,2,4]=>0101010=>[1,1,1,1,1,1,1]
[8,2,1,6,7,3,4,5]=>[1,7,8,3,2,6,5,4]=>0011011=>[2,2,1,2]
[2,7,8,5,4,1,3,6]=>[7,2,1,4,5,8,6,3]=>1100011=>[2,3,2]
[4,8,3,1,2,7,6,5]=>[5,1,6,8,7,2,3,4]=>1001100=>[1,2,2,2]
[3,5,2,7,4,1,8,6]=>[6,4,7,2,5,8,1,3]=>1010010=>[1,1,1,2,1,1]
[8,4,2,3,7,1,5,6]=>[1,5,7,6,2,8,4,3]=>0011011=>[2,2,1,2]
[2,8,4,7,1,3,5,6]=>[7,1,5,2,8,6,4,3]=>1010111=>[1,1,1,1,3]
[8,2,4,6,7,1,3,5]=>[1,7,5,3,2,8,6,4]=>0111011=>[1,3,1,2]
[3,5,2,7,6,1,8,4]=>[6,4,7,2,3,8,1,5]=>1010010=>[1,1,1,2,1,1]
[5,8,3,2,1,6,7,4]=>[4,1,6,7,8,3,2,5]=>1000110=>[1,3,2,1]
[5,8,7,3,4,6,2,1]=>[4,1,2,6,5,3,7,8]=>1001100=>[1,2,2,2]
[5,8,2,7,4,1,6,3]=>[4,1,7,2,5,8,3,6]=>1010010=>[1,1,1,2,1,1]
[5,1,4,2,8,7,6,3]=>[4,8,5,7,1,2,3,6]=>0101000=>[1,1,1,1,3]
[4,7,6,5,8,2,1,3]=>[5,2,3,4,1,7,8,6]=>1001001=>[1,2,1,2,1]
[5,3,7,1,6,2,8,4]=>[4,6,2,8,3,7,1,5]=>0101010=>[1,1,1,1,1,1,1]
[6,3,2,1,8,5,7,4]=>[3,6,7,8,1,4,2,5]=>0001010=>[3,1,1,1,1]
[3,8,4,1,5,6,7,2]=>[6,1,5,8,4,3,2,7]=>1001110=>[1,2,3,1]
[5,2,4,7,1,8,6,3]=>[4,7,5,2,8,1,3,6]=>0110100=>[1,2,1,1,2]
[8,3,2,4,6,5,1,7]=>[1,6,7,5,3,4,8,2]=>0011001=>[2,2,2,1]
[8,4,2,1,6,5,3,7]=>[1,5,7,8,3,4,6,2]=>0001001=>[3,1,2,1]
[8,6,4,2,1,5,3,7]=>[1,3,5,7,8,4,6,2]=>0000101=>[4,1,1,1]
[8,2,6,3,4,5,1,7]=>[1,7,3,6,5,4,8,2]=>0101101=>[1,1,1,2,1,1]
[5,8,4,7,6,2,3,1]=>[4,1,5,2,3,7,6,8]=>1010010=>[1,1,1,2,1,1]
[1,3,4,7,5,8,2,6]=>[8,6,5,2,4,1,7,3]=>1110101=>[3,1,1,1,1]
[1,3,5,2,4,8,7,6]=>[8,6,4,7,5,1,2,3]=>1101100=>[2,1,2,2]
[4,7,1,6,5,8,3,2]=>[5,2,8,3,4,1,6,7]=>1010100=>[1,1,1,1,1,2]
[2,8,5,1,4,7,6,3]=>[7,1,4,8,5,2,3,6]=>1001100=>[1,2,2,2]
[4,3,1,5,8,6,7,2]=>[5,6,8,4,1,3,2,7]=>0011010=>[2,2,1,1,1]
[4,1,3,5,8,6,7,2]=>[5,8,6,4,1,3,2,7]=>0111010=>[1,3,1,1,1]
[5,4,2,1,6,8,7,3]=>[4,5,7,8,3,1,2,6]=>0001100=>[3,2,2]
[6,8,4,3,2,7,1,5]=>[3,1,5,6,7,2,8,4]=>1000101=>[1,3,1,1,1]
[5,1,3,2,8,6,7,4]=>[4,8,6,7,1,3,2,5]=>0101010=>[1,1,1,1,1,1,1]
[5,2,3,1,6,8,7,4]=>[4,7,6,8,3,1,2,5]=>0101100=>[1,1,1,2,2]
[5,3,2,1,8,6,7,4]=>[4,6,7,8,1,3,2,5]=>0001010=>[3,1,1,1,1]
[5,2,1,3,6,8,7,4]=>[4,7,8,6,3,1,2,5]=>0011100=>[2,3,2]
[6,3,8,2,7,4,1,5]=>[3,6,1,7,2,5,8,4]=>0101001=>[1,1,1,1,2,1]
[3,5,1,7,8,4,2,6]=>[6,4,8,2,1,5,7,3]=>1011001=>[1,1,2,2,1]
[3,4,8,7,2,1,6,5]=>[6,5,1,2,7,8,3,4]=>1100010=>[2,3,1,1]
[6,4,3,8,7,2,1,5]=>[3,5,6,1,2,7,8,4]=>0010001=>[2,1,3,1]
[8,4,7,2,3,1,5,6]=>[1,5,2,7,6,8,4,3]=>0101011=>[1,1,1,1,1,2]
[8,4,7,1,3,2,5,6]=>[1,5,2,8,6,7,4,3]=>0101011=>[1,1,1,1,1,2]
[8,4,7,2,1,3,5,6]=>[1,5,2,7,8,6,4,3]=>0100111=>[1,1,2,3]
[8,6,4,2,1,3,7,5]=>[1,3,5,7,8,6,2,4]=>0000110=>[4,2,1]
[8,6,4,1,3,2,7,5]=>[1,3,5,8,6,7,2,4]=>0001010=>[3,1,1,1,1]
[8,6,4,2,3,1,7,5]=>[1,3,5,7,6,8,2,4]=>0001010=>[3,1,1,1,1]
[3,5,7,2,6,1,8,4]=>[6,4,2,7,3,8,1,5]=>1101010=>[2,1,1,1,1,1]
[6,1,3,8,5,7,2,4]=>[3,8,6,1,4,2,7,5]=>0110101=>[1,2,1,1,1,1]
[5,8,3,2,6,7,1,4]=>[4,1,6,7,3,2,8,5]=>1001101=>[1,2,2,1,1]
[2,8,1,5,4,7,6,3]=>[7,1,8,4,5,2,3,6]=>1010100=>[1,1,1,1,1,2]
[1,5,8,7,4,6,2,3]=>[8,4,1,2,5,3,7,6]=>1100101=>[2,2,1,1,1]
[2,1,7,6,4,5,8,3]=>[7,8,2,3,5,4,1,6]=>0100110=>[1,1,2,2,1]
[1,7,2,4,6,5,8,3]=>[8,2,7,5,3,4,1,6]=>1011010=>[1,1,2,1,1,1]
[3,5,1,7,6,8,2,4]=>[6,4,8,2,3,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,6,1,3,7,4]=>[4,1,7,3,8,6,2,5]=>1010110=>[1,1,1,1,2,1]
[6,3,5,8,7,2,1,4]=>[3,6,4,1,2,7,8,5]=>0110001=>[1,2,3,1]
[2,5,7,8,4,1,6,3]=>[7,4,2,1,5,8,3,6]=>1110010=>[3,2,1,1]
[4,1,5,2,6,8,7,3]=>[5,8,4,7,3,1,2,6]=>0101100=>[1,1,1,2,2]
[4,2,8,5,1,6,7,3]=>[5,7,1,4,8,3,2,6]=>0100110=>[1,1,2,2,1]
[4,1,8,5,2,6,7,3]=>[5,8,1,4,7,3,2,6]=>0100110=>[1,1,2,2,1]
[2,7,1,8,5,4,6,3]=>[7,2,8,1,4,5,3,6]=>1010010=>[1,1,1,2,1,1]
[5,8,6,2,1,3,7,4]=>[4,1,3,7,8,6,2,5]=>1000110=>[1,3,2,1]
[8,2,4,1,5,6,7,3]=>[1,7,5,8,4,3,2,6]=>0101110=>[1,1,1,3,1]
[3,4,5,6,8,2,1,7]=>[6,5,4,3,1,7,8,2]=>1111001=>[4,2,1]
[3,4,5,7,1,8,6,2]=>[6,5,4,2,8,1,3,7]=>1110100=>[3,1,1,2]
[3,4,5,7,8,2,6,1]=>[6,5,4,2,1,7,3,8]=>1111010=>[4,1,1,1]
[3,4,6,2,8,5,1,7]=>[6,5,3,7,1,4,8,2]=>1101001=>[2,1,1,2,1]
[3,4,6,8,1,5,2,7]=>[6,5,3,1,8,4,7,2]=>1110101=>[3,1,1,1,1]
[3,4,7,2,1,8,6,5]=>[6,5,2,7,8,1,3,4]=>1100100=>[2,2,1,2]
[3,4,8,2,1,5,6,7]=>[6,5,1,7,8,4,3,2]=>1100111=>[2,2,3]
[3,5,2,6,7,8,1,4]=>[6,4,7,3,2,1,8,5]=>1011101=>[1,1,3,1,1]
[3,5,2,7,8,4,6,1]=>[6,4,7,2,1,5,3,8]=>1011010=>[1,1,2,1,1,1]
[3,5,2,8,4,1,6,7]=>[6,4,7,1,5,8,3,2]=>1010011=>[1,1,1,2,2]
[3,5,6,2,8,4,1,7]=>[6,4,3,7,1,5,8,2]=>1101001=>[2,1,1,2,1]
[3,5,6,8,4,1,2,7]=>[6,4,3,1,5,8,7,2]=>1110011=>[3,2,2]
[3,5,7,2,4,8,6,1]=>[6,4,2,7,5,1,3,8]=>1101100=>[2,1,2,2]
[3,5,7,2,8,4,6,1]=>[6,4,2,7,1,5,3,8]=>1101010=>[2,1,1,1,1,1]
[3,5,7,8,4,1,6,2]=>[6,4,2,1,5,8,3,7]=>1110010=>[3,2,1,1]
[3,6,2,1,7,8,5,4]=>[6,3,7,8,2,1,4,5]=>1001100=>[1,2,2,2]
[3,6,2,1,8,5,4,7]=>[6,3,7,8,1,4,5,2]=>1001001=>[1,2,1,2,1]
[3,6,7,2,4,8,5,1]=>[6,3,2,7,5,1,4,8]=>1101100=>[2,1,2,2]
[3,6,7,2,8,5,4,1]=>[6,3,2,7,1,4,5,8]=>1101000=>[2,1,1,3]
[3,6,7,8,4,5,1,2]=>[6,3,2,1,5,4,8,7]=>1110101=>[3,1,1,1,1]
[3,6,8,2,4,5,1,7]=>[6,3,1,7,5,4,8,2]=>1101101=>[2,1,2,1,1]
[3,7,2,1,4,8,6,5]=>[6,2,7,8,5,1,3,4]=>1001100=>[1,2,2,2]
[3,7,2,1,8,5,6,4]=>[6,2,7,8,1,4,3,5]=>1001010=>[1,2,1,1,1,1]
[3,7,2,8,4,5,6,1]=>[6,2,7,1,5,4,3,8]=>1010110=>[1,1,1,1,2,1]
[3,7,8,2,4,5,6,1]=>[6,2,1,7,5,4,3,8]=>1101110=>[2,1,3,1]
[3,8,2,1,4,5,6,7]=>[6,1,7,8,5,4,3,2]=>1001111=>[1,2,4]
[4,1,5,6,7,8,3,2]=>[5,8,4,3,2,1,6,7]=>0111100=>[1,4,2]
[4,1,5,7,3,8,6,2]=>[5,8,4,2,6,1,3,7]=>0110100=>[1,2,1,1,2]
[4,1,6,3,7,8,5,2]=>[5,8,3,6,2,1,4,7]=>0101100=>[1,1,1,2,2]
[4,1,6,3,8,5,2,7]=>[5,8,3,6,1,4,7,2]=>0101001=>[1,1,1,1,2,1]
[4,1,6,7,3,8,5,2]=>[5,8,3,2,6,1,4,7]=>0110100=>[1,2,1,1,2]
[4,1,6,7,8,5,2,3]=>[5,8,3,2,1,4,7,6]=>0111001=>[1,3,2,1]
[4,1,6,8,3,5,2,7]=>[5,8,3,1,6,4,7,2]=>0110101=>[1,2,1,1,1,1]
[4,1,7,3,2,8,6,5]=>[5,8,2,6,7,1,3,4]=>0100100=>[1,1,2,1,2]
[4,1,7,8,3,5,6,2]=>[5,8,2,1,6,4,3,7]=>0110110=>[1,2,1,2,1]
[4,1,8,3,2,5,6,7]=>[5,8,1,6,7,4,3,2]=>0100111=>[1,1,2,3]
[4,5,2,6,7,8,3,1]=>[5,4,7,3,2,1,6,8]=>1011100=>[1,1,3,2]
[4,5,2,6,8,1,3,7]=>[5,4,7,3,1,8,6,2]=>1011011=>[1,1,2,1,2]
[4,5,6,3,8,1,2,7]=>[5,4,3,6,1,8,7,2]=>1101011=>[2,1,1,1,2]
[4,5,6,8,3,1,2,7]=>[5,4,3,1,6,8,7,2]=>1110011=>[3,2,2]
[4,5,7,3,8,1,6,2]=>[5,4,2,6,1,8,3,7]=>1101010=>[2,1,1,1,1,1]
[4,5,8,3,2,1,6,7]=>[5,4,1,6,7,8,3,2]=>1100011=>[2,3,2]
[4,6,2,3,7,8,5,1]=>[5,3,7,6,2,1,4,8]=>1011100=>[1,1,3,2]
[4,6,2,3,8,5,1,7]=>[5,3,7,6,1,4,8,2]=>1011001=>[1,1,2,2,1]
[4,6,2,7,3,8,5,1]=>[5,3,7,2,6,1,4,8]=>1010100=>[1,1,1,1,1,2]
[4,6,2,7,8,5,1,3]=>[5,3,7,2,1,4,8,6]=>1011001=>[1,1,2,2,1]
[4,6,7,3,2,8,5,1]=>[5,3,2,6,7,1,4,8]=>1100100=>[2,2,1,2]
[4,6,8,3,2,5,1,7]=>[5,3,1,6,7,4,8,2]=>1100101=>[2,2,1,1,1]
[4,7,2,3,1,8,6,5]=>[5,2,7,6,8,1,3,4]=>1010100=>[1,1,1,1,1,2]
[4,7,2,8,3,5,6,1]=>[5,2,7,1,6,4,3,8]=>1010110=>[1,1,1,1,2,1]
[4,7,8,3,2,5,6,1]=>[5,2,1,6,7,4,3,8]=>1100110=>[2,2,2,1]
[4,8,2,3,1,5,6,7]=>[5,1,7,6,8,4,3,2]=>1010111=>[1,1,1,1,3]
[5,1,2,6,8,4,3,7]=>[4,8,7,3,1,5,6,2]=>0111001=>[1,3,2,1]
[5,1,2,7,4,8,6,3]=>[4,8,7,2,5,1,3,6]=>0110100=>[1,2,1,1,2]
[5,1,2,7,8,4,6,3]=>[4,8,7,2,1,5,3,6]=>0111010=>[1,3,1,1,1]
[5,1,2,8,4,3,6,7]=>[4,8,7,1,5,6,3,2]=>0110011=>[1,2,2,2]
[5,1,6,3,8,4,2,7]=>[4,8,3,6,1,5,7,2]=>0101001=>[1,1,1,1,2,1]
[5,1,6,7,4,8,2,3]=>[4,8,3,2,5,1,7,6]=>0110101=>[1,2,1,1,1,1]
[5,1,6,7,8,4,2,3]=>[4,8,3,2,1,5,7,6]=>0111001=>[1,3,2,1]
[5,1,8,3,4,2,6,7]=>[4,8,1,6,5,7,3,2]=>0101011=>[1,1,1,1,1,2]
[5,6,2,3,8,4,1,7]=>[4,3,7,6,1,5,8,2]=>1011001=>[1,1,2,2,1]
[5,6,2,7,8,4,1,3]=>[4,3,7,2,1,5,8,6]=>1011001=>[1,1,2,2,1]
[5,6,8,3,4,2,1,7]=>[4,3,1,6,5,7,8,2]=>1101001=>[2,1,1,2,1]
[5,7,2,3,4,8,6,1]=>[4,2,7,6,5,1,3,8]=>1011100=>[1,1,3,2]
[5,7,8,3,4,2,6,1]=>[4,2,1,6,5,7,3,8]=>1101010=>[2,1,1,1,1,1]
[5,8,2,3,4,1,6,7]=>[4,1,7,6,5,8,3,2]=>1011011=>[1,1,2,1,2]
[6,1,2,3,7,8,5,4]=>[3,8,7,6,2,1,4,5]=>0111100=>[1,4,2]
[6,1,2,3,8,5,4,7]=>[3,8,7,6,1,4,5,2]=>0111001=>[1,3,2,1]
[6,1,2,7,8,5,4,3]=>[3,8,7,2,1,4,5,6]=>0111000=>[1,3,3]
[6,1,2,8,4,5,3,7]=>[3,8,7,1,5,4,6,2]=>0110101=>[1,2,1,1,1,1]
[6,1,7,3,4,8,5,2]=>[3,8,2,6,5,1,4,7]=>0101100=>[1,1,1,2,2]
[6,1,7,3,8,5,4,2]=>[3,8,2,6,1,4,5,7]=>0101000=>[1,1,1,1,3]
[6,1,7,8,4,5,3,2]=>[3,8,2,1,5,4,6,7]=>0110100=>[1,2,1,1,2]
[6,1,8,3,4,5,2,7]=>[3,8,1,6,5,4,7,2]=>0101101=>[1,1,1,2,1,1]
[6,7,2,3,8,5,4,1]=>[3,2,7,6,1,4,5,8]=>1011000=>[1,1,2,3]
[6,7,2,8,4,5,3,1]=>[3,2,7,1,5,4,6,8]=>1010100=>[1,1,1,1,1,2]
[6,8,2,3,4,5,1,7]=>[3,1,7,6,5,4,8,2]=>1011101=>[1,1,3,1,1]
[7,1,2,3,4,8,6,5]=>[2,8,7,6,5,1,3,4]=>0111100=>[1,4,2]
[7,1,2,8,4,5,6,3]=>[2,8,7,1,5,4,3,6]=>0110110=>[1,2,1,2,1]
[7,1,8,3,4,5,6,2]=>[2,8,1,6,5,4,3,7]=>0101110=>[1,1,1,3,1]
[6,4,1,8,2,3,7,5]=>[3,5,8,1,7,6,2,4]=>0010110=>[2,1,1,2,1]
[5,8,1,2,4,3,7,6]=>[4,1,8,7,5,6,2,3]=>1011010=>[1,1,2,1,1,1]
[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>1110101=>[3,1,1,1,1]
[3,5,8,6,1,2,4,7]=>[6,4,1,3,8,7,5,2]=>1100111=>[2,2,3]
[3,1,6,8,2,4,7,5]=>[6,8,3,1,7,5,2,4]=>0110110=>[1,2,1,2,1]
[3,6,2,8,1,5,7,4]=>[6,3,7,1,8,4,2,5]=>1010110=>[1,1,1,1,2,1]
[2,6,1,3,8,4,7,5]=>[7,3,8,6,1,5,2,4]=>1011010=>[1,1,2,1,1,1]
[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>1001111=>[1,2,4]
[2,7,5,1,3,8,4,6]=>[7,2,4,8,6,1,5,3]=>1001101=>[1,2,2,1,1]
[8,2,5,7,4,6,1,3]=>[1,7,4,2,5,3,8,6]=>0110101=>[1,2,1,1,1,1]
[8,2,1,3,7,6,4,5]=>[1,7,8,6,2,3,5,4]=>0011001=>[2,2,2,1]
[8,2,5,1,3,7,4,6]=>[1,7,4,8,6,2,5,3]=>0101101=>[1,1,1,2,1,1]
[8,2,7,5,3,1,6,4]=>[1,7,2,4,6,8,3,5]=>0100010=>[1,1,3,1,1]
[8,2,6,5,4,7,1,3]=>[1,7,3,4,5,2,8,6]=>0100101=>[1,1,2,1,1,1]
[7,6,5,2,4,8,1,3]=>[2,3,4,7,5,1,8,6]=>0001101=>[3,2,1,1]
[7,8,2,5,3,1,6,4]=>[2,1,7,4,6,8,3,5]=>1010010=>[1,1,1,2,1,1]
[7,1,8,6,3,2,4,5]=>[2,8,1,3,6,7,5,4]=>0100011=>[1,1,3,2]
[6,8,1,5,3,2,4,7]=>[3,1,8,4,6,7,5,2]=>1010011=>[1,1,1,2,2]
[1,6,7,5,3,2,4,8]=>[8,3,2,4,6,7,5,1]=>1100011=>[2,3,2]
[6,5,1,2,4,8,3,7]=>[3,4,8,7,5,1,6,2]=>0011101=>[2,3,1,1]
[7,8,1,6,4,2,3,5]=>[2,1,8,3,5,7,6,4]=>1010011=>[1,1,1,2,2]
[8,4,1,2,5,6,3,7]=>[1,5,8,7,4,3,6,2]=>0011101=>[2,3,1,1]
[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>1010011=>[1,1,1,2,2]
[8,1,3,7,2,6,4,5]=>[1,8,6,2,7,3,5,4]=>0110101=>[1,2,1,1,1,1]
[7,3,2,6,5,1,8,4]=>[2,6,7,3,4,8,1,5]=>0010010=>[2,1,2,1,1]
[7,8,4,2,5,6,1,3]=>[2,1,5,7,4,3,8,6]=>1001101=>[1,2,2,1,1]
[8,2,7,4,5,6,1,3]=>[1,7,2,5,4,3,8,6]=>0101101=>[1,1,1,2,1,1]
[8,2,3,6,5,1,7,4]=>[1,7,6,3,4,8,2,5]=>0110010=>[1,2,2,1,1]
[7,9,8,6,5,4,3,2,1]=>[3,1,2,4,5,6,7,8,9]=>10000000=>[1,7]
[6,9,8,7,5,4,3,2,1]=>[4,1,2,3,5,6,7,8,9]=>10000000=>[1,7]
[5,9,8,7,6,4,3,2,1]=>[5,1,2,3,4,6,7,8,9]=>10000000=>[1,7]
[4,9,8,7,6,5,3,2,1]=>[6,1,2,3,4,5,7,8,9]=>10000000=>[1,7]
[3,9,8,7,6,5,4,2,1]=>[7,1,2,3,4,5,6,8,9]=>10000000=>[1,7]
[2,9,8,7,6,5,4,3,1]=>[8,1,2,3,4,5,6,7,9]=>10000000=>[1,7]
[8,10,9,7,6,5,4,3,2,1]=>[3,1,2,4,5,6,7,8,9,10]=>100000000=>[1,8]
[6,9,7,8,5,4,3,2,1]=>[4,1,3,2,5,6,7,8,9]=>10100000=>[1,1,1,5]
[7,10,9,8,6,5,4,3,2,1]=>[4,1,2,3,5,6,7,8,9,10]=>100000000=>[1,8]
[4,8,6,5,7,3,2,1]=>[5,1,3,4,2,6,7,8]=>1001000=>[1,2,1,3]
[6,10,9,8,7,5,4,3,2,1]=>[5,1,2,3,4,6,7,8,9,10]=>100000000=>[1,8]
[3,8,7,5,4,6,2,1]=>[6,1,2,4,5,3,7,8]=>1000100=>[1,3,1,2]
[4,8,5,6,7,3,2,1]=>[5,1,4,3,2,6,7,8]=>1011000=>[1,1,2,3]
[5,10,9,8,7,6,4,3,2,1]=>[6,1,2,3,4,5,7,8,9,10]=>100000000=>[1,8]
[2,8,7,6,4,3,5,1]=>[7,1,2,3,5,6,4,8]=>1000010=>[1,4,1,1]
[4,10,9,8,7,6,5,3,2,1]=>[7,1,2,3,4,5,6,8,9,10]=>100000000=>[1,8]
[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>1000001=>[1,5,1]
[2,8,7,6,3,4,5,1]=>[7,1,2,3,6,5,4,8]=>1000110=>[1,3,2,1]
[2,9,8,7,6,5,3,4,1]=>[8,1,2,3,4,5,7,6,9]=>10000010=>[1,5,1,1]
[3,10,9,8,7,6,5,4,2,1]=>[8,1,2,3,4,5,6,7,9,10]=>100000000=>[1,8]
[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>1000011=>[1,4,2]
[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>10000001=>[1,6,1]
[2,10,9,8,7,6,5,4,3,1]=>[9,1,2,3,4,5,6,7,8,10]=>100000000=>[1,8]
[7,2,8,6,5,4,1,3]=>[2,7,1,3,4,5,8,6]=>0100001=>[1,1,4,1]
[7,2,8,5,4,6,1,3]=>[2,7,1,4,5,3,8,6]=>0100101=>[1,1,2,1,1,1]
[6,3,2,8,5,1,7,4]=>[3,6,7,1,4,8,2,5]=>0010010=>[2,1,2,1,1]
[8,4,7,2,5,6,3,1]=>[1,5,2,7,4,3,6,8]=>0101100=>[1,1,1,2,2]
[6,8,5,4,3,1,7,2]=>[3,1,4,5,6,8,2,7]=>1000010=>[1,4,1,1]
[5,8,6,4,1,3,7,2]=>[4,1,3,5,8,6,2,7]=>1000110=>[1,3,2,1]
[4,8,6,1,5,3,7,2]=>[5,1,3,8,4,6,2,7]=>1001010=>[1,2,1,1,1,1]
[3,6,1,8,5,2,7,4]=>[6,3,8,1,4,7,2,5]=>1010010=>[1,1,1,2,1,1]
[3,4,1,2,8,6,7,5]=>[6,5,8,7,1,3,2,4]=>1011010=>[1,1,2,1,1,1]
[6,8,3,5,4,1,7,2]=>[3,1,6,4,5,8,2,7]=>1010010=>[1,1,1,2,1,1]
[7,2,5,8,3,6,1,4]=>[2,7,4,1,6,3,8,5]=>0110101=>[1,2,1,1,1,1]
[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>1010101=>[1,1,1,1,1,1,1]
[7,2,6,8,5,3,1,4]=>[2,7,3,1,4,6,8,5]=>0110001=>[1,2,3,1]
[7,6,3,8,5,2,1,4]=>[2,3,6,1,4,7,8,5]=>0010001=>[2,1,3,1]
[7,2,6,4,8,3,1,5]=>[2,7,3,5,1,6,8,4]=>0101001=>[1,1,1,1,2,1]
[1,5,7,4,2,6,3,8]=>[8,4,2,5,7,3,6,1]=>1100101=>[2,2,1,1,1]
[4,2,3,1,7,8,5,6]=>[5,7,6,8,2,1,4,3]=>0101101=>[1,1,1,2,1,1]
[5,2,8,4,1,7,6,3]=>[4,7,1,5,8,2,3,6]=>0100100=>[1,1,2,1,2]
[8,6,3,4,7,2,5,1]=>[1,3,6,5,2,7,4,8]=>0011010=>[2,2,1,1,1]
[6,8,3,4,5,1,7,2]=>[3,1,6,5,4,8,2,7]=>1011010=>[1,1,2,1,1,1]
[2,5,1,8,4,3,7,6]=>[7,4,8,1,5,6,2,3]=>1010010=>[1,1,1,2,1,1]
[6,2,5,4,8,1,3,7]=>[3,7,4,5,1,8,6,2]=>0101011=>[1,1,1,1,1,2]
[4,3,1,6,5,8,2,7]=>[5,6,8,3,4,1,7,2]=>0010101=>[2,1,1,1,1,1]
[8,2,6,4,1,7,3,5]=>[1,7,3,5,8,2,6,4]=>0100101=>[1,1,2,1,1,1]
[7,3,8,4,5,2,1,6]=>[2,6,1,5,4,7,8,3]=>0101001=>[1,1,1,1,2,1]
[7,2,5,1,8,4,3,6]=>[2,7,4,8,1,5,6,3]=>0101001=>[1,1,1,1,2,1]
[5,4,6,8,1,2,7,3]=>[4,5,3,1,8,7,2,6]=>0110110=>[1,2,1,2,1]
[6,4,7,2,3,5,8,1]=>[3,5,2,7,6,4,1,8]=>0101110=>[1,1,1,3,1]
[3,4,7,8,6,2,5,1]=>[6,5,2,1,3,7,4,8]=>1110010=>[3,2,1,1]
[4,1,3,5,7,8,6,2]=>[5,8,6,4,2,1,3,7]=>0111100=>[1,4,2]
[6,5,1,8,4,7,3,2]=>[3,4,8,1,5,2,6,7]=>0010100=>[2,1,1,1,2]
[8,2,7,4,6,1,3,5]=>[1,7,2,5,3,8,6,4]=>0101011=>[1,1,1,1,1,2]
[8,7,3,6,1,5,2,4]=>[1,2,6,3,8,4,7,5]=>0010101=>[2,1,1,1,1,1]
[2,8,6,1,5,7,3,4]=>[7,1,3,8,4,2,6,5]=>1001101=>[1,2,2,1,1]
[5,7,3,2,4,1,8,6]=>[4,2,6,7,5,8,1,3]=>1001010=>[1,2,1,1,1,1]
[4,1,3,6,7,8,2,5]=>[5,8,6,3,2,1,7,4]=>0111101=>[1,4,1,1]
[3,8,1,5,6,2,7,4]=>[6,1,8,4,3,7,2,5]=>1011010=>[1,1,2,1,1,1]
[8,2,5,6,1,7,4,3]=>[1,7,4,3,8,2,5,6]=>0110100=>[1,2,1,1,2]
[7,1,5,2,8,6,4,3]=>[2,8,4,7,1,3,5,6]=>0101000=>[1,1,1,1,3]
[6,5,4,8,7,2,1,3]=>[3,4,5,1,2,7,8,6]=>0010001=>[2,1,3,1]
[1,8,6,4,5,2,7,3]=>[8,1,3,5,4,7,2,6]=>1001010=>[1,2,1,1,1,1]
[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>1001010=>[1,2,1,1,1,1]
[3,6,2,1,7,5,8,4]=>[6,3,7,8,2,4,1,5]=>1001010=>[1,2,1,1,1,1]
[2,5,4,1,8,7,6,3]=>[7,4,5,8,1,2,3,6]=>1001000=>[1,2,1,3]
[4,7,2,6,5,8,1,3]=>[5,2,7,3,4,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[6,8,1,4,2,7,3,5]=>[3,1,8,5,7,2,6,4]=>1010101=>[1,1,1,1,1,1,1]
[6,3,4,7,1,8,2,5]=>[3,6,5,2,8,1,7,4]=>0110101=>[1,2,1,1,1,1]
[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>1011110=>[1,1,4,1]
[5,2,4,1,6,8,7,3]=>[4,7,5,8,3,1,2,6]=>0101100=>[1,1,1,2,2]
[5,3,4,1,7,6,8,2]=>[4,6,5,8,2,3,1,7]=>0101010=>[1,1,1,1,1,1,1]
[3,1,4,6,5,7,8,2]=>[6,8,5,3,4,2,1,7]=>0110110=>[1,2,1,2,1]
[1,4,7,3,5,6,8,2]=>[8,5,2,6,4,3,1,7]=>1101110=>[2,1,3,1]
[5,1,3,6,4,8,7,2]=>[4,8,6,3,5,1,2,7]=>0110100=>[1,2,1,1,2]
[1,3,2,7,5,8,6,4]=>[8,6,7,2,4,1,3,5]=>1010100=>[1,1,1,1,1,2]
[1,4,2,7,8,5,6,3]=>[8,5,7,2,1,4,3,6]=>1011010=>[1,1,2,1,1,1]
[5,1,2,6,8,4,7,3]=>[4,8,7,3,1,5,2,6]=>0111010=>[1,3,1,1,1]
[4,1,2,6,8,5,3,7]=>[5,8,7,3,1,4,6,2]=>0111001=>[1,3,2,1]
[1,5,2,4,8,7,6,3]=>[8,4,7,5,1,2,3,6]=>1011000=>[1,1,2,3]
[1,2,6,4,8,7,5,3]=>[8,7,3,5,1,2,4,6]=>1101000=>[2,1,1,3]
[1,2,7,4,8,6,5,3]=>[8,7,2,5,1,3,4,6]=>1101000=>[2,1,1,3]
[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>1010101=>[1,1,1,1,1,1,1]
[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>1101001=>[2,1,1,2,1]
[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>1110101=>[3,1,1,1,1]
[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>1110101=>[3,1,1,1,1]
[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>1110101=>[3,1,1,1,1]
[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>1110101=>[3,1,1,1,1]
[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>1110110=>[3,1,2,1]
[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>1011010=>[1,1,2,1,1,1]
[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>1101100=>[2,1,2,2]
[1,6,7,3,4,8,5,2]=>[8,3,2,6,5,1,4,7]=>1101100=>[2,1,2,2]
[3,8,4,1,5,7,2,6]=>[6,1,5,8,4,2,7,3]=>1001101=>[1,2,2,1,1]
[1,3,6,4,2,8,7,5]=>[8,6,3,5,7,1,2,4]=>1100100=>[2,2,1,2]
[1,3,8,4,2,7,6,5]=>[8,6,1,5,7,2,3,4]=>1100100=>[2,2,1,2]
[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>1101010=>[2,1,1,1,1,1]
[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>1101010=>[2,1,1,1,1,1]
[1,2,6,4,8,3,7,5]=>[8,7,3,5,1,6,2,4]=>1101010=>[2,1,1,1,1,1]
[1,5,2,4,8,3,7,6]=>[8,4,7,5,1,6,2,3]=>1011010=>[1,1,2,1,1,1]
[2,8,3,5,1,4,7,6]=>[7,1,6,4,8,5,2,3]=>1010110=>[1,1,1,1,2,1]
[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>1100101=>[2,2,1,1,1]
[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>1101011=>[2,1,1,1,2]
[1,2,6,8,5,3,7,4]=>[8,7,3,1,4,6,2,5]=>1110010=>[3,2,1,1]
[1,2,6,8,7,3,5,4]=>[8,7,3,1,2,6,4,5]=>1110010=>[3,2,1,1]
[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>1110011=>[3,2,2]
[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>1110011=>[3,2,2]
[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>1101011=>[2,1,1,1,2]
[1,3,7,6,2,8,4,5]=>[8,6,2,3,7,1,5,4]=>1100101=>[2,2,1,1,1]
[2,3,8,7,4,1,6,5]=>[7,6,1,2,5,8,3,4]=>1100010=>[2,3,1,1]
[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>1101001=>[2,1,1,2,1]
[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>1110001=>[3,3,1]
[5,2,6,7,3,4,8,1]=>[4,7,3,2,6,5,1,8]=>0110110=>[1,2,1,2,1]
[5,2,4,7,6,3,8,1]=>[4,7,5,2,3,6,1,8]=>0110010=>[1,2,2,1,1]
[5,6,2,1,7,8,3,4]=>[4,3,7,8,2,1,6,5]=>1001101=>[1,2,2,1,1]
[5,6,2,1,4,8,7,3]=>[4,3,7,8,5,1,2,6]=>1001100=>[1,2,2,2]
[2,6,1,4,5,8,7,3]=>[7,3,8,5,4,1,2,6]=>1011100=>[1,1,3,2]
[5,4,2,7,6,3,8,1]=>[4,5,7,2,3,6,1,8]=>0010010=>[2,1,2,1,1]
[2,3,7,6,4,5,8,1]=>[7,6,2,3,5,4,1,8]=>1100110=>[2,2,2,1]
[2,6,1,7,5,8,3,4]=>[7,3,8,2,4,1,6,5]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,7,4,8,5,3]=>[7,3,8,2,5,1,4,6]=>1010100=>[1,1,1,1,1,2]
[5,1,2,7,8,4,3,6]=>[4,8,7,2,1,5,6,3]=>0111001=>[1,3,2,1]
[2,6,1,7,4,8,3,5]=>[7,3,8,2,5,1,6,4]=>1010101=>[1,1,1,1,1,1,1]
[3,6,4,1,7,8,2,5]=>[6,3,5,8,2,1,7,4]=>1001101=>[1,2,2,1,1]
[5,4,6,1,3,8,7,2]=>[4,5,3,8,6,1,2,7]=>0101100=>[1,1,1,2,2]
[3,6,4,1,5,8,7,2]=>[6,3,5,8,4,1,2,7]=>1001100=>[1,2,2,2]
[2,6,1,5,4,8,7,3]=>[7,3,8,4,5,1,2,6]=>1010100=>[1,1,1,1,1,2]
[2,6,1,4,7,8,5,3]=>[7,3,8,5,2,1,4,6]=>1011100=>[1,1,3,2]
[5,1,2,4,8,6,7,3]=>[4,8,7,5,1,3,2,6]=>0111010=>[1,3,1,1,1]
[5,1,2,4,8,7,3,6]=>[4,8,7,5,1,2,6,3]=>0111001=>[1,3,2,1]
[5,1,2,4,8,7,6,3]=>[4,8,7,5,1,2,3,6]=>0111000=>[1,3,3]
[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>1110010=>[3,2,1,1]
[4,3,1,2,8,5,7,6]=>[5,6,8,7,1,4,2,3]=>0011010=>[2,2,1,1,1]
[2,1,5,3,8,6,4,7]=>[7,8,4,6,1,3,5,2]=>0101001=>[1,1,1,1,2,1]
[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>1110101=>[3,1,1,1,1]
[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>1110011=>[3,2,2]
[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>1110001=>[3,3,1]
[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>1110011=>[3,2,2]
[2,6,1,5,4,8,3,7]=>[7,3,8,4,5,1,6,2]=>1010101=>[1,1,1,1,1,1,1]
[5,1,2,4,8,6,3,7]=>[4,8,7,5,1,3,6,2]=>0111001=>[1,3,2,1]
[5,1,2,4,8,3,7,6]=>[4,8,7,5,1,6,2,3]=>0111010=>[1,3,1,1,1]
[5,6,3,1,4,8,2,7]=>[4,3,6,8,5,1,7,2]=>1001101=>[1,2,2,1,1]
[2,5,4,3,1,8,6,7]=>[7,4,5,6,8,1,3,2]=>1000101=>[1,3,1,1,1]
[5,4,6,3,1,8,7,2]=>[4,5,3,6,8,1,2,7]=>0100100=>[1,1,2,1,2]
[3,6,4,5,1,8,7,2]=>[6,3,5,4,8,1,2,7]=>1010100=>[1,1,1,1,1,2]
[3,6,5,4,1,8,7,2]=>[6,3,4,5,8,1,2,7]=>1000100=>[1,3,1,2]
[5,2,6,1,7,8,4,3]=>[4,7,3,8,2,1,5,6]=>0101100=>[1,1,1,2,2]
[5,1,6,2,8,7,3,4]=>[4,8,3,7,1,2,6,5]=>0101001=>[1,1,1,1,2,1]
[2,1,3,7,8,6,4,5]=>[7,8,6,2,1,3,5,4]=>0111001=>[1,3,2,1]
[2,1,3,7,8,5,6,4]=>[7,8,6,2,1,4,3,5]=>0111010=>[1,3,1,1,1]
[5,2,4,1,7,8,6,3]=>[4,7,5,8,2,1,3,6]=>0101100=>[1,1,1,2,2]
[4,3,1,2,8,6,7,5]=>[5,6,8,7,1,3,2,4]=>0011010=>[2,2,1,1,1]
[5,1,4,2,8,6,7,3]=>[4,8,5,7,1,3,2,6]=>0101010=>[1,1,1,1,1,1,1]
[2,1,3,6,8,5,7,4]=>[7,8,6,3,1,4,2,5]=>0111010=>[1,3,1,1,1]
[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>1110101=>[3,1,1,1,1]
[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>1110001=>[3,3,1]
[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>1110011=>[3,2,2]
[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>1110101=>[3,1,1,1,1]
[2,1,3,6,8,7,4,5]=>[7,8,6,3,1,2,5,4]=>0111001=>[1,3,2,1]
[5,4,1,2,8,7,6,3]=>[4,5,8,7,1,2,3,6]=>0011000=>[2,2,3]
[3,1,6,2,8,7,5,4]=>[6,8,3,7,1,2,4,5]=>0101000=>[1,1,1,1,3]
[1,2,3,4,5,9,6,7,8]=>[9,8,7,6,5,1,4,3,2]=>11111011=>[5,1,2]
[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>11110111=>[4,1,3]
[1,2,3,9,4,5,6,7,8]=>[9,8,7,1,6,5,4,3,2]=>11101111=>[3,1,4]
[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>11011111=>[2,1,5]
[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>111111101=>[7,1,1]
[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>11111001=>[5,2,1]
[1,2,3,4,5,6,10,7,8,9]=>[10,9,8,7,6,5,1,4,3,2]=>111111011=>[6,1,2]
[1,2,3,4,9,6,5,7,8]=>[9,8,7,6,1,4,5,3,2]=>11110011=>[4,2,2]
[1,2,3,4,5,10,6,7,8,9]=>[10,9,8,7,6,1,5,4,3,2]=>111110111=>[5,1,3]
[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>1101011=>[2,1,1,1,2]
[1,2,3,9,5,4,6,7,8]=>[9,8,7,1,5,6,4,3,2]=>11100111=>[3,2,3]
[1,2,3,4,10,5,6,7,8,9]=>[10,9,8,7,1,6,5,4,3,2]=>111101111=>[4,1,4]
[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>1010111=>[1,1,1,1,3]
[1,2,9,4,3,5,6,7,8]=>[9,8,1,6,7,5,4,3,2]=>11001111=>[2,2,4]
[1,2,3,10,4,5,6,7,8,9]=>[10,9,8,1,7,6,5,4,3,2]=>111011111=>[3,1,5]
[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>1000111=>[1,3,3]
[1,9,3,2,4,5,6,7,8]=>[9,1,7,8,6,5,4,3,2]=>10011111=>[1,2,5]
[1,2,10,3,4,5,6,7,8,9]=>[10,9,1,8,7,6,5,4,3,2]=>110111111=>[2,1,6]
[8,4,7,6,5,3,2,1]=>[1,5,2,3,4,6,7,8]=>0100000=>[1,1,5]
[8,4,7,5,6,3,2,1]=>[1,5,2,4,3,6,7,8]=>0101000=>[1,1,1,1,3]
[8,5,7,4,6,3,2,1]=>[1,4,2,5,3,6,7,8]=>0101000=>[1,1,1,1,3]
[8,7,6,3,5,4,2,1]=>[1,2,3,6,4,5,7,8]=>0001000=>[3,1,3]
[8,6,7,3,5,4,2,1]=>[1,3,2,6,4,5,7,8]=>0101000=>[1,1,1,1,3]
[8,5,7,3,6,4,2,1]=>[1,4,2,6,3,5,7,8]=>0101000=>[1,1,1,1,3]
[8,1,7,4,6,5,3,2]=>[1,8,2,5,3,4,6,7]=>0101000=>[1,1,1,1,3]
[8,1,7,3,6,5,4,2]=>[1,8,2,6,3,4,5,7]=>0101000=>[1,1,1,1,3]
[8,2,7,3,6,5,4,1]=>[1,7,2,6,3,4,5,8]=>0101000=>[1,1,1,1,3]
[8,3,7,2,6,5,4,1]=>[1,6,2,7,3,4,5,8]=>0101000=>[1,1,1,1,3]
[8,5,7,2,6,4,3,1]=>[1,4,2,7,3,5,6,8]=>0101000=>[1,1,1,1,3]
[8,6,7,2,5,4,3,1]=>[1,3,2,7,4,5,6,8]=>0101000=>[1,1,1,1,3]
[8,7,6,2,5,4,3,1]=>[1,2,3,7,4,5,6,8]=>0001000=>[3,1,3]
[8,4,7,1,6,5,3,2]=>[1,5,2,8,3,4,6,7]=>0101000=>[1,1,1,1,3]
[8,3,7,1,6,5,4,2]=>[1,6,2,8,3,4,5,7]=>0101000=>[1,1,1,1,3]
[8,2,7,1,6,5,4,3]=>[1,7,2,8,3,4,5,6]=>0101000=>[1,1,1,1,3]
[8,1,7,2,6,5,4,3]=>[1,8,2,7,3,4,5,6]=>0101000=>[1,1,1,1,3]
[8,7,6,2,5,3,4,1]=>[1,2,3,7,4,6,5,8]=>0001010=>[3,1,1,1,1]
[8,1,7,6,5,3,4,2]=>[1,8,2,3,4,6,5,7]=>0100010=>[1,1,3,1,1]
[8,3,7,6,5,2,4,1]=>[1,6,2,3,4,7,5,8]=>0100010=>[1,1,3,1,1]
[8,4,7,6,5,2,3,1]=>[1,5,2,3,4,7,6,8]=>0100010=>[1,1,3,1,1]
[8,5,7,6,4,2,3,1]=>[1,4,2,3,5,7,6,8]=>0100010=>[1,1,3,1,1]
[8,6,7,5,4,1,3,2]=>[1,3,2,4,5,8,6,7]=>0100010=>[1,1,3,1,1]
[8,5,7,6,4,1,3,2]=>[1,4,2,3,5,8,6,7]=>0100010=>[1,1,3,1,1]
[8,3,7,6,5,1,4,2]=>[1,6,2,3,4,8,5,7]=>0100010=>[1,1,3,1,1]
[8,7,6,4,5,1,3,2]=>[1,2,3,5,4,8,6,7]=>0001010=>[3,1,1,1,1]
[8,7,6,2,5,1,4,3]=>[1,2,3,7,4,8,5,6]=>0001010=>[3,1,1,1,1]
[8,7,6,1,5,2,4,3]=>[1,2,3,8,4,7,5,6]=>0001010=>[3,1,1,1,1]
[6,8,1,3,2,5,4,7]=>[3,1,8,6,7,4,5,2]=>1010101=>[1,1,1,1,1,1,1]
[6,8,1,4,2,5,3,7]=>[3,1,8,5,7,4,6,2]=>1010101=>[1,1,1,1,1,1,1]
[7,8,3,6,1,4,2,5]=>[2,1,6,3,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,5,3,6,1,4]=>[2,1,7,4,6,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[7,8,2,5,1,4,3,6]=>[2,1,7,4,8,5,6,3]=>1010101=>[1,1,1,1,1,1,1]
[7,8,1,4,3,6,2,5]=>[2,1,8,5,6,3,7,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,4,3,7,2,6]=>[4,1,8,5,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,5,1,4,3,7]=>[3,1,7,4,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,5,3,7,1,4]=>[3,1,7,4,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[6,8,2,5,4,7,1,3]=>[3,1,7,4,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[2,5,4,7,6,8,1,3]=>[7,4,5,2,3,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[2,5,3,7,6,8,1,4]=>[7,4,6,2,3,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,5,1,4,3,7,6,8]=>[7,4,8,5,6,2,3,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,4,3,7,5,8]=>[7,3,8,5,6,2,4,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,5,8,1,4,3,7]=>[7,3,4,1,8,5,6,2]=>1010101=>[1,1,1,1,1,1,1]
[2,6,1,5,3,7,4,8]=>[7,3,8,4,6,2,5,1]=>1010101=>[1,1,1,1,1,1,1]
[2,6,3,7,4,8,1,5]=>[7,3,6,2,5,1,8,4]=>1010101=>[1,1,1,1,1,1,1]
[2,6,4,7,5,8,1,3]=>[7,3,5,2,4,1,8,6]=>1010101=>[1,1,1,1,1,1,1]
[5,8,3,6,4,7,1,2]=>[4,1,6,3,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[5,8,2,6,4,7,1,3]=>[4,1,7,3,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,8,2,6,3,7,1,5]=>[5,1,7,3,6,2,8,4]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,5,3,7,2,6]=>[5,1,8,4,6,2,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,8,1,5,2,6,3,7]=>[5,1,8,4,7,3,6,2]=>1010101=>[1,1,1,1,1,1,1]
[4,8,3,7,1,5,2,6]=>[5,1,6,2,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[6,8,3,7,1,4,2,5]=>[3,1,6,2,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]
[5,8,1,3,2,6,4,7]=>[4,1,8,6,7,3,5,2]=>1010101=>[1,1,1,1,1,1,1]
[5,8,4,7,1,3,2,6]=>[4,1,5,2,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]
[6,8,4,7,1,3,2,5]=>[3,1,5,2,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]
[6,8,5,7,1,3,2,4]=>[3,1,4,2,8,6,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,7,6,8,2,4,1,3]=>[4,2,3,1,7,5,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,6,8,1,3,2,5]=>[5,2,3,1,8,6,7,4]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,8,1,3,2,6]=>[5,2,4,1,8,6,7,3]=>1010101=>[1,1,1,1,1,1,1]
[4,7,1,3,2,6,5,8]=>[5,2,8,6,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,4,2,6,5,8]=>[6,2,8,5,7,3,4,1]=>1010101=>[1,1,1,1,1,1,1]
[3,7,5,8,1,4,2,6]=>[6,2,4,1,8,5,7,3]=>1010101=>[1,1,1,1,1,1,1]
[3,7,6,8,1,4,2,5]=>[6,2,3,1,8,5,7,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,6,8,2,5,1,4]=>[6,2,3,1,7,4,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,7,6,8,2,5,1,3]=>[5,2,3,1,7,4,8,6]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,8,3,6,1,2]=>[5,2,4,1,6,3,8,7]=>1010101=>[1,1,1,1,1,1,1]
[4,7,5,8,2,6,1,3]=>[5,2,4,1,7,3,8,6]=>1010101=>[1,1,1,1,1,1,1]
[3,7,5,8,2,6,1,4]=>[6,2,4,1,7,3,8,5]=>1010101=>[1,1,1,1,1,1,1]
[3,7,4,8,2,6,1,5]=>[6,2,5,1,7,3,8,4]=>1010101=>[1,1,1,1,1,1,1]
[3,7,4,8,1,5,2,6]=>[6,2,5,1,8,4,7,3]=>1010101=>[1,1,1,1,1,1,1]
[3,7,1,5,2,6,4,8]=>[6,2,8,4,7,3,5,1]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,6,1,5,4,8]=>[6,2,7,3,8,4,5,1]=>1010101=>[1,1,1,1,1,1,1]
[3,7,2,6,5,8,1,4]=>[6,2,7,3,4,1,8,5]=>1010101=>[1,1,1,1,1,1,1]
[4,7,3,6,5,8,1,2]=>[5,2,6,3,4,1,8,7]=>1010101=>[1,1,1,1,1,1,1]
[3,6,5,8,4,7,1,2]=>[6,3,4,1,5,2,8,7]=>1010101=>[1,1,1,1,1,1,1]
[2,6,5,8,4,7,1,3]=>[7,3,4,1,5,2,8,6]=>1010101=>[1,1,1,1,1,1,1]
[2,6,5,8,3,7,1,4]=>[7,3,4,1,6,2,8,5]=>1010101=>[1,1,1,1,1,1,1]
[2,6,3,7,1,5,4,8]=>[7,3,6,2,8,4,5,1]=>1010101=>[1,1,1,1,1,1,1]
[7,6,4,2,8,5,3,1]=>[2,3,5,7,1,4,6,8]=>0001000=>[3,1,3]
[7,6,4,3,8,2,5,1]=>[2,3,5,6,1,7,4,8]=>0001010=>[3,1,1,1,1]
[7,6,4,8,5,2,3,1]=>[2,3,5,1,4,7,6,8]=>0010010=>[2,1,2,1,1]
[6,8,4,3,7,2,1,5]=>[3,1,5,6,2,7,8,4]=>1001001=>[1,2,1,2,1]
[6,8,3,7,5,2,4,1]=>[3,1,6,2,4,7,5,8]=>1010010=>[1,1,1,2,1,1]
[7,6,8,3,5,2,4,1]=>[2,3,1,6,4,7,5,8]=>0101010=>[1,1,1,1,1,1,1]
[7,6,3,8,2,4,1,5]=>[2,3,6,1,7,5,8,4]=>0010101=>[2,1,1,1,1,1]
[6,8,3,7,4,5,2,1]=>[3,1,6,2,5,4,7,8]=>1010100=>[1,1,1,1,1,2]
[6,7,3,5,8,4,2,1]=>[3,2,6,4,1,5,7,8]=>1011000=>[1,1,2,3]
[5,7,8,3,6,2,1,4]=>[4,2,1,6,3,7,8,5]=>1101001=>[2,1,1,2,1]
[5,8,3,6,7,2,1,4]=>[4,1,6,3,2,7,8,5]=>1011001=>[1,1,2,2,1]
[6,3,4,8,7,2,5,1]=>[3,6,5,1,2,7,4,8]=>0110010=>[1,2,2,1,1]
[6,3,8,4,7,2,1,5]=>[3,6,1,5,2,7,8,4]=>0101001=>[1,1,1,1,2,1]
[6,2,8,4,1,7,5,3]=>[3,7,1,5,8,2,4,6]=>0100100=>[1,1,2,1,2]
[6,2,7,4,1,5,3,8]=>[3,7,2,5,8,4,6,1]=>0100101=>[1,1,2,1,1,1]
[6,3,4,7,5,8,2,1]=>[3,6,5,2,4,1,7,8]=>0110100=>[1,2,1,1,2]
[5,7,3,6,8,2,1,4]=>[4,2,6,3,1,7,8,5]=>1011001=>[1,1,2,2,1]
[5,6,8,3,7,2,1,4]=>[4,3,1,6,2,7,8,5]=>1101001=>[2,1,1,2,1]
[4,6,7,8,3,5,2,1]=>[5,3,2,1,6,4,7,8]=>1110100=>[3,1,1,2]
[4,6,8,3,5,7,2,1]=>[5,3,1,6,4,2,7,8]=>1101100=>[2,1,2,2]
[4,7,3,5,6,8,2,1]=>[5,2,6,4,3,1,7,8]=>1011100=>[1,1,3,2]
[4,7,3,5,8,2,6,1]=>[5,2,6,4,1,7,3,8]=>1011010=>[1,1,2,1,1,1]
[5,3,4,7,8,2,1,6]=>[4,6,5,2,1,7,8,3]=>0111001=>[1,3,2,1]
[5,3,8,2,4,1,6,7]=>[4,6,1,7,5,8,3,2]=>0101011=>[1,1,1,1,1,2]
[5,3,4,8,2,6,1,7]=>[4,6,5,1,7,3,8,2]=>0110101=>[1,2,1,1,1,1]
[4,8,3,6,2,5,7,1]=>[5,1,6,3,7,4,2,8]=>1010110=>[1,1,1,1,2,1]
[4,8,3,5,7,2,6,1]=>[5,1,6,4,2,7,3,8]=>1011010=>[1,1,2,1,1,1]
[4,8,3,5,6,7,2,1]=>[5,1,6,4,3,2,7,8]=>1011100=>[1,1,3,2]
[4,7,8,3,5,6,2,1]=>[5,2,1,6,4,3,7,8]=>1101100=>[2,1,2,2]
[4,7,8,3,6,2,5,1]=>[5,2,1,6,3,7,4,8]=>1101010=>[2,1,1,1,1,1]
[4,8,3,6,7,2,5,1]=>[5,1,6,3,2,7,4,8]=>1011010=>[1,1,2,1,1,1]
[4,8,3,7,2,5,6,1]=>[5,1,6,2,7,4,3,8]=>1010110=>[1,1,1,1,2,1]
[5,3,8,2,4,1,7,6]=>[4,6,1,7,5,8,2,3]=>0101010=>[1,1,1,1,1,1,1]
[5,2,8,4,1,7,3,6]=>[4,7,1,5,8,2,6,3]=>0100101=>[1,1,2,1,1,1]
[6,4,2,5,1,8,7,3]=>[3,5,7,4,8,1,2,6]=>0010100=>[2,1,1,1,2]
[6,4,3,5,8,2,1,7]=>[3,5,6,4,1,7,8,2]=>0011001=>[2,2,2,1]
[6,3,5,8,7,2,4,1]=>[3,6,4,1,2,7,5,8]=>0110010=>[1,2,2,1,1]
[5,8,3,7,2,6,4,1]=>[4,1,6,2,7,3,5,8]=>1010100=>[1,1,1,1,1,2]
[5,8,4,2,3,1,6,7]=>[4,1,5,7,6,8,3,2]=>1001011=>[1,2,1,1,2]
[5,8,4,2,3,1,7,6]=>[4,1,5,7,6,8,2,3]=>1001010=>[1,2,1,1,1,1]
[6,4,5,3,8,2,1,7]=>[3,5,4,6,1,7,8,2]=>0101001=>[1,1,1,1,2,1]
[6,4,3,8,5,7,2,1]=>[3,5,6,1,4,2,7,8]=>0010100=>[2,1,1,1,2]
[6,4,2,8,5,3,1,7]=>[3,5,7,1,4,6,8,2]=>0010001=>[2,1,3,1]
[6,4,2,7,3,1,8,5]=>[3,5,7,2,6,8,1,4]=>0010010=>[2,1,2,1,1]
[6,4,3,7,8,5,2,1]=>[3,5,6,2,1,4,7,8]=>0011000=>[2,2,3]
[6,4,5,3,7,1,8,2]=>[3,5,4,6,2,8,1,7]=>0101010=>[1,1,1,1,1,1,1]
[5,6,3,7,1,8,2,4]=>[4,3,6,2,8,1,7,5]=>1010101=>[1,1,1,1,1,1,1]
[5,6,3,4,8,2,1,7]=>[4,3,6,5,1,7,8,2]=>1011001=>[1,1,2,2,1]
[6,3,5,7,4,8,2,1]=>[3,6,4,2,5,1,7,8]=>0110100=>[1,2,1,1,2]
[6,4,2,5,1,7,3,8]=>[3,5,7,4,8,2,6,1]=>0010101=>[2,1,1,1,1,1]
[5,3,7,2,4,1,6,8]=>[4,6,2,7,5,8,3,1]=>0101011=>[1,1,1,1,1,2]
[5,3,4,7,2,6,1,8]=>[4,6,5,2,7,3,8,1]=>0110101=>[1,2,1,1,1,1]
[4,7,3,6,2,5,8,1]=>[5,2,6,3,7,4,1,8]=>1010110=>[1,1,1,1,2,1]
[4,7,3,6,8,2,5,1]=>[5,2,6,3,1,7,4,8]=>1011010=>[1,1,2,1,1,1]
[4,6,7,3,5,8,2,1]=>[5,3,2,6,4,1,7,8]=>1101100=>[2,1,2,2]
[4,5,7,8,3,6,2,1]=>[5,4,2,1,6,3,7,8]=>1110100=>[3,1,1,2]
[4,5,8,3,6,7,2,1]=>[5,4,1,6,3,2,7,8]=>1101100=>[2,1,2,2]
[4,5,8,3,7,2,6,1]=>[5,4,1,6,2,7,3,8]=>1101010=>[2,1,1,1,1,1]
[5,3,4,6,8,2,1,7]=>[4,6,5,3,1,7,8,2]=>0111001=>[1,3,2,1]
[5,3,6,8,2,1,4,7]=>[4,6,3,1,7,8,5,2]=>0110011=>[1,2,2,2]
[4,6,3,5,7,8,2,1]=>[5,3,6,4,2,1,7,8]=>1011100=>[1,1,3,2]
[4,5,7,3,6,8,2,1]=>[5,4,2,6,3,1,7,8]=>1101100=>[2,1,2,2]
[4,5,6,8,3,7,2,1]=>[5,4,3,1,6,2,7,8]=>1110100=>[3,1,1,2]
[5,7,4,8,6,3,2,1]=>[4,2,5,1,3,6,7,8]=>1010000=>[1,1,1,4]
[3,2,6,5,1,8,7,4]=>[6,7,3,4,8,1,2,5]=>0100100=>[1,1,2,1,2]
[3,5,6,7,2,8,4,1]=>[6,4,3,2,7,1,5,8]=>1110100=>[3,1,1,2]
[7,6,9,8,5,4,3,2,1]=>[3,4,1,2,5,6,7,8,9]=>01000000=>[1,1,6]
[6,5,4,9,8,7,3,2,1]=>[4,5,6,1,2,3,7,8,9]=>00100000=>[2,1,5]
[6,8,5,9,7,4,3,2,1]=>[4,2,5,1,3,6,7,8,9]=>10100000=>[1,1,1,5]
[6,7,8,9,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9]=>11100000=>[3,5]
[5,4,3,2,9,8,7,6,1]=>[5,6,7,8,1,2,3,4,9]=>00010000=>[3,1,4]
[5,6,7,8,9,4,3,2,1]=>[5,4,3,2,1,6,7,8,9]=>11110000=>[4,4]
[4,8,3,2,1,9,7,6,5]=>[6,2,7,8,9,1,3,4,5]=>10001000=>[1,3,1,3]
[4,6,7,8,3,9,5,2,1]=>[6,4,3,2,7,1,5,8,9]=>11101000=>[3,1,1,3]
[4,5,6,7,8,9,3,2,1]=>[6,5,4,3,2,1,7,8,9]=>11111000=>[5,3]
[3,2,1,6,5,4,9,8,7]=>[7,8,9,4,5,6,1,2,3]=>00100100=>[2,1,2,1,2]
[3,2,5,4,7,6,9,8,1]=>[7,8,5,6,3,4,1,2,9]=>01010100=>[1,1,1,1,1,1,2]
[3,5,7,2,8,4,9,6,1]=>[7,5,3,8,2,6,1,4,9]=>11010100=>[2,1,1,1,1,2]
[3,4,5,6,7,8,9,2,1]=>[7,6,5,4,3,2,1,8,9]=>11111100=>[6,2]
[2,4,6,7,1,8,3,9,5]=>[8,6,4,3,9,2,7,1,5]=>11101010=>[3,1,1,1,1,1]
[2,4,5,6,7,8,1,9,3]=>[8,6,5,4,3,2,9,1,7]=>11111010=>[5,1,1,1]
[8,7,10,9,6,5,4,3,2,1]=>[3,4,1,2,5,6,7,8,9,10]=>010000000=>[1,1,7]
[8,9,10,7,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9,10]=>110000000=>[2,7]
[7,6,5,10,9,8,4,3,2,1]=>[4,5,6,1,2,3,7,8,9,10]=>001000000=>[2,1,6]
[7,8,9,10,6,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9,10]=>111000000=>[3,6]
[6,5,4,3,10,9,8,7,2,1]=>[5,6,7,8,1,2,3,4,9,10]=>000100000=>[3,1,5]
[5,4,3,2,1,10,9,8,7,6]=>[6,7,8,9,10,1,2,3,4,5]=>000010000=>[4,1,4]
[5,4,8,7,3,10,9,6,2,1]=>[6,7,3,4,8,1,2,5,9,10]=>010010000=>[1,1,2,1,4]
[5,6,7,8,9,10,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10]=>111110000=>[5,4]
[4,8,9,3,2,1,10,7,6,5]=>[7,3,2,8,9,10,1,4,5,6]=>110001000=>[2,3,1,3]
[4,3,2,7,6,5,10,9,8,1]=>[7,8,9,4,5,6,1,2,3,10]=>001001000=>[2,1,2,1,3]
[4,5,6,7,8,9,10,3,2,1]=>[7,6,5,4,3,2,1,8,9,10]=>111111000=>[6,3]
[3,6,7,8,9,2,1,10,5,4]=>[8,5,4,3,2,9,10,1,6,7]=>111100100=>[4,2,1,2]
[3,4,5,6,7,8,9,10,2,1]=>[8,7,6,5,4,3,2,1,9,10]=>111111100=>[7,2]
[2,4,6,1,8,3,9,5,10,7]=>[9,7,5,10,3,8,2,6,1,4]=>110101010=>[2,1,1,1,1,1,1,1]
[2,4,6,7,8,1,9,3,10,5]=>[9,7,5,4,3,10,2,8,1,6]=>111101010=>[4,1,1,1,1,1]
[2,4,5,6,7,8,9,1,10,3]=>[9,7,6,5,4,3,2,10,1,8]=>111111010=>[6,1,1,1]
[1,6,8,2,5,3,7,4]=>[8,3,1,7,4,6,2,5]=>1101010=>[2,1,1,1,1,1]
[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>1101010=>[2,1,1,1,1,1]
[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>1101011=>[2,1,1,1,2]
[1,6,8,2,3,5,4,7]=>[8,3,1,7,6,4,5,2]=>1101101=>[2,1,2,1,1]
[5,3,6,1,2,4,8,7]=>[4,6,3,8,7,5,1,2]=>0101110=>[1,1,1,3,1]
[7,1,5,8,4,2,3,6]=>[2,8,4,1,5,7,6,3]=>0110011=>[1,2,2,2]
[8,1,5,7,4,2,3,6]=>[1,8,4,2,5,7,6,3]=>0110011=>[1,2,2,2]
[7,1,4,5,8,2,3,6]=>[2,8,5,4,1,7,6,3]=>0111011=>[1,3,1,2]
[7,4,1,6,2,8,3,5]=>[2,5,8,3,7,1,6,4]=>0010101=>[2,1,1,1,1,1]
[8,4,1,7,2,6,3,5]=>[1,5,8,2,7,3,6,4]=>0010101=>[2,1,1,1,1,1]
[8,1,4,7,5,2,3,6]=>[1,8,5,2,4,7,6,3]=>0110011=>[1,2,2,2]
[8,1,5,4,7,2,3,6]=>[1,8,4,5,2,7,6,3]=>0101011=>[1,1,1,1,1,2]
[2,1,7,5,8,3,4,6]=>[7,8,2,4,1,6,5,3]=>0101011=>[1,1,1,1,1,2]
[7,1,5,4,8,2,3,6]=>[2,8,4,5,1,7,6,3]=>0101011=>[1,1,1,1,1,2]
[7,1,4,8,5,2,3,6]=>[2,8,5,1,4,7,6,3]=>0110011=>[1,2,2,2]
[6,4,1,7,2,3,8,5]=>[3,5,8,2,7,6,1,4]=>0010110=>[2,1,1,2,1]
[7,8,3,1,2,4,6,5]=>[2,1,6,8,7,5,3,4]=>1001110=>[1,2,3,1]
[8,7,1,6,4,2,3,5]=>[1,2,8,3,5,7,6,4]=>0010011=>[2,1,2,2]
[8,6,1,7,4,2,3,5]=>[1,3,8,2,5,7,6,4]=>0010011=>[2,1,2,2]
[7,6,1,8,4,2,3,5]=>[2,3,8,1,5,7,6,4]=>0010011=>[2,1,2,2]
[7,3,8,1,2,4,6,5]=>[2,6,1,8,7,5,3,4]=>0101110=>[1,1,1,3,1]
[8,3,7,1,2,4,6,5]=>[1,6,2,8,7,5,3,4]=>0101110=>[1,1,1,3,1]
[8,3,6,1,2,4,7,5]=>[1,6,3,8,7,5,2,4]=>0101110=>[1,1,1,3,1]
[8,3,7,5,1,2,4,6]=>[1,6,2,4,8,7,5,3]=>0100111=>[1,1,2,3]
[7,3,6,1,2,4,8,5]=>[2,6,3,8,7,5,1,4]=>0101110=>[1,1,1,3,1]
[6,7,1,8,4,2,3,5]=>[3,2,8,1,5,7,6,4]=>1010011=>[1,1,1,2,2]
[6,8,1,7,4,2,3,5]=>[3,1,8,2,5,7,6,4]=>1010011=>[1,1,1,2,2]
[7,1,8,5,4,2,3,6]=>[2,8,1,4,5,7,6,3]=>0100011=>[1,1,3,2]
[7,1,8,4,5,2,3,6]=>[2,8,1,5,4,7,6,3]=>0101011=>[1,1,1,1,1,2]
[2,1,7,8,5,3,4,6]=>[7,8,2,1,4,6,5,3]=>0110011=>[1,2,2,2]
[7,6,3,1,2,4,8,5]=>[2,3,6,8,7,5,1,4]=>0001110=>[3,3,1]
[6,1,2,3,8,7,5,4]=>[3,8,7,6,1,2,4,5]=>0111000=>[1,3,3]
[6,8,1,4,2,3,7,5]=>[3,1,8,5,7,6,2,4]=>1010110=>[1,1,1,1,2,1]
[6,8,3,1,2,7,4,5]=>[3,1,6,8,7,2,5,4]=>1001101=>[1,2,2,1,1]
[6,7,3,1,2,8,4,5]=>[3,2,6,8,7,1,5,4]=>1001101=>[1,2,2,1,1]
[6,7,1,4,2,3,8,5]=>[3,2,8,5,7,6,1,4]=>1010110=>[1,1,1,1,2,1]
[4,3,6,8,5,7,1,2]=>[5,6,3,1,4,2,8,7]=>0110101=>[1,2,1,1,1,1]
[6,1,2,5,4,8,3,7]=>[3,8,7,4,5,1,6,2]=>0110101=>[1,2,1,1,1,1]
[3,2,8,5,4,1,7,6]=>[6,7,1,4,5,8,2,3]=>0100010=>[1,1,3,1,1]
[7,8,2,1,4,6,3,5]=>[2,1,7,8,5,3,6,4]=>1001101=>[1,2,2,1,1]
[7,2,1,5,8,3,4,6]=>[2,7,8,4,1,6,5,3]=>0011011=>[2,2,1,2]
[2,4,8,5,1,3,6,7]=>[7,5,1,4,8,6,3,2]=>1100111=>[2,2,3]
[3,5,6,1,8,4,2,7]=>[6,4,3,8,1,5,7,2]=>1101001=>[2,1,1,2,1]
[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>1110001=>[3,3,1]
[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>1101011=>[2,1,1,1,2]
[2,6,1,5,8,3,4,7]=>[7,3,8,4,1,6,5,2]=>1011011=>[1,1,2,1,2]
[5,7,1,6,8,4,3,2]=>[4,2,8,3,1,5,6,7]=>1011000=>[1,1,2,3]
[4,8,1,2,5,7,3,6]=>[5,1,8,7,4,2,6,3]=>1011101=>[1,1,3,1,1]
[8,4,6,2,5,7,3,1]=>[1,5,3,7,4,2,6,8]=>0101100=>[1,1,1,2,2]
[8,3,6,4,7,2,5,1]=>[1,6,3,5,2,7,4,8]=>0101010=>[1,1,1,1,1,1,1]
[3,8,1,4,7,2,5,6]=>[6,1,8,5,2,7,4,3]=>1011011=>[1,1,2,1,2]
[1,7,8,4,6,2,5,3]=>[8,2,1,5,3,7,4,6]=>1101010=>[2,1,1,1,1,1]
[3,7,4,8,5,1,6,2]=>[6,2,5,1,4,8,3,7]=>1010010=>[1,1,1,2,1,1]
[3,7,1,6,5,4,8,2]=>[6,2,8,3,4,5,1,7]=>1010010=>[1,1,1,2,1,1]
[2,7,3,1,5,8,4,6]=>[7,2,6,8,4,1,5,3]=>1001101=>[1,2,2,1,1]
[2,7,4,6,8,1,3,5]=>[7,2,5,3,1,8,6,4]=>1011011=>[1,1,2,1,2]
[8,2,6,7,5,4,3,1]=>[1,7,3,2,4,5,6,8]=>0110000=>[1,2,4]
[3,8,7,1,6,4,5,2]=>[6,1,2,8,3,5,4,7]=>1001010=>[1,2,1,1,1,1]
[3,6,8,2,7,4,1,5]=>[6,3,1,7,2,5,8,4]=>1101001=>[2,1,1,2,1]
[1,5,2,8,7,4,6,3]=>[8,4,7,1,2,5,3,6]=>1010010=>[1,1,1,2,1,1]
[3,4,2,7,8,1,6,5]=>[6,5,7,2,1,8,3,4]=>1011010=>[1,1,2,1,1,1]
[6,5,8,7,1,4,2,3]=>[3,4,1,2,8,5,7,6]=>0100101=>[1,1,2,1,1,1]
[4,1,7,3,8,5,2,6]=>[5,8,2,6,1,4,7,3]=>0101001=>[1,1,1,1,2,1]
[7,2,8,4,1,6,3,5]=>[2,7,1,5,8,3,6,4]=>0100101=>[1,1,2,1,1,1]
[7,1,5,6,8,4,3,2]=>[2,8,4,3,1,5,6,7]=>0111000=>[1,3,3]
[6,7,1,3,4,5,8,2]=>[3,2,8,6,5,4,1,7]=>1011110=>[1,1,4,1]
[6,8,7,4,2,3,5,1]=>[3,1,2,5,7,6,4,8]=>1000110=>[1,3,2,1]
[3,6,4,5,2,8,7,1]=>[6,3,5,4,7,1,2,8]=>1010100=>[1,1,1,1,1,2]
[5,3,8,6,1,2,4,7]=>[4,6,1,3,8,7,5,2]=>0100111=>[1,1,2,3]
[2,5,3,6,8,7,4,1]=>[7,4,6,3,1,2,5,8]=>1011000=>[1,1,2,3]
[6,3,5,4,8,7,2,1]=>[3,6,4,5,1,2,7,8]=>0101000=>[1,1,1,1,3]
[4,7,6,2,5,3,8,1]=>[5,2,3,7,4,6,1,8]=>1001010=>[1,2,1,1,1,1]
[8,5,2,7,1,4,3,6]=>[1,4,7,2,8,5,6,3]=>0010101=>[2,1,1,1,1,1]
[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>1001011=>[1,2,1,1,2]
[5,1,7,2,4,3,8,6]=>[4,8,2,7,5,6,1,3]=>0101010=>[1,1,1,1,1,1,1]
[5,4,1,3,8,6,2,7]=>[4,5,8,6,1,3,7,2]=>0011001=>[2,2,2,1]
[5,1,8,6,3,4,2,7]=>[4,8,1,3,6,5,7,2]=>0100101=>[1,1,2,1,1,1]
[5,8,2,4,7,6,3,1]=>[4,1,7,5,2,3,6,8]=>1011000=>[1,1,2,3]
[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>1101011=>[2,1,1,1,2]
[7,1,3,5,8,2,6,4]=>[2,8,6,4,1,7,3,5]=>0111010=>[1,3,1,1,1]
[8,2,1,3,5,6,7,4]=>[1,7,8,6,4,3,2,5]=>0011110=>[2,4,1]
[4,1,3,8,2,6,7,5]=>[5,8,6,1,7,3,2,4]=>0110110=>[1,2,1,2,1]
[3,1,7,2,8,5,4,6]=>[6,8,2,7,1,4,5,3]=>0101001=>[1,1,1,1,2,1]
[3,6,1,4,7,2,8,5]=>[6,3,8,5,2,7,1,4]=>1011010=>[1,1,2,1,1,1]
[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>1101011=>[2,1,1,1,2]
[7,1,3,6,2,8,4,5]=>[2,8,6,3,7,1,5,4]=>0110101=>[1,2,1,1,1,1]
[2,1,8,4,5,7,3,6]=>[7,8,1,5,4,2,6,3]=>0101101=>[1,1,1,2,1,1]
[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>1010011=>[1,1,1,2,2]
[2,1,8,5,4,3,6,7]=>[7,8,1,4,5,6,3,2]=>0100011=>[1,1,3,2]
[7,4,8,6,2,3,1,5]=>[2,5,1,3,7,6,8,4]=>0100101=>[1,1,2,1,1,1]
[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>1110001=>[3,3,1]
[7,2,8,5,3,6,4,1]=>[2,7,1,4,6,3,5,8]=>0100100=>[1,1,2,1,2]
[8,4,7,5,2,3,6,1]=>[1,5,2,4,7,6,3,8]=>0100110=>[1,1,2,2,1]
[7,5,2,8,4,6,1,3]=>[2,4,7,1,5,3,8,6]=>0010101=>[2,1,1,1,1,1]
[6,7,5,1,2,8,3,4]=>[3,2,4,8,7,1,6,5]=>1001101=>[1,2,2,1,1]
[7,6,2,4,5,8,3,1]=>[2,3,7,5,4,1,6,8]=>0011100=>[2,3,2]
[2,6,3,8,4,7,5,1]=>[7,3,6,1,5,2,4,8]=>1010100=>[1,1,1,1,1,2]
[2,8,3,6,4,5,7,1]=>[7,1,6,3,5,4,2,8]=>1010110=>[1,1,1,1,2,1]
[5,8,1,2,6,4,7,3]=>[4,1,8,7,3,5,2,6]=>1011010=>[1,1,2,1,1,1]
[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>1100101=>[2,2,1,1,1]
[7,5,1,2,8,4,6,3]=>[2,4,8,7,1,5,3,6]=>0011010=>[2,2,1,1,1]
[5,4,8,3,6,2,7,1]=>[4,5,1,6,3,7,2,8]=>0101010=>[1,1,1,1,1,1,1]
[6,4,5,8,2,7,3,1]=>[3,5,4,1,7,2,6,8]=>0110100=>[1,2,1,1,2]
[5,7,3,6,4,8,2,1]=>[4,2,6,3,5,1,7,8]=>1010100=>[1,1,1,1,1,2]
[3,1,5,6,4,8,7,2]=>[6,8,4,3,5,1,2,7]=>0110100=>[1,2,1,1,2]
[1,3,6,2,5,7,8,4]=>[8,6,3,7,4,2,1,5]=>1101110=>[2,1,3,1]
[1,4,6,3,5,7,8,2]=>[8,5,3,6,4,2,1,7]=>1101110=>[2,1,3,1]
[3,5,1,6,4,7,8,2]=>[6,4,8,3,5,2,1,7]=>1010110=>[1,1,1,1,2,1]
[3,6,1,4,2,7,8,5]=>[6,3,8,5,7,2,1,4]=>1010110=>[1,1,1,1,2,1]
[2,4,6,3,1,7,8,5]=>[7,5,3,6,8,2,1,4]=>1100110=>[2,2,2,1]
[1,3,6,5,2,7,8,4]=>[8,6,3,4,7,2,1,5]=>1100110=>[2,2,2,1]
[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>1100101=>[2,2,1,1,1]
[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>1101100=>[2,1,2,2]
[2,3,5,1,8,4,7,6]=>[7,6,4,8,1,5,2,3]=>1101010=>[2,1,1,1,1,1]
[2,3,6,1,8,5,4,7]=>[7,6,3,8,1,4,5,2]=>1101001=>[2,1,1,2,1]
[1,2,7,4,6,8,3,5]=>[8,7,2,5,3,1,6,4]=>1101101=>[2,1,2,1,1]
[2,3,7,5,1,8,4,6]=>[7,6,2,4,8,1,5,3]=>1100101=>[2,2,1,1,1]
[4,7,2,5,3,8,6,1]=>[5,2,7,4,6,1,3,8]=>1010100=>[1,1,1,1,1,2]
[3,1,7,5,4,8,6,2]=>[6,8,2,4,5,1,3,7]=>0100100=>[1,1,2,1,2]
[1,2,7,6,4,8,5,3]=>[8,7,2,3,5,1,4,6]=>1100100=>[2,2,1,2]
[1,2,7,3,6,8,5,4]=>[8,7,2,6,3,1,4,5]=>1101100=>[2,1,2,2]
[2,3,6,1,8,5,7,4]=>[7,6,3,8,1,4,2,5]=>1101010=>[2,1,1,1,1,1]
[3,1,5,4,8,7,6,2]=>[6,8,4,5,1,2,3,7]=>0101000=>[1,1,1,1,3]
[1,2,5,8,4,7,3,6]=>[8,7,4,1,5,2,6,3]=>1110101=>[3,1,1,1,1]
[1,2,6,8,5,4,7,3]=>[8,7,3,1,4,5,2,6]=>1110010=>[3,2,1,1]
[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>1110010=>[3,2,1,1]
[3,5,7,4,8,2,1,6]=>[6,4,2,5,1,7,8,3]=>1101001=>[2,1,1,2,1]
[2,4,7,6,8,3,1,5]=>[7,5,2,3,1,6,8,4]=>1101001=>[2,1,1,2,1]
[1,4,6,8,3,5,2,7]=>[8,5,3,1,6,4,7,2]=>1110101=>[3,1,1,1,1]
[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>1110011=>[3,2,2]
[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>1110001=>[3,3,1]
[1,2,5,8,4,3,7,6]=>[8,7,4,1,5,6,2,3]=>1110010=>[3,2,1,1]
[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>1110110=>[3,1,2,1]
[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>1110101=>[3,1,1,1,1]
[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>1110011=>[3,2,2]
[3,5,7,4,8,1,2,6]=>[6,4,2,5,1,8,7,3]=>1101011=>[2,1,1,1,2]
[4,6,1,7,5,8,2,3]=>[5,3,8,2,4,1,7,6]=>1010101=>[1,1,1,1,1,1,1]
[2,3,6,7,5,8,1,4]=>[7,6,3,2,4,1,8,5]=>1110101=>[3,1,1,1,1]
[1,3,7,5,6,8,2,4]=>[8,6,2,4,3,1,7,5]=>1101101=>[2,1,2,1,1]
[2,3,6,5,8,1,7,4]=>[7,6,3,4,1,8,2,5]=>1101010=>[2,1,1,1,1,1]
[3,4,6,2,8,1,7,5]=>[6,5,3,7,1,8,2,4]=>1101010=>[2,1,1,1,1,1]
[3,5,4,6,8,2,1,7]=>[6,4,5,3,1,7,8,2]=>1011001=>[1,1,2,2,1]
[3,5,4,6,8,1,2,7]=>[6,4,5,3,1,8,7,2]=>1011011=>[1,1,2,1,2]
[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>1110101=>[3,1,1,1,1]
[1,2,6,7,4,8,3,5]=>[8,7,3,2,5,1,6,4]=>1110101=>[3,1,1,1,1]
[3,6,4,7,1,8,5,2]=>[6,3,5,2,8,1,4,7]=>1010100=>[1,1,1,1,1,2]
[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>1110100=>[3,1,1,2]
[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>1110100=>[3,1,1,2]
[3,1,5,7,6,8,4,2]=>[6,8,4,2,3,1,5,7]=>0110100=>[1,2,1,1,2]
[3,5,4,6,8,2,7,1]=>[6,4,5,3,1,7,2,8]=>1011010=>[1,1,2,1,1,1]
[4,2,6,1,8,7,5,3]=>[5,7,3,8,1,2,4,6]=>0101000=>[1,1,1,1,3]
[3,1,6,5,8,7,4,2]=>[6,8,3,4,1,2,5,7]=>0101000=>[1,1,1,1,3]
[2,3,6,5,8,7,1,4]=>[7,6,3,4,1,2,8,5]=>1101001=>[2,1,1,2,1]
[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>1101100=>[2,1,2,2]
[1,2,7,5,6,8,4,3]=>[8,7,2,4,3,1,5,6]=>1101100=>[2,1,2,2]
[3,1,6,7,5,8,4,2]=>[6,8,3,2,4,1,5,7]=>0110100=>[1,2,1,1,2]
[4,6,2,7,5,8,3,1]=>[5,3,7,2,4,1,6,8]=>1010100=>[1,1,1,1,1,2]
[3,5,7,4,8,2,6,1]=>[6,4,2,5,1,7,3,8]=>1101010=>[2,1,1,1,1,1]
[2,4,7,6,8,3,5,1]=>[7,5,2,3,1,6,4,8]=>1101010=>[2,1,1,1,1,1]
[1,4,6,8,3,5,7,2]=>[8,5,3,1,6,4,2,7]=>1110110=>[3,1,2,1]
[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>1110110=>[3,1,2,1]
[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>1110101=>[3,1,1,1,1]
[1,2,5,8,4,7,6,3]=>[8,7,4,1,5,2,3,6]=>1110100=>[3,1,1,2]
[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>1110010=>[3,2,1,1]
[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>1110001=>[3,3,1]
[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>1110011=>[3,2,2]
[5,7,1,2,8,6,4,3]=>[4,2,8,7,1,3,5,6]=>1011000=>[1,1,2,3]
[3,1,7,6,8,5,4,2]=>[6,8,2,3,1,4,5,7]=>0101000=>[1,1,1,1,3]
[1,2,6,8,5,7,4,3]=>[8,7,3,1,4,2,5,6]=>1110100=>[3,1,1,2]
[1,2,5,8,7,4,6,3]=>[8,7,4,1,2,5,3,6]=>1110010=>[3,2,1,1]
[1,2,4,8,7,6,3,5]=>[8,7,5,1,2,3,6,4]=>1110001=>[3,3,1]
[6,4,5,7,2,8,1,3]=>[3,5,4,2,7,1,8,6]=>0110101=>[1,2,1,1,1,1]
[5,3,6,2,7,1,4,8]=>[4,6,3,7,2,8,5,1]=>0101011=>[1,1,1,1,1,2]
[2,6,3,4,7,1,5,8]=>[7,3,6,5,2,8,4,1]=>1011011=>[1,1,2,1,2]
[2,7,3,4,5,8,1,6]=>[7,2,6,5,4,1,8,3]=>1011101=>[1,1,3,1,1]
[3,7,4,5,6,8,1,2]=>[6,2,5,4,3,1,8,7]=>1011101=>[1,1,3,1,1]
[4,7,6,2,3,8,1,5]=>[5,2,3,7,6,1,8,4]=>1001101=>[1,2,2,1,1]
[7,6,2,4,5,8,1,3]=>[2,3,7,5,4,1,8,6]=>0011101=>[2,3,1,1]
[5,3,1,2,8,4,7,6]=>[4,6,8,7,1,5,2,3]=>0011010=>[2,2,1,1,1]
[7,3,1,2,8,4,6,5]=>[2,6,8,7,1,5,3,4]=>0011010=>[2,2,1,1,1]
[6,4,1,3,8,5,7,2]=>[3,5,8,6,1,4,2,7]=>0011010=>[2,2,1,1,1]
[6,2,3,1,8,4,7,5]=>[3,7,6,8,1,5,2,4]=>0101010=>[1,1,1,1,1,1,1]
[7,1,6,2,3,4,5,8]=>[2,8,3,7,6,5,4,1]=>0101111=>[1,1,1,4]
[8,2,7,3,4,5,6,1]=>[1,7,2,6,5,4,3,8]=>0101110=>[1,1,1,3,1]
[8,1,6,2,3,4,5,7]=>[1,8,3,7,6,5,4,2]=>0101111=>[1,1,1,4]
[8,1,5,7,2,3,6,4]=>[1,8,4,2,7,6,3,5]=>0110110=>[1,2,1,2,1]
[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>1010110=>[1,1,1,1,2,1]
[7,2,1,8,3,4,5,6]=>[2,7,8,1,6,5,4,3]=>0010111=>[2,1,1,3]
[1,4,5,8,3,6,7,2]=>[8,5,4,1,6,3,2,7]=>1110110=>[3,1,2,1]
[6,2,7,1,8,4,5,3]=>[3,7,2,8,1,5,4,6]=>0101010=>[1,1,1,1,1,1,1]
[3,2,8,7,1,4,6,5]=>[6,7,1,2,8,5,3,4]=>0100110=>[1,1,2,2,1]
[3,8,1,7,2,4,5,6]=>[6,1,8,2,7,5,4,3]=>1010111=>[1,1,1,1,3]
[6,8,2,3,5,1,4,7]=>[3,1,7,6,4,8,5,2]=>1011011=>[1,1,2,1,2]
[2,8,6,1,3,4,5,7]=>[7,1,3,8,6,5,4,2]=>1001111=>[1,2,4]
[1,7,6,2,3,4,5,8]=>[8,2,3,7,6,5,4,1]=>1001111=>[1,2,4]
[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>1001111=>[1,2,4]
[2,8,7,3,4,5,6,1]=>[7,1,2,6,5,4,3,8]=>1001110=>[1,2,3,1]
[3,8,7,2,4,5,6,1]=>[6,1,2,7,5,4,3,8]=>1001110=>[1,2,3,1]
[7,8,3,6,2,4,5,1]=>[2,1,6,3,7,5,4,8]=>1010110=>[1,1,1,1,2,1]
[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>1100110=>[2,2,2,1]
[8,7,6,1,3,4,5,2]=>[1,2,3,8,6,5,4,7]=>0001110=>[3,3,